cssi/SciSciGPT-SciSciNet huggingface dataset:
Exploring the Effects of a Social Robot's Speech Entrainment and Backstory on Young Children's Emotion, Rapport, Relationship, and Learning

In positive human-human relationships, people frequently mirror or mimic each other's behavior. This mimicry, also called entrainment, is associated with rapport and smoother social interaction. Because rapport in learning scenarios has been shown to lead to improved learning outcomes, we examined whether enabling a social robotic learning companion to perform rapport-building behaviors could improve children's learning and engagement during a storytelling activity. We enabled the social robot to perform two specific rapport and relationship-building behaviors: speech entrainment and self-disclosure (shared personal information in the form of a backstory about the robot's poor speech and hearing abilities). We recruited 86 children aged 3-8 years to interact with the robot in a 2 × 2 between-subjects experimental study testing the effects of robot entrainment Entrainment vs. No entrainment and backstory about abilities Backstory vs. No Backstory. The robot engaged the children one-on-one in conversation, told a story embedded with key vocabulary words, and asked children to retell the story. We measured children's recall of the key words and their emotions during the interaction, examined their story retellings, and asked children questions about their relationship with the robot. We found that the robot's entrainment led children to show more positive emotions and fewer negative emotions. Children who heard the robot's backstory were more likely to accept the robot's poor hearing abilities. Entrainment paired with backstory led children to use more of the key words and match more of the robot's phrases in their story retells. Furthermore, these children were more likely to consider the robot more human-like and were more likely to comply with one of the robot's requests. These results suggest that the robot's speech entrainment and backstory increased children's engagement and enjoyment in the interaction, improved their perception of the relationship, and contributed to children's success at retelling the story.
On the Capacity Region of the Layered Packet Erasure Broadcast Channel with Feedback

In this paper the capacity region of the Layered Packet Erasure Broadcast Channel (LPE-BC) with Channel Output Feedback (COF) available at the transmitter is investigated. The LPE-BC is a high-SNR approximation of the fading Gaussian BC recently proposed by Tse and Yates, who characterized the capacity region for any number of users and any number of layers when there is no COF. This paper derives capacity inner and outer bounds for the LPE-BC with COF for the case of two users and any number of layers. The inner bounds generalize past results for the two-user erasure BC, which is a special case of the LPE-BC with COF with only one layer. The novelty lies in the use of inter-user &#x0026; inter-layer network coding retransmissions (for those packets that have only been received by the unintended user), where each random linear combination may involve packets intended for any user originally sent on any of the layers. Analytical and numerical examples show that the proposed outer bound is optimal for some LPE-BCs.
Degenerate Sklyanin algebras and generalized twisted homogeneous coordinate rings

Abstract In this work, we introduce the point parameter ring B, a generalized twisted homogeneous coordinate ring associated to a degenerate version of the three-dimensional Sklyanin algebra. The surprising geometry of these algebras yields an analogue to a result of Artin–Tate–van den Bergh, namely that B is generated in degree one and thus is a factor of the corresponding degenerate Sklyanin algebra.
Del Pezzo surfaces of degree 6 over an arbitrary field

Abstract We give a characterization of all del Pezzo surfaces of degree 6 over an arbitrary field F. A surface is determined by a pair of separable algebras. These algebras are used to compute the Quillen K-theory of the surface. As a consequence, we obtain an index reduction formula for the function field of the surface.
Jointly Learning to Construct and Control Agents using Deep Reinforcement Learning

The physical design of a robot and the policy that controls its motion are inherently coupled, and should be determined according to the task and environment. In an increasing number of applications, data-driven and learning-based approaches, such as deep reinforcement learning, have proven effective at designing control policies. For most tasks, the only way to evaluate a physical design with respect to such control policies is empirical—i.e., by picking a design and training a control policy for it. Since training these policies is time-consuming, it is computationally infeasible to train separate policies for all possible designs as a means to identify the best one. In this work, we address this limitation by introducing a method that jointly optimizes over the physical design and control network. Our approach maintains a distribution over designs and uses reinforcement learning to optimize a control policy to maximize expected reward over the design distribution. We give the controller access to design parameters to allow it to tailor its policy to each design in the distribution. Throughout training, we shift the distribution towards higher-performing designs, eventually converging to a design and control policy that are jointly optimal. We evaluate our approach in the context of legged locomotion, and demonstrate that it discovers novel designs and walking gaits, outperforming baselines across different settings.
Causality preserving information transfer measure for control dynamical system

