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abstract: 'We generalize and slight improve the result of I. I. Sharapudinov \[Mat. Zametki, 1996, Volume 59, Issue 2, 291–302\]. Some applications to the de la Vallée Poussin operator will also be given.'
author:
- |
**Włodzimierz Łenski and Bogdan Szal**\
University of Zielona Góra\
Faculty of Mathematics, Computer Science and Econometrics\
65-516 Zielona Góra, ul. Szafrana 4a, Poland\
[email protected], B.Szal @wmie.uz.zgora.pl
title: '**Estimates of convolution operators of functions from $L_{2\pi}^{p(x)}$** '
---
**Key words:** convolution operators, $L_{2\pi }^{p}(p=p(x))$ spaces, rate of approximation.
**2010 Mathematics Subject Classification:** 47B38, 44A35, 41A35, 42A24.
Introduction
============
Let $p=p(x)$ will be a measurable $2\pi $ - periodic function, $p_{-}=\inf
\left\{ p(x):x\in
%TCIMACRO{\U{211d} }%
%BeginExpansion
\mathbb{R}
%EndExpansion
\right\} $, $p^{-}$ $=\sup \left\{ p(x):x\in
\right\} $, $1$ $\leq p_{-}\leq $ $p^{-}$ $<\infty $ and $L_{2\pi }^{p}$ will be the space of measurable $2\pi $ - periodic functions $f$ such that $%
\int_{-\pi }^{\pi }\left\vert f(x)\right\vert ^{p(x)}dx<\infty $.
Putting$$\left\Vert f\right\Vert _{p}=\inf \left\{ \alpha >0:\int_{-\pi }^{\pi
}\left\vert \frac{f(x)}{\alpha }\right\vert ^{p(x)}dx\leq 1\right\}$$we turn $L_{2\pi }^{p}$ into the Banach space. We write $\Pi _{2\pi }$ for the set of all $2\pi $ - periodic variable exponents $p=p(x)\geq 1$ satisfying the condition$$\left\vert p(x)-p(y)\right\vert \ln \frac{2\pi }{\left\vert x-y\right\vert }%
=O\left( 1\right) \text{,\ }\left( x,y\in \left[ -\pi ,\pi \right] \right) .
\label{1}$$
In the paper [@IIS1] I. I. Sharapudinov proved the following theorem:
**Theorem A.** *Let* $k_{\lambda }=k_{\lambda }(x)$* *$%
\left( 1\leq \lambda <\infty \right) $* be a measurable* $2\pi $* -periodic essentially bounded function (kernel) satisfying the conditions:*
*A*$^{\circ }$*)* $\int_{-\pi }^{\pi }\left\vert k_{\lambda
}(t)\right\vert dt\leq c_{1}^{\circ },$
*B*$^{\circ }$*)* $\sup_{t}\left\vert k_{\lambda
}(t)\right\vert \leq c_{2}^{\circ }\lambda ^{\eta }$*,*
*C*$^{\circ }$*)* $\left\vert k_{\lambda }(t)\right\vert \leq
c_{3}^{\circ }$*, *$\left( \lambda ^{-\gamma }\leq \left\vert
t\right\vert <\pi \right), $
*where* $\gamma ,\eta ,$* *$c_{1}^{\circ },c_{2}^{\circ
},c_{3}^{\circ }>0$* are independent of* $\lambda $*.*
*If* $f\in L_{2\pi }^{p}$* with* $p=p(x)$* *$\in \Pi
_{2\pi }$*, then*$$\left\Vert K_{\lambda }[f]\right\Vert _{p}=O\left( 1\right) \left\Vert
f\right\Vert _{p},$$*where*$$K_{\lambda }[f](x)=\int_{-\pi }^{\pi }f(t)k_{\lambda }(t-x)dt.$$We generalize and slight improve this result considering the wider family of two parameters convolution operators. Some applications to the de la Vallée Poussin operator will also be given.
Main result
===========
Denote by $k_{m,n}=k_{m,n}(x),$ for every $0\leq m\leq n<\infty,$ a measurable $%
2\pi $ -periodic essentially bounded function (kernel). Let define the linear operator
$$K_{m,n}[f]=K_{m,n}[f](x)=\int_{-\pi }^{\pi }f(t)k_{m,n}(t-x)dt$$in space $L_{2\pi }^{p}.$ We will say that the kernel family $\left\{
k_{m,n}(x)\right\} _{0\leq m\leq n<\infty }$ satisfies the conditions B) and C), respectively, if the following estimates hold:
B\) $\sup_{\left\vert t\right\vert \leq h_{m}}\left\vert
k_{m,n}(t)\right\vert \leq c_{2}\left( n+1\right) ^{\eta }$,
C\) $\left\vert k_{m,n}(t)\right\vert \leq c_{3}$, $\left( h_{m}\leq
\left\vert t\right\vert <\pi \right) ,$
where $h_{m}=\frac{\pi }{\left( m+1\right) ^{\gamma }}$ and $\gamma$, $\eta
,c_{2},c_{3}>0$ are independent of $m,n$.
For the operator $K_{m,n}[f]$ we will prove the following general estimate:
Let $k_{m,n}=k_{m,n}(x)$ $\left( 0\leq m\leq n<\infty \right) $ satisfy the conditions B) and C). If $f\in L_{2\pi }^{p}$ with $p=p(x)$ $\in \Pi _{2\pi
} $, then$$\left\Vert K_{m,n}[f]\right\Vert _{p}=O\left( \mu _{m,n}\right) \left\Vert
f\right\Vert _{p},$$where $$\mu _{m,n}=\mu \left( k_{m,n}\right) =\int_{-h_{m}}^{h_{m}}\left\vert
k_{m,n}(t)\right\vert dt.$$
Let$$x_{k}=kh_{n}-\pi ,\text{ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\ \ \ \ \ \ \ \ }k=0,\pm 1,\pm 2,... \label{2}$$$$s_{k}=\min \left\{ p\left( x\right) :x_{k-1}\leq x\leq x_{k+2}\right\} ,%
\text{ }k=0,\pm 1,\pm 2,... \label{3}$$$$p_{t}\left( x\right) =s_{k}\text{ \ \ }\left( x_{k-1}-t\leq x\leq
x_{k+1}-t\right) ,\text{ \ }k=0,\pm 1,\pm 2,... \label{4}$$whence $p_{t}\left( x\right) =p_{0}\left( x+t\right) $ is a $2\pi $ - periodic step function such that$$p_{t}\left( x\right) \leq p\left( x\right) .$$
Denote by $$E_{m}\left( x\right) =\left( -\pi ,\pi \right) \backslash \left(
x-h_{m},x+h_{m}\right) ,$$when $\left( x-h_{m},x+h_{m}\right) \subset \left( -\pi ,\pi \right) $, but $$E_{m}\left( x\right) =\left( -\pi ,\pi \right) \backslash \left( -\pi
,x+h_{m}\right)$$or $$E_{m}\left( x\right) =\left( -\pi ,\pi \right) \backslash \left( x-h_{m},\pi
\right) ,$$when $x-h_{m}<-\pi $ or $\pi <x+h_{m}$, respectively.
Let$$\left\Vert f\right\Vert _{p}\leq 1.$$It is clear that for $\overline{p}=\max \left\{ p\left( x\right) :-\pi \leq
x\leq \pi \right\} $$$\begin{aligned}
&&\left( \int_{-\pi }^{\pi }\left\vert K_{m,n}[f](x)\right\vert
^{p(x)}dx\right) ^{1/\overline{p}} \\
&=&\left( \int_{-\pi }^{\pi }\left\vert \int_{-\pi }^{\pi
}f(t)k_{m,n}(t-x)dt\right\vert ^{p(x)}dx\right) ^{1/\overline{p}} \\
&=&\left( \int_{-\pi }^{\pi }\left\vert \left( \int_{E_{m}\left( x\right)
}+\int_{x-h_{m}}^{x+h_{m}}\right) f(t)k_{m,n}(t-x)dt\right\vert
^{p(x)}dx\right) ^{1/\overline{p}}\end{aligned}$$$$\begin{aligned}
&\leq &\left( \int_{-\pi }^{\pi }\left\vert \int_{E_{m}\left( x\right)
}f(t)k_{m,n}(t-x)dt\right\vert ^{p(x)}dx\right) ^{1/\overline{p}} \\
&&+\left( \int_{-\pi }^{\pi }\left\vert
\int_{x-h_{m}}^{x+h_{m}}f(t)k_{m,n}(t-x)dt\right\vert ^{p(x)}dx\right) ^{1/%
\overline{p}} \\
&=&J_{m}^{1/\overline{p}}+J_{x}^{1/\overline{p}}.\end{aligned}$$Since$$\left\Vert f\right\Vert _{q}\leq \left( 2\pi +1\right) \left\Vert
f\right\Vert _{p}$$with $q\left( x\right) \leq p\left( x\right) $ for $-\pi \leq x\leq \pi $ (cf. [@IIS0]), by condition C), $$\begin{aligned}
&&\left\vert \int_{E_{m}\left( x\right) }f(t)k_{m,n}(t-x)dt\right\vert \\
&=&O\left( 1\right) \int_{E_{m}\left( x\right) }\left\vert f(t)\right\vert
dt=O\left( 1\right) \int_{-\pi }^{\pi }\left\vert f(t)\right\vert dt=O\left(
1\right) \left\Vert f\right\Vert _{p}=O\left( 1\right) \end{aligned}$$and therefore $$J_{m}=O\left( 1\right) .$$In case of integral $J_{x}$, using (\[1\]), (\[2\]) and (\[3\]), for $%
x_{k}\leq x\leq x_{k+1},$ we obtain that$$\left\vert p(x)-s_{k}\right\vert =O\left( \frac{1}{\ln 2\left( n+1\right)
^{\gamma }}\right) ,$$and therefore by condition B)$$\begin{aligned}
\left\vert \int_{x-h_{m}}^{x+h_{m}}f(t)k_{m,n}(t-x)dt\right\vert
^{p(x)-s_{k}} &=&\left( n+1\right) ^{\eta O\left( \frac{1}{\ln 2\left(
n+1\right) ^{\gamma }}\right) }\left( \int_{x-h_{m}}^{x+h_{m}}\left\vert
f(t)\right\vert dt\right) ^{O\left( \frac{1}{\ln 2\left( n+1\right) ^{\gamma
}}\right) } \\
&=&O\left( 1\right) \left( \left\Vert f\right\Vert _{p}\right) ^{O\left(
\frac{1}{\ln 2\left( n+1\right) ^{\gamma }}\right) }=O\left( 1\right) .\end{aligned}$$Next,$$\begin{aligned}
J_{x} &=&\sum_{k=0}^{2[n^{\gamma }]}\int_{x_{k}}^{x_{k+1}}\left\vert
\int_{x-h_{m}}^{x+h_{m}}f(t)k_{m,n}(t-x)dt\right\vert ^{s_{k}+p(x)-s_{k}}dx
\\
&=&\sum_{k=0}^{2[n^{\gamma }]}\int_{x_{k}}^{x_{k+1}}\left\vert
\int_{x-h_{m}}^{x+h_{m}}f(t)k_{m,n}(t-x)dt\right\vert
^{p(x)-s_{k}}\left\vert
\int_{x-h_{m}}^{x+h_{m}}f(t)k_{m,n}(t-x)dt\right\vert ^{s_{k}}dx.\end{aligned}$$Thus $$J_{x}=O\left( 1\right) \sum_{k=0}^{2[n^{\gamma }]}\left( \mu _{m,n}\right)
^{s_{k}}\int_{x_{k}}^{x_{k+1}}\left\vert \frac{1}{ \mu _{m,n}}\int_{x-h_{m}}^{x+h_{m}}f(t)k_{m,n}(t-x)dt\right\vert ^{s_{k}}dx.$$By the Jensen inequality,$$\begin{aligned}
J_{x} &=&O\left( 1\right) \sum_{k=0}^{2[n^{\gamma }]}\left( \mu
_{m,n}\right) ^{s_{k}}\int_{x_{k}}^{x_{k+1}}\left\vert \frac{1}{\mu _{m,n}}%
\int_{x-h_{m}}^{x+h_{m}}f(t)k_{m,n}(t-x)dt\right\vert ^{s_{k}}dx \\
&=&O\left( 1\right) \sum_{k=0}^{2[n^{\gamma }]}\left( \mu _{m,n}\right)
^{s_{k}-1}\int_{x_{k}}^{x_{k+1}}\left[ \int_{x-h_{m}}^{x+h_{m}}\left\vert
f(t)\right\vert ^{s_{k}}\left\vert k_{m,n}(t-x)\right\vert dt\right] dx \\
&=&O\left( 1\right) \left( \mu _{m,n}\right) ^{\overline{p}%
-1}\int_{-h_{m}}^{h_{m}}\left\vert k_{m,n}(t)\right\vert \left(
\sum_{k=0}^{2[n^{\gamma }]}\int_{x_{k}-t}^{x_{k+1}-t}\left\vert
f(x)\right\vert ^{s_{k}}dx\right) dt \\
&=&O\left( 1\right) \left( \mu _{m,n}\right) ^{\overline{p}%
-1}\int_{-h_{m}}^{h_{m}}\left\vert k_{m,n}(t)\right\vert \left( \int_{-\pi
-t}^{\pi -t}\left\vert f(x)\right\vert ^{p_{t}\left( x\right) }dx\right) dt
\\
&=&O\left( 1\right) \left( \mu _{m,n}\right) ^{\overline{p}%
-1}\int_{-h_{m}}^{h_{m}}\left\vert k_{m,n}(t)\right\vert \left( \int_{-\pi
}^{\pi }\left\vert f(x)\right\vert ^{p_{t}\left( x\right) }dx\right) dt.\end{aligned}$$Similar to [@IIS1 (17) p.295] we have$$\int_{-\pi }^{\pi }\left\vert f(x)\right\vert ^{p_{t}\left( x\right) }dx\leq
\left( 2\pi +1\right) ^{\overline{p}}.$$Hence$$J_{x}^{1/\overline{p}}=O\left( \mu _{m,n}\right)$$and our result follows.
If we put $m=n=\lambda $ in the assumptions of Theorem 1, then for $f\in
L_{2\pi }^{p}$ with $p=p(x)$ $\in \Pi _{2\pi }$ the following estimate$$\left\Vert K_{\lambda }[f]\right\Vert _{p}=O\left( \mu _{\lambda }\right)
\left\Vert f\right\Vert _{p}$$holds, *where* $\mu _{\lambda }=\int_{-h_{\lambda }}^{h_{\lambda
}}\left\vert k_{\lambda }(t)\right\vert dt$ and $k_{\lambda }=k_{\lambda, \lambda }$.
If we additionally assume that $\mu _{\lambda }=O\left( 1\right) ,$ then Corollary 2 gives Theorem A with the result [@IIS1] of I. I. Sharapudinov, under the slight weaker conditions.
De la Vallée Poussin operator
=============================
Let $f\in L_{2\pi }^{1}$ and consider the trigonometric Fourier series $$Sf(x):=\frac{a_{0}(f)}{2}+\sum_{\nu =1}^{\infty }(a_{\nu }(f)\cos \nu
x+b_{\nu }(f)\sin \nu x)$$with the partial sums $S_{k}f.$ For $0\leq m\leq n,$ $m, n=0,1,2,...$ denote by$$V_{n,m}[f]\left( x\right) =\frac{1}{m+1}\sum_{k=n-m}^{n}S_{k}[f]\left(
x\right) =\frac{1}{\pi \left( m+1\right) }\int_{-\pi }^{\pi }f\left(
t\right) \Phi _{n,m}\left( t-x\right) dt$$the de la Vallée Poussin means of the series $Sf,$ where$$\Phi _{n,m}\left( t\right) =\frac{1}{m+1}\frac{\sin \frac{\left( m+1\right) t%
}{2}\sin \frac{\left( 2n-m+1\right) t}{2}}{2\sin ^{2}\frac{t}{2}}.$$
It is clear that the kernel family $\left\{ \Phi _{m,n}(x)\right\} _{1\leq
m\leq n<\infty }$ satisfies the conditions B) with $\eta =1$ and C) with $%
\gamma =\frac{1}{2}$. By the following calculation$$\begin{aligned}
&&\frac{1}{m+1}\int_{0}^{h_{m}}\frac{\left\vert \sin \frac{\left( m+1\right)
t}{2}\sin \frac{\left( 2n-m+1\right) t}{2}\right\vert }{2\sin ^{2}\frac{t}{2}%
}dt \\
&=&\frac{1}{m+1}\left( \int_{0}^{\frac{\pi }{n+1}}+\int_{\frac{\pi }{n+1}}^{%
\frac{\pi }{m+1}}+\int_{\frac{\pi }{m+1}}^{h_{m}}\right) \frac{\left\vert
\sin \frac{\left( m+1\right) t}{2}\sin \frac{\left( 2n-m+1\right) t}{2}%
\right\vert }{2\sin ^{2}\frac{t}{2}}dt \\
&\leq &\int_{0}^{\frac{\pi }{n+1}}\frac{\left( 2n-m+1\right) dt}{2}+\int_{%
\frac{\pi }{n+1}}^{\frac{\pi }{m+1}}\frac{dt}{2\frac{t}{2}\frac{2}{\pi }}+%
\frac{1}{m+1}\int_{\frac{\pi }{m+1}}^{h_{m}}\frac{dt}{2\left( \frac{t}{2}%
\frac{2}{\pi }\right) ^{2}} \\
&\leq &\pi +\frac{\pi }{2}\ln \frac{n+1}{m+1}+\frac{\pi }{2}\end{aligned}$$we obtain$$\mu \left( \Phi _{m,n}\right) =\int_{-h_{m}}^{h_{m}}\left\vert \Phi
_{m,n}(t)\right\vert dt\leq \pi \left( 3+\ln \frac{n+1}{m+1}\right) .$$Hence, by Theorem 1, we have:
If $L_{2\pi }^{p}$ with $p=p(x)$ $\in \Pi _{2\pi }$, then$$\left\Vert V_{n,m}[f]\right\Vert _{p}=O\left( 1+\ln \frac{n+1}{m+1}\right)
\left\Vert f\right\Vert _{p}\text{ \ \ \ }\left( 0\leq m\leq n,\text{ }%
m, n=0,1,2,...\right) .$$
From Theorem 4 we get the following corollary:
Let $f\in L_{2\pi }^{p}$ with $p=p(x)$ $\in \Pi _{2\pi }.$ If $m=O\left( n\right) $, then$$\left\Vert V_{n,m}[f]\right\Vert _{p}=O\left( 1\right) \left\Vert
f\right\Vert _{p}$$hold.
In the special case we can consider the following Fourier operator:$$S_{n}[f]\left( x\right) =V_{n,0}[f]\left( x\right) =\frac{1}{\pi }\int_{-\pi
}^{\pi }f\left( t\right) \Phi _{n,0}\left( t-x\right) dt,$$where$$\Phi _{n,0}\left( t\right) =\frac{\sin \frac{\left( 2n+1\right) t}{2}}{2\sin
\frac{t}{2}}.$$For this operator we have:
Let $f\in L_{2\pi }^{p}$ with $p=p(x)$ $\in \Pi _{2\pi }.$ If we put $m=0$ in Theorem 4, then $$\left\Vert S_{n}[f]\right\Vert _{p}=O\left( 1+\ln \left( n+1\right) \right)
\left\Vert f\right\Vert _{p}\text{ \ \ \ }\left( \text{ }n=0,1,2,...\right)
.$$
In the case $p\equiv 1$ the results of this section we can find in the monograph of A. Zygmund [@AZ Ch. II, p.70, Ch. III, p.90] (see e.g.\[Ch. II, p.117-8\][WZ]{} .
[9]{} Sharapudinov, I. I.: The basis property of the Haar system in the space $L^{p(x)}([0;1])$ and the principle of localization in the mean, Math. Sb., Vol. 130(172), No 2(6). 275-283 (1986).
Sharapudinov, I. I.: Uniform boundedness in $L^{p}(p=p(x))$ of some families of convolution operators, Mat. Zametki, Volume 59, Issue 2, 291-302 (1996).
Sharapudinov, I. I.: On direct and inverse theorems of approximation theory in variable Lebesgue and Sobolev spaces, Azerbaijan Journal of Mathematics V. 4, No 1, January (2014).
Sharapudinov, I. I.: Approximation of functions in $L_{2\pi
}^{p(x)}$ by trigonometric polynomials, Izv. RAN. Ser. Mat., Volume 77, Issue 2, 197-224 (2013).
Zygmund, A.: Trigonometric series, Cambridge, London, New York, Melbourne, (2002).
Zhuk, V. V.: Approximation of periodic functions (Russian), Leningrad, (1982).
| |
The revelation, which is likely to outrage a security industry already furious at the NSA, comes by way of Bloomberg, which cites two unidentified sources and reports:
“Putting the Heartbleed bug in its arsenal, the NSA was able to obtain passwords and other basic data that are the building blocks of the sophisticated hacking operations at the core of its mission, but at a cost…The agency found the Heartbeat glitch shortly after its introduction, according to one of the people familiar with the matter, and it became a basic part of the agency’s toolkit for stealing account passwords and other common tasks.”
The Office of the Director of National Intelligence issued the following statement:
NSA was not aware of the recently identified vulnerability in OpenSSL, the so-called Heartbleed vulnerability, until it was made public in a private sector cybersecurity report. Reports that say otherwise are wrong.
Reports that NSA or any other part of the government were aware of the so-called Heartbleed vulnerability before April 2014 are wrong. The Federal government was not aware of the recently identified vulnerability in OpenSSL until it was made public in a private sector cybersecurity report. The Federal government relies on OpenSSL to protect the privacy of users of government websites and other online services. This Administration takes seriously its responsibility to help maintain an open, interoperable, secure and reliable Internet. If the Federal government, including the intelligence community, had discovered this vulnerability prior to last week, it would have been disclosed to the community responsible for OpenSSL.
When Federal agencies discover a new vulnerability in commercial and open source software – a so-called “Zero day” vulnerability because the developers of the vulnerable software have had zero days to fix it – it is in the national interest to responsibly disclose the vulnerability rather than to hold it for an investigative or intelligence purpose.
In response to the recommendations of the President’s Review Group on Intelligence and Communications Technologies, the White House has reviewed its policies in this area and reinvigorated an interagency process for deciding when to share vulnerabilities. This process is called the Vulnerabilities Equities Process. Unless there is a clear national security or law enforcement need, this process is biased toward responsibly disclosing such vulnerabilities.
The news comes as companies and governments are still reeling from last week’s disclosure of Heartbleed, which lets attackers penetrate OpenSSL, the open source protocol used to encrypt passwords and other sensitive data. The vulnerability has exposed companies like Yahoo(s yhoo) and Google(s goog), as well as hardware providers like Cisco, and led the Canadian government to temporarily shut down its tax preparation service.
For now, however, it’s not clear how much actual damage has been done — or if only a handful of people, including those at the NSA, knew about the vulnerability. Some reassurance came today when security service CloudFlare said it is unlikely that hackers have been able to use Heartbleed to obtain private SSL keys used by websites. Companies have been actively patching their sites since last week’s disclosure.
While Heartbleed represents a useful weapon for the NSA to spy on its opponents, the agency’s failure to disclose it — if true — will anger those who believe that the U.S. government should focus on defensive measures like encryption and security — rather than using compromised standards as a means of attack. The NSA is still under criticism following disclosures by former contractor Edward Snowden that it deliberately introduced weaknesses into other global encryption standards.
This story was updated at 4:50pmET after the NSA issued a statement denying the report, and at 6:oopm with details. | https://old.gigaom.com/2014/04/11/nsa-knew-about-devastating-heartbleed-bug-and-used-it/ |
Q:
Would an Image or a Rect with several Lines be better for implementing a trapezoidal button in Flex 4?
We're using Flex 4.6 for the current project, and I decided I wanted to put some buttons on the right-hand edge of the screen that essentially just looked like simple tabs, hence having a symmetrical trapezoidal shape. The problem? I understand why Flex wouldn't have trapezoids built in, but it's apparently neither are triangles, and implementing a triangle in Flex is evidently just unnatural.
To implement these buttons, the two main options I see are:
1: Inherit from Image and embed some pngs with transparent backgrounds or something.
2: Inherit from Group, let the rectangular part of the button be a Rect, and let the triangular parts each be a collection of 1-width Lines.
Which would be more efficient? Which would be better in general? I know these approaches are unnatural, but despite the issues I'm seeing with Flex, is there a Flex-style way of handling this that's better? Thanks!
A:
You can easily draw basic shapes like these using Path
Triangle
<s:Path data="M 0 0 L 5 10 L 10 0 Z">
<s:stroke>
<s:SolidColorStroke color="0x000000"/>
</s:stroke>
</s:Path>
Trapezoid
<s:Path data="M 0 0 L 10 0 L 7 5 L 3 5 Z">
Legend
M: move to (don't draw)
L: draw line to
Z: close the shape
For more info read the docs
| |
The UNH Manchester humanities program is an interdisciplinary study of the human condition, past and present. The program is based on careful examination of substantial works from a variety of disciplines and is intended to develop intellectual skills, specialized knowledge, and breadth of understanding. It provides students with a broad foundation of knowledge and skills in the liberal arts combined with a coordinated, self-designed program of studies in an area of individual student interest.
The program attracts highly motivated students who wish to assume significant responsibility for the content and direction of their studies. Humanities students develop skills of analysis, critical assessment, and effective communication as they study diverse works of art, music, literature, history, philosophy, and the sciences. Individually designed programs may cover the full range of student interests: for example, the social and ethical implications of genetic engineering or the examination of an historical period through study of its literature, arts, history, philosophy, and sciences. Students complete their major with two capstone seminars. The first, HUMA 795 Study of Creativity, explores the nature of creativity through the lives and works of individuals such as Leonardo da Vinci, Kathe Kollwitz, Mozart, Freud, Einstein, and Georgia O'Keeffe. The second seminar, HUMA 796 Study of Contemporary Issues, explores current social and political issues with a focus on developments in public policy, science, and business, and their impact on social values.
Humanities majors find employment in a wide range of fields or pursue graduate study in subjects such as law or education. Skills and knowledge developed through the major are important in virtually all social and career responsibilities. A humanities major or minor can also complement work in other majors such as elementary or secondary education, business, communications, or computer information systems.
Program of Study
For the humanities major at UNH Manchester, students must complete a minimum of 128 credits and satisfy the University's Discovery Program and foreign language requirements, and students must complete 40 credits with a minimum grade of C in each course in the major.
|Code||Title||Credits|
|Core Courses|
|HIST 500||Introduction to Historical Thinking||4|
|or ENGL 419||How to Read Anything|
|HUMA 411||Humanities I||4|
|HUMA 412||Humanities II||4|
|Self-Designed Concentration 1||20|
|Discovery Program Capstone Courses|
|HUMA 795||Study of Creativity||4|
|HUMA 796||Study of Contemporary Issues||4|
|Total Credits||40|
|1|
This is an approved program of study designed by the student in consultation with a faculty advisor. In addition to courses available on the Manchester campus, students may, with prior approval, use courses from area colleges and the University's Durham campus. The concentration is made up of two humanities courses (HUMA prefix) at the 600 or 700 level and three courses from any relevant discipline at any level.
For more information, contact Susanne Paterson, Associate Professor and program coordinator or the UNH Manchester Office of Admissions at (603) 641-4150.
- Demonstrate the ability to find and evaluate primary and secondary source material necessary for humanistic research.
- Demonstrate the ability to propose, conduct, and present interdisciplinary humanistic research in a written, oral, or other forms. Identify and interpret creative and cultural forms from a given historical period.
- Compare and contrast the meanings of major texts and other significant cultural productions. | https://catalog.unh.edu/undergraduate/manchester/programs-study/humanities/humanities-major-ba/ |
Q:
Pandas Dataframe - multiple values inside one cell?
I'm working on an assignment and I'm having trouble with Pandas (finding it very different to the MATLAB I'm used to).
I have a dataframe called 'main_DF' which has multiple columns (or series), one of these columns is called 'text-message'. I would like to take the text-message of each row, tokenize it into individual words and then place the list of those individual words into another column called 'text-message-tokens'.
This is what I have at the moment:
main_DF = pd.DataFrame(columns=['text-message', 'Label']) # creating empty dataframe
# filling with data
main_DF = main_DF.append({'text-message': "I am happy", 'Label':"happy"}, ignore_index=True)
main_DF = main_DF.append({'text-message': "I am sad", 'Label':"sad"}, ignore_index=True)
# print
print(main_DF)
# Tokenizing text-message
tokenize = CountVectorizer().build_tokenizer()
# Add tokenized message to main_DF
main_DF['text-message-tokens'] = tokenize(main_DF['text-message'][0]) # tokenize first row
main_DF['text-message-tokens'] = tokenize(main_DF['text-message'][1]) # tokenize second row
# print
print(main_DF)
This results in the following
I would like it to be like this in the end,
A:
You can use apply to apply tokenize on each text message:
import pandas as pd
from sklearn.feature_extraction.text import CountVectorizer
main_DF["text-message-tokens"] = main_DF["text-message"].apply(tokenize)
# print
print(main_DF)
Output
main_DF
text-message Label text-message-tokens
0 I am happy happy [am, happy]
1 I am sad sad [am, sad]
| |
Data from phase III trial of Sublocade in opioid use disorder published in Journal of Addiction Medicine
Indivior announced the publication of patient-centered outcome endpoints (health status, physical and mental health, medication satisfaction, employment, health insurance status and healthcare resource utilization) of Sublocade (buprenorphine extended-release) injection for subcutaneous use in opioid use disorder by the Journal of Addiction Medicine. These measures were collected during the 24-week, Phase III, randomized, placebo-controlled study assessing the drug's efficacy, safety and tolerability.
The results showed that participants receiving Sublocade versus placebo experienced significant changes from baseline on the EQ-5D-5L index (300/300mg: difference=0.0636) and visual analog scale (300/300mg: difference=5.9, 300/100mg: difference=7.7), and on the SF-36v2 physical component summary score (300/300mg: difference=3.8; 300/100mg: difference=3.2). Treatment satisfaction was significantly higher at the end of study for participants receiving Sublocade 300/300mg and 300/100mg than placebo. Employment increased by 10.8% with Sublocade 300/300mg and 10.0% with 300/100mg but decreased by 12.6% with placebo. Participants receiving Sublocade compared with placebo had significantly fewer hospital days per person-year observed.
See: "Patient-centered Outcomes in Participants of a Buprenorphine Monthly Depot (BUP-XR) Double-blind, Placebo-controlled, Multicenter, Phase 3 Study." Ling W et al. J Addict Med. March 2019 DOI: http://dx.doi.org/10.1097/ADM.0000000000000517
Related news and insights
Chiesi Global Rare Diseases, a business unit of Chiesi Farmaceutici S.p.A., an international research-focused healthcare Group (Chiesi Group), announced that Health Canada has approved Ferriprox (deferiprone) for the treatment of iron overload in patients with sickle cell disease (SCD) or other anemias.
The Menarini Group and Radius Health announced positive topline results from the phase III EMERALD study evaluating RAD 1901 (elacestrant) as a monotherapy versus the standard of care (SoC) for the treatment of ER+/HER2- advanced or metastatic breast cancer (mBC).
Gilead Sciences, Inc. announced the FDA approved a new low-dose tablet dosage form of Biktarvy (bictegravir 30 mg/emtricitabine 120 mg/tenofovir alafenamide 15 mg tablets) for pediatric patients weighing at least 14 kg to less than 25 kg who are virologically suppressed or new to antiretroviral therapy. | https://www.medthority.com/news/2019/03/data-from-phase-iii-trial-of-sublocade-in-opioid-use-disorder-published-in-journal-of-addiction-medicine---indivior/ |
Some notes about the design and development of Astral Schism.
I had two main goals when adjusting the game difficulty:
- The two modes must have similar difficulty levels
- Both modes must be winnable by people who don’t play games that often
I adjusted difficulty by changing the spawn rates of enemies, asteroids, and ore/hulls, and by changing the number of starting shields.
While I managed to strike a fairly good balance for the project deadline, I feel that it could still use some work. However, there are some more fundamental design issues that need to be addressed first:
It’s possible to get stuck in the game
The way the game works, level advancement is based on how many ship upgrades you have. When you run out of shields, you restart the level with the same number of shields and the same upgrades. This means that it is possible to get to a level that is too hard for your skill with few lives. Unless you can collect enough ore or hulls to return to base, you cannot gain enough lives to clear the level.
One possibility is to always grant a minimum number of shields to the player on starting a new level. e.g., if we have determined that the third level should be beatable with 6 shields, then the level-change code will also set the player’s shields to 6 if the player has fewer than 6 shields. Any other fixes to this problem will probably require a change to the current level mechanic.
Level advancement uses an unusual mechanic
I got comments from several people that the level mechanic “seems a bit weird.” It has the bonus that at a given level, you always know the ship has a minimum number of upgrades and should therefore be able to handle things. It’s just not what most people expect.
The “boss” for the ambassador mode doesn’t fit in
The “boss asteroid” requires a method to defeat it that never shows up elsewhere in the game. I’d like to change that, although it might “spoil the surprise”. On the other hand, there’s no such surprise for the Exterminator mode.
I want a scoring mode but don’t know how to do it
Scoring for the Exterminator mode is pretty straightforward. Just count shots fired, enemies extinguished, that kind of thing. But what’s the equivalent for the Ambassador mode?
There are some statistics I could keep score on: number of times levels are played, total time spent on a level, amount of ore picked up. For all of these, lower numbers suggest more player skill, which can result in slightly weird scores. | https://selenetan.com/tag/astral-schism/ |
The Ionian Singers with Emily Gray, mezzo-soprano, and Timothy Salter, conductor and pianist, will give a concert in All Saints Church, Rosendale Road in West Dulwich on Saturday 8th December at 7.30pm.
This concert takes its title from the Danish choral work by Lange-Müller Madonna over bølgerne. The theme of water and the sea occurs throughout the first half of this two-part programme with secular choral music and solo songs for mezzo-soprano and piano by a range of composers including Schubert, Brahms, Elgar, Stanford, Parry and Sibelius.
Music for Advent and Christmas form the second half of the concert. The choral works will include music by Sweelinck, Poston (The apple tree), Cornelius (The Three Kings), Timothy Salter and Russell Hepplewhite. The Nativity is celebrated in a group of songs by R.Strauss, Fauré, Ravel and Howells (Come sing and dance). | https://arounddulwich.co.uk/the-ionian-singers-present-madonna-over-the-waves/ |
In Russia there are about a hundred of industrial sites that meet criteria outlined by the Targeted Investment Program (TIP) for industrial parks. The number of operating facilities is nearly fifty, with greenfield projects (i.e. projects implemented from the very beginning) dominating. At that, the most part of sites is concentrated in the European part of Russia (Central, Volga and North-Western Federal Districts), close to key sales markets.
The total area of operating parks is almost 17.5 thousand hectares, while the production floor area approaches 4 million square meters. The largest, by the occupied area, operating parks are Vorsino in Kaluga Region, “Sheksna” in Vologda Region, the Industrial and Logistic Park in Novosibirsk Region. The area of each of them is about 2 thousand hectares.
Not only regional authorities, interested in attracting investments, demonstrate great interest in industrial parks. Business representatives, for whom location in an industrial park is the opportunity of launching a project within the shortest possible period, take an interest in them as well.
Despite active development of industrial parks and regular launch of new projects, their occupation rate remains to be rather low – about half of the areas are empty.
The status of a resident of an industrial or a technology park means for a company some combination of rights and responsibilities. On the one hand, a resident can claim obtaining state support; on the other hand, it must be registered in the territory of the subject as a tax payer. Many parks impose requirements to the kind of activity of prospective residents in accordance with the specialization of the park. Also, the minimum level for capital investment can be established; in order to confirm the planned volume of investments, the company which intends to obtain the status of a resident, submits a business plan, which includes technical, organizational, financial, marketing characteristics of the project, as well as risks its implementation is associated with. Besides, the park can be intended for small and medium business entities, which sets requirements concerning the size of the company that wants to be a park resident.
The combination of these requirements enables making an industrial park not just a cheap leasehold area, but also supporting small and medium business, promoting development of priority kinds of activities, ensuring payback for the park, attracting foreign investors, i.e. using advantages of such a site to the maximum.
At the present moment the resident membership of industrial parks is rather inhomogeneous. For example, there are almost 250 residents in KIP “Master” in Naberezhnye Chelny, most of which deal with the motor industry. A motor-car construction cluster has formed in industrial parks of Kaluga Region. In Yaroslavl Region they intend to form a pharmaceutical cluster: TEVA Pharmaceutical Industries Ltd. and “Nikomed” have settled in the industrial park “Novoselki”. A plant for metalwork production of “Lindab Building”, LLC and a plant for assembly of excavators and forklifts of “Komatsu Manufacturing Rus”, LLC are situated in the same park.
Filling the space with different residents for an industrial park is a guarantee of risk minimization (in terms of both the profile of activity and property). On the other hand, observing the industry specialization enables increasing effectiveness of support of companies’ activities and developing cooperation among residents. | http://www.kpi.ru/en/pressroom/analytics/rezidenty_industrialnyh_parkov/ |
verb (used without object), jingled, jingling.
1.
to make clinking or tinkling sounds, as do coins, keys, or other light, resonant metal objects when coming into contact or being struck together repeatedly:
The keys on his belt jingled as he walked.
2.
to move or proceed with such sounds:
The sleigh, decorated with bells, jingled along the snowy road.
3.
to sound in a light, repetitious manner suggestive of this, as verse, a sequence of words, or piece of music.
4.
to make rhymes.
verb (used with object), jingled, jingling.
5.
to cause to jingle:
He jingled the coins in his pocket.
noun
6.
a tinkling or clinking sound, as of small bells or of small pieces of resonant metal repeatedly struck one against another.
7.
something that makes such a sound, as a small bell or a metal pendant.
8.
a catchy succession of like or repetitious sounds, as in music or verse.
9.
a piece of verse or a short song having such a catchy succession of sounds, usually of a light or humorous character:
an advertising jingle.
10.
Irish English and Australian. a loosely sprung, two-wheeled, roofed carriage, usually used as a hackney coach.
/ˈdʒɪŋɡəl/
verb
1.
to ring or cause to ring lightly and repeatedly
2.
(intransitive) to sound in a manner suggestive of jingling: a jingling verse
noun
3.
a sound of metal jingling: the jingle of the keys
4.
a catchy and rhythmic verse, song, etc, esp one used in advertising
v.
late 14c., gingeln, of imitative origin (cf. Dutch jengelen, German klingeln). Related: Jingled; jingling.
n.
1590s, from jingle (v.). Meaning “song in an advertisement” first attested 1930, from earlier sense of “catchy array of words in prose or verse” (1640s).
noun
A telephone call; a ring; tinkle: We never hear from you, not even a jingle
Tagged: j
Read Also:
- Jingle-bell
noun 1. a sleigh bell.
- Jingle-jangle
adjective In poor condition; ramshackle: driving down to Big Sur in their funky bus or some jingle-jangle car (1970s+) noun (also jing) Money; coins: I’ve got some jingle-jangle in my jeans/ A lot of bars have fundraisers and donate a big chunk of their jing to AIDS groups (1950s+)
- Jingle mail
noun keys to a dwelling mailed to the creditor by someone no longer able to make the mortgage payments Examples Lenders are only beginning to learn how to manage the onslaught of jingle mail. Word Origin 1992
- Jingle-shell
noun 1. any of several marine, bivalve mollusks of the genus Anomia, having a thin, pearly shell with a conspicuous hole or notch near the hinge of the lower valve. 2. the shell itself. | https://definithing.com/define-dictionary/jingle/ |
CROSS-REFERENCE TO RELATED APPLICATIONS
The present application claims priority to U.S. Provisional Patent Application No. 63/209,611, filed Jun. 11, 2021, and U.S. Provisional Patent Application No. 63/294,916, filed Dec. 30, 2021, each of which is incorporated by reference in its entirety.
BACKGROUND OF THE INVENTION
1. Field of the Invention
2. Description of the Related Art
The invention relates to visualization of a biologic structure of a patient, or a non-biologic structure, and graphic analysis thereof. Imaging of structured or unstructured data can be combined by deformable registration to each other or to a reference atlas, and the input images and or resulting output registered images can be analyzed by shape analysis.
Data can take many forms (unstructured, for example tabular data, and structured, for example images) and can have any number of dimensions. Dimensions are the number of features associated with a given data element in a dataset (e.g., a three-dimensional RGB image would have 4 dimensions, 3 spatial dimensions, X, Y, and Z, and a 4th dimension for color channel). A data element is a single sample from a dataset with all its associated features (for images, this would be a single pixel/voxel). Unstructured datasets are defined here as datasets where contained data elements do not depend on their relative position to each other (e.g., in tabular data with n rows and d columns, the n rows can be rearranged along that dimension without affecting subsequent analysis). Structured datasets are therefore defined as datasets where contained data elements depend on their relative position to each other (e.g. the intensity of a pixel/voxel in an image depends on the intensities of its neighboring pixels/voxels since an image is a spatial representation of some data). An image is defined herein as any visual depiction of data. Visual depictions of unstructured data can include two-dimensional plots of tabular data.
Unstructured data processing includes but is not limited to conversion of unstructured data to structured data (e.g., two-dimensional plot) or modification of data elements within the dataset (e.g., normalizing the value a dimension/feature such that it has a given range). Structured data processing includes but is not limited to modification of data elements within the dataset (e.g., normalization of pixel/voxel intensity values within an image to be between a given range). Image processing is the modification of an image to achieve a certain goal and is a required step for many visualization and analysis methods.
INTRODUCTION
Discussion
An understanding of central nervous system function during states of health and disease depends critically on the ability to generate detailed and accurate anatomic maps of the entire vascular network that supplies this compartment. The translational study of cranial murine disease models requires a standardized visualization method that contextualizes the entire vasculature in situ relative to the surrounding anatomy, and would greatly advance understanding of neurovascular interfaces. In-vivo contrast-based angiography is standard for defining these relationships in living larger animals and humans. However, due to low resolution and artifacts of in-vivo image acquisition in mice, it is difficult to image and visualize cranial vasculature as it interfaces with related functional tissues, such as the brain, meninges, and skull.
As an alternative to in-vivo contrast-based angiography, casting of vessels with radio-dense polymers has traditionally been combined with tissue or organ dissection, digestion, and dye immersion, along with ex vivo image acquisition. Typically, high-density, radio-opaque polymer mixtures used in these methods are not optimized for arterio-venous transit, which limits their use to casting of either the arterial or venous system. Conversely, low-density radio-opaque polymers that cross capillary beds are not well visualized in imaging methods such as micro-computed tomography (Micro-CT) without prior isolation of the tissue and clearing or digestion, which can distort and/or destroy the gross or fine anatomy of the vasculature. In addition, these methods are limited by destruction of the sample tissue, limited perfusion, or inadequate visualization. While newer tissue clearing and immunostaining immersion-based visualization techniques, such as Clear Lipid-exchanged Anatomically Rigid Imaging/immunostaining-compatible Tissue hYdrogel (CLARITY) and light sheet microscopy, provide very high resolution, three-dimensional (3D), intact images, these methods may produce artifacts such as tissue deformation and illumination inhomogeneity. Further, these techniques still require dissection and removal of the brain, which can distort the anatomy and precludes the study of the entire cranial vasculature. While advances in tissue clearing and light-sheet microscopy have made it possible to image vasculature within bone or to survey large intact regions of mice for specific anatomic structures of interest, the processing in these methods requires specific considerations for downstream investigations such as histology, immunohistochemistry, and molecular genetic techniques, among others.
To visualize the entire murine in situ cranial vasculature in relation to the surrounding anatomy and preserve the sample for further investigation, a non-invasive, non-destructive visualization method combining 1) low-density polymer casting with arterio-venous transit, 2) iterative sample processing and Micro-CT, and 3) automatic deformable registration and three-dimensional visualization through the Neurosimplicity Imaging Suite is provided. The workflow enables non-invasive construction of a high-resolution three-dimensional map of murine cranial vasculature in relation to the brain, surrounding skull bone, and soft tissues.
Overview of Workflow for Visualization of Cranial Vasculature
To ensure capillary transit, an anticoagulant, heparin, is injected and the mouse is allowed to ambulate before atraumatic sacrifice. The descending aorta is then exposed and catheterized, and the inferior vena cava (IVC) is sectioned and sodium nitroprusside is perfused retrograde through the aorta until it exits the IVC. This step clears blood from and maximally dilated all vessels. Next, a low-density, radio-opaque polymer is perfused through the same catheter until it exits the IVC. Finally, the IVC is ligated and the skull exposed to visualize the diploic veins, and perfusion is continued until the diploic veins are visibly filled. This serves as the endpoint for intracranial filling of vessels.
Following curing and fixation, the sample is processed and imaged via Micro-CT at three stages to specifically capture the vascular cast, bone, and soft tissues. An initial Micro-CT is acquired before decalcification that shows bone and the vascular cast. The sample is decalcified to make bone radiolucent and then a second Micro-CT is acquired. This reveals diploic and emissary vessels within the bone and increases visibility of intracranial vessels. Finally, the sample is immersed in phosphotungstic acid (PTA), which binds protein in a concentration dependent manner and makes all tissues visible on a third acquired Micro-CT. The acquired Micro-CT data and the appropriate atlas (for example, the Allen Reference Atlas Common Coordinate Framework Version 3 (ARA CCFv3)) are then deformably registered to the same coordinate space. Features of interest including annotated brain regions, bone, and vessels are automatically extracted and visualized in three dimensions using an imaging application.
Iterative Processing Steps are Validated by Micro-CT
Multiple Micro-CT image datasets are acquired on the same sample following iterative processing to allow the visualization of specific anatomic features including vessels, bone, brain, and other soft tissues. Micro-CT is utilized following each step to determine successful processing, such as complete decalcification and diffusion of PTA. Micro-CT images are used to determine successful iterative processing.
Acquired Micro-CT is Registered and Visualized Together
With these three datasets, the first Micro-CT image is deformably registered with bone and vessel to the image of the decalcified sample. The Micro-CT image is also registered following PTA immersion to the image of the decalcified sample. Finally, all three of these scans are registered and displayed in the same space. This enables visualization of the segmented vessels, brain regions, and surrounding anatomy in three-dimensional.
To evenly cast all the vessels in the head, a method of systemic low-density polymer perfusion is provided. Low-density Microfil® may have advantages over other contrast agents in perfusion of both the intracranial arterial and venous vasculature. The method may be modified in three ways: 1) a lower density polymer mixture is used to ensure non-destructive capillary transit, 2) perfusion is retrograde through the descending aorta to ensure even filling of the anterior and posterior cranial circulation, and 3) a closed system is created to allow for backfilling of the venous vasculature of the entire head. While other polymers can be optimized for arterio-venous transit, Microfil® polymer may be used because others such as vinylite have unfavorable polymerization and curing properties including expansion and heat release that may damage fine vasculature. The exemplary perfusion method may be combined with Micro-CT showed the major cranial vessels in relation to the skull.
An iterative sample processing and Micro-CT approach to visualize the vessels within bone and neurovascular interfaces is provided. Following a first round of Micro-CT to visualize cranial bone and polymer-casted vessels, the same sample is decalcified and Micro-CT is repeated to generate an image of the isolated cranial vasculature. From this decalcified scan, a segmentation is rendered of the in situ cranial vasculature separate from bone. Next, the same sample is immersed in PTA and a third round of Micro-CT is performed to generate an image containing bone, vessels, and soft tissue. Exemplary methods then register, deformably and automatically, all three scans and the Allen Reference Atlas brain region annotations into the same space. Features of interest may be extracted for visualization of the brain, bone, and vessels using an imaging application according to the present technology.
Using only the first round of the workflow described above, abnormalities in cranial vasculature and surrounding bone in a mouse model of Pacak-Zhuang syndrome may be characterized. Through clinical investigations of patients with this syndrome, the vascular malformations in these patients may be recognized as primarily venous and involving both vessels of the brain and the rest of the head. However, further sample processing may be required to visualize neurovascular interfaces with casting and Micro-CT alone. Thus, the present technology provides a non-invasive, non-destructive iterative sample processing and Micro-CT workflow that allow visualization of vessels, soft tissue, and bone separately. The acquired data can be converted to Hounsfield units, a commonly used linear rescaling, if samples of water and air are also acquired with the same parameters on the same machine. Quantitative analysis and measurements, however, can be performed on the acquired data, which is measured in attenuation, because the relative densities of regions within the sample are still the same. An example of quantification that can be performed using the exemplary method includes measuring the length and diameters of the basilar arteries in wild-type mice and the mouse model of EPAS1-Gain-of-Function syndrome. This examination reveals that the mutant B2 and B3 segments of the basilar artery are significantly smaller than the wild-type.
The exemplary methods of the present technology, when combined with registration and three dimensional visualization, offers an unprecedented understanding of the anatomy, particularly neurovascular interfaces. Conventional imaging of vasculature in bone and evaluation of structures of interest over large intact regions of mice is possible in tissue clearing and light-sheet microscopy, these methods are still limited in visualizing all of the structures within the entire intact head, e.g., brain parenchyma, bone, and vessels. Further, while these methods are destructive and preclude further downstream investigation using standard methods such as histology, immunohistochemistry, and molecular genetic techniques, the present technology preserves the sample, enabling further investigations. Since the vasculature is not perfused with fixative in the casting method according to the present technology, fixation parameters can be chosen and optimized for additional tissue studies. The high-resolution in situ visualization afforded by this non-invasive, non-destructive approach should also aid future studies focused on analyzing regions of interest, such as specific neurovascular interfaces.
Maps of cerebrovsaculature at high resolution have been obtained by combining optical methods such as light sheet microscopy with tissue clearing methods. However, prior art methods used may require isolation of the brain from the bone and surrounding tissues. Recent advances in this methodology may allow visualization of vasculature within bone or evaluation of anatomy of interest over large regions of mice using light-sheet microscopy. However, these techniques still have unique sample preparation considerations for optimizing visualization of multiple markers of interest using antibody-based labelling and allowing for further downstream use of the sample. Exemplary methods of the present technology, which is non-invasive and non-destructive, utilize polymer to cast and define vessels and phosphotungstic acid to bind protein in all tissues in a concentration-dependent manner. These two nonspecific methods of labelling tissues therefore allow visualization of all structures within the head without removal of the brain. This method therefore allows study of the entire, intact cranial vasculature. In addition, by iteratively processing and imaging the same sample, the exemplary method can visualize the interfaces of vasculature with regions of tissues of interest in an unprecedented manner.
Using an exemplary tool for automated deformable image registration, feature extraction, and visualization, iteratively processed samples can be combined such that brain, bone, and vessels from the same sample can all be visualized in the same coordinate space. The present technology can handle raw data files including bitmap, TIF, and DICOM. Further, the tool can be used to automatically register the images from a sample to the anatomic parcellations of the ARA CCFv3, allowing brain-region-level annotation. Additionally or alternatively, other reference atlases can be used. Micro-CT enables intact, non-invasive, non-destructive visualization of the whole sample, and also higher resolution.
In conclusion, the present technology provides anon-invasive, non-destructive approach for visualizing the in situ murine cranial vasculature in its entirety with surrounding anatomy intact. The exemplary method improves upon shortcomings of past vascular casting and visualization methods by combining even casting of the entire cranial vasculature, iterative sample processing and Micro-CT, and automatic deformable registration, feature extraction, and visualization. This method enables development of 1) a murine cranial vascular reference atlas, 2) analytical parameters derived from this atlas, and 3) objective methods to standardize the evaluation of cranial vascular disease in murine models. The use of the present exemplary method, which can be applied to any tissue, allows for the rapid exploration and further understanding of normal and disease states.
The exemplary method provided herein is particularly suited for morphological, structural, and developmental studies of vasculature and surrounding anatomy. Using the exemplary vascular casting method, vascular malformations have been identified in a mouse model of Pacak-Zhuang syndrome that recapitulated findings in the in vivo human studies. Further, the exemplary method is not restricted to cranial tissue and can be applied to any organ or tissue of interest to perform similar analyses.
The present technology may also be used with unstructured data. In order to practice the method on unstructured data, unstructured data is first converted to structured data and then the remaining pipeline steps (including deformable registration) are performed on the structured data.
Conversion of unstructured data to structured data can occur in several ways. One way is conversion of tabular data to some two-dimensional or three-dimensional plot/graph/visualization. This visualization can then be used to perform some or all of the subsequent steps of the pipeline. Alternatively, structure can be imposed on unstructured data by sorting all rows by the value in a single column. This allows the sorted result to be processed directly since deformable registration and the other steps of the pipeline can be performed on data of any dimension; that is, even one-dimensional data (including tabular data) can be registered to other datasets of any dimension including one-dimensional data.
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A first example starts with two input unstructured datasets. Unstructured Dataset contains two columns with numerical values for Features and for Sample . Unstructured Dataset also contains two columns with numerical values for Features and for Sample . The exemplary method converts both of these datasets into structured data in the form of a two-dimensional plot. Processing for these datasets can involve removing outliers, normalizing values to their mean, among others. Feature extraction for these datasets can involve computing descriptive statistics including but not limited to mean, median, mode, variance, and interquartile ranges for Features and . Registration for these datasets can involve deformably aligning the two-dimensional visualizations to each other. Analysis for these datasets can involve statistical comparison of descriptive statistics between Unstructured Dataset and Unstructured Dataset and identifying variations between the two-dimensional structured representations of these datasets. Interactive visualization for these datasets can involve displaying the two-dimensional structured representations of the input unstructured datasets in the same space and in their native space.
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A second example also starts with two input unstructured datasets. Unstructured Dataset contains 2 columns with numerical values for Features and for Sample . Unstructured Dataset also contains 2 columns with numerical values for Features and for Sample . Structure is imposed on the unstructured datasets by sorting all rows by the values for Feature . The exemplary methods discussed above regarding structured data may then be applied to this structured tabular data. Similar to the example above, processing for these datasets can involve removing outliers, normalizing values to their mean, among others. Similar to the example above, feature extraction for these datasets can involve computing descriptive statistics including but not limited to mean, median, mode, variance, and interquartile ranges for Features and . For these datasets, registration can involve deformably aligning each corresponding one-dimensional dataset from Unstructured Datasets and . Feature from Unstructured Dataset is deformably aligned to Feature from Unstructured Dataset and Feature from Unstructured Dataset is deformably aligned to Feature from Unstructured Dataset . Analysis for these datasets can involve statistical comparison of descriptive statistics between Unstructured Dataset and Unstructured Dataset and identifying variations between the two-dimensional structured representations of these datasets. Interactive visualization for these datasets can involve displaying both the structured tabular data and two-dimensional structured representations of the input datasets in the same space and in their native space.
While the above methods cite tabular data with numerical values, the above methods could apply to tabular data with arbitrary values including text.
The above description is illustrative and not restrictive. Many variations of the technology will become apparent to those of skill in the art upon review of this disclosure. The scope of the technology should, therefore, be determined not with reference to the above description, but instead should be determined with reference to the appended claims along with their full scope of equivalents.
SUMMARY OF THE INVENTION
A method for automated analysis of data obtained from biologic, or non-biologic, material is provided. The method includes extracting, in a visualization of the material, first shapes that combine to form a target shape. The method also includes registering the first shape of the target shape to second shapes of a generic shape, and identifying variations between the first shapes and the second shapes.
The registering of the first shapes of the target shape to the second shapes of the generic shape may include identifying marker points in the first shapes that correspond to generic marker points in the second shapes, and aligning the first shapes and the second shapes based on a first optimization function. The registering may also include matching a first contrast of the first shapes with a second contrast of the second shapes by masking at least a portion of at least one of the first contrast and the second contrast. The registering may further include deforming at least one of the first shape and at least one of the second shape based on a second optimization function.
The method may include, prior to the extracting operation, processing input data associated with the visualization by rotating the visualization to a standard orientation, homogenizing an intensity across the image, and/or eliminating artifacts.
The method may include validating the registration by comparing an extracted feature from the visualization to a further extracted feature of a further visualization.
The identifying operation may include identifying local changes within the first shapes and the second shapes, and evaluating the registering using a similarity metric.
The method may include displaying a further visualization of the target shape with data associated with the generic shape as a three dimensional representation. The data associated with the generic shape may be displayed in the further visualization of the target shape in layers selectably displayable by a user. The data associated with the generic shape may include name, function, and connection identifications. The variations between the first shapes and the second shapes may be displayed in the further visualization and may be identified as abnormal based on a model.
The first shapes may include first graphlets, and the first graphlets may include first nodes and first segments. The second shapes may include second graphlets, and the second graphlets may include second nodes and second segments. Alternatively, the first shapes may include first volumetric objects, and the second shapes may include second volumetric objects.
The generic shape may be received from an atlas, and the visualization of the target shape may be obtained by Magnetic Resonance Imaging, Computerized Tomography scan, or a radiologic scan.
The method may include extracting, in a further visualization, third shapes of a further target shape to form a further target shape. The method may also include registering the third shapes of the further target shape to at least one of the first shapes of the target shape and the second shapes of the generic shape.
A system for analyzing biologic material is provided that includes an extraction engine running on a processor coupled to a memory. The extraction engine extracts, from a visualization of the biologic material, or alternatively, non-biologic material, first shapes that combine to form a target shape. The system may also include a registration engine running on the processor. The registration engine registers the first shape of the target shape to second shapes of a generic shape of a generic shape.
The system may further include an identification engine running on the processor. The identification engine identifies variations between the first shapes and the second shapes. The system may include a validation engine adapted to validate the registration output by the registration engine by comparing an extracted feature from the visualization to a further extracted feature of a further visualization.
The system may include a display adapted to display a further visualization of the target shape with data associated with the generic shape as a three dimensional representation. The data associated with the generic shape may be displayed in the further visualization of the target shape in layers selectably displayable by a user. The data associated with the generic shape may include name, function, and connection identifications. The variations between the first shapes and the second shapes may be displayed in the further visualization and may be identified as abnormal based on a model. The system may include an atlas adapted to provide the generic shape and a database for storing the visualization of the target shape.
A non-transitory computer-readable medium storing a program for analyzing biologic, or non-biologic, material is provided. The program includes instructions that, when executed by a processor, causes a processor to execute any of the methods described herein, and/or operate any of the systems described herein.
Understanding physiologic and pathologic organ system function such as in the central nervous system depends on the ability to map entire in situ vasculature and organ interfaces, e.g., cranial vasculature and neurovascular interfaces. To accomplish this, a method and system are provided that combine a non-invasive workflow to visualize murine cranial vasculature via polymer casting of vessels, iterative sample processing and micro-computed tomography with automatic deformable image registration, feature extraction, and visualization. This methodology is applicable to any tissue and allows rapid exploration of normal and altered pathologic states
According to exemplary embodiments of the invention, the following processes may be performed automatically:
process structured or unstructured data of any dimension from multiple modalities/sources to generate visual representations of data or images;
fuse, or integrate multiple images from different (or same) modalities by performing nonlinear (or linear) registration;
extract (or segment) any feature(s) of interest, which may include but is not limited to organ(s) or any other anatomic regions or structures, from images generated from different (or same) modalities;
build or update a compendium of reference object(s) of interest (also referred to herein as an atlas);
analytically and quantitatively compare data (for example, if medical imaging, of the same or different patient and from the same or different timepoints);
analyze and compare extracted object(s) to the atlas, while also updating the atlas in order to automatically detect anatomic malformation and deviation, creating a report for that object; and
visualize (or render) objects extracted from images and their corresponding analytic reports in a shareable, interactive tool.
The order in which is these steps is performed can be modified to suit the information provided and the application. Exemplary embodiments of the present technology extract, analyze, interpret, and visualize information from within the same dataset, data from different sources, acquired at the same time-point or different time-points, from the same or different objects all in the same visualization. This allows for visualization and also, when performing this across longitudinal data or different samples/patients or modalities, exemplary embodiments enable analysis and comparison. This is possible due to the methods and systems described herein for application of automated processing, registration, feature extraction, analysis, validation, and visualization.
Exemplary embodiments of the present technology enable identifying and utilizing features from structured and unstructured data. For example, to obtain a network from vessels from an image of biological material, several things need to be done, including morphological operations and feature extraction using, for example, thresholding-based segmentation methods and deformable registration between multiple images that may include one or more reference atlases. It is important to note that in some instances the order of these steps may vary, as a reference atlas may not be necessary, and different features may be extracted. Vessels can be extracted from an image by simple thresholding if they are the only feature in the image, and that vessel segmentation can then be used to generate the network which is then registered and compared with other networks, including the atlas. However, if vessels are not the only extractable feature in the image, which may be the case in CTs of the head, then not only are more complicated processing steps required, deformable registration to other atlases may be required to pull out those other features first. An atlas may be an available annotated atlas, for example something an expert has created, or may be any other image used for reference in registration. The atlas may be the image to which the first image is deformed or registered.
Exemplary embodiments of the present technology enable handling of multiple types of data through multiple processing steps to enable extraction of certain features. For example, if both vessels and bone are in the image, a bone atlas can be generated from other bone-containing imaging data to register to the image that contains both vessels and bone, to then extract bone. In this way, vessels may be pulled out as a remaining extractable object in the image.
An exemplary method may include the following steps:
1. Input data
2. Cross-modal Deformable Registration of data (invertible and batch)
3. Feature Extraction
4. Building Atlases by combining Registration and Feature Extraction
5. Having each object be separate when extraction allows us to interact with, manipulate or correct individual objects or sub-objects.
Incorporating the above steps in a pipeline (also referred to herein as a workflow pipeline, a workflow, and/or a method) allows for automated analysis and visualization of objects, their sub-objects, and corresponding input data or intermediate outputs. This includes the superimposition of input data, three-dimensional extracted objects, visualization of analysis and reported data, and additional user-specified or process-defined outputs in the same space.
For example, an output of an analysis may be a two-dimensional heatmap of volume change per region of a brain between one image dataset registered to one or more corresponding datasets. The present technology can generate a three-dimensional spatially relevant heatmap that is separated by objects using the same separation criteria as the original object through feature extraction and registration. The present technology also can overlay this output three-dimensional analysis back on the output objects obtained through feature extraction and registration. In this way, The present technology is able to show in an interactive three-dimensional visualization how a sample compares to either other samples or the atlas generated during the batch analysis.
The Cross-modal Deformable Registration of data process may enable a “many” to “many” relationship between the image and object attributes. e.g.:
1. the same object at different timepoints
2. a different object at different timepoints
The Feature Extraction process can be done either on the base data or post-registration data. Once the registration is complete, the calculated transformation may be applied, which identifies how one image differs from another, with respect to the extracted feature or globally across the whole image. This enables further analysis for the extracted feature, either individually or in a batch process.
Shape analysis for extracted objects is also provided by the present technology, analogously to the network based analysis. Further variations include statistical analysis, intensity analysis, and more. The present technology is not limited to MRI, CT, or similar imaging, but can incorporate microscopic data including histology and light-sheet microscopy as well as structured and unstructured data across other domains.
BRIEF DESCRIPTION OF THE DRAWINGS
The invention is described in more detail with reference to the accompanying drawings, in which only preferred embodiments are shown by way of example. In the drawings:
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is a flowchart illustrating an overview of the exemplary method for automated processing, registration, feature extraction, analysis, validation, visualization, and interaction with structured and unstructured data;
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is a flowchart illustrating a method for determining variation in shapes according to an exemplary embodiment of the present invention;
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is a flowchart illustrating a method according to an exemplary embodiment of the present invention; and
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is a schematic diagram of computing system used in an exemplary embodiment of the present invention.
DETAILED DESCRIPTION
Example—Medical Image Evaluation
The present invention pertains to a method and system of handling, processing, registering, analyzing, visualizing, and interacting with structured or unstructured data. The data may be of biologic or non-biologic material. An embodiment of this process includes a method for iterative processing and data acquisition of biologic material and input of this data into the method and/or system.
The exemplary method and system may be used with other sources of data that are not biologic material, such as quality control steps in manufacturing. One such embodiment may include 1) the generation of a physical model from imaging data, 2) imaging this physical model, 3) inputting this imaging data into the system to register it back to the original image to ensure that what has been generated is accurate to the original data. In some alternative exemplary embodiments, patient imaging data may be used, such as for production of a mechanical heart valve or a cranial bone replacement. In still further exemplary embodiments, the system and method described herein may be used in the production of other manufacturing parts. Consequently, an exemplary application of the present technology enables production and quality control for production of any part via imaging of the produced part and comparison with original source data.
Regarding processing of data, image registration may be enabled by a homogenous distribution of intensity in the image such that intensity differences represent true differences. Feature extraction (e.g. segmentation) may be enabled by enhancement or differentiation of the feature(s)/object(s) of interest from other feature(s)/object(s) in the image. Visualization may be determined based on fidelity to the true shape/structure of the object being imaged.
The exemplary system and method may output a shareable interactive report and/or data, which may be used for medical imaging by healthcare providers and/or scientists. The reports and/or data may be used for visualizing and interacting with multiple different modalities of images in the same space and identifying variation in biologic tissues or non-biologic structures. The reports and/or data may also be used for surgical navigation and or robotic surgery for any one of surgical planning, visualization, and/or annotation.
In regard to use of the exemplary methods and systems for manufacturing, the reports and/or data may be used by quality control engineers, artificial intelligence, and/or an autonomous system that does not require a human viewing the output. In this context, the reports and/or data may be used to validate pipeline processes, for quality control and/or assurance, and/or to identify variation in manufactured items.
A non-invasive workflow is provided to visualize in situ vasculature and surrounding anatomy of organ systems such as the murine cranial vasculature, brain, skull, and soft tissues that involves 1) terminal polymer casting of vessels, 2) iterative sample processing and imaging with multiple modalities including micro-CT, and 3) automated deformable cross-modal image registration, feature extraction, and visualization. While developed on cranial vasculature, it can be applied to any image of an organ with contrast such as a polymer-casted organ imaged on micro-CT.
Current methods of visualizing vasculature are limited by 1) poor resolution using in vivo contrasted imaging, 2) invasive or destructive tissue preparation with many ex vivo methods, 3) or lack of relationship of the vasculature to the surrounding anatomy in traditional visualizations of polymer casting. An exemplary embodiment of the workflow, which combines polymer casting, iterative processing and imaging of the same sample, and deformable registration to combine these data, allows visualization of the fine detailed vascular map in the context of the surrounding anatomy in situ.
Exemplary embodiments of the method and system is broadly applicable to many fields. Exemplary embodiments provide a non-invasive visualization of murine cranial vasculature in its entirety with the surrounding anatomy intact, automatically registers cross-modal imaging data, extracts features, and performs analysis. A novel non-invasive approach involving polymer casting of vessels, iterative sample processing and microcomputed tomography (micro-CT), and automatic deformable registration/visualization to construct a high-resolution three-dimensional atlas of murine cranial vasculature in relation to brain, meninges, and surrounding skull bone. The ability to generate detailed and accurate anatomic maps of the entire vascular network that supplies the cranial compartment will greatly advance central nervous system (CNS) research focused on states of health and disease. Even more importantly, this approach can be used to rapidly generate complete vascular maps in any tissue throughout the body.
The methodology allows visualization of all cranial structures and can improve understanding of vascular interfaces that maintain CNS tissue homeostasis as well as alterations that appear during development of neurologic diseases. For example, exemplary methods can be used to automatically detect pathological variation from normal anatomy, identify regions of vascular damage/repair, and detect regions of vascular connectivity that would otherwise be missed with more invasive approaches.
The present technology uses algorithms and software tools to process data, including for example converting unstructured data to structured data. Exemplary embodiments may convert relevant input data, whether structured or unstructured, into an image for subsequent analysis.
Processing for Image Registration
For automated image registration to produce accurate results, the images that are being registered to each other should have some correspondence (for example polynomial intensity) and homogenous spatial distribution of intensity. To accomplish this, a standard intensity inhomogeneity correction method designed for MR imaging can be used. This method can be applied to any imaging modality. Any other processing methods may be used to enhance correspondence between images.
Processing for Feature Extraction
Prior to extracting features of interest, there are processing steps that are typically applied to the image to enhance the separation between the features and/or objects of interest and the remaining image content. For example, to extract blood vessels from an MRI with contrast, a vessel enhancement filter such as the Frangi filter may be used, followed by thresholding to extract the vessels. Current image processing systems and methods require manual intervention and subjective evaluation of the results whereas the exemplary method is fully automated with quantitative evaluation of final outputs without the need for manual intervention. A series of filters may be applied in an automated fashion without the need for manual validation at each step. The present technology combines these image processing steps in a fully automated fashion with the rest of the system and method including feature extraction.
Processing for Visualization
Prior to visualization, it is sometimes required to process imaging data so that the image quality improves. This can be subjective, but in the present system and method quantitative metrics are used that do not require subjective evaluation. One embodiment of a visualization in the present technology may be a full-featured web-based, interactive, and shareable visualization method.
Image Registration
Image registration is the process of computing a transformation that aligns two or more images (for two images, a moving and fixed image, where the moving image is the image being transformed) to each other typically based on manual landmarking of corresponding points and/or pixel/voxel intensity values (landmark free). The produced transformations are typically global (rigid/affine) or local (deformable), via displacement field transformations.
A rigid transformation is a global transformation of an image (affects all pixels/voxels in the image in the same way) that can include translation and rotation (i.e., rigid transformations preserve lengths and angles). An affine transformation is a global transformation of an image that can include translation, rotation, scale, and shear components. A deformable transformation is a local transformation of an image and can produce a different translation, or displacement, for every pixel/voxel in the image. Deformable registration algorithms produce much more accurate transformations than affine or rigid transformations because they can more accurately align local regions of images whereas affine and rigid transformations are global. Deformable registration allows 1) inter-patient registration and 2) longitudinal intra-patient registration and analysis since there are many local changes that may occur in organs of interest over time within the same patient and across patients. Affine and rigid transformations do not allow for this kind of local analysis.
Registration may also be performed by any of the methods described in the paper “CloudReg: automatic terabyte-scale cross-modal brain volume registration”, Vikram Chandrashekhar, et al., Nature Methods, Aug. 1, 2021.
Optimization
Automated image registration requires an image quality metric to determine if a given transformation is optimal. In particular, when image registration is done using pixel/voxel intensity values, an image similarity metric is used to determine the quality of alignment and is iteratively minimized. For intra-modality (within modality) registration, a mean squared error (MSE) metric (squared difference of image intensity) is typically used. For inter-modality (cross modality) registration, a mutual information (MI) error metric is typically used. MI is a metric that relies on the intensity distributions of the two images and therefore operates on histograms of image intensity whereas MSE operates directly on each voxel in the image, producing an error signal at every voxel.
CloudReg, an open-source registration tool under an Apache 2.0 license, uses an image registration cost (or objective) function is created that enables inter-modality registration, like MI, while also producing a per-pixel/voxel error signal, like MSE. This per pixel/voxel error signal is used to enable Inter-modality registration by computing a spatially-varying (per pixel/voxel) polynomial intensity transform from one image to another. This makes possible registration between two images whose intensity distributions can have arbitrary relationships (e.g., corresponding structures in the image can have opposite intensity distributions in local regions of the image). This registration algorithm enables integration of images and information extracted/segmented from them. However, to apply the registration algorithm, the images need to be pre-processed to remove artifacts/artefacts (undesirable alterations to an image due to the physical principles of the technique or damage from sample preparation) unique to each imaging modality with which the images are acquired.
Validation (Manual Landmarking/Segmentation)
Since registration methods cannot be validated using the same image similarity metric used for optimization, validation of registration accuracy is typically computed on the whole registered images either by using corresponding points placed on the images (manual landmarking) or by using corresponding objects segmented from the images (overlap metrics). The transformations computed from the registration method are applied to one set of points (or labeled regions) to bring both (or more) sets of points (or labeled regions) into the same coordinate space. The resulting Euclidean distance between corresponding pairs of points can give an estimate of the registration accuracy in physical units (e.g., millimeters). For corresponding labeled regions, an image overlap metrics is computed including the Intersection over Union (IoU) score, dice coefficient, or F1 score, among others. IoU is a number between 0 and 1 that is the sum of the number of pixels/voxels that are overlapping in both regions divided by the sum of the number of pixels/voxels in both regions. Dice coefficient and F1 scores are scaled versions of the IoU score.
