cssi/SciSciGPT-SciSciNet huggingface dataset:
Models and Representations of Gaussian Reciprocal and Conditionally Markov Sequences

Conditionally Markov (CM) sequences are powerful mathematical tools for modeling random phenomena. There are several classes of CM sequences one of which is the reciprocal sequence. Reciprocal sequences have been widely used in many areas including image processing, intelligent systems, and acausal systems. To use them in application, we need not only their applicable dynamic models, but also some general approaches to designing parameters of dynamic models. Dynamic models governing two important classes of nonsingular Gaussian (NG) CM sequences (called CML and CMF models), and a dynamic model governing the NG reciprocal sequence (called reciprocal CML model) were presented in our previous work. In this paper, these models are studied in more detail and general approaches are presented for their parameter design. It is shown that every reciprocal CML model can be induced by a Markov model and parameters of the reciprocal CML model can be obtained from those of the Markov model. Also, it is shown how NG CM sequences can be represented in terms of a NG Markov sequence and an independent NG vector. This representation provides a general approach for parameter design of CML and CMF models. In addition, it leads to a better understanding of CM sequences, including the reciprocal sequence.
Data Injection Attacks on Smart Grids With Multiple Adversaries: A Game-Theoretic Perspective

Data injection attacks have emerged as a significant threat on the smart power grid. By launching data injection attacks, an adversary can manipulate the real-time locational marginal prices to obtain economic benefits. Despite the surge of existing literature on data injection, most such works assume the presence of a single attacker and assume no cost for attack or defense. In contrast, in this paper, a model for data injection attacks with multiple adversaries and a single smart grid defender is introduced. To study the interactions between the defender and the attackers, two game models are considered. In the first, a Stackelberg game is proposed in which the defender acts as a leader that can anticipate the actions of the adversaries, that act as followers, before deciding on which measurements to protect. The existence and properties of the Stackelberg equilibrium of this game are studied. To find the equilibrium, a distributed learning algorithm that operates under limited system information is proposed and shown to converge to the game solution. In the second proposed game model, it is considered that the defender cannot anticipate the actions of the adversaries. To this end, a hybrid satisfaction equilibrium—Nash equilibrium game is proposed. To find the equilibrium of this hybrid game, a search-based algorithm is introduced. Numerical results using the IEEE 30-bus system are used to illustrate and analyze the strategic interactions between the attackers and defender. The results show that by defending a very small set of measurements, the grid operator can achieve an equilibrium through which the optimal attacks have no effect on the system. Moreover, the results also show how, at equilibrium, multiple attackers can play a destructive role toward each other by choosing to carry out attacks that cancel each other out, leaving the system unaffected. In addition, the obtained equilibrium strategies under the Stackelberg and the hybrid models are compared while characterizing the amount of loss that the defender endures due to its inability to anticipate the attackers’ actions.
Did You Really Just Have a Heart Attack?: Towards Robust Detection of Personal Health Mentions in Social Media

Millions of users share their experiences on social media sites, such as Twitter, which in turn generate valuable data for public health monitoring, digital epidemiology, and other analyses of population health at global scale. The first, critical, task for these applications is classifying whether a personal health event was mentioned, which we call the (PHM) problem. This task is challenging for many reasons, including typically short length of social media posts, inventive spelling and lexicons, and figurative language, including hyperbole using diseases like "heart attack»» or "cancer»» for emphasis, and not as a health self-report. This problem is even more challenging for rarely reported, or frequent but ambiguously expressed conditions, such as "stroke»». To address this problem, we propose a general, robust method for detecting PHMs in social media, which we call WESPAD, that combines lexical, syntactic, word embedding-based, and context-based features. WESPAD is able to generalize from few examples by automatically distorting the word embedding space to most effectively detect the true health mentions. Unlike previously proposed state-of-the-art supervised and deep-learning techniques, WESPAD requires relatively little training data, which makes it possible to adapt, with minimal effort, to each new disease and condition. We evaluate WESPAD on both an established publicly available Flu detection benchmark, and on a new dataset that we have constructed with mentions of multiple health conditions. Our experiments show that WESPAD outperforms the baselines and state-of-the-art methods, especially in cases when the number and proportion of true health mentions in the training data is small.
Descending price algorithm for determining market clearing prices in matching markets

A descending price algorithm based auction mechanism in a two-sided matching market is proposed in this paper to determine market clearing prices. For general valuations with a intelligent choice of reverse constricted sets, we prove that the algorithm converges in a finite number of rounds. Then specializing to the rank one valuations in sponsored search markets, the proposed algorithm yields the element-wise maximum market clearing price.
The invalidity of the Laplace law for biological vessels and of estimating elastic modulus from total stress vs. strain: a new practical method

