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Title: Efficient algorithms to discover alterations with complementary functional association in cancer,
Abstract: Recent large cancer studies have measured somatic alterations in an
unprecedented number of tumours. These large datasets allow the identification
of cancer-related sets of genetic alterations by identifying relevant
combinatorial patterns. Among such patterns, mutual exclusivity has been
employed by several recent methods that have shown its effectivenes in
characterizing gene sets associated to cancer. Mutual exclusivity arises
because of the complementarity, at the functional level, of alterations in
genes which are part of a group (e.g., a pathway) performing a given function.
The availability of quantitative target profiles, from genetic perturbations or
from clinical phenotypes, provides additional information that can be leveraged
to improve the identification of cancer related gene sets by discovering groups
with complementary functional associations with such targets.
In this work we study the problem of finding groups of mutually exclusive
alterations associated with a quantitative (functional) target. We propose a
combinatorial formulation for the problem, and prove that the associated
computation problem is computationally hard. We design two algorithms to solve
the problem and implement them in our tool UNCOVER. We provide analytic
evidence of the effectiveness of UNCOVER in finding high-quality solutions and
show experimentally that UNCOVER finds sets of alterations significantly
associated with functional targets in a variety of scenarios. In addition, our
algorithms are much faster than the state-of-the-art, allowing the analysis of
large datasets of thousands of target profiles from cancer cell lines. We show
that on one such dataset from project Achilles our methods identify several
significant gene sets with complementary functional associations with targets. | [
0,
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1,
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] |
Title: Laplace operators on holomorphic Lie algebroids,
Abstract: The paper introduces Laplace-type operators for functions defined on the
tangent space of a Finsler Lie algebroid, using a volume form on the
prolongation of the algebroid. It also presents the construction of a
horizontal Laplace operator for forms defined on the prolongation of the
algebroid. All of the Laplace operators considered in the paper are also
locally expressed using the Chern-Finsler connection of the algebroid. | [
0,
0,
1,
0,
0,
0
] |
Title: Recurrent Neural Filters: Learning Independent Bayesian Filtering Steps for Time Series Prediction,
Abstract: Despite the recent popularity of deep generative state space models, few
comparisons have been made between network architectures and the inference
steps of the Bayesian filtering framework -- with most models simultaneously
approximating both state transition and update steps with a single recurrent
neural network (RNN). In this paper, we introduce the Recurrent Neural Filter
(RNF), a novel recurrent variational autoencoder architecture that learns
distinct representations for each Bayesian filtering step, captured by a series
of encoders and decoders. Testing this on three real-world time series
datasets, we demonstrate that decoupling representations not only improves the
accuracy of one-step-ahead forecasts while providing realistic uncertainty
estimates, but also facilitates multistep prediction through the separation of
encoder stages. | [
1,
0,
0,
1,
0,
0
] |
Title: Counterexample-Guided k-Induction Verification for Fast Bug Detection,
Abstract: Recently, the k-induction algorithm has proven to be a successful approach
for both finding bugs and proving correctness. However, since the algorithm is
an incremental approach, it might waste resources trying to prove incorrect
programs. In this paper, we propose to extend the k-induction algorithm in
order to shorten the number of steps required to find a property violation. We
convert the algorithm into a meet-in-the-middle bidirectional search algorithm,
using the counterexample produced from over-approximating the program. The
preliminary results show that the number of steps required to find a property
violation is reduced to $\lfloor\frac{k}{2} + 1\rfloor$ and the verification
time for programs with large state space is reduced considerably. | [
1,
0,
0,
0,
0,
0
] |
Title: Andreev Reflection without Fermi surface alignment in High T$_{c}$-Topological heterostructures,
Abstract: We address the controversy over the proximity effect between topological
materials and high T$_{c}$ superconductors. Junctions are produced between
Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta}$ and materials with different Fermi
surfaces (Bi$_{2}$Te$_{3}$ \& graphite). Both cases reveal tunneling spectra
consistent with Andreev reflection. This is confirmed by magnetic field that
shifts features via the Doppler effect. This is modeled with a single parameter
that accounts for tunneling into a screening supercurrent. Thus the tunneling
involves Cooper pairs crossing the heterostructure, showing the Fermi surface
mis-match does not hinder the ability to form transparent interfaces, which is
accounted for by the extended Brillouin zone and different lattice symmetries. | [
0,
1,
0,
0,
0,
0
] |
Title: Structural Data Recognition with Graph Model Boosting,
Abstract: This paper presents a novel method for structural data recognition using a
large number of graph models. In general, prevalent methods for structural data
recognition have two shortcomings: 1) Only a single model is used to capture
structural variation. 2) Naive recognition methods are used, such as the
nearest neighbor method. In this paper, we propose strengthening the
recognition performance of these models as well as their ability to capture
structural variation. The proposed method constructs a large number of graph
models and trains decision trees using the models. This paper makes two main
contributions. The first is a novel graph model that can quickly perform
calculations, which allows us to construct several models in a feasible amount
of time. The second contribution is a novel approach to structural data
recognition: graph model boosting. Comprehensive structural variations can be
captured with a large number of graph models constructed in a boosting
framework, and a sophisticated classifier can be formed by aggregating the
decision trees. Consequently, we can carry out structural data recognition with
powerful recognition capability in the face of comprehensive structural
variation. The experiments shows that the proposed method achieves impressive
results and outperforms existing methods on datasets of IAM graph database
repository. | [
1,
0,
0,
1,
0,
0
] |
Title: Polynomiality for the Poisson centre of truncated maximal parabolic subalgebras,
Abstract: We show that the Poisson centre of truncated maximal parabolic subalgebras of
a simple Lie algebra of type B, D and E_6 is a polynomial algebra.
In roughly half of the cases the polynomiality of the Poisson centre was
already known by a completely different method.
For the rest of the cases, our approach is to construct an algebraic slice in
the sense of Kostant given by an adapted pair and the computation of an
improved upper bound for the Poisson centre. | [
0,
0,
1,
0,
0,
0
] |
Title: Row-Centric Lossless Compression of Markov Images,
Abstract: Motivated by the question of whether the recently introduced Reduced Cutset
Coding (RCC) offers rate-complexity performance benefits over conventional
context-based conditional coding for sources with two-dimensional Markov
structure, this paper compares several row-centric coding strategies that vary
in the amount of conditioning as well as whether a model or an empirical table
is used in the encoding of blocks of rows. The conclusion is that, at least for
sources exhibiting low-order correlations, 1-sided model-based conditional
coding is superior to the method of RCC for a given constraint on complexity,
and conventional context-based conditional coding is nearly as good as the
1-sided model-based coding. | [
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0
] |
Title: Planetesimal formation by the streaming instability in a photoevaporating disk,
Abstract: Recent years have seen growing interest in the streaming instability as a
candidate mechanism to produce planetesimals. However, these investigations
have been limited to small-scale simulations. We now present the results of a
global protoplanetary disk evolution model that incorporates planetesimal
formation by the streaming instability, along with viscous accretion,
photoevaporation by EUV, FUV, and X-ray photons, dust evolution, the water ice
line, and stratified turbulence. Our simulations produce massive (60-130
$M_\oplus$) planetesimal belts beyond 100 au and up to $\sim 20 M_\oplus$ of
planetesimals in the middle regions (3-100 au). Our most comprehensive model
forms 8 $M_\oplus$ of planetesimals inside 3 au, where they can give rise to
terrestrial planets. The planetesimal mass formed in the inner disk depends
critically on the timing of the formation of an inner cavity in the disk by
high-energy photons. Our results show that the combination of photoevaporation
and the streaming instability are efficient at converting the solid component
of protoplanetary disks into planetesimals. Our model, however, does not form
enough early planetesimals in the inner and middle regions of the disk to give
rise to giant planets and super-Earths with gaseous envelopes. Additional
processes such as particle pileups and mass loss driven by MHD winds may be
needed to drive the formation of early planetesimal generations in the planet
forming regions of protoplanetary disks. | [
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1,
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] |
Title: Hierarchical Bloom Filter Trees for Approximate Matching,
Abstract: Bytewise approximate matching algorithms have in recent years shown
significant promise in de- tecting files that are similar at the byte level.
This is very useful for digital forensic investigators, who are regularly faced
with the problem of searching through a seized device for pertinent data. A
common scenario is where an investigator is in possession of a collection of
"known-illegal" files (e.g. a collection of child abuse material) and wishes to
find whether copies of these are stored on the seized device. Approximate
matching addresses shortcomings in traditional hashing, which can only find
identical files, by also being able to deal with cases of merged files,
embedded files, partial files, or if a file has been changed in any way.
Most approximate matching algorithms work by comparing pairs of files, which
is not a scalable approach when faced with large corpora. This paper
demonstrates the effectiveness of using a "Hierarchical Bloom Filter Tree"
(HBFT) data structure to reduce the running time of
collection-against-collection matching, with a specific focus on the MRSH-v2
algorithm. Three experiments are discussed, which explore the effects of
different configurations of HBFTs. The proposed approach dramatically reduces
the number of pairwise comparisons required, and demonstrates substantial speed
gains, while maintaining effectiveness. | [
1,
0,
0,
0,
0,
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] |
Title: Pre-freezing transition in Boltzmann-Gibbs measures associated with log-correlated fields,
Abstract: We consider Boltzmann-Gibbs measures associated with log-correlated Gaussian
fields as potentials and study their multifractal properties which exhibit
phase transitions. In particular, the pre-freezing and freezing phenomena of
the annealed exponent, predicted by Fyodorov using a modified
replica-symmetry-breaking ansatz, are generalised to arbitrary dimension and
verified using results from Gaussian multiplicative chaos theory. | [
0,
1,
0,
0,
0,
0
] |
Title: Learning Combinatorial Optimization Algorithms over Graphs,
Abstract: The design of good heuristics or approximation algorithms for NP-hard
combinatorial optimization problems often requires significant specialized
knowledge and trial-and-error. Can we automate this challenging, tedious
process, and learn the algorithms instead? In many real-world applications, it
is typically the case that the same optimization problem is solved again and
again on a regular basis, maintaining the same problem structure but differing
in the data. This provides an opportunity for learning heuristic algorithms
that exploit the structure of such recurring problems. In this paper, we
propose a unique combination of reinforcement learning and graph embedding to
address this challenge. The learned greedy policy behaves like a meta-algorithm
that incrementally constructs a solution, and the action is determined by the
output of a graph embedding network capturing the current state of the
solution. We show that our framework can be applied to a diverse range of
optimization problems over graphs, and learns effective algorithms for the
Minimum Vertex Cover, Maximum Cut and Traveling Salesman problems. | [
1,
0,
0,
1,
0,
0
] |
Title: Critical well-posedness and scattering results for fractional Hartree-type equations,
Abstract: Scattering for the mass-critical fractional Schrödinger equation with a
cubic Hartree-type nonlinearity for initial data in a small ball in the
scale-invariant space of three-dimensional radial and square-integrable initial
data is established. For this, we prove a bilinear estimate for free solutions
and extend it to perturbations of bounded quadratic variation. This result is
shown to be sharp by proving the unboundedness of a third order derivative of
the flow map in the super-critical range. | [
0,
0,
1,
0,
0,
0
] |
Title: Value Propagation for Decentralized Networked Deep Multi-agent Reinforcement Learning,
Abstract: We consider the networked multi-agent reinforcement learning (MARL) problem
in a fully decentralized setting, where agents learn to coordinate to achieve
the joint success. This problem is widely encountered in many areas including
traffic control, distributed control, and smart grids. We assume that the
reward function for each agent can be different and observed only locally by
the agent itself. Furthermore, each agent is located at a node of a
communication network and can exchanges information only with its neighbors.
