cssi/SciSciGPT-SciSciNet huggingface dataset:
Exact and efficient algorithm to discover extreme stochastic events in wind generation over transmission Power Grids

In this manuscript we continue the thread of [M. Chertkov, F. Pan, M. Stepanov, Predicting Failures in Power Grids: The Case of Static Overloads, IEEE Smart Grid 2011] and suggest a new algorithm discovering most probable extreme stochastic events in static power grids associated with intermittent generation of wind turbines. The algorithm becomes EXACT and EFFICIENT (polynomial) in the case of the proportional (or other low parametric) control of standard generation, and log-concave probability distribution of the renewable generation, assumed known from the wind forecast. We illustrate the algorithm's ability to discover problematic extreme events on the example of the IEEE RTS-96 model of transmission with additions of 10%;20% and 30% of renewable generation. We observe that the probability of failure may grow but it may also decrease with increase in renewable penetration, if the latter is sufficiently diversified and distributed.
Tensor Product Generation Networks for Deep NLP Modeling

We present a new approach to the design of deep networks for natural language processing (NLP), based on the general technique of Tensor Product Representations (TPRs) for encoding and processing symbol structures in distributed neural networks. A network architecture — the Tensor Product Generation Network (TPGN) — is proposed which is capable in principle of carrying out TPR computation, but which uses unconstrained deep learning to design its internal representations. Instantiated in a model for image-caption generation, TPGN outperforms LSTM baselines when evaluated on the COCO dataset. The TPR-capable structure enables interpretation of internal representations and operations, which prove to contain considerable grammatical content. Our caption-generation model can be interpreted as generating sequences of grammatical categories and retrieving words by their categories from a plan encoded as a distributed representation.
Action of a scattering map on weighted Sobolev spaces in the plane

Abstract We consider a scattering map that arises in the ∂ ¯ approach to the scattering theory for the Davey–Stewartson II equation and show that the map is an invertible map between certain weighted L 2 Sobolev spaces.
Joint Actuator-Sensor Design for Stochastic Linear Systems

We investigate here the joint actuator-sensor design problem for stochastic linear control systems. Specifically, we address the problem of identifying a pair of sensor and actuator which gives rise to the minimum expected value of a time-averaged quadratic cost. It is well known that for the linear-quadratic-Gaussian (LQG) control problem, the optimal feedback control law can be obtained via the celebrated separation principle. Moreover, if the system is stabilizable and detectable, then the infinite-horizon time-averaged cost exists. But such a cost depends on the placements of the sensor and the actuator. We formulate in the paper the optimization problem about minimizing the time-averaged cost over admissible pairs of actuator and sensor under the constraint that their Euclidean norms are fixed. The problem is non-convex and is in general difficult to solve. We obtain in the paper a gradient descent algorithm (over the set of admissible pairs) which minimizes the time-averaged cost. Moreover, we show that the algorithm can lead to a unique local (and hence global) minimum point under certain special conditions.
Saturated fusion systems with parabolic families

Abstract Let G be a group; a finite p-subgroup S of G is a Sylow p-subgroup if every finite p-subgroup of G is conjugate to a subgroup of S. In this paper, we examine the relations between the fusion system over S which is given by conjugation in G and a certain chamber system C , on which G acts chamber transitively with chamber stabilizer N G ( S ) . Next, we introduce the notion of a fusion system with a parabolic family and we show that a chamber system can be associated to such a fusion system. We determine some conditions the chamber system has to fulfill in order to assure the saturation of the underlying fusion system. We give an application to fusion systems with parabolic families of classical type.
DenseNet for dense flow

Classical approaches for estimating optical flow have achieved rapid progress in the last decade. However, most of them are too slow to be applied in real-time video analysis. Due to the great success of deep learning, recent work has focused on using CNNs to solve such dense prediction problems. In this paper, we investigate a new deep architecture, Densely Connected Convolutional Networks (DenseNet), to learn optical flow. This specific architecture is ideal for the problem at hand as it provides shortcut connections throughout the network, which leads to implicit deep supervision. We extend current DenseNet to a fully convolutional network to learn motion estimation in an unsupervised manner. Evaluation results on three standard benchmarks demonstrate that DenseNet is a better fit than other widely adopted CNN architectures for optical flow estimation.
Watch What You Just Said: Image Captioning with Text-Conditional Attention

Attention mechanisms have attracted considerable interest in image captioning due to their powerful performance. However, existing methods use only visual content as attention and whether textual context can improve attention in image captioning remains unsolved. To explore this problem, we propose a novel attention mechanism, called text-conditional attention, which allows the caption generator to focus on certain image features given previously generated text. To obtain text-related image features for our attention model, we adopt the guiding Long Short-Term Memory (gLSTM) captioning architecture with CNN fine-tuning. Our proposed method allows joint learning of the image embedding, text embedding, text-conditional attention and language model with one network architecture in an end-to-end manner. We perform extensive experiments on the MS-COCO dataset. The experimental results show that our method outperforms state-of-the-art captioning methods on various quantitative metrics as well as in human evaluation, which supports the use of our text-conditional attention in image captioning.
Rigidity of pairs of quasiregular mappings whose symmetric part of gradient are close