There are strong medical motivations to measure changes in material properties of tubular organs, in vivo and in vitro. The current approach estimates hoop stress from intraluminal pressure using the Laplace law and identifies 'elastic modulus' as the slope of a curve fitted hoop stress plotted against strain data. We show that this procedure is fundamentally flawed because muscle and other soft tissue are closely incompressible, so that the total stress includes a volume-preserving material-dependent hydrostatic response that invalidates the method. Furthermore, we show that the Laplace law incorrectly estimates total stress in biological vessels. However, the great need to estimate elastic modulus leads us to develop an alternative practical method, based on shear stress-strain, i.e. insensitive to nonelastic response from incompressibility, but that uses the same measurement data as the current (incorrect) method. The individual material parameters in the underlying (unknown) constitutive relation combine into an effective shear modulus that is a true measure of elastic response, unaffected by incompressibility and without reference to the Laplace law. Furthermore, our effective shear modulus is determined directly as a function of deformation, rather than as the slope of a fitted curve. We validate our method by comparing effective shear moduli against exact shear moduli for four theoretical materials with different degrees of nonlinearity and numbers of material parameters. To further demonstrate applicability, we reanalyse an in vivo study with our new method and show that it resolves an inconsistent change in modulus with the current method.
Privacy-preserving prediction

Ensuring differential privacy of models learned from sensitive user data is an important goal that has been studied extensively in recent years. It is now known that for some basic learning problems, especially those involving high-dimensional data, producing an accurate private model requires much more data than learning without privacy. At the same time, in many applications it is not necessary to expose the model itself. Instead users may be allowed to query the prediction model on their inputs only through an appropriate interface. Here we formulate the problem of ensuring privacy of individual predictions and investigate the overheads required to achieve it in several standard models of classification and regression. We first describe a simple baseline approach based on training several models on disjoint subsets of data and using standard private aggregation techniques to predict. We show that this approach has nearly optimal sample complexity for (realizable) PAC learning of any class of Boolean functions. At the same time, without strong assumptions on the data distribution, the aggregation step introduces a substantial overhead. We demonstrate that this overhead can be avoided for the well-studied class of thresholds on a line and for a number of standard settings of convex regression. The analysis of our algorithm for learning thresholds relies crucially on strong generalization guarantees that we establish for all differentially private prediction algorithms.
Feature sampling strategies for action recognition

Although dense local spatial-temporal features with bag-of-features representation achieve state-of-the-art performance for action recognition, the huge feature number and feature size prevent current methods from scaling up to real size problems. In this work, we investigate different types of feature sampling strategies for action recognition, namely dense sampling, uniformly random sampling and selective sampling. We propose two effective selective sampling methods using object proposal techniques. Experiments conducted on a large video dataset show that we are able to achieve better average recognition accuracy using 25% less features, through one of the proposed selective sampling methods, and even maintain comparable accuracy while discarding 70% features.
Circular Pentagons and Real Solutions of Painlevé VI Equations

We study real solutions of a class of Painleve VI equations. To each such solution we associate a geometric object, a one-parametric family of circular pentagons. We describe an algorithm that permits to compute the numbers of zeros, poles, 1-points and fixed points of the solution on the interval $${(1,+\infty)}$$ and their mutual position. The monodromy of the associated linear equation and parameters of the Painleve VI equation are easily recovered from the family of pentagons.
A structure theorem for Leibniz homology

Abstract Presented is a structure theorem for the Leibniz homology, HL ⁎ , of an Abelian extension of a simple real Lie algebra g . As applications, results are stated for affine extensions of the classical Lie algebras sl n ( R ) , so n ( R ) , and sp n ( R ) . Furthermore, HL ⁎ ( h ) is calculated when h is the Lie algebra of the Poincare group as well as the Lie algebra of the affine Lorentz group. The structure theorem identifies all of these in terms of g -invariants.
Punny Captions: Witty Wordplay in Image Descriptions

Wit is a form of rich interaction that is often grounded in a specific situation (e.g., a comment in response to an event). In this work, we attempt to build computational models that can produce witty descriptions for a given image. Inspired by a cognitive account of humor appreciation, we employ linguistic wordplay, specifically puns, in image descriptions. We develop two approaches which involve retrieving witty descriptions for a given image from a large corpus of sentences, or generating them via an encoder-decoder neural network architecture. We compare our approach against meaningful baseline approaches via human studies and show substantial improvements. Moreover, in a Turing test style evaluation, people find the image descriptions generated by our model to be slightly wittier than human-written witty descriptions when the human is subject to similar constraints as the model regarding word usage and style.
FAST DIRECTIONAL COMPUTATION OF HIGH FREQUENCY BOUNDARY INTEGRALS VIA LOCAL FFTs

The boundary integral method is an efficient approach for solving time-harmonic acoustic obstacle scattering problems. The main computational task is the evaluation of an oscillatory boundary integral at each discretization point of the boundary. This paper presents a new fast algorithm for this task in two dimensions. This algorithm is built on top of directional low-rank approximations of the scattering kernel and uses oscillatory Chebyshev interpolation and local FFTs to achieve quasi-linear complexity. The algorithm is simple, fast, and kernel-independent. Numerical results are provided to demonstrate the effectiveness of the proposed algorithm.
Change detection in a dynamic stream of attributed networks