Using softmax temporal consistency and a decentralized optimization method, we
obtain a principled and data-efficient iterative algorithm. In the first step
of each iteration, an agent computes its local policy and value gradients and
then updates only policy parameters. In the second step, the agent propagates
to its neighbors the messages based on its value function and then updates its
own value function. Hence we name the algorithm value propagation. We prove a
non-asymptotic convergence rate 1/T with the nonlinear function approximation.
To the best of our knowledge, it is the first MARL algorithm with convergence
guarantee in the control, off-policy and non-linear function approximation
setting. We empirically demonstrate the effectiveness of our approach in
experiments. | [
1,
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1,
0,
0
] |
Title: Collect at Once, Use Effectively: Making Non-interactive Locally Private Learning Possible,
Abstract: Non-interactive Local Differential Privacy (LDP) requires data analysts to
collect data from users through noisy channel at once. In this paper, we extend
the frontiers of Non-interactive LDP learning and estimation from several
aspects. For learning with smooth generalized linear losses, we propose an
approximate stochastic gradient oracle estimated from non-interactive LDP
channel, using Chebyshev expansion. Combined with inexact gradient methods, we
obtain an efficient algorithm with quasi-polynomial sample complexity bound.
For the high-dimensional world, we discover that under $\ell_2$-norm assumption
on data points, high-dimensional sparse linear regression and mean estimation
can be achieved with logarithmic dependence on dimension, using random
projection and approximate recovery. We also extend our methods to Kernel Ridge
Regression. Our work is the first one that makes learning and estimation
possible for a broad range of learning tasks under non-interactive LDP model. | [
1,
0,
0,
0,
0,
0
] |
Title: Efficiency versus instability in plasma accelerators,
Abstract: Plasma wake-field acceleration is one of the main technologies being
developed for future high-energy colliders. Potentially, it can create a
cost-effective path to the highest possible energies for e+e- or
{\gamma}-{\gamma} colliders and produce a profound effect on the developments
for high-energy physics. Acceleration in a blowout regime, where all plasma
electrons are swept away from the axis, is presently considered to be the
primary choice for beam acceleration. In this paper, we derive a universal
efficiency-instability relation, between the power efficiency and the key
instability parameter of the trailing bunch for beam acceleration in the
blowout regime. We also show that the suppression of instability in the
trailing bunch can be achieved through BNS damping by the introduction of a
beam energy variation along the bunch. Unfortunately, in the high efficiency
regime, the required energy variation is quite high, and is not presently
compatible with collider-quality beams. We would like to stress that the
development of the instability imposes a fundamental limitation on the
acceleration efficiency, and it is unclear how it could be overcome for
high-luminosity linear colliders. With minor modifications, the considered
limitation on the power efficiency is applicable to other types of
acceleration. | [
0,
1,
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0,
0
] |
Title: Minimal Exploration in Structured Stochastic Bandits,
Abstract: This paper introduces and addresses a wide class of stochastic bandit
problems where the function mapping the arm to the corresponding reward
exhibits some known structural properties. Most existing structures (e.g.
linear, Lipschitz, unimodal, combinatorial, dueling, ...) are covered by our
framework. We derive an asymptotic instance-specific regret lower bound for
these problems, and develop OSSB, an algorithm whose regret matches this
fundamental limit. OSSB is not based on the classical principle of "optimism in
the face of uncertainty" or on Thompson sampling, and rather aims at matching
the minimal exploration rates of sub-optimal arms as characterized in the
derivation of the regret lower bound. We illustrate the efficiency of OSSB
using numerical experiments in the case of the linear bandit problem and show
that OSSB outperforms existing algorithms, including Thompson sampling. | [
1,
0,
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] |
Title: On Optimistic versus Randomized Exploration in Reinforcement Learning,
Abstract: We discuss the relative merits of optimistic and randomized approaches to
exploration in reinforcement learning. Optimistic approaches presented in the
literature apply an optimistic boost to the value estimate at each state-action
pair and select actions that are greedy with respect to the resulting
optimistic value function. Randomized approaches sample from among
statistically plausible value functions and select actions that are greedy with
respect to the random sample. Prior computational experience suggests that
randomized approaches can lead to far more statistically efficient learning. We
present two simple analytic examples that elucidate why this is the case. In
principle, there should be optimistic approaches that fare well relative to
randomized approaches, but that would require intractable computation.
Optimistic approaches that have been proposed in the literature sacrifice
statistical efficiency for the sake of computational efficiency. Randomized
approaches, on the other hand, may enable simultaneous statistical and
computational efficiency. | [
1,
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1,
0,
0
] |
Title: Fast Monte-Carlo Localization on Aerial Vehicles using Approximate Continuous Belief Representations,
Abstract: Size, weight, and power constrained platforms impose constraints on
computational resources that introduce unique challenges in implementing
localization algorithms. We present a framework to perform fast localization on
such platforms enabled by the compressive capabilities of Gaussian Mixture
Model representations of point cloud data. Given raw structural data from a
depth sensor and pitch and roll estimates from an on-board attitude reference
system, a multi-hypothesis particle filter localizes the vehicle by exploiting
the likelihood of the data originating from the mixture model. We demonstrate
analysis of this likelihood in the vicinity of the ground truth pose and detail
its utilization in a particle filter-based vehicle localization strategy, and
later present results of real-time implementations on a desktop system and an
off-the-shelf embedded platform that outperform localization results from
running a state-of-the-art algorithm on the same environment. | [
1,
0,
0,
0,
0,
0
] |
Title: Generalized two-field $α$-attractor models from geometrically finite hyperbolic surfaces,
Abstract: We consider four-dimensional gravity coupled to a non-linear sigma model
whose scalar manifold is a non-compact geometrically finite surface $\Sigma$
endowed with a Riemannian metric of constant negative curvature. When the
space-time is an FLRW universe, such theories produce a very wide
generalization of two-field $\alpha$-attractor models, being parameterized by a
positive constant $\alpha$, by the choice of a finitely-generated surface group
$\Gamma\subset \mathrm{PSL}(2,\mathbb{R})$ (which is isomorphic with the
fundamental group of $\Sigma$) and by the choice of a scalar potential defined
on $\Sigma$. The traditional two-field $\alpha$-attractor models arise when
$\Gamma$ is the trivial group, in which case $\Sigma$ is the Poincaré disk.
We give a general prescription for the study of such models through
uniformization in the so-called "non-elementary" case and discuss some of their
qualitative features in the gradient flow approximation, which we relate to
Morse theory. We also discuss some aspects of the SRST approximation in these
models, showing that it is generally not well-suited for studying dynamics near
cusp ends. When $\Sigma$ is non-compact and the scalar potential is
"well-behaved" at the ends, we show that, in the {\em naive} local one-field
truncation, our generalized models have the same universal behavior as ordinary
one-field $\alpha$-attractors if inflation happens near any of the ends of
$\Sigma$ where the extended potential has a local maximum, for trajectories
which are well approximated by non-canonically parameterized geodesics near the
ends, we also discuss spiral trajectories near the ends. | [
0,
1,
1,
0,
0,
0
] |
Title: $\overline{M}_{1,n}$ is usually not uniruled in characteristic $p$,
Abstract: Using etale cohomology, we define a birational invariant for varieties in
characteristic $p$ that serves as an obstruction to uniruledness - a variant on
an obstruction to unirationality due to Ekedahl. We apply this to
$\overline{M}_{1,n}$ and show that $\overline{M}_{1,n}$ is not uniruled in
characteristic $p$ as long as $n \geq p \geq 11$. To do this, we use Deligne's
description of the etale cohomology of $\overline{M}_{1,n}$ and apply the
theory of congruences between modular forms. | [
0,
0,
1,
0,
0,
0
] |
Title: Continuum Limit of Posteriors in Graph Bayesian Inverse Problems,
Abstract: We consider the problem of recovering a function input of a differential
equation formulated on an unknown domain $M$. We assume to have access to a
discrete domain $M_n=\{x_1, \dots, x_n\} \subset M$, and to noisy measurements
of the output solution at $p\le n$ of those points. We introduce a graph-based
Bayesian inverse problem, and show that the graph-posterior measures over
functions in $M_n$ converge, in the large $n$ limit, to a posterior over
functions in $M$ that solves a Bayesian inverse problem with known domain.
The proofs rely on the variational formulation of the Bayesian update, and on
a new topology for the study of convergence of measures over functions on point
clouds to a measure over functions on the continuum. Our framework, techniques,
and results may serve to lay the foundations of robust uncertainty
quantification of graph-based tasks in machine learning. The ideas are
presented in the concrete setting of recovering the initial condition of the
heat equation on an unknown manifold. | [
0,
0,
1,
1,
0,
0
] |
Title: Automatic Conflict Detection in Police Body-Worn Audio,
Abstract: Automatic conflict detection has grown in relevance with the advent of
body-worn technology, but existing metrics such as turn-taking and overlap are
poor indicators of conflict in police-public interactions. Moreover, standard
techniques to compute them fall short when applied to such diversified and
noisy contexts. We develop a pipeline catered to this task combining adaptive
noise removal, non-speech filtering and new measures of conflict based on the
repetition and intensity of phrases in speech. We demonstrate the effectiveness
of our approach on body-worn audio data collected by the Los Angeles Police
Department. | [
1,
0,
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1,
0,
0
] |
Title: LAMOST telescope reveals that Neptunian cousins of hot Jupiters are mostly single offspring of stars that are rich in heavy elements,
Abstract: We discover a population of short-period, Neptune-size planets sharing key
similarities with hot Jupiters: both populations are preferentially hosted by
metal-rich stars, and both are preferentially found in Kepler systems with
single transiting planets. We use accurate LAMOST DR4 stellar parameters for
main-sequence stars to study the distributions of short-period 1d < P < 10d
Kepler planets as a function of host star metallicity. The radius distribution
of planets around metal-rich stars is more "puffed up" as compared to that
around metal-poor hosts. In two period-radius regimes, planets preferentially
reside around metal-rich stars, while there are hardly any planets around
metal-poor stars. One is the well-known hot Jupiters, and the other is a
population of Neptune-size planets (2 R_Earth <~ R_p <~ 6 R_Earth), dubbed as
"Hoptunes". Also like hot Jupiters, Hoptunes occur more frequently in systems
with single transiting planets though the fraction of Hoptunes occurring in
multiples is larger than that of hot Jupiters. About 1% of solar-type stars
host "Hoptunes", and the frequencies of Hoptunes and hot Jupiters increase with
consistent trends as a function of [Fe/H]. In the planet radius distribution,
hot Jupiters and Hoptunes are separated by a "valley" at approximately Saturn
size (in the range of 6 R_Earth <~ R_p <~ 10 R_Earth), and this "hot-Saturn
valley" represents approximately an order-of-magnitude decrease in planet
frequency compared to hot Jupiters and Hoptunes. The empirical "kinship"
between Hoptunes and hot Jupiters suggests likely common processes (migration
and/or formation) responsible for their existence. | [
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1,
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] |
Title: Model enumeration in propositional circumscription via unsatisfiable core analysis,
Abstract: Many practical problems are characterized by a preference relation over
admissible solutions, where preferred solutions are minimal in some sense. For
example, a preferred diagnosis usually comprises a minimal set of reasons that
is sufficient to cause the observed anomaly. Alternatively, a minimal
correction subset comprises a minimal set of reasons whose deletion is
sufficient to eliminate the observed anomaly. Circumscription formalizes such
preference relations by associating propositional theories with minimal models.
