cssi/SciSciGPT-SciSciNet huggingface dataset:
Source-Target Inference Models for Spatial Instruction Understanding.

Models that can execute natural language instructions for situated robotic tasks such as assembly and navigation have several useful applications in homes, offices, and remote scenarios. We study the semantics of spatially-referred configuration and arrangement instructions, based on the challenging Bisk-2016 blank-labeled block dataset. This task involves finding a source block and moving it to the target position (mentioned via a reference block and offset), where the blocks have no names or colors and are just referred to via spatial location features. We present novel models for the subtasks of source block classification and target position regression, based on joint-loss language and spatial-world representation learning, as well as CNN-based and dual attention models to compute the alignment between the world blocks and the instruction phrases. For target position prediction, we compare two inference approaches: annealed sampling via policy gradient versus expectation inference via supervised regression. Our models achieve the new state-of-the-art on this task, with an improvement of 47% on source block accuracy and 22% on target position distance.
Measures and Dynamics on Noetherian Spaces

We give an explicit description of all finite Borel measures on Noetherian topological spaces X, and characterize them as objects dual to a space of functions on X. We use these results to study the asymptotic behavior of continuous dynamical systems on Noetherian spaces.
Benefits of depth in neural networks

For any positive integer $k$, there exist neural networks with $\Theta(k^3)$ layers, $\Theta(1)$ nodes per layer, and $\Theta(1)$ distinct parameters which can not be approximated by networks with $\mathcal{O}(k)$ layers unless they are exponentially large --- they must possess $\Omega(2^k)$ nodes. This result is proved here for a class of nodes termed "semi-algebraic gates" which includes the common choices of ReLU, maximum, indicator, and piecewise polynomial functions, therefore establishing benefits of depth against not just standard networks with ReLU gates, but also convolutional networks with ReLU and maximization gates, sum-product networks, and boosted decision trees (in this last case with a stronger separation: $\Omega(2^{k^3})$ total tree nodes are required).
Combinatorial formulas for certain sequences of multiple numbers

Multiple analogues of certain families of combinatorial numbers have been recently constructed by the author in terms of well-poised Macdonald functions, and some of their properties were developed. In this paper, we present combinatorial formulas for the rational Macdonald functions, the multiple bracket function, the multiple binomial coefficients, and the multiple Catalan and Lah number sequences.
Uncertainty Autoencoders: Learning Compressed Representations via Variational Information Maximization

Compressed sensing techniques enable efficient acquisition and recovery of sparse, highdimensional data signals via low-dimensional projections. In this work, we propose Uncertainty Autoencoders, a learning framework for unsupervised representation learning inspired by compressed sensing. We treat the low-dimensional projections as noisy latent representations of an autoencoder and directly learn both the acquisition (i.e., encoding) and amortized recovery (i.e., decoding) procedures. Our learning objective optimizes for a tractable variational lower bound to the mutual information between the datapoints and the latent representations. We show how our framework provides a unified treatment to several lines of research in dimensionality reduction, compressed sensing, and generative modeling. Empirically, we demonstrate a 32% improvement on average over competing approaches for the task of statistical compressed sensing of high-dimensional datasets.
The intersection of subgroups in free groups and linear programming

We study the intersection of finitely generated subgroups of free groups by utilizing the method of linear programming. We prove that if $$H_1$$ is a finitely generated subgroup of a free group F, then the WN-coefficient $$\sigma (H_1)$$ of $$H_1$$ is rational and can be computed in deterministic exponential time in the size of $$H_1$$ . This coefficient $$\sigma (H_1)$$ is the minimal nonnegative real number such that, for every finitely generated subgroup $$H_2$$ of F, it is true that $${\bar{\mathrm {r}}}(H_1, H_2) \le \sigma (H_1) {\bar{ \mathrm {r}}}(H_1) {\bar{\mathrm {r}}}(H_2)$$ , where $${\bar{ \mathrm{r}}} (H) := \max ( \mathrm{r} (H)-1,0)$$ is the reduced rank of H, $$\mathrm {r}(H)$$ is the rank of H, and $${\bar{\mathrm {r}}}(H_1, H_2)$$ is the reduced rank of the generalized intersection of $$H_1$$ and $$H_2$$ . We also show the existence of a subgroup $$H_2^* = H_2^*(H_1)$$ of F such that $${\bar{\mathrm {r}}}(H_1, H_2^*) = \sigma (H_1) {\bar{\mathrm {r}}}(H_1) {\bar{ \mathrm {r}}}(H_2^*)$$ , the Stallings graph $$\Gamma (H_2^*)$$ of $$H_2^*$$ has at most doubly exponential size in the size of $$H_1$$ and $$\Gamma (H_2^*)$$ can be constructed in exponential time in the size of $$H_1$$ .
Loop coproducts in string topology and triviality of higher genus TQFT operations