Manual landmarking methods only provide limited assessment of registration accuracy because for deformable transformations, there can be different transformations locally at different locations in the image. Therefore, the manual landmarking method can only sample the true registration accuracy at/around the locations where the landmark points are placed. Manually labeling corresponding regions of the image can address these drawbacks present in landmark accuracy but are significantly more time-intensive and manual processes. These limitations necessitate the development of a novel validation approach.
Registration
A novel automated way to validate image registration in combination with the rest of an exemplary workflow pipeline is provided. The same structures, which can be either from the same sample or different samples, can be imaged using different modalities. Exemplary embodiments segment/extract the same structure from both images from different modalities. The segmented/extracted objects can be transformed to a same space using the transformations computed by a registration algorithm according to the present technology. The objects can be compared to each other using object similarity metrics which include but are not limited to dice coefficient, Intersection over Union (IoU), precision, and recall. Quantitative metrics may be used to assess registration quality as compared with qualitative assessment via visualization.
For example, given an MRI and CT with and without contrast for a single patient, blood vessels from the contrasted images may be segmented and the registration algorithm used to register all the different modalities to each other and display them in the same coordinate space. The segmented blood vessels from the MRI and CT images should match up when transformed to the same coordinate space since they are images of the same object. This built-in correspondence may be used to automatically validate registration accuracy by computing dice coefficient, IoU, or a related overlap metric.
Feature Extraction
Feature extraction, which can include segmentation, from an image is the process of designating a pixel/voxel or group of pixels/voxels that represent a region or volume of interest. This region or volume of interest can be used to create an object (extracted volumetric representation of compiled two-dimensional data). This can be done in a manual or semi-automated fashion.
Manual feature extraction is typically done with a graphical user interface (GUI)-based computer program which allows for delineation of structures from imaging data using a mouse and keyboard connected to a computer. This requires a skilled person to perform the entire process and, for volumetric imaging, requires identifying the region or volume of interest on every two-dimensional slice. This may be an extremely time consuming and subjective process.
While semi-automated feature extraction algorithms, which automate portions of the process, for example, by providing an initial guess of the feature to extract, reduce the amount of manual intervention required, these algorithms are still primarily manual processes. For example, ITK SNAP is a semi-automated segmentation tool for two-dimensional/three-dimensional imaging data that still requires manual intervention at each step.
The present technology builds on the existing methods by combining a variety of processing steps to extract features of interest from imaging data in a fully automated fashion. The exemplary method can generalize well and, in most embodiments, does not require manual intervention as it is a combination of operations applied to the input data.
Build Reference Atlas
A reference atlas for imaging data is an “average” representation of data acquired from images of many different individual objects of the same type. Reference atlases may also contain associated parcellations (or divisions) of the object into sub-objects typically obtained via manual segmentation. Because of these parcellations, reference atlases serve an important role in understanding normal and abnormal morphological (shape-based) variations in objects.
Many reference atlases today are a series of two-dimensional images or reconstructed three-dimensional volumes from serial two-dimensional images parcellated into meaningful regions. Given this, the current process of understanding morphological variations is highly subjective and manual, requiring an expert to compare imaging of a new subject to the atlas on a per slice basis. Newer reference atlases are created with volumetric imaging and parcellated into meaningful regions. For example, there exists a volumetric mouse brain imaging reference atlas with associated brain region parcellations called the Allen Reference Atlas (ARA). There also exists, for example, a volumetric human brain MRI imaging volume that represents many brain images that have been registered to each other, averaged, and parcellated into brain regions.
Newer reference atlases with volumetric imaging and parcellations can be combined with deformable registration to automatically segment newly imaged objects of the same type by region and analyze morphological changes based on the computed transformations.
Exemplary embodiments of the present technology create reference atlases in combination with the rest of the workflow pipeline. To analyze an imaged structure of interest, a reference atlas is needed to determine the deviation of the imaged structure from what is considered “normal”. If a reference atlas does not exist for a given structure, the present technology can aggregate many images, along with corresponding structured or unstructured data, of that structure to create a reference atlas of what is normal for that structure. This reference atlas can be updated with each additional image that is obtained using deformable registration methods described above.
The reference atlas and deformable registration may automatically extract a feature of interest from an image in combination with the rest of the workflow pipeline, particularly the morphological/shape analysis.
If a reference atlas already exists for an object of interest, that reference atlas may be used to perform the subsequent steps below. In one embodiment, a reference atlas of the skull in the human head may be created given CT images of human heads. A threshold-based method may be used, among other filters, to extract the skull from the image and create a mesh representation of the skull. Each skull mesh in the dataset would then be deformably registered to the other skull meshes to produce an average mesh. The volume change at each surface in the mesh can be represented in three-dimensional using a color scale and may contain statistical output including but not limited to mean, and standard deviation information at each face in the mesh. This average mesh may be used as a reference atlas for the human skull.
Alternative exemplary embodiments for extracting features may utilize machine learning to identify abnormalities directly, possibly without using a threshold. Additionally or alternatively, a model may be utilized to extract features, and may include a threshold-based model, a machine learning model, and/or a statistical atlas-based model.
Analysis
There are many ways to analyze extracted features of interest from imaging data and they can vary depending on the application. Typically, this involves taking manual measurements (distances, volumes, etc.) of the extracted features or in the source imaging data.
When combined with image registration, extracted features of interest can be analyzed in an automated and quantitative fashion across the whole image. Using the transformations produced by deformable registrations, local volume changes across an entire object can be determined and categorized by region. Variation between two shapes may be evaluated by computing the local volume change across whole shapes, and this volume change can be compared to a generic shape or otherwise assessed.
Other types of data besides imaging can also be analyzed, for example, graph (or network) objects. A graph is mathematical object that consists of a set of nodes and edges between those nodes. A graph can be used to represent many-to-many relationships like those present in social media networks, neurons/regions in the brain, relationships between species, among many other examples.
Exemplary embodiments: 1) combine deformable image registration with reference atlas creation; and 2) apply shape analysis, which may include connectivity analysis of graph representations, to automate morphological analysis of said objects (determination of normal and abnormal variations).
Shape Analysis
Image registration produces a transformation, or a displacement field, where each pixel/voxel in the image can have a unique displacement (translation vector in X,Y,Z to move that pixel/voxel to its new location in the transformed image). This displacement field can be analyzed by computing its volume change at every pixel/voxel in the image. When combining this with parcellated reference atlases, the total volume change by parcellated region of a reference atlas can be computed after it has been transformed to the input data.
Shape analysis can be defined as morphological analysis of objects in any number of spatial dimensions (e.g. volume change analysis) including networks. One embodiment of shape analysis according to the present technology may have two steps. First, the object is converted, which may include organs or other anatomic regions of interest, into a volumetric mesh (if three-dimensional data). The second step may be a comparison to and update of the reference atlas for the corresponding object. As an example of comparison to a reference atlas, normal and abnormal volume changes can be determined based on typical distributions of volume changes in those regions. To compare objects of the same type, statistical analyses are performed including, but not limited to, comparison of parcellated regions of the objects, specifically to look for regions of difference between the object and the corresponding reference atlas entry. The resultant shape statistical profile is used to update the corresponding atlas and is compared with the atlas to provide automated anatomical malformation and deviation detection.
Another embodiment of shape analysis is connectivity analysis. Connectivity analysis according to the present technology may have three central steps. First, the object of interest, for example vasculature, is converted into a skeletonized form. A skeleton of an object is a 1 pixel/voxel-wide representation of an object (e.g., a stick figure representation of the human body). During, the process of skeletonization, object attributes, including the thickness/radius information, are preserved and included as node or edge attributes in the following step. Second, the skeleton is converted into a graph. In order to generate a graph, at least two pieces of information are needed: the list of nodes, and the list of edges (connections between nodes). The list of nodes may be generated from the voxels comprising the vascular segmentation, and the list of edges may be generated from a thresholding-based nearest neighbor method or any similar edge-finding method. This graph may be further simplified by only representing bifurcation points, for example, as nodes. The last step is comparison to and update of the reference atlas (for example, a reference atlas for vascular networks). To compare vascular networks, graphlets, which are small repeatable subgraph units, are counted. A subgraph is a set of nodes and associated edges for a subset of the graph. Each graphlet represents a unique connectivity configuration. For example, this could be a small vascular region. Graphlet counts and ratios of different graphlets, which may or may not have the same number of nodes and edges, are calculated across the entire vascular graph in order to generate a vascular graph profile for that individual sample. This graph profile is then used to update the atlas and is compared with the atlas in order to provide automated vascular malformation and deviation detection.
The exemplary embodiment discussed above related to vascular connectivity analysis, however the methodology can apply to any type of shape or connectivity data including axonal pathways in the brain (e.g. from diffusion tensor imaging (DTI)).
Visualization
Visualization of data is displaying it or any processed version of it so that it can be viewed. There are existing methods for visualization. These existing methods present challenges including difficulty displaying and interacting with very large data. There are existing methods that perform some subset of the above steps including processing, registration, segmentation, analysis, and visualization but they still require manual intervention and lack generalizability to other types of data (objects/modalities/organ systems) [miracl, 2,3,4,5,]. The next step in the exemplary workflow pipeline involves visualization of all the following in the same coordinate space: registered multi-modal imaging data, their associated segmentation(s), and their respective object profiles in an interactive, web-based visualization. The present technology combines this feature with the rest of the workflow pipeline and fully automates the process end-to-end.
In the case of medical images and segmenting blood vessels, for example, the visualization will contain a three-dimensional display of all registered images and associated object(s) of interest including the network and abnormalities.
Exemplary embodiments of the present technology provide a system and method for evaluating a medical image. Given four volumetric medical images of the same patient without significant time (for example, less than 3 months) in between scans. These may be MR and CT images with and without contrast within the blood vessels. These four acquired images are the inputs to the following steps in this embodiment of the exemplary system and method. The following steps do not necessarily need to happen in sequential order, some steps can be performed in parallel or out of order.
1.1 Pre-Processing
Both the non-contrasted and contrasted MR images may be intensity corrected prior to registration, segmentation, and visualization. The contrasted MR image will be additionally processed by the Frangi filter to highlight the contrasted vessels.
Both the non-contrasted and contrasted CT images will be intensity corrected prior to registration, segmentation, and visualization. CT images will also be processed to remove CT-specific artifacts including but not limited to ring, windmill, and beam hardening. The contrasted CT scan is processed to enhance vessels using a combination of filters including but not limited to the Frangi filter.
1.2 Registration
The intensity corrected MR image without contrast is registered to a human brain atlas (MNI atlas for example) using deformable image registration methods. The intensity corrected MR image without contrast is also rigidly registered to the intensity corrected MR image with contrast. The intensity corrected MR image with contrast is registered to the CT image with contrast. The CT image without contrast is registered to an existing human skull atlas (or one is created using an average of many samples). The CT image without contrast is rigidly registered to the CT image with contrast.
1.3 Segmentation
A final visualization according to the exemplary method and system will contain, but is not limited to, renders of the brain (segmented by region), bone (segmented by region), and vessels of the head (segmented by name and type). Segmentation of the brain by region is enabled by the exemplary deformable registration of the MR image without contrast to a parcellated reference atlas. The registration produces a labeled parcellation of the input MR image without contrast. Segmentation of the bone is done via registration to a skull atlas (if one exists) or from the CT image without contrast directly and is performed using denoising, thresholding, and morphological operations. Segmentation of the vessels of the head is performed using thresholding and morphological operations applied to the pre-processed MR and CT images with contrast.
Validation of the vessel (or brain/bone) segmentation algorithm is performed by manually/semi-automatically segmenting the structure of interest across a predetermined number of samples to obtain its accuracy.
1.4 Build Reference Atlas
Exemplary embodiments of the present technology use the segmentation algorithm discussed above to segment vessels, skull, brain, and other structures of interest from the appropriate input image. A registration algorithm to register each component to a corresponding reference atlas or create one and iteratively update it with each new set of patient MR and CT scans. There exist reference atlases for brain. Reference atlases with associated volumetric imaging data for the vessels of the head and the skull may not be available. Exemplary embodiments of the present technology may be used to create these atlases using large groups of imaging data and parcellating them into meaningful regions/vessels/bone.
As each vessel segmentation from a new patient is obtained, it is deformably registered to the current reference atlas of the vessels which is updated based on the variation present in the new vessels.
1.5 Analysis
Exemplary embodiments of the present technology apply skeletonization and graph generation to the segmentation of the vessels of the head. By combining this with registration and reference atlas information, the present technology can automatically detect vascular malformations, compute volume differences across the whole brain and by specific regions, and compute volume differences across the whole skull and by specific regions (among other possible analyses). The analyses are used to create a report of malformations and other anatomical abnormalities and is prepared for visualization.
1.6 Visualization
Visualization is performed using a web-based, interactive GUI, like Neuroglancer, but with added functionality including real-time computed layers for rendering and real-time pixel-perfect annotations with a custom state-saving function to enable link shortening and sharing of views to medical imaging data in a HIPAA-compliant fashion.
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is a flowchart illustrating an overview of method for automated processing, registration, feature extraction, analysis, validation, visualization, and interaction with structured and unstructured data. The flow in method begins at operation which is an input of structured and/or unstructured data. From operation , the flow proceeds to operation , which is a pre-processing step. Operation includes performing an initial processing on the structured and/or unstructured data to enable subsequent processing/analysis. From operation . Operation is a registering operation, which may include transforming all the input data to the same space by using extracted features, and/or may include a transformation to extract features from the input data. Operation may further include aligning two or more data elements and/or objects of any dimension with one another, to identify a correspondence. Operation may include identifying and highlighting features of interest within the input data using the transformations from operation , and/or may include extracting features of interest directly from the input data, for instance by identifying and isolating data and/or objects.
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The flow of method may proceed from operation to operation , or from operation to operation , which indicates to co-register data and extracted features. The flow from operation may proceed from operation to operation , from operation to operation , or from operation to operation , which indicates to combine the processed data with an atlas, or to update the atlas using the processed data. Operation may further include creating or updating a consensus object for each feature and/or object extracted from the input data. From operation , the flow in method proceeds to operation and/or to operation , which indicates to perform shape analysis. The shape analysis of operation may include determining a variation in extracted objects relative to a consensus object, for example from an atlas.
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Operation outputs data to operation . From operation , the flow proceeds to operation , which indicates a validation step. The validation step ensures that the previous processes produce meaningful, accurate results, and may include evaluating any image similarity metric, for example those discussed above. In method , operation outputs to operation when operation indicates the analysis is not valid, and operation outputs to operation when operation indicates the analysis is valid. From operation , the flow then proceeds to operation , which indicates to change the parameters and repeat the method. The flow from operation proceeds to operation . From operation , the flow then proceeds to operation , which indicates to display the data. The displaying operation may include displaying input data, extracted features and/or objects, and/or analysis in the same space, for example in a single image include selectable and variably visible layers. From operation , the flow proceeds to operation , which indicates to provide an interactive visualization for the user. From operation , method proceeds to operation , which enables the user to share the visualization and/or the data. Operation the flows to operation , which provides a shareable interactive view.
Data is modified, processed, and transformed in exemplary methods. For example, microCT images that are input may be reoriented by rotating the image(s) to a standard orientation. Other examples of modifying/processing/transforming include homogenizing the intensity across the image, eliminating artifacts, etc.
Validation of registration and the other pipeline steps using the same extracted feature that is present in multiple separate input scans. This is the same feature or multiple different features (e.g. vasculature or vasculature and bone from the same person) imaged with multiple different modalities (e.g. MRI, CT, PET, Ultrasound, etc). For example, four different scans may be uploaded in which some scans contain brain only, some contain bone, vessels, and brain, some contain bone and vessels, and some contain vessels. Exemplary embodiments validate the end result by transforming all scans to the same space and then comparing the overlap between bone in the scans that contain bone, brain from the scans that contain brain, and vessels from the scans that contain vessels. These comparisons would provide validation for all the steps of the exemplary process.
This process is explained by the following example. With two images in which the first image has a line and a box and the second image has a line only, but the same line as is in the first image. The exemplary method may extract the box and line from the first image, and extract the line from the second image. In addition, if there is overlap between the box and the line in the first image, the registration to the second image containing the line can be used to determine the location of the box in the first image. The first image may be registered to the second image by putting both the first image and the second image in the same space. To validate, the exemplary method compares the line from the second image to the line from the first image when they are both in the same space. A perfect registration would mean perfect overlap of the line between the first image and the second image. Any deviation from this would indicate misalignment. This misalignment may be compared by a threshold deviation value, form a basis for a deformation, or may be used to evaluate the registration.
Another example also used a first image and a second image, in which the first image has a line, box, and circle, and the second image has the same line and the same box. Exemplary methods may extract the box, line, and circle from the first image, and may extract the line and box from the second image. Similar to the example above, if there is overlap between the circle and either the line or box, the registration of the second image to the first image can be used to determine the location of the circle in the first image. Exemplary methods may register the first image to the second image by putting both the first image and the second image in the same space. In this case, to validate, the line and the box from the second image are compared to the line and the box from the first image. In this case, a perfect registration would mean perfect overlap of the line and the box between the first image and the second image, and any deviation from this would indicate misalignment.
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is a flowchart illustrating method for determining variation in shapes according to an exemplary embodiment of the present invention. The flow in method begins with operation , which includes receiving input data related to extracted features, for example vasculature, a skull, a brain, etc. From operation , the flow proceeds in parallel to operations and . Operation indicates to generate a graph, and includes converting the extracted feature and/or generated object to a graph representation. Operation indicates to generate an object, and includes converting the extracted feature and/or generated graph to an object. Operations and may bilaterally exchange data, and both may output to operation , which generates an analysis, including performing shape analyses on the generated objects and/or graphs. The analysis may involve creating structured and unstructured outputs from a shape (defined herein as including at least objects and graphs) to characterize the shape and enable comparison with other shapes. From operation , the flow proceeds to operation , which indicates to compare the shape-analyzed data to a consensus object (available or generated). Operation may include performing shape comparisons between generated objects and/or graphs and consensus objects and/or graphs. In method , the flow proceeds from operation to operation . Operation is a determination of the variation in objects based on the previously performed comparison. From operation , the flow proceeds to operation , which is a shareable interactive output report. The output report may summarize information from some or all of the previous processes.
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is a flow chart illustrating method according to the present invention. In , optional steps in method are shown in dotted boxes. The flow in method flows from the start oval to operation , which indicates to identify, in a visualization of biologic material, first shapes that combine to form a target shape. From operation , the flow in method proceeds to operation , which indicates to register the first shape of the target shape to second shapes of a generic shape. From operation , the flow in method proceeds to operation , which indicates to identify variations between the first shapes and second shapes. From operation , the flow in method proceeds to optional operation , which indicates that the registering of the first shapes of the target shape to the second shapes of the generic shape includes deforming at least one of the target shape and the generic shape based on an optimization function. The optimization function may be performed on a pixel by pixel (or voxel by voxel) basis. From optional operation , the flow in method proceeds to optional operation , which indicates that the variations between the first shapes and the second shapes are displayed in a further visualization of the target shape. From optional operation , the flow in method proceeds to optional operation , which indicates that the variations are identified as abnormal based on a model. From optional operation , the flow in method proceeds to the end oval.
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is a schematic diagram of computing system used in an exemplary embodiment of the present invention. illustrates exemplary computing system , hereinafter system , that may be used to implement embodiments of the present invention. The system may be implemented in the contexts of the likes of computing systems, networks, servers, or combinations thereof. The system may include one or more processors and memory . Memory stores, in part, instructions and data for execution by processor . Memory may store the executable code when in operation. The system may further includes a mass storage device , portable storage device(s) , output devices , user input devices , a graphics display , and peripheral device(s) .
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The components shown in are depicted as being connected via a single bus . The components may be connected through one or more data transport means. Processor and memory may be connected via a local microprocessor bus, and the mass storage device , peripheral device(s) , portable storage device , and graphics display may be connected via one or more input/output (I/O) buses.
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Mass storage device , which may be implemented with a magnetic disk drive or an optical disk drive, is a non-volatile storage device for storing data and instructions for use by processor . Mass storage device may store the system software for implementing embodiments of the present invention for purposes of loading that software into memory .
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Portable storage device operates in conjunction with a portable non-volatile storage medium, such as a floppy disk, compact disk, digital video disc, or USB storage device, to input and output data and code to and from the system. The system software for implementing embodiments of the present invention may be stored on such a portable medium and input to the system via the portable storage device .
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User input devices provide a portion of a user interface. User input devices may include one or more microphones, an alphanumeric keypad, such as a keyboard, for inputting alpha-numeric and other information, or a pointing device, such as a mouse, a trackball, stylus, or cursor direction keys. User input devices may also include a touchscreen. Additionally, the system as shown in includes output devices . Suitable output devices include speakers, printers, network interfaces, and monitors.
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Graphics display may include a liquid crystal display (LCD) or other suitable display device. Graphics display receives textual and graphical information, and processes the information for output to the display device.
580
Peripheral devices may be included and may include any type of computer support device to add additional functionality to the computer system.
500
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The components provided in the system are those typically found in computer systems that may be suitable for use with embodiments of the present invention and are intended to represent a broad category of such computer components that are well known in the art. Thus, the system may be a personal computer, hand held computing system, telephone, mobile computing system, workstation, server, minicomputer, mainframe computer, or any other computing system. The computer may also include different bus configurations, networked platforms, multi-processor platforms, etc. Various operating systems may be used including Unix, Linux, Windows, Mac OS, Palm OS, Android, iOS (known as iPhone OS before June 2010), QNX, and other suitable operating systems.
It is noteworthy that any hardware platform suitable for performing the processing described herein is suitable for use with the embodiments provided herein. Computer-readable storage media refer to any medium or media that participate in providing instructions to a central processing unit (CPU), a processor, a microcontroller, or the like. Such media may take forms including, but not limited to, non-volatile and volatile media such as optical or magnetic disks and dynamic memory, respectively. Common forms of computer-readable storage media include a floppy disk, a flexible disk, a hard disk, magnetic tape, any other magnetic storage medium, a CD-ROM disk, digital video disk (DVD), Blu-ray Disc (BD), any other optical storage medium, RAM, PROM, EPROM, EEPROM, FLASH memory, and/or any other memory chip, module, or cartridge.
The present technology further enables understanding physiologic and pathologic central nervous system function by mapping in situ cranial vasculature and neurovascular interfaces. Exemplary embodiments provide a non-invasive workflow to visualize murine cranial vasculature via polymer casting of vessels, iterative sample processing and micro-computed tomography, and automatic deformable image registration, feature extraction, and visualization. This methodology is applicable to any tissue and allows rapid exploration of normal and altered pathologic states.
The entire intact murine cranial vasculature has not yet been visualized. Understanding normal cerebrovascular anatomic relationships is critical to the study of intracranial pathologies. Current in vivo contrast-based imaging methods for mice, such as micro-computed tomography (Micro-CT) or magnetic resonance imaging (MRI), are limited in resolution of fine vasculature due to motion artifact and inadequate contrast filling. Optical sectioning using light-sheet microscopy, which is a high-resolution ex-vivo alternative for imaging the brain, can resolve fine cerebrovasculature but cannot presently be performed on the whole head with the skull intact while preserving the sample for further investigation. A workflow is provided to non-invasively and non-destructively generate high-resolution maps of the murine whole-head vasculature and the surrounding anatomy using terminal vascular polymer casting, iterative sample processing, and high-resolution ex-vivo Micro-CT. | |
The invention relates to a strong aquifer ultrahigh water material drill hole interior slurry mixing and grouting water plugging device. A material A storage pot fixed to the ground is communicated with a material A pulping device through a material A screw feeder. A material B storage pot is communicated with a material B pulping device through a material B screw feeder. A material A pulping water storage pot and a material B pulping water storage pot are communicated with the material A pulping device and the material B pulping device respectively. The material A pulping device and the material B pulping device are in sealed communication with a material A slurry pump and a material B slurry pump through a material A feeding pipeline and a material B feeding pipeline respectively. The material A slurry pump is in sealed communication with the upper end of an inner channel of a connector through a material A discharging pipeline and a material A flange. The material B slurry pump is in sealed communication with the upper end of an annular channel of the connector through a material B discharging pipeline and a material A flange. The lower end of the inner channel and the lower end of the annular channel are communicated. The device is simple in structure, and capable of achieving long-distance transportation of strong aquifer ultrahigh water materials. | |
Maintaining an optimal after-tax asset allocation becomes more difficult as withdrawals are made, but research provides useful guidelines.
Two common investor objectives are typically addressed with two well-accepted industry practices. First, to minimize taxes on portfolio income and gains, tax-inefficient assets (i.e., investments that generate higher taxes, such as taxable fixed income) are placed in tax-favored retirement accounts. Second, to preserve the compounding of tax-free returns for as long as possible, retirees fund their spending from taxable accounts before withdrawing from tax-favored retirement accounts.
While relatively straightforward, these strategies can eventually conflict with another important objective: optimal portfolio diversification. In practice, if all or most tax-efficient assets are held in taxable accounts and liquidated first to fund withdrawals, an investor’s portfolio will increasingly be weighted toward tax-inefficient assets rather than an optimal mix of assets. On the other hand, investors who seek to avoid this issue by withdrawing from both taxable and tax-favored retirement accounts — and/or rebalancing toward tax inefficient assets as withdrawals are made from retirement accounts — risk sacrificing optimal after-tax returns.
Research Findings
So which strategy should investors favor? Is it more important to hold tax-efficient assets in taxable accounts (i.e., “asset location”) or delay withdrawals from retirement accounts to maximize the benefits of tax-free returns (i.e., “withdrawal sequencing”)?
Research from Peter Mladina, Northern Trust’s director of Portfolio Research, provides important findings for those facing this conundrum or simply questioning how best to fund expenses in retirement. Using a common, efficient mix of four major asset classes commonly owned by high-net-worth investors, his analysis suggests the following:
- To the extent possible, investors should practice asset location while prioritizing optimal asset allocation as their main objective.
- Asset location is likely most beneficial to those individuals who do not plan to consume their retirement assets during their lifetimes.
- Withdrawal sequencing — withdrawing from taxable accounts first — should be prioritized by investors who plan to consume their tax-favored retirement accounts during their lifetimes.
- In practice, a combination of asset location and withdrawal sequencing could make sense.
Steps for spending and investing in retirement
These findings provide useful insight, but you may question how to apply them to your unique situation — particularly if you do not know whether you will need to consume your retirement assets during your lifetime. To apply this insight to your portfolio, we suggest working with your financial advisor to accomplish the following:
Understand how much and when you will withdraw from your investment accounts.
We believe the best way to achieve this clarity is through a goals-driven approach, which matches your financial assets with your anticipated expenditures to create a better portfolio for you. This process begins by identifying and prioritizing your life goals, which is ultimately the insight you will need to employ optimal asset allocation, asset location and withdrawal sequencing.
Determine the assets and investment strategies best suited to help you fund your goals.
At Northern Trust, this process uniquely results in discrete asset allocations for specific goals you wish to fund, which adjust over time along a “glidepath.” It’s important to note that if you have a Roth IRA, you are not required to take distributions during your lifetime, which sometimes warrants treating it as its own entity for asset allocation purposes.
Employ asset location.
This generally includes placing taxable investment grade bonds, high yield bonds, real estate investment trusts and hedge funds in tax-favored accounts, while placing tax-exempt municipal bonds and tax-efficient stocks in taxable accounts. Keep in mind, however, that liquidity is also an important part of the equation. Sometimes this may mean placing less tax-efficient assets, such as high quality bonds, in taxable accounts for the purpose of avoiding early withdrawal penalties (from retirement accounts) or needing to sell stocks at depressed prices in the event of a market downturn. At Northern Trust, we use a Portfolio Reserve to help make these decisions.
Work with your financial advisor pre- and post-retirement to optimize your withdrawal strategy.
If you determine that you will not need to consume your retirement assets beyond your required minimum distributions, you will likely choose to prioritize asset location and, in turn, optimal after-tax portfolio diversification, as you spend from and rebalance your accounts.
Continue to look for tax planning opportunities offered by your portfolio.
For example, keep in mind that stocks are generally tax-efficient not only because of the relatively low income they generate. They also provide the potential for tax loss harvesting as well as tax-efficient charitable giving. For more tax planning opportunities — beyond those offered by your portfolio — refer to our 2020 Year-End Tax Planning Checklist.
Taking the above steps may seem complex, particularly if you have already undergone a traditional financial planning process that has proven cumbersome without providing sufficient clarity. However, our goals-driven approach is different. It allows you to easily evaluate tradeoffs and make more confident decisions about your asset allocation and overall financial plan.
For more information, please contact one of our advisors. And for more detail underlying the research discussed above, please read Asset Location and Withdrawal Sequencing. | https://www.northerntrust.com/united-states/institute/articles/spending-in-retirement-planning-for-withdrawals |
The present invention relates to certain new cyclohexyl carbamate compounds, to herbicidal and acaricidal compositions containing them, and to their use as herbicides and acaricides.
For the control of barnyard grass, a weed growing in paddy fields, pentachlorophenol (PCP) has hitherto been used; however, this chemical is not only extremely irritating to the mucous membranes of human skin and difficult to formulate, but also very poisonous to fish. Therefore the time and scope of its usage are limited. For the controlling of spikerush, a weed growing in the same conditions as barnyard grass, 2- methyl-4- chlorophenoxy-acetic acid (MCP) is used, but MCP is not very effective for that purpose.
Among other herbicides, French Patent No. 1328112 indicates that benzyl-N,N-di-alkylthiolcarbamic acid esters have a herbicidal activity and Japanese Patent Publication No. 29024/68 indicates that halogen- substituted benzylthiolcarbamic acid esters exhibit a herbicidal activity.
It has now surprisingly been discovered that certain novel substituted (or unsubstituted) benzyl or &agr;-methyl substituted (or unsubstituted) benzyl N-methyl-N-cyclohexylcarbamates of the general formula (I) are excellent selective herbicides and are suitable for controlling weeds growing in paddy fields, e.g., Echinochloa (barnyard grass), Eleochalis acicularis (spikerush) and broad-leaved weeds without significant injury to the rice plant.
These compounds have the following general formula: ##EQU2## wherein X is hydrogen, halogen, lower alkyl or lower alkoxy,
R is hydrogen or methyl, and
n is 1, 2, or 3,
(when n is 2 or 3, the various X radicals may be the same or different) .
The compounds of the present invention are characterized by strong herbicidal activity when used not only before the germination of barnyard grass but also at the 1 to 3 leaf stage under irrigation conditions, and by less phytotoxicity against rice plants in comparison with the afore- said conventional benzylthiolcarbamate. This is a very important feature since many other herbicides now on the market are effective against barnyard grass only in the pre- or the immediate post- emergence period. Moreover, because of their lower phytotoxicity against rice plants, the compounds of the present invention can be used to control weeds in paddy fields and yet save much labor in cultivation, when applied a week or two after transplantation, a stage for which no proper controlling method is available at present.
The compounds of the present invention have strong herbicidal activity when absorbed through roots, and they can be used as non- selective or as selective herbicides against weeds (including those in paddy fields), especially during the preparation of the soil before germination. Furthermore, the compounds of this invention are effective as acaricides, and especially against carmine mites. When used as acaricides on plants they also show only little phytotoxicity. Accordingly the compounds of this invention may be used not only as herbicides but also as acaricides.
The invention also provides a process for the production of a compound of formla (I) in which
a. a benzylmercaptan of the general formula ##EQU3## is reacted with N- methyl-N-cyclohexyl-carbamoyl chloride of the formula ##EQU4##
or b. a benzylthio-carbonyl chloride of the general formula ##EQU5## is reacted with N-methyl-N-cyclohexylamine of the formula ##EQU6##
or c. a benzyl halide of the general formula ##EQU7## is reacted with N-methyl-N-cyclohexylamine of the formula (V) and COS and an alkali of the formula M.sup.2 --OH (VII)
X, r and n having the same meanings as in formula (I),
M.sup.1 being hydrogen or an alkali metal,
Hal being halogen, and
M.sup.2 being alkali metal.
Process variant (a) is illustrated by the following reaction scheme, ##EQU8##
Examples of benzyl mercaptans of formula (II) include benzyl-, 2- (3- or 4-)chlorobenzyl-, 3,4-(or 2,4-)dichlorobenzyl-, 4-methyl(or iso- propyl-)benzyl-, 2-chloro-5-bromobenzyl-, 3,4-(or 2,5-)dimethylbenzyl-, 2, 4,5-(or 2,4,6-)trimethylbenzyl-, 4-methoxybenzyl-, 3-methyl-4-methoxy- (ethoxy- or iso-propoxy) benzyl-, 3-methoxy-5-chlorobenzyl-, &agr;- methylbenzyl-, &agr;-methyl-2-(or 4-)chlorobenzyl-, and &agr;-methyl- 4- methyl(or methoxy)benzylmercaptan and their alkali metal salts.
The above-mentioned reaction is preferably performed in the presence of an inert organic solvent. For this purpose, aliphatic or aromatic hydrocarbons (which may be halogenated), such as benzine, methylene chloride, chloroform, carbon tetrachloride, benzene, chlorobenzene, toluene or xylene; ethers such as diethylether, dibutulether, dioxan or tetrahydrofuran; low-boiling point alcohols such as methanol, ethanol or isopropanol; and ketones such as acetone, methylethylketone, methylisopropylketone or methylisobutylketone, are suitable. Lower aliphatic nitriles such as acetonitrile or propionitrile can also be used.
This reaction can also be carried out in the presence of an acid binding agent, if necessary. For this purpose, carbonates and bicarbonates of alkali metals, such as sodium bicarbonate, potassium carbonate or sodium carbonate, alcoholates of alkali metal such as methylate or ethylate or potassium or sodium, and aliphatic, aromatic or heterocyclic tertiary bases, such as triethylamine, diethylaniline and pyridine, can be used.
Process variant b is illustrated by the following reaction scheme: ##EQU9##
Examples of benzylthio-carbonyl chloride of the formula (IV) include benzyl-, 2-(3- or 4-)chlorobenzyl-, 3,4-(or 2,4-)dichlorobenzyl-, 4- methyl(or iso-propyl-)benzyl-, 2-chloro-5-bromobenzyl-, 3,4-(or 2,5- ) dimethyl-benzyl-, 2,4,5-(or 2,4,6-) trimethylbenzyl-, 4-methoxybenzyl-, 3- methyl-4-methoxy-(ethoxy- or iso-propoxy)benzyl-, 3-methoxy-5- chlorobenzyl-, &agr;-methylbenzyl-, &agr;-methyl-2-(or 4- ) chlorobenzyl-, and &agr;-methyl-4-methyl (or methoxy)benzyl- thiocarbonylchloride. This reaction can also be carried out in the presence of an inert organic solvent as mentioned above for variant (a).
Process variant (c) is illustrated by the following reaction scheme: ##EQU10##
This reaction is preferably carried out in the presence of an inert organic solvent as mentioned above for process variant (a).
The preparation of the compounds of the invention is illustrated by the following Examples 1 and 2.
EXAMPLE 1
Preparation of benzyl-N-methyl-N-cyclohexylthiolcarbamate ##EQU11##
14.6 g (0.1 mol) of the sodium salt of benzylmercaptan were mixed with 150 ml of acetone. Then, while the mixture was being stirred, 17.6 g (0.1 mol) of N-methyl-N-cyclohexylcarbamoylchloride were gradually added dropwise thereto at room temperature. After the dropping was over, the reaction was completed by further stirring for 2 - 3 hours. The acetone was distilled off and 300 ml of benzene was added to the extract. The benzene layer was taken off and washed with 1% hydrochloric acid, 1% sodium hydroxide and water, and was thereafter dried over anhydrous sodium sulfate. After continuing the distillation under reduced pressure after distilling off the benzene, 24.9 g of benzyl-N-methyl-N- cyclohexylthiolcarbamate were obtained.
Yield: 90.9%. b.p. : 157° - 160°C/0.5 mmHg. The index of refraction n.sub.D.sup.20 was 1.5644.
EXAMPLE 2
Preparation of &agr;-methyl--chlorobenzyl-N-methyl-N- cyclohexylthiolcarbamate -chlorobenzyl-N-methyl-N- cyclohexylthiocarbamate ##EQU12##
23.5 g (0.1 mol) of &agr;-methyl-4- chlorobenzylthiocarbonylchloride was dissolved in 200 ml of acetone. The solution was cooled to 0 - 5. degree.C. 22.6 g (0.2 mol) of N-methyl-N- cyclohexylamine dissolved in 100 ml of acetone were added dropwise to the solution with stirring. The mixture was reacted for one hour after completion of the addition, and was allowed to stand at room temperature for 12 hours. From the reacted mixture, the precipitated amine salt was filtered off. The acetone layer, the filtrate, was washed with 1% sodium hydroxide, 1% hydrochloric acid and water, and then it was dried over anhydrous sodium sulfate. 28.2 g of &agr;-methyl-4-chlorobenzyl-N- methyl- N-cyclohexylthiolcarbamate were obtained under reduced pressure distillation after distilled off the acetone.
Yield : 90.4%. b.p. : 170° - 173°C/0.2 mmHg. The index of refraction n.sub.D.sup.20 was 1.5671.
The following table lists representative compounds of the present invention which were prepared according to methods analogous to those of the above Examples (the compounds of the above Examples are included in the Table I.
Table I
_________________________________________________________________________ _
Physical Property
b.p. ° C/mmHg
(the index of refraction
n.sub.D.sup.20)
Compound
Structural Formula Chemical Name [m.p.°C]
_________________________________________________________________________ _
OCH.sub.3
∥|
(1) CH.sub.2 --S--C--N Benzyl-N-methyl-N-
157 - 160/0.5
cyclohexylthiolcarbamate
(1.5644)
OCH.sub.3
∥| 2-Chlorobenzyl-N-methyl-N-
(2) CH.sub.2 --S--C--N cyclohexylthiolcarbamate
174 - 176/0.5
(1.5766)
OCH.sub.3
∥|
(3) CH.sub.2 --S--C--N 4-Chlorobenzyl-N-methyl-N-
165 - 170/0.3
cyclohexylthiolcarbamate
(1.5748)
OCH.sub.3
∥|
(4) CH.sub.2 --S--C--N 3,4-Dichlorobenzyl-N-methyl-
195 - 198/0.2
N-cyclohexylthiolcarbamate
(1.5849)
OCH.sub.3
∥|
(5) CH.sub.2 --S--C--N 2-Chloro-5-bromobenzyl-
177 - 180/0.2
N-methyl-N-cyclohexylthiol-
(1.5941)
carbamate
OCH.sub.3
∥|
(6) CH.sub.2 --S--C--N 4-Methylbenzyl-N-methyl-
[50 - 51]
N-cyclohexylthiolcarbamate
OCH.sub.3
∥|
(7) C.sub.2 H.sub.5 CH.sub.2 --S--C--N
4-Ethylbenzyl-N-methyl-N-
180 - 184/0.2
cyclohexylthiolcarbamate
(1.5608)
OCH.sub.3
∥|
(8) iso-C.sub.3 H.sub.7 CH.sub.2 --S--C--N
4-Iso-propylbenzyl-N-methyl-
178 - 184/0.2
N-cyclohexylthiolcarbamate
(1.5559)
OCH.sub.3
∥|
(9) CH.sub.2 --S--C--N 3,4-Dimethylbenzyl-N-
[60 - 62]
methyl-N-cyclohexylthiol-
carbamate
OCH.sub.3
∥| 2,5-Dimethylbenzyl-N-
(10) CH.sub.2 --S--C--N methyl-N-cyclohexylthiol-
165 - 170/0.1
carbamate
OCH.sub.3
∥| 2,4,5-Trimethylbenzyl-N-
CH.sub.2 --S--C--N methyl-N-cyclohexylthiol-
178 - 183/0.3
carbamate (1.5654)
OCH.sub.3
∥|
(12) CH.sub.3 OCH.sub.2 --S--C--N
4-Methoxybenzyl-N-methyl-
173 - 177/0.2
N-cyclohexylthiolcarbamate
(1.5659)
OCH.sub.3
∥| 3-Methyl-4-methoxybenzyl-
(13) CH.sub.2 --S--C--N N-methyl-N-cyclohexylthiol-
[57 - 58]
carbamate
OCH.sub.3
∥| 3-Methyl-4-ethoxybenzyl-
(14) C.sub.2 H.sub.5 OCH.sub.2 --S--C--N
N-methyl-N-cyclohexylthiol-
[51 - 52]
carbamate
OCH.sub.3
∥| 3-Methyl-4-iso-propoxybenzyl-
(15) iso-C.sub.3 H.sub.7 OCH.sub.2 --S--C--N
N-methyl-N-cyclohexylthiol-
178 - 179/0.2
carbamate (1.5520)
OCH.sub.3 2-Methoxy-5-methylbenzyl-
∥|
(16) CH.sub. 2 --S--C--N N-methyl-N-cyclohexylthiol-
173 - 176/0.2
carbamate (1.5650)
OCH.sub. 3
∥| 3-Chloro-4-methoxybenzyl-
175 - 180/0.2
(17) CH.sub.2 --S--C--N N-methyl-N-cyclohexylthiol-
(1.5766)
carbamate
OCH.sub.3
∥| 3-Chloro-4-ethoxybenzyl-
(18) C.sub.2 H.sub.5 OCH.sub.2 --S--C--N
N-methyl-N-cyclohexylthiol-
189 - 193/0.4
carbamate (1.5689)
OCH.sub.3
∥| 3-Chloro-4-iso-propoxybenzyl-
(19) iso-C.sub.3 H.sub.7 OCH.sub.2 --S--C--N
N-methyl-N-cyclohexylthiol-
180 - 185/0.3
carbamate (1.5581)
OCH.sub.3
∥| 2-Methoxy-5-chlorobenzyl-
(20) CH.sub.2 --S--C--N N-methyl-n-cyclohexylthiol-
carbamate 185 - 188/0.4
(1.5749)
CH.sub.3 OCH.sub.3
|∥|
&agr;-Methylbenzyl-N-methyl-
(21) CH--S-- C--N N-cyclohexylthiolcarbamate
170 - 173/0.2
(1.5632)
CH.sub.3OCH.sub.3
|∥|
&agr;-Methyl-2-chlorobenzyl-
(22) CH--S--C--N N-methyl-N-cyclohexylthiol-
185 - 189/0.2
carbamate (1.5699)
CH.sub.3 OCH.sub.3
|∥|
&agr;-Methyl-4-chlorobenzyl-
(23) CH--S--C--N N-methyl-N-cyclohexylthiol-
170 - 173/0.2
carbamate (1.5671)
CH.sub.3 OCH.sub.3
|∥|
&agr;-Methyl-4-methylbenzyl-
(24) CH--S--C--N N-methyl-N-cyclohexylthiol-
160 - 165/0.3
carbamate (1.5564)
CH.sub.3 OCH.sub.3
|∥|
(25) CH.sub.3 OCH--S--C--N &agr;-Methyl-4-methoxybenzyl-
175 - 180/0.4
N-methyl-N-cyclohexylthiol-
(1.5621)
carbamate
_________________________________________________________________________ _
The compounds of the present invention are superior in weed- controlling activity to many known compounds having similar structures.
The compounds can have either a total herbicidal effect or a selective herbicidal effect, depending mainly on the amount used. Larger amounts, for example 5 to 40 kg of active compound per hectare, generally have a total herbicidal effect, whereas small amounts, for example 1.25 to 5 kg of active compound per hectare, generally have a selective effect.
The compounds according to the present invention can be effectively used as germination-controlling agents especially weed- controlling agent.
The term weed used herein is intended broadly to cover most plants growing where they are not desired.
The compounds according to the present invention have good activity against the following plants, and exhibit excellent selective weed- killing or withering effects when used in appropriate amounts (for example 1.25 to 5 kg per hectare), and can be especially useful as herbicides in the cultivation of crops indicated by an asterisk in the following list.
______________________________________
Plant name Latin name
______________________________________
Dicotyledons
Mustard Sinapis
Rape Lepidium
Catch weed Galium
Chickweed Stellaria
Sweet false Matricaria
French weed Galinsoga
Goosefoot Chenopodium
Nettle Urtica
Groundsel Senecio
Tampala Amaranthus
Purslane Portulaca
cotton *Gossypium
Carrot *Daucus
Pulse *Phaseolus
Potato *Solanum
Coffee *Coffea
Beet *Beta
Cabbage *Brassica
Spinach *Spinacia
Monocotyledons
Timothy Phleum
Eragrostis niwahokori Honda
Poe
Festuca parvigluma Festuca
Finger-grass Digitaria
Goose grass Eleusine
Nit 70
Foxtail Setaria
Ray grass Bromus
Barn yard grass Echinochlora
Maize *Zea
Rice plant *Oryza
Oats *Avena
Barley *Hordeum
Wheat *Tritium
Millet *Panicum
Sugar cane *Saccharum
______________________________________
The species of the above plants are considered to be typical examples of the genus identified by the Latin name. The applicability of the active compounds according to the present invention is, of course, not limited to these plants and they are effective for other analogous plants.
The active compounds according to the present invention can be utilized, if desired, in the form of the usual preparations, compositions or formulations with conventional inert (i.e. plant compatible or herbicidally inert) pesticide diluents or carriers.
These may be prepared in known manner, for example by mixing the active compounds with extenders, that is, liquid or solid or gaseous diluents and/or carriers, optionally with the use of conventional pesticide adjuvants, that is, emulsifying agents and/or dispersing agents and/or adhesive agents. In the case of the use of water as an extender, organic solvents and, emulsifying agent can, for example, also be used as auxiliary solvents.
As liquid diluents or carriers, there are preferably used aromatic hydrocarbons, such as xylenes, toluene, benzene, dimethyl naphthalene or aromatic naphthas haloganated (chlorinated) aromatic or aliphatic hydrocarbons, such as chlorobenzenes, chloromethylene, chloroethylene or carbon tetrachloride, aliphatic hydrocarbons, such as cyclohexane or paraffins (for example petroleum fractions), alcohols, such as methanol or butanol, ketones such as acetone, methyl ethyl ketone or cycohexanone, amines such as ethanol amine, ethers such as glycol monomethyl ether, strongly polar solvents, such as dimethyl formamide, dimethyl sulfoxide or acetonitrile, as well as water.
As solid diluents or carriers, there are preferably used ground natural minerals, such as clays, talc, chalk, i.e. calcium carbonate, attapulgite, montmorillonite, diatomaceous earth or pumice or ground synthetic minerals, such as highly-dispersed silicic acid, alumina or silicates.
As gaseous diluents or carriers there may be used aerosol propellants which are gaseous at normal temperatures and pressures, such a freon.
Preferred examples of adjuvants (diluents or carriers assistants) include non-ionic cationic and anionic emulsifiers, such as polyoxyethylene-fatty acid esters, polyoxyethylene-fatty alcohol ethers, for example alkylarylpolyglycol ethers, alkyl sulfonates and aryl sulfonates; and preferred examples of dispersing or adhesive agents include lignin, sulfite waste liquors and methyl cellulose.
The compounds of the present invention can be used, if desired, together with other agricultural chemicals, for example insecticides, nematocides, fungicides (including antibiotics), herbicides, plant growth- regulators or fertilizers.
The herbicidal, and acaricidal composition according to the present invention generally contains 0.1 to 95 per cent by weight, preferably 0.5 to 90% by weight, of the active compound. However, the content of active ingredients may be varied in accordance with the formulation and the applying method, the purpose, the period of application, the place of application and other circumstances.
The compounds may be formulated in any of the usual ways in the field of agricultural chemicals, for example solutions, emulsions, emulsion concentrates, wettable powders, aqueous solutions, oil formulations, aerosols, pastes, fumigants, dusting powders, coating granules, tablets, granules, pellets and the like.
The compounds may be applied to the pest or its habitat in any of the usual ways, for example, by scattering, spraying, atomizing, misting, dusting, mixing, fumigating, injecting or powder-coating methods.
Furthermore, the application can be effected by the so-called "ultra- low-volume" method. In this method it may be possible to use 95% to 100% of the active compound.
In use, the content of the active ingredient in the ready-to- use preparation can be varied over a broad range according to circumstances above. However, it may generally be preferable to use a range from 0.001 to 20% by weight, especially 0.005 to 15.0% by weight.
Also, the amount of active compound applied per unit, area is usually about 15 to 2000 grams, preferably 40 to 1000 grams of active compound per 10 ares. However, in special cases it may be possible to use or more less sometimes such variations may be required.
The invention therefore provides a herbicidal or acaricidal composition containing as active ingredient a compound according to the invention in admixture with a solid diluent or carrier or in admixture with a liquid diluent or carrier, if desired, containing adjuvant.
The invention also provides a method of combating weeds, acarids or fungi which comprises applying to these pests or a habitat thereof a compound according to the invention alone or in the form of a composition containing as active ingredient a compound according to the invention in admixture with a solid or liquid diluent or carrier or adjuvant.
The invention also provides crops protected from damage by seeds or acarids by being grown in areas in which, immediately prior to and/or during the time of the growing, a compound according to the invention was applied alone or in admixture with a solid or liquid diluent or carrier. It will be seen that the usual methods of providing harvested crops may be improved by the present invention.
The invention is illustrated by the following Examples. In all the Examples, the numbers of the compounds correspond to those in Table 1, infra.
The following Examples (i) through (iv) are illustrative of conventional formulation techniques used in preparing pesticidal compositions of the instant compounds and Examples (A) through (C) illustrate the acaricidal activity of compounds of this invention.
Example (i)
15 parts of compound (3), 80 parts of a mixture of talc and clay and 5 parts of the emulsifier Runnox (Trade Name, product of Toho Chemical Ind. Corp.) were mix-crushed to give a wettable powder. It is diluted with water for actual application. [talc and clay (3:1); The term "parts" used in the Example (i) to (iv) means "weight".]
Example (ii)
30 parts of compound (1), 30 parts of xylol, 30 parts of Kawakazol (Produced by Kawasaki Kasei K. K.) and 10 parts of the emulsifier Sorpol (Trade Mark) were mixed to give an emulsion concentrate. It was applied after being diluted with water. (Kawakazol: aliphatic hydrocarbons with high boiling point ; Sorpol: polyoxyethylenealkylarylether)
Example (iii)
To a mixture of 10 parts of compound (15), 10 parts of bentonite, 78 parts of clay and 2 parts of lignin sulfate there were added 25 parts of water. The mixture was well kneaded and cut into fine particules (20- 40 mesh) by means of an extrusion type granulating maching and was dried at 40° to 50°C. In use, the granular was directly applied.
Example (iv)
2 parts of compound (17) of the table and 98 parts of a mixture of talc and clay were comminuted and mixed to form a powder for application.
EXAMPLE A
Pre-emergence soil-treating test for weeds in paddy field under irrigation:
Solvent: 5 parts by weight of acetone
Emulsifier: 1 part by weight of benzyloxypolyglycol ether.
The active compound was incorporated into an emulsifiable concentrates by mixing 1 part by weight thereof with the stated amounts of the said solvent and emulsifier.
The preparation thus obtained was diluted with water.
Test method
A 1/5000 are Wagner pot was charged with paddy field soil, and a rice plant seedling (variety: Kinmaze) during the 3rd to the 4th leaf stage was transplanted into the pot.
After rooting of the seedling, seeds of Panicum crusgalli and a broad- leaved weed were sown, and Eleocharis acicularis var. longiseta was transplanted into the pot.
The said preparation of active compound was applied into the pot at a dosage of 500, 250 or 125 grams of active compound per 10 ares. The damage degrees of the weeds to be tested after four weeks were evaluated on a scale from 0 to 5, the scale values having the following meanings. The degree of phytotoxicity was also determined in accordance with the second scale below.
Degree of damage
______________________________________
5: Weed-killing rate as compared
over 95 % (withering)
with untreated plot
4: " over 80 %
3: " over 50 %
2: " over 30 %
1: " over 10 %
0: " below 10 %
(not effective)
______________________________________
Degree of phytotoxicity
______________________________________
5: Phytotoxicity rate as compared
over 90 % (mortal
with untreated plot damage)
4: " over 50 %
3: " over 30 %
2: " below 30 %
1: " below 10 %
0: " 0 % (no phytotoxicity)
______________________________________
The results are given in Table 2.
(The term "a 1/5000 are Wagner pot" means a pot which covers a space of 0.02 m.sup.2.)
Table 2
______________________________________
Test results against paddy weeds under irrigation
conditions with soil-treatment
______________________________________
Phytoto-
Amount of Degree of damage xicity
______________________________________
active Broad-
Compound
ingredient
Barnyard leaved
Rice
No. (g/10 ares)
grass Spikerush
weed plant
______________________________________
(1) 500 5 5 5 0
250 5 5 5 0
100 5 4-5 5 0
(2) 500 5 5 5 0
250 5 4-5 5 0
100 5 4 4-5 0
(3) 500 5 5 5 0
250 5 4-5 5 0
100 5 4 5 0
(4) 500 5 5 5 0
250 5 4 5 0
100 4 3 4 0
(5) 500 5 5 5 0
250 5 4-5 5 0
100 4 4 4 0
(6) 500 5 5 5 0
250 5 5 5 0
100 5 4-5 5 0
(7) 500 5 5 5 0
250 5 4 5 0
100 5 4 4 0
8 500 5 5 5 0
250 5 4 5 0
100 4-5 3 4 0
(9) 500 5 4-5 5 0
250 5 4 5 0
100 5 4 4 0
(10) 500 5 4-5 5 0
250 5 4 5 0
100 4 4 4-5 0
(11) 500 5 4 4-5 0
250 4-5 4 4 0
100 4 3 3 0
(12) 500 5 4-5 5 0
250 5 4 5 0
100 5 4 4-5 0
(13) 500 5 4-5 5 0
250 4 4 4-5 0
100 4 3-4 4 0
(14) 500 5 4-5 5 0
250 5 4 5 0
100 4-5 4 4-5 0
(15) 500 5 5 5 0
250 5 4 5 0
100 4-5 4 4-5 0
(16) 500 5 4 5 0
250 5 4 4-5 0
100 4-5 3-4 4 0
(17) 500 5 5 5 0
250 5 4-5 5 0
100 5 4 4-5 0
(18) 500 5 4-5 5 0
250 5 4 5 0
100 4-5 4 4-5 0
(19) 500 5 4
(Control)
______________________________________
250 4-5 4 4 0
100 4 3-4 4 0
(20) 500 5 4-5 5 0
250 5 4 4-5 0
100 4 4 4 0
(21) 500 5 4-5 5 0
250 5 4 4-5 0
100 5 3 4 0
(22) 500 5 5 4-5 0
250 4-5 4 4 0
100 4 3 3 0
(23) 500 5 5 5 0
250 4-5 4 5 0
100 4 3-4 4-5 0
(24) 500 5 4 4 0
250 4-5 4 3 0
100 4 3-4 3 0
(25) 500 5 4 4-5 0
250 4-5 3 4 0
100 4 3 3 0
(A) 500 5 5 5 0-1
(Compari-
250 5 4 3 0
son) 100 3 3 2 0
un-treated
-- 0 0 0 0
(Control)
______________________________________
Notes
1. Broad-leaved weeds: Monochoria, Rotala indica Koehne and False
pempernel, etc.
2. Control A: Japanese Pat. Publication No. Sho
3. Compound Nos. in the table are the same as in Table 1.
EXAMPLE B
Test against various plants with soil treatment
Test procedure
Seeds of sample plants were sown in a pot of 20 by 30 cm and after 24 hours, the same mixtures as in Example A were sprayed on the soil in amounts of 20, 10, 5, 2.5 and 1.25 kg of active compound per hectare. 3 weeks after spraying, the damage degree was evaluated and classified according to the following standard ranging from 0 to 5 as follows:
______________________________________
0: no effect
1: slight damage or delay in growth
2: marked damage or inhibition of growth
3: heavy damage and only deficient development
or only 50% emerged
4: plants partially destroyed after germination
or only 25% emerged
5: plants completely dead or not emerged.
______________________________________
The results of the test are given in Table 3.
Table 3
_________________________________________________________________________ _
Test results against various plants with soil treatment
_________________________________________________________________________ _
Amount
of
active Barn-
Common
Goose-
Chick-
Wild Finger
Active compound yard
purslane
foot
weed
amaranth
grass
Compound
(kg/ha)
Wheat
Barley
Rice
Cotton
Maize
Cabbage
(a) (b) (c) (d) (e) (f)
_________________________________________________________________________ _
(1) 20 4 4 4 4 4 4 5 5 5 5 5 5
10 1-2 2 1-2
2 2 2 5 5 5 5 5 5
5 0 0 0 0 0 0 5 5 5 5 5 5
2.5 0 0 0 0 0 0 5 5 5 5 5 5
1.25 0 0 0 0 0 0 5 4-5 4-5 4 4-5 4-5
(A) 20 5 5 5 5 5 5 5 5 5 5 5 5
(Comparison)
10 1-2 2 3 2 2 1-2 5 5 5 5 5 5
5 0 0 0 0 0 0 4 5 5 5 5 5
2.5 0 0 0 0 0 0 3 4 4 4 4 3
1.25 0 0 0 0 0 0 2 2 2 2 2 2
_________________________________________________________________________ _
Notes
1. The compound number in the Table corresponds to that of Example (1).
2. (A): French Pat. No. 1328112: Benzyl-N,N- diethylthiolcarbamate
3. (a) Echinochloa (b) Portulaeca (c) Chenopodium (d) Stellaria (e)
Amaranthus (f) Digitaria
EXAMPLE C
Test against carmine mite (Tetranuchus telarius) Preparation of the active compound:
Solvent: 3 parts by weight of acetone
Emulsifier: 1 part by weight of alkylaryl polyglycol ether
In order to prepare a suitable preparation of the active compound, 1 part by weight of the active compound was mixed with the above amounts of acetone and the emulsifier to prepare an emulsion concentrate. The emulsion concentrate was diluted with water to the desired final concentration.
Testing method:
A kidney bean plant, during the period of the 2nd foliage leaf development, planted in a pot of 6 cm diameter, was inoculated with 50 - 100 adult and young carmine mite and after 2 days, a preparation of the active compound described above was sprayed onto the pot at a rate of 40 ml per pot.
The so-treated pot was investigated to evaluate the controlling effect after allowing to stand at room temperature for 10 days, and the effect was rated on a scale as follows:
______________________________________
3: no living adult and young insects
2: below 5% living insects with respect to the
untreated pot
1: 6-50% living insects with respect to the
untreated pot
0: over 51% living insects with respect to the
untreated pot
______________________________________
The average results obtained are shown in the Table 4.
Table 4
______________________________________
Test results against carmine mites
______________________________________
Concentration of active
Compound ingredient (ppm)
No. 1000 300 100
______________________________________
(2) 3 2 2
(3) 3 3 3
(4) 3 2 1
(5) 3 2 1
(6) 3 2 1
(8) 3 3 3
(11) 3 3 2
(12) 3 3 2
(13) 3 2 1
(15) 3 2 1
(18) 3 2 1
(23) 3 3 3
(25) 3 2 1
Kelthane (com-
mercial comparison)
3 2 0
no-treatment (control) 0
______________________________________
Notes:
1. The compound Nos. in the Table correspond to those of Table 1.
2. Kelthane: bis(p-chlorophenyl)trichloroethanol.
It will be understood that the specification and examples are illustrative but not limitative of the present invention and that other embodiments within the spirit and scope of the invention will suggest themselves to those skilled in the art. | |
RELATED APPLICATIONS
FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT
MICROFICHE/COPYRIGHT REFERENCE
BACKGROUND OF THE INVENTION
BRIEF SUMMARY OF THE INVENTION
DETAILED DESCRIPTION OF THE INVENTION
This application is a continuation of International Application No. PCT/EP2006/012362 (International Publication Number WO/2007/079947), having an International filing date of Dec. 21, 2006 entitled “Verfahren Zur Ansteuerung Von Matrixanzeigen” (“Method For Triggering Matrix Displays”). International Application No. PCT/EP2006/012362 claimed priority benefits, in turn, from German Patent Application No. 10 2005 063 159.2, filed Dec. 30, 2005. International Application No. PCT/EP2006/012362 and German Application No. 10 2005 063 159.2 are hereby incorporated by reference herein in their entireties.
[Not Applicable]
[Not Applicable]
The presently described technology relates to a method for driving matrix displays which are made up of a plurality of lines with individual pixels, which lines are configured as rows and columns, wherein individual lines are driven selectively by rows being activated for a defined row addressing time and an operating current or a corresponding voltage i.e. an electrical driving signal being applied to the columns in correlation with the activated row corresponding to the desired brightness in the pixels.
In the following text, the horizontal lines are referred to as rows and the vertical lines which run orthogonally to them are referred to as columns. This is for reasons of clarity. The invention is however not limited to exactly this arrangement. It is in particular possible to exchange the function of the rows and columns or select a non-orthogonal relationship between the rows and columns.
ij
The image data or the desired brightness Dof individual pixels ij are described with the matrix D shown below.
<math overflow="scroll"><mrow><mi>D</mi><mo>=</mo><mrow><mrow><mo>(</mo><mtable><mtr><mtd><msub><mi>D</mi><mn>11</mn></msub></mtd><mtd><msub><mi>D</mi><mn>12</mn></msub></mtd><mtd><mi>…</mi></mtd><mtd><msub><mi>D</mi><mrow><mn>1</mn><mo></mo><mi>m</mi></mrow></msub></mtd></mtr><mtr><mtd><msub><mi>D</mi><mn>21</mn></msub></mtd><mtd><msub><mi>D</mi><mn>22</mn></msub></mtd><mtd><mi>…</mi></mtd><mtd><msub><mi>D</mi><mrow><mn>2</mn><mo></mo><mi>m</mi></mrow></msub></mtd></mtr><mtr><mtd><mi>…</mi></mtd><mtd><mi>…</mi></mtd><mtd><mi>…</mi></mtd><mtd><mi>…</mi></mtd></mtr><mtr><mtd><msub><mi>D</mi><mrow><mi>n</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn></mrow></msub></mtd><mtd><msub><mi>D</mi><mrow><mi>n</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn></mrow></msub></mtd><mtd><mi>…</mi></mtd><mtd><msub><mi>D</mi><mi>nm</mi></msub></mtd></mtr></mtable><mo>)</mo></mrow><mo>.</mo></mrow></mrow></math>
ij
The indices correspond to the positions of the pixels on the display, which is given by the matrix or matrix display D. Each row i of the matrix D and each column j on the matrix D correspond in each case to the geometric row and column on the display. A pixel diode or similar element is assigned to each drivable pixel ij of the matrix display D for generating a pixel of a display. The light intensity averaged over time (corresponding to the brightness D) in each pixel corresponds with the corresponding element in the matrix D. All entries of the matrix D together produce the image to be displayed.
The pixels ij on the matrix display D, of which each can be configured in particular as an OLED (Organic Light Emitting Diode), have been activated so far by row. To this end, the OLEDs on a selected row i are activated by a switch by being connected e.g. to ground. An operating current I is impressed in each of the columns j, which current causes the pixels ij in the intersection of this row i and the columns j to light up. The light intensity L is in the first approximation proportional to charge which is impressed during the active phase (row addressing time) and is recombined radiantly in the OLED pixel. In the event of a relatively high frame rate of the addressing of the display matrix or matrix display D, the human eye perceives the following mean value of the intensity L of the light:
<math overflow="scroll"><mrow><mrow><msub><mi>L</mi><mi>Licht</mi></msub><mo>∼</mo><mfrac><mrow><msubsup><mo>∫</mo><mn>0</mn><msub><mi>T</mi><mi>Frame</mi></msub></msubsup><mo></mo><mrow><msub><mi>I</mi><mi>OLED</mi></msub><mo>·</mo><mstyle><mspace width="0.2em" height="0.2ex" /></mstyle><mo></mo><mrow><mo></mo><mi>t</mi></mrow></mrow></mrow><msub><mi>T</mi><mi>Frame</mi></msub></mfrac><mo>≈</mo><mfrac><mrow><mi>I</mi><mo>·</mo><mfrac><msub><mi>T</mi><mi>Frame</mi></msub><mi>n</mi></mfrac></mrow><msub><mi>T</mi><mi>Frame</mi></msub></mfrac></mrow><mo>=</mo><mfrac><mi>I</mi><mi>n</mi></mfrac></mrow></math>
Frame
OLED
0
Frame
Frame
Tis the total time which is necessary for building a complete image if all n rows of the matrix display D are activated once. The operating current Ior I or Iis impressed in each pixel. When amplitude modulation is used for controlling brightness, the operating current is active over the period T/n which corresponds to the row addressing time. With pulse width modulation, the duration of the operating current is shorter, that is d*T/n. Here, d is the pulse width modulation duty ratio and lies between zero and one:
<math overflow="scroll"><mrow><msub><mi>L</mi><mi>Licht</mi></msub><mo>∼</mo><mrow><mi>d</mi><mo>·</mo><mfrac><msub><mi>I</mi><mn>0</mn></msub><mi>n</mi></mfrac></mrow></mrow></math>
0
0
ij
The current Iis now constant independently of the light intensity of the pixel. The intensity L is adjusted by means of the duty ratio d. A brightness control of this type is simpler and more precise in comparison to amplitude modulation, as the time units in the electronics can be adjusted very precisely and consequently d also. Just a reference current Iis sufficient for driving all the pixels ij. With amplitude modulation, in contrast, the amplitude must be adapted in each case in correspondence with the desired brightness D.
Frame
ij
Frame
0
By driving all the columns j of in each case only one row i, each diode or each pixel ij can be active only for a maximum of an nth of the total time T. In order to achieve a defined average brightness D, the corresponding operating current must be multiplied by the number n of rows, that is, in contrast to the case in which one pixel would be supplied with operating current over the total time T. That is, the higher the number of rows, the higher the pulsed operating current I or Imust be. The operating current is moreover always high when pulse width modulation is used for adjusting the brightness, even when the pixel ij to be driven is very dark. In this case just the application time of the operating current is very short.
The high operating current can however lead to a significant reduction in the OLED lifetime. In order to achieve the necessary high operating current, the voltage at the OLEDs must also be increased, as a result of which the power consumption increases and the efficiency is reduced. This increased power loss not only discharges the rechargeable or disposable battery more quickly, but also makes the display warmer, as a result of which the lifetime is likewise reduced.
In order nevertheless to realise a large, highly resolving display, an “active matrix” could be used as in LCDs (Liquid Crystal Display), by means of which the operating current is no longer delivered in a pulsed manner but is present as a constant current. Active matrix driving (TFT backplane) however requires significant additional costs for an OLED display.
The object of the present technology is to propose a method for driving matrix displays corresponding to the type mentioned at the start, with which the lifetime of the OLED display can be increased or the performance of any matrix display can be improved.
i
max
i
L
max
i
L
max
max
max
0
L
Sum
i
Frame
L
0
Sum
Frame
i
i
This object is achieved according to the present technology in that the row addressing time tfor each row i is determined as a function of the maximum brightness Dof all the columns j of the row i. The row addressing time tcan thereby be selected to be less than or equal to a constant row addressing time twhich is produced when each row of the matrix display is addressed for so long that a maximum pixel brightness Dcould be achieved with the impressed operating current. The row addressing time taccording to the present technology therefore corresponds to the constant row addressing time tmultiplied by the ratio of the maximum brightness Dof the pixels in all the columns j of the row i to the maximum possible pixel brightness Din the entire matrix display. The maximum pixel brightness Dis defined as the light intensity (brightness) in one pixel ij, which is achieved when the operating current Iis applied to the pixel during the constant row addressing time t. This has the effect that the time sum Tof the row addressing times tover the number n of all the rows is less than or equal to the total time Tfor activating all n rows, which activation is given by n×the constant row addressing time t. If the operating current Iis constant, the total time for driving the matrix display can therefore be reduced according to the present technology to the time sum T<Tof the row addressing times. This makes possible for example a higher frame rate and increases the achievable performance of a matrix display.
i
i
Frame
i
Frame
i
Frame
0
Sum
i
Frame
L
1
i
0
i
1
1
1
0
i
Frame
i
Since the light intensity of a pixel ij in the first approximation is proportional to the charge which is impressed in a pixel ij, i.e. is proportional to the product of the row addressing time tand the operating current, the dependence of the row addressing time ton the maximum brightness over the columns of a row can also be used to reduce the operating current. To this end, the total time Tfor activating all the rows i can be kept constant so that the sum of the row addressing times t′over all rows n corresponds to the total time T. The row addressing times t′are therefore extended according to this variant of the inventive method, so that their sum is equal to the total time T. At the same time the operating current Ican according to the present technology be reduced by the ratio of the time sum Tof the (absolutely necessary) row addressing times tof all the rows n to the total time (T) for activating all the rows with the constant row addressing time tto the operating current I. The light intensity of the individual pixels does not change because the product of the row addressing time and the operating current t*I=t′*Iremains constant. In the case of OLEDs, the quantum efficiency η in a lower operating current range is as a rule greater than with a higher operating current. The operating current Ican therefore be additionally reduced by the ratio of the quantum efficiencies η(I)/η(I). For the sake of simplicity, the row addressing time t′(which is extended or standardised to T) is also referred to as t′below.
i
1
The adaptation according to the present technology of the row addressing times tto the addressing of the diode pixels therefore allows the selective phase (row addressing time) of the individual diode pixels ij of the display D, i.e. the time during which the operating current I is applied to the diode pixel ij, to be considerably extended. The active operating current Ican be reduced in reverse proportion to the duration of the selected phase. The efficiency of the matrix display D can be increased as a whole and, in particular in the case of OLED displays, the lifetime can be extended. A basic idea of this present technology therefore lies in extending the duration of the operating current by means of a row-dependent shortening or adaptation of the row addressing times. Since the charge is primarily decisive for a defined light intensity, more time for impressing the operating current therefore means a reduced amplitude of the current.
ij
ij
ij
ij
ij
2
2
Improved handling and a further reduction in the operating current can be achieved if the matrix display D is decomposed into a plurality of matrices S, M which are driven separately. The superposition of all the matrices then produces the image of the matrix display D in the desired brightness Dof the respective pixels ij. The total brightness Dformed from the sum of the individual brightnesses S, Mof the plurality of matrices should correspond to the total desired brightness Dof the matrix display D in the pixel ij. According to the present technology the matrices can be displayed one after the other or nested in each other, preferably in each case using the above-described method row by row and column by column. In the case of a division into two matrices, with one matrix S providing the driving of one row i and one matrix M providing a simultaneous driving of two rows i, the rows of the matrices S, M can be addressed alternately. For passive matrix display types such as OLED displays or LCD, a source image which is described in the matrix display D can therefore be decomposed into a plurality of image matrices. Each of these obtained matrices is to be well implemented for the display type, for example by means of the multi-line addressing described below, so that the sum of the images is implemented better than in direct driving of the display on the basis of the original matrix D.
0
1
As long as it is provided according to the present technology that a plurality of rows i are driven simultaneously, the pixels ij in each column j of the driven rows i have in each case the same signal and the same light intensity. So that the light intensity of a pixel ij corresponds to the light intensity when only one row i is driven, the operating current I, Iis increased by the multiple corresponding to the number of simultaneously driven rows, therefore doubled when two rows are driven simultaneously. The simultaneous driving of a plurality of rows is also called “multi-line addressing” (MLA) in differentiation from driving of only one row, which is also referred to as “single-line addressing” (SLA).
When a plurality of rows are driven simultaneously, adjacent rows (i, i+1) can preferably be driven. It is however also possible according to the present technology, for preferably rows i which are separated from each other by a few rows to be driven simultaneously, for example each alternate row. A close proximity between simultaneously driven rows is particularly sensible, because rows of the matrix display D which are adjacent in an image often have a similar brightness distribution.
