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Increases the time between an enemy's attacks by 25% and slows its movement by 50% for 15 sec. Movement speed reduced by 50%. Time between melee and ranged attacks increased by 25%. Casting time increased by 25%.
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Whenever we make graphs using Excel, they turn out pretty ugly. But, actually Excel charts don't have to be ugly. While the default options provided by Excel are downright hideous, you can clean them up with a few tricks. You can check out a primer to making your charts more appealing here. Here's the before and after of the same chart. The first version is the default version that Excel gives you. The second is after doing some magic to it. For those of you under the age of 15 that prefer seeing things in GIF format, here are some tips from Darkhorse Analytics that show the general process of making your charts look presentable.
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That continued Wednesday as the Browns continued their first week of organized team activities. , who spent the past three seasons with Buffalo and helped the Bills snap a 17-year playoff drought last , said it's ongoing Wholesale NBA Jerseys process but the more you show leadership on the field and the locker room even the weight room and the building, the easier it is that you grab everyone and let them know you're the leader. Landry gives 's offense a versatile weapon and fiery competitor. far, though, the dynamic veteran signal-caller has already earned the respect of his peers, both and old. , who spent the past three seasons with Buffalo and helped the Bills snap a 17-year playoff drought last , said it's ongoing process but the more you show leadership on the field and the Wholesale NFL Jerseys Free Shipping locker room even the weight room and the building, the easier it is that you grab everyone and let them know you're the leader. 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Wholesale NFL Jerseys Free Shipping goal is to eventually be No. , who spent the past three seasons with Buffalo and helped the Bills snap a 17-year playoff drought last , said it's ongoing process but the more you show leadership on the field and the locker room even the weight room and the building, the easier it is that you grab everyone and let them know you're the leader. goal is to eventually be No. It's been roughly two months since Browns quarterback Tyrod was traded to and even less since he's been able to Cheap Jerseys NFL workout with his new teammates. Since joining the team, Browns coach has made clear is their starting quarterback. far, though, the dynamic veteran signal-caller has already earned the respect of his peers, both and old. far, though, the dynamic veteran signal-caller has already earned the respect of his peers, both and Cheap Jerseys NFL old. The latter of those dynamics showed when asked if he agreed with his ranking the NFL's Top 100 Players list. The latter of those dynamics showed when asked if he agreed with his ranking the NFL's Top 100 Players list. That continued Wednesday as the Browns continued their first week of organized team activities. It's been roughly two months since Browns quarterback Tyrod was traded to and even less since he's been able to workout with his new teammates. far, though, the dynamic veteran signal-caller has already earned the respect of his peers, both and old. , who spent the NBA Jerseys Cheap past three seasons with Buffalo and helped the Bills snap a 17-year playoff drought last , said it's ongoing process but the more you show leadership on the field and the locker room even the weight room and the building, the easier it is that you grab everyone and let them know you're the leader. 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Since joining the team, Browns coach has made clear is their starting quarterback. Of course not. , 28, brings a track record of production and winning to . goal is to eventually be No. , who spent the past three seasons with Buffalo and helped the Bills snap a 17-year playoff drought last , said it's ongoing process but the more you show leadership on the field and the locker room even the weight room and the building, the easier it is that you grab everyone and let them know you're the leader. , 28, cheap jerseys brings a track record of production and winning Cheap Jerseys Wholesale to . Honestly, it's honor cheap jerseys to be recognized among all of the top players this league, to be recognized Nike NFL Jerseys Supply the top 100, but I think for any competitor. The latter of those dynamics showed when asked if he agreed with his ranking the NFL's Top 100 Players list. Of course not. Landry gives 's offense a versatile weapon and fiery competitor. , who spent the past three seasons with Buffalo and helped the Bills snap a 17-year playoff drought last , said it's ongoing process but the more you show leadership on the field and the locker room even the weight room and the building, the easier it is that you grab everyone and let them know you're the leader. far, though, the dynamic veteran signal-caller has already earned the respect of his peers, both and old. That continued Wednesday as the Browns continued their first week of organized team activities. , 28, brings a track record of production and winning to . goal is to eventually be No. Cheap Jerseys Wholesale The latter of those dynamics showed when asked if he agreed with his ranking the NFL's Top 100 Players list. Landry gives 's offense a versatile weapon and fiery competitor. goal is to eventually be No. far, though, the dynamic veteran signal-caller has already earned the respect of his peers, both and old. far, though, the dynamic veteran signal-caller has already earned the respect of his peers, both and old. Another new face to the team's locker room is wide receiver Landry, a three-time Wholesale Jerseys China Pro Bowler Miami and the league's receptions leader a year ago. That continued Wednesday as the Browns Cheap Baseball Jerseys continued their first week of organized team activities. Another new face to the team's locker room is Wholesale Jerseys China wide receiver Landry, a three-time Pro Bowler Miami and the league's receptions leader a year ago. Landry gives 's offense a versatile weapon and fiery competitor. Landry gives Cheap Jerseys For Sale 's offense a versatile weapon and fiery competitor. , 28, brings a track record of production and winning to . 1, Landry said with a wide smile. , who spent the past three seasons with Buffalo and helped the Bills snap a 17-year playoff drought Baseball Jerseys last , said it's ongoing process but the more you show leadership Cheap Calgary Flames Jerseys on the field and the locker room even the weight room and the building, the easier it is that you grab everyone and let them know you're the leader. far, though, the dynamic veteran signal-caller has already earned the respect of his peers, both and old. It's been roughly two months since Browns quarterback Tyrod was traded to and even less since he's been able to workout with his new teammates. far, though, the dynamic veteran signal-caller has already earned Cheap Jerseys NFL the respect of his peers, both and old. 1, Landry said with a wide smile. That continued Wednesday as the Browns continued their first week of organized team Cheap Jerseys NFL activities. Since joining the team, Browns coach has made clear is their starting quarterback. Landry gives 's offense a versatile weapon and fiery competitor. Honestly, it's honor to be recognized among all of the top players this league, to be recognized the top 100, but I think for any competitor. , 28, brings a track record of production and winning to . Another new face to the team's locker room is wide receiver Landry, a three-time Pro Bowler Baseball Jerseys For Sale Miami and the league's receptions leader a year ago. Since joining the team, Browns coach has made clear is their starting quarterback. Landry http://www.authenticsabresstore.com/pat-lafontaine-jersey_c-426.html gives 's offense a versatile weapon and fiery competitor. goal is to eventually be No. Landry gives 's offense a versatile weapon and fiery competitor. , 28, brings a track record of production and winning to . 1, Landry said with a wide smile. Honestly, it's honor to be recognized among all of the top players this league, to be recognized the top 100, but I think for any competitor. goal is to eventually be No. Another new face to the team's locker room is wide receiver Landry, a three-time Pro Bowler Miami and the league's receptions leader a year ago. goal is to eventually be No. Five things to know about Day 2 of the Browns' OTAs, http://www.officialbostonbruins.com/Adidas-Jaroslav-Halak-Jersey which were open to the news media… , who spent the past three seasons with Buffalo and helped the Bills snap a 17-year playoff drought Basketball Jerseys Cheap last , said Authentic Jaroslav Halak Jersey it's ongoing process but the more you show leadership on the field and the locker room even the weight room and the building, the easier it is that you grab everyone and let them know you're the leader. 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Another new face to the team's locker room is wide receiver Landry, a three-time Pro Bowler Miami and the league's receptions leader a year ago. goal is to eventually be No. far, though, the dynamic veteran signal-caller has already earned the respect of his peers, both and old. Another Baseball Jerseys Basketball Jerseys Cheap For Sale new face to the team's locker room is wide receiver Landry, a three-time Pro Bowler Miami and the league's receptions leader a year Authentic Pat Lafontaine Jersey ago. That continued Wednesday as the Browns continued their first week of organized team activities. , who spent the past three Basketball Jerseys Cheap seasons with Buffalo and helped the Bills snap a 17-year playoff drought last , said it's ongoing process but the more you show leadership on the field and the locker room even the weight room and the building, the easier it is that you grab everyone and let them know you're the leader. 1, Landry said with a wide smile. Since joining the team, Browns coach has made clear is Wholesale NFL Jerseys Cheap their starting quarterback. far, though, the dynamic veteran signal-caller has already earned the baseball jerseys respect of his peers, both and old. Landry gives 's offense a versatile weapon and fiery competitor. Of course not. , who spent the past three seasons with Buffalo and helped the Bills snap a 17-year playoff drought last , said it's ongoing process but the more you show NBA Jerseys Cheap leadership on the field and the locker room even the weight room and the building, the easier it is that you grab NBA Basketball Jerseys everyone and let them know you're the leader. Since joining the team, Browns coach has made clear is their starting quarterback. Landry gives 's offense a versatile weapon and fiery competitor. , 28, brings a track record of production and winning to . 1, Landry said with a wide smile. Landry gives 's offense a versatile weapon and fiery competitor. The latter of those dynamics showed when asked if he agreed with his ranking the NFL's Top 100 Players list. , 28, brings a track record Nike NFL Jerseys Size Chart of production and winning to . 1, Landry said with a wide smile. Of course not. , 28, brings a track record of production and winning NFL Jerseys China to . Cheap NFL Jerseys USA Landry gives 's offense a versatile weapon and fiery competitor. Of course not. Wholesale NFL Jerseys Cheap Since joining the team, Browns coach has made clear is their starting quarterback. goal is to eventually be No. Since joining the team, Browns coach has made clear is their starting quarterback. Five things to know about Day 2 of the Browns' NBA Basketball Jerseys OTAs, which were open to the news media… Another new face to the Nike NFL Jerseys Size Chart team's locker room is wide receiver NFL Jerseys China Landry, a three-time Pro Bowler Miami and the league's receptions leader a year ago. 1, Landry said with a wide smile. Landry gives 's offense a versatile weapon and fiery competitor. , who spent the past three seasons with Buffalo and helped the Bills snap a 17-year playoff drought last , said it's ongoing process but the more you show leadership on the field and the locker room even the weight room and the building, the easier it is that you Cheap NFL Jerseys USA grab everyone and let them know you're the leader. Since joining the team, Browns coach has made clear is their starting quarterback. 1, Landry said with a wide smile. , 28, brings a track record of production and winning to . It's been roughly two months since Browns quarterback NBA Basketball Jerseys Tyrod was traded to and even less since he's been able to workout with his new teammates. Honestly, it's honor to be recognized among all of the top players this league, to be recognized the top 100, but I think for any competitor. Landry gives 's offense a versatile weapon and fiery competitor. It's been roughly two months since Browns quarterback Tyrod was traded to and even less since he's been able to workout with his new teammates. It's been roughly two months since Browns quarterback Tyrod was traded to and even less since he's been able to workout with Nike NFL Jerseys Size Chart his new teammates. The latter of those dynamics showed when asked if he agreed with his NFL Jerseys China ranking the NFL's Top 100 Players list. 1, Landry said with a wide smile. Landry gives 's offense a versatile weapon and fiery competitor. goal Cheap NFL Jerseys USA is to eventually be No. Another new face to the team's locker room is wide receiver Landry, a three-time Pro Bowler Miami and the league's receptions leader a year Wholesale NFL Jerseys Cheap ago. , who spent the past three seasons with Buffalo and helped the Bills snap a 17-year playoff drought last , said it's ongoing process but the more you show leadership on the field and the NBA Jerseys Cheap locker room even the weight room and the building, the easier it is that you grab everyone and let them basketball jerseys cheap know you're the leader. Honestly, it's honor to be recognized among all of the top players this league, to be recognized the top 100, but I think for any competitor. Landry gives 's offense a versatile weapon and fiery competitor. 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HomeStatisticsTV StarsZoe Williams Height, Weight, Age, Body Statistics Zoe Williams Height, Weight, Age, Body Statistics Zoe Williams Quick Info Height 5 ft 10 in Date of Birth April 3, 1980 Boyfriend Stuart McKay Zoe Williams is an English television personality, physician, health educator, and sportsperson who shot to fame after appearing as the character Amazon in the TV series Gladiators (2009). She went on to get featured in several other television programs including the BBC Two documentary Trust Me, I'm a Doctor (2016-2020) where she had discussed all subjects relating to health and lifestyle. Williams has practiced as an NHS general practitioner in London. She has also played rugby, having participated with the Blaydon Women's Rugby Football Club in the Premiership National League level in the past. Zoe has garnered more than 108k followers on Instagram. Zoe Williams Zoe Williams having a lovely time on a boat in August 2020 (Dr Zoe Williams / Instagram) Burnley, Lancashire, England, United Kingdom In 2001 she enrolled at Newcastle University to study medicine, earning her Bachelor of Medicine and Bachelor of Surgery degree after passing the course with merit. She graduated from medical school in 2007. Zoe gained experience in various specialist fields within medicine like A&E, Cardiology, Respiratory and Acute Medicine, Surgery, and Gynaecology. Television Personality, Physician, Health Educator, Sportsperson Zoe Williams in February 2021 realizing that it is time to start her maternity clothes shopping (Dr Zoe Williams / Instagram) 5 ft 10 in or 178 cm She has dated – James Crossley Stuart McKay – She has been in a relationship with Stuart McKay. They welcomed a son together named Lisbon (b. May 31, 2021). Zoe Williams with her boyfriend and bundle of joy in August 2021 (Dr Zoe Williams / Instagram) She is of Grenadian descent. She often tends to dye her hair in different shades. Towering physical appearance Expressive eyes She has endorsed or promoted several brands such as Elastoplast. Zoe Williams Favorite Things Breakfast – Poached eggs with avocado and sourdough Source – The Sun Zoe Williams Facts She was brought up in the north of England, in Lancashire. Williams developed a passion for competitive sport from her childhood. While she was at school, she used to play hockey and netball at the county level. Her love of team sports continued when she attended Newcastle University, and she joined a rugby team. She has been an ardent fan of the sport and has represented Northumberland at rugby union. In 2009, she founded the organization named Sportsgirls, which has aimed to increase the physical activity of teenage girls by educating and encouraging them to be healthier and more active. In 2013, workshops were developed for boys as well and the group got renamed as Fit4Life. Williams has remembered that as a kid growing up in the 1990s, she used to watch the original Gladiators, and getting the opportunity to be one was one of the most incredible feeling she has ever had. Zoe has recalled that she was an F2 doctor when she had applied to be a contestant on Gladiators, which had led to the invitation to join the cast of the program. She was the "green Gladiator" and became the face of Sky's green campaign along with being an ambassador for environmentally friendly lifestyle choices. Her one-year break from medicine was like a whirlwind, but she had the most fun with the camera, lights, and costumes when shooting for Gladiators. Zoe has added that spending the months with the team of the show, and getting to know them as well as their stories had taught her about the huge impact physical activity can have on the life of a person, that included the emotional and psychological benefits too. Featured Image by Dr Zoe Williams / Instagram Television Personality Capone (Rapper) Height, Weight, Age, Body Statistics Spider Loc Height, Weight, Age, Body Statistics Lin Yi Height, Weight, Age, Body Statistics Kid Capri Height, Weight, Age, Body Statistics Mack Maine Height, Weight, Age, Body Statistics
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The European Insurance Law Review is a double-blind peer-reviewed journal dedicated to publishing both theoretical and applied works on a wide range of topics in the law of insurance and risk, including issues at the intersection of law, insurance economics and finance, actuarial science and other related areas. Founded in 2002, it is published by the Association for Insurance Law of Serbia, one of the national chapters of the International Association of Insurance Law (AIDA). Entire material is published in Serbian language, while papers from the foreign authors are published both in Serbian and in one of the AIDA languages. Abstracts in the journal are always published in english language regardless of what is original language of the paper. The Insurance Law Association of Serbia was founded 1961 as the Yugoslav Association for Insurance Law. More information about the work and activities of the Association can be found at: www.srbija-aida.org.Association for Insurance Law of Serbia is also a member of the International Association of Insurance Publishers (Presse Internationale des Assurances – PIA). Considering the aspirations of the Republic of Serbia to become a member of the European Union, in the last few years, the Insurance Law Association of Serbia has had extensive cooperation with a number of insurance experts from other EU members or candidate countries. This culminated in the appointment of the international Editorial board of the Review in 2012, consisting of prominent professors of insurance law from the major European universities. Domestic and international authors provide a valuable contribution to the analysis of current issues and trends in national law, especially in light of the harmonization of the national legal system with the EU system. In this context, the Insurance Law Association of Serbia has decided to change the title of the Review from "Insurance Law Review" into "European Insurance Law Review", starting from no. 1/2013, in order to gain international recognition. Insurance Law Association of Serbia has an exclusive right to permit or decline permission for copying the content or part of the content in and form published in the European Insurance Law Review. Your submissions should be made to these email addresses [email protected] [email protected] All manuscripts submitted to the European Insurance Law Review are double-blind reviewed. Since January 2016, European Insurance Law Review is indexed in ERIH PLUS listing of the journal (European Reference Index for the Humanities and the Social Sciences). Since December 2013, European Insurance Law Review is indexed in HeinOnline database, that include more than 1800 law and law-related periodicals. Also, the journal has been included in Ulrich's Periodicals Directory – Ulrich's Web. Considering the aspirations of the Republic of Serbia to become a member of the European Union, in the last few years the Insurance Law Association of Serbia has had extensive cooperation with a number of insurance experts from other EU member or candidate countries. This culminated in the appointment of the international editorial board of the Review in 2012, consisting of prominent professors of insurance law from the major European universities. Both domestic and international authors provide a valuable contribution to the analysis of current issues and trends in national law, especially in light of the harmonization of the national legal system with the EU system. In this context, the Insurance Law Association of Serbia has decided to change the title of the Review from "Insurance Law Review" into "European Insurance Law Review", starting from no. 1/2013, in order to gain international recognition. Scientific research databases Latest published articles Administrative law at a turning point and the legal nature of administrative activities: A review of some peculiarities of the supervision of insurance activities in Serbia Administrative law is increasingly faced with various challenges and growing social needs that require innovative solutions. The demands of social groups for greater efficiency of Comparative perspective in regulating rights among victims, tortfeasors, and uninsured motorist fund: Rights of subrogation In China, the State Council's rules have vested in the Uninsured Motorist Fund rights to reimburseits paid compensation to victims from the person who is Peculiarities of public relations in the field of banking and insurance This paper investigates public relations and specificities of public relations in the banking and insurance sector. Firstly, we define the notion and principles of public Insurance of public enforcement officers' professional liability With the introduction of public enforcement officer by the Law on Enforcement and Security in 2011, then a new judicial profession in the legal system Statement on originality Writing instructions Copyright © 2023. Association for Insurance Law of Serbia. All rights reserved. Europian Insurance Law Review Please fill out this form. Company Position Upon receipt of payment, the journal will be sent to your address.
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In 2017, we have seen four Atlantic storms rapidly intensify with three of those storms - Hurricane Harvey, Irma and Maria - making landfall. When hurricanes intensify a large amount in a short period, scientists call this process rapid intensification. This is the hardest aspect of a storm to forecast and it can be most critical to people's lives. While any hurricane can threaten lives and cause damage with storm surges, floods, and extreme winds, a rapidly intensifying hurricane can greatly increase these risks while giving populations limited time to prepare and evacuate. Music credits: 'Micro Currents' by Jean-Patrick Voindrot [SACEM], 'Sink Deep' by Andrew Michael Britton [PRS], David Stephen Goldsmith [PRS], Mikey Rowe [PRS] from Killer Tracks. Rapid intensification is the hardest aspect of a storm to forecast and it can be most critical to people's lives. This GIF is optimized for posting on Twitter. Rapidly intensifying storms typically occur up to twice in a hurricane season. But in 2017, we have seen four storms rapidly intensify and scientists attribute this to warmer ocean waters and favorable winds. This GIF is optimized for posting on Twitter.
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Quality assurance (QA) is often seen in higher education studies as a policy instrument of governments, and as a management tool with higher education institutions. However, in higher education systems with their professional 'production technology' (both when it comes to teaching and to research) quality and excellence are actually 'made' by the 'professionals' on the work floor, i.e. the academic staff members (Westerheijden, Hulpiau & Waeytens, 2007). Academics' cooperation in quality improvement to strive for excellence is therefore crucial. Hence, governmental, managerial and collegial features of QA co-exist. European developments in higher education are seen to have a transformative character in general and during the last 10 years several steps in relation to quality initiatives and excellence have been made within higher education institutions in Western Balkans. However, research and publications regarding quality practices and excellence in higher education is still sparse. Best practices need to travel. The aim of the post doc project was to identify various institutional initiatives and practices that further can enhance the quality of the higher education sector in the region. What quality policies and practices could one observe in Western Balkans' universities? Do differences exist between private and public universities? What accreditation procedures do private and public universities follow? Are there any differences in perceptions of excellence for the leaders, and quality assurance administrators between private and public universities? What are the design criteria and key indicators that will position WBCs' universities to address future challenges and opportunities? Do universities and stakeholders take into consideration data and indicators for policy development and if so, what type of data and indicators are collected for this purpose? This comparative post doc project applied a multiple, mixed methods research design and used several data-gathering techniques, including document analysis (policy documents, Tempus data etc.), surveys, and interviews with a variety of stakeholders. Concepts from neo-institutional theory along with organizational characteristics, and policymaking processes (design, formulation, implementation, and evaluation) helped us agnized today's Western Balkans higher education at national and institutional levels. * Antigoni Papadimitriou was a post-doc fellow University of Oslo, Department of Educational Research. She completed her PhD at the Center for Higher Education Policy Studies (CHEPS), University of Twente, in the Netherlands. Her primary field of interest is the study of higher education governance and organization, specifically focusing on quality, leadership, and organizational change. Her interests also center on the study of higher education policies (development, implementation, and evaluation). Her focus extends to quality assurance, internationalization, and comparative issues in higher education. In May 2011, she was elected as a member-at-large of the Council of International Higher Education in Association for the Study of Higher Education (ASHE). She also is a member of CIES Higher Education Sig (HESIG) Awards Committee. Currently is an Assistant Professor of Management and Leadership and Program Director at Hellenic College, Boston USA.
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I believe that great design is not only about aesthetics but about visually representing a brand strategically to get through to a specific demographic. Over 10 years of commercial experience in the design and advertising industry, I've enjoyed working with companies such as Redcactus, Unified, Farmers, cievents, Brandhub and Brandish Advertising (now known as Bettle & Associates), to create print and web collateral for various brands and products. I love every aspect of creative design from the tactical rationale behind a brand to the structural techniques of package design, the simple navigation of a website to the use of typographic hierarchy in a clean and legible layout. I strive for success and know that with hard work and dedication I can achieve my future goals and the goals of my clients. If you like what you see here, feel free to contact me for further details. You can also follow me on LinkedIn, Facebook, Twitter, Instagram and Pinterest.
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Portland Trail Blazers edge the Houston Rockets in Game 1 By Colin Flosi Image courtesy of Keith Allison/Wikimedia. Before the playoffs began, it was quietly understood that this Portland Trail Blazers and Houston Rockets series was perhaps the most even match-up, and I'll be damned if both teams didn't prove that in Game 1. Despite being perhaps the most poorly-officiated game in recent playoff memory, the game turned into an instant classic. Four players fouled out (LaMarcus Aldridge, Robin Lopez, Patrick Beverley and Dwight Howard), all on questionable calls, and as a result it came down to a battle of the scoring guards, with Damian Lillard taking advantage of Patrick Beverley's absence to propel the Blazers over the Rockets, 122-120. If both teams were so evenly-matched, then what was the difference-maker for the Blazers? LaMarcus Aldridge. Despite fouling out with 1:04 left in overtime, Aldridge put up a dominant line of 46 points and 18 rebounds, and proved that maybe, just maybe, he has had enough of the first-round exits. Aldridge and Lillard combined to score 77 points and grab 27 rebounds, and both players' clutch baskets helped them steal home-court advantage on a night where James Harden struggled to score late in the game. While Harden did score 27 points, it took him 28 shots to do so, and his 14 three-point attempts (of which he hit only three) illustrate his questionable shot selection. Chandler Parsons, Jeremy Lin, Terrence Jones and Howard all stepped up at different times on offense for the Rockets, but Harden's inability to hit the shots that he needed ultimately spelled defeat for Houston. The biggest loss may not have been on the scoreboard, however, as it was released that Beverley had re-injured his right knee and would receive an MRI on Monday. If he is unable to go, Jeremy Lin would most likely move back into the starting lineup, leaving the Rockets with limited point guard depth off the bench, and even more of a problem when it comes to handling Lillard due to Beverley's endline-to-endline ball pressure being absent. One thing is for certain though – if the rest of the series is as tight as Game 1 was, NBA fans are in for a treat. Related Items:bmf, bmfdm, chandler pasrsons, damian lillard, dwight howard, james harden, jeremy lin, lamarcus aldridge, nba, nba playoffs, nicolas batum, partick beverley, Robin Lopez, terrence jones, wesley matthews Grizzlies' Nick Calathes suspended for drug violation Miami Heat take Game 1 from the Charlotte Bobcats
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![Ruby](https://github.com/philihp/tarot/workflows/Ruby/badge.svg) [![Build Status](https://travis-ci.com/philihp/tarot.svg?branch=master)](https://travis-ci.com/philihp/tarot) # Tarot This is an implementation of Kingdominion that I wrote so I could write an AI to play against. ## Using it Fire up a console bin/console Then create an initial gamestate with state = Tarot::State.new You can check out the available moves with state.available_moves Or try out one of the moves with state2 = state.play_move(move: game.available_moves.sample) Each command you run should duplicate the state, muck around with the new one, and then freeze it, so you can also still keep doing this and try different moves state3 = state.play_move(move: game.available_moves.sample) state4 = state.play_move(move: game.available_moves.sample) state5 = state.play_move(move: game.available_moves.sample) ## Notes ### State Phases * `:init_claim` * `:init_commit` Repeat until all old_claims are taken * `:claim` * `:place` * `:commit` ### What's the deal with rand? It's important to explicitly define the random seed, so that the same gamelist can be played through repeatedly without having to reshuffle the tiles. However, the computer AI can't be allowed ot have knowledge of the tiles to be drawn, because the computer can't cheat. One method of tackling this would be to develop a heuristic where the computer looks at the distribution of tiles left; sort of like card counting in blackjack... however this really bakes in the strategy that the AI will use and makes it relatively predictable. The advantage here, however, is that it would allow us to go relatively deep in the game-state-space. Another strategy would a stochastic monte carlo search the same moves a handful of times. The idea here is that the move (especially a later-game move) might be good 50% of the time, so let's go for it, while a bad move might only be good 10% of the time. Usually it's going to pick a decent move. Another benefit of going about it this way is the computer will never play perfectly. Sometimes it will make a wildcard play that appears to be bad, even though in its imagined trials, it happened to luck out. ## Development After checking out the repo, run `bin/setup` to install dependencies. Then, run `rake spec` to run the tests. You can also run `bin/console` for an interactive prompt that will allow you to experiment. ## License The gem is available as open source under the terms of the [MIT License](http://opensource.org/licenses/MIT). ## Thanks * https://github.com/PragTob/rubykon - for his ruby implementation of MCTS, of which this was derived. * https://github.com/dbravender/tilerealm - for his python implementation of the game. It turns out enumerating possible places to drop a tile is hard.
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With it's tip dihedral and long fuselage the Red Zephyr is a nicely different design with plenty of character. It was originally designed by Herb Greenberg in 1937 and with it's flat bottom wing section and large elevators it is another Old Timer that can handle windy conditions. Proof (as if proof were needed!) that the RZ can handle a 'bit of breeze' came in 2002 when my pal Jim Turner took his own Red Zephyr with him when Liz (his boss at the time) suggested he do a 4 month tour to the Falkland Islands as part of his RAF duties. Now we all know that 'our lads' like to run the flag up and make themselves comfortable while they are away from home, so Jim packed his Red Zephyr in an adapted 'pack up' case and persuded a freindly loady to find a place for it on an outbound flight so it would be there when he arrived. After seeing how well the model flew some bright spark suggested that it should be possible to fly it from one of the airports on the island, Mount Pleasant, to the other, Port Stanley and as both of these airports are classed as international it may well be possible that this flight was the first flight by a model aeroplane from one international airport to another. That is unless you know different? Anyway back to the plot! The flight was arranged and cleared by ATC and Jim found himself sitting in an armchair which had been put in the back of an open backed Land Rover and after fuelling himself and the model they set off on the trip which was around 40 miles. Now as this was the end of summer the wind was both 'fresh' and chilly and the model had to land about half way for refuelling despite the OS 40 four stroke only sipping lightly at the tank. However the flight was completed on the next hop and Jim and his pals raised £600 for a local childrens charity! The picture shows Jim and his pals with the model at Port Stanley airport after arriving safely and just before they all retired to the Frog and Sprocket bar for a 'debriefing!
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Chicken Chewrros are made with USDA Certified Chicken Breast, Organic Carrot, and Organic Cottage Cheese. Chicken Chewrros are popular amongst our puppies, seniors, and cheese lovers of all ages! Plus, they are made without any preservatives or added salt. Our handcrafted delicacies will change the way you think of dog treats. Love your furbabies with MonMo Treats!
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Cake Decoration Tool. All rights reserved. Gallery View. Aluminum Alloy Power: All Categories. Contact Multiple Suppliers. Custom design Tableware picnic half Plastic Name: Best selling excellent quality wholesale cake decorations supplies. Custom Feature: About Delivery We respect contract terms and keep true to delivery time to win clients. Company Name. There seems to be a problem serving the request at this time. If there are bad products, we will promptly pay compensation to customers without any charge.
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Sakthi is a straightforward guy who keeps each and every routine simple.I have always been someone with a lot of questions in my mind, and he was patient enough to deal with my queries one by one.Our sessions were short, efficient affairs as he focused on my fitness goals.Over months spent at the gym, we were able to cut down on my belly fat and improve endurance through specific training sessions. I am more confident as well as energetic nowadays. Mr. Ravi is serious about his job. He respects your time and money and always makes sure to give you value. Approaches his training in a genuinely informed way. He truly knows his stuff and is a fabulous motivator. I would recommend him to anyone thinking of using his services. Very friendly trainer, with lot of knowledge about weight loss, muscle growth and food dietary. Very satisfactory and professional with the approach and method he uses. Have been training with Ganesh for a week now. He is down to earth listens to our needs and provides workout routines as per our requirements. Also the open places he chooses to train us is a break from gyms that are closed rooms with AC. He provides the right mix of cardio with strength training along with few yoga postures gives me a wholistic approach towards my fitness. Would definitely like to continue my association with him as a personal trainer. Looking to hire professionals near Madipakkam?
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\subsection{Proof of Correctness of Top-$K$ Max-Product} We now consider the top-$K$ max-product algorithm, shown in full generality in Algo.~\ref{algo:dp:topK:main}. The following proposition proves its correctness. \begin{proposition} \label{eq:prop:dp:topK_guarantee} Consider as inputs to Algo.~\ref{algo:dp:topK:main} an augmented score function $\psi(\cdot, \cdot ; \wv)$ defined on tree structured graph $\mcG$, and an integer $K > 0$. Then, the outputs of Algo.~\ref{algo:dp:topK:main} satisfy $\psi\pow{k} = \psi(\yv\pow{k}) = \maxK{k}{\yv \in \mcY} \psi(\yv)$. Moreover, Algo.~\ref{algo:dp:topK:main} runs in time $\bigO(pK\log K \max_{v\in\mcV} \abs{\mcY_v}^2)$ and uses space $\bigO(p K \max_{v\in\mcV} \abs{\mcY_v})$. \end{proposition} \begin{proof} For a node $v \in \mcV$, let $\tau(v)$ denote the sub-tree of $\mcG$ rooted at $v$. Let $\yv_{\tau(v)}$ denote $\big( y_{v'} \text{ for } v' \in \tau(v) \big)$. Define $\psi_{\tau(v)}$ as follows: if $v$ is a leaf, $\yv_{\tau(v)} = (y_v)$ and $\psi_{\tau(v)}(\yv_{\tau(v)}) := \psi_v(y_v)$. For a non-leaf $v$, define recursively \begin{align} \label{eq:dp:topk_proof:phi_subtree} \psi_{\tau(v)}(\yv_{\tau(v)}) := \psi_v(y_v) + \sum_{v' \in C(v)} \left[ \psi_{v, v'}(y_v, y_{v'}) + \psi_{\tau(v')}(\yv_{\tau(v')}) \right] \,. \end{align} We will need some identities about choosing the $k$th largest element from a finite collection. For finite sets $S_1, \cdots, S_n$ and functions $f_j: S_j \to \reals$, $h: S_1 \times S_2 \to \reals$, we have, \begin{gather} \label{eq:dp:topk_proof:bellman1} \maxK{k}{u_1 \in S_1, \cdots, u_n \in S_n} \left\{ \sum_{j=1}^n f_j(u_j) \right\} = \quad \maxK{k}{l_1, \cdots, l_n \in [k]} \left\{ \sum_{j=1}^n \maxK{l_j}{u_j \in S_j} f_j(u_j) \right\} \,, \\ \label{eq:dp:topk_proof:bellman2} \maxK{k}{u_1 \in S_1, u_2 \in S_2} \{ f_1(u_1) + h(u_1, u_2) \} = \quad \maxK{k}{u_1 \in S_1, l \in [k]} \left\{ f_1(u_1) + \maxK{l}{u_2 \in S_2} h(u_1, u_2) \right\} \,. \end{gather} The identities above state that for a sum to take its $k$th largest value, each component of the sum must take one of its $k$ largest values. Indeed, if one of the components of the sum took its $l$th largest value for $l > k$, replacing it with any of the $k$ largest values cannot decrease the value of the sum. Eq.~\eqref{eq:dp:topk_proof:bellman2} is a generalized version of Bellman's principle of optimality (see \citet[Chap. III.3.]{bellman1957dynamic} or \citet[Vol. I, Chap. 1]{bertsekas1995dynamic}). For the rest of the proof, $\yv_{\tau(v)} \backslash y_v$ is used as shorthand for $\{y_{v'} \, | \, v' \in \tau(v) \backslash \{v\} \}$. Moreover, $\max_{\yv_{\tau(v)}}$ represents maximization over $\yv_{\tau(v)} \in \bigtimes_{v' \in \tau(v)} \mcY_{v'}$. Likewise for $\max_{\yv_{\tau(v)} \backslash y_v}$. Now, we shall show by induction that for all $v \in \mcV$, $y_v \in \mcY_v$ and $k = 1,\cdots, K$, \begin{align} \label{eq:dp:topk_proof:ind_hyp} \maxK{k}{\yv_{\tau(v)}\backslash y_v} \psi_{\tau(v)}(\yv_{\tau(v)}) = \psi_v(y_v) + \maxK{k}{} \bigg\{ \sum_{v' \in C(v)} m_{v'}\pow{l_{v'}}(y_{v'}) \bigg| l_{v'} \in [K] \text{ for } v' \in C(v) \bigg\} \,. \end{align} The induction is based on the height of a node. The statement is clearly true for a leaf $v$ since $C(v) = \varnothing$. Suppose \eqref{eq:dp:topk_proof:ind_hyp} holds for all nodes of height $\le h$. For a node $v$ of height $h+1$, we observe that $\tau(v) \backslash v$ can be partitioned into $\{\tau(v') \text{ for } v' \in C(v)\}$ to get, \begin{gather} \nonumber \maxK{k}{\yv_{\tau(v)}\backslash y_v} \psi_{\tau(v)}(\yv_{\tau(v)}) - \psi_v(y_v) \stackrel{\eqref{eq:dp:topk_proof:phi_subtree}}{=} \maxK{k}{\yv_{\tau(v)}\backslash y_v} \bigg\{ \sum_{v' \in C(v)} \psi_{v, v'}(y_v, y_{v'}) + \psi_{\tau(v')}(\yv_{\tau(v')}) \bigg\} \\ \label{eq:eq:topk_proof:ind_hyp_todo} \stackrel{\eqref{eq:dp:topk_proof:bellman1}}{=} \maxK{k}{} \bigg\{ \sum_{v' \in C(v)} \underbrace{ \maxK{l_{v'}}{\yv_{\tau(v')}} \{ \psi_{v, v'}(y_v, y_{v'}) + \psi_{\tau(v')}(\yv_{\tau(v')}) \} }_{=:\mcT_{v'}(y_v)} \, \bigg| \, l_{v'} \in [K] \text{ for } v' \in C(v) \bigg\} \,. \end{gather} Let us analyze the term in the underbrace, $\mcT_{v'}(y_v)$. We successively deduce, with the argument $l$ in the maximization below taking values in $\{1, \cdots, K\}$, \begin{align*} \mcT_{v'}(y_v) &\stackrel{\eqref{eq:dp:topk_proof:bellman2}}{=} \maxK{l_{v'}}{y_{v'}, l} \bigg\{ \psi_{v, v'}(y_v, y_{v'}) + \maxK{l}{\yv_{\tau(v')}\backslash y_{v'}} \psi_{\tau(v')}(\yv_{\tau(v')}) \bigg\} \\ &\stackrel{\eqref{eq:dp:topk_proof:ind_hyp}}{=} \maxK{l_{v'}}{y_{v'}, l} \bigg\{ \begin{matrix} \psi_{v'}(y_{v'}) + \psi_{v, v'}(y_v, y_{v'}) + \\ \maxK{l}{} \big\{ \sum_{v'' \in C(v')} m_{v''}\pow{l_{v''}}(y_{v'}) \, | \, l_{v''} \in [K] \text{ for } v'' \in C(v') \big\} \end{matrix} \bigg\} \\ &\stackrel{\eqref{eq:dp:topk_proof:bellman2}}{=} \maxK{l_{v'}}{} \bigg\{ \begin{matrix} \psi_{v'}(y_{v'}) + \psi_{v', v}(y_{v'}, y_v) \\ + \sum_{v'' \in C(v')} m\pow{l_{v''}}_{v''}(y_{v'}) \end{matrix} \, \bigg| \, \begin{matrix} y_{v'} \in \mcY_{v'} \text{ and } \\ l_{v''} \in [K] \text{ for } v'' \in C(v) \end{matrix} \bigg\} \\ &\stackrel{\eqref{eq:dp:topk:algo:update}}{=} m\pow{l_{v'}}_{v'}(y_v) \, . \end{align*} Here, the penultimate step followed from applying in reverse the identity \eqref{eq:dp:topk_proof:bellman2} with $u_1, u_2$ being by $y_{v'}, \{ l_{v''} \text{ for } v'' \in C(v')\}$ respectively, and $f_1$ and $h$ respectively being $ \psi_{v'}(y_{v'}) + \psi_{v', v}(y_{v'}, y_v)$ and $ \sum_{v''} m\pow{l_{v''}}_{v''}(y_{v'})$. Plugging this into \eqref{eq:eq:topk_proof:ind_hyp_todo} completes the induction argument. To complete the proof, we repeat the same argument over the root as follows. We note that $\tau(r)$ is the entire tree $\mcG$. Therefore, $\yv_{\tau(r)} = \yv$ and $\psi_{\tau(r)} = \psi$. We now apply the identity \eqref{eq:dp:topk_proof:bellman2} with $u_1$ and $u_2$ being $y_r$ and $\yv_{\tau(r) \backslash r}$ respectively and $f_1 \equiv 0$ to get \begin{align*} \maxK{k}{\yv \in \mcY} \psi(\yv) & \stackrel{\eqref{eq:dp:topk_proof:bellman2}}{=} \maxK{k}{y_r, l} \left\{ \maxK{l}{\yv\backslash y_r} \psi(\yv) \right\} = \maxK{k}{y_r, l} \left\{ \maxK{l}{\yv_{\tau(r)} \backslash y_r} \psi_{\tau(r)}(\yv_{\tau(r)}) \right\} \\ &\stackrel{\eqref{eq:dp:topk_proof:ind_hyp}}{=} \maxK{k}{y_r, l} \bigg\{ \begin{matrix} \psi_{r}(y_{r}) + \maxK{l}{} \big\{ \sum_{v \in C(r)} m_{v}\pow{l_{v}}(y_r) \, | \, l_{v} \in [K] \text{ for } v \in C(r) \big\} \end{matrix} \bigg\} \\ &\stackrel{\eqref{eq:dp:topk_proof:bellman2}}{=} \maxK{k}{} \bigg\{ \begin{matrix} \psi_r(y_r) + \\ \sum_{v \in C(r)} m\pow{l_{v}}_{v}(y_r) \end{matrix} \, \bigg| \, \begin{matrix} y_{r} \in \mcY_{r} \text{ and } \\ l_{v} \in [K] \text{ for } v \in C(r) \end{matrix} \bigg\} \\ &\,= \psi\pow{k} \,, \end{align*} where the last equality follows from Line~\ref{line:algo:dp:topk:final_score_k} of Algo.~\ref{algo:dp:topK:main}. The algorithm requires storage of $m_v\pow{k}$, an array of size $\max_{v \in \mcV} \abs{\mcY_v}$ for each $k = 1,\cdots, K$, and $v \in \mcV$. The backpointers $\delta, \kappa$ are of the same size. This adds up to a total storage of $\bigO(pK \max_{v} \abs{\mcY_v})$. To bound the running time, consider Line~\ref{line:algo:dp:topk:message_k} of Algo.~\ref{algo:dp:topK:main}. For a fixed $v' \in C(v)$, the computation \begin{align*} \maxK{k}{y_v, l_{v'} } \left\{ \psi_v(y_v) + \psi_{v, \rho(v)}(y_v, y_{\rho(v)}) + m_{v'}^{(l_{v'})}(y_v) \right\} \end{align*} for $k= 1, \cdots, K$ takes time $\bigO(K \log K \max_v \abs{\mcY_v})$. This operation is repeated for each $y_v \in \mcY_v$ and once for every $(v, v')\in \mcE$. Since $\abs\mcE = p-1$, the total running time is $\bigO(p K \log K \max_v \abs{\mcY_v}^2)$. \end{proof} \subsection{Proof of Correctness of Entropy Smoothing of Max-Product} Next, we consider entropy smoothing. \begin{proposition}\label{eq:prop:dp:ent_guarantee} Given an augmented score function $\psi(\cdot, \cdot ; \wv)$ defined on tree structured graph $\mcG$ and $\mu > 0$ as input, Algo.~\ref{algo:dp:supp_exp} correctly computes $f_{-\mu H}(\wv)$ and $\grad f_{-\mu H}(\wv)$. Furthermore, Algo.~\ref{algo:dp:supp_exp} runs in time $\bigO(p \max_{v\in\mcV} \abs{\mcY_v}^2)$ and requires space $\bigO(p \max_{v\in\mcV} \abs{\mcY_v})$. \end{proposition} \begin{proof} The correctness of the function value $f_{- \mu H}$ follows from the bijection $f_{- \mu H}(\wv) = \mu \, A_{\psi/\mu}(\wv)$ (cf. Prop.~\ref{prop:smoothing:exp-crf}), where Thm.~\ref{thm:pgm:sum-product} shows correctness of $A_{\psi / \mu}$. To show the correctness of the gradient, define the probability distribution $ P_{\psi, \mu}$ as the probability distribution from Lemma~\ref{lemma:smoothing:first-order-oracle}\ref{lem:foo:exp} and $P_{\psi, \mu, v}, P_{\psi, \mu, v, v'}$ as its node and edge marginal probabilities respectively as \begin{align*} P_{\psi, \mu}(\yv ; \wv) &= \frac{ \exp\left(\tfrac{1}{\mu}\psi(\yv ; \wv)\right)} {\sum_{\yv' \in \mcY }\exp\left(\tfrac{1}{\mu}\psi(\yv' ; \wv)\right)} \,, \\ P_{\psi, \mu, v}(\overline y_v ; \wv) &= \sum_{\substack{ \yv \in \mcY \, : \\ y_v = \overline y_v} }P_{\psi, \mu}(\yv ; \wv) \quad \text{for } \overline y_v \in \mcY_v, v \in \mcV\,, \text{ and, } \\ P_{\psi, \mu, v, v'}(\overline y_v, \overline y_{v'} ; \wv) &= \sum_{\substack{ \yv \in \mcY : \\ y_v = \overline y_v, \\ y_{v'} = \overline y_{v'} } }P_{\psi, \mu}(\yv ; \wv) \quad \text{for } \overline y_v \in \mcY_v, \overline y_{v'} \in \mcY_{v'}, (v,v') \in \mcE \,. \end{align*} Thm.~\ref{thm:pgm:sum-product} again shows that Algo.~\ref{algo:dp:supp_sum-prod} correctly produces marginals $P_{\psi, \mu, v}$ and $P_{\psi, \mu, v, v'}$. We now start with Lemma~\ref{lemma:smoothing:first-order-oracle}\ref{lem:foo:exp} and invoke \eqref{eq:smoothing:aug_score_decomp} to get \begin{align*} \grad f_{-\mu H}(\wv) =& \sum_{\yv \in \mcY} P_{\psi, \mu}(\yv ; \wv) \grad \psi(\yv ; \wv) \\ {=}& \sum_{\yv \in \mcY} P_{\psi, \mu}(\yv ; \wv) \left( \sum_{v\in \mcV} \grad \psi_v(y_v ; \wv) + \sum_{(v, v')\in \mcE} \grad \psi_{v, v'}(y_v, y_{v'} ; \wv) \right) \,, \\ =& \sum_{v \in \mcV} \sum_{\yv \in \mcY} P_{\psi, \mu}(\yv ; \wv) \grad \psi_v( y_v ; \wv) + \sum_{(v,v') \in \mcE} \sum_{\yv \in \mcY} P_{\psi, \mu}(\yv ; \wv) \grad \psi_{v, v'}(y_v, y_{v'} ; \wv) \\ =& \sum_{v \in \mcV} \sum_{\overline y_v \in \mcY_v} \sum_{\yv \in \mcY \, : \,y_v = \overline y_v} P_{\psi, \mu}(\yv ; \wv) \grad \psi_v(\overline y_v ; \wv) \\ &\qquad+ \sum_{(v,v') \in \mcE} \sum_{\overline y_v \in \mcY_v} \sum_{\overline y_{v'} \in \mcY_{v'}} \sum_{\yv \in \mcY \, :\, \substack{ y_v = \overline y_v \\ y_{v'} = \overline y_{v'} } } P_{\psi, \mu}(\yv ; \wv) \grad \psi_{v, v'}(\overline y_v, \overline y_{v'} ; \wv) \\ =& \sum_{v \in \mcV} \sum_{\overline y_v \in \mcY_v} P_{\psi, \mu, v}(\overline y_v ; \wv) \grad \psi_{v}(\overline y_v ; \wv) \\ &\qquad+ \sum_{(v,v') \in \mcE} \sum_{\overline y_v \in \mcY_v} \sum_{\overline y_{v'} \in \mcY_{v'}} P_{\psi, \mu, v, v'}(\overline y_v, \overline y_{v'} ; \wv) \grad \psi_{v, v'}(\overline y_v, \overline y_{v'} ; \wv) \,. \end{align*} Here, the penultimate equality followed from breaking the sum over $\yv \in \mcY$ into an outer sum that sums over every $\overline y_v \in \mcY_v$ and an inner sum over $\yv \in \mcY : y_v = \overline y_v$, and likewise for the edges. The last equality above followed from the definitions of the marginals. Therefore, Line~\ref{line:algo:dp:exp:gradient} of Algo.~\ref{algo:dp:supp_exp} correctly computes the gradient. The storage complexity of the algorithm is $\bigO(p \max_v \abs{\mcY_v})$ provided that the edge marginals $P_{\psi, \mu, v, v'}$ are computed on the fly as needed. The time overhead of Algo.~\ref{algo:dp:supp_exp} after Algo.~\ref{algo:dp:supp_sum-prod} is $\bigO(p \max_v \abs{\mcY_v}^2)$, by noting that each edge marginal can be computed in constant time (Remark~\ref{remark:pgm:sum-prod:fast-impl}). \end{proof} \begin{algorithm}[ptbh] \caption{Sum-product algorithm} \label{algo:dp:supp_sum-prod} \begin{algorithmic}[1] \STATE {\bfseries Procedure:} \textsc{SumProduct} \STATE {\bfseries Input:} Augmented score function $\psi$ defined on tree structured graph $\mcG$ with root $r \in \mcV$. \STATE {\bfseries Notation:} Let $N(v) = C(v) \cup \{\rho(v)\}$ denote all the neighbors of $v \in \mcV$ if the orientation of the edges were ignored. \STATE {\bfseries Initialize:} Let $V$ be a list of nodes from $\mcV$ arranged in increasing order of height. \FOR{$v$ in $V \backslash \{r\}$} \STATE Set for each $y_{\rho(v)} \in \mcY_{\rho(v)}$: \label{line:dp:exp_dp:update} \[ m_{v \to \rho(v)}(y_{\rho(v)}) \leftarrow \sum_{y_v \in \mcY_v} \left[ \exp \left( \psi_v(y_v) + \psi_{v, \rho(v)}(y_v, y_{\rho(v)}) \right) \prod_{v' \in C(v)} m_{v' \to v}(y_v) \right] \,. \] \ENDFOR \STATE $A \leftarrow \log \sum_{y_r \in \mcY_r} \left[ \exp\left( \psi_r(y_r) \right) \prod_{v' \in C(r)} m_{v' \to r}(y_r) \right] $. \label{line:dp:exp_dp:log_part} \FOR{$v$ in $\mathrm{reverse}(V)$} \FOR{$v' \in C(v)$} \STATE Set for each $y_{v'} \in \mcY_{v'}$: \[ m_{v\to v'}(y_{v'}) = \sum_{y_v \in \mcY_v}\left[ \exp\left( \psi_v(y_v) + \psi_{v', v}(y_{v'}, y_v) \right) \prod_{v'' \in N(v)\backslash\{v'\}} m_{v'' \to v}(y_v) \right] \,. \] \ENDFOR \ENDFOR \FOR{ $v$ in $\mcV$} \STATE Set $P_v(y_v) \leftarrow \exp\left( \psi_v(y_v) - A \right) \prod_{v'' \in N(v)} m_{v''\to v}(y_v)$ for every $y_v \in \mcY_v$. \ENDFOR \FOR{$(v, v')$ in $\mcE$} \STATE For every pair $(y_v, y_{v'}) \in \mcY_v \times \mcY_{v'}$, set \label{line:algo:sum-prod:pair} \begin{align*} P_{v, v'}(y_v, y_{v'}) \leftarrow & \exp\left(\psi_v(y_v) + \psi_{v'}(y_{v'}) + \psi_{v, v'}(y_v, y_{v'}) - A \right) \\& \prod_{v'' \in N(v) \backslash \{v'\}} m_{v''\to v}(y_v) \prod_{v'' \in N(v') \backslash \{v\}} m_{v''\to v'}(y_{v'}) \,. \end{align*} \ENDFOR \RETURN $A, \{P_v \text{ for } v \in \mcV \}, \{P_{v, v'} \text{ for } (v, v') \in \mcE \}$. \end{algorithmic} \end{algorithm} Given below is the guarantee of the sum-product algorithm (Algo.~\ref{algo:dp:supp_sum-prod}). See, for instance, \citet[Ch. 10]{koller2009probabilistic} for a proof. \begin{theorem} \label{thm:pgm:sum-product} Consider an augmented score function $\psi$ defined over a tree structured graphical model $\mcG$. Then, the output of Algo.~\ref{algo:dp:supp_sum-prod} satisfies \begin{align*} A &= \log \sum_{\yv \in \mcY} \exp(\psi(\yv)) \,, \\ P_v(\overline y_v) &= \sum_{\yv \in \mcY\, :\, y_v = \overline y_v} \exp(\psi(\yv) - A) \, \quad \text{for all $\overline y_v \in \mcY_v, v \in \mcV$, and, }\, \\ P_{v, v'}(\overline y_v, \overline y_{v'}) &= \sum_{\yv \in \mcY\, : \, \substack{ y_v = \overline y_v, \\ y_{v'} = \overline y_{v'} } } \exp(\psi(\yv) - A) \, \quad \text{for all $\overline y_v \in \mcY_v, \overline y_{v'} \in \mcY_{v'}, (v,v') \in \mcE$.} \\ \end{align*} Furthermore, Algo.~\ref{algo:dp:supp_sum-prod} runs in time $\bigO(p \max_{v\in\mcV} \abs{\mcY_v}^2)$ and requires an intermediate storage of $\bigO(p \max_{v\in\mcV} \abs{\mcY_v})$. \end{theorem} \begin{remark} \label{remark:pgm:sum-prod:fast-impl} Line~\ref{line:algo:sum-prod:pair} of Algo.~\ref{algo:dp:supp_sum-prod} can be implemented in constant time by reusing the node marginals $P_v$ and messages $m_{v \to v'},m_{v' \to v}$ as \begin{align*} P_{v, v'}(y_v, y_{v'}) = \frac{P_v(y_v) P_{v'}(y_{v'}) \exp(\psi_{v, v'}(y_v, y_{v'}) + A)}{m_{v'\to v}(y_v) m_{v\to v'}(y_{v'}) } \,. \end{align*} \end{remark} \subsection{Review of Best Max-Marginal First} \label{sec:a:bmmf} If one has access to an algorithm $\mcM$ that can compute max-marginals, the top-$K$ oracle is easily implemented via the Best Max Marginal First (BMMF) algorithm of \citet{yanover2004finding}, which is recalled in Algo.~\ref{algo:top_k_map:general}. This algorithm requires computations of two sets of max-marginals per iteration, where a {\em set} of max-marginals refers to max-marginals for all variables $y_v$ in $\yv$. \paragraph{Details} The algorithm runs by maintaining a partitioning of the search space $\mcY$ and a table $\varphi\pow{k}(v, j)$ that stores the best score in partition $k$ (defined by constraints $\mcC\pow{k}$) subject to the additional constraint that $y_v = j$. In iteration $k$, the algorithm looks at the $k-1$ existing partitions and picks the best partition $s_k$ (Line~\ref{alg:bmmf:best_part}). This partition is further divided into two parts: the max-marginals in the promising partition (corresponding to $y_{v_k} = j_k$) are computed (Line~\ref{alg:bmmf:line:max-marg}) and decoded (Line~\ref{alg:bmmf:line:decoding}) to yield $k$th best scoring $\yv\pow{k}$. The scores of the less promising partition are updated via a second round of max-marginal computations (Line~\ref{alg:bmmf:line:update_score}). \begin{algorithm}[tb] \caption{Best Max Marginal First (BMMF)} \label{algo:top_k_map:general} \begin{algorithmic}[1] \STATE {\bfseries Input:} Augmented score function $\psi$, parameters $\wv$, non-negative integer $K$, algorithm $\mcM$ to compute max-marginals of $\psi$. \STATE {\bfseries Initialization:} $\mcC\pow{1} = \varnothing$ and $\mcU\pow{2} = \varnothing$. \FOR{$v \in [p]$} \STATE For $j \in \mcY_v$, set $\varphi\pow{1}(v;j) = \max \{ \psi(\yv ; \wv) \, | \, \yv \in \mcY \text{ s.t. } y_v = j \}$ using $\mcM$. \STATE Set $y\pow{1}_v = \argmax_{j \in \mcY_v} \varphi\pow{1}(v, j)$. \ENDFOR \FOR{$k = 2, \cdots, K$} \STATE Define search space $\mcS\pow{k} = \left\{ (v, j, s) \in [p] \times \mcY_v \times [k-1] \, \big| \, y\pow{s}_v \neq j, \text{ and } (v, j, s) \notin \mcU\pow{t} \right\}$. \label{alg:bmmf:part_search} \STATE Find indices $(v_k, j_k, s_k) = \argmax_{(v, j, s) \in \mcS\pow{k}} \varphi\pow{s}(v,j)$ and set constraints $\mcC\pow{k} = \mcC\pow{s_k} \cup \{ y_{v_k} = j_k \}$. \label{alg:bmmf:best_part} \FOR{$v\in[p]$} \STATE For each $j \in \mcY_v$, use $\mcM$ to set $\varphi\pow{k}(v, j) = \max \left\{ \psi(\yv ; \wv) \, | \, \yv \in \mcY \text{ s.t. constraints } \mcC\pow{k} \text{ hold and } y_v = j \right\}$. \label{alg:bmmf:line:max-marg} \STATE Set $y\pow{k}_v = \argmax_{j \in \mcY_v} \varphi\pow{k}(v, j)$. \label{alg:bmmf:line:decoding} \ENDFOR \STATE Update $\mcU\pow{k+1} = \mcU\pow{k} \cup \left\{ (v_k, j_k, s_k) \right\}$ and $\mcC\pow{s_k} = \mcC\pow{s_k} \cup \{ y_{v_k} \neq j_k \}$ and the max-marginal table $\varphi\pow{s_k}(v, j) = \max_{\yv \in \mcY, \mcC\pow{s_k}, y_v = j} \psi(\yv ; \wv)$ using $\mcM$. \label{alg:bmmf:line:update_score} \ENDFOR \RETURN $\left\{ \left(\psi(\yv\pow{k} ; \wv), \yv\pow{k} \right) \right\}_{k=1}^K$. \end{algorithmic} \end{algorithm} \paragraph{Guarantee} The following theorem shows that Algo.~\ref{algo:top_k_map:general} provably implements the top-$K$ oracle as long as the max-marginals can be computed exactly under the assumption of unambiguity. With approximate max-marginals however, Algo.~\ref{algo:top_k_map:general} comes with no guarantees. \begin{theorem}[\citet{yanover2004finding}] \label{thm:inference:topKmm} Suppose the score function $\psi$ is unambiguous, that is, $\psi(\yv' ; \wv) \neq \psi(\yv'' ;\wv)$ for all distinct $\yv', \yv'' \in \mcY$. Given an algorithm $\mcM$ that can compute the max-marginals of $\psi$ exactly, Algo.~\ref{algo:top_k_map:general} makes at most $2K$ calls to $\mcM$ and its output satisfies $\psi(\yv_k ; \wv) = \max\pow{k}_{\yv \in \mcY} \psi(\yv ; \wv)$. Thus, the BMMF algorithm followed by a projection onto the simplex (Algo.~\ref{algo:smoothing:top_K_oracle} in Appendix~\ref{sec:a:smoothing}) is a correct implementation of the top-$K$ oracle. It makes $2K$ calls to $\mcM$. \end{theorem} \paragraph{Constrained Max-Marginals} The algorithm requires computation of max-marginals subject to constraints of the form $y_v \in Y_v$ for some set $Y_v \subseteq \mcY_v$. This is accomplished by redefining for a constraint $y_v \in Y_v$: \[ \overline \psi(\yv) = \begin{cases} \psi(\yv), \, \text{ if } y_v \in Y_v \\ -\infty, \, \text{ otherwise} \end{cases} \,. \] \subsection{Max-Marginals Using Graph Cuts} \label{sec:a:graph_cuts} \begin{algorithm}[tb] \caption{Max-marginal computation via Graph Cuts} \label{algo:top_k_map:graph_cuts} \begin{algorithmic}[1] \STATE {\bfseries Input:} Augmented score function $\psi(\cdot, \cdot ; \wv)$ with $\mcY = \{0, 1\}^p$, constraints $\mcC$ of the form $y_v = b$ for $b \in \{0,1\}$. \STATE Using artificial source $s$ and sink $t$, set $V' = \mcV \cup \{s, t\}$ and $E' = \varnothing$. \FOR{$v \in [p]$} \STATE Add to $E'$ the (edge, cost) pairs $(s \to y_v, \theta_{v; 0})$ and $(y_v \to t, \theta_{v; 1})$. \ENDFOR \FOR{$v,v' \in \mcR$ such that $v < v'$} \STATE Add to $E'$ the (edge, cost) pairs $(s \to y_v , \theta_{vv'; 00})$, $(y_{v'} \to t , \theta_{vv'; 11})$, $(y_v \to y_{v'} , \theta_{vv'; 10})$, $(y_{v'} \to y_v , \theta_{vv'; 01} - \theta_{vv' ;00} - \theta_{vv' ; 11})$. \ENDFOR \FOR{constraint $y_v = b$ in $\mcC$} \STATE Add to $E'$ the edge $y_v \to t$ if $b=0$ or edge $s \to y_v$ if $b=1$ with cost $+\infty$. \label{line:algo:mincut:constr} \ENDFOR \STATE Create graph $G'=(V', E')$, where parallel edges are merged by adding weights. \STATE Compute minimum cost $s, t$-cut of $G'$. Let $C$ be its cost. \STATE Create $\widehat \yv \in \{0, 1\}^p$ as follows: for each $v \in \mcV$, set $\widehat y_v = 0$ if the edge $s\to v$ is cut. Else $\widehat y_v = 1$. \RETURN $-C, \widehat \yv$. \end{algorithmic} \end{algorithm} This section recalls a simple procedure to compute max-marginals using graph cuts. Such a construction was used, for instance, by \citet{kolmogorov2004energy}. \paragraph{Notation} In the literature on graph cut inference, it is customary to work with the energy function, which is defined as the negative of the augmented score $-\psi$. For this section, we also assume that the labels are binary, i.e., $\mcY_v = \{0,1\}$ for each $v\in[p]$. Recall the decomposition~\eqref{eq:smoothing:aug_score_decomp} of the augmented score function over nodes and edges. Define a reparameterization \begin{gather*} \theta_{v;z}(\wv) = -\psi_v(z ; \wv) \, \text{ for } v\in \mcV, z \in \{0,1\} \,\\ \theta_{vv';z,z'}(\wv) = -\psi_{v,v'}(z, z' ;\wv) \,, \, \text{ if } (v, v') \in \mcE \\ \text{ for } (v, v')\in \mcE, (z,z') \in \{0,1\}^2\,. \end{gather*} We then get \begin{gather*} -\psi(\yv) = \sum_{v=1}^p \sum_{z \in \{0,1\}} \theta_{v; z} \ind(y_v=z) + \sum_{v=1}^p \sum_{v'=i+1}^p \sum_{z, z' \in \{0,1\}} \theta_{vv'; z z'} \ind(y_v=z) \ind(y_{v'}=z') \ind((v,v') \in \mcE) \,, \end{gather*} where we dropped the dependence on $\wv$ for simplicity. We require the energies to be submodular, i.e., for every $v, v' \in [p]$, we have that \begin{align} \label{eq:top_k_map:submodular} \theta_{vv' ; 00} + \theta_{vv' ; 11} \le \theta_{vv' ; 01} + \theta_{vv' ; 10} \,. \end{align} Also, assume without loss of generality that $\theta_{v;z}, \theta_{vv';zz'}$ are non-negative \citep{kolmogorov2004energy}. \paragraph{Algorithm and Correctness} Algo.~\ref{algo:top_k_map:graph_cuts} shows how to compute the max-marginal relative to a single variable $y_v$. The next theorem shows its correctness. \begin{theorem}[\citet{kolmogorov2004energy}] \label{thm:top_k_map:graph_cuts} Given a binary pairwise graphical model with augmented score function $\psi$ which satisfies \eqref{eq:top_k_map:submodular}, and a set of constraints $\mcC$, Algo.~\ref{algo:top_k_map:graph_cuts} returns $\max_{\yv \in \mcY_\mcC} \psi(\yv ; \wv)$, where $\mcY_\mcC$ denotes the subset of $\mcY$ that satisfies constraints $\mcC$. Moreover, Algo.~\ref{algo:top_k_map:graph_cuts} requires one maximum flow computation. \end{theorem} \iffalse \begin{proof} Suppose first that there are no constraints. We shall use the following two facts about the graph $G'$ in Algo.~\ref{algo:top_k_map:graph_cuts}. \begin{fact} \label{fact:graphcuts:fact1} Every label $\yv \in \mcY$ corresponds to a minimal cut in the graph $G'$, where the energy of the labeling $-\psi(\yv ; \wv)$ equals the cost of the cut. \end{fact} This shows that there exists a cut that corresponds to the minimum energy label $\yv^* = \argmax_{\yv \in \mcY} \psi(\yv ; \wv)$. However, the minimum cut might not correspond to any $\yv \in \mcY$. \begin{fact} \label{fact:graphcuts:fact2} The minimum cut of graph $G'$ corresponds to a valid labeling $\widehat \yv \in \mcY$. This labeling can be decoded as follows: $\widehat y_v = 0$ if the edge $s\to v$ is cut. Else $\widehat y_v = 1$. \end{fact} From Facts~\ref{fact:graphcuts:fact1} and~\ref{fact:graphcuts:fact2}, we deduce that the minimum cut of $G'$ corresponds to the minimum energy assignment $\yv^*$ and that the cost of the cut equals $\psi(\yv^* ; \wv)$. When we have constraints, note that the infinite weight edges added in Line~\ref{line:algo:mincut:constr} of Algo.~\ref{algo:top_k_map:graph_cuts} are never cut, else the cost of the cut would be $+\infty$. This enforces the constraints, and the cost of the returned cut is therefore $\max_{\yv \in \mcY_\mcC} \psi(\yv ; \wv)$. \end{proof} Let us now prove Facts~\ref{fact:graphcuts:fact1} and~\ref{fact:graphcuts:fact2}. \begin{proof}[Fact~\ref{fact:graphcuts:fact1}] Suppose we have labeling $\yv \in \mcY$. For each $v \in [p]$, cut $s \to y_v$ if $y_v = 0$, else cut $y_v = t$. For edges $vv'$, if $y_v = 0$ and $y_{v'} = 1$, also cut the edge $v' \to v$. Else, if if $y_v = 1$ and $y_{v'} = 0$, cut instead the edge $v \to v'$. Clearly, this is a $s,t$-cut because every path from $s$ to $t$ has a cut edge. Moreover, the cut is {\em minimal} in that adding any one cut edge back to the graph results in a valid $s-t$ path. The cost of this cut $C$ is now, (each summation on $v, v'$ below runs from $1$ to $p$ unless mentioned otherwise) \begin{align*} \mathrm{cost}(C) =& \sum_{v} \theta_{v ; y_v} + \sum_{v}\sum_{v' > v}\theta_{vv' ; 00} \ind(y_v = 0) + \sum_{v}\sum_{v' < v} \theta_{v'v ; 11} \ind(y_v = 1) \\ &+ \sum_{v}\sum_{v' > v} \theta_{vv' ; 10} \ind(y_v = 1) \ind(y_{v'} = 0) + \sum_{v}\sum_{v' > v} \left( \theta_{vv' ; 01} - \theta_{vv' ; 00} - \theta_{vv' ; 11} \right) \ind(y_v = 0) \ind(y_{v'} = 1) \\ =& \sum_{v} \theta_{v ; y_v} + \sum_{v} \sum_{v' > v} \big[ \theta_{vv' ; 00} \ind(y_v = 0) \left( 1 - \ind(y_{v'} = 1) \right) + \theta_{vv' ; 11} \ind(y_{v'} = 1) \left( 1 - \ind(y_v = 0) \right) \\ &+ \theta_{vv' ; 10} \ind(y_v = 1) \ind(y_{v'} = 0) + \theta_{vv' ; 01} \ind(y_v = 0) \ind(y_{v'} = 1) \big] \\ =& \sum_{v} \theta_{v ; y_v} + \sum_{v} \sum_{v' > v} \big[ \theta_{vv' ; 00} \ind(y_v = 0) \ind(y_{v'} = 0) + \theta_{vv' ; 11} \ind(y_{v'} = 1) \ind(y_v = 1) \\ &+ \theta_{vv' ; 10} \ind(y_v = 1) \ind(y_{v'} = 0) + \theta_{vv' ; 01} \ind(y_v = 0) \ind(y_{v'} = 1) \big] \\ =& \sum_{v} \theta_{v ; y_v} + \sum_{v} \sum_{v' > v} \theta_{vv' ; y_v y_{v'}} = - \psi(\yv ; \wv) \,. \end{align*} \end{proof} Next, let us prove Fact~\ref{fact:graphcuts:fact2}. \begin{proof}[Fact~\ref{fact:graphcuts:fact2}] Call the minimum cut $C$. For every vertex $v$, there exists a path $s \to v \to t$. Therefore, one of $s \to v$ or $v \to t$ must be cut. Since each $\theta_{v ; z}$ is assumed to be non-negative, {\em exactly one} of $s \to v$ or $v \to t$ is cut in the min cost cut. If $s \to v$ is cut, set $\widehat y_v = 0$. Else set $\widehat y_v = 1$. The labeling $\widehat \yv$ so obtained corresponds to a minimal cut, say $C'$, by Fact~\ref{fact:graphcuts:fact1}. By construction, $C$ and $C'$ agree on which $s \to v$ and $v \to t$ edges to cut. Minimality of $C$ and $C'$ ensure that $C = C'$, up to zero weight edges. But zero weight edges do not impact the cost of the cut and therefore, $\mathrm{cost}(C) = \mathrm{cost}(C') = -\psi(\widehat \yv ; \wv)$. Therefore, the min cut $C$ corresponds to the labeling $\widehat \yv$. \end{proof} \fi \subsection{Max-Marginals Using Graph Matchings} \label{sec:a:graph_matchings} The alignment problem that we consider in this section is as follows: given two sets $V, V'$, both of equal size (for simplicity), and a weight function $\varphi: V \times V' \to \reals$, the task is to find a map $\sigma : V \to V'$ so that each $v \in V$ is mapped to a unique $z \in V'$ and the total weight $\sum_{v \in V} \varphi(v, \sigma(v))$ is maximized. For example, $V$ and $V'$ might represent two natural language sentences and this task is to align the two sentences. \paragraph{Graphical Model} This problem is framed as a graphical model as follows. Suppose $V$ and $V'$ are of size $p$. Define $\yv = (y_1, \cdots, y_p)$ so that $y_v$ denotes $\sigma(v)$. The graph $\mcG = (\mcV, \mcE)$ is constructed as the fully connected graph over $\mcV = \{1, \cdots, p\}$. The range $\mcY_v$ of each $y_v$ is simply $V'$ in the unconstrained case. Note that when considering constrained max-marginal computations, $\mcY_v$ might be subset of $V'$. The score function $\psi$ is defined as node and edge potentials as in Eq.~\eqref{eq:smoothing:aug_score_decomp}. Again, we suppress dependence of $\psi$ on $\wv$ for simplicity. Define unary and pairwise scores as \begin{align*} \psi_v(y_v) = \varphi(v, y_v) \quad \text{and} \quad \psi_{v, v'}(y_v, y_{v'}) = \begin{cases} 0, \text{ if } y_v \neq y_{v'} \\ -\infty, \text{ otherwise } \end{cases} \, . \end{align*} \paragraph{Max Oracle} The max oracle with $\psi$ defined as above, or equivalently, the inference problem \eqref{eq:pgm:inference} (cf. Lemma~\ref{lemma:smoothing:first-order-oracle}\ref{lem:foo:max}) can be cast as a maximum weight bipartite matching, see e.g., \citet{taskar2005discriminative}. Define a fully connected bipartite graph $G = (V \cup V', E)$ with partitions $V, V'$, and directed edges from each $v \in V$ to each vertex $z \in V'$ with weight $\varphi(v, z)$. The maximum weight bipartite matching in this graph $G$ gives the mapping $\sigma$, and thus implements the max oracle. It can be written as the following linear program: \begin{align*} \max_{\{\theta_{v,z} \text{ for } (v,z) \in E\}} \, & \sum_{(v,z) \in E} \varphi(v, z) \theta_{v, z} \,, \\ \mathrm{s.t.} \quad & 0 \le \theta_{v, z} \le 1 \, \forall (v, z) \in V \times V' \\ & \sum_{v \in V} \theta_{v, z} \le 1 \, \forall z \in V' \\ & \sum_{z \in V'} \theta_{v, z} \le 1 \, \forall v \in V \, . \end{align*} \paragraph{Max-Marginal} For the graphical model defined above, the max-marginal $\psi_{\bar v ; \bar z}$ is the constrained maximum weight matching in the graph $G$ defined above subject to the constraint that $\bar v$ is mapped to $\bar z$. The linear program above can be modified to include the constraint $\theta_{\bar v, \bar z} = 1$: \begin{align} \label{eq:top_k_map:graph_matchings:max-marg:def} \begin{aligned} \max_{\{\theta_{v,z} \text{ for } (v,z) \in E\}} \, & \sum_{(v,z) \in E} \varphi(v, z) \theta_{v, z} \,, \\ \mathrm{s.t.} \quad & 0 \le \theta_{v, z} \le 1 \, \forall (v, z) \in V \times V' \\ & \sum_{v \in V} \theta_{v, z} \le 1 \, \forall z \in V' \\ & \sum_{z \in V'} \theta_{v, z} \le 1 \, \forall v \in V \\ & \theta_{\bar v, \bar z} = 1 \, . \end{aligned} \end{align} \paragraph{Algorithm to Compute Max-Marginals} Algo.~\ref{algo:top_k_map:graph_matchings}, which shows how to compute max-marginals is due to \citet{duchi2007using}. Its running time complexity is as follows: the initial maximum weight matching computation takes $\bigO(p^3)$ via computation of a maximum flow~\citep[Ch.~10]{schrijver-book}. Line~\ref{line:top_k_map:graph_matching:all-pairs} of Algo.~\ref{algo:top_k_map:graph_matchings} can be performed by the all-pairs shortest paths algorithm \citep[Ch.~8.4]{schrijver-book} in time $\bigO(p^3)$. Its correctness is shown by the following theorem: \begin{theorem}[\citet{duchi2007using}] \label{thm:top_k_map:graph_matching} Given a directed bipartite graph $G$ and weights $\varphi: V \times V' \to \reals$, the output $\psi_{v ; z}$ from Algo.~\ref{algo:top_k_map:graph_matchings} are valid max-marginals, i.e., $\psi_{v ; z}$ coincides with the optimal value of the linear program \eqref{eq:top_k_map:graph_matchings:max-marg:def}. Moreover, Algo.~\ref{algo:top_k_map:graph_matchings} runs in time $\bigO(p^3)$ where $p = \abs{V} = \abs{V'}$. \end{theorem} \begin{algorithm}[tb] \caption{Max marginal computation via Graph matchings} \label{algo:top_k_map:graph_matchings} \begin{algorithmic}[1] \STATE {\bfseries Input:} Directed bipartite graph $G=(V \cup V', E)$, weights $\varphi: V \times V' \to \reals$. \STATE Find a maximum weight bipartite matching $\sigma^*$ in the graph $G$. Let the maximum weight be $\psi^*$. \STATE Define a weighted residual bipartite graph $\widehat G = (V \cup V', \widehat E)$, where the set $\widehat E$ is populated as follows: for $(v,z) \in E$, add an edge $(v,z)$ to $\widehat E$ with weight $1 - \ind(\sigma^*(v) = z)$, add $(z, v)$ to $\widehat E$ with weights $- \ind(\sigma^*(v) = z)$. \STATE Find the maximum weight path from every vertex $z\in V'$ to every vertex $v \in V$ and denote this by $\Delta(z, v)$. \label{line:top_k_map:graph_matching:all-pairs} \STATE Assign the max-marginals $\psi_{v ; z} = \psi^* + \ind(\sigma^*(v) \neq z) \, \left( \Delta(z, v) + \varphi(v, z) \right)$ for all $(v, z) \in V \times V'$. \RETURN Max-marginals $\psi_{v;z}$ for all $(v, z) \in V \times V'$. \end{algorithmic} \end{algorithm} \subsection{Proof of Proposition~\ref{prop:smoothing:max-marg:all}} \label{sec:a:proof-prop} \begin{proposition_unnumbered}[\ref{prop:smoothing:max-marg:all}] Consider as inputs an augmented score function $\psi(\cdot, \cdot ; \wv)$, an integer $K>0$ and a smoothing parameter $\mu > 0$. Further, suppose that $\psi$ is unambiguous, that is, $\psi(\yv' ; \wv) \neq \psi(\yv'' ;\wv)$ for all distinct $\yv', \yv'' \in \mcY$. Consider one of the two settings: \begin{enumerate}[label={\upshape(\Alph*)}, align=left, leftmargin=*] \item the output space $\mcY_v = \{0,1\}$ for each $v \in \mcV$, and the function $-\psi$ is submodular (see Appendix~\ref{sec:a:graph_cuts} and, in particular, \eqref{eq:top_k_map:submodular} for the precise definition), or, \item the augmented score corresponds to an alignment task where the inference problem~\eqref{eq:pgm:inference} corresponds to a maximum weight bipartite matching (see Appendix~\ref{sec:a:graph_matchings} for a precise definition). \end{enumerate} In these cases, we have the following: \begin{enumerate}[label={\upshape(\roman*)}, align=left, widest=iii, leftmargin=*] \item The max oracle can be implemented at a computational complexity of $\bigO(p)$ minimum cut computations in Case~\ref{part:prop:max-marg:cuts}, and in time $\bigO(p^3)$ in Case~\ref{part:prop:max-marg:matching}. \item The top-$K$ oracle can be implemented at a computational complexity of $\bigO(pK)$ minimum cut computations in Case~\ref{part:prop:max-marg:cuts}, and in time $\bigO(p^3K)$ in Case~\ref{part:prop:max-marg:matching}. \item The exp oracle is \#P-complete in both cases. \end{enumerate} \end{proposition_unnumbered} \begin{proof} A set of max-marginals can be computed by an algorithm $\mcM$ defined as follows: \begin{itemize} \item In Case~\ref{part:prop:max-marg:cuts}, invoke Algo.