While anomaly detection in static networks has been extensively studied, only recently have researchers focused on dynamic networks. This trend is mainly due to the capacity of dynamic networks to ...
Efficient Algorithms for Outlier-Robust Regression

We give the first polynomial-time algorithm for performing linear or polynomial regression resilient to adversarial corruptions in both examples and labels. Given a sufficiently large (polynomial-size) training set drawn i.i.d. from distribution D and subsequently corrupted on some fraction of points, our algorithm outputs a linear function whose squared error is close to the squared error of the best-fitting linear function with respect to D, assuming that the marginal distribution of D over the input space is \emph{certifiably hypercontractive}. This natural property is satisfied by many well-studied distributions such as Gaussian, strongly log-concave distributions and, uniform distribution on the hypercube among others. We also give a simple statistical lower bound showing that some distributional assumption is necessary to succeed in this setting. These results are the first of their kind and were not known to be even information-theoretically possible prior to our work. Our approach is based on the sum-of-squares (SoS) method and is inspired by the recent applications of the method for parameter recovery problems in unsupervised learning. Our algorithm can be seen as a natural convex relaxation of the following conceptually simple non-convex optimization problem: find a linear function and a large subset of the input corrupted sample such that the least squares loss of the function over the subset is minimized over all possible large subsets.
Mixed Linear Layouts of Planar Graphs

A k-stack (respectively, k-queue) layout of a graph consists of a total order of the vertices, and a partition of the edges into k sets of non-crossing (non-nested) edges with respect to the vertex ordering. In 1992, Heath and Rosenberg conjectured that every planar graph admits a mixed 1-stack 1-queue layout in which every edge is assigned to a stack or to a queue that use a common vertex ordering.
Rational approximation on spheres

We quantify the density of rational points in the unit sphere S n , proving analogues of the classical theorems on the embedding of ℚ n into ℝ n . Specifically, we prove a Dirichlet theorem stating that every point α ∈ S n is sufficiently approximable, the optimality of this approximation via the existence of badly approximable points, and a Khintchine theorem showing that the Lebesgue measure of approximable points is either zero or full depending on the convergence or divergence of a certain sum. These results complement and improve on previous results, particularly recent theorems of Ghosh, Gorodnik and Nevo.
Monotone Paths in Dense Edge-Ordered Graphs

The altitude of a graph $G$, denoted $f(G)$, is the largest integer $k$ such that under each ordering of $E(G)$, there exists a path of length $k$ which traverses edges in increasing order. In 1971, Chv\'atal and Koml\'os asked for $f(K_n)$, where $K_n$ is the complete graph on $n$ vertices. In 1973, Graham and Kleitman proved that $f(K_n) \ge \sqrt{n - 3/4} - 1/2$ and in 1984, Calderbank, Chung, and Sturtevant proved that $f(K_n) \le (\frac{1}{2} + o(1))n$. We show that $f(K_n) \ge (\frac{1}{20} - o(1))(n/\lg n)^{2/3}$.
Expressiveness of rectifier networks

Rectified Linear Units (ReLUs) have been shown to ameliorate the vanishing gradient problem, allow for efficient backpropagation, and empirically promote sparsity in the learned parameters. They have led to state-of-the-art results in a variety of applications. However, unlike threshold and sigmoid networks, ReLU networks are less explored from the perspective of their expressiveness. This paper studies the expressiveness of ReLU networks. We characterize the decision boundary of two-layer ReLU networks by constructing functionally equivalent threshold networks. We show that while the decision boundary of a two-layer ReLU network can be captured by a threshold network, the latter may require an exponentially larger number of hidden units. We also formulate sufficient conditions for a corresponding logarithmic reduction in the number of hidden units to represent a sign network as a ReLU network. Finally, we experimentally compare threshold networks and their much smaller ReLU counterparts with respect to their ability to learn from synthetically generated data.
A Finiteness Theorem Via the Mean Curvature Flow with Surgery

In this article, we use the recently developed mean curvature flow with surgery for 2-convex hypersurfaces to prove certain isotopy existence and finally extrinsic finiteness results (in the spirit of Cheeger’s finiteness theorem) for the space of 2-convex closed embedded hypersurfaces in $${\mathbb {R}}^{n+1}$$ .
Nonlinear statistical learning with truncated Gaussian graphical models

We introduce the truncated Gaussian graphical model (TGGM) as a novel framework for designing statistical models for nonlinear learning. A TGGM is a Gaussian graphical model (GGM) with a subset of variables truncated to be nonnegative. The truncated variables are assumed latent and integrated out to induce a marginal model. We show that the variables in the marginal model are non-Gaussian distributed and their expected relations are nonlinear. We use expectation-maximization to break the inference of the nonlinear model into a sequence of TGGM inference problems, each of which is efficiently solved by using the properties and numerical methods of multivariate Gaussian distributions. We use the TGGM to design models for nonlinear regression and classification, with the performances of these models demonstrated on extensive benchmark datasets and compared to state-of-the-art competing results.
Viscosity solutions of path-dependent integro-differential equations

