cssi/SciSciGPT-SciSciNet huggingface dataset:
Optimal sampling-based motion planning under differential constraints: The drift case with linear affine dynamics

In this paper we provide a thorough, rigorous theoretical framework to assess optimality guarantees of sampling-based algorithms for drift control systems: systems that, loosely speaking, can not stop instantaneously due to momentum. We exploit this framework to design and analyze a sampling-based algorithm (the Differential Fast Marching Tree algorithm) that is asymptotically optimal, that is, it is guaranteed to converge, as the number of samples increases, to an optimal solution. In addition, our approach allows us to provide concrete bounds on the rate of this convergence. The focus of this paper is on mixed time/control energy cost functions and on linear affine dynamical systems, which encompass a range of models of interest to applications (e.g., double-integrators) and represent a necessary step to design, via successive linearization, sampling-based and provably-correct algorithms for non-linear drift control systems. Our analysis relies on an original perturbation analysis for two-point boundary value problems, which could be of independent interest.
What Twitter Profile and Posted Images Reveal about Depression and Anxiety

Previous work has found strong links between the choice of social media images and users’ emotions, demographics and personality traits. In this study, we examine which attributes of profile and posted images are associated with depression and anxiety of Twitter users. We used a sample of 28,749 Facebook users to build a language prediction model of survey-reported depression and anxiety, and validated it on Twitter on a sample of 887 users who had taken anxiety and depression surveys. We then applied it to a different set of 4,132 Twitter users to impute language-based depression and anxiety labels, and extracted interpretable features of posted and profile pictures to uncover the associations with users’ depression and anxiety, controlling for demographics. For depression, we find that profile pictures suppress positive emotions rather than display more negative emotions, likely because of social media self-presentation biases. They also tend to show the single face of the user (rather than show her in groups of friends), marking increased focus on the self, emblematic for depression. Posted images are dominated by grayscale and low aesthetic cohesion across a variety of image features. Profile images of anxious users are similarly marked by grayscale and low aesthetic cohesion, but less so than those of depressed users. Finally, we show that image features can be used to predict depression and anxiety, and that multitask learning that includes a joint modeling of demographics improves prediction performance. Overall, we find that the image attributes that mark depression and anxiety offer a rich lens into these conditions largely congruent with the psychological literature, and that images on Twitter allow inferences about the mental health status of users.
Lithium NLP: A System for Rich Information Extraction from Noisy User Generated Text on Social Media.

In this paper, we describe the Lithium Natural Language Processing (NLP) system - a resource-constrained, high-throughput and language-agnostic system for information extraction from noisy user generated text on social media. Lithium NLP extracts a rich set of information including entities, topics, hashtags and sentiment from text. We discuss several real world applications of the system currently incorporated in Lithium products. We also compare our system with existing commercial and academic NLP systems in terms of performance, information extracted and languages supported. We show that Lithium NLP is at par with and in some cases, outperforms state-of-the-art commercial NLP systems.
Exotic Bailey–Slater SPT-functions I: Group A

Abstract We introduce several spt-type functions that arise from Bailey pairs. We prove simple Ramanujan type congruences for these functions which can be explained by a spt-crank-type function. The spt-crank-type functions are constructed by adding an extra variable z into the generating functions. We find dissections when z is a certain root of unity, as has been done for many rank and crank difference formulas of various partition type objects. Our formulas require an identity of S.H. Chan on generalized Lambert series.
Optimal Construction of Regenerating Code Through Rate-Matching in Hostile Networks

Regenerating code is a class of distributed storage codes that can optimally trade the bandwidth required to repair a failed node with the amount of data stored per node. There are two optimal points in the regeneration tradeoff curve: the minimum storage regeneration code and the minimum bandwidth regeneration code. However, in hostile networks where the storage nodes may be compromised, the storage capacity of the network can be significantly affected. In this paper, we propose two optimal regenerating code constructions through rate-matching to combat this kind of adversarial attacks in hostile networks. We first develop a two-layer rate-matched regenerating code construction. By matching the parameters of the full rate code and the partial rate code, we can optimize the overall storage efficiency while maintaining the corrupted node detection probability. Through comprehensive analysis, we show that the two-layer rate-matched regenerating code can achieve 70% higher storage efficiency than the universally resilient regenerating code. We then propose an optimal $m$ -layer regenerating code construction. While the principle remains the same as the two-layer code, it is designed to optimize the total number of detectable corrupted nodes of $m$ layers from which the errors can be corrected under the constraint of any given code efficiency. Compared with the universally resilient regenerating code with the same rate, our $m$ -layer code can detect 50% more corrupted nodes.
A geometric interpretation of the characteristic polynomial of reflection arrangements