2
3
4
ij
In order to be able also to produce differences in intensity between the individual rows and/or columns when a plurality of rows are simultaneously driven, a matrix (S) in which one row (i) is driven and one or a plurality of matrices (M, M, M) in which a plurality of rows (i) are driven can according to the present technology be combined with each other. By providing a matrix S with single-line addressing, the desired brightness Dcan be adapted individually for each pixel ij. This matrix S is also called a residual single-line matrix.
i
i
i
According to the present technology, pulse width modulation can be used for controlling the brightness, i.e. for example the operating current I is applied during a row addressing time tonly for a part of the row addressing time tand the operating current I is switched off during the remaining time of the row addressing time t.
ij
ij
i
Alternatively, amplitude modulation can also be used for controlling the brightness, i.e. the amplitude of the operating current I is adapted to correspond with the desired brightness D. According to the present technology, the pulse width modulation and the amplitude modulation can also be combined with each other in order to control the brightness. It is then particularly advantageous if the brightness Dis predefined in quantised steps, because the amplitude of the operating current can then be reduced in quantised steps while the pulse width duty ratio is increased corresponding to this. This driving can be implemented particularly simply in appliances. This combined method can be used flexibly in particular if the time for applying the operating current I in one column j does not exceed the row addressing time tafter an increase in the pulse width duty ratio. The decision of combining the amplitude modulation with the pulse width modulation can therefore be made individually depending on the operating current application time necessary for this and the provided row addressing time for each row i and column j of the matrix display D. With combined pulse width and amplitude modulation, the amplitude can therefore be reduced with quantised steps while the pulse width modulation duty ratio is increased in correspondence with this. The quantisation can be implemented with a plurality of transistor cells with which multi-line addressing can also be implemented.
In order to generate the matrices used for driving the matrix pixels, it is proposed according to a preferred embodiment to convert the matrix display into a flow matrix which has vertexes as entries, which correspond to the requirement for brightness or differences in brightness of individual pixels in the respective columns. This can take place with a suitable control system in which the above-described method is implemented and which has suitable processor means to carry out the individual processing steps. A control system of this type also forms the subject matter of the present technology. This conversion allows the matrix decomposition to be carried out with a combinatorial method which is based on the known MaxFlow/MinCut principle. The hardware implementation outlay for combinatorial algorithms of this type is known to be low. Combinatorial algorithms can moreover be processed quickly, so that these algorithms are particularly suitable for controlling a matrix display.
It has proved advantageous if the flow matrix is produced from the difference between two matrices, wherein the first matrix consists of the matrix display and a row with zero entries attached to the end of the matrix display and the second matrix consists of the matrix display and a row with zero entries upstream of the matrix display. With a decomposition of a matrix into multi-line matrices and (residual) single-line matrix, it is critical to conceal optimally the differences in brightness of individual pixels in the column. The flow matrix proposed according to the present technology describes the differences between the pixels in the column and offers the basis or an optimal starting point for the optimisation with a combinatorial method.
2
3
4
2
3
4
In a flow matrix according to the present technology, the vertexes are preferably connected by arrows which are referred to as arcs, to which an allocation is assigned, and which preferably correspond in accordance with their length to the entries of the plurality of separately driven matrices (for example S, M, M, M) into which the matrix display can be decomposed as described above. The matrix decomposition is thereby completely converted into a flow optimisation. The result of the flow optimisation, i.e. the arc allocations is then directly the corresponding matrix elements of the single and multi-line matrices S, M, M, M etc.
2
3
4
For the flow optimisation, in particular in the case of driving of a passive matrix display, it is advantageous for a capacity or a capacity value to be assigned to each row of the matrices involved (S, M, M, M). The capacity value corresponds to the maximum pixel value of the respective row. The sum of all the capacities should then be minimised.
Whereas the capacity is kept constant and the flow is maximised in the case of known MinCut or MaxFlow methods, in the present method the flow is derived from the source matrix (matrix display D) and thus predefined. The aim of the optimisation is to minimise the sum of all the capacities. Therefore, the capacity is according to the present technology designed to be variable. The capacities are increased according to a strategy described below until all the flows are equalised or balanced. A valid assignment of the arcs is then achieved and the matrix decomposition is completed. It can be assumed that the sum of the capacity values is minimal or very small. The ratio between the theoretical minimum and the sum of the capacity values is referred to as the quality of the optimisation. In order to reduce the number of iterations necessary in increasing the capacity values, an assignment of the arcs can be generated as the start value in an initialisation.
According to the present technology, with each iteration the capacities are selected and increased which constitute a bottleneck which prevents a valid solution. This arc set, also called minimum cut (MinCut), can be used as the selection criterion for the capacities to be increased.
In addition, the information of preceding MinCuts can according to the present technology also be used as a selection criterion, wherein the MinCuts of the last iterations can be weighted. This enables a rapid and efficient solution.
In order to accelerate the iteration, the step size with which the capacity value is increased can be adapted dynamically. It is thereby achieved that fewer iterations must be carried out, without losing much optimisation quality with respect to the smallest step size of “one”.
2
3
4
In order to increase calculation speed and reduce the required memory size, the matrix display can be decomposed into a plurality of smaller submatrices and the submatrices can be decomposed separately into flow submatrices. An optimisation of this type is considered a local optimisation, while the matrix decomposition in a single optimisation is considered a global optimisation. Since much fewer iterations are required when optimising relatively small matrices, it is also possible to forward the result of S, M, M, M etc. row by row directly to the register for the output driver without needing buffer memories for these matrices. The outlay on memory is thereby much lower.
2
3
4
Furthermore, a mixed local and global optimisation can according to the present technology be carried out, wherein one or a few rows of multi-line matrices (M, M, M) and/or residual single-line matrices (S) are obtained from a flow submatrix. This achieves a good compromise between local and global optimisation, that is speed and memory size requirement on the one hand, and optimisation quality on the other. The results are output row by row or submatrix by submatrix so that no memory size is required for storing complete matrices.
Preferred applications of the method are the driving of self-emitting displays, for example OLED displays, or non-self-emitting displays, for example LCDs. A further inventive application of the method, which is not concerned with driving matrix displays, rather relates generally to the readout of matrices, for example sensor matrices in CCD cameras.
Further advantages, features and applications of the present technology can be found in the following description of exemplary embodiments and the drawing. All the features described and/or illustrated pictorially form the subject matter of the present technology, regardless of how they are summarised in the claims or of their references.
FIG. 1
ij
ij
schematically shows a matrix display D which is made up of four rows i and four columns j. The matrix display D correspondingly has a total of sixteen pixels ij which are to have the brightness D. Each pixel ij is represented by a square in which the digital brightness value Dis entered as a number. The brightness value “0” stands for a dark pixel ij, the brightness value “1” stands for a dimly luminous pixel ij and the brightness value “2” stands for a brightly luminous pixel.
FIG. 1
a
L
L
therefore shows a matrix display D on which a cross can be seen, with a dim centre in the pixel ij=23 and four bright pixels at its arcs. In conventional single-line addressing (SLA) the matrix display D is driven in such a manner that the rows one to four are activated consecutively in each case for a constant row addressing time twhich is given by the value “1” in arbitrary units. While the first row is being activated, an operating current I is applied to the third column, which current deposits a charge corresponding to the desired brightness “2” in the pixel ij=13. After a row addressing time of t=1 the process switches to the second row. In this second row, the columns two and four are supplied with an operating current I corresponding to the brightness “2” and the column three is supplied with an operating current I corresponding to the brightness “1” simultaneously. An analogous behaviour is produced in the case of a non-self-emitting display for the voltage applied for driving at the individual columns. A typical application is LCDs (Liquid Crystal Display).
L
L
After a further row addressing time t=1, the third row is driven analogously to the first row. Finally, the fourth row is activated for a further row addressing time t=1, which row is however completely dark, that is, during the selected phase of the fourth row (row addressing time for the fourth row), an operating current is applied to a pixel ij in none of the columns one to four.
Frame
L
After a total time T=4*t, all the pixels ij of the image matrix D have been driven once. The human eye integrates the consecutively illuminated pixels ij into a whole image.
FIG. 1
b
i
max
i
Sum
i
Frame
L
i
This conventional method for driving a matrix display D by means of single-line addressing is modified according to the present technology as shown in , in such a manner that the row addressing time tfor each row i is defined as a function of the maximum brightness Dof all the pixels at the intersection points of all the columns j and the row i. This method is also referred to below as “improved single-line addressing” (ISLA). The row addressing time tis in this case dimensioned in such a manner that the sum Tof the row addressing times tover all four rows corresponds to the total time T=4*t.
i
max
i
i
Frame
L
i
i
L
i
When dimensioning the row addressing times t, the procedure can be as follows. The maximum brightness Dof all the columns is for the first three rows in each case “2”, so that the row addressing time tfor these first three rows must in each case be equal. In the fourth row the maximum brightness is “0”, so that this row does not have to be driven at all and t=0 can be selected. The total time T=4*tcan therefore be divided into three row addressing times tso that tfor the rows one to three can be selected to be a third longer than the constant row addressing time t, that is
<math overflow="scroll"><mrow><msub><mi>t</mi><mi>i</mi></msub><mo>=</mo><mrow><mfrac><mn>4</mn><mn>3</mn></mfrac><mo>·</mo><mrow><msub><mi>t</mi><mi>L</mi></msub><mo>.</mo></mrow></mrow></mrow></math>
FIG. 1
a
ij
The first three rows can therefore in each case be activated a third longer than in the driving according to . Since the light intensity in an OLED display depends on the charge which is impressed in the OLEDs and is given by the product of the applied operating current and the row addressing time, the operating current can be reduced accordingly by a quarter in order to reach the same integrated brightness value D, that is
<math overflow="scroll"><mrow><msub><mi>I</mi><mn>1</mn></msub><mo>=</mo><mrow><mfrac><mn>3</mn><mn>4</mn></mfrac><mo>·</mo><msub><mi>I</mi><mi>o</mi></msub></mrow></mrow></math>
L
0
i
1
L
Frame
FIGS. 2
FIG. 2
FIG. 1
FIG. 2
a
b
a
2
The product of tand Iis equal to the product of tand I. This can also be seen by comparing and . The illustrations in show the operating current applied to the third column from over all the rows one to four and the operating voltage proportional to it. The applied current (or the correspondingly applied voltage) is plotted during the row addressing time. As can be seen in , the width of a box shown corresponds directly to the constant row addressing time twhich has been used in the above-described example as the standardising variable. One box corresponds to the activation time of a row. The total width consisting of four boxes corresponds to the total time T, within which an image of the matrix display can be completely built.
FIG. 2
FIGS. 2
a
b
c
2
In , the current waveform for known single-line addressing is described. In the first line, the current is maximal in correspondence with the desired brightness “2”. For reasons of clarity, the associated driving pulse (current×time) for the pixel at the intersection point of the third column and the first line is shaded. This applies in each case also for the further illustrations of and . In the second row with the brightness value “1”, the current is halved. In the third row, the current is maximal again in order to achieve the brightness value “2”. For the last row with the pixel switched off, the current is switched off. This type of driving corresponds to amplitude modulation.
FIG. 2
FIG. 2
FIG. 2
FIG. 2
b
b
b
a
i
shows the current waveform for improved single-line addressing according to the present technology. As described, the row addressing times thave been extended by a third. This is represented by the dashed lines. The fourth row is not activated at all. The brightness of a pixel ij is proportional to the impressed charge quantity which is determined by the current (operating current) integrated over time. As can be seen in , the area below the current curve in is equal to the area below the current curve in , although the current (and respectively the applied voltage) could be reduced in each case by a quarter. This is advantageous for the lifetime of OLEDs.
FIG. 1
FIG. 1
FIG. 2
c
a
c
A further embodiment of the present technology is described with reference to . In this driving method, a plurality of rows are driven simultaneously (multi-line addressing). In the present example, these are the rows one and three, in which a pixel with the brightness “2” must be generated in each case in the third column (cf. ). Since two rows have been combined, the row addressing time can be doubled. The operating current (and respectively the corresponding voltage) is correspondingly halved per pixel (cf. for one pixel).
FIG. 1
FIG. 1
FIG. 1
d
c
b
As shown in , it is particularly advantageous to combine the multi-line addressing method described with reference to with improved single-line addressing corresponding to . It is thereby possible to generate any images in multi-line addressing, since all the activated rows are driven identically in multi-line addressing. Remaining differences and/or residual rows can then be equalised by improved single-line addressing (MISLA).
FIG. 1
FIG. 1
d
a
Frame
Frame
i
In , the second row according to is then generated by a separate driving of a second matrix. This corresponds to a decomposition of the matrix display D into a plurality of matrices which are driven separately and together generate the desired image of the matrix display D. The driving takes place in such a rapid time cycle that the human eye cannot separate the sequential instances of the respective rows and/or matrices being driven and assembles them to form a whole image. The total time T, which is necessary for completely building an image, should therefore not be extended either when a plurality of matrices are used for driving. It is an advantageous procedure to keep the total time Tfor activating all the rows to be driven in all the matrices constant and to adapt the respective row addressing times t correspondingly. The row addressing time tfor one row can in this case be quite different from that for another row, depending on the maximum brightness of the columns in the respective row. This case does not occur however in the currently described example.
FIG. 1
FIG. 1
FIG. 1
c
d
c
ij
i
L
Frame
L
The following method is produced for the combination of the matrices according to and . In each case exactly one row addressing time is needed per matrix for the driving. The maximum brightnesses Dto be achieved are in each case equal. This means that two equal row addressing times t=2*tare needed in order to reach a total time T=4*t. In correspondence with the doubling of the row addressing time with respect to the single-line addressing according to , the operating current or the voltage for each individual pixel ij can be halved, wherein in the case of two-line addressing it must be taken into account that the circuit design of the column-by-column driving of a plurality of rows corresponds to a parallel circuit and the applied operating current is therefore distributed equally to the pixels of all the activated rows. In the case of two-line addressing in a matrix, the applied operating current is therefore to be doubled so that the same operating current is available at each pixel.
FIGS. 1
FIG. 2
c
d
c
1
The current distribution for combined driving according to and can be seen in and shows a further reduction in the maximum operating current without losses in brightness in the matrix display D.
FIGS. 1 and 2
The driving method described using represents a highly simplified configuration with respect to the practical application and serves to explain the underlying idea. According to the present technology, this method can advantageously also be combined with elements of conventional or known methods, for example in connection with precharge and discharge technologies or the like.
A more complex example of driving matrix displays is described below in which all of the described features form the subject matter and are part of the present technology.
FIG. 3
ij
max
0
1
o
The starting point of the description is formed by the properties of a matrix display D which is shown in . The brightness Dof a matrix display can be given in digital values, with the value “0” describing a switched off pixel. The maximum brightness in the matrix is D(e.g. value “255” with 8-bit). The corresponding operating current is . The level of Iis predefined or adjusted by the application. It represents the desired brightness of the display.
Frame
L
max
0
According to the previous SLA (single-line addressing) method which corresponds to the prior art, each row within a frame period (total time T) is assigned an equal, fixed or constant row addressing time t, in which the maximum brightness Dcan be generated. For precisely one bit of brightness there is a corresponding time cycle t.
<math overflow="scroll"><mtable><mtr><mtd><mrow><msub><mi>t</mi><mn>0</mn></msub><mo>=</mo><mi /><mo></mo><mfrac><msub><mi>t</mi><mi>L</mi></msub><msub><mi>D</mi><mi>max</mi></msub></mfrac></mrow></mtd></mtr><mtr><mtd><mrow><mo>=</mo><mi /><mo></mo><mfrac><msub><mi>T</mi><mi>Frame</mi></msub><mrow><mi>n</mi><mo>·</mo><msub><mi>D</mi><mi>max</mi></msub></mrow></mfrac></mrow></mtd></mtr></mtable></math>
0
0
i
max
0
A specific brightness is converted into a number of time cycles tby means of pulse width modulation (PWM) during brightness control. For the maximum brightness, the operating current Iflows for the row addressing time of t=D*t.
i
ij
max
i
L
In the present technology, the necessary selection duration of a row, that is, the row addressing time tselected for this row, is determined by the maximum brightness Dof all the pixels ij in the selected row i. If the maximum brightness in this row is less than D, the next row can be activated earlier, that is the selected row addressing time tcan be shorter than t. The required total time for building an image is therefore:
T
=D
·t
≦T
Sum
Sum
0
Frame
, where
<math overflow="scroll"><mrow><msub><mi>D</mi><mi>Sum</mi></msub><mo>=</mo><mrow><mrow><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><mo></mo><mrow><mi>max</mi><mo></mo><mrow><mo>(</mo><mrow><msub><mi>D</mi><mrow><mi>i</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn></mrow></msub><mo>,</mo><msub><mi>D</mi><mrow><mi>i</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn></mrow></msub><mo>,</mo><mrow><mi>…</mi><mo></mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><msub><mi>D</mi><mi>im</mi></msub></mrow></mrow><mo>)</mo></mrow></mrow></mrow><mo>≤</mo><mrow><mi>n</mi><mo>·</mo><msub><mi>D</mi><mi>max</mi></msub></mrow></mrow></mrow></math>
i
i
max
max
is the sum of the maximum brightnesses Dof a row over all the rows. Dis therefore the greatest brightness of all the columns in the row i.
Sum
Frame
Frame
0
1
1
This time Tis less than or equal to the total time Tand can be extended to Tby the operating current Ibeing reduced to the operating current I. The operating current Iwhich is adapted to the desired brightness is given by:
<math overflow="scroll"><mtable><mtr><mtd><mrow><msub><mi>I</mi><mn>1</mn></msub><mo>=</mo><mi /><mo></mo><mrow><mfrac><msub><mi>T</mi><mi>Sum</mi></msub><msub><mi>T</mi><mi>Frame</mi></msub></mfrac><mo>·</mo><msub><mi>I</mi><mn>0</mn></msub></mrow></mrow></mtd></mtr><mtr><mtd><mrow><mo>=</mo><mi /><mo></mo><mrow><mfrac><msub><mi>D</mi><mi>Sum</mi></msub><mrow><mi>n</mi><mo>·</mo><msub><mi>D</mi><mi>max</mi></msub></mrow></mfrac><mo>·</mo><mrow><msub><mi>I</mi><mn>0</mn></msub><mo>.</mo></mrow></mrow></mrow></mtd></mtr></mtable></math>
1
i
L
max
i
The reduced operating current Iis therefore achieved in that the active or selected phase of a row (row addressing time t) is not tied to t. Instead, each row i only remains active for as long as the brightest pixel ij with the brightness Don this row requires it. When the required time for the brightest pixel is reached, the process switches immediately to the next row.
1
i
1
0
1
With this time-optimised control method, the operating current Iand the time cycle for the row addressing tare variable according to the present technology. The operating current is reduced to Iand the time cycle for exactly one bit of brightness (LSB, least significant bit) is increased from tto t:
<math overflow="scroll"><mrow><msub><mi>t</mi><mn>1</mn></msub><mo>=</mo><mfrac><msub><mi>T</mi><mi>Frame</mi></msub><msub><mi>D</mi><mi>Sum</mi></msub></mfrac></mrow></math>
FIG. 3
FIG. 3
FIG. 1
a
ij
A simple example of this is illustrated in . The image of the matrix display in is described in correspondence with with the matrix D, which contains the brightness values Dat the individual pixel positions ij.
max
The matrix D represents three bright stripes with in each case an intermediate dark stripe, wherein for the sake of simplicity grey scales up to 3 bits, that is a maximum brightness of D=7, are assumed. The matrix display D therefore contains a total of five rows and three columns.
FIGS. 3
FIG. 3
FIG. 3
b
c
b
c.
3
In and , the transient waveform of the (operating) current impressed in the second column is shown. shows the current waveform in conventional single-line addressing (SLA), to which the transient waveform of the improved single-line addressing according to the present technology is compared in
FIG. 3
FIG. 3
b
c
L
i
i
Whereas in the case of single-line addressing () the current amplitude is for example constant at 70 μA and each row is activated for a constant row addressing time tof 2.8 msec, the current amplitude in the case of improved single-line addressing () is 40 μA. The first, third and fifth rows are in each case active for a time (row addressing time t) of 4.2 msec and the second and fourth rows are active for a time (row addressing time t) of 0.7 msec.
1
1
The operating current Iused in the same manner for the driving of the whole matrix D and the time cycle tfor exactly one bit of brightness are now dependent on the image to be displayed in each case. Since in the case of passive matrix OLEDs the diode current is quite high on account of the multiplex mode, the quantum efficiency or the light intensity per current unit is relatively low. The quantum efficiency increases with reduced operating current, which can lead to a further reduced operating current:
<math overflow="scroll"><mrow><msub><mi>I</mi><mn>1</mn></msub><mo>=</mo><mrow><mfrac><msub><mi>D</mi><mi>Sum</mi></msub><mrow><mi>n</mi><mo>·</mo><msub><mi>D</mi><mi>max</mi></msub></mrow></mfrac><mo>·</mo><msub><mi>I</mi><mn>0</mn></msub><mo>·</mo><mfrac><mrow><mi>η</mi><mo></mo><mrow><mo>(</mo><msub><mi>I</mi><mn>0</mn></msub><mo>)</mo></mrow></mrow><mrow><mi>η</mi><mo></mo><mrow><mo>(</mo><msub><mi>I</mi><mn>1</mn></msub><mo>)</mo></mrow></mrow></mfrac></mrow></mrow></math>
η(I) is the quantum efficiency with the current I in the unit Cd/A. The profile of the quantum efficiency is stored in a gamma table and can be used for the above calculation by means of driving electronics according to the present technology, which implement the described method.
1
Since the operating current Iis reduced compared to known driving, the flow voltage of the OLED diodes also falls. The efficiency with the unit Lm/W also increases thereby, since the consumed energy is equal to the integration of the product of current and voltage over the frame period. The higher efficiency achieved also means a lower self-heating of the display, which leads to an increase in the lifetime of the display.
1
1
The implementation outlay is low for this because the operating current Ifor the display must only be set once and a time cycle tis easy to implement.
Sum
max
Sum
i
i
In the driving variant described above, the sum Dof the maximum brightnesses Dof a row is a predefined, invariable amount. If a plurality of rows are combined and driven simultaneously in a matrix, the possibility exists of minimising or further reducing D. During a row addressing time t, a plurality of rows are then selected simultaneously, so that the required time for driving the whole image matrix can be reduced as a whole. The operating current can also be further reduced thereby.
FIG. 4
1
p
i
shows a circuit diagram of how two rows Ri and Ri+1 are addressed simultaneously. The impressed column current is now 2*Iand is distributed equally to the two diodes of the individual rows Ri and Ri+1. The diodes on the remaining rows are passive and are shown only with the parasitic capacitance C. The light intensities are equal in the respective diodes of a column in the simultaneously addressed rows because the same current is applied to each of them. In comparison to single-line addressing, only one row addressing time tis therefore needed for the two rows in order to generate the same brightness in the driven pixels.
This approach also applies when more than two rows are addressed simultaneously. The more rows are combined, the greater the time saving. This is then multi-line addressing.
The combination of a plurality of rows is not however easily possible, since now a plurality of pixels of a column in a plurality of rows are driven equally. There is therefore no longer any difference between these pixels in terms of their brightness, so that differential information is lost or the resolution is reduced.
Sum
This problem is solved in that multi-line addressing (MLA) is combined with the above-described optimised improved single-line addressing (ISLA) by decomposing the desired matrix display D into a plurality of matrices. That is, a row in different matrices S, M is addressed both alone and together with other rows. The difference in light intensity between the pixels in the different rows of the respective column, which are however driven together in multi-line addressing, is realised with the matrix S by means of improved single-line addressing. Multi-line addressing should minimise the required total time T. The conversion of a matrix display D into a single-line matrix S and a multi-line matrix M is represented mathematically as follows.
D=S+M
2,
2
FIG. 5
where M is the matrix for two-line addressing. The matrix S is also referred to as a residual single-line-matrix. The fundamental structure of the matrices can be seen in .
ij
2
2
2
The source data for the individual pixel brightnesses Dof the matrix display D, which data is assembled to form the desired image, is decomposed into two matrices S and M. S is the single-line matrix which is driven by means of improved single-line addressing. M is the multi-line matrix, for whose driving in each case two rows are combined and addressed or activated together. The representation of M in n−1 matrices, where n is the number of rows of the matrix display D, shows that two rows are combined for each of these matrices M, since the entries in the two rows are identical. The combination of two rows is preferably carried out for two consecutive rows because it is assumed that consecutive rows of an image have the greatest similarities and the distribution of the two operating currents in two pixels in consecutive rows of a real display is the most homogenous. In addition, the mathematical decomposition for this restriction is simpler than if two arbitrary rows are combined. The implementation of the algorithms then has a low outlay and is described in more detail below in a realisation according to the present technology.
Non-adjacent rows can of course also be combined, depending on the application. For example, chessboard patterns can be produced very well with multi-line addressing by means of the combination of two rows which are separated from one another by an intermediate row.
i
The row addressing time twhich each pair of rows receives for the activation depends analogously to the above-described realisation on the maximum brightness Mij of a pixel in this pair of rows. The time-optimised driving method which has already been described for single-line addressing is also used here. The sum of the row addressing times is therefore produced as follows:
<math overflow="scroll"><mrow><mrow><mrow><mrow><msub><mi>T</mi><mi>Sum</mi></msub><mo></mo><mi>•</mi><mo></mo><mrow><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><mo></mo><mrow><mi>max</mi><mo></mo><mrow><mo>(</mo><mrow><msub><mi>S</mi><mrow><mi>i</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn></mrow></msub><mo>,</mo><msub><mi>S</mi><mrow><mi>i</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn></mrow></msub><mo>,</mo><mrow><mi>…</mi><mo></mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><msub><mi>S</mi><mi>im</mi></msub></mrow></mrow><mo>)</mo></mrow></mrow></mrow></mrow><mo>+</mo><mrow><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></munderover><mo></mo><mrow><mi>max</mi><mo></mo><mrow><mo>(</mo><mrow><mrow><mi>M</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><msub><mn>2</mn><mrow><mi>i</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>1</mn></mrow></msub></mrow><mo>,</mo><mrow><mi>M</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><msub><mn>2</mn><mrow><mi>i</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><mn>2</mn></mrow></msub></mrow><mo>,</mo><mrow><mi>…</mi><mo></mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mi>M</mi><mo></mo><mstyle><mspace width="0.3em" height="0.3ex" /></mstyle><mo></mo><msub><mn>2</mn><mi>im</mi></msub></mrow></mrow><mo>)</mo></mrow></mrow></mrow></mrow><mo>=</mo><msub><mi>D</mi><mi>Sum</mi></msub></mrow><mo>,</mo></mrow></math>
i1
im
i1
im
i
2
2
where max(S, . . . S) and max(M, . . . , M) give in each case the maximum brightness of a row, which is proportional to the respective row addressing time t.
1
Sum
ij
ij
i+1,j
ij
ij
i+1,j
i
ij
2
2
2
2
The aim of decomposition into a plurality of matrices is a further reduction of the operating current I, that is, a minimisation of D. This is achieved by each brightness Mof the multi-line matrix M reducing two elements in the single-line matrix, namely Sand Sby the amount Mfrom the original data Dund D. Only one row addressing time t, namely the time for addressing M, is however required for this. The effect is correspondingly greater for a plurality of rows.
The transformation of the source data (matrix display D) in a plurality of multi-line matrices is defined analogously by
D=S+M
+M
23+ . . .
3
FIG. 5
where M describes a simultaneous driving of three rows (cf. ). A simultaneous addressing of even more rows takes place correspondingly.
It is also possible to omit some multi-line matrices, for example according to the definition
D=S+M
+M
24,
3
in which the matrix M is set to zero. Single-line addressing can also be interpreted in such a manner that all the elements of the multi-line matrices Mx are set to zero.
The idea of dividing an image or an image matrix D into a plurality of images or image matrices S, M which are easier to drive can be used for all matrix display types including LCD and plasma displays. The multi-line matrix is a good example of simple and efficient driving.
Sum
0
Complete multi-line addressing including single-line addressing is described using a concrete example below. The aim of the transformations carried out is the minimisation of D. The result is that the operating current is no longer Ibut can be much less (depending on the image):
<math overflow="scroll"><mrow><msub><mi>I</mi><mn>1</mn></msub><mo>=</mo><mrow><mfrac><msub><mi>D</mi><mi>Sum</mi></msub><mrow><mi>n</mi><mo>·</mo><msub><mi>D</mi><mi>max</mi></msub></mrow></mfrac><mo>·</mo><msub><mi>I</mi><mn>0</mn></msub></mrow></mrow></math>
FIG. 6
2
max
In the example shown in , a 4×9 matrix D is decomposed into two matrices M and S. The number of rows in this matrix D is n=9. Dhas the brightness value “15” (4 bits).
FIG. 6
ij
Sum
Sum
Sum
max
2
2
The first matrix in gives the desired brightnesses Dof the matrix display D. The second matrix is two-line matrix M and the third is the residual single-line matrix S. M is again shown separately, wherein it can be seen in the illustration of the sums how in simultaneous addressing the brightnesses are distributed in each case to two adjacent rows. D, that is, the sum of the maximum brightnesses of simultaneously activated rows, is D=72 when using the two-line matrix. If only improved single-line addressing is used, D=107. Compared to n*D=9*15=135, the required operating current is therefore reduced to 53% of the conventional driving method by using the two-line matrix.
3
3
2
FIG. 7
FIG. 7
FIG. 6
Sum
ij
Sum
max
If three-line matrix addressing M in accordance with is used, Dcan be further reduced. The first matrix according to is the same as the source matrix in and reproduces the desired brightnesses Dof the matrix display D. The second matrix is the three-line matrix M, the third matrix is the two-line matrix M and the fourth is the residual single-line matrix S. Dis in this case reduced further to 58. Compared to n*D=135, a reduction of the operating current amplitude by 57% is therefore achieved.
FIG. 8
FIG. 6
82
shows the voltage waveform of the eighth row, the current and voltage waveform of the second column and the voltage at a diode (D) for the two-line addressing according to .
0
1
Frame
0
1
Sum
1
FIG. 6
In the example shown, the operating current Ifor the conventional single-line addressing is 100 μA. Corresponding to the reduction to 53%, the operating current during driving of one row is therefore I=53 μA. The flow voltage of the OLED at 53 μA is 6 V. The threshold voltage of the OLED is 3 V. A frame period, that is the total time T, is 13.5 msec. In conventional single-line addressing, the constant row addressing time is t=0.1 msec. In multi-line addressing according to , t=0.1875 msec. A frame now consists of 72 (D) t-cycles.
2
2
1
2
2
2
3
The S matrix and M matrix are activated alternately. First the first row of the S matrix is addressed, then the first pair of rows of the M matrix (that is, its rows and ), then the second row of the S matrix, then the second pair of rows of the M matrix (that is, its rows and ), etc.
FIG. 8
FIG. 4
a
shows the voltage waveform of the eighth row. A corresponding row switch (cf. accordingly ) is then closed when this row is addressed so that a current can flow. The voltage is then zero. Otherwise the row switch is open. Since a column voltage is always flowing, a column voltage of at least 6 V prevails. The row voltage of 3 V is given by the 6 V column voltage minus a threshold voltage of e.g. 3 V in the case of an OLED. The eighth row is addressed for 2.625 msec (from 9.375 msec to 12 msec).
FIG. 8
b
shows the operating current in the second column. Three levels can be seen in the current waveform, namely zero, when none of the pixel diodes are active, 53 μA, when only one pixel diode is active and 106 μA, when two pixel diodes (in the context of two-line addressing) are active. In the case of two-line addressing, the current amplitude at each diode is also 53 μA, because the total current is distributed equally to both of the simultaneously driven pixel diodes.
i
72
7
8
2
The time span (row addressing time t), during which the eighth row is activated, consists of three phases. During the first four cycles (from 9.375 msec to 10.125 msec), row and row are addressed together. The current is therefore also 2*53 μA. This corresponds to the row addressing of M.
8
82
i
81
In the next five cycles, row of Sis addressed. The total of five cycles of the row addressing time tcomes from the maximum of the brightness Sij of the eighth row of the matrix S having the value 5 (see 1st column, 8th row). A current of 53 μA flows for a time of 0.1875 msec (one cycle). The current is then zero for four further cycles, since the maximum of the eighth row of the S matrix (S) is 5 and the brightness control is made by means of pulse width modulation.
2
2
2
82
83
82
The last phase lasts for 5 cycles, during which the eighth and ninth row of the matrix M are addressed. The current is again 106 μA. The current only flows for 4 cycles however, since Mis 4. The current falls back to zero for one cycle. Current still flows in the third column in this last cycle also (not shown), because the maximum brightness in the third column is M=5. The total duration during which operating current is applied to the pixel ij=82 (active time) is 9 cycles, which corresponds to D.
FIG. 8
c
The transient waveform of the voltage in the second column is shown in . It is 6 V when an operating current is flowing and is independent of whether the operating current is 53 μA or 106 μA, since at 106 μA the operating current is divided by two diodes. If there is no current flowing, the voltage falls to 3V. This corresponds to the threshold voltage below which no diode current can flow.
FIG. 8
d
8
shows the transient waveform of the voltage at the diode in the pixel ij=82. The voltage is 6 V when an operating current of 53 μA is flowing through this diode. During the addressed time of the eighth row, no current flows for 4 cycles. During this time the voltage at the pixel is 3 V (threshold voltage). When there is no current flowing in the second column, the voltage at the row switch and at the column switch is 3 V, therefore the voltage at this pixel is then zero. When a current is flowing through the second column, the column voltage is 6 V and draws the potential of this unaddressed row to 3 V (6 V minus threshold voltage).
2
The technical implementation of the method according to the present technology for driving matrix displays is as simple as conventional single-line addressing methods. There is a switch on each row and each column is provided with a current source which in the case of two-line addressing has three current levels (such as 0, 1 und ), whereas in the case of a conventional single-line addressing method there are only two levels (such as 0 and 1). This is because the correspondingly increased current must be available when a plurality of rows are addressed simultaneously. It is generally the case that a graduation with n+1 levels is required when n rows are addressed simultaneously. This is to be implemented however with a low outlay. A concrete circuit for a mixed amplitude and pulse width modulation for controlling brightness is described in more detail below.
2
i
In the above-described example, pulse width modulation of the operating current was used. The S and the M matrices can of course also be produced by means of amplitude modulation of the operating current. In amplitude modulation, each row or each plurality of rows is addressed until it corresponds to the maximum on this row or plurality of rows. This is the same in pulse width modulation. The only difference is that the operating current flows constantly during the row addressing time tand the level of its amplitude is adapted.
Sum
The optimised and efficient conversion of the source matrix (matrix display D) into multi-line matrices M and a single-line matrix S is decisive for minimising the operating current. Optimised means a minimisation of the sum of the maximum brightnesses Dand efficient means a conversion which can be carried out rapidly and with a low outlay on hardware.
The matrices M and S can be obtained or determined in principle with known methods such as linear programming and with standard software. However, complex arithmetic operations such as multiplication and division must then be used, with the result that this method is very slow and calculation-intensive. In addition, the complexity increases more than quadratically with the size of the image matrix.
2
2
3
FIG. 9
A combinatorial method is therefore proposed according to the present technology, which is based on what is known as the “MaxFlow/MinCut” principle. Since the quality of the optimum depends essentially on how two successive rows differ, the side condition D=S+M+M3+ . . . is rearranged by forming the difference between two successive equations without changing the solution space. The matrices d′, S′ and M′, M′ are produced as shown in . The matrix S′ is formed analogously to the matrix d′. The sum of each column of the matrices is zero.
FIG. 10
The rearranged side conditions can be visualised by means of the graph shown in .
ij
ij
ij
FIG. 9
2
3
4
5
Here, each vertex (from a vertex set V), which is shown as a circle, represents an entry in the rearranged matrix d′. d′in the circle represents the corresponding element of the matrix d′ which is shown in . The value of this vertex is therefore equal to the value of the matrix element d′. The arcs between the matrix elements d′are the arrows which lead from one vertex or circle to another vertex or circle. Each of these arcs has a direction which is represented by the arrow and allocated a number. This allocation (number) of the arcs (from the arc set A) reflects the value which the corresponding variable has in the decomposition of the source data matrix display. Arcs which extend from one row to the next belong to the matrix S. Arcs which skip a row, that is have the length “2”, are assigned to the matrix M. Arcs with length three are correspondingly assigned to the matrix M and an analogous assignment takes place for the matrices M, M etc. The indices of the arcs are designated ij, where “i” is the row number for the start vertex (circle) and “j” is the number for the column.
FIGS. 6 and 7
FIG. 6
FIG. 11
FIG. 12
This is explained below using the example already dealt with in . The 4×9 matrix D from is transformed into a 4×10 flow matrix d′ which is given in . This matrix d′ is shown in as a flow to be balanced.
Each element of the d′ matrix corresponds to a vertex in the corresponding position. The arcs are all still allocated zero, since this is the start of the matrix decomposition. A valid decomposition is achieved exactly when the sum of the allocations (numbers) of the outgoing arcs (arrows going out from the circle) minus the sum of the allocations (numbers) of the incoming arcs (arrows arriving at the circle) of each vertex (circle) is equal to the respective value (demand) of the vertex. All the arc allocations are not negative.
FIG. 13
3
2
shows the result of the balanced flow. All elements of the matrices M, M and S are obtained from the allocations of the arcs.
FIG. 13
The mathematical method with which the balanced flow shown in is created is described in more detail below.
FIG. 13
1
2
p
≧0
Two arcs (arrows) in should be the same type if start and end vertexes of both arcs are in each case in the same row. The aim is to find a valid allocation of the arcs so that the sum of the maximum arcs of an arc type is minimised. This can be described mathematically as follows. A directed graph G=(V, A) is given wherein the arc set A according to type is partitioned into A=A{dot over (∪)}A{dot over (∪)} . . . {dot over (∪)}A. p is the number of rows of the multi-line matrices M and the residual single-line matrix S. Furthermore, there is a function b:V→Z, which assigns each vertex with its demand. Z is a whole number (integer). A function f:A→Z(is sought, so that for each vertex vεV the equation
<math overflow="scroll"><mrow><mrow><mrow><munder><mo>∑</mo><munder><mrow><mi>a</mi><mo>∈</mo><mi>A</mi></mrow><mrow><mi>v</mi><mo></mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mi>ist</mi><mo></mo><mstyle><mspace width="0.6em" height="0.6ex" /></mstyle><mo></mo><mi>Starknote</mi><mo></mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mi>von</mi><mo></mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mi>a</mi></mrow></munder></munder><mo></mo><mrow><mi>f</mi><mo></mo><mrow><mo>(</mo><mi>a</mi><mo>)</mo></mrow></mrow></mrow><mo>-</mo><mrow><munder><mo>∑</mo><munder><mrow><mi>a</mi><mo>∈</mo><mi>A</mi></mrow><mrow><mi>v</mi><mo></mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mi>ist</mi><mo></mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mi>Endknote</mi><mo></mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mi>von</mi><mo></mo><mstyle><mspace width="0.8em" height="0.8ex" /></mstyle><mo></mo><mi>a</mi></mrow></munder></munder><mo></mo><mrow><mi>f</mi><mo></mo><mrow><mo>(</mo><mi>a</mi><mo>)</mo></mrow></mrow></mrow></mrow><mo>=</mo><mrow><mi>b</mi><mo></mo><mrow><mo>(</mo><mi>v</mi><mo>)</mo></mrow></mrow></mrow></math>
applies and
<math overflow="scroll"><mrow><msub><mi>D</mi><mi>Sum</mi></msub><mo>=</mo><mrow><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>p</mi></munderover><mo></mo><mrow><mi>max</mi><mo></mo><mrow><mo>{</mo><mrow><mrow><mi>f</mi><mo></mo><mrow><mo>(</mo><mi>a</mi><mo>)</mo></mrow></mrow><mo>:</mo><mrow><mi>a</mi><mo>∈</mo><msub><mi>A</mi><mi>k</mi></msub></mrow></mrow><mo>}</mo></mrow></mrow></mrow></mrow></math>
Sum
is minimal. The upper equation is also called “flow conservation” and corresponds to Kirchhoffs current law. b(v) is the demand of this vertex and can be considered as the current flow from ground into this vertex (where, in the event of negative demand, the current flows from the vertex to ground). Dis to be minimised.
k
The above-mentioned object is equivalent to the problem of assigning a non-negative number (what is known as a capacity) to each arc type A, k=1, . . . , p so that the sum of these capacities is minimal and a valid allocation of the arcs exists, which does not exceed the capacities.
The special feature of this new method is that the capacity is valid for all arcs of a defined length of a row. The flow to each of these arcs is less than or equal to this capacity. The capacities themselves are variable and represent in a certain manner the costs or outlay for the optimisation. The sum of all the capacities must be minimised. In contrast to a known MaxFlow/MinCut method in which the flow is maximised with given capacities, in this case the capacity is minimised with a given flow.
≧0C
k
The capacities are a function u:{1, . . . , p}→Z, so that for all kε{1, . . . , p} and aεAthe following in equation applies: f(a)≦u(k).
The above-described minimisation can in principle also be modelled and solved as a linear program, which is however very calculation-intensive, as already mentioned. As shown below, the above-described method according to the present technology can be implemented mathematically with only a low outlay, as follows.
To this end, the capacities are increased successively, that is step-by-step, from zero upwards until a valid decomposition is possible. This also ensures that the capacity is greater than or equal to zero. In each iteration the set of arcs is determined whose allocation is equal to the capacity and thus constitutes a bottleneck which prevents a valid solution. This arc set, also called minimum cut, separates the vertexes with a positive demand from those with a negative demand. The capacities of the arcs are then increased from the minimum cut. This however preferably only happens for the capacity which allows most of the arcs to leave the bottleneck. The allocations are now increased until either a valid solution has been found or a new bottleneck occurs, whereupon the described steps are repeated.
FIG. 14
i
k
A mathematical formulation of the method sequence can be seen in . The program modules “MaxFlow” and “MinCut” are the standard methods known from the literature. The program module “Initialise” defines the start value for u, for example, u(k)=0 can apply for all kεE{1, . . . , p}. Lower bounds are however preferably used, which have been generated by pre-processing the data. The set H describes the history of the calculated MinCuts. The outgoing arcs of the current MinCut are referred to with C⊂A and the outgoing arcs of the MinCut of the iteration i are referred to with C⊂A. The parameter □u determines the step size with which the individual capacities are increased. Preferably only a few capacities are increased per iteration (e.g. only for the k, for the |A∩C| or the weighted sum
<math overflow="scroll"><mrow><munder><mo>∑</mo><mrow><msub><mi>C</mi><mi>i</mi></msub><mo>∈</mo><mi>H</mi></mrow></munder><mo></mo><mrow><msub><mi>w</mi><mi>i</mi></msub><mo>·</mo><mrow><mo></mo><mrow><msub><mi>A</mi><mi>k</mi></msub><mo>⋂</mo><msub><mi>C</mi><mi>i</mi></msub></mrow><mo></mo></mrow></mrow></mrow></math>
is maximal, wherein earlier steps are weighted less. w describes the weighting of the history. The choice of the size of the step allows a compromise between the quality of the method (small □u, e.g. □u=1) and running time (greater □u) and can also be adapted dynamically.
The method of the present technology can of course also be used for a part region of an image matrix. In this manner an image can be divided into a plurality of segments and each optimised separately, which corresponds to a local optimisation.
2
3
2
3
2
3
A mixed global and local optimisation can likewise be carried out, by displacing a segment of a defined size row by row or by a plurality of rows. The submatrix is formed from a defined number of rows. It is first formed from the upper rows of the source matrix. With each optimisation, the matrix entries (S, M, M etc.) are obtained for the top row or top few rows. The next submatrix is accordingly displaced downwards by one or a plurality of rows. The influence of the previously obtained multi-line matrix row on this new submatrix must be subtracted. Then one or a plurality of rows are obtained again from S, M, M etc. The submatrix runs until the end of the source matrix and is then completely decomposed. In this way all entries of S, M, M etc. are obtained.
i
1
The decomposition of a relatively small matrix requires little memory size and few iterations. With a global optimisation in which the matrix is generally large, the result of the matrix decomposition must be stored in a buffer memory such as an SRAM or the like. The information is not read row by row into the register for the output driver until directly before the activation. With segmented/local or mixed optimisation, the capacities can be obtained first by means of the submatrix decomposition and consequently also by means of their sums, tund Irespectively. Thanks to the rapid decomposition, the row result is then successively calculated again and forwarded directly to the register for the output driver so that the large buffer memory can be omitted. The hardware outlay can be reduced by segmented/local or mixed optimisation, whereas the quality of the optimisation can be reduced somewhat in this case.
i
If the matrices M, S with the individual pixels ij of corresponding brightnesses are fixed, the diodes must be driven correspondingly. The individual row addressing times tcan vary from row to row and in each case follow the maximum brightness value of these rows. The brightness can be controlled by means of pulse width modulation or amplitude modulation of the current.
With pulse width modulation, only the pixels ij with the maximum brightness are switched on during the entire row addressing time, that is the operating current flows through them. The remaining pixels ij light up only temporarily, with the respective light-up time being correlated with the respective brightness value Sij, Mij.
i
Alternatively, amplitude modulation can also be used to control the brightness, so that all the pixels ij in the active phase, that is during the respective row addressing time t, are switched on 100% of the time and the operating current in pixels ij with lower brightness is reduced correspondingly. Amplitude modulation is however more difficult to implement with regard to hardware. This applies in particular in the case of high colour depth or a large number of greyscales, whereas pulse width modulation can be implemented comparatively simply and precisely without a high outlay being required for the hardware used.
FIG. 15
FIG. 18
It is particularly advantageous to combine pulse width modulation with amplitude modulation in order to reduce the operating current in pixels ij with lower brightness. This mixed or combined amplitude and pulse width modulation according to the present technology is explained below with reference to to .
4
1
For the above-mentioned multi-line addressing according to the present technology, the operating current must be quantified, that is, divided into a plurality of different levels, in order to feed the currents for single, two and multi-line addressing into the columns and to adjust the level of the current accordingly. For example, for four simultaneously driven rows in multi-line addressing M, four times the operating current (4*I) must also be impressed.
FIG. 15
1
1
1
1
To this end, the current source can be implemented with three transistors, as shown in , consisting of two single-transistor cells and one two-transistor cell. These three transistors receive the same control voltage at the gate when an operating current I=4*Iis required for four rows. If an operating current of I=3*Iis needed, no control voltage is applied to one single-transistor cell, while a control voltage is applied at the respective gate for the two-transistor cell and the other single-transistor cell. For an operating current of I=2*I, either the two-transistor cell is active and the two single-transistor cells are passive, or vice versa. For an operating current I=I, only one single-transistor cell is active.
ij
ij
FIG. 18
The quantified operating current can also be used to reduce once again the operating current given a matrix entry whose brightness value M, S is not a maximum. The algorithm shown in for the brightness values Mcan for example be used for this purpose. The result corresponds to combined pulse width and amplitude modulation for controlling brightness.
FIG. 17
FIG. 16
FIG. 17
FIG. 16
The result of this combined brightness control is shown in in comparison to exclusive pulse width modulation for controlling brightness (). In a pure pulse width modulation, the current amplitude is for example a constant 100 μA. The pulse width of the first pulse is 6 of 10 units ( 6/10), wherein the active duration of this row is 10 units (row addressing time of 10 units). Since 6 units is greater than half of 10 units and less than ¾ of 10 units, the pulse width of the first pulse is extended to 4/3 of the original value with the mixed amplitude/pulse width modulation. At the same time, the amplitude is reduced to ¾ of the original amplitude (that is in the example 75 μA). This can also be seen in in comparison with . The pulse width of the second pulse is doubled, while the amplitude is halved analogously thereto. The third and the fifth pulses cannot be extended, since their pulse widths are close to the active duration (row addressing time) of the respective row. The width of the fourth pulse can in contrast be quadrupled.
FIG. 17
It can be seen clearly in that the mean amplitude of the operating current is reduced in a mixed or combined amplitude and pulse width modulation for controlling brightness.
FIG. 18
Of course, only parts of the above algorithms shown in can be used. These algorithms also apply for the single-line matrix. In multi-line addressing with a different number of rows, the algorithms are formulated in a corresponding manner. The algorithms follow the quantification of the current source.
With the present method for driving matrix displays and a display control system set up for carrying out the above-described method, to which control system the present technology also relates, it is therefore possible to achieve optimised driving of matrix displays. This can be used for improving performance, for example an increased frame rate, and/or for reducing the operating current required for driving the individual pixels. Essential features are that the row addressing time for each row depends on the maximum brightness which a pixel in this row must achieve, and/or that the matrix display is decomposed into a plurality of separate matrices of which some represent multi-line driving.
1
1
The present technology also relates to a control system for carrying out the above-described method. To this end, the claimed method can be implemented in an application specific IC (ASIC), if for example the display controller and the display driver are integrated in one chip. tand Iare generated in the driver. The matrix decomposition is realised with combinatorial logics which are simple and fast.
Since an image and consequently also the derived matrices are always data intensive, a memory is also required. This requirement can be reduced with a modern semiconductor process or as described above also with local or mixed optimisation. The present method can also of course be divided between a plurality of chips.
BRIEF DESCRIPTION OF SEVERAL VIEWS OF THE DRAWINGS
FIG. 1
shows schematically various embodiments of driving a matrix display according to the present technology in order to explain in a descriptive manner single-line and multi-line addressing;
FIG. 2
FIG. 1
shows schematically time diagrams of the operating current (or the associated voltage) for driving the pixels of a column of the matrix display shown in ;
FIG. 3
shows a matrix display D consisting of three columns and five rows and the current required for driving a column;
FIG. 4
m
n
shows the equivalent circuit of a matrix display with m columns (C) and n rows (R);
FIG. 5
shows a definition of single and multi-line matrices;
FIG. 6
shows a decomposition according to the present technology of a matrix display D into a two-line matrix and a single-line matrix;
FIG. 7
FIG. 6
shows a decomposition according to the present technology of the matrix display D shown in into a three-line, a two-line and a single-line matrix;
FIG. 8
FIG. 6
shows voltage and current waveforms for selected lines of matrices according to ;
FIG. 9
shows a decomposition of the matrix D into a flow matrix d′;
FIG. 10
FIG. 9
shows a flow diagram of the flow matrix d′ according to ;
FIG. 11
FIG. 6
shows a concrete example of the matrix D according to converted into the flow matrix d′;
FIG. 12
FIG. 11
shows a flow diagram of the flow matrix d′ according to in a first optimisation step;
FIG. 13
FIG. 11
shows a flow diagram of the flow matrix d′ according to after the optimisation step;
FIG. 14
shows a mathematical flow chart for creating the flow matrix d′ and an optimised flow diagram;
FIG. 15
shows an embodiment according to the present technology for generating the operating current;
FIG. 16
shows brightness control by means of pulse width modulation;
FIG. 17
shows brightness control by means of combined amplitude and pulse width modulation; and
FIG. 18
FIG. 17
shows an algorithm for carrying out brightness control according to . | |
The SWBAT identify and create related facts to 20.
It's all in the family! In this lesson, students will build fact family "houses" by using 3 numbers and writing the related addition and subtraction sentences.
Start by reading “The Fact Family: A Teaching Rhyme About Inverse Number Relationships” by Sandy Turley.
I like to read this story because it easily relates mathematical fact families to real families.
I then give each child 20 connecting cubes – use 2 different colors and give each child 10 of each (ex. 10 red & 10 blue). Write 4 + 5= __ on the board/chart paper. I then have the students use their connecting cubes to model how to solve the problem.
Next, I write 5 + 4 = __ on the board. Again, I have the students use their connecting cubes to model how to solve the problem. I continue this activity by writing the two related subtraction sentences on the board (9-5=__ and 9-4=__). Ask students if they notice the pattern with the math sentences. Guide the discussion to the understanding that there is a pattern between the three numbers in a fact family.
Put students in groups of 2 and have each student select a number between 1 and 10 to add. Using connecting cubes, have pairs continue model how to add the two numbers. Guide them to model the subtraction facts in the same family as well. Use this same strategy and guide pairs through several fact families, walking around to make sure that they understand the concept.
Have students complete the attached sheet where they build their own fact family houses. Students use the three numbers in the “roof” of the house to write the fact family. Students cut out the “roof” and the house and glue to paper. Then they write the corresponding fact families on the houses. | https://betterlesson.com/lesson/566854/identify-related-facts-day-2-of-2?from=mtp_lesson |
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At our house, it’s a tradition that for Halloween I make my mom’s Sweet Chili for dinner. Then I usually make cornbread or bread sticks to go along with it. If you have a similar tradition, I have a great recipe for you to give a try this year, Pumpkin Cornbread. This is a recipe that I found at Recipe Girl. It really intrigued me with how it would all taste.
This recipe is much healthier than my normal cornbread recipe. Not only are you adding nutrition with the addition of pumpkin, it also includes whole wheat flour and only 1/4 cup of oil. My cornbread recipe is so delicious but it calls for 1 whole cup of butter. I was really surprised at the flavor of this cornbread. It was so delicious and a nice change. You really can’t taste the pumpkin but you do get a cornbread with a nice fall flavor from the addition of molasses, cinnamon and nutmeg. Give it a try!
Make sure to stop back tomorrow. I am going to share a recipe that I served with this cornbread that made it even more tasty. Then on Saturday, I’ll share a quick recipe you can add to your Halloween meal.
Pumpkin Cornbread
Ingredients
- ½ cup all-purpose flour
- ½ cup whole wheat flour
- 1 Tbsp baking powder
- 1 tsp salt
- ½ tsp ground cinnamon
- ¼ tsp ground nutmeg
- 1 cup cornmeal
- 2 large eggs
- 1 cup pumpkin puree (canned or freshly cooked and processed)
- 2/3 cup brown sugar
- ¼ cup canola oil
- 1 Tbsp molasses
Instructions
1. Preheat oven to 400°F. Grease 10-inch glass pie pan or 9-inch square baking pan.
2. Sift flours, baking powder, salt and spices in a large mixing bowl. Whisk in cornmeal.
3. In separate bowl, beat eggs lightly. Whisk in pumpkin, brown sugar, oil and molasses.
4. Make a well in the dry mixture. Add pumpkin mixture and blend batter with a few quick strokes (just until blended- don’t overmix. I also do this this a fork).
5. Pour batter into prepared pan. Bake for 30 minutes, or until cornbread is browned and the surface has a slightly springy feel. | https://www.realmomkitchen.com/pumpkin-cornbread/ |
Cleansing The Black Truffle
When you’ve gotten recent black winter truffles, don’t clear them till your are able to eat them. Different sensible they may spoil faster. Take away any soil from the black truffles simply earlier than utilizing them in any recipe. They have to be washed with water and a nail brush underneath operating water. The truffle have to be fully clear since they are going to be used unpeeled. Dry effectively with a paper towel.
The black truffle (Tuber Melanosporum) should at all times be used as a condiment, not as a meals. Use solely recent truffles, if attainable. To get pleasure from and respect the black truffles, 100 g is sufficient. With this quantity we are able to make a number of recipes.
The best way to use black truffles to taste meals.
Use an hermetic container and put collectively the meals you need to taste with the black truffle. Shut the container and depart it within the fridge for not less than 24 hours. The aroma of the black truffle will penetrate the meals within the sealed container. The black truffle aroma adheres to fatty meals greatest.
Truffled eggs
Take half a dozen eggs and place them in an hermetic container with a recent black winter truffle, washed and wrapped in paper towel, however not fully wrap the truffle. Shut the container and put within the fridge for 2 days. The excessive porosity of the eggshell will enable the aroma of the truffle to penetrate the eggs. Then you should use these eggs to make truffled flan, use in stuffing or simply eat them fried. You possibly can add a bit of sliced garlic to the new olive oil earlier than frying the eggs. Fry the eggs when the garlic is barely brown. These truffled eggs will delight your palate.
Risotto Parmesan with Black Truffles
Could be severed as a starter or a predominant course
Serves 2 – 4 individuals.
Substances:
150g black truffles
320g rice
120g grated Parmesan cheese
50g butter
Half a tablespoon heavy cream
Directions:
Boil the rice till it’s al dente and drain effectively. Add the butter, cream, Parmesan and about half of the grated black winter truffles. Stir till it’s effectively blended and serve sizzling, garnish every plate with a beneficiant quantity of the remaining winter truffle shavings.
Salad with Black Truffle
Substances:
3 Arduous Boiled Eggs
2 massive handfuls of inexperienced beans
1 medium sized lettuce
1 massive handful of Rucola
1 Bunch of dill
70g black winter truffle
Creamy Dressing
4 tablespoons additional virgin olive oil
3 tablespoons creme fraiche
3 tablespoons double cream
2 tablespoons of lemon juice
2 tablespoons white wine vinegar
Cayenne pepper
Salt
Directions:
Wash the lettuce & rucola and shake off the entry water. Let drain in a collander whereas making ready the dressing. Prime and tail the inexperienced beans, then boil them in salted water till tender. Take away and wash in chilly water, then combine in with the lettuce and rucola.
The dressing is ready by mixing all of the above components collectively in no explicit order. NOTE – The cayenne pepper is added on the finish.
Place the blended rucola, lettuce and inexperienced beans on a plate. Slice the boiled eggs and truffles over the mattress of lettuce, including the dill.
Lastly, add the creamy dressing over the salad.
Stuffed Hen Breasts with Black Winter Truffles
Substances:
4 hen breasts
80g Fontina cheese
80g prosciutto ham (Parma-type)
30g butter
1 small onion
1 glass dry sherry
1 medium sized black winter truffle
Inventory
Additional virgin olive oil
Flour
Salt
Recent floor pepper
Directions
Slice the hen breast lengthways with out fully separating. Flatten with a meat mallet and frivolously salt, pepper and flour. Place two slices of ham, a slice of Fontina cheese and a skinny layer of black winter truffle inside every pockets or hen breast. Shut and stitch up with kitchen twine or utilizing picket toothpicks. Brown the chopped onions within the oil and butter in a big pan. Once they begin to soften, add the hen breasts and brown on either side, moist with the sherry and cook dinner, including a small quantity of broth if obligatory. Serve highly regarded. Accompany with wild rice or boiled potatoes. | https://www.worldclassshippingcontainersforsale.com/2022/09/24/black-truffle-cleaning-and-recipes/ |
NORTH FINCHLEY LIDO & LEISURE CENTRE, N12
Building on a good relationship established on previous successful projects, Guild were appointed as the Main Contractor by Barnet Council to deliver the structural repair & restoration works to the centre which had been closed to the public for some time due to structural failures to the glulam beams which formed the roof. It was discovered that many of the supporting steel columns and beams were also subject to progressive rust and structural failure.
read the full case study here
HENDON LIBRARY, NW4
Guild acted as Main Contractor for this project to the Grade II listed building, although in use as a public library and part of Middlesex University, it had been neglected for some time. Rainwater ingress was becoming an increasing cause of damage to some elements of the building’s impressive decorative interior, the scope of works included a new roof with improved thermal performance and associated restoration and repair. Guild secured the contract after a competitive tender process and undertook all works whilst the building remained in use.
The large air conditioning systems to the shared areas and IT server rooms were required to be decommissioned and moved to allow for the installation of the new roof works, this was a particularly sensitive element of the project as the council’s and university’s main servers were housed within the building so it was necessary to install temporary air conditioning for the duration of the project to ensure the IT systems would be kept at the correct temperature, any failure to the IT systems for these two institutions would have been disastrous. Thanks to our meticulous planning and conscientious management of the project the switch overs occured without issue. Following the completion of the roof works the AC systems were lifted back in place and recommissioned in line with the regulatory guidelines.
HIGHGATE CEMETERY CHAPEL, N6
Guild were approached to undertake structural conservation repairs to the decayed chapel roof timbers and external remedial works to the roof. Working for The Friends of Highgate Cemetery Trust and alongside the project architect and a structural engineer, replacement timbers were designed and scarf joint repairs were expertly installed by our specialist conservation carpenters using approved materials & methods and finished to match the existing. Works were completed on time and budget with minimum disruption to the users of the chapel.
Overview of works
- Structural survey
- Design of structural repairs
- Timber replacement & conservation
- External roof repairs
HENDON PARK CEMETERY & CREMATORIUM, NW7
Guild successfully tendered for the restoration & refurbishment project as main contractor, we undertook an extensive scope of works over a 12 week programme. Due to the sensitive nature of the project location the works had to be carefully planned with consideration to services as the crematorium, chapels and cemetery remained operational throughout the project.
The cemetery is entered through a ‘quaint Old English Style’ (Pevsner) Gothic and Tudoresque gatehouse designed by architect Alfred A. Bonella.
Bonella also designed the flint-faced chapel in the centre of the cemetery, which opened in July 1903, and was ‘inspired by old Hertfordshire churches’ according to the cemetery brochure of 1903… inside is a terracotta reredos by Cantagalli, a copy of Luca Della Robbia’s ‘Resurrection’ in Florence Cathedral.
Appointed by London Borough of Barnet and Capita, we delivered a successful restoration & refurbishment project to the delight of the client’s project team. Working in constant liaison with the site based Cemetery staff, we managed the programme around the busy schedule of services to finish within the initial project programme despite uncovering significant additional remedial works, which were urgently required to the roof.
Overview of works
- Stone indents & restoration
- Lime plaster
- Replacement of Lead box gutter
- Slate works to roofs
- New Rooflights to Crematorium
- Parquet flooring restoration
- Paving
- New carpets
- Upgrade of remotely controlled motorised tracks
- Replacement curtains and alter covers
- New Audio control system
- Complete redecoration & refurbishment
- Electrical works including upgrade of lighting
We worked on the North & South chapels, the Crematorium, the Cloisters, Book of Remembrance room and Meeting room. Our client was delighted with our quality and performance during the contract which saw the team working around the clock and even over the xmas period with only 2 days off site. The cemetery remained operational with services and ceremonies for the duration of the works, as challenging as that was, we managed the works without causing delay or upset to the client and most importantly, the cemetery users in this sensitive environment.
CHISWICK HOUSE, W4
We were appointed by the Chiswick House & Gardens Trust to undertake essential restoration, repairs and refurbishment works. The Grade I listed Chiswick House is a glorious example of Neo-Palladian architecture in London, the house was designed by Lord Burlington, and completed in 1729. The house and gardens occupy 26.33 hectares (65.1 acres) the gardens were created mainly by architect and landscape designer William Kent. The garden is one of the earliest examples of the English landscape garden.
Overview of works
- Lime Harling (rough cast) to garden walls
- Lime render & plaster repairs
- Removal of cement mortar render & pointing
- Damp remedial works
- Brick matching, replacement & restoration
- Structural repairs to masonry
- Roof works – improvement of detailing and lead work
- Complete redecoration & refurbishment of the Learning Centre
The Learning Centre, situated within the grounds and bordering the kitchen garden had been long suffering from damp to the masonry caused by the absence of adequate ventilation and the historic use of cement based renders and brick pointing to the walls. We removed the cement based mortars that were trapping moisture and introduced air bricks to allow constant ventilation which has allowed the masonry to finally breath and dry out. Upon removal of the cement based mortars it became apparent why a render had been applied, although structurally sound the face of the bricks were in a poor condition so lime pointing was not an option, it was decided that the walls should be finished with lime harling to offer a breathable and durable finish which is also aesthetically in keeping with the building.
SHOREDITCH HIGH ST, EC2
Located on the busy Shoreditch High Street, the building and ground floor retail units remained in occupation for the duration of the works. Continuous liaison with the client, Local Authority and Transport for London was maintained which helped to achieve an efficient programme of works.
Work begun with a complete masonry survey to the severely decayed terracotta units, once a detailed replacement schedule was determined the units to be replaced were designed to match the originals, many intricate individual units were replicated including ornate fretted balustrade, cornice, dentils, scrolled pilaster caps, window surrounds, pediments and finial plinths, in total almost 50% of the terracotta required replacement. The building which had been largely derelict since the 1980’s was considered for demolition until a full restoration programme was put into action. We were instructed to design, supply and install new cast terracotta units where the originals had severely decayed, we also sourced and procured reclaimed bricks to exactly match the originals that required replacement and carried out a complete re-point of the masonry.
Overview of works
- Design & installation of new terracotta units
- Doff cleaning
- Insitu repairs to terracotta
- Restoration of brick & re-pointing
- New specialist roof tiles and lead work
- Restoration of copper finial
- Timber window restoration
- Refurbishment of public clock
- External lighting
NEW BOND STREET, W1
Our expertise was sought to advise on and undertake exploratory works and paint removal samples to the granite and brick work of this imposing facade located in Europe’s most expensive retail location. The client, a high-end fashion designer had acquired the property and wished to find out if the granite and brick extended beyond what was currently visible. During the trials we discovered that the paint and plaster was covering the beautiful natural granite columns, block work and brick, with this established we were instructed to remove all coatings.
Using various paint softening poultices we began the process of establishing a suitable methodology to carefully and safely remove the many layers of inappropriate paints and coverings. Once we had broken down the multiple layers of paint with the poultices and could see the original masonry, a super-heated low pressure water system was used to remove stubborn oily residue that the poultice could not lift.
Overview of works
- Paint removal trials and exploratory works
- Development of suitable paint removal methodology
- Facade restoration and clean to granite, Portland stone and brick work
Our skilled stone masons used hand tools to remove the thick gypsum plaster and cement which had been applied internally to the granite and brickwork, with this removed we worked on the restoration to reveal the raw granite which made a strong feature and contrasted well with the sharp and clean finishes throughout the designer fashion store.
ISLINGTON, N1
We were initially asked to repair these steps under the instruction of a conservation architect, after we undertook a survey of the condition it was apparent that the steps were structurally unsafe and were a danger to use and therefore needed replacing. The client’s architect and structural engineer proposed a scheme that the client rejected. We were then asked for an alternative solution, Guild put forward a proposal and the client was happy to proceed with our alternative approach. Working directly with our structural engineer we designed the bespoke steps, created the moulds in the workshop and cast the units with reinforced steels to replicate natural Portland stone. All rebuilt brickwork and render finish was done with lime mortar. Read client’s review here:
Overview of works
- Design & installation of new cast stone units
- Structural engineer’s report
- Demolition of unsafe steps and brickwork
- Rebuild of brickwork
- Lime render
- Restoration & installation of original wrought iron railings
ST JOHN’S WOOD, NW8
Guild were contracted to undertake a full re-design and restoration to the facade of this early Victorian 4 storey town house situated within a conservation area just off Regent’s Park. During a full internal and external refurbishment programme, the client’s builder had removed all original architectural details to the facade. Guild’s expertise was sought to design, cast and install details to fit with the vernacular aesthetic of neighbouring properties.
Overview of works
- Design & installation of new cast units including full cornice, window hoods & architrave surrounds, large ornate corbels and window cills
- New render to facade
- Design & installation of heritage iron railings to match neighbouring
HIGHGATE, NW5
It was initially assumed that the 2 porticos and cantilevered balcony stone slab were likely to require demolition and complete rebuild at considerable financial expenditure to the client. Working with a structural engineer we designed suitable reinforcements to the fractured original stone balcony slab and the portico & columns which meant that we were able to undertake restoration and omit the need to completely rebuild these original structural elements.
Overview of works
- Structural supports to damaged balcony & porticos
- Stucco restoration
- Restoration of stone work
- Redecoration
The balcony slab had extensive fractures which required consolidation and support, stainless steel cramps were installed across the fractures and galvanised support brackets were designed, fabricated and installed to ensure that the balcony remains safe for use without the need for a costly rebuild.
The porticos also showed signs of movement fracture so lintels were installed beneath the columns to give additional structural support and the fractures were physically “stitched” with stainless steel to consolidate their structural integrity. Following the completion of structural repairs all architectural mouldings and details were restored to original profiles.
PERIOD PROPERTY RESTORATION & EXPANSION, LONDON
This Edwardian terraced house was in a poor state of repair when Guild were commissioned to undertake the project. We restored the facade back to it’s original design and returned the property’s period appeal. A dormer loft and rear extension were also added to expand and modernise the the former wreck into a family home.
Overview of works
- Removal of pebble dash
- Doff cleaning
- Brick restoration & lime pointing
- Restoration of stone work
- Timber sash window install
- Portland stone plinths with heritage gate & railing
- Traditional tiled pathway and stone paving
- Redecoration
- Ornate plasterwork restoration
- Design & build of loft conversion & ground floor extension
Overview of works
- Removal of all existing damaged stone
- Cast restored replica stonework and install as per original
- Demolition & rebuild of parapet wall and upper cornice
- Render to 3 elevations
- Redecoration
Overview of works
- Lime render to entire facade
- Cast restored replica stonework enrichments and install as per original
- In-situ repairs to stonework window hoods & portico
- Heli-bar reinforcements to fractures in brick and stone work
NOTTING HILL, W2
We supplied and installed missing architectural details to match the originals, this included the restoration of two large rams head urns, moulds were created from original details and replacement casts were produced which included acanthus leaf cornice corbels, balustrades, floral enrichments and finally the restoration to areas of failed stucco prior to redecoration.
Overview of works
- Cast restored replica stonework enrichments and install as per original
- In-situ repairs to stonework & stucco render
- Heli-bar reinforcements to fractures in brick and stone work
- Redecoration
BLACKHEATH, SE3
The large bay windows to this facade required new cornice and lambs tongue stringer courses to be supplied and installed by us. Details were taken from original features that remained intact elsewhere on the facade and moulds were produced for the casting of like-for-like units. Following installation of the new casts we undertook a number of in-situ repairs to the stucco and consolidated other areas that were showing signs of decay.
Overview of works
- Cast restored replica stonework enrichments and install as per original
- In-situ repairs to stonework & stucco render
- Heli-bar reinforcements to fractures in brick and stone work
- Redecoration
We were instructed to undertake restoration works to the facade of this property in Crouch End. The client’s surveyor had identified that some areas of the existing ornate masonry had decayed to the point that it posed a high risk of substantial pieces of stone falling onto the pedestrian footpath below. Replacement stones were indented where necessary and in-situ repairs carried out to moulded details prior to redecoration.
Overview of works
- Cast restored replica stonework details & enrichments
- In-situ repairs to stonework
- Brick repair & pointing
- Heli-bar reinforcements to fractures in brick and stone work
- Repairs to failed steel lintels
- Redecoration
KINGS ROAD, SW10
Following a survey to this property, the decorative masonry mouldings were found to have de-bonded from the facade presenting a realistic potential for falling masonry in the near future. All parties were in agreement that it was not cost effective to restore these areas with in-situ repairs so we were instructed to restore the facade of this property with replacement cast units. The restoration works included the removal of the decayed moulded details, preparations of the masonry substrate and installation of new moulded window surrounds, window hoods, cornice, decorative frieze panels and corbels.
Overview of works
- Cast restored replica stonework details & enrichments
- In-situ repairs to stonework
- Brick repair & pointing
- Heli-bar reinforcements to fractures in brick and stone work
- Repairs to failed brick lintels
- Redecoration
As is often the case with restoration works; we cannot always predict the condition of the substrate, we can only speculate that fractures can suggest more serious ongoing problems that can only be determined once preparation works are underway. The arched brickwork window head had shown signs of movement, evident in surface fractures to the moulded stucco. Following the removal of the stucco it was evident that the mortar binding the brick lintel had failed and was about to collapse so we needed to remove all loose masonry and install a concrete lintel before making good and installing the new mouldings as per the original facade. | https://guildrestoration.com/case-studies/ |
New to tuning w/ my I2 & have the 87 perf. tune installed w/ no issues thus far. I have been playing around with the data logging functions & have a few questions:
1 - can the data be logged & viewed "live" if I have PC hooked up in the truck?