Abstract We extend the notion of viscosity solutions for path-dependent PDEs introduced by Ekren et al. (2014) to path-dependent integro-differential equations and establish well-posedness, i.e., existence, uniqueness, and stability, for a class of semilinear path-dependent integro-differential equations with uniformly continuous data. Closely related are non-Markovian backward SDEs with jumps, which provide a probabilistic representation for solutions of our equations. The results are potentially useful for applications using non-Markovian jump–diffusion models.
Novel lower bounds on the entropy rate of binary hidden Markov processes

Recently, Samorodnitsky proved a strengthened version of Mrs. Gerber's Lemma, where the output entropy of a binary symmetric channel is bounded in terms of the average entropy of the input projected on a random subset of coordinates. Here, this result is applied for deriving novel lower bounds on the entropy rate of binary hidden Markov processes. For symmetric underlying Markov processes, our bound improves upon the best known bound in the very noisy regime. The nonsymmetric case is also considered, and explicit bounds are derived for Markov processes that satisfy the (1, ∞)-RLL constraint.
Abstract Stobjs and Their Application to ISA Modeling

We introduce a new ACL2 feature, the abstract stobj, and show how to apply it to modeling the instruction set architecture of a microprocessor. Benefits of abstract stobjs over traditional ("concrete") stobjs can include faster execution, support for symbolic simulation, more efficient reasoning, and resilience of proof developments under modeling optimization.
The Bernardi Process and Torsor Structures on Spanning Trees

Let G be a ribbon graph, i.e., a connected finite graph G together with a cyclic ordering of the edges around each vertex. By adapting a construction due to O. Bernardi, we associate to any pair (v,e) consisting of a vertex v and an edge e adjacent to v a bijection between spanning trees of G and elements of the set Pic^g(G) of degree g divisor classes on G, where g is the genus of G. Using the natural action of the Picard group Pic^0(G) on Pic^g(G), we show that the Bernardi bijection gives rise to a simply transitive action \beta_v of Pic^0(G) on the set of spanning trees which does not depend on the choice of e. A plane graph has a natural ribbon structure (coming from the counterclockwise orientation of the plane), and in this case we show that \beta_v is independent of v as well. Thus for plane graphs, the set of spanning trees is naturally a torsor for the Picard group. Conversely, we show that if \beta_v is independent of v then G together with its ribbon structure is planar. We also show that the natural action of Pic^0(G) on spanning trees of a plane graph is compatible with planar duality. These findings are formally quite similar to results of Holroyd et al. and Chan-Church-Grochow, who used rotor-routing to construct an action r_v of Pic^0(G) on the spanning trees of a ribbon graph G, which they show is independent of v if and only if G is planar. It is therefore natural to ask how the two constructions are related. We prove that \beta_v = r_v for all vertices v of G when G is a planar ribbon graph, i.e. the two torsor structures (Bernardi and rotor-routing) on the set of spanning trees coincide. In particular, it follows that the rotor-routing torsor is compatible with planar duality. We conjecture that for every non-planar ribbon graph G, there exists a vertex v with \beta_v \neq r_v.
Counter-RAPTOR: Safeguarding Tor Against Active Routing Attacks

Tor is vulnerable to network-level adversaries who can observe both ends of the communication to deanonymize users. Recent work has shown that Tor is susceptible to the previously unknown active BGP routing attacks, called RAPTOR attacks, which expose Tor users to more network-level adversaries. In this paper, we aim to mitigate and detect such active routing attacks against Tor. First, we present a new measurement study on the resilience of the Tor network to active BGP prefix attacks. We show that ASes with high Tor bandwidth can be less resilient to attacks than other ASes. Second, we present a new Tor guard relay selection algorithm that incorporates resilience of relays into consideration to proactively mitigate such attacks. We show that the algorithm successfully improves the security for Tor clients by up to 36% on average (up to 166% for certain clients). Finally, we build a live BGP monitoring system that can detect routing anomalies on the Tor network in real time by performing an AS origin check and novel detection analytics. Our monitoring system successfully detects simulated attacks that are modeled after multiple known attack types as well as a real-world hijack attack (performed by us), while having low false positive rates.
Real-world font recognition using deep network and domain adaptation

We address a challenging fine-grain classification problem: recognizing a font style from an image of text. In this task, it is very easy to generate lots of rendered font examples but very hard to obtain real-world labeled images. This realto-synthetic domain gap caused poor generalization to new real data in previous methods (Chen et al. (2014)). In this paper, we refer to Convolutional Neural Networks, and use an adaptation technique based on a Stacked Convolutional AutoEncoder that exploits unlabeled real-world images combined with synthetic data. The proposed method achieves an accuracy of higher than 80% (top-5) on a realworld dataset.
Throughput and Delay Scaling of Content-Centric Ad Hoc and Heterogeneous Wireless Networks