Abstract Cohen and Godin constructed a positive boundary topological quantum field theory (TQFT) structure on the homology of free loop spaces of oriented closed smooth manifolds by associating certain operations called string operations to orientable surfaces with parametrized boundaries. We show that all TQFT string operations associated to surfaces of genus at least one vanish identically. This is a simple consequence of properties of the loop coproduct which will be discussed in detail. One interesting property is that the loop coproduct is nontrivial only on the degree d homology group of the connected component of L M consisting of contractible loops, where d = dim M , with values in the degree 0 homology group of constant loops. Thus the loop coproduct behaves in a dramatically simpler way than the loop product.
State evolution for general approximate message passing algorithms, with applications to spatial coupling

We consider a class of approximated message passing (AMP) algorithms and characterize their highdimensional behavior in terms of a suitable state evolution recursion. Our proof applies to Gaussian matrices with independent but not necessarily identically distributed entries. It covers—in particular—the analysis of generalized AMP, introduced by Rangan, and of AMP reconstruction in compressed sensing with spatially coupled sensing matrices. The proof technique builds on that of Bayati & Montanari [2], while simplifying and generalizing several steps.
Information entropy and thermal entropy: apples and oranges

The frequent misunderstanding of information entropy is pointed out. It is shown that, contrary to fortuitous situations and common beliefs, there is no general interrelation between the information entropy and the thermodynamical entropy. We point out that the change of information entropy during measurement is determined by the resolution of the measurement instrument and these changes do not have a general and clear-cut interrelation with the change of thermal entropy. Moreover, these changes can be separated in space and time. We show classical physical considerations and examples to support this conclusion. Finally, we show that information entropy can violate the Third Law of Thermodynamics which is another indication of major differences from thermal entropy.
Solutions to certain linear equations in Piatetski-Shapiro sequences

Denote by $\text{PS}(\alpha)$ the image of the Piatetski-Shapiro sequence $n \mapsto \lfloor n^{\alpha} \rfloor$ where $\alpha > 1$ is non-integral and $\lfloor x \rfloor$ is the integer part of $x \in \mathbb{R}$. We partially answer the question of which bivariate linear equations have infinitely many solutions in $\text{PS}(\alpha)$: if $a, b \in \mathbb{R}$ are such that the equation $y=ax+b$ has infinitely many solutions in the positive integers, then for Lebesgue-a.e. $\alpha > 1$, it has infinitely many or at most finitely many solutions in $\text{PS}(\alpha)$ according as $\alpha 2$ (and $(a,b) \neq (1,0)$). We collect a number of interesting open questions related to further results along these lines.
An alternative softmax operator for reinforcement learning

A softmax operator applied to a set of values acts somewhat like the maximization function and somewhat like an average. In sequential decision making, softmax is often used in settings where it is necessary to maximize utility but also to hedge against problems that arise from putting all of one's weight behind a single maximum utility decision. The Boltzmann softmax operator is the most commonly used softmax operator in this setting, but we show that this operator is prone to misbehavior. In this work, we study a differentiable softmax operator that, among other properties, is a non-expansion ensuring a convergent behavior in learning and planning. We introduce a variant of SARSA algorithm that, by utilizing the new operator, computes a Boltzmann policy with a state-dependent temperature parameter. We show that the algorithm is convergent and that it performs favorably in practice.
Nuisance effects in inter-scan functional connectivity estimates before and after nuisance regression

In resting-state functional MRI, the correlation between blood-oxygenation-level-dependent (BOLD) signals across brain regions is used to estimate the functional connectivity (FC) of the brain. FC estimates are prone to the influence of nuisance factors including scanner-related artifacts and physiological modulations of the BOLD signal. Nuisance regression is widely performed to reduce the effect of nuisance factors on FC estimates on a per-scan basis. However, a dedicated analysis of nuisance effects on the variability of FC metrics across a collection of scans has been lacking. This work investigates the effects of nuisance factors on the variability of FC estimates across a collection of scans both before and after nuisance regression. Inter-scan variations in FC estimates are shown to be significantly correlated with the geometric norms of various nuisance terms, including head motion measurements, signals derived from white-matter and cerebrospinal regions, and the whole-brain global signal (GS) both before and after nuisance regression. In addition, it is shown that GS regression (GSR) can introduce GS norm-related fluctuations that are negatively correlated with inter-scan FC estimates. The empirical results are shown to be largely consistent with the predictions of a theoretical framework previously developed for the characterization of dynamic FC measures. This work shows that caution must be exercised when interpreting inter-scan FC measures across scans both before and after nuisance regression.
TF Boosted Trees: A Scalable TensorFlow Based Framework for Gradient Boosting

TF Boosted Trees (TFBT) is a new open-sourced framework for the distributed training of gradient boosted trees. It is based on TensorFlow, and its distinguishing features include a novel architecture, automatic loss differentiation, layer-by-layer boosting that results in smaller ensembles and faster prediction, principled multi-class handling, and a number of regularization techniques to prevent overfitting.
Policy Gradient as a Proxy for Dynamic Oracles in Constituency Parsing.