We consider projections of points onto fundamental chambers of finite real reflection groups. Our main result shows that for groups of types A n , B n , and D n , the coefficients of the characteristic polynomial of the reflection arrangement are proportional to the spherical volumes of the sets of points that are projected onto faces of a given dimension. We also provide strong evidence that the same connection holds for the exceptional, and thus all, reflection groups. These results naturally extend those of De Concini and Procesi, Stembridge, and Denham, which establish the relationship for 0-dimensional projections. This work is also of interest to the field of order-restricted statistical inference, where projections of random points play an important role.
A modern maximum-likelihood theory for high-dimensional logistic regression

Students in statistics or data science usually learn early on that when the sample size n is large relative to the number of variables p, fitting a logistic model by the method of maximum likelihood produces estimates that are consistent and that there are well-known formulas that quantify the variability of these estimates which are used for the purpose of statistical inference. We are often told that these calculations are approximately valid if we have 5 to 10 observations per unknown parameter. This paper shows that this is far from the case, and consequently, inferences produced by common software packages are often unreliable. Consider a logistic model with independent features in which n and p become increasingly large in a fixed ratio. We prove that (i) the maximum-likelihood estimate (MLE) is biased, (ii) the variability of the MLE is far greater than classically estimated, and (iii) the likelihood-ratio test (LRT) is not distributed as a χ2 The bias of the MLE yields wrong predictions for the probability of a case based on observed values of the covariates. We present a theory, which provides explicit expressions for the asymptotic bias and variance of the MLE and the asymptotic distribution of the LRT. We empirically demonstrate that these results are accurate in finite samples. Our results depend only on a single measure of signal strength, which leads to concrete proposals for obtaining accurate inference in finite samples through the estimate of this measure.
Long-time behavior of random and nonautonomous Fisher-KPP equations. Part II. Transition fronts

In the current series of two papers, we study the long-time behavior of the following random Fisher-KPP equation: ut = uxx + a(&#x1d703;tω)u(1 − u),x ∈ ℝ,(1.1) where ω ∈ Ω, (Ω,ℱ, ℙ) is a given probability ...
Cognitive Transfer Outcomes for a Simulation-Based Introductory Statistics Curriculum.

Cognitive transfer is the ability to apply learned skills and knowledge to new applications and contexts. This investigation evaluates cognitive transfer outcomes for a tertiary-level introductory statistics course using the CATALST curriculum, which exclusively used simulation-based methods to develop foundations of statistical inference. A common assessment instrument administered at the end of each course measured learning outcomes for students. CATALST students showed evidence of both near and far transfer outcomes while scoring as high, or higher than, on the assessed learning objectives when compared with peers enrolled in similar courses that emphasized parametric inferential methods (e.g., the t-test). First published November 2017 at Statistics Education Research Journal Archives
Convergence of the Stochastic Six-Vertex Model to the ASEP

In this note we establish the convergence of the stochastic six-vertex model to the one-dimensional asymmetric simple exclusion process, under a certain limit regime recently predicted by Borodin-Corwin-Gorin. This convergence holds for arbitrary initial data.
Recovering nonuniform planted partitions via iterated projection

Abstract In the planted partition problem, the n vertices of a random graph are partitioned into k “clusters,” and edges between vertices in the same cluster and different clusters are included with constant probability p and q, respectively (where 0 ≤ q p ≤ 1 ). We give an efficient spectral algorithm that recovers the clusters with high probability, provided that the sizes of any two clusters are either very close or separated by ≥ Ω ( n ) . We also discuss a generalization of planted partition in which the algorithm's input is not a random graph, but a random real symmetric matrix with independent above-diagonal entries. Our algorithm is an adaptation of a previous algorithm for the uniform case, i.e., when all clusters are size n / k ≥ Ω ( n ) . The original algorithm recovers the clusters one by one via iterated projection: it constructs the orthogonal projection operator onto the dominant k-dimensional eigenspace of the random graph's adjacency matrix, uses it to recover one of the clusters, then deletes it and recurses on the remaining vertices. We show herein that a similar algorithm works in the nonuniform case.
Higher rank lamplighter groups are graph automatic

Abstract We show that the higher rank lamplighter groups, or Diestel–Leader groups Γ d ( q ) for d ≥ 3 , are graph automatic. This introduces a new family of graph automatic groups which are not automatic.
Learning Context-Sensitive Convolutional Filters for Text Processing

Convolutional neural networks (CNNs) have recently emerged as a popular building block for natural language processing (NLP). Despite their success, most existing CNN models employed in NLP share the same learned (and static) set of filters for all input sentences. In this paper, we consider an approach of using a small meta network to learn context-sensitive convolutional filters for text processing. The role of meta network is to abstract the contextual information of a sentence or document into a set of input-sensitive filters. We further generalize this framework to model sentence pairs, where a bidirectional filter generation mechanism is introduced to encapsulate co-dependent sentence representations. In our benchmarks on four different tasks, including ontology classification, sentiment analysis, answer sentence selection, and paraphrase identification, our proposed model, a modified CNN with context-sensitive filters, consistently outperforms the standard CNN and attention-based CNN baselines. By visualizing the learned context-sensitive filters, we further validate and rationalize the effectiveness of proposed framework.
Optimal Resource Allocation for Competitive Spreading Processes on Bilayer Networks