The resulting enumeration problem is addressed here by means of a new algorithm
taking advantage of unsatisfiable core analysis. Empirical evidence of the
efficiency of the algorithm is given by comparing the performance of the
resulting solver, CIRCUMSCRIPTINO, with HCLASP, CAMUS MCS, LBX and MCSLS on the
enumeration of minimal models for problems originating from practical
applications.
This paper is under consideration for acceptance in TPLP. | [
1,
0,
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0
] |
Title: Variations on a Visserian Theme,
Abstract: A first order theory T is said to be "tight" if for any two deductively
closed extensions U and V of T (both of which are formulated in the language of
T), U and V are bi-interpretable iff U = V. By a theorem of Visser, PA (Peano
Arithmetic) is tight. Here we show that Z_2 (second order arithmetic), ZF
(Zermelo-Fraenkel set theory), and KM (Kelley-Morse theory of classes) are also
tight theories. | [
0,
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1,
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0
] |
Title: Improved Query Reformulation for Concept Location using CodeRank and Document Structures,
Abstract: During software maintenance, developers usually deal with a significant
number of software change requests. As a part of this, they often formulate an
initial query from the request texts, and then attempt to map the concepts
discussed in the request to relevant source code locations in the software
system (a.k.a., concept location). Unfortunately, studies suggest that they
often perform poorly in choosing the right search terms for a change task. In
this paper, we propose a novel technique --ACER-- that takes an initial query,
identifies appropriate search terms from the source code using a novel term
weight --CodeRank, and then suggests effective reformulation to the initial
query by exploiting the source document structures, query quality analysis and
machine learning. Experiments with 1,675 baseline queries from eight subject
systems report that our technique can improve 71% of the baseline queries which
is highly promising. Comparison with five closely related existing techniques
in query reformulation not only validates our empirical findings but also
demonstrates the superiority of our technique. | [
1,
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0,
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0
] |
Title: High-performance parallel computing in the classroom using the public goods game as an example,
Abstract: The use of computers in statistical physics is common because the sheer
number of equations that describe the behavior of an entire system particle by
particle often makes it impossible to solve them exactly. Monte Carlo methods
form a particularly important class of numerical methods for solving problems
in statistical physics. Although these methods are simple in principle, their
proper use requires a good command of statistical mechanics, as well as
considerable computational resources. The aim of this paper is to demonstrate
how the usage of widely accessible graphics cards on personal computers can
elevate the computing power in Monte Carlo simulations by orders of magnitude,
thus allowing live classroom demonstration of phenomena that would otherwise be
out of reach. As an example, we use the public goods game on a square lattice
where two strategies compete for common resources in a social dilemma
situation. We show that the second-order phase transition to an absorbing phase
in the system belongs to the directed percolation universality class, and we
compare the time needed to arrive at this result by means of the main processor
and by means of a suitable graphics card. Parallel computing on graphics
processing units has been developed actively during the last decade, to the
point where today the learning curve for entry is anything but steep for those
familiar with programming. The subject is thus ripe for inclusion in graduate
and advanced undergraduate curricula, and we hope that this paper will
facilitate this process in the realm of physics education. To that end, we
provide a documented source code for an easy reproduction of presented results
and for further development of Monte Carlo simulations of similar systems. | [
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1,
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] |
Title: Correlation decay in fermionic lattice systems with power-law interactions at non-zero temperature,
Abstract: We study correlations in fermionic lattice systems with long-range
interactions in thermal equilibrium. We prove a bound on the correlation decay
between anti-commuting operators and generalize a long-range Lieb-Robinson type
bound. Our results show that in these systems of spatial dimension $D$ with,
not necessarily translation invariant, two-site interactions decaying
algebraically with the distance with an exponent $\alpha \geq 2\,D$,
correlations between such operators decay at least algebraically with an
exponent arbitrarily close to $\alpha$ at any non-zero temperature. Our bound
is asymptotically tight, which we demonstrate by a high temperature expansion
and by numerically analyzing density-density correlations in the 1D quadratic
(free, exactly solvable) Kitaev chain with long-range pairing. | [
0,
1,
0,
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] |
Title: Dimensionality Reduction for Stationary Time Series via Stochastic Nonconvex Optimization,
Abstract: Stochastic optimization naturally arises in machine learning. Efficient
algorithms with provable guarantees, however, are still largely missing, when
the objective function is nonconvex and the data points are dependent. This
paper studies this fundamental challenge through a streaming PCA problem for
stationary time series data. Specifically, our goal is to estimate the
principle component of time series data with respect to the covariance matrix
of the stationary distribution. Computationally, we propose a variant of Oja's
algorithm combined with downsampling to control the bias of the stochastic
gradient caused by the data dependency. Theoretically, we quantify the
uncertainty of our proposed stochastic algorithm based on diffusion
approximations. This allows us to prove the asymptotic rate of convergence and
further implies near optimal asymptotic sample complexity. Numerical
experiments are provided to support our analysis. | [
0,
0,
0,
1,
0,
0
] |
Title: Efficient tracking of a growing number of experts,
Abstract: We consider a variation on the problem of prediction with expert advice,
where new forecasters that were unknown until then may appear at each round. As
often in prediction with expert advice, designing an algorithm that achieves
near-optimal regret guarantees is straightforward, using aggregation of
experts. However, when the comparison class is sufficiently rich, for instance
when the best expert and the set of experts itself changes over time, such
strategies naively require to maintain a prohibitive number of weights
(typically exponential with the time horizon). By contrast, designing
strategies that both achieve a near-optimal regret and maintain a reasonable
number of weights is highly non-trivial. We consider three increasingly
challenging objectives (simple regret, shifting regret and sparse shifting
regret) that extend existing notions defined for a fixed expert ensemble; in
each case, we design strategies that achieve tight regret bounds, adaptive to
the parameters of the comparison class, while being computationally
inexpensive. Moreover, our algorithms are anytime, agnostic to the number of
incoming experts and completely parameter-free. Such remarkable results are
made possible thanks to two simple but highly effective recipes: first the
"abstention trick" that comes from the specialist framework and enables to
handle the least challenging notions of regret, but is limited when addressing
more sophisticated objectives. Second, the "muting trick" that we introduce to
give more flexibility. We show how to combine these two tricks in order to
handle the most challenging class of comparison strategies. | [
1,
0,
0,
1,
0,
0
] |
Title: Toeplitz Inverse Covariance-Based Clustering of Multivariate Time Series Data,
Abstract: Subsequence clustering of multivariate time series is a useful tool for
discovering repeated patterns in temporal data. Once these patterns have been
discovered, seemingly complicated datasets can be interpreted as a temporal
sequence of only a small number of states, or clusters. For example, raw sensor
data from a fitness-tracking application can be expressed as a timeline of a
select few actions (i.e., walking, sitting, running). However, discovering
these patterns is challenging because it requires simultaneous segmentation and
clustering of the time series. Furthermore, interpreting the resulting clusters
is difficult, especially when the data is high-dimensional. Here we propose a
new method of model-based clustering, which we call Toeplitz Inverse
Covariance-based Clustering (TICC). Each cluster in the TICC method is defined
by a correlation network, or Markov random field (MRF), characterizing the
interdependencies between different observations in a typical subsequence of
that cluster. Based on this graphical representation, TICC simultaneously
segments and clusters the time series data. We solve the TICC problem through
alternating minimization, using a variation of the expectation maximization
(EM) algorithm. We derive closed-form solutions to efficiently solve the two
resulting subproblems in a scalable way, through dynamic programming and the
alternating direction method of multipliers (ADMM), respectively. We validate
our approach by comparing TICC to several state-of-the-art baselines in a
series of synthetic experiments, and we then demonstrate on an automobile
sensor dataset how TICC can be used to learn interpretable clusters in
real-world scenarios. | [
1,
0,
1,
0,
0,
0
] |
Title: A stencil scaling approach for accelerating matrix-free finite element implementations,
Abstract: We present a novel approach to fast on-the-fly low order finite element
assembly for scalar elliptic partial differential equations of Darcy type with
variable coefficients optimized for matrix-free implementations. Our approach
introduces a new operator that is obtained by appropriately scaling the
reference stiffness matrix from the constant coefficient case. Assuming
sufficient regularity, an a priori analysis shows that solutions obtained by
this approach are unique and have asymptotically optimal order convergence in
the $H^1$- and the $L^2$-norm on hierarchical hybrid grids. For the
pre-asymptotic regime, we present a local modification that guarantees uniform
ellipticity of the operator. Cost considerations show that our novel approach
requires roughly one third of the floating-point operations compared to a
classical finite element assembly scheme employing nodal integration. Our
theoretical considerations are illustrated by numerical tests that confirm the
expectations with respect to accuracy and run-time. A large scale application
with more than a hundred billion ($1.6\cdot10^{11}$) degrees of freedom
executed on 14,310 compute cores demonstrates the efficiency of the new scaling
approach. | [
1,
0,
0,
0,
0,
0
] |
Title: Asymptotic behaviour methods for the Heat Equation. Convergence to the Gaussian,
Abstract: In this expository work we discuss the asymptotic behaviour of the solutions
of the classical heat equation posed in the whole Euclidean space.
After an introductory review of the main facts on the existence and
properties of solutions, we proceed with the proofs of convergence to the
Gaussian fundamental solution, a result that holds for all integrable
solutions, and represents in the PDE setting the Central Limit Theorem of
probability. We present several methods of proof: first, the scaling method.
Then several versions of the representation method. This is followed by the
functional analysis approach that leads to the famous related equations,
Fokker-Planck and Ornstein-Uhlenbeck. The analysis of this connection is also
given in rather complete form here. Finally, we present the Boltzmann entropy
method, coming from kinetic equations.
The different methods are interesting because of the possible extension to
prove the asymptotic behaviour or stabilization analysis for more general
equations, linear or nonlinear. It all depends a lot on the particular
features, and only one or some of the methods work in each case.Other settings
of the Heat Equation are briefly discussed in Section 9 and a longer mention of
results for different equations is done in Section 10. | [
0,
0,
1,
0,
0,
0
] |
Title: Magnetization dynamics of weakly interacting sub-100 nm square artificial spin ices,
Abstract: Artificial Spin Ice (ASI), consisting of a two dimensional array of nanoscale
magnetic elements, provides a fascinating opportunity to observe the physics of
out of equilibrium systems. Initial studies concentrated on the static, frozen
state, whilst more recent studies have accessed the out-of-equilibrium dynamic,
fluctuating state. This opens up exciting possibilities such as the observation
of systems exploring their energy landscape through monopole quasiparticle
creation, potentially leading to ASI magnetricity, and to directly observe
unconventional phase transitions. In this work we have measured and analysed
the magnetic relaxation of thermally active ASI systems by means of SQUID
magnetometry. We have investigated the effect of the interaction strength on
the magnetization dynamics at different temperatures in the range where the
nanomagnets are thermally active and have observed that they follow an
Arrhenius-type Néel-Brown behaviour. An unexpected negative correlation of
the average blocking temperature with the interaction strength is also
observed, which is supported by Monte Carlo simulations. The magnetization
relaxation measurements show faster relaxation for more strongly coupled
nanoelements with similar dimensions. The analysis of the stretching exponents
obtained from the measurements suggest 1-D chain-like magnetization dynamics.