Abstract For A ∈ M 2 × 2 let S ( A ) = A T A , i.e. the symmetric part of the polar decomposition of A. We consider the relation between two quasiregular mappings whose symmetric part of gradient are close. Our main result is the following. Suppose v , u ∈ W 1 , 2 ( B 1 ( 0 ) : R 2 ) are Q-quasiregular mappings with ∫ B 1 ( 0 ) det ⁡ ( D u ) − p d z ≤ C p for some p ∈ ( 0 , 1 ) and ∫ B 1 ( 0 ) | D u | 2 d z ≤ π . There exists constant M > 1 such that if ∫ B 1 ( 0 ) | S ( D v ) − S ( D u ) | 2 d z = ϵ then ∫ B 1 2 ( 0 ) | D v − R D u | d z ≤ c C p 2 p ϵ p 2 M Q 5 log ⁡ ( 10 C p Q ) for some R ∈ SO ( 2 ) . Taking u = Id we obtain a special case of the quantitative rigidity result of Friesecke, James and Muller [13] . Our main result can be considered as a first step in a new line of generalization of Theorem 1 of [13] in which Id is replaced by a mapping of non-trivial degree.
An infinite class of Sparse-Yao spanners

Let P be a set of n points in the plane. The Yao graph for P is a geometric graph obtained by extending equally spaced rays from each point u e P, and connecting u to a closest neighbor in each sector formed by these rays. Associated to this graph is an integer parameter k > 1 defining the number of rays. The out-degree of the Yao graph is k, but the in-degree can be as large as n − 1. To overcome the problem of potential high in-degree, the Sparse-Yao graph (also known as Yao-Yao graph) eliminates from the Yao graph all but a shortest incoming edge in each sector. It has been established that the Yao graph defined by integer parameter k ≥ 6 is a t-spanner, for some real constant t > 1, meaning that it has a path between each pair of points in P of length at most t times the Euclidean distance between the two points. The constant t is called the stretch factor of the Yao graph. The problem of determining whether the Sparse-Yao graph is a spanner or not has been long open. In this paper we make progress on this problem by showing that the Sparse-Yao graph defined by integer parameter 6k, with k ≥ 6, is a spanner with stretch factor 11.67. With parameter k ≥ 8, the stretch factor drops to 4.75.
Statistical estimation with strategic data sources in competitive settings

In this paper, we introduce a preliminary model for interactions in the data market. Recent research has shown ways in which a single central data aggregator can design mechanisms to ensure it receives high quality data from a collection of users, even when the sources have an aversion to producing and reporting such estimates to the aggregator. However, we have shown that these mechanisms often break down in more realistic models, where multiple data aggregators are in competition for the users' data. We formulate the competition that arises between the aggregators as a game, and show this game admits either no Nash equilibria, or a continuum of Nash Equilibria. In the latter case, there is a fundamental ambiguity in who bears the burden of incentivizing different data sources. We are also able to calculate the price of anarchy, which measures how much social welfare is lost between the Nash equilibrium and the social optimum, i.e. between non-cooperative strategic play and cooperation.
Blocks of small defect

Abstract Let G be a finite solvable group, let p be a prime such that p ≥ 5 and O p ( G ) = 1 , and we denote | G | p = p n , then G contains a block of defect less than or equal to ⌊ 3 n 5 ⌋ . Let G be a finite solvable group and let p a be the largest power of p dividing χ ( 1 ) for an irreducible character χ of G, we show that | G : F ( G ) | p ≤ p 3 a for p ≥ 5 .
On the semi-simplicity of the quantum cohomology algebras of complete intersections

In this short note, we study the semi-simplicity of the quantum cohomology algebra H(V, C) of a Fano complete intersection V, and show that the subspace of H(V, C) generated by the hyperplane sections is semi-simple in the sense of Dubrovin when the degree of V satisfies certain conditions.
A Nice Example of Lebesgue Integration

We explore the properties of an interesting new example of a function which is Lebesgue integrable but not Riemann integrable.
Network equivalence in the presence of an eavesdropper

We consider networks of noisy degraded wiretap channels in the presence of an eavesdropper. For the case where the eavesdropper can wiretap at most one channel at a time, we show that the secrecy capacity region, for a broad class of channels and any given network topology and communication demands, is equivalent to that of a corresponding network where each noisy wiretap channel is replaced by a noiseless wiretap channel. Thus in this case there is a separation between wiretap channel coding on each channel and secure network coding on the resulting noiseless network. We show with an example that such separation does not hold when the eavesdropper can access multiple channels at the same time, for which case we provide upper and lower bounding noiseless networks.
Inoculation by Fine-Tuning: A Method for Analyzing Challenge Datasets.