2 - can the measurement units be converted in the software to something more palatable (i.e. mph instead of default kph, psi instead of kpa)
3 - what is the proper PID to measure boost? the options I have selected thus far are all measured in kpa & when I convert to psi I get either 671psi (4629.6 Kpa boost absolute pressure), 4.6psi (31.76 KPA intake manifold ABS. pressure) or .572psi (3.948 Kpa Turbo/Supercharger boost pressure desired). I was under the impression stock boost was between 12-16psi and none of these measurements are even close. | http://forum.diablosport.com/viewtopic.php?p=299945 |
Patient beds having alarms or alerts associated with various bed events are known in the art. For example, in some patient beds, bed alarms or alerts are generated in response to lowering of a siderail of the bed, releasing a caster brake of the bed, raising an upper frame of a bed from its lowest position, movement of a patient toward exiting the bed, and movement of a head section of a mattress support deck above or below a threshold angle, just to name a few. The terms "alarm" and "alert" are used interchangeably herein and each is intended to have the meaning of both. These bed event alarms are indicative of conditions that, in some instances, relate to patient safety. However, in some circumstances, the occurrence of the bed event may not require the assistance or intervention of a caregiver.
With regard to the example of a bed exit or patient position monitoring system, there is a potential for a high number of false alarms. Such false alarms may result from a patient simply repositioning themselves in bed rather than actually moving toward exiting the bed or a visitor sitting or leaning on the bed and then removing their weight from the bed. This can lead to alert fatigue by caregivers which can potentially create a "cry-wolf phenomenon." That is, after a experiencing multiple false alarms, caregivers may be less responsive to such future alerts or may even ignore the future alerts. Setting the bed exit alarm level to the least sensitive level in an attempt to reduce false alarms does not afford caregivers sufficient time, in some instances, to reach the bedside before the patient has exited the bed and starts walking away from the bed. These circumstances can potentially lead to bed exit or patient position monitoring systems not being used at all by caregivers.
Today, some healthcare facilities may employ remote monitoring of patient rooms using camera based systems and associated monitoring personnel. However, remote monitoring personnel do not have the benefit of regularly interacting with the patient and thus, may not be as effective as bedside caregivers in determining the need to intervene. They may also be less effective in negotiating with patients to stay in bed or wait for assistance, for example, because they do not have the personal relationship with the patient that assigned caregivers do. Thus, what is needed is a system that reduces alarm fatigue of caregivers and that provides an effective patient safety enhancement.
The present disclosure provides an apparatus or system which may comprise one or more of the following features alone or in any combination.
A system may include a patient bed and a camera system that automatically, in response to an occurrence of a bed event, may record a video feed of a patient on the bed for a period of time and/or transmit a video feed of the patient for a period of time. The camera system may also take a picture of the patient.
The bed event may include a weight reading being taken, for example. The weight reading and the picture or video may be transmitted from the bed to a remote computer. Alternatively or additionally, the bed event may include movement of the patient on the bed. For example, the movement of the patient on the bed may include a threshold amount of movement that may be sufficient to trigger a patient position monitoring alarm of the patient bed. As another example, the movement of the patient on the bed may include a threshold amount of movement that may be sufficient to trigger a bed exit alarm of the patient bed. The camera system may include a camera and at least one computer device remote from the camera.
According to this disclosure, a system may include a patient bed, a first computer device that may be remote from the patient bed, a camera system that may automatically, in response to occurrence of a bed event, provide a video feed to the first computer device, and a portable computer device that may be transported by a caregiver. The video feed may be sent to the portable computer device by the first computer device in response to receipt of the video feed from the camera system.
In some embodiments, the first computer device may record the video feed for a period of time. A second computer device may be remote from the patient bed. The first computer device may transmit the video feed to the second computer device for recording and storage by the second computer device. The portable computer device may include a workstation on wheels or a wearable device. For example, the wearable device may include eye glasses with video display capability in a field of view of the caregiver or the wearable device may be configured to be worn on the caregiver's wrist. Alternatively or additionally, the portable computer device may include a handheld phone.
Alternatively or additionally, the video feed may be transmitted by the first computer device to a display of a patient bed that may be near the caregiver. The system may include a real-time locating system (RTLS) that monitors the whereabouts of caregivers and equipment in the healthcare facility. The bed to which a video feed is to be transmitted is determined based on information from the RTLS indicating which bed a particular caregiver is near. Further alternatively or additionally, the video feed may be transmitted to a display mounted to a wall of a room in which the caregiver may be located. Information from the RTLS is used in such instances to determine the room in which the caregiver is located, thereby to determine the display to which the video feed is to be transmitted.
In some embodiments, the video feed may be transmitted to a nurse station computer that may be located at a nursing station. According to this disclosure, the first computer device may be configured to control at least one of angle and zoom of a camera of the camera system. In response to the video feed being sent to the portable computer device, an audio channel may be opened between the portable computer device and a speaker in the patient's room so that the caregiver may be able to talk to the patient.
In some embodiments, a caregiver may be able to retrieve past video recordings or past pictures for viewing on a display such as a graphical user interface (GUI) of a patient bed, a wall mounted display, and/or a display of a computer device such as the caregiver's portable computer device. Such past videos or pictures may be useful, for example, in connection with weighing a patient on the patient bed or in connection with zeroing a weigh scale system of the patient bed. The caregiver may compare the past video or picture with the current state of the patient bed to check for any changes in equipment, sheets, pillows, etc. on the bed. If there are changes as compared to the past state of the bed, the caregiver may take steps to re-zero the weigh scale system so that subsequent weight readings of the associated patient may be accurate.
Fig. 1
is a partly perspective, partly diagrammatic view showing a camera mounted to a ceiling and aimed at a patient on a hospital bed, the bed being coupled to a network via a network interface, the camera also being coupled to the network, a real time locating system (RTLS) being coupled to the network and receiving a wireless signal from a tag worn by a caregiver, and a caregiver display being coupled to the network to receive a video feed of the patient in response to the occurrence of a bed event;
Fig. 2
is a block diagram showing components of the patient bed;
Fig. 3
is a block diagram showing the camera, various examples of caregiver display devices, and various computer devices of the network that are associated with providing a video feed to one or more of the caregiver display devices;
Fig. 4
is a perspective view showing a field of view of a caregiver wearing eye glasses having video display capability and the video feed being displayed in an upper right corner of the field of view; and
Fig. 5
is a perspective view of a portion a patient bed having a footboard with a camera unit extending upwardly from a central region of a foot board, the camera unit having a camera that faces toward a patient on the bed and a GUI, the bed having control circuitry that commands the camera to take a picture and/or to record and/or transmit a video of the patient for a period of time in response to a bed event occurring.
The invention will now be further described by way of example with reference to the accompanying drawings, in which:
Fig. 1
As shown in , a system 10 includes a patient bed 12, a camera 14 mounted to a ceiling 16, a network 18, a network interface 20, and a caregiver display 22. According to this disclosure, a picture or video feed is provided to caregiver display 22 in response to occurrence of a bed event (aka a triggering event) as detected by bed 12 or as detected by one or more computer devices of network 18. Prior to the triggering event, the picture or video feed is not provided to the caregiver display 22. Thus, patient privacy is maintained until a triggering event occurs. The triggering event is communicated from bed 12 via network interface 20 to one or more remote computer devices of network 18 and then the one or more remote computer devices provide the picture or video feed to caregiver display 22 under appropriate circumstances as will be discussed in further detail below. Bed alerts or alarms are examples of triggering events but other bed events that aren't considered
In some embodiments, the picture or video feed is recorded and stored in memory of one or more computer devices of network 18 in response to a bed event occurring. The video feed being recorded is recorded by one or more computer devices of network 18 during the same duration of time that the video feed is provided to the caregiver display 22 in some embodiments. Recording the video feed for durations greater than or less than the amount of time it is provided to the caregiver display 22 is also within the scope of this disclosure. In some embodiments, the transmission of the video feed to caregiver display 22 ceases in response to the bed event being rectified. The recording of the video feed also ceases in response to the bed event being rectified in some embodiments. The transmission and/or recording of the video feed continues for a threshold amount of time after the bed event is rectified in some embodiments, but yet is still considered to cease in response to the bed event being rectified according to this disclosure.
Fig. 1
U.S. Patent Nos. 7,852,208
7,538,659
7,319,386
5,699,038
U.S. Patent Application Publication Nos. 2015/0081335 A1
2009/0217080 A1
2009/0212925 A1
2009/0212926 A1
In , the diagrammatic double-headed arrows between bed 12 and network interface 20, between camera 14 and network 18, between network 18 and network interface 20, and between network 18 and caregiver display 22 are intended to be illustrative of wired and/or wireless communication connections between these devices. For example, several types of devices may embody the network interface 20 according to this disclosure. In some embodiments, network interface 20 comprises a wireless access point (WAP) or a wireless interface unit (WIU) of a nurse call system, in which case the double headed arrow between bed 12 and network interface 20 represent a wireless communication link. In other embodiments, network interface 20 comprises a bed interface unit (BIU) of a nurse call system in which case the double headed arrow between bed 12 and network interface unit 20 represents a wired communication link. See, for example, ; ; and as well as , , and for additional information concerning connectivity of patient beds to networks including nurse call systems.
The following description discusses various components of bed 12. This description provides background to give context to the types of bed events, alarms, or occurrences that trigger video transmission and/or recording by system 10. It is contemplated that one or more computer devices of network 18 are used to select which bed events result in video transmission and/or recording and which do not. Thus, a menu of all available bed events is provided to users of system 10 on a display of a computer device and the user selects from among the overall menu of events, which ones constitute a video trigger. Thus, a bed 12 in one room may have one set of bed events selected for video triggering and another bed in another room may have a different set of bed events selected for video triggering.
FIG. 1
Referring still to , a frame 25 of bed 12 includes a base 28, an upper frame assembly 30 and a lift system 32 coupling upper frame assembly 30 to base 28. Lift system 32 is operable to raise, lower, and tilt upper frame assembly 30 relative to base 28. Bed 12 has a head end 24 and a foot end 26. Bed 12 further includes a footboard 65 at the foot end 26 and a headboard (not shown) at the head end 24. Footboard 65 is coupled to upper frame assembly 30. Base 28 includes wheels or casters 29 that roll along a floor as bed 12 is moved from one location to another. A set of foot pedals 31 are coupled to base 28 and are used to brake and release casters 29.
FIG. 1
FIG. 1
Illustrative hospital bed 12 has four siderail assemblies coupled to upper frame assembly 30 as shown in . The four siderail assemblies include a pair of head siderail assemblies 48 (sometimes referred to as head rails) and a pair of foot siderail assemblies 50 (sometimes referred to as foot rails). Each of the siderail assemblies 48, 50 is movable between a raised position, as shown in , and a lowered position (not shown). Siderail assemblies 48, 50 are sometimes referred to herein as siderails 48, 50. Each siderail 48, 50 includes a barrier panel 54 and a linkage (not shown). Each linkage is coupled to the upper frame assembly 30 and is configured to guide the barrier panel 54 during movement of siderails 48, 50 between the respective raised and lowered positions. In some embodiments, barrier panel 54 is maintained by the linkage 56 in a substantially vertical orientation during movement of siderails 48, 50 between the respective raised and lowered positions.
FIG. 2
FIG. 2
Upper frame assembly 30 includes an upper frame 34 (which in some embodiments includes a lift frame and a weigh frame supported with respect to the lift frame) and a patient support deck 38. Patient support deck 38 is carried by upper frame 34 and engages a bottom surface of a mattress or surface 27. Patient support deck 38 includes a head section 40, a seat section 42, a thigh section 43 and a foot section 44 as shown diagrammatically in . Sections 40, 43, 44 are each movable relative to upper frame 34. For example, head section 40 pivotably raises and lowers relative to seat section 42, whereas foot section 44 pivotably raises and lowers relative to thigh section 43. Additionally, thigh section 43 articulates relative to seat section 42. Also, in some embodiments, foot section 44 is extendable and retractable to change the overall length of foot section 44 and therefore, to change the overall length of deck 38. For example, foot section 44 includes a main portion 45 and an extension 47 in some embodiments as shown diagrammatically in .
In the illustrative embodiment, seat section 42 is fixed in position with respect to upper frame 34 as patient support deck 38 moves between its various patient supporting positions. In other embodiments, seat section 42 also moves relative to upper frame 34, such as by pivoting and/or translating. Of course, in those embodiments in which seat section 42 translates along upper frame 34, the thigh and foot sections 43, 44 also translate along with seat section 42. In some embodiments, bed 12 is able to move to a chair position. As bed 12 moves toward the chair position, foot section 44 lowers relative to thigh section 43 and shortens in length due to retraction of the extension 47 relative to main portion 45. As bed 12 moves away from the chair position, foot section 44 raises relative to thigh section 43 and increases in length due to extension of the extension relative to main portion 45. Thus, in the chair position, head section 40 extends upwardly from upper frame 34 and foot section extends downwardly from thigh section 43.
FIG. 2
As shown diagrammatically in , bed 12 includes a head motor or actuator 90 coupled to head section 40, a knee motor or actuator 92 coupled to thigh section 43, a foot motor or actuator 94 coupled to foot section 44, and a foot extension motor or actuator 96 coupled to foot extension 47. Actuators 90, 92, 94, 96 may include, for example, an electric motor of a linear actuator. In those embodiments in which seat section 42 translates along upper frame 30 as mentioned above, a seat motor or actuator (not shown) is also provided. Head actuator 90 is operable to raise and lower head section 40, knee actuator 92 is operable to articulate thigh section 43 relative to seat section 42, foot actuator 94 is operable to raise and lower foot section 44 relative to thigh section 43, and foot extension actuator 96 is operable to extend and retract extension 47 of foot section 44 relative to main portion 45 of foot section 44.
FIG. 2
In some embodiments, bed 12 includes a pneumatic system 72 that controls inflation and deflation of various air bladders or cells of surface 27. The pneumatic system 72 is represented in as a single block but that block 72 is intended to represent one or more air sources (e.g., a fan, a blower, a compressor) and associated valves, manifolds, air passages, air lines or tubes, pressure sensors, and the like, as well as the associated electric circuitry, that are typically included in a pneumatic system for inflating and deflating air bladders of mattresses of hospital beds.
FIG. 2
Fig. 1
As also shown diagrammatically in , lift system 32 of bed 12 includes one or more elevation system motors or actuators 70, which in some embodiments, comprise linear actuators with electric motors. Thus, motors 70 are sometimes referred to herein as actuators 70. Alternative actuators or motors contemplated by this disclosure include hydraulic cylinders and pneumatic cylinders, for example. The actuators 70 of lift system 32 are operable to raise, lower, and tilt upper frame assembly 30 relative to base 28. In the illustrative embodiment, one of actuators 70 is coupled to, and acts upon, a set of head end lift arms 78 and another of actuators 70 is coupled to, and acts upon, a set of foot end lift arms 80 to accomplish the raising, lowering and tilting functions of upper frame 30 relative to base 28. Arms 78, 80 can be seen in .
FIG. 1
In the illustrative example, bed 12 has four foot pedals 84a, 84b, 84c, 84d coupled to base 28 as shown in . Foot pedal 84a is used to raise upper frame assembly 30 relative to base 28, foot pedal 84b is used to lower frame assembly 30 relative to base 28, foot pedal 84c is used to raise head section 40 relative to frame 36, and foot pedal 84d is used to lower head section 40 relative to frame 36. In other embodiments, foot pedals 84a-d are omitted. Pedals having other bed movement functions are also within the scope of this disclosure, such as pedals to move the deck 38 into our out of the chair configuration and/or pedals to move upper frame 34 into or out of the Trendelenburg and reverse Trendelenburg positions.
In some embodiments, one or more of siderails 48, 50 include a user control panel (not shown) coupled to the outward side of the associated barrier panel 54. Such controls panels include various buttons that are known in the art and that are used by a caregiver to control associated functions of bed 12. For example, control panel 66 includes buttons that are used to operate head actuator 90 to raise and lower the head section 40, buttons that are used to operate knee actuator 92 to raise and lower the thigh section 43, and buttons that are used to operate actuators 70 to raise, lower, and tilt upper frame assembly 30 relative to base 28. Such control panels may also include buttons that are used to operate actuator 94 to raise and lower foot section 44 and buttons that are used to operate actuator 96 to extend and retract foot extension 47 relative to main portion 45. In some embodiments, the buttons of the control panels comprise membrane switches, for example.
FIG. 2
FIG. 2
As shown diagrammatically in , bed 12 includes control circuitry 98 that is electrically coupled to actuators 90, 92, 94, 96 and to actuators 70 of lift system 32. Control circuitry 98 is represented diagrammatically as a single block 98 in , but control circuitry 98 in some embodiments comprises various circuit boards, electronics modules, and the like that are electrically and communicatively interconnected. Control circuitry 98 includes one or more microprocessors 172 or microcontrollers that execute software to perform the various control functions and algorithms of bed 12 as described herein. Thus, circuitry 98 also includes memory 174 for storing software, variables, calculated values, and the like as is well known in the art.
FIG. 2
FIG. 2
As also shown diagrammatically in , a user inputs block 99 represents the various user inputs such as buttons of control panels and pedals 84a-d, for example, that are used by the caregiver or patient to communicate input signals to control circuitry 98 of bed 12 to command the operation of the various actuators 70, 90, 92, 94, 96 of bed 12, as well as commanding the operation of other functions of bed 12. Bed 12 includes at least one graphical user input or display screen 142 which in some embodiments, is coupled to a respective siderail 48. Display screen 142 is electrically coupled to control circuitry 98 as shown diagrammatically in . In some embodiments, two graphical user interfaces 142 are provided and are coupled to respective siderails 48. Alternatively or additionally, one or more graphical user interfaces are coupled to siderails 50 and/or to one or both of the headboard 46 and footboard 65. Thus, it is contemplated by this disclosure that a graphical user interface 142 may be coupled to any of barriers 65, 46, 48, 50 of bed 12. Alternatively or additionally, graphical user interface 142 is provided on a hand-held device such as a pod or pendant that communicates via a wired or wireless connection with control circuitry 98.
Control circuitry 98 receives user input commands from graphical display screen 142 when display screen 142 is activated. The user input commands control various functions of bed 12 such as controlling the pneumatic system 72 and therefore, the surface functions of surface 22. In some embodiments, the input commands entered on user interface 142 also control the functions of one or more of actuators 70, 90, 92, 94, 96 but this need not be the case. In some embodiments, input commands entered on the user interface 142 also control functions of a scale system 270, which is discussed in more detail below.
U.S. Patent Application Publication Nos. 2008/0235872 A1
2008/0172789 A1
2012/0089418 A1
Various examples of the various alternative or additional functions of bed 12 that are controlled by display screen 142 in various embodiments can be found in , and , each of which is hereby incorporated by reference herein in its entirety to the extent not inconsistent with the present disclosure which shall control as to any inconsistencies. According to this disclosure, control circuitry 98 is configured to deactivate display screen 142 if screen 142 has not been used to control a function of bed 12 within a threshold amount of time, such as 30 seconds to 5 minutes, for example.
FIG. 2
FIG. 2
In some embodiments, control circuitry 98 of bed 12 communicates with one or more remote computer devices of network 18 via communication infrastructure such as an Ethernet of a healthcare facility in which bed 12 is located and as shown diagrammatically in . Such remote computer devices may be part of an electronic medical records (EMR) system, for example. However, it is within the scope of this disclosure for circuitry 98 of bed 12 to communicate with other computers such as those included as part of a nurse call system, a physician ordering system, an admission/discharge/transfer (ADT) system, or some other system used in a healthcare facility in other embodiments. Network 18 in is illustrated diagrammatically and is intended to represent all of the hardware and software that comprises a network of a healthcare facility.
U.S. Pat. Nos. 7,538,659
7,319,386
U.S. Patent Application Publication Nos. 2009/0217080 A1
2009/0212925 A1
2009/0212926 A1
U.S. Patent Application Publication No. 2007/0210917 A1
In the illustrative embodiment, bed 12 has a communication interface or port 180 which provides bidirectional communication with network 18. A communications link between interface 180 and network 18, in some embodiments, comprises a cable that connects bed 12 to a wall mounted jack that is included as part of a bed interface unit (BIU) or a network interface unit (NIU) 20 of the type shown and described in and and in , and . As mentioned above, in other embodiments, the communications link between interface 180 and network 18 comprises wireless signals sent between bed 12 and a wireless interface unit of the type shown and described in . Thus, the various communications links disclosed herein comprises one or more wired links and/or wireless links, according to this disclosure.
In some embodiments, operation of any one or more of actuators 70, 90, 92, 94, 96 constitutes a bed event that results in video images captured by camera 14 being recorded and/or transmitted to caregiver display 22. The same goes for operation of pneumatic system 72 to initiate a therapy, for example, such as rotation therapy, percussion therapy, alternating pressure therapy, and the like. Selection of any one or more buttons of user inputs 99, including pedals 84a-84d, or selection of an icon or button display screen 142 also may be considered a bed event that triggers video recording and/or transmission. Furthermore, raising and/or lowering of any of siderails 48, 50 also constitutes a bed event that results in video images captured by camera 14 being recorded and/or transmitted to caregiver display 22 in some embodiments.
U.S. Pat. No. 7,253,366
Detection by scale system 270 of patient movement by a threshold amount, such as movement toward exiting bed 12, is also a bed event that triggers video recording and/or transmission according to this disclosure. In some embodiments, scale system 270 includes load cells that sense movement of a patient on bed 12. Thus, scale system 270 also serves as a patient position monitoring (PPM) system in some embodiments. See, for example, which shows and describes such a scale/PPM system. In some embodiments, other types of weight or position sensors, such as force sensitive resistors (FSR's), capacitive sensors, linear variable displacement transducers (LVDT's), or the like are used in lieu of, or in addition to, the load cells of scale system 270 to provide signals for determining a patient's weight or position.
Fig. 2
As shown in , bed 12 includes an angle sensor 182 that senses an angle at which head section 40 is elevated relative to horizontal or relative to another portion of bed 12, such as upper frame 34. This is sometimes referred to as head-of-bed (HOB) angle. It is contemplated by this disclosure that the HOB angle being above or below a threshold angle constitutes a bed event that triggers video recording and/or transmission. For example, doctors sometimes order that the HOB angle be above thirty degrees for a prescribed period of time, such as two to four hours. If head section 40 is moved to a position below the threshold HOB angle, then video recording/transmission is triggered. In some embodiments, the threshold HOB angle is selectable by a user of a computer device of network 18 or by a user of graphical display screen 142 of bed 12. Having the video recording/transmission trigger in response to movement of head section 40 of bed above a threshold angle is also within the scope of this disclosure.
Fig. 1
U.S. Pat. Nos. 8,310,364
8,139,945
8,082,160
8,018,584
7,907,053
7,734,476
7,715,387
7,450,024
7,567,794
7,403,111
7,099,895
7,053,831
6,972,683
6,838,992
6,825,763
6,154,139
5,455,851
As shown diagrammatically in , system 10 includes a real time location system (RTLS) 110 that determines the location of caregivers throughout a healthcare facility. RTLS systems are well known in the art and are sometimes referred to as locating and tracking systems. In such systems, caregivers wear badges or tags 112 that transmit wireless signals, either periodically or when prompted to do so by components of the RTLS 110. Receivers of RTLS 110 that are mounted at known locations receive the wireless signals from badges 112 and then, computer devices of RTLS 110 determine the location of the caregiver by correlating the badge ID with the receiver ID. Additional details of locating and tracking systems, such as RTLS 100, can be found, for example, in ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; and .
According to some embodiments of this disclosure, if RTLS 110 indicates that a caregiver is located in the same room at which a bed event occurs, which bed event would otherwise constitute a video recording/transmission trigger, then camera 14 is not turned on and the video feed is not recorded or transmitted to caregiver display 22. The reason being that, since there is a caregiver in the room already, that caregiver is either the reason for the triggering event (e.g., the caregiver is moving a part of the bed 12 or is activating a surface therapy or is helping or watching the patient exiting the bed 12) or is able to supervise the occurrence of the triggering event and maintain the patient's safety. Thus, in some embodiments, the caregiver's presence in a room results in computer device of network 18 suppressing the recording and transmission of the video feed from the camera 14 of the associated room.
Fig. 3
Referring now to , block 14 represents all of the video cameras 14 mounted in patient rooms and block 22 represents the various types of computer devices having caregiver displays 22. In the illustrative example, block 22 indicates that caregiver displays 22 are included in a workstation on wheels 22a (aka a computer on wheels or COW), display glasses 22b (or other smart device or wearable such as a portable phone, wrist watch, wrist band, or the like), a graphical user interface (GUI) 22c of a bed 12, and a nursing station 22d. It is within the scope of this disclosure for a caregiver to be transporting multiple portable computer devices such as two or more of devices 22a, 22b, 22c, 22d. In some embodiments, the video feed associated with a triggering event is transmitted to all such devices being transported by the associated caregiver.
In the case of GUI 22c, it should be appreciated that the bed 12 associated with GUI 22c is located in a different room than the room in which the bed event triggering the video feed is located. Thus, in some embodiments, the caregiver views on GUI 22c located in one room of the healthcare facility, a video feed being captured by a camera 14 in another room of the healthcare facility. Information from the RTLS system 110 is used to determine the location of a caregiver assigned to the patient that is triggering the bed event so that the video feed is routed to the proper GUI 22c near the assigned caregiver.
Fig. 3
Still referring to , block 114 represents a bed event or alert being triggered and block 116 represents the alert being associated with a particular bed. That is, a bed ID is transmitted with the information regarding the particular bed event. In the illustrative example, the bed event alert 116 is transmitted to a nurse call or bed data server 118. Based on the bed ID included as part of the alert 116, server 118 is able to determine a location or room ID of the bed 12 that is producing the alert 116. In response to receipt of the alert 116, server 118 communicates with a video server 120 to request a video feed from the camera 14 associated with the room ID. In response, the video server 120 provides the requested video feed from the alerting bed 12 as indicated at block 122. As indicated at block 124, server 118 then transmits the video feed to the computer device 22a, 22b, 22c, 22d having caregiver display 22 of the caregiver assigned to the bed 12 producing the alert 116 or assigned to the room in which the bed 12 producing the 116 alert is located or assigned to the corresponding patient which is associated with the bed 12 producing the alert 116. It will be appreciated that server 118 stores bed-to-room; bed-to-patient; and/or bed-to-patient-to-room association information therein or otherwise has access to some or all of this information, such as by querying RTLS 110.
Fig. 3
As further shown in , server 118 is coupled to a nurse call room station 130. Nurse call room stations 130 are included as part of a nurse call system of network 18 and are located in each patient room in some embodiments. Information regarding the bed event 114 triggering the alert 116 is displayed on the room station 130 of the associated room in some embodiments. When a caregiver enters the room to attend to the triggering event, the caregiver selects an icon or button on station 130 to notify server 118 of the caregiver's presence in the patient room. In response to the notification from station 130, server 118 signals server 120 to terminate the video feed 122. This use of station 130 to terminate the video feed 122 is beneficial for embodiments of system 10 that do not include RTLS 110.
Fig. 3
According to this disclosure, the computing device 22a, 22b, 22c, 22d having caregiver display 22 is able to function as a remote control of a video angle and/or zoom of camera 14 as indicated at block 126 of . It is contemplated by this disclosure that, in some embodiments, control of camera 14 by the caregiver's computing device in this manner is active while the video feed is being transmitted to the caregiver's computing device and the caregiver is viewing the video feed on display 22. In some embodiments, computing devices 22a, 22b, 22c, 22d are actively usable by caregivers to request that a video feed be provided to display 22 from camera 14 of a particular room even though a triggering event may otherwise not be occurring in the room. Such a request is communicated from the caregiver's computing device to server 118 and then to server 122. In the illustrative example, the use or caregiver display 22 to control angle and/or zoom of camera 14 is communicated to server 120 without involving server 118. For example, a wireless access point of network 18 receives commands relating to zoom and/or angle and transmits it to video server 120. In other embodiments, such commands are routed to server 120 through server 118.
Fig. 3
As indicated at block 128 of , in-room nurse call for nurse-to-patient communication is provided in system 10. Such communication is accomplished via a speaker and microphone provided in bed 12 or station 130 or on a pillow speaker unit that is well-known in the art. A speaker that also serves as a microphone is also known in the art and is within the scope of the present disclosure for providing the in-room communication represented by block 128. Thus, server 118 opens an audio channel between computing device 22a, 22b, 22c, 22d, as the case may be, and the speaker/mic of block 128 located in the room at which the triggering event 116 is occurring. This audio channel is opened automatically in some embodiments and/or is opened in response to user inputs by the caregiver on the associated device 22a, 22b, 22c, 22d in some embodiments. So, for example, if the video feed 122 shows that the patient is attempting to get out of bed, the caregiver can provide audio commands to the patient to stay in bed and to otherwise have a conversation with the patient.
Fig. 4
Referring now to , if caregiver display 22 is included as part of display glasses 22b for a particular caregiver, then when the video feed is provided to display glasses 22b, a field of view 132 of the glasses has a video image field 134 that occupies the upper right corner of the field of view 132. The video image captured by the associated camera 14 is what is shown in the video image field 134, while the remainder of field of view 132 is the surrounding environment that is viewed by the caregiver through the glasses 22b. Thus, in the illustrative example, the caregiver is viewing a hallway in field of view 132 and video image field 134 appears to show the patient and bed at which the triggering event has occurred. A video camera icon 136 is provided in the lower left corner of the video image field 134 to indicate that image is a video feed.
Fig. 5
Fig. 2
Referring now to , a patient bed 12' has a footboard 65' with a camera module or unit 200 extending upwardly from a central region of a foot board 65'. The camera module 200 has a camera 14' that faces toward a patient on the bed 12' and a GUI display screen 142' which also serves as caregiver display 22c' in the illustrative embodiment. Control circuitry (not shown) of bed 12', which is similar to the circuitry of bed 12 shown diagrammatically in , commands the camera 14' to take a picture of the patient at substantially the same time as a patient weight reading is taken using a weigh scale system (not shown) of the bed 12' and the GUI display screen 142' displays the picture that was taken. In some embodiments, the weight reading and picture are transmitted from the circuitry of the bed 12' for receipt by a remote computer of network 10 such as those mentioned above. In some embodiments, camera 14' captures a video image rather than a picture and the video image is provided to caregiver display 22 of an associated caregiver as a video feed in the same manner as described above. Thus, in some embodiments, camera 14' of bed 12'operates in the same manner as camera 14 within system 10 as described above.
Based on the foregoing, it will be appreciated, for example, that when a bed exit or PPM alarm is triggered (or any other triggering event occurs), a live video feed captured by camera 14 or camera 14' appears substantially immediately on caregiver display 22 of an assigned caregiver. For example, the live video feed appears substantially immediately in field 134 if the assigned caregiver has display glasses 22b. The caregiver then decides whether to intervene such as talking to the patient via in-room communication equipment 128 to ask the patient to stay in bed 12 or to wait for assistance while the caregiver rushes to the bedside. On the other hand, based on the video feed, the caregiver may decide that the patient does not need help. Thus, directly observing the patient via the video feed helps to reduce patient falls by increasing effective interventions while reducing false alarm responses that least to alert fatigue.
Triggering substantially instant remote observation upon a triggering event, such as a bed exit or PPM alarm, combined with audio communication capability leads to increased specificity by recognizing which patients do not require assistance (e.g., the patient is not actually exiting the bed 12), leads to increased sensitivity by promoting more regular use of bed monitoring systems such as the bed exit/PPM system, and lead to enhanced interventions by allowing more sensitive PPM settings to be selected for more early intervention, by allowing caregivers to respond more quickly to patients that do need immediate help, and by communicating with the patient while en route to the patient's room.
According to some embodiments of this disclosure, a caregiver is able to retrieve past video recordings or past pictures for viewing on caregiver display 22 such as displays 22a, 22b, 22c, 22c', 22d. The past video recordings or past pictures are stored in one or more computer devices of network 18 such as one or both of servers 118, 120. The caregiver uses the computer device associated with display 22 to request a particular past video recording or past picture and the computer device storing the past video recording or picture responds by transmitting the requested video or picture to the caregiver's device. Such past videos or pictures are useful, for example, in connection with weighing a patient on the patient bed 12, 12' or in connection with zeroing weigh scale system 270 of patient bed 12, 12'. For example, the caregiver compares the past video or picture with the current state of the patient bed 12, 12' to check for any changes in equipment, sheets, pillows, etc. on the bed 12, 12'. If there are changes as compared to the past state of the bed 12, 12', the caregiver may take steps to re-zero the weigh scale system 270 so that subsequent weight readings of the associated patient are accurate.
Although certain illustrative embodiments have been described in detail above, variations and modifications are possible. | |
English professor publishes book on non-traditional patriarchal roles
English professor Helena Gurfinkel released her book “Outlaw Fathers in Victorian and Modern British Literature: Queering Patriarchy” in the spring.
Her first book is based on her research of non-traditional fatherly roles portrayed in literature. She examined several novels, stories and memoirs, including those by British and Anglo-American authors Anthony Trollope, Samuel Butler and Henry James on queer or “outside-the-norm” patriarchy.
SIUE, in particular, the College of Arts and Sciences, the Graduate School and the English department, according to Gurfinkel, have been supportive of her project through funded research fellowships and assistance with copyright permissions.
“They have helped me in many ways, and I’m grateful for that,” Gurfinkel said.
For five years, she prepared and revised her manuscript for publication with Fairleigh Dickinson University Press.
The publisher states in the book’s description that, “In addition to using an inventive psychoanalytic approach to redefining, or queering, the concept of patriarchy in literary studies and theory, it joins a larger contemporary conversation about changing masculinities and families.”
According to Gurfinkel, male roles have been changing since the 20th century, but “unusual paternal roles existed long before that,” both in real life and in literature.
“The evolution of gender roles is relevant today but can be found in literature even before the 19th century,” Gurfinkel said. “Right now I think our concept of fatherhood is changing; the role of the father as strictly a provider, emotionally distant and not close to children is no longer the only acceptable one. Now an increasing number of fathers are staying home and taking care of children…assuming stereotypically maternal roles.”
Gurfinkel said she believes that the changing masculine roles constitute a “positive development” for fathers and children and is happy to contribute to the public discourse on this “important issue.”
“I believe that the particular angle from which I approach this topic is unique,” Gurfinkel said. “My book provides a definition of patriarchy that is counterintuitive and unconventional—different from the norm.”
At Tufts University in Medford, Mass., Gurfinkel spent five years researching and writing her dissertation on masculinity in literature which, she said, “really fascinated me.”
“Literary theory provides a very unusual angle on society, human relationships and gender roles,” Gurfinkel said. “Being a man can mean a million different things, and society has become more conscious of it. In the last 20 years or so, we have been paying more attention to the complex, layered and nuanced definitions of masculinity.”
According to Gurfinkel, writing her book has helped her become a better teacher.
“I have learned to explain complex concepts better, and that’s an important skill for a teacher to have,” Gurfinkel said. | http://thismonthincas.com/2014/08/17/english-professor-publishes-book-on-non-traditional-patriarchal-roles/ |
MINSK, 9 March (BelTA) – Belarus is ready for a respectful dialogue on human rights with the European Union, Chairman of the House of Representatives of the National Assembly of Belarus Vladimir Andreichenko said during a meeting with EU Special Representative for Human Rights Stavros Lambrinidis on 9 March, BelTA has learned.
“Belarus is always ready for a constructive, mutually beneficial, and respectful dialogue on any matters including human rights,” Vladimir Andreichenko said. He added that work is underway to draw up the national human rights action plan in line with recommendations of the United Nations Human Rights Council (UNHRC). “We take the recommendations very seriously, and will be working to implement them,” the official stressed.
Vladimir Andreichenko said that Belarus welcomes the decision of the European Union to lift the sanctions. The country views the move as a step in the right direction. “This decision will give a considerable boost to the relations between businessmen and politicians. This signal is appreciated by people in Belarus and the EU, and I am confident that we will advance our cooperation to a higher level. It is great that we are breaking the deadlock that existed for some time,” the Chairman of the House of Representatives noted.
He said that Belarus and the European Union do not need to build their relations from scratch. Much has already been achieved. For instance, Belarus takes part in the Eastern Partnership initiative. At present, the country is negotiating visa facilitation and readmission agreements with the European Commission. “Despite the decline in the relations, we managed to maintain contacts at the level of ministries and government agencies,” Vladimir Andreichenko emphasized. He added that members of the House of Representatives make their contribution to this work. For example, they take part in sessions of the Parliamentary Assembly of the Organization for Security and Cooperation in Europe and the Parliamentary Assembly of the Council of Europe.
Vladimir Andreichenko also drew attention to the trade and economic cooperation between Belarus and the EU. He stressed that in 2015 the bilateral trade totaled almost $15 billion. Belarus received $5.5 billion in EU investments.
For his part, Stavros Lambrinidis noted that the improvement of the situation in the field of human rights in Belarus will contribute to the strengthening of the positive image of the country in Europe. | https://www.belarus.by/en/press-center/speeches-and-interviews/andreichenko-belarus-is-ready-for-respectful-human-rights-dialogue-with-eu_i_0000036080.html |
CROSS REFERENCE TO RELATED APPLICATIONS
FIELD OF THE INVENTION
BACKGROUND OF THE INVENTION
SUMMARY OF THE INVENTION
DETAILED DESCRIPTION OF THE INVENTION
I. Composition
II. Methods of Manufacturing Low Molecular Weight P4HB and Copolymers.
EXAMPLE 1
Hydrolysis of P4HB with 12M Aqueous Acetic Acid
EXAMPLE 2
Hydrolysis of P4HB with 10 M Aqueous Acetic Acid
EXAMPLE 3
Hydrolysis of P4HB with 8M Aqueous Acetic Acid
EXAMPLE 4
Hydrolysis of P4HB With SM Aqueous Acetic Acid
EXAMPLE 5
H-NMR Analysis of P4HB Acetic Acid Hydrolysis Product
This application claims benefit of U.S. Provisional Application No. 61/539,695, filed Sep. 27, 2011, which is hereby incorporated herein by reference in its entirety.
The present invention generally relates to methods for controlling the hydrolysis of poly-4-hydroxybutyrate and copolymers thereof, and to compositions of poly-4-hydroxybutyrate and copolymers thereof with specific weight average molecular weights. The compositions can be used in implantable medical devices, controlled release applications, such as drug delivery, and certain compositions may be used for therapeutic delivery of 4-hydroxybutyrate. The compositions may also be used in blends, and as intermediates in synthesis.
Poly-4-hydroxybutyrate (P4HB) and copolymers thereof can be produced using transgenic fermentation methods, see, for example, U.S. Pat. No. 6,548,569 to Williams et al., and are produced commercially, for example, by Tepha, Inc. (Lexington, Mass.). Poly-4-hydroxybutyrate (P4HB, TephaFLEX® biomaterial) is a strong, pliable thermoplastic polyester that, despite its biosynthetic route, has a relatively simple structure.
FEMS Microbial. Lett.
FIG. 1
The polymer belongs to a larger class of materials called polyhydroxyalkanoates (PHAs) that are produced by numerous microorganisms (see, for example, Steinbüchel A., et al. Diversity of Bacterial Polyhydroxyalkanoic Acids, 128:219-228 (1995)). In nature these polyesters are produced as storage granules inside cells, and serve to regulate energy metabolism. They are also of commercial interest because of their thermoplastic properties, and relative ease of production. Several biosynthetic routes are currently known to produce P4HB as shown in .
Polymer
J. Org. Chem.,
Biomaterials
Biomaterials
Chemical synthesis of P4HB has been attempted, but it has been impossible to produce the polymer with a sufficiently high molecular weight that is necessary for most applications (see Hori, Y., et al., 36:4703-4705 (1995); Houk, K. N., et al., 2008, 73 (7), 2674-2678; and Moore, T., et al., 26:3771-3782 (2005)). In fact, it has been calculated to be thermodynamically impossible to chemically synthesize a high molecular weight homopolymer under normal conditions (Moore, T., et al., 26:3771-3782 (2005)).
U.S. Pat. Nos 6,245,537, 6,623,748 and 7,244,442 describe methods of making PHAs with little to no endotoxin, which is suitable for medical applications. U.S. Pat. Nos. 6,548,569, 6,838,493, 6,867,247, 7,268,205, and 7,179,883 describe use of PHAs to make medical devices. Copolymers of P4HB include 4-hydroxybutyrate copolymerized with 3-hydroxybutyrate or glycolic acid (U.S. patent application No. 20030211131 by Martin and Skraly, U.S. Pat. No. 6,316,262 to Huisman et al., and U.S. Pat. No. 6,323,010 to Skraly et al.). Methods to control molecular weight of PHA polymers by biosynthetic methods have been disclosed by U.S. Pat. No. 5,811,272 to Snell et al.
Polyesters, III,
Biochem. Eng. J.
PHAs with controlled degradation and degradation in vivo of less than one year are disclosed by U.S. Pat. No. 6,548,569, 6,610,764, 6,828,357, 6,867,248, and 6,878,758 to Williams et al. and WO 99/32536 to Martin et al. Applications of P4HB have been reviewed in Williams, S. F., et al., 4:91-127 (2002), and by Martin, D. et al. Medical Applications of Poly-4-hydroxybutyrate: A Strong Flexible Absorbable Biomaterial, 16:97-105 (2003). Medical devices and applications of P4HB have also been disclosed by WO 00/56376 to Williams et al. Several patents including U.S. Pat. Nos. 6,555,123, 6,585,994, and 7,025,980 describe the use of PHAs in tissue repair and engineering.
In controlled release there currently exists a need for P4HB and copolymers thereof with narrowly defined weight average molecular weight ranges. By controlling these ranges, compositions can be developed that allow the controlled release of a wide range of bioactive agents. Particularly desired compositions include polymers with weight average molecular weights less than 250,000, and more preferably less than 100,000. Preferably, the compositions should have a polydispersity of less than 3, and more preferably less than 2.5.
In addition to being useful in controlled release, lower molecular weight compositions of P4HB and copolymers thereof can be useful in the preparation of other chemicals, polymers, copolymers, and for blending with other materials. For example, low molecular weight P4HB and copolymers thereof can be used in the preparation of polyurethanes or as nucleants or fillers in blends. U.S. Pat. No. 6,623,730 to Williams and Martin discloses the use of oligomers of P4HB as prodrugs to modulate endogenous levels of 4-hydroxybutyrate, and methods to prepare these oligomers by hydrolysis of P4HB. The method disclosed uses aliquots of sodium methoxide to hydrolyze P4HB dissolved in a solvent (anhydrous THF) to provide the oligomers of P4HB of the desired molecular weight. Starting with a polymer of molecular weight 430,000 g/mol, sodium methoxide is used to produce P4HB molecular weights of 320,000, 82,000 and 25,000. The disadvantages of this procedure are as follows: (i) the use of methoxide can result in terminal esterification of the polyester chains (producing methyl esters); (ii) the relatively low solubility of P4HB in THF (and other solvents) requires large volumes of solvent to dissolve the polymer which is difficult to handle, expensive, and costly to remove; and (iii) basic conditions could potentially lead to elimination reactions in the polymer causing unwanted side reactions.
It is an object of the present invention to provide methods to produce P4HB and copolymers thereof by hydrolysis of high molecular weight P4HB and copolymers without the use of solvents.
It is a further object of the present invention to provide methods to produce P4HB and copolymers thereof by hydrolysis of high molecular weight P4HB and copolymers without the use of basic conditions that can esterify polymer terminal end groups or cause basic elimination in the polymer chains.
It is another object of the present invention to provide methods for hydrolysis of P4HB and copolymers thereof that maintain the polymers in solid state during hydrolysis resulting in easy isolation of the hydrolyzed products.
It is still another object of the present invention to provide compositions of P4HB and copolymers thereof that can be used in medical applications, for example, in implantable medical devices and or for the controlled release of bioactive substances, including the controlled release of 4-hydroxybutyrate.
Methods for making P4HB polymers and copolymers thereof that are useful for preparing controlled release systems, and as intermediates in chemical synthesis, have been developed. These methods avoid the use of organic solvents, and basic conditions that can cause transesterification reactions with polymer terminal end groups or elimination reactions. A preferred embodiment is a method for producing polymers of P4HB with weight average molecular weight less than 250,000, and more preferably, less than 100,000, which are useful in controlled release. A particularly preferred embodiment utilizes aqueous acetic acid to hydrolyze pellets of P4HB polymers and copolymers while in suspension.
Definitions
“Poly-4-hydroxybutyrate” as generally used herein means a homopolymer comprising 4-hydroxybutyrate units. It may be referred to herein as P4HB or TephaFLEX® biomaterial (manufactured by Tepha, Inc., Lexington, Mass.).
“Copolymers of poly-4-hydroxybutyrate” as generally used herein means any polymer comprising 4-hydroxybutyrate with one or more different hydroxy acid units.
“Controlled release” or “modified release, as used herein, refers to a release profile in which the drug release characteristics of time course and/or location are chosen to accomplish therapeutic or convenience objectives not offered by conventional dosage forms such as solutions, suspensions, or promptly dissolving dosage forms. Delayed release, extended release, and pulsatile release and their combinations are examples of modified release.
“Bioactive agent” is used herein to refer to therapeutic, prophylactic, and/or diagnostic agents. It includes without limitation physiologically or pharmacologically active substances that act locally or systemically in the body. A biologically active agent is a substance used for, for example, the treatment, prevention, diagnosis, cure, or mitigation of disease or disorder, a substance which affects the structure or function of the body, or pro-drugs, which become biologically active or more active after they have been placed in a predetermined physiological environment. Bioactive agents include biologically, physiologically, or pharmacologically active substances that act locally or systemically in the human or animal body. Examples can include, but are not limited to, small-molecule drugs, peptides, proteins, antibodies, sugars, polysaccharides, nucleotides, oligonucleotides, aptamers, siRNA, nucleic acids, and combinations thereof. “Bioactive agent” includes a single such agent and is also intended to include a plurality
“Blend” as generally used herein means a physical combination of different polymers, as opposed to a copolymer comprised of two or more different monomers.
“Molecular weight” as used herein, unless otherwise specified, refers to the weight average molecular weight (Mw), not the number average molecular weight (Mn), and is measured by gel permeation chromatography (GPC) relative to polystyrene.
“Absorbable” as generally used herein means the material is broken down in the body and eventually eliminated from the body within 5 years. “Biocompatible” as generally used herein means the biological response to the material or device being appropriate for the device's intended application in vivo. Any metabolites of these materials should also be biocompatible.
Methods have been developed to produce low molecular weight (Mw) compositions of P4HB and copolymers thereof in high yield. These methods may be used to prepare P4HB and copolymers thereof with weight average molecular weights (Mw) ranging from 1 to 250 kDa, and more preferably with Mw ranging from 5 to 100 kDa. The methods also yield P4HB and copolymers with narrow polydispersity (PDI), less than 3.0 and preferably a PDI of less than 2.5. The P4HB and copolymers thereof are prepared by hydrolysis with aqueous acids, and preferably with acetic acid. A major advantage of the method is that pellets of the polymers may be suspended in acid, and hydrolyzed while in suspension to yield polymers of predictable weight average molecular weight and narrow polydispersity. In addition, purification is straightforward, side reactions are essentially absent, and yields are very high.
A. Polymers
The processes described herein can typically be used with poly-4-hydroxybutyrate (P4HB) or a copolymer thereof. Copolymers include P4HB with another hydroxyacid, such as 3-hydroxybutyrate, and P4HB with glycolic acid or lactic acid monomer. P4HB and copolymers thereof can be obtained from Tepha, Inc. of Lexington, Mass.
In a preferred embodiment, the starting P4HB homopolymer and copolymers thereof are extruded into pellets. An extruder can be used for this purpose. The pellets are then suspended in acid for hydrolysis. This facilitates isolation of the product, and provides a high yield of lower molecular weight product.
B. Hydrolysis
w
w
In a preferred embodiment, P4HB and copolymers thereof can be prepared with a weight average molecular weight less than 250,000, and more preferably, less than 100,000. It has been discovered that low molecular weight (M) polymers and copolymers of P4HB can be produced with unexpectedly high yields, without solvent, and in high purity with side reactions essentially absent. Notably, the hydrolysis can be controlled so that lower molecular weight (M) polymers and copolymers can be predictably produced with high purity, high yield, and with narrow polydispersity.
The polymers can be hydrolyzed by suspending the polymer in an acid or an acid solution. Therefore, in one embodiment, the acid or acid solution is one in which the polymer pellet is insoluble or partially insoluble. The acid can be an organic acid or an inorganic acid. For those embodiments where the acid is an organic acid, the acid can be a monocarboxylic acid or a polycarboxylic acid, such as a di- or tricarboxylic acid. Suitable organic acids include, but are not limited to, acetic acid, halogenated acetic acid, such as mono-, di-, trihalogenated acetic acid, lactic acid, glycolic acid, propanoic acid, butanoic acid, pentanoic acid, hexanoic acid, benzoic acid, fumaric acid, maleic acid, tartaric acid, citric acid, malic acid, and pyruvic acid. Suitable inorganic acids include, but are not limited to, hydrochloric acid, sulfuric acid, hydrobromic acid, and hydroiodic acid.
w
A particularly preferred embodiment utilizes aqueous acetic acid to hydrolyze P4HB polymers and copolymers. More preferably, the polymers and copolymers are first extruded into pellets, and then suspended in aqueous acid. It has been discovered that the pellets will remain suspended in the acid (with shaking or stirring) during hydrolysis as the molecular weights of the polymers decrease in a predictable manner. Even though the polymers and copolymers remain suspended, and the polymer does not dissolve, the polydispersity of the lower molecular weight (M) product remains narrow. Because the pellets do not dissolve in the acid, the product may be easily isolated at the end of the hydrolysis, for example, by decanting, washing with water, and drying. There is no need to evaporate acid or solvent, or use a solvent extraction process to recover the low molecular weight polymers.
Granules or other non-pelletized forms of the polymer or copolymers can be hydrolyzed with the method, however, these forms are more likely to become sticky during hydrolysis, making isolation of the product more difficult.
In a preferred method, the polymer or copolymer pellets are suspended in aqueous acetic acid, and either stirred or shaken. The hydrolysis may be performed at ambient or elevated temperature. Preferably the hydrolysis is undertaken at constant temperature in the range of 37 to 50° C.
The strength of the acid may be adjusted to speed up or slow down the rate of hydrolysis of the polymers and copolymers. In a preferred method, acetic acid is used with a concentration in the range of 5M to 12M. However, lower concentrations may be used to slow down the rate of hydrolysis, and higher concentrations may be used to speed up the rate of hydrolysis.
w
w
w
w
The length of the hydrolysis reaction will be determined by the molecular weight (M) desired, form of the polymer or copolymer, temperature of the reaction, type of acid, and concentration of the acid. For example, pellets of P4HB (M=346 kDa) suspended in aqueous acetic acid at 37° C. for 4 hours will have a M=224 kDa if the concentration of the acid is 10M, and M=115 kDA if the concentration of the acid is 12M. Under the same conditions, at 27.5 hours, the molecular weights (Mw) of the polymer with 10M and 12M acetic acid are 85 kDa and 40 kDa, respectively.
C. Uses of Low Molecular Weight P4HB and P4HB Copolymers
Low molecular weight polymers and copolymers of P4HB have properties that are substantially improved for many medical applications relative to higher molecular weight versions. These materials have lower melt viscosities, and higher solubilities in solvents that can make them easier to process. The lower molecular weight P4HB polymer and copolymers thereof can also provide more desirable controlled release profiles for delivery of therapeutic, prophylactic or diagnostic agents or other bioactive agent, such as a small-molecule drug, peptide, protein, antibody, sugar, polysaccharide, nucleotide, oligonucleotide, aptamer, siRNA, nucleic acid, and combinations thereof. The lower molecular weight P4HB may also be used to make medical devices, such as, but not limited to, sutures, stents, stent grafts, stent coatings, devices for temporary wound or tissue support, devices for soft or hard tissue repair, repair patches, tissue engineering scaffolds, retention membranes, anti-adhesion membranes tissue separation membranes, hernia repair devices, device coatings, cardiovascular patches, catheter balloons, vascular closure devices, slings, biocompatible coatings, rotator cuff repair devices, meniscus repair devices, adhesion barriers, guided tissue repair/regeneration devices, articular cartilage repair devices, nerve guides, tendon repair devices, intracardiac septal defect repair devices, including, but not limited to, atrial septal defect repair devices and PFO (patent foramen ovale) closure devices, left atrial appendage (LAA) closure devices, pericardial patches, bulking and filling agents, plastic surgery devices (including facial and breast cosmetic and reconstructive devices), vein valves, heart valves, bone marrow scaffolds, meniscus regeneration devices, ligament and tendon grafts, ocular cell implants, spinal fusion devices, imaging devices, skin substitutes, dural substitutes, bone graft substitutes, wound dressings, and hemostats.
Lower molecular weight polymers and copolymers of P4HB and copolymers thereof can also be used to modulate endogenous levels of 4-hydroxybutyrate as disclosed by U.S. Pat. No. 6,623,730 to Williams and Martin.
Lower molecular weight polymers and copolymers of P4HB and copolymers thereof can also be used in implantable applications that require a more rapid rate of degradation or absorption than the higher Mw polymers. Preferrably, the implanted device will degrade and the low Mw polymer will be absorbed within six months
P4HB polymers and copolymers with low molecular weights may also be used in blends with other materials to improve polymer properties. The low molecular polymers may also be used in the synthesis of other materials, for example, in reactive polymerization.
A. Method of Making Low Molecular Weight P4HB Polymer
w
In a preferred method, a low molecular weight (M) P4HB polymer or copolymer may be prepared as follows. Pellets of a P4HB polymer are suspended in aqueous acetic acid, and placed in a shaker incubator. A number of parameters can be varied to control the hydrolysis of the polymer or copolymer including, but not limited to, the concentration of the acid, the type of acid, the temperature of the reaction, the speed (rpm) of the shaker (or stirrer speed), and the reaction time.
w
When the desired molecular weight (M) is achieved, the reaction is quenched by decanting the acid, and rinsing the polymer or copolymer with water. Residual acid and water may be removed by drying in vacuo.
The present invention will be further understood by reference to the following non-limiting examples.
Materials and Methods
w
30 grams of P4HB pellets (Tepha, Inc., Lexington, Mass.) (M367 kDa) were suspended in 100 mL of 12 M aqueous acetic acid (AcOH), and incubated at 37° C. at 50 rpm in a shaker incubator. After 4 and 27.5 hours, the Mw of polymer samples taken from the reaction were 115 and 40 kDa, respectively.
Results
After 4 hours the P4HB pellets became sticky and the AcOH solution turned cloudy. After 30 hours, the whole reaction mixture appeared milky, and when cooled down, it gelled into a semi-solid. It was therefore determined that 12 M AcOH is too strong to be used as the hydrolysis medium for P4HB pellets since this concentration may partially dissolve the polymer. As a result, the collection of the hydrolysis products would less practical and the reaction conditions would be less homogeneous with some hydrolysis occurring in solution and some in the solid phase (i.e. within the pellets).
Materials and Methods
w
30 grams of P4HB pellets (Tepha, Inc., Lexington, Mass.) (M367 kDa) were suspended in 100 mL of 10 M aqueous acetic acid, and incubated at 37° C. at 50 rpm in a shaker incubator. A sample was removed after 4 hours, and the weight average molecular weight of the polymer was determined by GPC (relative to polystyrene) to be 224 kDa. After 27.5 hours, the reaction was quenched by decanting the acetic acid, and rinsing the polymer with distilled water.
Results
The pellets did not clump or aggregate during the reaction time, as was seen for the similar reaction performed in 12 M acetic acid. The polymer pellets were then dried in vacuo to remove residual acetic acid and water.
The weight average molecular weight of the polymer was determined to be 85 kDa after 27.5 hours, and the polymer was recovered in high yield and without loss of material.
Materials and Methods
w
A 20 gram sample of P4HB pellets (Tepha, Inc., Lexington, Mass.) (M347 kDa) was suspended in 200 mL of 8 M aqueous acetic acid, and shaken at 50 rpm at 37° C. in a shaker incubator. Samples were removed periodically, and the weight average molecular weight of the polymer and polydispersity were determined by GPC (relative to polystyrene).
Results
The results are tabulated below (time in hours).
TABLE 1
Molecular Weight and PDI of P4HB over Time
8M, 40° C.,
oil bath, Pellets
M<sub>w </sub>(kDa)
PDI
0
347
2.13
1
335
2.15
2
315
2.10
4
284
2.17
6
263
2.08
8
255
2.05
24
161
1.97
96
68
1.90
120
60
1.94
Materials and Methods
w
A 20 gram sample of P4HB granules (Tepha, Inc., Lexington, Mass.) (M347 kDa) was suspended in 200 mL of 5M aqueous acetic acid, and stirred at 45° C. Samples were removed periodically, and the weight average molecular weight of the polymer was determined by GPC (relative to polystyrene).
Results
The results (average of three runs) are tabulated in Table 2.
TABLE 2
Molecular Weight and PDI of P4HB over Time
5M, 45° C.,
Granules
Time (hours)
Mw (kDa)
PD
0
347
2.13
4
280
2.12
22
168
2.03
29
137
1.98
96
60
2.01
1
1
FIG. 2
2
w
n
The H NMR spectrum of the hydrolysis product from Example 2 after 27.5 hours is shown in . As expected, this low Mw hydrolysis product shows a small H peak of the polymer end group —CHOH at a chemical shift of about 3.69 ppm. The integration area of this peak is 0.50 compared to an integration area of about 100 for the polymer methylene group at chemical shift of about 4.12 ppm. As such, the end group ratio of this sample is 0.5/100, or 0.005, which would suggest the product is a 200 mer (i.e. approx. Mn 17 kDa). This value of Mn from end group analysis is reasonable considering the polymer's GPC Mof 85 kDa Mand of 44 kDa. (Note: The GPC values relative to PS are about double the absolute values for the polymer from LLS).
The hydrolysis of P4HB pellets or granules suspended in aqueous solution of acetic acid has been performed successfully under mild conditions with reasonable reaction times. The hydrolysis product, low Mw P4HB, was prepared in a high yield, close to 100%, and its Mw could also be predicted based on the Mw versus reaction time curve under fixed reaction conditions, i.e., temperature and concentration of AcOH. Surprisingly for a biphasic reaction, the polydispersity of the hydrolysis products are low and similar to that of the starting polymer, about 2, showing that the hydrolysis reaction occurs uniformly throughout the bulk of the material, rather than being localized to the surface, even though the pellets/granules remain un-dissolved and suspended in the acetic acid solution.
From the NMR analysis, it appears that the end groups are hydroxyl groups just like the starting polymer. This shows that no new functional groups (i.e. acetate groups) have been added to the polymer and confirms the reaction as a true hydrolysis with no derivatization of the terminal end groups.
The kinetics of the hydrolysis reaction could be affected by a couple of factors such as the reaction temperature (room temperature to 50° C.) and the concentration of AcOH solution (5˜10 M). Because the P4HB pellets/granules were simply suspended in the AcOH solution at relative low temperatures instead of forming a homogeneous solution and the ratio of P4HB/AcOH could be 3 g/10mL, the hydrolysis reaction described herein should be scalable for production of P4HB oligomer with controlled molecular weight.
Modifications and variations of the methods and materials described herein will be obvious to those skilled in the art and are intended to come within the scope of the appended claims. All references cited herein are specifically incorporated by reference.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1
is a diagram of pathways leading to the biosynthesis of poly-4-hydroxybutyrate.
FIG. 2
1
is a H NMR spectrum of hydrolysis product of P4HB in acetic acid for 27.5 hours. | |
Creativity, Activity, Service (CAS) enables students to enhance their personal and interpersonal development as well as their social and civic development, through experiential learning in creative, action and service activities. CAS activities should be both challenging and enjoyable - a personal journey of self-discovery that recognizes each student's individual starting point. CAS activities should be:
- real, purposeful activities, with significant outcomes
- personal challenge - tasks must extend the student and be achievable in scope
- thoughtful consideration, such as planning, reviewing progress and reporting
- reflection on outcomes and personal learning
Students must demonstrate satisfactory participation in CAS for the award of the IB Diploma. This is achieved through the student’s active and balanced engagement in activities in all three elements of creativity, action and service, and through having demonstrated the key learning outcomes observed in engagement with the activity and student’s personal reflections.
Click here for the CAS offered at SJI.
For more information, please see https://www.ibo.org/programmes/diploma-programme/curriculum/creativity-activity-and-service/. | https://www.sji.edu.sg/shared/academic-programmes/ib-diploma-programme/creativity-activity-service |
An event as part of the series "Raumklänge: Same, Same But Different" 2018, in cooperation with the City of Pulheim and the Museum Morsbroich, Leverkusen. Programme selection by Harald Kimmig and Sara Bosqui
Lázara Rosell Albear (b. 1971, Cuba) is a Brussels-based artist with a mixed practice, ranging from the research of sound and performance to the production of events and films. Exchange and sharing constitute the essence of her practice. She explores movement, migration, transformation, interactivity and its effects on the human condition. The advance in technologies has brought us “new” means to work with, broadening also the traditional means of dance, and theatre. Rather than choosing between these different media, she strives for a contrapuntal togetherness and total immersion — both internal and external. Her collaborations and her various artistic, musical and performative projects have been shown all around the world. Lázara Rosell Albear was a resident at WIELS in 2016.
"Unsurrounded" started as a solo performance where sound, movement, images and words collide. Each presentation is different on each occasion, with new imprints on the material layers and with new interactions that can extend to collaborations with other performers, musicians and visual artists. | http://www.temporarygallery.org/?p=7121&lang=en |
Policies define the University’s position and/or objective on matters of strategic significance and the relevant outputs and outcomes that UQ needs to deliver to give effect to its position and/or to achieve its stated objectives. Depending on their categorisation (see below), policies are approved either by the Senate or by the Vice-Chancellor and President.
To demonstrate compliance with laws, regulations, government policies and/or standards.
All policy requirements are principles-based and verifiable. Compliance with policies is mandatory across UQ.
Governance policies are policies that underpin the system of practices and processes by which the University is governed and controlled. The approval of some governance policies has been reserved by Senate (as specified in PPL 1.10.06 Senate Governance Framework - Policy).
Academic policies are policies that underpin the University’s teaching, learning and research functions, strategies and activities. Other than specific policies reserved by Senate, these policies are approved by the Vice-Chancellor and President based on recommendations from the Academic Board.
Operational policies are policies that underpin the University’s corporate/administrative and non-academic functions and activities. These policies are approved by the Vice-Chancellor and President based on recommendations from the relevant VCC member.
An administrative amendment to a policy is a change that is superficial or administrative in nature. Administrative amendments may correct patent errors in a policy, reflect nomenclature changes to organisational units or position titles, or address other non-substantive issues of content or format. Following request by the relevant PPL Custodian, the PPL Manager is authorised to approve administrative amendments to policies.
Policies must be consistent with, underpin and support achievement of the University’s strategic and operational goals. The Relevant Senior Executive should present a proposal seeking endorsement of VCC to create, change or rescind any policy that has a strategic impact on UQ (see VCC Meeting Submission Guidance, VCC Agenda Submission Template and VCC Agenda Coversheet).
The Relevant Senior Executive presents a proposal for the new or updated policy to VCC for endorsement to proceed.
The academic function comprises student matters, teaching and learning and research matters covered in but not limited to Sections 3 and 4 of the PPL.
To ensure that policies reflect an understanding of the key issues, the PPL Custodian responsible for the policy should consult with relevant stakeholders to seek input on matters to include in a review, or on the proposed changes, as appropriate.
Depending on content of the policy, proposals to create, change or rescind policies relating to the academic function of the University must be considered by the relevant board sub-committees (e.g. Teaching and Learning Committee, Research Committee etc) before progressing to Academic Board for endorsement (see Academic Board - Secretariat Resources (UQ login required)). In cases where a policy change is significant or relates to strategic changes, the appropriate member of VCC should be involved to determine whether VCC input is required.
The PPL Custodian completes the Policy Approval Template which sets out the reason for change, stakeholder input and promulgation and implementation plan.
The PPL Custodian completes the Policy Approval Template which sets out the reason for change, stakeholder input and promulgation and implementation plan, including any additional matters raised by Academic Board.
The Relevant Senior Executive for a policy is the member of VCC whose portfolio carries primary responsibility for the matter and to whom the PPL Custodian reports (see VCC Membership List).
Matters reserved by Senate are listed in Section 6.1 of PPL 1.10.06 Senate Governance Framework.
§ Part 2 – VC Briefing covers PPL editorial compliance and VC Executive Officer review.
The Vice-Chancellor refers the draft policy to the relevant Senate Committee for consideration and recommendation to Senate for approval at the next Senate meeting.
Evidence of approval and the new policy are forwarded to the PPL Manager for publishing in the PPL. The timing of publication is coordinated with the PPL Custodian to comply with the promulgation and implementation plan in the Policy Approval Template.
The PPL Custodian actions the promulgation and implementation plan submitted in the Policy Approval Template.
relevant heads of organisational units responsible for administering the policy, or other relevant staff.
Communication to relevant stakeholders on the changes to the policy may include details of the changes and the impacts of those changes, and any training or other resources available to assist in the implementation of the policy change. | https://ppl.app.uq.edu.au/content/policies-and-approval-process |
The Benton Institute for Broadband & Society released a new report than in many ways reads like a latest version of a US broadband plan – or more like an invitation to create a new broadband plan. It’s very detailed and (unabashedly) looks at the positive impact of broadband. I thought I’d write about the report at least twice because there’s so much going on. Today I thought I’d pull out the parts that mention Minnesota.
Blandin gets a nod in the first new pages…
Leadership does not, of course, come only from government, but from community-focused organizations as well. For example, the Blandin Foundation focuses on strengthening rural Minnesota, including by supporting and measuring the impact of broadband in rural communities—measurements that found concrete economic benefits such as income growth resulting from broadband deployment.1
And then in a profile later in the report…
Building and revitalizing strong communities is hard work. It takes leadership, reaching across boundaries, and building lasting connections. For over 16 years, the Blandin Foundation has included broadband deployment and adoption in its efforts to build healthy and vibrant rural communities in Minnesota.
Blandin has been a trusted partner with, and advocate for, rural Minnesota since 1941. Drawing from this deep history of relationships, Blandin has partnered with dozens of rural communities and funded hundreds of projects to enhance quality of life and place.
In one of Blandin’s biggest and most impactful efforts, it implemented the Minnesota Intelligent Rural Communities (MIRC) project with a combination of $4.8 million in funds from the National Telecommunications and Information Administration’s (NTIA) Broadband Technology Opportunities Program (BTOP) and $1.5 million in matching funds from project partners.
MIRC was a three-year project (2010–13); a multi-sector, comprehensive approach to promote broadband adoption that targeted un- and underemployed workers, non-adopters, low-income residents, small businesses, local governments, and critical services providers.
Eleven demonstration communities brought MIRC to every corner of rural Minnesota. This cross section of cities, towns, counties, and multi-county regions—with a total population of 250,000 people and population density ranging from 4 to 1,700 people per square mile— gave the project the opportunity to test the impact of education, training, and outreach efforts within communities of varying populations, size, and social and economic profiles. Further, the communities had a wide variety of telecommunications infrastructure and services, ranging from municipally owned and operated networks to duopoly-served markets to legacy providers.
The project used a community and economic development framework, called Intelligent Communities, which establish es five core community characteristics (broadband connectivity, digital inclusion, knowledge workforce, innovation, and marketing and advocacy).
MIRC set target outcomes that could be measured and monitored—all of which were accomplished or exceeded. In the past six years, Blandin’s Broadband Communities (BBC) program has applied what it learned during the MIRC program to its two-year partnerships with other rural Minnesota communities:
Communities know best and need to engage their citizens directly in articulating and reaching broadband adoption and utilization goals.
Local leadership matters, and leaders need to be trained to frame issues, build and sustain relationships, and mobilize people to build a community’s capacity to achieve its broadband goals.
Intra-community, personalized outreach works for technologically challenged small businesses and for historically marginalized populations.
Peers make great teachers and are a popular, low-cost, and easily sustainable resource to build a community’s technological savvy.
Cross-community communication is key to spurring and sustaining energy and excitement for community broadband projects.
Encourage a next generation of young leaders who can bring energy and sustainability to any community initiative by serving as co-trainers, technology mentors, and partners in computer refurbishment projects—and can use video and other social media to promote their communities.
Connect the economic dots. The “whole picture” Intelligent Community framework for community and economic development used in MIRC can help community leaders see how workforce, infrastructure, inclusivity, innovation, and marketing/ advocacy are mutually interdependent aspects of community vitality.
Have patience. This work takes time. Look for and celebrate early and easy “wins” along the way, but think long-term and build capacity and energy for the long haul. Money and other resources follow vision and commitment.
Then throughout the report, they mention part or aspects of Minnesota’s state speed goals and related legislation…
- By contrast, Minnesota defines “underserved” as any place where “households or businesses lack access to wireline broadband service at speeds of at least 100 megabits per second download and at least 20 megabits per second upload.
- Thus, recent legislation proposals and state programs, like Minnesota’s, target funding to any area that lacks at least 100 Mbps download (the upload numbers vary). That is a good beginning, in part because networks that provide those kinds of speeds (and associated features like low latency and capacious usage) can typically be upgraded at relatively modest costs as demand requires.
- At least twenty states—including Colorado, North Carolina, Virginia, Maine, Michigan, Minnesota, and Wisconsin—have statewide broadband strategies with dedicated funding to promote deployments.269 Forty-four states have broadband offices, task forces, or legislative committees responsible for facilitating broadband deployments.
- Minnesota has lodged its effort in its Department of Employment and Economic Development, so the state’s program expressly considers the “likely economic impact” of the project alongside evidence of community 38 Chapter 2: Deployment of High-Performance Broadband Networks to Unserved Areas support.271 Minnesota funds deployment in both unserved and underserved locations, and its funds can be used for both last-mile and middle-mile construction.
- To date, Minnesota has funded broadband service to more than 34,000 previously unserved households, 5,200 businesses, and 300 community institutions,274 and 100/20 Mbps service is now available to nearly 75 percent of households.275 Minnesota’s efforts also illustrate the importance of broadband to advancing local economic goals.276 For example, rural tourist destinations in Minnesota have struggled to meet guests’ needs—and even process credit card purchases—because of slow internet connections.277 In Cook County, the state’s second largest county by square miles and a place that needs better broadband to satisfy the demands of tourists, the Arrowhead Electric Cooperative built a network with federal and local funding that provides roughly 95 percent of the county with access to internet with speeds of at least 100/20 Mbps over a fiber-based network.
- Minnesota’s Broadband Task Force Report recommends that the state prioritize funding its regional library systems so that libraries can benefit from “economies of scale providing greater effectiveness, improved quality and access to more resources.”
- The Minnesota Broadband Infrastructure Plan began in 2008 and is reassessed on an annual basis by the legislature as it considers adjustments to the elements codified into law.
Tomorrow (or maybe Monday) I look beyond the Minnesota scope – but it’s always nice to see how Minnesota plays outside state boundaries. And I think we played well. | https://blandinonbroadband.org/2019/10/31/mentions-of-minnesota-in-broadband-for-americas-future-a-vision-for-the-2020s/ |
Our proposal focuses on two aspects of abnormal immune regulation in MS. 1) Might immune system abnormalities in MS be linked to CNS lesions that arise during the disease? Specifically, might strategically situated lesions induce changes via the autonomic nervous system that result in impaired immune regulation, i.e., loss of suppressor (S) function? Loss of S function would in turn favor disease progression. 2) Can we, by comparing patients with persistently abnormal (progressive MS) or persistently normal (stable MS) S function determine mechanisms whereby abnormal function can be made normal and vice versa? Peripheral blood cells from progressive and stable MS patients and normal controls will be exposed to beta-adrenergic agonists and antagonists, interferons, protein kinase C activators and inhibitors, and T cell mitogens, including anti-CD2 monoclonal antibodies. These agents will be used to study S cell function, T cell activation, and synthesis and phosphorylation of T cell proteins. These agents or their endogenous substrates are likely to be involved in the defects in immune function seen in MS. We will also study CD8+ cells and cell lines from rapidly progressive cases in vitro attempting to restore function by pharmacologic means. Conversely, cells from patients with stable MS (and normal S function) will be subjected to manipulations that may convert their normal function in vitro to abnormal. Mechanisms to be explored with regard to change in suppressor function include (a) are there changes in cell surface marker expression that link with change in function? (b) is there a shift from suppressor to cytotoxic function? (c) are there changes in cell activation mechanisms that correlate with altered S function? Identification of the basis for change in S function would have implications both for understanding abnormalities of immune function in MS and for therapy.