~\ref{algo:top_k_map:graph_cuts} a total of $2p$ times, with $y_v =0$, and $y_v = 1$ for each $v \in \mcV$. This takes a total of $2p$ min-cut computations. \item In Case~\ref{part:prop:max-marg:matching}, $\mcM$ is simply Algo.~\ref{algo:top_k_map:graph_matchings}, which takes time $\bigO(p^3)$. \end{itemize} The max oracle can then be implmented by the decoding in Eq.~\eqref{eq:max-marg:defn}, whose correctness is guaranteed by Thm.~\ref{thm:a:loopy:decoding}. The top-$K$ oracle is implemented by invoking the BMMF algorithm with $\mcM$ defined above, followed by a projection onto the simplex (Algo.~\ref{algo:smoothing:top_K_oracle} in Appendix~\ref{sec:a:smoothing}) and its correctness is guaranteed by Thm.~\ref{thm:inference:topKmm}. Lastly, the result of exp oracle follows from \citet[Thm. 15]{jerrum1993polynomial} in conjunction with Prop.~\ref{prop:smoothing:exp-crf}. \end{proof} \subsection{Inference using branch and bound search} \label{sec:a:bb_search} Algo.~\ref{algo:top_k:bb} with the input $K=1$ is the standard best-first branch and bound search algorithm. Effectively, the top-$K$ oracle is implemented by simply continuing the search procedure until $K$ outputs have been produced - compare Algo.~\ref{algo:top_k:bb} with inputs $K=1$ and $K > 1$. We now prove the correctness guarantee. \begin{algorithm}[tb] \caption{Top-$K$ best-first branch and bound search} \label{algo:top_k:bb} \begin{algorithmic}[1] \STATE {\bfseries Input:} Augmented score function $\psi(\cdot, \cdot ; \wv)$, integer $K > 0$, search space $\mcY$, upper bound $\widehat \psi$, split strategy. \STATE {\bfseries Initialization:} Initialize priority queue with single entry $\mcY$ with priority $\widehat \psi(\mcY ; \wv)$, and solution set $\mcS$ as the empty list. \WHILE{$\abs{\mcS} < K$} \STATE Pop $\widehat \mcY$ from the priority queue. \label{line:algo:bbtopk:pq} \IF{${\widehat \mcY} = \{\widehat \yv\}$ is a singleton} \label{line:algo:bbtopk:1} \STATE Append $( \widehat \yv, \psi(\widehat \yv ; \wv) )$ to $S$. \ELSE \STATE $\mcY_1, \mcY_2 \leftarrow \mathrm{split}(\widehat \mcY)$. \STATE Add $\mcY_1$ with priority $\widehat \psi(\mcY_1 ; \wv)$ and $\mcY_2$ with priority $\widehat \psi(\mcY_2 ; \wv)$ to the priority queue. \ENDIF \ENDWHILE \RETURN $\mcS$. \end{algorithmic} \end{algorithm} \begin{proposition_unnumbered}[\ref{prop:smoothing:bb-search}] Consider an augmented score function $\psi(\cdot, \cdot, \wv)$, an integer $K > 0$ and a smoothing parameter $\mu > 0$. Suppose the upper bound function $\widehat \psi(\cdot, \cdot ; \wv): \mcX \times 2^{\mcY} \to \reals$ satisfies the following properties: \begin{enumerate}[label=(\alph*), align=left, widest=a, leftmargin=*] \item $\widehat \psi(\widehat \mcY ; \wv)$ is finite for every $\widehat \mcY \subseteq \mcY$, \item $\widehat \psi(\widehat \mcY ; \wv) \ge \max_{\yv \in \widehat \mcY} \psi(\yv ; \wv)$ for all $\widehat \mcY \subseteq \mcY$, and, \item $\widehat \psi(\{\yv\} ; \wv) = \psi(\yv ; \wv)$ for every $\yv \in \mcY$. \end{enumerate} Then, we have the following: \begin{enumerate}[label={\upshape(\roman*)}, align=left, widest=ii, leftmargin=*] \item Algo.~\ref{algo:top_k:bb} with $K=1$ is a valid implementation of the max oracle. \item Algo.~\ref{algo:top_k:bb} followed by a projection onto the simplex (Algo.~\ref{algo:smoothing:top_K_oracle} in Appendix~\ref{sec:a:smoothing}) is a valid implementation of the top-$K$ oracle. \end{enumerate} \end{proposition_unnumbered} \begin{proof} Suppose at some point during the execution of the algorithm, we have a $\widehat \mcY = \{\widehat \yv\}$ on Line~\ref{line:algo:bbtopk:1} and that $\abs{\mcS} = k$ for some $0 \le k < K$. From the properties of the quality upper bound $\widehat \psi$, and using the fact that $ \{\widehat \yv\}$ had the highest priority in the priority queue (denoted by $(*)$), we get, \begin{align*} \psi(\widehat\yv ; \wv) &= \widehat \psi(\{ \widehat \yv\} ; \wv) \\ &\stackrel{(*)}{\ge} \max_{Y \in \mcP} \widehat \psi(Y ; \wv) \\ &\ge \max_{Y \in \mcP} \max_{\yv \in Y} \psi(\yv ; \wv) \\ &\stackrel{(\#)}{=} \max_{\yv \in \mcY - \mcS} \psi(\yv ; \wv) \,, \end{align*} where the equality $(\#)$ followed from the fact that any $\yv \in \mcY$ exits the priority queue only if it is added to $\mcS$. This shows that if a $\widehat \yv$ is added to $\mcS$, it has a score that is no less than that of any $\yv \in \mcY - \mcS$. In other words, Algo.~\ref{algo:top_k:bb} returns the top-$K$ highest scoring $\yv$'s. \end{proof} \subsection{Behavior of the Sequence $(\alpha_k)_{k \ge 0}$} \label{sec:a:c_alpha_k} \begin{lemma_unnumbered}[\ref{lem:c:alpha_k}] Given a positive, non-decreasing sequence $(\kappa_k)_{k\ge 1}$ and $\lambda \ge 0$, consider the sequence $(\alpha_k)_{k \ge 0}$ defined by \eqref{eq:c:update_alpha}, where $\alpha_0 \in (0, 1)$ such that $\alpha_0^2 \ge \lambda / (\lambda + \kappa_1)$. Then, we have for every $k \ge 1$ that $0< \alpha_k \le \alpha_{k-1}$ and, $ \alpha_k^2 \ge {\lambda}/({\lambda + \kappa_{k+1}}) \,. $ \end{lemma_unnumbered} \begin{proof} It is clear that \eqref{eq:c:update_alpha} always has a positive root, so the update is well defined. Define sequences $(c_k)_{k \ge 1}, (d_k)_{k \ge 0}$ as \begin{align*} c_k = \frac{\lambda + \kappa_k}{\lambda + \kappa_{k+1}}\,, \quad \mbox{and} \quad d_k = \frac{\lambda}{\lambda + \kappa_{k+1}} \,. \end{align*} Therefore, we have that $c_k d_{k-1} = d_k$, $0 < c_k \le 1$ and $0 \le d_k < 1$. With these in hand, the rule for $\alpha_k$ can be written as \begin{align} \label{eq:lem:c:alpha_k} \alpha_k = \frac{ -(c_k \alpha_{k-1}^2 - d_k ) + \sqrt{ (c_k \alpha_{k-1}^2 - d_k )^2 + 4 c_k \alpha_{k-1}^2 }}{2} \,. \end{align} We show by induction that that $d_k \le \alpha_k^2 < 1$. The base case holds by assumption. Suppose that $\alpha_{k-1}$ satisfies the hypothesis for some $k \ge 1$. Noting that $\alpha_{k-1}^2 \ge d_{k-1}$ is equivalent to $c_k \alpha_{k-1}^2 - d_k \ge 0$, we get that \begin{align} \nonumber \sqrt{ (c_k \alpha_{k-1}^2 - d_k )^2 + 4 c_k \alpha_{k-1}^2 } &\le \sqrt{ (c_k \alpha_{k-1}^2 - d_k )^2 + 4 c_k \alpha_{k-1}^2 + 2 (c_k \alpha_{k-1}^2 - d_k) (2\sqrt{c_k} \alpha_{k-1}) } \\ &= c_k \alpha_{k-1}^2 - d_k + 2\sqrt{c_k} \alpha_{k-1} \,. \label{eq:lem:c:alpha_k_helper} \end{align} We now conclude from \eqref{eq:lem:c:alpha_k} and \eqref{eq:lem:c:alpha_k_helper} that \begin{align} \nonumber \alpha_k &\le \frac{ -(c_k \alpha_{k-1}^2 - d_k ) + (c_k \alpha_{k-1}^2 - d_k + 2\sqrt{c_k} \alpha_{k-1}) }{2} \\ &= \sqrt{c_k}{\alpha_{k-1}} \le \alpha_{k-1} < 1\,, \label{eq:lem:c:alpha_k_dec} \end{align} since $c_k \le 1$ and $\alpha_{k-1} < 1$. To show the other side, we expand out \eqref{eq:lem:c:alpha_k} and apply \eqref{eq:lem:c:alpha_k_helper} again to get \begin{align*} \alpha_k^2 - d_k &= \frac{1}{2}(c_k \alpha_{k-1}^2 - d_k)^2 + (c_k \alpha_{k-1}^2 - d_k) - \frac{1}{2}(c_k \alpha_{k-1}^2 - d_k) \sqrt{(c_k \alpha_{k-1}^2 - d_k)^2 + 4 c_k \alpha_{k-1}^2 } \\ &= \frac{1}{2}(c_k \alpha_{k-1}^2 - d_k) \left(2 + (c_k \alpha_{k-1}^2 - d_k) - \sqrt{(c_k \alpha_{k-1}^2 - d_k)^2 + 4 c_k \alpha_{k-1}^2 } \right) \\ &\ge \frac{1}{2}(c_k \alpha_{k-1}^2 - d_k) \left(2 + (c_k \alpha_{k-1}^2 - d_k) - (c_k \alpha_{k-1}^2 - d_k+ 2\sqrt{c_k} \alpha_{k-1}) \right) \\ &= (c_k \alpha_{k-1}^2 - d_k) ( 1- \sqrt{c_k}\alpha_{k-1}) \ge 0 \,. \end{align*} The fact that $(\alpha_{k})_{k\ge 0}$ is a non-increasing sequence follows from~\eqref{eq:lem:c:alpha_k_dec}. \end{proof} \subsection{Proofs of Corollaries to Theorem~\ref{thm:catalyst:outer}} \label{subsec:c:proofs_missing_cor} We rewrite \eqref{thm:c:main:main} from Theorem~\ref{thm:catalyst:outer} as follows: \begin{align} \label{eq:c:app:main} F&(\wv_k) - F^* \le \left( \prod_{j=1}^k \frac{1-\alpha_{j-1}}{1-\delta_j} \right) \left( F(\wv_0) - F^* + \frac{\gamma_0}{2} \normsq{\wv_0 - \wv^*} \right) + \mu_k D_\omega \\ &+ \frac{1}{1-\alpha_k} \left[ \left( \prod_{j=1}^k \frac{1-\alpha_j}{1-\delta_j} \right) (1 + \delta_1) \mu_1 D_\omega + \sum_{j=2}^k \left( \prod_{i=j}^k \frac{1-\alpha_i}{1-\delta_i} \right) \left( \mu_{j-1} - (1-\delta_j)\mu_j \right)D_\omega \right] \,, \nonumber \end{align} Next, we have proofs of Corollaries~\ref{cor:c:outer_sc} to~\ref{cor:c:outer_smooth_dec_smoothing}. \begin{corollary_unnumbered}[\ref{cor:c:outer_sc}] Consider the setting of Thm.~\ref{thm:catalyst:outer}. Let $q = \frac{\lambda}{\lambda + \kappa}$. Suppose $\lambda > 0$ and $\mu_k = \mu$, $\kappa_k = \kappa$, for all $k \ge 1$. Choose $\alpha_0 = \sqrt{q}$ and, $\delta_k = \frac{\sqrt{q}}{2 - \sqrt{q}} \,.$ Then, we have, \begin{align*} F(\wv_k) - F^* \le \frac{3 - \sqrt{q}}{1 - \sqrt{q}} \mu D + 2 \left( 1- \frac{\sqrt q}{2} \right)^k \left( F(\wv_0) - F^* \right) \,. \end{align*} \end{corollary_unnumbered} \begin{proof} Notice that when $\alpha_0 = \sqrt{q}$, we have, $\alpha_k = \sqrt{q}$ for all $k$. Moreover, for our choice of $\delta_k$, we get, for all $k, j$, $\frac{1-\alpha_k}{1-\delta_j} = 1 - \frac{\sqrt q}{2}$. Under this choice of $\alpha_0$, we have, $\gamma_0 = \lambda$. So, we get the dependence on initial conditions as \begin{align*} \Delta_0 = F(\wv_0) - F^* + \frac{\lambda}{2} \normsq{\wv_0 - \wv^*} \le 2( F(\wv_0) - F^*) \,, \end{align*} by $\lambda$-strong convexity of $F$. The last term of \eqref{eq:c:app:main} is now, \begin{align*} \frac{\mu D}{1-\sqrt {q}} \left[ \underbrace{\left( 1 - \frac{\sqrt q}{2} \right)^{k-1} }_{\le 1} + \underbrace{\frac{\sqrt q}{2} \sum_{j=2}^k \left( 1 - \frac{\sqrt q}{2} \right)^{k-j}}_{\stackrel{(*)}{\le} 1 } \right] \le \frac{2 \mu D}{1 - \sqrt q} \, , \end{align*} where $(*)$ holds since \begin{align*} \sum_{j=2}^k \left( 1 - \frac{\sqrt q}{2} \right)^{k-j} \le \sum_{j=0}^\infty \left( 1 - \frac{\sqrt q}{2} \right)^{j} = \frac{2}{\sqrt{q}} \,. \end{align*} \end{proof} \begin{corollary_unnumbered}[\ref{cor:c:outer_sc:decreasing_mu_const_kappa}] Consider the setting of Thm.~\ref{thm:catalyst:outer}. Let $q = \frac{\lambda}{\lambda + \kappa}, \eta = 1 - \frac{\sqrt q}{2}$. Suppose $\lambda > 0$ and $\kappa_k = \kappa$, for all $k \ge 1$. Choose $\alpha_0 = \sqrt{q}$ and, the sequences $(\mu_k)_{k \ge 1}$ and $(\delta_k)_{k \ge 1}$ as \begin{align*} \mu_k = \mu \eta^{{k}/{2}} \,, \qquad \text{and,} \qquad \delta_k = \frac{\sqrt{q}}{2 - \sqrt{q}} \,, \end{align*} where $\mu > 0$ is any constant. Then, we have, \begin{align*} F(\wv_k) - F^* \le \eta^{{k}/{2}} \left[ 2 \left( F(\wv_0) - F^* \right) + \frac{\mu D_\omega}{1-\sqrt{q}} \left(2-\sqrt{q} + \frac{\sqrt{q}}{1 - \sqrt \eta} \right) \right] \, . \end{align*} \end{corollary_unnumbered} \begin{proof As previously in Corollary~\ref{cor:c:outer_sc}, notice that under the specific parameter choices here, we have, $\gamma_0 = \lambda$, $\alpha_k = \sqrt{q}$ for each $k$, and $\frac{1 - \delta}{1 - \alpha} = 1 - \frac{\sqrt q}{2} = \eta$. By $\lambda$-strong convexity of $F$ and the fact that $\gamma_0 = \lambda$, the contribution of $\wv_0$ can be upper bounded by $2(F(\wv_0) - F^*)$. Now, we plugging these into \eqref{eq:c:app:main} and collecting the terms dependent on $\delta_k$ separately, we get, \begin{align} \label{eq:c:outer:sc:dec_smoothing} \nonumber F(\wv_k) - F^* \le & \underbrace{2 \eta^k (F(\wv_0) - F^*)}_{=: \mcT_1} + \underbrace{\mu_k D}_{=: \mcT_2} \\ &+ \frac{1}{1 - \sqrt{q}} \left( \underbrace{\eta^k \mu_1 D}_{=: \mcT_3} + \underbrace{\sum_{j=2}^k \eta^{k-j+1} (\mu_{j-1} - \mu_j)D}_{=:\mcT_4} + \underbrace{\sum_{j=1}^k \eta^{k-j+1} \mu_j \delta_j D}_{=: \mcT_5} \right) \,. \end{align} We shall consider each of these terms. Since $\eta^k \le \eta^{k/2}$, we get $\mcT_1 \le 2\eta^{k/2}(F(\wv_0) - F^*)$ and $\mcT_3 = \eta^k \mu_1 D \le \eta^k \mu D \le \eta^{k/2} \mu D$. Moreover, $\mcT_2 = \mu_k D = \eta^{k/2} \mu D$. Next, using $ 1- \sqrt \eta \le 1 - \eta = \frac{\sqrt q}{2}$, \begin{align*} \mcT_4 &= \sum_{j=2}^k \eta^{k-j+1}(\mu_{j-1} - \mu_j) D = \sum_{j=2}^k \eta^{k-j+1} \mu \eta^{\nicefrac{(j-1)}{2}} (1 - \sqrt\eta) D \\ &\le \frac{\sqrt{q}}{2} \mu D \sum_{j=2}^k \eta^{k - \frac{j-1}{2}} = \frac{\sqrt{q}}{2} \mu D \eta^{\nicefrac{(k+1)}{2}} \sum_{j=0}^{k-2} \eta^{j/2} \le \frac{\sqrt{q}}{2} \mu D \frac{\eta^{\nicefrac{(k+1)}{2}} }{1- \sqrt\eta} \\ &\le \frac{\sqrt{q}}{2} \mu D \frac{\eta^{\nicefrac{k}{2}} }{1- \sqrt\eta} \, . \end{align*} Similarly, using $\delta_j = \nicefrac{\sqrt q}{2\eta}$, we have, \begin{align*} \mcT_5 &= \sum_{j=1}^k \eta^{k-j+1} \mu \eta^{j/2} D \frac{\sqrt q}{2\eta} = \frac{\sqrt{q}}{2} \mu D\sum_{j=1}^k \eta^{\nicefrac{k-j}{2}} \le \frac{\sqrt{q}}{2} \mu D \frac{\eta^{\nicefrac{k}{2}} }{1- \sqrt\eta} \, . \end{align*} Plugging these into \eqref{eq:c:outer:sc:dec_smoothing} completes the proof. \end{proof} \begin{corollary_unnumbered}[\ref{cor:c:outer_smooth}] Consider the setting of Thm.~\ref{thm:catalyst:outer}. Suppose $\mu_k = \mu$, $\kappa_k = \kappa$, for all $k \ge 1$ and $\lambda = 0$. Choose $\alpha_0 = \frac{\sqrt{5}-1}{2}$ and $\delta_k = \frac{1}{(1 + k)^2} \,.$ Then, we have, \begin{align*} F(\wv_k) - F^* \le \frac{8}{(k+2)^2} \left( F(\wv_0) - F^* + \frac{\kappa}{2} \normasq{2}{\wv_0 - \wv^*} \right) + \mu D_\omega\left( 1 + \frac{12}{k+2} + \frac{30}{(k+2)^2} \right) \, . \end{align*} \end{corollary_unnumbered} \begin{proof Firstly, note that $\gamma_0 = \kappa \frac{\alpha_0^2}{1-\alpha_0} = \kappa$. Now, define \begin{align*} \mcA_k &= \prod_{i=0}^k (1- \alpha_i) \text{, and, } \mcB_k = \prod_{i=1}^k (1-\delta_i) \, . \end{align*} We have, \begin{align} \label{lem:c:b_k_1} \mcB_k = \prod_{i=1}^k \left( 1 - \frac{1}{(i+1)^2} \right) = \prod_{i=1}^k \frac{i(i+2)}{(i+1)^2} = \frac{1}{2} + \frac{1}{2(k+1)}\,. \end{align} Therefore, \begin{align*} F(\wv_k) - F^* \le& \frac{\mcA_{k-1}}{\mcB_k} \left( F(\wv_0) - F^* + \frac{\gamma_0}{2} \normsq{\wv_0 - \wv^*} \right) + \mu D \\ &+ \frac{\mu D}{1-\alpha_0} \left( \prod_{j=1}^k \frac{1-\alpha_{j-1}}{1-\delta_k} \right) (1 + \delta_1) + \mu D \sum_{j=2}^k \left( \prod_{i=j}^k \frac{1- \alpha_{i-1}}{1-\delta_i} \right) \frac{\delta_j}{1-\alpha_{j-1}} \\ \le& \underbrace{\frac{\mcA_{k-1}}{\mcB_k} \left( F(\wv_0) - F^* + \frac{\gamma_0}{2} \normsq{\wv_0 - \wv^*} \right)}_{=:\mcT_1} + \mu D \\ &+ \underbrace{ \frac{\tfrac{5}{4}\mu D}{1-\alpha_0} \frac{\mcA_{k-1}}{\mcB_k} }_{=:\mcT_2}+ \underbrace{\mu D \sum_{j=2}^k \frac{ \nicefrac{\mcA_{k-1}} {\mcA_{j-2}}} { \nicefrac{\mcB_k}{\mcB_{j-1}}} \frac{\delta_j}{1-\alpha_{j-1}}}_{=:\mcT_3} \,. \end{align*} From Lemma~\ref{lem:c:A_k:const_kappa}, which analyzes the evolution of $(\alpha_k)$ and $(\mcA_k)$, we get that $\frac{2}{(k+2)^2} \le \mcA_{k-1} \le \frac{4}{(k+2)^2}$ and $\alpha_k \le \frac{2}{k+3}$ for $k \ge 0$. Since $\mcB_k \ge \frac{1}{2}$, \begin{align*} \mcT_1 \le \frac{8}{(k+2)^2} \left( F(\wv_0) - F^* + \frac{\gamma_0}{2} \normsq{\wv_0 - \wv^*} \right) \,. \end{align*} Moreover, since $\alpha_0 \le 2/3$, \begin{align*} \mcT_2 \le \frac{30}{(k+2)^2} \,. \end{align*} Lastly, we have, \begin{align*} \mcT_3 &\le \sum_{j=2}^k \frac{4}{(k+2)^2} \times \frac{(j+1)^2}{2} \times 2\left( \frac{1}{2}+ \frac{1}{2j} \right) \times \frac{1}{(j+1)^2} \times \frac{1}{1 - \nicefrac{2}{j+2}} \\ &\le 2\frac{2}{(k+2)^2} \sum_{j=2}^k \frac{j+2}{j} \le \frac{4}{(k+2)^2} \left(k -1 + 2 \log k \right) \le \frac{12}{k+2} \, , \end{align*} where we have used the simplifications $\sum_{j=2}^k 1/k \le \log k$ and $ k-1+2\log k \le 3k$. \end{proof} \begin{corollary_unnumbered}[\ref{cor:c:outer_smooth_dec_smoothing}] Consider the setting of Thm.~\ref{thm:catalyst:outer} with $\lambda = 0$. Choose $\alpha_0 = \frac{\sqrt{5}-1}{2}$, and for some non-negative constants $\kappa, \mu$, define sequences $(\kappa_k)_{k \ge 1}, (\mu_k)_{k \ge 1}, (\delta_k)_{k \ge 1}$ as \begin{align*} \kappa_k = \kappa \, k\,, \quad \mu_k = \frac{\mu}{k} \quad \text{and,} \quad \delta_k = \frac{1}{(k + 1)^2} \,. \end{align*} Then, for $k \ge 2$, we have, \begin{align} F(\wv_k) - F^* \le \frac{\log(k+1)}{k+1} \left( 2(F(\wv_0) - F^*) + \kappa \normasq{2}{\wv_0 - \wv^*} + 27 \mu D_\omega \right) \,. \end{align} For the first iteration (i.e., $k = 1$), this bound is off by a constant factor $1 / \log2$. \end{corollary_unnumbered} \begin{proof Notice that $\gamma_0 = \kappa_1 \frac{\alpha_0^2}{1- \alpha_0} = \kappa$. As in Corollary~\ref{cor:c:outer_smooth}, define \begin{align*} \mcA_k &= \prod_{i=0}^k (1- \alpha_i)\,, \quad \text{and,} \quad \mcB_k = \prod_{i=1}^k (1-\delta_i) \, . \end{align*} From Lemma~\ref{lem:c:A_k:inc_kappa} and \eqref{lem:c:b_k_1} respectively, we have for $k \ge 1$, \begin{align*} \frac{1- \frac{1}{\sqrt 2}}{k+1} &\le \mcA_{k} \le \frac{1}{k+2}\,, \quad \text{and,} \quad \frac{1}{2} \le \mcB_{k} \le 1\, . \end{align*} Now, invoking Theorem~\ref{thm:catalyst:outer}, we get, \begin{align} \label{eq:cor:c:nsc:dec_smoothing_eq} F(\wv_k) - F^* \le& \nonumber \underbrace{\frac{\mcA_{k-1}}{\mcB_k} \left( F(\wv_0) - F^* + \frac{\gamma_0}{2} \normsq{\wv_0 - \wv^*} \right)}_{=:\mcT_1} + \underbrace{\mu_k D}_{=:\mcT_2} + \underbrace{\frac{1}{1 - \alpha_0} \frac{\mcA_{k-1}}{\mcB_k} \mu_1 D(1 + \delta_1)}_{=:\mcT_3} + \\ &\underbrace{\sum_{j=2}^k \frac{\mcA_{k-1}/\mcA_{j-1}}{\mcB_k / \mcB_{j-1}} (\mu_{j-1} - \mu_j) D}_{=:\mcT_4} + \underbrace{\sum_{j=2}^k \frac{\mcA_{k-1}/\mcA_{j-1}}{\mcB_k / \mcB_{j-1}} \delta_j \mu_j D }_{=:\mcT_5} \,. \end{align} We shall bound each of these terms as follows. \begin{gather*} \mcT_1 = \frac{\mcA_{k-1}}{\mcB_k} \left( F(\wv_0) - F^* + \frac{\gamma_0}{2} \normsq{\wv_0 - \wv^*} \right) = \frac{2}{k+1} \left( F(\wv_0) - F^* + \frac{\kappa _0}{2} \normsq{\wv_0 - \wv^*} \right) \,, \\ \mcT_2 = \mu_k D = \frac{\mu D}{k} \le \frac{2\mu D}{k+1} \, , \\ \mcT_3 = \frac{1}{1 - \alpha_0} \frac{\mcA_{k-1}}{\mcB_k} \mu_1 D(1 + \delta_1) \le 3 \times \frac{2}{k+1} \times {\mu} \times \frac{5}{4}D = \frac{15}{2} \frac{\mu D}{k+1} \,, \end{gather*} where we used the fact that $\alpha_0 \le 2/3$. Next, using $\sum_{j=2}^k {1}/({j-1}) = 1 + \sum_{j=2}^{k-1} {1}/{j} \le 1 + \int_{1}^{k-1}{dx}/{x} = 1 + \log(k-1)$, we get, \begin{align*} \nonumber {\mcT_4} &= \sum_{j=2}^k \frac{2}{k+1} \cdot \frac{j}{1- \frac{1}{\sqrt 2}} \left(\frac{\mu}{j-1} - \frac{\mu}{j}\right) D = 2\sqrt2(\sqrt2 + 1) \frac{\mu D}{k+1} \sum_{j=2}^k \frac{1}{j-1} \nonumber \\ &\le 2\sqrt2(\sqrt2 + 1) \mu D \left( \frac{1 + \log(k+1)}{k+1} \right) \,. \end{align*} Moreover, from $\sum_{j=2}^k {1}/{(j+1)^2} \le \int_{2}^{k+1} {dx}/{x^2} \le 1/2$, it follows that \begin{align*} \mcT_5 = \sum_{j=2}^k \frac{2}{k+1} \cdot \frac{j}{1- \frac{1}{\sqrt 2}} \frac{\mu}{j} \cdot \frac{1}{(j+1)^2} D = 2\sqrt2(\sqrt2+1) \frac{\mu D}{k+1} \sum_{j=2}^k \frac{1}{(j+1)^2} \le \sqrt2(\sqrt2 + 1) \frac{\mu D}{k+1} \, . \end{align*} Plugging these back into \eqref{eq:cor:c:nsc:dec_smoothing_eq}, we get \begin{align*} F(\wv_k) - F^* \le& \frac{2}{k+1} \left( F(\wv_k) - F^* + \frac{\kappa}{2} \normsq{\wv_0 - \wv^*} \right)+ \\ &\frac{\mu D}{k+1} \left(2 + \frac{15}{2} + \sqrt2(1 + \sqrt2) \right) + 2\sqrt2(1 + \sqrt2)\mu D \frac{1 + \log(k+1)}{k+1} \,. \end{align*} To complete the proof, note that $\log(k+1) \ge 1$ for $k\ge 2$ and numerically verify that the coefficient of $\mu D$ is smaller than 27. \end{proof} \subsection{Inner Loop Complexity Analysis for Casimir} \label{sec:c:proofs:inner_compl} Before proving Prop.~\ref{prop:c:inner_loop_final}, the following lemmas will be helpful. First, we present a lemma from \citet[Lemma 11]{lin2017catalyst} about the expected number of iterations a randomized linearly convergent first order methods requires to achieve a certain target accuracy. \begin{lemma} \label{lem:c:inner_loop} Let $\mcM$ be a linearly convergent algorithm and $f \in \mcF_{L, \lambda}$. Define $f^* = \min_{\wv \in \reals^d} f(\wv)$. Given a starting point $\wv_0$ and a target accuracy $\eps$, let $(\wv_k)_{k \ge 0}$ be the sequence of iterates generated by $\mcM$. Define $T(\eps) = \inf \left\{ k \ge 0 \, | \, f(\wv_k) - f^* \le \eps \right\} \,.$ We then have, \begin{align} \expect[T(\eps)] \le \frac{1}{\tau(L, \lambda)} \log \left( \frac{2C(L, \lambda)} {\tau(L,\lambda)\eps} (f(\wv_0) - f^*) \right) + 1 \,. \end{align} \end{lemma} This next lemma is due to \citet[Lemma 14, Prop.~15]{lin2017catalyst}. \begin{lemma \label{lem:c:inner_loop_restart} Consider $F_{\mu\omega, \kappa}(\cdot \, ;\zv)$ defined in Eq.~\eqref{eq:prox_point_algo} and let $\delta \in [0,1)$. Let $\widehat F^* = \min_{\wv \in \reals^d} F_{\mu\omega, \kappa}(\wv ;\zv)$ and $\widehat \wv^* = \argmin_{\wv \in \reals^d} F_{\mu\omega, \kappa}(\wv ;\zv)$. Further let $F_{\mu\omega}(\cdot \, ;\zv)$ be $L_{\mu\omega}$-smooth. We then have the following: \begin{gather*} F_{\mu\omega, \kappa}(\zv ;\zv) - \widehat F^* \le \frac{L_{\mu\omega} + \kappa}{2} \normasq{2}{\zv - \widehat \wv^*} \,, \quad \text{and,} \\ F_{\mu\omega, \kappa}(\widehat\wv ;\zv) - \widehat F^* \le \frac{\delta\kappa}{8} \normasq{2}{\zv - \widehat \wv^*} \, \implies \, F_{\mu\omega, \kappa}(\widehat\wv ;\zv) - \widehat F^* \le \frac{\delta\kappa}{2} \normasq{2}{\widehat \wv - \zv} \,. \end{gather*} \end{lemma} We now restate and prove Prop.~\ref{prop:c:inner_loop_final}. \begin{proposition_unnumbered}[\ref{prop:c:inner_loop_final}] Consider $F_{\mu\omega, \kappa}(\cdot \, ;\zv)$ defined in Eq.~\eqref{eq:prox_point_algo}, and a linearly convergent algorithm $\mcM$ with parameters $C$, $\tau$. Let $\delta \in [0,1)$. Suppose $F_{\mu\omega}$ is $L_{\mu\omega}$-smooth and $\lambda$-strongly convex. Then the expected number of iterations $\expect[\widehat T]$ of $\mcM$ when started at $\zv$ in order to obtain $\widehat \wv \in \reals^d$ that satisfies \begin{align}\label{eq:inner_stopping_criterion} F_{\mu\omega, \kappa}(\widehat\wv;\zv) - \min_\wv F_{\mu\omega, \kappa}(\wv;\zv)\leq \tfrac{\delta\kappa}{2} \normasq{2}{\wv - \zv} \end{align} is upper bounded by \begin{align*} \expect[\widehat T] \le \frac{1}{\tau(L_{\mu\omega} + \kappa, \lambda + \kappa)} \log\left( \frac{8 C(L_{\mu\omega} + \kappa, \lambda + \kappa)}{\tau(L_{\mu\omega} + \kappa, \lambda + \kappa)} \cdot \frac{L_{\mu\omega} + \kappa}{\kappa \delta} \right) + 1 \,. \end{align*} \end{proposition_unnumbered} \begin{proof In order to invoke Lemma~\ref{lem:c:inner_loop}, we must appropriately set $\eps$ for $\widehat\wv$ to satisfy \eqref{eq:inner_stopping_criterion} and then bound the ratio $(F_{\mu\omega, \kappa}(\zv ;\zv) - \widehat F^*) / \eps$. Firstly, Lemma~\ref{lem:c:inner_loop_restart} tells us that choosing $\eps = \frac{\delta_k \kappa_k}{8} \normasq{2}{\zv_{k-1} - \widehat \wv^*}$ guarantees that the $\widehat \wv$ so obtained satisfies \eqref{eq:inner_stopping_criterion}, where $\widehat \wv^* := \argmin_{\wv \in \reals^d} F_{\mu\omega, \kappa}(\wv ;\zv)$, Therefore, $(F_{\mu\omega, \kappa}(\zv ;\zv) - \widehat F^*) / \eps$ is bounded from above by ${4(L_{\mu\omega} + \kappa)}/{\kappa \delta}$. \end{proof} \subsection{Information Based Complexity of {Casimir-SVRG}} \label{sec:c:proofs:total_compl} Presented below are the proofs of Propositions~\ref{prop:c:total_compl_svrg_sc} to \ref{prop:c:total_compl_nsc:dec_smoothing} from Section~\ref{sec:catalyst:total_compl}. We use the following values of $C, \tau$, see e.g., \citet{hofmann2015variance}. \begin{align*} \tau(L, \lambda) &= \frac{1}{8 \tfrac{L}{\lambda} + n} \ge \frac{1}{8 \left( \tfrac{L}{\lambda} + n \right)}\\ C(L, \lambda) &= \frac{L}{\lambda} \left( 1 + \frac{n \tfrac{L}{\lambda}}{8 \tfrac{L}{\lambda} + n} \right)\,. \end{align*} \begin{proposition_unnumbered}[\ref{prop:c:total_compl_svrg_sc}] Consider the setting of Thm.~\ref{thm:catalyst:outer} with $\lambda > 0$ and fix $\eps > 0$. If we run Algo.~\ref{algo:catalyst} with SVRG as the inner solver with parameters: $\mu_k = \mu = \eps / {10 D_\omega}$, $\kappa_k = k$ chosen as \begin{align*} \kappa = \begin{cases} \frac{A}{\mu n} - \lambda \,, \text{ if } \frac{A}{\mu n} > 4 \lambda \\ \lambda \,, \text{ otherwise} \end{cases} \,, \end{align*} $q = {\lambda}/{(\lambda + \kappa)}$, $\alpha_0 = \sqrt{q}$, and $\delta = {\sqrt{q}}/{(2 - \sqrt{q})}$. Then, the number of iterations $N$ to obtain $\wv$ such that $F(\wv) - F^* \le \eps$ is bounded in expectation as \begin{align*} \expect[N] \le \widetilde \bigO \left( n + \sqrt{\frac{A_\omega D_\omega n}{\lambda \eps}} \right) \,. \end{align*} \end{proposition_unnumbered} \begin{proof We use shorthand $A:=A_\omega$, $D := D_\omega$, $L_\mu = \lambda + \nicefrac{A}{\mu}$ and $\Delta F_0 = F(\wv_0) - F^*$. Let $C, \tau$ be the linear convergence parameters of SVRG. From Cor.~\ref{cor:c:outer_sc}, the number of outer iterations $K$ required to obtain $F(\wv_K) - F^* \le \eps$ is \begin{align*} K \le \frac{2}{\sqrt{q}} \log\left(\frac{ 2 \Delta F_0}{\eps - c_q \mu D} \right)\, , \end{align*} where $c_q = (3 - \sqrt q)/(1 - \sqrt q)$. From Prop.~\ref{prop:c:inner_loop_final}, the number $T_k$ of inner iterations for inner loop $k$ is, from $\delta_k = {\sqrt q}/({2 - \sqrt{q}})$, \begin{align*} \expect[T_k] &\le \frac{1}{\tau(L_\mu + \kappa, \lambda + \kappa)} \log\left( \frac{8 C(L_\mu + \kappa, \lambda + \kappa)}{\tau(L_\mu + \kappa, \lambda + \kappa)} \cdot \frac{L_\mu + \kappa}{\kappa} \cdot \frac{2 - \sqrt{q}}{\sqrt{q}} \right) + 1 \\ &\le \frac{2}{\tau(L_\mu + \kappa, \lambda + \kappa)} \log\left( \frac{8 C(L_\mu + \kappa, \lambda + \kappa)}{\tau(L_\mu + \kappa, \lambda + \kappa)} \cdot \frac{L_\mu + \kappa}{\kappa} \cdot \frac{2 - \sqrt{q}}{\sqrt{q}} \right) \,. \end{align*} Let the total number $N$ of iterations of SVRG to obtain an iterate $\wv$ that satisfies $F(\wv) - F^* \le \eps$. Next, we upper bound $\expect[N] \le \sum_{i=1}^K \expect[T_k]$ as \begin{align} \label{eq:c:total_compl_sc} \expect[N] \le \frac{4}{\sqrt{q} \tau(L_\mu + \kappa, \lambda +\kappa)} \log \left( \frac{8 C(L_\mu + \kappa, \lambda + \kappa)}{\tau(L_\mu + \kappa, \lambda + \kappa)} \frac{L_\mu + \kappa}{\kappa} \frac{2 - \sqrt{q}}{\sqrt q} \right) \log\left( \frac{2(F(\wv_0) - F^*)}{\eps - c_q \mu D} \right)\,. \end{align} Next, we shall plug in $C, \tau$ for SVRG in two different cases: \begin{itemize} \item Case 1: $A > 4\mu \lambda n$, in which case $\kappa + \lambda = A / (\mu n)$ and $q < 1/4$. \item Case 2: $A \le 4 \mu \lambda n$, in which case, $\kappa = \lambda$ and $q = 1/2$. \end{itemize} We first consider the term outside the logarithm. It is, up to constants, \begin{align*} \frac{1}{\sqrt{q}} \left( n + \frac{A}{\mu(\lambda + \kappa)} \right) = n \sqrt{\frac{\lambda + \kappa}{\lambda}} + \frac{A}{\mu \sqrt{\lambda(\lambda + \kappa)}} \,. \end{align*} For Case 1, plug in $\kappa + \lambda = A / (\mu n)$ so this term evaluates to $\sqrt{{ADn}/({\lambda \eps})}$. For Case 2, we use the fact that $A \le 4 \mu \lambda n$ so that this term can be upper bounded by, \[ n\left( \sqrt{\frac{\lambda + \kappa}{\lambda}} + 4 \sqrt{ \frac{\lambda}{\lambda + \kappa}} \right) = 3\sqrt{2}n \,, \] since we chose $\kappa= \lambda$. It remains to consider the logarithmic terms. Noting that $\kappa \ge \lambda$ always, it follows that the first log term of \eqref{eq:c:total_compl_sc} is clearly logarithmic in the problem parameters. As for the second logarithmic term, we must evaluate $c_q$. For Case 1, we have that $q < 1/4$ so that $c_q < 5$ and $c_q \mu D < \eps / 2$. For Case 2, we get that $q = 1/2$ and $c_q < 8$ so that $c_q \mu D < 4\eps/5$. Thus, the second log term of \eqref{eq:c:total_compl_sc} is also logarithmic in problem parameters. \end{proof} \begin{proposition_unnumbered} [\ref{prop:c:total_compl_sc:dec_smoothing_main}] Consider the setting of Thm.~\ref{thm:catalyst:outer}. Suppose $\lambda > 0$ and $\kappa_k = \kappa$, for all $k \ge 1$ and that $\alpha_0$, $(\mu_k)_{k \ge 1}$ and $(\delta_k)_{k \ge 1}$ are chosen as in Cor.~\ref{cor:c:outer_sc:decreasing_mu_const_kappa}, with $q = \lambda/(\lambda + \kappa)$ and $\eta = 1- {\sqrt q}/{2}$. If we run Algo.~\ref{algo:catalyst} with SVRG as the inner solver with these parameters, the number of iterations $N$ of SVRG required to obtain $\wv$ such that $F(\wv) - F^* \le \eps$ is bounded in expectation as \begin{align*} \expect[N] \le \widetilde \bigO \left( n + \frac{A_\omega}{\mu(\lambda + \kappa)\eps} \left( F(\wv_0) - F^* + \frac{\mu D_\omega}{1-\sqrt{q}} \right) \right) \,. \end{align*} \end{proposition_unnumbered} \begin{proof { We continue to use shorthand $A:=A_\omega$, $D := D_\omega$. First, let us consider the minimum number of outer iterations $K$ required to achieve $F(\wv_K) - F^* \le \eps$. From Cor.~\ref{cor:c:outer_sc:decreasing_mu_const_kappa}, if we have $\eta^{-K/2} \Delta_0 \le \eps$, or, \[ K \ge K_{\min} := \frac{\log\left( {\Delta_0}/{\eps} \right)}{\log\left({1}/{\sqrt\eta}\right)} \,. \] For this smallest value, we have, \begin{align} \label{eq:c:min_smoother} \mu_{K_{\min}} = \mu \eta^{K_{\min}/2} = \frac{\mu \eps}{\Delta_0} \,. \end{align} Let $C, \tau$ be the linear convergence parameters of SVRG, and define $L_k := \lambda + {A}/{\mu_k}$ for each $k\ge 1$. Further, let $\mcT'$ be such that \[ \mcT' \ge \max_{k\in\{1, \cdots, K_{\min}\}} \log\left( 8 \frac{C(L_k + \kappa, \lambda + \kappa)}{\tau(L_k + \kappa, \lambda+\kappa)} \frac{L_k + \kappa}{\kappa\delta} \right) \,. \] Then, the total complexity is, from Prop.~\ref{prop:c:inner_loop_final}, (ignoring absolute constants) \begin{align} \nonumber \expect[N] &\le \sum_{k=1}^{K_{\min}} \left( n + \frac{\lambda + \kappa + \frac{A}{\mu_k}}{\lambda + \kappa} \right) \mcT' \\ \nonumber &= \sum_{k=1}^{K_{\min}} \left( n+1 + \frac{\nicefrac{A}{\mu}}{\lambda + \kappa} \eta^{-k/2} \right) \mcT' \\ \nonumber &= \left( K_{\min}(n+1) + \frac{\nicefrac{A}{\mu}}{\lambda + \kappa} \sum_{k=1}^{K_{\min}} \eta^{-k/2} \right) \mcT' \\ \nonumber &\le \left( K_{\min}(n+1) + \frac{\nicefrac{A}{\mu}}{\lambda + \kappa} \frac{\eta^{-K_{\min}/2}}{1 - \eta^{1/2} } \right) \mcT' \\ &= \left( (n+1)\frac{\log\left( \frac{\Delta_0}{\eps} \right)}{\log(\nicefrac{1}{\sqrt\eta})} + \frac{\nicefrac{A}{\mu}}{\lambda + \kappa} \frac{1}{1 - \sqrt\eta} \frac{\Delta_0}{\eps} \right) \mcT' \,. \end{align} It remains to bound $\mcT'$. Here, we use $\lambda + \frac{A}{\mu} \le L_k \le \lambda + \frac{A}{\mu_K}$ for all $k \le K$ together with \eqref{eq:c:min_smoother} to note that $\mcT'$ is logarithmic in $\Delta_0/\eps, n, AD, \mu, \kappa, \lambda\inv$. } \end{proof} \begin{proposition_unnumbered}[\ref{prop:c:total_compl_svrg_smooth}] Consider the setting of Thm.~\ref{thm:catalyst:outer} and fix $\eps > 0$. If we run Algo.~\ref{algo:catalyst} with SVRG as the inner solver with parameters: $\mu_k = \mu ={\eps}/{20 D_\omega}$, $\alpha_0 = \tfrac{\sqrt{5} - 1}{2}$, $\delta_k = {1}/{(k+1)^2}$, and $\kappa_k = \kappa = {A_\omega}/{\mu(n+1)}$. Then, the number of iterations $N$ to get a point $\wv$ such that $F(\wv) - F^* \le \eps$ is bounded in expectation as \begin{align*} \expect[N] \le \widetilde \bigO \left( n\sqrt{\frac{F(\wv_0) - F^*}{\eps}} + \sqrt{A_\omega D_\omega n} \frac{\norma{2}{\wv_0 - \wv^*}}{\eps} \right) \, . \end{align*} \end{proposition_unnumbered} \begin{proof We use shorthand $A:=A_\omega$, $D := D_\omega$, $L_\mu = \nicefrac{A}{\mu}$ and $\Delta F_0 = F(\wv_0) - F^* + \frac{\kappa}{2} \normsq{\wv_0 -\wv^*}$. Further, let $C, \tau$ be the linear convergence parameters of SVRG. In Cor.~\ref{cor:c:outer_smooth}, the fact that $K \ge 1$ allows us to bound the contribution of the smoothing as $10 \mu D$. So, we get that the number of outer iterations $K$ required to get $F(\wv_K) - F^* \le \eps$ can be bounded as \begin{align*} K+1 \le \sqrt{\frac{8\Delta F_0}{\eps - 10 \mu D}} \,. \end{align*} Moreover, from our choice $\delta_k = 1 / (k+1)^2$, the number of inner iterations $T_k$ for inner loop $k$ is, from Prop.~\ref{prop:c:inner_loop_final}, \begin{align*} \expect[T_k] &\le \frac{1}{\tau(L_\mu + \kappa, \kappa)} \log\left( \frac{8 C(L_\mu + \kappa, \kappa)}{\tau(L_\mu + \kappa, \kappa)} \cdot \frac{L_\mu + \kappa}{\kappa} \cdot (k+1)^2 \right) + 1\\ &\le \frac{2}{\tau(L_\mu + \kappa, \kappa)} \log\left( \frac{8 C(L_\mu + \kappa, \kappa)}{\tau(L_\mu + \kappa, \kappa)} \cdot \frac{L_\mu + \kappa}{\kappa} \cdot {\frac{8\Delta F_0}{\eps - 10 \mu D}} \right) \,. \end{align*} Next, we consider the total number $N$ of iterations of SVRG to obtain an iterate $\wv$ such that $F(\wv) - F^* \le \eps$. Using the fact that $\expect[N] \le \sum_{i=1}^K \expect[T_k]$, we bound it as \begin{align} \label{eq:c:total_compl_smooth} \expect[N] \le \frac{1}{\tau(L_\mu + \kappa, \kappa)} \sqrt{\frac{8 \Delta F_0}{\eps - 10\mu D}} \log \left( \frac{64 C(L_\mu + \kappa, \kappa)}{\tau(L_\mu + \kappa, \kappa)} \frac{L_\mu + \kappa}{\kappa} \frac{\Delta F_0}{\eps - 10\mu D} \right)\,. \end{align} Now, we plug into \eqref{eq:c:total_compl_smooth} the values of $C, \tau$ for SVRG. Note that $\kappa = {L_\mu}/({n+1})$. So we have, \begin{align*} \frac{1}{\tau(L_\mu + \kappa, \kappa)} &= 8 \left( \frac{L_\mu + \kappa }{\kappa} + n \right) = 16(n+1) \,, \text{ and, } \\ C(L_\mu+\kappa, \kappa) &= \frac{L_\mu + \kappa}{\kappa} \left( 1 + \frac{n \tfrac{L_\mu+\kappa}{\kappa}}{8\tfrac{L+\kappa}{\kappa} + n} \right) \le (n+2) \left(1 + \tfrac{n}{8} \right)\, . \end{align*} It now remains to assign $\mu = {\eps}/({20D})$ and plug $C, \tau$ from above into \eqref{eq:c:total_compl_smooth}, noting that $\kappa = {20A D}/({\eps(n+1)})$. \end{proof} \begin{proposition_unnumbered}[\ref{prop:c:total_compl_nsc:dec_smoothing}] Consider the setting of Thm.~\ref{thm:catalyst:outer}. Suppose $\lambda = 0$ and that $\alpha_0$, $(\mu_k)_{k\ge 1}$,$ (\kappa_k)_{k\ge 1}$ and $(\delta_k)_{k \ge 1}$ are chosen as in Cor.~\ref{cor:c:outer_smooth_dec_smoothing}. If we run Algo.~\ref{algo:catalyst} with SVRG as the inner solver with these parameters, the number of iterations $N$ of SVRG required to obtain $\wv$ such that $F(\wv) - F^* \le \eps$ is bounded in expectation as \begin{align*} \expect[N] \le \widetilde\bigO \left( \frac{1}{\eps} \left( F(\wv_0) - F^* + \kappa \normasq{2}{\wv_0 - \wv^*} + \mu D \right) \left( n + \frac{A_\omega}{\mu \kappa} \right) \right) \,. \end{align*} \end{proposition_unnumbered} \begin{proof Define short hand $A:= A_\omega$, $D := D_\omega$ and \begin{gather} \label{eq:c:nsc:dec_smoothing_1} \Delta_0 := 2(F(\wv_0) - F^*) + \kappa \normsq{\wv_0 - \wv^*} + 27 \mu D \, . \end{gather} From Cor.~\ref{cor:c:outer_smooth_dec_smoothing}, the number of iterations $K$ required to obtain $F(\wv_K) - F^* \le \frac{\log(K+1)}{K+1} \Delta_0 \le \eps$ is (see Lemma~\ref{lem:c:helper_logx}), \begin{align} \label{eq:c:nsc:dec_smoothing} K + 1 = \frac{2\Delta_0}{\eps} \log \frac{2\Delta_0}{\eps} \,. \end{align} Let $C, \tau$ be such that SVRG is linearly convergent with parameters $C, \tau$, and define $L_k := {A}/{\mu_k}$ for each $k \ge 1$. Further, let $\mcT'$ be such that \[ \mcT' \ge \max_{k\in\{1, \cdots, K\}} \log\left( 8 \frac{C(L_k + \kappa, \kappa)}{\tau(L_k + \kappa, \kappa)} \frac{L_k + \kappa}{\kappa \delta_k} \right) \, . \] Clearly, $\mcT'$ is logarithmic in $K, n, AD, \mu, \kappa $. From Prop.~\ref{prop:c:inner_loop_final}, the minimum total complexity is (ignoring absolute constants) \begin{align} \expect[N] &= \sum_{k=1}^K \left( n + \frac{\nicefrac{A}{\mu_k} + \kappa_k}{\kappa_k} \right) \mcT' \nonumber \\ &= \sum_{k=1}^K \left( n + 1 + \frac{A}{\mu_k\kappa_k} \right) \mcT' \nonumber \\ &= \sum_{k=1}^K \left( n + 1 + \frac{A}{\mu\kappa} \right) \mcT' \nonumber \\ &\le \left( n+ 1 + \frac{A}{\mu \kappa} \right)K \mcT' \,, \end{align} and plugging in $K$ from~\eqref{eq:c:nsc:dec_smoothing} completes the proof. \end{proof} \subsection{Prox-Linear Convergence Analysis} \label{sec:c:pl_struct_pred} We first prove Lemma~\ref{lem:pl:struct_pred} that specifies the assumption required by the prox-linear in the case of structured prediction. \begin{lemma_unnumbered}[\ref{lem:pl:struct_pred}] Consider the structural hinge loss $f(\wv) = \max_{\yv \in \mcY} \psi(\yv ; \wv) = h\circ \gv(\wv)$ where $h, \gv$ are as defined in \eqref{eq:mapping_def}. If the mapping $\wv \mapsto \psi(\yv ; \wv)$ is $L$-smooth with respect to $\norma{2}{\cdot}$ for all $\yv \in \mcY$, then it holds for all $\wv, \zv \in \reals^d$ that \begin{align*} |h(\gv(\wv+\zv)) - h(\gv(\wv) + \grad\gv(\wv) \zv)| \le \frac{L}{2}\normasq{2}{\zv}\,. \end{align*} \end{lemma_unnumbered} \begin{proof} For any $\Am \in \reals^{m \times d}$ and $\wv \in \reals^d$, and $\norma{2,1}{\Am}$ defined in~\eqref{eq:matrix_norm_defn}, notice that \begin{align} \label{eq:pl-struc-pred-pf:norm} \norma{\infty}{\Am\wv} \le \norma{2, 1}{\Am} \norma{2}{\wv} \,. \end{align} Now using the fact that max function $h$ satisfies $|h(\uv') - h(\uv)| \le \norma{\infty}{\uv' - \uv}$ and the fundamental theorem of calculus $(*)$, we deduce \begin{align} |h(\gv(\wv+\zv)) - h(\gv(\wv) + \grad\gv(\wv) \zv)| &\le \norma{\infty}{\gv(\wv+\zv)- \left( \gv(\wv) + \grad\gv(\wv) \zv \right) } \nonumber \\ &\stackrel{(*)}{\le} \norm*{\int_0^1 (\grad\gv(\wv + t\zv) - \grad\gv(\wv) )\zv \, dt }_{\infty} \nonumber \\ &\stackrel{\eqref{eq:pl-struc-pred-pf:norm}}{\le} \int_0^1 \norma{2,1}{\grad\gv(\wv + t\zv) - \grad\gv(\wv) } \norma{2}{\zv} \, dt \,. \label{eq:pl-struc-pred-pf:1} \end{align} Note that the definition \eqref{eq:matrix_norm_defn} can equivalently be stated as $\norma{2,1}{\Am} = \max_{\norma{1}{\uv}\le 1} \norma{2}{\Am\T \uv}$. Given $\uv \in \reals^m$, we index its entries $u_\yv$ by $\yv \in \mcY$. Then, the matrix norm in \eqref{eq:pl-struc-pred-pf:1} can be simplified as \begin{align*} \norma{2,1}{\grad\gv(\wv + t\zv) - \grad\gv(\wv) } &= \max_{\norma{1}{\uv} \le 1} \bigg\|{\sum_{\yv \in \mcY} u_\yv ( \grad \psi( \yv ; \wv + t\zv) - \grad \psi( \yv ; \wv)) } \bigg\|_2 \\ &\le \max_{\norma{1}{\uv} \le 1} \sum_{\yv \in \mcY} |u_\yv| \norma{2}{\grad \psi( \yv ; \wv + t\zv) - \grad \psi( \yv ; \wv)} \\ &\le L t \norma{2}{\zv} \,, \end{align*} from the $L$-smoothness of $\psi$. Plugging this back into \eqref{eq:pl-struc-pred-pf:1} completes the proof. The bound on the smothing approximation holds similarly by noticing that if $h$ is $1$-Lipschitz then $h_{\mu \omega}$ too since $\nabla h_{\mu\omega}(\uv) \in \dom h^*$ for any $\uv \in \dom h$. \end{proof} \subsection{Information Based Complexity of the Prox-Linear Algorithm with {Casimir-SVRG}} \label{sec:c:pl_proofs} \begin{proposition_unnumbered}[\ref{prop:pl:total_compl}] Consider the setting of Thm.~\ref{thm:pl:outer-loop}. Suppose the sequence $\{\eps_k\}_{k\ge 1}$ satisfies $\eps_k = \eps_0 / k$ for some $\eps_0 > 0$ and that the subproblem of Line~\ref{line:pl:algo:subprob} of Algo.~\ref{algo:prox-linear} is solved using {Casimir-SVRG}{} with the settings of Prop.~\ref{prop:c:total_compl_svrg_sc}. Then, total number of SVRG iterations $N$ required to produce a $\wv$ such that $\norma{2}{\bm{\varrho}_\eta(\wv)} \le \eps$ is bounded as \begin{align*} \expect[N] \le \widetilde\bigO\left( \frac{n}{\eta \eps^2} \left(F(\wv_0) - F^* + \eps_0 \right) + \frac{\sqrt{A_\omega D_\omega n \eps_0\inv}}{\eta \eps^3} \left( F(\wv_0) - F^* + \eps_0 \right)^{3/2} \right) \, . \end{align*} \end{proposition_unnumbered} \begin{proof First note that $\sum_{k=1}^{K} \eps_k \le \eps_0 \sum_{k=1}^K k\inv \le 4 \eps_0 \log K$ for $K \ge 2$. Let $\Delta F_0 := F(\wv_0) - F^*$ and use shorthand $A, D$ for $A_\omega, D_\omega$ respectively. From Thm.~\ref{thm:pl:outer-loop}, the number $K$ of prox-linear iterations required to find a $\wv$ such that $\norma{2}{\bm{\varrho}_\eta(\wv)} \le \eps$ must satisfy \begin{align*} \frac{2}{\eta K} \left( \Delta F_0 + 4\eps_0 \log K \right) \le \eps \,. \end{align*} For this, it suffices to have (see e.g., Lemma~\ref{lem:c:helper_logx}) \begin{align*} K \ge \frac{4(\Delta F_0 + 4 \eps_0)}{\eta\eps^2} \log\left( \frac{4(\Delta F_0 + 4 \eps_0)}{\eta\eps^2} \right) \,. \end{align*} Before we can invoke Prop.~\ref{prop:c:total_compl_svrg_sc}, we need to bound the dependence of each inner loop on its warm start: $F_\eta(\wv_{k-1} ; \wv_{k-1}) - F_\eta(\wv_{k}^* ; \wv_{k-1})$ in terms of problem parameters, where $\wv_k^* = \argmin_{\wv} F_\eta(\wv ; \wv_{k-1})$ is the exact result of an exact prox-linear step. We note that $F_\eta(\wv_{k-1} ; \wv_{k-1}) = F(\wv_{k-1}) \le F(\wv_0)$, by Line~\ref{line:pl:algo:accept} of Algo.~\ref{algo:prox-linear}. Moreover, from $\eta \le 1/L$ and Asmp.~\ref{asmp:pl:upper-bound}, we have, \begin{align*} F_\eta(\wv_k^* ; \wv_{k-1}) &= \frac{1}{n} \sum_{i=1}^n h \big( \gv\pow{i}(\wv_{k-1}) + \grad \gv\pow{i}(\wv_{k-1})(\wv_k^* - \wv_{k-1}) \big) + \frac{\lambda}{2}\normasq{2}{\wv_k^*} + \frac{1}{2\eta} \normasq{2}{\wv_k^* - \wv_{k-1}} \\ &\ge \frac{1}{n} \sum_{i=1}^n h \big( \gv\pow{i}(\wv_{k-1}) + \grad \gv\pow{i}(\wv_{k-1})(\wv_k^* - \wv_{k-1}) \big) + \frac{\lambda}{2}\normasq{2}{\wv_k^*} + \frac{L}{2} \normasq{2}{\wv_k^* - \wv_{k-1}} \\ &\ge \frac{1}{n} \sum_{i=1}^n h \big( \gv\pow{i}(\wv_k^*) \big) + \frac{\lambda}{2}\normasq{2}{\wv_k^*} \\ &= F(\wv_k^*) \ge F^* \,. \end{align*} Thus, we bound $F_\eta(\wv_{k-1} ; \wv_{k-1}) - F_\eta(\wv_{k}^* ; \wv_{k-1}) \le \Delta F_0$. We now invoke Prop.~\ref{prop:c:total_compl_svrg_sc} and collect all constants and terms logarithmic in $n$, $\eps\inv, \eps_0 \inv$, $\Delta F_0$, $\eta\inv$, $A_\omega D_\omega$ in $\mcT, \mcT', \mcT''$. We note that all terms in the logarithm in Prop.~\ref{prop:c:total_compl_svrg_sc} are logarithmic in the problem parameters here. Letting $N_k$ be the number of SVRG iterations required for iteration $k$, we get, \begin{align*} \expect[N] &= \sum_{k=1}^K \expect[N_k] \le \sum_{k=1}^K \left( n + \sqrt{\frac{\eta A D n}{\eps_k}} \right) \, \mcT \\ &\le \left[ nK + \sqrt{\frac{\eta A D n}{\eps_0}} \left( \sum_{k=1}^K \sqrt{k} \right) \right] \, \mcT \\ &\le \left[ nK + \sqrt{\frac{\eta A D n}{\eps_0}}\, K^{3/2} \right] \, \mcT' \\ &\le \left[ \frac{n}{\eta \eps^2} (\Delta F_0 + \eps_0) + \sqrt{\frac{\eta A D n}{\eps_0}}\, \left( \frac{\Delta F_0 + \eps_0}{\eta \eps^2} \right)^{3/2} \right] \, \mcT'' \\ &= \left[ \frac{n}{\eta \eps^2} (\Delta F_0 + \eps_0) + \frac{\sqrt{ADn}}{\eta \eps^3} \frac{(\Delta F_0 + \eps_0)^{3/2}}{\sqrt{\eps_0}} \right] \, \mcT'' \,. \end{align*} \end{proof} \subsection{Some Helper Lemmas} \label{subsec:a:catalyst:helper} The first lemma is a property of the squared Euclidean norm from \citet[Lemma 5]{lin2017catalyst}, which we restate here. \begin{lemma}\label{lem:c:helper:quadratic} For any vectors, $\wv, \zv, \rv \in \reals^d$, we have, for any $\theta > 0$, \begin{align*} \normsq{\wv - \zv} \ge (1-\theta) \normsq{\wv - \rv} + \left( 1 - \frac{1}{\theta} \right) \normsq{\rv - \zv} \,. \end{align*} \end{lemma} The next lemmas consider rates of the sequences $(\alpha_k)$ and $(A_k)$ under different recursions. \begin{lemma} \label{lem:c:A_k:const_kappa} Define a sequence $(\alpha_k)_{k \ge 0}$ as \begin{align*} \alpha_0 &= \frac{\sqrt 5 - 1}{2} \\ \alpha_k^2 &= (1 - \alpha_k) \alpha_{k-1}^2 \,. \end{align*} Then this sequence satisfies \begin{align*} \frac{\sqrt 2}{k+3} \le \alpha_k \le \frac{2}{k+3} \,. \end{align*} Moreover, $A_k := \prod_{j=0}^k (1-\alpha_k)$ satisfies \begin{align*} \frac{2}{(k+3)^2} \le A_k \le \frac{4}{(k+3)^2} \,. \end{align*} \end{lemma} \begin{proof} Notice that $\alpha_0$ satisfies $\alpha_0^2 = 1 - \alpha_0$. Further, it is clear from definition that $\alpha_k \in (0, 1)\, \forall k \ge 0$. Hence, we can define a sequence $(b_k)_{k\ge 0}$ such that $b_k := 1/\alpha_k$. It satisfies the recurrence, $b_k^2 - b_k = b_{k-1}^2$ for $k \ge 1$, or in other words, $b_k = \tfrac{1}{2}\left( 1 + \sqrt{1 + 4 b_{k-1}^2} \right)$. Form this we get, \begin{align*} b_k &\ge b_{k-1} + \frac{1}{2} \ge b_0 + \frac{k}{2} \ge \frac{3}{2} + \frac{k}{2} \,. \end{align*} since $b_0 = \frac{\sqrt 5 + 1}{2}$. This gives us the upper bound on $\alpha_k$. Moreover, unrolling the recursion, \begin{align} \label{eq:c:helper:2_} \alpha_k^2 = (1- \alpha_k) \alpha_{k-1}^2 = A_k \frac{\alpha_0^2}{1 - \alpha_0} = A_k \, . \end{align} Since $\alpha_k \le 2/(k+3)$, \eqref{eq:c:helper:2_} yields the upper bound on $A_k$. The upper bound on $\alpha_k$ again gives us, \begin{align*} A_k \ge \prod_{i=0}^k \left( 1 - \frac{2}{i+3} \right) = \frac{2}{(k+2)(k+3)} \ge \frac{2}{(k+3)^2} \,, \end{align*} to get the lower bound on $A_k$. Invoking \eqref{eq:c:helper:2_} again to obtain the lower bound on $\alpha_k$ completes the proof. \end{proof} The next lemma considers the evolution of the sequences $(\alpha_k)$ and $(A_k)$ with a different recursion. \begin{lemma} \label{lem:c:A_k:inc_kappa} Consider a sequence $(\alpha_k)_{k\ge 0}$ defined by $\alpha_0 = \frac{\sqrt{5}- 1}{2}$, and $\alpha_{k+1}$ as the non-negative root of \begin{align*} \frac{\alpha_k^2}{1 - \alpha_k} = \alpha_{k-1}^2 \frac{k}{k+1} \,. \end{align*} Further, define \begin{align*} A_k = \prod_{i=0}^k ( 1- \alpha_i) \, . \end{align*} Then, we have for all $k\ge 0$, \begin{align} \frac{1}{k+1} \left(1 - \frac{1}{\sqrt2} \right) \le A_k \le \frac{1}{k+2} \, . \end{align} \end{lemma} \begin{proof} Define a sequence $(b_k)_{k\ge 0}$ such that $b_k = 1/\alpha_k$, for each $k$. This is well-defined because $\alpha_k \neq 0$, which may be verified by induction. This sequence satisfies the recursion for $k\ge 1$: $b_k (b_k -1) = \left( \frac{k+1}{k} \right)b_{k-1}$. From this recursion, we get, \begin{align} \nonumber b_k &= \frac{1}{2} \left( 1 + \sqrt{1 + 4 b_{k-1}^2 \left( \frac{k+1}{k} \right)} \right) \\ \nonumber &\ge \frac{1}{2} + b_{k-1} \sqrt\frac{k+1}{k} \\ \nonumber &\ge \frac{1}{2}\left( 1 + \sqrt{\frac{k+1}{k}} + \cdots + \sqrt{\frac{k+1}{2}} \right) + b_0\sqrt{k+1} \\ \nonumber &= \frac{\sqrt{k+1}}{2} \left( 1/\sqrt 2 + \cdots + 1/\sqrt{k+1} \right) + b_0 \sqrt{k+1} \\ &\stackrel{(*)}{\ge} \sqrt{k+1}\left( \sqrt{k+2} + b_0 - \sqrt 2 \right) = \sqrt{k+1} \left( \sqrt{k+2} + b_0 - \sqrt 2 \right) \,, \end{align} where $(*)$ followed from noting that $1/\sqrt{2}+\cdots+1/\sqrt{k+1} \ge \int_2^{k+2} \frac{dx}{\sqrt x} = 2(\sqrt{k+2}-\sqrt 2)$\,. Since $b_0 = 1/\alpha_0 = \frac{\sqrt{5} + 1}{2} > \sqrt 2$, we have, for $k \ge 1$, \begin{align} \alpha_k \le \frac{1}{\sqrt{k+1}(\sqrt{k+2}+ b_0 - \sqrt{2})} \le \frac{1}{\sqrt{k+1}\sqrt{k+2}} \,. \end{align} This relation also clearly holds for $k=0$. Next, we claim that \begin{align} A_k = (k+1) \alpha_k^2 \le \frac{k+1}{(\sqrt{k+1}\sqrt{k+2})^2} = \frac{1}{k+2}\, . \end{align} Indeed, this is true because \begin{align*} \alpha_k^2 = (1 - \alpha_k) \alpha_{k-1}^2 \frac{k}{k+1} = A_k \frac{\alpha_0^2}{1 - \alpha_0} \frac{1}{k+1} = \frac{A_k}{k+1} \,. \end{align*} For the lower bound, we have, \begin{align*} A_k = \prod_{i=0}^k (1 - \alpha_i) \ge \prod_{i=0}^k \left(1 - \frac{1}{\sqrt{i+1}\sqrt{i+2}} \right) \ge \left( 1 - \frac{1}{\sqrt2} \right) \prod_{i=1}^k \left(1 - \frac{1}{i+1} \right) = \frac{1 - \frac{1}{\sqrt{2}}}{k+1} \, . \end{align*} \end{proof} \begin{lemma} \label{lem:c:helper_logx} Fix some $\eps > 0$. If $k \ge \frac{2}{\eps} \log \frac{2}{\eps}$, then we have that $\frac{\log k}{k} \le \eps$. \end{lemma} \begin{proof} We have, since $\log x \le x$ for $x > 0$, \begin{align*} \frac{\log k }{k} \le \frac{\log\frac{2}{\eps} + \log\log\frac{2}{\eps}}{\frac{2}{\eps} \log\frac{2}{\eps}} = \frac{\eps}{2} \left( 1 + \frac{\log\log\frac{2}{\eps}}{\log\frac{2}{\eps}} \right) \le \eps \,. \end{align*} \end{proof} \subsection{Related Work} \label{sec:related_work} \begin{table*}[t!] \caption{\small{Convergence rates given in terms of the number of calls to various oracles for different optimization algorithms on the learning problem~\eqref{eq:c:main:prob} in case of structural support vector machines~\eqref{eq:pgm:struc_hinge}. The rates are specified in terms of the target accuracy $\eps$, the number of training examples $n$, the regularization $\lambda$, the size of the label space~$\scriptsize{\abs\mcY}$, the max feature norm $R=\max_i \norma{2}{\Phi(\xv\pow{i},\yv) - \Phi(\xv\pow{i}, \yv\pow{i})}$ and $\widetilde R \ge R$ (see Remark~\ref{remark:smoothing:l2vsEnt} for explicit form). The rates are specified up to constants and factors logarithmic in the problem parameters. The dependence on the initial error is ignored. * denotes algorithms that make $\bigO(1)$ oracle calls per iteration. \vspace{2mm} }} \label{tab:rates} \footnotesize\setlength{\tabcolsep}{2pt} \begin{minipage}{.32\linewidth} \centering \begin{adjustbox}{width=1\textwidth} \begin{tabular}{|c|c|} \hline \rule{0pt}{10pt} \textbf{Algo.} (\textit{exp} oracle) & \textbf{\# Oracle calls} \\[0.45ex] \hline\hline \rule{0pt}{15pt} \begin{tabular}{c} Exponentiated \\ gradient* \\ \citep{collins2008exponentiated}\end{tabular} & $\dfrac{(n + \log |\mcY|) R^2 }{\lambda \eps}$ \\[2.54ex] \hline \rule{0pt}{15pt} \begin{tabular}{c} Excessive gap \\ reduction \\ \citep{zhang2014accelerated} \end{tabular} & $n R \sqrt{\dfrac{\log |\mcY|}{\lambda \eps}}$ \\[2.54ex] \hline \rule{0pt}{15pt} \begin{tabular}{c} Prop.~\ref{prop:c:total_compl_svrg_main}*, \\ entropy smoother \end{tabular} & $\sqrt{\dfrac{nR^2 \log\abs\mcY}{\lambda \eps}}$ \\[2.54ex] \hline \rule{0pt}{15pt} \begin{tabular}{c} Prop.~\ref{prop:c:total_compl_sc:dec_smoothing_main}*, \\ entropy smoother \end{tabular} & $n + {\dfrac{R^2 \log\abs\mcY}{\lambda \eps}}$ \\[2.54ex] \hline \end{tabular} \end{adjustbox} \end{minipage} \hspace{2.6mm}% \begin{minipage}{.35\linewidth} \centering \begin{adjustbox}{width=1\textwidth} \begin{tabular}{|c|c|} \hline \rule{0pt}{10pt} \textbf{Algo.} (\textit{max} oracle) & \textbf{\# Oracle calls} \\[0.45ex] \hline\hline \rule{0pt}{15pt} \begin{tabular}{c} BMRM \\ \citep{teo2009bundle}\end{tabular} & $\dfrac{n R^2}{\lambda \eps}$ \\[2ex] \hline \rule{0pt}{15pt} \begin{tabular}{c} QP 1-slack \\ \citep{joachims2009cutting} \end{tabular}& $\dfrac{n R^2}{\lambda \eps}$ \\[2ex] \hline \rule{0pt}{15pt} \begin{tabular}{c} Stochastic \\ subgradient* \\ \citep{shalev2011pegasos} \end{tabular}& $\dfrac{R^2}{\lambda \eps}$ \\[2ex] \hline \rule{0pt}{15pt} \begin{tabular}{c} Block-Coordinate \\ Frank-Wolfe* \\ \citep{lacoste2012block} \end{tabular} & $n + \dfrac{R^2}{\lambda \eps}$ \\[2ex] \hline \end{tabular} \end{adjustbox} \end{minipage} \hspace{2.2mm} \begin{minipage}{.25\linewidth} \centering \medskip \begin{adjustbox}{width=1\textwidth} \begin{tabular}{|c|c|} \hline \rule{0pt}{0pt} \begin{tabular}{c} \textbf{Algo.} \\ (\textit{top-$K$} oracle) \end{tabular} & \textbf{\# Oracle calls} \\[0.45pt] \hline\hline \rule{0pt}{12pt} \begin{tabular}{c} Prop.~\ref{prop:c:total_compl_svrg_main}*, \\ $\ell_2^2$ smoother \end{tabular} & $\sqrt{\dfrac{n{\widetilde R}^2}{\lambda \eps}}$ \\[2.54ex] \hline \rule{0pt}{12pt} \begin{tabular}{c} Prop.~\ref{prop:c:total_compl_sc:dec_smoothing_main}*, \\ $\ell_2^2$ smoother \end{tabular} & $n + {\dfrac{{\widetilde R}^2}{\lambda \eps}}$ \\[2.45ex] \hline \end{tabular} \end{adjustbox} \end{minipage}% \end{table*} \paragraph{Optimization for Structural Support Vector Machines} Table~\ref{tab:rates} gives an overview of different optimization algorithms designed for structural support vector machines. Early works~\citep{taskar2004max,tsochantaridis2004support,joachims2009cutting,teo2009bundle} considered batch dual quadratic optimization (QP) algorithms. The stochastic subgradient method operated directly on the non-smooth primal formulation~\citep{ratliff2007approximate,shalev2011pegasos}. More recently,~\citet{lacoste2012block} proposed a block coordinate Frank-Wolfe (BCFW) algorithm to optimize the dual formulation of structural support vector machines; see also~\citet{osokin2016minding} for variants and extensions. Saddle-point or primal-dual approaches include the mirror-prox algorithm~\citep{taskar2006structured,cox2014dual,he2015semi}.~\citet{palaniappan2016stochastic} propose an incremental optimization algorithm for saddle-point problems. However, it is unclear how to extend it to the structured prediction problems considered here. Incremental optimization algorithms for conditional random fields were proposed by~\citet{schmidt2015non}. We focus here on primal optimization algorithms in order to be able to train structured prediction models with affine or nonlinear mappings with a unified approach, and on incremental optimization algorithms which can scale to large datasets. \paragraph{Inference} The ideas of dynamic programming inference in tree structured graphical models have been around since the pioneering works of \citet{pearl1988probabilistic} and \citet{dawid1992applications}. Other techniques emerged based on graph cuts \citep{greig1989exact,ishikawa1998segmentation}, bipartite matchings \citep{cheng1996maximum,taskar2005discriminative} and search algorithms \citep{daume2005learning,lampert2008beyond,lewis2014ccg,he2017deep}. For graphical models that admit no such a discrete structure, techniques based on loopy belief propagation~\citep{mceliece1998turbo,murphy1999loopy}, linear programming (LP)~\citep{schlesinger1976syntactic}, dual decomposition \citep{johnson2008convex} and variational inference \citep{wainwright2005map,wainwright2008graphical} gained popularity. \paragraph{Top-$K$ Inference} Smooth inference oracles with $\ell_2^2$ smoothing echo older heuristics in speech and language processing~\citep{jurafsky2014speech}. Combinatorial algorithms for top-$K$ inference have been studied extensively by the graphical models community under the name ``$M$-best MAP''. \citet{seroussi1994algorithm} and \citet{nilsson1998efficient} first considered the problem of finding the $K$ most probable configurations in a tree structured graphical model. Later, \citet{yanover2004finding} presented the Best Max-Marginal First algorithm which solves this problem with access only to an oracle that computes max-marginals. We also use this algorithm in Sec.~\ref{subsec:smooth_inference_loopy}. \citet{fromer2009lp} study top-$K$ inference for LP relaxation, while \citet{batra2012efficient} considers the dual problem to exploit graph structure. \citet{flerova2016searching} study top-$K$ extensions of the popular $\text{A}^\star$ and branch and bound search algorithms in the context of graphical models. Other related approaches include diverse $K$-best solutions \citep{batra2012diverse} and finding $K$-most probable modes \citep{chen2013computing}. \paragraph{Smoothing Inference} Smoothing for inference was used to speed up iterative algorithms for continuous relaxations. \citet{johnson2008convex} considered smoothing dual decomposition inference using the entropy smoother, followed by \citet{jojic2010accelerated} and \citet{savchynskyy2011study} who studied its theoretical properties. \citet{meshi2012convergence} expand on this study to include $\ell_2^2$ smoothing. Explicitly smoothing discrete inference algorithms in order to smooth the learning problem was considered by \citet{zhang2014accelerated} and \citet{song2014learning} using the entropy and $\ell_2^2$ smoothers respectively. The $\ell_2^2$ smoother was also used by \citet{martins2016softmax}. \citet{hazan2016blending} consider the approach of blending learning and inference, instead of using inference algorithms as black-box procedures. Related ideas to ours appear in the independent works~\citep{mensch2018differentiable,niculae2018sparsemap}. These works partially overlap with ours, but the papers choose different perspectives, making them complementary to each other.~\citet{mensch2018differentiable} proceed differently when, {e.g.},~smoothing inference based on dynamic programming. Moreover, they do not establish complexity bounds for optimization algorithms making calls to the resulting smooth inference oracles. We define smooth inference oracles in the context of black-box first-order optimization and establish worst-case complexity bounds for incremental optimization algorithms making calls to these oracles. Indeed we relate the amount of smoothing controlled by $\mu$ to the resulting complexity of the optimization algorithms relying on smooth inference oracles. \paragraph{End-to-end Training of Structured Prediction} The general framework for global training of structured prediction models was introduced by~\cite{bottou1990framework} and applied to handwriting recognition by~\cite{bengio1995lerec} and to document processing by~\cite{bottou1997global}. This approach, now called ``deep structured prediction'', was used, e.g., by \citet{collobert2011natural} and \citet{belanger2016structured}. \subsection{Notation} Vectors are denoted by bold lowercase characters as $\wv \in \reals^d$ while matrices are denoted by bold uppercase characters as $\Am \in \reals^{d \times n}$. For a matrix $\Am \in \reals^{m \times n}$, define the norm for $\alpha,\beta \in \{1, 2, \infty\}$, \begin{align} \label{eq:matrix_norm_defn} \norma{\beta, \alpha}{\Am} = \max\{ \inp{\yv}{\Am\xv} \, | \, \norma{\alpha}{\yv} \le 1 \, , \, \norma{\beta}{\xv} \le 1 \} \,. \end{align} For any function $f: \reals^d \to \reals \cup \{ +\infty \}$, its convex conjugate $f^*:\reals^d \to \reals \cup \{+\infty\}$ is defined as \begin{align*} f^*(\zv) = \sup_{\wv \in \reals^d} \left\{ \inp{\zv}{\wv} - f(\wv) \right\} \, . \end{align*} A function $f : \reals^d \to \reals$ is said to be $L$-smooth with respect to an arbitrary norm $\norm{\cdot}$ if it is continuously differentiable and its gradient $\grad f$ is $L$-Lipschitz with respect to $\norm{\cdot}$. When left unspecified, $\norm{\cdot}$ refers to $\norma{2}{\cdot}$. Given a continuously differentiable map $\gv : \reals^d \to \reals^m$, its Jacobian $\grad \gv(\wv) \in \reals^{m \times d}$ at $\wv \in \reals^d$ is defined so that its $ij$th entry is $[\grad \gv(\wv)]_{ij} = \partial g_i(\wv) / w_j$ where $g_i$ is the $i$th element of $\gv$ and $w_j$ is the $j$th element of $\wv$. The vector valued function $\gv : \reals^d \to \reals^m$ is said to be $L$-smooth with respect to $\norm{\cdot}$ if it is continuously differentiable and its Jacobian $\grad \gv$ is $L$-Lipschitz with respect to $\norm{\cdot}$. For a vector $\zv \in \reals^m$, $z_{(1)} \ge \cdots \ge z_{(m)}$ refer to its components enumerated in non-increasing order where ties are broken arbitrarily. Further, we let $\zv_{[k]} = (z_{(1)}, \cdots, z_{(k)}) \in \reals^k$ denote the vector of the $k$ largest components of $\zv$. We denote by $\Delta^{m-1}$ the standard probability simplex in $\reals^{m}$. When the dimension is clear from the context, we shall simply denote it by $\Delta$. Moreover, for a positive integer $p$, $[p]$ refers to the set $\{1, \ldots,p\}$. Lastly, $\widetilde \bigO$ in the big-$\bigO$ notation hides factors logarithmic in problem parameters. \subsection{Structural Hinge Loss} On a given input-output pair $(\xv, \yv)$, the error of prediction of $\yv$ by the inference procedure with a score function $\phi(\cdot, \cdot; \wv)$, is measured by a task loss $\ell \big( \yv, \yv^*(\xv; \wv) \big)$ such as the Hamming loss. The learning procedure would then aim to find the best parameter $\wv$ that minimizes the loss on a given dataset of input-output training examples. However, the resulting problem is piecewise constant and hard to optimize. Instead, \citet{altun2003hidden,taskar2004max,tsochantaridis2004support} propose to minimize a majorizing surrogate of the task loss, called the structural hinge loss defined on an input-output pair $(\xv\pow{i}, \yv\pow{i})$ as \begin{align}\label{eq:pgm:struc_hinge} f\pow{i}(\wv) = \max_{\yv \in \mcY} \left\{ \phi(\xv\pow{i}, \yv ; \wv) + \ell(\yv\pow{i}, \yv) \right\} - \phi(\xv\pow{i}, \yv\pow{i} ; \wv) = \max_{\yv \in \mcY} \psi\pow{i}(\yv, \wv) \, . \end{align} where $\psi\pow{i}(\yv ; \wv) = \phi(\xv\pow{i}, \yv ; \wv) + \ell(\yv\pow{i}, \yv) - \phi(\xv\pow{i}, \yv\pow{i} ; \wv)$ is the augmented score function. This approach, known as {\em max-margin structured prediction}, builds upon binary and multi-class support vector machines~\citep{crammer2001algorithmic}, where the term $\ell(\yv\pow{i}, \yv)$ inside the maximization in \eqref{eq:pgm:struc_hinge} generalizes the notion of margin. The task loss $\ell$ is assumed to possess appropriate structure so that the maximization inside \eqref{eq:pgm:struc_hinge}, known as {\em loss augmented inference}, is no harder than the inference problem in \eqref{eq:pgm:inference}. When considering a fixed input-output pair $(\xv\pow{i}, \yv\pow{i}$), we drop the index with respect to the sample $i$ and consider the structural hinge loss as \begin{equation}\label{eq:struct_hinge} f(\wv) = \max_{\yv \in \mathcal{\mcY}} \psi(\yv;\wv), \end{equation} When the map $\wv \mapsto \psi(\yv ; \wv)$ is affine, the structural hinge loss $f$ and the objective $F$ from \eqref{eq:c:main:prob} are both convex - we refer to this case as the structural support vector machine. When $\wv \mapsto \psi(\yv ; \wv)$ is a nonlinear but smooth map, then the structural hinge loss $f$ and the objective $F$ are nonconvex. \subsection{Smoothing Strategy} A convex, non-smooth function $h$ can be smoothed by taking its infimal convolution with a smooth function~\citep{beck2012smoothing}. We now recall its dual representation, which \citet{nesterov2005smooth} first used to relate the amount of smoothing to optimal complexity bounds. \begin{definition} \label{defn:smoothing:inf-conv} For a given convex function $h:\reals^m \to \reals$, a smoothing function $\omega: \dom h^* \to \reals$ which is 1-strongly convex with respect to $\norma{\alpha}{\cdot}$ (for $\alpha \in \{1,2\}$), and a parameter $\mu > 0$, define \begin{align*} h_{\mu \omega}(\zv) = \max_{\uv \in \dom h^*} \left\{ \inp{\uv}{\zv} - h^*(\uv) - \mu \omega(\uv) \right\} \,. \end{align*} as the smoothing of $h$ by $\mu \omega$. \end{definition} \noindent We now state a classical result showing how the parameter $\mu$ controls both the approximation error and the level of the smoothing. For a proof, see \citet[Thm. 4.1, Lemma 4.2]{beck2012smoothing} or Prop.~\ref{prop:smoothing:difference_of_smoothing} of Appendix~\ref{sec:a:smoothing}. \begin{proposition} \label{thm:setting:beck-teboulle} Consider the setting of Def.~\ref{defn:smoothing:inf-conv}. The smoothing $h_{\mu \omega}$ is continuously differentiable and its gradient, given by \[ \grad h_{\mu \omega}(\zv) = \argmax_{\uv \in \dom h^*} \left\{ \inp{\uv}{\zv} - h^*(\uv) - \mu \omega(\uv) \right\} \] is $1/\mu$-Lipschitz with respect to $\normad{\alpha}{\cdot}$. Moreover, letting $h_{\mu \omega} \equiv h$ for $\mu = 0$, the smoothing satisfies, for all $\mu_1 \ge \mu_2 \ge 0$, \begin{align*} (\mu_1 - \mu_2) \inf_{\uv \in \dom h^*} \omega(\uv) \le h_{\mu_2 \omega}(\zv) - h_{\mu_1 \omega}(\zv) \le (\mu_1 - \mu_2) \sup_{\uv \in \dom h^*} \omega(\uv) \,. \end{align*} \end{proposition} \paragraph{Smoothing the Structural Hinge Loss} We rewrite the structural hinge loss as a composition \begin{equation}\label{eq:mapping_def} \gv:\ \begin{cases} \reals^d &\to \reals^m \\ \wv &\mapsto (\psi(\yv;\wv))_{\yv \in \mathcal{Y}}, \end{cases} \, \qquad h: \begin{cases} \reals^{m} &\to \reals \\ \zv &\mapsto \max_{i \in [m]} z_i, \end{cases} \end{equation} where $m= |\mcY|$ so that the structural hinge loss reads \begin{align} \label{eq:pgm:struc_hinge_vec} f(\wv) = h \circ \gv(\wv)\,. \end{align} We smooth the structural hinge loss~\eqref{eq:pgm:struc_hinge_vec} by simply smoothing the non-smooth max function $h$ as \begin{align*} f_{\mu \omega} = h_{\mu \omega} \circ \gv. \end{align*} When $\gv$ is smooth and Lipschitz continuous, $f_{\mu \omega}$ is a smooth approximation of the structural hinge loss, whose gradient is readily given by the chain-rule. In particular, when $\gv$ is an affine map $\gv(\wv) = \Am\wv + \bv$, if follows that $f_{\mu \omega}$ is $(\normasq{\beta,\alpha}{\Am} / \mu)$-smooth with respect to $\norma{\beta}{\cdot}$ (cf. Lemma~\ref{lemma:smoothing:composition} in Appendix~\ref{sec:a:smoothing}). Furthermore, for $\mu_1 \ge \mu_2 \ge 0$, we have, \[ (\mu_1 - \mu_2) \min_{\uv \in \Delta^{m-1}} \omega(\uv) \le f_{\mu_2\omega}(\wv) - f_{\mu_1 \omega}(\wv) \le (\mu_1 - \mu_2) \max_{\uv \in \Delta^{m-1}} \omega(\uv) \,. \] \subsection{Smoothing Variants} In the context of smoothing the max function, we now describe two popular choices for the smoothing function $\omega$, followed by computational considerations. \subsubsection{Entropy and $\ell_2^2$ smoothing} When $h$ is the max function, the smoothing operation can be computed analytically for the \emph{entropy} smoother and the $\ell_2^2$ smoother, denoted respectively as \begin{align*} -H(\uv) := \inp{\uv}{\log \uv} \qquad \mbox{and} \qquad \ell_2^2(\uv) := \tfrac{1}{2}(\normasq{2}{\uv} - 1) \,. \end{align*} These lead respectively to the log-sum-exp function~\citep[Lemma 4]{nesterov2005smooth} \[ h_{-\mu H}(\zv) = \mu \log\left(\sum_{i=1}^{m}e^{z_i/\mu}\right), \quad \nabla h_{-\mu H}(\zv) = \left[\frac{e^{z_i/\mu}}{\sum_{j=1}^{m}e^{z_j/\mu}}\right]_{i=1,\ldots,m} \,, \] and an orthogonal projection onto the simplex, \[ h_{\mu \ell_2^2}(\zv) = \langle \zv, \operatorname{proj}_{\Delta^{m-1}}(\zv/\mu) \rangle - \tfrac{\mu}{2}\|\operatorname{proj}_{\Delta^{m-1}}(\zv/\mu)\|^2 + \tfrac{\mu}{2}, \quad \nabla h_{\mu \ell_2^2}(\zv) = \operatorname{proj}_{\Delta^{m-1}}(\zv/\mu) \,. \] Furthermore, the following holds for all $\mu_1 \ge \mu_2 \ge 0$ from Prop.~\ref{thm:setting:beck-teboulle}: \[ 0 \le h_{-\mu_1 H}(\zv) - h_{-\mu_2 H}(\zv) \le (\mu_1 - \mu_2) \log m, \quad \text{and,} \quad 0 \le h_{\mu_1 \ell_2^2}(\zv) - h_{\mu_2 \ell_2^2}(\zv) \le \tfrac{1}{2}(\mu_1-\mu_2) \,. \] \subsubsection{Top-$K$ Strategy} Though the gradient of the composition $f_{\mu \omega} = h_{\mu \omega} \circ \gv$ can be written using the chain rule, its actual computation for structured prediction problems involves computing $\grad \gv$ over all $m = \abs{\mcY}$ of its components, which may be intractable. However, in the case of $\ell_2^2$ smoothing, projections onto the simplex are sparse, as pointed out by the following proposition. \begin{proposition} \label{prop:smoothing:proj-simplex-1} Consider the Euclidean projection $\uv^* = \argmin_{\uv \in \Delta^{m-1}}\normasq{2}{\uv -{\zv}/{\mu}} $ of $\zv/\mu \in \reals^m$ onto the simplex, where $\mu > 0$. The projection $\uv^*$ has exactly $k \in [m]$ non-zeros if and only if \begin{align} \label{eq:smooth:proj:simplex_1_statement} \sum_{i=1}^k \left(z_{(i)} - z_{(k)} \right) < \mu \le \sum_{i=1}^k \left(z_{(i)} - z_{(k+1)} \right) \,, \end{align} where $z_{(1)}\ge \cdots \ge z_{(m)}$ are the components of $\zv$ in non-decreasing order and $z_{(m+1)} := -\infty$. In this case, $\uv^*$ is given by \begin{align*} u_i^* = \max \bigg\{0, \, \tfrac{1}{k\mu }\sum_{j=1}^k \big( z_i - z_{(j)} \big) + \tfrac{1}{k} \bigg\} \,. \end{align*} \end{proposition} \begin{proof} The projection $\uv^*$ satisfies $u^*_i = (z_i/\mu + \rho^*)_+$, where $\rho^*$ is the unique solution of $\rho$ in the equation \begin{align} \label{eq:smooth:proj:simplex_1} \sum_{i=1}^m \left( \frac{z_i}{\mu} + \rho \right)_+ = 1 \,, \end{align} where $\alpha_+ = \max\{0, \alpha\}$. See, e.g., \citet{held1974validation} for a proof of this fact. Note that $z_{(i)}/\mu + \rho^* \le 0$ implies that $z_{(j)}/\mu + \rho^* \le 0$ for all $j \ge i$. Therefore $\uv^*$ has $k$ non-zeros if and only if $z_{(k)}/\mu + \rho^* > 0$ and $z_{(k+1)}/\mu + \rho^* \le 0$. Now suppose that $\uv^*$ has exactly $k$ non-zeros, we can then solve \eqref{eq:smooth:proj:simplex_1} to obtain $\rho^* = \varphi_k(\zv/\mu)$, which is defined as \begin{align} \label{eq:smooth:proj:simplex_1b} \varphi_k\left( \frac \zv \mu \right) := \frac{1}{k} - \frac{1}{k} \sum_{i=1}^k \frac{z_{(i)}}{\mu} \,. \end{align} Plugging in the value of $\rho^*$ in $z_{(k)}/\mu + \rho^* > 0$ gives $\mu > \sum_{i=1}^k \left(z_{(i)} - z_{(k)} \right)$. Likewise, $z_{(k+1)}/\mu + \rho^* \le 0$ gives $\mu \le \sum_{i=1}^k \left(z_{(i)} - z_{(k+1)} \right)$. Conversely assume~\eqref{eq:smooth:proj:simplex_1_statement} and let $\widehat \rho = \varphi_k(\zv/\mu)$. Eq. \eqref{eq:smooth:proj:simplex_1_statement} can be written as $z_{(k)}/\mu + \widehat\rho > 0$ and $z_{(k+1)}/\mu + \widehat\rho \le 0$. Furthermore, we verify that $\widehat\rho$ satisfies Eq.~\eqref{eq:smooth:proj:simplex_1}, and so $\widehat \rho = \rho^*$ is its unique root. It follows, therefore, that the sparsity of $\uv^*$ is $k$. \end{proof} Thus, the projection of $\zv /\mu$ onto the simplex picks out some number $K_{\zv/\mu}$ of the largest entries of $\zv / \mu$ - we refer to this as the sparsity of $\operatorname{proj}_{\Delta^{m-1}}(\zv/\mu)$. This fact motivates the {\em top-$K$ strategy}: given $\mu>0$, fix an integer $K$ {\em a priori} and consider as surrogates for $h_{\mu\ell_2^2}$ and $\grad h_{\mu\ell_2^2}$ respectively \[ h_{\mu, K}(\zv) := \max_{\uv \in \Delta^{K-1}} \left\{ \inp*{\zv_{[K]}}{\uv} - \mu \ell_2^2(\uv) \right\}\,, \quad \text{and,} \quad \widetilde \grad h_{\mu, K}(\zv) := \Omega_K(\zv)\T\operatorname{proj}_{\Delta^{K-1}}\left( \frac{\zv_{[K]}}{\mu} \right) \,, \] where $\zv_{[K]}$ denotes the vector composed of the $K$ largest entries of $\zv$ and $ \Omega_K : \reals^m \to \{0,1\}^{K \times m} $ defines their extraction, i.e., $\Omega_K(\zv) = (\ev_{j_1}\T, \ldots, \ev_{j_K} \T)^\top\in \{0, 1\}^{K \times m}$ where $j_1, \cdots, j_K$ satisfy $z_{j_1} \ge \cdots \ge z_{j_K}$ such that $ \zv_{[K]} = \Omega_K(\zv) \zv$ \,. A surrogate of the $\ell_2^2$ smoothing is then given by \begin{align} \label{eq:smoothing:fmuK_defn} f_{\mu, K} := h_{\mu, K} \circ \gv \,, \quad\text{and,}\quad \widetilde \grad f_{\mu, K}(\wv) := \grad \gv(\wv)\T \widetilde \grad h_{\mu, K}(\gv(\wv)) \,. \end{align} \paragraph{Exactness of Top-$K$ Strategy} We say that the top-$K$ strategy is {\em exact} at $\zv$ for $\mu>0$ when it recovers the first order information of $h_{\mu \ell_2^2}$, i.e. when $ h_{\mu \ell_2^2}(\zv) = h_{\mu, K}(\zv)$ and $\grad h_{\mu \ell_2^2}(\zv) = \widetilde \grad h_{\mu, K}(\zv)$. The next proposition outlines when this is the case. Note that if the top-$K$ strategy is exact at $\zv$ for a smoothing parameter $\mu>0$ then it will be exact at $\zv$ for any $\mu'<\mu$. \begin{proposition} \label{prop:smoothing:proj-simplex-2} The top-$K$ strategy is exact at $\zv$ for $\mu>0$ if \begin{align} \label{eq:smooth:proj:simplex_2} \mu \le \sum_{i=1}^K \left(\zv_{(i)} - \zv_{( {\scriptscriptstyle K}+1)} \right) \,. \end{align} Moreover, for any fixed $\zv \in \reals^m$ such that the vector $\zv_{[\scriptscriptstyle K+1]} = \Omega_{K+1}(\zv)\zv$ has at least two unique elements, the top-$K$ strategy is exact at $\zv$ for all $\mu$ satisfying $0 < \mu \le z_{(1)} - z_{({\scriptscriptstyle K}+1)}$. \end{proposition} \begin{proof} First, we note that the top-$K$ strategy is exact when the sparsity $K_{\zv/\mu}$ of the projection $\operatorname{proj}_{\Delta^{m-1}}(\zv/\mu)$ satisfies $K_{\zv/\mu} \le K$. From Prop.~\ref{prop:smoothing:proj-simplex-1}, the condition that $K_{\zv/\mu} \in \{1, 2, \cdots, K\}$ happens when \begin{align*} \mu \in \bigcup_{k=1}^K \left( \sum_{i=1}^k \left(z_{(i)} - z_{(k)} \right), \, \sum_{i=1}^k \left(z_{(i)} - z_{(k+1)} \right) \right] = \left( 0 , \sum_{i=1}^K \left(z_{(i)} - z_{({\scriptscriptstyle K}+1)} \right) \right] \,, \end{align*} since the intervals in the union are contiguous. This establishes \eqref{eq:smooth:proj:simplex_2}. The only case when \eqref{eq:smooth:proj:simplex_2} cannot hold for any value of $\mu > 0$ is when the right hand size of \eqref{eq:smooth:proj:simplex_2} is zero. In the opposite case when $\zv_{[{\scriptscriptstyle K} + 1]}$ has at least two unique components, or equivalently, $z_{(1)} - z_{({\scriptscriptstyle K}+1)} > 0$, the condition $0 < \mu \le z_{(1)} - z_{({\scriptscriptstyle K}+1)}$ implies \eqref{eq:smooth:proj:simplex_2}. \end{proof} If the top-$K$ strategy is exact at $\gv(\wv)$ for $\mu$, then \[ f_{\mu, K}(\wv) = f_{\mu \ell_2^2}(\wv) \quad \text{and} \quad \widetilde \grad f_{\mu, K}(\wv) = \grad f_{\mu \ell_2^2}(\wv) \,, \] where the latter follows from the chain rule. When used instead of $\ell_2^2$ smoothing in the algorithms presented in Sec.~\ref{sec:cvx_opt}, the top-$K$ strategy provides a computationally efficient heuristic to smooth the structural hinge loss. Though we do not have theoretical guarantees using this surrogate, experiments presented in Sec.