Several datasets have recently been constructed to expose brittleness in models trained on existing benchmarks. While model performance on these challenge datasets is significantly lower compared to the original benchmark, it is unclear what particular weaknesses they reveal. For example, a challenge dataset may be difficult because it targets phenomena that current models cannot capture, or because it simply exploits blind spots in a model’s specific training set. We introduce inoculation by fine-tuning, a new analysis method for studying challenge datasets by exposing models (the metaphorical patient) to a small amount of data from the challenge dataset (a metaphorical pathogen) and assessing how well they can adapt. We apply our method to analyze the NLI “stress tests” (Naik et al., 2018) and the Adversarial SQuAD dataset (Jia and Liang, 2017). We show that after slight exposure, some of these datasets are no longer challenging, while others remain difficult. Our results indicate that failures on challenge datasets may lead to very different conclusions about models, training datasets, and the challenge datasets themselves.
On a problem of Neumann

Abstract A conjecture widely attributed to Neumann is that all finite non-desarguesian projective planes contain a Fano subplane. In this note, we show that any finite projective plane of even order which admits an orthogonal polarity contains many Fano subplanes. The number of planes of order less than n previously known to contain a Fano subplane was O ( log n ) , whereas the number of planes of order less than n that our theorem applies to is not bounded above by any polynomial in n .
On random exchange-stable matchings

Abstract Consider the group of n men and n women, each with their own preference list for a potential marriage partner. The stable marriage is a bipartite matching such that no unmatched pair (man, woman) prefer each other to their partners in the matching. Its non-bipartite version, with an even number n of members, is known as the stable roommates problem. Jose Alcalde introduced an alternative notion of exchange-stable, one-sided, matching: no two members prefer each other’s partners to their own partners in the matching. Katarina Cechlarova and David Manlove showed that the e-stable matching decision problem is N P -complete for both types of matchings. We prove that the expected number of e-stable matchings is asymptotic to π n 2 1 ∕ 2 for two-sided case, and to e 1 ∕ 2 for one-sided case. However, the standard deviation of this number exceeds 1 . 1 3 n , ( 1 . 0 6 n resp.). As an obvious byproduct, there exist instances of preference lists with at least 1 . 1 3 n ( 1 . 0 6 n resp.) e-stable matchings. The probability that there is no matching which is stable and e-stable is at least 1 − e − n 1 ∕ 2 − o ( 1 ) , ( 1 − O ( 2 − n ∕ 2 ) resp.).
Persistence, Coexistence and Extinction in Two Species Chemotaxis Models on Bounded Heterogeneous Environments

In this paper, we consider two species chemotaxis systems with Lotka–Volterra type competition terms in heterogeneous media. We first find various conditions on the parameters which guarantee the global existence and boundedness of classical solutions with nonnegative initial functions. Next, we find further conditions on the parameters which establish the persistence of the two species. Then, under the same set of conditions for the persistence of two species, we prove the existence of coexistence states. Finally we prove the extinction phenomena in the sense that one of the species dies out asymptotically and the other reaches its carrying capacity as time goes to infinity. The persistence in general two species chemotaxis systems is studied for the first time. Several important techniques are developed to study the persistence and coexistence of two species chemotaxis systems. Many existing results on the persistence, coexistence, and extinction on two species competition systems without chemotaxis are recovered.
Information-Theoretic Lower Bounds on Bayes Risk in Decentralized Estimation

We derive lower bounds on the Bayes risk in decentralized estimation, where the estimator does not have direct access to the random samples generated conditionally on the random parameter of interest, but only to the data received from local processors that observe the samples. The received data are subject to communication constraints due to the quantization and the noisy communication channels from the processors to the estimator. We first derive general lower bounds on the Bayes risk using information-theoretic quantities, such as mutual information, information density, small ball probability, and differential entropy. We then apply these lower bounds to the decentralized case, using strong data processing inequalities to quantify the contraction of information due to communication constraints. We treat the cases of a single processor and of multiple processors, where the samples observed by different processors may be conditionally dependent given the parameter, for noninteractive and interactive communication protocols. Our results recover and improve recent lower bounds on the Bayes risk and the minimax risk for certain decentralized estimation problems, where previously only conditionally independent sample sets and noiseless channels have been considered. Moreover, our results provide a general way to quantify the degradation of estimation performance caused by distributing resources to multiple processors, which is only discussed for specific examples in existing works.
Hate Lingo: A Target-Based Linguistic Analysis of Hate Speech in Social Media