Dynamic oracles provide strong supervision for training constituency parsers with exploration, but must be custom defined for a given parser’s transition system. We explore using a policy gradient method as a parser-agnostic alternative. In addition to directly optimizing for a tree-level metric such as F1, policy gradient has the potential to reduce exposure bias by allowing exploration during training; moreover, it does not require a dynamic oracle for supervision. On four constituency parsers in three languages, the method substantially outperforms static oracle likelihood training in almost all settings. For parsers where a dynamic oracle is available (including a novel oracle which we define for the transition system of Dyer et al., 2016), policy gradient typically recaptures a substantial fraction of the performance gain afforded by the dynamic oracle.
A programmable CMOS transceiver for structural health monitoring

We describe a highly-integrated CMOS transceiver for active structural health monitoring (SHM). The chip actuates piezoelectric transducers and also senses ultrasound waves received by the same or another transducer. The transmitter uses an integer-N frequency synthesizer and pulse-width modulation (PWM) to generate low-distortion, band-limited waveforms up to 12.7 V pp with center frequency from ∼0.1–2.75 MHz. The integrated offset-canceling fully-differential receiver has programmable gain and bandwidth, and uses quadrature demodulation to extract both amplitude and phase of the received waveforms for further signal processing. The transceiver was fabricated in a 0.5 μm CMOS process and has been validated using (2D) damage localization on an SHM test bed.
Nonlinear basis pursuit

In compressive sensing, the basis pursuit algorithm aims to find the sparsest solution to an underdetermined linear equation system. In this paper, we generalize basis pursuit to finding the sparsest solution to higher order nonlinear systems of equations, called nonlinear basis pursuit. In contrast to the existing nonlinear compressive sensing methods, the new algorithm is based on convex relaxation and is not a greedy method. The novel algorithm enables the compressive sensing approach to be used for a broader range of applications where there are nonlinear relationships between the measurements and the unknowns.
User oriented assessment of vibration suppression by command shaping in a supernumerary wearable robotic arm

Supernumerary Robotic Limbs (SRLs) exhibit inherently compliant behavior due to the elasticity present at the intersection of human tissue and the robot. This compliance, can prominently influence the operation of some SRLs, depending on the application. In order to control the residual vibrations of SRLs, we have used an input-shaping method which is a computationally inexpensive approach. The effectiveness of this method in controlling the residual vibrations of a SRL has been proven using robustness analysis. User studies show that reducing the vibrations using input shaping directly increases the user satisfaction and comfort by at least 9%. It is also observed that 36% of the users preferred unshaped commands. We hypothesize that the shaped commands put a higher cognitive load on the user compared to unshaped commands. This shows that when dealing with human-robot interaction, user satisfaction becomes an equally important parameter as traditional performance criteria and should be taken into account while evaluating the success of any vibration-control method.
Spin Logic via Controlled Correlation in Nanomagnet–Dirac-Fermion Heterostructures

Exotic properties of topological insulators (TIs) and graphene have captivated many condensed matter physicists, but are practical outcomes actually within reach? The authors propose an efficient, beyond-CMOS spin logic platform exploiting the strong exchange coupling between a ferromagnet and the Dirac fermion states of a TI and of graphene. A detailed theoretical analysis illustrates the desired ultralow-power performance under realistic conditions, leading to predictions for practical devices to be controlled by signals as small as atto- (10${}^{-18}$) Joules!
3D Convolutional Neural Networks for Classification of Functional Connectomes

Resting-state functional MRI (rs-fMRI) scans hold the potential to serve as a diagnostic or prognostic tool for a wide variety of conditions, such as autism, Alzheimer’s disease, and stroke. While a growing number of studies have demonstrated the promise of machine learning algorithms for rs-fMRI based clinical or behavioral prediction, most prior models have been limited in their capacity to exploit the richness of the data. For example, classification techniques applied to rs-fMRI often rely on region-based summary statistics and/or linear models. In this work, we propose a novel volumetric Convolutional Neural Network (CNN) framework that takes advantage of the full-resolution 3D spatial structure of rs-fMRI data and fits non-linear predictive models. We showcase our approach on a challenging large-scale dataset (ABIDE, with \(N>2,000\)) and report state-of-the-art accuracy results on rs-fMRI-based discrimination of autism patients and healthy controls.
Multivariate Time Series Classification Using Dynamic Time Warping Template Selection for Human Activity Recognition

Accurate and computationally efficient means for classifying human activities have been the subject of extensive research efforts. Most current research focuses on extracting complex features to achieve high classification accuracy. We propose a template selection approach based on Dynamic Time Warping, such that complex feature extraction and domain knowledge is avoided. We demonstrate the predictive capability of the algorithm on both simulated and real smartphone data.
Gauge topology and confinement: an update

