cssi/SciSciGPT-SciSciNet huggingface dataset:
On matrix valued square integrable positive definite functions

In this paper, we study matrix valued positive definite functions on a unimodular group. We generalize two theorems of Godement on $$L^2$$ positive definite functions. We show that a matrix-valued continuous $$L^2$$ positive definite function can always be written as the convolution of a matrix-valued $$L^2$$ positive definite function with itself. We also prove that, given two $$L^2$$ matrix valued positive definite functions $$\Phi $$ and $$\Psi $$ , $$\int _G Tr(\Phi (g) \overline{\Psi (g)}^t) d g \ge 0$$ . In addition this integral equals zero if and only if $$\Phi * \Psi =0$$ . Our proofs are operator-theoretic and independent of the group.
A periodic isoperimetric problem related to the unique games conjecture

We prove the endpoint case of a conjecture of Khot and Moshkovitz related to the Unique Games Conjecture, less a small error. Let $n\geq2$. Suppose a subset $\Omega$ of $n$-dimensional Euclidean space $\mathbb{R}^{n}$ satisfies $-\Omega=\Omega^{c}$ and $\Omega+v=\Omega^{c}$ for any standard basis vector $v\in\mathbb{R}^{n}$. For any $x=(x_{1},\ldots,x_{n})\in\mathbb{R}^{n}$ and for any $q\geq1$, let $\|x\|_{q}^{q}=|x_{1}|^{q}+\cdots+|x_{n}|^{q}$ and let $\gamma_{n}(x)=(2\pi)^{-n/2}e^{-\|x\|_{2}^{2}/2}$ . For any $x\in\partial\Omega$, let $N(x)$ denote the exterior normal vector at $x$ such that $\|N(x)\|_{2}=1$. Let $B=\{x\in\mathbb{R}^{n}\colon \sin(\pi(x_{1}+\cdots+x_{n}))\geq0\}$. Our main result shows that $B$ has the smallest Gaussian surface area among all such subsets $\Omega$, less a small error: $$ \int_{\partial\Omega}\gamma_{n}(x)dx\geq(1-6\cdot 10^{-9})\int_{\partial B}\gamma_{n}(x)dx+\int_{\partial\Omega}\Big(1-\frac{\|N(x)\|_{1}}{\sqrt{n}}\Big)\gamma_{n}(x)dx. $$ In particular, $$ \int_{\partial\Omega}\gamma_{n}(x)dx\geq(1-6\cdot 10^{-9})\int_{\partial B}\gamma_{n}(x)dx. $$ Standard arguments extend these results to a corresponding weak inequality for noise stability. Removing the factor $6\cdot 10^{-9}$ would prove the endpoint case of the Khot-Moshkovitz conjecture. Lastly, we prove a Euclidean analogue of the Khot and Moshkovitz conjecture. The full conjecture of Khot and Moshkovitz provides strong evidence for the truth of the Unique Games Conjecture, a central conjecture in theoretical computer science that is closely related to the P versus NP problem. So, our results also provide evidence for the truth of the Unique Games Conjecture. Nevertheless, this paper does not prove any case of the Unique Games conjecture.
Optimal and adaptive off-policy evaluation in contextual bandits

We consider the problem of off-policy evaluation—estimating the value of a target policy using data collected by another policy—under the contextual bandit model. We establish a minimax lower bound on the mean squared error (MSE), and show that it is matched up to constant factors by the inverse propensity scoring (IPS) estimator. Since in the multi-armed bandit problem the IPS is suboptimal (Li et. al, 2015), our result highlights the difficulty of the contextual setting with non-degenerate context distributions. We further consider improvements on this minimax MSE bound, given access to a reward model. We show that the existing doubly robust approach, which utilizes such a reward model, may continue to suffer from high variance even when the reward model is perfect. We propose a new estimator called SWITCH which more effectively uses the reward model and achieves a superior bias-variance tradeoff compared with prior work. We prove an upper bound on its MSE and demonstrate its benefits empirically on a diverse collection of datasets, often seeing orders of magnitude improvements over a number of baselines.
On Discrimination Discovery and Removal in Ranked Data using Causal Graph

Predictive models learned from historical data are widely used to help companies and organizations make decisions. However, they may digitally unfairly treat unwanted groups, raising concerns about fairness and discrimination. In this paper, we study the fairness-aware ranking problem which aims to discover discrimination in ranked datasets and reconstruct the fair ranking. Existing methods in fairness-aware ranking are mainly based on statistical parity that cannot measure the true discriminatory effect since discrimination is causal. On the other hand, existing methods in causal-based anti-discrimination learning focus on classification problems and cannot be directly applied to handle the ranked data. To address these limitations, we propose to map the rank position to a continuous score variable that represents the qualification of the candidates. Then, we build a causal graph that consists of both the discrete profile attributes and the continuous score. The path-specific effect technique is extended to the mixed-variable causal graph to identify both direct and indirect discrimination. The relationship between the path-specific effects for the ranked data and those for the binary decision is theoretically analyzed. Finally, algorithms for discovering and removing discrimination from a ranked dataset are developed. Experiments using the real-world dataset show the effectiveness of our approaches.
Torsional Rigidity and Bergman Analytic Content of Simply Connected Regions