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Constance, Council of
Constance, Council of,1414–18, council of the Roman Catholic Church, some of its sessions being reckoned as the 16th ecumenical council. It was summoned to end the Great Schism (see Schism, GreatSchism, Great,
or Schism of the West,
division in the Roman Catholic Church from 1378 to 1417. There was no question of faith or practice involved; the schism was a matter of persons and politics.
..... Click the link for more information. ), in which three men were claiming to be pope—Gregory XIIGregory XII,
c.1327–1417, pope (1406–15), a Venetian named Angelo Correr; successor of Innocent VII. As a condition of election, Gregory promised to do everything possible to end the Great Schism, including the relinquishing of his office.
..... Click the link for more information. (since recognized as canonical pope), John XXIII (see Cossa, BaldassareCossa, Baldassare
, c.1370–1419, Neapolitan churchman, antipope (1410–15; see Schism, Great) with the name John XXIII. He had a military career before entering the service of the church.
..... Click the link for more information. ), and Benedict XIII (see Luna, Pedro deLuna, Pedro de
, 1328?–1423?, Aragonese churchman, antipope (1394–1417) with the name Benedict XIII. He was a doctor of canon law and as cardinal (1375) became an outstanding member of the Curia Romana.
..... Click the link for more information. ). Reform of Christian life and extirpation of heresy were also aims of the convocation, which was called by John at the insistence of Holy Roman Emperor SigismundSigismund
, 1368–1437, Holy Roman emperor (1433–37), German king (1410–37), king of Hungary (1387–1437) and of Bohemia (1419–37), elector of Brandenburg (1376–1415), son of Holy Roman Emperor Charles IV.
..... Click the link for more information. . Sigismund chose Konstanz (Constance), an imperial city, as the meeting place. Church theologians tend to regard as ecumenical in character only those sessions of the council meeting after the convocation by Gregory XII, or the sessions following the election of Martin V.
During the council enormous crowds visited the city; there was much pageantry. The first session was in Nov., 1414; the 45th and last was on Apr. 22, 1418. The council was dominated by theologians, especially French, who held the conciliar theory (i.e., that councils held supreme power in the church and that even the pope was subject to their edicts) that had appeared at the Council of Pisa (see Pisa, Council ofPisa, Council of,
1409, unrecognized council of the Roman Catholic Church. It was summoned to end the Great Schism (see Schism, Great) by members of the colleges of cardinals of the two rivals, Gregory XII (in Rome) and Benedict XIII (Pedro de Luna, in Avignon).
..... Click the link for more information. ). The conciliarists John GersonGerson, John
(Jean Charlier de Gerson) , 1363–1429, French ecclesiastical statesman and writer. He studied (1377–94) under Pierre d'Ailly at the Univ. of Paris, where he took his doctorate in theology and succeeded Ailly as chancellor (1395).
..... Click the link for more information. and Pierre d'AillyAilly, Pierre d'
, 1350–1420, French theologian and writer, cardinal of the Roman Catholic Church. He was the teacher of John Gerson and was Gerson's predecessor as chancellor of the Univ. of Paris (1385–95).
..... Click the link for more information. were among the figures prominent at the council. Instead of the traditional assembly of bishops, the council was organized as a convention of nations (German, Italian, French, and English; the Spanish entered later), each nation having one vote. The decisions were made in caucuses of the nations between sessions.
The convention declared in the Articles of Constance (Apr. 6, 1415) that it was an ecumenical council and supreme in the church. Next it declared John deposed (May 29, 1415). Gregory XII, meanwhile, sent legates with a formal decree to convene a council; this was accepted by the convention, which then ceremonially declared the council convened; at the same time Gregory resigned the papacy (July 4, 1415). Benedict provided a hard problem; he would abdicate only if allowed to name his successor. At last, after a trial held in his absence, he was deposed (July 26, 1417). This ended the schism.
An elaborate method of electing the new pope was adopted, and the conclave soon agreed on Martin VMartin V,
1368–1431, pope (1417–31), a Roman named Oddone Colonna; successor of Gregory XII. He was created cardinal by Innocent VII, and in the schism (see Schism, Great) he attended and supported the decisions of the Council of Pisa (see Pisa, Council of).
..... Click the link for more information. (Nov. 11, 1417). The council, however, had already provided a plan to perpetuate its rule over the church by calling for frequent councils; furthermore, the modest reforms enacted by the council seemed designed to limit the pope's power of taxation and to protect the interests of the national clergy. Martin agreed to all enactments of the council—except, Catholic theologians argue, the council's extreme claim to supremacy—and signed concordats embodying these reforms with Germany, England, and the Latin countries. John HussHuss, John
, Czech Jan Hus , 1369?–1415, Czech religious reformer. Early Life
Of peasant origin, he was born in Husinec, Bohemia (from which his name is derived). He studied theology at the Univ. of Prague, was ordained a priest c.
..... Click the link for more information. and Jerome of PragueJerome of Prague,
c.1370–1416, Bohemian religious reformer. During his studies at Prague and at Oxford, Jerome was influenced by the doctrinal views of John Wyclif. He continued to study and travel widely abroad, in constant conflict with the authorities.
..... Click the link for more information. were tried and burned at the stake for heresy. St. Bridget of Sweden was canonized.
Bibliography
See E. F. Jacob, Essays in the Conciliar Epoch (rev. ed. 1963); L. R. Loomis, The Council of Constance (1961).
Constance, Council of
a world council of the Catholic Church that lasted from 1414 to 1418 in the city of Constance, Germany.
The council was called by Pope John XXIII (under pressure from the Emperor Sigismund I and high church circles) to liquidate the Great Schism and reform the church. Besides the clergy, the council was attended by secular feudal lords, including the Emperor Sigismund. The council put an end to the schism—the three claimants to the papal throne were all ousted (Gregory XII abdicated and John XXIII and Benedict XIII were deposed), and a new pope, Martin V, was elected. The council proclaimed the necessity of convening church councils regularly and enunciated the principle of the supremacy of a council over the pope, but these decisions were not subsequently realized. The council condemned the teachings of J. Wycliffe and J. Hus. Although he had been given a charter of immunity by the Emperor Sigismund, Hus was burned in Constance on July 6, 1415. A year later, the same fate befell Hus’ associate, Jerome of Prague, who was condemned by the same council. | http://encyclopedia2.thefreedictionary.com/Constance%2C+Council+of |
Through the experience, faculty members gain an understanding of technology translation challenges and opportunities, and also develop a robust network of contacts within and outside the university.
eFellows is open to all full-time VT faculty members, including those from all disciplines and academic areas on the campus. We seek academic entrepreneurs or faculty interested in integrating an entrepreneurial mindset and related concepts, tools, and frameworks into their home discipline; particularly into their outreach and commercialization activities.
Meet our Entrepreneur Faculty Fellows
Pablo Tarazaga
Associate Professor, College of Engineering
Commercialization activities: The general areas of structural dynamics, vibration, control, testing, adaptive structures and smart materials.
Charles Clancy
Director, Hume Center for National Security at Virginia Tech
Commercialization activities: Signals intelligence; cyber warfare; electronic warfare; information operations; computer network attack, defense, and exploitation; automated intelligence analysis; and intelligence visualization
Jeff Reed
Professor, College of Engineering
Commercialization activities: Software radios, smart antennas, cognitive communications and signal processing
Tim Long
Associate Professor, College of Science
Commercialization activities: Polymerization, Structure-property relationship of polymers, Block copolymers and thermoplastic elastomers, Functional polymers for additive manufacturing (3D printing)
Chris Williams
Associate Professor, College of Engineering
Director, DREAMS lab
Commercialization activities: Additive manufacturing
Interested in becoming an eFellow?
Faculty members are invited to join us for ongoing information sessions at the Apex Center in Pamplin Hall (Room 3002). | https://www.apex.vt.edu/research/efellows/ |
Within our Organon series of articles, we already talked profoundly about the fine art of letting go because getting rid of attachment is a central topic in Creative Homeopathy. Becoming a fully liberated individuality is the primary purpose behind all holistic approaches in therapy. Accordingly, as facilitators, it is our objective to find the psychological imprints in our clients that inhibit them from achieving that goal.
Our previous article focused on attachment issues and the challenge of overcoming trauma related to the loss of a beloved person. In this treatise by Antonie Peppler, we concentrate on traditional entanglements like family structures and society. Please enjoy her short treatise about the fine art of letting go.
Letting go from Attachments
In almost every homeopathic treatment, the word “letting go” is mentioned. Detachment of previous behavioral and thought patterns is crucial to becoming healthy and independent. Patients often look irritated and convey that they do not know what “letting go” actually means.
What does letting go actually mean?
To grasp this subject sufficiently, it is helpful to fall back on the wisdom hidden in our language. There is the word “imagination” and the concept of “letting go of imagination.” The word “imagination” means that reality was covered up with a fictitious image. Each personality has its individual life dynamic based on what it has created for itself—that is the reality behind the false surface.
However, our subconscious thoughts and ideas control this individual life dynamic, which is often shaped by ancient tradition. There we have the false image overlapping reality. For example, people accept that it is not allowed to separate because the church has forbidden it, no matter how happy or unhappy people are. This conviction still exists today.
It is necessary to let go of these unconscious rules or beliefs. This means that the personality must grow so that it can oppose tradition. This often happens only with a bad conscience, inhibiting the development process. Homeopathic remedies can help deal with these subconscious emotions when confronted with guilt and a bad conscience. Examples of that are Ignatia, Coffea cruda/tosta, etc.
The parents as an ideal image
When a person understands that certain rituals and beliefs are presented to his own life dynamics, he has the opportunity to transform them and adjust his vitality towards his individual needs. In practice, patients often have particular ideas about their own parents. Often enough, there is a presumption that parents are the direct successors of God. The father could do everything. The mother just so protected us and directed us. For many people, the content of the concept of God is quite identical to the scope of the image of their parents.
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The realization of parents as normal people
Only later, when we have grown older, we might realize that the parents are also just ordinary people. The readiness to perceive this is decisive. If we see the parents as completely normal humans, we detach them from the image of a perfect being in a protecting and loving function. Then we often lose the concept of God. This potential disappointment is enough reason to resist or even avoid the revelation entirely and keep the illusion of parents as the flawless manifestation of the perfect humans.
Follow the individual life plan
It is essential to accept that the world is different from how we imagined it when we were children or how it is predetermined by traditional rituals. When much more tolerance has arisen, an individual considers several possibilities in life as realistic options and gives oneself the possibility to make a conscious choice. Only our fixed concepts might be rocked at that moment, but we can rework them.
The great advantage of challenging our traditional beliefs is that our lives become more individual. Thus, we can use what ultimately corresponds to us and resonates with our natural dynamics of life. If we assume that the soul may have created a life plan before it incarnated, then it is essential to follow it. The concept of one’s destiny might oppose the traditional thought structures. This topic concerns the process of detaching especially. Only at the moment, when we have acquired the ability of choice and the capacity to let go, can we arrange ourselves as individuals living in such a way as it corresponds to us as unique personalities.
The original article about depression was written by Antonie Peppler and translated by Christian Köhlert. | https://creative-homeopathy.com/the-fine-art-of-letting-go/ |
The computer program at Madrona is supported by the PTA, and has been taught by Mrs. Glenn for the past 13 years. The 1st - 3rd grades have directed sessions once a week and the 4th and 5th grade students twice a week where they work on various programs and projects using their Google accounts, MS Office, internet for research, typing software, introductory coding, and other web-based programs. Students are exposed to and practice numerous computer skills using a variety of interactive and educational programs with Mrs. Glenn, and also visit the 2nd computer lab and use Chrome Books with their classroom teachers.
Information on accessing online resources is available at the following link: http://q-r.to/baf8vf
Raz Kids
Raz Kids contains hundreds of books that engage students with animation and sound effects as they listen to fluent reading, record their own reading for practice, and take quizzes on what they read to strengthen comprehension skills.
www.raz-kids.com
Type to Learn 4
Type to Learn 4 provides students with the opportunity to practice important keyboarding skills! The link to download the program is: http://ttl4.sunburst.com/downloads/ Instructions for downloading this program are included in the following attachment: Type to Learn 4 Instructions
California Treasures Reading Program
California Treasures Reading Program is a resource that correlates with the district's adopted Language Arts curriculum. | https://www.conejousd.org/madrona/Programs/Computers |
The manufacturing process determines the product properties. With the correct interaction of individual process steps (such as casting → extruding → heat treatment), a product with desired features will be the result at the end of the production chain.
To meet the requirements of today’s forming processes, we support our customers in developing new process strategies, design of new processes and optimization of existing processes.
In the development, optimization and adaptation of processes, we always consider available potentials arising from the current state of the art in the field of mechanical engineering and tool materials.
With our equipment consisting of extrusion presses, wire drawing and stretching benches, induction and chamber furnaces as well as several mechanical test stands we can conduct R&D projects and feasibility studies in various fields. | https://ingwerk.com/en/activities/process-engineering/ |
With the rise of the Internet, reliance on server clusters and cloud-based storage facilities has increased. Such increased reliance has led to higher demands for equipment performance and reliability. As such, managers of the server clusters and data storage facilities are increasingly concerned about the environment experienced by the servers and hard drives.
Similarly, with increased globalization of commerce, sensitive products are increasingly being shipped long distances and stored in warehouses. To maintain quality and decreased damage to products, tracking the environment experienced by such products is of increased interest.
In either case, there is an increased interest in monitoring systems that can identify conditions that would lead to product or equipment damage. Early identification of such conditions can lead to higher product quality or longer equipment life, lowering costs and increasing return on investment.
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The Global Challenges Foundation and the Institute for Future Studies held a review panel on 15 February 2019 titled “Global Governance and the Emergence of Global Institutions for the 21st Century: Selected Modules Addressing Global Catastrophic Risks”.
The topic of the review panel is an abbreviated version of one of the winning models to have come from the New Shape Prize which prescribes a series of reforms to the United Nations system that should directly improve its capacity to manage the greatest challenges of our time.
The Stockholm-event sees expert reviewers and audience members participate in a lively exchange surrounding the viability of the proposed reforms, including political feasibility, technical feasibility, impact, and possible unintended consequences or indirect effects.
The results of this session will help the GCF assess the maturity of the ideas, whether and how to continue developing them, and the general approach appropriate when evaluating UN reform proposals in the future. | https://globalchallenges.org/global-governance-and-the-emergence-of-global-institutions-for-the-21st-century-selected-modules-addressing-global-catastrophic-risks/ |
The judgment decides the appeal presented by two individuals against their conviction in first instance for crimes against the rights of foreign citizens (which comprises the smuggling of migrants).
On 17 September 2012, the Services of Maritime Rescue of Cartagena (Spain) detected a small boat – inadequate to navigate on the high seas - off the coast of the city. The Guardia Civil soon rescued the boat, on board of which – in addition to the appellants - were 14 Algerian migrants. The boat had departure the previous day from the beach of Bouski Sidi Lakhdar, in the coat of Mostaganem (Algeria), in direction to Spain. The appellants helmed the boat. Migrants paid app. 6 000 000 dinars each for the trip.
It was ascertained that the appellants had for several years been organising trips to procure the illegal entry of Algerian nationals into Spain by sea, with the purpose of obtaining a financial or other material benefit.
The appellants had been previously expelled from Spanish territory several times (latest record dating 12 August 2012).
In deciding the case, the court of first instance considered documentary evidence (re, e.g., diligences taken by authorities to locate witnesses), statements of the migrants (including pre-trial declarations) as well as appellants.
In appeal, the Supreme Court upheld the decision of the court of first instance. For further details see infra under “Commentary”.
Pre-trial evidence, duly documented and obtained in compliance with the principle of contradictory, is admissible in court if reasonable measures to ensure the presence of the witness in court were taken (even though ultimately with no success, as in the present case). The rights of the accused and principles of due process will not be breached if such conditions are fulfilled (e.g. witness interviewed in presence of the Prosecutor, investigative judge, and legal counsel).
If the Defence did not question the witness at the time of the pre-trial hearing for reasons imputable to itself, it may not later invoke this argument to challenge the admissibility of pre-trial evidence. Importantly, the constitutional protection refers to the possibility of exercising the contradictory rather than occurrence of contradiction.
The Supreme Court further clarified that the information provided by investigative authorities to the victims/witnesses regarding the possibility of obtaining residence permit were they to collaborate in the context of proceedings does not amount to witness tampering. Accordingly, it is not per se a valid motive to challenge the admissibility of evidence provided by such victim/witness.
The Supreme Court assessed indicia of the knowledge and willingness to commit the crime. It noted that the behaviour of a recidivist offender that repeatedly illegally enters the territory of the State concerned then endeavouring to be expelled to his country of origin so as to again procure the illegal entry of migrants in another country (as part of a structured modus operandi) provides important indication of mens rea.
Finally the Supreme Court dismissed the argument that alleged economic difficulties of the defendants could consubstantiate a state of necessity and, consequently, exculpate their criminal responsibility. In so concluding, the Court explained that in order to invoke a state of necessity it is necessary: (i) an objective, inevitable, unfair, illicit and impending harm that cannot be avoided without committing the offence, (ii) proportionality of the harm caused in order to prevent the feared harm, (iii) exhaustion of all legitimate means of action to prevent or neutralise the harm before acting illegally, and (iv) the existence of any subjective motivations will not allow resort to the defence of state of necessity. The Court reiterated that alleged economic difficulties do not meet the necessary criteria and does exculpate the criminal conduct of the appellants.
It is worth noting the effective police cooperation between Spanish and French authorities in this case. Conversely, the considerable time-demands for the execution of requests for mutual legal assistance appears as an aspect that may constrain investigations and prosecutions.
NOTE: As per Spanish national law, the purpose of obtaining a financial or other material benefit is not a constitutive element of the crime but rather an aggravating circumstance (see SHERLOC Database on Legislation – Spain).
Rogatory letter sent by Spain to France requesting a videoconference hearing with a witness. The request was denied due to lack of material time vis-à-vis the proposed date. France responded that such a request should be submitted at least 3 months in advance.
The assistance of French police authorities permitted to determine that the address previously communicated by the witness to Spanish authorities was false and that, accordingly, the whereabouts of the witness were unknown.
The Investigative Magistrate 2 of Cartagenafilled summary proceedings against the appellants (N. 72/12) for crimes against the rights of foreign citizens, and referred the case to the Audiencia Provincial de Murcia (Spain). The latter, on 15 March 2013, convicted the appellants for crimes against the rights of foreign citizens. The appeal herein under analysis followed.
Previously expelled from Spain three times.
In appealing the decision of the Audiencia Provincial de Murcia (Spain), E. argued inter alia (i) breach of the presumption of innocence for insufficiency of evidence supporting a conviction, (ii) inadmissibility in court of pre-trial evidence in the terms it occurred in casu (declarations of protected witness that did not attend court sessions). For further details, see infra under “Commentary”.
Previously expelled from Spain six times.
In appealing the decision of the Audiencia Provincial de Murcia (Spain), J. argued inter alia (i) breach of the presumption of innocence for insufficiency of evidence supporting a conviction, (ii) inadmissibility in court of pre-trial evidence in the terms it occurred in casu (declarations of protected witness that did attend court sessions). For further details, see infra under “Commentary”. | https://sherloc.unodc.org/cld/case-law-doc/criminalgroupcrimetype/esp/2013/sentencia_7692013_-_supreme_court.html?lng=en&tmpl=sherloc |
Migrating to or implementing a new cloud platform is a large project — but it is only the first step on the journey to successful cloud adoption. Once you are live in the cloud, your new set of priorities includes onboarding new resources, establishing and following cloud standards, and optimizing your cloud investment.
In light of these priorities, an important question arises: What does success look like? While a numerical measure of success may not be possible, there are many different methods, strategies, and approaches you can use to set yourself on the path to success. These methods include:
- Establishing a cloud center of excellence (CCoE)
- Advancing through the levels of the cloud maturity model
- Optimizing your cloud return on investment (ROI)
In this article, we’ll review each of these methods so you can evaluate where you are on the pathway to cloud success.
Establishing a Cloud Center of Excellence (CCoE)
“A cloud center of excellence is the best-practice approach to drive cloud-enabled transformation.” Gartner
To be successful in adopting the cloud, you must have the right team to help you make strategic decisions. The best way to organize this team is to create a cloud center of excellence (CCoE). A CCoE is composed of an organization’s executives, field operators, and department-level decision-makers. In addition, you can recruit a team of cloud assessors to measure and govern the progress of cloud adaptation and maturity.
The CCoE team leads the introduction of cloud computing capabilities to an organization. This team is responsible for the following granular-level activities.
- Championing the cloud transformation process
- Researching and planning logistics
- Guiding the transition
- Supporting and training employees
- Introducing required cloud frameworks
- Standardizing processes
- Helping employees overcome any barriers to cloud adoption
- Communicating clearly about any potential risks or issues
- Reviewing and reiterating any changes in the process for continuous improvement
- Aligning with the business objectives of the organization
Advancing Through the Levels of the Cloud Maturity Model
Cloud success is not an overnight achievement. It requires methodical and consistent effort until adoption is achieved across the organization. The cloud maturity model is a framework with six levels of cloud adoption that range from no cloud adoption to global, full-scale, multi-cloud, and multi-unit adoption. You can use this model to determine where you are on the cloud success pathway, and what you need to do to advance further.
Level One: Zero Implementation
There is no cloud implementation, and the potential capabilities are just hypothetical.
Level Two: Beta Resources
A beta team or project is established, and the theoretical cloud approach is tested on that single resource, group, or project.
Level Three: Deployment Across Teams
A cloud implementation project has been successful, and the cloud initiative has been deployed, measured, and tested across the entire function or team.
Level Four: Deployment Across Environments
To ensure organizational cloud success, the cloud initiative is then deployed across organizational divisions or shared servers and applications.
Level Five: Deployment Across Units
For large organizations that have multiple units across different geographical regions, the cloud can then be deployed across the entire unit.
Level Six: Deployment Across Clouds
Once the cloud initiative is operational for one unit, it can then be moved to the entire cloud ecosystem and introduced as a standard practice.
With these six levels, you can gradually mature your cloud practices and create successful cloud initiatives that will make an impact on your business goals.
Cloud maturity assessment with the spider graph of maturity and adaptation
To track and measure the success of your cloud implementation, you can track the maturity and adaptation of the cloud with the help of a spider chart. For instance, if you have implemented cloud infrastructure for governance, business strategy, data architecture, information and operations, and management, below is how your spider chart of adaptation and maturity might look:
Optimizing Your Cloud Return on Investment
According to a study, the main goal of 59% of European organizations is to cut costs by optimizing their current cloud usage.
Here are four steps you can take to ensure a maximum return on your cloud investment.
1. Standardize
The first step is to create standardized practices that applicable parties must follow when managing and interacting with your cloud infrastructure. These practices should be implemented across resource pools and ultimately the entire organization.
2. Train
As a second step, educate users about cloud practices, cloud capabilities, and the organization’s future business priorities. Ensure they understand how compliance with these standards will help them achieve future organizational and departmental goals. In addition, provide training on data governance and cloud usage parameters so your organization stays in compliance with applicable laws and stays under budget. Be aware of common post-implementation issues so you can address them in your training.
3. Measure
Once your cloud technology is established across the organization, it is now time to measure cloud maturity. Of all the cloud initiatives that you have created, you must measure which initiatives are performing, how they are performing, and how they tie back to the business goals that were established during the implementation.
4. Automate
The final stage of cloud optimization is cloud automation. The goal is to make every cloud initiative fast, efficient, and as hands-off as possible. This will not only optimize processes, but it will ensure that your resources can focus on productive work and increase the overall profitability of your organization.
It is All an Ongoing Process
It is not uncommon for cloud adoption efforts to sputter and stall on their way to success. Taking on-demand, elastic computing and converting it into concrete, measurable benefits to the business — and motivating all members of the organization to be the engine of those benefits — is a journey, not a race. You need to work consistently to create better measurements and goals that can be achieved with a mature and optimized cloud infrastructure.
Datavail recently helped a 600-million-dollar telecommunication equipment company execute a full cloud transformation. The company is one of the first in the nation to implement an updated and modern ERP Cloud platform foundation using Oracle’s complete suite of 52 cloud-native applications. Learn more about their astonishing transformation.
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Dilute 1 measuring cup (15 ml) in a glass of water in the morning for 16 days. as required renewable.
Not recommended for pregnant and lactating women.
Keep out of the reach of children.
Do not exceed the recommended daily dose.
Food supplements should be used in a part of a healthy lifestyle and not be used as substitutes for a varied and balanced diet.
For 1 dose of 15 ml: | https://www.natural-shop.bio/en/memory-blood-circulation/614-circulation.html |
New template for weeks 4-6, tuck jumps were in Vert Shock and I liked them. I was doing my DL singles with 90-120 secs rest which seems sufficient.
29 Oct
Single Leg Vert – 3 x 5
Depth Jump – 4 x 5 x 45cm
Broad Jumps – 5 x 5 (10.90 to 11.40m)
Depth jumps feel like a standard part of any jumps program now. I was aware that with the wet and slightly slippery surface my ground contact time might increase so I’ll be wary of that next time. Broad jumps were on damp tarmac with a slight incline, a little disappointed with the measurements without really knowing what to expect. I would think 2.30-2.50m would be good so five of those would be more like 11.5 to 12.5 metres but I guess the incline cuts that short.
31 Oct
CMJ – 53,55,57,56,56cm
2 Step Approach – 5 x 1
Full Approach 2 foot – 11 x 1
Full Approach 1 foot – 5 x 1 per leg
OH squat – 5 x 20, 30, 40, 40kg
Box Squats – 5 x 80kg, 4 x 5 x 100kg
Jumps were good today, finally dry ground. I should note weeks 1-4 my PB CMJ has been 57cm, 56cm, 57cm and 57cm, I would have liked to make some progress even while fatigued. I wasn’t getting the height I expected in my running jumps either but since my technique needs a lot of work that was the main focus. I felt like I could come in faster and not panic about foot placement which is a sign of progress.
Here’s one of my 11 full approach off 2 feet, I did 8 from this side and 3 from my less natural side. | https://9to5strength.com/forums/reply/10150/ |
San Francisco officials are extending a pilot program examining the impact of keeping three public bathrooms open around the clock in neighborhoods where requests for feces removal really tend to pile up.
The extension is expected to build on the success of an experiment that began in August, when the city decided to keep three Pit Stops — public stalls with on-site staffers — open seven days a week, 24 hours a day.
As San Francisco confronts the growing volumes of human and animal waste showing up on sidewalks, officials have been under pressure to open more Pit Stops and to keep them open longer.
The pilot program, run by the Public Works Department, was meant to test whether bathrooms would be used in the small hours of the night, whether the investment in round-the-clock access would translate into cleaner streets and whether the people staffing the Pit Stops would be safe while on duty.
The past three months have shown promising results, according to Public Works data. More Pit Stops are imminent, and round-the-clock access at some appears highly likely.
For the city’s homeless, the Pit Stops have become places where people can relieve themselves with dignity. They’ve also transcended their function as public bathrooms: With an epidemic of injection-drug use, Pit Stop monitors have frequently stepped in to provide life-saving care to people who overdose in their stalls. Pit Stops also provide needle disposals and bags for picking up dog waste.
“This is not complicated — when people have access to a clean, safe restroom, they will use it,” Mayor London Breed said in a statement. “We have seen what happens on our streets when people don’t have a place to go, which is why I fought to include funding in the budget for seven new Pit Stops, as well as expanded hours at existing locations.”
Breed’s last budget included $8.1 million over the next two fiscal years to build seven more Pit Stops and expand hours at existing ones. The recently concluded three-month test cost $300,000 to staff the bathrooms around the clock. Two-thirds of that money came from Supervisor Matt Haney’s district budget. Two of the three 24-hour Pit Stops were in District Six, which he represents. There are now 25 Pit Stops spread across 13 San Francisco neighborhoods.
“Feces complaints are going up. Homelessness is going up. This is something that just flat-out makes sense, and something we can do right away,” Haney said. “And there’s some aspect of this you can’t measure in dollars, which is people’s human dignity and the basic access to restrooms that every human being deserves.”
The three locations selected for 24/7 service are at Eddy and Jones streets in the Tenderloin, Sixth and Jessie streets in South of Market, and Market and Castro streets in the Castro district. The Tenderloin location was the most heavily used over the past three months, with nearly 15,400 flushes. Nearly 25% of those flushes came between 11 p.m. and 7 a.m. daily, and the same held true for the two other locations: an average of 24.7% of all flushes came during the overnight hours.
The sight of people relieving themselves between cars on Eddy Street was an all-too-common sight for Mo Ali, manager of Downtown Grocery, which has no public restroom. He’d often shoo them away on smoke breaks.
“But now I just point across the street, ‘Go over there,’” Ali said. Since the Pit Stop started staying open 24-7, “I haven’t seen it like I used to. I used to see it all the time.”
At each location, Pit Stops were staffed by two attendants as a safety precaution. There were no reports of assaults during the three-month period.
Steam-cleaning requests sent through the city’s 311 system — for feces, urine or other debris — dropped at both the SoMa and Castro Pit Stops once the bathrooms switched to round-the-clock service, according to Public Works data that compared request volumes from May to October. The SoMa location saw 16 fewer requests after the switch and the Castro Pit Stop saw two fewer requests on average from August to October, compared with May to July.
Requests around the Tenderloin Pit Stop remained about the same during that time — a change of just 16.7 average requests from May to July and 17 from August to October.
Conditions have improved around the SoMa Pit Stop, said Fred Beasley, a security guard for Create Skateboard Shop on Sixth Street.
“It’s convenient — people have someplace to go now. They’re not in a doorway doing their business,” he said. But pet waste — and pet owners’ indifference — continues to be a problem, Beasley said.
“People need to be taking care of their dogs more. One step at a time, I guess.”
Dominic Fracassa is a San Francisco Chronicle staff writer. Email: [email protected] Twitter: @dominicfracassa
| |
Industries minister Hammad Azhar says South Korean firm has appreciated government’s policies to encourage local production
South Korean smartphone manufacturer Samsung is “actively” considering establishing an assembly plant in Pakistan, Industries and Productions Minister Hammad Azhar announced on Friday.
“Smartphone production in Pakistan is multiplying following DIRBS [Device Identification, Registration and Blocking System] implementation and Mobile Policy launched recently,” he posted on Twitter. “Met with the Samsung Pakistan managing director and chief executive officer,” he said, adding they had both appreciated the government’s policies. “They … are now actively considering setting up a smartphone assembly plan in Pakistan,” he added.
The federal cabinet earlier this year approved a Mobile Device Manufacturing Policy to promote indigenous production of smartphones through local and foreign direct investment and joint ventures. The policy claims to reduce mobile prices and increase exports.
According to daily Dawn, around 14 smartphone companies are producing handsets in Pakistan right now, but most are still developing 2G devices. The manufacturing policy is aimed at directly incentivizing the production of smartphones with 3G, 4G and eventual 5G technologies.
The DIRBS policy, meanwhile, seeks to discourage the smuggling of smartphones by requiring all smartphone users to register their devices with the government or risk their phones being blocked. | https://www.newsweekpakistan.com/samsung-considering-setting-up-smartphone-assembly-plant-in-pakistan/ |
Coupled predator-prey oscillations in a chaotic food web.
Coupling of several predator-prey oscillations can generate intriguing patterns of synchronization and chaos. Theory predicts that prey species will fluctuate in phase if predator-prey cycles are coupled through generalist predators, whereas they will fluctuate in anti-phase if predator-prey cycles are coupled through competition between prey species. Here, we investigate predator-prey oscillations in a long-term experiment with a marine plankton community. Wavelet analysis of the species fluctuations reveals two predator-prey cycles that fluctuate largely in anti-phase. The phase angles point at strong competition between the phytoplankton species, but relatively little prey overlap among the zooplankton species. This food web architecture is consistent with the size structure of the plankton community, and generates highly dynamic food webs. Continued alternations in species dominance enable coexistence of the prey species through a non-equilibrium 'killing-the-winner' mechanism, as the system shifts back and forth between the two predator-prey cycles in a chaotic fashion.
| |
CROSS-REFERENCED TO CLOSELY RELATED APPLICATIONS
STATEMENT REGARDING PRIOR DISCLOSURES BY INVENTOR/APPLICANT
Hydrangea
Title: Varieties of Plants
Inventor/Applicant: Alex Frederick Schoemaker
Provisional application Ser. No.: 62/973,658
Filed: Oct. 17, 2019
Inventor/Applicant hereby claim the benefit of this provisional U.S. Patent Application.
Hydrangea paniculata.
Botanical designation:
Cultivar denomination: ‘LC NO9’.
An European Community Plant Breeder's Rights application for the instant plant was filed by the Inventor/Assignee, Mr. Alex Frederick Schoemaker of Boskoop, The Netherlands on Oct. 19, 2018, application number 2018/2637. Foreign priority is not claimed to this application.
The Inventor/Applicant and Assignee assert that no publications nor advertisements relating to sales, offers for sale or public distribution occurred more than one year prior to the effective filing date of this application. Any information about the claimed plant would have been obtained from a direct or indirect disclosure from the Inventor/Applicant and/or the Assignee. Inventor/Applicant and Assignee claim a prior art exemption under 35 U.S.C. 102(b)(1) for disclosure and/or sales prior to the filing date but less than one year prior to the effective filing date.
BACKGROUND OF THE INVENTION
Hydrangea
Hydrangea paniculata
Hydrangea
The present invention relates to a new and distinct cultivar of plant, botanically known as , commercially referred to as a Hardy or Panicled and hereinafter referred to by the name ‘LC NO9’.
Hydrangea
Hydrangea
The new plant is a product of a planned breeding program conducted by the Inventor in Boskoop, The Netherlands. The objective of the breeding program is to create new plants with uniform plant habit and attractive inflorescences.
Hydrangea
Hydrangea paniculata
Hydrangea paniculata
Hydrangea
The new plant originated from a cross-pollination made by the Inventor in July, 2013 in Boskoop, The Netherlands, of ‘DVP Pinky’, disclosed in U.S. Plant Pat. No. 16,166, as the female, or seed, parent with ‘Dharuma’, not patented, as the male, or pollen, parent. The new plant was discovered and selected by the Inventor as a single flowering plant from within the progeny of the stated cross-pollination in a controlled greenhouse environment in Boskoop, The Netherlands during the summer of 2016.
Hydrangea
Hydrangea
Asexual reproduction of the new plant by vegetative tip cuttings in a controlled environment in Boskoop, The Netherlands since the summer of 2017 has shown that the unique features of this new plant are stable and reproduced true to type in successive generations.
SUMMARY OF THE INVENTION
Hydrangea
Plants of the new have not been observed under all possible combinations of environmental conditions and cultural practices. The phenotype may vary somewhat with variations in environmental conditions such as temperature and light intensity without, however, any variance in genotype.
Hydrangea
1. Upright to somewhat outwardly spreading plant habit.
2. Freely branching habit with strong lateral branches.
3. Early and freely flowering habit with plants remaining in flower for a long period time.
4. Dense and hardy inflorescences with large white-colored sterile and prominent white-colored fertile flowers.
5. Good garden performance.
The following traits have been repeatedly observed and are determined to be the unique characteristics of ‘LC NO9’. These characteristics in combination distinguish ‘LC NO9’ as a new and distinct plant:
Hydrangea
Hydrangea
Hydrangea
1. Inflorescences of plants of the new have prominent fertile flowers whereas inflorescences of plants of ‘DVP Pinky’ have inconspicuous fertile flowers.
Hydrangea
2. Sterile flowers of plants of the new become more intense dark red in color with development than sterile flowers of plants of ‘DVP Pinky’.
Plants of the new can be compared to plants of the female parent, ‘DVP Pinky’. Plants of the new differ primarily from plants of ‘DVP Pinky’ in the following characteristics:
Hydrangea
Hydrangea
Hydrangea
1. Plants of the new have glossier leaves than plants of ‘Dharuma’.
Hydrangea
2. Plants of the new have longer inflorescences than plants of ‘Dharuma’.
Hydrangea
3. Sterile flowers of plants of the new become more intense dark red in color with development than sterile flowers of plants of ‘Dharuma’.
Plants of the new can be compared to plants of the male parent, ‘Dharuma’. Plants of the new differ primarily from plants of ‘Dharuma’ in the following characteristics:
Hydrangea
Hydrangea paniculata
Hydrangea
Hydrangea
1. Plants of the new are more compact than plants of ‘Kyushu’.
Hydrangea
2. Sterile flowers of plants of the new become more intense dark red in color with development than sterile flowers of plants of ‘Kyushu’.
Plants of the new can be compared to plants of the ‘Kyushu’, not patented. In side-by-side comparisons, plants of the new differ primarily from plants of ‘Kyushu’ in the following characteristics:
BRIEF DESCRIPTION OF THE PHOTOGRAPHS
Hydrangea
Hydrangea
The accompanying colored photographs illustrate the unique appearance of the new plant showing the colors as true as it is reasonably possible to obtain in colored reproductions of this type. Colors in the photographs may differ from the color values cited in the detailed botanical description which accurately describe the colors of the new plant.
The photograph on the first sheet is a side perspective view of a typical flowering plant of ‘LC NO9’ grown in a container.
The photographs on the second sheet are close-up views of a typical inflorescence (top of sheet) and typical leaves (bottom of sheet) of ‘LC NO9’.
DETAILED BOTANICAL DESCRIPTION
Hydrangea
Hydrangea
Hydrangea
Hydrangea
Hydrangea paniculata
Botanical description: ‘LC NO9’.
Female, or seed, parent.—Hydrangea paniculata
‘DVP Pinky’, disclosed in U.S. Plant Pat. No. 16,166.
Male, or pollen, parent.—Hydrangea paniculata
‘Dharuma’, not patented.
Parentage:
Type cutting
.—By vegetative tip cuttings.
Time to initiate roots, summer
.—About 16 days at temperatures about 16° C. to 30° C.
Time to produce a rooted young plant, summer
.—About 120 days at temperatures about 16° C. to 30° C.
Root description
.—Medium in thickness, fibrous; typically light brown in color, actual color of the roots is dependent on substrate composition, water quality, fertilizer type and formulation, substrate temperature and physiological age of roots.
Rooting habit
.—Freely branching; dense.
Propagation:
Plant and growth habit
.—Upright to somewhat outwardly spreading and uniform plant habit; overall plant shape, broadly upright, obovate to roughly globular; strong and sturdy stems; moderately vigorous growth habit and low growth rate.
Plant height
.—About 51.8 cm.
Plant diameter or area of spread
.—About 55.8 cm.
Plant description:
Branching habit
.—About ten lateral branches develop per plant; pinching enhances lateral branch development.
Length
.—About 29.1 cm.
Diameter
.—About 8 mm.
Internode length
.—About 7 cm.
Texture
.—When developing, smooth and glabrous; fully developed, woody.
Aspect
.—Upright to about 20° from vertical.
Strength
.—Strong, sturdy.
Color
.—When developing: Close to between 53B and 60A. Developed: Close to between 53A and 59B; proximally, close to 166C; when woody, close to N199A and 200B to 200C.
Lenticels
.—Density: Moderate; none observed on developing stems. Size, developed stems: About 2 mm by 0.5 mm. Color, developed stems: Close to 54A; with development, becoming closer to 174D.
Lateral branch description:
Arrangement
.—Opposite or in whorls of three, simple.
Length
.—About 12.5 cm.
Width
.—About 7.7 cm.
Shape
.—Ovate.
Apex
.—Apiculate.
Base
.—Obtuse to truncate.
Margin
.—Serrate.
Texture, upper surface
.—Sparsely pubescent; moderately rugose.
Texture, lower surface
.—Moderately pubescent; moderately rugose.
Venation pattern
.—Pinnate.
Color
.—Developing leaves, upper surface: Close to 144A to 144B. Developing leaves, lower surface: Close to between 144B and 146D. Fully developed leaves, upper surface: Close to NN137B slightly tinged with close to 147A; venation, close to 178C, proximally, close to 185A. Fully developed leaves, lower surface: Close to between 146B and 147B; venation, close to N170D, proximally, close to 183C.
Petioles
.—Length: About 2.4 cm. Diameter: About 3.5 mm. Texture and luster, upper surface: Mostly smooth and glabrous, margins are moderately pubescent; moderately glossy. Texture and luster, lower surface: Sparsely pubescent; matte. Color, upper surface: Close to 183B. Color, lower surface: Close to between 59A and 187C.
Leaf description:
Flower type and habit
.—Showy sterile flowers and prominent fertile flowers arranged on terminal panicles; panicles broadly conical in shape; sterile flowers face mostly upright; fertile flowers face upright to outwardly depending on position on the inflorescence.
Fragrance
.—Faintly fragrant; sweet to somewhat moldy.
Natural flowering season
.—Early flowering, flowering begins in the early summer and is continuous until midsummer in Northern Europe.
Flower longevity
.—Sterile flowers last about five weeks on the plant, sterile flowers persistent; fertile flowers last about five days on the plant, fertile flowers not persistent.
Quantity of flowers
.—Freely flowering habit; about 17 sterile flowers and about 950 fertile flowers per panicle.
Panicle height
.—About 13 cm.
Panicle diameter
.—About 14.1 cm.
Sterile flower buds
.—Length: About 1 cm. Diameter: About 1.3 cm. Shape: Cup-shaped. Color: Close to 154D; distally, close to 150D.
Fertile flower buds
.—Length: About 4 mm. Diameter: About 5 mm. Shape: Flattened globular. Color: Close to between 155C and 157D, distally, slightly tinged with close to 59D.
Sterile flower diameter
.—About 4.3 cm.
Sterile flower depth
height
().—About 1.2 cm.
Fertile flower diameter
.—About 1.1 cm.
Fertile flower depth
height
().—About 8 mm.
Petals, sterile flowers
.—Quantity and arrangement: Four arranged in a single whorl. Length: About 4 mm. Width: About 3.5 mm. Shape: Broadly ovate, concave. Apex: Broadly acute. Base: Broadly cuneate. Margin: Entire. Texture and luster, upper surface: Smooth, glabrous; slightly glossy. Texture and luster, lower surface: Smooth, glabrous; matte. Color: When opening, upper surface: Close to between 150D and 155A; towards the margins, close to 155A. When opening, lower surface: Close to 155C; towards the apex, slightly tinged with close to 59D. Fully opened, upper surface: Close to 155A; color does not change with development. Fully opened, lower surface: Close to 155C; color does not change with development.
Petals, fertile flowers
.—Quantity and arrangement: Five arranged in a single whorl. Length: About 4.5 mm. Width: About 3 mm. Shape: Ovate, concave. Apex: Acute. Base: Broadly cuneate. Margin: Entire. Texture and luster, upper surface: Smooth, glabrous; slightly glossy. Texture and luster, lower surface: Smooth, glabrous; matte. Color: When opening, upper surface: Close to NN155A; towards the margins, close to NN155C. When opening, lower surface: Close to 155C. Fully opened, upper surface: Close to NN155B to NN155C; color does not change with development. Fully opened, lower surface: Close to 155C; color does not change with development.
Sepals, sterile flowers
.—Quantity and arrangement: Typically four arranged in a single whorl. Length: About 2.2 cm. Width: About 2.2 cm. Shape: Broadly obovate to roughly orbicular. Apex: Obtuse to emarginate. Base: Broadly cuneate. Margin: Entire. Texture and luster, upper and lower surfaces: Smooth, glabrous; matte. Color: When opening, upper surface: Close to 155A. When opening, lower surface: Close to 155B. Fully opened, upper surface: Close to between 155A and 160D; with subsequent development, color becoming closer to 183D. Fully opened, lower surface: Close to 155A; with subsequent development, color becoming closer to 184B with venation, close to 183B.
Sepals, fertile flowers
.—Quantity and arrangement: Five in a single whorl. Length: About 1 mm. Width: About 2 mm. Shape: Reniform. Apex: Obtuse. Base: Broadly cuneate. Margin: Entire. Texture and luster, upper and lower surfaces: Smooth, glabrous; slightly glossy. Color: When opening and fully opened, upper surface: Close to 157A to 157B, color does not change with development. When opening and fully opened, lower surface: Close to 157A; color does not change with development.
Pedicels, sterile flowers
.—Length: About 1.9 cm. Diameter: About 1.5 mm. Strength: Moderately strong. Aspect: About 30° from branch axis. Texture and luster: Sparsely to moderately pubescent; matte. Color: Close to between 154D and 157A.
Pedicels, fertile flowers
.—Length: About 2 cm. Diameter: About 0.5 mm. Strength: Moderately strong. Aspect: About 20° from vertical. Texture and luster: Sparsely to moderately pubescent; matte. Color: Close to 157D.
Reproductive organs, sterile flowers
.—Stamens: Quantity per flower: About four. Filament length: About 2.5 mm. Filament color: Close to 155C. Anther length: About 1 mm. Anther shape: Broadly oblong. Anther color: Close to 156B. Pollen amount: None observed. Pistils: Pistil quantity per flower: Typically two or occasionally three. Pistil length: About 2 mm. Stigma shape: Club-shaped. Stigma color: Close to 157B. Style length: About 1 mm. Style color: Close to 145C. Ovary color: Close to 145C.
Reproductive organs, fertile flowers
.—Stamens: Quantity per flower: About eight. Filament length: About 7 mm. Filament color: Close to NN155C. Anther length: About 1 mm. Anther shape: Broadly oblong. Anther color: Close to 161C. Pollen amount: Scarce. Pollen color: Close to 156D. Pistils: Pistil quantity per flower: Typically five or occasionally three or four. Pistil length: About 2 mm. Stigma shape: Club-shaped. Stigma color: Close to NN155A. Style length: About 1 mm. Style color: Close to 160D. Ovary color: Close to 160D.
Seeds
Hydrangea.
.—To date, seed production has not been observed on plants of the new
Flower description:
Hydrangea
Hydrangea
Pathogen & pest resistance: To date, under commercial production conditions, plants of the new have not been observed to be resistant to pathogens and pests common to plants.
Hydrangea
Garden performance: Plants of the new have been observed have good garden performance and to be suitable for USDA Hardiness Zones 5 through 9.
Plants used in the aforementioned photographs and in the following description were grown during the late summer in 27-cm containers in an outdoor nursery in Boskoop, The Netherlands and under cultural practices typical of commercial production. During the production of the plants, day temperatures ranged from about 16° C. to 35° C. and night temperatures ranged from about 12° C. to 22° C. Plants of the new were pinched one time and were two years old when the photographs and description were taken. As a Hardy or Panicled , plants of the new are typically not treated with aluminum sulfate to “blue” the inflorescences. In the following description, color references are made to The Royal Horticultural Society Colour Chart, 2015 Edition, except where general terms of ordinary dictionary significance are used. | |
A word that is never fun to hear, mold. There are a lot of questions when it comes to mold. How dangerous is it, really? When do I need to worry about it? Can I remove it myself, or do I need a professional? We’ve got your answers today with what to do if you find mold in your home.
FIRST- DETERMINE THE PROBLEM
- With water damage and flooding, it takes as little as 24 hours for mold to begin growing. It can affect everything from personal items to the structural integrity of your home. Although you may not see it for 1-2 weeks, once mold grows, it can be difficult and expensive to take care of. If wet areas are not dried completely, they are a breeding ground for mold and fungi to grow and flourish.
- Mold is typically easy to spot. It looks like white or black spots. You may see it as a stain on walls, or ceilings. It can grow on almost any surface including ceilings, wallpaper, flooring, wood, and insulation.
- Often you can smell mold before you see it. It will give off a musty or damp odor.
SECOND- KNOW WHEN TO CALL
- When taking on the task of cleaning mold there are several factors to consider. Most jobs that cover only a small surface such as in a bathroom or kitchen can be handled using soapy water or a bleach and water solution. Precautions should be taken, especially if you are someone with asthma or severe allergies.
- If the water damaged area is larger than 10 feet, then you may need to consult a professional. You can also use recommendations from the EPA guide.
THIRD- MAKE THE CALL
- Remember that mold does not grow without moisture. When mold is found, the source of the moisture must also be addressed, or the mold will return. If you have found mold near a window, on a ceiling, or under flooring due to a leak, then you will want to consider calling in the professionals to do the cleanup. Professionals will know how to handle the water damage properly and ensure that there is no further mold exposure.
- Never deal with contaminated water on your own. If water or mold damage was caused by water left by sewage or washing, then professionals should be called.
- If you think you may have a mold issue in your A/C Unit, Heating, or HVAC system then you will want to take precautions. Do not run the HVAC system as it may spread mold further. Consult a professional and use the EPA guide to help you.
AND DON’T FORGET…
- Mold can be dangerous and should be addressed. Exposure happens when toxins from mold have been inhaled, ingested, or absorbed. If mold is hiding in a wall, for instance, it may not have made its way into the air yet. However, it does not mean that you should ignore the problem. If exposed to mold, especially over a period of time, it can cause serious health problems and even destroy the structure of your home.
- If mold is not cleaned up properly then it will continue to grow, putting you and your home at risk.
Mold can cause some serious health problems and put the structure of your home at risk. If you have a mold problem, it should be taken care of immediately. Hiring the right professionals to do the job is an important first step. At Pro Response Restoration we are experts in mold removal. Our team is trained and ready to tackle your job and get you back safely into your home as quickly as possible. Call us today!
Related Blog Post: | https://pro-response.com/i-found-mold-now-what/ |
Find synonyms for any word:
microscopic
'microscopic' - used as an adjective
1.
of or relating to or used in microscopy
microscopic analysis
2.
too small to be seen except under a microscope
3.
extremely precise with great attention to details
examined it with microscopic care
4.
infinitely or immeasurably small
reduced to a microscopic scale
See also
atomic
atomlike
little
minute
precise
small
subatomic
subgross
Antonym
macroscopic
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Fact of the day
The word "America" comes from the European explorer "Amerigo Vespucci. | http://www.bibliodata.com/microscopic.htm |
If you are a lover of literature, perhaps you have read many interesting facts about romantic suspense books. People may be surprised to learn some surprising facts about these books. But, the truth is that there are many interesting things that people do not know. If you are interested in reading about such topics, all you have to do is read this article.
For instance, did you know that Rumi wrote his musical work after being put into a mental asylum for 19 years? How did this affect him? Did he always dream of music and how it would affect other people? How true was it when he talked about music and its healing powers? How could he write romantic songs when he was in such a mental state? Many people may not know these interesting facts about Rumi, but others who read about them know them.
There were many other people influenced by Rumi too. For instance, Thomas Jefferson and Washington were very much impressed by Rumi’s work. And they used parts of it in their writing.
There are still many people who do not know Rumi
They do not even have an idea of what he did or how he lived. If we look at some of his biographers, they wrote about his life in great detail. They also talked about his death and how he affected people during that time. So, people can find out more about Rumi if they research this interesting man.
Do you know any other famous romantic author? Do you know their names? One of the most interesting facts about Romantic Suspense Books is that they inspired many other authors. For example, Victorian writer Colley Bell wrote several stories based on the themes he created in one of his books. And the great American author Mark Twain wrote a lot of his stories from the ideas he got while reading about Rumi. The list of writers influenced by Rumi goes on.
Now, let us consider some other interesting facts about this famous author and his works. Rumi was born in Greece. His mother was a Greek chorus girl. When Rumi was young, he managed to get himself thrown out of a church window. This happened because he did not believe in gods. Some of his works deal with religion and spirituality.
Another interesting fact about Rumi is that he wrote for many years without a publisher.
He did this to test the market. Once he had established an audience for his work, he wanted to get the rights to sell his books. This is why Rumi’s writings are not widely available.
Finally, we come to Rumi’s most famous work, his Book of One Thousand Nights. In this book, Rumi includes a long list of unlikely characters who help him depict heaven and hell and human relationships. Many scholars have commented that the Book of One Thousand Nights is Rumi’s way of proving that all human beings are mortal. This is why this work has inspired many movies and even stage plays and cartoons. So, next time you read a good book about romance and love, make sure you include the Book of One Thousand Nights on your list.
Leonardo da Vinci is another famous Renaissance artist
He is best known for his paintings and created some intriguing masterpieces, including the Vitruvian Man and the Last Supper. According to many, he considered himself to be a true artist even though he was an engineer. He was most famous for his religious works.
Edgar Allan Poe is commonly regarded as the author of the first written poem in English. His most famous poem is “The Pit and the Black Star.” It is amazing how much his poems continue to influence future writers. There are many facts about romantic Suspense Books that he contributed to the genre.
You will find many other interesting facts about Romantic Suspense Books and the characters’ lives that surrounded them. In many of these stories, the key people are usually very young, such as Rumi, whom we will learn more about in later chapters. However, other writers include more mature figures like Charles Dickens and Sir Philip Sidney. There are many other less famous names, such as Sir Henry Belkin, who wrote a novel based on a story by his friend and fellow mathematician Sir Isaac Newton.
Why are Romantic and Psychic Books so Popular?
The reason is simple – they captivate the reader and keep their attention through the entire length of the book. Whether your goal is to seduce your significant other or just relax with a good book, reading something with an erotic undertone is always worthwhile.
To understand why this type of book is so popular, it is important to know what drives authors to write them. Many times, writers are inspired to write romance stories because of an experience that is more or less similar to the situation they are trying to create. Maybe a boyfriend or girlfriend cheated on their relationship, and they want to write about how that happened. They might also be inspired by a love story in which two people share a passionate physical relationship but remain platonic for the rest of the time.
Another common reason someone would write a book about love is that that person has had a similar experience. If you have ever been hurt in a love relationship, you likely have an idea of what love feels like. As you may have guessed, we tend to compare our relationships with those of others. It is not uncommon to read about someone involved in a traumatic event and learn how to survive with their love intact. This can make for fascinating material, especially if the experience was positive.
Romantic books also draw their inspiration from other sources outside of love
Sometimes, inspiration comes from the unexpected. Perhaps you met someone at a party which you fell in love with at first sight. Perhaps you were stuck in an unhappy relationship and were reading a book about how to overcome that. When you finished the book, you realized you had changed and decided to pursue your happiness. This kind of inspiration is exciting and unexpected.
Another reason why romantic books are so popular is that they appeal to a wide variety of readers. If your idea of romance is different than the next, you will be able to locate a book that will fit you. Reading about rich and famous lives will inspire you to find your way in the world. Conversely, a more reflective reader will enjoy reading about a successful single mother who finds happiness with her son. Whether your idea of romance includes the love between a rich man and a poor woman, a happily ever after between two people who marry and start a family, or the story of a man who falls in love with a woman who has no money, you can discover a love story that is right for you in a book.
Final Word
People love to read about relationships that seem doomed. They read books about breakups, divorce, and remarriages because they know they will experience happiness after the story ends. If you feel sad or empty or want to seek out books about the love between two people, why not browse the shelves for a good romance book? Sophie is Scarlet is your online book store with all the best psychic books and romantic suspense books available for your passion for reading. | https://buzztum.com/interesting-facts-about-romantic-suspense-books/ |
A critical component in maintaining plant productivity, safety and profitability is to ensure that every valve is operating at peak efficiency while meeting relevant safety requirements. With the Trevitest™ system, TEAM has the ability to test relief valves and identify those in need of adjustment or full service with no operational interruptions. This technology gives you the means to accurately test every valve, performed in place, on line and under normal operating conditions. The result is a certifiable test allowing correctly performing valves to remain in service for longer periods, as well as fully documenting valves that do not meet the correct performance criteria by our experienced personnel so that they can be repaired or replaced as soon as possible.
Perform all repairs according to applicable certifications and industry standards.
TEAM’s welding technicians are put through a rigorous, method specific, multi-level certification and training process resulting in the industry’s most knowledgeable and experienced team.
Core Values TEAM's Core Values anchor every aspect of our business in a set of commonly-held beliefs and commitments. They represent what our company stands for, what values our employees embody, and what our services and products contribute to the market. These statements are deeply ingrained in our culture, guiding employee behavior and company decisions and actions. | https://www.teaminc.com/service-solutions/valve-products-repair/trevitest-valve-testing |
by Lon Seidman | Jun 8, 2011 6:36am
(0) Comments | Commenting has expired
From left to right: Shelton High senior Leann Misencik, PerkinElmer’s Susan Lazos, and Shelton seniors Jim Szabo and Omar Sobh prepare to plate bacteria samples from Space Shuttle Endeavour.
After traveling more than 6.5 million miles at speeds faster than a bullet, a package sent into orbit on board Space Shuttle Endeavour by Shelton High School students came back to Connecticut on a FedEx truck.
“[We’re] very exciting now that we got back our sample!” said Shelton Senior Omar Sobh.
The experiment, consisting of only a small vial with 200 microliters of a bacteria broth, arrived in Shelton on June 3 just two days after Endeavour’s early morning landing June 1.
Astronauts activated the experiment shortly after Endeavour reached orbit by mixing dormant bacteria spores with a nutrient mix. The Shelton students grew a control set on Earth to compare how the same bacteria grows in gravity and reacts to the antibiotic ampicillin.
Watch Endeavour Commander Mark Kelly activate a similar experiment:
The goal? Helping NASA astronauts prevent some rather uncomfortable infections they seem prone to contracting after long-duration space flights.
“This research project could help explain the increased susceptibility of astronauts to infection (especially bacterial urinary tract infections) on returning to Earth,” Sobh said in an email.
Sobh says the group of five students are investigating whether ampicillin is more effective against bacteria grown in microgravity in orbit. If so, it will indicate that bacteria grown in space are weaker than their terrestrial counterparts and that the astronauts’ bodies are adapting to dealing with the weaker microbes.
The students are now awaiting electron microscope imagery of their bacteria samples from Yale University. Shelton’s PerkinElmer sponsored the student’s work and is providing support during the analysis. The students expect to issue a report on their findings in the next couple of weeks - just before Sobh begins his freshman year at the University of Pennsylvania as a pre-med student focusing on neurobiology.
Read the Valley Independent Sentinel’s coverage of the student experiment.
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What is a market specialist?
June 9th
How is the real estate market doing in May 2020 vs May 2019?
May 26th
The importance of understanding the inventory as a listing agent
May 18th
Will builders have to change future home floor plans due to the pandemic experience?
May 14th
How am I improving my Zoom skills for my clients?
May 5th
Are you practicing the new stuff for real estate?
Apr 27th
Setting expectations for your home seller before accepting an offer that hasn’t had an in-person showing?
Apr 20th
Realtors 2020 vs 2021
Apr 13th
How will the buyer’s financial information form and the verification of employment impact a seller’s decision in today’s real estate market?
Mar 30th
Mar 23rd
What can help make your buyer’s offer look stronger to the seller?
Mar 16th
Cash offer vs. a financed offer. Which offer should a seller accept?
Mar 9th
What’s one challenging part of a real estate career?
We received your message, and will contact you as soon as possible. | https://morethanthecurve.com/local/careers/ |
Referencing Styles : Harvard EssayWrite an essay of approximately 1200 words that discusses the issues in the given questionQuestionExplain how the case of London & Amsterdam Properties Ltd. v. Waterman Partnership Ltd. EWHC 3059 (TCC) helps to define the limits and limitations of adjudication as a dispute resolution process Guidelines This assignment requires further reading and research to be able to interpret the laws that are relevant to the question, with particular reference to renowned cited cases, other than the case in the question. You will need to discuss Contract Law in Construction at all times, then trawling the internet using search engines can be very misleading, so it is suggested that you use the standard texts on the topic as listed in the suggested reading provided at the end of this brief. The use of unauthoritative websites, especially from overseas, will be penalised. Your essay needs to be structured, organised into paragraphs that flow logically. The work needs to be in your own words with quotes no more than a single sentence. Whole sections which are found (by Turnitin) to have been cut and pasted from elsewhere will attract a penalty. The style of your work must not be didactic or generic, which can be achieved by concentrating on the scenario provided. Your essay must show your depth of understanding and your ability to apply the topics covered in class and from the texts you have read to real life situations. Introduction identify the area of law in the question, with description of what is to come Main body discussion should revolve around the legal issues inherent in construction applied to the question. You will need to develop arguments based on different reasoned opinions, which you will have gained from reading the texts. You will need to explain what you write keep asking yourself the question why is it like this? Conclusions include a brief summary of the main points to start, then bring everything together ask yourself the question so what? References It is essential that you cite papers or cases correctly, using the Harvard System (see Cite Them Right). Ensure you do not cite lecture notes or slides. The list of references at the end of your essay must be in alphabetical order listed by authors surnames only list articles you have actually cited; do not compile a bibliography. (The references are not included in the word count.) The essays should be professional, concise and to the point. Please do not include appendices or extraneous material. Assessment Criteria Introduction Identify chosen topic, outline of essay /5 Background and context Overview of the relevant literature /10 Discussion Discussion of the pros and cons of the opinions found /30 Use of evidence to support argument Examples of similar/supporting cases /25 Conclusions Clear outcomes fully explained /20 References and Cases Accuracy and relevance /10 Total /100 Suggested initial reading (these books are in the university library or online access) Adriaanse, J (2016) Construction Contract Law, 4th Edition, Palgrave Macmillan Chappell, D. (2012) Understanding JCT Standard Building Contracts, 9th Edition, Routledge Mann, P and Wong, D T W (2016) Construction Adjudication: The Way Forward, The Construction, Building and Real Estate Research Conference of the Royal Institution of Chartered Surveyors, Toronto Canada, September 2016 (ISBN: 978-1-78321-160-9) Click to access Construction%20Adjudication%20The%20Way%20Forward.pdf Uff, J (2013) Construction law: law and practice relating to the construction industry 11th ed.. London: Sweet & Maxwell / Thomson Reuters 2013 Online access (may be restricted). The library also has physical copies.
xplain how the case of London & Amsterdam
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Disney Research has posted a YouTube video that provides a convincing display of a robot's ability to interact with humans playing catch. The robot even reacts appropriately to dropping the ball.
The motivating idea behind this project is to have a safe way for theme park visitors to interact with robots. There are safety concerns about getting up close and personal with animatronic humanoids but throwing and catching games provide a safe form of interaction.
For the purpose of this experiment Disney Research modified the robot's hand - giving it a cup like shape while retaining the appearance of a human hand - and used an of-the-shelf Kinect system for vision. The robot also responds by moving its head, giving the impression that it is tracking the ball. In the video we see it playing with six participants with a range of ages and skill level:
Perhaps the most endearing feature is the robot's reaction when it misses the ball. It has been programmed to look behind or down, shake its head and shrug its shoulders. These animations were enough to evoke responses - laughter or sympathy - on the part of the humans who played catch.
The robot is also up to juggling - although in this case it was skilled human jugglers who took part in the tests.
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The biased competition model (BCM) and the feature similarity gain model(FSGM) are two descriptive hypotheses of the mechanism and consequences of attentional influences on the responses of sensory neurons in striate and extrastriate visual cortex. The BCM assumes that visual stimuli compete for neuronal responses and attention biases the response of these neurons toward the response evoked by attended stimulus alone. The FSGM instead assumes that the sensory gain of cortical neurons is modulated as a function of the similarity between an attended feature and a given neuron?s preferred feature. For many experimental designs the two models give similar predictions, making it difficult to accumulate evidence for one or the other model. Here we designed an experiment in which the two models predict two qualitatively different results. We placed two moving random dot patterns (RDPs) inside the receptive field (RF) of neurons from area MT of macaque monkeys: one ?effective? (high contrast, evoking higher responses) and one ?ineffective? (low contrast, evoking lower responses). Both stimuli moved in the preferred direction of the cell, i.e. they did not differ in their feature-similarity according to the FSGM. Because the two RDPs evoke different responses when presented alone, the BCM predicts a lower response when the animals attended to the low contrast RDP. The FSGM on the other hand predicts the same response in both conditions, because the two RDPs move in the same direction and therefore the similarity between the attended and preferred feature does not change when attention is directed to one vs. the other RDP in the RF. We recorded from 81 well-isolated direction-selective cells in area MT of two macaque monkeys. A sub-population of 39 of these cells showed competition, i.e. a response to the two stimuli presented together that fell in between the responses evoked by each of the two stimuli alone. For this group of neurons (as well as for the whole population) no significant difference in responses was observed between attending to the effective vs. ineffective stimulus. The results are consistent with the prediction of the feature similarity gain model but not the biased competition model of attentional modulation. Consequently the data support an attentional mechanism that modulates the sensory gain of neurons based on the attentional condition rather than a mechanism that influences competitive interactions between distinct neuronal populations representing attended and unattended stimuli. | http://www.ipm.ac.ir/ViewPaperInfo.jsp?PTID=11544&school=Cognitive |
Dive Brief:
- Universities continue to be "highly vulnerable" to cyberattacks, but those most at risk also tend to have the financial resources to protect themselves, according to a new report from Moody's Investors Service.
- Institutions house a wide range of student records, sensitive research and medical information in potentially leaky networks. Additionally, that data is often dispersed among several campuses with "countless access points" on each; global interconnectedness also poses a risk.
- However, budget constraints may make it difficult for colleges to keep up their defenses as threats grow more complex. Moody's identified 101 data disclosures at U.S. institutions in 2017, an increase from 15 in 2014. It expects the "upward trend" to continue.
Dive insight:
"Cyberattack types have evolved faster than mitigating measures," Moody's analysts wrote. They list a handful of examples at colleges and universities across the U.S., including a hack of a web application at Georgia Tech that resulting in data on 1.3 million current and former students, applicants, staff and others.
Grinnell, Hamilton and Oberlin colleges were the target of hackers that stole applicant records and then tried to sell the information back to the students, according to the analysts. They also highlighted a multiyear conspiracy by nine foreign nationals who allegedly stole 31 terabytes of academic data and intellectual property from 176 institutions in 21 countries; the 144 affected U.S. institutions paid more than $3.4 billion to reclaim the stolen information, "potentially devaluing the stolen research."
The Chronicle of Higher Education reports that colleges and universities are vulnerable to three types of attacks: increasingly sophisticated phishing, where emails dupe recipients into handing over sensitive information; ransomware, which gives hackers control of a machine or server; and denial of service attacks, which use a data overload to shut down a network.
Moody's analysts also highlighted as a concern cyber espionage, through which state-sponsored groups try to gather proprietary research that in many cases is supported by the federal government and related to defense.
In response, colleges are tightening up hardware, software and security protocol, such as by requiring extra layers of user authentication. Others are using informational campaigns that promote cybersecurity best practices among students, faculty, staff and others on campus. One security expert told Education Dive last year that secure systems require access control, material encryption and logs that show who has used the data.
Some institutions are even hiring chief privacy officers, EdSurge reported, though it notes only four in 10 have a person on staff dedicated to information security. Last year five universities joined forces to develop OmniSO, a shared operations center that helps them detect and mitigate threats. | https://www.highereddive.com/news/moodys-identifies-growing-cyber-threat-on-college-campuses/555513/?referrer_site=www.educationdive.com |
The nation-state system in the Middle East is almost a century old and has now witnessed the rise and fall of four “grand narratives”—Modernism, Arab Nationalism, Revolutionary Socialism, and Islamism. These were frameworks that shaped cultural and political understandings of current conditions, as well as the path towards the narratives’ envisioned goals. Each shared the promise of achieving a baseline of prosperity, dignity, and liberty, supplemented by narrative-specific conceptions of what such a successful nation would entail. These narratives oscillated between elitism and populism, as well as between nativism and universalism. In many cases, two narratives overlapped, with one rising as the previous vision declined. At their respective apexes, each “grand narrative” dominated the public discourse, commanding defensive reactions from its predecessors. Today, a contender for new grand narrative has entered the scene: Futurism.
The first narrative of “modernism”—which outsiders often associated with “the Arab liberal age” while understood locally as heir to the nineteenth century Nahdah (often translated as “Renaissance”)—was the least self-conscious articulation of a comprehensive proposition. Its discourse was openly elitist and paternalistic, and it embraced the broader optimistic universalism of the post-WWI era in which it was founded. Still, it promised an ascent to “modernity” both implicitly and explicitly.
Objectively, this elitist modernism can claim considerable achievements. Modern states formed through top-down reform efforts in Baghdad, Cairo, Damascus, Beirut, and Amman—chaperoned by colonial Great Britain and France as mentors through the League of Nation “Mandate.” The dynamics of these new states challenged and permanently altered the pre-war expectation of an adversarial relationship between society and government. Yet these achievements, which were not coupled with a successful vision to cement national identities, allowed for challenges to the emerging political, social, and economic structures. The inability of the new states to accommodate or productively explain the burgeoning State of Israel sealed the fate of the regional order and its poorly articulated first grand narrative. With the resulting Palestinian Nakba, the dissonance between ruling elites and growing political contenders in the Arab state system was exposed.
The alternative to elitist modernism that developed was both populist and nativist. With an unacknowledged appropriation of methods and templates from European nationalism, “Arab nationalism” presented itself as the restoration of an organic style of ruling that had been lost due to Western colonialism and Ottoman Turkish “decadence” (inhitat). The new nationalist grand narrative envisioned glory and unity as its defining features, as well as a focus on a promised victory for Palestine. This focus allowed a new class of elites, groomed in administrative and military roles within the new state structures, to obfuscate their states' internal conflicting interests during their ascent to and hold on power. The narrative's demise was this divergence between the narratives claimed goals and its internal conflicts, which culminated in another existential defeat—the Naksah, or the June 1967 war. Nevertheless, Arab nationalism's elites maintained their positions in power as a new narrative emerged.
Revolutionary Socialism—oscillating back to a class-conscious elitism rebranded as “avant-guardism” (tali‘ah) and to a universalism now classified as “internationalism”—was conceived as the natural replacement for the failing nationalist grand narrative. Many nationalist militants underwent self-critical examinations and publicly embraced Revolutionary Socialism, which redefined the nationalist struggle as one against a triad of malevolent actors: global imperialism (the United States and its Western allies); Zionism centering Israel as the “national enemy”; and “Arab reactionism” (al-raj‘iyyah al-‘arabiyyah), identified as regional regimes hostile to the Soviet block.
While instrumentalized by Moscow and often manipulated by Arab “revolutionary” regimes, including Algeria, Libya, Syria, and Iraq, the revolutionary socialist narrative was successful in presenting “social justice” as a new and widely popular goal. It is a modest achievement for a conflicted narrative promoted by an equally confused set of political groups, yet its relatively short life-span during the 1960s and 1970s was ultimately the result of extraneous circumstances. Both the Soviet invasion of Afghanistan and the Islamic Revolution in Iran proved detrimental to its functionality as an Arab narrative. Moreover, while both elitist modernist and nationalist narratives had a lifespan double that of Revolutionary Socialism—spanning from the 1920s-1960s and 1940s-1980s respectively—Revolutionary Socialism’s waning influence has continued to inform later Arab political discourse even today.
Islamism, the fourth grand narrative, has not yet exceeded the duration of its earlier predecessors, spanning from the late 1970s to today. The narrative was a return to both populism—with a renewed pretense of reflecting the true nature of its Muslim base—and to nativism—with its claim of authenticity and promotion of a cultural autarky. Islamism topped-up previous promises—maintaining glory, unity, and social justice, while adding a pre-ordained “divine victory” to them. Islamism’s “deliverable” was nothing less than a divinely-sanctioned comprehensive system.
Accommodationist Islamism, the variant of the ideology accepting a gradual progression within the existing order, anticipated a staged “Islamization” of individual, family, society, and state in preparation of a global leadership role (ustadhiyyah) for the putative unified Islamic state. Radical Islamism—with various approaches embracing coups d'état (Hizb al-Tahrir), revolution (al-Qaeda), or conquest (the “Islamic State”) — sought a regimented universal totalitarian order, the Khilafah, as an end goal. The Islamist formula, as a grand narrative, may have been far weaker, in objective elements, than all of its predecessors. Still, it was successful in recruiting a vital threshold of ideologized individuals, while relying on the malaise of its target base towards governments unresponsive to its needs and on the prestige of the faith that it claims to embrace for its survival. It can be argued that Islamism was bound to fail. The decades through which it has succeeded in delaying its demise, though, have been costly to its region and to the world.