We consider a competitive epidemic process in a bilayer network, and develop a framework to find an optimal allocation of control resources to eliminate one of the epidemics. We consider the $S I_1 S I_2 S$ model, a recent generalization of the popular $SIS$ model to the case of two competitive epidemics. We start our analysis by extending the standard $S I_1 S I_2 S$ formulation with homogeneous parameters to a heterogeneous setting with edge-dependent infection rates, and node-dependent recovery rates. We then find necessary and sufficient conditions under which the mean-field approximation of a chosen epidemic process stabilizes to extinction exponentially quickly. Leveraging this result, we develop a framework for the solution of two optimization problems. In the first, we find an optimal allocation of control resources in order to eradicate the chosen epidemic at a minimum cost. In the second, we are given a fixed budget and propose a method which provably attains the extinction condition when sufficient capital is available, and otherwise mitigates the spread of the unwanted epidemic as much as possible. We explore the efficacy of our methods through extensive simulation.
Fourier-Deligne transform and representations of the symmetric group

We calculate the Fourier-Deligne transform of the IC extension to ${\C}^{n+1}$ of the local system ${\mathcal L}_{\Lambda}$ on the cone over $\Conf_n(¶^1)$ associated to a representation $\Lambda$ of $S_n$, where the length $n-k$ of the first row of the Young diagram of $\Lambda$ is at least $\frac{|\Lambda|-1}{2}$. The answer is the IC extension to the dual vector space ${\C}^{n+1}$ of the local system ${\mathcal R}_{\lambda}$ on the cone over the $k$-th secant variety of the rational normal curve in $¶^n$, where ${\mathcal R}_{\lambda}$ corresponds to the representation $\lambda$ of $S_k$, the Young diagram of which is obtained from the Young diagram of $\Lambda$ by deleting its first row. We also prove an analogous statement for $S_n$-local systems on fibers of the Abel-Jacobi map. We use our result on the Fourier-Deligne transform to rederive a part of a result of Michel Brion on Kronecker coefficients.
Mining associated text and images with dual-wing harmoniums

We propose a multi-wing harmonium model for mining multimedia data that extends and improves on earlier models based on two-layer random fields, which capture bidirectional dependencies between hidden topic aspects and observed inputs. This model can be viewed as an undirected counterpart of the two-layer directed models such as LDA for similar tasks, but bears significant difference in inference/learning cost tradeoffs, latent topic representations, and topic mixing mechanisms. In particular, our model facilitates efficient inference and robust topic mixing, and potentially provides high flexibilities in modeling the latent topic spaces. A contrastive divergence and a variational algorithm are derived for learning. We specialized our model to a dual-wing harmonium for captioned images, incorporating a multivariate Poisson for word-counts and a multivariate Gaussian for color histogram. We present empirical results on the applications of this model to classification, retrieval and image annotation on news video collections, and we report an extensive comparison with various extant models.
High-spatial-resolution K-band Imaging of Select K2 Campaign Fields

NASA's K2 mission began observing fields along the ecliptic plane in 2014 (Howell et al. 2014). Each observing campaign lasts ~80 days, during which high-precision optical photometry of select astrophysical targets is collected by the Kepler spacecraft. Due to the 4 arcsec pixel scale of the Kepler photometer, significant blending between the observed targets can occur (especially in dense fields close to the Galactic plane). We therefore undertook a program to use the Wide Field Camera (WFCAM) on the 3.8 m United Kingdom InfraRed Telescope (UKIRT) (Casali et al. 2007) to collect high-spatial-resolution near-infrared images of targets in select K2 campaign fields, which we report here. These 0.4 arcsec resolution K-band images offer the opportunity to perform a variety of science, including vetting exoplanet candidates by identifying nearby stars blended with the target star (Figure 1) and estimating the size, color, and type of galaxies observed by K2.
Computably enumerable sets that are automorphic to low sets

We work with the structure consisting of all computably enumerable (c.e.) sets ordered by set inclusion. The question we will partially address is which c.e. sets are autormorphic to low (or low2) sets. Using work of R. Miller, we can see that every set with semilow complement is � 0 automorphic to a low set. While it remains open whether every set with semilow complement is effectively automorphic to a low set, we show that there are sets without semilow complement that are effectively automorphic to low sets. We also consider other lowness notions such as having a semilow1.5 complement, having the outer splitting property, and having a semilow2 complement. We show that in every nonlow c.e. degree, there are sets with semilow1.5 complements without semilow complements as well as sets with semilow2 complements and the outer splitting property that do not have semilow1.5 complements. We also address the question of which sets are automorphic to low2 sets.
Contact Structures with Distinct Heegaard Floer Invariants