~\ref{sec:expt} show its efficiency and its robustness to the choice of $K$. \subsection{Score Functions} \label{sec:inf_oracles:score_func} Structured prediction is defined by the structure of the output $\yv$, while input $\xv \in \mcX$ can be arbitrary. Each output $\yv \in \mcY$ is composed of $p$ components $y_1, \ldots, y_p$ that are linked through a graphical model $\mathcal{G} = (\mathcal{V}, \mathcal{E})$ - the nodes $\mcV=\{1,\cdots,p\}$ represent the components of the output $\yv$ while the edges $\mcE$ define the dependencies between various components. The value of each component $y_v$ for $v \in \mcV$ represents the state of the node $v$ and takes values from a finite set $\mcY_v$. The set of all output structures $\mcY = \mcY_1 \times \cdots \times \mcY_p$ is then finite yet potentially intractably large. The structure of the graph (i.e., its edge structure) depends on the task. For the task of sequence labeling, the graph is a chain, while for the task of parsing, the graph is a tree. On the other hand, the graph used in image segmentation is a grid. For a given input $\xv$ and a score function $\phi(\cdot, \cdot ; \wv)$, the value $\phi(\xv, \yv; \wv)$ measures the compatibility of the output $\yv$ for the input $\xv$. The essential characteristic of the score function is that it decomposes over the nodes and edges of the graph as \begin{align} \label{eq:setting:score:decomp} \phi(\xv, \yv ; \wv) = \sum_{v \in \mcV} \phi_v(\xv, y_v; \wv) + \sum_{(v,v') \in \mcE} \phi_{v,v'}(\xv, y_v, y_{v'} ; \wv) \,. \end{align} For a fixed $\wv$, each input $\xv$ defines a specific compatibility function $\phi(\xv, \cdot\, ; \wv)$. The nature of the problem and the optimization algorithms we consider hinge upon whether $\phi$ is an affine function of $\wv$ or not. The two settings studied here are the following: \begin{description} \item{\bfseries Pre-defined Feature Map.} In this structured prediction framework, a pre-specified feature map $\Phi: \mcX \times \mcY \to \reals^d$ is employed and the score $\phi$ is then defined as the linear function \begin{equation}\label{eq:pre_spec_feature_map} \phi(\xv, \yv ; \wv) = \inp{\Phi(\xv, \yv)}{\wv} = \sum_{v \in \mcV} \inp{\Phi_v(\xv, y_v)}{\wv} + \sum_{(v,v') \in \mcE} \inp{\Phi_{v,v'}(\xv, y_v, y_{v'})}{\wv}\,. \end{equation} \item{\bfseries Learning the Feature Map.} We also consider the setting where the feature map $\Phi$ is parameterized by $\wv_0$, for example, using a neural network, and is learned from the data. The score function can then be written as \begin{equation}\label{eq:deep_setting} \phi(\xv, \yv ; \wv) = \inp{\Phi(\xv, \yv; \wv_0)}{\wv_1} \end{equation} where $\wv = (\wv_0, \wv_1)$ and the scalar product decomposes into nodes and edges as above. \end{description} Note that we only need the decomposition of the score function over nodes and edges of the $\mcG$ as in Eq.~\eqref{eq:setting:score:decomp}. In particular, while Eq.~\eqref{eq:deep_setting} is helpful to understand the use of neural networks in structured prediction, the optimization algorithms developed in Sec.~\ref{sec:ncvx_opt} apply to general nonlinear but smooth score functions. This framework captures both generative probabilistic models such as Hidden Markov Models (HMMs) that model the joint distribution between $\xv$ and $\yv$ as well as discriminative probabilistic models, such as conditional random fields~\citep{lafferty2001conditional} where dependencies among the input variables $\xv$ do not need to be explicitly represented. In these cases, the log joint and conditional probabilities respectively play the role of the score $\phi$. \begin{example}[Sequence Tagging] \label{example:inf_oracles:viterbi_example} Consider the task of sequence tagging in natural language processing where each $\xv = (x_1, \cdots, x_p) \in \mcX$ is a sequence of words and $\yv = (y_1, \cdots, y_p) \in \mcY$ is a sequence of labels, both of length $p$. Common examples include part of speech tagging and named entity recognition. Each word $x_v$ in the sequence $\xv$ comes from a finite dictionary $\mcD$, and each tag $y_v$ in $\yv$ takes values from a finite set $\mcY_v = \mcY_{\mathrm{tag}}$. The corresponding graph is simply a linear chain. The score function measures the compatibility of a sequence $\yv\in\mcY$ for the input $\xv\in\mcX$ using parameters $\wv = (\wv_{\mathrm{unary}}, \wv_{\mathrm{pair}})$ as, for instance, \[ \phi(\xv, \yv; \wv) = \sum_{v =1}^p \inp{\Phi_{\mathrm{unary}}(x_v, y_v)}{\wv_{\mathrm{unary}}} + \sum_{v=0}^p \inp{\Phi_{\mathrm{pair}}(y_v, y_{v+1})}{\wv_{\mathrm{pair}}}\,, \] where, using $\wv_{\mathrm{unary}} \in \reals^{\abs\mcD\abs{\mcY_{\mathrm{tag}}}}$ and $\wv_{\mathrm{pair}} \in \reals^{\abs{\mcY_{\mathrm{tag}}}^2}$ as node and edge weights respectively, we define for each $v \in [p]$, \[ \inp{\Phi_{\mathrm{unary}}(x_v, y_v)}{\wv_{\mathrm{unary}}} = \sum_{x \in \mathcal{D},\, j \in \mcY_{\mathrm{tag}}} w_{\mathrm{unary},\, x, j} \ind(x = x_v) \ind(j = y_v) \,. \] The pairwise term $\inp{\Phi_{\mathrm{pair}}(y_v, y_{v+1})}{\wv_{\mathrm{pair}}}$ is analogously defined. Here, $y_0, y_{p+1}$ are special ``start'' and ``stop'' symbols respectively. This can be written as a dot product of $\wv$ with a pre-specified feature map as in~\eqref{eq:pre_spec_feature_map}, by defining \[ \Phi(\xv, \yv) = \big(\sum_{v=1}^p \ev_{x_v} \otimes \ev_{y_v} \big) \oplus \big(\sum_{v=0}^p \ev_{y_v} \otimes \ev_{y_{v+1}} \big) \,, \] where $\ev_{x_v}$ is the unit vector $(\ind(x = x_v))_{x \in \mcD} \in \reals^{\abs\mcD}$, $ \ev_{y_v}$ is the unit vector $(\ind(j=y_v))_{j \in \mcY_{\mathrm{tag}}} \in \reals^{\abs{\mcY_{\mathrm{tag}}}}$, $\otimes$ denotes the Kronecker product between vectors and $\oplus$ denotes vector concatenation. \end{example} \subsection{Inference Oracles} We define now inference oracles as first order oracles in structured prediction. These are used later to understand the information-based complexity of optimization algorithms. \subsubsection{First Order Oracles in Structured Prediction} A first order oracle for a function $f :\reals^d \to \reals$ is a routine which, given a point $\wv \in \reals^d$, returns on output a value $f(\wv)$ and a (sub)gradient $\vv \in \partial f(\wv)$, where $\partial f$ is the Fr\'echet (or regular) subdifferential \citep[Def. 8.3]{rockafellar2009variational}. We now define inference oracles as first order oracles for the structural hinge loss $f$ and its smoothed variants $f_{\mu \omega}$. Note that these definitions are independent of the graphical structure. However, as we shall see, the graphical structure plays a crucial role in the implementation of the inference oracles. \begin{definition} \label{defn:inf-oracles-all} Consider an augmented score function $\psi$, a level of smoothing $\mu > 0$ and the structural hinge loss $f(\wv) = \max_{\yv \in \mathcal{\mcY}} \psi(\yv;\wv)$. For a given $\wv \in \reals^d$, \begin{enumerate}[label={\upshape(\roman*)}, align=left, widest=iii, leftmargin=*] \item the {\em max oracle} returns $f(\wv)$ and $\vv \in \partial f(\wv)$. \item the {\em exp oracle} returns $f_{-\mu H}(\wv)$ and $\grad f_{-\mu H}(\wv)$. \item the {\em top-$K$ oracle} returns $f_{\mu, K}(\wv)$ and $\widetilde \grad f_{\mu, K}(\wv)$ as surrogates for $f_{\mu \ell_2^2}(\wv)$ and $\grad f_{\mu \ell_2^2}(\wv)$ respectively. \end{enumerate} \end{definition} \noindent Note that the exp oracle gets its name since it can be written as an expectation over all $\yv$, as revealed by the next lemma, which gives analytical expressions for the gradients returned by the oracles. \begin{lemma} \label{lemma:smoothing:first-order-oracle} Consider the setting of Def.~\ref{defn:inf-oracles-all}. We have the following: \begin{enumerate}[label={\upshape(\roman*)}, align=left, widest=iii, leftmargin=*] \item \label{lem:foo:max} For any $\yv^* \in \argmax_{\yv \in \mathcal{\mcY}} \psi(\yv;\wv)$, we have that $\grad_\wv \psi(\yv^* ; \wv) \in \partial f(\wv)$. That is, the max oracle can be implemented by inference. \item The output of the exp oracle satisfies $\grad f_{-\mu H}(\wv) = \sum_{\yv \in \mcY} P_{\psi, \mu}(\yv ; \wv) \grad \psi(\yv ; \wv)$, where \[P_{\psi, \mu}(\yv ; \wv) = \frac{ \exp\left(\tfrac{1}{\mu}\psi(\yv ; \wv)\right)} {\sum_{\yv' \in \mcY }\exp\left(\tfrac{1}{\mu}\psi(\yv' ; \wv)\right)} \,. \] \label{lem:foo:exp} \item \label{lem:foo:l2} The output of the top-$K$ oracle satisfies $ \widetilde \grad f_{\mu, K}(\wv) = \sum_{i=1}^K u_{\psi, \mu, i}^*(\wv) \grad \psi(\yv_{(i)}; \wv) \,, $ where $Y_K = \left\{\yv_{(1)}, \cdots, \yv_{(K)} \right\}$ is the set of $K$ largest scoring outputs satisfying \[ \psi(\yv_{(1)} ; \wv) \ge \cdots \ge \psi(\yv_{(K)} ; \wv) \ge \max_{\yv \in \mcY \setminus Y_K} \psi(\yv ; \wv)\,, \] and $ \uv^*_{\psi, \mu} = \operatorname{proj}_{\Delta^{K-1}} \left( \left[\psi(\yv_{(1)} ; \wv), \cdots, \psi(\yv_{(K)} ; \wv) \right]\T \right)$. \end{enumerate} \end{lemma} \begin{proof} Part~\ref{lem:foo:exp} deals with the composition of differentiable functions, and follows from the chain rule. Part~\ref{lem:foo:l2} follows from the definition in Eq.~\eqref{eq:smoothing:fmuK_defn}. The proof of Part~\ref{lem:foo:max} follows from the chain rule for Fr\'echet subdifferentials of compositions \citep[Theorem 10.6]{rockafellar2009variational} together with the fact that by convexity and Danskin's theorem \citep[Proposition B.25]{bertsekas1999nonlinear}, the subdifferential of the max function is given by $\partial h(\zv) = \conv \{ \ev_i \, | \, i \in [m] \text{ such that } z_i = h(\zv) \}$. \end{proof} \begin{figure*}[!t \centering \begin{subfigure}[b]{0.28\linewidth} \centering \adjincludegraphics[width=\textwidth,trim={0.11\width 0.2\height 0.11\width 0.2\height},clip]{fig/viterbi/viterbi-max.pdf} \caption{\small{Non-smooth.}} \label{subfig:viterbi:1:max} \end{subfigure} \hspace{5mm}% \begin{subfigure}[b]{0.28\linewidth} \centering \adjincludegraphics[width=\textwidth,trim={0.11\width 0.2\height 0.11\width 0.2\height},clip]{fig/viterbi/viterbi-K.pdf} \caption{\small{$\ell_2^2$ smoothing.}} \label{subfig:viterbi:1:l2} \end{subfigure} \hspace{5mm}% \begin{subfigure}[b]{0.28\linewidth} \centering \adjincludegraphics[width=\textwidth,trim={0.11\width 0.2\height 0.11\width 0.2\height},clip]{fig/viterbi/viterbi-exp.pdf} \caption{\small{Entropy smoothing.}} \label{subfig:viterbi:1:ent} \end{subfigure} \caption{\small{Viterbi trellis for a chain graph with $p=4$ nodes and 3 labels. }} \label{fig:viterbi:1} \end{figure*} \begin{example} \label{example:inf_oracles:viterbi_example_2} Consider the task of sequence tagging from Example~\ref{example:inf_oracles:viterbi_example}. The inference problem~\eqref{eq:pgm:inference} is a search over all $\abs{\mcY} = \abs{\mcY_{\mathrm{tag}}}^p$ label sequences. For chain graphs, this is equivalent to searching for the shortest path in the associated trellis, shown in Fig.~\ref{fig:viterbi:1}. An efficient dynamic programming approach called the Viterbi algorithm \citep{viterbi1967error} can solve this problem in space and time polynomial in $p$ and $\abs{\mcY_{\mathrm{tag}}}$. The structural hinge loss is non-smooth because a small change in $\wv$ might lead to a radical change in the best scoring path shown in Fig.~\ref{fig:viterbi:1}. When smoothing $f$ with $\omega = \ell_2^2$, the smoothed function $f_{\mu \ell_2^2}$ is given by a projection onto the simplex, which picks out some number $K_{\psi/\mu}$ of the highest scoring outputs $\yv \in \mcY$ or equivalently, $K_{\psi/\mu}$ shortest paths in the Viterbi trellis (Fig.~\ref{subfig:viterbi:1:l2}). The top-$K$ oracle then uses the top-$K$ strategy to approximate $f_{\mu \ell_2^2}$ with $f_{\mu, K}$. On the other hand, with entropy smoothing $\omega = -H$, we get the log-sum-exp function and its gradient is obtained by averaging over paths with weights such that shorter paths have a larger weight (cf. Lemma~\ref{lemma:smoothing:first-order-oracle}\ref{lem:foo:exp}). This is visualized in Fig.~\ref{subfig:viterbi:1:ent}. \end{example} \subsubsection{Exp Oracles and Conditional Random Fields} Recall that a {\em Conditional Random Field (CRF)}~\citep{lafferty2001conditional} with augmented score function $\psi$ and parameters $\wv \in \reals^d$ is a probabilistic model that assigns to output $\yv \in \mcY$ the probability \begin{align} \label{eq:smoothing:crf:def} \prob(\yv \mid \psi ; \wv) = \exp\left(\psi(\yv ; \wv) - A_\psi(\wv) \right) \,, \end{align} where $A_\psi(\wv)$ is known as the log-partition function, a normalizer so that the probabilities sum to one. Gradient-based maximum likelihood learning algorithms for CRFs require computation of the log-partition function $A_\psi(\wv)$ and its gradient $\grad A_\psi(\wv)$. Next proposition relates the computational costs of the exp oracle and the log-partition function. \begin{proposition} \label{prop:smoothing:exp-crf} The exp oracle for an augmented score function $\psi$ with parameters $\wv \in \reals^d$ is equivalent in hardness to computing the log-partition function $A_\psi(\wv)$ and its gradient $\grad A_\psi(\wv)$ for a conditional random field with augmented score function $\psi$. \end{proposition} \begin{proof} Fix a smoothing parameter $\mu > 0$. Consider a CRF with augmented score function $\psi'(\yv ; \wv) = \mu\inv \psi(\yv ; \wv)$. Its log-partition function $A_{\psi'}(\wv)$ satisfies $\exp(A_{\psi'}(\wv)) = \sum_{\yv \in \mcY} \exp \left( \mu\inv \psi(\yv ; \wv) \right)$. The claim now follows from the bijection $f_{- \mu H}(\wv) = \mu \, A_{\psi'}(\wv)$ between $f_{-\mu H}$ and $A_{\psi'}$. \end{proof} \subsection{Inference Oracles in Trees} \label{subsec:smooth_inference_trees} We first consider algorithms implementing the inference algorithms in trees and examine their computational complexity. \subsubsection{Implementation of Inference Oracles} \paragraph{Max Oracle} In tree structured graphical models, the inference problem~\eqref{eq:pgm:inference}, and thus the max oracle (cf. Lemma~\ref{lemma:smoothing:first-order-oracle}\ref{lem:foo:max}) can always be solved exactly in polynomial time by the max-product algorithm~\citep{pearl1988probabilistic}, which uses the technique of dynamic programming~\citep{bellman1957dynamic}. The Viterbi algorithm (Algo.~\ref{algo:dp:max:chain}) for chain graphs from Example~\ref{example:inf_oracles:viterbi_example_2} is a special case. See Algo.~\ref{algo:dp:supp} in Appendix~\ref{sec:a:dp} for the max-product algorithm in full generality. \paragraph{Top-$K$ Oracle} The top-$K$ oracle uses a generalization of the max-product algorithm that we name top-$K$ max-product algorithm. Following the work of \citet{seroussi1994algorithm}, it keeps track of the $K$-best intermediate structures while the max-product algorithm just tracks the single best intermediate structure. Formally, the $k$th largest element from a discrete set $S$ is defined as \begin{align*} \maxK{k}{x \in S} f(x) = \begin{cases} \text{$k$th largest element of $\{f(y)\, |\, y \in S\} $} & k \le |S| \\ -\infty, & k > |S| \,. \end{cases} \end{align*} We present the algorithm in the simple case of chain structured graphical models in Algo.~\ref{algo:dp:topK:chain}. The top-$K$ max-product algorithm for general trees is given in Algo.~\ref{algo:dp:topK:main} in Appendix~\ref{sec:a:dp}. Note that it requires $\widetilde\bigO(K)$ times the time and space of the max oracle. \paragraph{Exp oracle} The relationship of the exp oracle with CRFs (Prop.~\ref{prop:smoothing:exp-crf}) leads directly to Algo.~\ref{algo:dp:supp_exp}, which is based on marginal computations from the sum-product algorithm. \begin{algorithm}[tb] \caption{Max-product (Viterbi) algorithm for chain graphs } \label{algo:dp:max:chain} \begin{algorithmic}[1] \STATE {\bfseries Input:} Augmented score function $\psi(\cdot, \cdot; \wv)$ defined on a chain graph $\mcG$. \STATE Set $\pi_1(y_1) \leftarrow \psi_1(y_1)$ for all $y_1 \in \mcY_1$. \FOR{$v= 2, \cdots p$} \STATE For all $y_v \in \mcY_v$, set \begin{align} \label{eq:dp:viterbi:update} \pi_{v}(y_v) \leftarrow \psi_v(y_v) + \max_{y_{v-1} \in \mcY_{v-1}} \left\{ \pi_{v-1}(y_{v-1}) + \psi_{v, v-1}(y_v, y_{v-1}) \right\} \,. \end{align} \STATE Assign to $\delta_v(y_v)$ the $y_{v-1}$ that attains the $\max$ above for each $y_v \in \mcY_v$. \ENDFOR \STATE Set $\psi^* \leftarrow \max_{y_p \in \mcY_p} \pi_p(y_p)$ and store the maximizing assignments of $y_p$ in $y_p^*$. \FOR{$v= p-1, \cdots, 1$} \STATE Set $y_v^* \leftarrow \delta_{v+1}( y_{v+1})$. \ENDFOR \RETURN $\psi^*, \yv^*:=(y_1^*, \cdots, y_p^*) $. \end{algorithmic} \end{algorithm} \begin{algorithm}[tb] \caption{Top-$K$ max-product (top-$K$ Viterbi) algorithm for chain graphs} \label{algo:dp:topK:chain} \begin{algorithmic}[1] \STATE {\bfseries Input:} Augmented score function $\psi(\cdot, \cdot ; \wv)$ defined on chain graph $\mcG$, integer $K>0$. \STATE For $k=1,\cdots, K$, set $\pi_1\pow{k}(y_1) \leftarrow \psi_1(y_1)$ if $k=1$ and $-\infty$ otherwise for all $y_1 \in \mcY_1$. \FOR{$v= 2, \cdots p$ and $k=1,\cdots, K$} \STATE For all $y_v \in \mcY_v$, set \begin{align} \label{eq:dp:viterbi:topk:update} \pi_{v}\pow{k}(y_v) \leftarrow \psi_v(y_v) + \maxK{k}{y_{v-1} \in \mcY_{v-1}, \ell \in [K]} \left\{ \pi_{v-1}\pow{\ell}(y_{v-1}) + \psi_{v, v-1}(y_v, y_{v-1}) \right\} \,. \end{align} \STATE Assign to $\delta_v\pow{k}(y_v), \kappa_v\pow{k}(y_v)$ the $y_{v-1}, \ell$ that attain the $\max\pow{k}$ above for each $y_v \in \mcY_v$. \ENDFOR \STATE For $k=1,\cdots, K$, set $\psi\pow{k} \leftarrow \max\pow{k}_{y_p \in \mcY_p, k \in [K]} \pi_p\pow{k}(y_p)$ and store in $y_p\pow{k}, \ell\pow{k}$ respectively the maximizing assignments of $y_p , k$. \FOR{$v= p-1, \cdots 1$ and $k=1,\cdots, K$} \STATE Set $y_v\pow{k} \leftarrow \delta_{v+1}\pow{\ell\pow{k}} \big( y_{v+1}\pow{k} \big)$ and $\ell\pow{k} \leftarrow \kappa_{v+1}\pow{\ell\pow{k}} \big( y_{v+1}\pow{k} \big)$. \ENDFOR \RETURN $\left\{ \psi\pow{k}, \yv\pow{k}:=(y_1\pow{k}, \cdots, y_p\pow{k}) \right\}_{k=1}^K$. \end{algorithmic} \end{algorithm} \begin{algorithm}[tb] \caption{Entropy smoothed max-product algorithm} \label{algo:dp:supp_exp} \begin{algorithmic}[1] \STATE {\bfseries Input:} Augmented score function $\psi(\cdot, \cdot ; \wv)$ defined on tree structured graph $\mcG$, $\mu > 0$. \STATE Compute the log-partition function and marginals using the sum-product algorithm (Algo.~\ref{algo:dp:supp_sum-prod} in Appendix~\ref{sec:a:dp}) \[ A_{\psi/\mu}, \{P_v \text{ for } v \in \mcV\}, \{ P_{v, v'} \text{ for } (v, v') \in \mcE \} \leftarrow \textsc{SumProduct}\left( \tfrac{1}{\mu} \psi(\cdot \, ; \wv), \mcG \right) \,. \] \STATE Set $f_{-\mu H}(\wv) \leftarrow \mu A_{\psi /\mu}$ and \[ \grad f_{-\mu H}(\wv) \leftarrow \sum_{v \in \mcV} \sum_{y_v \in \mcY_v} P_v(y_v) \grad \psi_v(y_v ; \wv) + \sum_{(v, v') \in \mcE} \sum_{y_v \in \mcY_v} \sum_{y_{v'} \in \mcY_{v'}} P_{v,v'}(y_v, y_{v'})\grad \psi_{v, v'}(y_v ; \wv) \,. \] \label{line:algo:dp:exp:gradient} \RETURN $f_{-\mu H}(\wv), \grad f_{-\mu H}(\wv)$. \end{algorithmic} \end{algorithm} \begin{remark} We note that clique trees allow the generalization of the algorithms of this section to general graphs with cycles. However, the construction of a clique tree requires time and space exponential in the {\em treewidth} of the graph. \end{remark} \begin{example} Consider the task of sequence tagging from Example~\ref{example:inf_oracles:viterbi_example}. The Viterbi algorithm (Algo.~\ref{algo:dp:max:chain}) maintains a table $\pi_v(y_v)$, which stores the best length-$v$ prefix ending in label $y_v$. One the other hand, the top-$K$ Viterbi algorithm (Algo.~\ref{algo:dp:topK:chain}) must store in $\pi_v\pow{k}(y_v)$ the score of $k$th best length-$v$ prefix that ends in $y_v$ for each $k \in [K]$. In the vanilla Viterbi algorithm, the entry $\pi_v(y_v)$ is updated by looking the previous column $\pi_{v-1}$ following~\eqref{eq:dp:viterbi:update}. Compare this to update \eqref{eq:dp:viterbi:topk:update} of the top-$K$ Viterbi algorithm. In this case, the exp oracle is implemented by the forward-backward algorithm, a specialization of the sum-product algorithm to chain graphs. \end{example} \subsubsection{Complexity of Inference Oracles} The next proposition presents the correctness guarantee and complexity of each of the aforementioned algorithms. Its proof has been placed in Appendix~\ref{sec:a:dp}. \begin{proposition} \label{prop:dp:main} Consider as inputs an augmented score function $\psi(\cdot, \cdot ; \wv)$ defined on a tree structured graph $\mcG$, an integer $K>0$ and a smoothing parameter $\mu > 0$. \begin{enumerate}[label={\upshape(\roman*)}, align=left, widest=iii, leftmargin=*] \item The output $(\psi^*, \yv^*)$ of the max-product algorithm (Algo.~\ref{algo:dp:max:chain} for the special case when $\mcG$ is chain structured Algo.~\ref{algo:dp:supp} from Appendix~\ref{sec:a:dp} in general) satisfies $\psi^* = \psi(\yv^* ; \wv) = \max_{\yv \in \mcY} \psi(\yv ; \wv)$. Thus, the pair $\big(\psi^*, \grad \psi(\yv^* ; \wv)\big)$ is a correct implementation of the max oracle. It requires time $\bigO(p \max_{v\in\mcV} \abs{\mcY_v}^2)$ and space $\bigO(p \max_{v\in\mcV} \abs{\mcY_v})$. \item The output $\{ \psi\pow{k}, \yv\pow{k} \}_{k=1}^K$ of the top-$K$ max-product algorithm (Algo.~\ref{algo:dp:topK:chain} for the special case when $\mcG$ is chain structured or Algo.~\ref{algo:dp:topK:main} from Appendix~\ref{sec:a:dp} in general) satisfies $\psi\pow{k} = \psi(\yv\pow{k}) = \max\pow{k}_{\yv \in \mcY} \psi(\yv)$. Thus, the top-$K$ max-product algorithm followed by a projection onto the simplex (Algo.~\ref{algo:smoothing:top_K_oracle} in Appendix~\ref{sec:a:smoothing}) is a correct implementation of the top-$K$ oracle. It requires time $\bigO(pK\log K \max_{v\in\mcV} \abs{\mcY_v}^2)$ and space $\bigO(p K \max_{v\in\mcV} \abs{\mcY_v})$. \label{prop:dp:main:part:topk} \item Algo.~\ref{algo:dp:supp_exp} returns $\big(f_{-\mu H}(\wv), \grad f_{-\mu H}(\wv)\big)$. Thus, Algo.~\ref{algo:dp:supp_exp} is a correct implementation of the exp oracle. It requires time $\bigO(p \max_{v\in\mcV} \abs{\mcY_v}^2)$ and space $\bigO(p \max_{v\in\mcV} \abs{\mcY_v})$. \end{enumerate} \end{proposition} \subsection{Inference Oracles in Loopy Graphs} \label{subsec:smooth_inference_loopy} For general loopy graphs with high tree-width, the inference problem \eqref{eq:pgm:inference} is NP-hard \citep{cooper1990computational}. In particular cases, graph cut, matching or search algorithms can be used for exact inference in dense loopy graphs, and therefore, to implement the max oracle as well (cf. Lemma~\ref{lemma:smoothing:first-order-oracle}\ref{lem:foo:max}). In each of these cases, we find that the top-$K$ oracle can be implemented, but the exp oracle is intractable. Appendix~\ref{sec:a:smooth:loopy} contains a review of the algorithms and guarantees referenced in this section. \subsubsection{Inference Oracles using Max-Marginals} We now define a {\em max-marginal}, which is a constrained maximum of the augmented score $\psi$. \begin{definition} The max-marginal of $\psi$ relative to a variable $y_v$ is defined, for $j \in \mcY_v$ as \begin{align} \psi_{v; j}(\wv) := \max_{\substack{\yv \in \mcY \,: \, y_v = j}} \psi(\yv ; \wv)\, . \end{align} \end{definition} \noindent In cases where exact inference is tractable using graph cut or matching algorithms, it is possible to extract max-marginals as well. This, as we shall see next, allows the implementation of the max and top-$K$ oracles. When the augmented score function $\psi$ is {\em unambiguous}, i.e., no two distinct $\yv_1, \yv_2 \in \mcY$ have the same augmented score, the output $\yv^*(\wv)$ is unique can be decoded from the max-marginals as (see \citet{pearl1988probabilistic,dawid1992applications} or Thm.~\ref{thm:a:loopy:decoding} in Appendix~\ref{sec:a:smooth:loopy}) \begin{align} \label{eq:max-marg:defn} y_v^*(\wv) = \argmax_{j \in \mcY_v} \psi_{v ; j}(\wv) \,. \end{align} If one has access to an algorithm $\mcM$ that can compute max-marginals, the top-$K$ oracle is also easily implemented via the {\em Best Max-Marginal First (BMMF)} algorithm of \citet{yanover2004finding}. This algorithm requires computations of $2K$ sets of max-marginals, where a {\em set} of max-marginals refers to max-marginals for all $y_v$ in $\yv$. Therefore, the BMMF algorithm followed by a projection onto the simplex (Algo.~\ref{algo:smoothing:top_K_oracle} in Appendix~\ref{sec:a:smoothing}) is a correct implementation of the top-$K$ oracle at a computational cost of $2K$ sets of max-marginals. The BMMF algorithm and its guarantee are recalled in Appendix~\ref{sec:a:bmmf} for completeness. \paragraph{Graph Cut and Matching Inference} \citet{kolmogorov2004energy} showed that submodular energy functions \citep{lovasz1983submodular} over binary variables can be efficiently minimized exactly via a minimum cut algorithm. For a class of alignment problems, e.g., \citet{taskar2005discriminative}, inference amounts to finding the best bipartite matching. In both these cases, max-marginals can be computed exactly and efficiently by combinatorial algorithms. This gives us a way to implement the max and top-$K$ oracles. However, in both settings, computing the log-partition function $A_\psi(\wv)$ of a CRF with score $\psi$ is known to be \#P-complete~\citep{jerrum1993polynomial}. Prop.~\ref{prop:smoothing:exp-crf} immediately extends this result to the exp oracle. This discussion is summarized by the following proposition, whose proof is provided in Appendix~\ref{sec:a:proof-prop}. \begin{proposition} \label{prop:smoothing:max-marg:all} Consider as inputs an augmented score function $\psi(\cdot, \cdot ; \wv)$, an integer $K>0$ and a smoothing parameter $\mu > 0$. Further, suppose that $\psi$ is unambiguous, that is, $\psi(\yv' ; \wv) \neq \psi(\yv'' ;\wv)$ for all distinct $\yv', \yv'' \in \mcY$. Consider one of the two settings: \begin{enumerate}[label={\upshape(\Alph*)}, align=left, leftmargin=*] \item the output space $\mcY_v = \{0,1\}$ for each $v \in \mcV$, and the function $-\psi$ is submodular (see Appendix~\ref{sec:a:graph_cuts} and, in particular, \eqref{eq:top_k_map:submodular} for the precise definition), or, \label{part:prop:max-marg:cuts} \item the augmented score corresponds to an alignment task where the inference problem~\eqref{eq:pgm:inference} corresponds to a maximum weight bipartite matching (see Appendix~\ref{sec:a:graph_matchings} for a precise definition). \label{part:prop:max-marg:matching} \end{enumerate} In these cases, we have the following: \begin{enumerate}[label={\upshape(\roman*)}, align=left, widest=iii, leftmargin=*] \item The max oracle can be implemented at a computational complexity of $\bigO(p)$ minimum cut computations in Case~\ref{part:prop:max-marg:cuts}, and in time $\bigO(p^3)$ in Case~\ref{part:prop:max-marg:matching}. \item The top-$K$ oracle can be implemented at a computational complexity of $\bigO(pK)$ minimum cut computations in Case~\ref{part:prop:max-marg:cuts}, and in time $\bigO(p^3K)$ in Case~\ref{part:prop:max-marg:matching}. \item The exp oracle is \#P-complete in both cases. \end{enumerate} \end{proposition} Prop.~\ref{prop:smoothing:max-marg:all} is loose in that the max oracle can be implemented with just one minimum cut computation instead of $p$ in in Case~\ref{part:prop:max-marg:cuts}~\citep{kolmogorov2004energy}. \subsubsection{Branch and Bound Search} Max oracles implemented via search algorithms can often be extended to implement the top-$K$ oracle. We restrict our attention to best-first branch and bound search such as the celebrated Efficient Subwindow Search \citep{lampert2008beyond}. Branch and bound methods partition the search space into disjoint subsets, while keeping an upper bound $\widehat \psi: \mcX \times 2^{\mcY} \to \reals$, on the maximal augmented score for each of the subsets $\widehat \mcY \subseteq \mcY$. Using a best-first strategy, promising parts of the search space are explored first. Parts of the search space whose upper bound indicates that they cannot contain the maximum do not have to be examined further. The top-$K$ oracle is implemented by simply continuing the search procedure until $K$ outputs have been produced - see Algo.~\ref{algo:top_k:bb} in Appendix~\ref{sec:a:bb_search}. Both the max oracle and the top-$K$ oracle can degenerate to an exhaustive search in the worst case, so we do not have sharp running time guarantees. However, we have the following correctness guarantee. \begin{proposition} \label{prop:smoothing:bb-search} Consider an augmented score function $\psi(\cdot, \cdot ; \wv)$, an integer $K > 0$ and a smoothing parameter $\mu > 0$. Suppose the upper bound function $\widehat \psi(\cdot, \cdot ; \wv): \mcX \times 2^{\mcY} \to \reals$ satisfies the following properties: \begin{enumerate}[label=(\alph*), align=left, widest=a, leftmargin=*] \item $\widehat \psi(\widehat \mcY ; \wv)$ is finite for every $\widehat \mcY \subseteq \mcY$, \item $\widehat \psi(\widehat \mcY ; \wv) \ge \max_{\yv \in \widehat \mcY} \psi(\yv ; \wv)$ for all $\widehat \mcY \subseteq \mcY$, and, \item $\widehat \psi(\{\yv\} ; \wv) = \psi(\yv ; \wv)$ for every $\yv \in \mcY$. \end{enumerate} Then, we have the following: \begin{enumerate}[label={\upshape(\roman*)}, align=left, widest=ii, leftmargin=*] \item Algo.~\ref{algo:top_k:bb} with $K=1$ is a correct implementation of the max oracle. \item Algo.~\ref{algo:top_k:bb} followed by a projection onto the simplex (Algo.~\ref{algo:smoothing:top_K_oracle} in Appendix~\ref{sec:a:smoothing}) is a correct implementation of the top-$K$ oracle. \end{enumerate} \end{proposition} \noindent See Appendix~\ref{sec:a:bb_search} for a proof. The discrete structure that allows inference via branch and bound search cannot be leveraged to implement the exp oracle. \subsection{{Casimir}: Catalyst with Smoothing} The Catalyst~\citep{lin2017catalyst} approach minimizes regularized objectives centered around the current iterate. The algorithm proceeds by computing approximate proximal point steps instead of the classical (sub)-gradient steps. A proximal point step from a point $\wv$ with step-size $\kappa^{-1}$ is defined as the minimizer of \begin{equation}\label{eq:prox_point} \min_{\zv \in \reals^m} F(\zv) + \frac{\kappa}{2}\normasq{2}{\zv-\wv}, \end{equation} which can also be seen as a gradient step on the Moreau envelope of $F$ - see \citet{lin2017catalyst} for a detailed discussion. While solving the subproblem~\eqref{eq:prox_point} might be as hard as the original problem we only require an approximate solution returned by a given optimization method $\mathcal{M}$. The Catalyst approach is then an inexact accelerated proximal point algorithm that carefully mixes approximate proximal point steps with the extrapolation scheme of \citet{nesterov1983method}. The {Casimir}{} scheme extends this approach to non-smooth optimization. For the overall method to be efficient, subproblems~\eqref{eq:prox_point} must have a low complexity. That is, there must exist an optimization algorithm $\mathcal{M}$ that solves them linearly. For the {Casimir}{} approach to be able to handle non-smooth objectives, it means that we need not only to regularize the objective but also to smooth it. To this end we define \[ F_{\mu \omega}(\wv) := \frac{1}{n}\sum_{i=1}^n h_{\mu \omega}(\Am\pow{i} \wv + {\bm b}\pow{i}) + \frac{\lambda}{2} \normasq{2}{\wv} \] as a smooth approximation of the objective $F$, and, \[ F_{\mu \omega, \kappa}(\wv; \zv) := \frac{1}{n}\sum_{i=1}^n h_{\mu \omega}(\Am\pow{i} \wv + {\bm b}\pow{i}) + \frac{\lambda}{2} \normasq{2}{\wv} + \frac{\kappa}{2}\normasq{2}{\wv-\zv} \] a smooth and regularized approximation of the objective centered around a given point $\zv \in \reals^d$. While the original Catalyst algorithm considered a fixed regularization term $\kappa$, we vary $\kappa$ and $\mu$ along the iterations. This enables us to get adaptive smoothing strategies. The overall method is presented in Algo.~\ref{algo:catalyst}. We first analyze in Sec.~\ref{sec:catalyst:analysis} its complexity for a generic linearly convergent algorithm $\mcM$. Thereafter, in Sec.~\ref{sec:catalyst:total_compl}, we compute the total complexity with SVRG~\citep{johnson2013accelerating} as $\mcM$. Before that, we specify two practical aspects of the implementation: a proper stopping criterion~\eqref{eq:stopping_criterion} and a good initialization of subproblems (Line~\ref{line:algo:c:prox_point}). \paragraph{Stopping Criterion} Following~\citet{lin2017catalyst}, we solve subproblem $k$ in Line~\ref{line:algo:c:prox_point} to a degree of relative accuracy specified by $\delta_k \in [0, 1)$. In view of the $(\lambda+\kappa_k)$-strong convexity of $F_{\mu_k\omega, \kappa_k}(\cdot\,; \zv_{k-1})$, the functional gap can be controlled by the norm of the gradient, precisely it can be seen that $\normasq{2}{\grad F_{\mu_k\omega, \kappa_k}(\widehat\wv; \zv_{k-1})} \le (\lambda+\kappa_k)\delta_k \kappa_k \normasq{2}{\widehat \wv - \zv_{k-1}}$ is a sufficient condition for the stopping criterion \eqref{eq:stopping_criterion}. A practical alternate stopping criterion proposed by \citet{lin2017catalyst} is to fix an iteration budget $T_{\mathrm{budget}}$ and run the inner solver $\mcM$ for exactly $T_{\mathrm{budget}}$ steps. We do not have a theoretical analysis for this scheme but find that it works well in experiments. \paragraph{Warm Start of Subproblems} Rate of convergence of first order optimization algorithms depends on the initialization and we must warm start $\mcM$ at an appropriate initial point in order to obtain the best convergence of subproblem~\eqref{eq:prox_point_algo} in Line~\ref{line:algo:c:prox_point} of Algo.~\ref{algo:catalyst}. We advocate the use of the prox center $\zv_{k-1}$ in iteration $k$ as the warm start strategy. We also experiment with other warm start strategies in Section~\ref{sec:expt}. \begin{algorithm}[tb] \caption{The {Casimir}{} algorithm} \label{algo:catalyst} \begin{algorithmic}[1] \STATE {\bfseries Input:} Smoothable objective $F$ of the form \eqref{eq:cvx_pb} with $h$ simple, smoothing function $\omega$, linearly convergent algorithm $\mcM$, non-negative and non-increasing sequence of smoothing parameters $(\mu_k)_{k \ge 1}$, positive and non-decreasing sequence of regularization parameters $(\kappa_k)_{k\ge1}$, non-negative sequence of relative target accuracies $(\delta_k)_{k\ge 1}$ and, initial point $\wv_0$, $\alpha_0 \in (0, 1)$, time horizon $K$. \STATE {\bfseries Initialize:} $\zv_0 = \wv_0$. \FOR{$k=1$ \TO $K$} \STATE Using $\mcM$ with $\zv_{k-1}$ as the starting point, find \label{line:algo:c:prox_point} $\wv_{k} \approx \argmin_{\wv\in\reals^d} F_{\mu_k \omega, \kappa_k}(\wv; \zv_{k-1})$ where \begin{equation}\label{eq:prox_point_algo} F_{\mu_k \omega, \kappa_k}(\wv; \zv_{k-1}) := \frac{1}{n}\sum_{i=1}^n h_{\mu_k \omega}(\Am\pow{i} \wv + {\bm b}\pow{i}) + \frac{\lambda}{2} \normasq{2}{\wv} + \frac{\kappa_k}{2}\normasq{2}{\wv- \zv_{k-1}} \end{equation} such that \begin{align}\label{eq:stopping_criterion} F_{\mu_k\omega, \kappa_k}(\wv_k;\zv_{k-1}) - \min_\wv F_{\mu_k\omega, \kappa_k}(\wv;\zv_{k-1})\leq \tfrac{\delta_k\kappa_k}{2} \normasq{2}{\wv_k - \zv_{k-1}} \end{align} \STATE Solve for $\alpha_k \geq 0$ \begin{align} \label{eq:c:update_alpha} \alpha_k^2 (\kappa_{k+1} + \lambda) = (1-\alpha_k) \alpha_{k-1}^2 (\kappa_k + \lambda) + \alpha_k \lambda. \end{align} \STATE Set \begin{align} \label{eq:c:update_support} \zv_k = \wv_k + \beta_k (\wv_k - \wv_{k-1}), \end{align} where \begin{align} \label{eq:c:update_beta} \beta_k = \frac{ \alpha_{k-1}(1-\alpha_{k-1}) (\kappa_k + \lambda) } { \alpha_{k-1}^2 (\kappa_k + \lambda) + \alpha_k(\kappa_{k+1} + \lambda) }. \end{align} \ENDFOR \RETURN $\wv_K$. \end{algorithmic} \end{algorithm} \subsection{Convergence Analysis of Casimir} \label{sec:catalyst:analysis} We first state the outer loop complexity results of Algo.~\ref{algo:catalyst} for any generic linearly convergent algorithm $\mcM$ in Sec.~\ref{sec:catalyst:outer_compl}, prove it in Sec.~\ref{subsec:c:proof}. Then, we consider the complexity of each inner optimization problem~\eqref{eq:prox_point_algo} in Sec.~\ref{sec:catalyst:inner_compl} based on properties of $\mcM$. \subsubsection{Outer Loop Complexity Results} \label{sec:catalyst:outer_compl} The following theorem states the convergence of the algorithm for general choice of parameters, where we denote $\wv^* \in \argmin_{\wv\in\reals^d} F(\wv)$ and $F^* = F(\wv^*)$. \begin{theorem} \label{thm:catalyst:outer} Consider Problem~\eqref{eq:cvx_pb_finite_sum}. Suppose $\delta_k \in [0, 1)$ for all $k \ge 1$, the sequence $(\mu_k)_{k\ge 1}$ is non-negative and non-increasing, and the sequence $(\kappa_k)_{k \ge 1}$ is strictly positive and non-decreasing. Further, suppose the smoothing function $\omega: \dom h^* \to \reals$ satisfies $-D_\omega \le \omega(\uv) \le 0$ for all $\uv \in \dom h^*$ and that $\alpha_0^2 \ge \lambda / (\lambda + \kappa_1)$. Then, the sequence $(\alpha_k)_{k \ge 0}$ generated by Algo.~\ref{algo:catalyst} satisfies $0 < \alpha_k \le \alpha_{k-1} < 1$ for all $k \ge 1$. Furthermore, the sequence $(\wv_{k})_{k \ge 0}$ of iterates generated by Algo.~\ref{algo:catalyst} satisfies \begin{align} \label{thm:c:main:main} F(\wv_k) - F^* \le \frac{\mcA_0^{k-1}}{\mcB_1^k} \Delta_0 + \mu_k D_\omega + \sum_{j=1}^k \frac{\mcA_j^{k-1}}{\mcB_j^k} \left( \mu_{j-1} - (1-\delta_j)\mu_j \right) D_\omega \,, \end{align} where $\mcA_i^j := \prod_{r=i}^j (1-\alpha_r)$, $\mcB_i^j := \prod_{r=i}^j (1-\delta_r)$, $\Delta_0 := F(\wv_0) - F^* + \frac{(\kappa_1 + \lambda) \alpha_0^2 - \lambda \alpha_0 } {2(1 - \alpha_0)} \normasq{2}{\wv_0 - \wv^*}$ and $\mu_0 := 2\mu_1$. \end{theorem} Before giving its proof, we present various parameters strategies as corollaries. Table~\ref{tab:catalyst_corollaries_summary} summarizes the parameter settings and the rates obtained for each setting. Overall, the target accuracies $\delta_k$ are chosen such that $\mcB_j^k$ is a constant and the parameters $\mu_k$ and $\kappa_k$ are then carefully chosen for an almost parameter-free algorithm with the right rate of convergence. Proofs of these corollaries are provided in Appendix~\ref{subsec:c:proofs_missing_cor}. The first corollary considers the strongly convex case ($\lambda > 0$) with constant smoothing $\mu_k=\mu$, assuming that $\eps$ is known {\em a priori}. We note that this is, up to constants, the same complexity obtained by the original Catalyst scheme on a fixed smooth approximation $F_{\mu\omega}$ with $\mu = \bigO(\eps D_\omega)$. \begin{corollary} \label{cor:c:outer_sc} Consider the setting of Thm.~\ref{thm:catalyst:outer}. Let $q = {\lambda}/(\lambda + \kappa)$. Suppose $\lambda > 0$ and $\mu_k = \mu$, $\kappa_k = \kappa$, for all $k \ge 1$. Choose $\alpha_0 = \sqrt{q}$ and, $\delta_k = {\sqrt{q}}/({2 - \sqrt{q}}) \,.$ Then, we have, \begin{align*} F(\wv_k) - F^* \le \frac{3 - \sqrt{q}}{1 - \sqrt{q}} \mu D_\omega + 2 \left( 1- \frac{\sqrt q}{2} \right)^k \left( F(\wv_0) - F^* \right) \,. \end{align*} \end{corollary} \noindent Next, we consider the strongly convex case where the target accuracy $\eps$ is not known in advance. We let smoothing parameters $( \mu_k )_{k \ge 0}$ decrease over time to obtain an adaptive smoothing scheme that gives progressively better surrogates of the original objective. \begin{corollary} \label{cor:c:outer_sc:decreasing_mu_const_kappa} Consider the setting of Thm.~\ref{thm:catalyst:outer}. Let $q = {\lambda}/(\lambda + \kappa)$ and $\eta = 1 - {\sqrt q}/{2}$. Suppose $\lambda > 0$ and $\kappa_k = \kappa$, for all $k \ge 1$. Choose $\alpha_0 = \sqrt{q}$ and, the sequences $(\mu_k)_{k \ge 1}$ and $(\delta_k)_{k \ge 1}$ as \begin{align*} \mu_k = \mu \eta^{{k}/{2}} \,, \qquad \text{and,} \qquad \delta_k = \frac{\sqrt{q}}{2 - \sqrt{q}} \,, \end{align*} where $\mu > 0$ is any constant. Then, we have, \begin{align*} F(\wv_k) - F^* \le \eta^{{k}/{2}} \left[ 2 \left( F(\wv_0) - F^* \right) + \frac{\mu D_\omega}{1-\sqrt{q}} \left(2-\sqrt{q} + \frac{\sqrt{q}}{1 - \sqrt \eta} \right) \right] \, . \end{align*} \end{corollary} \noindent The next two corollaries consider the unregularized problem, i.e., $\lambda = 0$ with constant and adaptive smoothing respectively. \begin{corollary} \label{cor:c:outer_smooth} Consider the setting of Thm.~\ref{thm:catalyst:outer}. Suppose $\mu_k = \mu$, $\kappa_k = \kappa$, for all $k \ge 1$ and $\lambda = 0$. Choose $\alpha_0 = (\sqrt{5}-1)/{2}$ and $\delta_k = (k+1)^{-2} \,.$ Then, we have, \begin{align*} F(\wv_k) - F^* \le \frac{8}{(k+2)^2} \left( F(\wv_0) - F^* + \frac{\kappa}{2} \normasq{2}{\wv_0 - \wv^*} \right) + \mu D_\omega\left( 1 + \frac{12}{k+2} + \frac{30}{(k+2)^2} \right) \, . \end{align*} \end{corollary} \begin{corollary} \label{cor:c:outer_smooth_dec_smoothing} Consider the setting of Thm.~\ref{thm:catalyst:outer} with $\lambda = 0$. Choose $\alpha_0 = (\sqrt{5}-1)/{2}$, and for some non-negative constants $\kappa, \mu$, define sequences $(\kappa_k)_{k \ge 1}, (\mu_k)_{k \ge 1}, (\delta_k)_{k \ge 1}$ as \begin{align*} \kappa_k = \kappa \, k\,, \quad \mu_k = \frac{\mu}{k} \quad \text{and,} \quad \delta_k = \frac{1}{(k + 1)^2} \,. \end{align*} Then, for $k \ge 2$, we have, \begin{align*} F(\wv_k) - F^* \le \frac{\log(k+1)}{k+1} \left( 2(F(\wv_0) - F^*) + \kappa \normasq{2}{\wv_0 - \wv^*} + 27 \mu D_\omega \right) \,. \end{align*} For the first iteration (i.e., $k = 1$), this bound is off by a constant factor $1 / \log2$. \end{corollary} \begin{table*}[t!] \caption{\small{Summary of outer iteration complexity for Algorithm~\ref{algo:catalyst} for different parameter settings. We use shorthand $\Delta F_0 := F(\wv_0) - F^*$ and {$\Delta_0 = \norma{2}{\wv_0 - \wv^*}$}. Absolute constants are omitted from the rates. \vspace{2mm} }} \begin{adjustbox}{width=\textwidth} \label{tab:catalyst_corollaries_summary} \centering \begin{tabular}{|c||ccccc|c|c|} \hline {Cor.} & $\lambda>0$ & $\kappa_k$ & $\mu_k$ & $\delta_k$ & $\alpha_0$ & $F(\wv_k)-F^*$ & Remark \\ \hline\hline \ref{cor:c:outer_sc} & Yes & $\kappa$ & $\mu$ & $\frac{\sqrt{q}}{2-\sqrt{q}}$ & $\sqrt{q}$ & $\left(1- \frac{\sqrt{q}}{2}\right)^k \Delta F_0 + \frac{\mu D}{1-\sqrt{q}}$ & $q = \frac{\lambda}{\lambda+\kappa}$ \\ \hline \ref{cor:c:outer_sc:decreasing_mu_const_kappa} & Yes & $\kappa$ & $\mu \left( 1 - \frac{\sqrt{q}}{2} \right)^{k/2}$ & $\frac{\sqrt{q}}{2-\sqrt{q}}$ & $\sqrt{q}$ & $\left(1- \frac{\sqrt{q}}{2}\right)^{k/2} \left( \Delta F_0 + \frac{\mu D}{1-\sqrt{q}} \right)$ & $q = \frac{\lambda}{\lambda+\kappa}$ \\ \hline \rule{0pt}{12pt} \ref{cor:c:outer_smooth} & No & $\kappa$ & $\mu$ & $k^{-2}$ & $c$ & $\frac{1}{k^2} \left(\Delta F_0 + \kappa \Delta_0^2 \right) + \mu D$ & $c = (\sqrt 5 - 1)/ 2$ \\[3pt] \hline \rule{0pt}{12pt} \ref{cor:c:outer_smooth_dec_smoothing} & No & $\kappa \, k$ & $\mu /k$ & $k^{-2}$ & $c$ & $\frac{\log k}{k} (\Delta F_0 + \kappa \Delta_0^2 + \mu D )$ & $c = (\sqrt 5 - 1)/ 2$ \\[3pt] \hline \end{tabular} \end{adjustbox} \end{table*} \subsubsection{Outer Loop Convergence Analysis}\label{subsec:c:proof} We now prove Thm.~\ref{thm:catalyst:outer}. The proof technique largely follows that of \citet{lin2017catalyst}, with the added challenges of accounting for smoothing and varying Moreau-Yosida regularization. We first analyze the sequence $(\alpha_k)_{k \ge 0}$. The proof follows from the algebra of Eq.~\eqref{eq:c:update_alpha} and has been given in Appendix~\ref{sec:a:c_alpha_k}. \begin{lemma} \label{lem:c:alpha_k} Given a positive, non-decreasing sequence $(\kappa_k)_{k\ge 1}$ and $\lambda \ge 0$, consider the sequence $(\alpha_k)_{k \ge 0}$ defined by \eqref{eq:c:update_alpha}, where $\alpha_0 \in (0, 1)$ such that $\alpha_0^2 \ge \lambda / (\lambda + \kappa_1)$. Then, we have for every $k \ge 1$ that $0< \alpha_k \le \alpha_{k-1}$ and, $ \alpha_k^2 \ge {\lambda}/({\lambda + \kappa_{k+1}}) \,. $ \end{lemma} \noindent We now characterize the effect of an approximate proximal point step on $F_{\mu\omega}$. \begin{lemma} \label{lem:c:approx_descent} Suppose $\widehat \wv \in \reals^d$ satisfies $F_{\mu\omega, \kappa}(\widehat \wv ;\zv) - \min_{\wv \in \reals^d} F_{\mu\omega, \kappa}( \wv ;\zv) \le \widehat\eps$ for some $\widehat \eps > 0$. Then, for all $0 < \theta < 1$ and all $\wv \in \reals^d$, we have, \begin{align} \label{eq:c:approx_descent} F_{\mu\omega}(\widehat\wv) + \frac{\kappa}{2} \normasq{2}{\widehat\wv - \zv} + \frac{\kappa + \lambda}{2}(1-\theta) \normasq{2}{\wv - \widehat\wv} \le F_{\mu\omega}(\wv) + \frac{\kappa}{2} \normasq{2}{\wv - \zv} + \frac{\widehat\eps}{\theta} \,. \end{align} \end{lemma} \begin{proof Let $\widehat F^* = \min_{\wv \in \reals^d} F_{\mu\omega,\kappa}(\wv ; \zv)$. Let $\widehat \wv^*$ be the unique minimizer of $F_{\mu\omega,\kappa}(\cdot \,; \zv)$. We have, from $(\kappa + \lambda)$-strong convexity of $F_{\mu\omega,\kappa}(\cdot \,; \zv)$, \begin{align*} F_{\mu\omega,\kappa}(\wv ; \zv) &\ge \widehat F^* +\frac{\kappa +\lambda}{2} \normasq{2}{\wv - \widehat \wv^*} \\ &\ge \left( F_{\mu\omega,\kappa}(\widehat\wv ; \zv) - \widehat\eps \right) + \frac{\kappa + \lambda}{2}(1-\theta) \normasq{2}{\wv - \widehat\wv} - \frac{\kappa + \lambda}{2} \left( \frac{1}{\theta} - 1 \right) \normasq{2}{\widehat\wv - \widehat \wv^*} \,, \end{align*} where we used that $\widehat\eps$ was sub-optimality of $\widehat\wv$ and Lemma~\ref{lem:c:helper:quadratic} from Appendix~\ref{subsec:a:catalyst:helper}. From $(\kappa + \lambda)$-strong convexity of $F_{\mu\omega, \kappa}(\cdot ; \zv)$, we have, \begin{align*} \frac{\kappa + \lambda }{2} \normasq{2}{\widehat\wv - \widehat \wv^*} \le F_{\mu\omega,\kappa}(\widehat\wv ; \zv) - \widehat F^* \le \widehat\eps\,, \end{align*} Since $(1/\theta - 1)$ is non-negative, we can plug this into the previous statement to get, \begin{align*} F_{\mu\omega,\kappa}(\wv ; \zv) \ge F_{\mu\omega,\kappa}(\widehat\wv ; \zv) + \frac{\kappa + \lambda}{2} (1-\theta) \normasq{2}{\wv - \widehat\wv} - \frac{\widehat\eps}{\theta}\,. \end{align*} Substituting the definition of $F_{\mu\omega,\kappa}(\cdot \,; \zv)$ from \eqref{eq:prox_point_algo} completes the proof. \end{proof} We now define a few auxiliary sequences integral to the proof. Define sequences $(\vv_k)_{k \ge 0}$, $(\gamma_k)_{k \ge 0}$, $(\eta_k)_{k \ge 0}$, and $(\rv_k)_{k \ge 1}$ as \begin{align} \label{eq:c:v_defn_base} \vv_0 &= \wv_0 \, \\ \label{eq:c:v_defn} \vv_k &= \wv_{k-1} + \frac{1}{\alpha_{k-1}} (\wv_k - \wv_{k-1}) \,, \, k \ge 1 \,, \\ \label{eq:c:gamma_defn_base} \gamma_0 &= \frac{(\kappa_1 + \lambda) \alpha_0^2 - \lambda \alpha_0 } {1 - \alpha_0} \,, \\ \label{eq:c:gamma_defn} \gamma_k &= (\kappa_k + \lambda) \alpha_{k-1}^2 \, , \, k \ge 1 \,, \\ \label{eq:c:eta_defn} \eta_k &= \frac{\alpha_k \gamma_k}{\gamma_{k+1} + \alpha_k \gamma_k} \,, \, k\ge 0 \,, \\ \label{eq:c:ly_vec_defn} \rv_k &= \alpha_{k-1} \wv^* + ( 1- \alpha_{k-1}) \wv_{k-1} \, , \, k \ge 1\,. \end{align} One might recognize $\gamma_k$ and $\vv_k$ from their resemblance to counterparts from the proof of \citet{nesterov2013introductory}. Now, we claim some properties of these sequences. \begin{claim} \label{claim:c:sequences} For the sequences defined in \eqref{eq:c:v_defn_base}-\eqref{eq:c:ly_vec_defn}, we have, \begin{align} \label{eq:c:gamma_defn_2} \gamma_k &= \frac{(\kappa_{k+1} + \lambda) \alpha_k^2 - \lambda \alpha_k } {1 - \alpha_k} \, , \, k \ge 0\,, \\ \label{eq:c:gamma_defn_3} \gamma_{k+1} &= (1- \alpha_k) \gamma_k + \lambda \alpha_k \, , \, k \ge 0\,, \\ \label{eq:c:eta_defn_2} \eta_k &= \frac{\alpha_k \gamma_k}{\gamma_k + \alpha_k \lambda} \, , \, k \ge 0 \\ \label{eq:c:v_defn_2} \zv_k &= \eta_k \vv_k + (1- \eta_k) \wv_k \, , \, k \ge 0\,, \,. \end{align} \end{claim} \begin{proof Eq.~\eqref{eq:c:gamma_defn_2} follows from plugging in \eqref{eq:c:update_alpha} in \eqref{eq:c:gamma_defn} for $k\ge 1$, while for $k=0$, it is true by definition. Eq.~\eqref{eq:c:gamma_defn_3} follows from plugging \eqref{eq:c:gamma_defn} in \eqref{eq:c:gamma_defn_2}. Eq.~\eqref{eq:c:eta_defn_2} follows from \eqref{eq:c:gamma_defn_3} and \eqref{eq:c:eta_defn}. Lastly, to show \eqref{eq:c:v_defn_2}, we shall show instead that \eqref{eq:c:v_defn_2} is equivalent to the update \eqref{eq:c:update_support} for $\zv_k$. We have, \begin{align*} \zv_k &\,= \eta_k \vv_k + (1-\eta_k) \wv_k \\ &\stackrel{\eqref{eq:c:v_defn}}{=} \eta_k \left( \wv_{k-1} + \frac{1}{\alpha_{k-1}} (\wv_k - \wv_{k-1}) \right) + (1-\eta_k) \wv_k \\ &\,= \wv_k + \eta_k \left(\frac{1}{\alpha_{k-1}} - 1 \right) (\wv_{k} - \wv_{k-1}) \,. \end{align*} Now, \begin{align*} \eta_k \left(\frac{1}{\alpha_{k-1}} - 1 \right) &\stackrel{\eqref{eq:c:eta_defn}}{=} \frac{\alpha_k \gamma_k}{\gamma_{k+1} + \alpha_k \gamma_k } \cdot \frac{1-\alpha_{k-1}}{\alpha_{k-1}} \\& \stackrel{\eqref{eq:c:gamma_defn}}{=} \frac{\alpha_k (\kappa_k + \lambda) \alpha_{k-1}^2 } { \alpha_k^2 (\kappa_{k+1} + \lambda) +\alpha_k (\kappa_k + \lambda) \alpha_{k-1}^2 } \cdot \frac{1-\alpha_{k-1}}{\alpha_{k-1}} \stackrel{\eqref{eq:c:update_beta}}{=} \beta_k \, , \end{align*} completing the proof. \end{proof} \begin{claim} \label{claim:c:ly_sequence} The sequence $(\rv_k)_{k \ge 1}$ from \eqref{eq:c:ly_vec_defn} satisfies \begin{align} \label{eq:c:norm_ly_sequence} \normasq{2}{\rv_k - \zv_{k-1}} \le \alpha_{k-1} (\alpha_{k-1} - \eta_{k-1}) \normasq{2}{\wv_{k-1} - \wv^*} + \alpha_{k-1} \eta_{k-1} \normasq{2}{\vv_{k-1} - \wv^*} \,. \end{align} \end{claim} \begin{proof Notice that $\eta_k \stackrel{\eqref{eq:c:eta_defn_2}}{=} \alpha_k \cdot \frac{\gamma_k}{\gamma_k + \alpha_k \lambda} \le \alpha_k$. Hence, using convexity of the squared Euclidean norm, we get, \begin{align*} \normasq{2}{\rv_k - \zv_{k-1}} & \stackrel{\eqref{eq:c:v_defn_2}}{=} \normasq{2}{ (\alpha_{k-1} - \eta_{k-1})(\wv^* - \wv_{k-1}) + \eta_{k-1}(\wv^* - \vv_{k-1}) } \\ &\,= \alpha_{k-1}^2 \normsq*{ \left(1 - \frac{\eta_{k-1}}{\alpha_{k-1}} \right) (\wv^* - \wv_{k-1}) + \frac{\eta_{k-1}}{\alpha_{k-1}} (\wv^* - \vv_{k-1}) }_2 \\ &\stackrel{(*)}{\le} \alpha_{k-1}^2 \left(1 - \frac{\eta_{k-1}}{\alpha_{k-1}} \right) \normasq{2}{\wv_{k-1} - \wv^*} + \alpha_{k-1}^2 \frac{\eta_{k-1}}{\alpha_{k-1}} \normasq{2}{\vv_{k-1} - \wv^*} \\ &\,= \alpha_{k-1} (\alpha_{k-1} - \eta_{k-1}) \normasq{2}{\wv_{k-1} - \wv^*} + \alpha_{k-1} \eta_{k-1} \normasq{2}{\vv_{k-1} - \wv^*} \,. \end{align*} \end{proof} For all $\mu \ge \mu' \ge 0$, we know from Prop.~\ref{thm:setting:beck-teboulle} that \begin{align} 0 \le F_{\mu \omega}(\wv) - F_{\mu'\omega}(\wv) \le (\mu - \mu') D_\omega \,. \label{asmp:c:smoothing:1} \end{align} We now define the sequence $( S_k )_{k\ge0}$ to play the role of a potential function here. \begin{align} \label{eq:c:ly_fn_defn} \begin{split} S_0 &= (1 - \alpha_0) (F(\wv_0) - F(\wv^*)) + \frac{\alpha_0 \kappa_1 \eta_0}{2} \normasq{2}{\wv_0 - \wv^*}\,, \\ S_k &= (1-\alpha_k) ( F_{\mu_k \omega}(\wv_k) - F_{\mu_k \omega}(\wv^*)) + \frac{\alpha_k \kappa_{k+1} \eta_k}{2} \normasq{2}{\vv_k - \wv^*}\,, \, k\ge 1 \,. \end{split} \end{align} We are now ready to analyze the effect of one outer loop. This lemma is the crux of the analysis. \begin{lemma} \label{lem:c:one_step_ly} Suppose $F_{\mu_k\omega, \kappa_k}(\wv_k ;\zv) - \min_{\wv\in\reals^d} F_{\mu_k\omega, \kappa_k}(\wv ; \zv) \le \eps_k$ for some $\eps_k > 0$. The following statement holds for all $0 < \theta_k < 1$: \begin{align} \label{eq:c:one_step_ly} \frac{S_k}{1-\alpha_k} \le S_{k-1} + (\mu_{k-1} - \mu_k) D_\omega + \frac{\eps_k}{\theta_k} - \frac{\kappa_k}{2}\normasq{2}{\wv_k - \zv_{k-1}} + \frac{\kappa_{k+1}\eta_k \alpha_k \theta_k}{2(1-\alpha_k)} \normasq{2}{\vv_k - \wv^*} \,, \end{align} where we set $\mu_0 := 2 \mu_1$. \end{lemma} \begin{proof} For ease of notation, let $F_k := F_{\mu_k \omega}$, and $D := D_\omega$. By $\lambda$-strong convexity of $F_{\mu_k\omega}$, we have, \begin{align} \label{eq:c:proof:step_sc_r_k} F_k(\rv_k) \le \alpha_{k-1} F_k(\wv^*) + (1-\alpha_{k-1}) F_k(\wv_{k-1}) - \frac{\lambda \alpha_{k-1} (1-\alpha_{k-1})}{2} \normasq{2}{\wv_{k-1} - \wv^*} \,. \end{align} We now invoke Lemma~\ref{lem:c:approx_descent} on the function $F_{\mu_k \omega, \kappa_k}(\cdot ; \zv_{k-1})$ with $\widehat \eps = \eps_k$ and $\wv = \rv_k$ to get, \begin{align} \label{eq:c:proof:main_eq_unsimplified} F_k(\wv_k) + \frac{\kappa_k}{2} \normasq{2}{\wv_k - \zv_{k-1}} + \frac{\kappa_k + \lambda}{2}(1-\theta_k) \normasq{2}{\rv_k - \wv_k} \le F_k(\rv_k) + \frac{\kappa_k}{2} \normasq{2}{\rv_k - \zv_{k-1}} + \frac{\eps_k}{\theta_k} \, . \end{align} We shall separately manipulate the left and right hand sides of \eqref{eq:c:proof:main_eq_unsimplified}, starting with the right hand side, which we call $\mcR$. We have, using \eqref{eq:c:proof:step_sc_r_k} and~\eqref{eq:c:norm_ly_sequence}, \begin{align*} \mcR \le& \, (1- \alpha_{k-1}) F_k(\wv_{k-1}) + \alpha_{k-1} F_k(\wv^*) - \frac{\lambda \alpha_{k-1} (1-\alpha_{k-1})}{2} \normasq{2}{\wv_{k-1} - \wv^*} \\ &+ \frac{\kappa_k}{2} \alpha_{k-1}(\alpha_{k-1} - \eta_{k-1}) \normasq{2}{\wv_{k-1} - \wv^*} + \frac{\kappa_k \alpha_{k-1} \eta_{k-1}}{2} \normasq{2}{\vv_{k-1} - \wv^*} + \frac{\eps_k}{\theta_k} \,. \end{align*} We notice now that \begin{align} \alpha_{k-1} - \eta_{k-1} &\stackrel{\eqref{eq:c:eta_defn_2}}{=} \alpha_{k-1} - \frac{\alpha_{k-1}\gamma_{k-1}}{\gamma_k + \alpha_{k-1} \gamma_{k-1}} \nonumber\\ &\,= \alpha_{k-1} \left( \frac{\gamma_k - \gamma_{k-1} ( 1- \alpha_{k-1})}{\gamma_k + \alpha_{k-1} \gamma_{k-1}} \right) \nonumber\\ &\stackrel{\eqref{eq:c:gamma_defn_3}}{=} \frac{\alpha_{k-1}^2 \lambda}{\gamma_{k-1} + \alpha_{k-1}\lambda} \nonumber\\ &\stackrel{\eqref{eq:c:gamma_defn_2}}{=} \frac{\alpha_{k-1}^2 \lambda (1-\alpha_{k-1})} {(\kappa_k + \lambda) \alpha_{k-1}^2 - \lambda \alpha_{k-1} + (1-\alpha_{k-1})\alpha_{k-1}\lambda} \nonumber\\ &\,= \frac{\lambda}{\kappa_k}(1-\alpha_{k-1}) \,, \label{eq:c:one_step_ly_pf_1} \end{align} and hence the terms containing $\normasq{2}{\wv_{k-1} - \wv^*}$ cancel out. Therefore, we get, \begin{align} \label{eq:c:proof:main_eq:rhs:simplified} \mcR \le (1 - \alpha_{k-1}) F_k(\wv_{k-1}) + \alpha_{k-1} F_k(\wv^*) + \frac{\kappa_k \alpha_{k-1} \eta_{k-1}}{2} \normasq{2}{\vv_{k-1} - \wv^*} + \frac{\eps_k}{\theta_k} \,. \end{align} To move on to the left hand side, we note that \begin{align} \label{eq:c:one_step_ly_proof_prod} \alpha_k \eta_k \nonumber &\stackrel{\eqref{eq:c:eta_defn_2}}{=} \frac{\alpha_k^2 \gamma_k}{\gamma_k + \alpha_k \lambda} \stackrel{\eqref{eq:c:gamma_defn},\eqref{eq:c:gamma_defn_2}}{=} \frac{\alpha_k^2 \alpha_{k-1}^2 (\kappa_k + \lambda)} {\frac{(\kappa_{k+1} + \lambda) \alpha_k^2 - \lambda \alpha_k}{1-\alpha_k} + \alpha_k \lambda } \\ &\,=\frac{ (1-\alpha_k)(\kappa_k + \lambda) \alpha_{k-1}^2 \alpha_k^2}{(\kappa_{k+1} + \lambda)\alpha_k^2 - \lambda \alpha_k^2} = (1-\alpha_k) \alpha_{k-1}^2 \frac{\kappa_k + \lambda}{\kappa_{k+1}} \,. \end{align} Therefore, \begin{align} \label{eq:c:one_step_ly_pf_2} F_k(\wv_k) - F_k(\wv^*) + \frac{\kappa_k + \lambda}{2} \alpha_{k-1}^2 \normasq{2}{\vv_k - \wv^*} \stackrel{\eqref{eq:c:ly_fn_defn},\eqref{eq:c:one_step_ly_proof_prod}}{=} \frac{S_k}{1 - \alpha_{k}} \,. \end{align} Using $\rv_k - \wv_k \stackrel{\eqref{eq:c:v_defn}}{=} \alpha_{k-1}(\wv^* - \vv_{k})$, we simplify the left hand side of \eqref{eq:c:proof:main_eq_unsimplified}, which we call $\mcL$, as \begin{align} \label{eq:c:proof:main_eq:lhs:simplified} \nonumber \mcL &= F_k(\wv_k) - F_k(\wv^*) + \frac{\kappa_k}{2} \normasq{2}{\wv_k - \zv_{k-1}} + \frac{\kappa_k + \lambda}{2}(1-\theta_k) \alpha_{k-1}^2 \normasq{2}{\vv_k - \wv^*} \\ &\stackrel{\eqref{eq:c:one_step_ly_pf_2}}{=} \frac{S_k}{1-\alpha_k} + F_k(\wv^*) + \frac{\kappa_k}{2} \normasq{2}{\wv_k - \zv_{k-1}} - \frac{\kappa_{k+1} \alpha_k \eta_k \theta_k}{2 (1-\alpha_k)} \normasq{2}{\vv_k - \wv^*} \,. \end{align} In view of \eqref{eq:c:proof:main_eq:rhs:simplified} and \eqref{eq:c:proof:main_eq:lhs:simplified}, we can simplify \eqref{eq:c:proof:main_eq_unsimplified} as \begin{align} \label{eq:c:one_step_ly_pf_2_int} \begin{aligned} \frac{S_k}{1-\alpha_k} & + \frac{\kappa_k}{2} \normasq{2}{\wv_k - \zv_{k-1}} - \frac{\kappa_{k+1}\alpha_k\eta_k\theta_k}{2(1-\alpha_k)} \normasq{2}{\vv_k - \wv^*} \\&\le (1 - \alpha_{k-1})\left( F_k(\wv_{k-1}) - F_k(\wv^*) \right) + \frac{\kappa_k \alpha_{k-1} \eta_{k-1}}{2}\normasq{2}{\vv_{k-1} - \wv^*} + \frac{\eps_k}{\theta_k} \,. \end{aligned} \end{align} We make a distinction for $k \ge 2$ and $k=1$ here. For $k \ge 2$, the condition that $\mu_{k-1} \ge \mu_k$ gives us, \begin{align} \label{eq:c:one_step_ly_pf_3} F_k(\wv_{k-1}) - F_k(\wv^*) \stackrel{\eqref{asmp:c:smoothing:1}}{\le} F_{k-1}(\wv_{k-1}) - F_{k-1}(\wv^*) + (\mu_{k-1} - \mu_{k}) D \, . \end{align} The right hand side of \eqref{eq:c:one_step_ly_pf_2_int} can now be upper bounded by \begin{align*} (1 - \alpha_{k-1})(\mu_{k-1} - \mu_k) D + S_{k-1} + \frac{\eps_k}{\theta_k} \,, \end{align*} and noting that $1-\alpha_{k-1} \le 1$ yields \eqref{eq:c:one_step_ly} for $k \ge 2$. For $k=1$, we note that $S_{k-1} (= S_0)$ is defined in terms of $F(\wv)$. So we have, \begin{align*} F_1(\wv_0) - F_1(\wv^*) \le F(\wv_0) - F(\wv^*) + \mu_1 D = F(\wv_0) - F(\wv^*) + (\mu_0 - \mu_1) D\,, \end{align*} because we used $\mu_0 = 2\mu_1$. This is of the same form as \eqref{eq:c:one_step_ly_pf_3}. Therefore, \eqref{eq:c:one_step_ly} holds for $k=1$ as well. % \end{proof} \noindent We now prove Thm.~\ref{thm:catalyst:outer}. \begin{proof} [Proof of Thm.~\ref{thm:catalyst:outer}] We continue to use shorthand $F_k := F_{\mu_k \omega}$, and $D := D_\omega$. We now apply Lemma~\ref{lem:c:one_step_ly}. In order to satisfy the supposition of Lemma~\ref{lem:c:one_step_ly} that $\wv_k$ is $\eps_k$-suboptimal, we make the choice $\eps_k = \frac{\delta_k \kappa_k}{2} \normasq{2}{\wv_k - \zv_{k-1}}$ (cf.~\eqref{eq:stopping_criterion}). Plugging this in and setting $\theta_k = \delta_k < 1$, we get from~\eqref{eq:c:one_step_ly}, \begin{align*} \frac{S_k}{1-\alpha_k} - \frac{\kappa_{k+1} \eta_k \alpha_k \delta_k}{2(1 - \alpha_k)} \normasq{2}{\vv_k - \wv^*} \le S_{k-1} + (\mu_{k-1} - \mu_k) D \,. \end{align*} The left hand side simplifies to $ S_k \, ({1- \delta_k})/({1-\alpha_k}) + \delta_k ( F_k(\wv_k) - F_k(\wv^*))$. Note that $F_k(\wv_k) - F_k(\wv^*) \stackrel{\eqref{asmp:c:smoothing:1}}{\ge} F(\wv_k) - F(\wv^*) - \mu_k D \ge -\mu_k D$. From this, noting that $\alpha_k \in (0, 1)$ for all $k$, we get, \begin{align*} S_k \left(\frac{1-\delta_k}{1-\alpha_k} \right) \le S_{k-1} + \delta_k \mu_k D + (\mu_{k-1} - \mu_k) D\,, \end{align*} or equivalently, \begin{align*} S_k \le \left( \frac{1-\alpha_k}{1-\delta_k} \right) S_{k-1} + \left( \frac{1-\alpha_k}{1-\delta_k} \right) (\mu_{k-1} - (1-\delta_k) \mu_k) D\,. \end{align*} Unrolling the recursion for $S_k$, we now have, \begin{align} \label{eq:c:pf_thm_main_1} S_k \le \left( \prod_{j=1}^k \frac{1-\alpha_j}{1-\delta_j} \right) S_0 + \sum_{j=1}^k \left( \prod_{i=j}^k \frac{1-\alpha_i}{1-\delta_i} \right) (\mu_{j-1} - (1- \delta_j) \mu_j) D\,. \end{align} Now, we need to reason about $S_0$ and $S_k$ to complete the proof. To this end, consider $\eta_0$: \begin{align} \eta_0 &\stackrel{\eqref{eq:c:eta_defn}}{=} \frac{\alpha_0 \gamma_0}{\gamma_1 + \alpha_0 \gamma_0} \nonumber\\ &\stackrel{\eqref{eq:c:gamma_defn_base}}{=} \frac{\alpha_0 \gamma_0} {(\kappa_1 + \lambda)\alpha_0^2 + \tfrac{\alpha_0}{1-\alpha_0}\left( (\kappa_1 + \lambda)\alpha_0^2 - \lambda \alpha_0 \right)} \nonumber\\ &\, = \frac{\alpha_0 \gamma_0 (1-\alpha_0)}{(\kappa_1 + \lambda)\alpha_0^2 - \lambda \alpha_0^2} = (1-\alpha_0) \frac{\gamma_0}{\kappa_1 \alpha_0} \,. \label{eq:c:thm_pf_1} \end{align} With this, we can expand out $S_0$ to get \begin{align*} S_0 &\stackrel{\eqref{eq:c:ly_fn_defn}}{=} (1- \alpha_0) \left(F(\wv_0) - F(\wv^*)\right) + \frac{\alpha_0 \kappa_1 \eta_0}{2} \normasq{2}{\wv_0 - \wv^*} \\ &\stackrel{\eqref{eq:c:thm_pf_1}}{=} (1- \alpha_0) \left( F(\wv_0) - F^* + \frac{\gamma_0}{2}\normasq{2}{\wv_0 - \wv^*} \right) \,. \end{align*} Lastly, we reason about $S_k$ for $k \ge 1$ as, \begin{align*} S_k \stackrel{\eqref{eq:c:ly_fn_defn}}{\ge} (1-\alpha_k) \left(F_k(\wv_k) - F_k(\wv^*) \right) \stackrel{\eqref{asmp:c:smoothing:1}}{\ge} (1-\alpha_k) \left( F(\wv_k) - F(\wv^*) - \mu_k D \right) \,. \end{align*} Plugging this into the left hand side of \eqref{eq:c:pf_thm_main_1} completes the proof. \end{proof} \subsubsection{Inner Loop Complexity} \label{sec:catalyst:inner_compl} Consider a class $\mcF_{L, \lambda}$ of functions defined as \[ \mcF_{L, \lambda} = \left\{ f : \reals^d \to \reals \text{ such that $f$ is $L$-smooth and $\lambda$-strongly convex} \right\} \,. \] We now formally define a linearly convergent algorithm on this class of functions. \begin{definition} \label{defn:c:linearly_convergent} A first order algorithm $\mcM$ is said to be linearly convergent with parameters $C : \reals_+ \times \reals_+ \to \reals_+$ and $\tau : \reals_+ \times \reals_+ \to (0, 1)$ if the following holds: for all $L \ge \lambda > 0$, and every $f \in \mcF_{L, \lambda}$ and $\wv_0 \in \reals^d$, $\mcM$ started at $\wv_0$ generates a sequence $(\wv_k)_{k \ge 0}$ that satisfies: \begin{align} \label{eq:def:linearly_convergent_2} \expect f(\wv_k) - f^* \le C(L, \lambda) \left( 1 - \tau(L, \lambda) \right)^k \left( f(\wv_0) - f^* \right)\, , \end{align} where $f^* := \min_{\wv\in\reals^d} f(\wv)$ and the expectation is over the randomness of $\mcM$. \end{definition} The parameter $\tau$ determines the rate of convergence of the algorithm. For instance, batch gradient descent is a deterministic linearly convergent algorithm with $\tau(L, \lambda)\inv = L/\lambda$ and incremental algorithms such as SVRG and SAGA satisfy requirement~\eqref{eq:def:linearly_convergent_2} with $\tau(L,\lambda)\inv = c(n + \nicefrac{L}{\lambda})$ for some universal constant $c$. The warm start strategy in step $k$ of Algo.~\ref{algo:catalyst} is to initialize $\mcM$ at the prox center $\zv_{k-1}$. The next proposition, due to \citet[Cor. 16]{lin2017catalyst} bounds the expected number of iterations of $\mcM$ required to ensure that $\wv_k$ satisfies \eqref{eq:stopping_criterion}. Its proof has been given in Appendix~\ref{sec:c:proofs:inner_compl} for completeness. \begin{proposition} \label{prop:c:inner_loop_final} Consider $F_{\mu\omega, \kappa}(\cdot \, ;\zv)$ defined in Eq.~\eqref{eq:prox_point_algo}, and a linearly convergent algorithm $\mcM$ with parameters $C$, $\tau$. Let $\delta \in [0,1)$. Suppose $F_{\mu\omega}$ is $L_{\mu\omega}$-smooth and $\lambda$-strongly convex. Then the expected number of iterations $\expect[\widehat T]$ of $\mcM$ when started at $\zv$ in order to obtain $\widehat \wv \in \reals^d$ that satisfies \begin{align*} F_{\mu\omega, \kappa}(\widehat\wv;\zv) - \min_\wv F_{\mu\omega, \kappa}(\wv;\zv)\leq \tfrac{\delta\kappa}{2} \normasq{2}{\wv - \zv} \end{align*} is upper bounded by \begin{align*} \expect[\widehat T] \le \frac{1}{\tau(L_{\mu\omega} + \kappa, \lambda + \kappa)} \log\left( \frac{8 C(L_{\mu\omega} + \kappa, \lambda + \kappa)}{\tau(L_{\mu\omega} + \kappa, \lambda + \kappa)} \cdot \frac{L_{\mu\omega} + \kappa}{\kappa \delta} \right) + 1 \,. \end{align*} \end{proposition} \begin{table*}[t!] \caption{\small{Summary of global complexity of {Casimir-SVRG}, i.e., Algorithm~\ref{algo:catalyst} with SVRG as the inner solver for various parameter settings. We show $\expect[N]$, the expected total number of SVRG iterations required to obtain an accuracy $\eps$, up to constants and factors logarithmic in problem parameters. We denote $\Delta F_0 := F(\wv_0) - F^*$ and {$\Delta_0 = \norma{2}{\wv_0 - \wv^*}$}. Constants $D, A$ are short for $D_\omega, A_\omega$ (see \eqref{eq:c:A_defn}). \vspace{2mm} }} \begin{adjustbox}{width=\textwidth} \label{tab:sc-svrg_rates_summary} \centering \begin{tabular}{|c||cccc|c|c|} \hline \rule{0pt}{12pt} {Prop.} & $\lambda>0$ & $\mu_k$ & $\kappa_k$ & $\delta_k$ & $\expect[N]$ & Remark \\[3pt] \hline\hline \rule{0pt}{15pt} \ref{prop:c:total_compl_svrg_main} & Yes & $\sfrac{\eps}{D}$ & $\sfrac{A D}{\eps n} - \lambda$ & $\sqrt\frac{\lambda\eps n}{A D}$ & $n + \sqrt{\frac{A D n}{\lambda \eps}} $ & fix $\eps$ in advance \\[5pt] \hline \rule{0pt}{15pt} \ref{prop:c:total_compl_sc:dec_smoothing_main} & Yes & $\mu c^k $ & $\lambda$ & $c'$ & $ n + \frac{A}{\lambda\eps} \frac{\Delta F_0 + \mu D}{\mu}$ & $c,c'<1$ are universal constants \\[5pt] \hline \rule{0pt}{15pt} \ref{prop:c:total_compl_svrg_smooth_main} & No & $\sfrac{\eps}{D}$ & $\sfrac{A D}{\eps n}$ & $1/k^2$ & $n\sqrt{\frac{\Delta F_0}{\eps}} + \frac{ \sqrt{A D n} \Delta_0}{\eps} $ & fix $\eps$ in advance \\[5pt] \hline \rule{0pt}{15pt} \ref{prop:c:total_compl_nsc:dec_smoothing_main} & No & $\sfrac{\mu}{k}$ & $\kappa_0 \, k$ & $1/k^2$ & $\frac{\widehat\Delta_0}{\eps} \left( n + \frac{A}{\mu \kappa_0} \right) $ & $\widehat\Delta_0 = \Delta F_0 + \frac{\kappa_0}{2} \Delta_0^2 + \mu D$ \\[5pt] \hline \end{tabular} \end{adjustbox} \end{table*} \subsection{Casimir with SVRG} \label{sec:catalyst:total_compl} We now choose SVRG \citep{johnson2013accelerating} to be the linearly convergent algorithm $\mcM$, resulting in an algorithm called {Casimir-SVRG}{}. The rest of this section analyzes the total iteration complexity of {Casimir-SVRG}{} to solve Problem~\eqref{eq:cvx_pb_finite_sum}. The proofs of the results from this section are calculations stemming from combining the outer loop complexity from Cor.~\ref{cor:c:outer_sc} to~\ref{cor:c:outer_smooth_dec_smoothing} with the inner loop complexity from Prop.~\ref{prop:c:inner_loop_final}, and are relegated to Appendix~\ref{sec:c:proofs:total_compl}. Table~\ref{tab:sc-svrg_rates_summary} summarizes the results of this section. Recall that if $\omega$ is 1-strongly convex with respect to $\norma{\alpha}{\cdot}$, then $h_{\mu\omega}(\Am \wv + \bv)$ is $L_{\mu\omega}$-smooth with respect to $\norma{2}{\cdot}$, where $L_{\mu\omega} = \normasq{2,\alpha}{\Am} / \mu$. Therefore, the complexity of solving problem~\eqref{eq:cvx_pb_finite_sum} will depend on \begin{align} \label{eq:c:A_defn} A_\omega := \max_{i=1,\cdots,n} \normasq{2, \alpha}{\Am\pow{i}} \,. \end{align} \begin{remark} \label{remark:smoothing:l2vsEnt} We have that $\norma{2,2}{\Am} = \norma{2}{\Am}$ is the spectral norm of $\Am$ and $\norma{2,1}{\Am} = \max_j \norma{2}{\av_j}$ is the largest row norm, where $\av_j$ is the $j$th row of $\Am$. Moreover, we have that $\norma{2,2}{\Am} \ge \norma{2,1}{\Am}$. \end{remark} \noindent We start with the strongly convex case with constant smoothing. \begin{proposition} \label{prop:c:total_compl_svrg_sc} \label{prop:c:total_compl_svrg_main} Consider the setting of Thm.~\ref{thm:catalyst:outer} and fix $\eps > 0$. If we run Algo.~\ref{algo:catalyst} with SVRG as the inner solver with parameters: $\mu_k = \mu = \eps / {10 D_\omega}$, $\kappa_k = k$ chosen as \begin{align*} \kappa = \begin{cases} \frac{A}{\mu n} - \lambda \,, \text{ if } \frac{A}{\mu n} > 4 \lambda \\ \lambda \,, \text{ otherwise} \end{cases} \,, \end{align*} $q = {\lambda}/{(\lambda + \kappa)}$, $\alpha_0 = \sqrt{q}$, and $\delta = {\sqrt{q}}/{(2 - \sqrt{q})}$. Then, the number of iterations $N$ to obtain $\wv$ such that $F(\wv) - F(\wv^*) \le \eps$ is bounded in expectation as \begin{align*} \expect[N] \le \widetilde \bigO \left( n + \sqrt{\frac{A_\omega D_\omega n}{\lambda \eps}} \right) \,. \end{align*} \end{proposition} \noindent Here, we note that $\kappa$ was chosen to minimize the total complexity (cf. \citet{lin2017catalyst}). This bound is known to be tight, up to logarithmic factors \citep{woodworth2016tight}. \noindent Next, we turn to the strongly convex case with decreasing smoothing. \begin{proposition} \label{prop:c:total_compl_sc:dec_smoothing} \label{prop:c:total_compl_sc:dec_smoothing_main} Consider the setting of Thm.~\ref{thm:catalyst:outer}. Suppose $\lambda > 0$ and $\kappa_k = \kappa$, for all $k \ge 1$ and that $\alpha_0$, $(\mu_k)_{k \ge 1}$ and $(\delta_k)_{k \ge 1}$ are chosen as in Cor.~\ref{cor:c:outer_sc:decreasing_mu_const_kappa}, with $q = \lambda/(\lambda + \kappa)$ and $\eta = 1- {\sqrt q}/{2}$. If we run Algo.~\ref{algo:catalyst} with SVRG as the inner solver with these parameters, the number of iterations $N$ of SVRG required to obtain $\wv$ such that $F(\wv) - F^* \le \eps$ is bounded in expectation as \begin{align*} \expect[N] \le \widetilde \bigO \left( n + \frac{A_\omega}{\mu(\lambda + \kappa)\eps} \left( F(\wv_0) - F^* + \frac{\mu D_\omega}{1-\sqrt{q}} \right) \right) \,. \end{align*} \end{proposition} \noindent Unlike the previous case, there is no obvious choice of $\kappa$, such as to minimize the global complexity. Notice that we do not get the accelerated rate of Prop.~\ref{prop:c:total_compl_svrg_sc}. We now turn to the case when $\lambda = 0$ and $\mu_k = \mu$ for all $k$. \begin{proposition} \label{prop:c:total_compl_svrg_smooth} \label{prop:c:total_compl_svrg_smooth_main} Consider the setting of Thm.~\ref{thm:catalyst:outer} and fix $\eps > 0$. If we run Algo.~\ref{algo:catalyst} with SVRG as the inner solver with parameters: $\mu_k = \mu ={\eps}/{20 D_\omega}$, $\alpha_0 = (\sqrt{5} - 1)/{2}$, $\delta_k = {1}/{(k+1)^2}$, and $\kappa_k = \kappa = {A_\omega}/{\mu(n+1)}$. Then, the number of iterations $N$ to get a point $\wv$ such that $F(\wv) - F^* \le \eps$ is bounded in expectation as \begin{align*} \expect[N] \le \widetilde \bigO \left( n\sqrt{\frac{F(\wv_0) - F^*}{\eps}} + \sqrt{A_\omega D_\omega n} \frac{\norma{2}{\wv_0 - \wv^*}}{\eps} \right) \, . \end{align*} \end{proposition} \noindent This rate is tight up to log factors~\citep{woodworth2016tight}. Lastly, we consider the non-strongly convex case ($\lambda = 0$) together with decreasing smoothing. As with Prop.~\ref{prop:c:total_compl_sc:dec_smoothing}, we do not obtain an accelerated rate here. \begin{proposition} \label{prop:c:total_compl_nsc:dec_smoothing} \label{prop:c:total_compl_nsc:dec_smoothing_main} Consider the setting of Thm.~\ref{thm:catalyst:outer}. Suppose $\lambda = 0$ and that $\alpha_0$, $(\mu_k)_{k\ge 1}$,$ (\kappa_k)_{k\ge 1}$ and $(\delta_k)_{k \ge 1}$ are chosen as in Cor.~\ref{cor:c:outer_smooth_dec_smoothing}. If we run Algo.~\ref{algo:catalyst} with SVRG as the inner solver with these parameters, the number of iterations $N$ of SVRG required to obtain $\wv$ such that $F(\wv) - F^* \le \eps$ is bounded in expectation as \begin{align*} \expect[N] \le \widetilde\bigO \left( \frac{1}{\eps} \left( F(\wv_0) - F^* + \kappa \normasq{2}{\wv_0 - \wv^*} + \mu D \right) \left( n + \frac{A_\omega}{\mu \kappa} \right) \right) \,. \end{align*} \end{proposition} \subsection{The Prox-Linear Algorithm} \label{sec:pl:pl-algo} The exact prox-linear algorithm of \citet{burke1985descent} generalizes the proximal gradient algorithm (see e.g., \citet{nesterov2013introductory}) to compositions of convex functions with smooth mappings such as~\eqref{eq:n-cvx_pb}. When given a function $f=h\circ \gv$, the prox-linear algorithm defines a local convex approximation $f(\cdot \, ; \wv_k)$ about some point $\wv \in \reals^d$ by linearizing the smooth map $\gv$ as $ f(\wv; \wv_k) := h(\gv(\wv_k) + \grad\gv(\wv_k)(\wv - \wv_k)) \, . $ With this, it builds a convex model $F(\cdot \, ; \wv_k)$ of $F$ about $\wv_k$ as \[ F(\wv ; \wv_k) := \frac{1}{n}\sum_{i=1}^n h(\gv\pow{i}(\wv_k) + \grad\gv\pow{i}(\wv_k)(\wv - \wv_k)) + \frac{\lambda}{2} \normasq{2}{\wv}\,. \] Given a step length $\eta > 0$, each iteration of the exact prox-linear algorithm then minimizes the local convex model plus a proximal term as \begin{align} \label{eq:pl:exact_pl} \wv_{k+1} = \argmin_{\wv \in \reals^d} \left[ F_{\eta}( \wv ; \wv_k) := F(\wv ; \wv_k) + \frac{1}{2\eta}\normasq{2}{\wv-\wv_k} \right] \,. \end{align} \begin{algorithm}[tb] \caption{(Inexact) Prox-linear algorithm: outer loop} \label{algo:prox-linear} \begin{algorithmic}[1] \STATE {\bfseries Input:} Smoothable objective $F$ of the form \eqref{eq:n-cvx_pb} with $h$ simple, step length $\eta$, tolerances $( \epsilon_k )_{k\ge1}$, initial point $\wv_0$, non-smooth convex optimization algorithm, $\mcM$, time horizon $K$ \FOR{$k=1$ \TO $K$} \STATE Using $\mcM$ with $\wv_{k-1}$ as the starting point, find \begin{align} \label{eq:pl:algo:update} \nonumber \widehat \wv_k \approx \argmin_{\wv} \bigg[ F_\eta(\wv ; \wv_{k-1}) := \frac{1}{n} \sum_{i=1}^n & h\big(\gv\pow{i}(\wv_{k-1}) + \grad\gv\pow{i}(\wv_{k-1})(\wv - \wv_{k-1}) \big) \\ &+ \frac{\lambda}{2}\normasq{2}{\wv} + \frac{1}{2\eta}\normasq{2}{\wv-\wv_{k-1}} \,, \bigg] \end{align} such that \begin{align} \label{eq:pl:algo:stop} F_\eta(\widehat \wv_k ; \wv_{k-1}) - \min_{ \wv \in \reals^d} F_\eta(\wv ; \wv_{k-1}) \le \eps_k \,. \end{align} \label{line:pl:algo:subprob} \STATE Set $\wv_k = \widehat \wv_k$ if $F(\widehat \wv_k) \le F(\wv_{k-1})$, else set $\wv_k = \wv_{k-1}$. \label{line:pl:algo:accept} \ENDFOR \RETURN $\wv_K$. \end{algorithmic} \end{algorithm} Following \citet{drusvyatskiy2016efficiency}, we consider an inexact prox-linear algorithm, which approximately solves \eqref{eq:pl:exact_pl} using an iterative algorithm. In particular, since the function to be minimized in \eqref{eq:pl:exact_pl} is precisely of the form~\eqref{eq:cvx_pb}, we employ the fast convex solvers developed in the previous section as subroutines. Concretely, the prox-linear outer loop is displayed in Algo.~\ref{algo:prox-linear}. We now delve into details about the algorithm and convergence guarantees. \subsubsection{Inexactness Criterion} As in Section~\ref{sec:cvx_opt}, we must be prudent in choosing when to terminate the inner optimization (Line~\ref{line:pl:algo:subprob} of Algo.