We study the throughput and delay characteristics of wireless caching networks, where users are mainly interested in retrieving content stored in the network, rather than in maintaining source-destination communication. Nodes are assumed to be uniformly distributed in the network area. Each node has a limited-capacity content store, which it uses to cache contents. We propose an achievable caching and transmission scheme whereby requesters retrieve content from the caching point, which is closest in the Euclidean distance. We establish the throughput and delay scaling of the achievable scheme, and show that the throughput and delay performance are order-optimal within a class of schemes. We then solve the caching optimization problem, and evaluate the network performance for a Zipf content popularity distribution, letting the number of content types and the network size both go to infinity. Finally, we extend our analysis to heterogeneous wireless networks where, in addition to wireless nodes, there are a number of base stations uniformly distributed at random in the network area. We show that in order to achieve a better performance in a heterogeneous network in the order sense, the number of base stations needs to be greater than the ratio of the number of nodes to the number of content types. Furthermore, we show that the heterogeneous network does not yield performance advantages in the order sense if the Zipf content popularity distribution exponent exceeds 3/2.
Early-life social environment alters juvenile behavior and neuroendocrine function in a highly social cichlid fish

Abstract Early-life experiences can shape adult behavior, with consequences for fitness and health, yet fundamental questions remain unanswered about how early-life social experiences are translated into variation in brain and behavior. The African cichlid fish Astatotilapia burtoni, a model system in social neuroscience, is well known for its highly plastic social phenotypes in adulthood. Here, we rear juveniles in either social groups or pairs to investigate the effects of early-life social environments on behavior and neuroendocrine gene expression. We find that both juvenile behavior and neuroendocrine function are sensitive to early-life effects. Behavior robustly co-varies across multiple contexts (open field, social cue investigation, and dominance behavior assays) to form a behavioral syndrome, with pair-reared juveniles towards the end of syndrome that is less active and socially interactive. Pair-reared juveniles also submit more readily as subordinates. In a separate cohort, we measured whole brain expression of stress and sex hormone genes. Expression of glucocorticoid receptor 1a was elevated in group-reared juveniles, supporting a highly-conserved role for the stress axis mediating early-life effects. The effect of rearing environment on androgen receptor α and estrogen receptor α expression was mediated by treatment duration (1 vs. 5 weeks). Finally, expression of corticotropin-releasing factor and glucocorticoid receptor 2 decreased significantly over time. Rearing environment also caused striking differences in gene co-expression, such that expression was tightly integrated in pair-reared juveniles but not group-reared or isolates. Together, this research demonstrates the important developmental origins of behavioral phenotypes and identifies potential behavioral and neuroendocrine mechanisms.
Algebraic cycles representing cohomology operations

In this paper we will show that certain universal homology classes which are fundamental in topology are algebraic. To be specific, the products of Eilenberg–MacLane spaces \({\mathcal K}_{2q}\equiv K(\mathbf Z,{2}) \times K(\mathbf Z,{4}) \times \cdots \times K(\mathbf Z,{2q}) \) have models which are limits of complex projective varieties. Precisely, we have \({\mathcal K}_{2q}= \varinjlim \nolimits _{d\rightarrow \infty }\mathcal C^{q}_{d}(\mathbf P^{n})\) where \(\mathcal C^{q}_{d}(\mathbf P^{n})\) denotes the Chow variety of effective cycles of codimension q and degree d on \(\mathbf P_{\mathbf C}^{n}\). It is natural to ask which elements in the homology of \({\mathcal K}_{2q}\) are represented by algebraic cycles in these approximations. In this paper we find such representations for the even dimensional classes which are known as Steenrod squares (as well as their Pontrjagin and join products). These classes are dual to the cohomology classes which correspond to the basic cohomology operations also known as the Steenrod squares.
Developments around positive sectional curvature

This is not in any way meant to be a complete survey on positive curvature. Rather it is a short essay on the fascinating changes in the landscape surrounding positive curvature. In particular, details and many results and references are not included, and things are not presented in chronological order.
The Traveling Salesman Theorem in Carnot groups

Let $${\mathbb {G}}$$ be any Carnot group. We prove that, if a subset of $${\mathbb {G}}$$ is contained in a rectifiable curve, then it satisfies Peter Jones’ geometric lemma with some natural modifications. We thus prove one direction of the Traveling Salesman Theorem in $${\mathbb {G}}$$ . Our proof depends on new Alexandrov-type curvature inequalities for the Hebisch–Sikora metrics. We also apply the geometric lemma to prove that, in every Carnot group, there exist $$-\,1$$ -homogeneous Calderon–Zygmund kernels such that, if a set $$E \subset {\mathbb {G}}$$ is contained in a 1-regular curve, then the corresponding singular integral operators are bounded in $$L^2(E)$$ . In contrast to the Euclidean setting, these kernels are nonnegative and symmetric.
HIGHER INDICATORS FOR SOME GROUPS AND THEIR DOUBLES