We prove that the contact structures on Y= dX induced by non-homotopic Stein structures on the 4-manifold X have distinct Heegaard Floer invariants.
A refinement of strong multiplicity one for spectra of hyperbolic manifolds

Let M1 and M2 denote two compact hyperbolic man- ifolds. Assume that the multiplicities of eigenvalues of the Lapla- cian acting on L 2 (M1) and L 2 (M2) (respectively, multiplicities of lengths of closed geodesics in M1 and M2) are the same, except for a possibly infinite exceptional set of eigenvalues (respectively lengths). We define a notion of density for the exceptional set and show that if it is below a certain threshold, the two manifolds must be iso-spectral.
Differentially private convex optimization with piecewise affine objectives

Differential privacy is a recently proposed notion of privacy that provides strong privacy guarantees without any assumptions on the adversary. The paper studies the problem of computing a differentially private solution to convex optimization problems whose objective function is piecewise affine. Such problems are motivated by applications in which the affine functions that define the objective function contain sensitive user information. We propose several privacy preserving mechanisms and provide an analysis on the trade-offs between optimality and the level of privacy for these mechanisms. Numerical experiments are also presented to evaluate their performance in practice.
Topological Skeletonization and Tree-Summarization of Neurons Using Discrete Morse Theory

Neuroscientific data analysis has classically involved methods for statistical signal and image processing, drawing on linear algebra and stochastic process theory. However, digitized neuroanatomical data sets containing labelled neurons, either individually or in groups labelled by tracer injections, do not fully fit into this classical framework. The tree-like shapes of neurons cannot mathematically be adequately described as points in a vector space (eg, the subtraction of two neuronal shapes is not a meaningful operation). There is therefore a need for new approaches. Methods from computational topology and geometry are naturally suited to the analysis of neuronal shapes. Here we introduce methods from Discrete Morse Theory to extract tree-skeletons of individual neurons from volumetric brain image data, or to summarize collections of neurons labelled by localized anterograde tracer injections. Since individual neurons are topologically trees, it is sensible to summarize the collection of neurons labelled by a localized anterograde tracer injection using a consensus tree-shape. This consensus tree provides a richer information summary than the regional or voxel-based "connectivity matrix" approach that has previously been used in the literature. The algorithmic procedure includes an initial pre-processing step to extract a density field from the raw volumetric image data, followed by initial skeleton extraction from the density field using a discrete version of a 1-(un)stable manifold of the density field. Heuristically, if the density field is regarded as a mountainous landscape, then the 1-(un)stable manifold follows the "mountain ridges" connecting the maxima of the density field. We then simplify this skeleton-graph into a tree using a shortest-path approach and methods derived from persistent homology. The advantage of this approach is that it uses global information about the density field and is therefore robust to local fluctuations and non-uniformly distributed input signals. To be able to handle large data sets, we use a divide-and-conquer approach. The resulting software DiMorSC is available on Github. To the best of our knowledge this is currently the only publicly available code for the extraction of the 1-unstable manifold from an arbitrary simplicial complex using the Discrete Morse approach.
Energy-efficient wireless interconnection framework for multichip systems with in-package memory stacks

Multichip systems with memory stacks and various processing chips are at the heart of platform based designs such as servers and embedded systems. Full utilization of the benefits of these integrated multichip systems need a seamless, and scalable in-package interconnection framework. However, state-of-the-art inter-chip communication requires long wireline channels which increases energy consumption and latency while decreasing data bandwidth. Here, we propose the design of an energy-efficient, seamless wireless interconnection network for multichip systems. We demonstrate with cycle-accurate simulations that such a design reduces the energy consumption and latency while increasing the bandwidth in comparison to modern multichip integration systems.
Inverse Optimization with Noisy Data

Inverse optimization refers to the inference of unknown parameters of an optimization problem based on knowledge of its optimal solutions. This paper considers inverse optimization in the setting w...
On the List-Decodability of Random Linear Rank-Metric Codes

The list-decodability of random linear rank-metric codes is shown to match that of random rank-metric codes. Specifically, an $\mathbb{F}_{q}$ -linear rank-metric code over $\mathbb{F}_{q}^{m\times n}$ of rate $R=(1-\rho)(1-\frac{n}{m}\rho)-\varepsilon$ is shown to be (with high probability) list-decodable up to fractional radius $\rho\in(0,1)$ with lists of size at most $\frac{C_{p,q}}{\varepsilon}$ , where $C_{\rho,q}$ is a constant depending only on $\rho$ and $q$ . This matches the bound for random rank-metric codes (up to constant factors). The proof adapts the approach of Guruswami, Hastad, Kopparty (STOC 2010), who established a similar result for the Hamming metric case, to the rank-metric setting. A full version of this paper is accessible at https://arxiv.org/abs/1710.11516
Point leaf maximal singular Riemannian foliations in positive curvature