In the instanton ensemble the fermionic zero modes collectivize and break chiral symmetry. Recent studies of resulting zero mode zone confirm its very small width and overall importance for lattice simulations. Confinement however has been related with completely different topological objects, the magnetic monopoles. Instanton constituents ‐ instanton dyons, discovered at nonzero holonomy by Pierre van Baal and others ‐ are able to explain both confinement and chiral symmetry breaking. The talk summarizes recent works deriving the instanton-dyon mutual interactions, and statistical studies of their ensemble. At high density the screening is robust enough to do it analytically, in the mean-field-type approach: we call this limit Dense Dyonic Plasma (DDP). Above Tc the classical interaction between the dyons induce strong correlations and should be studied by direct numerical simulations. Those works are now in progress.
General methods of elliptic minimization

We provide general methods in the calculus of variations for the anisotropic Plateau problem in arbitrary dimension and codimension. Given a collection of competing “surfaces” that span a given “bounding set” in an ambient metric space, we produce one minimizing an elliptic area functional. The collection of competing surfaces is assumed to satisfy a set of geometrically-defined axioms. These axioms hold for collections defined using any combination of homological, cohomological or linking number spanning conditions. A variety of minimization problems can be solved, including sliding boundaries.
Overlapped list successive cancellation approach for hardware efficient polar code decoder

This paper presents an efficient hardware design approach for list successive cancellation (LSC) decoding of polar codes. By applying path-overlapping scheme, for LSC with list size l (l > 1), the l instances of successive cancellation (SC) decoder can be cut down to only one. This results in a dramatic reduction of the hardware complexity without any decoding performance loss. We also develop novel approaches to reduce the latency associated with the pipeline scheme. Simulation results show that with proposed design approach the hardware efficiency is increased significantly over the recently proposed LSC decoders.
Gromov hyperbolicity, the Kobayashi metric, and $\mathbb{C}$-convex sets

In this paper we study the global geometry of the Kobayashi metric on domains in complex Euclidean space. We are particularly interested in developing necessary and sufficient conditions for the Kobayashi metric to be Gromov hyperbolic. For general domains, it has been suggested that a non-trivial complex affine disk in the boundary is an obstruction to Gromov hyperbolicity. This is known to be the case when the set in question is convex. In this paper we first extend this result to $\mathbb{C}$-convex sets with $C^1$-smooth boundary. We will then show that some boundary regularity is necessary by producing in any dimension examples of open bounded $\mathbb{C}$-convex sets where the Kobayashi metric is Gromov hyperbolic but whose boundary contains a complex affine ball of complex codimension one.
Graphical Models for Non-Negative Data Using Generalized Score Matching

A common challenge in estimating parameters of probability density functions is the intractability of the normalizing constant. While in such cases maximum likelihood estimation may be implemented using numerical integration, the approach becomes computationally intensive. In contrast, the score matching method of Hyvarinen (2005) avoids direct calculation of the normalizing constant and yields closed-form estimates for exponential families of continuous distributions over Rm. Hyvarinen (2007) extended the approach to distributions supported on the non-negative orthant Rm+. In this paper, we give a generalized form of score matching for non-negative data that improves estimation efficiency. We also generalize the regularized score matching method of Lin et al. (2016) for non-negative Gaussian graphical models, with improved theoretical guarantees.
Energy of harmonic functions and Gromov's proof of Stallings' theorem

© 2014 by De Gruyter 2014. We provide details for Gromov's proof of Stallings' theorem on groups with infinitely many ends using harmonic functions. The main technical result of the paper is a compactness theorem for a certain family of harmonic functions.
Coherence-based performance guarantees of Orthogonal Matching Pursuit

In this paper, we present coherence-based performance guarantees of Orthogonal Matching Pursuit (OMP) for both support recovery and signal reconstruction of sparse signals when the measurements are corrupted by noise. In particular, two variants of OMP either with known sparsity level or with a stopping rule are analyzed. It is shown that if the measurement matrix X ∊ Cn×p satisfies the strong coherence property, then with n ≳ O(k log p), OMP will recover a k-sparse signal with high probability. In particular, the performance guarantees obtained here separate the properties required of the measurement matrix from the properties required of the signal, which depends critically on the minimum signal to noise ratio rather than the power profiles of the signal. We also provide performance guarantees for partial support recovery. Comparisons are given with other performance guarantees for OMP using worst-case analysis and the sorted one step thresholding algorithm.
Dimensionality reduction for acoustic vehicle classification with spectral embedding

We propose a method for recognizing moving vehicles, using data from roadside audio sensors. This problem has applications ranging widely, from traffic analysis to surveillance. We extract a frequency signature from the audio signal using a short-time Fourier transform, and treat each time window as an individual data point to be classified. By applying a spectral embedding, we decrease the dimensionality of the data sufficiently for K-nearest neighbors to provide accurate vehicle identification.
Selection for synchronized cell division in simple multicellular organisms.