We exploit the equality of Bergman analytic content and torsional rigidity of a simply connected domain to develop a new method for calculating these quantities. This method is particularly suitable for the case when the region in question is a polygon. A large number of examples are computed in explicit detail to demonstrate the utility of our ideas.
Online Boosting Algorithms for Multi-label Ranking

We consider the multi-label ranking approach to multi-label learning. Boosting is a natural method for multi-label ranking as it aggregates weak predictions through majority votes, which can be directly used as scores to produce a ranking of the labels. We design online boosting algorithms with provable loss bounds for multi-label ranking. We show that our first algorithm is optimal in terms of the number of learners required to attain a desired accuracy, but it requires knowledge of the edge of the weak learners. We also design an adaptive algorithm that does not require this knowledge and is hence more practical. Experimental results on real data sets demonstrate that our algorithms are at least as good as existing batch boosting algorithms.
Singular integral equations with two fixed singularities and applications to fractured composites

A symmetric characteristic singular integral equation with two fixed singularities at the endpoints in the class of functions bounded at the ends is analyzed. It reduces to a vector Hilbert problem for a half-disc and then to a vector Riemann-Hilbert problem on a real axis with a piecewise constant matrix coefficient that has two points of discontinuity. A condition of solvability and a closed-form solution to the integral equation are derived. For the Chebyshev polynomials of the first kind in the right hand-side, the solution of the integral equation is expressed in terms of two nonorthogonal polynomials with associated weights. Based on this new generalized spectral relation for the singular operator with two fixed singularities an approximate solution to the complete singular integral equation is derived by recasting it as an infinite system of linear algebraic equations of the second kind. The method is illustrated by solving two problems of fracture mechanics, the antiplane and plane strain problems for a finite crack in a composite plane. The plane is formed by a strip and two half-planes; the elastic constants of the strip are different from those of the half-planes. The crack is orthogonal to the interfaces, and it is located in the strip with the ends lying in the interfaces. Numerical results are reported and discussed.
A presentation theorem for continuous logic and metric abstract elementary classes

We give a presentation theorem for continuous first-order logic and Metric Abstract Elementary classes in terms of $L_{\omega_1, \omega}$ and Abstract Elementary Classes, respectively. This presentation is accomplished by analyzing dense subsets that are closed under functions. We extend this correspondence to types and saturation.
A simple approach to temporal cloaking

In recent years a remarkable progress was made in the construction of spatial cloaks using the methods of transformation optics and metamaterials. The temporal cloaking, i.e. the cloaking of an event in spacetime, was also widely studied by using transformations on spacetime domains. We propose a simple and general method for the construction of temporal cloaking using the change of time variables only.
Prestructuring sparse matrices with dense rows and columns via null space methods

Several applied problems may produce large sparse matrices with a small number of dense rows and/or columns, which can adversely affect the performance of commonly used direct solvers. By posing the problem as a saddle point system, an unconventional application of a null space method can be employed to eliminate dense rows and columns. The choice of null space basis is critical in retaining the overall sparse structure of the matrix. A one-sided application of the null space method is also presented to eliminate either dense rows or columns. These methods can be considered techniques that modify the nonzero structure of the matrix before employing a direct solver, and may result in improved direct solver performance.
Multiwave tomography with reflectors: Landweber's iteration

We use the Landweber method for numerical simulations for the multiwave tomography problem with a reflecting boundary and compare it with the averaged time reversal method. We also analyze the rate of convergence and the dependence on the step size for the Landweber iterations on a Hilbert space.
Symbolic powers of ideals defining F-pure and strongly F-regular rings

Given a radical ideal $I$ in a regular ring $R$, the Containment Problem of symbolic and ordinary powers of $I$ consists of determining when the containment $I^{(a)} \subseteq I^b$ holds. By work of Ein-Lazersfeld-Smith, Hochster-Huneke and Ma-Schwede, there is a uniform answer to this question, but the resulting containments are not necessarily best possible. We show that a conjecture of Harbourne holds when $R/I$ is F-pure, and prove tighter containments in the case when $R/I$ is strongly F-regular.
Graph convolutional policy network for goal-directed molecular graph generation

Generating novel graph structures that optimize given objectives while obeying some given underlying rules is fundamental for chemistry, biology and social science research. This is especially important in the task of molecular graph generation, whose goal is to discover novel molecules with desired properties such as drug-likeness and synthetic accessibility, while obeying physical laws such as chemical valency. However, designing models to find molecules that optimize desired properties while incorporating highly complex and non-differentiable rules remains to be a challenging task. Here we propose Graph Convolutional Policy Network (GCPN), a general graph convolutional network based model for goal-directed graph generation through reinforcement learning. The model is trained to optimize domain-specific rewards and adversarial loss through policy gradient, and acts in an environment that incorporates domain-specific rules. Experimental results show that GCPN can achieve 61% improvement on chemical property optimization over state-of-the-art baselines while resembling known molecules, and achieve 184% improvement on the constrained property optimization task.
Efron's coins and the Linial arrangement