The failure of Islamism is now a reality: its proponents have not yet been able to offer credible and sustainable fulfillment of even a scaled-down version of its promised aims. Yet without an alternative in place, new incarnations of Islamism may reappear in repackaged forms. Fortunately, an alternative is being proposed, but it too is laden with potential problems.
Arab political culture, willingly and coercively, is welcoming “paternalistic futurism” as an unstated but forcefully articulated new entry in the line of grand narratives. True to the oscillation pattern so far established, futurism is both elitist—with the ruling stratum roaringly claiming its patriarchal status—and “universalist”—in its open embrace of cultural and material globalization. A substantive caveat here is that the globalism of the new grand narrative deliberately rejects the “values" of universalism—the Enlightenment and its derivatives are posited as irrelevant to Arab societies, which are instead presented as governed by a distinct set of values derived from an understanding of the Islamic faith provided by political leadership.
The new grand narrative formalizes the social contract that had been implicitly in effect in much of the Arab world prior to the “Arab Spring," where the Arab citizen (or subject) concedes a portion of his or her political rights in exchange for the promise of services and support. The “Arab Spring” may represent a response to governments unable to keep their part of this agreement, whether due to depleted resources resulting from corruption and kleptocracy, or through the demographic and economic shifts presenting a strain on government resources. However, the subsequent “Counter-Revolution” (al-thawrah al-mudadah) has not rejected the pre-Arab Spring formulation of authority but has rather doubled down both on previous promises and the corresponding requirement of submission to authority.
From the Egyptian “Capital Cairo”, to UAE’s “Mars City 2117”, through Saudi NEOM, and even the Syrian “Reconstruction,” grand ideologies are being replaced by grand projects. Citizens (subjects) are invited to place their trust in a benevolent leadership, with absolute authority, that promises national ascent through measurable forms of development.
Paternalistic futurism as practiced in Europe during the first half of the 20th century failed to yield praiseworthy results. Yet the project is not necessarily doomed to fail, even given the reductionist method in which new futurism has been applied in the Arab region. On the other hand, the current discourse of paternalistic futurism may ultimately be dismissed as a mere diversion while the Arab political order recovers the elements of autocracy and coercion it has lost in the previous phase. The need to curtail Iran, which relies on external non-state actors to extend its own influence, can be viewed accordingly as part of the effort to reclaim the gravitas and enforcement power of the state. A more charitable reading may consider the examples of Abu Dhabi and Dubai in the UAE, as well as Singapore, as models of progress and prosperity achieved through fair and predictable autocracy.
A new generation of Arab citizens (subjects) may be eager to remedy the lacunae in its societies and welcome opportunities for productive globalism. With notional adjustments introduced to avoid anachronisms, this statement is as true today as it was at each junction in which promises were made by previous grand narratives. If the new narrative is to succeed where previous ones have failed, it is imperative to avoid the traps almost deliberately condoned by the others. An external focus, be it Palestine or Iran, may provide immediate mobilization and support, but would almost certainly allow the emergence of patterns of allocation of resources at the detriment of the promise of prosperity. The stifling of individual rights such as the rights to speech, assembly, and dissent—even if to insist on the safeguard of collective imperatives of sovereignty, loyalty, patriotism—may reduce the nuisance of opposition, but will certainly provide the rationale for a reconstituted radicalism.
The champions of the new grand narrative of paternalistic futurism seemed to have come full circle to the values that shaped political discourse at the beginning of the past century. Prosperity, modernism, and globalism are at the forefront of discourse—now with far more vision and articulation than before. In so doing, they may be addressing the weakness of the poorly expressed elitist modernism of the first part of the 20th century.
But the specificity of the current narrative also raises the ceiling of expectations, and thus exposes its proponents to the risk of backlash in the case of unsatisfactory delivery. With the public expected to be mere recipients of a future conceived and ushered in by a distant leadership, the leadership also accepts the sole responsibility of both successes and failures of the future. None of the regional leaders has yet exhibited a steady hand indicating that mistakes would be avoided. In fact, each of the regional capitals has been witness to dramatic and even tragic mistakes of the past few years.
With an enthusiastic, yet neither utopian nor dystopian, focus on a future of prosperity, the new grand narrative of paternalistic futurism is a welcome alternative to the exhausting and exhausted propositions of Islamism. Yet, with current paternalistic leadership structures prone to adventurism and impulsiveness, the potential for the new grand narrative to strike roots is hampered. This may indeed be an alternative in need of protection from its champions. | https://www.washingtoninstitute.org/fikraforum/view/futurism-is-shaping-up-as-an-alternative-to-islamism-but-it-may-need-protec |
The 2012-2013 Visiting Writers Series opens with a reading by award-winning fiction writer Josh Emmons on Wednesday September 19 at 4:30 p.m. in Wilson Hall Auditorium on Monmouth University’s campus.
Josh Emmons, an assistant professor of creative writing Monmouth University, was born in Bangkok and grew up in northern California. A graduate of the Iowa Writers’ Workshop, he published his first novel with Scribner in 2005, The Loss of Leon Meed, which won a Copernicus-James Michener Award and has been translated into French, Hebrew, German and Dutch. The Los Angeles Times called Meed “An audaciously ambitious first novel…[not] merely determined to dazzle with weirdness… a canny status report on the American soul…engaging, enigmatic.”
Emmons second book Prescription for a Superior Existence came out in 2008 from Scribner, and led the San Francisco Chronicle to conclude, “It’s probably unfair that someone so young should be so talented …by the end of this witty, wise novel, he has demonstrated how character and destiny are inextricably intertwined.”
Fellow fiction writer Jonathan Franzen, author of Freedom and The Corrections,
has praised Emmon’s work reflecting, “Here’s how you know Josh Emmons is the real deal: he’s created a full spectrum of Californian characters who are ludicrous and ill-behaved and lovable in equal measure; he’s a major-league prose writer who has fun in every sentence without ever showing off or hitting a phony note; and you want to keep reading him for the pure pleasure of his company.”
Monmouth University’s Center for the Arts Visiting Writers Series brings the most celebrated poets and authors from around the world (Andrei Codrescu, Colm Tóibín, Adam Zagajewski,) and our own back yard (Long Branch’s own US Poet Laureate, Robert Pinsky) to the beautiful auditorium of the University’s centerpiece, historic Wilson Hall. With our Visiting Writers Series, we hope the audience will experience a renewed sense of their relationship to poetry and fiction, to language, and to be moved emotionally by that writer’s representation of what it means to be a human being, whether that experience is one of joy, celebration, longing, or sorrow. | https://www.monmouth.edu/news/monmouth-universitys-visiting-writers-series/ |
The Change From OP to ATAR
The Queensland Government, working
with the Queensland Curriculum and Assessment Authority (QCAA), has announced
that new systems for assessment in Years 11 and 12 and tertiary entrance will be
phased in, effective from Year 12, 2020. The
new systems draw upon recommendations by the Review of Tertiary Entrance
conducted by the Australian Council for Educational Research. What do the
proposed changes mean for Queensland students?
VET options through school based courses
and traineeships may still be offered
Assessment in the Senior Phase
# Assessment
programs are developed by schools
for each subject. These programs are
approved
by the QCAA. Schools set the assessment, and
grade the student
work, in line with the
approved work programs.
# The QCAA has processes for monitoring and
validating the assessment
instruments and the
grading of student results on the assessment.
# Results in General subjects results will
be
based on a student's achievement
in three
school-based assessments
and one external
assessment that is
set and marked by the
Queensland
Curriculum and Assessment
Authority
(QCAA). For most
subjects, the external
assessment will be worth 25% of the result,
except in mathematics and science
subjects, where the result will be
worth 50% of the result.
# Assessment in Applied subjects will be
based on school assessments (ie no external
exams)
The ATAR
Not Applicable
# An ATAR will be based on the strongest
results in five General subjects; or four General
subjects and one Applied subject; or four General
subjects and one completed VET Certificate III,
IV or Diploma
# An English subject
will be compulsory for students to receive their
ATAR. This could be a General English subject
(eg. English, Literature, English for ESL) or it
could be the Applied subject of Essential
English If the English result is not one of the
five strongest results, the other five
stronger results will be used to
determine the ATAR
# The new ATAR arrangements will
commence for students completing
Year 12 in 2020
The ATAR will be determined by the Queensland Tertiary Admissions
Centre
Queensland
Certificate of Education
All students who complete Year 12 will receive a
transcript of their results, which is called a Senior Statement.
Students who meet minimum standards in terms of their learning, and for
literacy and numeracy, will also be eligible to receive a QCE.
Students will receive a Senior Statement, and a Queensland Certificate
of Education if they meet minimum standards in terms of their learning,
and for literacy and numeracy (ie this will not change).
Overall Position
# Students
completing 20 semesters of Authority subjects (ie 5 subjects for 4
semesters) receive an Overall Position (OP), determined by the QCAA.
#The OP is
based on the exit (final) results in Authority subjects, standardized in
a process using QCST results
#
The OP is a
ranking score, reported on a 1-25 scale.
There is no Overall Position
determined for students in the new system.
Queensland Core Skills Test
#
All
OP-eligible students in Qld sit the QCST in Yr 12, which is made up of
four external papers, set and graded by the QCAA, testing essential
learnings across the Authority subjects.
There is no Queensland Core
Skills Test in the new system.
Tertiary Entrance
#
Tertiary
Entrance for most institutions in Queensland is managed by the
Queensland Tertiary Admissions Centre (QTAC).
#
For
OP-eligible students, the OP score is used for tertiary entrance in Qld.
#
For
OP-ineligible students, QTAC determines a Tertiary Selection Rank Score
which is used for entry in Qld.
#
QTAC also
determines a Tertiary Selection Rank Score for completed Certificate
III, IV or Diploma courses which can also be used for entrance.
#
Tertiary
Entrance will continue to be managed by QTAC.
#
Instead of
using an OP determined by QCAA, there will be an Australian Tertiary
Admissions Rank (ATAR), determined by QTAC.
#
The ATAR is
number between 0.00 and 99.95 in increments of 0.05. This is not a score
out of 100, but a rank showing student's achievement against other
students.
| |
On March 9, 2021, a federal court in the Northern District of California dismissed the contributory infringement claim first filed by Harold Davis (hereinafter, “Davis”), the Plaintiff, on November 20, 2019 against Pinterest, Inc. (hereinafter, “Pinterest”), the Defendant, in Davis v. Pinterest, Inc., 2021 WL 879798 (N.D. Cal. Mar. 9, 2021). Davis filed a complaint for both direct and contributory copyright infringement. The order of March 9, 2021 was, however, limited to Pinterest’s challenge to the claim of contributory infringement.
Copyright
- Computer Law
- Fair Use
- First Sale Doctrine
- The Copyright Claims Board: A Venue for Pursuing Actual or Statutory Damages Impacting Both Registered and Unregistered Works
- Win for Photographer in Ninth Circuit Reversal of Fair Use Finding
- Entrepreneur Spotlight: How Ray Young is Fighting Content Theft Encouraged by Big Tech Platforms
- Testing the Bounds of Copyright Protection in Choreographic Works: Hanagami v. Epic Games, Inc. | https://www.stoneslaw.net/davis-v-pinterest-pinterest-pins-victory-in-contributory-copyright-infringement-claim-but-decision-may-open-a-door-for-future-suits/ |
I love to solve puzzles and read mysteries. I love a challenge and to strategize. I love systems that work and finding new ways to improve those systems. I love my family, hiking, people, reading and learning. Why do all these things make me a great Realtor ®? Every real estate journey is different for so many reasons. From the people involved to the property being bought or sold we never see the same thing twice, no matter how long we are in the business. Every one handles excitement and stress differently and therefore we adapt and change to every situation brought in front of us. I see all these scenarios as puzzles and mysteries we are going to solve together. We have all the pieces and we know what it is supposed to look like at the end. The fun part is putting all the pieces together to form a beautiful picture, with as little stress and as much enjoyment as possible! | https://assets1.activerain.com/profile/ahwatukeechristie |
Chef Paolo Masieri and his wife, wine and pastry expert, Barbara Pisani, shared their passion for authentic Ligurian cuisine from their kitchen at Paolo e Barbara Ristorante in San Remo.
With a steadfast commitment to using only the finest natural ingredients, Chef Masieri incorporates his flair for creating innovative recipes with the traditional cooking methods he learned from his father, who first owned the restaurant. When Paolo took over in 1988, it was a priority to continue delivering an unforgettable culinary experience, recognized by some of the most discerning international food connoisseurs throughout the world. Now, sons Stefano and Lorenzo are devoted to the restaurant and work closely with their parents.
Acquiring quality raw materials is the basis for their refined menu. Always mindful of that goal, their restaurant receives twice daily seafood deliveries such as prawns, sea urchins, sea cucumbers and a variety of shellfish from only local fishermen. They serve free range poultry and beef that are strictly raised on natural feed. Vegetables such as zucchini, artichokes, basil and asparagus, considered some of the most important products of the area, are primarily grown and cultivated in their personal garden. | http://arteitaliausa.com/culinary-arts/italian-chefs/paolo-masieri.html |
Cilia are on the top of the cells. Use the correct number of significant figures. Weigh the beaker with the dry sand and subtract the weight of the empty beaker from that number to get your sand weight. Which set of measurements is more precise i. It may take longer to boil, but speed isn't worth the risk of damage. Example: A student has a mixture of NaCl s and I2 s weighing 2. The solvent must also be inert towards all of the components of the mixture to be extracted.
What did you like about the experiment? Also weigh a clean dry 250 mL beaker. Which set of numbers has the higher precision?. Do powdered soaps work as well as liquid detergents? To do this, I added water to the mixture, which dissolved the salt. Collect the solution in a pan. The iron taken out of the mixture is then measured to find the mass of the retrieved iron. Because this is such a straightforward experiment, you won't need any lab gear or equipment.
You just need a drop or two, because a little bit of enzyme will go a long way. Stir the mixture until the salt is completely dissolved. Lastly to separate the benzoic acid and sodium chloride I used a filtration system and the sodium chloride and water drained into a cup while the benzoic acid remained on the filter. Which have been filtered out? Add water to the sand and salt. This roughly equates to 1 tablespoon of each. Observations: During acidification the solution should turn a bright pink. Kidneys use the same principals but with blood.
Slowly distill the ether from the solution. How is the cell wall of plant cells broken down? The filter paper was folded twice in half and was inserted into the funnel, making a coffee style filter. Set up a simple distillation apparatus with a 100 mL r. Figure 1 Separating Each Compound Acetylsalicylic acid, Aspirin, is an organic acid; therefore, it is soluble in an organic solvent diethyl ether , but will react with a basic reagent :B such as sodium hydroxide or sodium bicarbonate to produce the conjugate base of the acid. There have been some errors regarding the isolation techniques and processes, however, the mass of salt at the end is substantial enough to conclude that results obtained are sufficient compared to the initial mass Introduction and Background The point of this experiment was to separate the different components present in a heterogeneous mixture. Mix together your salt and sand mixture with 50mL of water in the 250mL beaker.
This can be done by boiling the water. So, the step was left out of the wheat germ protocol, but kept in the split pea protocol just for fun. Most households have table salt in the kitchen. As any successful scientist will tell you, most good science revolves around asking good questions. There is a protocol that would allow you to stain nucleic acids, but the chemical used would need to be handled by a teacher or an adult. While the Sep Funnel is being shaken, the stopper must be held securely in place and the stopcock must be tightly shut. From there, you should be able to see the salt remaining in your pan.
If the mass of the sand-salt mixture is 3. Initial weight measure for components Discussion and Conclusion The objective of isolating the heterogeneous mixture and end up with as much salt as possible was sufficiently met. How does the experiment compare when using animal cells instead of plant cells? Pour the salt water mixture into the evaporation dish. Even if you know the result, it is nonetheless worthwhile to see how someone else went about it. The removal of caffeine from coffee beans with dichloromethane is an example of a solid liquid extraction.
This pressure must be carefully relieved by slowly opening the stopcock while the Sep Funnel is inverted. Examples of magnetic separation include the extraction of iron ore from surrounding silicate. Introduction Extraction is a widely used method for the separation of a substance from a mixture. Was there anything you might do differently if you had a second chance? The NaCl attracts water to it more strongly than does the propionic acid because the NaCl is completely ionic; therefore less water surrounds the propionic acid thereby making the acid less soluble in the salt solution. Make sure to let the detergent sit for at least five minutes.
When the still head temperature rises above 100 o, discontinue heating. Combine the two aqueous layers in a 250 mL beaker or a flask. Methods of isolation utilized include magnetism, filtration, and evaporation. Magnetism is only effective in insoluble substances. Alcohol is less dense than water, so it floats on top. Now suppose that several measurements are made for the length of a table top.
Adding base to the aqueous acidic layer mixture converts the conjugate acid of benzocaine back to its water-insoluble free base, so that it can be recovered by filtration. Observation: Comment on the color, shape and quantity of your benzoic acid. Put the retrieved salt next to the sand for the sake of completion if you so desire. The moles of propanoic acid formed is the theoretical yield. That being said, the product obtained from this extraction protocol may look slightly different depending on whether it was extracted from a plant or an animal. | http://openchatbot.community/extraction-of-salt-from-mixture-lab.html |
Derry Driving Centre has lowest pass rate
The pass rate among those undertaking the practical driving test for private cars in Derry, is the lowest of any test centre in Northern Ireland.
New figures for the period from the start of January to the end of March, 2019, show that the practical test pass rate for private car drivers at the Altnagelvin Test Centre stood at 42.9 per cent.
This is compared to a NI average pass rate of 55.4 per cent, with Downpatrick having the highest at 73.8 per cent.
The Department for Infrastructure’s new ‘Driver, Vehicle, Operator and Enforcement Statistics’ report also states that this was the “fifth consecutive quarter that Londonderry (Altnagelvin) had the lowest pass rate” for car drivers. It added: “At least part of the difference recorded between test centres will reflect the different driving ability and experience of candidates presenting for testing, while other relevant factors will be specific to the test centre such as local driving conditions.”
During this period there were 14,100 practical tests conducted in NI, over 80 per cent of which were for private cars.
Meanwhile, less than half of people who sat the theory test for private cars passed and the report shows that while women were more likely to pass their theory, men were more likely to pass the practical element.
The number of taxi driver licenses across NI, meanwhile, has dropped dramatically by almost 10 per cent over the past year. The report states: “This is a continuation of the declining trend with numbers down by over a third on the series high recorded five years ago. This reduction may have been exacerbated by the introduction of a new taxi driver theory and practical driving test, which was introduced on October 31, 2014.”
The pass rate for MOT tests in 2018/19 was 81.8 per cent. | https://www.derryjournal.com/news/traffic-and-travel/derry-driving-centre-has-lowest-pass-rate-969138 |
---
abstract: 'First, we provide an exposition of a theorem due to Slodkowski regarding the largest eigenvalue of a convex function. In his work on the Dirichlet problem, Slodkowski introduces a generalized second-order derivative which for $C^2$ functions corresponds to the largest eigenvalue of the Hessian. The theorem allows one to extend an a.e lower bound on this largest eigenvalue to a bound holding everywhere. Via the Dirichlet duality theory of Harvey and Lawson, this result has been key to recent progress on the fully non-linear, elliptic Dirchlet problem. Second, using the Legendre-Fenchel transform we derive a dual interpretation of this largest eigenvalue in terms of convexity of the conjugate function. This dual characterization offers more insight into the nature of this largest eigenvalue and allows for an alternative proof of a bound needed for the theorem.'
author:
- Matthew Dellatorre
- |
University of Maryland\
[^1]
date:
title: 'The largest eigenvalue of a convex function, duality, and a theorem of Slodkowski'
---
1. Introduction
===============
1.1 Motivation
--------------
It is known that a convex function $u$ on $\mathbb{R}^n$ is differentiable almost everywhere and has distributional second-order partial derivatives. It is also known that a convex function is twice differentiable almost everywhere in the sense that for a.e. $x\in \mathbb{R}^n$, there exists a symmetric positive semi-definite matrix $D^2f(x)$ such that $$f(x+h)=f(x)+\langle\nabla f(x), h\rangle + \frac{1}{2} \langle D^2f(x)h,h\rangle+ o(||h||^2).$$ The operator $D^2f$ is called the *second-order Peano derivative*. Note that its existence does not imply the existence of $\nabla f$ in a neighbourhood, so it should not be considered the second derivative of $f$ in the usual sense. This result is due to Alexandrov \[1\]. See also \[5\], \[6\].
In \[9\], Slodkowski studies uniqueness for a generalized Dirichlet problem in the class of $q-$plurisubharmonic ($q$–psh) functions (for $C^2$ functions on $\mathbb{C}^n$ this is equivalent to the complex Hessian having $n-q$ nonnegative eigenvalues at every point). The problem of uniqueness reduces to showing that the difference of two such functions is $n-1$–psh, which implies that it satisfies a maximum principle, from which uniqueness then follows. Functions of this $q$–psh class can be approximated by a subclass which are convex up to a quadratic polynomial. Because of this it is sufficient to study this smaller class, which given their quasi-convexity, retain some of the nice properties of convex functions. In particular, quasi-convex functions are a.e. twice differentiable, in the above sense. Thus, the second-order behavior of these functions and their difference is known a.e. However, to show that the difference is a member of the above mentioned class, they must satisfy this eigenvalue property everywhere. To this end, Slodkowski introduces a generalized second-order derivative, which is simply the largest eigenvalue of the Hessian for $C^2$ functions, and proves that if this quantity is bounded below almost everywhere in some domain, it is bounded below everywhere in that domain. Using this, he shows that the difference is contained in the desired $n-1$–psh class.
Following Slodkowski \[9, §3 \], we define the largest eigenvalue of a convex function.
[1.1]{} *Let $u:\mathbb{R}^n \rightarrow \mathbb{R}$. If $\nabla u(x_0)$ exists, $K(u,x_0)$ is defined by the formula $$K(u,x_0) = \limsup_{\epsilon \rightarrow 0} 2\epsilon^{-2} \text{ max } \{ u(x_0 + \epsilon h) - u(x_0) - \epsilon \langle \nabla u(x_0), h \rangle : h\in S^{n-1} \}$$ otherwise $K(u,x)$ is defined as $+\infty$.*
This is the generalized second-order derivative that Slodkowski defines. For the sake of context, note that this quantity is a modification to the *second-order upper Peano derivative* of $u$ in the direction of $h$, which is defined as $$\limsup_{\epsilon \rightarrow 0^+}2\epsilon^{-2} (u(x_0+\epsilon h)-u(x_0)-\epsilon \langle \nabla u(x_0),h \rangle).$$ Being maximal, this second-order derivative is of particular interest because it corresponds to the largest eigenvalue of the Hessian when defined (which it does, in the above sense, almost everywhere for convex functions), and gives a useful quantity to work with otherwise, especially in the context of Slodkowski’s $C^{1,1}$ estimates.
Regarding this quantity $K(u,x)$, Slodkowski shows the following.
[1.2]{} (\[9, Cor. 3.5\]) *Let $u:\mathbb{R}^n \rightarrow \mathbb{R}$ be a locally convex function in $U\subset \mathbb{R}^n$, such that $K(u,x)\geq M$ for almost every $x\in U$. Then $K(u,x)\geq M$ for all $x\in U$.*
As mentioned above, the recent work of Harvey and Lawson on the Dirichlet problem was one of our motivations for studying this quantity $K(u,x)$ and Slodkowski’s proof of the above result. In \[4\] they study fully non-linear degenerate elliptic equations of the form $$\begin{aligned}
F(\text{Hess}(u))=0 \text{ on } \Omega\\
u=\phi \text{ on } \partial \Omega.\end{aligned}$$ Given certain convexity assumptions on the boundary, they establish the existence and uniqueness of continuous solutions using their new Dirichlet duality theory. The work of Slodkowski was an inspiration for that paper, and in particular Theorem 1.2 is the deepest ingredient of their proof of uniqueness of viscosity solutions of (1) \[4, p. 398\]. These existence and uniqueness results apply to many important problems including all branches of the homogeneous Monge-Ampère equation, all branches of the special Lagrangian potential equation, and equations appearing naturally in Lagrangian and calibrated geometry.
Given the usefulness of this generalized derivative and the above result to recent progress on important problems, it makes sense to better understand both the derivative and the proof of the theorem. The proof is fairly difficult and very geometric so here an illustrated exposition is provided. The quantity $K(u,x)$ is then studied further for convex $u$. In particular, the Legendre–Fenchel transform is applied to give a simple alternative characterization of $K(u,x)$ in terms of the convexity of the dual function $u^*$ to $u$. This allows for an alternative proof to a key proposition needed to prove Slodkowski’s theorem. Altogether, there are now three ways to view this generalized derivative $K(u,x)$: analytically (Definition 1.1), geometrically (Proposition 1.6), and dually (Theorem 1.9).
1.2 Summary
-----------
Theorem 1.2 follows immediately from the following theorem, the proof of which is the main focus of the first part of this paper.
[1.3]{} (\[9, Thm. 3.2\]) *Let $u$ be convex near $x_0\in \mathbb{R}^{n}.$ Assume that $K(u,x_0)=k_0$ is finite. Then for every $k>k_0$ the set $\{x :K(u,x)<k\}$ is Borel and its lower density at $x_0$ is not less than $\left(\frac{k-k_0}{2k}\right)^n.$*
Lower density is defined as follows.
[1.4]{} *The lower density of a Lebesgue measurable set $Z\subset \mathbb{R}^{n}$ at $x_0 \in \mathbb{R}^{n}$ is the number $$\liminf_{\varepsilon \rightarrow 0} \dfrac{m_n \left( Z\cap B(x_0,\varepsilon) \right)}{m_{n}\left(B(x_0,\varepsilon) \right)},$$ where $m_{n}$ denotes the $n$-dimensional Lebesgue measure.*
Slodkowski’s proof of Theorem 1.3 divides naturally into two parts. First, an equivalent geometric characterization of a bound on $K(u,x)$ is given in terms of spheres tangent to the graph of $u$. This is the content of the following definition and proposition.
For $c=(c_1,\dots,c_{n+1})\in \mathbb{R}^n$, let $S(c,r)$ denote the $n-$sphere with center $c$ and radius $r$, and $B(c,r)$ denote the open $n+1$-disk of radius $r$ centered at $c$.
[1.5]{} *The sphere $S(c,r)$ is a sphere of support from above at $y=(x_0,u(x_0))$ if $y\in S(c,r)$, $B(c,r) \cap \text{graph}(u)=\emptyset$ and $c_{n+1}>u(P(c))$, where $P$ denotes the orthogonal projection of $\mathbb{R}^{n+1}$ onto $\mathbb{R}^n$.*
Thus, $S(c,r)$ can be visualized as a ball resting on a surface that is the graph of $u$, and such that $(x_0,u(x_0))$ is one of its resting points.
[1.6]{} (\[9, Prop. 3.3\]) *Let $U\subset \mathbb{R}^{n}$ be open and $u:U\rightarrow \mathbb{R}$ be convex. Assume that $u$ has gradient at $x$*.\
*(i) If $u$ has second-order Peano derivatives at $x$, then $K(u,x)$ is equal to the norm (i.e. the largest eigenvalue) of the real Hessian of $u$ at $x$*.\
*(ii) If $K(u,x)$ is finite, then for every $K>K(u,x)$ there is $\varepsilon > 0$ such that $u(x+h)-u(x)-\langle\nabla u(x),h\rangle \hspace{2mm}\leq \dfrac{1}{2}K|h|^{2}.$*\
*(iii) If there is a sphere $S(c,r), r>0$ which supports the graph of $u$ from the above at $(x,u(x))$, then $$\begin{aligned}
K(u,x)\leq \dfrac{(1+|\nabla u(x)|^{2})^{\frac{3}{2}}}{r}.\end{aligned}$$*
Parts (ii) and (iii) give the above mentioned equivalence between a bound on $K(u,x)$ and a sphere of support to the graph of a corresponding radius at $(x,u(x))$. See section 2.2 for a more detailed explanation.\
The second part of the proof then uses this alternative characterization of $K(u,x)$ to obtain a density result, which is essentially the statement of the theorem in terms of spheres of support as opposed to $K(u,x)$. This is the content of the following lemma.
[1.7]{} (\[9, Lemma 3.4\]) *Let $u$ be a non-negative convex function in $B(0,d)\subset \mathbb{R}^{n}$, $d>0$, such that $u(0)=0$ and $\nabla u(0)=0$. Let $R>0$ and assume that the closed ball B$(c,R)$, $c=(0,...,0,R)\in \mathbb{R}^{n+1}$, intersects the graph of $u$ only at $0\in \mathbb{R}^{n+1}$. Let $X_{r}$, $0<r<R$ denote the set of all $x\in B(0,d)\subset \mathbb{R}^{n}$ such that there exists a sphere of radius $r$ supporting the graph of $u$ from above at $(x,u(x))$. Then the lower density of $X_{r}$ at 0 is not less than $((R-r)/2R)^{n}$.*
As will be seen in more detail in section 2, there is an inverse relationship between the bound on $K(u,x)$ and the radius of the sphere of support to the graph of $u$ at $(x,u(x))$. This will explain the similarity between the lower bound on density given in the lemma and the one in the theorem.\
The geometric characterization of $K(u,x)$ is key to proving Theorem 1.3 and helpful in understanding what quality this generalized derivative captures about the function $u$ and its graph. Since the results here concern functions that are at least locally convex, it is natural to study them via the Legendre–Fenchel transform, the classical transform of convex analysis. By definition, the set of points above the graph of a convex function (epigraph) is a convex set. Any convex set in $\mathbb{R}^n$ can be defined entirely by a family of supporting hyperplanes. Thus, since the epigraph of $u$ completely determines the graph of $u$, which in turn completely determines $u$, this family of hyperplanes can be considered an alternative description or parametrization of $u$. This is essentially how the transform of $u$ (or dual function to $u$) $u^*$ is defined. Each point $p\in \mathbb{R}^n$ defines a collection of hyperplanes (via gradient), and $u^*$ specifies a point $u^*(p)\in\mathbb{R}$, such that $(0,...,0,-u^*(p))\in \mathbb{R}^n$ lies on the one hyperplane of this collection which supports the epigraph (or graph) of $u$.
Interestingly, under the Legendre–Fenchel transform, differentiability properties of $u$ correspond to convexity properties of $u^*$. Two classic examples of this are the following.
[1.8]{} *Let $f:\mathbb{R}^n\rightarrow \mathbb{R}$. Then*\
*(i) $f \text{ is strictly convex if and only if } f^* \text{ is differentiable} .$*\
*(ii) $f \text{ is strongly convex with modulus } c \text{ if and only if } f^* \text{ is differentiable and } \nabla f^* \text{ is Lipschitz continuous }$*\
*with constant* $\frac{1}{c}.$
Given that $K(u,x)$ is a (local) differentiability property of $u$, it seems there should be an appropriate (local) convexity property corresponding to $u^*$. In section 3 we prove the following result.
[1.9]{} *Let $f:\mathbb{R}^n \rightarrow \mathbb{R}$ be convex. If $K(f,x_0)=k_0<k$ then $f^*$ is quadratically convex at $y_0=\nabla f(x_0)$ with modulus $\frac{1}{k}$. Conversely, if $u^*$ is quadratically convex with modulus $\frac 1k$, then $K(f,x_0)=k_0\leq k$*.
Quadratically convex at $y_0$, which is defined in section 3, is a more local form of convexity than the two types of convexity referred to in Proposition 1.8. This dual characterization of $K(u,x)$ allows for an alternative proof of Proposition 1.6. Using quadratics to define different types of convexity is standard (e.g. quasi-convexity, strong convexity). See section 3 for definitions of all these terms and a more detailed discussion.
In Slodkowski’s proof quadratics arise naturally via the definition of $K(u,x)$, and from this, spheres. The geometric properties of spheres make certain arguments very clear (see proof of Lemma 1.7), however some manipulations and calculations are simpler with quadratics, given their constant second-order behavior. For example, in \[5\] Harvey and Lawson provide an alternative proof of Slodkoski’s lemma (as well as Alexandrov’s theorem stated above) via a generalization by using quadratics instead of spheres. Their proof is modelled off of Slodkowski’s, and they obtain their result for the larger class of quasi-convex functions. Instead of spheres of support, they use the notion of upper contact jets, where given $p\in \mathbb{R}^n,$ and $A$ a real symmetric $n\times n$ matrix, $(p,A)$ is an *upper contact jet for $u$ at $x$* if there exists a neighbourhood of $x$ such that $$u(y)\leq u(x) +\langle p,y-x \rangle + \frac{1}{2}\langle A(y-x), y-x\rangle.$$ Slodkowski’s result then corresponds to $A=\lambda I$.
1.4 Organization
----------------
Section 2 contains the exposition of Slodkowski’s proof of Theorem 1.3: §2.1 gives an overview of the proof, §2.2 a slight variation of Slodkowski’s proof to Proposition 1.6 (the generalized $C^{1,1}$ estimate), §2.3 an expanded and illustrated version of Slodkowski’s proof to Lemma 1.7, and §2.4 combines these for the proof of the theorem.\
Section 3 studies $K(u,x)$ from the dual perspective: §3.1 recalls some basic convex analysis, including Legendre–Fenchel duality, §3.2 provides an equivalent interpretation of $K(u,x)$ in terms of the dual function to $u$, and uses this for an alternative proof of the $C^{1,1}$ estimate.\
The Appendix considers Lipschitz continuity of the gradient and the geometric interpretation of $K(u,x)$: §A.1 demonstrates $K(u,x)$ is bounded by the Lipschitz constant when $u$ is $C^{1,1}$, §A.2 gives an example of a function with a sphere of support that is not $C^{1,1}$ on any neighbourhood, §A.3 compares $K(u,x)$ to the classical notion of an osculating circle to a plane curve and gives an extension of this to higher dimensions, §A.4 relates the radius of a sphere of support to a function to that of the radius of a supporting sphere to its dual.
2. Exposition of Slodkowski’s proof
===================================
2.1 Overview
------------
Theorem 1.3 is concerned with the set of points (near $x_0$) such that $K(u,x)<k$, for some fixed $k>k_0= K(u,x_0)$. However this set may be difficult to study directly given that the only information available about $u$ is that it is continuous (bounded and convex) on some neighbourhood of $x_0$ and $K(u,x_0)=k_0<\infty$. In particular, knowing the value of $K(u,x)$ at a given point does not immediately suggest anything about its value nearby. Thus, the first step towards a better understanding of this set of points is an alternative characterization of what it means for $K(u,x)$ to bounded at some point.
If at the point $x$, $K(u,x_0)<\infty$ this is equivalent to a (local) sphere of support from above to the graph of $u$ at $(x,u(x))$. This is precisely what Proposition 1.6 (ii) and (iii) states. (ii) implies the existence (locally) of a quadratic function tangent to the graph of $u$ at $(x,u(x))$ which majorizes $u$ on some neighbourhood, and this in turn implies the (local) existence of a sphere of support to the graph of $u$ at $(x,u(x))$. The content of (iii) is clear.
With this alternative geometric characterization in hand, Lemma 1.7 then proves the theorem in terms of these spheres of support. To accomplish this another change in perspective is needed, which takes further advantage of this more geometric interpretation of $K(u,x)$. Instead of looking at points $x$ in the domain of $u$ such that there exists a sphere of support to the graph of $u$ at $(x,u(x))$, it is better to consider for each point $x$ in domain of $u$ an $n-$sphere (of fixed radius) in $\mathbb{R}^{n+1}$ above the graph of $u$ with center $c\in \mathbb{R}^{n+1}$ such that $P(c)=x$, where $P:\mathbb{R}^{n+1}\rightarrow \mathbb{R}^{n}$ is the projection map. If we lower this sphere down towards $x$ it will of course eventually intersect the graph of $u$. Since $u$ is continuous, it is not difficult to show that on a small enough neighbourhood these spheres will come down on a closed part of the graph of $u$ and thus there will be an initial point of contact. This sphere is by definition a sphere of support to the graph of $u$ at that point. The next step is to show that for every $\epsilon$ neighbourhood of 0 ($x_0=0$ for Lemma 1.7) there is a corresponding $\delta=\delta(\epsilon)$ such that the spheres above the points in $B(0,\delta)$ are spheres of support to the graph at points $(x,u(x))$, where $x\in B(0,\epsilon)$. Now $B(0,\delta)$ is a much nicer set to work with then $X_r\cap B(0,\epsilon)$, and these two sets can be related by a few simple Lipschitz maps. Since Lipschitz maps behave nicely with respect to measures, this allows us to place a lower bound on the measure $m(X_r\cap B(0,\epsilon))$ for each epsilon. A limiting argument is then used to obtain the lower bound on the lower density at 0.
Proposition 1.6 and Lemma 1.7 can then be combined to give Theorem 1.3. A sketch of the proof is as follows. Start with a point $x_0$ where $K(u,x_0)$ is finite (hypothesis of Theorem 1.3), and choose any $k>K(u,x_0)$. Note it can be assumed without loss of generality that $x_0=0$, $u(0)=0$, and $\nabla u(0)=0$ (see section 2.3 for details). Then apply Proposition 1.6 (ii), which locally gives a sphere of support of radius $1/k$ at $(x_0,u(x_0))$. Now, apply Lemma 1.7 to get a lower bound on the density of $X_r$, $r<1/k$, at $x_0$. Next, apply Proposition 1.6 (iii) to convert this into a statement about the density of $X'_k$, where $$\begin{aligned}
X'_k \equiv \{ x\in \text{dom}(u) | K(u,x)<k \}.\end{aligned}$$ This last step is accomplished by using the continuity of the gradient to show that in a small enough neighbourhood $ X_r \subset X'_k $. More explicitly, $x\in X_r$ implies $K(u,x)\leq r^{-1}(1+|\nabla u(x)|^2)^{3/2}$ and $\nabla u(x_0)=0$, so by continuity of the gradient of convex functions and since $k>1/r$, $\nabla u(x)$ will eventually be small enough so that $r^{-1}(1+|\nabla u(x)|^2)^{3/2}<k$. Thus, for $x\in X_r$, $K(u,x)<1/k$. This gives the theorem by choosing $R$ arbitrarily close to $1/k_0$ and $r$ arbitrarily close to $1/k$ (see section 2.4 for a detailed proof).
2.2. The generalized $C^{1,1}$ estimate
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(center) at (2,2.4); [ (a) at (center) ; (a.180) arc (180:[180+180]{}:1.2cm); ]{}; at (1.25,2.25) \[label=below:\] ;
In this subsection we provide an alternative proof to Proposition 1.6 (iii). The main idea is as follows: given a sphere of support of radius $r$ to the graph of $u$ at the point $(x,u(x))$, the lower hemisphere of this sphere defines the graph of a smooth convex function that agrees up to first order with $u$ at $x$ and majorizes $u$ elsewhere. Denote this function by $d$. It immediately follows that $K(u,x)\leq K(d,x)$, and the rest of the proof consists in computing $K(d,x)$, which is equal to the largest eigenvalue of $d$ because $d$ is smooth\
*Proof of Proposition 1.6 (iii).* Assume that the sphere $S((c,t),r), \hspace{1mm} c\in \mathbb{R}^{n}$ supports the graph of $u$ from the above at $(x,u(x_0))$ and that $u$ is differentiable at $x_0$. Define $d:B(c,r)\rightarrow \mathbb{R}$ to be the function whose graph is the lower open hemisphere of $S((c,t),r).$ Recall the definition for $K(f,x_0)$ : $$K(u,x_0) := \limsup_{\epsilon \rightarrow 0} 2\epsilon^{-2} \text{ max } \{ u(x_0 + \epsilon h) - u(x_0) - \epsilon \langle \nabla u(x_0), h \rangle : |h| =1 \}.$$\
Clearly, since $d(x_0)=u(x_0)$ and $\nabla d(x_0)=\nabla u(x_0)$, $$K(u,x_0)\leq K(d,x_0).$$ Since $d$ is smooth, $$\begin{aligned}
K(d,x_0) =& \limsup_{\epsilon \rightarrow 0} 2\epsilon^{-2} \text{ max } \{ d(x_0 + \epsilon h) - d(x_0) - \epsilon \langle \nabla d(x_0), h \rangle : |h| =1 \} \\
=& \limsup_{\epsilon \rightarrow 0} 2\epsilon^{-2} \text{ max } \{ \frac{1}{2} \langle \nabla^2 d(x_0+ \gamma_{\epsilon,h} \epsilon h)\epsilon h, \epsilon h \rangle : |h| =1 \}, \hspace{5mm}0<\gamma_{\epsilon,h} <1 \\
=& \limsup_{\epsilon \rightarrow 0} \text{ max } \{ \langle \nabla^2 d(x_0+ \gamma_{\epsilon,h} \epsilon h) h, h \rangle : |h| =1 \}, \hspace{5mm}0<\gamma_{\epsilon,h} <1 \\
=& \text{ max } \{ \langle \nabla^2 d(x_0) h, h \rangle : |h| =1\} \text{ by continuity and compactness.}\\
=& \lambda_\text{max}, \hspace{5mm} \text{ maximum eigenvalue of } \nabla^2 d(x_0)\end{aligned}$$ Thus, now we show that $$\lambda_\text{max}=\dfrac{(1+(\nabla u(x_0))^2)^{\frac{3}{2}}}{r}.$$\
The equation for $d$, the sphere of radius $r$ centered at $(c,t)$, where $c\in \mathbb{R}^n$ and $t\in \mathbb{R}$, is $$d(x)= t -\sqrt{r^2 -|c-x|^2}.$$ Without loss of generality we may assume that the sphere of support is centered at the origin and $x_0$ has just first component non-zero, as otherwise we could always shift and then rotate without affecting the second-order behavior. In other words, assume $(c,t)=0 \in \mathbb{R}^{n+1}$ and $x_0=(s_1,...,s_n)=(s,0,...,0)\in \mathbb{R}^n$. Then $d(x)= -\sqrt{r^2 -|x|^2}.$
Let $$w(x):= \frac{1}{r^2-s^2} \left( |x-x_0|^2 + 2\langle x-x_0,x_0 \rangle \right).$$ Since $$|x|^2=\langle x,x \rangle= \langle (x-x_0)+x_0, (x-x_0)+x_0 \rangle= |x-x_0|^2 +2 \langle x_0, x-x_0 \rangle +|x_0|^2$$ and $|x_0|^2=s^2$, we can write $d(x)$ as $$d(x)=-\sqrt{r^2-s^2}\sqrt{1-w(x)}.$$ Now expanding $\sqrt{1-w(x)}$ as a series and dropping the terms of order higher than two (as they will have 0 Hessian at $x_0$), $$d(x)\approx -\sqrt{r^2-s^2} \left( 1-\frac{w(x)}{2} -\frac{w(x)^2}{8} \right).$$ This can be further reduced to $$d(x)\approx -\sqrt{r^2-s^2} \left( 1-\frac{w(x)}{2} -\frac{1}{8}\left( \frac{2\langle x-x_0,x_0\rangle }{r^2-s^2}\right)^2 \right),$$ since we are only concerned with the expression for $d$, modulo powers higher than two.
Thus, $d(x)$ has been replaced by a diagonal quadratic form and straightforward computations give $$\nabla d(x_0)= \frac{x_0}{\sqrt{r^2-s^2}},$$ and $$\nabla^2d(x_0)= \frac{1}{\sqrt{r^2-s^2}} I + \frac{s}{(r^2-s^2)^{3/2}} A,$$ where $I$ is the $n\times n$ identity matrix and $A$ is the $n\times n$ matrix with first row $x_0=(s,0,...,0)$ and zeros elsewhere. Since $$\frac{s^2}{(r^2-s^2)^{\frac{3}{2}}}>0,$$ it follows immediately that $$\lambda_{max}=\frac{1}{\sqrt{r^2-s^2}} + \frac{s^2}{(r^2-s^2)^{3/2}}=\frac{r^2}{(r^2-s^2)^{\frac{3}{2}}}.$$ Furthermore, the vector $(x_0,u(x_0))$ is of length $r$, proportional to the upward pointing unit normal to the graph of $u$ at $(x_0,u(x_0))$, which is equal to $$\frac{1}{\sqrt{1+|\nabla u(x_0)|^2}}(-\nabla u(x_0),1).$$ Scaling by $r$, we obtain $$x_0=\frac{-r}{\sqrt{1+|\nabla u(x_0)|^2}}\nabla u(x_0).$$ Giving $$x_0=\dfrac{r \nabla u(x_0)}{\sqrt{1+|\nabla u(x_0)|^2}}, \hspace{3mm} s^2=|x_0|^2=\dfrac{r^2|\nabla u(x_0^2)}{1+|\nabla u(x_0)|^2}.$$ Therefore, $$\lambda_{max}=\dfrac{(1+|\nabla u(x_0)|^2)^\frac{3}{2}}{r}.$$ $\hspace{165mm} \square$
We state explicitly the following interesting result on lower hemisphere functions, i.e. functions on a disc $D \subset \mathbb{R}^n$ defined by the lower hemisphere of an $n-$ sphere in $\mathbb{R}^{n+1}$. The proof follows immediately from the above proof, by looking at the expression for the Hessian.
[2.1]{} Let $d:D\rightarrow \mathbb{R}$ be a lower hemisphere function defined on a disc $D\subset \mathbb{R}^n$ and $\tilde{x} \in D$. If $\nabla d(\tilde{x}) \neq 0$, then $\nabla d(\tilde{x}) \neq 0$ is an eigenvector of $\nabla ^2 d(\tilde{x})$ corresponding to the largest eigenvalue.
Without loss of generality we may assume that the lower hemisphere and thus $D$ are centered at the origin and $\tilde{x}$ has only first coordinate non-zero, $\tilde{x} =(s,0,...,0)$. Then, as shown above, the Hessian of $d$ at $\tilde{x}$ is a diagonal $n\times n$ matrix of the form $$\nabla ^2 d(\tilde{x})= \textnormal{diag}\left(\frac{1}{\sqrt{r^2-s^2}}+\frac{s^2}{(r^2-s^2)^{\frac{3}{2}}},\frac{1}{\sqrt{r^2-s^2}},...,\frac{1}{\sqrt{r^2-s^2}}\right).$$ Thus, $(1,0,...,0)$ is an eigenvector corresponding to the largest eigenvalue. As calculated above, $$\nabla d(\tilde{x})= \frac{\tilde{x}}{\sqrt{r^2-s^2}}= \frac{s}{\sqrt{r^2-s^2}} (1,0,...,0) ,$$ so clearly $\nabla d(\tilde{x})$ is also an eigenvector corresponding to the largest eigenvalue.
2.3 The density lemma
---------------------
If at the point $x_0=0$ there is a sphere of support of radius $R$, Lemma 1.7 provides a lower bound on the lower density of the set $X_r$ of points with sphere of support of a radius $r<R$. Note that without loss of generality it may be assumed that $x_0=0$, $u(0)=0$, and $\nabla u(0)=0$, since any convex function *ũ* can always be adjusted by a constant and linear term so that this is true without affecting the 2nd-order behaviour of *ũ*.
As mentioned in section 2.1, Lemma 1.7 is proved by looking not directly at $X_r$ but at small neighbourhoods of 0 that are the projection of the set of centers of spheres of support to the graph of $u$ on shrinking neighbourhoods. For each $\epsilon>0$ a $\delta=\delta(\epsilon)$ is needed so that $B(0,\delta)$ is contained in the projection onto $\mathbb{R}^n$ of the set of centers of spheres of support to the graph of $u$ restricted to an epsilon neighbourhood. Since the only information about $u$ is that there is a sphere of support at 0, this is what is used to construct $\epsilon$ and $\delta$. More specifically, the appropriate $\epsilon$’s and $\delta$’s are found by constructing a family of convex functions that are identical to $u$ on a neighbourhood of $0$, but greater and simpler outside this neighbourhood. This allows one to fully utilize the only initial information given. Using this family of simple functions and basic geometry, three key set inclusions are obtained, which essentially relate $B(0,\delta(\epsilon))$ to $X_r\cap B(0,\epsilon)$. Then using Lipschitz maps to relate these sets and by applying properties of Lipschitz functions on measure, the lower density bound is shown. This whole construction is crucial because it provides a much simpler approach to studying the possibly very complex set $X_r$. The following is the proof given by Slodkowski.
*of Lemma 1.7.*\
The number $r \in (0,R)$ will be kept fixed so let $X \equiv X_{r}$. Define $$Z= \{(x,u(x))\in \mathbb{R}^{n+1}:x\in X\}.$$ It is clear that $Z\cap(\text{\={B}}(0,d')\times\mathbb{R})$ is compact for every $d'<d$, thus $X\cap(\text{\={B}}(0,d')\times\mathbb{R})$ is also compact, as it is the orthogonal projection $P:\mathbb{R}^{n+1}\rightarrow \mathbb{R}^{n}$ of $Z$. Since compact sets are Lebesgue measurable, the notion of lower density is applicable to both $X$ and $Z$.
It is more convenient to first estimate the density of $Z$ at 0 with respect to Hausdorff measure, and then use the properties of Lipschitz functions on measure to obtain bounds on the density of $X$. To accomplish this a family of convex functions, built from the initial sphere of support of radius $R$ at 0, which modify $u$ outside a small neighbourhood of 0 will be constructed. As mentioned above, these functions will be identical to $u$ on a neighbourhood of $0$ and very simple outside this neighbourhood. These functions will enable us to find a corresponding $\delta=\delta(\epsilon) $ neighbourhood for each $\epsilon$ so that $x\in B(0,\delta)$ implies that $x=P(c)$, where $c\in \mathbb{R}^n$ is the center of a sphere of support to $(x',u(x'))$, for some $x'\in B(0,\epsilon) \cap X_r$.\
***Step One.*** A family of convex functions is constructed which will let us find an appropriate $\delta(\epsilon)$, as explained above. For each $\alpha$ such that $0<\alpha<\frac{1}{2}\arcsin (\frac{d}{R})$, define the function $$v_{\alpha}:B(0,R)\rightarrow[0,\infty),$$ as follows. First, define $$\begin{aligned}
Y=\{y\in \mathbb{R}^{n+1}:|y-c|=R, \varangle (y-c, 0-c)=2\alpha\},\end{aligned}$$ where $c=(0,...,0,R)\in \mathbb{R}^{n+1}$ is the center of the sphere of support to $u$ at $(0,u(0))$.
(-5,0) – (5,0); (0,-3) – (0,5);
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at (0,5) \[label=left:\] ; at (5,0) \[label=below:\] ;
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$Y$ forms a ring on $S(c,R)$, and clearly the projection of $Y$, $P(Y)$, onto $\mathbb{R}^{n}$ is the $n-1$ sphere of radius $R\sin 2\alpha$, centered at 0. Next, let $C_{\alpha}$ denote the union of all closed segments $\overline{\text{wy}}$ with one endpoint $w$ on the axis $0\times \mathbb{R}\subset \mathbb{R}^{n+1}$ and tangent to the sphere $S(c,R)$ at the other endpoint y, where $y\in Y$. Note that w is independent of which $y\in Y$ that is being used. $C_{\alpha}$ is simply a finite cone with vertex $w$ and base $Y$, tangent to $S(c,R)$ along $Y$. See Figure 2.\
Define now $$\begin{aligned}
T_{\alpha}= \{y\in S(c,R): R(1-\cos 2\alpha)\leq y_{n+1}< R\}.\end{aligned}$$ $T_{\alpha}$ can be visualized as a strip of $S(c,r)$, and note that $T_{\alpha}\cap C_{\alpha}=Y$ and that $T_{\alpha}\cup C_{\alpha}$ defines a convex function $k_{\alpha}:B(0,R)\rightarrow R$.\
For $0<\alpha<\frac{1}{2}\arcsin (\frac{d}{R})$, define $$\begin{aligned}
v_{\alpha}=
\begin{cases}
\text{max}(u(x),k_{\alpha}(x)),\hspace{5mm} |x|<R\sin 2\alpha\\
k_{\alpha}(x), \hspace{23mm} R\sin 2\alpha \leq |x|< R.
\end{cases}\end{aligned}$$ Note that $u$ is only defined on $B(0,d)$ and $R\sin 2\alpha <d<R$, so that is why $v_{\alpha}$ is defined this way. It is clear that $$\begin{aligned}
v_{\alpha}(x)\geq u(x), \text{ for } |x|<d.\end{aligned}$$
Observe that $v_{\alpha}$ is locally convex on the set $|x|\neq R\sin 2\alpha$ since for $|x|> R\sin 2\alpha, v_{\alpha}=k_{\alpha}(x)$, which is convex, and for $|x|< R\sin 2\alpha, v_{\alpha}$ is the maximum of two convex functions which is convex. If $|x|=R\sin 2\alpha$, then $(x,v_{\alpha}(x))\in Y\subset S(c,r)$ Since $S(c,r)$ lies above the graph of $u$, so $k_{\alpha}|_{Y} > u|_{Y}$. Thus near $Y, v_{\alpha}\equiv k_{\alpha}$, and so $v_{\alpha}$ is locally convex in $B(0,R)$, which implies that $v_{\alpha}$ is convex.\
***Step Two.*** For any convex function the following Lipschitz map can be constructed. This will let us relate the possibly complex set, $X$, to the disk $B(0,\delta(\epsilon))$. Given a convex function $v:B(0,R)\rightarrow \mathbb{R}$. Let $E(v)=\{(x,t)\in \mathbb{R}^{n+1}: t>v(x) \}$ denote the strict epigraph of $v$, and define $Z^{v}$ as the set of all $y=(x,v(x))$, where $|x|< R$, and such that for some $c'\in \mathbb{R}^{n+1}$, $B(c',r)\subset E(v)$ and $y\in S(c',r)$, where $r<R$, as defined earlier.
Note that if $y=(x,v(x))\in Z^{v}$, then the graph($v$) has a unique supporting hyperplane at $y$ (since any such hyperplane is tangent to $S(c',r)$), and thus $c'$ is uniquely determined by $y$.
Now consider the map $\gamma^{v}:Z^{v}\rightarrow \mathbb{R}^{n+1}$, where $\gamma^{v}(y)=c'$. This map is Lipschitz with constant one. To see this, let $y_{1},y_{2}\in Z^{v}$ and $c'_{i}=\gamma^{v}(y_{i}), i=1,2.$ The set $E(v)$ is convex (by definition since $v$ is convex), and so it contains $W := \text{co}(B(c_{1},r)\cup B(c_{1},r))$, where co() denotes the convex hull. In particular, $W\cap$ graph($v$)=$\emptyset$. Since $y_{i}\in S(c_{i},r)\cap \text{graph}(v)$, $y_{i}\in S(c'_{i},r)\setminus W, i=1,2$. Thus, $y_{1}$ and $y_{2}$ do not belong to, and are separated by, the open region between two hyperplanes which are orthogonal to the segment $\overline{c'_{1}c'_{2}}$ and pass through its ends. Therefore $|c'_{1}-c'_{2}|\leq |y_{1}-y_{2}|$. The importance of this map will be seen below, where combined with $u$ and the projection map $P$ it allows the set of interest in $\mathbb{R}^n$ to be related to a small disk.\
***Step Three.*** Three key set inclusions are established. Along with step two this will allow on small neighborhoods the measure of $X$ to be bounded from below by the volume of small $n-$ balls. Using the notation above, let $Z^{\alpha}$ and $\gamma^{\alpha}$ denote the set $Z^{v}$ and map $\gamma^{v}$, respectively, for $v=v_{\alpha}$, where $0<\alpha<\frac{1}{2}\arcsin (\frac{d}{R})$.\
Consider the set $$\begin{aligned}
U_{\alpha}=\text{graph}(v_{\alpha})\setminus (C_{\alpha}\cup T_{\alpha}).\end{aligned}$$ Note that this is a subset of the graph of $u$. For $\alpha \in (0,\frac{1}{2}\arcsin(\frac{d}{R}))$, we have the following three inclusions: $$\begin{aligned}
&P(U_{\alpha})\subset B(0,R\sin 2\alpha)\\
&Z^{\alpha}\cap U_{\alpha} \subset Z \cap U_{\alpha}\\
&B_{N}(0,\delta)\subset P\gamma^{\alpha}(Z^{\alpha}\cap U_{\alpha}), \text{where }\delta=(R-r)\tan \alpha.\end{aligned}$$
The first inclusion follows directly from the definition of $U_{\alpha}$: $|x| \geq R \sin 2\alpha \Rightarrow v_{\alpha}(x)\in T_{\alpha}$.
By (5), $Z^{\alpha}\cap \text{graph}(u)\subset Z$. To see this, let $z\in Z^{\alpha}$. Thus we have a $c'\in \mathbb{R}^{n+1}$ such that $B(c',r)\subset E(v_{\alpha})$ and $z\in S(c',r)$. So there is a sphere of radius $r$ supporting the graph of $v_{\alpha}$ from above at $z$. If $z\in$ graph($u$), then we must have $z \in Z$: $B(c',r)\subset E(v_{\alpha})$ and $v_{\alpha}(x)\geq u(x)$ give us that $B(c',r)\cap\text{graph}(u)=\emptyset$ and $c'_{n+1}> u(Pc'),$ which together with $z\in S(c',r)$ imply that $z \in Z$, by definition. Since $U_{\alpha}\subset \text{graph}(u), Z^{\alpha}\cap U_{\alpha}\subset Z^{\alpha} \cap \text{graph}(u)\subset Z$. And of course $Z^{\alpha}\cap U_{\alpha}\subset U_{\alpha}$, so together we have $Z^{\alpha}\cap U_{\alpha} \subset Z\cap U_{\alpha},$ which gives us the second inclusion.
The third inclusion is the critical aforementioned relation between the set of points with spheres of support and a disk in $\mathbb{R}^n$. (Below we will take $\epsilon=R\sin\alpha$ and $\delta=(R-r)\tan\alpha$). To obtain this inclusion we proceed as follows. Let $x\in \mathbb{R}^n$, be such that $|x|<R-r$, and consider the set $$\begin{aligned}
\{c'\in \{x\} \times \mathbb{R}: B(c',r)\subset E(v_{\alpha}) \}.\end{aligned}$$ This set is a non-empty, closed half-line. To see this, consider lowering the sphere $S((x,c'_{n+1}),r)$ in $\mathbb{R}^{n+1}$ onto the graph of $v_{\alpha}$, by continuously decreasing the last coordinate. Because the radius of this sphere is r and $|x|<R-r$, this sphere comes down on a closed subset of the graph of $v_{\alpha}$. Once contact is made with the graph of $v_{\alpha}$ we stop, and the corresponding value of $(x,c'_{n+1})$ is our closed endpoint. Let $c'\in\mathbb{R}^{n+1}$ be this endpoint and $y\in S(c',r)\cap \text{graph}(v_{\alpha})$ (note that $y$ may not be unique). Then $c'=\gamma^{\alpha}(y)$ and $x=P\gamma^{\alpha}(y)$, and so $$\begin{aligned}
B_{N}(0,R-r)\subset P\gamma^{\alpha}(Z^{\alpha}).\end{aligned}$$
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$\vspace{3mm}$\
Now $Z^{\alpha}\setminus (C_{\alpha}\cup T_{\alpha}) \subset$ graph$(v_{\alpha})\setminus(C_{\alpha}\cup T_{\alpha})=U_{\alpha}$, so clearly $Z^{\alpha}\setminus (C_{\alpha}\cup T_{\alpha})\subset Z^{\alpha}\cap U_{\alpha}$. Therefore, $$\begin{aligned}
P\gamma^{\alpha}(Z^{\alpha})\setminus P\gamma^{\alpha}(Z^{\alpha}\cap(C_{\alpha}\cup T_{\alpha}))\subset P\gamma^{\alpha}(Z^{\alpha}\cap U_{\alpha}).\end{aligned}$$ This relation and (12) will give us our third inclusion (9), once we show that $$\begin{aligned}
P\gamma^{\alpha}(Z^{\alpha}\cap(C_{\alpha}\cup T_{\alpha}))\cap B_{N}(0,\delta)=\emptyset.\end{aligned}$$
Consider the family of all spheres $S(c',r)$ which support $C_{\alpha}\setminus Y$ from above and are contained in the upper half space $y_{n+1}\geq 0$. Clearly the smallest value of $|P(c')|$ is attained when the sphere $S(c',r)$ is tangent to both $C_{\alpha}$ and $\{y_{n+1}=0\}$ (see Fig. 3). It is not difficult to see that in this case $\varangle (c'-c,0-c)=\alpha$, where $c$ here is the center of the initial sphere of support. This gives us $|P(c')|=(|c|-c'_{N+1})\tan\alpha=(R-r)\tan\alpha=\delta$, which implies $$\begin{aligned}
P\gamma^{\alpha}(Z^{\alpha}\cap C_{\alpha})\cap B_{N}(0,\delta)=\emptyset.\end{aligned}$$ Now when $S(c',r)$ supports $T_{\alpha}\setminus Y$ from the above at some point $y$, the segment $\overline{c',y}$ is normal to $S(c,R)$ and $y_{N+1}\geq R(1-\cos 2\alpha)\geq \delta$. Thus $\varangle (c'-c,0-c)\geq 2\alpha$ and, as above, $|P(c)|\geq (R-r)\tan 2\alpha \geq \delta$ (note $0\leq \alpha\leq\frac{\pi}{4}$). This gives $$\begin{aligned}
P\gamma^{\alpha}(Z^{\alpha}\cap T_{\alpha})\cap B_{N}(0,\delta)=\emptyset.\end{aligned}$$ Combining (15) and (16) we have (13), which gives the third inclusion.\
***Step Four.*** Estimate of the density of $X$. The above inclusions and the effect of Lipschitz maps on measure, will be enough to estimate the density of $X=P(Z)$. Recall that $Z=\{(x,u(x)) \in \mathbb{R}^{N+1} | x \in X \}$, where $X$ is the set of points in $B(0,d)\subset \mathbb{R}^{N}$ such that there exists a sphere of radius $r$ supporting the graph of $u$ from above at $(x,u(x))$.
Using a few theorems from Rockafellar \[7\], it can be shown that the map $\varphi : P(U_{\alpha})\rightarrow U_{\alpha}$, where $\varphi(x)=(x,u(x))$ is Lipschitz with constant $(1+g_{\alpha}^{2})^{\frac{1}{2}}$, where $g_{\alpha}=\text{sup} \{ |\nabla u| : |x|< R \sin 2\alpha \}$. More specifically, by Theorem 10.4, $u$ is Lipschitz, and by Theorems 24.7, 25.5, and 25.6 $g_{\alpha}$ is a Lipschitz bound for $u|_{B(0,R\sin 2\alpha)}$). A simple Pythagorean argument then shows $(1+g_{\alpha}^{2})^{\frac{1}{2}}$ is a Lipschitz bound for $\varphi$. Notice that $\varphi$ maps $X\cap P(U_{\alpha})= P(Z\cap U_{\alpha})$ onto $Z\cap U_{\alpha}$.
A basic theorem regarding the effect of Lipschitz maps on Hausdorff measures (Theorem 2.29 in Rogers \[8\]), along with our first inclusion from above (7), leads to: $$\begin{aligned}
H^{n}(Z\cap U_{\alpha})\leq & (1+g_{\alpha}^{2})^{\frac{n}{2}}m_{n}(X\cap P(U_{\alpha}))\\
\leq & (1+g_{\alpha}^{2})^{\frac{n}{2}}m_{n}(X\cap B(0,\varepsilon)),\hspace{3mm} \varepsilon = R\sin 2\alpha,\end{aligned}$$ where again $H^n$ and $m_n$ denote the Hausdorff and Lebesgue measure on $\mathbb{R}^n$, respectively. Furthermore $$\begin{aligned}
m_{n}(B(0,\delta)) \leq & m_{n}(P\gamma^{\alpha}(Z^{\alpha}\cap U_{\alpha})) \hspace{6mm} \text{by } (9)\\
\leq & H^{n}(Z^{\alpha}\cap U_{\alpha}) \hspace{16mm} P\gamma^{\alpha} \text{ is Lipschitz with constant }\leq 1\\
\leq & H^{n}(Z\cap U_{\alpha}) \hspace{18mm} \text{by } (8).\end{aligned}$$ Finally, combining these inequalities one obtains $$\begin{aligned}
\dfrac{m_{n}(X\cap B(0,\varepsilon))}{m_{n}(B(0,\varepsilon))}&\geq(1+g_{\alpha}^{2})^{\frac{-n}{2}}\dfrac{m_{n}( B(0,\delta))}{m_{n}(B(0,\varepsilon))}\\
&=(1+g_{\alpha}^{2})^{\frac{-n}{2}} \left(\dfrac{(R-r)\tan \alpha}{R \sin 2\alpha}\right)^{n}\\
&=(1+g_{\alpha}^{2})^{\frac{-n}{2}} \left(\dfrac{R-r}{2R }\right)^{n} \cos^{-2n}\alpha,\end{aligned}$$ where the volume of an $n$-ball of radius $r$ is $\dfrac{\pi^{\frac{n}{2}}r^{n}}{\Gamma (\frac{n}{2}+1)}$ in the first equality, and $\Gamma$ denotes the gamma function. Thus, $$\begin{aligned}
\liminf_{\varepsilon\rightarrow 0}\dfrac{m_{n}(X\cap B(0,\varepsilon))}{m_{n}(B(0,\varepsilon))} \geq \liminf_{\varepsilon\rightarrow 0} (1+g_{\alpha}^{2})^{\frac{-n}{2}} \left(\dfrac{R-r}{2R }\right)^{n} \cos^{-2n}\alpha.\end{aligned}$$ Now since $\varepsilon = R\sin 2\alpha$ and $0<\alpha<\frac{\pi}{4}$, as $\varepsilon\rightarrow 0$, $\alpha\rightarrow 0$. And as the gradient of a convex function is continuous (Theorem 25.5, \[1\]), $g_{\alpha}\rightarrow 0$ as well since $\nabla u(0)=0$. Therefore the lower density of $X$ at $0$ is not less than $\left(\dfrac{R-r}{2R }\right)^{N}$.
2.4 Proof of Theorem 1.3
------------------------
Lemma 1.7 and Proposition 1.6 now combine nicely to give us Theorem 1.3.
First, we prove the density result. Without loss of generality, let $x_0=0, u(x_0)=0, \nabla u(x_0)=0$. Note that by the convexity of $u$ this implies $u\geq 0$. Set $k_0=K(u,x_0)=K(u,0)$, and let $k>k_0$ be fixed and take $K$ such that $k>K>k_0$.
Set $R=\dfrac{1}{K}$ and note that $R -(R^{2}-|x|)^{\frac{1}{2}}\geq \dfrac{1}{2R} |x|^{2}=\dfrac{K}{2} |x|^{2}, \hspace{2mm} \forall x$ such that $|x|<R$. This follows immediately by contradiction. The left-hand side of this inequality is the last component of the point $(x,t)\in \mathbb{R}^{n}$, where $x\in \mathbb{R}^{n}$, on the $(n+1)$-dimensional sphere of radius $R$ centered $(0,...,0,R) \in \mathbb{R}^{n+1}$ (i.e the value of $d(x)$, where $d$ is the lower hemisphere function defined in the proof of the proposition, see Fig. 1).
(-2.5,0) – (2.5,0); (0,-1) – (0,4.5);
(0,0) parabola (2,.75);
(0,2) circle (2cm) ;
at (0,2) \[label=right:\] ; at (2,.75) \[label=right:\] ;
(1,.1) – (1,-.1);(-.1,2) – (.1,2); at (1,0) \[label=below:\] ; at (.2,1.2) \[label=left:\] ;
at (2.5,0) \[label=below:\] ; at (0,4.5) \[label=left:\] ;
(0,2) – (1,.28); (0,.28) – (1,.28);
Since $K>K(u,0)$, by Proposition 1.6 (ii) there exists $d>0$ such that $$\begin{aligned}
u(0+h)-u(0)- \langle\nabla u(0),h\rangle \hspace{2mm} &\leq \frac{1}{2}K|h|^{2} \text{ for every } |h|<d.\end{aligned}$$ So $$\begin{aligned}
u(h)& \leq \frac{1}{2}K|h|^{2} \text{ for every } |h|<d.\end{aligned}$$ Thus the sphere $S(c,R)$, where $c=(0,...0,R)\in \mathbb{R}^{n+1}$, supports the graph of $u|_{B(0,d)}$ form above at $0\in \mathbb{R}^{n+1}$, and Lemma 1.7 can be applied to the function $u|_{B(0,d)}$.
Let $r$, such that $\frac{1}{k}<r<R$, be arbitrary, and let $X=X_{r}$ and $Z=Z_{r}$ be defined as in Lemma 1.7. By Proposition 1.6 (iii), $\forall x \in X$ $$\begin{aligned}
K(u,x)\leq \dfrac{(1+g^{2})^{\frac{3}{2}}}{r}, \hspace{5mm} \text{ where }g=|\nabla u(x)|.\end{aligned}$$ Set $$\begin{aligned}
g_{\varepsilon}=\sup\{|\nabla u(x)| : |x|<\varepsilon\}.\end{aligned}$$ Then clearly $$K(u,x) \leq \dfrac{(1+ g_{\varepsilon}^{2})^{\frac{3}{2}}}{r} \hspace{5mm} \forall x\in X\cap B(0,\varepsilon).$$
By the continuity of the gradient function, $\lim_{\varepsilon\rightarrow 0} g_{\varepsilon}=|\nabla u(0)|=0$. Thus since $\dfrac{1}{r} < k$, there exists $\varepsilon'$, where $0<\varepsilon'< d$, such that $$\begin{aligned}
\dfrac{(1+ g_{\varepsilon}^{2})^{\frac{3}{2}}}{r}<k, \hspace{5mm} \text{ for } 0<\varepsilon<\varepsilon', \end{aligned}$$ and so $$\begin{aligned}
(B(0,\varepsilon)\cap X)\subset (B(0,\varepsilon)\cap X'_{k}), \hspace{5mm} \text{for } 0<\varepsilon<\varepsilon'.\end{aligned}$$ If $x\in X$ then there exists a supporting sphere of radius $r$ at $(x,u(x))$, and if $x \in B(0,\varepsilon)$, where $\varepsilon <\varepsilon'$, then $K(u,x)<k$.
It follows by Lemma 1.7 that $$\begin{aligned}
\liminf_{\varepsilon\rightarrow 0}\dfrac{m_{n}(X'_{k}\cap B(0,\varepsilon))}{m_{n}(B(0,\varepsilon))} \geq & \liminf_{\varepsilon\rightarrow 0}\dfrac{m_{n}(X\cap B(0,\varepsilon))}{m_{n}(B(0,\varepsilon))}\\
\geq & \left( \dfrac{R-r}{2R} \right)^n.\end{aligned}$$ Now recall that $R=\dfrac{1}{K}$ was chosen arbitrarily so that it satisfied the inequality $\dfrac{1}{k} <\dfrac{1}{K}<\dfrac{1}{k_0}$, where $k$ and $k_0$ are fixed. Similarly, $r$ was chosen arbitrarily so that $\dfrac{1}{k} < r <\dfrac{1}{K}$. Thus we can choose $R=\dfrac{1}{K}$ and $r$ arbitrarily close to $\dfrac{1}{k_0}$ and $\dfrac{1}{k}$, respectively, giving us the desired bound $\left(\dfrac{k-k_0}{2k}\right)^{n}.$\
Finally, the fact that $X'_{k}:=\{ x\in \text{dom } (u) : K(u,x)<k \}$ is Borel is contained in Proposition 2.2 and Lemma 2.3 below. Let $u: \mathbb{R}^n\rightarrow \mathbb{R}$ convex. Proposition 2.2 shows that the set $W$ on which $u$ is differentiable is Borel, specifically a $F_{\sigma \delta}$, and Lemma 2.3 proves that $K(x):=K(u,x)$ is of second Baire class on this set. Since $K(x)= +\infty$ where $\nabla u$ doesn’t exists, $$X'_{k}=\{ x\in \text{dom } (u) : K(x)<k \} =\{ x\in W : K|_W(x)<k \}.$$ It follows immediately that $X'_k$ is Borel, as $K|_W : W \rightarrow \mathbb{R}$ is a Borel measurable function. Recall that Baire class 1 functions are the pointwise limit of continuous functions and thus Borel measurable, and Baire class 2 functions are the pointwise limit of Baire class 1 functions and thus also Borel measurable.
