cssi/SciSciGPT-SciSciNet huggingface dataset:
The background field method on the lattice

The background field method has been used successfully to determine hadron electromagnetic polarizabilities. Recently questions have been raised regarding the proper way to deal with the electric field on the lattice. In this paper, we show how the presence of a background electric field affects the quark hopping matrix. We use this formulation to carry out simulations on quenched configurations, and we present the results for neutron electric polarizability for pion masses as low as 500MeV. We find that the polarizability is roughly constant for the quark masses considered, α ∼ 1.5×10−4 fm3. While the polarizability is positive, it is significantly smaller than the experimental value due to the fact that the quark masses used are too large.
The IBM 2016 English Conversational Telephone Speech Recognition System

We describe a collection of acoustic and language modeling techniques that lowered the word error rate of our English conversational telephone LVCSR system to a record 6.6% on the Switchboard subset of the Hub5 2000 evaluation testset. On the acoustic side, we use a score fusion of three strong models: recurrent nets with maxout activations, very deep convolutional nets with 3x3 kernels, and bidirectional long short-term memory nets which operate on FMLLR and i-vector features. On the language modeling side, we use an updated model "M" and hierarchical neural network LMs.
An Inverse Theorem for an Inequality of Kneser

Let G = (G, +) be a compact connected abelian group, and let μG denote its probability Haar measure. A theorem of Kneser (generalising previous results of Macbeath, Raikov, and Shields) establishes the bound μG(A + B) ≥ min(μG(A) + μG(B), 1) whenever A and B are compact subsets of G, and A + B:= {a + b: a ∈ A, b ∈ B} denotes the sumset of A and B. Clearly one has equality when μG(A) + μG(B) ≥ 1. Another way in which equality can be obtained is when A = φ−1(I) and B = φ−1(J) for some continuous surjective homomorphism φ: G → ℝ/ℤ and compact arcs I, J ⊂ ℝ/ℤ. We establish an inverse theorem that asserts, roughly speaking, that when equality in the above bound is almost attained, then A and B are close to one of the above examples. We also give a more “robust” form of this theorem in which the sumset A + B is replaced by the partial sumset A +eB:= {1A * 1B ≥ e} for some small e > 0. In a subsequent paper with Joni Teravainen, we will apply this latter inverse theorem to establish that certain patterns in multiplicative functions occur with positive density.
Adversarial Robustness: Softmax versus Openmax.

Deep neural networks (DNNs) provide state-of-the-art results on various tasks and are widely used in real world applications. However, it was discovered that machine learning models, including the best performing DNNs, suffer from a fundamental problem: they can unexpectedly and confidently misclassify examples formed by slightly perturbing otherwise correctly recognized inputs. Various approaches have been developed for efficiently generating these so-called adversarial examples, but those mostly rely on ascending the gradient of loss. In this paper, we introduce the novel logits optimized targeting system (LOTS) to directly manipulate deep features captured at the penultimate layer. Using LOTS, we analyze and compare the adversarial robustness of DNNs using the traditional Softmax layer with Openmax, which was designed to provide open set recognition by defining classes derived from deep representations, and is claimed to be more robust to adversarial perturbations. We demonstrate that Openmax provides less vulnerable systems than Softmax to traditional attacks, however, we show that it can be equally susceptible to more sophisticated adversarial generation techniques that directly work on deep representations.
The Value of Side-Information in Secondary Spectrum Markets

We consider a secondary spectrum market where primaries set prices for their unused channels. The payoff of a primary then depends on the availability of channels for its competitors, which a primary might not have information about. We study a model where a primary can acquire this competitor’s channel state information (C-CSI) at a cost. We formulate a game between two primaries, where each primary decides whether to acquire the C-CSI or not and then selects its price based on that. We first characterize the Nash equilibrium of this game for a symmetric model where the C-CSI is perfect. We show that the payoff of a primary is independent of the C-CSI acquisition cost. We then generalize our analysis to allow for imperfect estimation and cases, where the two primaries have different C-CSI costs or different channel availabilities. Our results show interestingly that the payoff of a primary increases when there is estimation error. We also show that surprisingly the expected payoff of a primary may decrease when the C-CSI acquisition cost decreases or primaries have different availabilities.
MaestROB: A Robotics Framework for Integrated Orchestration of Low-Level Control and High-Level Reasoning