We characterize the tournaments that are dominance graphs of sets of (unfair) coins in which each coin displays its larger side with greater probability. The class of these tournaments coincides with the class of tournaments whose vertices can be numbered in a way that makes them semiacyclic, as defined by Postnikov and Stanley. We provide an example of a tournament on nine vertices that cannot be made semiacyclic, yet it may be represented as a dominance graph of coins, if we also allow coins that display their smaller side with greater probability. We conclude with an example of a tournament with 81 vertices that is not the dominance graph of any system of coins.
Tailoring light-matter interaction with a nanoscale plasmon resonator.

We propose and demonstrate a new approach for achieving enhanced light-matter interactions with quantum emitters. Our approach makes use of a plasmon resonator composed of defect-free, highly crystalline silver nanowires surrounded by patterned dielectric distributed Bragg reflectors. These resonators have an effective mode volume (Veff) 2 orders of magnitude below the diffraction limit and a quality factor (Q) approaching 100, enabling enhancement of spontaneous emission rates by a factor exceeding 75 at the cavity resonance. We also show that these resonators can be used to convert a broadband quantum emitter to a narrow-band single-photon source with color-selective emission enhancement.
On a proof of the Labastida-Marino-Ooguri-Vafa conjecture

We outline a proof of a remarkable conjecture of Labastida-Mari\~no-Ooguri-Vafa about certain new algebraic structures of quantum link invariants and the integrality of infinite family of new topological invariants. Our method is based on the cut-and-join analysis and a special rational ring characterizing the structure of the Chern-Simons partition function.
Deep Biaffine Attention for Neural Dependency Parsing

This paper builds off recent work from Kiperwasser & Goldberg (2016) using neural attention in a simple graph-based dependency parser. We use a larger but more thoroughly regularized parser than other recent BiLSTM-based approaches, with biaffine classifiers to predict arcs and labels. Our parser gets state of the art or near state of the art performance on standard treebanks for six different languages, achieving 95.7% UAS and 94.1% LAS on the most popular English PTB dataset. This makes it the highest-performing graph-based parser on this benchmark---outperforming Kiperwasser Goldberg (2016) by 1.8% and 2.2%---and comparable to the highest performing transition-based parser (Kuncoro et al., 2016), which achieves 95.8% UAS and 94.6% LAS. We also show which hyperparameter choices had a significant effect on parsing accuracy, allowing us to achieve large gains over other graph-based approaches.
EmojiNet: An Open Service and API for Emoji Sense Discovery

This paper presents the release of EmojiNet, the largest machine-readable emoji sense inventory that links Unicode emoji representations to their English meanings extracted from the Web. EmojiNet is a dataset consisting of: (i) 12,904 sense labels over 2,389 emoji, which were extracted from the web and linked to machine-readable sense definitions seen in BabelNet; (ii) context words associated with each emoji sense, which are inferred through word embedding models trained over Google News corpus and a Twitter message corpus for each emoji sense definition; and (iii) recognizing discrepancies in the presentation of emoji on different platforms, specification of the most likely platform-based emoji sense for a selected set of emoji. The dataset is hosted as an open service with a REST API and is available at http://emojinet.knoesis.org/. The development of this dataset, evaluation of its quality, and its applications including emoji sense disambiguation and emoji sense similarity are discussed.
Machine learning inverse problem for topological photonics

Topology opens many new horizons for photonics, from integrated optics to lasers. The complexity of large-scale devices asks for an effective solution of the inverse problem: how best to engineer the topology for a specific application? We introduce a machine-learning approach applicable in general to numerous topological problems. As a toy model, we train a neural network with the Aubry–Andre–Harper band structure model and then adopt the network for solving the inverse problem. Our application is able to identify the parameters of a complex topological insulator in order to obtain protected edge states at target frequencies. One challenging aspect is handling the multivalued branches of the direct problem and discarding unphysical solutions. We overcome this problem by adopting a self-consistent method to only select physically relevant solutions. We demonstrate our technique in a realistic design and by resorting to the widely available open-source TensorFlow library. Topological photonics is a growing field with applications spanning from integrated optics to lasers. This study presents a machine learning method to solve the inverse problem that may help finding optimized solutions to engineer the topology for each specific application
Honest signaling in zero-sum games is hard, and lying is even harder

We prove that, assuming the exponential time hypothesis, finding an epsilon-approximately optimal symmetric signaling scheme in a two-player zero-sum game requires quasi-polynomial time. This is tight by [Cheng et al., FOCS'15] and resolves an open question of [Dughmi, FOCS'14]. We also prove that finding a multiplicative approximation is NP-hard. We also introduce a new model where a dishonest signaler may publicly commit to use one scheme, but post signals according to a different scheme. For this model, we prove that even finding a (1-2^{-n})-approximately optimal scheme is NP-hard.
Fibered faces, veering triangulations, and the arc complex