While social media empowers freedom of expression and individual voices, it also enables anti-social behavior, online harassment, cyberbullying, and hate speech. In this paper, we deepen our understanding of online hate speech by focusing on a largely neglected but crucial aspect of hate speech -- its target: either directed towards a specific person or entity, or generalized towards a group of people sharing a common protected characteristic. We perform the first linguistic and psycholinguistic analysis of these two forms of hate speech and reveal the presence of interesting markers that distinguish these types of hate speech. Our analysis reveals that Directed hate speech, in addition to being more personal and directed, is more informal, angrier, and often explicitly attacks the target (via name calling) with fewer analytic words and more words suggesting authority and influence. Generalized hate speech, on the other hand, is dominated by religious hate, is characterized by the use of lethal words such as murder, exterminate, and kill; and quantity words such as million and many. Altogether, our work provides a data-driven analysis of the nuances of online-hate speech that enables not only a deepened understanding of hate speech and its social implications, but also its detection.
Attacking the Madry Defense Model with $L_1$-based Adversarial Examples

The Madry Lab recently hosted a competition designed to test the robustness of their adversarially trained MNIST model. Attacks were constrained to perturb each pixel of the input image by a scaled maximal $L_\infty$ distortion $\epsilon$ = 0.3. This discourages the use of attacks which are not optimized on the $L_\infty$ distortion metric. Our experimental results demonstrate that by relaxing the $L_\infty$ constraint of the competition, the elastic-net attack to deep neural networks (EAD) can generate transferable adversarial examples which, despite their high average $L_\infty$ distortion, have minimal visual distortion. These results call into question the use of $L_\infty$ as a sole measure for visual distortion, and further demonstrate the power of EAD at generating robust adversarial examples.
Upper bounds on the second largest prime factor of an odd perfect number

Acquaah and Konyagin showed that if N is an odd perfect number with prime factorization N = p1a1p2a2⋯pkak, where p1 < p2⋯ < pk, then one must have pk < 31/3N1/3. Using methods similar to theirs, we...
On the evaluation of prolate spheroidal wave functions and associated quadrature rules

Abstract As demonstrated by Slepian et al. in a sequence of classical papers (see Slepian (1983) [33] , Slepian and Pollak (1961) [34] , Landau and Pollak (1961) [18] , Slepian and Pollak (1964) [35] , Slepian (1965) [36] ), prolate spheroidal wave functions (PSWFs) provide a natural and efficient tool for computing with bandlimited functions defined on an interval. Recently, PSWFs have been becoming increasingly popular in various areas in which such functions occur – this includes physics (e.g. wave phenomena, fluid dynamics), engineering (signal processing, filter design), etc. To use PSWFs as a computational tool, one needs fast and accurate numerical algorithms for the evaluation of PSWFs and related quantities, as well as for the construction of corresponding quadrature rules, interpolation formulas, etc. During the last 15 years, substantial progress has been made in the design of such algorithms – see, for example, Xiao et al. (2001) [40] (see also Bowkamp (1947) [6] , Slepian and Pollak (1961) [34] , Landau and Pollak (1961) [18] , Slepian and Pollak (1964) [35] for some classical results). The complexity of many of the existing algorithms, however, is at least quadratic in the band limit c. For example, the evaluation of the nth eigenvalue of the prolate integral operator requires O ( c 2 + n 2 ) operations (see e.g. Xiao et al. (2001) [40] ); the construction of accurate quadrature rules for the integration (and associated interpolation) of bandlimited functions with band limit c requires O ( c 3 ) operations (see e.g. Cheng et al. (1999) [8] ). Therefore, while the existing algorithms are satisfactory for moderate values of c (e.g. c ⩽ 10 3 ), they tend to be relatively slow when c is large (e.g. c ⩾ 10 4 ). In this paper, we describe several numerical algorithms for the evaluation of PSWFs and related quantities, and design a class of PSWF-based quadratures for the integration of bandlimited functions. While the analysis is somewhat involved and will be published separately (currently, it can be found in Osipov and Rokhlin (2012) [27] ), the resulting numerical algorithms are quite simple and efficient in practice. For example, the evaluation of the nth eigenvalue of the prolate integral operator requires O ( n + c ⋅ log c ) operations; the construction of accurate quadrature rules for the integration (and associated interpolation) of bandlimited functions with band limit c requires O ( c ) operations. All algorithms described in this paper produce results essentially to machine precision. Our results are illustrated via several numerical experiments.
Dimensionality Reduction with Subspace Structure Preservation

Modeling data as being sampled from a union of independent subspaces has been widely applied to a number of real world applications. However, dimensionality reduction approaches that theoretically preserve this independence assumption have not been well studied. Our key contribution is to show that 2K projection vectors are sufficient for the independence preservation of any K class data sampled from a union of independent subspaces. It is this non-trivial observation that we use for designing our dimensionality reduction technique. In this paper, we propose a novel dimensionality reduction algorithm that theoretically preserves this structure for a given dataset. We support our theoretical analysis with empirical results on both synthetic and real world data achieving state-of-the-art results compared to popular dimensionality reduction techniques.
Masking Strategies for Image Manifolds