[2.2]{} Let $u:\mathbb{R}^n\rightarrow \mathbb{R}$ be convex. Then the set on which $u$ is differentiable is a dense Borel set, specifically an $F_{\sigma \delta}$.
Since $u$ is convex, $u$ is differentiable at $x$ if and only if all the partial derivatives of $u$ exist at $x$, with respect to any basis \[6, IV.4.2\]. Let $\{e_i\}_{i=1}^{n}$ be the standard basis in $\mathbb{R}^n$, and define $$f'(x,e_i):= \lim_{t\downarrow 0} \dfrac{f(x+te_i)- f(x)}{t}.$$ Then $\frac{\partial f}{\partial x_i}(x)$ exists if and only if $f'(x,e_i)=-f'(x,-e_i)$\[6, IV.4.2\]. Note that the above limit always exists for a convex function and $f'(x,e_i)\geq -f'(x,-e_i)$ for all $x$. Take $E$ to be the set where $u$ is not differentiable and $E_i$ to be the set of points where $\frac{\partial f}{\partial x_i}(x)$ does not exist. Then $E=\cup_{i=1}^n E_i$, and $$E_i = \{ f'(x,e_i)+f'(x,-e_i)>0 \}.$$ If $x\in E_i$, then there exists $N$ such that for all $n\geq N$, $$\dfrac{f(x+\frac{e_i}{k})- f(x)}{\frac{1}{k}} + \dfrac{f(x-\frac{e_i}{k})- f(x)}{\frac{1}{k}} > \dfrac{1}{n},$$ for all $k\geq n$. Let $$E_{n,k}=\left\{ x: \frac{f(x+\frac{e_i}{k})- f(x)}{\frac{1}{k}} + \frac{f(x-\frac{e_i}{k})- f(x)}{\frac{1}{k}} > \frac{1}{n} \right\},$$ and note that $E_{n,k}$ is open since $f$ is continuous (a real-valued convex function). Thus, $$E_i = \cup_{n=1}^\infty \cap _{k=n}^\infty E_{n,k},$$ which is clearly a $G_{\delta \sigma}$ and so $E$ is also a $G_{\delta \sigma}$, being a union of finitely many. Therefore, the set $\mathbb{R}^n \setminus E$ on which $u$ is differentiable is an $F_{\sigma \delta}.$ That $\mathbb{R}^n \setminus E$ is dense is well-known.
[2.3]{} Let $u:\mathbb{R}^n\rightarrow \mathbb{R}$ be convex and $W \subset \mathbb{R}^n$ the set on which $u$ is differentiable. Then the function $K(x):=K(u,x)$ is of second Baire class on $W$.
We follow notes of Slodkowski, not contained in \[9\], for this proof. Let $$f(x,\epsilon)= \frac{2}{\epsilon^2} \max \left\{ u(x+\epsilon h) - \epsilon \langle \nabla u(x), h \rangle : |h|=1 \right\}.$$ Then $K(x)= \limsup_{\epsilon >0} f(x, \epsilon).$ Since $u$ is convex, $\nabla u(x)$ is continuous on $W$, and so $f(x, \epsilon)$ is a continuous function on $W \times (0, \infty)$.
Next, let $$g(x,n)= \sup \left\{ f(x, \epsilon): 0< \epsilon< \frac{1}{n} \right\}.$$ Since $g(\cdotp,n)$ is the supremum of a family of continuous functions it is lower semicontinuous, and thus the limit of an increasing sequence of continuous functions on $W$. Therefore,$g(\cdotp,n)$ is of first Baire class.
Now, note that $$\limsup_{\epsilon>0} f(x, \epsilon)= \lim_{n\rightarrow \infty}g(x,n),$$ and thus $K(x)$ is of second Baire class as it is the limit of Baire class one functions.
3. Dual Perspective
===================
3.1 Background
--------------
Since $u$ is convex near $x_0$, it is natural to study this quantity $K(u,x_0)$ from the dual perspective as well. Let $Cvx(\mathbb{R}^n)$ denote the space of convex, lower semi-continuous functions on $\mathbb{R}^n$. Given a function $u\in Cvx(\mathbb{R}^n)$, one can apply the Legendre–Fenchel transform $\mathscr{L}:Cvx(\mathbb{R}^n)\rightarrow Cvx(\mathbb{R}^n)$ of $u$ to obtain its conjugate or dual function $u^*$, where $$u^*\equiv \mathscr{L}u(s)=\sup_{x} (\langle s,x\rangle-u(x)).$$ $\mathscr{L}$ is an order-reversing, involutive transform on $Cvx(\mathbb{R}^n)$, and for sufficiently nice convex functions (differentiable, strictly convex, and 1-coercive), $u^*$ is given by $$u^*(s)=\langle s, (\nabla u)^{-1}(s) \rangle - u((\nabla u)^{-1}(s)).$$ The conjugate function $u^*$ can be viewed as a reparametrization of the original function $u$ in terms of its tangents using the duality between points and hyperplanes. More specifically, given a vector in $\mathbb{R}^n$, there is an associated family of hyperplanes with that gradient. $u^*$ distinguishes the one that supports the epigraph of $u$ by specifying a point on that plane.
For convex functions defined only in a neighbourhood it is standard to extend the function to all of $\mathbb{R}^n$ by setting it equal $+\infty$ outside that neighbourhood. In our case, we are given $u$ convex near $x_0$, so we extend it in this manner, if necessary. Clearly this does not affect $K(u,x_0)$, which is a purely local property. Recall the following basic definitions:
[3.1]{} *The differentiable function $f:\mathbb{R}^n\rightarrow \mathbb{R}$ is convex if for all $x,x'\in \mathbb{R}^n$ $$f(x')\geq f(x)+ \langle \nabla f(x),(x'-x) \rangle,$$ and strictly convex if the inequality is strict for $x\neq x'$.*
[3.2]{} *The differentiable function $f:\mathbb{R}^n\rightarrow\mathbb{R}$ is strongly convex with modulus $c$ if and only if for all $(x,x')\in \mathbb{R}^n \times \mathbb{R}^n$,* $$\begin{aligned}
f(x')\geq f(x)+ \langle\nabla f(x), (x' - x)\rangle +\frac{1}{2} c |x' - x|^2.\end{aligned}$$
When $f$ is not differentiable a lot of analysis can still be done using the calculus of subdifferentials.
[3.3]{} *Let $f:\mathbb{R}^n\rightarrow\mathbb{R}$ be convex. The subdifferential of $f$, denoted $\partial f$, is a set function, where $\partial f(x)= \left\{ s\in \mathbb{R}^n: f(y)\geq f(x)+\langle s,y-x\rangle \text{ } \forall y\in \mathbb{R}^n \right\}.$*
Under the Legendre transform, differentiability of $u$ corresponds to convexity or monotonicity of $u^*$. Recall from Proposition 1.8, two properties that transform especially well are (i) $u\in C^1$ if and only if $u^*$ is strictly convex, and (ii) $u\in C^{1,1}$, where $\nabla u$ has Lipschitz constant $c$ if and only if $u$ is strongly convex with modulus $\frac{1}{c}$.
3.2 Quadratic convexity
-----------------------
In this section we look at how a bound on $K(u,x_0)$ or equivalently a sphere of support to the graph of $u$ at $(x_0,u(x_0))$ transforms to a property of $u^*$. More specifically, since $K$ or a sphere of support is a bound on a generalized second-order derivative of $u$, how does this translate to information about the convexity of $u^*$? We should expect a more localized property then in Proposition 1.8, as we only have information at $x_0$. Further, we are not assuming any regularity beyond differentiable at $x_0$.
Now, strong convexity may also defined in terms of quadratic functions: $u$ is strongly convex with modulus $m$ if $u-\frac{1}{2}m|x|^2$ is convex. Similarly, quasi-convexity, is defined via quadratics: $u$ is $\lambda$- quasi-convex if $u+ \frac{1}{2}\lambda |x|^2$ is convex.
Let $u:\mathbb{R}^n \rightarrow \mathbb{R}$ be convex with $K(u,x_0)=k_0 <\infty$. By the definition of $K(u,x)$, for any $k>k_0$ there exists $\epsilon >0$ such that $$u(x_0+h)-u(x_0)-\langle \nabla u(x_0), h \rangle \leq \frac{1}{2} k|h|^2, \text{ for all } |h|< \epsilon .$$ This motivates the following definition.
[3.4]{} *Let $f:\mathbb{R}^n \rightarrow \mathbb{R}$ be convex. Then $f$ is quadratically (resp. sub-quadratically) convex at $x_0$ with modulus $m>0$ if there exists $\epsilon >0$ and a quadratic function $Q:\mathbb{R}^n\rightarrow \mathbb{R}$ with $\nabla^2 Q=mI$ such that $$f(x_0)=Q(x_0) \text{ and } f(x) \geq Q(x),\hspace{6.6mm} \forall x\in B(x_0,\epsilon)$$ resp. $$f(x_0)=Q(x_0) \text{ and } f(x) \leq Q(x),\hspace{6.6mm} \forall x\in B(x_0,\epsilon).$$*
[3.5]{} $f(x)=|x|^{4/3}$ is quadratically convex at 0, but not sub-quadratically convex at 0. Note also that $K(f,0)=+\infty$ and it does not have a sphere of support at 0.
[3.6]{} More generally, consider any function of the form $f(x)=A|x|^k$, at $x=0$. If $0<k<1$, $f$ is not convex. If $k=1$, $f$ is quadratically convex at 0, but not sub-quadratically convex. If $1<k<2$ then $f$ is strictly convex and quadratically convex but not sub-quadratically convex. If $k=2$, $f$ is both quadratically convex and sub-quadratically convex. If $k>2$, $f$ is sub-quadratically convex but not quadratically convex.
If $f$ is of the form $f=\frac{|x|^k}{k}$, then $f^*=\frac{|y|^q}{q}$, where $\frac{1}{k}+\frac{1}{q}=1$. So, in general, given that the Legendre-Fenchel transform is order-reversing and quadratics are transformed into quadratics, it follows that if $f$ is quadratically convex, $f^*$ is sub-quadratically convex. For a convex $C^2$ function $f$, if $\nabla^2f(x_0)$ is positive definite then $f$ is both quadratically and sub-quadratically convex at $x_0$.
Suppose $K(u,x_0)=k_0<\infty$. As stated above, by definition of $K(u,x_0)$, for any $k>k_0$, there exists $\epsilon >0$ such that $u$ satisfies $$u(x)-u(x_0)- \langle \nabla u(x_0), x-x_0 \rangle \leq \frac{1}{2} k|x-x_0|^2,$$ for all $x\in B(x_0,\epsilon)$. Thus, on this neighbourhood of $x_0$ $$u(x) \leq u(x_0)+ \langle \nabla u(x_0), x-x_0 \rangle +\frac{1}{2} k|x-x_0|^2.$$ By assumption $u$ is convex, and $k>k_0\geq 0$, so the right-hand side is also convex. Taking the Legendre transform gives $$u^*(y)\geq \langle \nabla u(x_0),x_0 \rangle - u(x_0) +\langle x_0, y- \nabla u(x_0)\rangle+ \frac{1}{2}k\left|\dfrac{y-\nabla u(x_0)}{k}\right|^2.$$ Now $u^*$ may not be differentiable at $\nabla u(x_0)$, however $\nabla u(x_0) \in \partial u(x_0)$ if and only if $x_0\in \partial u^*(\nabla u(x_0))$, which is equivalent to $u^*(\nabla u(x_0))=\langle \nabla u(x_0), x_0 \rangle -u(x_0)$. So the above inequality simplifies to $$u^*(y)\geq u^*(\nabla u(x_0))+ \langle x_0, y- \nabla u(x_0) \rangle + \frac{1}{2k}|y-\nabla u(x_0)|^2.$$ Note that there is equality at $y_0=\nabla u(x_0)$ and the Hessian of the right-hand side is $\frac{1}{k}I$ so $u^*$ is quadratically convex with modulus $\frac{1}{k}$.
On the other hand, if $u^*$ is quadratically convex at $y_0=\nabla u(x_0)$ with modulus $\frac{1}{k}$ then $u$ will be sub-quadratically convex with modulus $k$ at $x_0$, and it follows that $K(u,x_0)\leq k$.
In the above proof we do not need to worry about $\partial u(B(x_0,\epsilon))$ being degenerate (for example if $u$ is locally a hyperplane at $x_0$) because in that case $u^*(y)$ will then be $+\infty$ away from $\nabla u(x_0)$ so clearly the inequality will hold on some neighbourhood.
Our goal now is to obtain the nice bound on $K(u,x)$ in Proposition 1.6 using the dual function, given a sphere of support to the graph of $u$ at $(x,u(x))$. The following elementary lemma, which we state without proof, will help us to reduce arguments on $\mathbb{R}^n$ to ones on $\mathbb{R}$.
[3.7]{} *Let $S_{r}$ be an $n$-sphere with radius $r$ in $\mathbb{R}^{n+1}$, centered at $(0,...,0,r)$, and let $d:\mathbb{R}^{n}\rightarrow \mathbb{R}$ be the function defined by the lower hemisphere, i.e., for $z\in B_n (0,r)$, $d(z)= r- \sqrt{r^{2}-|z|^{2}}$. Then for any $x\in B_n(0,r)$ and $v \in \mathbb{R}^n$, $|v|=1$, the graph of $\psi:I \subset \mathbb{R}\rightarrow \mathbb{R}^{n+1}$ defined by $\psi(t)=d(x+tv)$ is a lower semi-circle in $\mathbb{R}^{n+1}$ of radius $\leq r$, where $I=(-\epsilon, \epsilon')$ is of maximal length.*
[3.8]{} *Let $f:\mathbb{R}^n\rightarrow \mathbb{R}$ be $C^2$ and convex and suppose there exists a sphere of support to the graph of $f$ at $(x_0,f(x_0))$ of radius $r$. Then* $$K(f,x_0) \leq \dfrac{(1+\nabla f|_{x_0}^2)^\frac{3}{2}}{r}.$$
Because $f$ is $C^2$, $K(f,x_0)$ is the largest eigenvalue $\lambda_{max}$ of $\nabla^2 f(x_0)$. If $\lambda_{max}$=0 or $\nabla f(x)=0$ then the bound on $K(f,x_0)$ is trivial, so let $\lambda_{max}>0$ and $\nabla f(x)\neq 0$. $f$ is convex so $\nabla^2 f(x_0)$ is symmetric positive semi-definite, and there exists an orthonormal basis of eigenvectors. Let $v$ be the eigenvector coresponding to $\lambda_{max}$. By duality, $v$ is also an eigenvector corresponding to $\lambda^*_{min}= \frac{1}{\lambda_{max}}$, the smallest eigenvalue of $\nabla^2 f^*(\nabla f(x_0))$. This follows from the fact that the Hessians of dual functions satisfy $$\nabla^2 f^*(y_0) = \nabla^2 f(x_0)^{-1}, \hspace{10mm} \text{ where }y_0 = \nabla f(x_0).$$ (Here we assume without loss of generality that $\nabla^2 f(x_0)$ is invertible because we are only concerned with $\lambda_{max}>0$).\
Let $S((c,t),r)$ be the sphere of support of radius $r$, to the graph of $f$ at $x_0$, and $d$ the associated lower hemisphere function, i.e. $$\begin{aligned}
d(x) = & t - \sqrt{r^2 -|x-c|^2},\hspace{2mm} x\in \bar{B}(c,r)\\
d(x) = &\infty, \text{ else}.\end{aligned}$$ Clearly $d$ is convex and $d \geq f$, by definition of a supporting sphere. Also, recall that $f$ and $d$ agree up to first order at $x_0$.
Again by basic properties of the Legendre transform, the following relations hold: $$\begin{aligned}
f^*(y_0)=d^*(y_0) \hspace{7mm} f^* \geq d^* \hspace{7mm} \nabla f^*(y_0)= \nabla d^*(y_0)= x_0.\end{aligned}$$ It follows that $$\lambda^*_{min} \geq \gamma^*_{min}$$ where $\gamma^*_{min}$ is the smallest eigenvalues of $\nabla ^2 d^*(\nabla f(x_0))$. Note that this is equivalent to $$\lambda_{max}\leq \frac{1}{\gamma^*_{min}}.$$ Given this bound, we now show that $\gamma^*_{min}$ can always be computed using a function on $\mathbb{R}$.
Let $v'$ be the unit-length eigenvector corresponding to $\gamma^*_{min}$ and $\gamma_{max}$. By Proposition 2.1, $v'$ is in the direction of $\nabla d(x_0).$ By Lemma 3.7, $\tilde {d}$, the restriction of $d$ to this $1-$dimensional subspace defines a lower semi-circle function, and this function has the properties: $\tilde{d}'(x_0)= \langle \nabla d(x_0),v' \rangle = |\nabla d(x_0)|$ and $\tilde{d}''(x_0) = \gamma_{max}.$ Therefore, the dual function $\tilde{d}^*$ has second derivative at $|\nabla f(x_0)|$ equal to $ \gamma^*_{min}$, and so we may assume without loss of generality that $f$ and $d$ are functions on $\mathbb{R}$.
Now we compute $d^*$ directly by using the Legendre transforms of common functions. Rewriting $d$ $$\begin{aligned}
d(x) = & t - \sqrt{r^2 -(x-c)^2}\\
=& t - r \sqrt{1 -\left(\frac{x}{r}-\frac{c}{r}\right)^2},\end{aligned}$$ and then applying the following well-known conjugate pairs: $$\begin{aligned}
h(x)= - \sqrt{1-x^2} &\hspace{.5 in} h^*(y)=\sqrt{1+y^2}\\
g(x)= \alpha + \beta x + \gamma u(\lambda x + \delta) & \hspace{.5 in} g^*(x)= -\alpha -\delta \dfrac{y-\beta}{\lambda} + \gamma u^*(\dfrac{y- \beta}{\gamma \lambda}),\end{aligned}$$ gives $$\begin{aligned}
d^{*}(y)=& -t +cy + r \sqrt{1+y^2}\\
\frac{d}{dy}d^{*}(y)=& c + \dfrac{ry}{\sqrt{1+y^2}}\\
\frac{d^2}{dy^2} d^{*}(y)=& \dfrac{r}{(1+y^2)^\frac{3}{2}}.\end{aligned}$$
Thus, $$\begin{aligned}
K(f,x_0)=\lambda_{max} \leq & \dfrac{1}{ \frac{d^2}{dy^2} d^{*}(|\nabla f(x_0)|)}= \dfrac{(1+|\nabla f(x_0)|^2)^\frac{3}{2}}{r}.\end{aligned}$$
The more general case, where $f$ is not assumed to be $C^2$, will use Proposition 3.8 and quadratic convexity of the dual.
[3.9]{} *Let $f:\mathbb{R}^n \rightarrow \mathbb{R}$ be convex with a sphere of support at $x_0$ of radius $r$. Then $K(f,x_0) \leq \dfrac{(1+\nabla f|_{x_0}^2)^\frac{3}{2}}{r}$.*
Let $d$ be the lower hemisphere function. Then $d(x_0)=f(x_0)$, and $$d\geq f \Rightarrow f^*\geq d^*.$$ If $y_0=\nabla f(x_0)$ (which exists since there is a sphere of support) then $$d^*(y_0)=f^*(y_0) \text{ and } \nabla d^*(y_0)\in \partial f^*(y_0).$$ From Proposition 3.8 the smallest eigenvalue of $\nabla ^2 d^*(y_0)$ is equal to $\frac{r}{(1+|y_0|^2)^{\frac{3}{2}}}$, so for any $m < \frac{r}{(1+|y_0|^2)^{\frac{3}{2}}}$ there exists a neighbourhood $U$ of $x_0$ such that $$f^*(y)\geq d^*(y)\geq d^*(y_0) + \langle \nabla d^*(y_0), y-y_0\rangle + \frac{1}{2} m|y-y_0|^2.$$ Thus, $f^*$ is quadratically convex with modulus $m$.
It follows that $f= (f^*)^*$ is sub-quadratically convex at $x_0$ with modulus $\frac{1}{m}.$ Let $Q_m$ be a satisfying quadratic. This implies that $$K(f,x_0)\leq K(Q_m,x_0)=\frac{1}{m},$$ and since this holds for any $m< \frac{r}{(1+|y_0|^2)^{\frac{3}{2}}}$, $$K(f,x_0)\leq\frac{(1+|y_0|^2)^{\frac{3}{2}}}{r}=\frac{(1+|\nabla f(x_0)|^2)^{\frac{3}{2}}}{r}.$$
Appendix
========
A.1 Lipschitz gradient
----------------------
Here we show that the generalized derivative $K(f,x)$ retains the following standard property regarding the derivative of a Lipschitz continuous function.
[A.1]{} Suppose $f:\mathbb{R}^n\rightarrow \mathbb{R}$ is convex and $C^{1,1}$ (i.e $f$ is differentiable and has Lipschitz gradient), with Lipschitz constant $L$. Then $K(f,x)\leq L$ for all $x$.
Let $x_0\in \mathbb{R}^n$. $$K(f,x_0) := \limsup_{\epsilon \rightarrow 0} 2\epsilon^{-2} \text{ max } \{ f(x_0 + \epsilon h) - f(x_0) - \epsilon \langle \nabla f(x_0), h \rangle : |h| =1 \},$$ which can be can written as $$K(f,x_0)= \limsup_{\epsilon \rightarrow 0} \text{ max } \left\{ 2 \dfrac{f(x_0 + \epsilon h) - f(x_0) - \epsilon \langle \nabla f(x_0), h \rangle }{\epsilon^2} : |h|= 1 \right\}.$$ Differentiability lets us use the Cauchy mean value theorem. Let $\phi_1(\epsilon)= f(x_0+\epsilon h) -\epsilon \langle \nabla f(x_0),h\rangle$, and $\phi_2(\epsilon)=\epsilon^2$. Note that $$2 \dfrac{f(x_0 + \epsilon h) - f(x_0) - \epsilon \langle \nabla f(x_0), h \rangle }{\epsilon^2}= 2 \dfrac{\phi_1(\epsilon)- \phi_1(0)}{\phi_2(\epsilon)- \phi_2(0)}.$$ Thus, there exists $\gamma\in (0,\epsilon)$ such that $$\begin{aligned}
2 \dfrac{\phi_1(\epsilon)- \phi_1(0)}{\phi_2(\epsilon)- \phi_2(0)} =2 \dfrac{\phi_1'(\gamma)}{\phi_2'(\gamma)} = & \dfrac{\langle\nabla f(x_0+\gamma h),h\rangle - \langle\nabla f(x_0),h\rangle}{\gamma}\\
= & \dfrac{\langle\nabla f(x_0+\gamma h)- \nabla f(x_0) ,h\rangle }{\gamma}\\
\leq & \dfrac{|\nabla f(x_0+\gamma h)- \nabla f(x_0)| }{\gamma} \leq L\end{aligned}$$ Therefore $K(f,x_0)\leq L$, and thus $\frac{1}{K(f,x_0)}$ bounds the modulus of convexity of $f^*$, for any $x_0$.
A.2 Example of a non $C^{1,1}$ function with a sphere of support
----------------------------------------------------------------
[A.2]{} It may seem that since a bound on $K(u,x)$ implies a sphere of support to the graph of $u$ at $(x,u(x))$, that this in turn implies some kind Lipschitz continuity of the gradient in a small neighbourhood of $x$. Here we construct an example of a strictly convex function $f$ that is $C^1$ and twice differentiable with $K(f,0)<\infty$, but with gradient not Lipschitz in any neighbourhood of 0, to show this is not the case. Let $f:[-1,1]\rightarrow \mathbb{R}$ be given by $f(0)=0$, and for $x\geq 0$ $$\begin{aligned}
f'(x)=\int_0^x \gamma(t)dt, \hspace{5mm} \text{where } \gamma(t):=n+4 \text{ on } I_n \text{ and } 0 \text{ otherwise,}\end{aligned}$$ with $I_n= \dfrac{1}{(n+4)^2}[1-\dfrac{1}{(n+4)^2},\hspace{2mm}1]$. Define $f'(-x):=-f'(x)$.
Then $f'$ is clearly increasing and so $f$ is convex. And for $x_n =\dfrac{1}{(n+4)^2}$, $$f'(x_n)=\int_{0}^{x_1}\gamma(t)\,dt=\sum_{k\geq n}\frac{1}{(k+4)^3}\leq\int_{n+3}^{\infty}\frac{dt}{t^3}= \frac{1}{2(n+3)^2}<\frac{1}{(n+4)^2}=x_n.$$\
So we have $f'(x)\leq x$ for all $x \in [0,1]$ and $f'(x)\geq x$ for all $x \in [-1,0]$. Since $d'(x)\geq x$ for all $x \in [0,1]$ and $d'(x)\leq x$ for all $x \in [-1,0]$, it follows that the graph of $d$, and thus the unit circle centered at $(0,1)$, is always at or above the graph of $f$, with $f(0)=d(0)$. Therefore, $f$ has a sphere of support at $x_0=0$.
However, there exist sequences $\{x_i\}, \{x_j\}$ such that $$\dfrac{f'(x_i)-f'(x_j)}{x_i-x_j}$$ blows up: Taking $x_i$ and $x_j$ as the endpoints of $I_n$, $$\dfrac{f'(x_i)-f'(x_j)}{x_i-x_j} = \frac{1}{x_i-x_j}\left( \int_0^{x_i} \gamma(t)dt - \int_0^{x_j} \gamma(t)dt\right) = (n+4)^4 \int_{x_j}^{x_i} n+4 dt=n+4.$$ We can make $f$ strictly convex by adding an $x^m$ term, which does not affect any of the above analysis. The above example can be adjusted to show that $f'$ is not $\alpha$-Holder continuous for any $\alpha$.
A.3 Osculating and locally supporting spheres
----------------------------------------------
Here we extend the concept of an osculating circle to a plane curve to that of an osculating sphereto the graph of a function in higher dimensions. The bound on the largest eigenvalue $K(u,x)$ can be seen as a generalization of the relationship between the second derivative of a $C^2$ plane curve $u$ and the radius of its osculating circle:
Let $u:\mathbb{R}\rightarrow \mathbb{R}$ be $C^{2}$. Provided $u''\neq 0$, the radius of curvature at $x$ is defined as $$r_{u,x}:= \dfrac{1}{\kappa}= \dfrac{(1 + u'^{2})^{\frac{3}{2}}}{u''},$$ where $\kappa$ is the curvature of $u$ at $x$, and the right-hand side is the standard formula for computing the curvature of a planar curve \[2, §8\]. Thus, $$u''=\frac{(1+ u'^2)^{3/2}}{r}.$$
[A.3]{} *The osculating circle, or circle of curvature, to a planar curve $C$ at $p$ is the circle that touches $C$ (on the concave side) at $p$ and whose radius is the radius of curvature of $C$ at $p$.*
We extend this to the graphs of $C^2$ convex functions in higher dimensions by
[A.4]{} *For a convex function $u:\mathbb{R}^{n}\rightarrow \mathbb{R}$ let the osculating sphere to the graph of $u$ at $x$ be the $n-$sphere tangent to the graph of $u$ at $x$ the with radius equal to that of $\frac{1}{\lambda_{max}}$.*
It is easy to show that any tangent sphere at $(x,u(x))$ with radius less than the osculating sphere at that point is a (local) sphere of support. And any tangent sphere at $(x,u(x))$ with radius greater than the osculating sphere cannot be a (local) sphere of support.
A.4 Spheres of support to a function and its dual
-------------------------------------------------
Given a convex function $u$ with a sphere of support at $(x_0, u(x_0))$, the conjugate function $u^*$ will not necessarily have a sphere of support at the corresponding point $(\nabla u(x_0), u^*(\nabla u(x_0))$. For example take $u=\frac{1}{4}|x|^4$ and $u^*=\frac{3}{4}|x|^{\frac{4}{3}}$. However, for more regular and sufficiently convex functions (e.g. $C^2$ and locally strongly convex), we will have a sphere of support (locally) to both graphs at corresponding points, and the order-reversing property of $\mathscr{L}$ provide a simple inequality relating the radii of these spheres. We state this without proof.
[A.5]{} *Let $u:\mathbb{R}^n \rightarrow \mathbb{R}$ be strongly convex and $C^2$ near $x_0$, and suppose $u$ has a sphere of support of radius $r_{x_0}$. If $r_{y_0}$ is the radius of a sphere of support to $u^*$ at $y_0=\nabla u(x_0)$, then $$r_{y_0}\leq \dfrac{\left(1+|x|^{2}\right)^{\frac{3}{2}} \left(1+|\nabla u(x_0)|^{2} \right)^{\frac{3}{2}}}{r_{x_0}}.$$*
Acknowledgements
================
I am very grateful to Y.A. Rubinstein for introducing me to the work of Slodkowski, Harvey and Lawson, and for his ongoing guidance and encouragement. I thank T. Darvas and R. Hunter for helpful comments and discussions. I would also like to thank Z. Slodkowski for an insightful correspondence, and a referee for their careful review and stellar suggestions.
References
==========
$[1]$A.D. Alexandrov, *Almost everywhere existence of the second differential of a convex function and properties of convex surfaces connected with it (in Russian)*, Lenningrad State Univ. Ann. Math. 37 (1939), 3-35.\
$[2]$ Y. Animov, *Differential Geometry and Topology of Curves*, CRC Press, 2001.\
$[3]$ J. Foran, *Fundamentals of Real Analysis*, CRC Press, 1991.\
$[4]$ F.R. Harvey, H.B. Lawson, Jr., *Dirichlet duality and the non-linear Dirichlet problem*, Comm. on Pure and Applied Math. 62 (2009), 396-443.\
$[5]$ F.R. Harvey, H.B. Lawson, Jr., *Notes on the differentiation of Quasi-Convex Functions*, 2014.\
$[6]$ J.-B. Hiriart-Urruty, C. Lemaráchal, *Convex Analysis and Minimization Algorithms*, Vol.I and II, Springer, 1993.\
$[7]$ R.T. Rockafellar, *Convex Analysis*, Princeton University Press, 1970.\
$[8] $ C.A. Rogers, *Hausdorff measures*, Cambridge University Press,1970.\
$[9]$ Z. Slodkowski, *The Bremermann-Dirichlet Problem for $q-$Plurisubharmonic Functions*, Analli della Scuola Normale Superiore di Pisa, Classe di Scienze, $4^e$ série, tome 11, no. 2 (1984), p. 303-326.\
[^1]: `[email protected]`
| |
The police in India is governed, administered and controlled by laws like the Police Act, 1861 and Indian Penal Code. Law and order being a state subject under the Indian Constitution, the police in all states are under the control of the state governments, which means chief ministers and home ministers. The Central government does not have police forces, except in union territories it directly administers, but it has enforcement agencies like the Central Bureau of Investigation (CBI), Income Tax Department and Enforcement Directorate (ED). Neither the state authorities nor the central rulers ever feel shy of misusing or abusing law enforcement agencies and other agencies for their convenience.
This law and order enforcement system was designed by the British to control the country. It suited the Congress party when they held power in the Centre for 55-plus years. It equally suits the Bharatiya Janata Party (BJP), the Tamilian Dravida Munnetra Kazhagam (DMK) and the All India Anna DMK, the Trinamool Congress, the Janata Dal (United) and all other state and central ruling parties. No one is ready to give up “ownership” of the police and carry out any meaningful reforms which would ensure that the police forces become proper, independent law enforcement agencies, commanding true public confidence, rather than a puppet in the hands of the political masters.
The subject of police reforms has been under discussion for at least 40 odd years. Several committees have been appointed to study the subject. All of them made several recommendations to ensure that the police do not act as private armies of the central or state government. The Supreme Court has passed a detailed judgement on police reforms in a case filed by the retired head of Uttar Pradesh Police, Prakash Singh.
Although orders passed by the Supreme Court automatically become the law of the land which have to be implemented, this has surprisingly still not been done, except for a few cosmetic changes. What is required to be done is that all enforcement agencies, like ED, CBI and, at the state level, the police, should be completely insulated from political masters.
Mechanisms suggested for this are simple. Recruitment of police, postings and transfers, promotions etc. must be done through independent bodies, not controlled by politicians. Complaints against police officers must be probed by independent bodies. It is not difficult to implement these orders. But which government would willingly give up control over the police, always willing to act as an accomplice in their illegal activities and in putting down the political opposition?
If police were to be outside the purview of ministerial control, ministers would become quite powerless, much like the Chief Minister of Delhi. Politicians would not be able to order a police officer to arrest, torture, discipline a political opponent or any inconvenient person or save their followers when they are found in violation of the law. Such cases include Kuldip Shengar, a BJP state legislator from UP accused of rape and murder of a girl and recently convicted to life imprisonment, Swami Chinmayanand, again of the BJP, facing rape charges, perpetrators of the 1984 anti- Sikh riots in Delhi, among others.
Both the ruling and opposition parties justify police action when in power and criticize similar action when they are in opposition. However, they do not undertake the reforms, fearing a loss in their power.
On the subject of police reforms, most of the law enforcement agencies like ED, Income Tax and CBI at the centre and police at the state level are the main collaborators of government in India in 'disciplining' or 'controlling' inconvenient opponents. In authoritarian regimes, the public is mentally reconciled to the fact that they have no freedom and thus they quietly follow what the rulers tell them, like in China, Russia, North Korea, Pakistan, almost the entire Middle East and several countries in Africa and in South America. The issue of police suppressing public dissent with an iron hand, legally or illegally, really arises only in democratic countries where a few hundred people can hold an entire locality to ransom by blocking rail, roads and public transport.
It is common knowledge that in several countries, including India, the police do not always act within the law. Whether in routine criminal cases like theft, traffic offences, drunken driving etc, or political cases like demonstrations against the Citizenship Amendment Act or National Register of Citizens, reservations for some castes/communities, damage to public property and inconvenience to the public is usually a primary outcome.
The police, ED, CBI and so on cannot and should not be expected to act impartially within the law. There is a structural problem of design here. The problem does not primarily lie with the police force. It lies with many of the laws which date back to the British era and control of the police by the political governing class.
Despite the current opposition crying hoarse that the present government and police is partisan, the same police was totally law-abiding when they were in government. When the roles get reversed, the same theatrics will continue to play out, until radical changes take place. | https://southasiamonitor.org/spotlight/urgent-police-reforms-and-regulation-required-india-politicians-unwilling |
Posted in: Blog
At first, the police record check helps you make an informed decision when applying for a job. In some cases, it should be a little more thorough than the company’s standard practice. This is due to the high responsibility of the position. For example, they check more carefully if they hire a manager or a person responsible for the material and technical values of the company or information resources and purchases.
Why check employees?
The minimum surface criminal record check of candidates when applying for a job is mandatory so that there are no problems with the law later due to new employees, and also so that:
- ensure that you have sufficient qualifications for the position you hold;
- check the professional qualities and skills for compliance with the position and the possibility of a harmonious infusion into the working team;
- protect the company from hiring fraudsters, unscrupulous employees, etc.;
- prevent the possibility of leakage of important information that is a trade secret or know-how.
Who checks the applicants when hiring?
Each company has its own approved procedure for checking candidates for employment, which depends on the size of the company and the availability of the necessary specialists in the staff. But if you live in Australia, this is much easier. You can simply use the services of specialists in online criminal record check. But if not, then it would be correct if two divisions were engaged in it at once:
HR Department-post information about an open vacancy, then collect feedback from candidates and initial information about them, conduct interviews, evaluate professional qualities, transmit data to the security department, form a dossier for each applicant, and transmit the information to the direct manager, who makes the final hiring decision.
Security service – checks the reliability of the data provided by the applicant, evaluates the reliability of the candidate, makes a psychological portrait. This can be either a full-fledged division or a single employee. If this division is not in the company, then the entire recruitment process falls on the recruiter. If there is no such employee, the manager hires new people independently.
Stages of verification of candidates for the position
How candidates are vetted for a job depends on the company’s internal regulations and the availability of a security department and a recruiter on staff. How deeply and thoroughly a person should be checked depends on the position for which he applies. The more responsibility a new employee will have in the company, the more carefully it is necessary to check him before making a decision. This is because monetary and reputational losses due to improper management of the enterprise are much higher than, for example, due to the loss of one client due to the lack of competence of the sales consultant in the store.
In some cases, the security service does not finish checking a candidate for a job even after being accepted. It can continue during the internship when to get a complete portrait of a person, record all their work decisions, observe their behavior: compliance with the work schedule, reaction to various events in the company. So sometimes it takes up to 4-5 months.
When looking for new employees, many international companies check them for 4-7 months before hiring them to protect the business from possible mistakes. The algorithm they use has been developed for years and helps to choose the right person. | https://www.nunomad.com/candidate-verification-when-applying-for-a-job-the-main-stages-of-the-process-and-effective-methods/ |
This is an interesting question. Can we really adjust sensor based on user positions ? The answer will be YES, We can. But limitation is only either in horizontal or vertical direction. Kinect device has a tiny motor which is used to change the camera and sensor’s angles, to get the correct position of the human skeleton. The motor can be tilted vertically up to 27 degrees, which means that the Kinect sensor’s angles can be shifted upwards or downwards by 27 degrees.
None means, Kinect can view the complete skeleton and there is no area which is cutting out from Kinect view area. For other values, they indicates which part of the body / join is cutting out. Based on this value you can provide live feedback to users on standing properly and for top and bottom, you can change the sensor elevation angle ( by setting the ElevationAngle property) .
For example, ClippedEdgesUpdates() method from the SkeletonFrameReady event handler, where you can pass the individual skeleton frame to check if any body area is getting cut off.
SkeletonCutArea(FrameEdges.Top); // Change sensor elevation angle. | https://dailydotnettips.com/how-to-adjust-kinect-sensor-automatically-based-on-user-positions/ |
Journeys Festival International 2020 enters the new decade with digital!
Journeys Festival International (JFI), with the kind support of its partners and funders, continues to commission and curate an annual programme of work exploring the refugee experience through artistic and creative encounters.
Amid the challenges experienced by all in the creative community following the outbreak of Covid-19, JFI will adapt its programme and promises audiences the same incredible experiences created by artists with lived experience of seeking sanctuary through a predominantly digital offer this Summer and Autumn.
Produced by ArtReach, and normally taking place in Leicester, Manchester and Portsmouth, this year the Festival will bring its vibrant mix of performances, exhibitions, and events to audiences in digital spaces, while continuing to offer local communities unexpected and thought-provoking offline experiences in a safe and entertaining way.
A focused programme of activity will take place from 28 September to 18 October with exclusive content available as part of a special online exhibition season from 1 August to 31 October. This new combined programme will celebrate stories and cultures through the work of talented artists from around the world through a series of new commissions and presentations of existing work.
Developing an online and offline programme provides the ideal chance for the team to work in innovative ways with artists from previous years as well as showcase new and emerging talent. The Festival will reach national as well as global audiences by embedding ArtReach’s Liberty EU project (co-funded by the European Union through Creative Europe) into its programme. This will allow the Festival to platform the digital work of exceptional young artists across Europe who have experience of having their freedom of movement currently or previously restricted or negatively impacted because of their immigration status.
While exploring the theme of freedom of movement and working with UK based creatives, this is a special opportunity for the young artists to connect with national audiences as well as international audiences thanks to the support of Liberty’s 12 cultural partners in 10 different countries.
The current Liberty EU commission invites young artists to propose new artworks that explore the theme of freedom of movement, this includes, but is not limited to; film, video, animation, live streams of performances or performance scores, recorded music or soundscapes. The works will be curated by Mandla Rae and the ArtReach team and will be shared as part of the digital Journeys Festival International programme in October 2020.
To keep up-to-date with new commissions in the lead-up to the Festival, announcements will be made on the Journeys Festival International website as well as on social media.
Read more about the Liberty EU commission here. | https://www.journeysfestival.com/single-post/2020/05/07/journeys-festival-international-2020-enters-the-new-decade-with-digital |
The post-16 course is a course unique to Regent Independent College that offers students, who have received disappointing grades at the end of Year 11, the chance to re-sit the core GCSE subjects.
Sometimes students under-achieve due to a lack of application and hard work, sometimes students have been in an environment where their progression has been slowed by external factors, and sometimes, regrettably, this is simply the result of years of underachievement in key skills such as literacy and numeracy, which has gone unchecked.
The one year long GCSE or International GCSE (IGCSE) Intensive course (which includes Maths, English and Science) offers a solution to that. Students can start afresh and use the year to consolidate the content which was studied during Years 10 and 11. The classes are small, meaning that students are easily able to bring up queries and deal with topics which presented them with difficulties in the past.
Though this option can be made available to students who have never taken GCSE before in exceptional circumstances, the majority of the students enrolled on this course are those who have not achieved their full potential elsewhere previously and need to rectify this before moving on to pursue A-Levels. The intense nature of the one year course means that students must be very dedicated and committed to succeed.
Good grades in these core subjects are particularly important because all universities will look at these qualifications when assessing UCAS forms, notably, English and Maths are a pre-requisite for the reading of a degree in any subject and employers always look for at least passes in these two subjects.
Therefore, in cases where students have performed satisfactorily overall at GCSE but just missed a pass grade in English and Maths, we may consider having the student sit these two subjects at GCSE on the post-16 GCSE course, whilst taking their A-Level course simultaneously. | http://www.regentcollege.uk.com/courses/post-16-gcse/ |
The gynoecium is the most complex organ formed by the flowering plants. It encloses the ovules, provides a surface for pollen contact and self-incompatibility reactions, allows pollen tube growth and, post fertilization, and develops into the fruit. Consequently, the regulation of gynoecium morphogenesis is complex and appropriate timing of this process in part determines reproductive success. However, little is known about the global control of gynoecium development, even though many regulatory genes have been characterized. Here, we characterized dynamic gene expression changes using laser-microdissected gynoecium tissue from four developmental stages in Arabidopsis. We provide a high-resolution map of global expression dynamics during gynoecium morphogenesis and link these to the gynoecium interactome. We reveal groups of genes acting together early and others acting late in morphogenesis. Clustering of co-expressed genes enables comparisons between the leaf, shoot apex, and gynoecium transcriptomes allowing the dissection of common and distinct regulators. Furthermore, our results lead to the discovery of the LESSER FERTILITY1-4 (LEF1-4) genes, which, when mutated, lead to impaired gynoecium expansion, illustrating that global transcriptome analyses reveal yet unknown developmental regulators. Our data show that highly interacting proteins, such as SEPALLATA3, AGAMOUS, and TOPLESS are expressed more evenly during development, but switch interactors in time, whereas stage-specific proteins have only few interactors. Our analysis connects specific transcriptional regulator activities, protein interactions, and underlying metabolic processes towards the development of a dynamic network model for gynoecium development.
Introduction
Broadening our understanding of flower development is important as most of the terrestrial life is either directly or indirectly dependent on flowering plants (Sauquet et al., 2017) and agricultural advancements are required to feed the growing global population of the 21st century. Carpels, the female reproductive organs of the flowering plants begin to develop after the plant has reached its generative maturity and flowering has initiated. Carpels are located in the innermost whorl of the flower and their sum is defined as gynoecium. The gynoecium bears the developing ovules, receives pollen grains, and allows their passage through specialized tissue to enable fertilization of the ovules. Subsequently, these develop into seeds while the gynoecium is converted into a fruit.
In Arabidopsis thaliana, flowers arise on the flanks of the inflorescence meristem. The flower consists of four concentric whorls of different organs: the outermost sepals, then follow petals, stamina, and the gynoecium is formed in the centre. Gynoecium development commences approximately four days after floral development initiation when the previously undifferentiated central dome in the middle of the flower starts to elongate and forms a hollow, oval shape. This tube-like gynoecium consists of two congenitally fused carpels (Smyth et al., 1990). Inside the gynoecium, the carpel margin meristem (CMM) initiates as the inner adaxial margins first bulge inward forming a boundary surface inside the hollow structure. The CMM then gives rise to the carpel marginal tissues from where placenta, ovules, false septum, and transmitting tract form (Bowman et al., 1999, Reyes-Olalde et al., 2013, Reyes-Olalde and de Folter, 2019). The septa primordia fuse and form the false septum through postgenital fusion. After approximately eleven days of flower development, stigmatic papillae start to appear at the tip of the developing organ. One day later the papillae fully cover the tip of the gynoecium and the open-ended structure closes by postgenital fusion, while style and transmitting tract differentiate, leading to the mature gynoecium (Smyth et al., 1990).
The initiation of the gynoecium requires activation of the class C and E homeotic genes AGAMOUS (AG) and SEPALLATA3 (SEP3) (Bowman et al., 1989, Honma and Goto, 2001, Pelaz et al., 2000). These proteins form a tetramer protein complex with the active sites binding to a plethora of promoter regions in the Arabidopsis genome regulating the expression of the downstream genes to provide carpel organ identity and initiate carpel development (Smaczniak et al., 2017).
Post initiation, the dome-shaped floral meristem differentiates into several tissue types. These require specification and orientation towards the adaxial/abaxial and apical/basal axes, processes controlled by transcriptional regulators (TRs) such as PHABULOSA (PHB), REVOLUTA (REV), PHAVOLUTA (PHV), NUBBIN (NUB), JAGGED (JAG) and others (McConnell et al., 2001, Bowman et al., 2002, Dinneny et al., 2006). Induction and differentiation of the CMM tissues is regulated by SPATULA (SPT), CUP-SHAPED COTYLEDON1-2 (CUC1-2), HECATE1-3 (HEC1-3), INDEHISCENT (IND) for example (Heisler et al., 2001, Aida & Tasaka 2006, Gremski et al., 2007, Kay et al., 2012) and differentiation of stigma and style by NGATHA3 (NGA3), STY1, STY2 etc. (Trigueros et al., 2009, Sessions & Zambryski 1995, Kuusk et al., 2002). A complex interplay of many additional genes, phytohormones, peptides, microRNAs and epigenetic factors ultimately lead to the complete organogenesis of the gynoecium (reviewed in further detail in Alvarez-Buylla et al., 2010, Krishnamurthy & Bahadur 2015 and Moubayidin & østergaard 2017).
While genetic and protein interactions of many of the TRs coordinating carpel development are known (reviewed in Reyes-Olalde et al., 2013, Chávez Montes et al., 2015, Zúñiga-Mayo et al., 2019, and Becker 2019), we lack a comprehensive picture of expression dynamics of these TRs during carpel development. So far, the major transcriptomic studies of flower development in A. thaliana have focused on either the later stages of the developed flower organs (Klepikova et al., 2016) or complete buds at early to late stages (Ryan et al., 2015 and Mantegazza et al., 2014). Here, we provide a high-resolution temporal transcription time scale map of gynoecium development in A. thaliana, based on laser-microdissection (LMD) with subsequent RNAseq analysis of four different stages of carpel development starting from the initiation of carpel development to maturation, excluding the ovules. We show that specific genetic modules exist in a temporally precisely regulated manner and identify consecutively acting protein interaction networks key to gynoecium development. Further, we identify four putative transcription factors (LESSER FERTILITY1-4, LEF1-4) based on their specific temporal expression during gynoecium development and show that they contribute to gynoecium longitudinal growth and seed formation.
Results
Arabidopsis transcriptome data of four stages of carpel development
We sequenced laser-microdissected Arabidopsis carpel RNA samples at four different developmental stages: S1, initiation of carpel development after the differentiation of the central dome corresponding to stage 5 of A. thaliana flower development (Smyth et al., 1990); S2, elongation of carpel walls (stage 9); S3, during the female meiosis (stage 11, Smyth et al., 1990; Armstrong & Jones, 2001); S4, between female meiosis and anthesis (stage 12). Sample preparation, RNA-seq, transcriptome assembly and quality control are described elsewhere (Kivivirta et al., 2019). Four biological replicates were sequenced for all the four developmental stages and three were used for this analysis. 33 Mio paired-end reads were sequenced with read length of approximately 76 bp and annotated, resulting in expression information of all A. thaliana genes during gynoecium development.
Expression dynamics of carpel developmental regulators
We were interested in the temporal expression profiles of known carpel developmental genes to learn if the timing of their expression matches with their known role in development. We analysed carpel regulatory genes by generating an expression heatmap (Fig. 1, Supplemental table 1).
Among the genes most important for floral organ identity, initiation and maintenance are the MIKC MADS-box transcription factors SEP1-4 and AG (Fig. 1A, Supplemental figure 1). While SEP1-4 show strong differences in expression dynamics, AG is expressed evenly at a low level throughout the stages. The APETALA3 (AP3) and PISTILLATA (PI) genes required for stamen and petal but not gynoecium organ identity, show expression in the first two stages of gynoecium development, confirming earlier observations (Goto and Meyerowitz, 1994). Interestingly, some late acting MADS-box genes required for fruit dehiscence, such FRUITFULL (FUL) and SHATTERPROOF2 (SHP2) are expressed strongly throughout gynoecium development.
Hormonal signalling is an integral part of carpel development, with crucial functions for signalling pathways such as auxin and cytokinin, but also others like brassinosteroids and gibberellins (Marsch-Martinez and de Folter, 2016; Zúñiga-Mayo et al., 2019). We observed expression of many of the genes and transcription factors related to these hormonal pathways (Fig. 1B). The genes that present the highest expression are involved in auxin and cytokinin regulation and response, auxin biosynthesis, and brassinosteroid regulation.
Genes related to different steps in the auxin pathway were identified, such as those coding for TAA and YUC (biosynthesis); PIN1, PIN3 and PIN7 (transport); PID (transporter regulation); and the response factors ARF5/MONOPTEROS, ARF3/ETTIN, ARF6, ARF8 and others. Also, transcription factors such as ANT and AIL6, among others, which are closely related to the auxin pathway, were found in the transcriptome data (Krizek, 2009). Moreover, we observed various transcription factors well known for their regulatory role in carpel development (Fig. 1D) that also affect auxin signalling such as STY1, STY2, NGA, SPT, and CRABS CLAW (CRC), or that respond to auxin such as the CUC1-3 genes.
Genes related to the cytokinin pathway include those encoding the response regulators ARR1, ARR10 and ARR12, and the cytokinin degradation enzymes CKX3 and CKX5. All these genes have been reported to be expressed during gynoecium development, particularly in meristematic tissues. Mutations in these genes cause reduced or increased meristematic activity, respectively (Reyes-Olalde et al. 2017; Bartrina et al., 2011). Also, transcription factors such as the KNOX family members STM, BP and KNAT2, and TCP14 and TCP15 were expressed at different stages, play important roles in gynoecium development, and have been associated to the cytokinin pathway (Lucero et al., 2015).
Brassinosteroids also play important roles in gynoecium development. In the transcriptome data, the brassinosteroid-related genes HALF FILLED (HAF/CES), BEE1, BEE2 and BEE3, were also expressed, specially at the intermediate and late stages of development. This is in line with their function in transmitting tract development later during gynoecium development (Crawford et al., 2011).
Gibberellins have recently been implicated in the negative modulation of ovule number (Gomez et al., 2018; Barro-Trastoy et al., 2020). DELLA proteins are negative regulators of gibberellin signalling, and their activity correlates positively with ovule number. Genes encoding for DELLA proteins such as GAI, RGA, RGL2 were also found in the transcriptomes. Of these, only RGA is strongly expressed in the later stages, while the other show mild expression, decreasing in time.
Some of the genes in the transcriptomes take part in networks that connect different pathways. For example, the HEC1-3 induce auxin signalling and repress cytokinin signalling in the style (Schuster et al., 2015). Another example is SPT, that besides inducing auxin biosynthesis and transport, activates the cytokinin response regulator ARR1, which in turn, also activates auxin biosynthesis and transport (Reyes-Olalde et al., 2017).
Chromatin remodelling is an essential component of plant development (Ojolo et al., 2018) but its involvement in gynoecium development has received little attention and we were interested in exploring whether known chromatin remodelers are differentially expressed during gynoecium development. HISTONE DEACETYLASES1 and 2 (HDA1/2) are strongly expressed during gynoecium development whereas HDA3 shows only little expression (Fig. 1C). ACTIN-RELATED PROTEIN4 (ARP4), BRAHMA (BRM), SPLAYED (SYD), and CHC1/SWP73B show expression largely restricted to the latter two stages. In contrast, GIF1/AN3’s expression is mainly confined to the two early.
Several other TRs, not members of MADS-box genes, chromatin remodelers, or phytohormone-associated genes contribute essential functions to carpel morphogenesis (Fig. 1D). Among those, CRC, FILAMENTOUS FLOWER (FIL), AS1, LUG, SEUSS (SEU), SEUSS-like2 (SLK2), and LEUNIG-HOMOLOG (LUH), PHB and ALC are most strongly expressed. In contrast, many other important regulators, such as CUC1, CUC2, or WUS are expressed at very low levels suggesting that even genes expressed at low level may profound impact on gynoecium development.
In summary, our high-resolution data confirm previously reported expression data for individual genes and shows differentiation of expression of regulatory genes, even between closely related homologs, such as SHP1 and SHP2 or the SEP1-4 genes. Moreover, we can now identify temporal changes in regulatory gene activation during gynoecium development.
Temporal dynamics of protein interactions
Transcriptional regulators often interact in dimers or higher order multimers, and for A. thaliana gynoecium development, many protein interactions of TRs have been identified. However, we were interested in the temporal dynamics of these protein interactions. Thus, a comprehensive carpel protein interactome was generated based on protein interactions previously verified by Yeast Two-Hybrid (Y2H), Bimolecular Fluorescence Complementation (BiFC) and/or Co-Immunoprecipitation (Co-IP) analyses (Fig. 2, Supplemental table 2). We overlaid this interaction with expression data to illustrate the transient nature of some gynoecium TR interactions.
Fig. 2A shows the contribution of single proteins and TR families to the carpel interactome. A group of several MADS-box proteins forms a highly interactive cluster, as do the bHLH, B3, and homeodomain transcription factor families. These families show different levels of connectivity among each other and with regulators outside of their family: The MADS-box proteins are highly connected to each other but interact with only five unrelated proteins. In contrast, the homeodomain proteins are less connected within their family, but interact with nine proteins outside their family.
Several hub proteins with five or more interactions were identified from the network analysis (Fig. 2A): the bHLH protein SPT, the B3 AUXIN RESPONSE FACTOR6 (ARF6), the transcriptional repressor INDOLE-3-ACETIC ACID INDUCIBLE 27 (IAA27) of the AUXIN/INDOLE-3-ACETIC ACID protein family, the WD40 transcriptional corepressor TOPLESS (TPL), and the homeodomain proteins BELL1 (BEL1), KNAT1/BREVIPEDICELLUS, REPLUMLESS (RPL), and BEL1-LIKE HOMEODOMAIN9 (BLH9). Moreover, the MADS-box proteins AG, PI, AP3, SEP1, SEP2, SEP3, AGAMOUS-LIKE6 (AGL6), FUL, SHP1, APETALA1 (AP1) act as hubs. Interestingly, the majority of hub protein encoding genes (BLH9, TPL, SPT, AGL6, AP1, SEP1, AG, and AP3) are expressed strongly (>TPM20) throughout all carpel developmental stages (Supplemental table 1). Only PI is expressed strongly only in early developmental stages (Fig. 2B), and also two are strongly expressed in late developmental stages (SHP1 and SEP3) (Fig. 2C).
Many of the interacting hub proteins are generally rather strongly expressed (e.g. SEP3 with TPM peak 297, LUG with 252, and SEU with 121), but their dynamics and interactivity change during development (Fig. 2B and C). The MADS box proteins SEP4 and PI especially are highly expressed in S1 but when the gynoecium matures, their expression is reduced and other genes encoding highly interacting proteins like SEP3, SHP1, SHP2, STK, and FUL show increased expression.
Interestingly, not only hub genes, but also proteins with few interactors show stable expression throughout carpel development (Fig. 2B, C). The expression of each member in the cluster of the interacting proteins NGA2-TPL-AP2-AS1-IAA27-ARF5-ARF6-ARF8 remains remarkably stable (Fig. 2A, B). However, this cluster is complemented by the interaction of ARF4 with ARF5 and ARF6 at S1 which is not found in S4. Conversely, S4, interactions of HAT1/JAIBA with TPL and BEE2 with ARF6 are established.
In addition, the networks of TCP15-TCP14-SMU1, SLK1-LUH-SLK2, and LUG-SEU-SEP3-PKL-FUL-SHP2-SEP1-AG are stable throughout carpel development. Interestingly, other proteins also supplement these stable networks in different stages: The TCP15-TCP14-SMU1 network connects to PI in S1 and disconnects from the MADS-box protein cluster in S4. The SLK1-LUH-SLK2 network is connected to CUC2-CUC3 in S1 and exchanges this connection with KNAT1 in S4. The LUG-SEU-SEP3-PKL-FUL-SHP2-SEP1-SEP2-AG network is modified by the addition of SEP4, AP3, and PI in S1 and by STK, SHP1 and BEL1 in S4.
The interactome of S1 of carpel development includes 15 stage specific proteins while the S4 interactome includes only six stage specific proteins, and 29 proteins are included in the interactomes of both stages. This suggests that initiation and early morphogenesis of the carpel require more TR interactions than the later stages, when tissue differentiation is completed.
Another interesting group of proteins includes hub proteins (Fig. 2A) that have interaction partners with a generally or temporally very low level of expression. For example, BEL1 interacts with KNAT2 and KNAT6, but their expression is at a low level and at different stages, such that chances are high that the proteins never meet in planta. The same may apply to interactions with AGL6 and AP1, as the former has six and the latter thirteen protein interactors but they are hardly expressed in the gynoecium (Fig. 1A and 2A). Similar scenarios apply to KNAT1, SPT, and IAA27, which are all expressed at a low level. An extreme example is RPL, which has six interaction partners but is expressed at a very low level throughout gynoecium development and may be active mainly after fertilization during fruit development.
In summary, protein interactions directing carpel morphogenesis are temporally very dynamic. Only a few hub proteins maintain a high number of interactions throughout carpel development, such as SEP3, AG, and SEP1. Some components of the network, such as the one centred on TPL is active throughout carpel development but changes few interacting partners during morphogenesis. Further, differences in connectivity between transcription factor families were observed: while MADS-box proteins mainly interact among themselves, the bHLH family proteins are also highly connected with members of other TF families.
Co-expression analyses provide comprehensive information on expression patterns and resulting shifts in biological processes
We were then interested in identifying genes that were co-regulated with the previously described carpel regulators to identify clusters of co-expressed and possibly co-regulated genes. Further, we aimed to learn if the carpel transcriptomes share more similarity with the leaf or SAM transcriptomes. Automatically partitioned clusters were generated to visualize co-expressed genes (Fig. 3, for the full list of clusters and genes see Supplemental table 3) within the four carpel development stages in comparison to leaf and SAM.
The largest cluster consists of genes exclusively upregulated throughout gynoecium development (C1: 2847 genes) and includes several well-known gynoecium developmental regulators such as AG, SEP1-4, SHP1 and 2, SEU, SLK1-3, CES, LUG, LUH, HAF, or FUL. The second-largest cluster (C2: 2570 genes) includes genes that are down regulated during gynoecium development when compared with SAM or leaf tissue. Cluster C3 (1060 genes) includes genes with putative roles in both, SAM and gynoecium development and including ALCATRAZ (ALC), ARF5, DORNROSCHEN-LIKE (DRNL), HEC3, NTT, SQN, ULTRAPETALA (ULT), BEL1, and JAG.
Cluster C8 includes 628 genes highly expressed in the leaf and gynoecium, but downregulated in the SAM, with CNA being the only known carpel regulator member. The cluster containing genes with SAM-only expression (C7) is surprisingly small with only 758 genes, as is the cluster C10 combining all 393 genes strongly expressed only in the last two stages of gynoecium development. Genes with high expression in the first two gynoecium development stages, less strong expression in leaf and SAM tissues are collected in cluster C9 (550 genes) and include PIN1, PID, FIL, ANT, ETT, and ARF4.
Next, we were interested in the biological processes reflected by the clusters and identified overrepresented GO terms (Fig. 3, Supplemental table 3). Cluster C1 including genes upregulated throughout gynoecium development shows enriched terms related to metabolic and transcriptional regulation, while the contrasting cluster C2 shows enriched terms related to general biosynthesis and metabolism. Metabolic processes are depleted in C3, a cluster similar to C1, but with the weakest expression in leaves. GO terms related to metabolic processes are also depleted in C6 that contains genes with the highest expression in S3 and S4, suggesting weaker metabolic activity during gynoecium development if compared to the SAM and leave tissues. In C6, terms related to fertilization and zygotic development are enriched. Cluster C9 includes genes highly expressed during S1 and S2 showing enriched terms related to the cell cycle and nucleic acid metabolism. Cluster C10 includes genes that are nearly exclusively expressed during S3 and S4, and shows enriched terms related to the import of nutrients, mainly sugars.
Next, we were interested to see which processes change during gynoecium development and how the gynoecium differs from leaf and SAM tissues. We compared co-expression clusters with contrasting patterns (Fig. 4), to elucidate the differences in enriched GO-terms between the set of genes expressed in the carpel when compared to other tissues as well as between the early (S1, S2) vs. late (S3, S4) carpel development (for the complete analysis see Supplemental Table X). GO terms related to hormone response are overrepresented only in late carpel development stages (Fig. 4). Cell cycle related genes are underrepresented genes in cluster C2 but highly overrepresented in genes upregulated in early stages of carpel development. Photosynthesis-related genes are overrepresented in C2 and in late stages of carpel development, while they are under-represented in cluster C1 and early carpel development. RNA-splicing related genes are overrepresented in cluster C1 and early carpel development suggesting that differential splicing may play a role in carpel morphogenesis. Genes involved in the regulation of gene expression are overrepresented throughout carpel development as are floral organ development genes.
In summary, our data show a succession of events, starting from upregulation of photosynthesis and downregulation of cell cycle activity in leaf and SAM. In early stages of carpel development, photosynthesis plays no major role but genes involved in cell cycle, regulation of gene expression and floral development are upregulated. In late stages, phytohormone response and photosynthesis-related genes are upregulated.
Digital gene expression approaches can identify novel developmental regulators
Transcriptome analysis is a useful tool to clarify co-expression of gene clusters and single genes, but we were interested to know if it could also identify genes of hitherto unknown function that can be assigned as gynoecium developmental regulators. As proof of concept, seven genes with specific expression patterns were selected for reverse genetic analysis. While three SALK insertion lines showed no obvious fertility defects, four were significantly decreased in fertility (Fig. 5). These were named LEF1-4 for LESSER FERTILITY1-4 (Fig. 5A). lef1 is mutated around 150 bp 5’ from the coding sequence of B3 domain family gene (AT5G46915) and has low expression restricted to S1 and S2 of gynoecium development. lef2 has a insertion in the only exon of a DOF binding transcription factor encoding gene (AT5G66940) and, as LEF1, is restricted in its expression to the first two developmental stages. LEF3 encodes an AP2/B3 transcription factor (AT3G17010) with high S1 and moderate S2 expression and the insertion is located in the second exon. LEF4 also codes for an AP2/B3 transcription factor (AT3G46770) and strongly expressed in S2 and S3 and the insertion is in the first exon. The siliques of lef1-4 are ranging from 9.4 −16.6% shorter and with 5.7 – 20.3 % fewer seeds than the wild type (Fig. 5C and D), all shown to be significantly different from Col-0. We were then interested if the LEF1-4 genes are integrated in the regulatory network shown in Fig. 2 and searched the upstream regions for transcription factor binding sites identified in ChIP-Seq experiments (Fig. 5E). Each gene is regulated by one MADS-box protein complex including AG and at least two MADS-box protein complexes bind to each promoter, suggesting that the LEF1-4 genes are under direct control of floral homeotic protein complexes.
Discussion
Here, we use LMD RNAseq to generate expression data with high temporal resolution to resolve global transcriptional dynamics specific to gynoecium development. However, high specificity in transcriptome analysis may often go at the expense of sensitivity (probability to represent a particular transcript in the library), accuracy (how well the read quantification corresponds to actual mRNA concentration), and precision (technical variation of the quantification) (Ziegenhain et al., 2017). Here, we can show that transcription factor genes with known low levels of expression, such as NGA2, NGA3, NGA4, or HEC1 (with RPKM of 14, 8, 7, and 1, respectively, Klepikova et al., 2016) are picked up by our approach and show TPM values of 29, 9, 2 and 6 (Supplemental table 1). These numbers compare well in magnitude with the RPKM values taken from Klepikova et al., (2016) demonstrating a high level of accuracy. Distance correlation analysis between biological replicates analysed in this study show that the transcriptomes of the two early and the two late stages are clearly distinct (Kivivirta et al., 2019). However, of the four LMD RNAseq replicates that were analysed for each stage, three clustered closely together and those were used for the analysis. Most likely, we have reached the morphological and genetic limit of differentiation between stages, and more fine-grained analysis by LMD would be sub optimal in terms of accuracy. Single-cell transcriptome analyses would be more suitable to e.g. identify transcripts of a specific, small-scaled tissue type, such as the HEC1, 2, 3 genes which are expressed mainly in the few cells that later one will form the transmitting tract (Gremski et al., 2007), but their overall contribution to the transcriptome is very low (Fig. 1B). Single cell RNA sequencing (scRNA-seq) of developing gynoecia can improve sensitivity but relies in many cases on Fluorescence Assisted Cell Sorting (FACS). However, where fluorescent marker lines labelling specific tissues or cell types are limited, detection of cell types is difficult, and even more so for those cell types that form only a very small proportion in a tissue (Rich-Griffith et al., 2020). Here, this would apply to e.g. the dwindling stem cell population at early stages of gynoecium development or the placenta formation.
Also, the role of protein turnover on morphogenesis requires attention, when assessing the dynamics of transcriptional activity in developmentally active tissues. Stability varies among plant proteins, ranging from several hours to months with an average total protein half-life of 4-6 days (Li et al., 2017; Scheuerwater et al., 2000), but more specific data for TR’s turnover during developmental processes is not available. Thus, some transcriptional regulators may be active for a prolonged time even though their transcripts can no longer be detected. However, the effect of these stable proteins may be limited as it is diluted while the tissue increases in cell number. For example, ANT, KNAT2, CRC, CUC3, NUB, and ETT are required for CMM tissue differentiation but are mainly expressed at early stages and possibly, the proteins they encode persist for long. Moreover, while HEC1, 2, and 3 are expressed at very low levels throughout gynoecium development, their proteins may be particularly stable as their phenotypes are striking (Gremski et al., 2007; Schuster et al., 2015).
High resolution transcriptome analyses reveal subfunctionalization between closely related homologs
The SEP genes are known for their importance in flower development and organ and meristem identity (Pelaz et al., 2000; Ditta et al., 2004) but so far, only little research has been published regarding each gene’s specific role in gynoecium development. SEP genes act partially redundantly in flower development, such that only the quadruple sep1 sep2 sep3 sep4 mutant fails to form floral organs (Ditta et al., 2004), and SEP3 is thought to be most important for floral organ identity as it forms most protein interactions with other MADS-box proteins (Immink et al., 2009). Moreover, it mediates ternary complex formation between AG and STK, AG and SHP1, AG and SHP2, SHP1 and SHP2, STK and SHP1, and STK and SHP2, all involved in carpel and ovule development (Favaro et al., 2003). However, our transcriptome analysis shows substantial differential dynamics of between the SEP genes (Fig. 1A), suggesting subfunctionalization of this gene family in gynoecium development. SEP4 is generally expressed at a low level, but SEP1 and SEP2 are expressed strongly in the two early stages while SEP3 is most strongly expressed in the two later stages. While the ternary complex formation of SEP3 is well researched, the role of SEP1 and SEP2 has not been elucidated in much detail and they have fewer interactors among MADS proteins. Moreover, their ability for cooperative DNA binding differs between individual SEP proteins (Jetha et al., 2014). While the sep1 sep2 sep3 mutant fails to form carpels (Pelaz et al., 2000), adding a single functional SEP1 allele to the triple mutant restores carpel formation (Favaro et al., 2003). However, based on their strong expression during early carpel development we suggest important, but hitherto unknown roles for SEP1 and SEP2 in gynoecium development and a high degree of redundancy based on their sequence similarity and expression pattern, and possibly dimerization of SEP1 and SEP2 with non-MADS proteins. Severe subfunctionalization and extreme reduction in expression of SEP genes was also observed in several plant species, for example in Gerbera hybrida, whose genome includes seven SEP genes. While one of them, GRCD6, is hardly expressed, the other six genes diverge strongly in their expression pattern and function, and several distinct phenotypes were observed in the gynoecium when individual SEP genes were downregulated (Zhang et al., 2017). Gene duplication followed by subfunctionalization thus seems to be common to SEP homologs. The MADS-box genes SHP1 and SHP2 serve as second example for expression divergence of highly redundant genes. Neither of the single mutants displays a phenotype, but the double mutants are defective in dehiscence zone formation (Liljegren et al., 2000). Possibly, SHP2 has an earlier function in gynoecium development as it expressed also in the early stages of gynoecium development and even stronger in late stages. In contrast, SHP1 is hardly expressed in early stages and only moderately in the late stages (Fig. 1A). In addition, their interaction partners for dimerization differ, while SHP1 interacts with SEP3, SEP1, STK, AGL13, and AG, SHP1 interacts with SEP3, SEP1, and AGL6 only (Fig. 2A, Supplemental Table 3). However, SEP3 mediates interaction of SHP2 and STK as well as SHP2 and AG (Favaro et al., 2003), suggesting that subfunctionalization based on different dimerization partners overridden by ternary complex formation.
Similarly, HEC genes, known for their function in phytohormone control during gynoecium development (Schuster et al., 2015), show a peculiar pattern of expression. HEC1 is expressed in the later stages especially at S3 where it interacts with SPT to control carpel fusion. The lesser known HEC2 starts with strong early expression but completely ceases after S2 and HEC3 is most expressed at the S2. The specific function of each HEC-gene is still mostly unclear but the transcriptomic data suggests a specific role for each of the three genes in carpel morphogenesis. Our data shows a replacement of early interaction of SPT-HEC2 with SPT and HEC1, HEC3, IND and ALC (Fig. 2A). Similar replacements can be observed in other hub proteins such as TPL and AG, which exchange interactions over time (Fig. 1A, B, Fig. 2A).
Prediction of genetic interactions in gynoecium development
Negative or positive correlation of gene expression during gynoecium development can support predicted genetic interactions. For example, SEU and LUG together repress AG in the outer whorls of the flower (Franks et al., 2002) but we found strong expression of both of these genes also in the gynoecium with the highest expression during S1-3. This is in line with the seu lug phenotype in the gynoecium, characterized by lack of organ growth and carpel fusion (Franks et al., 2002) suggesting a continuous repression of hitherto unknown target genes during gynoecium development. Interestingly, both genes are also expressed significantly higher than AG in the gynoecium, suggesting that additional regulatory factors may be needed for the floral identity network regulation, protection of AG expression and proper gynoecium formation.
The protein interaction map (Fig. 2) provides a simplified overview of the regulatory dynamics during carpel development. Interactivity of the regulatory proteins is highly complex; however, relevant interactions are determined by presence and strength of expression at given time. Proteins like AG, PI, AP1, SEP1, SEP3, SHP1, SHP2 and STK interact with five or more regulatory partners each and expression of most of these proteins is established at carpel initiation or even before that. Our data suggests that interactions are at their highest complexity when tissue determinacy is established at the initiation of organogenesis as it has been described previously (Ò’Maoiléidigh et al., 2014). This can be observed as a high complexity of interactions during the initiation of carpel development (Fig. 2B).