We study the connections between subsurface projections in curve and arc complexes in fibered 3-manifolds and Agol’s veering triangulation. The main theme is that large-distance subsurfaces in fibers are associated to large simplicial regions in the veering triangulation, and this correspondence holds uniformly for all fibers in a given fibered face of the Thurston norm.
An Unoriented Variation on de Bruijn Sequences

For positive integers k, n, a de Bruijn sequence B(k, n) is a finite sequence of elements drawn from k characters whose subwords of length n are exactly the $$k^n$$ words of length n on k characters. This paper studies the unoriented de Bruijn sequence uB(k, n), an analog to de Bruijn sequences, but for which the sequence is read both forwards and backwards to determine the set of subwords of length n. We show that nontrivial unoriented de Bruijn sequences of optimal length exist if and only if k is two or odd and n is less than or equal to 3. Unoriented de Bruijn sequences for any k, n may be constructed from certain Eulerian trails in Eulerizations of unoriented de Bruijn graphs.
Regular Labelings and Geometric Structures

Three types of geometric structure—grid triangulations, rectangular subdivisions, and orthogonal polyhedra—can each be described combinatorially by a regular labeling: an assignment of colors and orientations to the edges of an associated maximal or near-maximal planar graph. We briefly survey the connections and analogies between these three kinds of labelings, and their uses in designing efficient geometric algorithms.
Stochastic Burgers' equation on the real line: regularity and moment estimates

In this project, we investigate the stochastic Burgers' equation with multiplicative space-time white noise on an unbounded spatial domain. We give a random field solution to this equation by defin...
Effortless data exploration with zenvisage: an expressive and interactive visual analytics system

Data visualization is by far the most commonly used mechanism to explore and extract insights from datasets, especially by novice data scientists. And yet, current visual analytics tools are rather limited in their ability to operate on collections of visualizations---by composing, filtering, comparing, and sorting them---to find those that depict desired trends or patterns. The process of visual data exploration remains a tedious process of trial-and-error. We propose zenvisage, a visual analytics platform for effortlessly finding desired visual patterns from large datasets. We introduce zenvisage's general purpose visual exploration language, ZQL ("zee-quel") for specifying the desired visual patterns, drawing from use-cases in a variety of domains, including biology, mechanical engineering, climate science, and commerce. We formalize the expressiveness of ZQL via a visual exploration algebra---an algebra on collections of visualizations---and demonstrate that ZQL is as expressive as that algebra. zenvisage exposes an interactive front-end that supports the issuing of ZQL queries, and also supports interactions that are "short-cuts" to certain commonly used ZQL queries. To execute these queries, zenvisage uses a novel ZQL graph-based query optimizer that leverages a suite of optimizations tailored to the goal of processing collections of visualizations in certain pre-defined ways. Lastly, a user survey and study demonstrates that data scientists are able to effectively use zenvisage to eliminate error-prone and tedious exploration and directly identify desired visualizations.
Efficient and Invariant Convolutional Neural Networks for Dense Prediction

Convolutional neural networks have shown great success on feature extraction from raw input data such as images. Although convolutional neural networks are invariant to translations on the inputs, they are not invariant to other transformations, including rotation and flip. Recent attempts have been made to incorporate more invariance in image recognition applications, but they are not applicable to dense prediction tasks, such as image segmentation. In this paper, we propose a set of methods based on kernel rotation and flip to enable rotation and flip invariance in convolutional neural networks. The kernel rotation can be achieved on kernels of 3 × 3, while kernel flip can be applied on kernels of any size. By rotating in eight or four angles, the convolutional layers could produce the corresponding number of feature maps based on eight or four different kernels. By using flip, the convolution layer can produce three feature maps. By combining produced feature maps using maxout, the resource requirement could be significantly reduced while still retain the invariance properties. Experimental results demonstrate that the proposed methods can achieve various invariance at reasonable resource requirements in terms of both memory and time.
A multi-strain virus model with infected cell age structure: Application to HIV

Abstract A general mathematical model of a within-host viral infection with n virus strains and explicit age-since-infection structure for infected cells is considered. In the model, multiple virus strains compete for a population of target cells. Cells infected with virus strain i ∈ { 1 , … , n } die at per-capita rate δ i ( a ) and produce virions at per-capita rate p i ( a ) , where δ i ( a ) and p i ( a ) are functions of the age-since-infection of the cell. Viral strain i has a basic reproduction number, R i , and a corresponding positive single strain equilibrium, E i , when R i > 1 . If R i 1 , then the total concentration of virus strain i will converge to 0 asymptotically. The main result is that when max i R i > 1 and all of the reproduction numbers are distinct, i.e. R i ≠ R j ∀ i ≠ j , the viral strain with the maximal basic reproduction number competitively excludes the other strains. As an application of the model, HIV evolution is considered and simulations are provided.
Second-Guessing in Tracing Tasks Considered Harmful?