We consider the problem of selecting an optimal mask for an image manifold, i.e., choosing a subset of the pixels of the image that preserves the manifold’s geometric structure present in the original data. Such masking implements a form of compressive sensing through emerging imaging sensor platforms for which the power expense grows with the number of pixels acquired. Our goal is for the manifold learned from masked images to resemble its full image counterpart as closely as possible. More precisely, we show that one can indeed accurately learn an image manifold without having to consider a large majority of the image pixels. In doing so, we consider two masking methods that preserve the local and global geometric structure of the manifold, respectively. In each case, the process of finding the optimal masking pattern can be cast as a binary integer program, which is computationally expensive but can be approximated by a fast greedy algorithm. Numerical experiments show that the relevant manifold structure is preserved through the data-dependent masking process, even for modest mask sizes.
Revealing Network Structure, Confidentially: Improved Rates for Node-Private Graphon Estimation

Motivated by growing concerns over ensuring privacy on social networks, we develop new algorithms and impossibility results for fitting complex statistical models to network data subject to rigorous privacy guarantees. We consider the so-called node-differentially private algorithms, which compute information about a graph or network while provably revealing almost no information about the presence or absence of a particular node in the graph. We provide new algorithms for node-differentially private estimation for a popular and expressive family of network models: stochastic block models and their generalization, graphons. Our algorithms improve on prior work [15], reducing their error quadratically and matching, in many regimes, the optimal nonprivate algorithm [37]. We also show that for the simplest random graph models (G(n, p) and G(n, m)), node-private algorithms can be qualitatively more accurate than for more complex models—converging at a rate of 1/ e^2 n^3 instead of 1/e^2 n^2. This result uses a new extension lemma for differentially private algorithms that we hope will be broadly useful.
On the Evaluation of Semantic Phenomena in Neural Machine Translation Using Natural Language Inference

We propose a process for investigating the extent to which sentence representations arising from neural machine translation (NMT) systems encode distinct semantic phenomena. We use these representations as features to train a natural language inference (NLI) classifier based on datasets recast from existing semantic annotations. In applying this process to a representative NMT system, we find its encoder appears most suited to supporting inferences at the syntax-semantics interface, as compared to anaphora resolution requiring world knowledge. We conclude with a discussion on the merits and potential deficiencies of the existing process, and how it may be improved and extended as a broader framework for evaluating semantic coverage
Stability properties of the colored Jones polynomial

It is known that the colored Jones polynomial of a +-adequate link has a well-defined tail consisting of stable coefficients, and that the coefficients of the tail carry geometric and topological i...
Gradually Updated Neural Networks for Large-Scale Image Recognition

Depth is one of the keys that make neural networks succeed in the task of large-scale image recognition. The state-of-the-art network architectures usually increase the depths by cascading convolutional layers or building blocks. In this paper, we present an alternative method to increase the depth. Our method is by introducing computation orderings to the channels within convolutional layers or blocks, based on which we gradually compute the outputs in a channel-wise manner. The added orderings not only increase the depths and the learning capacities of the networks without any additional computation costs, but also eliminate the overlap singularities so that the networks are able to converge faster and perform better. Experiments show that the networks based on our method achieve the state-of-the-art performances on CIFAR and ImageNet datasets.
Differential equations in automorphic forms

Physicists such as Green, Vanhove, et al show that differential equations involving automorphic forms govern the behavior of gravitons. One particular point of interest is solutions to $(\Delta-\lambda)u=E_{\alpha} E_{\beta}$ on an arithmetic quotient of the exceptional group $E_8$. We establish that the existence of a solution to $(\Delta-\lambda)u=E_{\alpha}E_{\beta}$ on the simpler space $SL_2(\mathbb{Z})\backslash SL_2(\mathbb{R})$ for certain values of $\alpha$ and $\beta$ depends on nontrivial zeros of the Riemann zeta function $\zeta(s)$. Further, when such a solution exists, we use spectral theory to solve $(\Delta-\lambda)u=E_{\alpha}E_{\beta}$ on $SL_2(\mathbb{Z})\backslash SL_2(\mathbb{R})$ and provide proof of the meromorphic continuation of the solution. The construction of such a solution uses Arthur truncation, the Maass-Selberg formula, and automorphic Sobolev spaces.
Proactive Defense Against Physical Denial of Service Attacks Using Poisson Signaling Games