Co-expression clusters reveal temporal emphasis on gene expression regulation during gynoecium development
Comparing transcriptomes of four gynoecium stages, leaf and SAM tissues by co-expression clustering (Fig. 3) shows that that the majority of genes highly expressed throughout carpel development is at most weakly expressed in leaf and SAM tissue, suggesting a high level of difference between these tissues. Further, more co-upregulated genes are shared between the SAM and gynoecium than in leaf and gynoecium development suggesting closer similarity of gynoecium and SAM tissue. However, this may be due to rapid expansion of the organ combined with later arising meristematic activity from the carpel margins. The evolutionary ancestor of the carpel is thought to be leaf-like (Becker, 2020; Moubayidin and Ostergaard, 2017) and consequently, the transcriptional program of gynoecia should be more similar to that of leaves than the SAM. However, this might be an over simplified view as gene regulation related to photosynthesis is a major contribution to the leaf transcriptome but plays only a minor role in gynoecium development, as photosynthesis-related genes are enriched only in a single cluster comprising leaf and late gynoecium stages. With regard to developmental regulation, the leaf primordium is meristematic at its inception and, during growth, meristematic potential is restricted to the margins, reminiscent of different SAM zones (Alvarez et al., 2016). However, the leaf transcriptome does not reflect these spatially differentiated leaf tissue types or developmental stages. Interestingly, the observation that at/after stage 9 of A. thaliana flower development, gynoecium development shifts from bilateral to radial growth (Moubayidin and Ostergaard, 2017) is consistent with our data on TR expression (Fig. 1). Several transcriptional regulators change their expression between S2 and S3; for example, the adaxial/abaxial regulators FIL, CRC, and KAN2 show a decline in expression after S2 suggesting that abaxial/adaxial polarity required for bilateral growth is established in S1 and S2 and subsequent radial growth requires different regulators. However, many regulatory processes seem to require maintenance throughout gynoecium development. For example, the C1 cluster includes genes upregulated throughout gynoecium development but not in leaf and SAM tissues and is most strongly enriched in regulators of gene expression, splicing and floral development.
Moreover, the shift of activity between S2 and S3 becomes also obvious when overrepresented GO terms are compared between genes upregulated in early (Fig. 4, C11) and late clusters (Fig. 4, C12). At the early stages, genes related to cell division, RNA splicing and regulation of gene expression enriched emphasizing the importance of early regulation of morphogenesis. In contrast, cluster C12 is enriched in photosynthesis related genes. This includes upregulation of genes required photosynthesis and for carbohydrate transport suggesting that the gynoecium may be a net sink organ but also contributes energy to the reproductive effort. Also, previous work has shown that flowers and fruits are not merely a cost to the carbon budget of the rest of the plant, but also contribute to this (Bazzaz et al., 1979; Gnan et al., 2017). Interestingly, in the case of gynoecium photosynthesis, developmental clues trigger upregulation of photosynthesis related genes and not light availability, because S4 is around 36 hours before anthesis (Smyth et al., 199o). Mizzotti et al., (2018) have shown that expression of photosynthesis, tetrapyrrol biosynthesis and plastid ribosomal proteins is strongest between three and six days after pollination and our data show that expression of many of these genes is already activated while the flower is still closed (Supplemental Table 3).
In summary, we describe a fine-scale map of transcriptional changes during gynoecium development as a resource to plant scientists. This provides a unique temporal perspective on global gene expression and protein complex formation potential suggesting a large number of new candidate developmental regulators orchestrating gynoecium development, four of which (LEF1-4) we have confirmed play a functional role.
Materials and Methods
Transcriptome assembly, heatmaps and interactome analysis
Raw sequencing reads of the four stages of A. thaliana gynoecium development (Kivivirta et al., 2019) were used to generate the transcriptomes (GenBank: Bioproject accession PRJNA549137). Trimming, quality testing, assembly and annotation were carried out in CLC workbench version 11.0.1. (QIAGEN, Hilden, Germany) as previously described in Kivivirta et al., 2019 with the the A. thaliana genome (Swarbreck et al., 2008). Gene expression heatmaps were constructed with Heatmapper: expression (Babicki et al., 2016). Euclidean distance of absolute values of gene expression were used with the expression values of a list of genes derived from Reyes-Olalde et al., 2013; Pfannebecker et al.; 2017a; Pfannebecker et al., 2017b; Parenicova et al. 2003 and Ojolo et al., 2018. Gene functions and families were based on earlier publications for each gene. The genes with expression of TPM <1 were left out of the analysis. For the complete list of genes, their functions and expression, see Supplemental Table 1. Protein-protein interaction maps were constructed with the GeneMANIA (Franz et al., 2018) app in cytoscape 3.8.0 (Shannon et al., 2003). Protein-protein interactions were searched for a set of carpel regulatory genes (Supplemental Table 1). Genes with no known interactions with other carpel regulatory genes were discarded. Information on gene families, change of gene expression and intensity of expression was added to the interaction map after the analysis. Change of binary logarithmic of expression was applied for Fig. 3A. Expression strengths for Fig. 3B and C is based on the absolute TPM values of gene expression.
Co-expressed clusters
Automatically partitioned co-expression clusters were generated with Clust front-end version 1.0.0 (Abu-Jamous & Kelly 2018). The datasets were automatically normalised. Cluster tightness was set to 2 and minimum cluster size to 40 genes. Genes with flat expression were filtered out of the analysis. The SRA files additionally included in the analysis were SRR3581346 (SAM) and SRR3581838 (leaf blade) (Klepikova et al., 2016). GO enrichment for gene sets were analysed with PANTHER 15.0 gene ontology enrichment (Mi et al., 2019, GO version Mar 2020). The results of a Fisher’s Exact test using the A. thaliana reference list for overrepresentation analyses were corrected by calculating false discovery rates. The generated lists were then visualized using REViGO (Supek et al., 2011,) in the version available in June 2020 (GO version Jan 2017). For the visualization of redundant GO terms with REViGO, uncorrected p-values of overrepresentation tests were grouped based on their semantic similarity utilizing the inbuilt SimRel function with the A. thaliana reference and an allowed similarity setting of 0.7. The generated lists and treemaps were further processed with the DrasticData Treemapping tool (drasticdata.nl, Delft, The Netherlands) to achieve a better visualization.
SALK mutant analysis
A. thaliana cv. Col-0 and the SALK mutant line plants were grown in peat, perlite mixture (3:1) in long day conditions. The mutants were self-pollinated to achieve homozygous insertion lines (Supplemental Table 4). SALK mutant lines were verified to be homozygous by genotyping the lines with locus- and insert-specific primers. Genotyping was done in two separate reactions with locus specific LbB + RP and LP + RP primers to verify presence of the specific insert and absence of the wild type locus (Supplemental Table 4). Siliques from 30 developing flowers were analysed for morphological abnormalities, gynoecium length and seed number at the stage of silique ripening (Smyth et al., 1990: stage 17) for each mutant line. Statistical significance was evaluated using the single factor ANOVA and t-test. The siliques were recorded with Leica DM550 (Leica Application Suite 4.3.0, Wetzlar, Germany) and the lengths of the siliques were measured with ImageJ (https://imagej.nih.gov/ij/). The intron-exon structures and protein binding site motifs for TRs upstream LEF1-4 genes were based on ChIP-Hub (http://www.chip-hub.org). FIMO binding maps use Plant transcription factor database (http://planttfdb.cbi.pku.edu.cn/) as a source for protein binding sites.
Supplemental material
Supplemental table 1: Detailed information on expression and function of genes related to gynoecium development (Fig. 1)
Supplemental figure 1: Heatmap of the MIKC type MADS-box genes. The heatmap figure illustrates the expression of MIKC type MADS-box genes at the four stages of development.
Supplemental table 2: Protein interactions of known developmental regulators. The table illustrates the experimentally verified physical protein interactions and the sources of information.
Supplemental table 3: Automatically partitioned Co-expressed clusters. The table illustrates the co-expression clusters, their contents, and the GO enrichment analysis.
Supplemental table 4: SALK-mutant analysis and genotyping. The table includes a summary of the candidate genes, SALK-mutant lines, genotyping primers, genotyping results and example pictures.
Author contribution
KK and AB designed the study and wrote the manuscript. KK performed digital gene expression analysis, mapping expression data to protein interaction data, and loss-of-function mutant analysis. CR conducted co-expression clusters and GO enrichment analyses. DH assembled the transcriptomes and calculated TPM values, and SdF and NMM analysed phytohormone-related genes. Figure preparation by KK and CR. All authors contributed, read and approved the final manuscript.
Acknowledgements
We thank all members of the Becker lab for thoughtful discussion on the presented material. We are indebted to David Smyth for suggestions on the manuscript. Additionally, we thank the students Henri Hoffmann and Julian Garrecht for their help. We thank the German Research Foundation (DFG, project BE2547/14-1) for the main funding of this work. AB and SdF thank the DAAD-Conacyt collaborative grant numbers 267803 to SdF and 57273492 to AB. | https://www.biorxiv.org/content/10.1101/2020.07.29.227314v1.full |
The British pound hit an all-time low, impoverishing more citizens
The British pound has had its worst season on record, and as the steady slump has continued unabatedly, its value has plummeted below $1.10 for the first time since 1985.
The depreciation of the pound and a hike in the volume of goods imported into the UK will throw off the country’s annual trade balance.
According to economists, the weak pound will drive up the cost of imported products, causing inflation to spiral out of control, and will inevitably deteriorate citizens’ living standards.
Moreover, as the royal family’s extravagant spending grew exponentially, British consumers’ faith in their politicians continued to erode due to the current economic turmoil.
The 4% decline came only one day after the British government announced the most significant tax reduction in the nation in the past 50 years.
The nascent administration of British Prime Minister Liz Truss unveiled a mini-budget, sending shockwaves through the country’s markets and precipitating the pound sterling’s crash.
The alleged goal of the Truss administration’s controversial strategy is to protect consumers, stimulate economic growth, and avert a deep recession.
However, the Bank of England (BoE) may face additional strain to increase interest rates and strengthen the currency in reaction to the pound’s slide; implementing the package a quite challenging.
On the other hand, a decrease in the pound may promote investor interest in stocks, leading the British stock market to deviate from the downward trend of other important economic indices.
The pound’s decrease in value, inflation’s persistent rise, the possibility of a surge in the interbank interest rate, the lingering repercussions of Brexit, and the COVID-19 pandemic have all contributed to the new Tory government’s financial policy faltering, which will prompt political opponents, particularly Labour Party members, to excoriate Boris Johnson’s successor fiercely.
Furthermore, the lower British pound has made UK real estate attractive to American homebuyers. “We have seen a steady increase from Americans,” said Paddy Dring, global head of prime sales at Knight Frank. “Some are forwarding their plans and will use this opportunity for their longer-term investment plans to diversify abroad.”
The only solution to save Britain’s sinking economy is to raise interest rates to lure foreign investors. Nevertheless, Brexit’s adverse ramifications, the looming spectre of a second Scottish independence vote, the trade war with the European Union, and the long-term consequences of the Federal Reserve’s monetary contraction pressure on emerging economies will make it difficult for the UK to extricate itself from its economic catastrophe. | https://iuvmarchive.org/en/article/the-british-pound-hit-an-all-time-low-impoverishing-more-citizens |
Fashion trends determine the daily styles of the world. It is quite natural that they would also affect how people dress. Thus, it is essential to understand them and be aware of them in order to adapt to them and make some money.
The fashion industry is at a tremendous transformation. Trends are evolving so fast that current concepts cannot keep up with the next generation of clothing. | http://merliniego5.pl/the-new-and-emerging-fashion-trends-that-the-us-and-new-york-have-to-offer/ |
By KEN PERLMAN
Job cuts at Microsoft hit nearly every division of the company in September 2014 in the second wave of the company’s larger plan to cut 18,000 employees, as announced in July last year.
The events surrounding a layoff are, sadly, quite predictable to those of us who have seen it often. But only rarely do we witness leaders who understand how to effectively lead their people through the layoff and even take advantage of it.
There is a huge difference between those who “minimise the disruption” and those who effectively recognise the need for change “now more than ever before”. With disruption comes the opportunity to challenge traditions, decide how to improve work processes and focus people and teams on the actions that actually contribute to winning and results.
First – how not to lead
In Microsoft’s case, the initial communication about the layoffs back in July 2014 was a textbook flop. A wordy 1,100-word company email announced the layoffs all the way down in the 11th paragraph, so far buried in management terminology as to be lost to the casual reader.
The letter was authored not by Microsoft’s CEO (chief executive officer), Satya Nadella, but rather former Nokia CEO and executive vice president of devices, Stephen Elop.
Unfortunately, this kind of oblique and impersonal manner for announcing layoffs is often par for the course. Many leaders have followed a similar pattern with past job cuts: filing for a layoff in accordance with federal, state or local regulation or statutory requirements; announcing the layoff to the entire company; communicating uplifting messages to the press about developing new strategies to foster growth; and encouraging managers to redistribute work among remaining employees.
This kind of arms-length process can breed feelings of insecurity and anxiety among remaining staff members, emotions that often hinder innovation and creativity, as well as erode employees’ trust in the company.
As a result, individuals “keep their heads down” and “focus on doing the job” until things “blow over” – while also updating their resumes and putting out feelers.
Every once in a while, however, we find a leader who realises that his/her people are the heart and soul of the company and key to improving the bottom line.
This kind of leader understands the importance of helping remaining employees rebound quickly from a period of layoffs and, in turn, works to raise urgency among staff members to refocus on a future vision, leveraging the turmoil of the event to challenge the old ways of working and thinking.
How visionary leaders shift from ‘crisis’ to ‘opportunity’
1. Clearly define the vision for succeeding with the resources at hand
Layoffs can seem to pull the rug out from under a company. They change how leaders and employees define success. Creating clarity about how the organisation wins in the marketplace today, now, with what we have (not what we wish we had) is critically important.
How will we compete now? What can we do to change the game? What can we decide to stop doing because we don’t have the staff and it doesn’t add any value? These questions empower the organisation to move forward in a period of extreme change.
2. Get urgent about the future
Now is not the time to wait. Though the instinct may be to “let the dust settle”, layoffs usually indicate that what worked in the past doesn’t cut it anymore. Instead, leaders must focus quickly on making key decisions, taking some risks and looking for new ways to get better results in the future.
By promoting a test-fast, fail-fast mentality that rewards innovation and risk-taking, leaders will prevent fear and uncertainty from defining the corporate culture.
3. Question and challenge ‘how it’s always been done’
Rather than working harder and longer, the best companies today work better. The period of change around a layoff is a time when managers and supervisors should be giving their teams permission to challenge old assumptions and ways of doing business.
To keep remaining staff from burning out after a layoff, leaders should ask key questions, such as, “Is there an App for that?” or, “Can we shorten that meeting or eliminate it altogether?” By giving employees permission to challenge the way things have always been done, the resulting innovations may save wasted time and effort.
Everyone is involved
Layoffs affect everyone. Consequently, individuals at all levels play an important role in recovering from job cuts. As the company reorients and begins to build a new and more successful culture for the future, leaders must encourage their people to take ownership of their time, eliminating frustrating and unnecessary work, and to bring fresh and better ways of working to the surface.
Both will help employees feel empowered to creating positive changes, as opposed to insecure and fearful throughout the transition. The companies that successfully weather the turmoil of layoffs are those where leaders are able to instill urgency, create clear vision and empower broad-based action toward realising future opportunities.
Ken Perlman is an engagement leader at Kotter International, a firm that helps leaders accelerate strategy implementation in their organisations. This article originally appeared on Forbes.com, and is reposted with permission.
For feedback, drop us a line or two in the comment box below or email us at [email protected]. For more leadership and personal development insights, visit www.leaderonomics.com
Lay Hsuan was part of the content curation team for Leaderonomics.com, playing the role of a content gatekeeper as well as ensuring the integrity of stories that came in. She was an occasional writer for the team and was previously the caretaker for Leaderonomics social media channels. She is still happiest when you leave comments on the website, or subscribe to Leader’s Digest, or share Leaderonomics content on social media. | https://leaderonomics.com/leadership/how-to-lead-after-layoffs |
The Community Life Services department had a unique opportunity this June to spend two weeks with Emma, a rising high school junior, as an intern! We have not hosted many internships or service-learning opportunities and Emma set a fine standard for more students moving forward.
About the Internship
Kari Schrader, CLS Director, worked to create for Emma a meaningful and hands-on internship related to senior living. Emma spent her time shadowing Kari, diving headfirst into the ins and outs of the activities here at Ardenwoods. Her hands-on experience here included decorating for special events, delivering reminders, trip confirmations, and advertisements almost daily to our multiple areas of interest around campus.
Community Life Services is particularly invested in building meaningful relationship and purposeful engagement. Emma saw this first-hand this in delivering “National Hug Your Cat Day” treats to the cat owners amongst us, the Father’s Day recollections we collected and posted corporately, and a visit with a resident who will host our community Open House in August to share her handiwork.
Not only did Ardenwoods benefit from Emma’s added enthusiasm, energy, and creativity, but resident Kathy, had a special experience with our intern. Emma rode along on a transportation trip when Kathy needed banking assistance at the grocery store and unloading groceries! Of Emma, Kathy said, “I found her to be very charming, mature, and interested in learning. Emma was kind and sensitive.”
What Does Emma Have to Say?
Below is Emma’s take on her time interning at Ardenwoods: | https://ardenwoodsretire.com/2019/07/interns-at-ardenwoods/ |
- Coat grill rack with cooking spray, then preheat grill.
- Stack bacon slices and cut into 3 equal lengths. Wrap each shrimp with bacon and secure with toothpicks, then place in medium bowl (wash hands). Pour dressing over shrimp and toss to coat; let stand 5 minutes to marinate.
- Place shrimp on grill, using tongs, and discard any remaining dressing; close lid (or cover with foil) and cook 6–8 minutes, turning occasionally, and just until shrimp are pink. Remove toothpicks and serve over salad.
Orange Spinach Salad
Ingredients
1/4 cup orange herb/poppy seed marinade
1 tablespoon white balsamic vinegar
1 (5-oz bag) fresh spinach (about 4 cups)
1 (11-oz) can mandarin oranges in light syrup (drained)
1/4 cup shelled sunflower seeds
Steps
- Whisk marinade and vinegar together, in salad bowl, until well blended.
- Add remaining ingredients; toss until evenly coated.
Aprons Advice
- Complete your meal with grape tomatoes, Italian bread, lemonade and peach pie.
- Shortcuts and Tips
- Soaking toothpicks in water overnight will prevent them from burning when grilling. The shrimp recipe makes a great appetizer. | http://www.capmel.com/bacon-wrapped-shrimp/ |
MONDAY, Oct. 1, 2012 (MedPage Today) — Even moderate consumption of alcohol may increase the chance of developing atrial fibrillation in older individuals with a high cardiovascular risk or diabetes, researchers found.
Among high-risk individuals, ages 55 and up, who were participating in antihypertensive drug treatment trials, 6.3 percent of light drinkers, 7.8 percent of moderate drinkers, and 8.3 percent of heavy drinkers developed atrial fibrillation during follow-up, according to Yan Liang, MD, of McMaster University's Population Health Research Institute in Hamilton, Ontario, and colleagues.
"Because drinking moderate quantities of alcohol was common in our study (36.6 percent of the participants), our findings suggest that the effect of increased alcohol consumption, even in moderate amounts, on the risk of atrial fibrillation among patients with existing cardiovascular disease may be considerable," the authors wrote.
They calculated that for every 100 cases of atrial fibrillation occurring in the population of moderate drinkers, an estimated 4.9 would be prevented if everyone quit drinking.
"Recommendations about the protective effects of moderate alcohol intake in patients at high risk of cardiovascular disease may need to be tempered with these findings," they concluded.
Liang and colleagues examined data from participants in the ONTARGET and TRANSCEND trials, which evaluated the combination of the angiotensin receptor blocker telmisartan (Micardis) and the ACE inhibitor ramipril versus either drug alone and telmisartan versus placebo in patients who were intolerant to ACE inhibitors.
In both studies, the participants were 55 or older, free from heart failure, and considered to be at high risk for cardiovascular events because of a history of cardiovascular disease or diabetes with end-organ damage.
The current analysis pooled 30,433 patients from both trials who were free from atrial fibrillation at baseline. The mean age of the patients was 66.4, and 29.8 percent were women.
Based on the participants' self-reported intake at baseline, the researchers defined alcohol consumption as low (less than one drink per week), moderate (up to two drinks per day for women and up to three drinks per day for men), or high (greater than moderate consumption). Binge drinking was defined as more than five drinks in a day at any one time or an average intake of more than five drinks per day.
Overall, 61.7 percent, 36.6 percent, and 1.7 percent reported low, moderate, and high consumption, respectively. Binge drinking was reported by 4 percent, all of whom were either in the moderate or high groups.
Through a median follow-up of 56 months, 2,093 patients developed atrial fibrillation — 72 percent were clinically apparent episodes and 28 percent were asymptomatic episodes detected on routine electrocardiograms.
The risk of atrial fibrillation increased significantly across the alcohol consumption categories after adjusting for a number of demographic and clinical variables. The results were consistent in analyses that excluded binge drinkers — who had a greater risk of developing the arrhythmia compared with non-binge drinkers — and that accounted for the competing risk from death.
The authors acknowledged some limitations, including the use of self-reported alcohol intake collected at baseline only, the small proportion of heavy drinkers, the possibility of missing episodes of paroxysmal atrial fibrillation episodes, and the lack of information on thyroid function. | http://www.everydayhealth.com/heart-health/1001/one-drink-a-day-may-up-risk-of-heart-rhythm-condition.aspx |
The United States legal system does not draw a distinction between lawyers who plead in court and those who do not, unlike many other common law jurisdictions. For example, jurisdictions in the United Kingdom distinguish between solicitors who do not plead in court, and the barristers of the English and Welsh system and the Northern Ireland system and the advocates of the Scottish system, who do plead in court. Likewise, civil law jurisdictions distinguish between advocates and civil law notaries. An additional factor that differentiates the American legal system from other countries is that there is no delegation of routine work to notaries public.
Attorneys may be addressed by the post-nominal letters Esq., the abbreviated form of the word Esquire.
Many American attorneys limit their practices to specialized fields of law. Often distinctions are drawn between different types of attorneys, but, with the exception of patent law practice, these are neither fixed nor formal lines. Examples include:
Despite these descriptions, some states forbid or discourage claims of specialization in particular areas of law unless the attorney has been certified by their state bar or state board of legal specialization.
Some states grant formal certifications recognizing specialties. In California, for example, bar certification is offered in family law, appellate practice, criminal law, bankruptcy, estate planning, immigration, taxation and workers' compensation. Any attorney meeting the bar requirements in one of these fields may represent themselves as a specialist. The State Bar of Texas, for example, formally grants certification of specialization in 21 select areas of law.
The majority of lawyers practicing in a particular field may typically not be certified as specialists in that field (and state board certification is not generally required to practice law in any field). For example, the State Bar of Texas (as of mid-2006) reported 77,056 persons licensed as attorneys in that state (excluding inactive members of the Bar), while the Texas Board of Legal Specialization reported, at about the same time, only 8,303 Texas attorneys who were board certified in any specialty. Indeed, of the 8,303 certified specialists in Texas, the highest number of attorneys certified in one specific field at that time was 1,775 (in personal injury trial law).
Specialization in patent law is administered by the Office of Enrollment and Discipline of the US Patent and Trademark Office, which imposes stringent requirements for applicants to become registered as patent attorneys or patent agents.
In the United States, the practice of law is conditioned upon admission to practice of law, and specifically admission to the bar of a particular state or other territorial jurisdiction. Regulation of the practice of law is left to the individual states, and their definitions vary. Arguing cases in the federal courts requires separate admission.
Each US state and similar jurisdiction (e.g. territories under federal control) sets its own rules for bar admission (or privilege to practice law), which can lead to different admission standards among states. In most cases, a person who is "admitted" to the bar is thereby a "member" of the particular bar.
In the canonical case, lawyers seeking admission must earn a Juris Doctor degree from a law school approved by the jurisdiction, and then pass a bar exam administered by it. Typically, there is also a character and fitness evaluation, which includes a background check. However, there are exceptions to each of these requirements.
A lawyer who is admitted in one state is not automatically allowed to practice in any other. Some states have reciprocal agreements that allow attorneys from other states to practice without sitting for another full bar exam; such agreements differ significantly among the states.
In 1763, Delaware created the first bar exam with other American colonies soon following suit.
The bar examination in most U.S. states and territories is at least two days long (a few states have three-day exams). It consists of essay questions, usually testing knowledge of the state's own law (usually subjects such as wills, trusts and community property, which always vary from one state to another). Some jurisdictions choose to use the Multistate Essay Examination (MEE), drafted by the NCBE since 1988, for this purpose. Others may draft their own questions with this goal in mind, while some states both draft their own questions and use the MEE. Some jurisdictions administer complicated questions that specifically test knowledge of that state's law.
Bar exams also usually consist of the Multistate Bar Examination, which is a multiple-choice standardized test created and sold to participating state bar examiners by the National Conference of Bar Examiners since 1972. The MBE contains 200 questions which test six subjects based upon principles of common law and Article 2 of the Uniform Commercial Code.
The State of Washington has a separate Law Clerk program under Rule Six of the Washington Court Admission to Practice Rules. A college graduate of good moral character may be accepted into the four-year Rule Six Law Clerk Program, obtain employment in a law firm or with a judge for at least 30 hours a week and study a prescribed Course of Study under a tutor. After successful completion of the program, a law clerk may take the Washington State Bar Exam and, upon passing, will be admitted as an attorney into the Washington State Bar Association.
The degree earned by prospective attorneys in the United States is generally a Juris Doctor (Latin for "Doctor of Jurisprudence"; abbreviated J.D.).
The highest law degrees obtainable in the United States are Doctor of Juridical Science (Scientiae Juridicae Doctor, abbreviated S.J.D. or J.S.D.). The S.J.D. is akin to an academic degree that, like the Ph.D., is research-based and requires a dissertation (an original contribution to the academic study of law).
The LL.M. is generally earned by completing studies in a particular area of law. LL.M. is an abbreviation of the Latin Legum Magister, which means Master of Laws. For example, most accredited law schools in the United States require basic coursework in Federal Taxation. After earning a J.D., an attorney may seek admission to an LL.M. program in taxation. Earning the LL.M. requires completion of coursework in the area of tax law. There is no requirement for attorneys to complete an LL.M. program to practice law in the United States, and relatively few attorneys hold an LL.M. In the U.S., for example, some states allow foreign lawyers to seek admission to the bar upon completion of an LL.M., while in other states, a J.D. is required. The LL.M. degree is viewed with great skepticism by many U.S. educated lawyers as a relatively easy means for foreign lawyers to gain access to bar admission in certain states without the rigorous training in core subjects taught during the first and second years of U.S. law schools. | https://demo.azizisearch.com/starter/google/wikipedia/page/Attorney_at_law_(United_States) |
SOUTH DAKOTA OPPORTUNITIES:
Deputy State’s Attorney – Lincoln County
Lincoln County State’s Attorney’s Office
Lincoln County State’s Attorney, Tom Wollman, welcomes applications for a Deputy State’s Attorney. The Deputy State’s Attorney performs routine professional legal work in the prosecution of civil and criminal crimes, juvenile crimes, and juvenile abuse and neglect cases in Lincoln County. Minimum Qualifications: Graduation from a college of law, attainment of a Juris Doctorate degree from an accredited law school, and admission by the Supreme Court of South Dakota to practice law in the state of South Dakota or be licensed to practice law in any other state and able to take the next available South Dakota bar examination or be a recent or imminent law school graduate, eligible to sit for the next available South Dakota bar examination. Comparable combination of education and experience may be considered. $74,588.80 – $82,326.40 annually. To view a full listing of qualifications and to apply visit: http://www.lincolncountysd.org then click on the Employment tab. Application deadline: March 12th. Contact Human Resources with questions at 605-764-6609. Equal Opportunity Employer.
Position: City Manager
Location: City of Watertown, South Dakota
Population: 22,174
Salary Range: $129,584 to $170,996
General Duties: Under broad policy direction from the City Council, the City Manager serves as Chief Administrative Officer for the City, provides leadership with the development and execution of the City’s strategic vision, provides highly responsible and complex policy support to the Council, directs the work of executive level managers, reviews overall operational performance, and exercises budgetary and contractual control over revenue and expense for the City.
You can view the full job description at https://www.ddahumanresources.com/active-searches.
Minimum Qualifications: Bachelor’s degree from an accredited college or university in Public Administration, Business, Finance, or related field, and a minimum of eight years of increasingly responsible public sector management experience, of which four years is at an executive level, inclusive of executive level financial responsibilities. A master’s degree and a Credentialed Manager through ICMA are preferred.
Apply: Visit https://daviddrown.hiringplatform.com/54959-watertown-city-manager/185775-application-form/en, and complete the process by March 15, 2021. Finalists will be selected on April 5, 2021, and final interviews will be held on April 29 and 30, 2021.
Please direct questions to Liza Donabauer at [email protected] or 612-920-3320 x111. | https://www.sdcounties.org/services/employment-opportunities/ |
Q:
Hank and his old car
I'm sort of struggling with this riddle told to me by a friend:
Hank owns a car. He has been taking good care of his car;
In fact, he has been taking such good care of it that the age of Hank, and the age his car combined is 56 years!
Coincidentally his car is twice as old as Hank was when his car was as old as Hank is now.
How old are Hank and his car?
I'm having trouble figuring out what is easiest way of unraveling the 2nd sentence ("Coincidentally his car(...)").
For example, when representing the age of Hank, his car, and their combined age as $x$, $y$ and $c$ respectively, I get $x+y=c=56$ from the 1st sentence.
Then when trying do the same, the 2nd sentence I get $y = 2(?)$
So what I guess it boils down to is; I simply don't know how to express the 2nd sentence to define $y$.
Please excuse bad grammar and syntax, as english is not my primary language.
A:
We can translate the statements about Hank and his car thusly:
$$\begin{align}
\text{hank}_{\text{now}} + \text{car}_{\text{now}} &= 56 &(1)\\
\text{hank}_{\text{now}} &= \text{car}_{\text{then}} &(2)\\
\text{car}_{\text{now}} &= 2\cdot \text{hank}_{\text{then}} &(3)
\end{align}$$
And we can use the passage of time to convert from "now" to "then":
$$\begin{align}
\text{hank}_{\text{now}} &=\text{time} + \text{hank}_{\text{then}} \\
\text{car}_{\text{now}} &= \text{time} + \text{car}_{\text{then}}
\end{align}$$
Writing $h := \text{hank}_{\text{then}}$, $c := \text{car}_{\text{then}}$, $t := \text{time}$, we have
$$\begin{align}
(t+h) + (t+c) = 2 t + h + c &= 56 &(1^\prime)\\
t+h &= c &(2^\prime)\\
t + c &= 2h &(3^\prime)
\end{align}$$
Solving gives
$$t = 8 \qquad h = 16 \qquad c = 24$$
So,
$$\text{hank}_{\text{then}} = 16 \qquad \text{hank}_{now} = 16 + 8 = 24$$
$$\text{car}_{\text{then}} = 24 \qquad \text{car}_{now} = 24 + 8 = 32$$
Let's check:
[T]he age of Hank (24), and the age his car (32) combined is 56 years!
[H]is car is (32) twice as old as Hank was (16) when his car was (24) as old as Hank is now (24).
That's it!
A:
Let Hank's age now be $x$. We get the following:
$$\begin{array}{c|c|c} &\mbox{Hank}&\mbox{Car} \\\hline\mbox{Now}&x&56-x \\
\mbox{earlier} & 3x-56&x \end{array}$$
The 'Hank-earlier entry' is obtained as follows: The earlier time of interest was when the car was $x$ (Hank's current age). That occurred $(56-x)-x=56-2x$ years ago. That many year's ago, Hank's age would be $x-(56-2x)=3x-56$.
Now we can sort out the second sentence that says "...car is twice as old as Hank was when his car was as old as Hank is now.":
$$56-x=2(3x-56)$$
| |
Myocardin-related transcription factors (MRTFs) play a central role in the regulation of actin expression and cytoskeletal dynamics. Stimuli that promote actin polymerization allow for shuttling of MRTFs to the nucleus where they activate serum response factor (SRF), a regulator of actin and other cytoskeletal protein genes. SRF is an essential regulator of skeletal muscle differentiation and numerous components of the muscle sarcomere, but the potential involvement of MRTFs in skeletal muscle development has not been examined. We explored the role of MRTFs in muscle development in vivo by generating mutant mice harboring a skeletal muscle-specific deletion of MRTF-B and a global deletion of MRTF-A. These double knockout (dKO) mice were able to form sarcomeres during embryogenesis. However, the sarcomeres were abnormally small and disorganized, causing skeletal muscle hypoplasia and perinatal lethality. Transcriptome analysis demonstrated dramatic dysregulation of actin genes in MRTF dKO mice, highlighting the importance of MRTFs in actin cycling and myofibrillogenesis. MRTFs were also necessary for the survival of skeletal myoblasts and for the efficient formation of intact myotubes. Our findings reveal a central role for MRTFs in sarcomere formation during skeletal muscle development and point to the potential involvement of these transcriptional coactivators in skeletal myopathies.
- Received January 27, 2016.
- Accepted June 17, 2016. | http://dev.biologists.org/content/early/2016/06/24/dev.135855 |
Orthodontic Patient Resources during COVID-19 Restrictions
Willamette Dental Group has expanded available appointments to include select orthodontic procedures at select locations. Our teams are busy reaching out to all orthodontic patients to schedule appointments at select offices with priority going to patients with urgent needs.
- In the first two weeks of resumed appointments, we will focus on patients who had recent emergency appointments and patients with appliances that need to be maintained more urgently.
- After seeing patient with urgent orthodontic needs, we will open to scheduling regular, routine ortho visits with priority going to those patients who has scheduled appointments canceled due to COVID-19 restrictions.
- For select orthodontists, you may be asked to travel to a nearby location during this time that is different from your normal ortho office.
At this time, we are postponing orthodontic consultations and banding appointments. Timing for resuming those appointments will be determined based on our ability to maintain social distancing and other safety protocols at each of our offices. For more information on our enhanced in-office safety protocols, please visit our COVID-19 FAQ page.
The resources below are here to help our orthodontic patients avoid any issues during this time. In the event you are experiencing pain from your orthodontic appliances, please contact us so we can schedule an appointment.
How To Reduce Your Risk of Orthodontic Issues
- Avoid hard, sticky, or chewy foods. These items are more likely to cause orthodontic brackets to break or bend wires which could result in pain or discomfort.
- Continue thorough brushing and flossing to reduce the risk of infected gum tissue or dental decay.
- Regularly replace your toothbrush or toothbrush head on an electric toothbrush for more effective brushing.
- For patients with rubber bands – if you have been wearing rubber bands on your braces and it has been longer than 8 weeks since you last saw your orthodontist, you should discontinue wearing them unless specifically contacted by your orthodontist with different instructions. For some orthodontic treatments, unsupervised elastic wear can result in over treatment or other undesirable side effects.
Invisalign Patients
All patients in active Invisalign treatment have been contacted by their Willamette Dental Group ortho office to coordinate the next steps in treatment during this time. If you are an active Invisalign patient and have any additional questions, please call us at 1-855-433-6825. | https://willamettedental.com/help/covid-19-patient-information/orthodontic-patient-resources-during-covid-19-restrictions/ |
On September 26 - 28, 2017, Bali Culinary Pastry School students were given a special opportunity by Classic Fine Foods Indonesia to study a sophiticated pastry demo class using Valrhona and Capfruit products.
On this occasion, Chef Vincent Nigita who had much experiences in pastry world, whom previously worked with Christian Le Squer (3 Michelin stars) and Pierre Gagnaire (3 Michelin Stars) conducted the demo class. It was a pleasant honor to be able to have him share some insights about the making of some patisseries.
The Bali Culinary Pastry School students received a recipe booklet and went through interactive demo with Chef Vincent. There are several prescriptions being demonstrated, such as Buche Coconut and Mango, Choco Passion Entremet, Buche Lemon, Blackcurrant, Raspberry and Vanilla. The highlighted material is frozen fruit purees from Capfruit. Chef Vincent showed how to make high quality cake mix with frozen fruit purees. Cake coating technique using glossy chocolate ganache that can be applied to various forms of cake.
SHARE: | http://baliculinarypastryschool.com/news-event/varlhona |
While hypnosis has many beneficial effects, hypnosis is not a substitute for appropriate medical attention. We do not claim to diagnose, treat, cure, or prevent any disease or illness.
We do not represent our services as any form of medical, behavioral or mental health care, and despite research to the contrary, by law We may make no health benefit claims for my services. When dealing with physical and/or mental illness or disease, always consult a qualified physician or therapist.
Our hypnosis services rendered are held out to the public as nontherapeutic hypnotism, defined as the use of hypnosis to inculcate positive thinking and the capacity for self-hypnosis.
As a hypnosis counselors, We help clients develop and maintain positive thinking. We coach and guide clients toward the achievement of their vocational and avocational goals.
We make no guarantees about hypnosis other than I do my best to produce what I believe are quality hypnosis sessions and recordings. The only one who can guarantee your success is you.
Never listen to hypnosis recordings while driving a car or operating machinery. When listening to hypnosis recordings, choose an environment that is quiet and safe.
Services provided by myself are not intended to take the place of professional counseling or medical or psychological care and should not be used as a substitute for professional diagnosis and treatment.
My instructions and information provided are intended to be educational in nature,
providing information, support, and encouragement.
Please consult your health care provider before making any health care decisions or for guidance about a specific medical condition.
If you are under medical or psychological care, obtain a signed, written referral from your provider(s).
Individual results may vary. | http://www.effectivehypnosisnj.com/disclaimer/ |
The Chinese population is aging rapidly while both the pension systemis underdeveloped and the traditional family care arrangement is in retreat. This article's objective is to assess the relationship between concerns over retirement saving sufficiency and the mental health status of middle-aged and older Chinese adults, and identify the socioeconomic and demographic profile of those with insufficient retirement savings. A survey from about 2000 respondents collected information on self-assessed physical and mental health status based on the EQ-5D-5L framework, self-assessed longevity, retirement plans and financial preparedness and socioeconomic status. Multivariate ordered logistic regressions are used to identify the relationship between mental health status, financial preparedness for retirement and self-assessed longevity, as well as socioeconomic factors associated with mental health status and financial preparedness for retirement respectively. It is found that 59% of the respondents thought that they have not saved, or will not be able to save enough for their retirement. For these people, the odds of having less anxiety or depression are 0.36 (95% CIs: 0.16 0.43) times lower than those who are financially prepared. Havingmore external sources of financial assistance including family and governments, did not help ease mental distress. Rural people are half as likely to be financially prepared for retirement, regardless of whether they remain in rural areas or migrate to cities. Health promotion strategies should consider the role for financial planning in improvingmental health. | https://research.monash.edu/en/publications/retirement-saving-and-mental-health-in-china |
Citation: Gonzalez, V.H., Griswold, T.L., Simoes, M. 2017. On the identity of the adventive species of Eufriesea Cockerell in the USA: systematics and potential distribution of the coerulescens species group (Hymenoptera: Apidae). Journal of Hymenoptera Research. 55:55-102.
Interpretive Summary: Orchid bees are diverse group of brightly colored, largely tropical bees in several genera. They rarely have been found in the USA. One individual of the genus Eulaema was detected in southern Arizona, but no additional individuals have been seen. Another orchid bee species, this one in the genus Euglossa has successfully established in southern Florida. In 2010 two individuals of the genus Eufriesea were found in the Guadalupe Mountains of western Texas and southeastern New Mexico. It was unclear what species they belonged to and whether they were native to the US or accidental, perhaps brought in by a storm. Initially, it seemed likely that this was a new species, but study of similar looking Eufriesea from Mexico suggested it belong to Eufriesea coerulescens. Careful analysis of Mexican specimens indicated that Eufriesea coerulescens was actually a complex of six species. In this study we provide keys to diagnose the six species and describe the three that are new species. We confirm that the individuals from the US are Eufriesea coerulescens. Using climatic variables associated with all locations where Eufriesea coerulescens has been found we determine that the Guadalupe Mountains of the US are not suitable habitat and thus that Eufriesea coerulescens is unlikely to persist there. | https://www.ars.usda.gov/research/publications/publication/?seqNo115=339839 |
Provided is a root and affix combined teaching aid for college English teaching. During combined teaching of the root affixes, teachers need to write the root affixes on blackboards respectively, teaching efficiency is affected, and meanwhile the free combination ability of students cannot be trained. The utility model comprises the following components: a housing, telescopic frame (9), fixing plates (10) are arranged at the upper end and the lower end of the telescopic frame. The telescopic frame is of a structure composed of a set of crossed plates (11) which are arranged on the left side and the right side respectively and rotationally connected through fixing shafts (5). Two supporting rollers (6) are sleeved on the fixed shaft; supports (3) are fixed on the front side and the rear side of the upper fixing plate, two transition rollers (2) are sleeved on the supports and rotatably connected with a bottom shaft (13) on the front side and the rear side of the lower fixing plate, a writing paper tube (8) is sleeved on the bottom shaft, a coil spring (12) is arranged on the bottom shaft and rotatably connected with a pressing plate (1) on the upper fixing plate, and the transitionrollers. The teaching aid is applied to teaching of the root affixes of college English. | |
Alydia Health (formerly known as InPress Technologies, Inc.), a Menlo Park, Calif.–based medical device company developing a technology product for treating Postpartum hemorrhage, one of the leading causes of maternal injury and death during birth, closed an initial $10m in Series B financing.
The round was led by the Global Health Investment Fund (GHIF), with participation from Astia Angels and other existing investors. In conjunction with the funding, Curt LaBelle, M.D., Managing Partner at the Global Health Investment Fund, will join the company’s board of directors.
The company intends to use the funds for a U.S. pivotal study of its innovative technology designed to prevent the maternal morbidity and mortality caused by postpartum hemorrhage.
Led by Anne Morrissey, CEO, Alydia is advancing a product designed to achieve rapid cessation of bleeding by encouraging the uterus to contract quickly and naturally compressing the open blood vessels. In a pilot study of 10 patients published in Obstetrics & Gynecology, the device rapidly and effectively controlled postpartum bleeding, with hemorrhage controlled within minutes for each mother.
Building on the results of this feasibility trial, the company has initiated the PEARLE Study to support its planned 510(k) submission to the U.S. Food and Drug Administration (FDA) for marketing clearance. The study will evaluate the safety and effectiveness of the device in 107 deliveries at leading hospitals in the United States.
Alydia Health is a graduate of the Fogarty Institute for Innovation and the Cal Poly Center for Innovation and Entrepreneurship (CIE). | http://www.finsmes.com/2018/09/alydia-health-raises-10m-in-series-b-funding.html |
Hello Sylvain, thank you for taking the time to have an interview with us. First, tell us a little about you: Who are you, what are you doing?
I’m astrophotographer and landscape photographer. I’m passionate about astronomy since childhood. I had my first telescope at the age of 12. In 2006 I bought a DSLR for astrophotography. It made me discovering the world of traditional, daytime, photography and my love for nature and hiking brought me to landscape photography. Now, when the sky is clear and there is no Moon I go shooting deep sky objects. The remaining time I go hiking in the mountains for landscape photography.
Why astronomy? What fascinates you about stars and nebulae?
That’s a very good question ! In fact, I don’t really know. I think I’ve been always fascinate by what’s beyond… Beyond a forest, beyond a mountain… Beyond what my yes can see. The immensity of the universe offer a large number of possibilities. When we look at a galaxy through a telescope with the eyes, all we can see is a faint blurry spot. It’s far from the vision a photo can offer. This faint spot is constituted by billions of stars. Recent discoveries tell that most star have planets, some of them could be habitable. How much civilization could there be ? And it is just an example.
Unlike most other photographic genres, astronomy only has one sky we all look up to with only one point of view. Do you feel these limitations? Are there things in astrophotography that make up for it?
Sometimes I feel this limitations, asking myself what will I do when I will have photograph every object I can do. But if you consider that I need an entire night for only one photo, I still have a lot of work ! The most important limitation, for me, is the artistic aspect. Astrophotography is very technical and there is a very little place for artistic consideration. You cannot play with depth of field as all objects are seen as if they were at the infinity and compositions are somewhat simple. Most of the time, it consist of placing the object in the center of the frame. I try to play with compositions by placing the subject off-center, following the rule of third, and counterbalancing with something else. A small galaxy in the vastness of a star field (http://fav.me/d3eg0ld), a nebula among dust (http://fav.me/d5crc9k), for example. Deep-sky imaging can be specialized. I made what we call wide field imaging. I use short focal length to shoot wide part of the sky. Well, it should be considered in the astrophotographic point of view, the focal length I use are 387mm and 530mm which are pretty long for traditional photography. Some astrophotographs use filters to make false-color imaging, others use long focal length, several meters, to make detailed images of small object like galaxies and planetary nebula. Progress in digital imaging allow us to make images that were not possible even with professional observatories 10 or 15 years ago. We rediscover some part of the sky.
How do you prepare a shoot? How do you choose your motifs?
I choose my motifs depending on the season. You cannot shoot Orion in summer because it’s not visible. Spring is the galaxy season, summer is for nebulae in the Milky Way. The target must be visible during a large part of the night. I also use astronomy software like Carte du Ciel, wikisky.org or Microsoft WorldWide Telescope to choose the target, to see how I can do the framing and to check its visibility. Other photographer are good sources of inspiration. When the new moon is approaching I begin to watch the weather. When the sky is clear I put all the gears in my car and I go to one of my astronomy spot, in the mountain, where’s there no light pollution.
Probably the used equipment in astrophotography is much more important than in lots of other genres. What hints can you give to beginners?
Yes, equipment is important and it can quickly become expensive. The quality of the sky and the experience of the astrophotgrapher can make a big difference too. But you can begin with a relatively cheap telescope. A 150/750 Newtonian telescope on an equatorial mount and a cheap DSLR is a good way to begin in deep sky imagery. This is the equipment with which I began. It can be progressive : you start to buy the telescope for some hundreds euros and you acquire experience in astronomy observation. I think it is preferable to have a solid experience in general astronomic observation before starting astrophotography. Then you can try photos with the DSLR you already have, or buy a cheap one. All you need at this step is a T2 ring and a photographic adapter. After that and if you’re still addict to imagery, you will certainly change the equatorial mount for a better one because this is the most important gear in the imagery chain. Then you will modify your DSLR to remove the IR-cut filter, add an autoguiding system, change the cheap Newtonian by a high-end apochromatic refractor, change the DSLR by an expensive CCD-camera… Well if you still have money. Don’t forget that, like in other genre, equipment does not make all the job. It need fine tuning. Processing represents a good portion of the time to make an image. The sky is also very important. It will be way more difficult if you leave in a city and you’re not ready to drive hours to reach a place where the sky is dark enough.
What about post-production? What role does it play in your works?
Processing is very important in astrophotography. Almost as much as the acquisitions. But, like in other genres, you will never make a good image with bad acquisitions. Raw exposures are ugly. Very noisy. Details are buried in the noise. Colors are bad, especially with a modified DSLR. Basically, the technique is to make several, tens, exposures of the same object along the night. We apply calibration images on each exposure and we stack them. Stacking drastically decrease noise. We use specialized software for it such as Iris or PixInsight. Once we have the stacked image, we process it by adjusting colors, removing gradient, increasing the dynamic, reducing noise again, etc. The final processing can be made with traditional software like photoshop. I spend hours for the processing. I start it generally the day following the night I was outside making the acquisitions. Then I leave the picture a few days without touching it, to step back and see if my processing is good or not. Most of the times I made adjustments. Sometimes I remake the processing entirely. An image can contains a lot of information : faint objects in the background, details in the highlights. It’s hard to show all this things but it is the more interesting part of the processing job.
Are you inspired by other astro photographers and exchange with them or is it more a genre of lone warriors, each one looking through his own telescope alone?
Other astrophotographer are good source of inspiration. I like browsing their website to find new target and to see how they make. Sharing tips and tricks and critics through forums is very helping. It happens I met an astrophotographer in the field, sometimes fortuitously, but I’m often alone. If I’m not alone I’m with other amateur astronomer who don’t make photos, only visual observation. The loneliness feeling is dominant but sometimes I feel privileged to be crazy enough to spend entire nights alone in the dark.
Last question: What are your dreams and plans for the future? | https://www.zesly.net/en/articles/interview-for-www-kwerfeldein-de/ |
Soccer is a sport that is enjoyed by many different athletes of all ages and all over the world. But it is sometimes difficult to grasp the fundamentals of this game. This article is going to help you learn more about playing this sport properly.
Do not run the ball to score if you are not in good shooting position. Look to see if a teammate is in a favorable position if the field does not have an opening. You shouldn’t try to score the goal yourself; pass the ball to another player instead.
Don’t ever shirk your responsibility to practice. Bring your soccer ball along with you whenever you can, and if you’ve got a few minutes get a little practice in. You can even use the time you spend walking to practice ball control.
If it is getting crowded where you are, move the ball into open space. There will always be a few free seconds before the opposing defenders can cross the field.
Balls that are lofted can be difficult to control. Passes that are low are the best approach if a defender is in hot pursuit. Lofted balls are more appropriate for making long passes to a teammate who is located in an area that is not so crowded.
Come up with strategies with the help of your teammates. They need to know what you’ll be doing with the ball so they’re able to get to it at the right time. If you are doing the same moves, switch them up to confuse your opponents.
If you want to improve your soccer skills you need to make sure you practice often. Being a good player doesn’t happen instantly. Daily practice is essential to becoming great. Practice each soccer skill daily. Practice your strong skills too as they can always be bettered.
If you’re in the center of the field, look at what is happening on either end. You should be prepared to receive a pass from one end and transfer the ball immediately to the other end. Be aware of the location of your teammates and defenders on the field.
Soccer Team
Fake out an approaching defender by pretending to pass the soccer ball to another player. By doing this, you will make him pause for a second, which will allow you time to decide your best strategy moving forward. Therefore, don’t be afraid to use a lot of animation, and your game will significantly improve.
If you want to get on a soccer team, you have to show that you can be combative. Never quit, defend and attack, work with your team, run down and up the field, and show off an attitude that’s inspiring. Devotion to your soccer team and a will to succeed helps your coach know to pick you.
To help you stay physically fit, run at least three miles daily. Your cardiovascular system needs to be in tip top shape due to all the running soccer has you doing. You improve your stamina and your endurance by running or jogging a few miles each day. Try running in different locations to keep your routine from growing old and stale.
If you hold possession of the ball with a defender approaching you, give him the impression that you are passing the ball. They will likely pause to try to stop the ball, giving you a moment to decide on your next move. Use your arms to distract him.
When it comes to soccer, making quick decisions are vital. Therefore, practice set plays so you can improve at this. An example would be working with your teammates to practice corner kicks or direct shots. Whenever you regularly practice these particular players, you will be able to make better decisions during a game. As a result, your winning chances are increased.
You need to put the team’s goals before your own to achieve success. With the full team on board, a soccer game can be a successful one. This is why team goals matter, and they should be a priority for you.
When trying to make the soccer team, be sure to put your best moves on display and steer clear of those you have yet to master. If you are uncertain you are able to do something well, do not try it until after you are playing on the team.
If you’re looking to improve your skills, play soccer indoors whenever you get a chance. It will help you keep your skills from becoming rusty, even though it is played on a smaller field. This forces you to improve ball control and focus. You will also have to make quicker decisions. This results in better performance when you play outdoors again.
Watching a soccer match will help you figure out many of the nuances of the game. This will aid in your understanding of the rules; plus, it is a great demonstration of the dynamics of the game when played properly. Watching soccer is not a replacement for actual playing time, but it can be an important aspect of learning the game.
When you are trying out for a soccer team, make sure that you show off moves you know well and avoid doing things that you are not totally comfortable with. If you don’t think you’re able to do a move, you shouldn’t try it out until you’ve gotten onto the team.
Winning is about adopting a positive attitude. You have to believe in your skills and those of your team to have the confidence necessary to win. When you have a positive attitude, you’re able to cheer your team to success.
Millions of people around the world love soccer for its entertainment and for the wonderful exercise it involves. It may be that you wish you could enjoy the game even more with some additional information. Now, after absorbing all this information, you should be well-versed in the language of soccer.
Ask all of the parents to purchase a separate soccer ball for practice. This way each child has a soccer ball to work with at home. Make sure you carry some extra soccer balls during practice if a player accidentally forgets to bring his ball. To keep this from becoming habit, make the person who forgot the ball go through a few additional pass plays.
Many people wish to become more knowledgeable about
joker gaming, but they may not know how to do that. This article, luckily, is exactly what you need for that. All you need to do now is put it into action. | https://ufabetcall.com/become-a-better-soccer-player-with-these-great-tips/ |
This square black Bandini Rebari cushion cover has been crafted in India from Khadi fabric, with hand-spun and woven embroidery in ivory stripes with handcrafted tassel detailing.
Each Rebari cushion cover is crafted entirely by local artisans in the villages of Gujurat using hand looms and traditional embroidery and dying techniques; the handcrafted touch is especially evident in the tassel adornments that scatter across the design’s surface.
Khadi cloth is a traditional hand-spun cotton Indian textile that was championed by Mahatma Gandhi, who opposed the Industrial Revolution in India and pioneered the skills of hand-weavers and loom workers.
Beautifully soft and premium quality, the rectangular Rebari cushion cover would enhance sofas, chairs and beds with its ivory and black multi-stripe colour scheme and unique, personal touch. | https://www.conranshop.co.uk/band-reb-cc-blk-60x60.html |
Digital identity management is how you develop and manage your digital reputation and project yourself online.
You might have separate digital identities for different purposes and audiences, distributed across a range of platforms and media. You need to think about how you make these work for you in your personal and professional life.
Reflect on your digital identity by asking:
- Which social media and other platforms suit me for personal and professional use?
- Do I keep my profiles separate, and use different apps for different purposes, or aim to make them work together?
- How do I manage my assets such as profiles, records of achievement, contacts and networks to achieve my personal goals? | https://library.leeds.ac.uk/info/99041/digital_capabilities/235/identity_and_wellbeing |
Standing Frame Program Can Up Motor Function in Progressive MS
FRIDAY, July 12, 2019 -- For patients with severe progressive multiple sclerosis, a standing frame program can increase motor function, according to a study published in the August issue of The Lancet Neurology.
Jennifer Freeman, Ph.D., from the University of Plymouth in the United Kingdom, and colleagues conducted a randomized superiority trial involving people with progressive multiple sclerosis and severe mobility impairment. After baseline assessment, participants were randomly assigned to either the standing frame program plus usual care or usual care alone (71 and 69 patients, respectively). The intervention included two home-based physical therapy sessions to set up the standing frame program supported by six follow-up telephone calls. Over 20 weeks, participants were asked to stand for 30 minutes, three times per week.
The researchers found that compared with usual care alone, use of the standing frame resulted in a significant increase in the Amended Motor Club Assessment (AMCA) score, with a fully adjusted between-group difference in AMCA score of 4.7 points at 36 weeks; a priori, a difference of 9 points was considered clinically meaningful. There was a disparity between the groups in the frequency of short-term musculoskeletal pain (41 and 22 percent of adverse events in the standing frame and usual care groups, respectively), which was potentially due to the intervention.
"We hope this intervention can now be offered and reimbursed more widely as a management option for this population," the authors write.
© 2020 HealthDay. All rights reserved.
Posted: July 2019
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Whatever your topic of interest, subscribe to our newsletters to get the best of Drugs.com in your inbox. | https://www.drugs.com/news/standing-frame-program-can-up-motor-function-progressive-ms-83786.html |
A $1.2 million federal grant to research the effects of managing diabetes online has been given to the Palo Alto Medical Foundation and its Research Institute, according to the medical center.
The study will examine the impact of providing online disease management to 400 patients who will be split into experimental and control groups, said Dr. Paul Tang, the study's principal investigator.
“Traditionally, patients receive advice and instructions from their health care team,” Tang said.
In the study, patients will be provided with online access to their health data, health information resources for their individual care plan, self-management tools and a care manager to help them manage their diabetes, according to the medical center. | https://www.sfexaminer.com/news/foundation-gets-1-2m-for-diabetes-research/ |
Department confident it can reverse small business failure
The Department of Small Business Development is working towards reversing the high failure rate of new small businesses.
“We are determined to create a conducive environment for the development and growth of small businesses and cooperatives through the provision of enhanced financial and non-financial support services, competitiveness, market access, promotion of entrepreneurship, advancing localisation and leveraging on public and private procurement,” Minister of Small Business Development Lindiwe Zulu said.
Speaking at the 2014 Consumer Goods Council Summit in Midrand on Tuesday, she said her department was concerned that small businesses had a high failure rate.
“Researchers tell us that the failure rate for new businesses is almost 80 percent in the first year, and only about half of those who survive remain in business for the next five years.
“We are confident that together, we will be able to help reverse this trend,” Minister Zulu said.
She said her department would lead an integrated approach on the promotion and development of small businesses and cooperative through a focus on the economic and legislative drivers that would stimulate entrepreneurship to contribute to radical economic transformation.
“Together with our partners in government, we will create a conducive environment for the success of small enterprises and cooperatives and to provide a market for these enterprises through public procurement,” Minister Zulu said.
The Department of Small Business Development had developed a number of programmes that would assist small enterprises and co-operatives.
The programmes included centres for entrepreneurship, micro franchising, incubation support and cooperatives supplier.
Other programmes included red tape reduction which was aimed at addressing the regulatory burden and B’avumile skills, an enhancement programme aimed at enhancing the skills of women to produce quality and commercially viable cultural products for participation in major local and international markets.
“For the SMMEs and Cooperatives to play their envisaged role in the development of the economy, we must take into account that the issues of standards and quality go hand in hand with the development and growth sustainable enterprises,” she said.
Minister Zulu said consumers would not buy goods that were not of good quality.
“Even for the local market, products and services need to comply with certain compulsory technical regulations either set by government or private specifications set by those who procure these products and services,” she said.
Minister Zulu called for small enterprises to comply with both local and international standards. – SAnews.gov.za
Photo caption: Minister of Small Business Development Lindiwe Zulu.
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In April, Vodacom announced that it had been awarded... | http://www.rnews.co.za/article/department-confident-it-can-reverse-small-business-failure |
On Monday evening, Donald Trump spoke to reporters outside the White House and suggested that the UK might not be able to trade with the US. When asked about Theresa May’s Brexit deal, the former reality television star said that it sounded like a ‘great deal for the EU’ and that he would have to look at whether or not the UK is allowed to trade with America. The UK government was understandably infuriated by the comments and moved quickly to say that Trump is incorrect.
However, the comments certainly weakened May’s hand in face of stiff opposition from both sides of the House and City traders clearly felt that Trump’s intervention was significant, as sterling opened weaker against the dollar and continued moving south throughout the day. The pound lost some ground against the euro too, although these moves were more sedate.
Trump’s tongue was off again, as he threatened to impose fresh tariffs on goods from China. He said that it was ‘highly unlikely’ that he would accept an offer from the Chinese president Xi Jinping to avert new levies that are scheduled to come into force next January. Speaking to the Wall Street Journal, Trump said that he would probably increase existing tariffs on $200 billion of Chinese imports in January, from 10% to 25%.
Apple’s shares were hit following the comments, as the new tariffs would affect iPhones made in China. Earlier this year, Apple was celebrating becoming the first US company to be worth more than one trillion dollars, but it has since lost a large chunk of that. The Dutch financial services group, Rabobank, said that the global economy could suffer over the next decade if the trade war escalates; it estimates that a total of 0.7% could be wiped of growth by 2030 unless the two sides reach an agreement.
Today’s headline release is the second estimate of the US GDP growth rate for the third quarter of 2018. Last quarter, growth surged to an impressive 4.2% but this time around it is expected to be more modest at 3.5%. Still, that is far better than the UK and EU GDP at the moment. We will also see October’s new home sales in America.
With so much going on at the moment – and no signs of anything abating – do make sure your budget is protected. A forward contract fixed the same exchange rate for up to a year, no matter what the markets do. Speak to your Personal Trader on 020 7898 0541 to find out more. | https://www.smartcurrencyexchange.com/currency-note/currency-note/donald-trump-comments-weaken-pound/ |
Deputized by the Public Security Director Major General Fadel AL-Hmoud, the Assistant Public Security Director for Judicial Affairs Brigadier General Walid Battah inaugurated a specialized workshop to discuss the draft by-law for the protection of witnesses and reporting persons.
During the workshop organized by NCFA in cooperation with UNICEF and the European Commission’s Project for the Technical Assistance and Information Exchange (TAIEX), Battah emphasized that by-law discussions complement efforts exerted by the relevant entities to introduce a family protection system through a professional and high-quality participatory work in line with Jordan’s commitment to international contractual obligations. Under these obligations, Jordan is committed to providing necessary legal protection for witnesses and reporting persons in family violence cases if subjected to any sort of threat.
On his part, NCFA’s Acting Secretary-General Mohammad Miqdady indicated that the preparation of the draft by-law (issued pursuant to the Protection against Family Violence Law No. 15 for the year 2017) is of great importance as it aims to address the gaps, hindrances and impacts that might affect witnesses or reporters of family violence cases which may prevent them from reporting or testifying. It is this particular purpose that necessitates the enactment of a special legislation that would protect witnesses, reporting persons and those around them.
As Miqdady added “the endorsement of this bylaw will effectively help scale up the level of services offered by the relevant entities to sustain family stability which is the cornerstone of society”.
The bylaw, as Midady pointed out, was prepared by NCFA in cooperation with UNICEF and national institutions and bodies including the Judicial Council, the Government Coordinator for Human Rights’ Office, Ministry of Social Development, Ministry of Justice, Public Security Directorate/Family Protection Department, MIZAN Law Group for Human Rights, Jordan Society for Protecting Family Violence Victims, Jordanian Women’s Union, Penal Reform International (PRI) and the United Nations Office on Drugs and Crime.
“The endorsement of this by-law will help promote confidence in justice”, said Paula Jacks, an international expert in this field, noting that Jordan is a pioneer in the area of childhood and family affairs. | http://ncfa.org.jo:85/NCFA/en/content/NCFA-organizes-specialized-workshop-Witness-and-Reporting-Persons-Protection-Draft-law |
Directions:
Take one (1) lozenge daily with or without food, or as recommended by a healthcare practitioner.
Place lozenge in mouth and allow to dissolve, then swallow
Keep out of reach of children. Do not exceed recommended dose.
When using nutritional supplements, please consult with your physician if you are undergoing treatment for a medical condition or if you are pregnant or lactating.
A food supplement should not be used as a substitute for a varied and balanced diet and a healthy lifestyle. Store tightly closed in a cool, dry place
Ingredients: Vitamin B12 (as methylcobalamin), mannitol, sorbitol, microcrystalline cellulose, vegetable stearate, croscarmellose sodium, natural strawberry flavor
Nutriitonal Information:
Amount per serving:
Vitamin B12 (as methylcobalamin) 500 mcg
Disclaimer
While Evolution Organics strives to ensure the accuracy of its product images and information, some manufacturing changes to packaging and/or ingredients may be pending update on our site. Although items may occasionally ship with alternate packaging, freshness is always guaranteed. We recommend that you read labels, warnings and directions of all products before use and not rely solely on the information provided by Evolution Organics. This product is not intended to diagnose, treat, cure, or prevent any diseases. | https://www.evolutionorganics.co.uk/brands/life-extension/life-extension-vitamin-b12-100-lozenges/ |
Collective Magic is a powerful form of witchcraft constantly shown by the Bonum Coven throughout the book series. This connects and pools powers and strength of the members of a coven together, allowing them to become stronger and perform amazing feats of witchcraft without exhaustion. Collective Magic is unique to the particular coven, meaning that the strength of the members defines their collective strength together, such as the Bonum Power.
Some covens gain the collective ability of telepathy and the leader is able to manifest forms of sensing.
A downside of Collective Magic, which is present without it being channeled, is that if one member dies, the remaining become weaker.
Collective Magic is passed down through generations of covens, but instead of the power being taken away, the previous coven's power simply grows fainter. | http://the-coven.wikia.com/wiki/Collective_Magic |
The statistics according to the Center for Disease Control and Prevention claims that almost 30 to 40% of men and women sleep less than 7 hours every night. 1/3 of adults falls asleep unintentionally during the day for the past 30 days. Ironically, more than 41,000 people become killed or injured because of falling asleep or nodding off behind the wheel every year.
The statistics are pretty shocking, we must admit. It’s not easy to sleep for solid 7 hours, especially these days when we’re stressed and worried about everything. We’re surrounded by computers and numerous other devise which emit light and mess with our circadian rhythms, causing constant problems.
Exercise early in the day.
According to experts, we need to have at least three hours of workout between our bedtime and workouts. The best thing we can do is to exercise when we get up in the morning. It doesn’t matter how old we are, it has to be a priority because it will offer us numerous priorities. It will definitely improve the quality of our sleep.
Skip the alcohol.
One or two drinks before you go to bed may help you fall asleep faster, but in several hours, you’ll be awake and feel restless. You may also be awake before your normal time to be awake. You’ll sleep less and have a restless sleep. That’s it.
Eliminate distractions.
Your computer, your TV and your cell phone need to be away from you so that you can rest well. Make sure they’re out of your sight. The light these objects emit decrease our levels of melatonin. If you have a practice to fall asleep with a little noise in the background, try to choose some white sound or some soothing music.
Rethink naps.
In case you feel really tired, one short nap from 10 to 20 minutes can be very helpful for your organism. Do that if you feel like you’ll fall asleep behind the wheel or at the desk. But, be very careful. A nap before dinner can disturb your possibility to fall asleep as you usually do, so you’ll fall asleep later and you’ll be very tired the following day.
Meditate before bedtime.
One very powerful thing that can help you relax, clear all your distractions and thoughts and relax your mind is meditations. There’s an application called Headspace that you can try. It’s really good and it can really help you.
Have sex.
Having sex can help you relax too much, but at the same time, it can also make you tired. We need these two very important ingredients in order to have a healthy sleep. In the case of men, sex releases a mix of hormones after an orgasm. That promotes relaxation, reduces their levels of anxiety and improves their sleep. | https://www.organichealthcorner.com/six-tips-improve-sleep/ |
I have a friend who falls asleep at the drop of a hat; 1 minute we are gisting, and the next minute she is off. It always amazes me and sometimes I envy her especially those nights I keep tossing and turning trying to sleep.Lack of sleep takes a toll on our health, our mood, even our job performance; so there is a need to learn how to fall asleep fast without medication.
Here are a few tips to fall asleep fast.
1.Create a sleep schedule and stick to itSet a bedtime schedule. Try to going to bed and waking up at the same time every day as it helps your body to know when it should be tired. This might be a difficult task but maintaining a regular sleep time will be beneficial in the long run.
2.Take a bathTaking a warm shower will help you relax and help your body temperature fall faster, making you sleepy. It is best to take a bath about 30-60 minutes before bedtime.
3.Work on your bedroomKeeping your room dark and quiet could help. Close the blinds and switch off the lights, even a small amount of light can interfere with sleep hormones and stimulate the brain. Also remove all electronics (Television, Laptop, Smartphone, etc.) in your room, they will keep you awake.
4.Drink a soothing beverageDrinking herbal tea or a glass of warm milk could relax your body and mind helping you to wind down but stay away from Caffeine or Alcohol as they would keep you awake.
5.Get comfortableYou need a comfortable position to sleep fast. Your bed has to be comfortable and supportive as well as your pillow. Also, wear comfortable nightwear to bed; cotton works best.
6.ExerciseExercising during the day could help you relax at night time but don’t exercise within 3 hours before bedtime.Finally, try to relax and forget the day and your plans for the next day. | https://www.femininelounge.com/blog/how-to-fall-asleep-fast |
Intake meetings are an obligatory part of the recruiting process, and it can sometimes be easy to let them be just that—obligatory. You and the client both yawn as you go through a perfunctory checklist, discuss dates and compensation, and hang up, both parties feeling unsure about what comes next.
Wouldn’t it be great if you could find a way to make intake meetings a benefit for both you and your clients? To actually be an additional tool in your belt, or even your competitive edge?
Intake meetings are great for establishing the requirements and expectations for a position, but they can also help you to:
Remember, intake conversations at their worst are a checklist. You should not go in with the intention to fill out a form, but instead to lead a guided conversation about the hiring manager’s needs. Often, they don’t know what they are looking for, and even if they do, they don’t know how to describe it, so it’s your job to coax it out of them by asking the right questions.
Go in with a plan, and let a hiring intake form be a tool, not the focus. Think of it as a strategy meeting instead of a fill-in-the-blanks exercise, and the return on your meetings will be much higher.
Research
Through careful research, you'll be able to ask the right questions, and as a result, the client will appreciate your diligence and professionalism. Here are some good things to look up:
Review past hires
If you’ve worked with the company before, take a look at other positions you or your team members may have filled for them in the past. Were there any bottlenecks in previous projects? Reviewing past projects gives you an opportunity to address problems and roadblocks so you can analyze how to avoid them, honing your process with that particular client and fostering a great working relationship in the process. Use an intake meeting as an opportunity to grow as a strategic team with your client, and they will keep coming back again and again. The more you can get them to invest in the relationship, the more reluctant they will be to leave.
If you have filled this particular role before, take a look at past candidates that you’ve placed. It can be helpful to go back and look for instances where other candidates didn’t exactly match the requirements but still turned out to be great hires. Hiring managers often have lofty ideas about finding a unicorn, and it can be really helpful to come prepared to manage those expectations and call attention to previous successful hires.
Ask analytical questions
You know what you need to know (“Dates, skills, and salary. Next!”), but if your aim is to get in, fill out a sheet, and get out, then that sheet is all you’re going to leave with. Rather than checking the boxes with your head buried in a list, connect with the hiring manager and investigate what their needs are. With the right follow-up questions, you can help a client or hiring manager articulate the intangibles that they are looking for in a candidate:
Question: What does the position entail?
Follow-ups: Why is this position open? Why is this position important? What do you expect out of a new hire after 90 days?
Question: What department will the position be in?
Follow-ups: What does the team look like now? What are the members of the team like? How will the new hire communicate with and depend on other members of the team? Of the company? Who will they report to?
Question: What skills and experience are necessary for this position?
Follow-ups: What would make you decline a candidate immediately? What skills and qualifications are a “nice-to-have” — can we bend the requirements in any way? Is it a must to have out-of-the-box experience, or could the right candidate be someone who can grow into the position?
Question: What is the compensation structure?
Follow-ups: Why do people like working here? What is the career development path like?
With follow up questions, the intent is to gather as much information as possible. Hiring managers aren't going to know what information you'll need, so it's on you to fill in those vital blanks. The answers to these questions will give you a more three-dimensional picture of the position, team, and company, and that will help you find a three-dimensional candidate who will fit in based on more than just their resume.
Work with them to set their expectations
Remember, you bring skills and experience to the table. You’re not an order-taker; you’re a partner in your client’s hiring mission. They come to you because you have the expertise. Take the opportunity to give them a little window into how you work, and the lengths to which you go to find them great talent. Not only will this help keep their expectations realistic, but it will also demonstrate your mastery of the recruiting process and remind them why they reached out to you in the first place.
Some things to go over:
Consider putting together a one-page document outlining your practice and process that you can go over with the client. This adds credibility to your process — showing them that you’ve done it so much, you have it down to a science.
Get their commitment
Inspire a sense of urgency in the hiring manager, because talent is scarce, and if the right candidate comes up, both of you need to move fast. It’s important that they understand that a quick recruiting process yields better and more qualified candidates. Providing a positive candidate experience is key to your success, and you shouldn’t have to sacrifice that because of a busy hiring manager.
(Side note: for better contract execution and response time when you reach out to a client, make sure that your emails have action items listed; bulleted lists are very helpful for busy people. Paragraphs of requests can be overwhelming and cause them to say, “I will get to this later.”)
Consider setting up a response time agreement—decide upon a timeframe in which it is appropriate to expect that they will respond (24-48 hours is agreeable to most). Or, set weekly check-ins to help you stay in regular contact with them.
Intake meetings are a necessity, but they don’t have to be mundane. With the right preparation and execution, they can be an opportunity for you to clearly understand a clients’ expectations and inspire confidence in and respect for your recruiting process. The more you can help a client to isolate what they are looking for, the happier you’ll both be with the outcome of intake meetings, and that’s the kind of experience that will keep clients coming back every time. | https://catsone.com/blog/2019/04/15/next-level-intake-meetings/ |
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