In this paper, we show through examples, how the existing definitions of information transfer, namely directed information and transfer entropy fail to capture true causal interaction between states in control dynamical system. Furthermore, existing definitions are shown to be too weak to have any implication on two of the most fundamental concepts in system theory, namely controllability and observability. We propose a new definition of information transfer, based on the ideas from dynamical system theory, and show that this new definition can not only capture true causal interaction between states, but also have implication on system controllability and observability properties. In particular, we show that non-zero transfer of information from input-to-state and state-to-output implies structural controllability and observability properties of the control dynamical system respectively. Analytical expression for information transfer between state-to-state, input-to-state, state-to-output, and input-to-output are provided for linear system. There is a natural extension of our proposed definition to define information transfer over n time steps and average information transfer over infinite time step. We show that the average information transfer in feedback control system between plant output and input is equal to the entropy of the open loop dynamics thereby re-deriving the Bode fundamental limitation results using the proposed definition of transfer.
Rigidity results in general relativity: A review

In this survey we review the progress made in the last ten years in understanding the Black Hole Rigidity problem in the setting of smooth spacetimes. We review both local and global results and discuss the main mathematical ideas behind them.
WPaxos: Wide Area Network Flexible Consensus

WPaxos is a multileader Paxos protocol that provides low-latency and high-throughput consensus across wide-area network (WAN) deployments. WPaxos uses multileaders, and partitions the object-space among these multileaders. Unlike statically partitioned multiple Paxos deployments, WPaxos is able to adapt to the changing access locality through object stealing. Multiple concurrent leaders coinciding in different zones steal ownership of objects from each other using phase-1 of Paxos, and then use phase-2 to commit update-requests on these objects locally until they are stolen by other leaders. To achieve fast phase-2 commits, WPaxos adopts the flexible quorums idea in a novel manner, and appoints phase-2 acceptors to be close to their respective leaders. We implemented WPaxos and evaluated it over WAN deployments across 5 AWS regions. The dynamic partitioning of the object-space and emphasis on zone-local commits allow WPaxos to significantly outperform both partitioned Paxos deployments and leaderless Paxos approaches.
Neural Particle Smoothing for Sampling from Conditional Sequence Models

We introduce neural particle smoothing, a sequential Monte Carlo method for sampling annotations of an input string from a given probability model. In contrast to conventional particle filtering algorithms, we train a proposal distribution that looks ahead to the end of the input string by means of a right-to-left LSTM. We demonstrate that this innovation can improve the quality of the sample. To motivate our formal choices, we explain how neural transduction models and our sampler can be viewed as low-dimensional but nonlinear approximations to working with HMMs over very large state spaces.
Understanding Deep Neural Networks with Rectified Linear Units

In this paper we investigate the family of functions representable by deep neural networks (DNN) with rectified linear units (ReLU). We give an algorithm to train a ReLU DNN with one hidden layer to *global optimality* with runtime polynomial in the data size albeit exponential in the input dimension. Further, we improve on the known lower bounds on size (from exponential to super exponential) for approximating a ReLU deep net function by a shallower ReLU net. Our gap theorems hold for smoothly parametrized families of "hard" functions, contrary to countable, discrete families known in the literature. An example consequence of our gap theorems is the following: for every natural number $k$ there exists a function representable by a ReLU DNN with $k^2$ hidden layers and total size $k^3$, such that any ReLU DNN with at most $k$ hidden layers will require at least $\frac{1}{2}k^{k+1}-1$ total nodes. Finally, for the family of $\mathbb{R}^n\to \mathbb{R}$ DNNs with ReLU activations, we show a new lowerbound on the number of affine pieces, which is larger than previous constructions in certain regimes of the network architecture and most distinctively our lowerbound is demonstrated by an explicit construction of a *smoothly parameterized* family of functions attaining this scaling. Our construction utilizes the theory of zonotopes from polyhedral theory.
Sequential Experiment Design for Hypothesis Verification

Hypothesis testing is an important problem with applications in target localization, clinical trials etc. Many active hypothesis testing strategies operate in two phases: an exploration phase and a verification phase. In the exploration phase, selection of experiments is such that a moderate level of confidence on the true hypothesis is achieved. Subsequent experiment design aims at improving the confidence level on this hypothesis to the desired level. In this paper, the focus is on the verification phase. A confidence measure is defined and active hypothesis testing is formulated as a confidence maximization problem in an infinite-horizon average-reward Partially Observable Markov Decision Process (POMDP) setting. The problem of maximizing confidence conditioned on a particular hypothesis is referred to as the hypothesis verification problem. The relationship between hypothesis testing and verification problems is established. The verification problem can be formulated as a Markov Decision Process (MDP). Optimal solutions for the verification MDP are characterized and a simple heuristic adaptive strategy for verification is proposed based on a zero-sum game interpretation of Kullback-Leibler divergences. It is demonstrated through numerical experiments that the heuristic performs better in some scenarios compared to existing methods in literature.
Even-primitive vectors in induced supermodules for general linear supergroups and in costandard supermodules for Schur superalgebras