~\ref{algo:prox-linear}). Function value suboptimality is used as the inexactness criterion here. In particular, for some specified tolerance $\eps_k > 0$, iteration $k$ of the prox-linear algorithm accepts a solution $\widehat \wv$ that satisfies $F_\eta(\widehat \wv_k ; \wv_{k-1}) - \min_{ \wv} F_\eta(\wv ; \wv_{k-1}) \le \eps_k$. \paragraph{Implementation} In view of the $(\lambda + \eta\inv)$-strong convexity of $F_\eta(\cdot \, ; \wv_{k-1})$, it suffices to ensure that $(\lambda + \eta\inv) \normasq{2}{\vv} \le \eps_k$ for a subgradient $\vv \in \partial F_\eta(\widehat \wv_k ; \wv_{k-1})$. \paragraph{Fixed Iteration Budget} As in the convex case, we consider as a practical alternative a fixed iteration budget $T_{\mathrm{budget}}$ and optimize $F_\eta(\cdot\, ; \wv_k)$ for exactly $T_{\mathrm{budget}}$ iterations of $\mcM$. Again, we do not have a theoretical analysis for this scheme but find it to be effective in practice. \subsubsection{Warm Start of Subproblems} As in the convex case, we advocate the use of the prox center $\wv_{k-1}$ to warm start the inner optimization problem in iteration $k$ (Line~\ref{line:pl:algo:subprob} of Algo.~\ref{algo:prox-linear}). \subsection{Convergence analysis of the prox-linear algorithm} \label{sec:pl:convergence} We now state the assumptions and the convergence guarantee of the prox-linear algorithm. \subsubsection{Assumptions} For the prox-linear algorithm to work, the only requirement is that we minimize an upper model. The assumption below makes this concrete. \begin{assumption} \label{asmp:pl:upper-bound} The map $\gv\pow{i}$ is continuously differentiable everywhere for each $i \in [n]$. Moreover, there exists a constant $L > 0$ such that for all $\wv, \wv' \in \reals^d$ and $i\in [n]$, it holds that \begin{align*} h\big(\gv\pow{i}(\wv') \big) \le h\big(\gv\pow{i}(\wv) + \grad\gv\pow{i}(\wv) (\wv'-\wv) \big) + \frac{L}{2}\normasq{2}{\wv'-\wv} \,. \end{align*} \end{assumption} \noindent When $h$ is $G$-Lipschitz and each $\gv\pow{i}$ is $\widetilde L$-smooth, both with respect to $\norma{2}{\cdot}$, then Assumption~\ref{asmp:pl:upper-bound} holds with $L = G\widetilde L$ \citep{drusvyatskiy2016efficiency}. In the case of structured prediction, Assumption~\ref{asmp:pl:upper-bound} holds when the augmented score $\psi$ as a function of $\wv$ is $L$-smooth. The next lemma makes this precise and its proof is in Appendix~\ref{sec:c:pl_struct_pred}. \begin{lemma} \label{lem:pl:struct_pred} Consider the structural hinge loss $f(\wv) = \max_{\yv \in \mcY} \psi(\yv ; \wv) = h\circ \gv(\wv)$ where $h, \gv$ are as defined in \eqref{eq:mapping_def}. If the mapping $\wv \mapsto \psi(\yv ; \wv)$ is $L$-smooth with respect to $\norma{2}{\cdot}$ for all $\yv \in \mcY$, then it holds for all $\wv, \zv \in \reals^d$ that \begin{align*} |h(\gv(\wv+\zv)) - h(\gv(\wv) + \grad\gv(\wv) \zv)| \le \frac{L}{2}\normasq{2}{\zv}\,. \end{align*} \end{lemma} \subsubsection{Convergence Guarantee} Convergence is measured via the norm of the {\em prox-gradient} $\bm{\varrho}_\eta(\cdot)$, also known as the {\em gradient mapping}, defined as \begin{align} \bm{\varrho}_\eta(\wv) = \frac{1}{\eta} \left( \wv - \argmin_{\zv \in \reals^d} F_\eta(\zv ; \wv) \right) \,. \end{align} The measure of stationarity $\norm{\bm{\varrho}_\eta(\wv)}$ turns out to be related to the norm of the gradient of the Moreau envelope of $F$ under certain conditions - see \citet[Section 4]{drusvyatskiy2016efficiency} for a discussion. In particular, a point $\wv$ with small $\norm{\bm{\varrho}_\eta(\wv)}$ means that $\wv$ is close to $\wv' = \argmin_{\zv \in \reals^d} F_\eta(\zv ; \wv)$, which is nearly stationary for $F$. The prox-linear outer loop shown in Algo.~\ref{algo:prox-linear} has the following convergence guarantee \citep[Thm.~5.2]{drusvyatskiy2016efficiency}. \begin{theorem} \label{thm:pl:outer-loop} Consider $F$ of the form~\eqref{eq:n-cvx_pb} that satisfies Assumption~\ref{asmp:pl:upper-bound}, a step length $0 < \eta \le 1/L$ and a non-negative sequence $(\eps_k)_{k\ge1}$. With these inputs, Algo.~\ref{algo:prox-linear} produces a sequence $(\wv_k)_{k \ge 0}$ that satisfies \begin{align*} \min_{k=0, \cdots, K-1} \normasq{2}{\bm{\varrho}_\eta(\wv_k)} \le \frac{2}{\eta K} \left( F(\wv_0) - F^* + \sum_{k=1}^{K} \eps_k \right) \,, \end{align*} where $F^* = \inf_{\wv \in \reals^d} F(\wv)$. In addition, we have that the sequence $(F(\wv_k))_{k\ge0}$ is non-increasing. \end{theorem} \begin{remark} Algo.~\ref{algo:prox-linear} accepts an update only if it improves the function value (Line~\ref{line:pl:algo:accept}). A variant of Algo.~\ref{algo:prox-linear} which always accepts the update has a guarantee identical to that of Thm.~\ref{thm:pl:outer-loop}, but the sequence $(F(\wv_k))_{k\ge0}$ would not guaranteed to be non-increasing. \end{remark} \subsection{Prox-Linear with {Casimir-SVRG}{}} \label{sec:pl:total-compl} We now analyze the total complexity of minimizing the finite sum problem~\eqref{eq:n-cvx_pb} with {Casimir-SVRG}{} to approximately solve the subproblems of Algo.~\ref{algo:prox-linear}. For the algorithm to converge, the map $\wv \mapsto \gv\pow{i}(\wv_k) + \grad \gv\pow{i}(\wv_k)(\wv - \wv_k)$ must be Lipschitz for each $i$ and each iterate $\wv_k$. To be precise, we assume that \begin{align} A_\omega := \max_{i=1,\cdots,n} \sup_{\wv \in \reals^d} \normasq{2, \alpha}{\grad \gv\pow{i}(\wv)} \end{align} is finite, where $\omega$, the smoothing function, is 1-strongly convex with respect to $\norma{\alpha}{\cdot}$. When $\gv\pow{i}$ is the linear map $\wv \mapsto \Am\pow{i}\wv$, this reduces to \eqref{eq:c:A_defn}. We choose the tolerance $\eps_k$ to decrease as $1/k$. When using the {Casimir-SVRG}{} algorithm with constant smoothing (Prop.~\ref{prop:c:total_compl_svrg_sc}) as the inner solver, this method effectively smooths the $k$th prox-linear subproblem as $1/k$. We have the following rate of convergence for this method, which is proved in Appendix~\ref{sec:c:pl_proofs}. \begin{proposition} \label{prop:pl:total_compl} Consider the setting of Thm.~\ref{thm:pl:outer-loop}. Suppose the sequence $(\eps_k)_{k\ge 1}$ satisfies $\eps_k = \eps_0 / k$ for some $\eps_0 > 0$ and that the subproblem of Line~\ref{line:pl:algo:subprob} of Algo.~\ref{algo:prox-linear} is solved using {Casimir-SVRG}{} with the settings of Prop.~\ref{prop:c:total_compl_svrg_sc}. Then, total number of SVRG iterations $N$ required to produce a $\wv$ such that $\norma{2}{\bm{\varrho}_\eta(\wv)} \le \eps$ is bounded as \begin{align*} \expect[N] \le \widetilde\bigO\left( \frac{n}{\eta \eps^2} \left(F(\wv_0) - F^* + \eps_0 \right) + \frac{\sqrt{A_\omega D_\omega n \eps_0\inv}}{\eta \eps^3} \left( F(\wv_0) - F^* + \eps_0 \right)^{3/2} \right) \, . \end{align*} \end{proposition} \begin{remark} \label{remark:pl:choosing_eps0} When an estimate or an upper bound $B$ on $F(\wv_0) - F^*$, one could set $\eps_0 = \bigO(B)$. This is true, for instance, in the structured prediction task where $F^* \ge 0$ whenever the task loss $\ell$ is non-negative (cf.~\eqref{eq:pgm:struc_hinge}). \end{remark} \subsection{Dataset and Task Description} \label{subsec:expt:task_description} For each of the tasks, we specify below the following: (a) the dataset $\{ (\xv\pow{i}, \yv\pow{i})\}_{i=1}^n$, (b) the output structure $\mcY$, (c) the loss function $\ell$, (d) the score function $\phi(\xv, \yv ; \wv)$, (e) implementation of inference oracles, and lastly, (f) the evaluation metric used to assess the quality of predictions. \subsubsection{CoNLL 2003: Named Entity Recognition} Named entities are phrases that contain the names of persons, organization, locations, etc, and the task is to predict the label (tag) of each entity. Named entity recognition can be formulated as a sequence tagging problem where the set $\mcY_{\mathrm{tag}}$ of individual tags is of size 7. Each datapoint $\xv$ is a sequence of words $\xv = (x_1, \cdots, x_p)$, and the label $\yv = (y_1, \cdots, y_p) \in \mcY(\xv)$ is a sequence of the same length, where each $y_i \in \mcY_{\mathrm{tag}}$ is a tag. \paragraph{Loss Function} The loss function is the Hamming Loss $\ell(\yv, \yv') = \sum_i \ind(y_i \neq y_i')$. \paragraph{Score Function} We use a chain graph to represent this task. In other words, the observation-label dependencies are encoded as a Markov chain of order 1 to enable efficient inference using the Viterbi algorithm. We only consider the case of linear score $\phi(\xv, \yv ; \wv) = \inp{\wv}{\Phi(\xv, \yv)}$ for this task. The feature map $\Phi$ here is very similar to that given in Example~\ref{example:inf_oracles:viterbi_example}. Following \citet{tkachenko2012named}, we use local context $\Psi_i(\xv)$ around $i$\textsuperscript{th} word $x_i$ of $\xv$. In particular, define $\Psi_i(\xv) = \ev_{x_{i-2}} \otimes \cdots \otimes \ev_{x_{i+2}}$, where $\otimes$ denotes the Kronecker product between column vectors, and $\ev_{x_i}$ denotes a one hot encoding of word $x_i$, concatenated with the one hot encoding of its the part of speech tag and syntactic chunk tag which are provided with the input. Now, we can define the feature map $\Phi$ as \begin{align*} \Phi(\xv, \yv) = \left[ \sum_{v=1}^p \Psi_v(\xv) \otimes \ev_{y_v} \right] \oplus \left[ \sum_{i=0}^p \ev_{y_{v}} \otimes \ev_{y_{v+1}} \right] \,, \end{align*} where $\ev_y \in \reals^{\abs{\mcY_{\mathrm{tag}}}}$ is a one hot-encoding of $y \in \mcY_{\mathrm{tag}}$, and $\oplus$ denotes vector concatenation. \paragraph{Inference} We use the Viterbi algorithm as the max oracle (Algo.~\ref{algo:dp:max:chain}) and top-$K$ Viterbi algorithm (Algo.~\ref{algo:dp:topK:chain}) for the top-$K$ oracle. \paragraph{Dataset} The dataset used was CoNLL 2003 \citep{tjong2003introduction}, which contains about $\sim 20K$ sentences. \paragraph{Evaluation Metric} We follow the official CoNLL metric: the $F_1$ measure excluding the `O' tags. In addition, we report the objective function value measured on the training set (``train loss''). \paragraph{Other Implementation Details} The sparse feature vectors obtained above are hashed onto $2^{16} - 1$ dimensions for efficiency. \subsubsection{PASCAL VOC 2007: Visual Object Localization} Given an image and an object of interest, the task is to localize the object in the given image, i.e., determine the best bounding box around the object. A related, but harder task is object detection, which requires identifying and localizing any number of objects of interest, if any, in the image. Here, we restrict ourselves to pure localization with a single instance of each object. Given an image $\xv \in \mcX$ of size $n_1 \times n_2$, the label $\yv \in \mcY(\xv)$ is a bounding box, where $\mcY(\xv)$ is the set of all bounding boxes in an image of size $n_1 \times n_2$. Note that $\abs{\mcY(\xv)} = \bigO(n_1^2n_2^2)$. \paragraph{Loss Function} The PASCAL IoU metric \citep{everingham2010pascal} is used to measure the quality of localization. Given bounding boxes $\yv, \yv'$, the IoU is defined as the ratio of the intersection of the bounding boxes to the union: \begin{align*} \mathrm{IoU}(\yv, \yv') = \frac{\mathrm{Area}(\yv \cap \yv')}{\mathrm{Area}(\yv \cup \yv')} \,. \end{align*} We then use the $1 - \mathrm{IoU}$ loss defined as $\ell(\yv, \yv') = 1 - \mathrm{IoU}(\yv, \yv')$. \paragraph{Score Function} The formulation we use is based on the popular R-CNN approach \citep{girshick2014rich}. We consider two cases: linear score and non-linear score $\phi$, both of which are based on the following definition of the feature map $\Phi(\xv, \yv)$. \begin{itemize} \item Consider a patch $\xv|_\yv$ of image $\xv$ cropped to box $\yv$, and rescale it to $64\times 64$. Call this $\Pi(\xv|_\yv)$. \item Consider a convolutional neural network known as AlexNet \citep{krizhevsky2012imagenet} pre-trained on ImageNet \citep{ILSVRC15} and pass $\Pi(\xv|_\yv)$ through it. Take the output of {\tt conv4}, the penultimate convolutional layer as the feature map $\Phi(\xv, \yv)$. It is of size $ 3 \times 3\times 256$. \end{itemize} In the case of linear score functions, we take $\phi(\xv, \yv ; \wv) = \inp{\wv}{\Phi(\xv, \yv)}$. In the case of non-linear score functions, we define the score $\phi$ as the the result of a convolution composed with a non-linearity and followed by a linear map. Concretely, for $\thetav \in \reals^{H \times W \times C_1}$ and $\wv \in \reals^{C_1 \times C_2}$ let the map $\thetav \mapsto \thetav \star \wv \in \reals^{H \times W \times C_2}$ denote a two dimensional convolution with stride $1$ and kernel size $1$, and $\sigma: \reals \to \reals$ denote the exponential linear unit, defined respectively as \begin{align*} [\thetav \star \wv]_{ij} = \wv\T [\thetav]_{ij} \quad \text{and} \quad \sigma(x) = x \, \ind(x \ge 0) + (\exp(x) - 1) \, \ind(x < 0) \,, \end{align*} where $[\thetav]_{ij} \in \reals^{C_1}$ is such that its $l$th entry is $\thetav_{ijl}$ and likewise for $[\thetav \star \wv]_{ij}$. We overload notation to let $\sigma:\reals^d\to \reals^d$ denote the exponential linear unit applied element-wise. Notice that $\sigma$ is smooth. The non-linear score function $\phi$ is now defined, with $\wv_1 \in \reals^{256\times16}, \wv_2 \in \reals^{16\times3\times3}$ and $\wv=(\wv_1, \wv_2)$, as, \begin{align*} \phi(\xv, \yv ; \wv) = \inp{\sigma(\Phi(\xv, \yv) \star \wv_1)}{\wv_2} \,. \end{align*} \paragraph{Inference} For a given input image $\xv$, we follow the R-CNN approach~\citep{girshick2014rich} and use selective search~\citep{van2011segmentation} to prune the search space. In particular, for an image $\xv$, we use the selective search implementation provided by OpenCV~\citep{opencv_library} and take the top 1000 candidates returned to be the set $\widehat{\mcY}(\xv)$, which we use as a proxy for $\mcY(\xv)$. The max oracle and the top-$K$ oracle are then implemented as exhaustive searches over this reduced set $\widehat\mcY(\xv)$. \paragraph{Dataset} We use the PASCAL VOC 2007 dataset \citep{everingham2010pascal}, which contains $\sim 5K$ annotated consumer (real world) images shared on the photo-sharing site Flickr from 20 different object categories. For each class, we consider all images with only a single occurrence of the object, and train an independent model for each class. \paragraph{Evaluation Metric} We keep track of two metrics. The first is the localization accuracy, also known as CorLoc (for correct localization), following \citet{deselaers2010localizing}. A bounding box with IoU $> 0.5$ with the ground truth is considered correct and the localization accuracy is the fraction of images labeled correctly. The second metric is average precision (AP), which requires a confidence score for each prediction. We use $\phi(\xv, \yv' ; \wv)$ as the confidence score of $\yv'$. As previously, we also plot the objective function value measured on the training examples. \paragraph{Other Implementation Details} For a given input-output pair $(\xv, \yv)$ in the dataset, we instead use $(\xv, \widehat \yv)$ as a training example, where $\widehat\yv = \argmax_{\yv' \in \widehat\mcY(\xv)} \mathrm{IoU}(\yv, \yv')$ is the element of $\widehat\mcY(\xv)$ which overlaps the most with the true output $\yv$. \subsection{Methods Compared} \label{subsec:expt:competing_methods} The experiments compare various convex stochastic and incremental optimization methods for structured prediction. \begin{itemize} \item {\bfseries SGD}: Stochastic subgradient method with a learning rate $\gamma_t = \gamma_0 / (1 + \lfloor t / t_0 \rfloor)$, where $\eta_0, t_0$ are tuning parameters. Note that this scheme of learning rates does not have a theoretical analysis. However, the averaged iterate $\overline \wv_t = {2}/(t^2+t)\sum_{\tau=1}^t \tau \wv_\tau$ obtained from the related scheme $\gamma_t = 1/(\lambda t)$ was shown to have a convergence rate of $\bigO((\lambda \eps)\inv)$ \citep{shalev2011pegasos,lacoste2012simpler}. It works on the non-smooth formulation directly. \item {\bfseries {BCFW}}: The block coordinate Frank-Wolfe algorithm of \citet{lacoste2012block}. We use the version that was found to work best in practice, namely, one that uses the weighted averaged iterate $\overline \wv_t = {2}/(t^2+t)\sum_{\tau=1}^t \tau \wv_\tau$ (called {\tt bcfw-wavg} by the authors) with optimal tuning of learning rates. This algorithm also works on the non-smooth formulation and does not require any tuning. \item {\bfseries {SVRG}}: The SVRG algorithm proposed by \citet{johnson2013accelerating}, with each epoch making one pass through the dataset and using the averaged iterate to compute the full gradient and restart the next epoch. This algorithm requires smoothing. \item {\bfseries {Casimir-SVRG-const}}: Algo.~\ref{algo:catalyst} with SVRG as the inner optimization algorithm. The parameters $\mu_k$ and $\kappa_k$ as chosen in Prop.~\ref{prop:c:total_compl_svrg_sc}, where $\mu$ and $\kappa$ are hyperparameters. This algorithm requires smoothing. \item {\bfseries {Casimir-SVRG-adapt}}: Algo.~\ref{algo:catalyst} with SVRG as the inner optimization algorithm. The parameters $\mu_k$ and $\kappa_k$ as chosen in Prop.~\ref{prop:c:total_compl_sc:dec_smoothing}, where $\mu$ and $\kappa$ are hyperparameters. This algorithm requires smoothing. \end{itemize} On the other hand, for non-convex structured prediction, we only have two methods: \begin{itemize} \item {\bfseries SGD}: The stochastic subgradient method \citep{davis2018stochastic}, which we call as SGD. This algorithm works directly on the non-smooth formulation. We try learning rates $\gamma_t = \gamma_0$, $\gamma_t = \gamma_0 /\sqrt{t}$ and $\gamma_t = \gamma_0 / t$, where $\gamma_0$ is found by grid search in each of these cases. We use the names SGD-const, SGD-$t^{-1/2}$ and SGD-$t^{-1}$ respectively for these variants. We note that SGD-$t^{-1}$ does not have any theoretical analysis in the non-convex case. \item {\bfseries {PL-Casimir-SVRG}}: Algo.~\ref{algo:prox-linear} with {Casimir-SVRG-const}{} as the inner solver using the settings of Prop.~\ref{prop:pl:total_compl}. This algorithm requires smoothing the inner subproblem. \end{itemize} \subsection{Hyperparameters and Variants} \label{subsec:expt:hyperparam} \paragraph{Smoothing} In light of the discussion of Sec.~\ref{sec:smooth_oracle_impl}, we use the $\ell_2^2$ smoother $\omega(\uv) = \normasq{2}{\uv} / 2$ and use the top-$K$ strategy for efficient computation. We then have $D_\omega = 1/2$. \paragraph{Regularization} The regularization coefficient $\lambda$ is chosen as $\nicefrac{c}{n}$, where $c$ is varied in $\{ 0.01, 0.1, 1, 10\}$. \paragraph{Choice of $K$} The experiments use $K = 5$ for named entity recognition where the performance of the top-$K$ oracle is $K$ times slower, and $K=10$ for visual object localization, where the running time of the top-$K$ oracle is independent of $K$. We also present results for other values of $K$ in Fig.~\ref{fig:plot_ner_K} and find that the performance of the tested algorithms is robust to the value of $K$. \paragraph{Tuning Criteria} Some algorithms require tuning one or more hyperparameters such as the learning rate. We use grid search to find the best choice of the hyperparameters using the following criteria: For the named entity recognition experiments, the train function value and the validation $F_1$ metric were only weakly correlated. For instance, the 3 best learning rates in the grid in terms of $F_1$ score, the best $F_1$ score attained the worst train function value and vice versa. Therefore, we choose the value of the tuning parameter that attained the best objective function value within 1\% of the best validation $F_1$ score in order to measure the optimization performance while still remaining relevant to the named entity recognition task. For the visual object localization task, a wide range of hyperparameter values achieved nearly equal performance in terms of the best CorLoc over the given time horizon, so we choose the value of the hyperparameter that achieves the best objective function value within a given iteration budget. \subsubsection{Hyperparameters for Convex Optimization} This corresponds to the setting of Section~\ref{sec:cvx_opt}. \paragraph{Learning Rate} The algorithms {SVRG}{} and {Casimir-SVRG-adapt}{} require tuning of a learning rate, while SGD requires $\eta_0, t_0$ and {Casimir-SVRG-const}{} requires tuning of the Lipschitz constant $L$ of $\grad F_{\mu\omega}$, which determines the learning rate $\gamma = 1/(L + \lambda + \kappa)$. Therefore, tuning the Lipschitz parameter is similar to tuning the learning rate. For both the learning rate and Lipschitz parameter, we use grid search on a logarithmic grid, with consecutive entries chosen a factor of two apart. \paragraph{Choice of $\kappa$} For {Casimir-SVRG-const}{}, with the Lipschitz constant in hand, the parameter $\kappa$ is chosen to minimize the overall complexity as in Prop.~\ref{prop:c:total_compl_svrg_sc}. For {Casimir-SVRG-adapt}{}, we use $\kappa = \lambda$. \paragraph{Stopping Criteria} Following the discussion of Sec.~\ref{sec:cvx_opt}, we use an iteration budget of $T_{\mathrm{budget}} = n$. \paragraph{Warm Start} The warm start criterion determines the starting iterate of an epoch of the inner optimization algorithm. Recall that we solve the following subproblem using SVRG for the $k$th iterate (cf. \eqref{eq:prox_point_algo}): \begin{align*} \wv_k \approx \argmin_{\wv \in \reals^d} F_{\mu_k\omega, \kappa_k}(\wv_k;\zv_{k-1}) \,. \end{align*} Here, we consider the following warm start strategy to choose the initial iterate $\widehat \wv_0$ for this subproblem: \begin{itemize} \item {\tt Prox-center}: $\widehat \wv_0 = \zv_{k-1}$. \end{itemize} In addition, we also try out the following warm start strategies of \citet{lin2017catalyst}: \begin{itemize} \item {\tt Extrapolation}: $\widehat \wv_0 = \wv_{k-1} + c(\zv_{k-1} - \zv_{k-2})$ where $c = \frac{\kappa}{\kappa + \lambda}$. \item {\tt Prev-iterate}: $\widehat \wv_0 = \wv_{k-1}$. \end{itemize} We use the {\tt Prox-center} strategy unless mentioned otherwise. \paragraph{Level of Smoothing and Decay Strategy} For {SVRG}{} and {Casimir-SVRG-const}{} with constant smoothing, we try various values of the smoothing parameter in a logarithmic grid. On the other hand, {Casimir-SVRG-adapt}{} is more robust to the choice of the smoothing parameter (Fig.~\ref{fig:plot_ner_smoothing}). We use the defaults of $\mu = 2$ for named entity recognition and $\mu = 10$ for visual object localization. \subsubsection{Hyperparameters for Non-Convex Optimization} This corresponds to the setting of Section~\ref{sec:ncvx_opt}. \paragraph{Prox-Linear Learning Rate $\eta$} We perform grid search in powers of 10 to find the best prox-linear learning rate $\eta$. We find that the performance of the algorithm is robust to the choice of $\eta$ (Fig.~\ref{fig:ncvx:pl_lr}). \paragraph{Stopping Criteria} We used a fixed budget of 5 iterations of {Casimir-SVRG-const}{}. In Fig.~\ref{fig:ncvx:inner-iter}, we experiment with different iteration budgets. \paragraph{Level of Smoothing and Decay Strategy} In order to solve the $k$th prox-linear subproblem with {Casimir-SVRG-const}{}, we must specify the level of smoothing $\mu_k$. We experiment with two schemes, (a) constant smoothing $\mu_k = \mu$, and (b) adaptive smoothing $\mu_k = \mu / k$. Here, $\mu$ is a tuning parameters, and the adaptive smoothing scheme is designed based on Prop.~\ref{prop:pl:total_compl} and Remark~\ref{remark:pl:choosing_eps0}. We use the adaptive smoothing strategy as a default, but compare the two in Fig.~\ref{fig:ncvx_smoothing}. \paragraph{Gradient Lipschitz Parameter for Inner Optimization} The inner optimization algorithm {Casimir-SVRG-const}{} still requires a hyperparameter $L_k$ to serve as an estimate to the Lipschitz parameter of the gradient $\grad F_{\eta, \mu_k\omega}(\cdot\,; \wv_k)$. We set this parameter as follows, based on the smoothing strategy: (a) $L_k = L_0$ with the constant smoothing strategy, and (b) $L_k = k\, L_0$ with the adaptive smoothing strategy (cf. Prop.~\ref{thm:setting:beck-teboulle}). We note that the latter choice has the effect of decaying the learning rate as $~1/k$ in the $k$th outer iteration. \begin{figure}[t!] \centering \includegraphics[width=\textwidth]{plots/ner_cvx/ner_best.pdf} \caption{Comparison of convex optimization algorithms for the task of Named Entity Recognition on CoNLL 2003.}\label{fig:plot_all_ner} \end{figure} \begin{figure}[!thb] \centering \includegraphics[width=0.93\textwidth]{plots/loc_cvx/loc_all_best_1E+01_0.pdf} \caption{Comparison of convex optimization algorithms for the task of visual object localization on PASCAL VOC 2007 for $\lambda=10/n$. Plots for all other classes are in Appendix~\ref{sec:a:expt}.}\label{fig:plot_all_loc} \end{figure} \begin{figure}[!thb] \centering \includegraphics[width=0.93\textwidth]{plots/loc_ncvx/loc_best_all_1E+00_0.pdf} \caption{Comparison of non-convex optimization algorithms for the task of visual object localization on PASCAL VOC 2007 for $\lambda=1/n$. Plots for all other classes are in Appendix~\ref{sec:a:expt}.}\label{fig:plot_ncvx_loc} \end{figure} \subsection{Experimental study of different methods} \label{subsec:expt:competing_results} \paragraph{Convex Optimization} For the named entity recognition task, Fig.~\ref{fig:plot_all_ner} plots the performance of various methods on CoNLL 2003. On the other hand, Fig.~\ref{fig:plot_all_loc} presents plots for various classes of PASCAL VOC 2007 for visual object localization. The plots reveal that smoothing-based methods converge faster in terms of training error while achieving a competitive performance in terms of the performance metric on a held-out set. Furthermore, BCFW and SGD make twice as many actual passes as SVRG based algorithms. \paragraph{Non-Convex Optimization} Fig.~\ref{fig:plot_ncvx_loc} plots the performance of various algorithms on the task of visual object localization on PASCAL VOC. \subsection{Experimental Study of Effect of Hyperparameters: Convex Optimization} We now study the effects of various hyperparameter choices. \paragraph{Effect of Smoothing} Fig.~\ref{fig:plot_ner_smoothing} plots the effect of the level of smoothing for {Casimir-SVRG-const}{} and {Casimir-SVRG-adapt}{}. The plots reveal that, in general, small values of the smoothing parameter lead to better optimization performance for {Casimir-SVRG-const}. {Casimir-SVRG-adapt}{} is robust to the choice of $\mu$. Fig.~\ref{fig:plot_ner_smoothing-2} shows how the smooth optimization algorithms work when used heuristically on the non-smooth problem. \begin{figure}[!thb] \centering \begin{subfigure}[b]{0.88\linewidth} \centering \includegraphics[width=\textwidth]{plots/ner_cvx/plot_smoother_main.pdf} \caption{\small{Effect of level of smoothing.}} \label{fig:plot_ner_smoothing} \end{subfigure} \begin{subfigure}[b]{0.88\linewidth} \centering \includegraphics[width=\textwidth]{plots/ner_cvx/plot_nonsmooth_svrg_main.pdf} \caption{\small{Effect of smoothing: use of smooth optimization with smoothing (labeled ``smooth'') versus the heuristic use of these algorithms without smoothing (labeled ``non-smooth'') for $\lambda = 0.01/n$.}} \label{fig:plot_ner_smoothing-2} \end{subfigure} \begin{subfigure}[b]{0.88\linewidth} \centering \includegraphics[width=\textwidth]{plots/ner_cvx/plot_warm_start.pdf} \caption{\small{Effect of warm start strategies for $\lambda=0.01/n$ (first row) and $\lambda = 1/n$ (second row).}} \label{fig:plot_ner_warm-start} \end{subfigure} \begin{subfigure}[b]{0.88\linewidth} \centering \includegraphics[width=\textwidth]{plots/ner_cvx/plot_K_main.pdf} \caption{\small{Effect of $K$ in the top-$K$ oracle ($\lambda = 0.01/n$).}} \label{fig:plot_ner_K} \end{subfigure} \caption{Effect of hyperparameters for the task of Named Entity Recognition on CoNLL 2003. C-SVRG stands for Casimir-SVRG in these plots.}\label{fig:plot_cvx_hyperparam} \end{figure} \paragraph{Effect of Warm Start Strategies} Fig.~\ref{fig:plot_ner_warm-start} plots different warm start strategies for {Casimir-SVRG-const}{} and {Casimir-SVRG-adapt}. We find that {Casimir-SVRG-adapt}{} is robust to the choice of the warm start strategy while {Casimir-SVRG-const}{} is not. For the latter, we observe that {\tt Extrapolation} is less stable (i.e., tends to diverge more) than {\tt Prox-center}, which is in turn less stable than {\tt Prev-iterate}, which always works (cf. Fig.~\ref{fig:plot_ner_warm-start}). However, when they do work, {\tt Extrapolation} and {\tt Prox-center} provide greater acceleration than {\tt Prev-iterate}. We use {\tt Prox-center} as the default choice to trade-off between acceleration and applicability. \paragraph{Effect of $K$} Fig.~\ref{fig:plot_ner_K} illustrates the robustness of the method to choice of $K$: we observe that the results are all within one standard deviation of each other. \subsection{Experimental Study of Effect of Hyperparameters: Non-Convex Optimization} We now study the effect of various hyperparameters for the non-convex optimization algorithms. All of these comparisons have been made for $\lambda = 1/n$. \paragraph{Effect of Smoothing} Fig.~\ref{fig:ncvx_smoothing:1} compares the adaptive and constant smoothing strategies. Fig.~\ref{fig:ncvx_smoothing:2} and Fig.~\ref{fig:ncvx_smoothing:3} compare the effect of the level of smoothing on the the both of these. As previously, the adaptive smoothing strategy is more robust to the choice of the smoothing parameter. \begin{figure}[!thb] \centering \begin{subfigure}[b]{\linewidth} \centering \includegraphics[width=\textwidth]{plots/loc_ncvx/loc_fixed-vs-adapt-smth_sheep_1E+00.pdf} \caption{Comparison of adaptive and constant smoothing strategies.} \label{fig:ncvx_smoothing:1} \end{subfigure} \begin{subfigure}[b]{\linewidth} \centering \includegraphics[width=\textwidth]{plots/loc_ncvx/loc_smoother-decay_sheep_1E+00.pdf} \caption{Effect of $\mu$ of the adaptive smoothing strategy.} \label{fig:ncvx_smoothing:2} \end{subfigure} \begin{subfigure}[b]{\linewidth} \centering \includegraphics[width=\textwidth]{plots/loc_ncvx/loc_smoother-const_sheep_1E+00.pdf} \caption{Effect of $\mu$ of the constant smoothing strategy.} \label{fig:ncvx_smoothing:3} \end{subfigure} \caption{Effect of smoothing on {PL-Casimir-SVRG}{} for the task of visual object localization on PASCAL VOC 2007.}\label{fig:ncvx_smoothing} \end{figure} \begin{figure}[!thb] \centering \begin{subfigure}[b]{\linewidth} \centering \includegraphics[width=\textwidth]{plots/loc_ncvx/loc_pl-lr_sheep_1E+00.pdf} \caption{\small{Effect of the hyperparameter $\eta$.}}\label{fig:ncvx:pl_lr} \end{subfigure} \begin{subfigure}[b]{\linewidth} \centering \includegraphics[width=\textwidth]{plots/loc_ncvx/loc_inner-iter_sheep_1E+00.pdf} \caption{\small{Effect of the iteration budget of the inner solver.}}\label{fig:ncvx:inner-iter} \end{subfigure} \begin{subfigure}[b]{\linewidth} \centering \includegraphics[width=\textwidth]{plots/loc_ncvx/loc_warmstart_sheep_1E+00.pdf} \caption{\small{Effect of the warm start strategy of the inner {Casimir-SVRG-const}{} algorithm.}} \label{fig:ncvx:warm-start} \end{subfigure} \caption{Effect of hyperparameters on {PL-Casimir-SVRG}{} for the task of visual object localization on PASCAL VOC 2007.}\label{fig:ncvx_hyperparam} \end{figure} \paragraph{Effect of Prox-Linear Learning Rate $\eta$} Fig.~\ref{fig:ncvx:pl_lr} shows the robustness of the proposed method to the choice of $\eta$. \paragraph{Effect of Iteration Budget} Fig.~\ref{fig:ncvx:inner-iter} also shows the robustness of the proposed method to the choice of iteration budget of the inner solver, {Casimir-SVRG-const}. \paragraph{Effect of Warm Start of the Inner Solver} Fig.~\ref{fig:ncvx:warm-start} studies the effect of the warm start strategy used within the inner solver {Casimir-SVRG-const}{} in each inner prox-linear iteration. The results are similar to those obtained in the convex case, with {\tt Prox-center} choice being the best compromise between acceleration and compatibility. \section{Introduction} \input{sections/01_intro} \section{Smooth Structured Prediction} \label{sec:setting} \input{sections/02_struct_pred} \section{Inference Oracles} \label{sec:inference_oracles} \input{sections/03_inf_oracles} \section{Implementation of Inference Oracles} \label{sec:smooth_oracle_impl} \input{sections/04_smoothing} \section{The Casimir Algorithm} \label{sec:cvx_opt} \input{sections/05_Casimir} \section{Extension to Non-Convex Optimization} \label{sec:ncvx_opt} \input{sections/06_proxlin} \section{Experiments} \label{sec:expt} \input{sections/08_expt} \section{Future Directions} \input{sections/09_conclusion} \paragraph{Acknowledgments} This work was supported by NSF Award CCF-1740551, the Washington Research Foundation for innovation in Data-intensive Discovery, and the program ``Learning in Machines and Brains'' of CIFAR. \clearpage \newpage
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President Obama stays the course Amidst street protests and a gloomy national mood, supporters of Obama turned out in force for last week's town-hall meeting. By Mitch Perry on Wed, Feb 3, 2010 at 5:00 am Tracy May OBAMA IN THE HOUSE: The president doffed his jacket to take questions from the audience at UT's Bob Martinez Sports Center. "I think President Obama is the most visionary president we've had since Eisenhower." Unlikely praise coming from any quarters these days, but especially from a Republican whose wife is running for the Florida GOP gubernatorial nomination. But the 76-year-old Doc Dockery (husband of Paula) is not just any Republican. He fought for 28 years and spent millions of dollars to have high-speed rail come to the Sunshine State, and helped pass a constitutional amendment in 2000 to create a high-speed rail authority that ultimately was repealed in 2004. So he was understandably pleased last Thursday when he attended the president's town-hall meeting at the University of Tampa, where Obama and Vice President Joe Biden announced a $1.25 billion grant to begin construction of a high-speed rail line from Tampa to Orlando. Though it wasn't the complete $2.56 billion that ConnectUs' Ed Turanchik and other Florida lawmakers had been lusting for, it's considered to be a dynamic first installment toward providing thousands of construction jobs to a state economy suffering as bad as any in the country. Of course, Dockery was not alone in expressing support for the president last week. Thunderous applause greeted him when he appeared on stage at the Bob Martinez Sports Center, and he rose to the occasion with a typically rousing speech. But even amidst the town-hall camaraderie, there was no way for Obama to escape his or the country's troubles. With unemployment at lows not seen in Florida since before the creation of the Tampa Bay Buccaneers, one particular question-and-answer exchange seemed to epitomize the quandary that Obama faces, both in style and substance. Clearwater small business owner Steve Gordon expressed his frustration at the difficulties of obtaining a business loan. He wondered why the Small Business Administration couldn't lend the money, instead of the banks. "Why can't you use the SBA just like you lent directly to Wall Street, you lent directly to the automakers, you lent directly to the banks — why can't the government make small business [grants] available directly to us?" Gordon asked. The president struggled mightily to answer the question in a way that would make Gordon, and the partisan audience, feel better. But in a sound-bite world, his 793-word response — explaining that the majority of small business loans would have to come from the private sector — made some reporters literally yawn. With a struggling economy, and with health care reform in possible critical condition, much of the political press has characterized the Obama administration, only a year in office, as a presidency in crisis. But many of Obama's supporters are staying the course. Among the thousands eagerly waiting to hear him speak last week was health care activist Doug Hickman from Redington Shores. Though he's frustrated that there isn't a health care bill ready to be signed, he's keeping the faith. "Is it hard not to get discouraged?" he asked rhetorically. "Sure, it's hard. We're trying to change what began with Ronald Reagan. You don't change 28 years in a year. Am I still on board? You betcha." Hickman said that part of Obama's struggles is that he's tried to end "the imperial presidency," by allowing Congress to make the laws. "You advise and consent with them, and he tried that. But who would have thought he'd end up with a party of no, and not a second party?" Similar sentiments were heard from others who'd waited for hours in line, none of them as disillusioned or disappointed as the national political class. Ashley Southern is an art therapy major at UT, part of the generation inspired by Obama's "Yes We Can" mantra in 2007-2008. Southern said being green to the political process has its pros and cons. "A lot of his [Obama's] ideas are idealistic, and the kids in our age group are drawn to that because they're big ideas, and more power to him if it happens, but I think older generations think that it's not so possible. And maybe we don't realize it as much?" One reason that some progressives are skeptical is the administration's failure so far to produce a health care bill. But some observers wonder whether the real problem was the decision to pursue reform in the first place, especially at a time when there were so many other pressing concerns. Kaki Caruson, a professor of political science at USF, believes that the motivation to achieve a universal health care system made sense a year ago, but thinks the devastating economic downturn wrecked those plans. "I think if we were in a robust economy and we didn't have the same type of mortgage and banking crises," she said, "perhaps people might have been more open to health care change. Instead, she says, "I think it was a tough time to tackle this issue...the climate was difficult to enact this much change." Caruson said that Ronald Reagan's famous line — "Are you better off than you were four years ago?" — is as good a standard as any for assessing a president or governor. "People don't think they're better off," she says. "They don't see wages getting better. But economic recovery beats to its own beat, and there's only so much you can do." Leading the opposition all year in the streets has been the Tea Party movement, which made its presence felt with a protest alongside Kennedy Boulevard near the UT campus. One proud member of the movement, a woman who wanted to be identified only as Barbara from Orlando, carried a sign in support of Supreme Court Justice Samuel Alito, who was seen on television during the State of the Union address scoffing at Obama's criticism of the recent campaign finance decision. "I'm just pointing out that there are people in official positions that also understand when they're being lied to," she remarked. She called the State of the Union address divisive. "I didn't like the 'party of no,'" she said. When asked what she made of the president's plan to meet with Republicans, she was equally dismissive. "He'll meet with him, but he's not going to get off his rock. This is the hill he wants to die on." It's a hill that still carries large Democratic Party majorities in the House and Senate, despite the Washington insider talk that having 41 votes in the minority somehow trumps 59 in the majority. And it's evident that in Tampa, there are plenty of people who still have Obama's back, despite the naysayers. Check with them in another year and it may not be the same feeling, but as Obama said last week, "I don't quit." Many of his supporters aren't ready to quit either — not just yet. University of Tampa, Tampa Bay, Tampa, republicans, president barack obama, mitch perry, Hillsborough County, high-speed rail, Democrats, bob martinez sports complex
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Fastrac was a division of RAC aimed at making motor vehicle finance simple for the average motorist. Fastrac approached us with a desire to revamp its corporate identity as it moved forward with its business. Our job was to design a complete brand and collateral identity that was strong and contemporary.
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2013 CCI Commencement By CCI May 9, 2013 CCI Commencement on May 9, 2013 marked the end of another academic year for the college. Over 300 students graduated this spring and many will soon be starting their new careers. Monica Langley, esteemed Wall Street Journal writer, gave the commencement address to the students and guests attending the ceremony. In her address she shared her three guiding principles: people, persistance and passion. With her stories from 25 years at the WSJ and her early days as an intern copy clerk at the Knoxville News Sentinel, she captured the graduates attention with her practical and timely guidance. Click here to view her commencement address: http://sf.ites.utk.edu/utk/Play/186f9361b3a145e49a0069dcadb64c361d. The ceremony was punctuated with an incredible performance by Angelia Onulha as she sang "I Hope You Dance." CCI graduate Ashley Wright was commissioned into the United States Airforce by Lieutenant Colonel Brian J. Delamater. The senior gift was presented to the college in honor of Professor and Director Margie Morrison and will be used once fully funded to purchase a seat in the CCI auditorium in her memory. Angelia Onuoha CCI Commencement Monica Langley
{ "redpajama_set_name": "RedPajamaCommonCrawl" }
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package gov.va.isaac.gui.listview; import gov.va.isaac.AppContext; import gov.va.isaac.config.profiles.UserProfileManager; import gov.va.isaac.init.SystemInit; import gov.va.isaac.interfaces.gui.ApplicationWindowI; import gov.va.isaac.interfaces.gui.views.DockedViewI; import java.io.File; import javafx.application.Application; import javafx.concurrent.Task; import javafx.scene.Scene; import javafx.stage.Stage; import org.glassfish.hk2.api.Rank; import org.jvnet.hk2.annotations.Service; /** * {@link ListViewRunner} * * @author <a href="mailto:[email protected]">Dan Armbrust</a> */ @Service @Rank (value = -50) public class ListViewRunner extends Application implements ApplicationWindowI { Stage primaryStage_; /** * @see javafx.application.Application#start(javafx.stage.Stage) */ @Override public void start(Stage primaryStage) throws Exception { primaryStage_ = primaryStage; ListBatchView lv = AppContext.getService(ListBatchView.class); primaryStage.setScene(new Scene(lv.getView(), 1024, 800)); primaryStage.show(); } public static void main(String[] args) throws Exception { Exception dataStoreLocationInitException = SystemInit.doBasicSystemInit(new File("../../isaac-pa/app/")); if (dataStoreLocationInitException != null) { System.err.println("Configuration of datastore path failed. DB will not be able to start properly! " + dataStoreLocationInitException); System.exit(-1); } AppContext.getService(UserProfileManager.class).configureAutomationMode(new File("profiles")); launch(args); } /** * @see gov.va.isaac.interfaces.gui.ApplicationWindowI#getPrimaryStage() */ @Override public Stage getPrimaryStage() { return primaryStage_; } /** * @see gov.va.isaac.interfaces.gui.ApplicationWindowI#ensureDockedViewIsVisble(gov.va.isaac.interfaces.gui.views.DockedViewI) */ @Override public void ensureDockedViewIsVisble(DockedViewI view) { } /** * @see gov.va.isaac.interfaces.gui.ApplicationWindowI#browseURL(java.lang.String) */ @Override public void browseURL(String url) { } @Override public void addBackgroundTask(Task<?> task) { } }
{ "redpajama_set_name": "RedPajamaGithub" }
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This presence schedule tells you when you can expect to find ValeriMair available online on XloveCam®. Online availability statistics are automatically calculated based on the last 45 days and are based on the actual publication time of the ValeriMair's webcam. where have you gone ? mi sono trovato molto bene con la modella..
{ "redpajama_set_name": "RedPajamaC4" }
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In partnership with Macmillan Cancer Support and as a member of the Improving the Cancer Journey network in Fife, Fife Cultural Trust are launching volunteer-led Cancer Information and Support Centres across ONFife Libraries to provide practical and emotional support for people affected by cancer in their local communities. A strong volunteer network will be key to the success of these Macmillan Cancer Information and Support Centres, so you will be responsible for recruiting, training and supporting a team of volunteers to provide an effective drop-in support service for people affected by cancer. You will also support the Macmillan Project Officer to plan, promote, implement and evaluate the Macmillan Cancer Information and Support Centres to ensure long term sustainability of the support service for people affected by cancer in Fife. Please note the closing date for applications is Sunday 10 February 2019.
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Bed and Breakfasts Saint-Loup-des-Chaumes B&B - Vacation Rental Saint-Loup-des-Chaumes Chambres d'h�tes au Ch�teau De Preuil Vallenay B&B Set in a landscaped park in Vallenay, 33 km from Bourges, Ch�teau De Preuil features free WiFi access and free private parking. All rooms feature a connected flat-screen TV, free WiFi access and a private bathroom fitted with a shower. The bathroom is equipped with free toiletries and a hair dryer. You will find a shared lounge at the property. An array of activities are offered in the area, such as horse riding, cycling and fishing. La Berthoderie Morlac B&B A charming family-run 19th century farmhouse, offering bed and breakfast and optional gourmet country dinners, located in the department of Cher, in the heart of France. We offer a special discount of 20%, starting from the third night. A peaceful retreat, where you can visit castles, gardens, a superb Cistercian Abbey and Roman churches. Bourges, a medieval city, with its famous cathedral, is just forty kilometers away. La Berthoderie is just eighteen kiliometres from the 17th century fortress of Saint-Amand Montrond and many other interesting places. We are located just outside the quaint village of Morlac, in a big forested park. We can arrange some excellent lake fishing for you. No pets please. La Berthoderie is only a ten minute drive from the A71 Motorway from Paris to Clermont-Ferrand, then to Montpellier(A75) passing the Millau viaduct. Melitine Saint-Amand-Montrond B&B & Gite Featuring a garden and a terrace, Melitine provides accommodation in Saint-Amand-Montrond with free WiFi and city views. The property features garden views and is 2.1 km from Orval. This apartment is equipped with 2 bedrooms, a kitchen with a microwave and a fridge, a flat-screen TV, a seating area and 1 bathroom with a shower. Guests at the apartment can enjoy a continental breakfast. The nearest airport is Chateauroux-Centre Airport, 67 km from Melitine. BB Fleurie Saint-Amand-Montrond B&B Bed & Breakfast Fleurie is set in the centre of Saint-Amand-Montrond, 45 km from Bourges. It offers a terrace and views of the garden. Every room features a flat-screen TV and free WiFi. Certain rooms include a sitting area or desk for your convenience. Every room has a private bathroom fitted with a walk-in shower. Homemade meals are available upon reservation and can be served on the terrace. There is a shared lounge at the property. Montlu�on is one-hour drive away from BB Fleurie. Chambre d�h�tes �cureuil Boasting a terrace, Chambre d�h�tes �cureuil features accommodation in Saint-Amand-Montrond with free WiFi and city views. The bed and breakfast has garden views and is 3.1 km from Orval. A flat-screen TV is available. The bed and breakfast offers a continental or � la carte breakfast. Guests at Chambre d�h�tes �cureuil can enjoy hiking and cycling nearby, or make the most of the garden. The nearest airport is Chateauroux-Centre, 68 km from the accommodation, and the property offers a free shuttle service. Amphore du Berry Amphore du Berry B&B is located in Saint-Amand-Montrond, just 3 km from the Cit� de l�Or gold production and exhibition centre. It features a large furnished garden and a heated indoor swimming pool. Each room has a seating area with a sofa, a TV and a private bathroom with a bath or shower. A continental breakfast is served daily and catering services are available at an extra cost. Massages are also available on request. Le Moulin Du Pont Mar�ais B&B A 19th-century house on the site of an old watermill,in beautiful grounds with lawns and flowers. There is a twin-bedded room, a double, and a family suite for 4, all with private shower room and WC. A quiet and peaceful place, with a very friendly welcome. Meals by reservation. Le Moulin De La Pr�e Morlac B&B & Gite La Chaume des Buis La Chaume des Buis, a remodelled 18th-century house, is a B&B located in the Gallo-Roman village of Drevant, 4.5 km out of Saint-Amand-Montrond. It features a floral garden and orchard and is located 200 metres from the River Cher. The guest rooms are decorated with care and they include antique furniture. All rooms have tea and coffee facilities. Breakfast consists of homemade jam using fruit grown in the garden. An additional feature of this B&B is the private wine cellar stocked with regional wines. There is a gourmet restaurant 300 metres away. An array of activities can be enjoyed on site or in the surroundings, including cycling, hiking and fishing. Free private parking is available on site. Le Grand Champiau St Pierre-les-bois B&B & Gite A charming 4-bedroomed rural gite, sleeping up to 8, with shared pool and jacuzzi (with adjoining gite, Le petit Champiau, sleeping up to 4). Appartement Duplex Totalement Meuble Et Equipe Ligni�res B&B & Gite Featuring a shared lounge, Appartement Duplex Totalement Meuble Et Equipe features accommodation in Ligni�res with free WiFi and city views. The air-conditioned accommodation is 24 km from Orval. Boasting a Blu-ray player, the apartment has a kitchen with a dishwasher, a microwave and a fridge, a living room with a seating area and a dining area, 2 bedrooms, and 2 bathrooms with a hot tub and a shower. A flat-screen TV with cable channels and a DVD player are available. Guests at the apartment can enjoy a continental breakfast. Bourges is 46 km from Appartement Duplex Totalement Meuble Et Equipe, while Ch�teauroux is 41 km from the property. The nearest airport is Chateauroux-Centre Airport, 41 km from the accommodation. Chambres d'h�tes L'Ange Blanc Ligni�res B&B Located just 3 km from Ch�teau Ligni�re in the Cher region, L�Angle Blanc offers a covered, heated swimming pool, a garden and a terrace. It is a 45-minute drive from Chateauroux and 63 km from the Brenne Regional Park. All rooms features a flat-screen TV, DVD player, electric kettle and ironing facilities. The en suite bathroom includes free toiletries. A breakfast is provided every morning at L�Ange Blanc. Guests can also sample the local cuisine in a shared meal with the hosts, upon request. Additional features include billiards, bike rental and free Wi-Fi access throughout. The A71 motorway is ideally located 20 km away and free private parking is possible on site. Chambre d�h�tes La Reserve Saint-Pierre-les-Bois B&B Set on a 1-hectare garden in Saint-Pierre-les-Bois, La Reserve is 20 km from the Ch�teau de Meillant and 15 km from Noirlac Abbey. It offers an outdoor swimming pool, a terrace and self-catering suites with free Wi-Fi. Each suite features a wardrobe, a seating area and garden views. The private bathroom is complete with a hairdryer and a shower. The Family Suite has a mezzanine. Guests are invited to enjoy a daily continental breakfast at La Reserve. Each suite includes a kitchenette with kitchenware, a fridge and an oven. This property is 20 km from the Ch�teau d�Ainay-le-Vieil and 12 km from Ch�teau de Culan. Free private parking is available on site. Maisonnais B&B & Gite Maison des Arts is located in Maisonnais and offers a garden, barbecue facilities and a terrace. Montlu�on is 50 km from the apartment, while Orval is 26 km away. The nearest airport is Chateauroux-Centre Airport, 53 km from Maison des Arts. L'Amalgam' Ainay-le-Vieil B&B Located in Ainay-le-Vieil, L'Amalgam' offers garden, free WiFi, room service, and a shared lounge. With garden views, this accommodation features a swimming pool. The air-conditioned bed and breakfast also provides a flat-screen TV and 1 bathroom with a bath. A continental breakfast is available daily at the bed and breakfast. A barbecue and a terrace are available for guests at L'Amalgam' to use. Montlu�on is 42 km from the accommodation, while Orval is 13 km away. The nearest airport is Chateauroux-Centre Airport, 78 km from L'Amalgam'. Maison Les Galettes Rezay B&B Located in Rezay, 28 km from Orval, Maison Les Galettes provides free bikes and free WiFi. There is a fully equipped private bathroom with shower and a hairdryer. A continental breakfast is available daily at the bed and breakfast. Maison Les Galettes offers a children's playground. An outdoor swimming pool can be found at the accommodation, along with a garden. The nearest airport is Chateauroux-Centre Airport, 52 km from Maison Les Galettes. Chateau Igny La Perche B&B Situated in La Perche, Chateau Igny features free WiFi, and guests can enjoy an outdoor swimming pool, a garden and a shared lounge. A continental breakfast is available each morning at the bed and breakfast. Chateau Igny offers a children's playground. Guests at the accommodation can enjoy table tennis on site, or go hiking or cycling in the surroundings. Montlu�on is 36 km from Chateau Igny, while Orval is 18 km from the property. The nearest airport is Chateauroux-Centre Airport, 84 km from the bed and breakfast. Domaine Levignot Braize Braize B&B Featuring a swimming pool, a garden and a terrace and views of the garden, Domaine Levignot Braize is set in Braize and offers accommodation with free WiFi. Guests at the bed and breakfast can enjoy a continental breakfast. Domaine Levignot Braize offers a children's playground. If you would like to discover the area, cycling is possible in the surroundings and the accommodation can arrange a bicycle rental service. Montlu�on is 40 km from Domaine Levignot Braize, while Orval is 20 km away. The nearest airport is Chateauroux-Centre Airport, 85 km from the bed and breakfast. Le Pr� de Luceau Blet B&B Le Pr� de Luceau is located in Blet. The bed and breakfast, set in a building dating from 19th century, provides free WiFi. Featuring garden views, the bed and breakfast comes with a flat-screen TV, a seating area, a wardrobe and 1 bathroom. A continental breakfast is available daily at the bed and breakfast. After a day of hiking or cycling, guests can relax in the garden or in the shared lounge area. Bourges is 36 km from Le Pr� de Luceau, while Orval is 31 km away. The nearest airport is Chateauroux-Centre Airport, 97 km from the accommodation. Saint Amand Montrond B&B AMPHORE DU BERRY is situaed in center of town. you see swimming pool, rooms very confortable. Vesdun B&B Providing lake views, Amaryllis in Vesdun provides accommodation, an outdoor swimming pool, a garden, a bar, a shared lounge and a terrace. Free WiFi is provided. There is a fully equipped private bathroom with shower and a hairdryer. Guests at the bed and breakfast can enjoy a buffet breakfast. Cycling can be enjoyed nearby. Montlu�on is 34 km from Amaryllis, while Orval is 24 km away. The nearest airport is Chateauroux-Centre Airport, 88 km from the accommodation. Maisonlaventure Bommiers B&B Set in Bommiers, 36 km from Saint-Maur, Maisonlaventure offers a seasonal outdoor swimming pool and free WiFi. There is a fully equipped private bathroom with shower and a hairdryer. Continental and buffet breakfast options are available every morning at the bed and breakfast. Maisonlaventure offers a sun terrace. Guests can also relax in the garden or in the shared lounge area. Ch�teauroux is 30 km from the accommodation, while Orval is 40 km from the property. The nearest airport is Chateauroux-Centre Airport, 29 km from Maisonlaventure. La Petite Barre Bessais Le Fromental B&B 2 comfortable B&B's, one will accommodate a family of 4. Both en-suite. 45 mins from Magny Cours and Lurcy Levis racing circuits. Motorbike friendly. Clos Charmille Meaulne B&B Situated in Meaulne in the Auvergne Region, 29 km from Montlu�on, Clos Charmille features a sun terrace and views of the garden. Free WiFi is featured throughout the property and free private parking is available on site. Some units include a seating area for your convenience. You will find a coffee machine in the room. Extras include bathrobes and free toiletries. You will find a shared lounge at the property. A continental breakfast is served every morning at Clos Charmille, cheeses and cold cuts can be requested for an extra fee. Homemade meals and picnics are available upon request for an extra charge. You can play tennis at the bed and breakfast. Featuring a seasonal outdoor swimming pool, a garden, and a shared lounge, Rive Droite features accommodation in Meaulne with free WiFi and garden views. Boasting a private pool, the bed and breakfast is in an area where guests can engage in activities such as hiking and cycling. The bed and breakfast also provides a seating area, washing machine and 1 bathroom with a shower. Guests at the bed and breakfast can enjoy a continental breakfast. Rive Droite offers a terrace. Montlu�on is 31 km from the accommodation, while Orval is 21 km away. The nearest airport is Chateauroux-Centre Airport, 86 km from Rive Droite. The Jones We are situated in the center of France countryside known as the BERRY REGION, INDRE. We are offering a cosy GITE/ COTTAGE self-catering which sleeps two to six people comfortably. We also are offering Bed & Breakfast rooms ensuite, one or two nights special discounts if pre booked. Only 20mins from the motorway A20 one nights stays welcome and pets, break up your journey or come for a very relaxing holiday.We have a splash pool, barbecue, games, a small lake for those who like to fish with carp stocked.There are lots of places to see and activities within a short drive We provide evening meals menus start from 10 euros per person. Nearest village is ST.AOUT, the Towns of LA CHATRE AND ISSOUDUN are twenty minutes drive.Our main aim is to make you feel welcome and to enjoy your holiday. Domaine de la Rue La Berthenoux B&B Located in La Berthenoux, Domaine de la Rue offers accommodation with a flat-screen TV. Complimentary WiFi is provided. There is a fully equipped private bathroom with shower and a hair dryer. Guests at the bed and breakfast can enjoy a continental breakfast. Domaine de la Rue offers a terrace. Hiking can be enjoyed nearby. Ch�teauroux is 38 km from the accommodation. Chateauroux-Centre Airport is 49 km from the property. Maison de L`Etang Tron�ais B&B & Gite Maison de L`Etang offers accommodation in Tron�ais. Guests can fish in the lake beside the property. The property features views of the lake and is 47 km from Moulins. Free private parking is provided. The apartment comes with a seating area and a kitchenette complete with an oven and a microwave. There is a bathroom. A flat-screen TV with satellite channels is provided. Other facilities at Maison de L`Etang include a barbecue. The area is popular for hiking, cycling, horse riding and birdwatching. Water sports and tennis facilities are available in the surrounding area. Montlu�on is 35 km from Maison de L`Etang, while Orval is 21 km away. Clermont-Ferrand Auvergne Airport is 125 km away. Ch�teaumeillant B&B & Gite Le Paradis is set in Ch�teaumeillant. Montlu�on is 46 km from the apartment, while Orval is 35 km from the property. The nearest airport is Chateauroux-Centre Airport, 64 km from Le Paradis. Le Moulin De St Leger Issoudun B&B A beautiful and tranquil Bed and Breakfast located in the picturesque Loire Indre Valley. Perfectly located for stopovers on the way to the south of France or Spain, being 5 hours from Le Harvre and 6 hours from Calais. There's a beautiful garden in front of the river where guests can take their breakfast. Evening meals are available on request and there is also a BBQ area for guests to do their own thing. le Matou Roux Isle-et-Bardais B&B Situated in Isle-et-Bardais, 25 km from St Amand Montrond, le Matou Roux features free WiFi access and free private parking. Guests have access to a shared lounge with a refrigerator, tea and coffee making facilities and kitchenware. You can engage in various activities, such as horse riding and cycling. The bed and breakfast also offers free use of bicycles. Montlu�on is 41 km from le Matou Roux, while Nevers is 44 km from the property. The nearest airport is Chateauroux-Centre Airport, 83 km from the property. Manoir du mortier Surrounded by a 50-hectare park, this 18th-century manor house offers an outdoor swimming pool and elegant rooms each one located in a different tower. Free Wi-Fi is available in the public areas of Manoir du Mortier. With a refined d�cor, each room includes a spacious private bathroom with bathrobe, slippers and hairdryer. Some have a panoramic view of the Bourbonnais countryside, the orchard and the horse pen. Breakfast is included in the rate and served each morning. At an additional cost, the owner can also prepare traditional French dinners made with home-grown vegetables. You can relax on the poolside lounge area or go picking the mushrooms in the nearby Tron�ais forest. Several hiking paths start from the manor and a tennis course is available 6 km away in Saint-Bonnet-de-Tron�ais. The A71 Motorway is 12 km away. La Fleurette Isle Et Bardais B&B La Fleurette is settled in the Allier, in the heart of France, only 300 km away from Paris. The bed and breakfast is part of a long�re, a large old farm (1850), and has its own front door. The farm is situated on the marketplace of Isle et Bardais, a very small village in the neighbourhood of the For�t de Tron�ais. B&B Ch�teau de Peufeilhoux Vallon-en-Sully B&B Located 5 km from Vallon-en-Sully and set in a castle surrounded by 74 acres of forest, B&B Ch�teau de Peufeilhoux offers an outdoor pool as well as spacious rooms with a fireplace and free WiFi access. Decorated with period furniture, each room here offers a seating area, views of the garden and a private bathroom with a bathtub or a shower, a hairdryer, free toiletries and bathrobes. A buffet breakfast with homemade produce is available every morning and includes tea, coffee, honey, eggs, cakes, hot chocolate and brioche. At B&B Ch�teau de Peufeilhoux, guests can also find meeting facilities and relax in the shared lounge. Golfing, cycling and fishing can be enjoyed in the surroundings. Montlu�on Train Station is a 35-minute drive from the property. inattendue Augy-sur-Aubois B&B Offering an outdoor pool and views of the garden, inattendue is located in Augy-sur-Aubois, 48 km from Bourges. Free WiFi is featured and free private parking is available on site. Some rooms have a seating area where you can relax. A flat-screen TV is offered. Dinners are available upon request and at an extra cost. You can engage in various activities, such as fishing and hiking. The bed and breakfast also offers free use of bicycles. Moulins is 44 km from inattendue, while Nevers is 33 km away. The nearest airport is Chateauroux-Centre Airport, 85 km from the property. G�te De Langeron Augy Sur Aubois B&B & Gite Cottage for 9 people with private outdoor space Ferme Auberge Des Pirodelles Augy Sur Aubois B&B Berry in the door of the Auvergne, discover our beautiful region full of rich In a working farm. We welcome you to our three guest rooms, located above the room Ferme Auberge, You can enjoy the quiet of the countryside and discover the life of the farm. Here you can enjoy our hearty breakfasts consist of a maximum of home products. If you wish, you can also dine, enjoy delicious regional cuisine, prepared with produce from the farm. Logis De Chezelles Sidiailles B&B 4 cottages 3�pis comfortable lodgings of France and quiet of the countryside Berry Les Fruits du Passau Saint-D�sir� B&B Located in Saint-D�sir�, a 16-minute drive from the A71 motorway and a 21-minutes from the N145 motorway and Montlu�on, this residence is in the countryside and has a terrace. Each room in the B&B at the Les Fruits du Passau is individually decorated, two of the rooms have a view over the garden and a private bathroom. The tents all have refrigerators and a view of the playground. A continental breakfast is served daily and there is a restaurant available for lunches and dinners upon reservation. A children�s playground, heated seasonal outdoor pool and free Wi-Fi in public areas are available. Free private parking is provided. odyss�e La Grave B&B Located in La Grave in the Auvergne region, odyss�e provides accommodation with free WiFi. Montlu�on is 23 km from the bed and breakfast, while Orval is 36 km away. The nearest airport is Chateauroux-Centre Airport, 98 km from odyss�e. Saint-�loy-d?Allier B&B Situated in Saint-�loy-d?Allier, les glycines features accommodation with free WiFi and a garden. There is a fully equipped private bathroom with shower and a hairdryer. A � la carte breakfast is available each morning at the bed and breakfast. Montlu�on is 28 km from les glycines, while Orval is 35 km from the property. The nearest airport is Chateauroux-Centre Airport, 88 km from the accommodation. ChampduTaillis Couleuvre B&B Featuring a hot tub and a seasonal outdoor pool, ChampduTaillis is a guest house in Couleuvre, 40 km from Moulins. Free private parking is available on site and free WiFi is provided throughout the property. Each room has a private terrace and garden views. All rooms have a private bathroom with a shower and a hairdryer. Bed linen and towels are provided. Guests have shared access to a kitchen with a fridge, microwave, oven and stovetop. There are also table tennis facilities and a barbecue. Free use of bicycles is available at this bed and breakfast and the area is popular for cycling. Montlu�on is 44 km from ChampduTaillis, while Nevers is 41 km away. The nearest airport is Chateauroux-Centre Airport, 87 km from ChampduTaillis. la grange aux hirondelles Sancoins B&B Offering views of the garden, la grange aux hirondelles is situated in Sancoins in the Centre Region, 50 km from Bourges. Free private parking is available on site. Every room comes with a flat-screen TV. You will find a coffee machine and a kettle in the room. You will find a shared lounge at the property. A range of activities are offered in the area, such as cycling and hiking. Moulins is 42 km from la grange aux hirondelles, while Nevers is 31 km away. Chateauroux-Centre Airport is 89 km from the property. Nohant-Vic B&B This B&B is in Nohant-Vic, a 4-minute drive from the house of the writer George Sand, where the artist Delacroix had a studio. Set in a 1-hectare garden it has a terrace and free Wi-Fi. Each guest room at La Grange is decorated with the colours of flowers, in tones of pale blue, yellow or red. All the rooms have an en suite bathroom and a view of the surrounding area. Breakfast is provided every morning in the breakfast room. Guests can enjoy the large, private garden, furnished with outdoor furniture and parasols or read newspapers on the sofa on the mezzanine. La Grange offers free, private parking and is 36 km south-east of Ch�teauroux and the A20 motorway. There is a swimming pool 12 minutes� drive away. La Platriere Lurcy-levis B&B & Gite La Platriere is a newly converted farmhouse offering peaceful holidays and short breaks in the heart of France. The main house offers bed & breakfast, with evening meals available with advanced notice. The House sits in 3 acres of gardens, with a large outdoor swimming pool, petanque and childrens play area. Situated at the top of a hill, La Platriere, offers stunning views of the surrounding countryside. La Platriere is large enough to cater for individuals, as well as large group bookings. We have 6 bedrooms, all beautifully decorated, some with exposed beams, and all with views overlooking the garden and countryside beyond. Each bedroom has a private en-suite shower room, central heating, and complimentary tea/coffee. Our bedrooms vary in size, we have a large spacious family room which can sleep up to 5, two double rooms with queen size beds, two twin-bedded rooms, and one single bedroom. Prices start from 35 euros to 110 euros per night inclusive of breakfast. Guests are free to use all facilities at La Platriere, including large guest lounge (open log fire in winter), swimming pool and gardens. Meals can either be taken indoors in the dining room or outside on the sun terrace. G�te And Bed And Breakfast Accommodation. La Platriere Retreat is a farmhouse, renovated to a high standard, offering Bed and Breakfast accommodation with 5 guest rooms, and a Cottage which sleeps up to 6 people. Having 3 acres of gardens and a swimming pool, La Platriere Retreat offers stunning views of the surrounding countryside. Situated in the Allier department in the region of Auvergne, La Platriere is close to the Troncais Forest, and the borders of Cher and the Nievre, offering the easy reach of the diversity of 3 different regions for the visitor to explore. AU BORD DE LA FORET Featuring a swimming pool, a garden and a bar and views of the garden, AU BORD DE LA FORET is located in Couleuvre and provides accommodation with free WiFi. All units come with a seating area, a flat-screen TV with satellite channels and a private bathroom with free toiletries and shower. Guests at the bed and breakfast can enjoy a continental or a buffet breakfast. AU BORD DE LA FORET features a terrace. Moulins is 45 km from the accommodation, while Orval is 37 km away. The nearest airport is Chateauroux-Centre Airport, 103 km from AU BORD DE LA FORET. Le Grenier Du Luisant Germigny L'exempt B&B Guest room with living room, adjoining bathroom, upstairs property located in the heart of a quiet little village of Berry Welcome in English and Dutch
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More than 40 per cent of "underperforming" secondary schools would no longer fall into the category if progress measures were re-weighted to account for pupils' backgrounds, new research reveals. And a fifth of secondary schools would see their position in national league tables change by more than 500 places, researchers at the University of Bristol have found. Now they have warned league tables are "punishing and rewarding the wrong schools", echoing headteachers who have already said the government's progress measures are unhelpful for schools with high proportions of disadvantaged pupils. The researchers have produced an "adjusted" Progress 8 which re-weights a pupil's progress score according to factors such as their ethnicity, free school eligibility and gender, so that their progress is compared with others in their group rather than with an overall national average. Under the adjusted measure, 123 (41 per cent) of the 303 schools that were judged in 2016 to be underperforming or "well below average", meaning their Progress 8 score fell below the floor standard of -0.5, would move out of that category. Eight of the schools would get an average Progress 8 score, and 115 schools would only be "below average" and not below floor standard. The paper, which analysed the Progress 8 scores of the 3,098 secondary schools in the 2016 league tables, also found almost one-fifth would move up or down the national league tables by 500 or more ranks. Four per cent of schools would move more than 1,000 ranks. "Bearing in mind there are only 3,000 secondary schools nationally, these changes are very large indeed," said the report. The researchers, George Leckie and Harvey Goldstein, have now called for the government to publish a league table with their adjusted progress measure, "side-by-side with the current measure" to present a more informative picture of schools' performance. Progress 8 was introduced in 2016 as a new headline accountability measure, designed to measure the improvement that pupils make between their key stage 2 tests and GCSEs. The new research also reveals what happens to progress scores at different types of school, such as university technical colleges and studio schools, when pupils' backgrounds are accounted for. For instance the average score for university technical colleges (UTCs) improves from -0.66 to -0.57 after being adjusted. For studio schools the score improves from -0.90 to -0.71. The report explained that UTCs are disadvantaged in progress measures because 76 per cent of their pupils are boys, who perform worse than girls. Studio schools are put at a disadvantage by teaching a high percentage of SEN pupils (33 per cent), the report found. Meanwhile under the adjusted Progress 8, "the apparent benefit of attending a grammar school is reduced by almost a third", with pupil progress scores dropping from 0.33 to 0.24, according to the research. Grammar schools are especially advantaged by having a low percentage of poor pupils (6.8 per cent) and to a lesser extent SEN pupils (5.6 per cent), while having disproportionately large proportions of pupils from high-progress ethnic groups, said the report. Finally, the average pupil progress in all-girls schools drops from 0.31 to 0.10 when pupil background is accounted for. In contrast, the average pupil progress in all-boys schools increases from 0.15 to 0.19.