While the Internet of things (IoT) promises to improve areas such as energy efficiency, health care, and transportation, it is highly vulnerable to cyberattacks. In particular, distributed denial-of-service (DDoS) attacks overload the bandwidth of a server. But many IoT devices form part of cyber-physical systems (CPS). Therefore, they can be used to launch “physical” denial-of-service attacks (PDoS) in which IoT devices overflow the “physical bandwidth” of a CPS. In this paper, we quantify the population-based risk to a group of IoT devices targeted by malware for a PDoS attack. In order to model the recruitment of bots, we develop a “Poisson signaling game,” a signaling game with an unknown number of receivers, which have varying abilities to detect deception. Then we use a version of this game to analyze two mechanisms (legal and economic) to deter botnet recruitment. Equilibrium results indicate that (1) defenders can bound botnet activity, and (2) legislating a minimum level of security has only a limited effect, while incentivizing active defense can decrease botnet activity arbitrarily. This work provides a quantitative foundation for proactive PDoS defense.
Fredholm Operators in the Toeplitz Algebra {\mathcal {I}}(QC)

We will give a complete description of \({\mathcal {I}}\) the set of all invertible quasicontinuous functions on the unit circle. In particular we will show that \({\mathcal {I}}\) has uncountably many path-connected components. We will also characterize \({\mathcal {F}}\) the set of Fredholm operators of the C\(^*\)-algebra generated by the Toeplitz operators \(T_\phi \) with quasicontinuous symbols \(\phi \). Finally we will classify the path-connected components of \({\mathcal {F}}\) and show that \({\mathcal {F}}\) has uncountably many path-connected components.
Crime Event Embedding with Unsupervised Feature Selection

We present a novel event embedding algorithm for crime data that can jointly capture time, location, and the complex free-text component of each event. The embedding is achieved by regularized Restricted Boltzmann Machines (RBMs), and we introduce a new way to regularize by imposing a ` 1 penalty on the conditional distributions of the observed variables of RBMs. This choice of regularization performs feature selection and it also leads to efficient computation since the gradient can be computed in a closed form. The feature selection forces embedding to be based on the most important keywords, which captures the common modus operandi (M.O.) in crime series. Using numerical experiments on a large-scale crime dataset, we show that our regularized RBMs can achieve better event embedding and the selected features are highly interpretable from human understanding.
Wireless Software Synchronization of Multiple Distributed Cameras

We present a method for precisely time-synchronizing the capture of image sequences from a collection of smartphone cameras connected over WiFi. Our method is entirely software-based, has only modest hardware requirements, and achieves an accuracy of less than 250 µs on unmodified commodity hardware. It does not use image content and synchronizes cameras prior to capture. The algorithm operates in two stages. In the first stage, we designate one device as the leader and synchronize each client device’s clock to it by estimating network delay. Once clocks are synchronized, the second stage initiates continuous image streaming, estimates the relative phase of image timestamps between each client and the leader, and shifts the streams into alignment. We quantitatively validate our results on a multi-camera rig imaging a high-precision LED array and qualitatively demonstrate significant improvements to multi-view stereo depth estimation and stitching of dynamic scenes. We release as open source libsoftwaresync, an Android implementation of our system, to inspire new types of collective capture applications.
The myth of modularity in rule-based systems

In this paper, we examine the concept of modularity, an often cited advantage of the ruled-based representation methodology. We argue that the notion of modularity consists of two distinct concepts which we call syntactic modularity and semantic modularity. We argue that when reasoning under uncertainty, it is reasonable to regard the rule-based approach as both syntactically and semantically modular. However, we argue that in the case of plausible reasoning, rules are syntactically modular but are rarely semantically modular. To illustrate this point, we examine a particular approach for managing uncertainty in rule-based systems called the MYCIN certainty factor model. We formally define the concept of semantic modularity with respect to the certainty factor model and discuss logical consequences of the definition. We show that the assumption of semantic modularity imposes strong restrictions on rules in a knowledge base; we argue that such restrictions are rarely valid in practical applications. Finally, we suggest how the concept of semantic modularity can be relaxed in a manner that makes it appropriate for plausible reasoning.
Effective Implementation of the Weak Galerkin Finite Element Methods for the Biharmonic Equation

Abstract The weak Galerkin (WG) methods have been introduced in Mu et al. (2013, 2014), [14] for solving the biharmonic equation. The purpose of this paper is to develop an algorithm to implement the WG methods effectively. This can be achieved by eliminating local unknowns to obtain a global system with significant reduction of size. In fact, this reduced global system is equivalent to the Schur complements of the WG methods. The unknowns of the Schur complement of the WG method are those defined on the element boundaries. The equivalence of the WG method and its Schur complement is established. The numerical results demonstrate the effectiveness of this new implementation technique.
S2: An Efficient Graph Based Active Learning Algorithm with Application to Nonparametric Classification

This paper investigates the problem of active learning for binary label prediction on a graph. We introduce a simple and label-efficient algorithm called S for this task. At each step, S selects the vertex to be labeled based on the structure of the graph and all previously gathered labels. Specifically, S queries for the label of the vertex that bisects the shortest shortest path between any pair of oppositely labeled vertices. We present a theoretical estimate of the number of queries S needs in terms of a novel parametrization of the complexity of binary functions on graphs. We also present experimental results demonstrating the performance of S on both real and synthetic data. While other graph-based active learning algorithms have shown promise in practice, our algorithm is the first with both good performance and theoretical guarantees. Finally, we demonstrate the implications of the S algorithm to the theory of nonparametric active learning. In particular, we show that S achieves near minimax optimal excess risk for an important class of nonparametric classification problems.
People mover's distance: Class level geometry using fast pairwise data adaptive transportation costs