Let $$G=GL(m|n)$$ be the general linear supergroup over an algebraically closed field K of characteristic zero, and let $$G_{ev}=GL(m)\times GL(n)$$ be its even subsupergroup. The induced supermodule $$H^0_G(\lambda )$$, corresponding to a dominant weight $$\lambda $$ of G, can be represented as $$H^0_{G_{ev}}(\lambda )\otimes \Lambda (Y)$$, where $$Y=V_m^*\otimes V_n$$ is a tensor product of the dual of the natural GL(m)-module $$V_m$$ and the natural GL(n)-module $$V_n$$, and $$\Lambda (Y)$$ is the exterior algebra of Y. For a dominant weight $$\lambda $$ of G, we construct explicit $$G_{ev}$$-primitive vectors in $$H^0_G(\lambda )$$. Related to this, we give explicit formulas for $$G_{ev}$$-primitive vectors of the supermodules $$H^0_{G_{ev}}(\lambda )\otimes \otimes ^k Y$$. Finally, we describe a basis of $$G_{ev}$$-primitive vectors in the largest polynomial subsupermodule $$\nabla (\lambda )$$ of $$H^0_G(\lambda )$$ (and therefore in the costandard supermodule of the corresponding Schur superalgebra S(m|n)). This yields a description of a basis of $$G_{ev}$$-primitive vectors in arbitrary induced supermodule $$H^0_G(\lambda )$$.
A statistical perspective on randomized sketching for ordinary least-squares

We consider statistical as well as algorithmic aspects of solving large-scale least-squares (LS) problems using randomized sketching algorithms. For a LS problem with input data (X, Y) ∈ Rn×p × Rn, sketching algorithms use a "sketching matrix," S ∈ Rr×n, where r ≪ n. Then, rather than solving the LS problem using the full data (X, Y), sketching algorithms solve the LS problem using only the "sketched data" (SX, SY). Prior work has typically adopted an algorithmic perspective, in that it has made no statistical assumptions on the input X and Y, and instead it has been assumed that the data (X, Y) are fixed and worst-case (WC). Prior results show that, when using sketching matrices such as random projections and leverage-score sampling algorithms, with p ≲ r ≪ n, the WC error is the same as solving the original problem, up to a small constant. From a statistical perspective, we typically consider the mean-squared error performance of randomized sketching algorithms, when data (X, Y) are generated according to a statistical linear model Y = Xβ+e, where e is a noise process. In this paper, we provide a rigorous comparison of both perspectives leading to insights on how they differ. To do this, we first develop a framework for assessing, in a unified manner, algorithmic and statistical aspects of randomized sketching methods. We then consider the statistical prediction efficiency (PE) and the statistical residual efficiency (RE) of the sketched LS estimator; and we use our framework to provide upper bounds for several types of random projection and random sampling sketching algorithms. Among other results, we show that the RE can be upper bounded when p ≲ r ≪ n while the PE typically requires the sample size r to be substantially larger. Lower bounds developed in subsequent results show that our upper bounds on PE can not be improved.
M -statistic for kernel change-point detection

Detecting the emergence of an abrupt change-point is a classic problem in statistics and machine learning. Kernel-based nonparametric statistics have been proposed for this task which make fewer assumptions on the distributions than traditional parametric approach. However, none of the existing kernel statistics has provided a computationally efficient way to characterize the extremal behavior of the statistic. Such characterization is crucial for setting the detection threshold, to control the significance level in the offline case as well as the average run length in the online case. In this paper we propose two related computationally efficient M-statistics for kernel-based change-point detection when the amount of background data is large. A novel theoretical result of the paper is the characterization of the tail probability of these statistics using a new technique based on change-of-measure. Such characterization provides us accurate detection thresholds for both offline and online cases in computationally efficient manner, without the need to resort to the more expensive simulations such as bootstrapping. We show that our methods perform well in both synthetic and real world data.
Optimal Control Via Neural Networks: A Convex Approach

Control of complex systems involves both system identification and controller design. Deep neural networks have proven to be successful in many identification tasks, however, from model-based control perspective, these networks are difficult to work with because they are typically nonlinear and nonconvex. Therefore many systems are still identified and controlled based on simple linear models despite their poor representation capability. In this paper we bridge the gap between model accuracy and control tractability faced by neural networks, by explicitly constructing networks that are convex with respect to their inputs. We show that these input convex networks can be trained to obtain accurate models of complex physical systems. In particular, we design input convex recurrent neural networks to capture temporal behavior of dynamical systems. Then optimal controllers can be achieved via solving a convex model predictive control problem. Experiment results demonstrate the good potential of the proposed input convex neural network based approach in a variety of control applications. In particular we show that in the MuJoCo locomotion tasks, we could achieve over 10% higher performance using 5* less time compared with state-of-the-art model-based reinforcement learning method; and in the building HVAC control example, our method achieved up to 20% energy reduction compared with classic linear models.
Sequential Relaxation of Unit Commitment with AC Transmission Constraints