In this paper we explicitly determine all indicators for groups isomorphic to the semidirect product of two cyclic groups by an automorphism of prime order, as well as the generalized quaternion groups. We then compute the indicators for the Drinfel'd doubles of these groups. This first family of groups include the dihedral groups, the non-abelian groups of order pq, and the semidihedral groups. We find that the indicators are all integers, with negative integers being possible in the first family only under certain specific conditions.
Laplacian eigenproblems on product regions and tensor products of Sobolev spaces

Abstract Characterizations of eigenvalues and eigenfunctions of the Laplacian on a product domain Ω p : = Ω 1 × Ω 2 are obtained. When zero Dirichlet, Robin or Neumann conditions are specified on each factor, then the eigenfunctions on Ω p are precisely the products of the eigenfunctions on the sets Ω 1 , Ω 2 separately. There is a related result when Steklov boundary conditions are specified on Ω 2 . These results enable the characterization of H 1 ( Ω p ) and H 0 1 ( Ω p ) as tensor products and descriptions of some orthogonal bases of the spaces. A different characterization of the trace space of H 1 ( Ω p ) is found.
Data-efficient off-policy policy evaluation for reinforcement learning

In this paper we present a new way of predicting the performance of a reinforcement learning policy given historical data that may have been generated by a different policy. The ability to evaluate a policy from historical data is important for applications where the deployment of a bad policy can be dangerous or costly. We show empirically that our algorithm produces estimates that often have orders of magnitude lower mean squared error than existing methods--it makes more efficient use of the available data. Our new estimator is based on two advances: an extension of the doubly robust estimator (Jiang & Li, 2015), and a new way to mix between model based and importance sampling based estimates.
A Convergence Theory for Deep Learning via Over-Parameterization

Deep neural networks (DNNs) have demonstrated dominating performance in many fields, e.g., computer vision, natural language progressing, and robotics. Since AlexNet, the neural networks used in practice are going wider and deeper. On the theoretical side, a long line of works have been focusing on why we can train neural networks when there is only one hidden layer. The theory of multi-layer neural networks remains somewhat unsettled. We present a new theory to understand the convergence of training DNNs. We only make two assumptions: the inputs do not degenerate and the network is over-parameterized. The latter means the number of hidden neurons is sufficiently large: polynomial in n, the number of training samples and in L, the number of layers. We show on the training dataset, starting from randomly initialized weights, simple algorithms such as stochastic gradient descent attain 100% accuracy in classication tasks, or minimize regression loss in linear convergence rate, with a number of iterations that only scale polynomial in n and L. Our theory applies to the widely-used but non-smooth ReLU activation, and to any smooth and possibly non-convex loss functions. In terms of network architectures, our theory at least applies to fully-connected neural networks, convolutional neural networks (CNN), and residual neural networks (ResNet).
Achievable rate region based on coset codes for multiple access channel with states

We derive a new achievable rate region for the problem of communicating over a multiple access channel with states. Our coding technique is based on the ensemble of nested coset codes and the technique of typicality decoding. Exploiting structure in this ensemble, we analyze a more efficient decoding strategy to improve upon the rate region achievable using unstructured codes. We identify examples for which the achievable rate region based on nested coset codes is strictly larger than the ones achievable using random unstructured codes.
Giving Attention to the Unexpected: Using Prosody Innovations in Disfluency Detection

Disfluencies in spontaneous speech are known to be associated with prosodic disruptions. However, most algorithms for disfluency detection use only word transcripts. Integrating prosodic cues has proved difficult because of the many sources of variability affecting the acoustic correlates. This paper introduces a new approach to extracting acoustic-prosodic cues using text-based distributional prediction of acoustic cues to derive vector z-score features (innovations). We explore both early and late fusion techniques for integrating text and prosody, showing gains over a high-accuracy text-only model.
An Energy Approach to Uniqueness for Higher-Order Geometric Flows

We describe a simple, direct method to prove the uniqueness of solutions to a broad class of parabolic geometric evolution equations. Our argument, which is based on a prolongation procedure and the consideration of certain natural energy quantities, does not require the solution of any auxiliary parabolic systems. In previous work, we used a variation of this technique to give an alternative proof of the uniqueness of complete solutions to the Ricci flow of uniformly bounded curvature. Here we extend this approach to curvature flows of all orders, including the \(L^2\)-curvature flow and a class of quasilinear higher-order flows related to the obstruction tensor. We also detail its application to the fully nonlinear cross-curvature flow.
A model of consistent node types in signed directed social networks