[Context and motivation] Trace matrices are lynch pins for the development of mission- and safety-critical software systems and are useful for all software systems, yet automated methods for recovering trace links are far from perfect. This limitation makes the job of human analysts who must vet recovered trace links more difficult. [Question/Problem] Earlier studies suggested that certain analyst behaviors when performing trace recovery tasks lead to decreased accuracy of recovered trace relationships. We propose a three-step experimental study to: (a) determine if there really are behaviors that lead to errors of judgment for analysts, (b) enhance the requirements tracing software to curtail such behaviors, and (c) determine if curtailing such behaviors results in increased accuracy. [Principal ideas/results] We report on a preliminary study we undertook in which we modified the user interface of RETRO.NET to curtail two behaviors indicated by the earlier work. We report on observed results. [Contributions] We describe and discuss a major study of potentially unwanted analyst behaviors and present results of a preliminary study toward determining if curbing these behaviors with enhancements to tracing software leads to fewer human errors.
Synchronization of Kuramoto Oscillators via Cutset Projections

Synchronization in coupled oscillators networks is a remarkable phenomenon of relevance in numerous fields. For Kuramoto oscillators, the loss of synchronization is determined by a tradeoff between coupling strength and oscillator heterogeneity. Despite extensive prior work, the existing sufficient conditions for synchronization are either very conservative or heuristic and approximate. Using a novel cutset projection operator, we propose a new family of sufficient synchronization conditions; these conditions rigorously identify the correct functional form of the tradeoff between coupling strength and oscillator heterogeneity. To overcome the need to solve a nonconvex optimization problem, we then provide two explicit bounding methods, thereby obtaining 1) the best-known sufficient condition for unweighted graphs based on the 2-norm, and 2) the first-known generally applicable sufficient condition based on the $\infty$ -norm. We conclude with a comparative study of our novel $\infty$ -norm condition for specific topologies and IEEE test cases; for most IEEE test cases, our new sufficient condition is one to two orders of magnitude more accurate than previous rigorous tests.
The structure of evolved representations across different substrates for artificial intelligence

Artificial neural networks (ANNs), while exceptionally useful for classification, are vulnerable to misdirection. Small amounts of noise can significantly affect their ability to correctly complete...
Differentially Private Testing of Identity and Closeness of Discrete Distributions

We study the fundamental problems of identity testing (goodness of fit), and closeness testing (two sample test) of distributions over $k$ elements, under differential privacy. While the problems have a long history in statistics, finite sample bounds for these problems have only been established recently. In this work, we derive upper and lower bounds on the sample complexity of both the problems under $(\varepsilon, \delta)$-differential privacy. We provide optimal sample complexity algorithms for identity testing problem for all parameter ranges, and the first results for closeness testing. Our closeness testing bounds are optimal in the sparse regime where the number of samples is at most $k$. Our upper bounds are obtained by privatizing non-private estimators for these problems. The non-private estimators are chosen to have small sensitivity. We propose a general framework to establish lower bounds on the sample complexity of statistical tasks under differential privacy. We show a bound on differentially private algorithms in terms of a coupling between the two hypothesis classes we aim to test. By constructing carefully chosen priors over the hypothesis classes, and using Le Cam's two point theorem we provide a general mechanism for proving lower bounds. We believe that the framework can be used to obtain strong lower bounds for other statistical tasks under privacy.
Concentration of distances in Wigner matrices

Abstract It is well-known that distances in random iid matrices are highly concentrated around their mean. In this note we extend this concentration phenomenon to Wigner matrices. Exponential bounds for the lower tail are also included.
Smooth solutions and singularity formation for the inhomogeneous nonlinear wave equation

Abstract We study the nonlinear inhomogeneous wave equation in one space dimension: v t t − T ( v , x ) x x = 0 . By constructing some “decoupled” Riccati type equations for smooth solutions, we provide a singularity formation result without restrictions on the total variation of the data, which generalizes earlier singularity results of Lax and the first author. We apply these results to compressible Euler flows with a general pressure law and elasticity in an inhomogeneous medium.
Indecomposable vector-valued modular forms and periods of modular curves

We classify the three-dimensional representations of the modular group that are reducible but indecomposable, and their associated spaces of holomorphic vector-valued modular forms. We then demonstrate how such representations may be employed to compute periods of modular curves. This technique obviates the use of Hecke operators, and therefore provides a method for studying noncongruence modular curves as well as congruence.
Toward Extractive Summarization of Online Forum Discussions via Hierarchical Attention Networks.

Forum threads are lengthy and rich in content. Concise thread summaries will benefit both newcomers seeking information and those who participate in the discussion. Few studies, however, have examined the task of forum thread summarization. In this work we make the first attempt to adapt the hierarchical attention networks for thread summarization. The model draws on the recent development of neural attention mechanisms to build sentence and thread representations and use them for summarization. Our results indicate that the proposed approach can outperform a range of competitive baselines. Further, a redundancy removal step is crucial for achieving outstanding results.
Cooperative communication based on random beamforming strategy in wireless sensor networks

This paper presents a two-phase cooperative communication strategy and an optimal power allocation strategy to transmit sensor observations to a fusion center in a large-scale sensor network. Outage probability is used to evaluate the performance of the proposed system. Simulation results demonstrate that: 1) when signal-to-noise ratio is low, the performance of the proposed system is better than that of the multiple-input and multiple-output system over uncorrelated slow fading Rayleigh channels; 2) given the transmission rate and the total transmission SNR, there exists an optimal power allocation that minimizes the outage probability; 3) on correlated slow fading Rayleigh channels, channel correlation will degrade the system performance in linear proportion to the correlation level.
Flow-GAN: Combining Maximum Likelihood and Adversarial Learning in Generative Models.