This paper describes a framework called MaestROBe It is designed to make the robots perform complex tasks with high precision by simple high-level instructions given by natural language or demonstration. To realize this, it handles a hierarchical structure by using the knowledge stored in the forms of ontology and rules for bridging among different levels of instructions. Accordingly, the framework has multiple layers of processing components; perception and actuation control at the low level, symbolic planner and Watson APIs for cognitive capabilities and semantic understanding, and orchestration of these components by a new open source robot middleware called Project Intu at its core. We show how this framework can be used in a complex scenario where multiple actors (human, a communication robot, and an industrial robot) collaborate to perform a common industrial task. Human teaches an assembly task to Pepper (a humanoid robot from SoftBank Robotics) using natural language conversation and demonstration. Our framework helps Pepper perceive the human demonstration and generate a sequence of actions for UR5 (collaborative robot arm from Universal Robots), which ultimately performs the assembly (e.g. insertion) task.
Estimation of KL Divergence: Optimal Minimax Rate

The problem of estimating the Kullback–Leibler divergence $D(P\|Q)$ between two unknown distributions $P$ and $Q$ is studied, under the assumption that the alphabet size $k$ of the distributions can scale to infinity. The estimation is based on $m$ independent samples drawn from $P$ and $n$ independent samples drawn from $Q$ . It is first shown that there does not exist any consistent estimator that guarantees asymptotically small worst case quadratic risk over the set of all pairs of distributions. A restricted set that contains pairs of distributions, with density ratio bounded by a function $f(k)$ is further considered. An augmented plug-in estimator is proposed, and its worst case quadratic risk is shown to be within a constant factor of $(({k}/{m})+({kf(k)}/{n}))^{2}+({\log ^{2}\!\!f(k)}/{m})+({f(k)}/{n})$ , if $m$ and $n$ exceed a constant factor of $k$ and $kf(k)$ , respectively. Moreover, the minimax quadratic risk is characterized to be within a constant factor of $((k/(m \log k))+(k f(k)/(n \log k)))^{2}+({\log ^{2}\!\!f(k)}/{m})+({f(k)}/{n})$ , if $m$ and $n$ exceed a constant factor of $k/\log (k)$ and $kf(k)/\log k$ , respectively. The lower bound on the minimax quadratic risk is characterized by employing a generalized Le Cam’s method. A minimax optimal estimator is then constructed by employing both the polynomial approximation and the plug-in approaches.
Weak null singularities in general relativity

We construct a class of spacetimes (without symmetry assumptions) satisfying the vacuum Einstein equations with singular boundaries on two null hypersurfaces intersecting in the future on a 2-sphere. The metric of these spacetimes extends continuously beyond the singularities while the Christoffel symbols fail to be square integrable in a neighborhood of any point on the singular boundaries. The construction shows moreover that the singularities are stable in a suitable sense. These singularities are stronger than the impulsive gravitational spacetimes considered by Luk-Rodnianski and are conjecturally the generic type of singularity in the interior of black holes arising from gravitational collapse.
A note on the ultrahyperbolic wave equation in 3+3 dimensions

This note proves a conjecture of Sparling [Germ of a synthesis: space-time is spinorial, extra dimensions are time-like. Proc R Soc Lond Ser A Math Phys Eng Sci. 2007;463(2083):1665–1679; The Ξ-tra...
Hierarchical mixtures-of-experts for exponential family regression models with generalized linear mean functions: a survey of approximation and consistency results

We investigate a class of hierarchical mixtures-of-experts (HME) models where exponential family regression models with generalized linear mean functions of the form ψ(α + xT β) are mixed. Here ψ(ċ) is the inverse link function. Suppose the true response y follows an exponential family regression model with mean function belonging to a class of smooth functions of the form ψ(h(x)) where h(ċ) ∈ W∞2 (a Sobolev class over [0, 1]s). It is shown that the HME probability density functions can approximate the true density, at a rate of O(m-2/s) in Lp, norm, and at a rate of O(m-4/s) in Kullback-Leibler divergence. These rates can be achieved within the family of HME structures with no more than s-layers, where s is the dimension of the predictor x. It is also shown that likelihood-based inference based on HME is consistent in recovering the truth, in the sense that as the sample size n and the number of experts m both increase, the mean square error of the predicted mean response goes to zero. Conditions for such results to hold are stated and discussed.
Mathematical Symbolism in a Russian Literary Masterpiece