This indicates that the nature of the interactions between nanoelements lowers
the dimensionality of the ASI from 2-D to 1-D. Finally, we present a way to
quantify the effective interaction energy of a square ASI system, and compare
it to the interaction energy calculated from a simple dipole model and also to
the magnetostatic energy computed with micromagnetic simulations. | [
0,
1,
0,
0,
0,
0
] |
Title: Structured Connectivity Augmentation,
Abstract: We initiate the algorithmic study of the following "structured augmentation"
question: is it possible to increase the connectivity of a given graph G by
superposing it with another given graph H? More precisely, graph F is the
superposition of G and H with respect to injective mapping \phi: V(H)->V(G) if
every edge uv of F is either an edge of G, or \phi^{-1}(u)\phi^{-1}(v) is an
edge of H. We consider the following optimization problem. Given graphs G,H,
and a weight function \omega assigning non-negative weights to pairs of
vertices of V(G), the task is to find \varphi of minimum weight
\omega(\phi)=\sum_{xy\in E(H)}\omega(\phi(x)\varphi(y)) such that the edge
connectivity of the superposition F of G and H with respect to \phi is higher
than the edge connectivity of G. Our main result is the following "dichotomy"
complexity classification. We say that a class of graphs C has bounded
vertex-cover number, if there is a constant t depending on C only such that the
vertex-cover number of every graph from C does not exceed t. We show that for
every class of graphs C with bounded vertex-cover number, the problems of
superposing into a connected graph F and to 2-edge connected graph F, are
solvable in polynomial time when H\in C. On the other hand, for any hereditary
class C with unbounded vertex-cover number, both problems are NP-hard when H\in
C. For the unweighted variants of structured augmentation problems, i.e. the
problems where the task is to identify whether there is a superposition of
graphs of required connectivity, we provide necessary and sufficient
combinatorial conditions on the existence of such superpositions. These
conditions imply polynomial time algorithms solving the unweighted variants of
the problems. | [
1,
0,
0,
0,
0,
0
] |
Title: Transition probability of Brownian motion in the octant and its application to default modeling,
Abstract: We derive a semi-analytic formula for the transition probability of
three-dimensional Brownian motion in the positive octant with absorption at the
boundaries. Separation of variables in spherical coordinates leads to an
eigenvalue problem for the resulting boundary value problem in the two angular
components. The main theoretical result is a solution to the original problem
expressed as an expansion into special functions and an eigenvalue which has to
be chosen to allow a matching of the boundary condition. We discuss and test
several computational methods to solve a finite-dimensional approximation to
this nonlinear eigenvalue problem. Finally, we apply our results to the
computation of default probabilities and credit valuation adjustments in a
structural credit model with mutual liabilities. | [
0,
0,
0,
0,
0,
1
] |
Title: Block-Sparse Recurrent Neural Networks,
Abstract: Recurrent Neural Networks (RNNs) are used in state-of-the-art models in
domains such as speech recognition, machine translation, and language
modelling. Sparsity is a technique to reduce compute and memory requirements of
deep learning models. Sparse RNNs are easier to deploy on devices and high-end
server processors. Even though sparse operations need less compute and memory
relative to their dense counterparts, the speed-up observed by using sparse
operations is less than expected on different hardware platforms. In order to
address this issue, we investigate two different approaches to induce block
sparsity in RNNs: pruning blocks of weights in a layer and using group lasso
regularization to create blocks of weights with zeros. Using these techniques,
we demonstrate that we can create block-sparse RNNs with sparsity ranging from
80% to 90% with small loss in accuracy. This allows us to reduce the model size
by roughly 10x. Additionally, we can prune a larger dense network to recover
this loss in accuracy while maintaining high block sparsity and reducing the
overall parameter count. Our technique works with a variety of block sizes up
to 32x32. Block-sparse RNNs eliminate overheads related to data storage and
irregular memory accesses while increasing hardware efficiency compared to
unstructured sparsity. | [
1,
0,
0,
1,
0,
0
] |
Title: Fast Rates for Bandit Optimization with Upper-Confidence Frank-Wolfe,
Abstract: We consider the problem of bandit optimization, inspired by stochastic
optimization and online learning problems with bandit feedback. In this
problem, the objective is to minimize a global loss function of all the
actions, not necessarily a cumulative loss. This framework allows us to study a
very general class of problems, with applications in statistics, machine
learning, and other fields. To solve this problem, we analyze the
Upper-Confidence Frank-Wolfe algorithm, inspired by techniques for bandits and
convex optimization. We give theoretical guarantees for the performance of this
algorithm over various classes of functions, and discuss the optimality of
these results. | [
0,
0,
1,
1,
0,
0
] |
Title: Ages and structural and dynamical parameters of two globular clusters in the M81 group,
Abstract: GC-1 and GC-2 are two globular clusters (GCs) in the remote halo of M81 and
M82 in the M81 group discovered by Jang et al. using the {\it Hubble Space
Telescope} ({\it HST}) images. These two GCs were observed as part of the
Beijing--Arizona--Taiwan--Connecticut (BATC) Multicolor Sky Survey, using 14
intermediate-band filters covering a wavelength range of 4000--10000 \AA. We
accurately determine these two clusters' ages and masses by comparing their
spectral energy distributions (from 2267 to 20000~{\AA}, comprising photometric
data in the near-ultraviolet of the {\it Galaxy Evolution Explorer}, 14 BATC
intermediate-band, and Two Micron All Sky Survey near-infrared $JHK_{\rm s}$
filters) with theoretical stellar population-synthesis models, resulting in
ages of $15.50\pm3.20$ for GC-1 and $15.10\pm2.70$ Gyr for GC-2. The masses of
GC-1 and GC-2 obtained here are $1.77-2.04\times 10^6$ and $5.20-7.11\times
10^6 \rm~M_\odot$, respectively. In addition, the deep observations with the
Advanced Camera for Surveys and Wide Field Camera 3 on the {\it HST} are used
to provide the surface brightness profiles of GC-1 and GC-2. The structural and
dynamical parameters are derived from fitting the profiles to three different
models; in particular, the internal velocity dispersions of GC-1 and GC-2 are
derived, which can be compared with ones obtained based on spectral
observations in the future. For the first time, in this paper, the $r_h$ versus
$M_V$ diagram shows that GC-2 is an ultra-compact dwarf in the M81 group. | [
0,
1,
0,
0,
0,
0
] |
Title: Graphons: A Nonparametric Method to Model, Estimate, and Design Algorithms for Massive Networks,
Abstract: Many social and economic systems are naturally represented as networks, from
off-line and on-line social networks, to bipartite networks, like Netflix and
Amazon, between consumers and products. Graphons, developed as limits of
graphs, form a natural, nonparametric method to describe and estimate large
networks like Facebook and LinkedIn. Here we describe the development of the
theory of graphons, for both dense and sparse networks, over the last decade.
We also review theorems showing that we can consistently estimate graphons from
massive networks in a wide variety of models. Finally, we show how to use
graphons to estimate missing links in a sparse network, which has applications
from estimating social and information networks in development economics, to
rigorously and efficiently doing collaborative filtering with applications to
movie recommendations in Netflix and product suggestions in Amazon. | [
1,
1,
0,
0,
0,
0
] |
Title: Bayesian Methods in Cosmology,
Abstract: These notes aim at presenting an overview of Bayesian statistics, the
underlying concepts and application methodology that will be useful to
astronomers seeking to analyse and interpret a wide variety of data about the
Universe. The level starts from elementary notions, without assuming any
previous knowledge of statistical methods, and then progresses to more
advanced, research-level topics. After an introduction to the importance of
statistical inference for the physical sciences, elementary notions of
probability theory and inference are introduced and explained. Bayesian methods
are then presented, starting from the meaning of Bayes Theorem and its use as
inferential engine, including a discussion on priors and posterior
distributions. Numerical methods for generating samples from arbitrary
posteriors (including Markov Chain Monte Carlo and Nested Sampling) are then
covered. The last section deals with the topic of Bayesian model selection and
how it is used to assess the performance of models, and contrasts it with the
classical p-value approach. A series of exercises of various levels of
difficulty are designed to further the understanding of the theoretical
material, including fully worked out solutions for most of them. | [
0,
1,
0,
1,
0,
0
] |
Title: Information Extraction in Illicit Domains,
Abstract: Extracting useful entities and attribute values from illicit domains such as
human trafficking is a challenging problem with the potential for widespread
social impact. Such domains employ atypical language models, have `long tails'
and suffer from the problem of concept drift. In this paper, we propose a
lightweight, feature-agnostic Information Extraction (IE) paradigm specifically
designed for such domains. Our approach uses raw, unlabeled text from an
initial corpus, and a few (12-120) seed annotations per domain-specific
attribute, to learn robust IE models for unobserved pages and websites.