Abstract The evolution of multicellularity was a major transition in the history of life on earth. Conditions under which multicellularity is favored have been studied theoretically and experimentally. But since the construction of a multicellular organism requires multiple rounds of cell division, a natural question is whether these cell divisions should be synchronous or not. We study a population model in which there compete simple multicellular organisms that grow by either synchronous or asynchronous cell divisions. We demonstrate that natural selection can act differently on synchronous and asynchronous cell division, and we offer intuition for why these phenotypes are generally not neutral variants of each other.
Dileptons and Chiral Symmetry Restoration

Abstract We report on recent work relating the medium effects observed in dilepton spectra in heavy-ion collisions to potential signals of chiral symmetry restoration. The key connection remains the approach to spectral function degeneracy between the vector-isovector channel with its chiral partner, the axialvector-isovector channel. Several approaches are discussed to elaborate this connection, namely QCD and Weinberg sum rules with input for chiral order parameters from lattice QCD, and chiral hadronic theory to directly evaluate the medium effects of the axialvector channel and the pertinent pion decay constant as function of temperature. A pattern emerges where the chiral mass splitting between ρ and a 1 burns off and is accompanied by a strong broadening of the spectral distributions.
Global Convergence of a Grassmannian Gradient Descent Algorithm for Subspace Estimation

It has been observed in a variety of contexts that gradient descent methods have great success in solving low-rank matrix factorization problems, despite the relevant problem formulation being non-convex. We tackle a particular instance of this scenario, where we seek the d-dimensional subspace spanned by a streaming data matrix. We apply the natural first order incremental gradient descent method, constraining the gradient method to the Grassmannian. In this paper, we propose an adaptive step size scheme that is greedy for the noiseless case, that maximizes the improvement of our metric of convergence at each data index t, and yields an expected improvement for the noisy case. We show that, with noise-free data, this method converges from any random initialization to the global minimum of the problem. For noisy data, we provide the expected convergence rate of the proposed algorithm per iteration.
Schrödinger operators and associated hyperbolic pencils

Abstract For a large class of Schrodinger operators, we introduce the hyperbolic quadratic pencils by making the coupling constant dependent on the energy in the very special way. For these pencils, many problems of scattering theory are significantly easier to study. Then, we give some applications to the original Schrodinger operators including one-dimensional Schrodinger operators with L 2 -operator-valued potentials, multidimensional Schrodinger operators with slowly decaying potentials.
Computational mechanisms in genetic regulation by RNA

The evolution of the genome has led to very sophisticated and complex regulation. Because of the abundance of non-coding RNA (ncRNA) in the cell, different species will promiscuously associate with each other, suggesting collective dynamics similar to artificial neural networks. A simple mechanism is proposed allowing ncRNA to perform computations equivalent to neural network algorithms such as Boltzmann machines and the Hopfield model. The quantities analogous to the neural couplings are the equilibrium constants between different RNA species. The relatively rapid equilibration of RNA binding and unbinding is regulated by a slower process that degrades and creates new RNA. The model requires that the creation rate for each species be an increasing function of the ratio of total to unbound RNA. Similar mechanisms have already been found to exist experimentally for ncRNA regulation. With the overall concentration of RNA regulated, equilibrium constants can be chosen to store many different patterns, or many different input-output relations. The network is also quite insensitive to random mutations in equilibrium constants. Therefore one expects that this kind of mechanism will have a much higher mutation rate than ones typically regarded as being under evolutionary constraint.
The reciprocal Mahler ensembles of random polynomials

We consider the roots of uniformly chosen complex and real reciprocal polynomials of degree N whose Mahler measure is bounded by a constant. After a change of variables, this reduces to a generalization of Ginibre’s complex and real ensembles of random matrices where the weight function (on the eigenvalues of the matrices) is replaced by the exponentiated equilibrium potential of the interval [−2, 2] on the real axis in the complex plane. In the complex (real) case, the random roots form a determinantal (Pfaffian) point process, and in both cases, the empirical measure on roots converges weakly to the arcsine distribution supported on [−2, 2]. Outside this region, the kernels converge without scaling, implying among other things that there is a positive expected number of outliers away from [−2, 2]. These kernels as well as the scaling limits for the kernels in the bulk (−2, 2) and at the endpoints {−2, 2} are presented. These kernels appear to be new, and we compare their behavior with related kernels wh...
The structure of the Mitchell order—I

We isolate here a wide class of well-founded orders called tame orders, and show that each such order of cardinality at most κ can be realized as the Mitchell order on a measurable cardinal κ, from a consistency assumption weaker than o(κ) = κ+.
Inconsistent Node Flattening for Improving Top-Down Hierarchical Classification