Andrei Bely's modernist novel "Petersburg," first published in 1913, is considered a pinnacle of the Symbolist movement. Nabokov famously ranked it as one of the four greatest masterpieces of 20th-century prose. The author's father, Bugaev, was an influential mathematician and for 12 years served as the president of the Moscow Mathematical Society; he was also a source of inspiration for one of the main characters in the son's novel. While the philosophical views and political leanings of the mathematicians surrounding Bely, and their impact on "Petersburg," have been a topic of recent academic interest, there has not yet been a direct investigation of the surprisingly frequent and sophisticated mathematical passages in the book itself. We attempt here to rectify this gap in the scholarly literature, and in doing so find a rich tapestry of mathematical ideas and allusions.
Asymptotic expansion in Gevrey spaces for solutions of Navier–Stokes equations

In this paper, we study the asymptotic behavior of solutions to the threedimensional incompressible Navier-Stokes equations (NSE) with periodic boundary conditions and potential body forces. In particular, we prove that the Foias-Saut asymptotic expansion for the regular solutions of the NSE in fact holds in all Gevrey classes . This strengthens the previous result obtained in Sobolev spaces by Foias-Saut. By using the Gevrey-norm technique of Foias-Temam, the proof of our improved result simplifies the original argument of Foias-Saut, thereby, increasing its adaptability to other dissipative systems. Moreover, the expansion is extended to Leray-Hopf weak solutions and the exponential decay rate for each of its remainders is calculated explicitly.
Routing Networks: Adaptive Selection of Non-Linear Functions for Multi-Task Learning

Multi-task learning (MTL) with neural networks leverages commonalities in tasks to improve performance, but often suffers from task interference which reduces the benefits of transfer. To address this issue we introduce the routing network paradigm, a novel neural network and training algorithm. A routing network is a kind of self-organizing neural network consisting of two components: a router and a set of one or more function blocks. A function block may be any neural network - for example a fully-connected or a convolutional layer. Given an input the router makes a routing decision, choosing a function block to apply and passing the output back to the router recursively, terminating when a fixed recursion depth is reached. In this way the routing network dynamically composes different function blocks for each input. We employ a collaborative multi-agent reinforcement learning (MARL) approach to jointly train the router and function blocks. We evaluate our model against cross-stitch networks and shared-layer baselines on multi-task settings of the MNIST, mini-imagenet, and CIFAR-100 datasets. Our experiments demonstrate a significant improvement in accuracy, with sharper convergence. In addition, routing networks have nearly constant per-task training cost while cross-stitch networks scale linearly with the number of tasks. On CIFAR-100 (20 tasks) we obtain cross-stitch performance levels with an 85% reduction in training time.
Linguistic Markers of Influence in Informal Interactions.

There has been a long standing interest in understanding ‘Social Influence’ both in Social Sciences and in Computational Linguistics. In this paper, we present a novel approach to study and measure interpersonal influence in daily interactions. Motivated by the basic principles of influence, we attempt to identify indicative linguistic features of the posts in an online knitting community. We present the scheme used to operationalize and label the posts as influential or non-influential. Experiments with the identified features show an improvement in the classification accuracy of influence by 3.15%. Our results illustrate the important correlation between the structure of the language and its potential to influence others.
Locally-Optimized Inter-Subject Alignment of Functional Cortical Regions

Inter-subject registration of cortical areas is necessary in functional imaging (fMRI) studies for making inferences about equivalent brain function across a population. However, many high-level visual brain areas are defined as peaks of functional contrasts and it is usually difficult to identify clear anatomical landmarks and boundaries for these areas, due to large variability in their cortical position. As a consequence, previous methods usually fail to accurately map such functional regions of interest (ROIs) across participants. To address this problem, we propose a locally optimized registration method that directly predicts the location of a seed ROI on a separate target cortical sheet by maximizing the functional correlation between regions and simultaneously constraining the global structure of the mapping, while allowing for non-local deformations in its topology. Our registration method outperformed two canonical baselines (anatomical landmark-based AFNI alignment and cortical curvature-based FreeSurfer alignment) in the percentage of overlap between predicted region and ground truth LOC. Furthermore, the maps obtained using our method are more consistent across subjects than both baseline measures. Consequently, our method has the ability to directly and immediately improve the quality of group maps for high-level visual areas in countless fMRI studies. This would dramatically increase the statistical power of such studies, as a more accurate mapping to a common space implies less smoothing and larger effect sizes.
On the normality of secant varieties