Abstract We generalize the notion of fixed point homogeneous isometric group actions to the context of singular Riemannian foliations. We find that in some cases, positively curved manifolds admitting these so-called point leaf maximal SRF's are diffeo/homeomorphic to compact rank one symmetric spaces. In all cases, manifolds admitting such foliations are cohomology CROSSes or finite quotients of them. Among non-simply connected manifolds, we find examples of such foliations which are non-homogeneous.
Rees algebras of diagonal ideals

There is a natural epimorphism from the symmetric algebra to the Rees algebra of an ideal. When this epimorphism is an isomorphism, we say that the ideal is of linear type. Given two determinantal rings over a field, we consider the diagonal ideal, kernel of the multiplication map. We prove in many cases that the diagonal ideal is of linear type and recover the defining ideal of the Rees algebra. In our cases, the special fiber rings of the diagonal ideals are the homogeneous coordinate rings of the join varieties.
Harnack Inequalities and Heat Kernel Estimates for Degenerate Diffusion Operators Arising in Population Biology

This paper continues the analysis, started in [2, 3], of a class of degenerate elliptic operators defined on manifolds with corners, which arise in Population Biology. Using techniques pioneered by J. Moser, and extended and refined by L. Saloff-Coste, Grigoryan, and Sturm, we show that weak solutions to the parabolic problem defined by a sub-class of these operators, which consists of those that can be defined by Dirichlet forms and have non-vanishing transverse vector field, satisfy a Harnack inequality. This allows us to conclude that the solutions to these equations belong, for positive times, to the natural anisotropic Holder spaces, and also leads to upper and, in some cases, lower bounds for the heat kernels of these operators. These results imply that these operators have a compact resolvent when acting on $C^0$ or $L^2.$ The proof relies upon a scale invariant Poincare inequality that we establish for a large class of weighted Dirichlet forms, as well as estimates to handle certain mildly singular perturbation terms. The weights that we consider are neither Ahlfors regular, nor do they generally belong to the Muckenhaupt class $A_2.$
The Bayesian Case Model: A Generative Approach for Case-Based Reasoning and Prototype Classification

We present the Bayesian Case Model (BCM), a general framework for Bayesian case-based reasoning (CBR) and prototype classification and clustering. BCM brings the intuitive power of CBR to a Bayesian generative framework. The BCM learns prototypes, the "quintessential" observations that best represent clusters in a dataset, by performing joint inference on cluster labels, prototypes and important features. Simultaneously, BCM pursues sparsity by learning subspaces, the sets of features that play important roles in the characterization of the prototypes. The prototype and subspace representation provides quantitative benefits in interpretability while preserving classification accuracy. Human subject experiments verify statistically significant improvements to participants' understanding when using explanations produced by BCM, compared to those given by prior art.
On the Sub-Packetization Size and the Repair Bandwidth of Reed-Solomon Codes

Reed-Solomon (RS) codes are widely used in distributed storage systems. In this paper, we study the repair bandwidth and sub-packetization size of RS codes. The repair bandwidth is defined as the amount of transmitted information from surviving nodes to a failed node. The RS code can be viewed as a polynomial over a finite field $GF(q^\ell)$ evaluated at a set of points, where $\ell $ is called the sub-packetization size. Smaller bandwidth reduces the network traffic in distributed storage, and smaller $\ell $ facilitates the implementation of RS codes with lower complexity. Recently, Guruswami and Wootters proposed a repair method for RS codes when the evaluation points are the entire finite field. While the sub-packetization size can be arbitrarily small, the repair bandwidth is higher than the minimum storage regenerating (MSR) bound. Tamo, Ye, and Barg achieved the MSR bound but the sub-packetization size grows faster than the exponential function of the number of the evaluation points. In this paper, we present code constructions and repair schemes that extend these results to accommodate different sizes of the evaluation points. In other words, we design schemes that provide points in between. These schemes provide a flexible tradeoff between the sub-packetization size and the repair bandwidth. In addition, we generalize our schemes to manage multiple failures.
Parametrizing quartic algebras over an arbitrary base

We parametrize quartic commutative algebras over any base ring or scheme (equivalently finite, flat degree four $S$-schemes), with their cubic resolvents, by pairs of ternary quadratic forms over the base. This generalizes Bhargava's parametrization of quartic rings with their cubic resolvent rings over $\mathbb{Z}$ by pairs of integral ternary quadratic forms, as well as Casnati and Ekedahl's construction of Gorenstein quartic covers by certain rank 2 families of ternary quadratic forms. We give a geometric construction of a quartic algebra from any pair of ternary quadratic forms, and prove this construction commutes with base change and also agrees with Bhargava's explicit construction over $\mathbb{Z}$.
Automatic Detection and Uncertainty Quantification of Landmarks on Elastic Curves