Large-scale classification of data where classes are structurally organized in a hierarchy is an important area of research. Top-down approaches that exploit the hierarchy during the learning and prediction phase are efficient for large-scale hierarchical classification. However, accuracy of top-down approaches is poor due to error propagation i.e., prediction errors made at higher levels in the hierarchy cannot be corrected at lower levels. One of the main reason behind errors at the higher levels is the presence of inconsistent nodes that are introduced due to the arbitrary process of creating these hierarchies by domain experts. In this paper, we propose two different data-driven approaches (local and global) for hierarchical structure modification that identifies and flattens inconsistent nodes present within the hierarchy. Our extensive empirical evaluation of the proposed approaches on several image and text datasets with varying distribution of features, classes and training instances per class shows improved classification performance over competing hierarchical modification approaches. Specifically, we see an improvement upto 7% in Macro-F1 score with our approach over best TD baseline. SOURCE CODE: http://www.cs.gmu.edu/ mlbio/InconsistentNodeFlattening.
Rational curves on hypersurfaces

Let $(X,D)$ be a pair where $X$ is a projective variety. We study in detail how the behavior of rational curves on $X$ as well as the positivity of $-(K_X+D)$ and $D$ influence the behavior of rational curves on $D$. In particular we give criteria for uniruledness and rational connectedness of components of $D$.
Three Revolutions in The Kernel Are Worse Than One

An example is constructed of a purely unrectiable measure for which the singular integral associated to the kernel K(z) = z z2 is bounded in L 2 ( ). The singular integral fails to exist in the sense of principal value -almost everywhere. This is in sharp contrast with the results known for the kernel 1 (the Cauchy transform).
Distributed Bayesian Filtering using Logarithmic Opinion Pool for Dynamic Sensor Networks

The discrete-time Distributed Bayesian Filtering (DBF) algorithm is presented for the problem of tracking a target dynamic model using a time-varying network of heterogeneous sensing agents. In the DBF algorithm, the sensing agents combine their normalized likelihood functions in a distributed manner using the logarithmic opinion pool and the dynamic average consensus algorithm. We show that each agent’s estimated likelihood function globally exponentially converges to an error ball centered on the joint likelihood function of the centralized multi-sensor Bayesian filtering algorithm. We rigorously characterize the convergence, stability, and robustness properties of the DBF algorithm. Moreover, we provide an explicit bound on the time step size of the DBF algorithm that depends on the time-scale of the target dynamics, the desired convergence error bound, and the modeling and communication error bounds. Furthermore, the DBF algorithm for linear-Gaussian models is cast into a modified form of the Kalman information filter. The performance and robust properties of the DBF algorithm are validated using numerical simulations.
A free boundary problem on three-dimensional cones

Abstract We consider a free boundary problem on cones depending on a parameter c and study when the free boundary is allowed to pass through the vertex of the cone. We show that when the cone is three-dimensional and c is large enough, the free boundary avoids the vertex. We also show that when c is small enough but still positive, the free boundary is allowed to pass through the vertex. This establishes 3 as the critical dimension for which the free boundary may pass through the vertex of a right circular cone. In view of the well-known connection between area-minimizing surfaces and the free boundary problem under consideration, our result is analogous to a result of Morgan that classifies when an area-minimizing surface on a cone passes through the vertex.
Tracing the Use of Practices through Networks of Collaboration

An active line of research has used on-line data to study the ways in which discrete units of information---including messages, photos, product recommendations, group invitations---spread through social networks. There is relatively little understanding, however, of how on-line data might help in studying the diffusion of more complex {\em practices}---roughly, routines or styles of work that are generally handed down from one person to another through collaboration or mentorship. In this work, we propose a framework together with a novel type of data analysis that seeks to study the spread of such practices by tracking their syntactic signatures in large document collections. Central to this framework is the notion of an "inheritance graph" that represents how people pass the practice on to others through collaboration. Our analysis of these inheritance graphs demonstrates that we can trace a significant number of practices over long time-spans, and we show that the structure of these graphs can help in predicting the longevity of collaborations within a field, as well as the fitness of the practices themselves.
Importance Sampling Policy Evaluation with an Estimated Behavior Policy

We consider the problem of off-policy evaluation in Markov decision processes. Off-policy evaluation is the task of evaluating the expected return of one policy with data generated by a different, behavior policy. Importance sampling is a technique for off-policy evaluation that re-weights off-policy returns to account for differences in the likelihood of the returns between the two policies. In this paper, we study importance sampling with an estimated behavior policy where the behavior policy estimate comes from the same set of data used to compute the importance sampling estimate. We find that this estimator often lowers the mean squared error of off-policy evaluation compared to importance sampling with the true behavior policy or using a behavior policy that is estimated from a separate data set. Intuitively, estimating the behavior policy in this way corrects for error due to sampling in the action-space. Our empirical results also extend to other popular variants of importance sampling and show that estimating a non-Markovian behavior policy can further lower large-sample mean squared error even when the true behavior policy is Markovian.
Scalar curvature and uniruledness on projective manifolds