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News, Tech OnePlus 8 Release Date Is Closer Than You Think, Could Be Next Month Image: CashKro & OnLeaks OnePlus fans are eagerly awaiting the launch of the OnePlus 8 series. What makes it even more interesting is the rumor that OnePlus could launch a OnePlus 8 Lite, in addition to OnePlus 8 and OnePlus 8 Pro. Popular leakster Ishan Agarwal recently revealed some details about the upcoming OnePlus 8 on Twitter, and it's certainly a piece of good news for OnePlus fans. According to Agarwal, OnePlus 8 could be released sooner than expected. Usually, OnePlus follows a cycle as per which it releases a flagship in May and the T-edition in December. I'm excited for the green. Is it gonna be Olive Green, like the OnePlus 7T was actually supposed to come in? https://t.co/08uo2j1zAU — Ishan Agarwal (@ishanagarwal24) February 9, 2020 This time, we could see OnePlus 8 being released in late March or April if the tweet is to be believed. There is no concrete information about the OnePlus 8 release date yet. Another tidbit that we got about OnePlus 8 is that it could be available in a new green color option for both 8 and 8 Pro. Also Read: List Of OnePlus Devices Receiving OxygenOS 10 (Android 10) Update As per the ongoing OnePlus 8 rumors, we could expect OnePlus 8 to feature Snapdragon 865, a 120Hz refresh rate display, and a revamped camera. A video by TrueTech, which is circulating on the internet, has almost confirmed the OnePlus 8 Pro design. The video shows the 120Hz screen refresh rate and punch-hole camera design. TrueTech OnePlus recently announced that it has plans to bring major upgrades to the camera and videography features on its current and upcoming smartphones. Also, OnePlus recently became a 'full member' of the Wireless Power Consortium. This hints that wireless charging could be one of the key features of OnePlus 8/ 8 Pro. Keep following Fossbytes and we'll update you about the OnePlus 8 release date once it's announced.
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Will Arnett explains that playing Batman in The LEGO Batman Movie allowed him to bend the rules around the character, and make him a little bit goofier while still maintaining his familiar characteristics. He talks about Batman and The Joker's complicated relationship, and how the film explores what might happen if they realized they cannot live without the other. Will shares his excitement upon learning that he would be co-starring with Michael Cera, whom he previously worked with on Arrested Development. Will says that he wants people to come to the film to laugh, to connect to the story, and ultimately, have a good time. The LEGO Batman Movie Clip - "Batman Will Stop You" The LEGO Batman Movie Clip - "Snake Clowns" The LEGO Batman Movie Clip - "Raise Your Son" The LEGO Batman Movie Clip - "I Know Who You Are"
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Q: use apply file list for a function in R I've created this function to get some information from two different files create_distance_to_strand <- function(data, data2, nameCsv) { newData <- data %>% select(seqnames, start, end, V4, seqnames, geneStart, geneEnd, geneStrand, distanceToTSS, SYMBOL, geneLength)%>% rename(peak = V4) joined_df <- merge(newData , closest_dist, by.x = "peak", by.y = "peak", all.x = TRUE, all.y = TRUE) %>% drop_na() write.table(joined_df , nameCsv, sep = "\t") return(joined_df) } closest_dist = read.csv("closest_distance", header = T, sep ="\t") annotation = read.csv("results_annotation", header = T, sep ="\t") myDistanceToStrand <- create_distance_to_strand(annotation, closest_dist, "frame.csv") It works as expected. However, I'm trying to make it more efficient in case I'd have different "closest_dist" files, in order to apply the function to all the files. I've tried this: files <- list.files(pattern = "closest*") proof = lapply(files, create_distance_to_strand(annotation, closest_dist, "proof.csv")) But does not work Error in h(simpleError(msg, call)) : error in evaluating the argument 'y' in selecting a method for function 'merge': object 'closest_dist' not found Any advice? Thank you A: Since you have different closest_dist files which are saved in files, you can use lapply to pass them one by one. We can use an anonymous function here - files <- list.files(pattern = "closest*") proof = lapply(files, function(x) create_distance_to_strand(annotation, x, "proof.csv")) To have a separate output file you may pass different nameCsv value as well. Map(function(x, y) create_distance_to_strand(annotation, x, y), files, sprintf('proof%d.csv', seq_along(files)))
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Who sells jabra evolve 65 uc stereo cheap, the product is a well-liked item this season. this product is a new item sold by Jabra Singapore store and shipped from Singapore. Jabra Evolve 65 UC Stereo is sold at lazada.sg having a very cheap price of SGD266.00 (This price was taken on 23 May 2018, please check the latest price here). what are the features and specifications this Jabra Evolve 65 UC Stereo, let's examine the details below. For detailed product information, features, specifications, reviews, and guarantees or other question that is certainly more comprehensive than this Jabra Evolve 65 UC Stereo products, please go straight to the vendor store that is due Jabra Singapore @lazada.sg. Jabra Singapore can be a trusted seller that already practical knowledge in selling Headphones & Headsets products, both offline (in conventional stores) and internet based. lots of their clients are very satisfied to buy products from your Jabra Singapore store, that may seen with the many five star reviews given by their buyers who have obtained products from the store. So you do not have to afraid and feel concerned about your products or services not up to the destination or not according to what is described if shopping within the store, because has numerous other clients who have proven it. Moreover Jabra Singapore also provide discounts and product warranty returns when the product you get won't match what you ordered, of course using the note they feature. Including the product that we're reviewing this, namely "Jabra Evolve 65 UC Stereo", they dare to give discounts and product warranty returns if the products they offer don't match what's described. So, if you need to buy or seek out Jabra Evolve 65 UC Stereo i then recommend you buy it at Jabra Singapore store through marketplace lazada.sg. Why should you buy Jabra Evolve 65 UC Stereo at Jabra Singapore shop via lazada.sg? Naturally there are many benefits and advantages that you can get when shopping at lazada.sg, because lazada.sg is a trusted marketplace and also have a good reputation that can present you with security from all forms of online fraud. Excess lazada.sg compared to other marketplace is lazada.sg often provide attractive promotions for example rebates, shopping vouchers, free freight, and frequently hold flash sale and support that's fast and that's certainly safe. and what I liked is simply because lazada.sg can pay on the spot, that has been not there in almost any other marketplace.
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La Rastrojero Conosur était une voiture conçue à-partir du châssis de la deuxième génération du petit camion pick-up utilitaire Rastrojero 68, lui aussi produit par la société gouvernementale argentine de construction d'avions (et d'autos) IAME - Industrias Aeronáuticas y Mecánicas del Estado - (Industries aéronautiques et mécaniques de l'État). Caractéristiques Basée sur la version à moteur Diesel de ce dernier, cette automobile destinée à l'usage exclusif des flottes de taxis fut construite de 1974 à 1979, année où toutes les opérations de l'entreprise furent arrêtées. La voiture était esthétiquement assez proche du Rastrojero 68 Diesel à double cabine, exceptée sa partie arrière. En effet, l'endroit où se trouvait normalement le compartiment cargo arrière possédait un coffre dessiné avec une légère pente, abandonnant les lignes assez anguleuses du modèle original. La mécanique était strictement identique à celle du pick-up, moteur Diesel Indenor XD 4.88 fabriqué par Borgward sous licence Peugeot-Ricardo dans la version de DIN, doté d'une injection indirecte Bosch EP/VA et accouplé à une boîte de vitesses manuelle Borgward à 4 rapports. Sa production cessa le , en-même temps que toute la chaîne de montage et les autres produits Rastrojero. Les modèles ont été commercialisés uniquement auprès les flottes de taxis, même si, de nos jours, quelques exemplaires commencent à être restaurés pour être utilisés comme véhicules privés. Références Voir aussi Articles connexes IAME Rastrojero Liens externes Fiches techniques gamme Rastrojero & Conosur. La gamme des modèles IAME Transport routier Automobile des années 1970 IAME
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Celeb Listing NFL superstar's former Central Austin home spirals onto market for $1.89 million Apr 17, 2020 | 3:10 pm Drew Brees may be best known as the quarterback who led the New Orleans Saints to Super Bowl victory in 2010, but he grew up throwing passes in Austin. He perfected his game on the nearly half-acre lot of a four-bedroom, two-bath home in North University, to be more precise. Brees grew up in 3501 Woodrow St., which has now hit the market for $1,890,000 and is represented by Suzanne Pringle of Kuper Sotheby's International Realty "I can just see Drew and his brother throwing passes in the backyard," Pringle told Realtor.com. The 3,000-square foot home was originally built in 1933 but boasts several updates, including central air conditioning, a guesthouse, pool, and enlarged three-car garage. There are still lots of original features, though, from the Craftsman-style wood-burning fireplace in the formal living room to the floor-to-ceiling bookcases in the family room. Original wood floors run throughout, and period-style cabinetry adds a touch of historic charm to the otherwise updated kitchen. "For someone who loves old houses, it still has a lot of the original character," Pringle said. The current owners bought the 3,000-square-foot home from Brees' former stepfather, Harley Clark, in 1993. Clark is best known for introducing the "hook 'em horns" hand signal in 1955, as the University of Texas at Austin's head cheerleader. Born in Dallas, Brees grew up in Austin and, according to Pringle, attended a nearby elementary school. He went on to play football for Westlake High School before heading to college at Purdue. It probably helped that he had all that space on which to run around and play ball on. The park-like backyard features a covered porch, expansive decks, and a gazebo, all backing up to Waller Creek. "It's almost half an acre," says Pringle. "You just never find that in town. It's on the higher end of the [price] range, because of all the land that comes with it." Despite its secluded feel, the home is close to many popular Hyde Park restaurants, a five-minute walk to Russell Lee Elementary School, and only eight blocks from UT. The home was built in 1933 and retains much of its original charm. celebritieshome-for-salesports Donut Worry, Darling Austin donut shop reportedly recovers stolen food truck amid holiday rollercoaster Jan 4, 2023 | 4:07 pm Lots of Austinites had things stolen over the holidays, so they're certainly not alone. At Gourdough's Donuts, the thieves were after more than just the dough; over Christmas, the entire Airstream trailer was removed from its paved home. The company took to social media to ask Austinites to keep their eyes peeled for the glistening donut factory, and it actually worked. Some commenters on the post reported seeing the trailer off of Highway 21 and thinking the location was odd. (Now that the trailer is recovered, donuts in a field sounds like a great way to celebrate.) The post offered a cash reward for information via direct message. News of the recovery was delivered by KVUE's Ford Sanders, who tweeted that the owner had contacted him directly. The donut shop has been quiet since the initial post, wishing people a happy new year on January 1, before Sanders' announcement. Gourdough's is likely eager to leave 2022 behind. The restaurant celebrated a decade simultaneously with its own closure in November, permanently ending brick-and-mortar service at the South Lamar location. Brunch, lunch, and dinner all sold out according to an update on the Instagram announcement. During its tenure, Gourdough's became known for its brazen willingness to put anything on a donut: fried chicken, steak, gravy, eggs, avocado, and, believe it or not, strawberries. Although the dessert donuts are exciting in their own right — often piled high with several toppings outside the sprinkles and glaze mainstream — there is often little need to indulge after the main course. Thankfully for the fried-meats-on-donuts niche, which in Austin is essentially only occupied by this whimsical Austin business, the plan was to keep donuts coming through the original trailer and more mobile locations coming soon. dessertsbrunchlunchdinnerclosings
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Q: What do we call definitions we keep using for objects whose nature has changed? Is there a name for "definitional drift," meaning a word we've used to define something in the past, but the object of definition has changed over time, yet we keep using the same word? For example, "phone." Back in the 80s, we had phones that were connected to walls with cords. Phones were...well, phones. Now, we call the device we carry a "phone," even though it's barely a phone. It's primarily designed to a million things other than make phone calls, and if we list the things we do it by frequency, making or taking a phone call would likely be near the bottom of the list. This is clearly a thing that happens. Is there a name for it? Can you think of other classic examples of it? Edit: another example is when we record video on our phone (ha!), we often say we "taped it," or we "have it on tape." But magnetic tape has nothing to do with it anymore. A: It's a form of semantic drift. Semantic change (also semantic shift, semantic progression, semantic development, or semantic drift) is the evolution of word usage—usually to the point that the modern meaning is radically different from the original usage. - wikipedia In Blank's typology, the semantic drift of phone, for example, looks like it's based on Metonymy: Change based on contiguity between concepts, e.g., horn "animal horn" → "musical instrument". - ibid The meaning of the word "phone" has changed because each stage of the development from voice-call phones to smart phones has retained enough similarity to the previous stage for the name to be broadly recognisable and associated with the new device.
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hey guys just wondering how promising or fulfilling this could become and wanted to know if this is going to be more in demand due to certain music genres on the rise or has it reached its peak ? Hey there, we can only speak on behalf of our experience and thus far, the demand for live visuals in performance events (live music, art, plays, etc.) has increased in demand in recent years. There are environmental factors involved depending on where you live, but it's somewhat becoming expected as part of a "complete" show even in non-electronic music. If you notice a lack of show visuals in your area, it's worth exposing it to enhance events and provide a unique experience for show-goers in an area where it might be lacking. Cheers!
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Breadcrumbs Section. Click here to navigate to respective pages. Computing in the Regulated Environment DOI link for Computing in the Regulated Environment Computing in the Regulated Environment book ByGraham Ogg BookA Practical Guide to Quality Management in Clinical Trial Research Click here to navigate to parent product. First Published 2005 Imprint CRC Press The early eighties was a period of mass adoption of personal computers, and the enthusiasm continues. The main difference today is that they are cheaper and more powerful. Many instruments of that time, such as the HPLC machines, used the microcomputer to control such things as gradient elution. Today, most such instruments have their logic and processor units built into them. The electronic revolution has provided us with the paperless office that we were promised back then. Taylor & Francis Group Logo Taylor & Francis Online CogentOA Taylor & Francis Group Students/Researchers Librarians/Institutions Registered in England & Wales No. 3099067 5 Howick Place | London | SW1P 1WG© 2022 Informa UK Limited
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Tag: Apollo Emma's Anticipated Treasures, Most Anticipated 2023 – Historic & Gothic Delights Post date 6th Jan 2023 No Comments on Emma's Anticipated Treasures, Most Anticipated 2023 – Historic & Gothic Delights Historical and gothic fiction is, for me, a joint favourite genre with thrillers. So I'm very excited about the books on today's list. What do you think of my choices? A Marriage of Fortune by Anne O'Brien England. 1469. A fortunate marriage will change history. A scandal could destroy everything… Margaret Paston, matriarch of the Paston family, knows that a favourable match for one of her unruly daughters is the only way to survive the loss of their recently acquired Caister Castle. But as the War of the Roses rages on, dangerous enemies will threaten even her best laid plans. Margery Paston, her eldest daughter, has always strived to uphold the Paston name and do her mother proud. But when she loses her heart to a man below her station, she must make a terrible choice: will she betray her family and risk everything for a chance at true love? Anne Haute, first cousin to the Queen, is embroiled in a longstanding betrothal to Sir John Paston, the eldest son and heir to the Paston seat. But despite his promises, Anne can't help but doubt that he will ever keep his word and make her his wife… In the midst of civil war, each of these women must decide: Head or heart? Love or duty? Reputation- or scandal? Published January 19th by Orion Pre-order here* The Whispering Muse by Larua Purcell Be careful what you wish for… it may just come true. At The Mercury Theatre in London's West End, rumours are circulating of a curse. It is said that the lead actress Lilith has made a pact with Melpomene, the tragic muse of Greek mythology, to become the greatest actress to ever grace the stage. Suspicious of Lilith, the jealous wife of the theatre owner sends dresser Jenny to spy on her, and desperate for the money to help her family, Jenny agrees. What Jenny finds is a woman as astonishing in her performance as she is provocative in nature. On stage, it's as though Lilith is possessed by the characters she plays, yet off stage she is as tragic as the Muse who inspires her, and Jenny, sorry for her, befriends the troubled actress. But when strange events begin to take place around the theatre, Jenny wonders if the rumours are true, and fears that when the Muse comes calling for payment, the cost will be too high. Published February 2nd by Raven The Snow Hare by Paula Lichtarowicz Lena has her life mapped out. While her sister obsesses about fortune-telling gypsies and marriage, Lena studies the way the heart works. She isn't going to let being a girl stop her from becoming one of Poland's first female doctors. But the world has other plans for Lena. Instead of university she finds herself a reluctant army wife, lonely and unmoored by the emotions of motherhood. And as she tries to accept a different future from the one she wanted, the threat of global war becomes reality. Lena must face just how unpredictable life can be. Deemed Enemies of State by the invading Soviets, she and her family are exiled from their Polish village to a work camp in the freezing hell of Siberia. It's here, despite the hunger and back-breaking work, Lena learns something remarkable; it is possible to fall in love even at the edge of life. And for that love, Lena must make a decision, the consequences of which will haunt her for ever. Tender, brutal and passionate, The Snow Hare is about living with impossible choices and our incredible ability to cultivate hope in the darkest places. Published February 2nd by John Murray Press A Gift of Poison by Bella Ellis (The Bronte Mysteries 4) Haworth 1847 – Anne and Emily Brontë have had their books accepted for publication, while Charlotte's has been rejected everywhere, creating a strained atmosphere at the parsonage. At the same time, a shocking court case has recently concluded, acquitting a workhouse master of murdering his wife by poison. Everyone thinks this famously odious and abusive man is guilty. However, he insists he is many bad things but not a murderer. When an attempt is made on his life, he believes it to be the same person who killed his wife and applies to the detecting sisters for their help. Despite reservations, they decide that perhaps, as before, it is only they who can get to the truth and prove him innocent – or guilty – without a shadow of doubt. Published February 9th by Hodder & Stoughton The Shadow of Perseus by Claire Heywood The myth of Perseus, told through the story of the three women who knew him best – his mother Danae, his wife Andromeda, and his victim, Medusa. History remembers him as a hero. But the women who knew him best remember a different man… Perseus grows up wanting to be a hero, but he cannot become one if his mother Danae still sees him as a boy. When his stepfather Polydektes casts him away on a voyage across the sea, Perseus is determined to fulfil the great destiny of the son of a god and the grandson of a king. But the line between heroism and monstrosity is thin, and when Perseus attempts to seduce first gentle Medusa and then beautiful Andromeda, before finally reuniting with Danae, they each learn of the dangers of resisting a boy prepared to risk it all for greatness . . . Published February 21st by Hodder & Stoughton The Book of Eve by Meg Clothier In the name of the Father, not a word of this. Her letters are forbidden. Beatrice is the convent's librarian. For years, she has shunned the company of her sisters, finding solace only with her manuscripts. Then, one carnival night, two women, bleeding and stricken, are abandoned outside the convent's walls. Moments from death, one of them presses something into Beatrice's hands: a bewitching book whose pages have a dangerous life of their own. But men of the faith want the book destroyed, and a zealous preacher has tracked it to her door. Her sisters' lives – or her obsession. Beatrice must decide. The book's voice is growing stronger. An ancient power uncoils. Will she dare to listen? Published March 2nd by Wildfire The Londonn Seance Society by Sarah Penner From the author of the intoxicating bestseller The Lost Apothecary comes an entrancing exploration of the blurred lines between truth and illusion and the grave risks women take to avenge the ones they love. May mercy be upon the man who finds himself the enemy of a vengeful medium… 1873. At an abandoned château on the outskirts of Paris, a dark séance is about to take place, led by acclaimed spiritualist Vaudeline D'Allaire. Known worldwide for her talent in conjuring the spirits of murder victims to ascertain the identities of the people who killed them, she is highly sought after by widows and investigators alike. Lenna Wickes has come to Paris to find answers about her sister's death, but to do so, she must embrace the unknown and overcome her own logic-driven bias against the occult. When Vaudeline is beckoned to England to solve a high-profile murder, Lenna accompanies her as an understudy. But as the women team up with the powerful men of London's exclusive Séance Society to solve the mystery, they begin to suspect that they are not merely out to solve a crime, but perhaps entangled in one themselves… Published March 21st by Legend Press The Lodger by Helen Scarlett This second novel from the author of The Deception of Harriet Fleet takes us back to the aftermath of the Great War in another haunting, atmospheric Gothic tale. London in 1919 was a city of ghosts and absences, haunted by the men who marched away but never came back from 'the war to end all wars.' Grace Armstrong believes that she has come to terms with her own loss, the death of her fiancé, the brilliant and dazzling best friend of her brother. He was declared Missing in Action during the Battle of the Somme, but he starts to reappear both in her waking life and dreams. Grace is appalled when a body, dragged from the Thames, is identified as Elizabeth Smith, who has lodged with Grace and her family for the last eight years before suddenly disappearing. Elizabeth had been more than a lodger; she had become a close friend to Grace, who feels compelled to find out what happened. In doing so she is drawn reluctantly into the sordid and dangerous underbelly of London and a scandal that rocked Edwardian society. Soon Grace finds herself under threat, and the only person prepared to listen is the brooding Tom Monaghan. But Tom has dark shadows of his own to navigate before being able to put his past behind him to help Grace in her quest for the truth. Published March 23rd by Quercus The Valkyrie by Kate Heartfield From SUNDAY TIMES bestselling author Kate Heartfield comes a glorious, lyrical retelling of one of Norse mythology's greatest epics Brynhild is a Valkyrie: shieldmaiden of the Allfather, chooser of the slain. But now she too has fallen, flightless in her exile. Gudrun is a princess of Burgundy, a daughter of the Rhine, a prize for an invading king – a king whose brother Attila has other plans, and a dragon to call upon. And in the songs to be sung, there is another hero: Sigurd, a warrior with a sword sharper than the new moon. As the legends tell, these names are destined to be lovers, fated as enemies. But here on Midgard, legends can be lies… For not all heroes are heroic, nor all monsters monstrous. And a shieldmaiden may yet find that love is the greatest weapon of all. Kate Heartfield's book 'The Embroidered Book' was a Sunday Times bestseller w/c 14-02-2022. Published March 30th by HarperVoyager The House of Whispers by Anna Mazzola A creepy, chilling story – another Anna Mazzola triumph!' JENNIFER SAINT Sometimes the secrets of the past are more dangerous than the present… Rome, 1938. As the world teeters on the brink of war, talented pianist Eva Valenti enters the house of widower Dante Cavallera to become his new wife. On the outside, the forces of Fascism are accelerating, but in her new home, Eva fears that something else is at work, whispering in the walls and leaving mysterious marks on Dante's young daughter. Soon she starts to wonder whether the house itself is trying to give up the secrets of its mysterious past – secrets that Dante seems so determined to keep hidden. However, Eva must also conceal the truth of her own identity, for if she is discovered, she will be in greater danger than she could ever have imagined… Published April 6th by Orion Atalanta by Jennifer Saint The mesmerising story of the only female Argonaut, told by Jennifer Saint, the bestselling author of ELEKTRA and ARIADNE . When a daughter is born to the King of Arcadia, she brings only disappointment. Left exposed on a mountainside, the defenceless infant Atalanta is left to the mercy of a passing mother bear and raised alongside the cubs under the protective eye of the goddess Artemis. Swearing that she will prove her worth alongside the famed heroes of Greece, Atalanta leaves her forest to join Jason's band of Argonauts. But can she carve out her own place in the legends in a world made for men? Published April 13th by Widlfire From the bestselling author of The Clockmaker's Daughter, Kate Morton, comes a breathtaking mystery of love, lies and a cold case come back to life, told with her trademark intricacy and beauty. Adelaide Hills, Christmas Eve, 1959. At the end of a scorching hot day, beside a creek in the grounds of a grand and mysterious mansion, a local delivery man makes a terrible discovery. A police investigation is called and the small town of Tumbilla becomes embroiled in one of the most shocking and perplexing murder cases in the history of South Australia. Sixty years later, Jess is a journalist in search of a story. Having lived and worked in London for almost twenty years, she now finds herself laid off from her full-time job and struggling to make ends meet. A phone call out of nowhere summons her back to Sydney, where her beloved grandmother, Nora, who raised Jess when her mother could not, has suffered a fall and been raced to the hospital. At a loose end in Nora's house, Jess does some digging into her past. In Nora's bedroom, she discovers a true crime book, chronicling the police investigation into a long-buried tragedy: the Turner Family Tragedy of Christmas Eve, 1959. It is only when Jess skims through the book that she finds a shocking connection between her own family and this once-infamous crime – a crime that has never been truly solved. And for a journalist without a story, a cold case might be the best distraction she can find . . . An epic novel that spans generations, Homecoming asks what we would do for those we love, and how we protect the lies we tell. It explores the power of motherhood, the corrosive effects of tightly held secrets, and the healing nature of truth. Published April 13th by Mantle Prize Women by Caroline Lea The gripping and unforgettable new novel from Caroline Lea, based on one of history's most shocking but largely untold scandals 'Gorgeous. Prize Women . . . took my breath away. I haven't stopped thinking about it' JENNIFER SAINT, bestselling author of ARIADNE Masterful. Caroline Lea is a superb storyteller, and Prize Women deserves a huge readership. So good, I had to pull myself away' ELIZABETH MACNEAL, bestselling author of THE DOLL FACTORY Toronto, Canada, 1926 Best friends Lily di Marco and Mae Thebault were once inseparable. They lived under the same roof and cared for each other's children. But with mouths to feeds and demanding husbands to keep happy, both women are forced into terrible decisions as the Great Depression tightens its grip. When lawyer Charles Vance Miller's will promises a handsome sum of money to the woman who can produce the most babies in the next ten years, it is initially dismissed as a vanity project. But as the Great Depression worsens, and times get increasingly tough across the world, for the most desperate in society this contest known as The Great Stork Derby suddenly seems like a way out. Ten years later, Lily and Mae couldn't be further apart. And as The Great Stork Derby continues to make headlines, for all the wrong reasons, both these women must face up to their part in it, and the consequences… Published April 27th by Michael Joseph The Woman on the Bridge by Sheila O'Flanagan A stunning historical novel from multi-million-copy bestselling author Sheila O'Flanagan Dublin. The 1920s. As war tears Ireland apart, two young people are caught up in events that will bring love, tragedy – and the hardest of choices. In a country fighting for freedom, it's hard to live a normal life. Winnie O'Leary supports the cause, but she doesn't go looking for trouble. Then rebel Joseph Burke steps into her workplace. Winnie is furious with him about a broken window. She's not interested in romance. But love comes when you least expect it. Joseph's family shelter fugitives and transport weapons. Joseph would never ask Winnie to join the fight; but his mother and sisters demand commitment. Will Winnie choose Joseph, and put her own loved ones in deadly danger? Or wait for a time of peace that may never come? Ireland's tumultuous independence struggle is the backdrop for an unforgettable story of courage and heartbreak, in which heroes are made of ordinary people. Inspired by the story of Sheila O'Flanagan's grandmother, The Woman on the Bridge is the unmissable, compulsive new novel from a bestselling author. Published April 27th by Headline Review A Lady's Guide to Scandal by Sophie Irwin The captivating new historical novel from the author of the Sunday Times bestseller A Lady's Guide to Fortune-Hunting Pre-order the most delightful, escapist historical of the year from the Sunday Times bestselling author! Recently widowed from her marriage of convenience, Eliza, now Dowager Countess of Somerset, is bequeathed a fortune, hers to keep as long as she can steer clear of scandal. It should be simple – Eliza has spent a lifetime following the rules – but now that she is rich, titled and independent, misbehaviour is much more tempting… Published May 11th by Harper Collins The Ghost Theatre by Mat Osman TO LOVE IS TO FALL . . . On a rooftop in Elizabethan London two worlds collide. Shay is a messenger-girl and trainer of hawks who sees the future in the patterns of birds. Nonesuch is the dark star of the city's fabled child theatre scene, as famous as royalty yet lowly as a beggar. Together they create The Ghost Theatre: a troupe staging magical plays in London's hidden corners. As their hallucinatory performances incite rebellion among the city's outcasts, the pair's relationship sparks and burns against a backdrop of the plague and a London in flames. Their growing fame sweeps them up into the black web of the Elizabethan court, where Shay and Nonesuch discover that if they fly too high, a fall is sure to come. Fantastical and captivating, The Ghost Theatre charts the rise and dramatic destruction of a dream born from love and torn apart by betrayal. Published May 11th by Bloomsbury Stealing by Margaret Verble A gripping, gut-punch of a novel about a Cherokee child removed from her family and sent to a Christian boarding school in the 1950s—an ambitious, eye-opening reckoning of history and small-town prejudices from Pulitzer Prize finalist Margaret Verble. Since her mother's death, Kit Crockett has lived with her grief-stricken father, spending lonely days far out in the country tending the garden, fishing in a local stream, and reading Nancy Drew mysteries from the library bookmobile. One day when Kit discovers a mysterious and beautiful woman has moved in just down the road, she is intrigued. Kit and her new neighbor Bella become fast friends. Both outsiders, they take comfort in each other's company. But malice lurks near their quiet bayou and Kit suddenly finds herself at the center of tragic, fatal crime. Soon, Kit is ripped from her home and Cherokee family and sent to Ashley Lordard, a religious boarding school. Along with the other Native students, Kit is stripped of her heritage, force-fed Christian indoctrination, and is sexually abused by the director. But Kit, as strong-willed and shrewd as ever, secretly keeps a journal recounting what she remembers—and revealing just what she has forgotten. Over the course of Stealing, she slowly unravels the truth of how she ended up at the school—and plots a way out. In swift, sharp, and stunning prose, Margaret Verble spins a powerful coming-of age tale and reaffirms her place as an indelible storyteller and chronicler of history. Vita and the Birds by Polly Crosby A haunting mystery for fans of Eve Chase, Kate Morton and Kate Mosse. 1938: Lady Vita Goldsborough lives in the shadow of her controlling older brother, Aubrey. Trapped and isolated on the East Anglian coast, Vita takes solace in watching the birds that fly over the marshes. But then she meets local artist Dodie Blakeney. The two women form a close bond, and Vita finally glimpses a chance to escape Aubrey's grasp and be as free as the birds she loves. 1997: Decades later and in the wake of her mother's death, Eve Blakeney returns to the coast where she spent childhood summers with her beloved grandmother, Dodie. Eve hopes the visit will help make sense of her grief. The last thing she expects to find is a bundle of letters that hint at the heart-breaking story of Dodie's relationship with a woman named Vita. Eve and Vita's stories are linked by a shattering secret that echoes through the decades, and when Eve discovers the truth, it will overturn everything she thought she knew about her family – and change her life forever. Published May 25th by HQ Mrs Porter Calling by AJ Pearce (The Emmy Lake Chronicles) The heartwarming, moving and uplifting new story of friendship, love and finding courage when all seems lost from AJ Pearce, TheSunday Times bestselling author of Dear Mrs Bird and Yours Cheerfully. London, April 1943. Emmy Lake is an agony aunt at Woman's Friend magazine, doing all she can to help readers as they face the challenges of wartime life. With her column thriving and a team of women behind her, Emmy finally feels she is Doing Her Bit. But when the glamourous new owner arrives, everything changes. Charming her way around editor Guy Collins, Emmy quickly realises the Honourable Mrs Cressida Porter plans to destroy everything readers love about the magazine. With her best friends by her side, Emmy must work out how she can bring everyone together and save Woman's Friend before it's too late. Published May 25th by Picador Hokey Pokey by Kate Mascarenhas A grand hotel, a famous opera star and a psychoanalyst with a hidden agenda. Kate Mascarenhas's third novel offers her readers a glamorous, thrilling ride through murder, madness and the darkest recesses of the mind. February, 1929. The Regent Hotel in Birmingham is a place of deception and glamour. Behind its six-storeyed façade, guests sip absinthe cocktails on velvet banquettes, while the hotel's red-jacketed staff scurry through its lavish corridors to ensure the finest service is always at hand. In the early evening, a psychoanalyst checks in under a pseudonym: Nora Dickinson. Nora is young, diligent and ambitious. Though she doesn't see herself as a liar, she is travelling with an agenda. Having followed the famous opera singer, Berenice Oxbow, from Zurich to Birmingham, she's determined not to let her out of her sight. But when a terrible snow storm isolates the hotel – and its guests – from the outside world, the lines between nightmare and reality begin to blur… Published June 8th by Apollo The Good Liars by Anita Frank From the author of stunning historical fiction books comes a new story of crime, deceit, and murder, set in the early 1920s… In the hot summer of 1914 a boy vanishes, never to be seen again. Now, in 1920, the once esteemed Stilwell family of Darkacre Hall find their already troubled lives thrown into disarray when new evidence leads to the boy's case being reopened – and this time they themselves are under police scrutiny. As the dead return to haunt the living, old resentments resurface and loyalties are tested, while secrets risk being unearthed that could destroy them all. Published June 8th by HQ The Fascination by Essie Fox Exploring universal themes of love and loss, the power of redemption and what it means to be unique,The Fascination is an evocative,glittering and bewitching gothic novel that brings alive Victorian London and darkness and deception that lies beneath… Victorian England. A world of rural fairgrounds and glamorous London theatres. A world of dark secrets and deadly obsessions… Twin sisters Keziah and Tilly Lovell are identical in every way, except that Tilly hasn't grown a single inch since she was five. Coerced into promoting their father's quack elixir as they tour the country fairgrounds, at the age of fifteen the girls are sold to a mysterious Italian known as 'Captain'. Theo is an orphan, raised by his grandfather, Lord Seabrook, a man who has a dark interest in anatomical freaks and other curiosities … particularly the human kind. Resenting his grandson for his mother's death in childbirth, when Seabrook remarries and a new heir is produced, Theo is forced to leave home without a penny to his name. Unable to train to be a doctor as he'd hoped, Theo finds employment in Dr Summerwell's Museum of Anatomy in London, and here he meets Captain and his theatrical 'family' of performers, freaks and outcasts. But it is Theo's fascination with Tilly and Keziah that will lead all of them into a web of dark deceits, exposing the darkest secrets and threatening everything they know… Exploring universal themes of love and loss, the power of redemption and what it means to be unique, The Fascination is an evocative, glittering and bewitching gothic novel that brings alive Victorian London and darkness and deception that lies beneath… Published June 22nd by Orenda Books The Square of Sevens by Laura Shepherd-Robinson 'The queen of the historical crime novel' – CJ Tudor 'My father had spelt it out to me. Choice was a luxury I couldn't afford. This is your story, Red. You must tell it well . . .' A girl known only as Red, the daughter of a Cornish fortune-teller, travels with her father making a living predicting fortunes using the ancient method: the Square of Sevens. When her father suddenly dies, Red becomes the ward of a gentleman scholar. Now raised as a lady amidst the Georgian splendour of Bath, her fortune-telling is a delight to high society, but she cannot ignore the questions that gnaw at her soul: who was her mother? How did she die? And who are the mysterious enemies her father was always terrified would find him? The pursuit of these mysteries takes her from Cornwall and Bath to London and Devon, from the rough ribaldry of the Bartholemew Fair to the grand houses of two of the most powerful families in England. And while Red's quest brings her the possibility of great reward, it also leads into her grave danger . . . Laura Shepherd-Robinson's The Square of Sevens is an epic and sweeping novel set in Georgian high society, a dazzling story offering up mystery, intrigue, heartbreak, and audacious twists. Published June 22nd by Mantle The Birdcage Library by Freya Berry A mystery lies hidden within an old book… Unlock the secrets of The Birdcage Library. 'Gothic, gorgeous and vividly atmospheric; an immersive literary page-turner to be swept up in' Ellery Lloyd, New York Times bestselling author A rich, beguiling story of long-buried secrets and dark obsession, The Birdcage Library is the dazzling new novel from Freya Berry, author of The Dictator's Wife, as seen on BBC2 Between the Covers. Dear Reader, the man I love is trying to kill me… Emily Blackwood, adventuress and plant hunter, travels north for a curious new commission. A gentleman has written to request she catalogue his vast collection of taxidermied creatures before sale. On arrival, Emily finds a ruined castle, its owner haunted by a woman who vanished years before. And when she discovers the ripped pages of a diary, crammed into the walls, she realises dark secrets lie here, waiting to entrap her too…. Discover a mystery within a mystery in The Birdcage Library, a novel that will hold you in its spell until the final page. Published June 22nd by Headline The Illusions by Liz Hyder At a time of extraordinary change, two women must harness their talents to take control of their own destiny . . . Bristol, 1896. Used to scraping a living as the young assistant to an ageing con artist, Cecily Marsden's life is turned upside down when her master suddenly dies. Believing herself to blame, could young Cec somehow have powers she little understands? Meanwhile Eadie Carleton, a pioneering early film-maker, struggles for her talent to be taken seriously in a male-dominated world, and a brilliant young magician, George Perris, begins to see the potential in moving pictures. George believes that if he can harness this new technology, it will revolutionise the world of magic forever – but in order to achieve his dreams, he must first win over Miss Carleton . . . As a group of illusionists prepare for a grand spectacle, Cec, Eadie and George's worlds collide. But as Cec falls in love with the bustling realm of theatre and magic, she faces the fight of her life to save the performance from sabotage and harness the element of real magic held deep within her. THE ILLUSIONS is the captivating new novel from the much-lauded author of THE GIFTS. Inspired by real-life illusionists and early film pioneers, this astonishing story of women and talent, magic and power, sweeps you into a world where anything is possible and nothing is quite as it seems . . . Published June 22nd by Manilla Press 73 Dove Street by Julie Owen Moylan When Edie Budd arrives at a shabby West London boarding house in October 1958, carrying nothing except a broken suitcase and an envelope full of cash, it's clear she's hiding a terrible secret. And she's not the only one; the other women of 73 Dove Street have secrets of their own . . . Tommie, who lives on the second floor, waits on the eccentric Mrs Vee by day. After dark, she harbours an addiction to seedy Soho nightlife – and a man she can't quit. Phyllis, 73 Dove Street's formidable landlady, has set fire to her husband's belongings after discovering a heart-breaking betrayal – yet her fierce bravado hides a past she doesn't want to talk about. At first, the three women keep to themselves. But as Edie's past catches up with her, Tommie becomes caught in her web of lies – forcing her to make a decision that will change everything . . . Published July 20th by Michael Joseph The Only One Left by Riley Sager Bestselling author Riley Sager returns with a Gothic chiller about a young caregiver assigned to work for a woman accused of a Lizzie Borden-like massacre decades earlier. At seventeen, Lenora Hope Hung her sister with a rope Now reduced to a schoolyard chant, the Hope family murders shocked the Maine coast one bloody night in 1929. While most people assume seventeen-year-old Lenora was responsible, the police were never able to prove it. Other than her denial after the killings, she has never spoken publicly about that night, nor has she set foot outside Hope's End, the cliffside mansion where the massacre occurred. Stabbed her father with a knife Took her mother's happy life It's now 1983, and home-health aide Kit McDeere arrives at a decaying Hope's End to care for Lenora after her previous nurse fled in the middle of the night. In her seventies and confined to a wheelchair, Lenora was rendered mute by a series of strokes and can only communicate with Kit by tapping out sentences on an old typewriter. One night, Lenora uses it to make a tantalizing offer–I want to tell you everything. Published July 20th by Dutton Fair Rosaline by Natasha Solomons BEFORE ROMEO LOVED JULIET, HE LOVED FAIR ROSALINE . . . Was the greatest ever love story really a lie? Romeo Montague is handsome and charming and the first time he sees young Rosaline Capulet, who has secretly snuck into his family's masquerade summer ball, he falls instantly in love. At first Rosaline is unsure of Romeo's attentions but with her father determined that she join the nunnery, Romeo offers her the chance of a different life. Gradually he convinces her that only true love could make him feel this way, that he is enraptured by her beauty. Indeed, he cannot live without her! And so begins the story of Romeo and Rosaline. These star-crossed lovers must keep everything hidden from Rosaline's family, at least until they are wed. But when a destitute young girl appears, claiming to be carrying Romeo's child, Rosaline starts to doubt all that she has been told. And as whispers of more girls reach her ears, what once felt like a courtship begins to feel more like a pursuit. As Rosaline recognises Romeo for the villain he truly is, his gaze turns suddenly towards Rosaline's adored and beautiful cousin, thirteen-year old Juliet. Can Rosaline save Juliet from her Romeo? Or can this story only ever end one way . . ? Hamnet meets My Dark Vanessa in this fierce, feminist, intensely gripping, unmissable novel; captivating and chillingly relevant, FAIR ROSALINE takes everything you thought you knew about Romeo and Juliet and turns it on its head . . . Published August 3rd by Manilla Press House of Odysseus by Claire North 'CLAIRE NORTH BRINGS A POWERFUL, FRESH AND UNFLINCHING VOICE TO ANCIENT MYTH' Jennifer Saint, author of Sunday Times bestseller Ariadne Following the critically acclaimed Ithaca comes House of Odysseus, the second novel in Claire North's Songs of Penelope trilogy – an exquisite, gripping tale that breathes life into ancient myth. This is the story of Penelope of Ithaca, famed wife of Odysseus, as it has never been told before. On the island of Ithaca, queen Penelope maintains a delicate balance of power. Many years ago, her husband Odysseus sailed to war with Troy and never returned. In his absence, Penelope uses all her cunning to keep the peace – but this is shattered with the arrival of Orestes, King of Mycenae. Orestes, son of Agamemnon, is mad. Wracked with guilt for putting his own mother to death, he grows ever more unhinged. But a king cannot be seen to be weak. To keep him safe from the ambitious men of Mycenae, his sister Elektra brings him to Ithaca to recover under the protection of Penelope. But no sooner has Orestes arrived then his uncle Menelaus, the blood-soaked king of Sparta, comes looking for him. Menelaus hungers for Orestes' throne – and if he can seize it, no one will be safe from his violent whims. Caught between Sparta and Mycenae, Penelope must protect Ithaca from two mad kings on the edge of war. Her only allies are Elektra, desperate to protect her brother, and Helen of Troy, Menelaus' wife. Each woman has a secret, and their secrets will shape the world . . . Published August 24th by Orbit Learned by Heart by Emma Donoghue Inspired by the real-life diaries of Eliza Raine and Anne Lister – 'the first modern lesbian,' also known as Gentleman Jack – Donoghue's mesmerising historical novel is a tour de force of rich characterisation and period detail. Published August 24th by Pan Macmillan The Black Feathers by Rebecca Netley PRE ORDER THE NEXT CHILLING AND TWISTY GHOST STORY FROM THE AUTHOR OF THE WHISTLING Where ghosts tread, black feathers fall . . . When Annie marries widower Edward Stonehouse and arrives at Guardbridge, his estate on the Yorkshire moors, she thinks she has finally put darkness behind her. She is mistaken. Edward's sister, Iris, still lives in the family home. A taxidermist and medium, she urges Annie to watch out for black feathers – claiming that they mark the spot where a spirt has visited. At first, Annie dismisses her warnings. But, before long, she begins to feel haunted. What exactly happened to Edward's first wife? Why is Iris so disturbed? And should Annie really be watching for signs from the dead – or is she the one being watched? SET ON THE YORKSHIRE MOORS IN THE 1800S, THE BLACK FEATHERS IS A GHOSTLY TALE OF MAGIC AND WICKEDNESS. Published October 12th by Michael Joseph The Temple of Fortuna by Elodie Harper (The Wolf Den Triolgy 3) The final instalment in Elodie Harper's Sunday Times bestselling Wolf Den Trilogy 'Beautiful, moving, captivating.' Jennifer Saint 'Vivid, unsentimental and compelling.' The Times Amara's journey has taken her far; from a slave in Pompeii's wolf den to a high-powered courtesan in Rome… though her story is not over yet. While Amara plays for power in Rome's imperial palace, those dearest to her remain in Pompeii. But it is AD 79, and mighty Mount Vesuvius is about to make itself known… Published November 23rd by Apollo Tags 73 Dove Street, A Gift of Poison, A Marriage of Fortune, AJ Pearce, Anita Frank, Anna Mazzola, Anne O'Brien, Apollo, Atalanta, Bella Ellis, Bloomsbury, Caroline Lea, Claire Heywood, Claire North, Dutton, Elodie Harper, Emma Donoghue, Essie Fox, Freya Berry, Harper Collins UK, Harper Voyager, Head of Zeus, Headline, Headline Review, Helen Scarlett, Hodder & Stoughton, Hokey Pokey, Homecoming, House of Odysseus, HQ, Jennifer Saint, John Murray Press, Julie Owen Moylan, Kate Heartfield, Kate Mascerenhas, Kate Morton, Laura Purcell, Laura Shepherd-Robinson, Learned By Heart, Liz Hyder, Manilla Press, Mantle, Margaret Verble, Mat Osman, Meg Clothier, Michael Joseph, Mrs Porter Calling, Natasha Solomons, Orbit, Orenda Books, Orion, Paula Lichtarowicz, Picador, Polly Crosby, Prize Women, Quercus, Raven, Rebecca Netley, Riley Sager, Sarah Penner, Sheila O'Flanagan, Sophie Irwin, Stealing, The Birdcage Library, The Black Feathers, The Book of Eve, The Bronte Mysteries, The Emmy Lake Chronicles, The Fascination, The Ghost Theare, The Good Liars, The House of Whispers, The Illusions, The Lodger, The London Seance Society, The Only One Left, The Shadow of Perseus, The Snow Hare, The Square of Sevens, The Temple of Fortuna, The Valkyrie, The Whispering Muse, The Wolf Den Series, The Woman on the Bridge, Vita and the Birds, Wildfire Emma's Anticipated Treasures – November 2022 Post date 22nd Oct 2022 1 Comment on Emma's Anticipated Treasures – November 2022 We're edging closer to the end of the year and the number of releases is slowling down a little, but there are still a number of exciting books to look forward to. Here are the ones I'm most excited about being released next month. The Prisoner by B. A. Paris Published: November 3rd Genre: Psychological Thriller, Suspense Secrets. Suspicion. Survival. No one writes relationships better than B.A. PARIS Amelie has always been a survivor, from losing her parents as a child in Paris to making it on her own in London. As she builds a career for herself in the magazine industry, she meets, and agrees to marry, Ned Hawthorne. Amelie wakes up in a pitch-black room, not knowing where she is. Why has she been taken? Who are her mysterious captors? And why does she soon feel safer here, imprisoned, than she had begun to feel with her husband Ned? In true B.A. Paris style, The Prisoner is a gripping survival story, a twisted love story and at its dark heart a thriller to keep you up all night. The Book of the Most Precious Substance by Sara Gran Publisher: Faber & Faber Genre: Thriller, Psychological Thriller, Paranormal Fiction A book with all of life's answers, if only you can find it… 'Extravagant, sexy and compelling. I loved it.' LAUREN BEUKES Rare book dealer Lily Albrecht has just been given a tip-off about The Book of the Most Precious Substance, a 17th century manual rumoured to be the most powerful occult book ever written, if it really exists at all. With some of the wealthiest people in the world willing to pay Lily a fortune to track it down, she embarks on a journey from New York to New Orleans to Munich to Paris. If she finds it, Lily stands to gain more than just money. This could erase the greatest tragedy of her life. But will Lily's quest help her find some answers, or will she lose everything in search of a ghost? The Ones We Burn by Rebecca Mix Published: November 8th Genre: Fantasy Fiction, Dark Fantasy, High Fantasy I am the monster. I am the shield. I am the knife in the dark. Ranka is tired of death. All she wants now is to be left alone, living out her days in Witchik's wild north with the coven that raised her, attempting to forget the horrors of her past. But when she is named Bloodwinn, the next treaty bride to the human kingdom of Isodal, her coven sends her south with a single directive: kill him. Easy enough, for a blood-witch whose magic compels her to kill. Except the prince is gentle, kind, and terrified of her. He doesn't want to marry Ranka; he doesn't want to be king at all. And it's his sister – the wickedly smart, infuriatingly beautiful Princess Aramis – who seems to be real threat. But when witches start turning up dead, murdered by a mysterious, magical plague, Aramis makes Ranka an offer: help her develop a cure, and in return, she'll teach Ranka to contain her deadly magic. But as the coup draws nearer and the plague spreads, Ranka is forced to question everything she thought she knew about her power, her past, and who she's meant to fight for. Soon, she will have choose between the coven that raised her – and the princess who sees beyond the monster they shaped her to be. But as the bodies pile up, a monster may be exactly what they need. Dawnlands by Philippa Gregory (Fairmile Series Book 3) Genre: Historical Fiction, Myths, Fairy Tale, Domestic Fiction The spellbinding Fairmile series continues as the fiercely independent Alinor and her family find themselves entangled in palace intrigue, political upheaval, and life-changing secrets in seventeenth-century England. It is 1685, England is on the brink of a renewed civil war against the Stuart kings and many families are bitterly divided. Ned Ferryman cannot persuade his sister Alinor that he is right to return from America with his Pokanoket servant Rowan to join the rebel army. Instead, Alinor has been coaxed by the manipulative Livia to save the queen from the coming siege. The rewards are life-changing: the family could return to their beloved Tidelands, and Alinor could rule where she was once lower than a servant. Alinor's son, Rob, is determined to stay clear of the war, but when he and his nephew set out to free Ned from execution for treason and Rowan from a convict deportation to Barbados, they find themselves enmeshed in the creation of an imposter Prince of Wales – a surrogate baby to the queen. From the last battle in the desolate Somerset Levels to the hidden caves on the slave island of Barbados, this third volume of an epic story follows a family from one end of the empire to another, to find a new dawn in a world which is opening up before them with greater rewards and dangers than ever before. Heart of the Sun Warrior by Sue Lynn Tan (The Celestial Kingdom Book 2) Published: November 10th Genre: Fairy Tale, High Fantasy, Historical Fantasy, Myths & Legends, Fantasy Series The stunning conclusion to the Celestial Kingdom Duology An unspeakable terror is sweeping across the realm as the Celestial Emperor tightens his grip on power. The fragile peace Xingyin fought so hard for when freeing her mother is under threat. Forced to flee her home, Xingyin ventures into the unexplored lands of the Immortal Realm to seek aid in her fight, but, with alliances shifting quicker than the tides, she has to overcome past grudges and enmities to forge a new path forward, seeking aid where she never imagined. Xingyin must uncover the truth of her heart and claw her way through devastation – to rise against evil before it destroys everything she holds dear, and the worlds she has grown to love … even if doing so demands the greatest price of all. The stunning sequel to the Sunday Times bestselling Daughter of the Moon Goddess delves deeper into beloved Chinese mythology, concluding the epic story of Xingyin – the daughter of Chang'e and the mortal archer Houyi – as she battles a grave new threat to the realm, in this powerful tale of love, sacrifice, and hope. Murder on the Christmas Express by Alexandra Benedict Genre: Mystery, Cozy Mystery, Crime Fiction, Domestic Fiction, Holiday Fiction, Adventure Fiction **COULD YOU SOLVE THE CASE? PRE-ORDER NOW FOR THE PUZZLING CHRISTMAS MYSTERY OF THE YEAR** Eighteen passengers. Seven stops. One killer. In the early hours of Christmas Eve, the sleeper train to the Highlands is derailed, along with the festive plans of its travellers. With the train stuck in snow in the middle of nowhere, a killer stalks its carriages, picking off passengers one by one. Those who sleep on the sleeper train may never wake again. Can former Met detective Roz Parker find the killer before they kill again? All aboard for . . . Murder on the Christmas Express The Pain Tourist by Paul Cleave Publisher: Orenda Books Genre: Thriller, Medical Thriller, Police Procedural A young man wakes from a coma to find himself targeted by the men who killed his parents, while someone is impersonating a notorious New Zealand serial killer … the latest chilling, nerve-shredding, twisty thriller from the author of The Quiet People… James Garrett was critically injured when he was shot following his parents' execution, and no one expected him to waken from a deep, traumatic coma. When he does, nine years later, Detective Inspector Rebecca Kent is tasked with closing the case that her now retired colleague, Theodore Tate, failed to solve all those years ago. But between that, and hunting for Copy Joe – a murderer on a spree, who's imitating Christchurch's most notorious serial killer – she's going to need Tate's help … especially when they learn that James has lived out another life in his nine-year coma, and there are things he couldn't possibly know, including the fact that Copy Joe isn't the only serial killer in town… The Buried by Sharon Bolton Genre: Mystery, Suspense, Crime Fiction, Psychological Thriller, Horror Fiction, Crime Series AN OLD ENEMY IS LAID TO REST . . . AND A NEW CRIME IS DISCOVERED Florence Lovelady, the most senior serving policewoman in Britain, visits convicted serial killer Larry Glassbrook in prison. Larry is coming to the end of his life but has one last task for Florence: to learn the identity of the remains discovered at children's home Black Moss Manor. The town Florence escaped narrowly with her life still holds many secrets. Will she finally learn the truth? Or will time run out for her first? The latest Florence Lovelady thriller, set shortly after the bestselling first novel The Craftsman in the chilling, new series from Richard and Judy bestseller Sharon Bolton The Picture Bride by Lee Guem-yi Publisher: Scribe UK Could you marry a man you've never met? Three Korean women in 1918 make a life-changing journey to Hawaii, where they will marry, having seen only photographs of their intended husbands. Different fates await each of these women. Hong-ju, who dreams of a marriage of 'natural love', meets a man who looks twenty years older than his photograph; Song-hwa, who wants to escape from her life of ridicule as the granddaughter of a shaman, meets a lazy drunkard. And then there's Willow, whose 26-year-old groom, Taewan, looks just like his image … Real life doesn't always resemble a picture, but there's no going back. And while things don't turn out quite as they'd hoped, even for Willow, they do find something that makes their journey worthwhile ― each other. The Vicious Circle by Katherine St. John Publisher: William Morrow Genre: Thriller, Suspense, Adventure Fiction For fans of Lucy Foley and Liane Moriarty, a twisty, escapist suspense about a mysterious retreat center harboring violent secrets. A perfect paradise? Or a perfect nightmare? On a river deep in the Mexican jungle stands the colossal villa Xanadu, a wellness center that's home an ardent spiritual group devoted to self-help guru Paul Bentzen and his enigmatic wife Kali. But when Paul mysteriously dies, his entire estate—including Xanadu—is left not to Kali, but to his estranged niece Sveta. Shocked and confused, Sveta travels from New York City to Mexico to pay her respects. At first, Xanadu seems like a secluded paradise with its tumbling gardens, beautiful people, and transcendent vibe. But soon the mystical façade wears thin, revealing a group of brainwashed members drunk on promises of an impossible utopia, guided by a disturbing belief system and a charismatic, dangerously capable leader. As the sinister forces surrounding Sveta become apparent, she realizes, too late, she can't escape. Frantic and terrified, she discovers her only chance of survival is to put her confidence in the very person she trusts the least. The Weather Woman by Sally Gardner Genre: Historical Fiction, Historical Romance, Historical Fantasy, Fantasy Fiction, Regency Romance The rich and atmospheric new novel from prize-winning author Sally Gardner, set in the 18th century between the two great Frost Fairs. Neva Friezland is born into a world of trickery and illusion, where fortunes can be won and lost on the turn of a card. She is also born with an extraordinary gift. She can predict the weather. In Regency England, where the proper goal for a gentlewoman is marriage and only God knows the weather, this is dangerous. It is also potentially very lucrative. In order to debate with the men of science and move about freely, Neva adopts a sophisticated male disguise. She foretells the weather from inside an automaton created by her brilliant clockmaker father. But what will happen when the disguised Neva falls in love with a charismatic young man? It can be very dangerous to be ahead of your time. Especially as a woman. The People Before by Charlotte Northedge Publisher: Harper Collikns UK Genre: Mystery, Suspense, Psychological Thriller, Crime Fiction, Horror Fiction What if your dream house became your worst nightmare? Jess and her husband need a new start. So when the chance to buy a rambling old house in the Suffolk countryside comes up, they leap at it. But not everyone in Suffolk is welcoming. The locals know a secret about the Maple House, and soon, Jess realises they've made a huge mistake. Something bad happened in that house. Something nobody wants to talk about. Something to do with the people before… Murder Most Royal by S. J. Bennett (Her Majesty Investigates Book 3) Publisher: Zaffre Genre: Mystery, Cozy Mystery, Cozy Mystery Series THE ROYALLY BRILLIANT THIRD BOOK IN THE HER MAJESTY THE QUEEN INVESTIGATES MYSTERY SERIES Christmas at Sandringham is going to be murder . . . A human hand and a bag of drugs are found washed up on a beach next to the Queen's estate at Sandringham The Queen identifies the 70-year-old victim, Edward St Cyr, from his signet ring. But the search for his killer is not so straightforward. Suspects include the Queen's horse groom, a shady land agent, an aristocrat neighbour, as well as the victim's many cousins and relations. The investigation leads the Queen – and her trusted assistant, Rozie – to a local pigeon racing club, back to London, and to the ancient, moated Godwick Hall. But how do the seemingly disparate pieces of the puzzle fit together? And who is the next victim? Agatha Christie meets The Crown in MURDER MOST ROYAL, the much-anticipated third book in the 'Her Majesty The Queen Investigates' mystery series by SJ Bennett – for fans of The Thursday Murder Club by Richard Osman, Agatha Christie and M.C. Beaton's Agatha Raisin. The Christmas Wish by Lindsey Kelk Publisher: Harper Collins UK Genre: Romance Novel, Contemporary Romance, Humorous Fiction, Holiday Fiction Ever wished it could be Christmas every day? Wish again… Newly single lawyer Gwen Baker is hoping that a family Christmas – countryside, a mountain of food and festive films – will salve the sting of her career hanging by a thread and her heart being trampled on. Because everyone else has their life sorted: even Dev, her boy-next-door crush, is now a tall, dark and handsome stranger with a fiancée. She can't help wishing her future was clearer. Then Gwen wakes up to discover it's Christmas day all over again. Like Groundhog Day but with turkey. And family arguments. On repeat. As she figures out how to escape her own particular Christmas hell, Dev is the one bright spot. He might be all grown-up but underneath he's just as kind and funny as she remembers. Maybe, just maybe, her heart can be mended after all. But how do you fall in love with someone who can't remember you from one day to the next? Mad Honey by Jodi Picoult and Jennifer Finney Boylan Genre: Contemporary Fiction, Literary Fiction Olivia fled her abusive marriage to return to her hometown and take over the family beekeeping business when her son Asher was six. Now, impossibly, her baby is six feet tall and in his last year of high school, a kind, good-looking, popular ice hockey star with a tiny sprite of a new girlfriend. Lily also knows what it feels like to start over – when she and her mother relocated to New Hampshire it was all about a fresh start. She and Asher couldn't help falling for each other, and Lily feels happy for the first time. But can she trust him completely? Then Olivia gets a phone call – Lily is dead, and Asher is arrested on a charge of murder. As the case against him unfolds, she realises he has hidden more than he's shared with her. And Olivia knows firsthand that the secrets we keep reflect the past we want to leave behind ­­- and that we rarely know the people we love well as we think we do. The Lindbergh Nanny by Mariah Fredericks Publisher: Review Genre: Historical Fiction, Mystery, Historical Mystery, Biographical Fiction SHE WAS THE LAST PERSON TO SEE THE BABY… You may not know Betty Gow's name – but 'the Lindbergh nanny' is infamous. In 1932, all eyes are on Charles and Anne Morrow Lindbergh, the most glamorous and intriguing couple in America. But who was paying attention when, one evening in early March, their baby son was stolen from the family home? The Lindbergh nanny is the first person to discover Charlie missing… and the last to see him that night. With the world watching on, Betty must discover the truth about what really happened to young Charlie, to clear her own name – and to find justice for the little boy she loves. A propulsive re-imagining of America's most notorious crime of the twentieth century, told through the eyes of the young woman who found herself at the heart of the case. The Dazzle of Light by Georgina Clarke Publisher: Verve Books Genre: Mystery, Crime Fiction, Historical Mystery Ruby Mills is ruthlessly ambitious, strikingly beautiful – and one of the Forty Thieves' most talented members. Harriet Littlemore writes the women's section in a local newspaper. She's from a 'good' London family and engaged to an up-and-coming Member of Parliament – but she wants a successful career of her own. After witnessing Ruby fleeing the scene of a robbery, Harriet develops a fascination with the elusive young thief that extends beyond journalistic interest. As their personal aspirations bring them into closer contact than society's rules usually allow, Ruby and Harriet's stories become increasingly intertwined. Their magnetic dynamic, fraught with envy and desire, tells a compulsive, cinematic story about class, morality and the cost of being an independent woman in 1920s London. Suicide Thursday by Will Carver Genre: Mystery, Thriller, Suspense, Psychological Thriller, Hardboiled, Noir Fiction A disenchanted man struggles to get beyond the first chapter of the books he's writing, and to separate fact from fiction in his own life. His friend's suicide changes everything … The mind-blowing, heart-rending new thriller from cult bestselling author Will Carver. Eli Hagin can't finish anything. He hates his job, but can't seem to quit. He doesn't want to be with his girlfriend, but doesn't know how end things with her, either. Eli wants to write a novel, but he's never taken a story beyond the first chapter. Eli also has trouble separating reality from fiction. When his best friend kills himself, Eli is motivated, for the first time in his life, to finally end something himself, just as Mike did… Except sessions with his therapist suggest that Eli's most recent 'first chapters' are not as fictitious as he had intended … and a series of text messages that Mike received before his death point to something much, much darker… Happy New Year by Malin Stehn Genre: Mystery, Suspense, Psychological Thriller, Domestic Fiction IT SHOULD HAVE BEEN THE PARTY OF THE SEASON. BUT SHE NEVER CAME HOME. It's New Year's Eve. The best night of the year. As old friends the Wiksells and the Anderssons raise their glasses, their teenage children host their own party across town, finally free to let loose. But the next morning, seventeen-year-old Jennifer Wiksell is missing. The hours tick by. The police get involved. And no one knows who to trust. These two families have a lot to hide. Could the answer to Jennifer's disappearance lie close to home? The Sanctuary by Emma Haughton Very few people get the opportunity to stay here. And some don't get to leave … Zoey doesn't remember anything about last night. But she knows something went badly wrong. For she is no longer in New York. She's woken up in the desert, in a white building she doesn't recognise, and she's alone. When she discovers she's been admitted to The Sanctuary, a discreet, mysterious, isolated refuge from normal life, to avoid jail, she is stunned. She knows she has secrets, troubles, but she thought she had everything under control. But as she spends more time with other residents, she begins to open up about what she's running from. Until she realises that not everyone in The Sanctuary has her best interests at heart, and someone might even be a killer . . . The Locked Attic by B P Walter Genre: Thriller, Mystery, Suspense, Psychological Thriller, Crime Fiction, Domestic Fiction There's something in my neighbour's attic. Something steeped in shadows. A secret to everyone. Seen by no one… He stands sometimes at the window. Hidden in the corner of my eye. I know he's there. I know he's watching. Now my son is dead. My neighbour is not. And I'm going to find out why. The Judas Tree by Amanda Jennings Genre: Suspense, Thriller, Psychological Fiction, Coming-of-Age Story Childhood betrayal casts a long shadow… From the author of The Haven and The Cliff House, this is a devastating thriller set in a Cornish boarding school. 'A gripping page-turner' Tammy Cohen, author of The Wedding Party At a bleak boys' boarding school in Cornwall in the eighties when bullying is rife, Will and his best friend, Luke, are involved in a horrific incident that results in Luke leaving. Twenty-five years later their paths cross again and memories of a painful childhood come flooding back to haunt them both. Will's wife, Harmony, is struggling after a miscarriage that has hit her hard, and wishes Will would open up about what happened. But as Will withdraws further, she finds herself drawn to the charismatic stranger from her husband's past, Luke, and soon all three are caught in a tangled web of guilt and desire . . . From Amanda Jennings, author of The Cliff House, comes a haunting thriller about betrayal and revenge. Alone with You in the Ether by Olivie Blake Genre: Contemporary Romance, Disability Fiction Chicago, sometime. Two people meet in the armory of the Art Institute by chance. Prior to their encounter, he is a doctoral student who manages his destructive thoughts with compulsive calculations about time travel; she is a bipolar counterfeit artist undergoing court-ordered psychotherapy. After their meeting, those things do not change. Everything else, however, is slightly different. Both obsessive, eccentric personalities, Aldo Damiani and Charlotte Regan struggle to be without each other from the moment they meet. The truth – that he is a clinically depressed, anti-social theoretician and she is a manipulative liar with a history of self-sabotage – means the deeper they fall in love, the more troubling their reliance on each other becomes. Alone With You in the Ether by Olivie Blake is a glimpse into the nature of love, what it means to be unwell, and how to face the fractures of yourself and still love as if you're not broken. Publisher: Literary Fiction Genre: Scribner UK From the author of A Little Hope comes an enormously powerful and life-affirming novel about three individuals whose lives intersect in unforeseen ways. Set in a close-knit Pennsylvania suburb in the grip of winter, A Quiet Life follows three people grappling with loss and finding a tender wisdom in their grief. Chuck Ayers used to look forward to nothing so much as his annual trip to Hilton Head with his wife, Cat–that yearly taste of relaxation they'd become accustomed to in retirement, after a lifetime of working and raising two children. Now, just months after Cat's death, Chuck finds that he can't let go of her things–her favorite towel, the sketchbooks in her desk drawer–as he struggles to pack for a trip he can't imagine taking without her. Ella Burke delivers morning newspapers and works at a bridal shop to fill her days while she anxiously awaits news–any piece of information–about her missing daughter. Ella adjusts to life in a new apartment and answers every call on her phone, hoping her daughter will reach out one day. After the sudden death of her father, Kirsten Bonato set aside her veterinary school aspirations, finding comfort in the steady routine of working at an animal shelter. But as time passes, old dreams and new romantic interests begin to surface–and Kirsten finds herself at another crossroads. In this beautifully crafted and profoundly moving novel, three parallel narratives converge in poignant and unexpected ways, as each character bravely presses onward, trying to recover something they have lost. Emotionally riveting and infused with hope, A Quiet Life celebrates humanity in the midst of uncertainty. My Husband's Killer by Laura Marshall Genre: Mystery, Suspense, Psychological Thriller, Holiday Fiction Three couples. One murder. A holiday to die for . . . We arrived at a villa on the Amalfi Coast, ready to enjoy a sun-soaked weekend with our oldest friends – and one new face. By the end of the weekend, my husband is found dead. But how can I mourn him, when on the day of his funeral I discover he was having an affair? The only suspects are the women we went on holiday with. My oldest, closest friends. Do I really want to dig into my husband's secret? Do I really want to know who betrayed me? And as I start to unravel their secrets . . . do I really believe his death was an accident? Tags A Quiet Life, Alexandra Benedict, Alone With You in the Ether, Amanda Jennings, Apollo, B. A. Paris, B. P. Walter, Charlotte Northedge, Dawnlands, Emma Haughton, Emma's Anticipated Treasures, Ethan Joella, Faber & Faber, Fairmile Series, Georgina Clarke, Happy New Year, Harper Collins UK, Harper Voyager, Heart of the Sun Warrior, Her Majest Investigates Series, Hodder & Stoughton, HQ, Jennifer Finney Boylan, Jodi Picoult, Katherine St. John, Laura Marshall, Lee Guem-yi, Lindsey Kelk, Mad Honey, Malin Stehn, Mariah Fredericks, Michael Joseph, Murder Most Royal, Murder on the Christmas Express, My Husband's Killer, November 2022, November Books, Olivie Blake, One More Chapter, Orenda Books, Orion, Paul Cleave, Philippa Gregory, Rebecca Mix, Review, S. J. Bennett, Sally Gardner, Sara Gran, Scribe UK, Scribner UK, Sharon Bolton, Simon & Schuster UK, Sphere, Sue Lynn Tan, Suicide Thursday, The Book of Most Precious Substance, The Buried, The Celestial Kingdom Series, The Christmas Wish, The Dazzle of the Light, The Judas Tree, The Lindbergh Nanny, The Locked Attic, The Ones We Burn, The Pain Tourist, The People Before, The Picture Bride, The Prisoner, The Sanctuary, The Vicious Circle, Tor, Verve Books, Will Carver, William Morrow, Zaffre Blog Tours book reviews Emma's Anticipated Treasures BLOG TOUR: The Marsh House by Zoe Somerville Post date 11th Mar 2022 4 Comments on BLOG TOUR: The Marsh House by Zoe Somerville Published: March 3rd 2022 Genre: Historical Fiction, Suspense, Thriller, Historical Romance, Psychological Fiction, Coming-of-Age Story Format: Hardcover, Kindle, Audiobook Welcome to my stop on the blog tour for this mesmerising and haunting tale. Thank you to Head of Zeus for the invitation to take part and the gifted copy of the book. "No-one had lived in the house for years afore they arrived last winter. Not since all that fuss in thirty-four… I weren't surprised to see her though. Oh, no, it was her all right. We'd been waiting for her." OMG. This book! I expected it to be good after hearing so much praise for Zoe Somerville's debut novel, but I was unprepared for the chilling gothic masterpiece that lurked between these pages. I inhaled this book in one sitting, staying up until 3am in a desperate need for answers. It was totally worth it and I have no doubt that this will make it into my top books of the year when December rolls around. December 1962. Malorie has rented a remote house on the Norfolk coast hoping to create a magical and memorable Christmas for her daughter Franny after a difficult year. Known as The Marsh House, its eerie atmosphere looms over them from the moment they cross the threshold. While looking for Christmas decorations in the attic they come across an old suitcase filled with papers and notebooks. Upon closer inspection, Malorie discovers that the notebooks are the diaries of Rosemary Wright, a teenage girl who lived at the house thirty years earlier. Curiosity taking over, Malorie begins to read and becomes fixated on the mysterious past of this young girl. But what secrets are waiting to be uncovered inside Rosemary's diaries? "I knew she'd found something and what she'd be looking for. She wanted evidence. Proof. Facts. As if it would all be there for her and she could lay it all out and it would make sense. But it's never as simple as that. The graves are elsewhere. The bones are dust. It's not graves that tell you a history, a story of a life. That's much harder to find, but if you know where to look, you can find it. It will reveal itself." The Marsh House is literary gothic fiction at its best. The perfect combination of lyrical prose, page turning plot, chilling atmosphere and gripping tension, this haunting tale had me on the edge of my seat from beginning to end. Creepily claustrophobic and almost dreamlike in places, there is a sense of the otherworldly about it. The snow storm adds to the sense of isolation and increases the fear when strange and inexplicable occurrences begin to make Marlorie question her own sanity. Zoe Somerivlle is a gifted storyteller and the style of this book was spot on for me. I loved the short, cryptic chapters from an unknown narrator who is watching Malorie and Franny and Rosemary's diary was an inspired choice that brought Rosemary alive and allowed us to connect with her. Just like Malorie I was enthralled and desperate to know what happened next in her story. The story moves between the two timelines smoothly, punctuated by the short chapters from the mysterious narrator that sent shivers down my spine each time they appeared. There was no chance of me putting this book down until I had all the answers. Malorie and Rosemary are great narrators who capture the imagination and hold you in the palm of their hand as the story unfolds. They are fascinating, flawed and real, a whole world of heartbreak, fear, regret and guilt to be found in these women. And their internal conflict and pain is told so vividly that I could feel it in my own soul. From the start we know Malorie believes there to be a connection between her father and Marsh House so I spent the book looking for clues and trying to guess how he might be connected. I had my theories, one of which was correct, but what I loved is how the author creates just enough doubt to make you second guess and not feel sure until the moment just before the big reveal, adding to the mystery and suspense. "There was something rotten that had been hiding in front of her and it was revealing itself." Mesmerising, chilling and immersive, this is a clear your schedule and read it in one sitting kind of book. An easy five stars from me, I can't recommend it highly enough. I will be reading Zoe's first book as soon as possible and am excited to watch this talented author's star undoubtedly rise. Rating: ✮✮✮✮✮ Zoë Somerville is originally from Norfolk, but has settled with her husband and children in the West Country. She works as an English teacher. Zoë began her debut novel, The Night of the Flood on the Bath Spa Creative Writing MA in 2016. It was published in September 2020. Her second novel, The Marsh House, a ghost story and mystery is published in March 2022. She is currently writing her third novel. Waterstones*| Amazon*| Bookshop.org* *These are affiliate links Thanks for reading Bibliophiles 😊 Emma xxx Please check out the reviews from the other bloggers taking part in the tour. Tags 5 star reads, Apollo, Blog Tour, Book Review, Coming-of-Age Story, Emma's Anticipated Treasures, Head of Zeus, historical fiction, Historical Romance, March 2022, March books, Psychological fiction, suspense, thriller Emma's Anticipated Treasures: Most Anticipated of 2022 – Next in Series Post date 23rd Dec 2021 3 Comments on Emma's Anticipated Treasures: Most Anticipated of 2022 – Next in Series We aren't even out of 2021 yet, but 2022 is overflowing with so many exciting books that I have had to create three lists to share the ones I'm most anticipating: Most Anticipated, Most Anticipated Debuts and Next in Series. Today I'm sharing my final list of anticipated books. These are all the next books in a series that are I'm most looking forward to next year. I am a big fan of a good series and some of my favourites have another installment out next year. There are also some great follow-ups to books that were a standalone but have been so popular that the author has revisited the story a second time (eg The Miniaturist and Rachel's Holiday). So here's my most anticipated next installments in a series being released in 2022: Demon (Six Stories 6) by Matt Wesolowski Scott King's podcast investigates the 1995 cold case of a demon possession in a rural Yorkshire village, where a 12-year-old boy was murdered in cold blood by two children. Book six in the chilling, award-winning Six Stories series. In 1995, the picture-perfect village of Ussalthwaite was the site of one of the most heinous crimes imaginable, in a case that shocked the world. Twelve-year-old Sidney Parsons was savagely murdered by two boys his own age. No reason was ever given for this terrible crime, and the 'Demonic Duo' who killed him were imprisoned until their release in 2002, when they were given new identities and lifetime anonymity. Elusive online journalist Scott King investigates the lead-up and aftermath of the killing, uncovering dark stories of demonic possession, and encountering a village torn apart by this unspeakable act. And, as episodes of his Six Stories podcast begin to air, and King himself becomes a target of media scrutiny and the public's ire, it becomes clear that whatever drove those two boys to kill is still there, lurking, and the campaign of horror has just begun… Published January 20th by Orenda. Buy here. Marion Lane and the Deadly Rose by T. A. Willberg The envelope was tied with three delicate silk ribbons: "One of the new recruits is not to be trusted…" It's 1959 and a new killer haunts the streets of London, having baffled Scotland Yard. The newspapers call him The Florist because of the rose he brands on his victims. The police have turned yet again to the Inquirers at Miss Brickett's for assistance, and second year Marion Lane is assigned the case. But she's already dealing with a mystery of her own, having received an unsigned letter warning her that one of the three new recruits should not be trusted. She dismisses the letter at first, focusing on The Florist case, but her informer seems to be one step ahead, predicting what will happen before it does. But when a fellow second-year Inquirer is murdered, Marion takes matters into her own hands and must come face-to-face with her informer-who predicted the murder-to find out everything they know. Until then, no one at Miss Brickett's is safe and everyone is a suspect. With brilliant twists and endless suspense, all set within the dazzling walls and hidden passageways of Miss Brickett's, Marion Lane and the Deadly Rose is a deliciously fun new historical mystery you won't be able to put down. Published February 3rd by Orion. Buy here* Night of Demons and Saints by Menna van Praag And then there were three . . . Three years ago, the sisters confronted their demon father in that strange other-world called Everwhere. It was a battle that ended in a devastating loss, and the scars they carry seem to have slowly pushed the sisters apart . . . One sister, still raw with grief, is now a near recluse but determined to use her powers to resurrect what she has lost. Another has made the journey to learn more of her family, her culture and her roots. And another seems to have turned her back on what she is and opted to lead a more normal life. But now the sisters are about to be brought together once more. Because when the clock strikes midnight, when October ticks into November, when autumn wilts into winter, when All Hallows' Eve becomes All Saints' Day, the sisters Grimm will turn twenty-one and reach the zenith of their powers. And on this night, at this time, in this place called Everwhere, anything is possible . . . Published February 3rd by Bantam Press. Buy here* House of Sky and Breath (Crescent City 2) by Sarah J. Maas Sequel to the #1 New York Times bestseller. Sarah J. Maas's sexy, groundbreaking CRESCENT CITY series continues with this second installment. Bryce Quinlan and Hunt Athalar have made a pact. As they process the events of the Spring they will keep things . platonic . until the Solstice. But can they resist when the crackling tension between them is enough to set the whole of Crescent City aflame? And they are not out of danger yet. Dragged into a rebel movement they want no part of, Bryce, Hunt and their friends find themselves pitted against the terrifying Asteri – whose notice they must avoid at all costs. But as they learn more about the rebel cause, they face a choice: stay silent while others are oppressed, or fight. And they've never been very good at staying silent. In this sexy, action-packed sequel to the #1 bestseller House of Earth and Blood, Sarah J. Maas weaves a captivating story of a world about to explode – and the people who will do anything to save it. Published February 15th by Bloomsbury. Buy here* Again, Rachel by Marian Keyes Twenty-five years after the iconic, 1.5 million-copy bestseller Rachel's Holiday burst into our lives, Rachel's BACK! Back in the long ago nineties, Rachel Walsh was a mess. But a spell in rehab transformed everything. Life became very good, very quickly. These days, Rachel has love, family, a great job as an addiction counsellor, she even gardens. Her only bad habit is a fondness for expensive trainers. But with the sudden reappearance of a man she'd once loved, her life wobbles. She'd thought she was settled. Fixed forever. Is she about to discover that no matter what our age, everything can change? Is it time to think again, Rachel? Published February 17th by Michael Joseph. Buy here* One for Sorrow (DI Callanach 7) by Helen Fields Published March 3rd by Avon. Buy here* Four Aunties and a Wedding by Jesse Sutanto Published March 3rd by HQ. Buy here* The Blood Isles (Pantheon 2) by C. F. Barrington The second in an action-packed adventure thriller series, where modern-day recruits compete in an ancient fight to the death in the streets of Edinburgh. New Season. New Rules. Same deadly game… The Pantheon Games are the biggest underground event in the world, followed by millions online. New recruits must leave behind their twenty-first century lives and vie for dominance in a gruelling battle to the death armed only with ancient weapons – and their wits. Last season's new recruits Tyler and Lana have lived to fight another day, but now they face a series of even more lethal clashes before the Grand Battle that will end the Season. It's survival of the fittest, in the most brutal fashion imaginable. Lana must face the demons of her past, and Tyler has the mother of all targets on his back. This action-packed adventure thriller is perfect for fans of Pierce Brown's Red Rising, Battle Royale and The Running Man. Published March 3rd by Head of Zeus. Buy here* A Life for a Life (Detective Kate Young 3) by Carol Wyer Published March 15th by Thomas & Mercer. Buy here* House with the Golden Door (The Wolf Den 2) by Elodie Harper The life of a courtesan in Pompeii is glittering, yet precarious… Amara has escaped her life as a slave in the town's most notorious brothel, but now her existence depends on the affections of her patron: a man she might not know as well as she once thought. At night she dreams of the wolf den, still haunted by her past. Amara longs for the women she was forced to leave behind and worse, finds herself pursued by the man who once owned her. In order to be free, she will need to be as ruthless as he is. Amara knows her existence in Pompeii is subject to Venus, the goddess of love. Yet finding love may prove to be the most dangerous act of all. We return to Pompeii for the second instalment in Elodie Harper's Wolf Den Trilogy, reimagining the lives of the women from the town's lupanar. Published May 12th by Apollo. Buy here* Cold Reckoning (DS Adam Tyler 3) by Russ Thomas The new must-read novel from the bestselling and highly acclaimed author of FIREWATCHING and NIGHTHAWKING A body is discovered in a frozen lake, its wrists bound. When it is linked to a case from 2002, Tyler, DC Rabbani and the CCRU team are called in. But fresh blood is soon discovered at the scene and the disturbing events from all those years ago are dragged sharply into the present . . . Published May 12th by Simon and Schuster. Buy here* The Dark (Lacy Flint 5) by Sharon Bolton HE'S WATCHING HER. AND SHE HAS NO IDEA… When a baby is snatched from its pram, off-duty police officer Lacey Flint is there to prevent disaster. But who would want to hurt a child? Lacey's colleague, DI Mark Joesbury, has been expecting something like this. Monitoring a complex network of dark web sites, Joesbury and his team have detected a new terrorist threat from an extremist group, known online as 'incels'. Joesbury's team are tracking the growing incel movement online, trying to infiltrate the ring of power at its core, but the dark web is built for anonymity, and the incel army is vast. The team soon come under pressure when they discover that the snatched child was just the first in a series of violent attacks designed to terrorise women. Even worse, the leaders of the movement seem to have singled out Lacey as the embodiment of everything they hate, placing her in terrible danger… Published May 26th by Orion. Buy here* DI Helen Grace Book 11 by M. J. Arlidge THE BRAND NEW, UTTERLY GRIPPING DI HELEN GRACE THRILLER FROM BESTSELLING AUTHOR MJ ARLIDGE COMING SOON . . . Published June 9th by Orion. Buy here* From the Ashes (DI Eve Hunter 3) by Deborah Masson It only takes one spark to reignite an old mystery . . . DI Eve Hunter and her team are called to the scene of a fire that has destroyed a home for underprivileged children in Aberdeen. No-one knows how the blaze started; all they know is that one person didn't make it out in time. Her team have dealt with their fair share of tragedies but this case affects them each deeply – particularly when they start to suspect that everyone at the home, from the residents to the staff, has something to hide. And when a horrific discovery is unearthed in the ruins of the property, the team must ask themselves – did someone have a secret worth killing for? Published June 23rd by Transworld. Buy here* The House of Fortune by Jessie Burton The sequel to Jessie Burton's million-copy bestseller The Miniaturist. In the golden city of Amsterdam, in 1705, Thea Brandt is turning eighteen, and she is ready to welcome adulthood with open arms. At the city's theatre, Walter, the love of her life, awaits her, but at home in the house on the Herengracht, all is not well – her father Otto and Aunt Nella argue endlessly, and the Brandt family are selling their furniture in order to eat. On Thea's birthday, also the day that her mother Marin died, the secrets from the past begin to overwhelm the present. Nella is desperate to save the family and maintain appearances, to find Thea a husband who will guarantee her future, and when they receive an invitation to Amsterdam's most exclusive ball, she is overjoyed – perhaps this will set their fortunes straight. And indeed, the ball does set things spinning: new figures enter their life, promising new futures. But their fates are still unclear, and when Nella feels a strange prickling sensation on the back of her neck, she remembers the miniaturist who entered her life and toyed with her fortunes eighteen years ago. Perhaps, now, she has returned for her . . . The House of Fortune is a glorious, sweeping story of fate and ambition, secrets and dreams, and one young woman's determination to rule her own destiny. Published July 7th by Picador. Buy here* Listen to Me (Rizzoli and Isles 13) by Tess Gerritsen Rizzoli & Isles return, in the nail-biting new thriller from Sunday Times bestselling author Tess Gerritsen. Detective Jane Rizzoli and Forensic Pathologist Maura Isles are investigating the gruesome murder of a nurse, whilst also protecting a young student from a stalker. But immersed in their day jobs, will they lose sight of something sinister happening much closer to home? Published July 7th by Bantam Press. Buy here* All About Evie (Evie Epworth 2) by Matson Taylor EVIE EPWORTH IS TEN YEARS OLDER. BUT IS SHE ANY WISER? Ten years on from the events of THE MISEDUCATION OF EVIE EPWORTH, Evie is settled in London and working as a production assistant for the BBC. She has everything she has ever dreamed of (a career, a leatherette portfolio briefcase and an Ossie Clark poncho). Following an unfortunate incident involving a pregnancy test, a Hornsea china mug and Princess Anne, however, Evie is forced to seek other opportunities. After a brief sojourn into the world of art, Evie talks her way into her dream job working for Right On!, a weekly magazine that tells the hip and happening of London all they need to know about the latest cultural goings-on about town. There are gaps in her knowledge, though, that a jealous colleague threatens to expose, and her disastrous love life leaves her worrying that she may be condemned to a life of eternal spinsterdom (as Evie observes, 'even Paul had married Linda by the time he was 26'). But with the help of friends, both old and new, she may find a way through her messy 20s and finally discover just exactly who it is she is meant to be. Published July 21st by Scribner UK. Buy here* The Family Remains by Lisa Jewell The Family Upstairs has gripped audiences around the world, becoming a smash hit with readers everywhere. In 2022 no. 1 bestselling author Lisa Jewell will publish a sequel. Published July 21st by Century. Buy here* Cold, Cold Bones (Temperance Brenan 21) by Kathy Reichs Sometimes, revisiting the past is the only way to rescue the present . . . Winter has come to North Carolina and, with it, a drop in crime. For a while, temporarily idle forensic anthropologist Tempe Brennan is content to dote on her daughter Katy, finally returned to civilian life from the army. But when mother and daughter meet at Tempe's place one night for dinner, they find a box on the back porch. Inside: a very fresh human eyeball. GPS coordinates etched into the eyeball lead to a Benedictine Monastery where an equally macabre discovery awaits. Soon after, Tempe examines a mummified corpse in a state park, and her anxiety deepens. There seems to be no pattern to these random killings, except that each mimics in some way a killing that a younger Tempe witnessed, analyzed, or barely escaped. Who or what is targeting her, and why? Helping Tempe discover the answers is Detective Erskine 'Skinny' Slidell, retired but still volunteering with the CMPD cold case unit – and still displaying his gallows humour. But as the two infiltrate a bizarre survivalist's lair, even Skinny's mood darkens. And then Tempe's daughter Katy disappears. Electrifying, heart-stopping and compulsive, this is Tempe's most personal and dangerous case yet . . . Published July 21st by Simon & Schuster. Buy here* Hope To Die (DC Adam Fawley 5) by Cara Hunter Midnight. A callout to an isolated farm outside Oxford. A body, shot at point blank range in the kitchen. It looks like a burglary gone wrong, but DC Adam Fawley suspects there's something more to it. Who exactly was the aggressor here? When the police discover a connection to a high-profile case from years ago, involving a child's murder and an alleged miscarriage of justice, the press go wild. Suddenly Fawley's team are under more scrutiny than ever before. And when you dig up the past, you're sure to find a few skeletons… Published July 21st by Penguin UK. Buy here* A Slayton Thriller Book 2 by Caroline Mitchell The Night Whispers are coming… Don't miss the thrilling next book in the exciting new Slayton series from #1 bestselling author Caroline Mitchell. Perfect for fans of C. J. Tudor and Stephen King. Published July 28th by Embla Books. Buy here* The Dragons Promise (Six Crimson Cranes) by Elizabeth Lim Shiori's adventure continues in the stunning follow up to Six Crimson Cranes. Published August 30th by Hodder & Stoughton. Buy here* The Thursday Murder Club Book 3 by Richard Osman A new mystery is afoot in the third book in the Thursday Murder Club series from million-copy bestselling author Richard Osman. Coming Autumn 2022! Pre-order your copy now. Published September 15h by Viking. Buy here* Murder Most Royal (Her Majesty the Queen Investigates 3) by S.J. Bennett THE ROYALLY BRILLIANT THIRD BOOK IN THE HER MAJESTY THE QUEEN INVESTIGATES MYSTERY SERIES – NOW AVAILABLE TO PRE-ORDER IN HARDBACK, EBOOK AND AUDIOBOOK! Published November 10th by Zaffre. Buy here* The Court of Miracles 2 by Kester Grant The Sunday Times bestselling adventure inspired by Les Miserables continues.Return to a dark and dangerous alternate Paris in book 2 of The Court of Miracles Trilogy. Published December 8th by Harper Voyager. Buy here* Are you planning to read any of these? What series are you excited to continue reading in 2022? Let me know in the comments. Tags A Life For A Life, Adam Tyler Series, All About Evie, Apollo, August 2022, Avon Books UK, Bantam Press, Bloomsbury UK, book series, C. F. Barrington, Cara Hunter, Carol Wyer, Caroline Mitchell, Century, Cold Cold Bones, Cold Reckoning, Crescent City Series, Crime series, DC Adam Fawley, Deborah Masson, December 2022, Demon, DI Callanach, DI Eve Hunter, DI Helen Grace Series, Elizabeth Lim, Elodie Harper, Embla Books, Evie Epworth, Fantasy Series, February 2022, Four Aunties and a Wedding, From the Ashes, Head of Zeus, Helen Fields, Hope To Die, House of Sky and Breath, House with the Golden Door, HQ, January 2022, Jesse Sutanto, Jessie Burton, July 2022, June 2022, Kate Marshall Series, Kathy Reichs, Kester Grant, Lacy Flint Series, Lisa Jewell, Listen To Me, M. J. Arlidge, March 2022, Marian Keyes, Marion Lane and the Deadly Rose, Marion Lane Mysteries, Matson Taylor, Matt Wesolowski, May 2022, Menna van Praag, Michael Joseph, Most Anticipated 2022: Next in Series, Murder Most Royal, Night of Demons and Saints, November 2022, One For Sorrow, Orenda, Orenda Books, Orion, Penguin UK, Picador, Richard osman, Rizzoli & Isles Series, Russ Thomas, S. J. Bennett, Sarah J. Maas, Scribner UK, September 2022, Sharon Bolton, Simon & Schuster UK, Sisters Grimm Series, Six Crimson Cranes, Six Stories Series, Slayton Series, T. A. Willberg, Temperance Brenan, Temperance Brenan Series, Tess Gerritsen, The Blood Isles, The Court of Miracles Series, The Dark, The Dragon's Promise, The Family Remains, the Her Majesty the Queen Investigates Series, The House of Fortune, The Pantheon Series, The Thursday Murder Club Series, The Wolf Den Series, Transworld, Transworld Publishing, Viking, Walsh Family Series Emma's Anticipated Treasures: Most Anticipated in 2022 – Back Again Post date 20th Dec 2021 3 Comments on Emma's Anticipated Treasures: Most Anticipated in 2022 – Back Again We aren't even out of 2021 yet, but 2022 is overflowing with so many exciting books that I have had to create three lists to share the ones I'm most anticipating: Back Again, The Debuts and Next in Series. I'm starting by sharing my list of books by authors I love or who have already had a book published, the ones who are back again – hence the title. There are a lot of books on this list, 47 in total even after narrowing it down as much as possible. And doing that was no simple task. It took me days! So, without further ado, here are the books I'm most looking forward to being released in 2022: The Unravelling by Polly Crosby A darkly beautiful dual-timeline novel with a captivating mystery, for fans of Diane Setterfield and Kiran Millwood Hargrave When Tartelin Brown accepts a job with the reclusive Marianne Stourbridge, she finds herself on a wild island with a mysterious history. Tartelin is tasked with hunting butterflies for Marianne's research. But she quickly uncovers something far more intriguing than the curious creatures that inhabit the landscape. Because the island and Marianne share a remarkable history, and what happened all those years ago has left its scars, and some terrible secrets. As Tartelin pieces together Marianne's connection to the island, she must confront her own reasons for being there. Can the two women finally face up to the painful memories that bind them so tightly to the past? Atmospheric and deeply emotional, The Unravelling is the captivating novel from the author of The Illustrated Child. Published January 6th by HQ. Buy here* To Paradise by Hanya Yanagihara From the author of the modern classic A Little Life, a bold, brilliant novel spanning three centuries and three different versions of the American experiment, about lovers, family, loss and the elusive promise of utopia. 