Empirically, we demonstrate that our approach can outperform feature-centric
Conditional Random Field baselines by over 18\% F-Measure on five annotated
sets of real-world human trafficking datasets in both low-supervision and
high-supervision settings. We also show that our approach is demonstrably
robust to concept drift, and can be efficiently bootstrapped even in a serial
computing environment. | [
1,
0,
0,
0,
0,
0
] |
Title: A Tutorial on Kernel Density Estimation and Recent Advances,
Abstract: This tutorial provides a gentle introduction to kernel density estimation
(KDE) and recent advances regarding confidence bands and geometric/topological
features. We begin with a discussion of basic properties of KDE: the
convergence rate under various metrics, density derivative estimation, and
bandwidth selection. Then, we introduce common approaches to the construction
of confidence intervals/bands, and we discuss how to handle bias. Next, we talk
about recent advances in the inference of geometric and topological features of
a density function using KDE. Finally, we illustrate how one can use KDE to
estimate a cumulative distribution function and a receiver operating
characteristic curve. We provide R implementations related to this tutorial at
the end. | [
0,
0,
0,
1,
0,
0
] |
Title: Optimizing expected word error rate via sampling for speech recognition,
Abstract: State-level minimum Bayes risk (sMBR) training has become the de facto
standard for sequence-level training of speech recognition acoustic models. It
has an elegant formulation using the expectation semiring, and gives large
improvements in word error rate (WER) over models trained solely using
cross-entropy (CE) or connectionist temporal classification (CTC). sMBR
training optimizes the expected number of frames at which the reference and
hypothesized acoustic states differ. It may be preferable to optimize the
expected WER, but WER does not interact well with the expectation semiring, and
previous approaches based on computing expected WER exactly involve expanding
the lattices used during training. In this paper we show how to perform
optimization of the expected WER by sampling paths from the lattices used
during conventional sMBR training. The gradient of the expected WER is itself
an expectation, and so may be approximated using Monte Carlo sampling. We show
experimentally that optimizing WER during acoustic model training gives 5%
relative improvement in WER over a well-tuned sMBR baseline on a 2-channel
query recognition task (Google Home). | [
1,
0,
0,
1,
0,
0
] |
Title: Stochastic Canonical Correlation Analysis,
Abstract: We tightly analyze the sample complexity of CCA, provide a learning algorithm
that achieves optimal statistical performance in time linear in the required
number of samples (up to log factors), as well as a streaming algorithm with
similar guarantees. | [
1,
0,
0,
1,
0,
0
] |
Title: Status maximization as a source of fairness in a networked dictator game,
Abstract: Human behavioural patterns exhibit selfish or competitive, as well as
selfless or altruistic tendencies, both of which have demonstrable effects on
human social and economic activity. In behavioural economics, such effects have
traditionally been illustrated experimentally via simple games like the
dictator and ultimatum games. Experiments with these games suggest that, beyond
rational economic thinking, human decision-making processes are influenced by
social preferences, such as an inclination to fairness. In this study we
suggest that the apparent gap between competitive and altruistic human
tendencies can be bridged by assuming that people are primarily maximising
their status, i.e., a utility function different from simple profit
maximisation. To this end we analyse a simple agent-based model, where
individuals play the repeated dictator game in a social network they can
modify. As model parameters we consider the living costs and the rate at which
agents forget infractions by others. We find that individual strategies used in
the game vary greatly, from selfish to selfless, and that both of the above
parameters determine when individuals form complex and cohesive social
networks. | [
1,
0,
0,
0,
0,
1
] |
Title: On Dziobek Special Central Configurations,
Abstract: We study the special central configurations of the curved N-body problem in
S^3. We show that there are special central configurations formed by N masses
for any N >2. We then extend the concept of special central configurations to
S^n, n>0, and study one interesting class of special central configurations in
S^n, the Dziobek special central configurations. We obtain a criterion for them
and reduce it to two sets of equations. Then we apply these equations to
special central configurations of 3 bodies on S^1, 4 bodies on S^2, and 5
bodies in S^3. | [
0,
0,
1,
0,
0,
0
] |
Title: Learning from a lot: Empirical Bayes in high-dimensional prediction settings,
Abstract: Empirical Bayes is a versatile approach to `learn from a lot' in two ways:
first, from a large number of variables and second, from a potentially large
amount of prior information, e.g. stored in public repositories. We review
applications of a variety of empirical Bayes methods to several well-known
model-based prediction methods including penalized regression, linear
discriminant analysis, and Bayesian models with sparse or dense priors. We
discuss `formal' empirical Bayes methods which maximize the marginal
likelihood, but also more informal approaches based on other data summaries. We
contrast empirical Bayes to cross-validation and full Bayes, and discuss hybrid
approaches. To study the relation between the quality of an empirical Bayes
estimator and $p$, the number of variables, we consider a simple empirical
Bayes estimator in a linear model setting.
We argue that empirical Bayes is particularly useful when the prior contains
multiple parameters which model a priori information on variables, termed
`co-data'. In particular, we present two novel examples that allow for co-data.
First, a Bayesian spike-and-slab setting that facilitates inclusion of multiple
co-data sources and types; second, a hybrid empirical Bayes-full Bayes ridge
regression approach for estimation of the posterior predictive interval. | [
0,
0,
0,
1,
0,
0
] |
Title: Runout transition and clustering instability observed in binary-mixture avalanche deposits,
Abstract: Binary mixtures of dry grains avalanching down a slope are experimentally
studied in order to determine the interaction among coarse and fine grains and
their effect on the deposit morphology. The distance travelled by the massive
front of the avalanche over the horizontal plane of deposition area is measured
as a function of mass content of fine particles in the mixture, grain-size
ratio, and flume tilt. A sudden transition of the runout is detected at a
critical content of fine particles, with a dependence on the grain-size ratio
and flume tilt. This transition is explained as two simultaneous avalanches in
different flowing regimes (a viscous-like one and an inertial one) competing
against each other and provoking a full segregation and a split-off of the
deposit into two well-defined, separated deposits. The formation of the distal
deposit, in turn, depends on a critical amount of coarse particles. This allows
the condensation of the pure coarse deposit around a small, initial seed
cluster, which grows rapidly by braking and capturing subsequent colliding
coarse particles. For different grain-size ratios and keeping a constant total
mass, the change in the amount of fines needed for the transition to occur is
found to be always less than 7%. For avalanches with a total mass of 4 kg we
find that, most of the time, the runout of a binary avalanche is larger than
the runout of monodisperse avalanches of corresponding constituent particles,
due to lubrication on the coarse-dominated side or to drag by inertial
particles on the fine-dominated side. | [
0,
1,
0,
0,
0,
0
] |
Title: A Simple Convex Layers Algorithm,
Abstract: Given a set of $n$ points $P$ in the plane, the first layer $L_1$ of $P$ is
formed by the points that appear on $P$'s convex hull. In general, a point
belongs to layer $L_i$, if it lies on the convex hull of the set $P \setminus
\bigcup_{j<i}\{L_j\}$. The \emph{convex layers problem} is to compute the
convex layers $L_i$. Existing algorithms for this problem either do not achieve
the optimal $\mathcal{O}\left(n\log n\right)$ runtime and linear space, or are
overly complex and difficult to apply in practice. We propose a new algorithm
that is both optimal and simple. The simplicity is achieved by independently
computing four sets of monotone convex chains in $\mathcal{O}\left(n\log
n\right)$ time and linear space. These are then merged in
$\mathcal{O}\left(n\log n\right)$ time. | [
1,
0,
0,
0,
0,
0
] |
Title: Fundamental solutions for Schrodinger operators with general inverse square potentials,
Abstract: In this paper, we classify the fundamental solutions for a class of
Schrodinger operators. | [
0,
0,
1,
0,
0,
0
] |
Title: An Efficient Load Balancing Method for Tree Algorithms,
Abstract: Nowadays, multiprocessing is mainstream with exponentially increasing number
of processors. Load balancing is, therefore, a critical operation for the
efficient execution of parallel algorithms. In this paper we consider the
fundamental class of tree-based algorithms that are notoriously irregular, and
hard to load-balance with existing static techniques. We propose a hybrid load
balancing method using the utility of statistical random sampling in estimating
the tree depth and node count distributions to uniformly partition an input
tree. To conduct an initial performance study, we implemented the method on an
Intel Xeon Phi accelerator system. We considered the tree traversal operation
on both regular and irregular unbalanced trees manifested by Fibonacci and
unbalanced (biased) randomly generated trees, respectively. The results show
scalable performance for up to the 60 physical processors of the accelerator,
as well as an extrapolated 128 processors case. | [
1,
0,
0,
0,
0,
0
] |
Title: NSML: A Machine Learning Platform That Enables You to Focus on Your Models,
Abstract: Machine learning libraries such as TensorFlow and PyTorch simplify model
implementation. However, researchers are still required to perform a
non-trivial amount of manual tasks such as GPU allocation, training status
tracking, and comparison of models with different hyperparameter settings. We
propose a system to handle these tasks and help researchers focus on models. We
present the requirements of the system based on a collection of discussions
from an online study group comprising 25k members. These include automatic GPU
allocation, learning status visualization, handling model parameter snapshots
as well as hyperparameter modification during learning, and comparison of
performance metrics between models via a leaderboard. We describe the system
architecture that fulfills these requirements and present a proof-of-concept
implementation, NAVER Smart Machine Learning (NSML). We test the system and
confirm substantial efficiency improvements for model development. | [
1,
0,
0,
0,
0,
0
] |
Title: High order local absorbing boundary conditions for acoustic waves in terms of farfield expansions,
Abstract: We devise a new high order local absorbing boundary condition (ABC) for
radiating problems and scattering of time-harmonic acoustic waves from
obstacles of arbitrary shape. By introducing an artificial boundary $S$
enclosing the scatterer, the original unbounded domain $\Omega$ is decomposed
into a bounded computational domain $\Omega^{-}$ and an exterior unbounded
domain $\Omega^{+}$. Then, we define interface conditions at the artificial
boundary $S$, from truncated versions of the well-known Wilcox and Karp
farfield expansion representations of the exact solution in the exterior region
$\Omega^{+}$. As a result, we obtain a new local absorbing boundary condition
(ABC) for a bounded problem on $\Omega^{-}$, which effectively accounts for the
outgoing behavior of the scattered field. Contrary to the low order absorbing
conditions previously defined, the order of the error induced by this ABC can
easily match the order of the numerical method in $\Omega^{-}$. We accomplish
this by simply adding as many terms as needed to the truncated farfield
expansions of Wilcox or Karp. The convergence of these expansions guarantees
that the order of approximation of the new ABC can be increased arbitrarily
without having to enlarge the radius of the artificial boundary. We include
numerical results in two and three dimensions which demonstrate the improved
accuracy and simplicity of this new formulation when compared to other
absorbing boundary conditions. | [
0,
1,
1,
0,
0,
0
] |
Title: Bootstrapping Exchangeable Random Graphs,
Abstract: We introduce two new bootstraps for exchangeable random graphs. One, the
"empirical graphon", is based purely on resampling, while the other, the
"histogram stochastic block model", is a model-based "sieve" bootstrap. We show
that both of them accurately approximate the sampling distributions of motif
densities, i.e., of the normalized counts of the number of times fixed
subgraphs appear in the network. These densities characterize the distribution
of (infinite) exchangeable networks. Our bootstraps therefore give, for the
first time, a valid quantification of uncertainty in inferences about
fundamental network statistics, and so of parameters identifiable from them. | [
0,
0,
0,
1,
0,
0
] |
Title: The Discrete Stochastic Galerkin Method for Hyperbolic Equations with Non-smooth and Random Coefficients,
Abstract: We develop a general polynomial chaos (gPC) based stochastic Galerkin (SG)
for hyperbolic equations with random and singular coefficients. Due to the
singu- lar nature of the solution, the standard gPC-SG methods may suffer from
a poor or even non convergence. Taking advantage of the fact that the discrete
solution, by the central type finite difference or finite volume approximations
in space and time for example, is smoother, we first discretize the equation by
a smooth finite difference or finite volume scheme, and then use the gPC-SG
approximation to the discrete system. The jump condition at the interface is
treated using the immersed upwind methods introduced in [8, 12]. This yields a
method that converges with the spectral accuracy for finite mesh size and time
step. We use a linear hyperbolic equation with discontinuous and random
coefficient, and the Liouville equation with discontinuous and random
potential, to illustrate our idea, with both one and second order spatial
discretizations. Spectral convergence is established for the first equation,
and numerical examples for both equations show the desired accu- racy of the
method. | [
0,
0,
1,
0,
0,
0
] |
Title: Seasonal evolution of $\mathrm{C_2N_2}$, $\mathrm{C_3H_4}$, and $\mathrm{C_4H_2}$ abundances in Titan's lower stratosphere,
Abstract: We study the seasonal evolution of Titan's lower stratosphere (around
15~mbar) in order to better understand the atmospheric dynamics and chemistry
in this part of the atmosphere. We analysed Cassini/CIRS far-IR observations
from 2006 to 2016 in order to measure the seasonal variations of three
photochemical by-products: $\mathrm{C_4H_2}$, $\mathrm{C_3H_4}$, and
$\mathrm{C_2N_2}$. We show that the abundances of these three gases have
evolved significantly at northern and southern high latitudes since 2006. We
measure a sudden and steep increase of the volume mixing ratios of
$\mathrm{C_4H_2}$, $\mathrm{C_3H_4}$, and $\mathrm{C_2N_2}$ at the south pole
from 2012 to 2013, whereas the abundances of these gases remained approximately
constant at the north pole over the same period. At northern mid-latitudes,
$\mathrm{C_2N_2}$ and $\mathrm{C_4H_2}$ abundances decrease after 2012 while
$\mathrm{C_3H_4}$ abundances stay constant. The comparison of these volume
mixing ratio variations with the predictions of photochemical and dynamical
models provides constraints on the seasonal evolution of atmospheric
circulation and chemical processes at play. | [
0,
1,
0,
0,
0,
0
] |
Title: Systems, Actors and Agents: Operation in a multicomponent environment,
Abstract: Multi-agent approach has become popular in computer science and technology.