This paper proposes a sequential convex relaxation method for obtaining feasible and near-globally optimal solutions for unit commitment (UC) with AC transmission constraints. First, we develop a second-order cone programming (SOCP) relaxation for AC unit commitment. To ensure that the resulting solutions are feasible for the original non-convex problem, we incorporate penalty terms into the objective of the proposed SOCP relaxation. We generalize our penalization method to a sequential algorithm which starts from an initial point (not necessarily feasible) and leads to feasible and near-optimal solutions for AC unit commitment. Once a feasible point is attained, the algorithm preserves feasibility and improves the objective value until a near optimal point is obtained. The experimental results on IEEE 57, IEEE 118, and IEEE 300 bus benchmark cases from Matpower [1] demonstrate the performance of the proposed method in solving challenging instances of AC unit commitment.
Fighting Offensive Language on Social Media with Unsupervised Text Style Transfer.

We introduce a new approach to tackle the problem of offensive language in online social media. Our approach uses unsupervised text style transfer to translate offensive sentences into non-offensive ones. We propose a new method for training encoder-decoders using non-parallel data that combines a collaborative classifier, attention and the cycle consistency loss. Experimental results on data from Twitter and Reddit show that our method outperforms a state-of-the-art text style transfer system in two out of three quantitative metrics and produces reliable non-offensive transferred sentences.
DeepMove: Learning Place Representations through Large Scale Movement Data

Understanding and reasoning about places and their relationships are critical for many applications. Places are traditionally curated by a small group of people as place gazetteers and are represented by an ID with spatial extent, category, and other descriptions. However, a place context is described to a large extent by movements made from/to other places. Places are linked and related to each other by these movements. This important context is missing from the traditional representation.We present DeepMove, a novel approach for learning latent representations of places. DeepMove advances the current deep learning based place representations by directly model movements between places. We demonstrate DeepMove’s latent representations on place categorization and clustering tasks on large place and movement datasets with respect to important parameters. Our results show that DeepMove outperforms state-of-the-art baselines. Without sophisticated weighting schemes, DeepMove’s representations can provide up to 15% higher than competing methods in matching rate of place category and result in up to 39% higher silhouette coefficient value for place clusters evaluated on a dataset with 19,194 point of interests (POIs) and 14 million trips.DeepMove is spatial and temporal context aware. It is scalable. It outperforms competing models using much smaller training dataset (a month or 1/12 of data). These qualities make it suitable for a broad class of real-world applications.
THE LINK OF {f(x, y) + z n = 0} AND ZARISKI'S CONJECTURE

We consider suspension hypersurface singularities of type g = f(x,y) + z n , where f is an irreducible plane curve singularity. For such germs, we prove that the link of g determines completely the Newton pairs of f and the integer n except for two pathological cases, which can be completely described. Even in the pathological cases, the link and the Milnor number of g determine uniquely the Newton pairs of f and n. In particular, for such g, we verify Zariski's conjecture about the multiplicity. The result also supports the following conjecture formulated in the paper. If the link of an isolated hypersurface singularity is a rational homology 3-sphere then it determines the embedded topological type, the equivariant Hodge numbers and the multiplicity of the singularity. The conjecture is verified for weighted homogeneous singularities too.
Spin nilHecke algebras of classical type

Abstract We formulate and study the spin nilHecke algebras NH n – b and NH n – d of type B/D, which differ from the usual nilHecke algebras by some odd signs. The type B spin nilHecke algebra is a nil version of the spin type B Hecke algebra introduced earlier by the second author and Khongsap, but not for the type D one. We construct faithful polynomial representations Pol n – of the nilHecke algebras via odd Demazure operators. We formulate the spin Schubert polynomials, and use them to show that the spin nilHecke algebras are matrix algebras with entries in a subalgebra of Pol n – consisting of spin symmetric polynomials. All these results have their counterparts for the usual nilHecke algebras over the rational field. Our work is a generalization of results of Lauda and Ellis–Khovanov–Lauda in usual/spin type A.
Compact representation of the full Broyden class of quasi‐Newton updates

In this paper, we present the compact representation for matrices belonging to the the Broyden class of quasi-Newton updates, where each update may be either rank-one or rank-two. This work extends previous results solely for the restricted Broyden class of rank-two updates. In this article, it is not assumed the same Broyden update is used each iteration; rather, different members of the Broyden class may be used each iteration. Numerical experiments suggest that a practical implementation of the compact representation is able to accurately represent matrices belonging to the Broyden class of updates. Furthermore, we demonstrate how to compute the compact representation for the inverse of these matrices, as well as a practical algorithm for solving linear systems with members of the Broyden class of updates. We demonstrate through numerical experiments that the proposed linear solver is able to efficiently solve linear systems with members of the Broyden class of matrices to high accuracy. As an immediate consequence of this work, it is now possible to efficiently compute the eigenvalues of any limited-memory member of the Broyden class of matrices, allowing for the computation of condition numbers and the ability perform sensitivity analysis.
A Euclidean Skolem-Mahler-Lech-Chabauty method