'To Paradise is a transcendent, visionary novel of stunning scope and depth. A novel so layered, so rich, so relevant, so full of the joys and terrors – the pure mystery – of human life, is not only rare, it's revolutionary.' – Michael Cunningham In an alternate version of 1893 America, New York is part of the Free States, where people may live and love whomever they please (or so it seems). The fragile young scion of a distinguished family resists betrothal to a worthy suitor, drawn to a charming music teacher of no means. In a 1993 Manhattan besieged by the AIDS epidemic, a young Hawaiian man lives with his much older, wealthier partner, hiding his troubled childhood and the fate of his father. And in 2093, in a world riven by plagues and governed by totalitarian rule, a powerful scientist's damaged granddaughter tries to navigate life without him – and solve the mystery of her husband's disappearances. These three sections are joined in an enthralling and ingenious symphony, as recurring notes and themes deepen and enrich one another: A townhouse in Washington Square Park in Greenwich Village; illness, and treatments that come at a terrible cost; wealth and squalor; the weak and the strong; race; the definition of family, and of nationhood; the dangerous righteousness of the powerful, and of revolutionaries; the longing to find a place in an earthly paradise, and the gradual realization that it can't exist. What unites not just the characters, but these Americas, are their reckonings with the qualities that make us human: Fear. Love. Shame. Need. Loneliness. To Paradise is a fin–de–siecle novel of marvellous literary effect, but above all it is a work of emotional genius. The great power of this remarkable novel is driven by Yanagihara's understanding of the aching desire to protect those we love – partners, lovers, children, friends, family and even our fellow citizens – and the pain that ensues when we cannot. Published January 11th by Picador. Buy here* The Twyford Code by Janice Hallett It's time to solve the murder of the century… Forty years ago, Steven Smith found a copy of a famous children's book by disgraced author Edith Twyford, its margins full of strange markings and annotations. Wanting to know more, he took it to his English teacher Miss Iles, not realising the chain of events that he was setting in motion. Miss Iles became convinced that the book was the key to solving a puzzle, and that a message in secret code ran through all Twyford's novels. Then Miss Iles disappeared on a class field trip, and Steven has no memory of what happened to her. Now, out of prison after a long stretch, Steven decides to investigate the mystery that has haunted him for decades. Was Miss Iles murdered? Was she deluded? Or was she right about the code? And is it still in use today? Desperate to recover his memories and find out what really happened to Miss Iles, Steven revisits the people and places of his childhood. But it soon becomes clear that Edith Twyford wasn't just a writer of forgotten children's stories. The Twyford Code has great power, and he isn't the only one trying to solve it… Perfect for fans of Richard Osman, Alex Pavesi and S.J. Bennett, The Twyford Code will keep you up puzzling late into the night. Published January 13th by Viper. Buy here* The Key in the Lock by Beth Underdown I still dream, every night, of Polneath on fire. Smoke unravelling from an upper window, and the terrace bathed in a hectic orange light . . . Now I see that the decision I made at Polneath was the only decision of my life. Everything marred in that one dark minute. By day, Ivy Boscawen mourns the loss of her son Tim in the Great War. But by night she mourns another boy – one whose death decades ago haunts her still. For Ivy is sure that there is more to what happened all those years ago: the fire at the Great House, and the terrible events that came after. A truth she must uncover, if she is ever to be free. But once you open a door to the past, can you ever truly close it again? From the award-winning author of The Witchfinder's Sister comes a captivating story of burning secrets and buried shame, and of the loyalty and love that rises from the ashes. Published January 13th by Viking. Buy here* Violeta by Isabel Allende One extraordinary woman. One hundred years of history. One unforgettable story. Violeta comes into the world on a stormy day in 1920, the first daughter in a family of five boisterous sons. From the start, her life is marked by extraordinary events, for the ripples of the Great War are still being felt, even as the Spanish flu arrives on the shores of her South American homeland almost at the moment of her birth. Through her father's prescience, the family will come through that crisis unscathed, only to face a new one as the Great Depression transforms the genteel city life she has known. Her family loses all and is forced to retreat to a wild and beautiful but remote part of the country. There, she will come of age, and her first suitor will come calling. In a letter to someone she loves above all others, Violeta recounts devastating heartbreak and passionate affairs, times of both poverty and wealth, terrible loss and immense joy, and a life shaped by some of the most important events of history: the fight for women's rights, the rise and fall of tyrants and, ultimately, not one but two pandemics. Through the eyes of a woman whose unforgettable passion, determination, and sense of humour will carry her through a lifetime of upheaval, Isabel Allende once more brings us an epic that is both fiercely inspiring and deeply emotional. Published January 25th by Bloomsbury Publishing. Buy here* The Couple at the Table by Sophie Hannah You're on your honeymoon at an exclusive couples-only resort. You receive a note warning you to 'Beware of the couple at the table nearest to yours'. At dinner that night, five other couples are present, and none of their tables is any nearer or further away than any of the others. It's as if someone has set the scene in order to make the warning note meaningless – but why would anyone do that? You have no idea. You also don't know that you're about to be murdered, or that once you're dead, all the evidence will suggest that no one there that night could possibly have committed the crime. So who might be trying to warn you? And who might be about to commit the perfect impossible murder? Published January 27th by Hodder & Stoughton. Buy here* Em and Me by Beth Morrey A mother. A daughter. A secret waiting to be discovered. 'Glorious! A wonderful book, such a joy!' Clare Pooley For too long – since the sudden death of her mother as a teenager, since the birth of her daughter, Em, when she was just seventeen – Delphine has been unable to let go of the past, obsessed with protecting Em and clinging to a secret that could ruin everything. She's been living life in safe shades of grey. The day that Delphine finally stands up for herself is the day that changes everything. Delphine begins to remember what it's like to want more: rediscovering her singing voice, opening herself to friendship, and reviving not only her mother's roots, but her mother's memories. As her life begins to fill with colour, can she be brave for herself and for Em? And what would happen if she finally told the truth? A big-hearted, hopeful novel about finding second chances – and taking them. Published February 3rd by Harper Collins. Buy here* The Hemlock Cure by Joanne Burn It is 1665 and the women of Eyam keep many secrets. Isabel Frith, the village midwife, walks a dangerous line with her herbs and remedies. There are men in the village who speak of witchcraft, and Isabel has a past to hide. So she tells nobody her fears about Wulfric, the pious, reclusive apothecary. Mae, Wulfric's youngest daughter, dreads her father's rage if he discovers what she keeps from him. Like her feelings for Rafe, Isabel's ward, or that she studies from Wulfric's forbidden books at night. But others have secrets too. Secrets darker than any of them could have imagined. When Mae makes a horrifying discovery, Isabel is the only person she can turn to. But helping Mae will place them both in unspeakable peril. And meanwhile another danger is on its way from London. One that threatens to engulf them all . . . Based on the real history of an English village during the Great Plague, The Hemlock Cure is an utterly beguiling tale of fear and ambition, betrayal, self-sacrifice and the unbreakable bond between two women. Published February 10th by Sphere. Buy here* Off Target by Eve Smith When a one-night stand leads to a long-desired pregnancy, Susan will do anything to ensure her husband won't find out … including the unthinkable. But when something horrendous is unleashed around the globe, her secret isn't the only thing that is no longer safe… A longed-for baby An unthinkable decision A deadly mistake In an all-too-possible near future, when genetic engineering has become the norm for humans, not just crops, parents are prepared to take incalculable risks to ensure that their babies are perfect … altering genes that may cause illness, and more… Susan has been trying for a baby for years, and when an impulsive one-night stand makes her dream come true, she'll do anything to keep her daughter and ensure her husband doesn't find out … including the unthinkable. She believes her secret is safe. For now. But as governments embark on a perilous genetic arms race and children around the globe start experiencing a host of distressing symptoms – even taking their own lives – something truly horrendous is unleashed. Because those children have only one thing in common, and people are starting to ask questions… Bestselling author of The Waiting Rooms, Eve Smith returns with an authentic, startlingly thought-provoking, disturbing blockbuster of a thriller that provides a chilling glimpse of a future that's just one modification away… Published February 17th by Orenda. Buy here Breathless by Amy McCullock IT'S ICE COLD. YOU'RE MILES FROM HELP. AND ONE OF YOU WILL BE NEXT . . . Pre-order next year's most gripping thriller now, and ensure you're the first to read the book that everyone will be talking about 'A high-altitude, high-stakes thriller that combines fascinating, authentic mountaineering experience with pure thriller entertainment. I loved it' MATT HAIG, Sunday Times bestselling author of THE MIDNIGHT LIBRARY When struggling journalist Cecily Wong is invited to join an expedition to climb one of the world's tallest mountains, it seems like the chance of a lifetime. She doesn't realise how deadly the climb will be. As their small team starts to climb, things start to go wrong. There's a theft. Then an accident. Then a mysterious note, pinned to her tent: there's a murderer on the mountain. The higher they get, the more dangerous the climb becomes, and the more they need to trust one another. And that's when Cecily finds the first body . . . The Gifts by Liz Hyder The luminous debut adult novel from the Waterstones Prize Winner, perfect for fans of The Mermaid and Mrs Hancock, The Essex Serpent and The Doll Factory In an age defined by men, it will take something extraordinary to show four women who they truly are . . . October 1840. A young woman staggers alone through a forest in Shropshire as a huge pair of impossible wings rip themselves from her shoulders. Meanwhile, when rumours of a 'fallen angel' cause a frenzy across London, a surgeon desperate for fame and fortune finds himself in the grip of a dangerous obsession, one that will place the women he seeks in the most terrible danger . . . THE GIFTS is the astonishing debut adult novel from the lauded author of BEARMOUTH. A gripping and ambitious book told through five different perspectives and set against the luminous backdrop of nineteenth century London, it explores science, nature and religion, enlightenment, the role of women in society and the dark danger of ambition. Published February 17th by Manilla Press. Buy here* The Girl Who Fell Beneath the Sea by Axie Oh Deadly storms. An ancient curse. Will her sacrifice save them all? For generations, deadly storms have ravaged Mina's homeland. Her people believe the Sea God, once their protector, now curse them with death and despair. To appease him, each year a maiden is thrown into the sea, in the hopes that one day the 'true bride' will be chosen and end the suffering. Many believe Shim Cheong – Mina's brother's beloved – to be the legendary true bride. But on the night Cheong is sacrificed, Mina's brother follows her, even knowing that to interfere is a death sentence. To save her brother, Mina throws herself into the water in Cheong's stead. Swept away to the Spirit Realm, a magical city of lesser gods and mythical beasts, Mina finds the Sea God, trapped in an enchanted sleep. With the help of a mysterious young man and a motley crew of demons, gods and spirits, Mina sets out to wake him and bring an end to the storms once and for all. But she doesn't have much time: a human cannot live long in the land of the spirits. And there are those who would do anything to keep the Sea God from waking . . . The Girl Who Fell Beneath the Sea is a magical feminist retelling of a classic Korean legend, perfect for fans of Uprooted and Miyazaki's Spirited Away. Published February 22nd by Hodder & Stoughton. Buy here* Nasty Little Cuts by Tina Baker WHO WILL SURVIVE THE NIGHT? A nightmare jolts Debs awake. She leaves the kids tucked up in their beds and goes downstairs. There's a man in her kitchen, holding a knife. But it's not an intruder. This is her husband Marc, the father of her children. A man she no longer recognises. Once their differences were what drew them together, what turned them on. Him, the ex-army officer from a good family. Her, the fitness instructor who grew up over a pub. But now these differences grate to the point of drawing blood. Marc screams in his sleep. And Debs hardly knows the person she's become, or why she lets him hurt her. Neither of them is completely innocent. Neither is totally guilty. Marc is taller, stronger, and more vicious, haunted by a war he can't forget. But he has no idea what Debs is capable of when her children's lives are at stake… A powerful exploration of a relationship built on passion, poisoned by secrets and violence. Perfect for readers of Blood Orange and Big Little Lies. Published February 24th by Viper. Buy here* Published March 3rd by Orion. Buy here* Where nothing goes unseen. And everyone has a story to unlock. Something terrible happened here last night. Only you – and the killer – hold the key . . . Published March 3rd by Harper Collins. Buy here* July, 1931. Rosemary lives in the Marsh House with her austere father, surrounded by unspoken truths and rumours. So when the glamorous Lafferty family move to the village, she succumbs easily to their charm. Dazzled by the beautiful Hilda and her dashing brother, Franklin, Rosemary fails to see the danger that lurks beneath their bright façades… Published March 3rd by Apollo. Buy here* Published March 10th by Viper. Buy here* 'An echo of Daphne du Maurier' Independent Published March 17th by Hodder & Stoughton. Buy here* First Born by Will Dean THE LAST THING A TWIN EXPECTS IS TO BE ALONE … Molly lives a quiet, contained life in London. Naturally risk averse, she gains comfort from security and structure. Every day the same. Her identical twin Katie is her exact opposite: gregarious and spontaneous. They used to be inseparable, until Katie moved to New York a year ago. Molly still speaks to her daily without fail. But when Molly learns that Katie has died suddenly in New York, she is thrown into unfamiliar territory. Katie is part of her DNA. As terrifying as it is, she must go there and find out what happened. As she tracks her twin's last movements, cracks begin to emerge. Nothing is what it seems. And a web of deceit is closing around her. Delivering the same intensity of pace and storytelling that made THE LAST THING TO BURN a word-of-mouth sensation, FIRST BORN will surprise, shock and enthral. Published April 14th by Hodder & Stoughton. Buy here* Into the Dark by Fiona Cummins Into the Dark is the new dark and gripping crime thriller from Fiona Cummins about revenge, greed, ambition and the true cost of friendship. THE PLACE: Seawings, a beautiful Art Deco home overlooking the sweep of the bay in Midtown-on-Sea. THE CRIME: The gilded Holden family – Piper and Gray and their two teenage children, Riva and Artie – has vanished from the house without a trace. THE DETECTIVE: DS Saul Anguish, brilliant but with a dark past, treads the narrow line between light and shade. One late autumn morning, Piper's best friend arrives at Seawings to discover an eerie scene – the kettle is still warm, all the family's phones are charging on the worktop, the cars are in the garage. But the house is deserted. In fifteen-year-old Riva Holden's bedroom, scrawled across the mirror in blood, are three words: Published April 14th by Pan Macmillan. Buy here* Elektra by Jennifer Saint An exciting and equally lyrical new retelling from Jennifer Saint, the Sunday Times bestselling author of ARIADNE 'Saint's immersive novel thrusts the reader straight into the heart of Greek mythology' ipaper on Ariadne The House of Atreus is cursed. A bloodline tainted by a generational cycle of violence and vengeance. This is the story of three women, their fates inextricably tied to this curse, and the fickle nature of men and gods. Clytemnestra The sister of Helen, wife of Agamemnon – her hopes of averting the curse are dashed when her sister is taken to Troy by the feckless Paris. Her husband raises a great army against them and determines to win, whatever the cost. Princess of Troy, and cursed by Apollo to see the future but never to be believed when she speaks of it. She is powerless in her knowledge that the city will fall. The youngest daughter of Clytemnestra and Agamemnon, Elektra is horrified by the bloodletting of her kin. But can she escape the curse, or is her own destiny also bound by violence? Published April 28th by Wildfire. Buy here* The No-Show by Beth O'Leary The funny, heart-breaking and uplifting new novel from the bestselling author of The Flatshare Three women. Three dates. One missing man… 8.52 a.m. Siobhan is looking forward to her breakfast date with Joseph. She was surprised when he suggested it – she normally sees him late at night in her hotel room. Breakfast on Valentine's Day surely means something … so where is he? 2.43 p.m. Miranda's hoping that a Valentine's Day lunch with Carter will be the perfect way to celebrate her new job. It's a fresh start and a sign that her life is falling into place: she's been dating Carter for five months now and things are getting serious. But why hasn't he shown up? 6.30 p.m. Joseph Carter agreed to be Jane's fake boyfriend at an engagement party. They've not known each other long but their friendship is fast becoming the brightest part of her new life in Winchester. Joseph promised to save Jane tonight. But he's not here… Meet Joseph Carter. That is, if you can find him. The No-Show is the brilliantly funny, heart-breaking and joyful new novel from Beth O'Leary about dating, and waiting, and the ways love can find us. An utterly extraordinary tearjerker of a book, this is O'Leary's most ambitious novel yet. Published April 28th by Quercus. Buy here* The Birdcage by Eve Chase Some secrets need to be set free . . . When half-sisters Kat, Flora and Lauren are unexpectedly summoned to Rock Point, the remote Cornish house where they spent their childhood summers, it is the first time they have been there together since their artist father painted them in the celebrated Girls and Birdcage. Since then they have drifted apart into wildly different lives, each one determined to forget the fateful summer of twenty years ago. But when they arrive at Rock Point it is clear they are not alone. Someone is lurking in the shadows, watching their every move. Someone who remembers what they did, and has been waiting for their return. As the events of that summer rise closer to the surface, will the three sisters escape unscathed for a second time? Or are some secrets too powerful to remain under lock and key? An emotional mystery full of dark secrets and twists, transporting the reader to the rugged remote landscape of north Cornwall. Published April 28th by Michael Joseph. Buy here* Miss Aldridge Regrets by Louise Hare From the author of This Lovely City comes a new historical murder mystery, this time set on board the Queen Mary Lena Aldridge is wondering if life has passed her by. The dazzling theatre career she hoped for hasn't worked out. Instead, she's stuck singing in a sticky-floored basement club in Soho and her married lover has just left her. She has nothing to look forward to until a stranger offers her the chance of a lifetime: a starring role on Broadway and a first-class ticket on the Queen Mary bound for New York. After a murder at the club, the timing couldn't be better and Lena jumps at the chance to escape England. Until death follows her onto the ship and she realises that her greatest performance has already begun. Because someone is making manoeuvres behind the scenes, and there's only one thing on their mind… Miss Aldridge Regrets is the exquisite new novel from Louise Hare, the author of This Lovely City. A brilliant murder mystery, it also explores class, race and pre-WWII politics, and will leave readers reeling from the beauty and power of it. Published April 28th by HQ. Buy here* Beggar's Abbey by V.L. Valentine A dark house filled with darker secrets… Winter 1954, and in a dilapidated apartment in Brooklyn, Sam Cooper realises that she has nothing left. Her mother is dead, she has no prospects, and she cannot afford the rent. But as she goes through her mother's things, Sam finds a stack of hidden letters that reveal a family and an inheritance that she never knew she had, three thousand miles away in Yorkshire. Begars Abbey is a crumbling pile, inhabited only by Sam's crippled grandmother, Lady Cooper, a housekeeper and a handful of servants. Sam cannot understand why her mother kept its very existence a secret, but her diaries offer a glimpse of a young girl growing increasingly terrified. As is Sam herself. Built on the foundations of an old convent, Begars moves and sings with the biting wind. Her grandmother cannot speak, and a shadowy woman moves along the corridors at night. For there are dark places in the hidden tunnels beneath Begars. And they will not give up their secrets easily… Perfect for readers of Laura Purcell and Natasha Pulley, Begars Abbey will keep you up at night. Published April 28th by Viper. Buy here* Idol by Louise O'Neill 'Follow your heart and speak your truth.' For Samantha Miller's young fans – her 'girls' – she's everything they want to be. She's an oracle, telling them how to live their lives, how to be happy, how to find and honour their 'truth'. And her career is booming: she's just hit three million followers, her new book Chaste has gone straight to the top of the bestseller lists and she's appearing at sell-out events. Determined to speak her truth and bare all to her adoring fans, she's written an essay about her sexual awakening as a teenager, with her female best friend, Lisa. She's never told a soul but now she's telling the world. The essay goes viral. But then – years since they last spoke – Lisa gets in touch to say that she doesn't remember it that way at all. Her memory of that night is far darker. It's Sam's word against Lisa's – so who gets to tell the story? Whose 'truth' is really a lie? 'You put yourself on that pedestal, Samantha. You only have yourself to blame.' Riveting, compulsive and bold, IDOL interrogates our relationship with our heroes and explores the world of online influencers, asking how well we can ever really know those whose carefully curated profiles we follow online. And it asks us to consider how two memories of the same event can differ, and how effortlessly we choose which stories to believe. Published May 12th by Bantam Press. Buy here* Wrong Place, Wrong Time by Gillian McAllister Can you stop a murder after it's already happened? It's every parent's nightmare. Your happy, funny, innocent son commits a terrible crime: murdering a complete stranger. You don't know who. You don't know why. You only know your teenage boy is in custody and his future lost. That night you fall asleep in despair. Until you wake . . . . . . and it is yesterday. Every morning you wake up a day earlier, another day before the murder. Another chance to stop it. Somewhere in the past lie the answers,and you don't have a choice but to find them . . . Published May 12th by Michael Joseph. Buy here* Take My Hand by Dolen Perkins-Valdez 'Shot through with spirit and hope, it's one hell of a book' Stylist, Books You Can't Miss in 2022 A nurse at the Family Planning Clinic in Montgomery Alabama, Civil Townsend is passionate about putting choice into women's hands. She brings the option of birth control to their doorsteps, and with it the right to determine their own destinies. Or so she believes. When she is assigned to administer birth control to two school-age Black girls, the Williams sisters, who live off an old unpaved road in a shack without running water, Civil can't help but feel uneasy. She grows close to the family and becomes fiercely invested in their well-being. And then she makes a shocking discovery: the girls have been involuntarily sterilized. Civil is horrified that such a terrible mistake could have taken place, and vows to get to the bottom of it. She soon learns that this is no isolated event but a pattern, far more serious than she could ever have imagined, targeting poor Black women. Could her clinic be responsible? Had she and her fellow Black nurses been complicit? No matter how ugly, Civil is determined for the truth to be brought to light. Based on true events, Take My Hand brims with hope, compassion, and the burning pursuit of justice. Published May 12th by Phoenix. Buy here* The Dance Tree by Kiran Millwood-Hargrave In Strasbourg, in the boiling hot summer of 1518, a plague strikes the women of the city. First it is just one – a lone figure, dancing in the main square – but she is joined by more and more and the city authorities declare an emergency. Musicians will be brought in. The devil will be danced out of these women. Just beyond the city's limits, pregnant Lisbet lives with her mother-in-law and husband, tending the bees that are their livelihood. Her best friend Ida visits regularly and Lisbet is so looking forward to sharing life and motherhood with her. And then, just as the first woman begins to dance in the city, Lisbet's sister-in-law Nethe returns from six years' penance in the mountains for an unknown crime. No one – not even Ida – will tell Lisbet what Nethe did all those years ago, and Nethe herself will not speak a word about it. It is the beginning of a few weeks that will change everything for Lisbet – her understanding of what it is to love and be loved, and her determination to survive at all costs for the baby she is carrying. Lisbet and Nethe and Ida soon find themselves pushing at the boundaries of their existence – but they're dancing to a dangerous tune . . . From Kiran Millwood Hargrave, the bestselling author of The Mercies, The Dance Tree is a heart-stopping story of family secrets, forbidden love and women pushed to the edge. Published May 12th by Picador. Buy here* Do No Harm by Jack Jordan My son has been taken. And I've been given a choice… Kill a patient on the operating table. Or never see him again. The man lies on the table in front of me. As a surgeon, it's my job to save him. As a mother, I know I must kill him. You might think that I'm a monster. But there really is only one choice. I must get away with murder. Or I will never see my son again. I'VE SAVED MANY LIVES. WOULD YOU TRUST ME WITH YOURS? DON'T MISS THE HEART-STOPPING THRILLER OF 2022 #DONOHARM Madwoman by Louisa Treger In 1887 young Nellie Bly sets out for New York and a career in journalism, determined to make her way as a serious reporter, whatever that may take. But life in the city is tougher than she imagined. Down to her last dime and desperate to prove her worth, she comes up with a dangerous plan: to fake insanity and have herself committed to the asylum that looms on Blackwell's Island. There, she will work undercover to document – and expose – the wretched conditions faced by the patients. But when the asylum door swings shut behind her, she finds herself in a place of horrors, governed by a harshness and cruelty she could never have imagined. Cold, isolated and starving, her days of terror reawaken the traumatic events of her childhood. She entered the asylum of her own free will – but will she ever get out? An extraordinary portrait of a woman way ahead of her time, Madwoman is the story of a quest for the truth that changed the world. Published by Bloomsbury. Buy here* The Set-Up by Lizzie Dent He thinks it's fate. She set the whole thing up. Mara wants to believe in fate – she's just never had a good reason to. Until now… After a case of mistaken identity, and the appearance of Joe – a gorgeous Austrian cellist – Mara has the chance to set up her own destiny. But life is complicated… The lido where she works is under threat and her new housemate, Mike, proves to be more than she bargained for. Will Mara manage to arrange her own happiness? And what if true love is closer to home than she thinks? Published June 9th by Viking. Buy here* No Place To Run by Mark Edwards No synopsis available. Published June 21st by Thomas & Mercer. Buy here* The Bay by Allie Reynolds There's a darkness inside all of us and The Bay has a way of bringing it out. Everyone here has their secrets but we don't go looking for them. Because sometimes it's better not to know. The waves are to die for at The Bay. It's a paradise they would kill to keep. The Beach meets Point Break in the thriller of the summer by Allie Reynolds. Kenna arrives in Sydney to surprise her best friend, shocked to hear she's going to marry a guy she's only just met. But Mikki and her fiancé Jack are about to head away on a trip, so Kenna finds herself tagging along for the ride. Sorrow Bay is beautiful, wild and dangerous. A remote surfing spot with waves to die for, cut off from the rest of the world. Here Kenna meets the mysterious group of people who will do anything to keep their paradise a secret. Sky, Ryan, Clemente and Victor have come to ride the waves and disappear from life. How will they feel about Kenna turning up unannounced? As Kenna gets drawn into their world, she sees the extremes they are prepared to go to for the next thrill. And everyone seems to be hiding something. What has her best friend got involved in and how can she get her away? But one thing is rapidly becoming clear about The Bay: nobody ever leaves. Published June 23rd by Headline. Buy here* The Guest House by Ronin Morga-Bentley KEEP YOUR FAMILY SAFE. WHATEVER THE COST… Jamie and Victoria are expecting their first baby. With a few weeks to go, they head off for a final weekend break in a remote part of the North Pennines. The small and peaceful guesthouse is the ideal location to unwind together before becoming parents. Upon arrival, they are greeted by Barry and Fiona, the older couple who run the guesthouse. They cook them dinner and show them to their room before retreating to bed themselves. The next morning, Jamie and Victoria wake to find the house deserted. Barry and Fiona are nowhere to be seen. All the doors are locked. Both their mobile phones and car keys have disappeared. Even though it's a few weeks early, Victoria knows the contractions are starting. The baby is coming, and there's no way out. Published June 23rd by Orion. Buy here* The Guilty Couple by C.L. Taylor The Sunday Times and million copy bestseller returns with her most pulse-pounding, page-turning book yet. Five years ago, Olivia Sutherland was wrongfully convicted of plotting to murder her husband. Now she's finally free, Olivia has three goals: repair her relationship with her teenage daughter, clear her name, and bring down her husband – the man who framed her. Just how far is she willing to go to get what she wants? And how far will her husband go to stop her? Because his lies run deeper than Olivia could ever have imagined – and this time it's not her freedom that's in jeopardy, but her life… Published June 23rd by Avon. Buy here* The Museum of Ordinary People by Mike Gayle Inspired by a box of mementos found abandoned in a skip following a house clearance, The Museum of Ordinary People is a poignant, thought-provoking but ultimately uplifting story of memory and love, grief, loss and the things we leave behind. It is another brilliant novel from an author who seems to have the absolute knack of writing topical, engaging, heartwarming stories which really connect with readers. Published July 7th by Hodder & Stoughton. Buy here* My Other Husband by Dorothy Koomson What if your murderous fantasies start to come true? Someone is trying to frame me for murder. They're hurting people in the ways I write about – and making sure I'm the prime suspect. I think I know why. But I can't tell the police or even use my rock-solid alibi . . . Because then I'd have to confess about my other husband. A series of terrifying murders. A set of complex lies. And a woman with no way to clear her name. My Other Husband is the latest gripping thriller from the Queen of The Big Reveal. Published July 7th by Headline. Buy here* Truly Darkly Deeply by Victoria Selman 12-year-old Sophie and her mother, Amelia-Rose, move to London from Massachusetts where they meet the charismatic Matty Melgren, who quickly becomes an intrinsic part of their lives. But as the relationship between the two adults fractures, a serial killer begins targeting young women with a striking resemblance to Amelia-Rose. When Matty is eventually sent down for multiple murders, questions remain as to his guilt — questions which ultimately destroy both women. Nearly twenty years later, Sophie receives a letter from Battlemouth Prison informing her Matty is dying and wants to meet. It looks like Sophie might finally get the answers she craves. But will the truth set her free — or bury her deeper? Published July 7th by Quercus. Buy here* Things We Do in the Dark by Jennifer Hillier Things We Do in the Dark is a brilliant new thriller from Jennifer Hillier, the award-winning author of the breakout novels Little Secrets and Jar of Hearts. Paris Peralta is suspected of killing her celebrity husband, and her long-hidden past now threatens to destroy her future. When Paris Peralta is arrested in her own bathroom–covered in blood, holding a straight razor, her celebrity husband dead in the bathtub behind her–she knows she'll be charged with murder. But as bad as this looks, it's not what worries her the most. With the unwanted media attention now surrounding her, it's only a matter of time before someone from her long hidden past recognizes her and destroys the new life she's worked so hard to build, along with any chance of a future. Twenty-five years earlier, Ruby Reyes, known as the Ice Queen, was convicted of a similar murder in a trial that riveted Canada in the early nineties. Reyes knows who Paris really is, and when she's unexpectedly released from prison, she threatens to expose all of Paris's secrets. Left with no other choice, Paris must finally confront the dark past she escaped, once and for all. Because the only thing worse than a murder charge are two murder charges. Published July 19th by Minotaur Books. Buy here* The Retreat by Sarah Pearse Most are here to recharge and refresh. But someone's here for revenge . . . The addictive new thriller from the global bestselling author of The Sanatorium. An eco-wellness retreat has opened on an island off the coast of Devon, promising rest and relaxation – but the island itself, known locally as Reaper's Rock, has a dark past. Once the playground of a serial killer, it's rumoured to be cursed. DS Elin Warner is called to the retreat when a young woman's body is found on the rocks below the yoga pavilion, in what seems to be a tragic fall. But the victim wasn't a guest – she wasn't meant to be on the island at all. When a man drowns in a diving incident the following day, Elin starts to suspect that there's nothing accidental about these deaths. But why would someone target the retreat – and who else is in danger? Elin must find the killer – before the island's history starts to repeat itself . . . Published July 21st by Bantam Press. Buy here* That Bonesetter Woman by Frances Quinn It's usual, they say, for a young person coming to London for the first time to arrive with a head full of dreams. Well, Endurance Proudfoot did not. When she stepped off the coach from Sussex, on a warm and sticky afternoon in the summer of 1757, it never occurred to her that the city would be the place where she'd make her fortune; she was just very annoyed to be arriving there at all. Meet Endurance Proudfoot, the bonesetter's daughter: clumsy as a carthorse, with a tactless tongue and a face she's sure only a mother could love. Durie only wants one thing in life – to follow her father and grandfather into the family business of bonesetting. It's a physically demanding job, requiring strength, nerves of steel and discretion – and not the job for a woman. But Durie isn't like other women. She's strong and stubborn and determined to get her own way. And she finds that she has a talent at bonesetting – her big hands and lack of grace have finally found their natural calling. So, when she is banished to London with her sister, who is pretty, delicate and exactly the opposite to Durie in every way, Durie will not let it stop her realising her dreams. And while her sister will become one of the first ever Georgian celebrities, Durie will become England's first and most celebrated female bonesetter. But what goes up must come down, and Durie's elevated status may well become her undoing… Published August 4th by Simon and Schuster. Buy here* The Last Party by Clare Macintosh On New Year's Eve, Rhys Lloyd has a house full of guests. His lakeside holiday homes are a success, and he's generously invited the village to drink champagne with their wealthy new neighbours. This will be the party to end all parties. But not everyone is there to celebrate. By midnight, Rhys will be floating dead in the freezing waters of the lake. On New Year's Day, DC Ffion Morgan has a village full of suspects. The tiny community is her home, so the suspects are her neighbours, friends and family – and Ffion has her own secrets to protect. With a lie uncovered at every turn, soon the question isn't who wanted Rhys dead . . . but who finally killed him. In a village with this many secrets, a murder is just the beginning. Published August 4th by Sphere. Buy here* Daisy Darker by Alice Feeney Daisy Darker is an all-consuming tale of psychological suspense with a spectacular twist from the internationally bestselling author Alice Feeney Daisy Darker's family were as dark as dark can be, when one of them died all of them lied and pretended not to see . . . Daisy Darker is arriving at her grandmother's house for her eightieth birthday. It is Halloween, and Seaglass – the crumbling Cornish house perched upon its own tiny private island – is at one with the granite rocks it sits on. The Darker family haven't all been in the same place for over a decade, and when the tide comes in they'll be cut off from the rest of the world for eight hours. When the tide goes back out, nothing will ever be the same again, because one of them is a killer . . . Published August 18th by Pan MacMillan. Buy here* Something Wicked by Laura Purcell From the Sunday Times bestselling author comes a gripping tale of obsession, superstition and ambition, set against the atmospheric backdrop of Victorian London. Be careful what you wish for… it may just come true. By the pricking of my thumbs… Published August 25th by Raven Books. Buy here* The Girl on the 88 Bus by Freya Sampson When Libby Nicholls arrives in London, broken-hearted and with her life in tatters, the first person she meets on the bus is elderly pensioner Frank. He tells her about the time in 1962 he met a girl on the number 88 bus with beautiful red hair just like her own. They made plans for a date at the National Gallery, but Frank lost the ticket with her number written on it. For the past sixty years, he's ridden the same bus trying to find her. Libby is inspired by the story and, with the help of an unlikely companion, she makes it her mission to help Frank's search. As she begins to open her guarded heart to strangers and new connections, Libby's tightly controlled world expands. But with Frank's dementia progressing quickly, their chance of finding the girl on the number 88 bus is slipping away. More than anything, Libby wants Frank to see his lost love one more time. But their quest also shows Libby just how important it is to embrace her own chances for happiness – before it's too late. A beautifully uplifting novel about how one chance meeting can change the course of your life Published September 8th by Zaffre. Buy here* So what do you think? Will you be adding any of these to your tbr? Let me know in the comments. Thanks for reading Bibliophiles ☺️ Emma xxx Tags Alice Feeney, Allie Reynolds, Amy McCulloch, Anna Mazzola, Anticipated Treasures 2022, Apollo, April 2022, August 2022, Avon, Avon Books UK, Axie Oh, Bantam Press, Begar's Abbey, Beth Morrey, Beth O'Leary, Beth Underdown, Bloomsbury Publishing, Bloomsbury UK, Bonnier Zaffre, Breathless, C.L. Taylor, Catriona Ward, Clare Macintosh, Daisy Darker, Do No Harm, Dolen Perkins-Valdez, Dorothy Koomson, Elektra, Emma's Anticipated Treasures, Eve Chase, Eve Smith, February 2022, Fiona Cummins, First Born, Frances Quinn, Freya Sampson, Gillian McAllister, Girl on the 88 Bus, Hanya Yanagihara, Harper Collins UK, Headline, Hodder & Stoughton, HQ, Idol, Into The Dark, Isabel Allende, Jack Jordan, Janice Hallett, January 2022, Jennifer Hillier, Jennifer Saint, Joanne Burn, July 2022, June 2022, Kiran Millwood Hargrave, Laura Purcell, Liz Hyder, Louisa Treger, Louise Hare, Louise O'Neill, Lucy Foley, Madwoman, Manilla Press, March 2022, Mark Edwards, May 2022, Michael Joseph, Mike Gayle, Minotaur Books, Miss Aldridge Regrets, Most Anticipated 2022, Nasty Little Cuts, No Place To Run, Off Target, Orenda, Orenda Books, Orion, orion books, Pan Macmillan, Phoenix, Picador, Polly Crosby, Quercus, Quercus books, Robin Morgan-Bentley, Sarah Maine, Sarah Pearse, September 2022, Simon & Schuster UK, Something Wicked, Sophie Hannah, Sphere, Sundial, Take My Hand, That Bonesetter Woman, The Awakenings, The Bay, The Birdcage, The Clockwork Girl, The Couple at the Table, The Dance Tree, The Gifts, The Girl Who Fell Beneath The Sea, The Guest House, The Guilty Couple, The Hemlock Cure, The Key in the Lock, The Last Party, The Marsh House, The Museum of Ordinary People, The No-Show, The Other Husband, The Paris Apartment, The Retreat, The Twyford Code, The Unravelling, Things We Do in the Dark, Thomas & Mercer, Tina Baker, To Paradise, Truly Darkly Deeply, V. L. Valentine, Victoria Selman, Viking, Violeta, Viper, Viper Books, Wildfire, Will Dean, Wrong Place, Wrong Time, Zaffre, Zoe Somerville Blog Tour: Lemon by Kwon Yeo-sun (Translated by Janet Hong) Post date 14th Oct 2021 1 Comment on Blog Tour: Lemon by Kwon Yeo-sun (Translated by Janet Hong) Published: October 14th, 2021 Genre: Literary Crime Fiction, Contemporary Fiction, Thriller, Translated Fiction Format: Hardcover, Kindle, Audio Happy Publication Day to this intriguing and thought-provoking novel. Thank you to Jade at Head of Zeus for the invitation to take part and the gifted ARC. In the summer of 2002, nineteen-year-old Kim Hae-on was murdered in what became known as the High School Beauty Murder. There were two suspects: Shin Jeongjun, who had a rock-solid alibi, and Han Manu, to whom no evidence could be pinned. The case went cold. Seventeen years pass without justice, and the grief and uncertainty take a cruel toll on her younger sister, Da-on, in particular. Unable to move on with her life, Da-on tries in her own twisted way to recover some of what she's lost, ultimately setting out to find the truth of what happened. Told at different points in time from the perspectives of Da-on and two of Hae-on's classmates, Lemon is a piercing psychological portrait that takes the shape of a crime novel and is a must-read novel of 2021. "And so began the revenge of the yellow angel. Lemon, I muttered. Like a chant of revenge, I muttered: Lemon, lemon, lemon." Set in Korea, Lemon examines the murder of nineteen-year-old Kim Hae-on in July 2002 and the impact it had on those left behind. Told by a trio of narrators, the story begins with the interrogation of one of the two boys suspected of her murder, and then follows chronologically to the present day as her sister searches for the truth of what happened that summer night. The story unfolds from three different perspectives: the victim's sister, Da-on, and two of her classmates and each has a unique voice that makes them easy to distinguish from one another. But it is Da-on whose voice is the loudest of them all. Hae-on was the beautiful older sister and when she was killed Da-on was left feeling even more inadequate in comparison. To try and fill the void of her sister's absence Da-on resorted to extreme measures, including extensive plastic surgery, to try and emulate her sister. But it didn't work and she is still left struggling to move on. Over the years she becomes increasingly focused on Han Manu, one of the boys suspected of Hae-on's murder, and embarks on an obsessive search for answers and revenge. It would be impossible not to feel for Da-on, her pain so vivid and raw that it makes you want to weep. And while I didn't always agree with her actions, I did understand them. An intriguing and compelling read, there is a dark, haunting atmosphere that pervades each page. Beautifully written, I loved how the author used different writing styles for the different narrators yet still manages to make it all blend together and flow seamlessly. I particularly loved the chapter titled 'Rope' as it just felt so unique, so different to anything else I've read. But I have to confess that I have been left with mixed feelings about this one and think it will be a bit of a marmite book. I was all set to give this a five star rating but then it ended in such a sudden and ambiguous way. I was left feeling stunned, like I must have missed something as surely that couldn't be it. I've been pondering on it ever since I finished and I still feel the same way. While I think this is a great book that is worth reading, I would caution anyone who reads it to be prepared for a cryptic climax that will make you think about what you just read. While it is a short read at just 148 pages, this is a book packed with emotion that examines a variety of topics. Not only does it look at the impact of Hae-on's death on those still living over the years, but it also looks at how families were torn apart and lives ruined by suspicion. It also explores how a desire for justice can lead to a quest for vengeance and asks if healing is ever really served by doing so. Is it better to sometimes leave things without closure than cause further hurt and pain by focusing on the past? A thought-provoking and fascinating read, Lemon is a striking and reflective story that will linger long after that final page. Rating: ✯✯✯✯✰ Kwon Yeo-sun was born in Andong, North Gyeongsang Province of South Korea in 1965. Kwon enjoyed a brilliant literary debut in 1996 when her novel Niche of Green was awarded the Sangsang Literary Award. At the time, novels that reflected on the period of the democratization movement in South Korea, were prevalent. MEET THE TRANSLATOR: Janet Hong is a writer and translator based in Vancouver, Canada. She received the 2018 TA First Translation Prize for her translation of Han Yujoo's The Impossible Fairy Tale, which was also a finalist for both the 2018 PEN Translation Prize and the 2018 National Translation Award. She has translated Ha Seong-nan's Flowers of Mold, Ancco's Bad Friends, and Keum Suk Gendry-Kim's Grass. Waterstones*| Bookshop.org*| Amazon| Google Books| Apple Books| Kobo Thanks for reading Bibliophiles😊 Emma xxx Tags Apollo, Blog Tour, Book Review, contemporary fiction, Emma's Anticipated Treasures, Four star reads, Janet Hong, Kwon Yeo-Sun, Lemon, Literary Crime Fiction, October 2021, October Books, thriller, Translated Fiction Emma's Anticipated Treasures – October 2021 Post date 24th Sep 2021 No Comments on Emma's Anticipated Treasures – October 2021 Can you believe that we are almost in October? The nights are drawing in, the air is cooler and spooky season is upon us in the book world. And I'm thrilled! I'm also looking forward that the Christmassy books are starting to be released too. It comes together to make this month's anticipated releases an eclectic and exciting mix. The Spirit Engineer by A. J. West Publisher: Duckworth Genre: Ghost Story SYNOPISIS: A CHILLING DEBUT TEEMING WITH SPIRITS, SÉANCES AND SCANDAL. Belfast, 1914. Two years after the sinking of the Titanic, high society has become obsessed with spiritualism, attending séances in the hope they might reach their departed loved ones. William Jackson Crawford is a man of science and a sceptic, but one night with everyone sitting around the circle, voices come to him – seemingly from beyond the veil – placing doubt in his heart and a seed of obsession in his mind. Could the spirits truly be communicating with him or is this one of Kathleen's parlour tricks gone too far? Based on the true story of Professor William Jackson Crawford and famed medium Kathleen Goligher, and with a cast of characters including Sir Arthur Conan Doyle and Harry Houdini, The Spirit Engineer conjures a haunted, twisted tale of power, paranoia, and one ultimate, inescapable truth… Buy the book here* Fall by West Camel Genre: Psychological Fiction, Urban Fiction, Coming-of-Age Story Estranged brothers are reunited over plans to develop the tower block where they grew up, but the desolate estate becomes a stage for reliving the events of one life-changing summer. Twins Aaron and Clive have been estranged for forty years. Aaron still lives in the empty, crumbling tower block on the riverside in Deptford where they grew up. Clive is a successful property developer, determined to turn the tower into luxury flats. But Aaron is blocking the plan and their petty squabble becomes something much greater when two ghosts from the past – twins Annette and Christine – appear in the tower. At once, the desolate estate becomes a stage on which the events of one scorching summer are relived – a summer that shattered their lives, and changed everything forever… Grim, evocative and exquisitely rendered, Fall is a story of friendship and family – of perception, fear and prejudice, the events that punctuate our journeys into adulthood, and the indelible scars they leave – a triumph of a novel that will affect you long after the final page has been turned. The Room in the Attic by Louise Douglas Publisher: Boldwood Books Genre: Ghost Horror, Domestic Fiction A child who does not know her name… In 1903 fishermen find a wrecked boat containing a woman, who has been badly beaten, and a young girl. An ambulance is sent for, and the two survivors are taken to All Hallows, the imposing asylum, hidden deep on Dartmoor. The woman remains in a coma, but the little girl, Harriet, awakens and is taken to an attic room, far away from the noise of the asylum, and is put in the care of Nurse Emma Everdeen. Two motherless boys banished to boarding school… In 1993, All Hallows is now a boarding school. Following his mother's death and his father's hasty remarriage, Lewis Tyler is banished to Dartmoor, stripped of his fashionable clothes, shorn of his long hair, and left feeling more alone than ever. There he meets Isak, another lost soul, and whilst refurbishment of the dormitories is taking place, the boys are marooned up in the attic, in an old wing of the school. Cries and calls from the past that can no longer be ignored… All Hallows is a building full of memories, whispers, cries from the past. As Lewis and Isak learn more about the fate of Harriet, and Nurse Emma's desperate fight to keep the little girl safe, it soon becomes clear there are ghosts who are still restless. Are they ghosts the boys hear at night in the room above, are they the unquiet souls from the asylum still caught between the walls? And can Lewis and Isak bring peace to All Hallows before the past breaks them first… The Midnight Man by Caroline Mitchell Publisher: Embla Books Genre: Mystery, Thriller, Suspense From number one bestselling author Caroline Mitchell, comes the first chilling Slayton thriller for fans of C. J. Tudor and Stephen King. If you open your door to the Midnight Man, hide with a candle wherever you can. Try not to scream as he draws near, because one of you won't be leaving here… On Halloween night in Slayton, five girls go to Blackhall Manor to play the Midnight Game. They write their names on a piece of paper and prick their fingers to soak it in blood. At exactly midnight they knock on the door twenty-two times – they have invited the Midnight Man in. It was supposed to be a game, but only four girls come home. Detective Sarah Noble has just returned to the force, and no one knows more about Blackhall Manor than her. It's a case that will take Sarah back to everything she's been running from, and shake her to the core. Will she be ready to meet the Midnight Man? The Whistling by Rebecca Netley Genre: Ghost Story, Horror Fiction Alone in the world, Elspeth Swansome has taken the position of nanny to a family on the remote Scottish island of Skelthsea. Her charge, Mary, is a troubled child. Distracted and secretive, she hasn't uttered a word since the sudden death of her twin, William – just days after their former nanny disappeared. With Mary defiantly silent, Elspeth turns to the islanders. But no one will speak of what happened to William. Just as no one can explain the hypnotic lullabies sung in empty corridors. Nor the strange dolls that appear in abandoned rooms. Nor the faint whistling that comes in the night . . . As winter draws in and passage to the mainland becomes impossible, Elspeth finds herself trapped. But is this house haunted by the ghosts of the past? OR THE SECRETS OF THE LIVING..? Chilling, twisty and emotionally gripping, The Whistling is an atmospheric page-turner with shades of the classics, yet a unique character of its own. Perfect for fans of Susan Hill and Laura Purcell. We Are Not Like Them by Christine Pride and Jo Piazza Genre: Thriller, Contemporary Fiction THE MOST IMPORTANT NOVEL YOU'LL READ THIS YEAR Not every story is black and white. Riley and Jen have been best friends since they were children, and they thought their bond was unbreakable. It never mattered to them that Riley is black and Jen is white. And then Jen's husband, a Philadelphia police officer, is involved in the shooting of an unarmed black teenager and everything changes in an instant. This one act could destroy more than just Riley and Jen's friendship. As their community takes sides, so must Jen and Riley, and for the first time in their lives the lifelong friends find themselves on opposing sides. But can anyone win a fight like this? We Are Not Like Them is about friendship and love. It's about prejudice and betrayal. It's about standing up for what you believe in, no matter the cost. Lemon by Kwon Yeo-Sun Genre: Mystery, Thriller, Psychological Fiction, Crime Fiction, Domestic Fiction The Party Crasher by Sophie Kinsella Publisher: Bantam Press Genre: Contemporary Romance, Humorous Fiction The Talbots are having one last party at their family home. But Effie hasn't been invited . . . Effie's still not over her parents splitting up a year ago. Her dad and his new girlfriend are posting their PDAs all over Instagram – and no one should have to deal with photos of their dad with the hashtags #viagraworks and #sexinyoursixties. Now they're selling the beloved family home and holding a 'house-cooling' party. When Effie receives only a last-minute 'anti-invitation', she decides to give it a miss. Until she remembers her precious Russian dolls, safely tucked away up a chimney. She'll have to go back for them – but not as a guest. She'll just creep in, grab the dolls and make a swift exit. No one will know she was ever there. Of course, nothing goes to plan. Not only does Effie bump into her ex-boyfriend (who she's very much not over), she can't find the dolls. And as she secretly clambers around dusty attics, hides under tables and mournfully eyes up the dessert table, she discovers unexpected truths about her family – and even about herself. With time (and hiding places) running out, Effie starts to wonder if she'd be better off simply crashing the party. Perhaps that's the only way to find out what's really going on with her family… Expect shocking secrets, hilarious mix-ups and an unforgettable romance. Welcome to the party of the year! Black Drop by Leonora Nattrass Genre: Historical Fiction, Mystery, Crime Fiction This is the confession of Laurence Jago. Clerk. Gentleman. Reluctant spy. July 1794, and the streets of London are filled with rumours of revolution. Political radical Thomas Hardy is to go on trial for treason, the war against the French is not going in Britain's favour, and negotiations with the independent American colonies are on a knife edge. Laurence Jago – clerk to the Foreign Office – is ever more reliant on the Black Drop to ease his nightmares. A highly sensitive letter has been leaked to the press, which may lead to the destruction of the British Army, and Laurence is a suspect. Then he discovers the body of a fellow clerk, supposedly a suicide. Blame for the leak is shifted to the dead man, but even as the body is taken to the anatomists, Laurence is certain both of his friend's innocence, and that he was murdered. But after years of hiding his own secrets from his powerful employers, and at a time when even the slightest hint of treason can lead to the gallows, how can Laurence find the true culprit without incriminating himself? A thrilling historical mystery, perfect for readers of C.J. Sansom, Andrew Taylor, Antonia Hodgson and Laura Shepherd-Robinson. The Watchers by A.M. Shine Genre: Fairy Tale, Horror Fiction A spine-chilling Irish horror adventure set in the remote unknown forests of Galway, from debut Irish author A.M. Shine. You can't see them. But they can see you. This forest isn't charted on any map. Every car breaks down at its treeline. Mina's is no different. Left stranded, she is forced into the dark woodland only to find a woman shouting, urging Mina to run to a concrete bunker. As the door slams behind her, the building is besieged by screams. Mina finds herself in a room with a wall of glass, and an electric light that activates at nightfall, when the Watchers come above ground. These creatures emerge to observe their captive humans and terrible things happen to anyone who doesn't reach the bunker in time. Afraid and trapped among strangers, Mina is desperate for answers. Who are the Watchers and why are these creatures keeping them imprisoned, keen to watch their every move? Perfect for fans of Francine Toon, Paul Tremblay and Andrew Michael Hurley. The Hiding Place by Amanda Mason Genre: Thriller, Gothic Fiction, Ghost Story, Horror Fiction Some secrets can never be concealed . . . Nell Galilee, her husband and twelve year old step-daughter Maude rent a holiday cottage by the sea, needing time and space away from home. Nell grew up in this small, wind-blown town and has mixed feelings about returning, and it isn't long before she is recognised by a neighbour, seemingly desperate to befriend her. The cottage has been empty for some time, and from the start Nell feels uncomfortable there. Something isn't quite right about this place . . . Maude, furious about being brought here against her will, soon finds herself beguiled by the house's strange atmosphere. There are peculiar marks in the roof beams above her bedroom, and in another room, a hiding place, concealing a strange, unnerving object. As the house gradually reveals its secrets, Nell becomes increasingly uneasy – and Maude spellbound. But these women – and the women that surround them – are harbouring their own secrets too, and soon events will come to a terrible head . . . A brilliant, unsettling and chilling novel of mothers and daughters, truth and deception and the lengths people will go to, to obtain power over their own lives, The Hiding Place is the second chilling novel from the acclaimed author of The Wayward Girls. The Opposite of Butterfly Hunting by Evanna Lynch Publisher: Headline Genre: Memoir 'Gradually, I began to feel this dawning awareness that womanhood was coming for me, that it was looming inevitably, and it didn't feel safe…' Evanna Lynch has long been viewed as a role model for people recovering from anorexia and the story of her casting as Luna Lovegood in the Harry Potter films has reached almost mythic proportions. Here, in her fascinating new memoir, Evanna confronts all the complexities and contradictions within herself and reveals how she overcame a life-threatening eating disorder, began to conquer her self-hate and confronted her fear of leaving the neatness and safety of girlhood for the unpredictable journey of being a woman, all in the glare of the spotlight of international fame. Delving into the very heart of a woman's relationship with her own body, Evanna explores the pivotal moments and choices in her life that led her down the path of creativity and dreaming and away from the empty pursuit of perfection, and reaches towards acceptance of the wild, sensual and unpredictable reality of womanhood. This is a story of the tragedy and the glory of growing up, of mourning girlhood and stepping into the unknown, and how that act of courage is the most magical and creatively liberating thing a woman can do. I Know You by Claire McGowan In this tense thriller from the bestselling author of What You Did and The Other Wife, a woman finds a dead body. Will she make the same mistake as last time? When Rachel stumbles upon a body in the woods, she knows what she has to do: run. Get away. Do not be found at the scene. Last time, she didn't know, and she ended up accused of murder. But when this victim is identified as her boyfriend's estranged wife, Rachel realises she's already the prime suspect. With mounting evidence against her, Rachel's only hope is to keep the truth about herself well hidden. Because twenty years ago she was someone else―Casey, a young nanny trying to make it as an actress in Los Angeles. When the family she worked for were brutally murdered, all the evidence pointed to her and she went to prison. Back then, she narrowly escaped the death penalty and managed to free herself on appeal. Now she's fighting to save the life she's spent years piecing back together. But with her behaviour raising suspicion and the police closing in, Rachel can't help wondering: Was her discovery in the woods really just an awful coincidence, or is someone framing her for murder? Someone who knows who she is, and wants revenge… The Haunting Season Published: October 21st, 2021 Genre: Historical Fiction, Historical Fantasy, Horror Fiction, Ghost Story Eight bestselling, award-winning authors return to the time-honoured tradition of the seasonal ghost story in this dazzling new collection. This is your indispensable companion to the long, dark nights this October Long before Charles Dickens and Henry James popularized the tradition, the shadowy nights of winter have been a time for people to gather together by the flicker of candlelight and experience the intoxicating thrill of a ghost story. Now eight bestselling, award-winning authors-all of them master storytellers of the sinister and the macabre-bring the tradition to vivid life in a spellbinding new collection of original spine-tingling tales. Taking you from the frosty Fens to the wild Yorkshire moors, to the snow-covered grounds of a haunted estate, to a bustling London Christmas market, these mesmerizing stories will capture your imagination and serve as your indispensable companion to cold, dark nights. So curl up, light a candle, and fall under the spell of winters past. . . Murder Isn't Easy by Carla Valentine Genre: Biography, True Crime While other children were devouring the works of Enid Blyton and Beatrix Potter, Carla Valentine was poring through the pages of Agatha Christie novels. It was this early fascination that led to her job as a pathology technician, trained in forensics and working in mortuaries. Nearly every Agatha Christie story involves one – or, more commonly, several – dead bodies, and for a young Carla, a curious child already fascinated with biology, these stories and these bodies were perfect puzzles. Of course, Agatha herself didn't talk of 'forensics' in the way we use it now, but in each tale she writes of twists and turns with her expert weave of human observation, ingenuity and genuine science of the era. Through the medium of the 'whodunnit', Agatha Christie was a pioneer of forensic science, and in Murder Isn't Easy Carla illuminates all of the knowledge of one of our most beloved authors. Care For Me by Farah Cook Publisher: Hodder Studio Genre: Thriller, Suspense, Psychological Fiction When Amira takes her mother Afrah to Ravenswood Lodge Care Home, she thinks they will both be safe. But the past is just around the corner . . . Amira is struggling to look after her mother, Afrah. So when they arrive at Ravenswood Lodge Care Home, beautiful and imposing against the background of the Scottish Highlands, she hopes it is the right decision for them both. But soon Afrah insists her belongings are being stolen, her photographs, her jewellery, her pill boxes, Amira and the staff are convinced it's just Afrah's imagination, it's just her memory. But Afrah knows Ravenswood Lodge isn't a safe place. Could it have something to do with the past? She remembers newspaper clippings, hazy images of a fire years ago, a memory she's spent years forgetting and now she just wants to remember. Someone wants her gone. But first, she needs to convince Amira of the truth. The compelling, heartbreaking debut novel by Farah Cook, about mothers and daughters, and secrets that are never really forgotten . . . The Judge's List by John Grisham Genre: Thriller, Suspense, Legal Thriller, Political Fiction From the Sunday Times and New York Times bestselling author, a new legal thriller about a man who might be the most criminal sitting judge in American history. In The Whistler, Lacy Stoltz investigated a corrupt judge who was taking millions in bribes from a crime syndicate. She put the criminals away, but only after being attacked and nearly killed. Three years later, and approaching forty, she is tired of her work for the Florida Board on Judicial Conduct and ready for a change. Then she meets a mysterious woman who is so frightened she uses a number of aliases. Jeri Crosby's father was murdered twenty years earlier in a case that remains unsolved and that has grown stone cold. But Jeri has a suspect whom she has become obsessed with and has stalked for two decades. Along the way, she has discovered other victims. Suspicions are easy enough, but proof seems impossible. The man is brilliant, patient, and always one step ahead of law enforcement. He is the most cunning of all serial killers. He knows forensics, police procedure, and most important: he knows the law. He is a judge, in Florida – under Lacy's jurisdiction. He has a list, with the names of his victims and targets, all unsuspecting people unlucky enough to have crossed his path and wronged him in some way. How can Lacy pursue him, without becoming the next name on his list? The Judge's List is by any measure John Grisham's most surprising, chilling novel yet. Daughters of a Dead Empire by Carolyn Tara O'Neil Publisher: Roaring Brook Press Genre: Historical Fiction, Historical Mystery, Young Adult Fiction From debut author Carolyn Tara O'Neil comes a thrilling alternate history set during the Russian Revolution. Russia, 1918: With the execution of Tsar Nicholas, the empire crumbles and Russia is on the edge of civil war–the poor are devouring the rich. Anna, a bourgeois girl, narrowly escaped the massacre of her entire family in Yekaterinburg. Desperate to get away from the Bolsheviks, she offers a peasant girl a diamond to take her as far south as possible–not realizing that the girl is a communist herself. With her brother in desperate need of a doctor, Evgenia accepts Anna's offer and suddenly finds herself on the wrong side of the war. Anna is being hunted by the Bolsheviks, and now–regardless of her loyalties–Evgenia is too. Daughters of a Dead Empire is a harrowing historical thriller about dangerous ideals, loyalty, and the price we pay for change. An imaginative retelling of the Anastasia story. Medusa by Jessie Burton Publisher: Bloomsbury YA Genre: Folklore and Mythology, Greek Mythology, Young Adult Fiction A dazzling, feminist retelling of Greek myth from the internationally bestselling author of The Miniaturist, stunningly illustrated by Olivia Lomenech Gill. Exiled to a far-flung island by the whims of the gods, Medusa has little company except the snakes that adorn her head instead of hair. But when a charmed, beautiful boy called Perseus arrives on the island, her lonely existence is disrupted with the force of a supernova, unleashing desire, love and betrayal. Filled with glorious full-colour illustrations by award-winning Olivia Lomenech Gill, this astonishing retelling of Greek myth is perfect for readers of Circe and The Silence of the Girls. Illuminating the girl behind the legend, it brings alive Medusa for a new generation. Midnight in Everwood by M. A. Kuzniar Genre: Fairytale, Magical Realism, Historical Fantasy, Fantasy Fiction, Coming-of-Age Story In the darkness of night, magic awaits… The Nutcracker for adults, perfect for fans of Robert Dinsdale's The Toymakers, Erin Morgenstern's The Night Circus and Stephanie Garber's Caraval 'It was a rainy day that the magic came, and once magic has entered your life, you stay in its glittering clutch forever' Nottingham, 1906 Marietta Stelle longs to be a ballerina but as Christmas draws nearer, her dancing days are numbered. At the wishes of her family, she will be obligated to marry and take up her place in society in the New Year. But when a mysterious toymaker, Dr Drosselmeier, purchases a neighbouring townhouse, it heralds the arrival of magic and wonder in her life. Although Drosselmeier's magic is darker than Marietta could have imagined… When he constructs an elaborate theatrical set for her final ballet performance, Marietta discovers it carries a magic all of its own. As the clock chimes midnight, Marietta finds herself walking through a land of snow-topped fir trees leading to a frozen sugar palace silent with secrets and must find a way to return home. In the darkness of night, magic awaits and you will never forget what you find here… Under the Whispering Door by T. J. Klune Genre: Fantasy Fiction, Contemporary Fantasy, Gay Fiction Witty, haunting, and kind, Under the Whispering Door is a gift for troubled times. TJ Klune brings us a warm hug of a story about a man who spent his life at the office – and his afterlife building a home. Welcome to Charon's Crossing. The tea is hot, the scones are fresh and the dead are just passing through. When a reaper comes to collect Wallace from his own sparsely-attended funeral, Wallace is outraged. But he begins to suspect she's right, and he is in fact dead. Then when Hugo, owner of a most peculiar tea shop, promises to help him cross over, Wallace reluctantly accepts the truth. Yet even in death, he refuses to abandon his life – even though Wallace spent all of it working, correcting colleagues and hectoring employees. He'd had no time for frivolities like fun and friends. But as Wallace drinks tea with Hugo and talks to his customers, he wonders if he was missing something. The feeling grows as he shares jokes with the resident ghost, manifests embarrassing footwear and notices the stars. So when he's given one week to pass through the door to the other side, Wallace sets about living a lifetime in just seven days. The Christmas Bookshop by Jenny Colgan Genre: Contemporary, Fiction Contemporary Romance The brand new feel-good Christmas novel from Sunday Times top ten bestselling author, Jenny Colgan. Carmen has always worked in her local department store. So, when the gorgeous old building closes its doors for good, she is more than a little lost. When her sister, Sofia, mentions an opportunity in Edinburgh – a cute little bookshop, the spare room in her house – Carmen is reluctant, she was never very good at accepting help. But, short on options, she soon finds herself pulling into the snowy city just a month before Christmas. What Sofia didn't say is that the shop is on its last legs and that if Carmen can't help turn things around before Christmas, the owner will be forced to sell. Privately, Sofia is sure it will take more than a miracle to save the store, but maybe this Christmas, Carmen might surprise them all… The Ripping Tree by Nikki Gemmell Publisher: The Borough Press Genre: Historical Fiction, Historical Mystery, Thriller GET OUT. BEFORE THEY SAVE YOU. Early 1800s. Thomasina Trelora is on her way to the colonies. Her fate: to be married to a clergyman she's never met. As the Australian coastline comes into view a storm wrecks the ship and leaves her lying on the rocks, near death. She's saved by an Aboriginal man who carries her to the door of a grand European house, Willowbrae. Tom is now free to be whoever she wants to be and a whole new life opens up to her. But as she's drawn deeper into the intriguing life of this grand estate, she discovers that things aren't quite as they seem. She stumbles across a horrifying secret at the heart of this world of colonial decorum – and realises she may have exchanged one kind of prison for another. The Ripping Tree is an intense, sharp shiver of a novel, which brings to mind such diverse influences as The Turn of the Screw, Rebecca and the film Get Out as much as it evokes The Secret River. A powerful and gripping tale of survival written in Nikki Gemmell's signature lyrical and evocative prose, it examines the darkness at the heart of early colonisation. Unsettling, audacious, thrilling and unputdownable. The Cult by Abby Davies Genre: Thriller, Psychological Thriller, Hardboiled The gripping new thriller that will have you on the edge of your seat from the first page to the last! A hidden community… Thirty years ago, in the English countryside, a commune was set up. Led by Uncle Saviour, it was supposed to be a place of love, peace and harmony. But what started out as paradise turned into hell. A shocking abduction… Now, two young children have vanished from their home in the middle of the night. Their parents are frantic, the police are at a loss. A twisting case… DI Ottoline is leading the search – her only clue a mask found in the woods. Could the key lie in events that took place decades ago, when a dream of a new way of life became something far more sinister? Thanks for reading Bibliophiles😊 See you next month for more of Emma's Anticipated Treasures xxx Tags A. J. West, A. M. Shine, Abby Davies, Amanda Mason, Apollo, Bantam Press, Bloomsbury YA, Boldwood Books, Care For Me, Carla Valentine, Caroline Mitchell, Carolyn Tara O'Neil, Christine Pride, Claire McGowan, Daughters of a Dead Empire, Embla Books, Emma's Anticipated Treasures, Evanna Lynch, Fall, Farah Cook, Harper Collins UK, Head of Zeus, Headline, Hodder & Stoughton, Hodder Sudio, HQ, HQ Stories, I Know You, Jenny Colgan, Jessie Burton, Jo Piazza, John Grisham, Kwon Yeo-Sun, Lemon, Leonora Nattrass, Louise Douglas, M. A.. Kuzniar, Medusa, Michael Joseph, Midnight in Everwood, Murder Isn't Easy, October 2021, October Books, Orenda, Orenda Books, Rebecca Netley, Roaring Brook Press, Sophie Kinsella, Sphere, T. J. Klune, The Borough Press, The Christmas Bookshop, The Cult, The Haunting Season, The Hiding Place, The Judge's List, The Midnight Man, The Party Crasher, The Room in the Attic, The Spirit Engineer, The Watchers, The Whistling, Thomas & Mercer, Under the Whispering Door, Viper, Viper Books, We Are Not Like Them, Zaffre
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The former The Bachelor star has admitted he never should've selected Robertson, a 29-year-old model from Santa Monica, CA, over some -- if not all -- of the other 24 competing girls at the conclusion of his edition, which was filmed in November 2011 and aired in March. "I should apologize to all those women and say, 'Sorry I didn't see it,'" Flajnik told Life & Style. "I really have lost all respect for this person that I thought I knew and that I was in love with at one point." Flajnik's former bachelorettes saw right through Robertson's alleged act and even tried to warn the 30-year-old winemaker from Sonoma, CA that she wasn't a nice girl at heart, and now, Flajnik seemingly wishes he had listened more intently. "She just had me fooled," he told the magazine. "I talk to my friends all the time and they're like, 'Maybe she was just really good at it. She got all of us fooled, too, Ben. You weren't the only one.'" Flajnik's family was reportedly a little hesitant about Robertson as well, as they requested the former The Bachelor star to think hard about whether they should actually tie the knot before the couple eventually called it quits in October. "I wanted to see it through on my own. I knew if it was going to work or not. It just took a little bit longer," Flajnik told Life & Style. "You know, hindsight is 20/20." Robertson told Life & Style earlier this month that Flajnik treated her "so badly" and she was "miserable with Ben" during their 10-month relationship. She's currently dating Arie Luyendyk Jr. from Emily Maynard's season of The Bachelorette, leaving the winemaker a little surprised and speechless. "[I'm not dating again], not as quickly as she is," Flajnik told the magazine shortly after discovering Robertson's bashing comments and new relationship.
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An exquisite cool blue denim hue is brought to perfection by nature in this 1.07 carat SI1 cushion cut Natural Fancy Intense Blue diamond. Radiant brilliance and fire animate the comely cushion cut diamond. An elongated cushion cut, this Fancy Intense Blue diamond was made to sit in the center of a ring or pendant. Its rich blue color is a true blue that lacks any grey tones. At 1.07 carats, it is just the right size for capturing the attention of others, which it is very sure to do. The saturated color of this Fancy Intense Blue diamond is rare and difficult to find, particularly in this size. Diamonds represent eternal love and strength. Give the gift of this stunning diamond to your loved one and she will certainly appreciate and cherish your one-of-a-kind gift for many years to come. GIA-certified.
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Investigators in Ocean County believe murder-suicide likely links the deaths of a man found hanging from a Comcast bucket truck and a woman found beaten to death on his kitchen floor. Police in Holmdel found 32-year-old Tyree Johnson of Jackson hanging from the truck on Wednesday just after 7:30 a.m. Police found no one at his Lexington Court home in Jackson, when they went to notify relatives about his death. Officers used Johnson's key to go inside the home and a strong odor led them to the kitchen. There they found 29-year-old Christy Keronen of Lakewood dead with apparent head trauma. The Ocean County Prosecutor's Office says Keronen's brother had reported her missing earlier in the day. She was last seen Sunday around 9 a.m. Officials have not said how the two may be connected.