However, the conventional models of multi-agent and multicomponent systems
implicitly or explicitly assume existence of absolute time or even do not
include time in the set of defining parameters. At the same time, it is proved
theoretically and validated experimentally that there are different times and
time scales in a variety of real systems - physical, chemical, biological,
social, informational, etc. Thus, the goal of this work is construction of a
multi-agent multicomponent system models with concurrency of processes and
diversity of actions. To achieve this goal, a mathematical system actor model
is elaborated and its properties are studied. | [
1,
0,
0,
0,
0,
0
] |
Title: The Painlevé property of $\mathbb{C}P^{N-1}$ sigma models,
Abstract: We test the $\mathbb{C}P^{N-1}$ sigma models for the Painlevé property.
While the construction of finite action solutions ensures their meromorphicity,
the general case requires testing. The test is performed for the equations in
the homogeneous variables, with their first component normalised to one. No
constraints are imposed on the dimensionality of the model or the values of the
initial exponents. This makes the test nontrivial, as the number of equations
and dependent variables are indefinite. A $\mathbb{C}P^{N-1}$ system proves to
have a $(4N-5)$-parameter family of solutions whose movable singularities are
only poles, while the order of the investigated system is $4N-4$. The remaining
degree of freedom, connected with an extra negative resonance, may correspond
to a branching movable essential singularity. An example of such a solution is
provided. | [
0,
1,
0,
0,
0,
0
] |
Title: A comment on Stein's unbiased risk estimate for reduced rank estimators,
Abstract: In the framework of matrix valued observables with low rank means, Stein's
unbiased risk estimate (SURE) can be useful for risk estimation and for tuning
the amount of shrinkage towards low rank matrices. This was demonstrated by
Candès et al. (2013) for singular value soft thresholding, which is a
Lipschitz continuous estimator. SURE provides an unbiased risk estimate for an
estimator whenever the differentiability requirements for Stein's lemma are
satisfied. Lipschitz continuity of the estimator is sufficient, but it is
emphasized that differentiability Lebesgue almost everywhere isn't. The reduced
rank estimator, which gives the best approximation of the observation with a
fixed rank, is an example of a discontinuous estimator for which Stein's lemma
actually applies. This was observed by Mukherjee et al. (2015), but the proof
was incomplete. This brief note gives a sufficient condition for Stein's lemma
to hold for estimators with discontinuities, which is then shown to be
fulfilled for a class of spectral function estimators including the reduced
rank estimator. Singular value hard thresholding does, however, not satisfy the
condition, and Stein's lemma does not apply to this estimator. | [
0,
0,
1,
1,
0,
0
] |
Title: Static and Fluctuating Magnetic Moments in the Ferroelectric Metal LiOsO$_3$,
Abstract: LiOsO$_3$ is the first example of a new class of material called a
ferroelectric metal. We performed zero-field and longitudinal-field $\mu$SR,
along with a combination of electronic structure and dipole field calculations,
to determine the magnetic ground state of LiOsO$_3$. We find that the sample
contains both static Li nuclear moments and dynamic Os electronic moments.
Below $\approx 0.7\,$K, the fluctuations of the Os moments slow down, though
remain dynamic down to 0.08$\,$K. We expect this could result in a frozen-out,
disordered ground state at even lower temperatures. | [
0,
1,
0,
0,
0,
0
] |
Title: Ranking with Adaptive Neighbors,
Abstract: Retrieving the most similar objects in a large-scale database for a given
query is a fundamental building block in many application domains, ranging from
web searches, visual, cross media, and document retrievals. State-of-the-art
approaches have mainly focused on capturing the underlying geometry of the data
manifolds. Graph-based approaches, in particular, define various diffusion
processes on weighted data graphs. Despite success, these approaches rely on
fixed-weight graphs, making ranking sensitive to the input affinity matrix. In
this study, we propose a new ranking algorithm that simultaneously learns the
data affinity matrix and the ranking scores. The proposed optimization
formulation assigns adaptive neighbors to each point in the data based on the
local connectivity, and the smoothness constraint assigns similar ranking
scores to similar data points. We develop a novel and efficient algorithm to
solve the optimization problem. Evaluations using synthetic and real datasets
suggest that the proposed algorithm can outperform the existing methods. | [
0,
0,
0,
1,
0,
0
] |
Title: Identities and central polynomials of real graded division algebras,
Abstract: Let $A$ be a finite dimensional real algebra with a division grading by a
finite abelian group $G$. In this paper we provide finite basis for the
$T_G$-ideal of graded identities and for the $T_G$-space of graded central
polynomials for $A$. | [
0,
0,
1,
0,
0,
0
] |
Title: Two-Dimensional Large Gap Topological Insulators with Large Rashba Spin-Orbit Coupling in Group-IV films,
Abstract: Rashba spin orbit coupling in topological insulators has attracted much
interest due to its exotic properties closely related to spintronic devices.
The coexistence of nontrivial topology and giant Rashba splitting, however, has
rare been observed in two-dimensional films, limiting severely its potential
applications at room temperature. Here, we propose a series of inversion
asymmetric group IV films, ABZ2, whose stability are confirmed by phonon
spectrum calculations. The analyses of electronic structures reveal that they
are intrinsic 2D TIs with a bulk gap as large as 0.74 eV, except for GeSiF2,
SnSiCl2, GeSiCl2 and GeSiBr2 monolayers which can transform from normal to
topological phases under appropriate tensile strains. Another prominent
intriguing feature is the giant Rashba spin splitting with a magnitude reaching
0.15 eV, the largest value reported in 2D films. These results present a
platform to explore 2D TIs for room temperature device applications. | [
0,
1,
0,
0,
0,
0
] |
Title: Assumption-Based Approaches to Reasoning with Priorities,
Abstract: This paper maps out the relation between different approaches for handling
preferences in argumentation with strict rules and defeasible assumptions by
offering translations between them. The systems we compare are: non-prioritized
defeats i.e. attacks, preference-based defeats, and preference-based defeats
extended with reverse defeat. | [
1,
0,
0,
0,
0,
0
] |
Title: On the Impact of Transposition Errors in Diffusion-Based Channels,
Abstract: In this work, we consider diffusion-based molecular communication with and
without drift between two static nano-machines. We employ type-based
information encoding, releasing a single molecule per information bit. At the
receiver, we consider an asynchronous detection algorithm which exploits the
arrival order of the molecules. In such systems, transposition errors
fundamentally undermine reliability and capacity. Thus, in this work we study
the impact of transpositions on the system performance. Towards this, we
present an analytical expression for the exact bit error probability (BEP)
caused by transpositions and derive computationally tractable approximations of
the BEP for diffusion-based channels with and without drift. Based on these
results, we analyze the BEP when background is not negligible and derive the
optimal bit interval that minimizes the BEP. Simulation results confirm the
theoretical results and show the error and goodput performance for different
parameters such as block size or noise generation rate. | [
1,
0,
1,
0,
0,
0
] |
Title: Uniform $L^p$-improving for weighted averages on curves,
Abstract: We define variable parameter analogues of the affine arclength measure on
curves and prove near-optimal $L^p$-improving estimates for associated
multilinear generalized Radon transforms. Some of our results are new even in
the convolution case. | [
0,
0,
1,
0,
0,
0
] |
Title: Finite Sample Differentially Private Confidence Intervals,
Abstract: We study the problem of estimating finite sample confidence intervals of the
mean of a normal population under the constraint of differential privacy. We
consider both the known and unknown variance cases and construct differentially
private algorithms to estimate confidence intervals. Crucially, our algorithms
guarantee a finite sample coverage, as opposed to an asymptotic coverage.
Unlike most previous differentially private algorithms, we do not require the
domain of the samples to be bounded. We also prove lower bounds on the expected
size of any differentially private confidence set showing that our the
parameters are optimal up to polylogarithmic factors. | [
1,
0,
1,
1,
0,
0
] |
Title: Muon Spin Rotation Analysis of the Internal Magnetic Field of Heavy Fermion System Uranium Beryllium-13,
Abstract: Uranium beryllium-13 is a heavy fermion system whose anomalous behavior may
be explained by its poorly understood internal magnetic structure. Here,
uranium beryllium-13's magnetic distribution is probed via muon spin
spectroscopy ($\mu$SR)-a process where positive muons localize at magnetically
unique sites in the crystal lattice and precess at characteristic Larmor
frequencies, providing measurements of the internal field. Muon spin
experiments using the transverse-field technique conducted at varying
temperatures and external magnetic field strengths are analyzed via statistical
methods on ROOT. Two precession frequencies are observed at low temperatures
with an amplitude ratio in the Fourier transform of 2:1, enabling muon stopping
sites to be traced at the geometric centers of the edges of the crystal
lattice. Characteristic strong and weak magnetic sites are deduced,
additionally verified by mathematical relationships. Results can readily be
applied to other heavy fermion systems, and recent identification of quantum
critical points in a host of heavy fermion compounds show a promising future
for the application of these systems in quantum technology. Note that this
paper is an analysis of data, and all experiments mentioned here are conducted
by a third party. | [
0,
1,
0,
0,
0,
0
] |
Title: Unitary Groups as Stabilizers of Orbits,
Abstract: We show that a finite unitary group which has orbits spanning the whole space
is necessarily the setwise stabilizer of a certain orbit. | [
0,
0,
1,
0,
0,
0
] |
Title: Algebras of generalized dihedral type,
Abstract: We provide a complete classification of all algebras of generalised dihedral
type, which are natural generalizations of algebras which occurred in the study
of blocks with dihedral defect groups. This gives a description by quivers and
relations coming from surface triangulations. | [
0,
0,
1,
0,
0,
0
] |
Title: Average whenever you meet: Opportunistic protocols for community detection,
Abstract: Consider the following asynchronous, opportunistic communication model over a
graph $G$: in each round, one edge is activated uniformly and independently at
random and (only) its two endpoints can exchange messages and perform local
computations. Under this model, we study the following random process: The
first time a vertex is an endpoint of an active edge, it chooses a random
number, say $\pm 1$ with probability $1/2$; then, in each round, the two
endpoints of the currently active edge update their values to their average. We
show that, if $G$ exhibits a two-community structure (for example, two
expanders connected by a sparse cut), the values held by the nodes will
collectively reflect the underlying community structure over a suitable phase
of the above process, allowing efficient and effective recovery in important
cases.