Abstract In this paper, we show that the secant variety to a smooth projective variety embedded by a sufficiently positive line bundle is normal. As an application, we deduce that the secant variety to a general canonical curve of genus at least 7 is normal.
Inexactness of the Hydro-Thermal Coordination Semidefinite Relaxation

Hydro-thermal coordination is the problem of determining the optimal economic dispatch of hydro and thermal power plants over time. The physics of hydroelectricity generation is commonly simplified in the literature to account for its fundamentally nonlinear nature. Advances in convex relaxation theory have allowed the advent of Shor’s semidefinite programming (SDP) relaxations of quadratic models of the problem. This paper shows how a recently published SDP relaxation is only exact if a very strict condition regarding turbine efficiency is observed, failing otherwise. It further proposes the use of a set of convex envelopes as a strategy to successfully obtain a stricter lower bound of the optimal solution. This strategy is combined with a standard iterative convex-concave procedure to recover a stationary point of the original non-convex problem.
Spectral clustering based on local PCA

We propose a spectral clustering method based on local principal components analysis (PCA). After performing local PCA in selected neighborhoods, the algorithm builds a nearest neighbor graph weighted according to a discrepancy between the principal subspaces in the neighborhoods, and then applies spectral clustering. As opposed to standard spectral methods based solely on pairwise distances between points, our algorithm is able to resolve intersections. We establish theoretical guarantees for simpler variants within a prototypical mathematical framework for multi-manifold clustering, and evaluate our algorithm on various simulated data sets.
Individualized rank aggregation using nuclear norm regularization

In recent years rank aggregation has received significant attention from the machine learning community. The goal of such a problem is to combine the (partially revealed) preferences over objects of a large population into a single, relatively consistent ordering of those objects. However, in many cases, we might not want a single ranking and instead opt for individual rankings. We study a version of the problem known as collaborative ranking. In this problem we assume that individual users provide us with pairwise preferences (for example purchasing one item over another). From those preferences we wish to obtain rankings on items that the users have not had an opportunity to explore. The results here have a very interesting connection to the standard matrix completion problem. We provide a theoretical justification for a nuclear norm regularized optimization procedure, and provide high-dimensional scaling results that show how the error in estimating user preferences behaves as the number of observations increase.
Multihead Multitrack Detection With Reduced-State Sequence Estimation

In shingled magnetic recording, the multihead multitrack (MHMT) detector can better combat the effect of intertrack interference than the single-head single-track detector. Such a detector, however, has prohibitive implementation complexity. In this paper, we propose to use the reduced-state sequence estimation algorithm to significantly reduce the complexity, and render MHMT practical. A commonly used symmetric two-head two-track channel model is considered in this paper. Well-structured reduced-state trellises are constructed by evaluating the effective symbol pair distances and designing proper set partitioning principles. Different trellis configurations are obtained based on the desired performance/complexity tradeoff. Simulation results show that the MHMT detector can achieve near maximum-likelihood performance with a small fraction of the original number of trellis states.
Speech-driven Animation with Meaningful Behaviors

Abstract Conversational agents (CAs) play an important role in human computer interaction (HCI). Creating believable movements for CAs is challenging, since the movements have to be meaningful and natural, reflecting the coupling between gestures and speech. Studies in the past have mainly relied on rule-based or data-driven approaches. Rule-based methods focus on creating meaningful behaviors conveying the underlying message, but the gestures cannot be easily synchronized with speech. Data-driven approaches, especially speech-driven models, can capture the relationship between speech and gestures. However, they create behaviors disregarding the meaning of the message. This study proposes to bridge the gap between these two approaches overcoming their limitations. The approach builds a dynamic Bayesian network (DBN), where a discrete variable is added to constrain the behaviors on the underlying constraint. The study implements and evaluates the approach with two constraints: discourse functions and prototypical behaviors. By constraining on the discourse functions (e.g., questions), the model learns the characteristic behaviors associated with a given discourse class learning the rules from the data. By constraining on prototypical behaviors (e.g., head nods), the approach can be embedded in a rule-based system as a behavior realizer creating trajectories that are timely synchronized with speech. The study proposes a DBN structure and a training approach that (1) models the cause-effect relationship between the constraint and the gestures, and (2) captures the differences in the behaviors across constraints by enforcing sparse transitions between shared and exclusive states per constraint. Objective and subjective evaluations demonstrate the benefits of the proposed approach over an unconstrained baseline model.
Parameterized approximation algorithms for some location problems in graphs