Using the theory of o-minimality we show that the p-adic method of Skolem-Mahler-Lech-Chabauty may be adapted to prove instances of the dynamical Mordell-Lang conjecture for some real analytic dynamical systems. For example, we show that if f1, . . . , fn is a finite sequence of real analytic functions fi : (−1, 1)→ (−1, 1) for which fi(0) = 0 and | f ′ i (0)| ≤ 1 (possibly zero), a = (a1, . . . , an) is an n-tuple of real numbers close enough to the origin and H(x1, . . . , xn) is a real analytic function of n variables, then the set {m ∈N : H( f ◦m 1 (a1), . . . , f ◦m n (an)) = 0} is either all of N, all of the odd numbers, all of the even numbers, or is finite.
Learning Abstractions for Program Synthesis

Many example-guided program synthesis techniques use abstractions to prune the search space. While abstraction-based synthesis has proven to be very powerful, a domain expert needs to provide a suitable abstract domain, together with the abstract transformers of each DSL construct. However, coming up with useful abstractions can be non-trivial, as it requires both domain expertise and knowledge about the synthesizer. In this paper, we propose a new technique for learning abstractions that are useful for instantiating a general synthesis framework in a new domain. Given a DSL and a small set of training problems, our method uses tree interpolation to infer reusable predicate templates that speed up synthesis in a given domain. Our method also learns suitable abstract transformers by solving a certain kind of second-order constraint solving problem in a data-driven way. We have implemented the proposed method in a tool called Atlas and evaluate it in the context of the Blaze meta-synthesizer. Our evaluation shows that (a) Atlas can learn useful abstract domains and transformers from few training problems, and (b) the abstractions learned by Atlas allow Blaze to achieve significantly better results compared to manually-crafted abstractions.
Visualization of collaborative data

Collaborative data consist of ratings relating two distinct sets of objects: users and items. Much of the work with such data focuses on filtering: predicting unknown ratings for pairs of users and items. In this paper we focus on the problem of visualizing the information. Given all of the ratings, our task is to embed all of the users and items as points in the same Euclidean space. We would like to place users near items that they have rated (or would rate) high, and far away from those they would give low ratings. We pose this problem as a real-valued non-linear Bayesian network and employ Markov chain Monte Carlo and expectation maximization to find an embedding. We present a metric by which to judge the quality of a visualization and compare our results to Eigentaste, locally linear embedding and co-occurrence data embedding on three real-world datasets.
Optimal Error Rates for Interactive Coding II: Efficiency and List Decoding

We study coding schemes for error correction in interactive communications. Such interactive coding schemes simulate any n-round interactive protocol using N rounds over an adversarial channel that corrupts up to ρ N transmissions. Important performance measures for a coding scheme are its maximum tolerable error rate ρ, communication complexity N, and computational complexity. We give the first coding scheme for the standard setting which performs optimally in all three measures: Our randomized non-adaptive coding scheme has a near-linear computational complexity and tolerates any error rate δ < 1/4 with a linear N = Θ(n) communication complexity. This improves over prior results [1]–[4] which each performed well in two of these measures. We also give results for other settings of interest, namely, the first computationally and communication efficient schemes that tolerate ρ < 2/7 adaptively, ρ < 1/3 if only one party is required to decode, and ρ < 1/2 if list decoding is allowed. These are the optimal tolerable error rates for the respective settings. These coding schemes also have near linear computational and communication complexity. These results are obtained via two techniques: We give a general black-box reduction which reduces unique decoding, in various settings, to list decoding. We also show how to boost the computational and communication efficiency of any list decoder to become near linear1.
Online Human-Bot Interactions: Detection, Estimation, and Characterization

Increasing evidence suggests that a growing amount of social media content is generated by autonomous entities known as social bots. In this work we present a framework to detect such entities on Twitter. We leverage more than a thousand features extracted from public data and meta-data about users: friends, tweet content and sentiment, network patterns, and activity time series. We benchmark the classification framework by using a publicly available dataset of Twitter bots. This training data is enriched by a manually annotated collection of active Twitter users that include both humans and bots of varying sophistication. Our models yield high accuracy and agreement with each other and can detect bots of different nature. Our estimates suggest that between 9% and 15% of active Twitter accounts are bots. Characterizing ties among accounts, we observe that simple bots tend to interact with bots that exhibit more human-like behaviors. Analysis of content flows reveals retweet and mention strategies adopted by bots to interact with different target groups. Using clustering analysis, we characterize several subclasses of accounts, including spammers, self promoters, and accounts that post content from connected applications.
Effectivity of dynatomic cycles for morphisms of projective varieties using deformation theory