A population quantity of interest in statistical shape analysis is the location of landmarks, which are points that aid in reconstructing and representing shapes of objects. We provide an automated...
Self-Attention with Relative Position Representations

Relying entirely on an attention mechanism, the Transformer introduced by Vaswani et al. (2017) achieves state-of-the-art results for machine translation. In contrast to recurrent and convolutional neural networks, it does not explicitly model relative or absolute position information in its structure. Instead, it requires adding representations of absolute positions to its inputs. In this work we present an alternative approach, extending the self-attention mechanism to efficiently consider representations of the relative positions, or distances between sequence elements. On the WMT 2014 English-to-German and English-to-French translation tasks, this approach yields improvements of 1.3 BLEU and 0.3 BLEU over absolute position representations, respectively. Notably, we observe that combining relative and absolute position representations yields no further improvement in translation quality. We describe an efficient implementation of our method and cast it as an instance of relation-aware self-attention mechanisms that can generalize to arbitrary graph-labeled inputs.
THE PILLOWCASE AND TRACELESS REPRESENTATIONS OF KNOT GROUPS II: A LAGRANGIAN-FLOER THEORY IN THE PILLOWCASE

We dene an elementary relatively Z=4 graded Lagrangian-Floer chain complex for restricted immersions of compact 1-manifolds into the pillowcase, and apply it to the intersection diagram obtained by taking traceless SU(2) character varieties of 2-tangle de- compositions of knots. Calculations for torus knots are explained in terms of pictures in the punctured plane. The relation to the reduced instanton homology of knots is explored.
Reward augmented maximum likelihood for neural structured prediction

A key problem in structured output prediction is direct optimization of the task reward function that matters for test evaluation. This paper presents a simple and computationally efficient approach to incorporate task reward into a maximum likelihood framework. By establishing a link between the log-likelihood and expected reward objectives, we show that an optimal regularized expected reward is achieved when the conditional distribution of the outputs given the inputs is proportional to their exponentiated scaled rewards. Accordingly, we present a framework to smooth the predictive probability of the outputs using their corresponding rewards. We optimize the conditional log-probability of augmented outputs that are sampled proportionally to their exponentiated scaled rewards. Experiments on neural sequence to sequence models for speech recognition and machine translation show notable improvements over a maximum likelihood baseline by using reward augmented maximum likelihood (RML), where the rewards are defined as the negative edit distance between the outputs and the ground truth labels.
Topological complexity of symplectic 4-manifolds and Stein fillings

We prove that there exists no a priori bound on the Euler characteristic of a closed symplectic 4-manifold coming solely from the genus of a compatible Lefschetz pencil on it, nor is there a similar bound for Stein fillings of a contact 3-manifold coming from the genus of a compatible open book --- except possibly for a few low genera cases. To obtain our results, we produce the first examples of factorizations of a boundary parallel Dehn twist as arbitrarily long products of positive Dehn twists along non-separating curves on a fixed surface with boundary. This solves an open problem posed by Auroux, Smith and Wajnryb, and a more general variant of it raised by Korkmaz, Ozbagci and Stipsicz, independently.
Rotational virtual knots and quantum link invariants

This paper studies rotational virtual knot theory and its relationship with quantum link invariants. Every quantum link invariant for classical knots and links extends to an invariant of rotational virtual knots and links. We give examples of non-trivial rotational virtuals that are undectable by quantum invariants.
Bi-local holography in the SYK model: perturbations

We continue the study of the Sachdev-Ye-Kitaev model in the Large N limit. Following our formulation in terms of bi-local collective fields with dynamical reparametrization symmetry, we perform perturbative calculations around the conformal IR point. These are based on an e expansion which allows for analytical evaluation of correlators and finite temperature quantities.
An Influence-Receptivity Model for Topic Based Information Cascades

We consider the problem of estimating the latent structure of a social network based on observational data on information diffusion processes, or cascades. Here for a given cascade, we only observe the time a node/agent is infected but not the source of infection. Existing literature has focused on estimating network diffusion matrix without any underlying assumptions on the structure of the network. We propose a novel model for inferring network diffusion matrix based on the intuition that an information datum is more likely to propagate among two nodes if they are interested in similar topics, which are common with the information. In particular, our model endows each node with an influence vector (how authoritative they are on each topic) and a receptivity vector (how susceptible they are on each topic). We show how this node-topic structure can be estimated from observed cascades. The estimated model can be used to build recommendation system based on the receptivity vectors, as well as for marketing based on the influence vectors.
Coarse Grid Projection Methodology: A Partial Mesh Refinement Tool for Incompressible Flow Simulations