In more detail, we first provide a first-moment analysis showing that, for a
large class of almost-regular clustered graphs that includes the stochastic
block model, the expected values held by all but a negligible fraction of the
nodes eventually reflect the underlying cut signal. We prove this property
emerges after a mixing period of length $\mathcal O(n\log n)$. We further
provide a second-moment analysis for a more restricted class of regular
clustered graphs that includes the regular stochastic block model. For this
case, we are able to show that most nodes can efficiently and locally identify
their community of reference over a suitable time window. This results in the
first opportunistic protocols that approximately recover community structure
using only polylogarithmic work per node. Even for the above class of regular
graphs, our second moment analysis requires new concentration bounds on the
product of certain random matrices that are technically challenging and
possibly of independent interest. | [
1,
0,
0,
0,
0,
0
] |
Title: Provably Accurate Double-Sparse Coding,
Abstract: Sparse coding is a crucial subroutine in algorithms for various signal
processing, deep learning, and other machine learning applications. The central
goal is to learn an overcomplete dictionary that can sparsely represent a given
input dataset. However, a key challenge is that storage, transmission, and
processing of the learned dictionary can be untenably high if the data
dimension is high. In this paper, we consider the double-sparsity model
introduced by Rubinstein et al. (2010b) where the dictionary itself is the
product of a fixed, known basis and a data-adaptive sparse component. First, we
introduce a simple algorithm for double-sparse coding that can be amenable to
efficient implementation via neural architectures. Second, we theoretically
analyze its performance and demonstrate asymptotic sample complexity and
running time benefits over existing (provable) approaches for sparse coding. To
our knowledge, our work introduces the first computationally efficient
algorithm for double-sparse coding that enjoys rigorous statistical guarantees.
Finally, we support our analysis via several numerical experiments on simulated
data, confirming that our method can indeed be useful in problem sizes
encountered in practical applications. | [
1,
0,
0,
1,
0,
0
] |
Title: Sequential two-fold Pearson chi-squared test and tails of the Bessel process distributions,
Abstract: We find asymptotic formulas for error probabilities of two-fold Pearson
goodness-of-fit test as functions of two critical levels. These results may be
reformulated in terms of tails of two-dimensional distributions of the Bessel
process. Necessary properties of the Infeld function are obtained. | [
0,
0,
1,
1,
0,
0
] |
Title: Tracking Gaze and Visual Focus of Attention of People Involved in Social Interaction,
Abstract: The visual focus of attention (VFOA) has been recognized as a prominent
conversational cue. We are interested in estimating and tracking the VFOAs
associated with multi-party social interactions. We note that in this type of
situations the participants either look at each other or at an object of
interest; therefore their eyes are not always visible. Consequently both gaze
and VFOA estimation cannot be based on eye detection and tracking. We propose a
method that exploits the correlation between eye gaze and head movements. Both
VFOA and gaze are modeled as latent variables in a Bayesian switching
state-space model. The proposed formulation leads to a tractable learning
procedure and to an efficient algorithm that simultaneously tracks gaze and
visual focus. The method is tested and benchmarked using two publicly available
datasets that contain typical multi-party human-robot and human-human
interactions. | [
1,
0,
0,
0,
0,
0
] |
Title: Magnetic properties in ultra-thin 3d transition metal alloys II: Experimental verification of quantitative theories of damping and spin-pumping,
Abstract: A systematic experimental study of Gilbert damping is performed via
ferromagnetic resonance for the disordered crystalline binary 3d transition
metal alloys Ni-Co, Ni-Fe and Co-Fe over the full range of alloy compositions.
After accounting for inhomogeneous linewidth broadening, the damping shows
clear evidence of both interfacial damping enhancement (by spin pumping) and
radiative damping. We quantify these two extrinsic contributions and thereby
determine the intrinsic damping. The comparison of the intrinsic damping to
multiple theoretical calculations yields good qualitative and quantitative
agreement in most cases. Furthermore, the values of the damping obtained in
this study are in good agreement with a wide range of published experimental
and theoretical values. Additionally, we find a compositional dependence of the
spin mixing conductance. | [
0,
1,
0,
0,
0,
0
] |
Title: Detection of Anomalies in Large Scale Accounting Data using Deep Autoencoder Networks,
Abstract: Learning to detect fraud in large-scale accounting data is one of the
long-standing challenges in financial statement audits or fraud investigations.
Nowadays, the majority of applied techniques refer to handcrafted rules derived
from known fraud scenarios. While fairly successful, these rules exhibit the
drawback that they often fail to generalize beyond known fraud scenarios and
fraudsters gradually find ways to circumvent them. To overcome this
disadvantage and inspired by the recent success of deep learning we propose the
application of deep autoencoder neural networks to detect anomalous journal
entries. We demonstrate that the trained network's reconstruction error
obtainable for a journal entry and regularized by the entry's individual
attribute probabilities can be interpreted as a highly adaptive anomaly
assessment. Experiments on two real-world datasets of journal entries, show the
effectiveness of the approach resulting in high f1-scores of 32.93 (dataset A)
and 16.95 (dataset B) and less false positive alerts compared to state of the
art baseline methods. Initial feedback received by chartered accountants and
fraud examiners underpinned the quality of the approach in capturing highly
relevant accounting anomalies. | [
1,
0,
0,
0,
0,
0
] |
Title: Alternate Estimation of a Classifier and the Class-Prior from Positive and Unlabeled Data,
Abstract: We consider a problem of learning a binary classifier only from positive data
and unlabeled data (PU learning) and estimating the class-prior in unlabeled
data under the case-control scenario. Most of the recent methods of PU learning
require an estimate of the class-prior probability in unlabeled data, and it is
estimated in advance with another method. However, such a two-step approach
which first estimates the class prior and then trains a classifier may not be
the optimal approach since the estimation error of the class-prior is not taken
into account when a classifier is trained. In this paper, we propose a novel
unified approach to estimating the class-prior and training a classifier
alternately. Our proposed method is simple to implement and computationally
efficient. Through experiments, we demonstrate the practical usefulness of the
proposed method. | [
0,
0,
0,
1,
0,
0
] |
Title: Rate Optimal Binary Linear Locally Repairable Codes with Small Availability,
Abstract: A locally repairable code with availability has the property that every code
symbol can be recovered from multiple, disjoint subsets of other symbols of
small size. In particular, a code symbol is said to have $(r,t)$-availability
if it can be recovered from $t$ disjoint subsets, each of size at most $r$. A
code with availability is said to be 'rate-optimal', if its rate is maximum
among the class of codes with given locality, availability, and alphabet size.
This paper focuses on rate-optimal binary, linear codes with small
availability, and makes four contributions. First, it establishes tight upper
bounds on the rate of binary linear codes with $(r,2)$ and $(2,3)$
availability. Second, it establishes a uniqueness result for binary
rate-optimal codes, showing that for certain classes of binary linear codes
with $(r,2)$ and $(2,3)$-availability, any rate optimal code must be a direct
sum of shorter rate optimal codes. Third, it presents novel upper bounds on the
rates of binary linear codes with $(2,t)$ and $(r,3)$-availability. In
particular, the main contribution here is a new method for bounding the number
of cosets of the dual of a code with availability, using its covering
properties. Finally, it presents a class of locally repairable linear codes
associated with convex polyhedra, focusing on the codes associated with the
Platonic solids. It demonstrates that these codes are locally repairable with
$t = 2$, and that the codes associated with (geometric) dual polyhedra are
(coding theoretic) duals of each other. | [
1,
0,
1,
0,
0,
0
] |
Title: Occupation times for the finite buffer fluid queue with phase-type ON-times,
Abstract: In this short communication we study a fluid queue with a finite buffer. The
performance measure we are interested in is the occupation time over a finite
time period, i.e., the fraction of time the workload process is below some
fixed target level. We construct an alternating sequence of sojourn times
$D_1,U_1,...$ where the pairs $(D_i,U_i)_{i\in\mathbb{N}}$ are i.i.d. random
vectors. We use this sequence to determine the distribution function of the
occupation time in terms of its double transform. | [
0,
0,
1,
0,
0,
0
] |
Title: Affine forward variance models,
Abstract: We introduce the class of affine forward variance (AFV) models of which both
the conventional Heston model and the rough Heston model are special cases. We
show that AFV models can be characterized by the affine form of their cumulant
generating function, which can be obtained as solution of a convolution Riccati
equation. We further introduce the class of affine forward order flow intensity
(AFI) models, which are structurally similar to AFV models, but driven by jump
processes, and which include Hawkes-type models. We show that the cumulant
generating function of an AFI model satisfies a generalized convolution Riccati
equation and that a high-frequency limit of AFI models converges in
distribution to the AFV model. | [
0,
0,
0,
0,
0,
1
] |
Title: Measurement of the muon-induced neutron seasonal modulation with LVD,
Abstract: Cosmic ray muons with the average energy of 280 GeV and neutrons produced by
muons are detected with the Large Volume Detector at LNGS. We present an
analysis of the seasonal variation of the neutron flux on the basis of the data
obtained during 15 years. The measurement of the seasonal variation of the
specific number of neutrons generated by muons allows to obtaine the variation
magnitude of of the average energy of the muon flux at the depth of the LVD
location. The source of the seasonal variation of the total neutron flux is a
change of the intensity and the average energy of the muon flux. | [
0,
1,
0,
0,
0,
0
] |
Title: A sub-super solution method for a class of nonlocal problems involving the p(x)-Laplacian operator and applications,
Abstract: In the present paper we study the existence of solutions for some nonlocal
problems involving the p(x)-Laplacian operator. The approach is based on a new
sub-supersolution method | [
0,
0,
1,
0,
0,
0
] |
Title: A Las Vegas algorithm to solve the elliptic curve discrete logarithm problem,
Abstract: In this paper, we describe a new Las Vegas algorithm to solve the elliptic
curve discrete logarithm problem. The algorithm depends on a property of the
group of rational points of an elliptic curve and is thus not a generic
algorithm. The algorithm that we describe has some similarities with the most
powerful index-calculus algorithm for the discrete logarithm problem over a
finite field. | [
1,
0,
1,
0,
0,
0
] |
Title: Spectral sequences via examples,
Abstract: These are lecture notes for a short course about spectral sequences that was
held at Málaga, October 18--20 (2016), during the "Fifth Young Spanish
Topologists Meeting". The approach was to illustrate the basic notions via
fully computed examples arising from Algebraic Topology and Group Theory. | [
0,
0,
1,
0,
0,
0
] |
Title: A Note on Prediction Markets,
Abstract: In a prediction market, individuals can sequentially place bets on the
outcome of a future event. This leaves a trail of personal probabilities for
the event, each being conditional on the current individual's private
background knowledge and on the previously announced probabilities of other
individuals, which give partial information about their private knowledge. By
means of theory and examples, we revisit some results in this area. In
particular, we consider the case of two individuals, who start with the same
overall probability distribution but different private information, and then
take turns in updating their probabilities. We note convergence of the
announced probabilities to a limiting value, which may or may not be the same
as that based on pooling their private information. | [
0,
0,
1,
1,
0,
0
] |
Title: A recurrence relation for the odd order moments of the Fabius function,
Abstract: A simple recurrence relation for the even order moments of the Fabius
function is proven. Also, a very similar formula for the odd order moments in
terms of the even order moments is proved. The matrices corresponding to these
formulas (and their inverses) are multiplied so as to obtain a matrix that
correspond to a recurrence relation for the odd order moments in terms of
themselves. The theorem at the end gives a closed-form for the coefficients. | [
0,
0,
1,
0,
0,
0
] |
Title: Performance of Range Separated Hybrids: Study within BECKE88 family and Semilocal Exchange Hole based Range Separated Hybrid,
Abstract: A long range corrected range separated hybrid functional is developed based
on the density matrix expansion (DME) based semilocal exchange hole with
Lee-Yang-Parr (LYP) correlation. An extensive study involving the proposed
range separated hybrid for thermodynamic as well as properties related to the
fractional occupation number is compared with different BECKE88 family
semilocal, hybrid and range separated hybrids. It has been observed that using
Kohn-Sham kinetic energy dependent exchange hole several properties related to
the fractional occupation number can be improved without hindering the
thermochemical accuracy. The newly constructed range separated hybrid
accurately describe the hydrogen and non-hydrogen reaction barrier heights. The
present range separated functional has been constructed using full semilocal
meta-GGA type exchange hole having exact properties related to exchange hole
therefore, it has a strong physical basis. | [
0,
1,
0,
0,
0,
0
] |
Title: Manifold Mixup: Learning Better Representations by Interpolating Hidden States,
Abstract: Deep networks often perform well on the data distribution on which they are
trained, yet give incorrect (and often very confident) answers when evaluated
on points from off of the training distribution. This is exemplified by the
adversarial examples phenomenon but can also be seen in terms of model
generalization and domain shift. Ideally, a model would assign lower confidence
to points unlike those from the training distribution. We propose a regularizer
which addresses this issue by training with interpolated hidden states and
encouraging the classifier to be less confident at these points. Because the
hidden states are learned, this has an important effect of encouraging the
hidden states for a class to be concentrated in such a way so that
interpolations within the same class or between two different classes do not
intersect with the real data points from other classes. This has a major
advantage in that it avoids the underfitting which can result from
interpolating in the input space. We prove that the exact condition for this
problem of underfitting to be avoided by Manifold Mixup is that the
dimensionality of the hidden states exceeds the number of classes, which is
often the case in practice. Additionally, this concentration can be seen as
making the features in earlier layers more discriminative. We show that despite
requiring no significant additional computation, Manifold Mixup achieves large
improvements over strong baselines in supervised learning, robustness to
single-step adversarial attacks, semi-supervised learning, and Negative
Log-Likelihood on held out samples. | [
0,
0,
0,
1,
0,
0
] |
Title: Small Resolution Proofs for QBF using Dependency Treewidth,
Abstract: In spite of the close connection between the evaluation of quantified Boolean
formulas (QBF) and propositional satisfiability (SAT), tools and techniques
which exploit structural properties of SAT instances are known to fail for QBF.