Given an endomorphism of a projective variety, by intersecting the graph and the diagonal varieties we can determine the set of periodic points. In an effort to determine the periodic points of a given minimal period, we follow a construction similar to cyclotomic polynomials. The resulting zero-cycle is called a dynatomic cycle and the points in its support are called formal periodic points. This article gives a proof of the effectivity of dynatomic cycles for morphisms of projective varieties using methods from deformation theory.
Decentralized Control via Dynamic Stochastic Prices: The Independent System Operator Problem

A smart grid connects several electricity consumers/producers, e.g., wind/solar/storage farms, fossil-fuel plants, industrial/commercial loads, or load-serving aggregators, all modeled as stochastic dynamical systems. In each time period, each consumes/supplies some electrical energy. Each such agent's utility is the benefit accrued from its consumption or the negative of its generation cost. The social welfare, the sum of all these utilities, is the total benefit accrued from all consumption minus the total cost of generation. The independent system operator is charged with maximizing the social welfare subject to total generation equalling consumption in each time period, but without the agents revealing their system states, dynamic models, utility functions, or uncertainties. It has to announce prices after interacting with agents via bid-price interactions. This paper examines the case where the agents respond in a compliant price-taking manner. It is shown that there is an iterative bid-price interaction, where agents respond to price announcements by complying to the requirement to announce their optimal responses according to their true stochastic model, or, in the case where the agents are linear quadratic Gaussian (LQG) systems, according to deterministic versions of their true stochastic models, that leads to the same global maximum value of social welfare attainable if all agents had pooled their information. In the important LQG case, the bid-price iteration is dramatically simple, exchanging only real-valued vectors of future prices and consumptions/generations at each time step. Agents need not even know of the existence of other agents. DC power flow equations can also be incorporated. The results may be of broader interest vis-a-vis general equilibrium theory of economics for stochastic dynamic agents.
THE PICARD CROSSED MODULE OF A BRAIDED TENSOR CATEGORY

For a finite braided tensor category C we introduce its Picard crossed module P(C) consisting of the group of invertible C-module categories and the group of braided tensor autoequivalences of C. We describe P(C) in terms of braided autoequivalences of the Drinfeld center of C. As an illus- tration, we compute the Picard crossed module of a braided pointed fusion category.
Regularity criterion and energy conservation for the supercritical Quasi-Geostrophic equation

This paper studies the regularity and energy conservation problems for the 2D supercritical quasi-geostrophic (SQG) equation. We apply an approach of splitting the dissipation wavenumber to obtain a new regularity condition which is weaker than all the Prodi–Serrin type regularity conditions. Moreover, we prove that any viscosity solution of the supercritical SQG in $$L^2(0,T; B^{1/2}_{2,c(\mathbb N)})$$ satisfies energy equality.
Expected reliability of communication protocols

Abstract We consider the problem of sending a message from a sender s to a receiver r through an unreliable network by specifying in a protocol what each vertex is supposed to do if it receives the message from one of its neighbors. A protocol for routing a message in such a graph is finite if it never floods r with an infinite number of copies of the message. The expected reliability of a given protocol is the probability that a message sent from s reaches r when the edges of the network fail independently with probability 1 − p . We discuss, for given networks, the properties of finite protocols with maximum expected reliability in the case when p is close to 0 or 1, and we describe networks for which no one protocol is optimal for all values of p . In general, finding an optimal protocol for a given network and fixed probability is challenging and many open problems remain.
Jointly Predicting Predicates and Arguments in Neural Semantic Role Labeling

Recent BIO-tagging-based neural semantic role labeling models are very high performing, but assume gold predicates as part of the input and cannot incorporate span-level features. We propose an end-to-end approach for jointly predicting all predicates, arguments spans, and the relations between them. The model makes independent decisions about what relationship, if any, holds between every possible word-span pair, and learns contextualized span representations that provide rich, shared input features for each decision. Experiments demonstrate that this approach sets a new state of the art on PropBank SRL without gold predicates.
A multi-modal graph-based semi-supervised pipeline for predicting cancer survival

Cancer survival prediction is an active area of research that can help prevent unnecessary therapies and improve patient's quality of life. Gene expression profiling is being widely used in cancer studies to discover informative biomarkers that aid predict different clinical endpoint prediction. We use multiple modalities of data derived from RNA deep-sequencing (RNA-seq) to predict survival of cancer patients. Despite the wealth of information available in expression profiles of cancer tumors, fulfilling the aforementioned objective remains a big challenge, for the most part, due to the paucity of data samples compared to the high dimension of the expression profiles. As such, analysis of transcriptomic data modalities calls for state-of-the-art big-data analytics techniques that can maximally use all the available data to discover the relevant information hidden within a significant amount of noise. In this paper, we propose a pipeline that predicts cancer patients' survival by exploiting the structure of the input (manifold learning) and by leveraging the unlabeled samples using Laplacian support vector machines, a graph-based semi supervised learning (GSSL) paradigm. We show that under certain circumstances, no single modality per se will result in the best accuracy and by fusing different models together via a stacked generalization strategy, we may boost the accuracy synergistically. We apply our approach to two cancer datasets and present promising results. We maintain that a similar pipeline can be used for predictive tasks where labeled samples are expensive to acquire.
Sequence-Based Multi-Lingual Low Resource Speech Recognition