Adversarial learning of probabilistic models has recently emerged as a promising alternative to maximum likelihood. Implicit models such as generative adversarial networks (GAN) often generate better samples compared to explicit models trained by maximum likelihood. Yet, GANs sidestep the characterization of an explicit density which makes quantitative evaluations challenging. To bridge this gap, we propose Flow-GANs, a generative adversarial network for which we can perform exact likelihood evaluation, thus supporting both adversarial and maximum likelihood training. When trained adversarially, Flow-GANs generate high-quality samples but attain extremely poor log-likelihood scores, inferior even to a mixture model memorizing the training data; the opposite is true when trained by maximum likelihood. Results on MNIST and CIFAR-10 demonstrate that hybrid training can attain high held-out likelihoods while retaining visual fidelity in the generated samples.
Video Summarization with Long Short-Term Memory

We propose a novel supervised learning technique for summarizing videos by automatically selecting keyframes or key subshots. Casting the task as a structured prediction problem, our main idea is to use Long Short-Term Memory (LSTM) to model the variable-range temporal dependency among video frames, so as to derive both representative and compact video summaries. The proposed model successfully accounts for the sequential structure crucial to generating meaningful video summaries, leading to state-of-the-art results on two benchmark datasets. In addition to advances in modeling techniques, we introduce a strategy to address the need for a large amount of annotated data for training complex learning approaches to summarization. There, our main idea is to exploit auxiliary annotated video summarization datasets, in spite of their heterogeneity in visual styles and contents. Specifically, we show that domain adaptation techniques can improve learning by reducing the discrepancies in the original datasets’ statistical properties.
Minimal actuator placement with optimal control constraints

We introduce the problem of minimal actuator placement in a linear control system so that a bound on the minimum control effort for a given state transfer is satisfied while controllability is ensured. We first show that this is an NP-hard problem following the recent work of Olshevsky [1]. Next, we prove that this problem has a supermodular structure. Afterwards, we provide an efficient algorithm that approximates up to a multiplicative factor of O(log n), where n is the size of the multi-agent network, any optimal actuator set that meets the specified energy criterion. Moreover, we show that this is the best approximation factor one can achieve in polynomial-time for the worst case. Finally, we test this algorithm over large Erdős-Renyi random networks to further demonstrate its efficiency.
Grothendieck's Theorem, past and present

Probably the most famous of Grothendieck’s contributions to Banach space theory is the result that he himself described as “the fundamental theorem in the metric theory of tensor products”. That is now commonly referred to as “Grothendieck’s theorem” (GT in short), or sometimes as “Grothendieck’s inequality”. This had a major impact first in Banach space theory (roughly after 1968), then, later on, in C ¤ -algebra theory, (roughly after 1978). More recently, in this millennium, a new version of GT has been successfully developed in the framework of “operator spaces” or non-commutative Banach spaces. In addition, GT independently surfaced in several quite unrelated fields: in connection with Bell’s inequality in quantum mechanics, in graph theory where the Grothendieck constant of a graph has been introduced and in computer science where the Grothendieck inequality is invoked to replace certain NP hard problems by others that can be treated by “semidefinite programming’ and hence solved in polynomial time. In this expository paper, we present a review of all these topics, starting from the original GT. We concentrate on the more recent developments and merely outline those of the first Banach space period since detailed accounts of that are already available, for instance the author’s 1986 CBMS notes.
Multi-objective Maximization of Monotone Submodular Functions with Cardinality Constraint

We consider the problem of multi-objective maximization of monotone submodular functions subject to cardinality constraint, often formulated as $\max_{|A|=k}\min_{i\in\{1,\dots,m\}}f_i(A)$. While it is widely known that greedy methods work well for a single objective, the problem becomes much harder with multiple objectives. In fact, Krause et al.\ (2008) showed that when the number of objectives $m$ grows as the cardinality $k$ i.e., $m=\Omega(k)$, the problem is inapproximable (unless $P=NP$). On the other hand, when $m$ is constant Chekuri et al.\ (2010) showed a randomized $(1-1/e)-\epsilon$ approximation with runtime (number of queries to function oracle) $n^{m/\epsilon^3}$. %In fact, the result of Chekuri et al.\ (2010) is for the far more general case of matroid constant. We focus on finding a fast and practical algorithm that has (asymptotic) approximation guarantees even when $m$ is super constant. We first modify the algorithm of Chekuri et al.\ (2010) to achieve a $(1-1/e)$ approximation for $m=o(\frac{k}{\log^3 k})$. This demonstrates a steep transition from constant factor approximability to inapproximability around $m=\Omega(k)$. Then using Multiplicative-Weight-Updates (MWU), we find a much faster $\tilde{O}(n/\delta^3)$ time asymptotic $(1-1/e)^2-\delta$ approximation. While the above results are all randomized, we also give a simple deterministic $(1-1/e)-\epsilon$ approximation with runtime $kn^{m/\epsilon^4}$. Finally, we run synthetic experiments using Kronecker graphs and find that our MWU inspired heuristic outperforms existing heuristics.
Nonlinear polarization and efficiency droop in hexagonal InGaN/GaN disk-in-wire LEDs