It is a basic tenet in complex geometry that {\it negative} curvature corresponds, in a suitable sense, to the absence of rational curves on, say, a complex projective manifold, while {\it positive} curvature corresponds to the abundance of rational curves. In this spirit, we prove in this note that a projective manifold $M$ with a Kahler metric with positive total scalar curvature is uniruled, which is equivalent to every point of $M$ being contained in a rational curve. We also prove that if $M$ possesses a Kahler metric of total scalar curvature equal to zero, then either $M$ is uniruled or its canonical line bundle is torsion. The proof of the latter theorem is partially based on the observation that if $M$ is not uniruled, then the total scalar curvatures of all Kahler metrics on $M$ must have the same sign, which is either zero or negative.
Decouplings for curves and hypersurfaces with nonzero Gaussian curvature

We prove two types of results. First we develop the decoupling theory for hypersurfaces with nonzero Gaussian curvature, which extends our earlier work from [4]. As a consequence of this, we obtain sharp (up to e losses) Strichartz estimates for the hyperbolic Schrodinger equation on the torus. Our second main result is an l 2 decoupling for nondegenerate curves, which has implications for Vinogradov’s mean value theorem.
Distributed Observers for LTI Systems

We consider the problem of distributed state estimation of a linear time-invariant (LTI) system by a network of sensors. We develop a distributed observer that guarantees asymptotic reconstruction of the state for the most general class of LTI systems, sensor network topologies, and sensor measurement structures. Our analysis builds upon the following key observation—a given node can reconstruct a portion of the state solely by using its own measurements and constructing appropriate Luenberger observers; hence, it only needs to exchange information with neighbors (via consensus dynamics) for estimating the portion of the state that is not locally detectable. This intuitive approach leads to a new class of distributed observers with several appealing features. Furthermore, by imposing additional constraints on the system dynamics and network topology, we show that it is possible to construct a simpler version of the proposed distributed observer that achieves the same objective while admitting a fully distributed design phase. Our general framework allows extensions to time-varying networks that result from communication losses, and scenarios including faults or attacks at the nodes.
Classification of weighted networks through mesoscale homological features

As complex networks find applications in a growing range of disciplines, the diversity of naturally occurring and model networks being studied is exploding. The adoption of a well-developed collection of network taxonomies is a natural method for both organizing this data and understanding deeper relationships between networks. Most existing metrics for network structure rely on classical graph-theoretic measures, extracting characteristics primarily related to individual vertices or paths between them, and thus classify networks from the perspective of local features. Here, we describe an alternative approach to studying structure in networks that relies on an algebraic-topological metric called persistent homology, which studies intrinsically mesoscale structures called cycles, constructed from cliques in the network. We present a classification of 14 commonly studied weighted network models into four groups or classes, and discuss the structural themes arising in each class. Finally, we compute the persistent homology of two real-world networks and one network constructed by a common dynamical systems model, and we compare the results with the three classes to obtain a better understanding of those networks.
Distributed sequence memory of multidimensional inputs in recurrent networks

Recurrent neural networks (RNNs) have drawn interest from machine learning researchers because of their effectiveness at preserving past inputs for time-varying data processing tasks. To understand the success and limitations of RNNs, it is critical that we advance our analysis of their fundamental memory properties. We focus on echo state networks (ESNs), which are RNNs with simple memoryless nodes and random connectivity. In most existing analyses, the short-term memory (STM) capacity results conclude that the ESN network size must scale linearly with the input size for unstructured inputs. The main contribution of this paper is to provide general results characterizing the STM capacity for linear ESNs with multidimensional input streams when the inputs have common low-dimensional structure: sparsity in a basis or significant statistical dependence between inputs. In both cases, we show that the number of nodes in the network must scale linearly with the information rate and poly-logarithmically with the input dimension. The analysis relies on advanced applications of random matrix theory and results in explicit non-asymptotic bounds on the recovery error. Taken together, this analysis provides a significant step forward in our understanding of the STM properties in RNNs.
A dichotomy for the injective dimension of $F$-finite $F$-modules and holonomic $D$-modules

AbstractLet M be either a holonomic D-module over a formal power series ring with coefficients in a field of characteristic zero, or an F-finite F-module over a noetherian regular ring of character...
On Approximating Maximum Independent Set of Rectangles

We study the Maximum Independent Set of Rectangles (MISR) problem: given a set of n axis-parallel rectangles, find a largest-cardinality subset of the rectangles, such that no two of them overlap. MISR is a basic geometric optimization problem with many applications, that has been studied extensively. Until recently, the best approximation algorithm for it achieved an O(log log n)-approximation factor. In a recent breakthrough, Adamaszek and Wiese provided a quasi-polynomial time approximation scheme: a (1-e)-approximation algorithm with running time nO(poly(log n)/e). Despite this result, obtaining a PTAS or even a polynomial-time constant-factor approximation remains a challenging open problem. In this paper we make progress towards this goal by providing an algorithm for MISR that achieves a (1-e)-approximation in time nO(poly(log logn/e)). We introduce several new technical ideas, that we hope will lead to further progress on this and related problems.
Most Correlated Arms Identification

We study the problem of finding the most mutually correlated arms among many arms. We show that adaptive arms sampling strategies can have significant advantages over the non-adaptive uniform sampling strategy. Our proposed algorithms rely on a novel correlation estimator. The use of this accurate estimator allows us to get improved results for a wide range of problem instances.
Receptor uptake arrays for vitamin B12, siderophores, and glycans shape bacterial communities.