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(function(root, factory) { if (typeof define === 'function' && define.amd) { // AMD. Register as an anonymous module. define(['ApiClient', 'model/JobIgesOutputPayload', 'model/JobObjOutputPayload', 'model/JobObjOutputPayloadAdvanced', 'model/JobStepOutputPayload', 'model/JobStlOutputPayload', 'model/JobSvfOutputPayload', 'model/JobThumbnailOutputPayload'], factory); } else if (typeof module === 'object' && module.exports) { // CommonJS-like environments that support module.exports, like Node. module.exports = factory(require('../ApiClient'), require('./JobIgesOutputPayload'), require('./JobObjOutputPayload'), require('./JobObjOutputPayloadAdvanced'), require('./JobStepOutputPayload'), require('./JobStlOutputPayload'), require('./JobSvfOutputPayload'), require('./JobThumbnailOutputPayload')); } else { // Browser globals (root is window) if (!root.ForgeModelDerivative) { root.ForgeModelDerivative = {}; } root.ForgeModelDerivative.JobPayloadItem = factory(root.ForgeModelDerivative.ApiClient, root.ForgeModelDerivative.JobIgesOutputPayload, root.ForgeModelDerivative.JobObjOutputPayload, root.ForgeModelDerivative.JobObjOutputPayloadAdvanced, root.ForgeModelDerivative.JobStepOutputPayload, root.ForgeModelDerivative.JobStlOutputPayload, root.ForgeModelDerivative.JobSvfOutputPayload, root.ForgeModelDerivative.JobThumbnailOutputPayload); } }(this, function(ApiClient, JobIgesOutputPayload, JobObjOutputPayload, JobObjOutputPayloadAdvanced, JobStepOutputPayload, JobStlOutputPayload, JobSvfOutputPayload, JobThumbnailOutputPayload) { 'use strict'; /** * The JobPayloadItem model module. * @module model/JobPayloadItem * @version 2.0.0 */ /** * Constructs a new <code>JobPayloadItem</code>. * Output description object, depends of the type * @alias module:model/JobPayloadItem * @class * @implements module:model/JobSvfOutputPayload * @implements module:model/JobThumbnailOutputPayload * @implements module:model/JobStlOutputPayload * @implements module:model/JobStepOutputPayload * @implements module:model/JobIgesOutputPayload * @implements module:model/JobObjOutputPayload * @param type {module:model/JobObjOutputPayload.TypeEnum} The requested output types. Possible values include `svf`, `thumbnai`, `stl`, `step`, `iges`, or `obj`. For a list of supported types, call the [GET formats](https://developer.autodesk.com/en/docs/model-derivative/v2/reference/http/formats-GET) endpoint. */ var exports = function(type) { var _this = this; JobSvfOutputPayload.call(_this, type); JobThumbnailOutputPayload.call(_this, type); JobStlOutputPayload.call(_this, type); JobStepOutputPayload.call(_this, type); JobIgesOutputPayload.call(_this, type); JobObjOutputPayload.call(_this, type); }; /** * Constructs a <code>JobPayloadItem</code> from a plain JavaScript object, optionally creating a new instance. * Copies all relevant properties from <code>data</code> to <code>obj</code> if supplied or a new instance if not. * @param {Object} data The plain JavaScript object bearing properties of interest. * @param {module:model/JobPayloadItem} obj Optional instance to populate. * @return {module:model/JobPayloadItem} The populated <code>JobPayloadItem</code> instance. */ exports.constructFromObject = function(data, obj) { if (data) { obj = obj || new exports(); JobSvfOutputPayload.constructFromObject(data, obj); JobThumbnailOutputPayload.constructFromObject(data, obj); JobStlOutputPayload.constructFromObject(data, obj); JobStepOutputPayload.constructFromObject(data, obj); JobIgesOutputPayload.constructFromObject(data, obj); JobObjOutputPayload.constructFromObject(data, obj); } return obj; } // Implement JobSvfOutputPayload interface: /** * The requested output types. Possible values include `svf`, `thumbnai`, `stl`, `step`, `iges`, or `obj`. For a list of supported types, call the [GET formats](https://developer.autodesk.com/en/docs/model-derivative/v2/reference/http/formats-GET) endpoint. * @member {module:model/JobSvfOutputPayload.TypeEnum} type */ exports.prototype['type'] = undefined; /** * @member {Array.<module:model/JobSvfOutputPayload.ViewsEnum>} views */ exports.prototype['views'] = undefined; // Implement JobThumbnailOutputPayload interface: /** * The requested output types. Possible values include `svf`, `thumbnai`, `stl`, `step`, `iges`, or `obj`. For a list of supported types, call the [GET formats](https://developer.autodesk.com/en/docs/model-derivative/v2/reference/http/formats-GET) endpoint. * @member {module:model/JobThumbnailOutputPayload.TypeEnum} type */ exports.prototype['type'] = undefined; /** * @member {module:model/JobThumbnailOutputPayloadAdvanced} advanced */ exports.prototype['advanced'] = undefined; // Implement JobStlOutputPayload interface: /** * The requested output types. Possible values include `svf`, `thumbnai`, `stl`, `step`, `iges`, or `obj`. For a list of supported types, call the [GET formats](https://developer.autodesk.com/en/docs/model-derivative/v2/reference/http/formats-GET) endpoint. * @member {module:model/JobStlOutputPayload.TypeEnum} type */ exports.prototype['type'] = undefined; /** * @member {module:model/JobStlOutputPayloadAdvanced} advanced */ exports.prototype['advanced'] = undefined; // Implement JobStepOutputPayload interface: /** * The requested output types. Possible values include `svf`, `thumbnai`, `stl`, `step`, `iges`, or `obj`. For a list of supported types, call the [GET formats](https://developer.autodesk.com/en/docs/model-derivative/v2/reference/http/formats-GET) endpoint. * @member {module:model/JobStepOutputPayload.TypeEnum} type */ exports.prototype['type'] = undefined; /** * @member {module:model/JobStepOutputPayloadAdvanced} advanced */ exports.prototype['advanced'] = undefined; // Implement JobIgesOutputPayload interface: /** * The requested output types. Possible values include `svf`, `thumbnai`, `stl`, `step`, `iges`, or `obj`. For a list of supported types, call the [GET formats](https://developer.autodesk.com/en/docs/model-derivative/v2/reference/http/formats-GET) endpoint. * @member {module:model/JobIgesOutputPayload.TypeEnum} type */ exports.prototype['type'] = undefined; /** * @member {module:model/JobIgesOutputPayloadAdvanced} advanced */ exports.prototype['advanced'] = undefined; // Implement JobObjOutputPayload interface: /** * The requested output types. Possible values include `svf`, `thumbnai`, `stl`, `step`, `iges`, or `obj`. For a list of supported types, call the [GET formats](https://developer.autodesk.com/en/docs/model-derivative/v2/reference/http/formats-GET) endpoint. * @member {module:model/JobObjOutputPayload.TypeEnum} type */ exports.prototype['type'] = undefined; /** * @member {module:model/JobObjOutputPayloadAdvanced} advanced */ exports.prototype['advanced'] = undefined; return exports; }));
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Der Gißübelturm in Lauingen, einer Stadt im schwäbischen Landkreis Dillingen an der Donau, war ein Teil der ehemaligen Stadtbefestigung. Der Wehrturm, neben dem Haus Oberes Brunnental 16, ist ein geschütztes Baudenkmal. Beschreibung Der viergeschossige Rundturm an der südöstlichen Ecke der Stadtmauer wurde um 1413 errichtet. Er wird vom Lauinger Schloss mit seinen Türmen überragt. Der viergeschossige Turm besitzt ein spitzes Kegeldach. An den beiden oberen Geschossen sind Schießscharten unter gerahmten Rechteckblenden vorhanden. Unter dem Dach verläuft ein zweimal gestuftes Traufgesims. Literatur Die Kunstdenkmäler des Landkreises Dillingen an der Donau. Bearbeitet von Werner Meyer (= Die Kunstdenkmäler von Bayern. Die Kunstdenkmäler von Schwaben. Band VII. Landkreis Dillingen an der Donau). R. Oldenbourg Verlag, München 1972, ISBN 3-486-43541-8, S. 583. Weblinks Baudenkmal in Lauingen (Donau) Stadtbefestigung in Lauingen (Donau) Wehrturm in Bayern Erbaut in den 1410er Jahren Turm in Europa Bauwerk in Lauingen (Donau)
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<manifest xmlns:android="http://schemas.android.com/apk/res/android" package="com.wms.opensource.images3android.demo" android:versionCode="1" android:versionName="1.0" > <uses-sdk android:minSdkVersion="11" android:targetSdkVersion="22" /> <uses-permission android:name="android.permission.INTERNET"></uses-permission> <uses-permission android:name="android.permission.ACCESS_NETWORK_STATE"></uses-permission> <uses-permission android:name="android.permission.ACCESS_WIFI_STATE"></uses-permission> <uses-permission android:name="android.permission.WRITE_EXTERNAL_STORAGE" /> <uses-permission android:name="android.permission.CAMERA" /> <uses-permission android:name="android.permission.SET_WALLPAPER" /> <uses-permission android:name="com.android.launcher.permission.INSTALL_SHORTCUT"/> <application android:allowBackup="true" android:icon="@drawable/ic_launcher" android:label="@string/app_name" android:theme="@style/Theme.AppCompat.Light.DarkActionBar" > <activity android:name="com.wms.opensource.images3android.activity.UploadImageActivity" android:label="@string/uploadImageActivityTitle" android:screenOrientation="portrait"> <intent-filter> <action android:name="android.intent.action.MAIN"></action> <category android:name="android.intent.category.LAUNCHER"></category> </intent-filter> <intent-filter> <action android:name="android.intent.action.CREATE_SHORTCUT"></action> <category android:name="android.intent.category.DEFAULT" /> </intent-filter> </activity> <activity android:name="com.wms.opensource.images3android.activity.ImageListFragmentActivity" android:label="@string/imageListActivityTitle" android:screenOrientation="portrait" android:configChanges="keyboardHidden|orientation" android:windowSoftInputMode="stateVisible|adjustResize"> </activity> </application> </manifest>
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Permit pain leaves park a 'wasteland' posted by Sentinel-Times September 29, 2015 News Michael Tsaousidis claims Bass Coast Shire Council has thwarted attempts to turn a former Corinella amusement park into a market site. The council disagrees. G023915 BASS resident and businessman Michael Tsaousidis had grand plans in mind when he bought a prime piece of Corinella real estate back in 2012. The 59-acre property at 1996 Bass Highway, surrounding by tall cyclone fencing, is well-known to locals as the former site of The Swagman's Hat – an amusement park which opened in the late 1980s and closed after just a few years. When Mr Tsaousidis bought the property at auction, a real estate website listing described the land as "a blank canvas" with many benefits including "a current permit to trade retail." Three years after handing over $600,000 for the property, the site remains an overgrown wasteland with nothing but a few dozen cattle grazing amid remnants of decaying park infrastructure. None of Mr Tsaousidis's dreams have come to fruition – and he lays the blame solely at the feet of Bass Coast Shire Council. "I've been trying to open something here for the community and all I've had is three years of setbacks," he told the Sentinel-Times. "I was told there was a permit in place to trade retail when I bought the property, but no one at the council has helped me. "Whenever I've tried to do something at the property, they make me do backflips." Mr Tsaousidis's initial idea for the site was to open a caravan park, but he eventually settled with a proposal to open the front of the property up for a 'trash and treasure' market every Sunday instead. With a left-hand turning lane to the site's broad entrance already in place – plus a huge colourbond shed where stallholders could trade undercover – he thought the plan was a no-brainer. But he claims his proposal was thwarted by "miscommunication" from the shire and a lack of support. "I put in an application for the market and they told me I needed things like a traffic report and vegetation report," he said, exasperated. "Plus they wanted to know how I was going to construct car parking. "All it was going to be was a simple Sunday market so I could finally do something with the place. "I thought the council was here to help, not hinder." Armed with a stack of dog-eared permit paperwork dating back years, Mr Tsaousidis says his battle with the shire seems never-ending. So what has gone wrong between the landowner and the shire, exactly? Council's general manager of sustainable development and growth, Allison Jones, confirmed an application for a market was lodged in October of last year, but says the document "did not contain basic information such as a copy of the title and business plan." "Mr Tsaousidis failed to provide a comprehensive application; most of the information council and other agencies such as VicRoads would need to assess the proposed use was missing," she explained. "A car parking and traffic management plan was requested as was a vegetation and landscape plan. "Mr Tsaousidis was sent a detailed further information request in early November 2014. " "This has not been responded to and, as a result, the application has lapsed. "Mr Tsaousidis has not lodged another application since the previous application was lapsed in late 2014 nor has he undertaken any pre-application discussions with council." Mr Tsaousidis claims he "never received" additional information in the mail. Ms Jones confirmed a permit for a retail premises was issued back in 2003, but it was in relation to equine supplies only.
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Car suspected in deadly Rankin Co. hit-and-run found as family and friends mourn Car suspected in fatal hit and run found as community mourns By Roslyn Anderson | August 29, 2019 at 8:50 PM CDT - Updated August 29 at 8:50 PM RANKIN COUNTY, Miss. (WLBT) - A deadly hit and run rocked the Rankin County community Thursday, including relatives of the victim. A cross now marks the spot where Michael Jerom Crumbly took his last breaths. He was just across the street from his home on Greenfield Circle, an area residents say is plagued with speeders. A community of largely family on Greenfield Circle is left reeling following the tragic death of "Big Mike". The 44-year-old concrete worker was walking home when a witness says he was hit by a speeding car. Bennie Courtney had just said goodnight to Crumbly and was walking home in the opposite direction when he said he was forced off the roadway by the speeding car. "I said 'Mike I'll see you tomorrow' and I heard that boom, boom and I thought it was the dog, and that was Mike," said Courtney. Deborah Rhodes is a registered nurse and Crumbly's cousin. She and her son rushed to the scene and performed CPR until first responders arrived. "Somebody hit him and whoever did this needs to come up, turn themselves in, report this," urged Rhodes. "Big Mike is gone and it's not gonna bring him back, but at least have justice for Big Mike." "I hope whoever did this you seeing this on TV and just turn yourself in, turn yourself in," added Courtney as tears ran down his face. "Because that Mike was a good person, and you can't do this. The Lord knows that you're going to suffer if you don't turn yourself in." Rankin County Sheriff Bryan Bailey said a gold Chevy Malibu was found by Jackson police Wednesday afternoon on Shirley Drive in Jackson and it's believed to be the vehicle involved. It had damage to the front bumper, hood and windshield. A suspect has been developed and is being sought. Roslyn Anderson Roslyn Anderson is a reporter at WLBT and Fox40 News in Jackson, MS.
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Q: change select value when press button i'm still Beginner at this i have table and i select data between two date range using this code and its working fine for me $StartDate = "2016-01-01"; $EndDate = "2016-12-30"; $result = mysql_query("SELECT *FROM users where submit_date BETWEEN '$StartDate' AND '$EndDate'") or die(mysql_error()); then i added 2 data picker and button echo "<form method=post action=><table>". "<tr><td>Start Date : </td><td><input type=date name=StartDate value=$StartDate></td></tr>". "<tr><td>End Date : </td><td><input type=date name=EndDate value=$EndDate></td></tr>". "<tr><td colspan=2><input type=submit name=UpdateSelect value=Set></td></tr>". "</table></form>"; now i need help with this how to update the page when i press the sumbit button to start selecting from the new start date and end date. i'm sorry for my bad english. and thanks A: A small demo of your problem hope will help you and solve your problem. I assume you are using mysqli connection object. if (isset($_POST['submit_btn'])) { $start_date = $_POST['start_date']; $end_date = $_POST['end_date']; $sql = "SELECT * FROM users where submit_date BETWEEN '$start_date' AND '$end_date'"; $result = $conn->query($sql); } $conn->close(); ?> <html> <head> <title></title> </head> <body> <form action="" method="post"> <table> <tr> <td><input type="date" name="start_date" value=""/></td> </tr> <tr> <td><input type="date" name="end_date" value=""/></td> </tr> <tr> <td><input type="submit" name="submit_btn" value="Set"/></td> </tr> </table> </form> <!-- here your data manupulation logic --> <?php if (isset($result) && !empty($result)) { if ($result->num_rows > 0) { // output data of each row while($row = $result->fetch_assoc()) { echo "id: " . $row["id"];. " - Name: " . $row["firstname"]. " " . $row["lastname"]. "<br>"; } } else { echo "0 results"; } } ?> </body> </html> The is used for input fields that should contain a date. Depending on browser support, a date picker can show up in the input field.
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Age-related increase of VGF-expression … Advance Online Publications Publication Ethics and Publication Malpractice Statements Research Paper Volume 6, Issue 6 pp 440—453 Age-related increase of VGF-expression in T lymphocytes Stefan Busse1, , Johann Steiner1,2,3, , Justus Micheel1, , Henrik Dobrowolny1, , Christian Mawrin4, , Tim J. Krause1, , Michael Adamaszek5, , Bernhard Bogerts1,2, , Ursula Bommhardt6, , Roland Hartig6, , Mandy Busse7, , 1 Department of Psychiatry, University of Magdeburg, Magdeburg, Germany 2 Center for Behavioral Brain Sciences, Magdeburg, Germany 3 Pembroke College, University of Cambridge, Cambridge, UK 4 Department of Neuropathology, University of Magdeburg, Magdeburg, Germany 5 Center of Neurological Rehabilitation, University of Leipzig, Leipzig, Germany 6 Institute of Immunology, University of Magdeburg, Magdeburg, Germany 7 Department of Pediatric Pulmonology, Allergology & Neonatology, Medical University of Hannover, Hannover, Germany * Equal contribution Received: January 6, 2014 Accepted: April 30, 2014 Published: May 4, 2014 https://doi.org/10.18632/aging.100656 Busse S, Steiner J, Micheel J, Dobrowolny H, Mawrin C, Krause TJ, Adamaszek M, Bogerts B, Bommhardt U, Hartig R, Busse M, . Age-related increase of VGF-expression in T lymphocytes. Aging (Albany NY). 2014; 6:440-453 . https://doi.org/10.18632/aging.100656 Copy or Download citation: Select the format you require from the list below Click to copy this citation from the text box above or download the citation: Citation | Citation & Abstract Copyright: © 2014 Busse et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. VGF is a protein expressed by neurons and processed into several peptides. It plays a role in energy homeostasis and promotes growth and survival. Recently, VGF mRNA was detected in peripheral leukocytes. Since it is known that aging is associated with a decrease in the development and function of neuronal as well as immune cells, we addressed the question whether a peripheral expression of VGF by CD3+ T cells and CD56+ NK cells is correlated with age. Therefore, the frequency of VGF+CD3+ and VGF+CD56+ cells was determined in mentally healthy volunteers aged between 22 and 88. We found an age-dependent increase in the number of VGF+CD3+ T cells that correlated with HbA1c and the body mass index (BMI). VGF-expression by NK cells was age-independent. Blockade of VGF reduced proliferation and secretion of cytokines such as IL-2, IL-17A, IL-1β, IL-10 and TNF by CD3+ T cells and PBMCs. Rapamycin-mediated T cell blockade significantly reduced the frequency of VGF-expressing T cells. We conclude that VGF contributes to survival and function of peripheral T cells. The age-dependent increase in VGF-expression could serve as mechanism that counterregulates the decrease in functionality of T lymphocytes. Aging is becoming of increasing importance, because the cohort of older adults constitutes the fastest growing population in the world for the first time in history. It has been predicted that about by the year 2025 the population older than 65 years will be increasing 3.5 times as rapidly as the total population [1]. Therefore, studies of the age-dependent molecular and cellular mechanisms are of rising interest. Aging is associated with a decline in the function of the immune system, characterized by dramatic changes on the cellular and systemic level that affect the innate as well as the adaptive immune system: The innate immune system, represented e.g. by natural killer (NK) cells, macro-phages and dendritic cells (DCs), shows an age-associated impaired function to trigger T-cell responses [2]. The output of naive T cells, part of the adaptive immunity, declines with age as a result of the thymic involution [3]. However, elderly people have significantly higher number of T cells that are specific for persistent viruses, such as EBV and CMV [4]. This so-called immunosenescence is further characterized by an inverted CD4+/CD8+ T cell ratio, a shift from Th1 to Th2 cell induction following T cell activation that influences the balance between humoral and cell-mediated immune responses. This altered cytokine profile is probably the result of an increased ratio of memory to naive T cells [5, 6]. The cytokine milieu is modulated during aging also in another direction: elevated levels of circulating proinflammatory cytokines, like IL-6 and TNFα [7] were detected in elderly people. It is known that chronic inflammation has a negative impact on tissues, organs, and health in general. Increased levels of IL-6 and TNFα and their receptors are significant independent risk factors for mortality and morbidity in the aged population [8]. As a consequence of immunosenescence, there is an increased incidence of age-related pathologies [9-12]: Senescent T cells may play a role of cardiovascular disease [13], atherosclerosis [14], myocardial infarction [15] and type 2 diabetes mellitus (T2DM) [16]. There is abundant communication between the central nervous system (CNS) and the immune system. For instance, T cells are important in functions of the healthy brain such as spatial learning and memory [17, 18] and adult neurogenesis [19]. Senescent T cells are also involved in neurodegenerative disorders such as Alzheimer's disease [20, 21] or vascular dementia [22]. Therefore, new therapeutic treatment options for neurodegenerative diseases are needed, such as Rapamycin. Rapamycin, a macrolide immuno-suppressant used to prevent rejections following organ transplantation via inhibition of T and B cell proliferation, was shown to reduce amyloid-beta levels, to abolish cognitive deficits in mouse models of Alzheimer's disease [23] and to suppress brain aging in rats [24]. www.impactaging.com 441 AGING, June 2014, Vol. 6 No.6VGF is a neuronal polypeptide first identified as a cDNA clone from plate V of the nerve growth factor (NGF)-induced rat pheochromocytoma (PC12) cell cDNA library [25]. The VGF protein is widely expressed in the neurons in brain and hippocampal synaptic activity [26] and is subsequently processed into more than 10 different peptides; these peptides play an important role by improving plasticity, neurogenesis, energy homeostasis, pain modulation and sexual behaviour (for a recent review, see [27]). VGF is abundantly expressed in the thalamus and promotes dendritic growth and survival of cortical neurons [28]. Certain VGF peptides are also involved in the regulation of food uptake and energy balance. VGF- deficient mice are smaller and thinner than wild type mice [29]. However, some VGF peptides like TLQP-21 have an opposite effect on fat deposition and trigger lipolysis or induce resistance to obesity by reducing fat accumulation [30]. After enzymatic processing, smaller VGF-derived peptides are secreted into the cerebrospinal fluid (CSF) or blood. Therefore, some VGF fragments were considered as biomarkers for neurological and psychiatric disorders, such as Alzheimer's disease, frontotemporal dementia and schizophrenia [31]. Recently, Cattaneo et al. detected VGF mRNA expression also in human leukocytes [32]. Since it was shown that peripheral T cells express several neurotransmitter receptors, proteins and metabolites originally identified in cells of the nervous system [33], we wondered if T cells express VGF as well. Moreover, we questioned if blocking of VGF has any functional consequences and whether VGF levels are age-dependent. Therefore, we investigated the VGF expression in T cells of mentally healthy persons aged between 22 and 88 years using flow cytometry. Obesity is the hallmark of the metabolic syndrome that represents a cluster of different disorders which predispose people for the development of chronic metabolic diseases including T2DM and cardiovascular diseases [34]. As a consequence of a sedentary lifestyle and increased energy uptake, an enlargement of adipose tissue takes place that is associated with an inflammatory immune response which leads to adipose tissue dysfunction [35]. The number of CD4+ and CD8+ T cells are elevated in obese human adipose tissue, which indicates changes in T-cell infiltration in human adipose tissue [36]. Therefore, the T-cell compartment balance is important for the regulation of adipose tissue homeostasis. Since VGF potentially influences energy homeostasis, we evaluated the association between HbA1c and the body mass index (BMI) and the VGF expression in T cells. Furthermore, we determined the frequency of VGF-expressing CD56+ NK cells during senescence. We detected an increase of VGF-expressing CD3+ T cells during aging. This increase was correlated with the level of HbA1c and the BMI. In vitro blockade of VGF using an antibody reduced proliferation and the cytokine production by CD3+ T cells and peripheral blood mononuclear cells (PBMCs). However, we detected no changes in the expression of VGF by NK cells with increasing age. Our data suggest that VGF could contribute to survival and function of peripheral T cells. We speculate that the age-dependent increase in VGF-expression could serve as a mechanism that counterregulates the decrease in functionality of T cells during senescence. Study cohort 42 healthy gender-matched volunteers (23 females, age 22-88 years; 19 males; 22-86 years) were included in the study. The demographic features of the mentally healthy volunteers are summarized in suppl. table 1. Routine blood parameters including lipid status of all volunteers were analyzed and no changes were found indicating a severe illness. Most of the younger volunteers had no underlying disease and used no medication, while some of the older suffered from arterial hypertension, hyperlipidemia, hypothyroidism, chronic obstructive pulmonary disease, cardiac insufficiency, hyperuricemia or osteoporosis and had to be under medication. Mini mental status-test (MMST) of all volunteers was 29 or 30 (suppl. table 1). Age-dependent expression of VGF by CD3+ T cells and CD56+ NK cells A flow cytometry approach was used to determine the expression of VGF-positive CD3+ T cells (VGF+CD3+; an example is shown in suppl. fig. 1) and CD56+ NK cells (VGF+CD56+). The number of CD3+ T cells tended to decrease with age (p=0.069; Figure 1a). The frequency of VGF-expressing CD3+ T lymphocytes among the CD3+ lymphocytes (VGF+CD3+/ CD3+) ranged between 1.62% and 27.85% and showed an age-dependent increase (p=0.001; Figure 1b; suppl. table 2 and suppl. fig. 2). This increase was more pronounced in female (p=0.001) than in male volunteers (p=0.087). The number of CD56+ NK cells was not age-dependent (p=0.423; Figure 1a). The percentage of VGF-expressing CD56+ NK cells in the CD56+ NK cell population (VGF+CD56+/ CD56+) ranged between 5.30% and 80.77%, but this increase did not correlate with age, neither in the female nor in the male cohort (Figure 1c; suppl. table 2 and suppl. fig. 2). Figure 1. Expression of VGF on CD3+ T cells and CD56+ NK cells. PBMCs isolated from 42 healthy volunteers aged between 22 and 88 years without psychiatric diagnosis were stained with anti-VGF (D20) and anti-CD3 or anti-CD56 and were analyzed using flow cytometry. The numbers of CD3+ T cells and CD56+ NK cells depending on the age of the persons is shown in (a). The frequency of VGF-expressing CD3+ cells within the T lymphocytes population is correlated with the age of the cohort (b; left) and further subdivided according to the gender (b; right). The proportion of VGF-expressing CD56+ cells within the NK cell population is shown in dependence with the age of the cohort (c; left) and further subdivided according to the gender (c; right). Figure 2. Correlation between HB1Ac and VGF-expressing CD3+ T cells. The HbA1c (glycated haemoglobin) level provides an integrated average blood glucose measure and was determined during routine blood analysis. The HbA1c value of the cohort increased with age and was positively correlated with frequency of VGF-expressing CD3+ cells within the T cell population (a). Also the body mass index (BMI) increased with a rising number of VGF+CD3+ T cells (b). Correlation between HB1Ac, BMI and VGF-expressing CD3+ T cells Glycated haemoglobin (HbA1c) levels provide an 8–12 week integrated average blood glucose measure and were determined during routine blood analysis. The HbA1c values of the volunteers increased statistically with age (p=0.001). Therefore, a positive correlation between HbA1c and VGF+CD3+/ CD3+ T lymphocytes (p=0.003) and the body mass index (BMI; not from all volunteers available; p=0.003) and the frequency of VGF+CD3+/ CD3+ T cells was calculated. For regression analysis, we used VGF+CD3+/ CD3+ as dependent factor and HB1Ac, BMI and age as independent variables. When considering all three confounders, age is the significant and relevant factor. VGF induces proliferation and cytokine production by T cells We addressed the question whether the inhibition of VGF has any functional consequences for CD3+ T cells. Therefore, isolated CD3+ T cells were stimulated with Dynabeads Human T-Activator CD3/CD28 (and PMA/Ionomycin as positive control) in the presence of either anti-VGF Ab or an isotype-matched control for three days and then the cytokine levels in the supernatant were measured. To determine proliferation, CD3+ T cells were additionally labeled with CFSE before culturing (Figure 3a). The treatment of T cells with anti-VGF during stimulation with aCD3/CD28 diminished the production of the T cell survival factor IL-2, but also of the Th17-mediated cytokine IL-17A, the Th1-associated cytokine IL-1β and the Treg/ Th2-cytokine IL-10 (Figure 3b). Blockade of VGF also strongly inhibited the proliferation of CD3+ T cells. Figure 3. VGF induces proliferation and cytokine production by T cells and PBMCs. Isolated T cells were stimulated with aCD3/28 or PMA/Ionomycin (as positive control) or were left untreated (medium control) for 3 days in the presence of anti-VGF (D20; red) or an isotype-matched control Ab (blue). Division of cells is detected by loss of fluorescence intensity of cells labeled with CFSE. Blockade of VGF inhibited the proliferation of T cells stimulated with aCD3/28 or PMA/Ionomycin (a) and reduced the production of cytokines in T cell cultures stimulated with aCD3/28 (b). Blocking of VGF diminished the division of PBMCs stimulated with PHA or PMA/Ionomycin (as positive control; c) and also the secretion of cytokines in PHA-stimulated PBMC cultures. VGF induces proliferation and cytokine production in PBMCs Stimulation of CD3+ T cells with aCD3/CD28 acts independent of the presence of antigen-presenting cells (APCs). Whether VGF also influenced the interaction between T cells and APCs was determined by stimulation of PBMCs with PHA (and PMA/Ionomycin as positive control) in the presence of either anti-VGF Ab or an isotype-matched control. CFSE-labeled PBMCs were used to determine proliferation (Figure 3c). The treatment of PHA-stimulated PBMCs with anti-VGF Ab inhibited the secretion of TNF-α and IL-10 and decreased the production of IL-2 and IL-1β. However, the level of IL-17A, which is also produced by other cell types such as macrophages or monocytes, was unchanged (Figure 3d). Blockage of VGF severely diminished the proliferation of the PBMCs induced by PHA. VGF expression is reduced upon rapamycin treatment Rapamycin and cyclosporine A are both immunosuppressive drugs which inhibit the activation of T cells and therefore are used to prevent organ rejections. To determine their function in the expression of VGF by T cells, PBMC were incubated in medium with or without rapamycin or cyclosporine A. Treatment with rapamycin reduced the expression of VGF (p=0.0154, Figure 4) compared to medium. Also cyclosporine A was able to reduce the frequency of VGF+CD3+ T cells, however only to a smaller extent. Figure 4. Rapamycin-treated T cells down-regulate VGF. Isolated PBMCs were cultured in medium in the presence or absence of either Rapamycin or Cyclosporine A for 24h. Afterwards, the frequency of VGF-expressing CD3+ T cells was determined using flow cytometry (*p<0.05; one-way ANOVA). To our knowledge this is the first report showing that the neuronal polypeptide VGF is expressed by peripheral T cells and, to a smaller extent, by NK cells. The expression of VGF by T lymphocytes increased with age. It was shown that T cells protect neurons from degeneration and this neuroprotective effect is mediated via the production of neurotrophins [37, 38], the modulation of glutamate release by astrocytes and microglia [39, 40], the regulation of innate immunity at the site of injury [41]. Other still unexplored mechanisms may be involved. Since it was described that immune cells express a broad range of receptors specific for adrenaline, noradrenaline and dopamine it was also shown that these neurotransmitters are involved in both the propagation and resolution of immune responses, splenic T cells are able to produce acetylcholine [42]. T cells can also secrete dopamine by themselves. Dopamine signalling through D1 and D5 receptors in Treg cells attenuated their suppressive properties [43]. Moreover, pro-cognitive functions of T cells were discussed as well (reviewed in [44]). Furthermore, neurotransmitters and neuropeptides can modulate the functions of immune cells such as T cells, myeloid cells or dendritic cells when released from the CSF into the blood. Therefore the aim of our study was to explore further hints for an involvement of T cells in the interaction between the CNS and the immune system. Changes in the expression of VGF in the brain or CSF are associated with schizophrenia [45], depressive disorders [46], Parkinson's and Alzheimer's disease [47, 48]. Since Cattaneo et al. [32] showed VGF expression by leukocytes on mRNA level, we used flow cytometry to detect VGF expression on protein level. Our study showed that blockade of VGF in vitro dampened the proliferation and cytokine production by T cells and PBMCs. It is known that senescent T cells have shortened telomeres and increased telomerase activity [49-51] and a dramatically decreased IL-2 production [52]. The important costimulatory molecule CD28 is downregulated while CTLA-4 is upregulated [53-56]. Both molecules bind to CD80 and CD86, and another stimulatory surface molecule, CD27, is absent and this event is coupled with upregulation of the inhibitory molecule CD57. The TCR signal transduction pathways are significantly altered as well [57], resulting in impaired transcription of key effector T cell genes. The result of these events is a decline of T cell immune function in elderly persons such as a blunted immune response to vaccination intended to prevent infections and a reduced ability to fight actual infections. Blocking VGF in vitro decreased the secretion of IL-2 indicating that VGF stimulates the production of IL-2. This finding may suggest that VGF has a positive net effect on T cell survival and function. Moreover, inhibition of T cell activation by rapamycin reduced the expression of VGF by T cells. The importance of TOR, the target of rapamycin, insulin and insulin-like growth factor 1 (IGF-1) signaling pathways for aging was shown by Mikhail V. Blagosklonny, who proposed the hyperfunction theory of aging [58, 59]. According to this new, challenging idea aging is the consequence of continued activity of processes which evolved to optimize development in adulthood, especially excess biosynthesis. TOR regulates biomass within the cell; it inhibits autophagy and promotes protein translation, thereby TOR controls aging. Consequently, intervention in TOR signalling has several anti-aging effects: it increased life span and slowed progression of age-related pathologies in female S6K1 mice [60]. Rapamycin was shown to delay cellular senescence [61, 62], to extent the lifespan in both male and female mice [63] and to suppress brain aging and neurodegeneration in rats [24]. Therefore, Rapamycin could serve as a new therapeutic approach for the treatment of Alzheimer's disease. TOR is also a key molecular interplayer in nutrient sensing, and calorie restriction is an important aging-delaying intervention. We detected a positive correlation between glycated haemoglobin (HbA1c) and VGF+CD3+/CD3+ T lymphocytes as well between the BMI and the number of VGF-expressing T cells. VGF is involved in maintaining energy balance [64]. Previous studies have shown that VGF knockout mice are thin, small, hypermetabolic and of reduced fat stores [29]. The expression of VGF is not only induced by NGF, BDNF, neurotrophin 3 and fibroblast growth factors, but also by insulin. CD4+ and CD8+ T cells infiltrate obese human adipose tissue and induce local and systemic inflammation with an increased production of proinflammatory cytokines and provide a major link to the pathogenesis of insulin resistance [65]. Of particular interest are Th17 cells: the percentage of Th17 cells is elevated in blood of T2D patients and was correlated with human BMI, as a measure of adiposity in T2D patients [66]. Moreover, the IL-17 production by T cells correlates also with T2D severity (as measured by HbA1c), further supporting a likely relationship between the Th17 cells and metabolic imbalance. Blocking of VGF in CD3+ T cell cultures stimulated with aCD3/CD28 reduced the level of secreted IL-17 indicating that VGF promotes IL-17 production by T cells. Taken together, our data support Blagosklonny's hyperfunction hypothesis of aging, implicating that T cells are involved in the pathogenesis of insulin resistance and add VGF as a novel biomarker which becomes upregulated by rising HbA1c and the BMI. Immunosenescence is a complex process that we are just beginning to explore. The age-dependent increase in VGF-expression could serve as a mechanism that counterregulates the decrease in functionality of T lymphocytes to prevent more severe damaging effects during aging. Compared with T cells, the percentage and also the absolute number of NK cells with a mature phenotype enhances with age [67-69]. No age-dependent changes in the number of VGF-expressing CD56+ NK or total NK cells could be detected. Further investigation will be needed to characterize the nature and function of the VGF-expressing CD3+ T cells in immunosenescence and in age-related pathologies as well. The study has certain limitations that have to be considered. First, we investigated the expression of VGF in T lymphocytes and NK cells. However, CD3-negative and CD56-negative cells also express VGF. Therefore, a comparative analysis of monocytes and B cells would be important as well. Second, the isolation of T cells by MACS technology resulted in a purity of about 95%. Therefore we do not know how blocking VGF in T cell cultures was influenced by contaminating APCs. Third, we found out that BMI and Hb1Ac influences the expression of VGF in T cells. However, it has to be explored in the future cell culture studies if the supply with nutrients (or starvation) has a direct regulatory effect on the expression of VGF in T cells. By using the N-terminal antibody (D-20) against VGF, we detected three bands by Western Blot in PBMC and CD3+ T cells, as we had already described for human hypothalamic tissue, which were located at the molecular weights of approximately 90, 60, and 34 kDa [45]. While the 90 kDa protein corresponds to intact VGF, the other bands are proteolytic cleavage products of VGF. However, changes in the presence of the protein/ peptides and the associated meaning for aging and age-related diseases (dementia) are still unknown and currently under intensive investigation. The study was performed in accordance with German laws, the Declaration of Helsinki, and the guidelines of the local institutional review board (159/11). Written consent was obtained from all healthy persons. We collected 10 ml EDTA blood from 42 healthy persons aged between 22 and 88 years without psychiatric diagnosis. Routine blood analysis (including differential blood cell count, levels of C-reactive protein, glucose, lipids, liver enzymes and thyroid hormones) were performed. None of the persons had to be excluded because of changes of the routine blood values. No volunteer had a known history of immune disease, immunomodulating treatment, cancer, chronic terminal disease, severe cardiovascular disorder, substance abuse or severe trauma. Preparation of peripheral blood mononuclear cells (PBMC) PBMCs were separated by standard density gradient centrifugation (Ficoll Paque; Biochrom AG, Berlin) for 20 min, 375x g, RT) from freshly drawn blood collected in lithium heparin-treated tubes (BD Vacutainer; BD Biosciences, San Jose, CA, USA), which was diluted 1:1 with phosphate-buffered saline (PBS). The cell ring was harvested and the cell suspension was washed twice in PBS. Cells were then suspended in FACS staining buffer and cell number was counted. Isolated PBMC were washed once and then incubated with fluorescently-labeled antibodies for 20 min at 4° C in staining buffer (PBS + 0.5% BSA). Antibodies used in this study included reagents specific for: CD3 (UCHT1) and CD56 (B159) from BD Pharmingen (San Diego, CA); VGF (D-20) and the detection antibody, donkey anti-goat IgG FITC, from Santa Cruz Biotechnology (Dallas, Texas, USA). Afterwards, data were collected on a FACS flow cytometer (Fortessa, BD Biosciences, Mountain View, CA) and analyzed using FACS DIVA software 6.1.3 (BD Biosciences, Mountain View, CA) and using FlowJo software (Treestar Inc., Ashland, OR). The data were analyzed using biexponential transformation function for complete data visualization. Stimulation of PBMC and CD3+ T cells in vitro CD3+ T cells were isolated using Pan T cell isolation kit (Miltenyi Biotech, Bergisch Gladbach, Germany) and AutoMACS separation. PBMC and CD3+ T cells were resuspended in RPMI medium supplemented with 10% FCS and 1% antibiotics and plated at a density of 1×106 cells/ml. PBMCs were stimulated with PMA/ Ionomycin (1mg/ml) and PHA (1mg/ml), CD3+ T cells with Dynabeads Human T-Activator CD3/CD28 (Lifetechnology Inc, Darmstadt, Germany) for 3 days. For inhibition of VGF-mediated effects, anti-VGF (D20) or an isotype-matched control antibody was added to the cultures at day 0. Measurement of cell proliferation To measure cell proliferation, PBMC and CD3+ T cells were stained with CSFE (5,6 Carboxyfluorescein Diacetate, Succinimidyl Ester; Molecular Probes, Lifetechnology Inc, Darmstadt, Germany) according to standard protocols. Cells were stimulated as described above. Cell proliferation was detected using flow cytometry. Measurement of cytokine production After 3d stimulation, supernatants from PBMC and CD3+ T cells were harvested and stored at -20°C. The cytokine production was detected using a human Th1/Th2 Multiplex assay (affymetrix eBioscience, San Diego, CA, USA) according to the manufacturer's instructions. Treatment with rapamycin and cyclosporine A Isolated PBMC were cultured for 24h in complete RPMI medium with or without the addition of rapamycin (200 ng/ml) or cyclosporine A (200 ng/ml). Afterwards, the cells were harvested and the expression of VGF on CD3+ T cells was detected using flow cytometry. 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Ribosomal protein S6 kinase 1 signaling regulates mammalian life span. Science (New York, NY. 2009; 326:140-144.. 61. Demidenko ZN, Zubova SG, Bukreeva EI, Pospelov VA, Pospelova TV, Blagosklonny MV. Rapamycin decelerates cellular senescence. Cell cycle Georgetown, Tex. 2009; 8:1888-1895.. 62. Leontieva OV, Lenzo F, Demidenko ZN, Blagosklonny MV. Hyper-mitogenic drive coexists with mitotic incompetence in senescent cells. Cell cycle (Georgetown, Tex. 11:4642-4649.. 63. Harrison DE, Strong R, Sharp ZD, Nelson JF, Astle CM, Flurkey K, Nadon NL, Wilkinson JE, Frenkel K, Carter CS, Pahor M, Javors MA, Fernandez E, et al. Rapamycin fed late in life extends lifespan in genetically heterogeneous mice. Nature. 2009; 460:392-395. [PubMed] 64. Salton SR, Ferri GL, Hahm S, Snyder SE, Wilson AJ, Possenti R, Levi A. VGF: a novel role for this neuronal and neuroendocrine polypeptide in the regulation of energy balance. Frontiers in neuroendocrinology. 2000; 21:199-219. [PubMed] 65. Olefsky JM and Glass CK. Macrophages, inflammation, and insulin resistance. Annual review of physiology. 72:219-246.. 66. Jagannathan-Bogdan M, McDonnell ME, Shin H, Rehman Q, Hasturk H, Apovian CM, Nikolajczyk BS. Elevated proinflammatory cytokine production by a skewed T cell compartment requires monocytes and promotes inflammation in type 2 diabetes. J Immunol. 186:1162-1172. [PubMed] 67. Facchini A, Mariani E, Mariani AR, Papa S, Vitale M, Manzoli FA. Increased number of circulating Leu 11+ (CD 16) large granular lymphocytes and decreased NK activity during human ageing. Clin Exp Immunol. 1987; 68:340-347. [PubMed] 68. Vitale M, Zamai L, Neri LM, Galanzi A, Facchini A, Rana R, Cataldi A, Papa S. The impairment of natural killer function in the healthy aged is due to a postbinding defcient mechanism. Cell Immunol. 1992; 145:1-10. [PubMed] 69. Borrego F, Alonso C, Galiani M, Carracedo J, Ramirez R, Ostos B, Pena J, Solana R. NK phenotypic markers and IL2 response in NK cells from elderly people. Experimental gerontology. 1999; 34:253-265. [PubMed] Stefan Busse, MD [email protected] aging CD3 lymphocytes VGF expression Rapamycin All site content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 License (CC BY 3.0).
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Paul Harvey and the Reign of Heaven – Foreign Courts Doing Business Here! Fraud! The unincorporated entity known as The United States of America and the incorporated entity also calling itself "The United States of America" are NOT THE SAME entities just because they appear to have the same name. They are fundamentally different in nature, jurisdiction, and law. Trying to obfuscate this in any way just slows down any solution to the problem this country faces. It will also be seen that the quasi-military offices such as "Postmaster General" were NEVER part of the lawful government of the actual United States and have instead existed in the Territorial United States and Municipal United States — that is, in international jurisdiction of the sea prior to the Civil War and afterward usurped upon the land as part of the Territorial United States' administration. But if you don't know that there are three versions of "United States"— our version, the Territorial United States and the Municipal United States (both of which routinely just refer to themselves as "the United States" also) — it's nigh on unto impossible for people to wrap their heads around which entity and which offices of which entity you are talking about. This is just another example of "similar names deceits" being used by lawyers to create deliberate confusions and wrong assumptions and keep us all at each other's throats and unable to square off and deal with the actual problem. If there is a stain on the record of our forefathers, one dark hour in the earliest history of the American colonies, it would be the hanging of the so-called "witches" at Salem. But that was a pinpoint in place and time, a brief lapse into hysteria. For the most part, our seventeenth century colonists were scrupulously fair, even in fear. There was one group of people they feared with reason – a society, you might say, whose often insidious craft had claimed a multitude of victims, ever since the Middle Ages in Europe. One group of people hated and feared from Massachusetts Bay to Virginia. The magistrates would not burn them at the stake, although surely a great many of the colonists might have recommended such a solution. Our forefathers were baffled by them. In the first place, where did they come from? Of all who sailed from England to Plymouth in 1620, not one of those two-legged vermin was aboard. That's what the colonists called them. Parasites who fed on human misery, spreading sorrow and confusion wherever they went. And still, they were permitted co-existence with the colonists. Of course, there were colonial laws prohibiting the practice of their infamous craft. Somehow a way was always found around those laws. In 1641, Massachusetts Bay Colony took a novel approach to the problem. The governors attempted to starve those "devils" out of existence through economic exclusion. They were denied wages, and thereby it was hoped that they would perish. Four years later Virginia followed the example of Massachusetts Bay, and for a while, it seemed that the dilemma had been resolved. Somehow the parasites managed to survive, and the mere nearness of them made the colonists' skin crawl. The "treacherous ones" were cast out of the colony. At last, after decades of enduring the psychological gloom, the sun came out and birds sang and all was right with the world. And the elation continued for a generation. I'm not sure why the Virginians eventually allowed the outcasts to return, but they did. In 1680, after twenty-two years, the despised ones were readmitted to the colony on the condition that they be subjected to the strictest surveilance. For indeed, over the next half-century or so, the imposed restrictions were slowly, quietly swept away. And those whose treachery had been feared since the Middle Ages ultimately took their place in society. You see, the "vermin" that once infested colonial America, the parasites who preyed on the misfortune of their neighbors until finally they were officially banished from Virginia, those dreaded, despised and inevitably outcast masters of confusion were – LAWYERS! Claim in bold Quotes by Anna, — rebuttal in Italics by the Reign of Heavens. Where is the evidence of this claim? There are no links or documents, nothing….. This is the first time that the Government of The United States of America has ever heard of such a claim or the subject matter. Keith Livingway never claimed that he attended a bankruptcy trustee sale, nor did he ever claim to have bought the office of Postmaster General. Where is the evidence? Where is a publication of the claim? There isn't any because it is a complete lie. The whole scenario was completely made up by Anna Von Reitz and Paul Stramer. Everyone can see that "Postmaster General" did, in fact, exist before the civil war, and here is the link to the successor of Ebeneezer Hazard: LINK The Postmaster General credentials are towards the bottom of the page. The National Assembly did create a department of the General Post Office to operate as a Government agency, however, that was done to protect the original General Post Office of 1775 from foreign powers when doing business with them. The National Assembly has that right and power to create such agencies when doing business with foreign powers. Further, everyone can see that Benjamin Franklin did, in fact, hold the office of Postmaster General and not this made up difference in spelling and land/sea jurisdiction garbage. All surveys require both, metes and bounds and seaward boundaries in order to be legitimate. No one can land lock a country. IT IS DECLARED THAT; the office of the Postmaster General of the Confederacy of The United States of America of 1775, first held by Doctor Benjamin Franklin on 26th of July 1775, was succeeded by Richard Bache on November 7th, 1776, succeeded by Ebenezer Hazard on the 28th day of January 1782, and died in the year of 1817 without naming a successor. The office of the Postmaster General of the Confederacy of The United States of America of 1775 was vacant from the year 1817 until the year 2010." as published April 2nd, 2012 at the link above. Keith Livingway is not and has never claimed to personally own any office, however he was appointed successor of Ebeneezer Hazard as stated in the Declaration of Chain of Title here: LINK by the National Assembly to the office of the Postmaster General and or Post Master General of the General Post Office of the original Confederacy of 1781 back to 1775 and now the Government of The United States of America. The appointment is for life or until succeeded to keep the chain of title to the country known as The United States of America. These facts as stated in blue may be a source of distress, jealousy, embarrassment or otherwise to Anna Von Reitz and Paul Stramer. Those emotions do not give them the right to print lies, deceive people, or slander people. Neither of them has the right to attack people personally with lies and deceit. Neither of them called to verify the facts of their documents, ever…That is called libel and others that are parroting these lies and twisting the facts are also libel. All of this back and forth really needs to end because it is beginning to have the look and feel of high school all over again. The office of the Postmaster General of the Government of The United States of America will never be vacated or released into the hands of proprietors seeking to use Patriot tricks to gain control of the country on behalf of foreign powers. Upon the death of the current aforesaid office holder, the chain of title reverts back to the National Assembly to appoint a new successor and further, there exist other protections of said office that is privileged information. Further, it is a very serious crime to attack the General Post Office of the country. THE T-ROH SHOW will broadcast and cover the real story and facts about how all of this came about when it pertains to the General Post Office and the original Government when more important issues are already covered. Next Next post: What I Think. Really.
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https://www.sfgate.com/news/article/Mural-missed-Mission-miffed-3068653.php Mural missed, Mission miffed Tyche Hendricks, OF THE EXAMINER STAFF Published 4:00 am PDT, Wednesday, September 23, 1998 1998-09-23 04:00:00 PDT SAN FRANCISCO -- WITH A passionate display of street theater, a handful of Mission District artists resurrected for one evening the spirit of the Lilli Ann mural, a brightly colored, four-story artwork that was wiped out this summer with a coat of white paint. And with a bit of community organizing and a lawsuit, they hope to restore it permanently. More than two dozen local artists and area residents gathered Tuesday evening before the now-blank wall at 17th and Harrison streets for a theatrical mourning of the beloved mural. Amid rattling of bones, they cast a tongue-in-cheek hex on the building that for 12 years had been the site of an abstract painting commissioned by The City and designed by renowned San Francisco muralist Jesus "Chuy" Campusano. On July 25, the 5,000 square feet of swirling geometric shapes in green, yellow, red and purple were painted over with an acrylic sealant by commercial real estate developers Robert and Vera Cort, who bought the vacant building two years ago and have spent $1.5 million renovating it. The Corts say they had to seal up the wall to protect the building from the elements. "It was leaking like a sieve. That's why we sealed it," Vera Cort said. "We didn't do anything maliciously." She added that she and her husband had planned to make the wall available as display space for one of her new tenants, the multimedia company University Games, which makes Carmen Sandiego products. But to the Mission's Latino artists, the whitewashing of the mural is nothing less than an assault on the cultural heritage of a struggling neighborhood, another manifestation of the gentrification that threatens to make the area unaffordable for the artists and immigrant families who have long called it home. Jaime Cortez, a staff member at Galeria de la Raza on 24th Street, convened the "protest funeral" Tuesday evening with a shout. "Perhaps Robert Cort thought he could indulge in cultural clear-cutting in the Mission without consequences. Wrong!" he declared. "Some of our Mission neighborhoods may be a bit decrepit, but our murals are our flowers." The Lilli Ann mural, which got its name because the building once housed the Lilli Ann garment factory, is part of the Mission's rich tradition of public art, and one of the first major abstract murals in The City, he said. Though Campusano died last year, his children and Elias Rocha, the artist who executed the painting, have sued the Robert J. Cort Trust in hopes of forcing the restoration of the mural. As dusk fell on 17th Street, Cortez asked his audience, "Do you remember Lilli Ann?" "Yes!" hollered the crowd. "What was she like?" Cortez asked. "Colorful and bold!" one replied. "One of a kind!" another said. Then, as the group chanted "Lilli Ann, Lilli Ann," the "ghost of the murdered mural" appeared in the form of Monica Praba Pilar, a performance artist dressed all in white, with skeletal face paint and a headdress made from a frilly pink doll. "I was cut down in my prime," she wailed. "I've been down in the land of the dead with all the other dead art." "The spirit of the community will heal you," chanted the crowd, some placing flowers in her arms, others ringing the bells on their bicycles. At that, Gerardo Perez, another artist, dressed as a Mexican peasant brujo, or witch, in straw hat and sandals, clacked a pair of bones and symbolically hexed the building and "the greed of developers," crying "el hambre de la muerte te llama" ( "the hunger of death is calling you" ) as he raised his arms and bowed down on the sidewalk. "We stand here today to remind everyone that being poor does not mean that we will stand by passively as monied developers and corporate interests attempt to push us out, price us out or paint us out of existence," Cortez concluded. "The community demands and deserves respect, and we will take to the streets to get it." But Vera Cort said she was troubled by the "greedy developer" label she had been tagged with. She and her husband took great pains to restore the rundown, 90-year-old building that originally was built for the McCroskey mattress company, she said, giving it a new roof and foundation and replacing the windows, plumbing and wiring. "We're good landlords, very hands-on property owners," she said, adding that the Corts were third-generation San Franciscans. "We're willing to devote time and be part of the community, but we're not going to be pushed into a corner by a few activists." Cort said she was unaware of the California Art Preservation Act or the federal Visual Artists' Rights Act that require giving the artist or his heirs 90 days notice before removing an artwork. "These laws basically balance the rights of real property owners against the moral right of artists to protect their work," said Brooke Oliver, the attorney for the Campusano family. The protection of the law hinges on whether or not the artwork can be removed, though. If it can, it belongs to the artist. If not, the property owners can do with it as they please. So last weekend, the plaintiffs brought restoration expert Nathan Zakheim up from Los Angeles to see whether it was possible to save and remove the mural. He found that the sealant could be wiped off with a solvent, restoring the mural beneath, and that the mural itself could be removed in 1-foot-square segments, using a laborious chemical technique, and remounted on another surface. Cort said she was relieved that the mural was not destroyed, but "whether they can reassemble 5,000 square feet remains to be seen." The plaintiffs and neighborhood activists want the colorful painting to stay right where it has always been. "We'd like to see it restored," said Campusano's widow, Dianne Dimoss. "That would make my son and daughter happy. And it would set a precedent that people cannot come into a neighborhood and destroy art." <
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We're not really that glib. But the question does sort of answer itself. If you don't really know the reasons for having a blog, chances are good that you won't be using the blog in ways that can helpful to your organization. And if you're not using it well, you've just created an online space where – rather than seeing how capable and informed and expert your company is – readers may instead see apathy, lack of purpose, or outdated material. So, what are some of the good reasons for establishing and maintaining a blog? You have lots of good content to share and a plan for sharing it. If this isn't the case, stop now; your blogging efforts will be for naught. You've got to have something to say and you've got to have a plan for getting it written out and on the blog. If you're not going to write – at the very least – one quality blog per month, don't set on up. Even better, post every other week or weekly. And have a internal plan for how this happens. Is the blog responsibility of one person in the organization? Will you have multiple writers? Calendar this out and get it set in stone. In terms of what to write about, the possibilities are endless if you start brainstorming: new product descriptions, case studies about projects, jobs, or initiatives your organization tackled, staff profiles, shared articles from other places about industry trends or developments, and much more. You're seeking to boost your search rankings. More content on your website means more pages that can be indexed and trolled by the search engines. So it can always help to be adding fresh, new content to your website via a blog. As you do so, you'll also be wanting to write blog posts that are rich with key words that you're guessing folks will type into a search engine. It also can help to have your blog cross promoted or referenced on other blogs around similar topics, so look to partner with other bloggers who can give you a boost. You want your audience to engage and dialogue with you. Perhaps you want some feedback and interaction with the readers of your website – whether through comments on blog articles, surveys, short quizzes, or some other means. In this case, a moderated blog can be a good thing. Readers can respond to what you've written and to one another's comments. Most blog platforms will also allow you to moderate comments, approving them before they're posted, so that nothing unseemly appears on the blog and so that WWIII doesn't break out for some reason. You want to convey subject expertise or mastery of your trade. Regular blog articles are a great way to showcase some of the work you're doing or some of the innovations you're making in your company. A blog can also be a place to share what you're reading from other writers, a way to demonstrate that you're "keeping up" on the latest thought patterns or trends in your industry. With the rate of change skyrocketing in almost every market and sphere, the more you can evidence that you are aware and thinking through the ramifications for your business and organization, the more potential clients or members can believe that you'll have the same mindfulness around your interactions with them. The reasons for starting and maintaining a blog are many – and we could easily write 500 more words on further arguments for keeping one. But the bottom line is this: have a reason and have a plan. Otherwise, spend your time and energy on a marketing effort better suited to the goals you need to accomplish.
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Hopa.com features over 60 flash scratch card games and scratch off tickets. Register with Hopa using our bonus code and you are in for some free cash no deposit required to test the games. Who knows, you might even win something, as every 1 in 3 cards is a winning card. The 200,000 EUR scratch jackpot is waiting for you. In order to bet online with Hopa you must create an account first. If you don't have an account yet click here to visit Hopa.com, and hit the option "Play now". At registration, use the Hopa.com bonus code as shown below for a guaranteed bonus. YES. You will get the stated bonus provided you will use correctly the bonus code at registration and you will deposit for the first time a minimum of $10. Please note that Hopa wagering requirements apply in order to cash out the bonus. Hopa.com terms and conditions apply. NEXT bonus codes and Hopa.com are in a strategic partnership in order to bring you the best promos and authorized bonus codes. Should you have any problems in redeeming your bonus please contact Hopa.com Customer Service stating the bonus code used or contact us and we will solve any related issues for you in the shortest time possible. The Hopa.com bonus code was reviewed in 2018 by NEXTbonuscodes.com and received a 5 / 5 rating. We hope you are pleased using the bonus code for Hopa and you will recommend it to your friends as well.
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keywords: John Warhurst Is Professor Of Political Science At The Australian National University And A Canberra Rallies take the good fight to Canberra John Warhurst Political rallies are on the rise. That is a good thing. The ones that should really make governments take notice are those that contain not just rusted on party supporters, but people who really are considering changing their vote from the Gillard-Abbott election in 2010. ASIO and me I received the documents in a battered brown suitcase. They were from a time of high drama within the Movement and the Labor Party concerning the Labor Split. In the course of my research, I wrote to several international sources. This brought me to the attention of the CIA and ASIO. Gillard's chaplaincy challenge In the midst of debates about same sex marriage that will test and probably break relations between the Gillard Government and some Christian communities, the chaplaincy program is seen by both camps as a win-win. A challenge to be considered by the High Court this month could change all that. Labor's poor political antennae The Government's free set-top box scheme is facing community and Opposition claims that it is wasteful and will tempt rorters and shysters. What should be a feel-good scheme has become a cavalcade of the disgruntled. This tells us a lot about politics and policy-making. Greens' and Abbott's guilt by association Political alliances can be strategically useful, but leaders must be careful not to appear too close to extreme groups. Tony Abbott and the NSW Greens have experienced 'guilt by association' in recent times, but the concept has a long history in Australian politics. Small parties, big ideas More Labor and Coalition MPs than Green MPs are pro gay marriage and pro euthanasia. It is these major party social progressives who should be most feared by opponents of gay marriage and euthanasia. The Greens will only ever play a ginger-group role. Old men behaving badly Old men are hard to top when it comes to abuse of power: Egypt's Mubarak is 82, Italy's Berlusconi is 74, and Zimbabwe's Mugabe is 88. There are good arguments for removing leaders once they reach 'a certain age', even in relatively benign democracies such as Australia. Lessons about Australian identity from 'The King's Speech' Some advocates of monarchy have jumped on the film The King's Speech as evidence that Australia needs a monarch. Monarchists often argue like this when they want to personalise the constitutional debate by concentrating on a member of the Royal family with attractive features. Political opposition need not be nasty Adversarial politics can be seen as a necessary and positive aspect of Westminster style parliamentary politics. This does not include needless aggression that is expressed in a nasty tone and apparent anger. Rehabilitating Rudd and Turnbull Kevin Rudd and Malcolm Turnbull's past faults and misdemeanours have been forgotten and they have been charged with new responsibilities at the heart of Australia's domestic and international futures. The new leaders must wish their vanquished colleagues great success. But not too much. The election Rudd could have won The result suggests some fascinating questions. Prime among them is whether Labor panicked and threw away this election when it deposed Kevin Rudd and replaced him with Julia Gillard in June. Would Rudd have done better? The answer is probably yes. Nothing underhanded about Labor-Greens deal Appearing last week on ABC1's Q+A, Julie Bishop claimed that following a preference deal with the Labor Party, the Greens were now effectively a Labor faction. Preference deals are as old as the preferential system itself. The impact of these deals should not be exaggerated.
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KCC Architecture is a young firm with an integrated vision of the architecture practice. As the design process unfolds we actively engage in the integration of a clear intention, open communication, target dates, budget control, best professional practices and inspiring creativity. We strive to provide a platform where each team member can bring forward the best of themselves to achieve a common goal. Karla moved to Vancouver from Guadalajara Mexico in 2002. With her masters in architecture and following her dream, she attained the registration as an architect in 2011. Enthusiastic, focused, business oriented and with 20 years experience she inspires every day commitment to excellence, beauty and sustainability. Driven to lead creative teams with a clear visions and ultimately delivering successful projects.
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Shirly Pinto, Ph.D. VP, Drug Discovery-Biology Shirly joined Kallyope as VP and Head of Biology, Drug Discovery in March 2017. At Kallyope, she is responsible for leading a discovery platform involving in vivo, in vitro, and biomarker systems and is accountable for multiple drug discovery programs. Prior to joining Kallyope, Shirly gained in-depth knowledge of drug discovery from target validation to lead optimization in multiple therapeutic areas related to cardio-metabolism and tissue injury spanning 12 years at Merck. In recent years at Merck, Shirly established and executed the scientific strategy for fibrosis and diabetic complications related to renal diseases. She was accountable for a diverse portfolio spanning multiple modalities. Prior to that, Shirly led numerous drug discovery small molecule/peptide programs in the areas of obesity, diabetes, and atherosclerosis. Over the years, Shirly has been a strong driver for successfully leading collaborations with multiple partners in academia and industry and is the author/co-author of 40 publications. Shirly joined Merck after a postdoctoral appointment with Jeff Friedman at the Rockefeller University, where she demonstrated hypothalamic neuronal plasticity in response to leptin. She received her Ph.D., from Weil Cornell Graduate School of Medical Sciences. She worked with Tim Tully at Cold Spring Harbor Laboratory studying the genetic role of a Drosophila gene associated with learning defects. Kallyope Inc. • 430 East 29th Street, 10th Floor, New York, NY 10016 © 2016 Kallyope
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Some years ago, Henri Matisse's signature was discovered in the visitors' book at the Nasrid monument, showing that he had visited the Alhambra in December 1910 during his trip to Andalusia when he was 41. To commemorate the centenary of that visit, the Granada Museum of Fine Arts, housed in the Palace of Charles V in the Alhambra complex, is holding an exhibition of his works. The exhibition, 'Matisse and the Alhambra', contains around 100 exhibits, including 34 oils, drawings and lithographs and one of the painter's sculptures. Also on show are the artist's letters, postcards and personal photographs and works of Islamic art, from ceramics to tapestries and miniatures. The exhibition is running until the end of this month so art lovers are still just in time to see Matisse's colourful works and personal effects in spectacular surroundings. Granada's Alhambra is a palace and fortress complex constructed during the mid 14th century by the Moorish rulers of 'Al-Andalus'. It is the jewel in the crown of what was to be 700 years of Muslim rule in most of Spain. Designated a UNESCO World Heritage Site as housing the country's most important Islamic architecture, the Alhambra is now one of Spain's major tourist attractions. Don't miss this opportunity to view the harmony of two different cultures from two different eras.
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<!DOCTYPE html> <html> <head> <meta http-equiv="Content-type" content="text/html; charset=utf-8" /> <title>JQuery Validation Engine</title> <link rel="stylesheet" href="../css/validationEngine.jquery.css" type="text/css"/> <link rel="stylesheet" href="../css/template.css" type="text/css"/> <link rel="stylesheet" href="http://labs.abeautifulsite.net/jquery-selectBox/jquery.selectBox.css" type="text/css" /> <script src="../js/jquery-1.8.2.min.js" type="text/javascript"></script> <script src="../js/languages/jquery.validationEngine-en.js" type="text/javascript" charset="utf-8"></script> <script src="../js/jquery.validationEngine.js" type="text/javascript" charset="utf-8"></script> <script src="http://labs.abeautifulsite.net/jquery-selectBox/jquery.selectBox.js" type="text/javascript"></script> <script> jQuery(document).ready(function() { var prefix = "selectBox_" // binds form submission and fields to the validation engine jQuery("#formID").validationEngine({ prettySelect : true, usePrefix: prefix }); $("select").selectBox(); // By default, selectBox does not create an id to the newly created element - We need to add this manually $('select').each(function(){ // The jquery validation engine needs an id on the "a" element created by selectBox plugin $(this).next('a.selectBox') // Since id needs to be unique, we use a prefix here (can use suffix - up to you) .attr("id", prefix + this.id ) // By default, all classes are passed on to the new element - Important: We need to remove it .removeClass("validate[required]"); }) // This demo is for hidden elements in the form $('#hidden_samples').change(function(){ var value = $(this).val(); if (value != '') $('#section_' +value).show().siblings().hide(); else $('#hidden_elements').children().hide(); }); }); </script> <style type="text/css"> select {width: 250px} div {margin-top: 20px} </style> </head> <body> <p> <a href="../index.html" onclick="">Back to index</a> </p> <p> This demonstration shows the validation with the <a href="https://github.com/claviska/jquery-selectBox">jQuery SelectBox plugin</a> </p> <form id="formID" class="formular" method="post" action=""> <fieldset> <legend> Select single </legend> <label> <select name="country" id="country" class="validate[required]"> <option value="">- Please Select -</option> <option value="United States">United States</option> <option value="United Kingdom">United Kingdom</option> <option value="Afghanistan">Afghanistan</option> <option value="Albania">Albania</option> <option value="Algeria">Algeria</option> <option value="American Samoa">American Samoa</option> <option value="Andorra">Andorra</option> <option value="Angola">Angola</option> <option value="Anguilla">Anguilla</option> <option value="Antarctica">Antarctica</option> <option value="Antigua and Barbuda">Antigua and Barbuda</option> <option value="Argentina">Argentina</option> <option value="Armenia">Armenia</option> <option value="Aruba">Aruba</option> <option value="Australia">Australia</option> <option value="Austria">Austria</option> <option value="Azerbaijan">Azerbaijan</option> <option value="Bahamas">Bahamas</option> <option value="Bahrain">Bahrain</option> <option value="Bangladesh">Bangladesh</option> <option value="Barbados">Barbados</option> <option value="Belarus">Belarus</option> <option value="Belgium">Belgium</option> <option value="Belize">Belize</option> <option value="Benin">Benin</option> <option value="Bermuda">Bermuda</option> <option value="Bhutan">Bhutan</option> <option value="Bolivia">Bolivia</option> <option value="Bosnia and Herzegovina">Bosnia and Herzegovina</option> <option value="Botswana">Botswana</option> <option value="Bouvet Island">Bouvet Island</option> <option value="Brazil">Brazil</option> <option value="British Indian Ocean Territory">British Indian Ocean Territory</option> <option value="Brunei Darussalam">Brunei Darussalam</option> <option value="Bulgaria">Bulgaria</option> <option value="Burkina Faso">Burkina Faso</option> <option value="Burundi">Burundi</option> <option value="Cambodia">Cambodia</option> <option value="Cameroon">Cameroon</option> <option value="Canada">Canada</option> <option value="Cape Verde">Cape Verde</option> <option value="Cayman Islands">Cayman Islands</option> <option value="Central African Republic">Central African Republic</option> <option value="Chad">Chad</option> <option value="Chile">Chile</option> <option value="China">China</option> <option value="Christmas Island">Christmas Island</option> <option value="Cocos (Keeling) Islands">Cocos (Keeling) Islands</option> <option value="Colombia">Colombia</option> <option value="Comoros">Comoros</option> <option value="Congo">Congo</option> <option value="Congo, The Democratic Republic of The">Congo, The Democratic Republic of The</option> <option value="Cook Islands">Cook Islands</option> <option value="Costa Rica">Costa Rica</option> <option value="Cote D'ivoire">Cote D'ivoire</option> <option value="Croatia">Croatia</option> <option value="Cuba">Cuba</option> <option value="Cyprus">Cyprus</option> <option value="Czech Republic">Czech Republic</option> <option value="Denmark">Denmark</option> <option value="Djibouti">Djibouti</option> <option value="Dominica">Dominica</option> <option value="Dominican Republic">Dominican Republic</option> <option value="Ecuador">Ecuador</option> <option value="Egypt">Egypt</option> <option value="El Salvador">El Salvador</option> <option value="Equatorial Guinea">Equatorial Guinea</option> <option value="Eritrea">Eritrea</option> <option value="Estonia">Estonia</option> <option value="Ethiopia">Ethiopia</option> <option value="Falkland Islands (Malvinas)">Falkland Islands (Malvinas)</option> <option value="Faroe Islands">Faroe Islands</option> <option value="Fiji">Fiji</option> <option value="Finland">Finland</option> <option value="France">France</option> <option value="French Guiana">French Guiana</option> <option value="French Polynesia">French Polynesia</option> <option value="French Southern Territories">French Southern Territories</option> <option value="Gabon">Gabon</option> <option value="Gambia">Gambia</option> <option value="Georgia">Georgia</option> <option value="Germany">Germany</option> <option value="Ghana">Ghana</option> <option value="Gibraltar">Gibraltar</option> <option value="Greece">Greece</option> <option value="Greenland">Greenland</option> <option value="Grenada">Grenada</option> <option value="Guadeloupe">Guadeloupe</option> <option value="Guam">Guam</option> <option value="Guatemala">Guatemala</option> <option value="Guinea">Guinea</option> <option value="Guinea-bissau">Guinea-bissau</option> <option value="Guyana">Guyana</option> <option value="Haiti">Haiti</option> <option value="Heard Island and Mcdonald Islands">Heard Island and Mcdonald Islands</option> <option value="Holy See (Vatican City State)">Holy See (Vatican City State)</option> <option value="Honduras">Honduras</option> <option value="Hong Kong">Hong Kong</option> <option value="Hungary">Hungary</option> <option value="Iceland">Iceland</option> <option value="India">India</option> <option value="Indonesia">Indonesia</option> <option value="Iran, Islamic Republic of">Iran, Islamic Republic of</option> <option value="Iraq">Iraq</option> <option value="Ireland">Ireland</option> <option value="Israel">Israel</option> <option value="Italy">Italy</option> <option value="Jamaica">Jamaica</option> <option value="Japan">Japan</option> <option value="Jordan">Jordan</option> <option value="Kazakhstan">Kazakhstan</option> <option value="Kenya">Kenya</option> <option value="Kiribati">Kiribati</option> <option value="Korea, Democratic People's Republic of">Korea, Democratic People's Republic of</option> <option value="Korea, Republic of">Korea, Republic of</option> <option value="Kuwait">Kuwait</option> <option value="Kyrgyzstan">Kyrgyzstan</option> <option value="Lao People's Democratic Republic">Lao People's Democratic Republic</option> <option value="Latvia">Latvia</option> <option value="Lebanon">Lebanon</option> <option value="Lesotho">Lesotho</option> <option value="Liberia">Liberia</option> <option value="Libyan Arab Jamahiriya">Libyan Arab Jamahiriya</option> <option value="Liechtenstein">Liechtenstein</option> <option value="Lithuania">Lithuania</option> <option value="Luxembourg">Luxembourg</option> <option value="Macao">Macao</option> <option value="Macedonia, The Former Yugoslav Republic of">Macedonia, The Former Yugoslav Republic of</option> <option value="Madagascar">Madagascar</option> <option value="Malawi">Malawi</option> <option value="Malaysia">Malaysia</option> <option value="Maldives">Maldives</option> <option value="Mali">Mali</option> <option value="Malta">Malta</option> <option value="Marshall Islands">Marshall Islands</option> <option value="Martinique">Martinique</option> <option value="Mauritania">Mauritania</option> <option value="Mauritius">Mauritius</option> <option value="Mayotte">Mayotte</option> <option value="Mexico">Mexico</option> <option value="Micronesia, Federated States of">Micronesia, Federated States of</option> <option value="Moldova, Republic of">Moldova, Republic of</option> <option value="Monaco">Monaco</option> <option value="Mongolia">Mongolia</option> <option value="Montenegro">Montenegro</option> <option value="Montserrat">Montserrat</option> <option value="Morocco">Morocco</option> <option value="Mozambique">Mozambique</option> <option value="Myanmar">Myanmar</option> <option value="Namibia">Namibia</option> <option value="Nauru">Nauru</option> <option value="Nepal">Nepal</option> <option value="Netherlands">Netherlands</option> <option value="Netherlands Antilles">Netherlands Antilles</option> <option value="New Caledonia">New Caledonia</option> <option value="New Zealand">New Zealand</option> <option value="Nicaragua">Nicaragua</option> <option value="Niger">Niger</option> <option value="Nigeria">Nigeria</option> <option value="Niue">Niue</option> <option value="Norfolk Island">Norfolk Island</option> <option value="Northern Mariana Islands">Northern Mariana Islands</option> <option value="Norway">Norway</option> <option value="Oman">Oman</option> <option value="Pakistan">Pakistan</option> <option value="Palau">Palau</option> <option value="Palestinian Territory, Occupied">Palestinian Territory, Occupied</option> <option value="Panama">Panama</option> <option value="Papua New Guinea">Papua New Guinea</option> <option value="Paraguay">Paraguay</option> <option value="Peru">Peru</option> <option value="Philippines">Philippines</option> <option value="Pitcairn">Pitcairn</option> <option value="Poland">Poland</option> <option value="Portugal">Portugal</option> <option value="Puerto Rico">Puerto Rico</option> <option value="Qatar">Qatar</option> <option value="Reunion">Reunion</option> <option value="Romania">Romania</option> <option value="Russian Federation">Russian Federation</option> <option value="Rwanda">Rwanda</option> <option value="Saint Helena">Saint Helena</option> <option value="Saint Kitts and Nevis">Saint Kitts and Nevis</option> <option value="Saint Lucia">Saint Lucia</option> <option value="Saint Pierre and Miquelon">Saint Pierre and Miquelon</option> <option value="Saint Vincent and The Grenadines">Saint Vincent and The Grenadines</option> <option value="Samoa">Samoa</option> <option value="San Marino">San Marino</option> <option value="Sao Tome and Principe">Sao Tome and Principe</option> <option value="Saudi Arabia">Saudi Arabia</option> <option value="Senegal">Senegal</option> <option value="Serbia">Serbia</option> <option value="Seychelles">Seychelles</option> <option value="Sierra Leone">Sierra Leone</option> <option value="Singapore">Singapore</option> <option value="Slovakia">Slovakia</option> <option value="Slovenia">Slovenia</option> <option value="Solomon Islands">Solomon Islands</option> <option value="Somalia">Somalia</option> <option value="South Africa">South Africa</option> <option value="South Georgia and The South Sandwich Islands">South Georgia and The South Sandwich Islands</option> <option value="South Sudan">South Sudan</option> <option value="Spain">Spain</option> <option value="Sri Lanka">Sri Lanka</option> <option value="Sudan">Sudan</option> <option value="Suriname">Suriname</option> <option value="Svalbard and Jan Mayen">Svalbard and Jan Mayen</option> <option value="Swaziland">Swaziland</option> <option value="Sweden">Sweden</option> <option value="Switzerland">Switzerland</option> <option value="Syrian Arab Republic">Syrian Arab Republic</option> <option value="Taiwan, Republic of China">Taiwan, Republic of China</option> <option value="Tajikistan">Tajikistan</option> <option value="Tanzania, United Republic of">Tanzania, United Republic of</option> <option value="Thailand">Thailand</option> <option value="Timor-leste">Timor-leste</option> <option value="Togo">Togo</option> <option value="Tokelau">Tokelau</option> <option value="Tonga">Tonga</option> <option value="Trinidad and Tobago">Trinidad and Tobago</option> <option value="Tunisia">Tunisia</option> <option value="Turkey">Turkey</option> <option value="Turkmenistan">Turkmenistan</option> <option value="Turks and Caicos Islands">Turks and Caicos Islands</option> <option value="Tuvalu">Tuvalu</option> <option value="Uganda">Uganda</option> <option value="Ukraine">Ukraine</option> <option value="United Arab Emirates">United Arab Emirates</option> <option value="United Kingdom">United Kingdom</option> <option value="United States">United States</option> <option value="United States Minor Outlying Islands">United States Minor Outlying Islands</option> <option value="Uruguay">Uruguay</option> <option value="Uzbekistan">Uzbekistan</option> <option value="Vanuatu">Vanuatu</option> <option value="Venezuela">Venezuela</option> <option value="Viet Nam">Viet Nam</option> <option value="Virgin Islands, British">Virgin Islands, British</option> <option value="Virgin Islands, U.S.">Virgin Islands, U.S.</option> <option value="Wallis and Futuna">Wallis and Futuna</option> <option value="Western Sahara">Western Sahara</option> <option value="Yemen">Yemen</option> <option value="Zambia">Zambia</option> <option value="Zimbabwe">Zimbabwe</option> </select> </label> </fieldset> <fieldset> <legend> Hidden Form Sections </legend> <label> <select name="hidden_samples" id="hidden_samples" class="validate[required]"> <option value="">- Please Select -</option> <option value="1">Show Option 1</option> <option value="2">Show Option 2</option> </select> </label> <div id="hidden_elements"> <div id="section_1" style="display:none"> <label> This is the hidden option for "Show Option 1" <select name="hidden_samples" id="hidden_samples_1" class="validate[required]"> <option value="">- Please Select -</option> <option value="1">Show Option 1</option> <option value="2">Show Option 2</option> </select> </label> </div> <div id="section_2" style="display:none"> <label> This is the hidden option for "Show Option 2" <select name="hidden_samples" id="hidden_samples_2" class="validate[required]"> <option value="">- Please Select -</option> <option value="1">Show Option 1</option> <option value="2">Show Option 2</option> </select> </label> </div> </div> </fieldset> <input class="submit" type="submit" value="Validate &amp; Send the form!"/> <hr/> </form> </body> </html>
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PCN Flight West: WA/DL Capt. Henry 'Ted' T. Weidemueller Jr. WA/DL Capt. Henry 'Ted' T. Weidemueller Jr. USAF veteran, WA/DL Capt. Henry T. Weidemueller Jr. Notification with the passing of retired Western/Delta pilot Captain Henry 'Ted' T. Weidemueller Jr., age 78. Captain Weidemueller joined Western Airlines 04-22-1968 and retired with Delta Air Lines in 2000 as F/O, based 030/LAX. Henry T. Weidemueller, 78, entered into glory on Monday, August 20. After graduation from George Washington University in his hometown of St. Louis, Missouri, Henry served his country in the United States Air Force from 1962 to1967. After completion of his service, Captain Weidemueller began his 32-year career as a pilot for Delta Air Lines. He retired in 2000. Henry – or Ted, as he was known to many -- was devoted to his neighborhood church, Holy Nativity Episcopal Church in Westchester (Los Angeles). For 50 years, Ted served his church in countless unselfish ways. He was a Vestry member, also serving as both junior and senior warden. He served faithfully at the altar, assisting in both services on Sundays. He was also the church's unofficial caretaker. Besides caring for the church, Ted was best known for his warm, munificent "big" hugs on Sunday mornings -- an expression of his generous and caring spirit. Now we entrust him to the care of God, leaning on God's everlasting arms. A celebration of Ted's life will be held at Holy Nativity, 6700 West 83rd Street in Westchester on Saturday, September 1, at 10:00 A.M. Interment at Holy Cross Cemetery, 5835 West Slauson Avenue, Culver City, will follow the service. All are welcome to a reception at Holy Nativity following the interment. In keeping with Ted's wishes, in lieu of flowers, gifts can be made to Holy Nativity Episcopal Church in thanksgiving for Ted's life.
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The focal point is created by the crystal chandelier in your room. The gorgeous outlook is very nice to be decorated in certain room with formal arrangement. The special features come with the beautiful performance and unique shape. The lighting will give the pretty effect that will be created by these chandeliers of crystal. Do you love the lovely style of these lights? You should consider these types of the lighting for adorning your room décor. Let's take a look for the lovely chandeliers. The hundreds lighting reflections comes with beautiful effects that is made from the crystal chandelier. That may be expensive. But the formal lighting will make the room will be nice and elegant. The living room is very good to be hung this type of the chandelier with crystals. That is so nice to make the harmony performance on the living room with modern design or just the opposite. The elements of the crystal chandelier are created with different and varied features. That will be fitted to the room that needs these types of the lights. You may use this kind of the light for the bedroom. The shade lighting is very nice for this room, because the great shade reflections are able to make you have the comfy sleep at the bedroom. That is the important thing for your daily routine. Crystal chandelier with the gorgeous will be wanted by many people that can be hung for some other rooms like dining room, bathroom and meeting room. The classic features are able to bring the vintage styles for the room that hung these lights. The bright and shade lights are available. The contemporary design and the vintage style are also available. You may have one of them that are suitable to the styles of your room and your interior designs.
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Holy Resurrection Cathedral (Tokyo, Japan) Revision as of 13:27, June 10, 2008 by Θεοδωρος (talk | contribs) Orthodoxy in Japan Timeline of Orthodoxy in Japan Church of Japan Nicholas of Japan Andronik of Perm Sergius (Tikhomirov) Nicholas (Ono) Benjamin (Basalyga) Ireney (Bekish) Nikon (de Greve) Vladimir (Nagosky) Theodosius (Nagashima) Seraphim (Sigrist) of Sendai Daniel (Nushiro) of Japan Seraphim (Tsujie) of Sendai Fr Paul Sawabe Fr Simeon Michiro Mii Fr Anatoly Tikhai Yakov Tikhai Victor Pokrovsky Irina Yamashita Holy Resurrection Cathedral Holy Resurrection Cathedral as completed in 1891 The Holy Resurrection Cathedral, commonly called Nikolai-do, in Surugadai, Kanda district, Tokyo, Japan is the main cathedral of the Japanese Orthodox Church. It is located on Surugadai knoll in Kanda, on property purchased in 1872 by the future Archbishop Nicholas (Kasatkin), now St. Nicholas of Japan, for his mission headquarters to preach Orthodox Christianity to the Japanese people. Construction of the cathedral began in 1884, to plans prepared by Michael A. Shchurupov, a Moscow architect. It took seven years for the Japanese artisans to complete the edifice, which followed the classic Byzantine church design. The cathedral was consecrated on March 8, 1891. The Cathedral ruins after the Great Kanto earthquake of September 1923 The original cathedral was seriously damaged in the Great Kanto Earthquake of September 1923. The earthquake caused the main bell tower to fall onto the central dome, collapsing it, and thus causing major damage to the building. Fire further damaged and destroyed the iconostasis and the interior of the building. Rebuilding the cathedral became a major task for the then ruling bishop, Archbishop Sergii (Tikhomirov), who succeeded St. Nicholas after he died in 1912. Since Russia could no longer be looked to as a source of funding, Archbishop Sergii had to look for funding within Japan. A significant amount of funds was raised by numerous concerts by the cathedral choir, led by Victor A. Pokrovsky. The re-built cathedral was re-consecrated on December 15, 1929, with a shorter bell tower, a modified dome that was more in keeping with Archbishop Nicholas' original desires, and a less ornate interior. The re-built cathedral was designed by the Japanese architect, Shinito Okada. The Cathedral as re-built in 1929 Holy Resurrection Cathedral is known more popularly as Nikolai-do (Nicorai-do, as pronounced in Japanese), meaning The Temple (or House) of Nicholas, which reflects his popularity in Japan. In the world before the 1960s Nikolai-do was a prominent building that overlooked the Imperial palace, but now it is hidden among the many tall buildings erected since the 1960s. Holy Resurrection Cathedral today Orthodox Church singing in Japan Retrieved from "https://en.orthodoxwiki.org/index.php?title=Holy_Resurrection_Cathedral_(Tokyo,_Japan)&oldid=71192" Categories > Places > Churches Categories > Places > Churches > Churches in Japan Categories > Places > Orthodoxy by country > Orthodoxy in Japan
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I'm in the middle of an EMOTIONAL weekend. Yesterday was my last day at work which was very sad because I loved that job. The owners of the business took me back so readily after I was made redundant (I worked here before the theatre) and I think that is the nicest thing. I was showered with presents (Charlotte, my lovely colleague, got me a Waterstones voucher because 'I know you love books'. Yeh, that provoked the feels) and good wishes and hugs from everyone and I am still quite overwhelmed. Then tonight is my leaving party with my girls and the boy. I can only imagine the state of me when the alcohol is a-flowing. So thinking about the fact that I am leaving my home town and moving to the big city on Monday is threatening to push me over the edge and smother me with feels. But I am nothing if not British and my stiff upper lip is working overtime. June has been good. Busy, but good. I have been to America and London, started my new job, got a new reviewing job and been offered freelance writing work by my (ex-)employers. I am going to be a busy bee but I function better that way. I am still behind on reviewing these but they're coming, don't fret. I have many MANY thoughts. I have read some stonkers this month and I am still thoroughly enjoying AK. I have a weird crush on Levin but I have a suspicion that change somewhat in the course of the rest of the book. So far I'm just imagining this fit Russian farmer joining his peasants, doing the mowing, getting all sweaty and slowly removing his layers of Russian clothing...AHEM. Well, that's sounding altogether too Lawrencian for my tastes. Let's move on. On Monday, July 1st I am packing my life into a van and hitting the motorway to move to London. Monday is also my birthday (I've reached the big 23) so it will be an interesting day. Birthday's have never meant much to me but I think this one may be quite memorable. I've got a whole evening planned for when we finally get there. My brother, his girlfriend and housemate will come across from Essex, I'll be with my sister and our housemate and my boyfriend will come up from Taunton. I'm thinking takeaway and cider. Healthy, as always. I have a question for you all, particularly for Wilkie lovers out there. I have a couple of Wilkie novels on my Classics Club list (The Moonstone and No Name) and I have been considering organising a readalong. Any thoughts? Some of you have already expressed an interest but if anyone had any ideas of which book to choose then please let me know. I'm thinking it wouldn't run until autumn/winter because I think his novels match the stormy days and dark evenings rather well. Anyway, just talk to me people. I hope June has treated everyone well. How has your reading gone? Let's see how the second half of the year pans out for us all. Who doesn't love a blogger picture? Wow, your move has come around quickly, how exciting! I agree with you that Levin is the most interesting character in Anna K, too. Hey, all this emotional stuff only means there are many people who care about you, and that's a good thing! I wish you good luck with the move and no doubt London will be awesome. I'd definitely join for Moonstone read event, because it's in my classics list, but many people have probably read this one so you might want to pick something else. Duuuuude, it is totally normal to have a crush on Levin because he is THE BEST. I love him so. And lookit you doing Big Life Things (on your birthday, no less!) Very exciting stuff. Good luck in your new endeavors! I'm impressed with how much you've read. Especially with all of the things going on. Thinking of you as the move gets underway! Hope your move goes really well Ellie. And it sounds like you've got some great work stuff going on too. Happy birthday!