Signed directed social networks, in which the relationships between users can be either positive (indicating relations such as trust) or negative (indicating relations such as distrust), are increasingly common. Thus the interplay between positive and negative relationships in such networks has become an important research topic. Most recent investigations focus upon edge sign inference using structural balance theory or social status theory. Neither of these two theories, however, can explain an observed edge sign well when the two nodes connected by this edge do not share a common neighbor (e.g., common friend). In this paper we develop a novel approach to handle this situation by applying a new model for node types. Initially, we analyze the local node structure in a fully observed signed directed network, inferring underlying node types. The sign of an edge between two nodes must be consistent with their types; this explains edge signs well even when there are no common neighbors. We show, moreover, that our approach can be extended to incorporate directed triads, when they exist, just as in models based upon structural balance or social status theory. We compute Bayesian node types within empirical studies based upon partially observed Wikipedia, Slashdot, and Epinions networks in which the largest network (Epinions) has 119K nodes and 841K edges. Our approach yields better performance than state-of-the-art approaches for these three signed directed networks.
Lie algebras and higher torsion in p-groups

Abstract The primary aim of this paper is to study exceptional torsion in the integral cohomology of a family of p-groups associated to p-adic Lie algebras. A spectral sequence E r ⁎ , ⁎ [ g ] is defined for any Lie algebra g which models the Bockstein spectral sequence of the corresponding group in characteristic p. This spectral sequence is then studied for complex semisimple Lie algebras like sl n ( C ) and the results there are transferred to the corresponding p-group via the intermediary arithmetic Lie algebra defined over Z . The results obtained this way for a fixed Lie algebra scheme like sl n ( − ) hold in a range in the corresponding Bockstein spectral sequence for all but finitely many primes depending on the chosen range. Over C , it is shown that E 1 ⁎ , ⁎ [ g ] = H ⁎ ( g , U ( g ) ⁎ ) = H ⁎ ( Λ BG ) where U ( g ) ⁎ is the (filtered) dual of the universal enveloping algebra of g equipped with the dual adjoint action and ΛBG is the free loop space of the classifying space of an associated compact, connected real form Lie group G to g . When passing to characteristic p, in the corresponding Bockstein spectral sequence, a char 0 to char p phase transition is observed. For example, it is shown that the algebra E 1 ⁎ , ⁎ [ sl 2 [ F p ] ] requires at least 17 generators unlike its characteristic zero counterpart which only requires two.
Multi-channel opportunistic access: A case of restless bandits with multiple plays

This paper considers the following stochastic control problem that arises in opportunistic spectrum access: a system consists of n channels where the state (“good” or “bad”) of each channel evolves as independent and identically distributed Markov processes. A user can select exactly k channels to sense and access (based on the sensing result) in each time slot. A reward is obtained whenever the user senses and accesses a “good” channel. The objective is to design a channel selection policy that maximizes the expected discounted total reward accrued over a finite or infinite horizon. In our previous work we established the optimality of a greedy policy for the special case of k=1 (i.e., single channel access) under the condition that the channel state transitions are positively correlated over time. In this paper we show under the same condition the greedy policy is optimal for the general case of k≥1; the methodology introduced here is thus more general. This problem may be viewed as a special case of the restless bandit problem, with multiple plays. We discuss connections between the current problem and existing literature on this class of problems.
Shifted vertex operator algebras

We study the properties of shifted vertex operator algebras, which are vertex algebras derived from a given theory by shifting the conformal vector. In this way, we are able to exhibit large numbers of vertex operator algebras which are regular(rational and C_2-cofinite) and yet are pathological in one way or another.
Comparison of modern Langevin integrators for simulations of coarse-grained polymer melts

For a wide range of phenomena, current computational ability does not always allow for atomistic simulations of high-dimensional molecular systems to reach time scales of interest. Coarse-graining ...
A Biomechanical Study on the Use of Curved Drilling Technique for Treatment of Osteonecrosis of Femoral Head

Osteonecrosis occurs due to the loss of blood supply to the bone, leading to spontaneous death of the trabecular bone. Delayed treatment of the involved patients results in collapse of the femoral head, which leads to a need for total hip arthroplasty surgery. Core decompression, as the most popular technique for treatment of the osteonecrosis, includes removal of the lesion area by drilling a straight tunnel to the lesion, debriding the dead bone and replacing it with bone substitutes. However, there are two drawbacks for this treatment method. First, due to the rigidity of the instruments currently used during core decompression, lesions cannot be completely removed and/or excessive healthy bone may also be removed with the lesion. Second, the use of bone substitutes, despite its biocompatibility and osteoconductivity, may not provide sufficient mechanical strength and support for the bone. To address these shortcomings, a novel robot-assisted curved core decompression (CCD) technique is introduced to provide surgeons with direct access to the lesions causing minimal damage to the healthy bone. In this study, with the aid of finite element (FE) simulations, we investigate biomechanical performance of core decompression using the curved drilling technique in the presence of normal gait loading. In this regard, we compare the result of the CCD using bone substitutes and flexible implants with other conventional core decompression techniques. The study finding shows that the maximum principal stress occurring at the superior domain of the neck is smaller in the CCD techniques (i.e., 52.847 MPa) compared to the other core decompression methods; furthermore, the peak value of normal stress at the interface for the CCD model is substantially smaller than traditional and advanced core decompression techniques (89% and 76%, respectively). FE results demonstrate the superior performance of CCD compared to the other approaches without any compromise to patient’s safety and markedly reducing the risk of femoral fracture in the postoperative phase for normal gait loading.
Semantic similarity analysis—A computer-based study of meaning in noun phrases