Abstract In this paper, we computationally evaluate the influence of nonlinear piezoelectricity in a recently reported hexagon shaped In0.25Ga0.75N/GaN disk-in-wire light emitting diode (LED). To calculate the single-particle electronic states and the interband optical transition rates, we have employed a fully atomistic valence force field (VFF)-sp3s∗ tight-binding framework coupled with a recently proposed (first-principles based) polarization model from Prodhomme et al. (2013). The microscopically determined transition parameters are then incorporated into an LED simulator to investigate how atomicity, strain relaxation, and the net polarization field affect the internal quantum efficiency and lead to a degraded droop characteristic.
Maximum Likelihood Upper Bounds on the Capacities of Discrete Information Stable Channels

Motivated by generating information stable processes greedily, we prove a universal maximum likelihood (ML) upper bound on the capacities of discrete information stable channels. The bound is derived leveraging a system of equations obtained via the Karush-Kuhn-Tucker (KKT) conditions. Intriguingly, for some discrete memoryless channels (DMCs), for instance, the BEC and BSC, the associated upper bounds are tight and equal to their capacities. Furthermore, for discrete channels with memory, as a particular example, we apply the ML bound to the BDC. The derived upper bound is a sum-max function related to counting the number of possible ways that a length-m binary subsequence that can be obtained by deleting n – m bits (with n – m close to nd and d denotes the deletion probability) of a length-n binary sequence. A full version of this paper is accessible at [1].
Abhyankar’s conjectures in Galois theory: Current status and future directions

In this paper, we survey the major contributions of Abhyankar to the development of the theory of fundamental groups and Galois covers in positive characteristic. We first discuss the current status of four conjectures of Abhyankar about Galois covers in positive characteristic. Then we discuss research directions inspired by Abhyankar's work, including many open problems.
The r^{p}-Weighted Energy Method of Dafermos and Rodnianski in General Asymptotically Flat Spacetimes and Applications

In [11], Dafermos and Rodnianski presented a novel approach to establish uniform decay rates for solutions $${\upvarphi }$$ to the scalar wave equation $$\square _{g}{\upvarphi }=0$$ on Minkowski, Schwarzschild and other asymptotically flat backgrounds. This paper generalises the methods and results of [11] to a broad class of asymptotically flat spacetimes $$(\mathcal {M},g)$$ , including Kerr spacetimes in the full subextremal range $$|a|<M$$ , but also radiating spacetimes with no exact symmetries in general dimension $$d+1$$ , $$d\ge 3$$ . As a soft corollary, it is shown that the Friedlander radiation field for $${\upvarphi }$$ is well defined on future null infinity. Moreover, polynomial decay rates are established for $${\upvarphi }$$ , provided that an integrated local energy decay statement (possibly with a finite loss of derivatives) holds and the near region of $$(\mathcal {M},g)$$ satisfies some mild geometric conditions. The latter conditions allow for $$(\mathcal {M},g)$$ to be the exterior of a black hole spacetime with a non-degenerate event horizon (having possibly complicated topology) or the exterior of a compact moving obstacle in an ambient globally hyperbolic spacetime satisfying suitable geometric conditions.
On tangent cones in Wasserstein space

If M is a smooth compact Riemannian manifold, let P(M) denote the Wasserstein space of probability measures on M. If S is an embedded submanifold of M, and $\mu$ is an absolutely continuous measure on S, then we compute the tangent cone of P(M) at $\mu$.
Movement-Efficient Sensor Deployment in Wireless Sensor Networks

We study a mobile wireless sensor network (MWSN) consisting of multiple mobile sensors or robots. Two key issues in MWSNs - energy consumption, which is dominated by sensor movement, and sensing coverage - have attracted plenty of attention, but the interaction of these issues is not well studied. To take both sensing coverage and movement energy consumption into consideration, we model the sensor deployment problem as a constrained source coding problem. Our goal is to find an optimal sensor deployment to maximize the sensing coverage with specific energy constraints. We derive necessary conditions to the optimal sensor deployment with (i) total energy constraint and (ii) network lifetime constraint. Using these necessary conditions, we design Lloyd-like algorithms to provide a trade-off between sensing coverage and energy consumption. Simulation results show that our algorithms outperform the existing relocation algorithms.
The MIP Ensemble Simulation: Local Ensemble Statistics in the Cosmic Web