Abstract We address the problem of defining a network graph on a large collection of classes. Each class is comprised of a collection of data points, sampled in a non i.i.d. way, from some unknown underlying distribution. The application we consider in this paper is a large scale high dimensional survey of people living in the US, and the question of how similar or different are the various counties in which these people live. We use a co-clustering diffusion metric to learn the underlying distribution of people, and build an approximate earth mover's distance algorithm using this data adaptive transportation cost.
Streaming PCA and Subspace Tracking: The Missing Data Case

For many modern applications in science and engineering, data are collected in a streaming fashion carrying time-varying information, and practitioners need to process them with a limited amount of memory and computational resources in a timely manner for decision making. This often is coupled with the missing data problem, such that only a small fraction of data attributes are observed. These complications impose significant, and unconventional, constraints on the problem of streaming principal component analysis (PCA) and subspace tracking, which is an essential building block for many inference tasks in signal processing and machine learning. This survey article reviews a variety of classical and recent algorithms for solving this problem with low computational and memory complexities, particularly those applicable in the big data regime with missing data. We illustrate that streaming PCA and subspace tracking algorithms can be understood through algebraic and geometric perspectives, and they need to be adjusted carefully to handle missing data. Both asymptotic and nonasymptotic convergence guarantees are reviewed. Finally, we benchmark the performance of several competitive algorithms in the presence of missing data for both well-conditioned and ill-conditioned systems.
Change of Monetary Regime, Contracts, and Prices: Lessons from the Great Depression, 1932-1935

Abstract In this paper I analyze the process leading to the abandonment of the gold standard in the U.S. in 1933, and the devaluation of the dollar in 1934. I argue that most changes of monetary regime have an impact on contracts. In this specific case, contracts that were written in terms of gold, or “gold equivalent,” were rewritten in paper dollars. Congress did this on June 5, 1933, when it abrogated the “gold clause” retroactively. The Supreme Court validated the move in February 1935. The result was a very large transfer of wealth from creditors to debtors. I use daily data on commodity prices to investigate the extent to which these policies contributed to ending deflation. I find that commodity prices reacted strongly to the announcement of policy changes, and to legal procedures involving contracts. These results are consistent with the “change in regime” hypothesis of Sargent.
The role of transmitter cooperation in linear interference networks with block erasures

In this work, we explore the potential and optimal use of transmitter cooperation in wireless interference networks with deep fading conditions. We consider a linear interference network with K transmitter-receiver pairs, where each transmitter can be connected to two neighboring receivers. Long-term fluctuations (shadow fading) in the wireless channel can lead to any link being erased with probability p. Each receiver is interested in one unique message that can be available at two transmitters. The considered rate criterion is the average per user degrees of freedom (puDoF) as K goes to infinity. Prior to this work, the optimal assignment of messages to transmitters were identified in the two limits p → 0 and p → 1. We identify new schemes that achieve average puDoF values that are higher than the state of the art for a significant part of the range 0 < p < 1. The key idea to our results is to understand that the role of cooperation shifts from increasing the probability of delivering a message to its intended destination at high values of p, to interference cancellation at low values of p. Our schemes are based on an algorithm that achieves the optimal DoF value in any network realization, when restricted to a given message assignment as well as the use of zero-forcing schemes.
A Subspace Pursuit Method to Infer Refractivity in the Marine Atmospheric Boundary Layer

Inferring electromagnetic (EM) propagation characteristics within the marine atmospheric boundary layer (MABL) from data in real time is crucial for modern maritime navigation and communications. The propagation of EM waves is well modeled by a partial differential equation (PDE): a Helmholtz equation. A natural way to solve the MABL characterization inverse problem is to minimize what is observed and what is predicted by the PDE. However, this optimization is difficult because it has many local minima. We propose an alternative solution that relies on the properties of the PDE but does not involve solving the full forward model. Ducted environments result in an EM field which can be decomposed into a few propagating, trapped modes. These modes are a subset of the solutions to a Sturm–Liouville eigenvalue problem. We design a new objective function that measures the distance from the observations to a subspace spanned by these eigenvectors. The resulting optimization problem is much easier than the one that arises in the standard approach, and we show how to solve the associated nonlinear eigenvalue problem efficiently, leading to a real-time method.
Compression of the electron repulsion integral tensor in tensor hypercontraction format with cubic scaling cost