Molecular variants of vitamin B12, siderophores, and glycans occur. To take up variant forms, bacteria may express an array of receptors. The gut microbe Bacteroides thetaiotaomicron has three different receptors to take up variants of vitamin B12 and 88 receptors to take up various glycans. The design of receptor arrays reflects key processes that shape cellular evolution. Competition may focus each species on a subset of the available nutrient diversity. Some gut bacteria can take up only a narrow range of carbohydrates, whereas species such as B. thetaiotaomicron can digest many different complex glycans. Comparison of different nutrients, habitats, and genomes provides opportunity to test hypotheses about the breadth of receptor arrays. Another important process concerns fluctuations in nutrient availability. Such fluctuations enhance the value of cellular sensors, which gain information about environmental availability and adjust receptor deployment. Bacteria often adjust receptor expression in response to fluctuations of particular carbohydrate food sources. Some species may adjust expression of uptake receptors for specific siderophores. How do cells use sensor information to control the response to fluctuations? This question about regulatory wiring relates to problems that arise in control theory and artificial intelligence. Control theory clarifies how to analyze environmental fluctuations in relation to the design of sensors and response systems. Recent advances in deep learning studies of artificial intelligence focus on the architecture of regulatory wiring and the ways in which complex control networks represent and classify environmental states. I emphasize the similar design problems that arise in cellular evolution, control theory, and artificial intelligence. I connect those broad conceptual aspects to many testable hypotheses for bacterial uptake of vitamin B12, siderophores, and glycans.
An Improved Convergence Analysis of Stochastic Variance-Reduced Policy Gradient.

We revisit the stochastic variance-reduced policy gradient (SVRPG) method proposed by Papini et al. (2018) for reinforcement learning. We provide an improved convergence analysis of SVRPG and show that it can find an $\epsilon$-approximate stationary point of the performance function within $O(1/\epsilon^{5/3})$ trajectories. This sample complexity improves upon the best known result $O(1/\epsilon^2)$ by a factor of $O(1/\epsilon^{1/3})$. At the core of our analysis is (i) a tighter upper bound for the variance of importance sampling weights, where we prove that the variance can be controlled by the parameter distance between different policies; and (ii) a fine-grained analysis of the epoch length and batch size parameters such that we can significantly reduce the number of trajectories required in each iteration of SVRPG. We also empirically demonstrate the effectiveness of our theoretical claims of batch sizes on reinforcement learning benchmark tasks.
A Surprisingly Effective Fix for Deep Latent Variable Modeling of Text

When trained effectively, the Variational Autoencoder (VAE) is both a powerful language model and an effective representation learning framework. In practice, however, VAEs are trained with the evidence lower bound (ELBO) as a surrogate objective to the intractable marginal data likelihood. This approach to training yields unstable results, frequently leading to a disastrous local optimum known as posterior collapse. In this paper, we investigate a simple fix for posterior collapse which yields surprisingly effective results. The combination of two known heuristics, previously considered only in isolation, substantially improves held-out likelihood, reconstruction, and latent representation learning when compared with previous state-of-the-art methods. More interestingly, while our experiments demonstrate superiority on these principle evaluations, our method obtains a worse ELBO. We use these results to argue that the typical surrogate objective for VAEs may not be sufficient or necessarily appropriate for balancing the goals of representation learning and data distribution modeling.
Earlier isn't always better: Sub-aspect Analysis on Corpus and System Biases in Summarization

Despite the recent developments on neural summarization systems, the underlying logic behind the improvements from the systems and its corpus-dependency remains largely unexplored. Position of sentences in the original text, for example, is a well known bias for news summarization. Following in the spirit of the claim that summarization is a combination of sub-functions, we define three sub-aspects of summarization: position, importance, and diversity and conduct an extensive analysis of the biases of each sub-aspect with respect to the domain of nine different summarization corpora (e.g., news, academic papers, meeting minutes, movie script, books, posts). We find that while position exhibits substantial bias in news articles, this is not the case, for example, with academic papers and meeting minutes. Furthermore, our empirical study shows that different types of summarization systems (e.g., neural-based) are composed of different degrees of the sub-aspects. Our study provides useful lessons regarding consideration of underlying sub-aspects when collecting a new summarization dataset or developing a new system.
Valid Inference Corrected for Outlier Removal

Ordinary least square (OLS) estimation of a linear regression model is well-known to be highly sensitive to outliers. It is common practice to (1) identify and remove outliers by looking at the dat...