We develop efficient parameterized, with additive error, approximation algorithms for the (Connected) r-Domination problem and the (Connected) p-Center problem for unweighted and undirected graphs. Given a graph G, we show how to construct a (connected) \(\big (r + \mathcal {O}(\mu ) \big )\)-dominating set D with \(|D| \le |D^*|\) efficiently. Here, \(D^*\) is a minimum (connected) r-dominating set of G and \(\mu \) is our graph parameter, which is the tree-breadth or the cluster diameter in a layering partition of G. Additionally, we show that a \(+ \mathcal {O}(\mu )\)-approximation for the (Connected) p-Center problem on G can be computed in polynomial time. Our interest in these parameters stems from the fact that in many real-world networks, including Internet application networks, web networks, collaboration networks, social networks, biological networks, and others, and in many structured classes of graphs these parameters are small constants.
Numerical analysis on mixing processes for transcritical real-fluid simulations

The accurate and robust simulation of transcritical real-fluid flows is crucial for many engineering applications. Diffused interface methods are frequently employed and several numerical schemes have been developed for simulating transcritical flows. These schemes can be categorized into two types, namely fully conservative and quasi-conservative schemes. An adaptive scheme which is a hybrid of the two is developed in this study. By considering several numerical test cases, it is shown that different schemes predict distinctly different mixing behaviors. It is shown that the mixing processes follow the isobaric-adiabatic and isobaric-isochoric mixing models for fully and quasi-conservative schemes, respectively, and the adaptive scheme yields a mixing behavior that spans both models. The distinct mixing behaviors are a consequence of numerical diffusion instead of physical diffusion and can be attributed to insufficient numerical spatial resolution. This work provides a better understanding on the interpretation of numerical simulation results and the mixing models that are commonly used to study transcritical flows.
Diagonalizing the Hamiltonian of $\lambda \phi^4$ Theory in 2 Space-Time Dimensions

Abstract We propose a new non-perturbative technique for calculating the scattering amplitudes of field-theory directly from the eigenstates of the Hamiltonian . Our method involves a discretized momentum space and a momentum cutoff, thereby truncating the Hilbert space and making numerical diagonalization of the Hamiltonian achievable. We show how to do this in the context of a simplified λ ϕ 4 theory in two space–time dimensions. We present the results of our diagonalization, its dependence on time, its dependence on the parameters of the theory and its renormalization.
Dissolving knot surgered 4-manifolds by classical cobordism arguments

The purpose of this note is to show that classical cobordism arguments, which go back to the pioneering works of Mandelbaum and Moishezon, provide quick and unified proofs of any knot surgered comp...
Time analyticity with higher norm estimates for the 2D Navier–Stokes equations

This paper establishes bounds on norms of all orders for solutions on the global attractor of the 2D Navier-Stokes equations, complexified in time. Specifically, for periodic boundary conditions on [0, L], and a force g ∈ D(A α−1 2 ), we show there is a fixed strip about the real time axis on which a uniform bound ∣Aαu∣ < mανκα0 holds for each α ∈ N. Here ν is viscosity, κ0 = 2π/L , and mα is explicitly given in terms of g and α. We show that if any element in A is in D(Aα), then all of A is in D(Aα), and likewise with D(Aα) replaced by C∞(Ω). We demonstrate the universality of this “all for one, one for all” law on the union of a hierarchal set of function classes. Finally, we treat the question of whether the zero solution can be in the global attractor for a nonzero force by showing that if this is so, the force must be in a particular function class.
Regularized Spectral Clustering under the Degree-Corrected Stochastic Blockmodel

Spectral clustering is a fast and popular algorithm for finding clusters in networks. Recently, Chaudhuri et al. [1] and Amini et al. [2] proposed inspired variations on the algorithm that artificially inflate the node degrees for improved statistical performance. The current paper extends the previous statistical estimation results to the more canonical spectral clustering algorithm in a way that removes any assumption on the minimum degree and provides guidance on the choice of the tuning parameter. Moreover, our results show how the "star shape" in the eigenvectors-a common feature of empirical networks-can be explained by the Degree-Corrected Stochastic Blockmodel and the Extended Planted Partition model, two statistical models that allow for highly heterogeneous degrees. Throughout, the paper characterizes and justifies several of the variations of the spectral clustering algorithm in terms of these models.
Complexity bounds for the controllability of temporal networks with conditions, disjunctions, and uncertainty