Techniques for multi-lingual and cross-lingual speech recognition can help in low resource scenarios, to bootstrap systems and enable analysis of new languages and domains. End-to-end approaches, in particular sequence-based techniques, are attractive because of their simplicity and elegance. While it is possible to integrate traditional multi-lingual bottleneck feature extractors as front-ends, we show that end-to-end multi-lingual training of sequence models is effective on context independent models trained using Connectionist Temporal Classification (CTC) loss. We show that our model improves performance on Babel languages by over 6% absolute in terms of word/phoneme error rate when compared to mono-lingual systems built in the same setting for these languages. We also show that the trained model can be adapted cross-lingually to an unseen language using just 25% of the target data. We show that training on multiple languages is important for very low resource cross-lingual target scenarios, but not for multi-lingual testing scenarios. Here, it appears beneficial to include large well prepared datasets.
Measuring the quality of exercises

This work explores the problem of exercise quality measurement since it is essential for effective management of diseases like cerebral palsy (CP). This work examines the assessment of quality of large amplitude movement (LAM) exercises designed to treat CP in an automated fashion. Exercise data was collected by trained participants to generate ideal examples to use as a positive samples for machine learning. Following that, subjects were asked to deliberately make subtle errors during the exercise, such as restricting movements, as is commonly seen in cases of patients suffering from CP. The quality measurement problem was then posed as a classification to determine whether an example exercise was either “good” or “bad”. Popular machine learning techniques for classification, including support vector machines (SVM), single and double-layered neural networks (NN), boosted decision trees, and dynamic time warping (DTW), were compared. The AdaBoosted tree performed best with an accuracy of 94.68% demonstrating the feasibility of assessing exercise quality.
Arrangements of minors in the positive Grassmannian and a triangulation of the hypersimplex

The structure of zero and nonzero minors in the Grassmannian leads to rich combinatorics of matroids. In this paper, we investigate an even richer structure of possible equalities and inequalities between the minors in the positive Grassmannian. It was previously shown that arrangements of equal minors of largest value are in bijection with the simplices in a certain triangulation of the hypersimplex that was studied by Stanley, Sturmfels, Lam and Postnikov. Here, we investigate the entire set of arrangements and its relations with this triangulation. First, we show that second largest minors correspond to the facets of the simplices. We then introduce the notion of cubical distance on the dual graph of the triangulation and study its relations with the arrangement of t-th largest minors. Finally, we show that arrangements of largest minors induce a structure of a partially ordered set on the entire collection of minors. We use this triangulation of the hypersimplex to describe a two-dimensional grid structure on this poset.
Latent Multi-group Membership Graph Model

We develop the Latent Multi-group Membership Graph (LMMG) model, a model of networks with rich node feature structure. In the LMMG model, each node belongs to multiple groups and each latent group models the occurrence of links as well as the node feature structure. The LMMG can be used to summarize the network structure, to predict links between the nodes, and to predict missing features of a node. We derive efficient inference and learning algorithms and evaluate the predictive performance of the LMMG on several social and document network datasets.
Integral bases for the universal enveloping algebras of map superalgebras

Abstract Let g be a finite dimensional complex simple classical Lie superalgebra and A be a commutative, associative algebra with unity over C . In this paper we define an integral form for the universal enveloping algebra of the map superalgebra g ⊗ A , and exhibit an explicit integral basis for this integral form.
Tensor Completion Algorithms in Big Data Analytics

Tensor completion is a problem of filling the missing or unobserved entries of partially observed tensors. Due to the multidimensional character of tensors in describing complex datasets, tensor completion algorithms and their applications have received wide attention and achievement in areas like data mining, computer vision, signal processing, and neuroscience. In this survey, we provide a modern overview of recent advances in tensor completion algorithms from the perspective of big data analytics characterized by diverse variety, large volume, and high velocity. We characterize these advances from the following four perspectives: general tensor completion algorithms, tensor completion with auxiliary information (variety), scalable tensor completion algorithms (volume), and dynamic tensor completion algorithms (velocity). Further, we identify several tensor completion applications on real-world data-driven problems and present some common experimental frameworks popularized in the literature along with several available software repositories. Our goal is to summarize these popular methods and introduce them to researchers and practitioners for promoting future research and applications. We conclude with a discussion of key challenges and promising research directions in this community for future exploration.
Large Scale Constrained Linear Regression Revisited: Faster Algorithms via Preconditioning