We discuss coarse grid projection (CGP) methodology as a guide for partial mesh refinement of incompressible flow computations for the first time. Based on it, if for a given spatial resolution the numerical simulation diverges or the velocity outputs are not accurate enough, instead of refining both the advection–diffusion and the Poisson grids, the CGP mesh refinement suggests to only refine the advection–diffusion grid and keep the Poisson grid resolution unchanged. The application of the novel mesh refinement tool is shown in the cases of flow over a backward-facing step and flow past a cylinder. For the backward-facing step flow, a three-level partial mesh refinement makes a previously diverging computation numerically stable. For the flow past a cylinder, the error of the viscous lift force is reduced from 31.501 to 7.191% (with reference to the standard mesh refinement results) by the one-level partial mesh refinement technique.
Towards unifying hamiltonian Monte Carlo and Slice sampling

We unify slice sampling and Hamiltonian Monte Carlo (HMC) sampling, demonstrating their connection via the Hamiltonian-Jacobi equation from Hamiltonian mechanics. This insight enables extension of HMC and slice sampling to a broader family of samplers, called Monomial Gamma Samplers (MGS). We provide a theoretical analysis of the mixing performance of such samplers, proving that in the limit of a single parameter, the MGS draws decorrelated samples from the desired target distribution. We further show that as this parameter tends toward this limit, performance gains are achieved at a cost of increasing numerical difficulty and some practical convergence issues. Our theoretical results are validated with synthetic data and real-world applications.
Evaluation of Parallel Tempering to Accelerate Bayesian Parameter Estimation in Systems Biology

Models of biological systems often have many unknown parameters that must be determined in order for model behavior to match experimental observations. Commonly-used methods for parameter estimation that return point estimates of the best-fit parameters are insufficient when models are high dimensional and under-constrained. As a result, Bayesian methods, which treat model parameters as random variables and attempt to estimate their probability distributions given data, have become popular in systems biology. Bayesian parameter estimation often relies on Markov Chain Monte Carlo (MCMC) methods to sample model parameter distributions, but the slow convergence of MCMC sampling can be a major bottleneck. One approach to improving performance is parallel tempering (PT), a physics-based method that uses swapping between multiple Markov chains run in parallel at different temperatures to accelerate sampling. The temperature of a Markov chain determines the probability of accepting an unfavorable move, so swapping with higher temperatures chains enables the sampling chain to escape from local minima. In this work we compared the MCMC performance of PT and the commonly-used Metropolis- Hastings (MH) algorithm on six biological models of varying complexity. We found that for simpler models PT accelerated convergence and sampling, and that for more complex models, PT often converged in cases MH became trapped in non-optimal local minima. We also developed a freely-available MATLAB package for Bayesian parameter estimation called PTEMPEST (http://github.com/RuleWorld/ptempest), which is closely integrated with the popular BioNetGen software for rule-based modeling of biological systems.
Multi-Level Feature Abstraction from Convolutional Neural Networks for Multimodal Biometric Identification

In this paper, we propose a deep multimodal fusion network to fuse multiple modalities (face, iris, and fingerprint) for person identification. The proposed deep multimodal fusion algorithm consists of multiple streams of modality-specific Convolutional Neural Networks (CNNs), which are jointly optimized at multiple feature abstraction levels. Multiple features are extracted at several different convolutional layers from each modality-specific CNN for joint feature fusion, optimization, and classification. Features extracted at different convolutional layers of a modality-specific CNN represent the input at several different levels of abstract representations. We demonstrate that an efficient multimodal classification can be accomplished with a significant reduction in the number of network parameters by exploiting these multi-level abstract representations extracted from all the modality-specific CNNs. We demonstrate an increase in multimodal person identification performance by utilizing the proposed multi-level feature abstract representations in our multimodal fusion, rather than using only the features from the last layer of each modality-specific CNNs. We show that our deep multi-modal CNNs with multimodal fusion at several different feature level abstraction can significantly outperform the unimodal representation accuracy. We also demonstrate that the joint optimization of all the modality-specific CNNs excels the score and decision level fusions of independently optimized CNNs.
Growth rates of permutation classes: from countable to uncountable

We establish that there is an algebraic number $\xi\approx 2.30522$ such that while there are uncountably many growth rates of permutation classes arbitrarily close to $\xi,$ there are only countably many less than $\xi$. Central to the proof are various structural notions regarding generalized grid classes and a new property of permutation classes called concentration. The classification of growth rates up to $\xi$ is completed in a subsequent paper.
Reconstructions in ultrasound modulated optical tomography

The work of both authors was partially supported by NSF grant DMS-0604778 and Award No. KUS-C1-016-04 made by King Abdullah University of Science and Technology (KAUST). The work of the second author was also partially supported by U.S. Department of Energy grant DE-FG07-07ID14767 and by an Alfred P. Sloan Research Fellowship. We wish to express our gratitude to these sources of support. We would also like to thank Prof. P. Kuchment, who suggested the approach for proving linear stability in Section 5.
An Improved Approximate Consensus Algorithm in the Presence of Mobile Faults