This is especially true for the structural parameter treewidth, which has
allowed the design of successful algorithms for SAT but cannot be
straightforwardly applied to QBF since it does not take into account the
interdependencies between quantified variables.
In this work we introduce and develop dependency treewidth, a new structural
parameter based on treewidth which allows the efficient solution of QBF
instances. Dependency treewidth pushes the frontiers of tractability for QBF by
overcoming the limitations of previously introduced variants of treewidth for
QBF. We augment our results by developing algorithms for computing the
decompositions that are required to use the parameter. | [
1,
0,
0,
0,
0,
0
] |
Title: Lattice thermal expansion and anisotropic displacements in urea, bromomalonic aldehyde, pentachloropyridine and naphthalene,
Abstract: Anisotropic displacement parameters (ADPs) are commonly used in
crystallography, chemistry and related fields to describe and quantify thermal
motion of atoms. Within the very recent years, these ADPs have become
predictable by lattice dynamics in combination with first-principles theory.
Here, we study four very different molecular crystals, namely urea,
bromomalonic aldehyde, pentachloropyridine, and naphthalene, by
first-principles theory to assess the quality of ADPs calculated in the
quasi-harmonic approximation. In addition, we predict both thermal expansion
and thermal motion within the quasi-harmonic approximation and compare the
predictions with experimental data. Very reliable ADPs are calculated within
the quasi-harmonic approximation for all four cases up to at least 200 K, and
they turn out to be in better agreement with experiment than the harmonic ones.
In one particular case, ADPs can even reliably be predicted up to room
temperature. Our results also hint at the importance of normal-mode
anharmonicity in the calculation of ADPs. | [
0,
1,
0,
0,
0,
0
] |
Title: Modal operators and toric ideals,
Abstract: In the present paper we consider modal propositional logic and look for the
constraints that are imposed to the propositions of the special type $\Box a$
by the structure of the relevant finite Kripke frame. We translate the usual
language of modal propositional logic in terms of notions of commutative
algebra, namely polynomial rings, ideals, and bases of ideals. We use
extensively the perspective obtained in previous works in Algebraic Statistics.
We prove that the constraints on $\Box a$ can be derived through a binomial
ideal containing a toric ideal and we give sufficient conditions under which
the toric ideal fully describes the constraints. | [
0,
0,
1,
0,
0,
0
] |
Title: Metadynamics for Training Neural Network Model Chemistries: a Competitive Assessment,
Abstract: Neural network (NN) model chemistries (MCs) promise to facilitate the
accurate exploration of chemical space and simulation of large reactive
systems. One important path to improving these models is to add layers of
physical detail, especially long-range forces. At short range, however, these
models are data driven and data limited. Little is systematically known about
how data should be sampled, and `test data' chosen randomly from some sampling
techniques can provide poor information about generality. If the sampling
method is narrow `test error' can appear encouragingly tiny while the model
fails catastrophically elsewhere. In this manuscript we competitively evaluate
two common sampling methods: molecular dynamics (MD), normal-mode sampling
(NMS) and one uncommon alternative, Metadynamics (MetaMD), for preparing
training geometries. We show that MD is an inefficient sampling method in the
sense that additional samples do not improve generality. We also show MetaMD is
easily implemented in any NNMC software package with cost that scales linearly
with the number of atoms in a sample molecule. MetaMD is a black-box way to
ensure samples always reach out to new regions of chemical space, while
remaining relevant to chemistry near $k_bT$. It is one cheap tool to address
the issue of generalization. | [
0,
1,
0,
1,
0,
0
] |
Title: Multi-timescale memory dynamics in a reinforcement learning network with attention-gated memory,
Abstract: Learning and memory are intertwined in our brain and their relationship is at
the core of several recent neural network models. In particular, the
Attention-Gated MEmory Tagging model (AuGMEnT) is a reinforcement learning
network with an emphasis on biological plausibility of memory dynamics and
learning. We find that the AuGMEnT network does not solve some hierarchical
tasks, where higher-level stimuli have to be maintained over a long time, while
lower-level stimuli need to be remembered and forgotten over a shorter
timescale. To overcome this limitation, we introduce hybrid AuGMEnT, with leaky
or short-timescale and non-leaky or long-timescale units in memory, that allow
to exchange lower-level information while maintaining higher-level one, thus
solving both hierarchical and distractor tasks. | [
1,
0,
0,
1,
0,
0
] |
Title: Dynamical structure of entangled polymers simulated under shear flow,
Abstract: The non-linear response of entangled polymers to shear flow is complicated.
Its current understanding is framed mainly as a rheological description in
terms of the complex viscosity. However, the full picture requires an
assessment of the dynamical structure of individual polymer chains which give
rise to the macroscopic observables. Here we shed new light on this problem,
using a computer simulation based on a blob model, extended to describe shear
flow in polymer melts and semi-dilute solutions. We examine the diffusion and
the intermediate scattering spectra during a steady shear flow. The relaxation
dynamics are found to speed up along the flow direction, but slow down along
the shear gradient direction. The third axis, vorticity, shows a slowdown at
the short scale of a tube, but reaches a net speedup at the large scale of the
chain radius of gyration. | [
0,
1,
0,
0,
0,
0
] |
Title: Current induced magnetization switching in PtCoCr structures with enhanced perpendicular magnetic anisotropy and spin-orbit torques,
Abstract: Magnetic trilayers having large perpendicular magnetic anisotropy (PMA) and
high spin-orbit torques (SOTs) efficiency are the key to fabricate nonvolatile
magnetic memory and logic devices. In this work, PMA and SOTs are
systematically studied in Pt/Co/Cr stacks as a function of Cr thickness. An
enhanced perpendicular anisotropy field around 10189 Oe is obtained and is
related to the interface between Co and Cr layers. In addition, an effective
spin Hall angle up to 0.19 is observed due to the improved antidamping-like
torque by employing dissimilar metals Pt and Cr with opposite signs of spin
Hall angles on opposite sides of Co layer. Finally, we observed a nearly linear
dependence between spin Hall angle and longitudinal resistivity from their
temperature dependent properties, suggesting that the spin Hall effect may
arise from extrinsic skew scattering mechanism. Our results indicate that 3d
transition metal Cr with a large negative spin Hall angle could be used to
engineer the interfaces of trilayers to enhance PMA and SOTs. | [
0,
1,
0,
0,
0,
0
] |
Title: Quantum Black Holes and Atomic Nuclei are Hollow,
Abstract: The quantum Schrodinger-Newton equation is solved for a self-gravitating Bose
gas at zero temperature. It is derived that the density is non-uniform and a
central hollow cavity exists. The radial distribution of the particle momentum
is uniform. It is shown that a quantum black hole can be formed only above a
certain critical mass. The temperature effect is accounted for via the
Schrodinger-Poisson-Boltzmann equation, where low and high temperature
solutions are obtained. The theoretical analysis is extended to a strong
interacting gas via the Schrodinger-Yukawa equation, showing that the atomic
nuclei are also hollow. Hollow self-gravitating Fermi gases are described by
the Thomas-Fermi equation. | [
0,
1,
0,
0,
0,
0
] |
Title: Learning Non-Discriminatory Predictors,
Abstract: We consider learning a predictor which is non-discriminatory with respect to
a "protected attribute" according to the notion of "equalized odds" proposed by
Hardt et al. [2016]. We study the problem of learning such a non-discriminatory
predictor from a finite training set, both statistically and computationally.
We show that a post-hoc correction approach, as suggested by Hardt et al, can
be highly suboptimal, present a nearly-optimal statistical procedure, argue
that the associated computational problem is intractable, and suggest a second
moment relaxation of the non-discrimination definition for which learning is
tractable. | [
1,
0,
0,
0,
0,
0
] |
Title: Pinned, locked, pushed, and pulled traveling waves in structured environments,
Abstract: Traveling fronts describe the transition between two alternative states in a
great number of physical and biological systems. Examples include the spread of
beneficial mutations, chemical reactions, and the invasions by foreign species.
In homogeneous environments, the alternative states are separated by a smooth
front moving at a constant velocity. This simple picture can break down in
structured environments such as tissues, patchy landscapes, and microfluidic
devices. Habitat fragmentation can pin the front at a particular location or
lock invasion velocities into specific values. Locked velocities are not
sensitive to moderate changes in dispersal or growth and are determined by the
spatial and temporal periodicity of the environment. The synchronization with
the environment results in discontinuous fronts that propagate as periodic
pulses. We characterize the transition from continuous to locked invasions and
show that it is controlled by positive density-dependence in dispersal or
growth. We also demonstrate that velocity locking is robust to demographic and
environmental fluctuations and examine stochastic dynamics and evolution in
locked invasions. | [
0,
0,
0,
0,
1,
0
] |
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