We present a new technique that allows us to compute ensemble statistics on a local basis, directly relating halo properties to their local environment. This is achieved by the use of a correlated ensemble in which the Large Scale Structure is common to all realizations while having each an independent halo population. The correlated ensemble can be stacked, effectively increasing the halo number density by an arbitrary factor, thus breaking the fundamental limit in the halo number density given by the haloe mass function. This technique allows us to compute \textit{local ensemble statistics} of the matter/haloe distribution at any position in the simulation box, while removing the intrinsic stochasticity in the halo formation process and directly relating halo properties to their environment. We introduce the \textit{Multum In Parvo} (MIP) correlated ensemble simulation consisting of 220 realizations on a 32 h$^{-1}$ Mpc box with $256^3$ particles each. This is equivalent in terms of effective volume and number of particles to a box of $\sim 193$ h$^{-1}$ Mpc of side with $\sim 1540^3$ particles containing $\sim 5\times 10^6$ haloes with a minimum mass of $3.25 \times 10^9$ h$^{-1}$ M$_{\odot}$. The potential of the technique presented here is illustrated by computing the local ensemble statistics of the halo ellipticity and halo shape-LSS alignment. We show that, while there are general trends in the ellipticity and alignment of haloes with their LSS, there are also significant spatial variations which has important implications for observational studies of galaxy shape and alignment.
On intrinsic isometries to Euclidean space

I consider compact metric spaces which admit intrinsic isometries to Euclidean d-space. The main result roughly states that the class of these spaces coincides with class of inverse limits of Euclidean d-polyhedra.
Toward a diagnostic toolkit for linear models with Gaussian-process distributed random effects.

Author(s): Bose, Maitreyee; Hodges, James S; Banerjee, Sudipto | Abstract: Gaussian processes (GPs) are widely used as distributions of random effects in linear mixed models, which are fitusing the restricted likelihood or the closely related Bayesian analysis. This article addresses two problems. First, we proposetools for understanding how data determine estimates in these models, using a spectral basis approximation to the GP underwhich the restricted likelihood is formally identical to the likelihood for a gamma-errors GLM with identity link. Second,to examine the data’s support for a covariate and to understand how adding that covariate moves variation in the outcomey out of the GP and error parts of the fit, we apply a linear-model diagnostic, the added variable plot (AVP), both to theoriginal observations and to projections of the data onto the spectral basis functions. The spectral- and observation-domainAVPs estimate the same coefficient for a covariate but emphasize low- and high-frequency data features respectively and thushighlight the covariate’s effect on the GP and error parts of the fit, respectively. The spectral approximation applies to dataobserved on a regular grid; for data observed at irregular locations, we propose smoothing the data to a grid before applyingour methods. The methods are illustrated using the forest-biomass data of Finley et al. (2008).
An adiabatic theorem for resonances

We prove a robust extension of the quantum adiabatic theorem. The theorem applies to systems that have resonances instead of bound states and to systems for which just an approximation to a bound state is known. To demonstrate the theorem’s usefulness in a concrete situation, we apply it to shape resonances. © 2011 Wiley Periodicals, Inc.
Mnemo: Boosting Memory Cost Efficiency in Hybrid Memory Systems

For hosting data-serving and caching workloads based on key-value stores in clouds, the cost of memory represents a significant portion of the hosting expenses. The emergence of cheaper, but slower, types of memories, such as NVDIMMs, opens opportunities to reduce the hosting costs for such workloads. The question explored in this paper is how to determine adequate allocations of different memory types in future systems with heterogeneous memory components, so as to retain desired performance SLOs and maximize the cost efficiency of the memory resource. We develop Mnemo, a memory sizing and data tiering consultant, that permits quick exploration of the cost-benefit tradeoffs associated with different configurations of the hybrid memory components used by key-value store workloads. Using experimental evaluation with different workload patterns, Mnemo is able to afford applications such as Redis, Memcached and DynamoDB, with substantial reduction in their hosting costs, at negligible impact on application performance, thus improving the overall system memory cost efficiency.
Mechanisms for Integrated Feature Normalization and Remaining Useful Life Estimation Using LSTMs Applied to Hard-Disks

In this paper we focus on application of data-driven methods for remaining useful life estimation in components where past failure data is not uniform across devices, i.e. there is a high variance in the minimum and maximum value of the key parameters. The system under study is the hard disks used in computing cluster. The data used for analysis is provided by Backblaze as discussed later. In the article, we discuss the architecture of of the long short term neural network used and describe the mechanisms to choose the various hyper-parameters. Further, we describe the challenges faced in extracting effective training sets from highly unorganized and class-imbalanced big data and establish methods for online predictions with extensive data pre-processing, feature extraction and validation through online simulation sets with unknown remaining useful lives of the hard disks. Our algorithm performs especially well in predicting RUL near the critical zone of a device approaching failure. With the proposed approach we are able to predict whether a disk is going to fail in next ten days with an average precision of 0.8435. We also show that the architecture trained on a particular model is generalizable and transferable as it can be used to predict RUL for devices in other models from same manufacturer.