This paper explores the problem of reaching approximate consensus in synchronous point-to-point networks, where each pair of nodes is able to communicate with each other directly and reliably. We consider the mobile Byzantine fault model proposed by Garay ’94 – in the model, an omniscient adversary can corrupt up to f nodes in each round, and at the beginning of each round, faults may “move” in the system (i.e., different sets of nodes may become faulty in different rounds). Recent work by Bonomi et al. ’16 proposed a simple iterative approximate consensus algorithm which requires at least \(4f+1\) nodes. This paper proposes a novel technique of using “confession” (a mechanism to allow other nodes to ignore past behavior) and a variant of reliable broadcast to improve the fault-tolerance level. In particular, we present an approximate consensus algorithm that requires only \(\lceil 7f/2\rceil + 1\) nodes, an \(\lfloor f/2 \rfloor \) improvement over the state-of-the-art algorithms. Moreover, we also show that the proposed algorithm is optimal within a family of round-based algorithms.
Exact regularity and the cohomology of tiling spaces

The Exact Regularity Property was introduced recently as a property of homological Pisot substitutions in one dimension. In this paper, we consider exact regularity for arbitrary tiling spaces. Let ${T}$ be a $d$ dimensional repetitive tiling, and let $\Omega_{T}$ be its hull. If $\check H^d(\Omega_{T}, Q) = Q^k$, then there exist $k$ patches whose appearance govern the number of appearances of every other patch. This gives uniform estimates on the convergence of all patch frequencies to the ergodic limit. If the tiling ${T}$ comes from a substitution, then we can quantify that convergence rate. If ${T}$ is also one-dimensional, we put constraints on the measure of any cylinder set in $\Omega_{T}$.
Being Negative but Constructively: Lessons Learnt from Creating Better Visual Question Answering Datasets

Visual question answering (Visual QA) has attracted a lot of attention lately, seen essentially as a form of (visual) Turing test that artificial intelligence should strive to achieve. In this paper, we study a crucial component of this task: how can we design good datasets for the task? We focus on the design of multiple-choice based datasets where the learner has to select the right answer from a set of candidate ones including the target (i.e., the correct one) and the decoys (i.e., the incorrect ones). Through careful analysis of the results attained by state-of-the-art learning models and human annotators on existing datasets, we show that the design of the decoy answers has a significant impact on how and what the learning models learn from the datasets. In particular, the resulting learner can ignore the visual information, the question, or both while still doing well on the task. Inspired by this, we propose automatic procedures to remedy such design deficiencies. We apply the procedures to re-construct decoy answers for two popular Visual QA datasets as well as to create a new Visual QA dataset from the Visual Genome project, resulting in the largest dataset for this task. Extensive empirical studies show that the design deficiencies have been alleviated in the remedied datasets and the performance on them is likely a more faithful indicator of the difference among learning models. The datasets are released and publicly available via http://www.teds.usc.edu/website_vqa/.
Swarm Engineering Through Quantitative Measurement of Swarm Robotic Principles in a 10,000 Robot Swarm

When designing swarm-robotic systems, systematic comparison of algorithms from different domains is necessary to determine which is capable of scaling up to handle the target problem size and target operating conditions. We propose a set of quantitative metrics for scalability, flexibility, and emergence which are capable of addressing these needs during the system design process. We demonstrate the applicability of our proposed metrics as a design tool by solving a large object gathering problem in temporally varying operating conditions using iterative hypothesis evaluation. We provide experimental results obtained in simulation for swarms of over 10,000 robots.
Positive entropy actions of countable groups factor onto Bernoulli shifts

We prove that if a free ergodic action of a countably infinite group has positive Rokhlin entropy (or, less generally, positive sofic entropy) then it factors onto all Bernoulli shifts of lesser or equal entropy. This extends to all countably infinite groups the well-known Sinai factor theorem from classical entropy theory.
The Materials Science Procedural Text Corpus: Annotating Materials Synthesis Procedures with Shallow Semantic Structures

Materials science literature contains millions of materials synthesis procedures described in unstructured natural language text. Large-scale analysis of these synthesis procedures would facilitate deeper scientific understanding of materials synthesis and enable automated synthesis planning. Such analysis requires extracting structured representations of synthesis procedures from the raw text as a first step. To facilitate the training and evaluation of synthesis extraction models, we introduce a dataset of 230 synthesis procedures annotated by domain experts with labeled graphs that express the semantics of the synthesis sentences. The nodes in this graph are synthesis operations and their typed arguments, and labeled edges specify relations between the nodes. We describe this new resource in detail and highlight some specific challenges to annotating scientific text with shallow semantic structure. We make the corpus available to the community to promote further research and development of scientific information extraction systems.