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Thysanozoon nigropapillosum, le ver plat ciel étoilé, est une espèce de vers plats polyclades de la famille des Pseudocerotidae. Répartition Cette espèce se rencontre dans l'Océan Indien et l'Ouest de l'Océan Pacifique tropical. Elle est notamment présente sur les côtes des Maldives, de l'Inde, du Sri Lanka, de Singapour, de Taiwan, de l'Indonésie, de la Nouvelle Guinée, des Îles Salomon, de l'île de Guam, des îles Palaos et de l'atoll d'Ifalik. Habitat Cette espèce est généralement observée dans les eaux côtières du récif à des profondeurs comprises entre 1 et 30 mètres. Elle affectionne la zone continuellement immergée, les mares de l'estran et le dessous des débris. Description Thysanozoon nigropapillosum est une espèce qui mesure de l'ordre de 15 à de long. Le corps est long et large avec une surface dorsale noir profond et une surface ventrale brun foncé. La bordure, légèrement ondulée, est d'un blanc vif opaque. La surface dorsale comprend de nombreuses papilles arrondies, à répartition uniforme, à pointes jaunes de différentes tailles. Une paire de pseudo-tentacules plissés en forme d'oreille est placée au milieu de la partie antérieure. Un groupe de taches oculaires cérébrales, disposées en forme de fer à cheval, est présent derrière les pseudo-tentacules mais sont difficilement visibles en raison de la couleur noire du dos. Le pharynx est simplement plié au niveau antérieur. L'ouverture de la bouche est placée en arrière du milieu du pharynx. Une paire de pores mâles est située derrière le pharynx, suivie de pores femelles médians et d'une ventouse postérieure aux pores femelles. La vésicule séminale est oblongue. Le canal déférent est non ramifié. Le canal éjaculatoire est enroulé. La prostate est ovale. le stylet est long en forme de cône. L'antrum mâle et femelle est peu profond. Éthologie Comportement Cette espèce est rarement observée la nuit. Soumis à des courants forts, ces vers plats peuvent nager rapidement par contractions et ondulation de leur marge corporelle. Nutrition Thysanozoon nigropapillosum se nourrit de tuniciers en utilisant sa bouche. Parce qu'il possède un grand pharynx, il peut engloutir les tuniciers coloniaux comme, par exemple, Didemnum sp.. Reproduction Au début de la rencontre, les deux individus, hermaphrodites, s'encerclent l'un l'autre. Ensuite l'un des partenaires étend son double pénis vers l'autre et le saisit à l'aide de celui-ci par le bord latéral comme avec des baguettes. Dans le cas de figure observé, l'insémination est unilatérale et après que le spermatophore est déposé sur l'épiderme, le donneur de sperme part sans recevoir de sperme de son partenaire. Publication originale Hyman, L. H. 1959. A further study of Micronesian polyclad flatworms. Proceedings of the United States National Museum, 108: 543–597. (pdf) Taxononie L'espèce Thysanozoon nigropapillosum a été décrite par la zoologiste américaine Libbie Henrietta Hyman en 1959 sous le protonyme Acanthozoon nigropapillosum puis transférée dans le genre Thysanozoon par le zoologiste allemand Anno Faubel en 1984. Espèce similaire Thysanozoon nigropapillosum est assez similaire à Thysanozoon flavomaculatum qui se rencontre en mer rouge. Notes et références Notes Références Liens externes Pseudocerotidae
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<?php class SPVIDEOLITE_IMP_Vk implements SPVIDEOLITE_CLASS_IImporter { private static $regexp = '#vk\.com.*/video(\-?\d+_\d+)#i'; private static $regexpIdIndex = 1; private static $embedTemplate = '<iframe src="//vk.com/video_ext.php?oid={ownerId}&id={videoId}&hash={hash}&hd=1" width="640" height="360" frameborder="0"></iframe>'; public static function getRegExp() { return self::$regexp; } public static function getRegExpIdentifierIndex() { return self::$regexpIdIndex; } public static function embedApplyVideoId($videoId) { $ids = explode('_', $videoId); $oid = $ids[0]; $id = $ids[1]; $hash = $ids[2]; $code = str_replace('{videoId}', $id, self::$embedTemplate); $code = str_replace('{ownerId}', $oid, $code); $code = str_replace('{hash}', $hash, $code); return $code; } public static function getClipIdentifier( $url ) { $matches = array(); if (preg_match(self::$regexp, $url, $matches)) { return $matches[self::$regexpIdIndex]; } else { throw new Exception('Unmatched URL of service'); } } public static function getClipDetailByUrl( $url ) { $id = self::getClipIdentifier( $url ); return self::getClipDetailByIdentifier($id); } public static function getClipDetailByIdentifier( $id ) { $video = new stdClass; # XML data URL $file_data = 'http://vk.com/video'.$id; $video->html_url = $file_data; # XML $html = file_get_contents($file_data); $matches = array(); $jsonRegex = '#var\svars\s=\s(.*?)\\\\n#i'; preg_match_all($jsonRegex, $html, $matches); $json = $matches[1][0]; $json = stripcslashes($json); if (substr($json, -1) == ';') $json = substr($json, 0, -1); $json = json_decode($json, true); # Title $video->title = $json['md_title'] ? strval($json['md_title']) : null; # Description $description_query = '#<div class="video_row_info_description">(.*?)<\/div>#i'; $description = array(); preg_match_all($description_query, $html, $description); $description = isset($description[1][0])?$description[1][0]:false; $video->description = $description ? strval(trim($description)) : null; # Tags $video->tags = null; # Duration $video->duration = null; # Author & author URL $video->author_url = null; # Publication date $video->date_published = null; # Last update date $video->date_updated = null; # Thumbnails $thumbnail = new stdClass; $thumbnail->url = preg_replace("/(http\:\/\/|https\:\/\/)/", "//", $json['jpg']); $thumbnail->width = 320; $thumbnail->height = 240; $video->thumbnails[] = $thumbnail; # Player URL $video->player_url = null; # FLV file URL $video->files = array(); # Embed Code $video->embedCode = self::embedApplyVideoId($id . '_' . $json['hash2']); return $video; } }
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Making ABM work for your startup. It's the scaled-back, prospect-focused approach of ABM that's key to effectively engaging your targets and maximizing your team's efficiency. Each success you have with a targeted account will offer you new insights, skills and tools that will help you expand your marketing efforts as your startup grows. 1. Don't be a one-trick pony. Since 2013, Amazon has been the king of curating product recommendations. You can thank its ultrapersonalized home pages, in part, for teaching targets to ignore email blasts and banner ads that don't speak directly to them. That's why ABM emphasizes seizing their attention through personalized messages and customized brand experiences. 2. Take a course in social intelligence. What really sets ABM -- and potentially your brand -- apart is how you can make each account feel seen, heard, understood and appreciated. Doing so is vital to keeping your contacts satisfied. In fact, 84 percent of marketers told ITSMA that ABM has the highest return on investment of any marketing strategy or program, showing that ABM's customer-driven approach is key for marketers in retaining and growing business relationships. We all know that networking can be helpful in business. But when you're working on a smaller scale, recognizing and capitalizing on business connections are frequently a pivotal part of building enduring relationships. It's often that "we run with the same crowd, so let's be friends" connection that pushes target accounts to choose your startup over your competitors.
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Diversified Association Management is a full service HOA management company with offices in Colorado Springs and Denver, Colorado. We have been in business for 9 years and feel we have a solid track record helping Homeowners manage their day to day. Below you will find some of the many reasons Diversified should be your only choice for HOA management in Colorado. Flexibility as well as open communication is imperative for a well-functioning HOA community. Diversified Property Managements business depends on the happiness of residents overall, it is in our best interest to make sure the communities we manage are kept safe, clean, and well-maintained. We are constantly striving to maintain an open line of communication with residents. We are truly believers in an "open door" policy. All of our staff have direct phone lines and we take into consideration residents' concerns and desires, not just simply tell them to "follow the rules," because they're in place. We believe volunteer Board Members are the cornerstone of their communities. A successful Board promotes the concept of "community". Living in a HOA brings continuity and order to the association. Diversified Property Management works closely with Board members to facilitate the needs of the association. This includes overseeing fiscal management, vendors, covenants etc. Diversified Property Management only works with vendors that are licensed and insured. This gives us the assurance that the vendor is credible and knowledgeable in their field. A well written RFP outlining the scope of work that can be incorporated into a contract and is the first step in hiring the right vendor. Because we are a locally owned and operated company, we also look to hire local vendors first! We are constantly updating our consolidated list of professionals in order to serve the communities we manage and to meet the expectations of our Boards. We create and promote a team-based approach in every aspect of our company. Our employees are empowered, not micromanaged. By empowering our team members, it promotes resourcefulness, creativity, flexibility—an environment that is constantly looking for ways to improve how things are done. We believe this ultimately creates strong work ethic, loyalty and pride. We are a strong, service-oriented and happy team that genuinely cares for each other, as well as—most importantly—the communities who have hired us to the HOA. Thanks for mentioning how HOA's are generally flexible when it comes to helping their residents. I like how you said that they try to be good at communicating with everyone as well. My husband and I are looking into real estate with good HOA management. Thanks for your post!
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Goldstock's distributed sporting goods to the Schenectady area since 1896. After closing the doors, the remaining inventory (in trade lots) from Goldstock's Sporting Goods, along with all furniture, fixtures and equipment is being sold at auction. Please check back for detailed list, terms, and link for online bidding. TERMS: All sales final. Items sold as-is. Cash, credit card or approved check. Applicable sales tax unless in possession of a valid exemption certificate. No store credits, returns or certificates. Unsold inventory, FF&E to be sold at auction on Tuesday, April 30.
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Yesterday I got a direct message on twitter from a high profile coach whom I have admired for years. She told me that she had heard really good things about me from a few of my colleagues and clients. I love it when people talk behind my back. I love talking awesome about other people behind their backs too.
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From skincare to exercise, these podcasts will guide you towards a better understanding of your body. There is so much information on the internet about health, however, it can be hard to find sources that are reputable, and easy to understand. Podcasts are a super helpful and an effortless way to learn more while on the go. Some health professionals are using podcasts to educate a greater number of people across the globe. All you need to start learning is an Internet connection and maybe a pair of earphones. If you're interested in learning about how your body works or looking for ideas on self-care, look no further! Below are some of the most exciting, informative, and easy to listen to podcasts that will keep you updated on the latest health news. The V-Word is revolutionary for people who haven't had a proper sexual education or for those who are just curious about lady bits. This podcast is hosted by two gynecologists who talk about all things vaginas. With episodes between 20 – 40 minutes long, these two women cover a lot of ground tackling topics ranging from birth plans to human trafficking. This is a great place to go if you want to become more acquainted with women's health and the stigmas around it. Birthday Skin is a podcast that is dedicated to your largest organ, your skin! Two friends with a passion for skincare have teamed up to create a podcast that answers all your skincare queries. They discuss the latest fads, everyday skin care as well as skin conditions such as rosacea. The podcast feels like an informative, yet light and casual conversation between friends. A lot of people have succumbed to diet culture and have a strained relationship with food. This podcast on intuitive eating will get real about the dangers of societal expectations on human bodies. The host, Dr. Stefani Reinold, is charismatic and is a certified psychiatrist and eating disorders specialist. She talks about how our bodies are smart and know their needs better than the nutritionists, sports gurus or magazines. This podcast is great for anyone who has a problem with food and body image. Want to start loving and being kind to your body, Rebecca Scritchfield can help with that! Her podcast Body Kindness focuses on loving yourself in the form you are in at the moment and pursuing health instead of unattainable body standards. Bernie Salazar, a former Biggest Loser "winner", is a regular guest on the show and he shares why he's happier and healthier as a fat man. Ali Feller interviews influential fitness figures and delves into their psyches on her podcast "Ali on the Run ". Sometimes the conversation turns away from fitness, but nonetheless, the conversation remains inspirational. Maybe you can stretch, meditate, or run while listening to this podcast? The conversation is always professional and easy to keep up with. This podcast may motivate you to begin moving more! This list is not exhaustive, however, it's a starting point for those of you who want to learn more about your bodies, health, and fitness. Delve into these podcasts to discover the biological miracle that is the human body. Bobby Jindal, was it ever really your time to shine?
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// .NAME vtkArcSource - create a circular arc // .SECTION Description // vtkArcSource is a source object that creates an arc defined by two // endpoints and a center. The number of segments composing the polyline // is controlled by setting the object resolution. // Alternatively, one can use a better API (that does not allow for // inconsistent nor ambiguous inputs), using a starting point (polar vector, // measured from the arc's center), a normal to the plane of the arc, // and an angle defining the arc length. // Since the default API remains the original one, in order to use // the improved API, one must switch the UseNormalAndAngle flag to TRUE. // The development of an improved, consistent API (based on point, normal, // and angle) was supported by CEA/DIF - Commissariat a l'Energie Atomique, // Centre DAM Ile-De-France, BP12, F-91297 Arpajon, France, and implemented // by Philippe Pebay, Kitware SAS 2012. // .SECTION See Also // vtkEllipseArcSource #ifndef vtkArcSource_h #define vtkArcSource_h #include "vtkFiltersSourcesModule.h" // For export macro #include "vtkPolyDataAlgorithm.h" class VTKFILTERSSOURCES_EXPORT vtkArcSource : public vtkPolyDataAlgorithm { public: static vtkArcSource *New(); vtkTypeMacro(vtkArcSource,vtkPolyDataAlgorithm); void PrintSelf(ostream& os, vtkIndent indent); // Description: // Set position of the first end point. vtkSetVector3Macro(Point1,double); vtkGetVectorMacro(Point1,double,3); // Description: // Set position of the other end point. vtkSetVector3Macro(Point2,double); vtkGetVectorMacro(Point2,double,3); // Description: // Set position of the center of the circle that defines the arc. // Note: you can use the function vtkMath::Solve3PointCircle to // find the center from 3 points located on a circle. vtkSetVector3Macro(Center,double); vtkGetVectorMacro(Center,double,3); // Description: // Set the normal vector to the plane of the arc. // By default it points in the positive Z direction. // Note: This is only used when UseNormalAndAngle is ON. vtkSetVector3Macro(Normal,double); vtkGetVectorMacro(Normal,double,3); // Description: // Set polar vector (starting point of the arc). // By default it is the unit vector in the positive X direction. // Note: This is only used when UseNormalAndAngle is ON. vtkSetVector3Macro(PolarVector,double); vtkGetVectorMacro(PolarVector,double,3); // Description: // Arc length (in degrees), beginning at the polar vector. // The direction is counterclockwise by default; // a negative value draws the arc in the clockwise direction. // Note: This is only used when UseNormalAndAngle is ON. vtkSetClampMacro(Angle,double,-360.0,360.0); vtkGetMacro(Angle,double); // Description: // Define the number of segments of the polyline that draws the arc. // Note: if the resolution is set to 1 (the default value), // the arc is drawn as a straight line. vtkSetClampMacro(Resolution,int,1,VTK_INT_MAX); vtkGetMacro(Resolution,int); // Description: // By default the arc spans the shortest angular sector point1 and point2. // By setting this to true, the longest angular sector is used instead // (i.e. the negative coterminal angle to the shortest one). // Note: This is only used when UseNormalAndAngle is OFF. False by default. vtkSetMacro(Negative, bool); vtkGetMacro(Negative, bool); vtkBooleanMacro(Negative, bool); // Description: // Activate the API based on a normal vector, a starting point // (polar vector) and an angle defining the arc length. // The previous API (which remains the default) allows for inputs that are // inconsistent (when Point1 and Point2 are not equidistant from Center) // or ambiguous (when Point1, Point2, and Center are aligned). // Note: false by default. vtkSetMacro(UseNormalAndAngle, bool); vtkGetMacro(UseNormalAndAngle, bool); vtkBooleanMacro(UseNormalAndAngle, bool); // Description: // Set/get the desired precision for the output points. // vtkAlgorithm::SINGLE_PRECISION - Output single-precision floating point. // vtkAlgorithm::DOUBLE_PRECISION - Output double-precision floating point. vtkSetMacro(OutputPointsPrecision,int); vtkGetMacro(OutputPointsPrecision,int); protected: vtkArcSource(int res=1); ~vtkArcSource() {} int RequestData(vtkInformation *, vtkInformationVector **, vtkInformationVector *); int RequestInformation(vtkInformation *, vtkInformationVector **, vtkInformationVector *); double Point1[3]; double Point2[3]; double Center[3]; double Normal[3]; double PolarVector[3]; double Angle; int Resolution; bool Negative; bool UseNormalAndAngle; int OutputPointsPrecision; private: vtkArcSource(const vtkArcSource&) VTK_DELETE_FUNCTION; void operator=(const vtkArcSource&) VTK_DELETE_FUNCTION; }; #endif
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Street Journeys Film Reviewed by Kam Williams Street Journeys (2011) Director: Tracy Christian Kenya, 2011, Duration 58 min., English & Swahili In the heart of Nairobi, where abandoned children wander the streets with no relief from the grim realities of poverty, hope for the future is dim, until renowned Kenyan actress Anne Wanjugu restores the children's spirit through the healing power of theater. But when an unexpected event puts their resilience to the test, it's up to the children to draw on their strength, and glean lessons of faith, family, and the rising of the spirit without their mentor. "On a trip to Kenya in March 2000 I met Anne Wanjugu. In 1994, Anne started an orphanage called Shangilia to rescue Nairobi's street children. Our initial meeting inspired me to make a documentary film about her life and the children whose lives she was transforming through theater. Anne died suddenly in 2002 but her legacy to heal through the arts continues in her absence. In December of 2007 twenty-five of the current orphans made their theatrical debut at The Kennedy Center, on Broadway, and in concert alongside Hugh Masekela and the late Odetta in New York City. Anne taught me that compassion requires action and that with faith and hope anything is possible. Thank you for the opportunity to share the children's story. They continue to inspire me with their courage." Tracy Christian Read More AALBC.com Film Reviews
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Унбинилијум (), такође познат и као () или једноставно елемент120 (), хемијски је елемент са атомским бројем 120 и симболом -{Ubn}-. Унбинилијум и -{Ubn}- је привремено систематско -{IUPAC}- име односно симбол, док стално име не буде одабрано у будућности. У периодном систему елемената, очекује се да ће да се смести у , и то као земноалкални метал и други елемент у осмој периоди. Било је неколико покушаја од стране америчких, немачких и руских научника да синтетишу овај елемент; сви су били неуспешни. Његова позиција као седмог земноалкалног метала говори да би имао слична својства као и ови до сада откривени метали (берилијум, магнезијум, калцијум, стронцијум, баријум и радијум); међутим, релативистички ефекти можда ће да изазову девијације у неким од својстава овог елемента у односу на оно што се очекује директном применом периодичних законитости. На пример, очекује се да ће унбинилијум да буде мање реактиван од баријума и радијума и да ће да се понаша сличније стронцијуму; елемент би требало да покаже карактеристично +2 стање оксидације земноалкалних метала, али такође је предвиђена могућност да ће стање оксидације да буде +4 што је до сада непрепознато стање код било ког од земноалкалних метала. Референце Хемијски елементи Земљани алкални метали
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England kicked-off. Ireland won the toss. Capt: Jack Hudson, only captaincy Selectors: The Football Association Committee following trial games, with Secretary Charles W. Alcock having the primary influence, on Friday, 16th February 1882. team notes: Norman Bailey (Clapham Rovers FC), Jack Hargreaves (Blackburn Rovers FC) and Clem Mitchell (Upton Park FC) all withdrew from the England line-up on 21 February. Hudson, Cobbold and Arthur Bambridge were replacements. Arthur Cursham and Bambridge then dropped out, replaced by Whateley and Pawson. By being four days younger than Alf Lyttelton, Nevill Cobbold became the youngest player to score on his debut (a record that will not be broken for another 51 years by Stan Matthews). This is the second time (1878-79) that England have won two matches in a row, but only the first time they have not conceded a goal for two matches in a row. Cursham, Cobbold, Goodhart, Dunn, Whateley, Pawson. ELO rating 4th Colours: St. Patrick blue shirts, white shorts. team notes: James Buckle and Alexander Dill were in the original starting eleven. There places went to Reid and Spiller. Davison, McWha, Morrow, Potts, Reid, Spiller. Blackburn Olympic's F.A Cup run continued as they brushed aside Druids, the Welsh Cup holders, 4-1 to progress to the semi-finals for the first time. They went on to become the first northern club to lift the trophy. It was on 23 February 1883 that Charles Parnell, the leader of the Irish Parliamentary Party, defiantly tried to deflect criticism of his suspected support of the violent attacks on opponents of the Irish Land League.
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Q: Finding Binet form in Mathematica Suppose I have a linear recurrence* and I want to find its closed-form 'Binet' representation. Is there a good way to do this in Mathematica? It seems like a very basic request, and there are certainly many natural ways to ask Mathematica to do it for me. But so far everything I've tried has failed: it churns until its memory use is so high the operating system is obliged to close it, or it gives warnings that it does not know how to simplify simple expressions†, or the like. I could understand this if the question was hard, but it's not—factor the characteristic equation, find the roots, and solve a linear system. The most recent time I tried this (and had the program crash) was on a degree-9 example, and I just don't think a 9-by-9 linear system should be that hard to solve. Surely I'm not the only one who need to do this from time to time! What is the right way to do this? I lost my session so I don't have the exact code I tried. One solution created a List with the recurrence and its initial points and used RSolve. Another found and factored the characteristic equation and took appropriate roots to the n-th power multiplied by polynomials of degree corresponding to the multiplicity with coefficients generated from C[i]. I also tried Solve and Reduce in various ways. * Or a rational generating function. Actually I'll start from a List of numbers which are described by a recurrence of less than half its length, and FindLinearRecurrence or FindGeneratingFunction can do the not-too-difficult conversion. † For example, when I asked it to solve one recurrence it choked on sin^2 (3pi/14) + cos^2(3pi/14) in the course of the calculation, saying that ran out of precision. You'd think it could symbolically simplify something like that, but no. A: I have no knowledge of Binet form, but addressing your concern regarding simplification: expr = Sin[3 pi/14]^2 + Cos[3 pi/14]^2; Simplify[expr] 1 A: I'm not sure if this is what you had in mind, but you could do something like Binet[ker_List, init_List] := Module[{charp, roots, polynomials, coeffs, base, p}, roots = Tally[ N@Eigenvalues[ PadLeft[Append[IdentityMatrix[Length[ker] - 1], Reverse[ker]]]]]; coeffs = Table[p[i, j], {i, Length[roots]}, {j, roots[[i, 2]]}]; polynomials = Table[(Evaluate[i.#^Range[0, Length[i] - 1]]) &, {i, coeffs}]; base = roots[[All, 1]]; {polynomials /. Solve[Table[ Through[polynomials[n]].base^n == init[[n + 1]], {n, 0, Length[init] - 1}], Flatten[coeffs]][[1]], base}] Then for a linear recurrence kernel and initial values init, Binet[kernel, init] returns two lists. The first one contains the polynomials and the second the roots of the characteristic polynomial. The n-th entry in the recurrence table is then equal to a[kernel, init][n] with a[kernel_, init_] := Evaluate@Module[{p, b}, {p, b} = Binet[kernel, init]; Through[p[#]].b^#] & So for example for the Fibonacci sequence you would get kernel = {1, 1}; init = {1, 1}; {p, b} = Binet[kernel, init] (* ==> {{0.723607 &, 0.276393 &}, {1.61803, -0.618034}} *) With[{sol = a[{1, 1}, {1, 1}]}, Table[Chop@sol[n], {n, 0, 10}]]; (* ==> {1., 1., 2., 3., 5., 8., 13., 21., 34., 55., 89.} *)
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Posted June 23rd, 2015 by SDerr. Click on the link below to access an application in English or Spanish. You may also pick up an application at any one of our centers or at our administration office, or call one of our locations and have an application mailed to you. Applications should be filled out completely, signed, and returned to our administration office along with proof of income. Proof of income should include a copy of your current tax return, W-2, verification of child support, unemployment and/or disability income. Verification of any of the following services automatically makes you income eligible: MDHHS Child Care Reimbursements, SSI, FIP Payments, Work First, Foster Child Status. Please contact Holland Day Care at (616) 298-2361 and/or fill out the application using the link below (choose English or Spanish). Child Care services are available for children ages 6 weeks-5 years. DHHS payments are accepted. Sliding fee scale available based on income. Schedule: Full day (minimum of 6 hours), year-round, Monday through Friday.
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Posts Tagged 'iPhone' a domestic slight, a screw, concept script, in the middle of the night, iPhone, Langston Huges, Langston Hughes, neighbors creep, storytelling, the handyman, the Mrs., The write right, unfaithful partner, up to write The Write Right: A domestic slight In Communication, Griot, News, Science on June 20, 2016 at 5:02 am The Write Right — Langston Hughes had it. I have it. We all have the right to communicate via song or say, by voice, text or write. Please say what you feel inside, because I always do. If a situation needs too much stroking – I call that a screw. 😀 Oooo! Don't even get me started, after all I do have "The Write." I like to do mine when most are asleep. I own the dark of the night. When you decide to 'lay you down to sleep,' and your unfaithful partner is contemplating a "creep," I'm the one with the iphone in voice record mode, the light in the window. Stories of late night creeping tweak my scripted flow. No. I don't know where the male neighbor is 'off to' or where he ever goes, though it is good food for my literary soul to see nocturnal activity – like so. As he crept into the night, my mind yielded to the characters in my script and they started talking they said, "if his wife gets up and cuts on the light — evidence will be on display and squawking. Carried away in mind, the Mrs. may glance out of the front door to see what's going on, that's when she'll peep my silhouette in the window across the street — with the light on. Ding dong! Looking at me. My light'll go off, but I'm rarely s'ked. I just don't need her piping up. She should go back to bed. That man ain't no mono-homebody. He likes to keep it plural. The city is a nice place to play. Her man was raised in the country rural. Me? I was raised in the Dallas/Fort Worth in stitched boots, a wide brim and a nifty little skirt. I'm up early and my night hours run late. I stay awake to keep watch of my plate. My plate is my life, my journey, my purpose and what I am doing here. The Mrs. will fancy coming over tomorrow to verse, but I will not be here. I am a writer, a recorder of history. Invoked by realism I jot it down, add in a little provocative mystique and we've got a concept script in the round. Who's sneaking out to see who, and go where? My neighbor is on point 3-days a week. However, between the hours of 8am-3pm, the handyman works "the domestic recon creep." The Mrs. across the street finds the handyman to be a treat. He doesn't mind the work; he doesn't mind the heat. Once I asked her if her A/C or something was on the blink, she said no, but there are "pipe issues" with her sink. She said the handyman is good with her pipes. She said his mannerism is one that she likes. She said he doesn't charge her for all services all of the time. She said if I wanted him to stop by my home, that would be fine. I replied, "Mine? Oh honey, never mind, my pipes are fine," — besides the help that he's giving her can be seen by the blind." She laughed – me too and then she said, "What's the name of your site? And do you enjoy spending your time upstairs writing all night?" I told her, "I do," and that "the night hours are best." I told her "more pops-off in the wee hours of night while the majority of folks are at rest." She smiled and began to walk back across the street, looking over her shoulder in great delight, she said, "you do what you and I'll do what I do." I agreed, and then produced this write. She has the right to continue to do whatever she is doing, and he has the right to continue creep-creeping and night screwing, and I have the right to be vocal and record on my iphone… I love the night life, I am so rarely alone. And so with The Write Right, I do believe this to be true, and if I didn't stay up to jot it down, who'd ever find the time to write about you? Keep doing what you do. If it's "on the low" – I guarantee someone is watching you. Apple Rocks Relocation, Ashton Kutcher, Herberger Theater, iPhone, JOBS the biopic, Joshua Michael Stern, Matt Whiteley, Rock Center, Steve Jobs, Sundance, Video The Defining 30 years of Steve Jobs' Life In Communication, Griot, Movies, Networking, News, Science, Technology on December 7, 2012 at 8:24 am Whatever did we do before the iPhone came out? Verizon held the coveted brand, 'Can you hear me now?' There were hundreds of mobile phones out, but none were better than the others. Then Steve Jobs hit the scene and iPhone became the coveted mother. Do you FACETIME? I do! Thanks to Steve my phone shares the view. [FoxNews.com/Tech] — The first film on the life of Apple co-founder Steve Jobs since his death, with Ashton Kutcher in the title role, is to make its debut at the Sundance Film Festival. The movie, which is called jOBS and is directed by Joshua Michael Stern, chronicles "the defining 30 years of Steve Jobs' life," according to the Sundance Institute. The film, which was written by Matt Whiteley, is described as a "candid, inspiring and personal portrait of the one who saw things differently". The movie aims to tell the story of Jobs' life from wayward hippie to co-founder of Apple and revered creative entrepreneur. A Facebook page for the film said jOBS is an "incredibly powerful and true story of the visionary who set out to change the world, and did". Sony Pictures is also developing a movie about Jobs, based on the bestselling book by Walter Isaacson that was released after the Apple chief's death last year. It will be scripted by Social Network writer Aaron Sorkin. Kutcher, 34, was best known for TV shows including That 70s Show and Punk'd before he replaced Charlie Sheen last May on Two And A Half Men. Steve Jobs died October 5, 2011 at the age of 56 after a long battle with cancer. Kutcher's movie, which closes the festival, which runs from January 17 to 27 in Park City in Utah, is one of 18 star-studded premieres announced for Robert Redford's independent cinema showcase. Lovelace, a movie about porn star Linda Lovelace, is also on the bill. Amanda Seyfried plays the title role in Rob Epstein and Jeffrey Friedman's portrait of the Deep Throat actress who tured her back on the industry became an anti-porn crusader. Adding to the premieres list is Before Midnight, director Richard Linklater's third film collaborating with Ethan Hawke and Julie Delpy after Before Sunrise and Before Sunset, in which the audience encounters their characters nine years later in Greece. Australian actresses Nicole Kidman, Mia Wasikowska and Jacki Weaver star in psychological thriller Stoker, which marks South Korean director Park Chan-wook's English-language debut. Behind-the-scenes tales of pornography will also be explored in British director Michael Winterbottom's The Look Of Love, starring Steve Coogan and based on British adult magazine publisher and entrepreneur Paul Raymond. Read more: http://www.foxnews.com/tech/2012/12/05/kutcher-as-steve-jobs-sundance-debuts-biopic/#ixzz2EFPYwdxy I recently saw a live production at Herberger Theater via Intel That told the story of APPLE & Steve Jobs — and told the story well. I was so caught up in the detail divvy of the shiny apple of wealth that I felt like it was Steve Jobs telling the tale himself. I never knew as much about Steve's pioneering – he was no whiner. We also learned a great deal about APPLE's manufacturing in China. Immediately as we were leaving the theater, news broke loose that Chinese workers were rioting – APPLE's golden egg goose. The timing couldn't have been more perfect to validate the details of the show. Steve Jobs imagination was a mob, but outsourcing wasn't the best way to go. Workers in China were working 18-hour days under intense pressure with very few breaks. And if a piece of merchandise were to drop and break, it was the ass of the worker that the forman would take. One guy was beaten pretty bad, because a device could not be found. Then "allegedly" committed suicide while in security custody and bound. The workers had no benefits and iPhone 5 productions were pressing. The revelation of how workers were living, without a doubt was very depressing. I sat on my seat, with my iPhone 4S in hand and seriously considered abandoning the APPLE band. I'm into film production and my MacBook Pro is one of my best friends. For it with Final Cut is just what produced NO COUNTRY FOR OLD MEN. Post the awesome theater production, I put the story on my back and told everyone who loved the iPhone – about the human rights issue that outsourcing lacked. Though I am happy to report today, due to President Obama vowing to tax all who outsource US company work — APPLE production is coming back. The next story will divvy more info on that…. APPLE ROCKS RELOCATION By Ronnie Polidoro Apple CEO Tim Cook revealed that one of the existing Mac lines will be manufactured exclusively in the United States next year, making the comments during an exclusive interview with Brian Williams broadcast Thursday night on NBC's "Rock Center." Mac fans will have to wait to see which Mac line it will be because Apple, widely known for its secrecy, left it vague. ROCK CENTER EXCLUSIVE — "We've been working for years on doing more and more in the United States," Cook told Williams. This announcement comes a week after recent rumors in the blogosphere sparked by iMacs inscribed in the back with "Assembled in USA." It was Timothy D. Cook's first television interview since taking over from his visionary former boss, Steve Jobs, who resigned due to health reasons in August 2011. Jobs died on October 5, 2011, after a long battle with pancreatic cancer. The announcement could be good news for a country that has been struggling with an unemployment rate of around 8 percent for some time and has been bleeding good-paying factory jobs to lower-wage nations such as China. Cook, who joined Apple in 1998, said he believes it's important to bring more jobs to the United States. Apple would not reveal where exactly the Macs will be manufactured. "When you back up and look at Apple's effect on job creation in the United States, we estimate that we've created more than 600,000 jobs now," said Cook. Those jobs, not all Apple hires, vary from research and development jobs in California to retail store hires to third-party app developers. Apple already has data centers in North Carolina, Nevada and Oregon and plans to build a new one in Texas. Apple has taken a lot of heat over the past couple of years after a rash of suicides at plants in China run by Foxconn drew attention to working conditions at the world's largest contract supplier. Apple and other manufacturers who have their gadgets produced by Foxconn were forced to defend production in China. Earlier this year, Apple hired the nonprofit Fair Labor Association to examine working conditions at Foxconn, which makes some of Apple's most popular products: iPhones, iPods and iPads. Given that, why doesn't Apple leave China entirely and manufacture everything in the U.S.? "It's not so much about price, it's about the skills," Cook told Williams. WATCH VIDEO: Apple CEO announces 'Made in America' plans Echoing a theme stated by many other companies, Cook said he believes the U.S. education system is failing to produce enough people with the skills needed for modern manufacturing processes. He added, however, that he hopes the new Mac project will help spur others to bring manufacturing back to the U.S. "The consumer electronics world was really never here," Cook said. "It's a matter of starting it here." Cook said he still misses Jobs, his friend and mentor, but that Jobs' advice to him before he died was to do the things he thinks are right and not try to guess "what Steve would do." "I loved Steve dearly, and miss him dearly," Cook told Williams. "And one of the things he did for me, that removed a gigantic burden that would have normally existed, is he told me, on a couple of occasions before he passed away, to never question what he would have done. Never ask the question, 'What Steve would do,' to just do what's right." Apple today is worth about 43 percent more than when Cook took over. Under his leadership, Apple has released three new iMac models, two iPhones, two iPads, and the iPad mini. That's not to say there haven't been some speed bumps. Most notable was the release of "Apple Maps," which replaced the Google Maps app on the iPhone and was widely panned for misleading directions. Cook admits they screwed up. "On Maps, a few years ago, we decided that we wanted to provide customers features that we didn't have in the current edition of Maps," Cook said, "It [Maps] didn't meet our customers' expectation, and our expectations of ourselves are even higher than our customers'. However, I can tell you, so we screwed up." The Maps debacle led to the defenestration of some company executives, including reportedly Richard Williamson, who oversaw the mapping team. "We screwed up and we are putting the weight of the company behind correcting it," Cook told Williams. Customers still snapped up the iPhone 5, however. According to Apple, five million of them were sold in their first weekend after the device's launch in September. Speed bump No. 2 was the redesigned connector for the iPhone 5, which was widely criticized by many because it didn't fit many of the accessories Apple fans had already purchased for their earlier iPhone versions. It forced them to purchase an adapter, which some criticized as an inelegant solution. Others argue, however, that the new connector was worth it because it allowed Apple to make a smaller device. "It was one of those things where we couldn't make this product with that connector," Cook said, "But let me tell you, the product is so worth it." What's next for Apple? Did Cook leave us with a clue? "When I go into my living room and turn on the TV, I feel like I have gone backwards in time by 20 to 30 years," Cook told Williams. "It's an area of intense interest. I can't say more than that." Click here to watch Brian Williams' exclusive interview with Apple CEO Tim Cook from Rock Center.
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You know that song that's been stuck in your head; the one that Lady Gaga belts out when Bradley Cooper brings her up on stage in the trailer for the upcoming musical drama "A Star Is Born?" It's called "Shallow" and it just dropped. Gaga premiered the earworm on Apple Music's Beats 1 radio on Thursday, in addition to releasing a much-anticipated video. Most of the music on the soundtrack is original, written in part by Cooper and Gaga, who duet in "Shallow." Cooper, who also directed the film, famously insisted that the music in the drama be recorded live. Gaga wrote "Shallow" with Mark Ronson, Andrew Wyatt, and Anthony Rossomando, and co-produced it with Benjamin Rice. It's already drawing Oscar buzz. Warner Bros. previewed the full track listing for the soundtrack in late August leading up to the movie's grand Venice Film Festival debut. "A Star Is Born's" soundtrack will be released on Oct. 5 — the day the film hits theaters.
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Sakura Chorus, formerly "Nichigo Chorus" is a Japanese chorus group consisting of only women. It was originally formed in 1991 by Rev. Hanaoka who was then the Senior Pastor at SJUMC. It began as a SJUMC outreach program designed to reach a diverse group of Japanese women regardless of their religious beliefs. There are currently 15 members with a variety of backgrounds – from housewives to successful business professionals, active and retired. The group not only enjoys singing Japanese traditional and spiritual songs, but also values introducing Japanese culture and tradition to the local community. The group occasionally performs during worship service at SJUMC. We also extend our efforts to local community service by providing bi-annual concerts and visiting the Asian nursing home. It also belongs to the Northern California Choral Association and participates in its choral festival every other year in the Bay Area. On June 20, 2010 the group held a bi-annual concert in the SJUMC sanctuary, which was a great success with more than 200 people attending. Some proceeds were donated to UMCOR through SJUMC to help victims of earthquakes in Haiti and Chile. Ayako Marshall at 422-5848 or Michiyo Laing at 967-8998.
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FORMER UNLV QUARTERBACK HERRING JOINING REBEL RADIO TEAM LAS VEGAS (UNLVRebels.com) – Former record-setting UNLV quarterback Caleb Herring has been hired as the football program's new radio analyst, the athletics department and its multimedia rightsholder Learfield announced Thursday. Herring will join sixth-year play-by-play voice Russ Langer in the booth and at the weekly... ATLANTIC 10 SELECTS LEARFIELD AS MULTI-MEDIA RIGHTS PARTNER NEWPORT NEWS, Va.— The Atlantic 10 Conference announced today it has selected Learfield as its comprehensive multimedia rights holder in a multi-year agreement, beginning with the 2017-18 athletic season. Learfield will hold exclusive multimedia rights to the men's and women's basketball championship and all 19 Atlantic... DAVE SOUTH MAKES 2017-18 HIS FINAL SEASON BEHIND THE MICROPHONE FOR FOOTBALL AND MEN'S BASKETBALL COLLEGE STATION — Dave South, the legendary voice of Texas A&M athletics since 1985, has decided to make the 2017 Aggie football season and the 2017-18 men's basketball season his final year behind the microphone calling the radio play-by-play for Learfield's Texas A&M Ventures. The following... IMG LEARFIELD TICKET SOLUTIONS TEAMS UP WITH INDIANAPOLIS COLTS INDIANAPOLIS - The Indianapolis Colts today announced that IMG Learfield Ticket Solutions (IMGLTS) will support the team's ticket sales throughout the 2017 NFL season with a focus on group sales at regular season home games. The IMGLTS staff will work from the company's dedicated sales... CONTRACT EXTENSION CONTINUES EAGLE GAME BROADCASTS WITH KXLY BROADCAST GROUP Learfield, KXLY & EWU agree on new agreement which will have games aired live through 2019-20 season on 700-AM ESPN & 105.3-FM CHENEY, Wash. - Learfield's Eagles Sports Properties, multimedia rights holder for Eastern Washington University Athletics, has reached a multi-year extension to continue radio broadcasts...
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Tree nurseries are the focus of TreeNurseries.us. This website describes tree nurseries and explains why trees are important. It lists the types of trees often raised at tree nurseries and highlights the differences between retail and wholesale tree nurseries. Convenient links to retail and wholesale tree nurseries, landscape contractor information, and general tree planting resources are also included. Find a broad selection of fruit trees, shade trees, evergreens and flowering shrubs at selected retail and wholesale nurseries. Captioned photos on this website include young trees at a tree farm, trees planted in nursery pots, a beautiful maple tree, and tree root balls in burlap. All information on website TreeNurseries.us is provided "as is." This website contains reference information and resource links about tree nurseries and the trees they grow. By using this website, you agree that Zeducorp is not responsible for errors or omissions, and shall have no liability for damages of any kind, including special, indirect, or consequential damages, arising out of or resulting from any information, product, or service made available hereunder or the use or modification thereof. Thank you for visiting the TreeNurseries.us website. We trust that you have found our website useful, and we invite you to place a link to TreeNurseries.us on your website. Simply copy the following HTML link and paste it on one of your website pages to reference this informative website. We appreciate your consideration. TreeNurseries.us, a division of Zeducorp. TreeNurseries.us is a Chosen Sites™ resource.
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Customer service jobs are unlikely to become automated because of the human need for empathy. Throughout history, different eras have begotten different heroes of productivity in industry. In the 80s, the stock broker was the rock star of the business world. In the late 90s and 2000s, it was the computer programmer. For the last decade or so, it's been the data scientist. As the work of data scientists and engineers creates the Automation Age, the next industrial rock star will be the customer service specialist. Before you scoff at the idea of what may be considered a lower-level job today, ask yourself what happened to the stock broker? When's the last time you talked to one or even heard of one? Jobs ebb, flow, and disappear. The importance of a function today is not equivalent to the importance of that same function tomorrow, and it never will be. Humans have three core capabilities with which robots cannot compete: creativity, community, and empathy. As we enter the Automation Age, where the fear of robots replacing human work is likely to come true, those three skills will enable the future of human productivity. The last of the three, empathy, should well be considered the most important. Empathy is what most makes us human - the capacity for mutual understanding. As the Automation Age eliminates rote and some not-so-rote tasks, it will create an opportunity for humans to capitalize on empathy. The manifestation of empathy in industry is through unique and memorable customer service, no matter the business. Welcome to the Empathy Economy. The Empathy Economy is an intentional spin on the Sharing Economy. Just as the Sharing Economy was a byproduct of a super connected world via the Internet and smartphones, the Empathy Economy will arise through the result of job loss from automation. Uber, Airbnb, WeWork, and countless other business have changed the way humans think about asset ownership and even asset leasing. If users own assets, they want to get more out of them. If users need assets, they want instant access to them on demand without the burden of ownership. The Sharing Economy, as with all functional economies, is efficient in matching two complementary desires. The Empathy Economy will similarly match humans or businesses who desire empathic services with those willing to offer them. Services that augment human empathy: For example, a lightweight CRM tool that enables employees to instantly recognize customers when they walk in the door, remember details about their lives, and know their preferences for service at the business. Services that build empathy: For example, a simulated environment that puts trainees through various situations to help them understand why another person feels a certain way and how to best serve them. Marketplaces that match buyers and sellers of empathy: For example, a platform that makes freelance customer service experts available for various tasks that might require a human touch to differentiate and enhance a particular service. Today's businesses must adopt automation technologies and embrace the Empathy Economy simultaneously by leveraging empathic customer service specialists as the face of their automated tools. In other words, people will act as a truly human skin on the work being produced by robots. In the future, H&R Block will leverage AI to automate every customer's taxes, but it's also likely that they'll need a human, who may only have cursory knowledge about accounting, present the sensitive reality that a customer owes the government a few thousand dollars in taxes; or perhaps the joy that they'll be getting a few thousand dollars in refund. Either way, the human presentation creates a differentiated customer experience that can be distinctly H&R Block. Using only automation as their selling point, which every other tax prep service will also have and may only vary slightly, will necessitate a race to the bottom in price. In this example, H&R Block could benefit by adopting services that help augment and build empathy as the core skill of their customer service specialists. Another outcome of the Empathy Economy could be Target leveraging a marketplace for freelance workers with specific product expertise and high empathic qualities to deliver orders to local customers with personalized service. Similar to the tax example, this moves the discussion away from price towards experience, which can command a premium. You may be wondering why empathy is the greatest opportunity in the triumvirate of uniquely human traits. Creativity and community already exist in a structured sense in our societies. Creativity has always been a democracy, but the Internet made the distribution of creativity available to all. There are numerous ways, both online and offline, to share creativity and get paid for it, YouTube and Patreon as examples. These platforms will only become more important in the Automation Age. As for community, traditional institutions provide this now - governments, churches, schools, local businesses, etc. Technology will help these institutions continue to evolve with automation; however, trusting relationships between people will remain the heart of community because, by definition, it has to. Empathy doesn't yet seem to have a defined structure for application in our world. We know it's important and the best businesses find ways to implement empathy into their culture, but it's still a nebulous, unmeasurable thing. The Empathy Economy will change that. It's cliché to say that empathy is in short supply today because every generation probably has the same sentiment. The good news is that automation will force humans to be more human, and the Empathy Economy will create opportunities for humans to monetize a uniquely human capability. True empathy isn't easy, but it's the most powerful expression of humanity. In a world full of robots, empathy can only become more valuable. Doug Clinton is a managing partner at Loup Ventures, a research-driven venture capital firm focused on investing in frontier technology.
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Joan Ganz Cooney Center - Sarah Vaala, Ph.D. Home → About Us → Our People → Senior Fellows → Sarah Vaala, Ph.D. Dr. Vaala is a Research Associate at Vanderbilt University, where she is currently focused on developing mobile and internet tools to boost problem-solving skills among teens living with chronic illness. She completed her Ph.D. in Communication Studies at the Annenberg School for Communication at the University of Pennsylvania. As a graduate student Sarah worked on an RTL-funded research team which examined young children's television-viewing and language learning. She is interested in the diverse educational and health implications of media in the lives of children and adolescents, as well as the ways caregivers perceive and make decisions about their children's media use. Sarah served as the 2011-2012 Joan Ganz Cooney Center research fellow. Sarah's focus on children's informal learning was first sparked while working as a deckhand and educational guide on an Erie Canal packet-boat. As a Psychology major at Davidson College, her focus narrowed in on the intersections between media and child development. Sarah's passion for child-focused research was forged while working as an EEG research technician at Mt. Hope Family Center in Rochester, N.Y.
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5 Minutes Tops Wraps With Regional Competition As a business teacher, Lucas Schrauben wanted to get his students pumped about entrepreneurship. He thought introducing a unit devoted to entrepreneurial endeavours would be awesome but sadly, only a few students agreed. "Most just saw it as another school project," says Lucas. But, as he listened to many of them prepare to get crummy… As a business teacher, Lucas Schrauben wanted to get his students pumped about entrepreneurship. He thought introducing a unit devoted to entrepreneurial endeavours would be awesome but sadly, only a few students agreed. "Most just saw it as another school project," says Lucas. But, as he listened to many of them prepare to get crummy summer jobs, he became more and more determined to help them see the value of entrepreneurship and how it could essentially help them create their own summer jobs. "The show Shark Tank was a huge help," says Lucas. He began using it as a model and held a pitch competition, giving the kids Monopoly money to invest in each other's businesses. As the students got more excited, so did the rest of the community. When he mentioned the program to the Grand Ledge Business Alliance, they decided to put up some actual money and the first round of the 5 Minutes Tops Business Competition were born. That was three years ago. Now, Lucas is a Career Development coordinator with Eaton RESA Career Preparation Center and he has watched local 5 Minutes Tops Events pop up all over the region giving students 5 minutes to pitch their business idea and the opportunity to win money. This year, they had 71 students register from all over Michigan. Winners of the local competitions competed last week in the final, regional event against a handful of other students who were competing for the first time. The regional event gave out $3500 in prizes. Checking out #pitches at the 5 Minutes Tops Competition pic.twitter.com/zfY9LIhA5s — Startup Lansing (@StartupLansing) March 10, 2016 The winner, Emily Newborn of Emily's Farm, impressed the judges with her detailed financial plan for her chicken and rabbit farm. Her livestock is fed a balanced diet of food grown on her own farm and she went into great detail about her costs, her profit margins and how much she saves using her own feed. "The judges were impressed with her understanding of it all," says Lucas. Pitch Competitions give students real world experience they will be able to apply in the working world — Startup Lansing (@StartupLansing) March 10, 2016 While a farming project was the winner, Lucas was impressed with the diversity of the ideas. "There was everything from farms to technology," he says. And the audience and judges saw products such as solar panels and ceramics. Businesses in #Michigan are ready to grow but can't always find capable talent. These programs help solve that. And now, for the students who didn't get a chance to compete, and many of those that did, the next step is the Youth Startup Expo on March 24. More of a trade show than a competition, students who didn't get to pitch at 5 Minutes Tops will be able to show off their businesses at the expo. "The competition," says Lucas, "Was first built simply to engage students in entrepreneurship, and now it's grown in both monetary amounts and participation." 5 Minutes Tops encourages students to spread their entrepreneurial wings and step outside their comfort zones — Startup Lansing (@StartupLansing) March 10, 2016 Entrepreneurs are all about making passions into businesses and that is evident in these #student #pitches
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This repo contains materials for a 90-minute introductory D3 guest lecture with the Spring Data Science Immersive at [General Assembly DC](https://generalassemb.ly/education/data-science-immersive). # Getting Started 1. [Download Brackets](http://brackets.io/) > After installing: open --> click on brick on right --> search for 'Emmet' --> install 2. Create a folder for today's D3 project (i.e. documents/d3-intro) # Session Goals - Introducing key vocabulary and concepts of visualization library D3.js - Identifying fundamentals of writing code for the web - Creating an example visualization using D3 - Preparing to make use of the vast library of D3 resources and knowledge available to you ![header](https://github.com/ayrenay/d3-rough-sketches-class/blob/master/rough-sketches-cover.PNG)
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Show your appreciation or recognize a job well done with custom awards. Very responsive and as I didn't have a template to use for my sign, I gave it my best shot. But they also offered me a redesigned layout which was far superior to my original attempt. Really, the whole transaction could not have gone better and the finished product looks great! Cleopatra is terrific to work with and patient in providing proofs and tweaking designs to choose from, so we can get exactly the look we want. Her graphic design folks are amazing! It's high quality work with excellent customer service and we've been very happy with the outcome on all the signs and wall graphic work they've done for our building. They do great work!
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If you're planning for your upcoming retirement, you've probably thought a lot about aged care and how that fits into your plan. If you're planning for your upcoming retirement, you've probably thought a lot about aged care and how that fits into your plan. Retirement villages do tend to conjure up images of aged care horror stories, which is hardly what you want your retirement to be. The good news is, providers like Evermore are changing how we see retirement villages, and revamping aged care to help people make the most out of their retirement years. It all starts with retirement villages in Forster. Retirement to the Evermore team is all about lifestyle, and that's why they've thought of everything in their retirement villages. Located in Forster, a community mid-way between Newcastle and Port Macquarie, Evermore Living is affordable retirement living with five-star quality. Luxurious 1 and 2 bedroom apartments allow you to enjoy your retirement in comfort and relaxation, while keeping you connected to the people around you and offering aged care services when you need them. All the Evermore apartments are self-contained, so you can do your own cooking and entertain as you please. Families (including children) are more than welcome at Evermore, and within the retirement villages are a wide range of activities to keep you, and any visitors, busy. Retirement villages do not need to be sterile and soulless environments. Evermore offers an on-site restaurant, gym, pool, movie theatre, BBQ terrace, club lounge, bar and tropical garden. There's even a hair salon, a men's shed, and arts and craft activities for those interested. It's retirement with a social focus if you want it, or retirement for relaxation if that's what you would prefer. When it comes to aged care Forster residents at Evermore know that independence and choice is a core focus. Residents in retirement villages don't always get to choose what they need and when, but they do at Evermore. You choose if you want to do your own cooking or housekeeping, what activities you want to be involved in, and what level of aged care service you need. The kind of aged care Forster offers means you can access in-home consultations with Evermore's registered nurse, access supported living, and work with experts to develop an aged care plan that suits you. Your resort style apartment is close to everything you need, and the town of Forster is perfectly located between Newcastle and Port Macquarie providing a gateway to the best of the mid-north coast. Tucked away in the retirement-friendly town of Forster, halfway between Newcastle and Port Macquarie, Evermore's aged care retirement villages are far beyond what most people hope for in their golden years. Independence, choice, and a lifestyle that your families will be jealous of, this is the aged care Forster folks can expect at Evermore. When it comes to aged care Forster encourages activity and enjoyment the way only coastal living can. Within easy reach of shopping and airports (at both Newcastle and Port Macquarie), this is the best aged care Forster wide, and among the best on the mid-north coast. At Evermore residents have access to beaches, ocean baths, quality medical precincts, shopping centres, lakes, bowls clubs, golf, sports centres and so much more. It's a location where you can actually enjoy your retirement, no matter what your aged care needs might be. If you're interested in exploring a coastal retirement at Evermore's retirement village, contact Evermore today to find out more. You can register your interest online, where you can also see more information and apartment plans, or give the team a call to talk with them about availability and cost.
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The International Conference on Similarity Search and Applications (SISAP) is an annual forum for researchers and application developers in the area of similarity data management. It aims at the technological problems shared by numerous application domains, such as data mining, information retrieval, multimedia, computer vision, pattern recognition, computational biology, geography, biometrics, machine learning, and many others that make use of similarity search as a necessary supporting service. From its roots as a regional workshop in metric indexing, SISAP has expanded to become the only international conference entirely devoted to the issues surrounding the theory, design, analysis, practice, and application of content-based and feature-based similarity search. The SISAP initiative has also created a repository serving the similarity search community. Source code for similarity indexes, as well as experimental test beds and benchmark data sets, are made available to all researchers wishing to evaluate and compare new applications, databases, indexes and algorithms for similarity search.
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Q: Show text box when checkbox clicked and keep showing after page reload I have written a JavaScript function that shows a text input field when a checkbox is clicked. The essence of the function is basically to change the text box display property from "none", to "block" on checkbox click. This works fine, and thus when I check the box I see the text field, and when I uncheck the box, the text box hides. Now, I am trying to figure out how to keep the text box showing after the page is refreshed. This is where I am stuck. Any suggestions? Thanks! Please let me know if I need to clarify anything! A: Best way is to store your state in a cookie and read it after load to get back to the same state : Set cookie and get cookie with JavaScript
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Christopher Smith 6 years ago Remembering Brock Yates: Outspoken Journalist, Purveyor Of Performance, Automotive Legend Brock Yates passed away October 5 at the age of 82, but his mark in the automotive world will endure for generations. It's entirely possible that many of you don't know who Brock Yates is. Or rather, was - he passed away yesterday from complications of Alzheimer's at the age of 82, which in this day and age is still entirely too soon. Anyway, for those who aren't familiar with Mr. Yates, let me introduce you: "The Cannonball Run" released in 1981 was accurately based on American coast-to-coast races Yates established in the 1970s. No, he wasn't a movie star, though he did pen this film and also made a cameo appearance. What many of you may not realise is that this movie is based on something he actually did. Back in 1971 Yates came up with the Cannonball Baker Sea-To-Shining-Sea Memorial Trophy Dash, and joined racing legend Dan Gurney to drive a Ferrari Daytona from New York to Los Angeles in 35 hours. After the run, Gurney was famously quoted as saying "at no time did we exceed 175 mph." The unofficial race across America was held four more times, the last race taking place in 1979. Yes, it was certainly illegal. And as later races would prove through the 1970s, they were also a touch flamboyant. Many of the events depicted in the film actually happened in real Cannonball races, including racers disguised as priests. The ambulance driven by Burt Reynolds in the movie was the actual ambulance that Yates and two co-drivers used in the final 1979 race. His wife Pamela went along as the "critical patient that couldn't be flown." So yes, Brock was a motoring enthusiast to the core. And while the Cannonball races are certainly a big part of his legacy, he was first and foremost a hard-hitting auto journalist. He spent decades as an editor at noted American magazine Car and Driver, talking about everything from the latest cars to thrashing the management of American automakers. His writing style was as straight-forward as he was, often trading eloquence for to-the-point phrases that made you feel like you were talking with him instead of reading something. To see what I mean, read this classic Yates article from 1983 about a Mexican road trip gone awry. Yates was a powerful influence in the automotive realm. He was certainly a major influence in my writing career, and I would bet every single penny of Ralph Nader's net wealth that Yates influenced thousands of auto writers like me. More importantly, he inspired and entertained millions of auto fanatics around the world. I never had a chance to meet Brock Yates. I would've liked to. We're all fortunate to have his articles and books to read and re-read, and because of that, I suspect he will continue to influence many generations of writers and petrolheads for years to come. Here's hoping there aren't speed limits in Heaven. Because if there are, God will hear about it. Thanks for everything Brock. Recommended Blog Classic F1 V10 Noise Makes Verstappen & Hamilton's Battle Even Better Car Throttle Submit Your Videos To Get Featured On Our Social Channels Blog There's A Subaru WRX Engine In This Tiny Porsche 914 Blog Would You Buy This Cut-Price VeilSide Honda NSX? Blog The Triumph Tiger Sport 660 Is Probably The Best £9000 You Can Spend On Personal Transport Blog My 188bhp Skoda Karoq Test Car Is So Good I Might Buy One Blog How 'My' Skoda Kodiaq Rescued Our Terrible G-Wiz EV
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US sanctions South Sudan's vice president over abuses in AP News, National JOHANNESBURG (AP) — The United States has imposed sanctions on South Sudan's First Vice President Taban Deng Gai, citing his involvement in serious human rights abuses. The statement Wednesday is one of the sharpest actions taken by the U.S. against the South Sudan government amid Washington's frustration over the country's failure to achieve a stable peace after its civil war. The Treasury Department statement asserts that Deng has been involved in the disappearance and deaths of civilians. It also asserts that he has acted to divide the armed opposition in South Sudan, extending the country's five-year civil war that killed nearly 400,000 people. South Sudan's government could not immediately be reached for comment. The U.S. is among the countries pressuring South Sudan's rival leaders to form a coalition government. A deadline for that looms next month after the parties failed to make one in November. More than 50 days into the 100-day extension, the U.S. statement said, "there have been no concrete steps to create the security conditions conducive to implementing a peace deal." It added that the U.S. "will continue to apply pressure on the senior leadership of South Sudan to take concrete measures to bring peace and stability to the country." The U.S., which backed the fight for South Sudan's independence from Sudan, achieved in 2011, has been increasingly frustrated by the inability of President Salva Kiir and rival Riek Machar to reach a lasting peace. Meanwhile, the government faces widespread accusations by critics of mismanagement and corruption. "Today's action represents a significant and important ratcheting up of U.S. financial pressure designed to break the impasse in South Sudan and hold those impeding peace accountable," John Prendergast, co-founder of The Sentry, said in a statement. The Washington-based investigative group has often reported on alleged corruption by South Sudanese officials. "Over the past two years, the United States has sustained a campaign of pressure that is now appropriately directed at senior officials like Taban Deng, who have benefited financially and politically from conflict. These measures should continue until lasting peace is realized," Prendergast said. Matt Lee in Washington contributed. Ukrainian airliner crashes in Iran, killing all 176 aboard The Latest: Trump: New sanctions on Iran after base strike 12-18-19 WTMJ Nights with Scott Warras and Sarah Hauer 12-17-19 WTMJ Nights with Martin Moore and Dasha Kelly 12-12-19 WTMJ Nights with Pete Schwaba and Brian Noonan 12-11-19 WTMJ Nights with Derrell Connor
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Pycnosiphorus pallidocinctus is een keversoort uit de familie vliegende herten (Lucanidae). De wetenschappelijke naam van de soort is voor het eerst geldig gepubliceerd in 1861 door Fairmaire & Germain. Vliegende herten
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Women's Institute St Helens (WISH) Stand By Your Jam National WI Lancashire WI Denman College Allotment News Meeting Roundup When WISH went to the Royal Garden Party Last month, ladies from every WI in the country descended on Buckingham Palace to attend a special Royal Garden Party, hosted by Camilla, Duchess of Cornwall to mark the Centenary of the WI. One of our members, Teresa was lucky enough to have one of the golden tickets and has kindly told us all about her day: Attending the WI Royal Garden Party was a wonderful, once in a lifetime experience which I will never forget. I met some amazing ladies from all around the country – some who, like me, had only been WI members for a couple of years, while others had been involved for over forty years. Most of our conversations took place in the queue to get into the Palace which, although it took over an hour, was a very good humoured affair, if a little windy at times! Photos were not allowed inside the palace so all of mine were taken while queuing. Everyone had to show ID, which explains the long wait, but we were all too excited to notice the time. Once through the Palace rooms, we found ourselves looking down onto the lawns from a beautiful terrace. It was just a sea of colourful hats and fascinators, with the striking outfits of the Yeomen of the Guard dotted around. We managed to see each member of the Royal party as they made their way down to the Royal Tea Tent: Camilla, Duchess of Cornwall, Sophie, Countess of Wessex, Princess Alexandra and the Duchess of Gloucester. They spent time chatting to people and each of them seemed warm and friendly. The biggest cheer of all, though, was saved for the Calendar Girls as they also made their way to the Royal Tent. The rest of us were content with the Main Tea Tent, which did not disappoint: a fabulous array of tiny cakes and pastries, plus finger sandwiches of course – delicious! Time flew by and it was soon time for the Royal party to process across the lawns as they departed – we managed to get a front row spec (at last) and were able to get a great view as they passed. Someone near me began to sing 'Jerusalem' at that very moment, and soon everyone joined in – I found it extremely emotional and felt an incredible bond towards the other ladies (all 8,000 of them!) I loved every minute of my time at the Garden Party and am extremely grateful for the opportunity to be part of such a wonderful event in the history of the WI – I just wish we could have all been there! Teresa Turton Tags: Buckingham Palace garden party,Guest post,Royal Garden Party,WI Centenary Celebrations « WISH Centenary Exhibition WISH & The Dirty Rotten Scoundrels » Back to Top Contact Us Share on Facebook Tweet this Post Email to a Friend The Road to Success with the WISH Bursary The Girls at The Lowry WISH & The Dirty Rotten Scoundrels WISH Centenary Exhibition – 2013 Completed Activities 2012 Completed Activities 50 days to Fit Calendar About Meetings/How to Join Secret Knitting The WI Story © 2019 Women's Institute St Helens (WISH)|ProPhoto Website by NetRivet, Inc.
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This is a prebuilt Heavy Duty ATR robot with 10 inch tires. The Heavy Duty ATR supports each wheel shaft with two sealed ball bearings and is chain driven with a 10:15 reduction. See the HD ATR ATR building support page for more details. We have included everything to make it ready to run including batteries, controllers, chargers, etc. This robot is built and ready to go! Please allow 1-2 days for packaging prior to shipment. This robot has two functional encoders included with the motors, but they are not hooked up. We have included a RC controller with it, but it could be replaced with a microcontroller or a larger channel radio for pan and tilt camera system, etc.
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CEAM Response to State Board of Education Vote By voting to grant Provisional Accreditation status to the Riverview Gardens School District (RGSD) last week, the Missouri State Board of Education (SBOE) has taken away a critical education lifeline to families in that district. The transfer option provided under Missouri Revised Statute 167.131 grants students in unaccredited school districts the right to transfer from their home district to a higher performing, neighboring district. In making the decision, the SBOE turned a blind eye to RGSD's low student academic performance results in favor of a rising Annual Performance Report (APR) percentage. The Children's Education Alliance of Missouri (CEAM) has previously voiced concern over the Missouri APR formula. The decision to reaccredit the Riverview Gardens School District stands in stark contrast to these 2016 state test results: Math – 14% proficient or advanced English Language Arts – 25% proficient or advanced Science – 14.4% proficient or advanced While the APR formula provides the option to use Status Points, Growth Points, or Progress Points to churn out an APR score, families are left with no options for the education of their children. "Removing educational options from families in low performing school districts doesn't help anyone. What we've witnessed through the implementation of the transfer law is a critical focus on the unaccredited districts that has helped spur change and attempts at improvement. Moving forward most families in Riverview Gardens will have no choice but to send their children to an underperforming school district. Now the SBOE is telling families that despite what we know about performance results, these schools are good enough for your children," said CEAM Associate Executive Director Peter Franzen. CEAM stands at-the-ready to help RGSD families navigate this process. No transfer law means no transportation for transfer students. Even though area school districts have agreed upon a plan to allow some existing transfer students to continue attending their transfer district for anywhere from one to four years, current transfer families without the ability to drive their children to school will be forced to return to RGSD. Families are encouraged to contact their school district for more information. Families interested in becoming advocates for more educational options may contact CEAM Outreach Manager Cici Tompkins at [email protected]. For more information on this topic, click here – http://www.stltoday.com/news/local/education/riverview-gardens-regains-state-accreditation/article_133be158-72e2-57f5-9910-ec78e8d7e490.html –http://news.stlpublicradio.org/post/riverview-gardens-transfer-parents-react-district-s-classification-upgrade#stream/0 « Previous Post: Missouri Education Funding Formula and Interactive Maps » Next Post: The Calculus on Course Access: Part 1
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They come and they go. They generally don't stay long. The Continental Football League. The World Football League. The United States Football League. The World League of American Football. NFL Europe. The XFL (more about that it in a minute). The United Football League (which once employed yours truly). These leagues, whether designed as challengers to the NFL or as "feeder" leagues to develop talent, never find the tricky balance between fast fan acceptance, revenues and expenses. Expenses always get them – travel, medical, housing, insurance, stadium rental. And now the Alliance of American Football falls on that same sharp sword. Dundon had said last week the AAF needed cooperation from the NFL Players Association if it were to succeed. The AAF wanted to be able to sign and use players who are on NFL practice squads or signed to futures contracts. The NFLPA turned the AAF down, saying such moves could violate the labor agreement with the NFL and injuries could shorten or end player careers. As a side note, can you name three players in the AAF? Didn't think so. If the AAF doesn't make it back and your hunger for spring football cannot be sated, relax. And wait a year. The XFL, which played one season in 2001, returns in 2020, backed by World Wrestling Entertainment and its boss, Vince McMahon. Hope springs eternal. Spring football? Ah, as short-lived as the bloom of your crocuses.
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Isha Sacred Walks are a tremendous possibility for spiritual transformation – do not miss this year's sacred journeys! Mount Kailash and Lake Manasarovar cannot be described in words; one must bathe in their presence to understand the significance of such spaces. Considered as the spiritual center of the universe by five religions, they are subjects of innumerable myths and legends. The journey sets across some of the most beautiful places in Nepal and Tibet. It includes a trek to Mount Kailash and Lake Manasarovar, an opportunity to surrender on one's way to freedom. The Himalayas are venerated as the abode of the Enlightened, and are of great significance for spiritual seekers. The ten-day sojourn comprises meditations and treks to some of the most picturesque and powerful places in the Garhwal region of the Indian Himalayas, such as the sacred sites of Gangotri, Kedarnath, Badrinath, and Hardwar, the gateway to the mystical Himalayas. This is an opportunity to soak in the immense energies of these majestic mountains. Varanasi is a city older than history. Considered among the holiest cities in the world, it receives hundreds of thousands of seekers yearly. It is filled with places of tremendous spiritual significance, such as the Kashi Vishwanath Temple, the Vishalakshi temple, and Manikarnika Ghat. The Varanasi sojourn also includes a visit to two significant places in Gautama the Buddha's life – Sarnath and Bodhgaya – the ancient University of Nalanda, as well as various other sites. Varanasi was consecrated by Adiyogi Shiva himself, as a phenomenal yantra to "download the cosmos." It is a living testimony to the variety and exuberance of the spiritual paths India has given birth to, and is a must visit for any seeker today. The yogis and mystics of Southern India have created many tools for one to reach their ultimate nature. Perhaps the most famous of these were an intricately connected system of temples and sacred places – the Pancha Bhuta Sthalas. These five temples, marvels in terms of energy and architectural brilliance, were each created for one of the five elements – the temple at Srikalahasti for air, at Kanchipuram for earth, at Thiruvannamalai for fire, at Chidambaram for space and at Thiruvanaikaval for water. This is a rare privilege to experience the explosive power of these five temples, unravelling the ultimate potential within. There is no mention anywhere about the cost of these walks, approximately how much do these walks cost?
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Anonsage. Think. Do. Learn.: Level Up - Construct 2: Don't Confuse "+" And "&" I just spent over an hour debugging a problem in my Construct 2 code. Suffice to say the solution is now ingrained in my brain. Now, I want to explain a little intricacy of C2. TLDR: In Construct 2, whenever you are dealing with text and you want to concatenate/append additional text (or a variable), then you need to use the ampersand "&" symbol. Using the plus "+" symbol will cause a silent error/bug, i.e. the program won't tell you that there is a bug. Ex: If I try to set text to "Score: " + PlayerScore, then the value of the variable `PlayerScore` will not appear. The correct way to set the text would have been: "Score: " & PlayerScore. Note, the only difference between the two codes was the plus and ampersand. Other programming languages have "overloaded" concatenaters, meaning the "+" symbol in some languages like Java are contextual. Depending on the value to the right and left of the plus sign, it will act a different way rather than not working at all, as in C2. In Construct 2, the only time that you should use the plus symbol is when you want to add two numbers together. That is it. Anyways, the issue that I was trying to solve for over an hour involved using WebStorage and Functions with programmatically assigned parameters. Saving and retrieving values was working great, just not exactly the way I wanted it to. I had a highscores table for easy, medium, and hard difficulties, but they were all staying the same values across each of them. My buggy code included lots of ampersands surrounding the entire area, but basically, this is what it looked like: Save("HighScore" + LevelDifficulty, PlayerPoints). Note: The plus sign is wrong. No programming languages I use have the ampersand as a String concatenate. So, when I viewed the code snippets a few times, even completely writing them, my mind knew exactly that String + String should be working. If I hadn't already read the manual/documentation before this point, then I probably wouldn't have found the answer myself. Experience built through learned mistakes. ps - Just in case I haven't said it enough yet... When you are using Construct 2 and dealing with text, use the ampersand, &. Don't use the plus, +, sign!
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Lionise is a luxury rental platform where women can rent sarees, lehengas, gowns, anarkali's, dresses and jumpsuits. I rented this outfit for my engagement and it was a dream come true! My outfit was the perfect fit and delivered on time! Lionise has some of the best designer pieces available on rent. Thank You for the lovely Crop Top and Skirt in such a short time. I will be recommending Lionise to all my friends! I loved the outfit! It was too beautiful. I will be ordering alll my ethnic wear from Lionise now! gonna rcommend you to all my friends! Their Customer Service Team is very helpful and responsive. I absolutely loved this indo-western gown! Hassle free experience and amazing collection! Dressing up made so much easier and affordable by Lionise. The shoot was amazing! I ordered two outfits for my shoot, and i loved it! Thank You Lionise, for a wonderful experience! I rented this beautiful Lehenga for my friend's wedding! Loved the look and fit! gorgeously packaged and fit perfectly! Great fit, Timely Delivery and the Superior Hygiene Standards! Lionise is my go-to wedding wardrobe! to every woman who wants to wear the latest designer colection.
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A charming two bedroom terrace cottage retaining many character features and offering deceptively spacious accommodation, situated in a highly convenient location for local amenities and Bat and Ball station, offered to the market with no onward chain. This charming two bedroom cottage, situated in a highly convenient location, offers generous living accommodation and has retained much of its character, including beams to ceilings and beautiful stripped wood doors. An enclosed entrance porch with multi-paned bay window to front and wood entrance door with stained glass panels leads through to a spacious open plan living/ dining room with open staircase, French doors to rear leading to garden, open fireplace in the living area with exposed brick chimney breast and arches in alcoves with display shelves. A terracotta tiled floor runs through from the dining room to a well fitted kitchen with window to rear overlooking the garden, and comprises roll top work surfaces with a range of wall and base units incorporating a white sink with mixer tap and drainer. Integrated appliances include a fridge, freezer, four ring gas hob, double oven and there is space for a washing machine and microwave. Wall mounted combi-boiler. To the first floor a half landing leads to a generous size bathroom with suite comprising paneled bath, corner tiled shower cubicle, low level wc with concealed cistern, wash hand basin with vanity cupboard beneath and airing cupboard with slatted shelving. Off the landing are two double bedrooms, bedroom one with stripped wood wardrobe, dressing table and chest of drawers to one wall. Externally there is a garden to the rear with right of way providing access to the front. The majority of the garden is laid to lawn with mature hedging and shrubs and a path leads up the garden to a useful timber storage shed. The roof of the property was replaced in 2014. Viewing is highly recommended to fully appreciate the accommodation on offer which has the benefit of no onward chain. From Sevenoaks High Street proceed in a northerly direction and at the traffic lights continue straight on down Dartford Road which becomes St Johns Hill. At the traffic lights at Bat and Ball proceed straight on and take the first turning on the right into Bat and Ball Road and first right again into Chatham Hill Road where the property will be found a short distance along on the left hand side.
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RENE MEULENSTEEN admits he cannot guarantee Dimitar Berbatov will still be at Fulham in January despite the striker proving his worth in the 2-0 win over Aston Villa. Berbatov slotted an audacious penalty to double Fulham's advantage after Steve Sidwell had opened the scoring against his old club. But Meulensteen refused to discuss the Bulgarian's future after being asked about the prospects of Berbatov remaining at Craven Cottage once the January transfer window open. "I can't, couldn't, wouldn't and don't want to answer that, it's my decision to do that with the people who are relevant to discuss these things," said Meulensteen. Having ended a run of six league games without victory, Meulensteen preferred to praise Berbatov's focus against Villa. "I think the word is focus, anyone who has a good focus will know what the job is in hand, and you focus on the performance," Meulensteen added. Dejected Villa boss Paul Lambert questioned the penalty decisions that went against his side, particularly Aaron Hughes' challenge on Gabriel Agbonlahor. "I don't think we did enough to win the game," said Lambert.
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Vaudoncourt és un municipi francès, situat al departament dels Vosges i a la regió del Gran Est. L'any 2007 tenia 132 habitants. Demografia Població El 2007 la població de fet de Vaudoncourt era de 132 persones. Hi havia 56 famílies, de les quals 12 eren unipersonals (8 homes vivint sols i 4 dones vivint soles), 24 parelles sense fills i 20 parelles amb fills. La població ha evolucionat segons el següent gràfic: Habitants censats Habitatges El 2007 hi havia 65 habitatges, 56 eren l'habitatge principal de la família, 6 eren segones residències i 3 estaven desocupats. 62 eren cases i 3 eren apartaments. Dels 56 habitatges principals, 48 estaven ocupats pels seus propietaris, 6 estaven llogats i ocupats pels llogaters i 2 estaven cedits a títol gratuït; 5 tenien tres cambres, 10 en tenien quatre i 41 en tenien cinc o més. 49 habitatges disposaven pel capbaix d'una plaça de pàrquing. A 25 habitatges hi havia un automòbil i a 28 n'hi havia dos o més. Piràmide de població La piràmide de població per edats i sexe el 2009 era: Economia El 2007 la població en edat de treballar era de 83 persones, 70 eren actives i 13 eren inactives. De les 70 persones actives 68 estaven ocupades (36 homes i 32 dones) i 2 estaven aturades (1 home i 1 dona). De les 13 persones inactives 7 estaven jubilades i 6 estaven classificades com a «altres inactius». Ingressos El 2009 a Vaudoncourt hi havia 57 unitats fiscals que integraven 136,5 persones, la mediana anual d'ingressos fiscals per persona era de 20.101 €. Activitats econòmiques Dels 7 establiments que hi havia el 2007, 1 era d'una empresa extractiva, 3 d'empreses de construcció, 1 d'una empresa de transport, 1 d'una empresa d'hostatgeria i restauració i 1 d'una empresa de serveis. Dels 2 establiments de servei als particulars que hi havia el 2009, 1 era una lampisteria i 1 electricista. L'any 2000 a Vaudoncourt hi havia 9 explotacions agrícoles que ocupaven un total de 395 hectàrees. Poblacions més properes El següent diagrama mostra les poblacions més properes. Referències Résumé statistique Fitxa resum de dades estadístiques de Vaudoncourt a l'INSEE. Évolution et structure de la population Fitxa amb el detall de dades de Vaudoncourt a l'INSEE France par commune Dades detallades de tots els municipis de França accessibles a partir del mapa. Municipis dels Vosges
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As befitting a company that forsook the plodding world of energy production for a high-flying life of the spread, trading, retailing and — it turns out — creative-accounting its way to Wall Street glory, the decline and fall of Enron has been a clatter of dominoes. The $1.2 billion hit from a shady partnership venture gone bad. The SEC investigation into how Enron hid massive amounts of debt off its books where Wall Street couldn't see it. The frantic talks with banks, creditors, and a suitor/savior, fellow Houston giant and erstwhile competitor Dynegy. All framed by a spectacular slide in Enron's stock price from over $80 in January to $30 in October to less than $4 at Wednesday�s opening bell — and punctuated only hours later with the one-two punch that looks to have finished Enron off. That would be the downgrade Wednesday morning of Enron�s corporate debt to "junk" status — a bit of paperwork that instantly adds something like $10 billion in debt to Enron�s towering stack of bills — and the abrupt termination by Dynegy of the planned rescue. [an error occurred while processing this directive] The move surprised Wall Street, which even after the debt downgrade was whispering that the deal — after some very heavy renegotiations, of course — was as good as done, and Dynegy CEO Chuck Watson wouldn't get specific with reporters afterwards about why he killed it. Some reports indicate a fear — or a discovery — of more skeletons lurking in Enron's apparently spacious creative-accounting closet. But it seems more likely that Enron had simply ceased to be worth the trouble. Why buy a corpse when you�ve already pulled the boots off — and it�s starting to rot? Dynegy got into the Enron deal for three reasons. The first — that Enron stock was dirt cheap — went sour when Enron's stock continued to slide even faster than Dynegy's, but the renegotiations looked likely to rectify that. The other two were about structure — Dynegy wanted to take over as the energy-trading honcho by folding its own trading operation into Enron's powerhouse, and it wanted to beef up its real energy-production assets by acquiring Enron subsidiary Northern Natural Gas, a pipeline network that runs from the upper Midwest down to Texas. But three weeks later, Enron's trading operation is a shell of its former self, having been steadily deserted by leery clients as each day brought further doubt how long Enron itself was going to be a viable company. And the pipeline? As part of the original merger deal, Dynegy handed Enron $1.5 billion in badly needed capital — in exchange for preferred stock in Northern Natural Gas. And now that the merger is terminated, guess what? Dynegy has the right to buy the rest of the pipeline�s stock. "Sometimes a company's best deals are the ones they didn't do," Watson said Wednesday — especially if you�ve already gotten what you wanted. Once Enron's credit rating went "junk" Wednesday — essentially condemning Enron to a takeover or bankruptcy — Dynegy didn't see anything left to buy that it couldn't get cheaper at the gone-out-of-business sale, including the thousands of Enron traders and other employees for whom the commute to the Houston office is already a daily routine. And life will go on. The NNG pipeline will simply change hands, and probably get more attention from Dynegy than Enron ever gave it. Other energy retailers, starting with Dynegy, will happily fill in the trading space — that's what markets do. And Enron, once No. 7 on the FORTUNE 500, will file for bankruptcy, sell off its assets, and very likely disappear, having found (like derivatives-slinger Long-Term Capital Investment of yesteryear) that in the high-wire life of trading for profits, too much leverage, too-clever accounting and a few bad breaks can be a lethal combination.
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Nicola Notaris (* 5. Juli 1727 in Santa Caterina dello Ionio; † 8. Juli 1802 in Squillace), auch Nicola Notariis, Nicolas Notariis, Nikolaus Notari und Nicolò de Notari war ein italienischer römisch-katholischer Geistlicher und Bischof von Umbriatico und danach von Squillace in Kalabrien. Leben Nicola Notaris wurde am 5. Juli 1727 als Sohn des Domenico Notaris und seiner Frau Antonia Mandarani in Santa Caterina dello Ionio (Provinz Catanzaro, Kalabrien) geboren. Am 25. August 1752 wurde er von Bischof Ferdinando Mandarini von Oppido Mamertina zum Priester geweiht. Papst Pius VI. ernannte ihn am 28. Juli 1777 zum Bischof von Umbriatico. Die Bischofsweihe fand am 3. August 1777 statt. Hauptkonsekrator war Kardinal Francesco Saverio de Zelada, Kardinalpriester von Santi Silvestro e Martino ai Monti in Rom. Als Mitkonsekratoren fungierten (Titular-)Erzbischof Giuseppe Maria Contesini von Athen und (Titular-)Erzbischof Girolamo Volpi von Neocaesarea in Ponto. Am 20. Juli 1778 wurde er bereits zum Bischof von Squillace ernannt. In seiner Amtszeit ließ er 1798 den Dom in Squillace neu aufbauen. Nicolas Notaris starb am 8. Juli 1802 in Squillace. Einzelnachweise Römisch-katholischer Bischof (18. Jahrhundert) Historische Person (Italien) Geboren 1727 Gestorben 1802 Mann
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Teaming up with a person on the web is okay but you need to be truthful concerning the reason. As talking on the world wide web is the major type of communication it is perfectly fine to send an email to this man who has the copy motives. When you speak to a Chinese girl online remember to emphasize your wisdom and abilities. Internet dating is so amazing if you stop by the appropriate direction. Internet dating is in an all-time high among singles today. Internet dating makes it simple to get in touch with people from all over the Earth, and it is one of the many explanations for why women and men go online daily. A great deal of such online dating websites such as Mirabela Executive Dating additionally provide elite single dating options for women and men that are searching for a selective and top-notch treatment. By definition, relationship on the web is the institution of two individuals throughout the web. It can mean meeting people of various cultures and backgrounds so remember to know how to respect them. Online dating is extremely handy. Internet relationship protects your personal space. Internet dating is a superb venue for timid types. Internet dating has been shown to be a prosperous process of meeting people and establishing dates. Dating on the internet could be equally tricky for men because it is for you. Another reason online dating is the outstanding option is that you are able to meet men and women in light of something apart from their own appearances. Internet dating programs from India are meant to spark a connection, and they allow you to locate people with the exact pursuits, principles, etc.. Internet dating isn't the normal dating so it's just normal to talk with more than 1 person as you're not dating any person solely just yet. It is a true blessing for us. It's played a very important role in modernizing human life. If a web site is not user friendly, members more frequently than notcheck other relationship sites that may give a simpler navigation, precision and simplicity of usage. Dating sites are primarily meant for one individual to satisfy another. Internet dating websites are the perfect place to discover friends, that you can search for men and women having the exact interests as you. The free internet dating site is even more popular because it is not only convenient but is highly economical. You don't have to be overly suspecting about the people which are in the relationship site. A good deal of people might think that the senior people would not participate in any online dating website. Internet dating sites furnish you with matchmaking cases that are not monitored, via the usage of your notebook computer, Internet link and also in latter days, your cell phone. There are lots of internet dating services all around the world that assists senior citizens all over the world in looking the perfect foreign dating sites choice in their view. Additionally, there are many services for online matchmaking in Australia. Dating isn't running a marathon, it is all about fun and enjoying somebody else's business. In the event you believe internet dating solutions can assist you just in the way it has helped lots of people, you would have to make a web-based profile and search profile for dating. Perhaps by now you'll have enrolled with your very first internet dating agency.
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"Thank you so much for the truly beautiful dress that you made me for our wedding. It was perfection in every way and when I put it on I honestly felt like a 1920's movie star! Thank you for making the whole process so fun and enjoyable. Each of you made me and my dress feel so special and important. Thank you. In return, I will recommend you to every newly engaged girl I meet!
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Edward Weir, the son of a Scottish rivetter in Belfast's shipyards, died on 14th January 1947 after treatment in the UVF Hospital, Upper Galwally, Belfast. Private Edward Weir served in World War One with 1st Battalion, Royal Irish Rifles and enlisted again with the 6th Battalion, Royal Ulster Rifles during the Second World War. Private Edward Weir (D/24547) served in 6th Battalion Royal Ulster Rifles during World War Two. Born on 3rd September 1888, he was the son of Robert Weir and Margaret Weir (née McLarnon) of Belfast, Co. Down. The Weir's resided at 17 Club Row Lane, Belfast, Co. Down. Club Row Lane or Club Row Loanin is now Dee Street. Edward was the husband of Agnes Weir of Belfast, Co. Antrim. His eldest siblings were born in Renfrewshire, Scotland where Robert Weir worked as a ship's riveter; Christina Weir born on 29th May 1874, Mary Weir born in 1877, Ann Weir born on 25th August 1881. The Weir family then moved to Belfast where shipbuilding was an emerging industry in the mid-1880s. A son, Archibald Weir was born on 25th May 1885. Edward also had younger brothers; George Weir born on 3rd July 1891, Peter Weir born in June 1894, and Henry "Harry" Weir born on 21st October 1896. On 31st March 1901, the Irish census records the family at 123 Church Street East, Belfast, Co. Down. By the time of the next census on 2nd April 1911, Edward is serving with 1st Battalion Royal Irish Rifles in England. Edward died on 14th January 1947 aged 57 years old. His place of death was the UVF Hospital, Upper Galwally, Belfast, Co. Antrim. At the time, Weir lived nearby in 2 Earl Haig Park, houses established for World War One veterans. A funeral took place two days later on 16th January 1947 in Dundonald, Co. Down. Resting where no shadows fall. If you enjoyed this post on "Edward Weir", please share with your friends and followers.
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