The purpose of this paper is to present a method by which a computerized data base which contains phrases of natural language information can be created and interrogated in the semantic domain for multiple uses and users. The method takes into account both the individual user’s needs and concepts of similarity in meaning of textual material represented by the stored data. The method is applicable to arbitrary bodies of natural language text which occur in the syntactic format of the noun phrase. The method was developed and tested, however, using noun phrases of medical text since its capabilities are directly applicable to needs in that area.
Brown measure support and the free multiplicative Brownian motion

Abstract The free multiplicative Brownian motion b t is the large-N limit of Brownian motion B t N on the general linear group GL ( N ; C ) . We prove that the Brown measure for b t —which is an analog of the empirical eigenvalue distribution for matrices—is supported on the closure of a certain domain Σ t in the plane. The domain Σ t was introduced by Biane in the context of the large-N limit of the Segal–Bargmann transform associated to GL ( N ; C ) . We also consider a two-parameter version, b s , t : the large-N limit of a related family of diffusion processes on GL ( N ; C ) introduced by the second author. We show that the Brown measure of b s , t is supported on the closure of a certain planar domain Σ s , t , generalizing Σ t , introduced by Ho. In the process, we introduce a new family of spectral domains related to any operator in a tracial von Neumann algebra: the L p n -spectrum for n ∈ N and p ≥ 1 , a subset of the ordinary spectrum defined relative to potentially-unbounded inverses. We show that, in general, the support of the Brown measure of an operator is contained in its L 2 2 -spectrum.
Neuromorphic Acceleration for Approximate Bayesian Inference on Neural Networks via Permanent Dropout

As neural networks have begun performing increasingly critical tasks for society ranging from driving cars to identifying candidates for drug development, the value of their ability to perform uncertainty quantification (UQ) in their predictions has risen commensurately. Permanent dropout, a popular method for neural network UQ, involves injecting stochasticity into the inference phase of the model and creating many predictions for each of the test data. This shifts the computational and energy burden of deep neural networks from the training phase to the inference phase. Recent work has demonstrated near-lossless conversion of classical deep neural networks to their spiking counterparts. We use these results to demonstrate the feasibility of conducting the inference phase with permanent dropout on spiking neural networks, mitigating the technique's computational and energy burden, which is essential for its use at scale or on edge platforms. We demonstrate the proposed approach via the Nengo spiking neural simulator on a combination drug therapy dataset for cancer treatment, where UQ is critical. Our results indicate that the spiking approximation gives a predictive distribution practically indistinguishable from that given by the classical network.
The single-cell transcriptomic landscape of early human diabetic nephropathy

Diabetic nephropathy is characterized by damage to both the glomerulus and tubulointerstitium, but relatively little is known about accompanying cell-specific changes in gene expression. We performed unbiased single-nucleus RNA sequencing (snRNA-seq) on cryopreserved human diabetic kidney samples to generate 23,980 single-nucleus transcriptomes from 3 control and 3 early diabetic nephropathy samples. All major cell types of the kidney were represented in the final dataset. Side-by-side comparison demonstrated cell-type–specific changes in gene expression that are important for ion transport, angiogenesis, and immune cell activation. In particular, we show that the diabetic thick ascending limb, late distal convoluted tubule, and principal cells all adopt a gene expression signature consistent with increased potassium secretion, including alterations in Na+/K+-ATPase, WNK1, mineralocorticoid receptor, and NEDD4L expression, as well as decreased paracellular calcium and magnesium reabsorption. We also identify strong angiogenic signatures in glomerular cell types, proximal convoluted tubule, distal convoluted tubule, and principal cells. Taken together, these results suggest that increased potassium secretion and angiogenic signaling represent early kidney responses in human diabetic nephropathy.
Predicting Stochastic Human Forward Reachable Sets Based on Learned Human Behavior

With the recent surge of interest in introducing autonomous vehicles to the everyday lives of people, developing accurate and generalizable algorithms for predicting human behavior becomes highly crucial. Moreover, many of these emerging applications occur in a safety-critical context, making it even more urgent to develop good prediction models for human-operated vehicles. This is fundamentally a challenging task as humans are often noisy in their decision processes. Hamilton-Jacobi (HJ) reachability is a useful tool in control theory that provides safety guarantees for collision avoidance. In this paper, we first demonstrate how to incorporate information derived from HJ reachability into a machine learning problem which predicts human behavior in a simulated collision avoidance context, and show that this yields a higher prediction accuracy than learning without this information. Then we propose a framework to generate stochastic forward reachable sets that flexibly provides different safety probabilities and generalizes to novel scenarios. We demonstrate that we can construct stochastic reachable sets that can capture the trajectories with probability from 0.75 to 1.