In this paper, we revisit the large-scale constrained linear regression problem and propose faster methods based on some recent developments in sketching and optimization. Our algorithms combine (accelerated) mini-batch SGD with a new method called two-step preconditioning to achieve an approximate solution with a time complexity lower than that of the state-of-the-art techniques for the low precision case. Our idea can also be extended to the high precision case, which gives an alternative implementation to the Iterative Hessian Sketch (IHS) method with significantly improved time complexity. Experiments on benchmark and synthetic datasets suggest that our methods indeed outperform existing ones considerably in both the low and high precision cases.
A geometric characterization of a sharp Hardy inequality

Abstract In this paper, we prove that the distance function of an open connected set in R n + 1 with a C 2 boundary is superharmonic in the distribution sense if and only if the boundary is weakly mean convex . We then prove that Hardy inequalities with a sharp constant hold on weakly mean convex C 2 domains. Moreover, we show that the weakly mean convexity condition cannot be weakened. We also prove various improved Hardy inequalities on mean convex domains along the line of Brezis and Marcus (1997) [7] .
Constructible sheaves on simplicial complexes and Koszul duality

We obtain a linear algebra data presentation of the category of constructible with respect to perverse triangulation sheaves on a finite simplicial complex. We also establish Koszul duality between the above mentioned category and the category of perverse sheaves constructible with respect to the triangulation
Approximating C 1;0 -foliations

We extend the Eliashberg-Thurston theorem on approximations of taut oriented $C^2$-foliations of 3-manifolds by both positive and negative contact structures to a large class of taut oriented $C^{1,0}$-foliations, where by $C^{1,0}$ foliation, we mean a foliation with continuous tangent plane field. These $C^{1,0}$-foliations can therefore be approximated by weakly symplectically fillable, universally tight, contact structures. This allows applications of $C^2$-foliation theory to contact topology and Floer theory to be generalized and extended to constructions of $C^{1,0}$-foliations.
Optimal ridge detection using coverage risk

We introduce the concept of coverage risk as an error measure for density ridge estimation. The coverage risk generalizes the mean integrated square error to set estimation. We propose two risk estimators for the coverage risk and we show that we can select tuning parameters by minimizing the estimated risk. We study the rate of convergence for coverage risk and prove consistency of the risk estimators. We apply our method to three simulated datasets and to cosmology data. In all the examples, the proposed method successfully recover the underlying density structure.
Falsification of dark energy by fluid mechanics

The 2011 Nobel Prize in Physics has been awarded for the discovery from observations of increased supernovae dimness interpreted as distance, so that the Universe expansion rate has changed from a rate decreasing since the big bang to one that is now increasing, driven by anti-gravity forces of a mysterious dark energy material comprising 70% of the Universe mass-energy. Fluid mechanical considerations falsify both the accelerating expansion and dark energy concepts. Kinematic viscosity is neglected in current standard models of self-gravitational structure formation, which rely on cold dark matter CDM condensations and clusterings that are also falsified by fluid mechanics. Weakly collisional CDM particles do not condense but diffuse away. Photon viscosity predicts superclustervoid fragmentation early in the plasma epoch and protogalaxies at the end. At the plasma-gas transition, the plasma fragments into Earth-mass gas planets in trillion planet clumps (proto-globular-star-cluster PGCs). The hydrogen planets freeze to form the dark matter of galaxies and merge to form their stars. Dark energy is a systematic dimming error for Supernovae Ia caused by dark matter planets near hot white dwarf stars at the Chandrasekhar carbon limit. Evaporated planet atmospheres may or may not scatter light from the events depending on the line of sight.
Recurrent Binary Embedding for GPU-Enabled Exhaustive Retrieval from Billion-Scale Semantic Vectors

Rapid advances in GPU hardware and multiple areas of Deep Learning open up a new opportunity for billion-scale information retrieval with exhaustive search. Building on top of the powerful concept of semantic learning, this paper proposes a Recurrent Binary Embedding (RBE) model that learns compact representations for real-time retrieval. The model has the unique ability to refine a base binary vector by progressively adding binary residual vectors to meet the desired accuracy. The refined vector enables efficient implementation of exhaustive similarity computation with bit-wise operations, followed by a near-lossless k-NN selection algorithm, also proposed in this paper. The proposed algorithms are integrated into an end-to-end multi-GPU system that retrieves thousands of top items from over a billion candidates in real-time. The RBE model and the retrieval system were evaluated with data from a major paid search engine. When measured against the state-of-the-art model for binary representation and the full precision model for semantic embedding, RBE significantly outperformed the former, and filled in over 80% of the AUC gap in-between. Experiments comparing with our production retrieval system also demonstrated superior performance. While the primary focus of this paper is to build RBE based on a particular class of semantic models, generalizing to other types is straightforward, as exemplified by two different models at the end of the paper.