Electron repulsion integral tensor has ubiquitous applications in electronic structure computations. In this work, we propose an algorithm which compresses the electron repulsion tensor into the tensor hypercontraction format with O ( n N 2 log ? N ) computational cost, where N is the number of orbital functions and n is the number of spatial grid points that the discretization of each orbital function has. The algorithm is based on a novel strategy of density fitting using a selection of a subset of spatial grid points to approximate the pair products of orbital functions on the whole domain.
Interpretable apprenticeship learning with temporal logic specifications

Recent work has addressed using formulas in linear temporal logic (LTL) as specifications for agents planning in Markov Decision Processes (MDPs). We consider the inverse problem: inferring an LTL specification from demonstrated behavior trajectories in MDPs. We formulate this as a multiobjective optimization problem, and describe state-based (“what actually happened”) and action-based (“what the agent expected to happen”) objective functions based on a notion of “violation cost”. We demonstrate the efficacy of the approach by employing genetic programming to solve this problem in two simple domains.
Cayley Graphs with an Infinite Heesch Number

We construct a 2-generated group $\Gamma $ such that its Cayley graph possesses finite connected subsets with arbitrarily large finite Heesch number. Thus we obtain an example of a Cayley graph with an infinite Heesch number.
Explicit integration of extremely stiff reaction networks: quasi-steady-state methods

A preceding paper by Guidry et al 2013 Comput. Sci. Disc. 6 015001 demonstrated that explicit asymptotic methods generally work much better for extremely stiff reaction networks than has previously been shown in the literature. There we showed that for systems well removed from equilibrium, explicit asymptotic methods can rival standard implicit codes in speed and accuracy for solving extremely stiff differential equations. In this paper, we continue the investigation of systems well removed from equilibrium by examining quasi-steady-state (QSS) methods as an alternative to asymptotic methods. We show that for systems well removed from equilibrium, QSS methods also can compete with, or even exceed, standard implicit methods in speed, even for extremely stiff networks, and in many cases give a somewhat better integration speed than for asymptotic methods. As for asymptotic methods, we will find that QSS methods give correct results, but with a non-competitive integration speed as equilibrium is approached. Thus, we find that both asymptotic and QSS methods must be supplemented with partial equilibrium methods as equilibrium is approached to remain competitive with implicit methods.
Control synthesis for nonlinear optimal control via convex relaxations

This paper addresses the problem of control synthesis for nonlinear optimal control problems in the presence of state and input constraints. The presented approach relies upon transforming the given problem into an infinite-dimensional linear program over the space of measures. To generate approximations to this infinite-dimensional program, a sequence of Semi-Definite Programs (SDP)s is formulated in the instance of polynomial cost and dynamics with semi-algebraic state and bounded input constraints. A method to extract a polynomial control function from each SDP is also given. This paper proves that the controller synthesized from each of these SDPs generates a sequence of values that converge from below to the value of the optimal control of the original optimal control problem. In contrast to existing approaches, the presented method does not assume that the optimal control is continuous while still proving that the sequence of approximations is optimal. Moreover, the sequence of controllers that are synthesized using the presented approach are proven to converge to the true optimal control. The performance of the presented method is demonstrated on three examples.
Law of the First Passage Triple of a Spectrally Positive Strictly Stable Process

For a spectrally positive and strictly stable process with index in (1, 2), a series representation is obtained for the joint distribution of the “first passage triple” that consists of the time of first passage and the undershoot and the overshoot at first passage. The result leads to several corollaries, including (1) the joint law of the first passage triple and the pre-passage running supremum, and (2) at a fixed time point, the joint law of the process’ value, running supremum, and the time of the running supremum. The representation can be decomposed as a sum of strictly positive functions that allow exact sampling of the first passage triple.
Equivariant perturbation in Gomory and Johnson's infinite group problem (V). Software for the continuous and discontinuous 1-row case

We present software for investigations with cut-generating functions in the Gomory–Johnson model and extensions, implemented in the computer algebra system SageMath.
LEVEL REPULSION IN INTEGRABLE SYSTEMS

We provide evidence that level repulsion in semiclassical spectrum is not just a feature of classically chaotic systems, but classically integrable systems as well. While in chaotic systems level repulsion develops on a scale of the mean level spacing, regardless of the location in the spectrum, in integrable systems it develops on a much longer scale — such as geometric mean of the mean level spacing and the running energy in the spectrum for hard wall billiards. We show that at this scale level correlations in integrable systems have a universal dependence on the level separation, as well as discuss their exact form at any scale. These correlations have dramatic consequences, including deviations from the Poissonian statistics in the nearest level spacing distribution and persistent oscillations of the level number variance over an energy interval as a function of the interval width. We illustrate our findings on two specific models — rectangular infinite well and a modified Kepler problem — that serve as generic types of a hard wall billiard and a potential problem without extra symmetries. Our theory and numerical work are based on the concept of parametric averaging that allows sampling of a statistical ensemble of integrable systems at a given spectral location (running energy).