Abstract In temporal planning, many different temporal network formalisms are used to model real world situations. Each of these formalisms has different features which affect how easy it is to determine whether the underlying network of temporal constraints is consistent. While many of the simpler models have been well-studied from a computational complexity perspective, the algorithms developed for advanced models which combine features have very loose complexity bounds. In this paper, we provide tight completeness bounds for strong, weak, and dynamic controllability checking of temporal networks that have conditions, disjunctions, and temporal uncertainty. Our work exposes some of the subtle differences between these different structures and, remarkably, establishes a guarantee that all of these problems are computable in PSPACE.
BGG reciprocity for current algebras

Abstract We study the category I gr of graded representations with finite-dimensional graded pieces for the current algebra g ⊗ C [ t ] where g is a simple Lie algebra. This category has many similarities with the category O of modules for g and in this paper, we formulate and study an analogue of the famous BGG duality. We recall the definition of the projective and simple objects in I gr which are indexed by dominant integral weights. The role of the Verma modules is played by a family of modules called the global Weyl modules. We show that in the case when g is of type s l 2 , the projective module admits a flag in which the successive quotients are finite direct sums of global Weyl modules. The multiplicity with which a particular Weyl module occurs in the flag is determined by the multiplicity of a Jordan–Holder series for a closely associated family of modules, called the local Weyl modules. We conjecture that the result remains true for arbitrary simple Lie algebras. We also prove some combinatorial product–sum identities involving Kostka polynomials which arise as a consequence of our theorem.
Adaptive sign error control

Abstract In multiple testing scenarios, typically the sign of a parameter is inferred when its estimate exceeds some significance threshold in absolute value. Typically, the significance threshold is chosen to control the experimentwise type I error rate, family-wise type I error rate or the false discovery rate. However, controlling these error rates does not explicitly control the sign error rate. In this paper, we propose two procedures for adaptively selecting an experimentwise significance threshold in order to control the sign error rate. The first controls the sign error rate conservatively, without any distributional assumptions on the parameters of interest. The second is an empirical Bayes procedure, and achieves optimal performance asymptotically when a model for the distribution of the parameters is correctly specified. We also discuss an adaptive procedure to minimize the sign error rate when the experimentwise type I error rate is held fixed.
Sobolev Extensions of Lipschitz Mappings into Metric Spaces

Wenger and Young proved that the pair $(\mathbb{R}^m,\mathbb{H}^n)$ has the Lipschitz extension property for $m \leq n$ where $\mathbb{H}^n$ is the sub-Riemannian Heisenberg group. That is, for some $C>0$, any $L$-Lipschitz map from a subset of $\mathbb{R}^m$ into $\mathbb{H}^n$ can be extended to a $CL$-Lipschitz mapping on $\mathbb{R}^m$. In this paper, we construct Sobolev extensions of such Lipschitz mappings with no restriction on the dimension $m$. We prove that any Lipschitz mapping from a compact subset of $\mathbb{R}^m$ into $\mathbb{H}^n$ may be extended to a Sobolev mapping on any bounded domain containing the set. More generally, we prove this result in the case of mappings into any Lipschitz $(n-1)$-connected metric space.
Optimal convergence and adaptation for utility optimal opportunistic scheduling

This paper considers the fundamental convergence time for opportunistic scheduling over time-varying channels. The channel state probabilities are unknown and algorithms must perform some type of estimation and learning while they make decisions to optimize network utility. Existing schemes can achieve a utility within ∊ of optimality, for any desired ∊ > 0, with convergence and adaptation times of O(1/∊2). This paper shows that if the utility function is concave and smooth, then O(log(1/∊)/∊) convergence time is possible via an existing stochastic variation on the Frank-Wolfe algorithm, called the RUN algorithm. Next, a converse result is proven to show it is impossible for any algorithm to have convergence time better than O(1/∊), provided the algorithm has no a-priori knowledge of channel state probabilities. Hence, RUN is within a logarithmic factor of convergence time optimality. However, RUN has a vanishing stepsize and hence has an infinite adaptation time. Using stochastic Frank-Wolfe with a fixed stepsize yields improved O(1/∊2) adaptation time, but convergence time increases to O(1/∊2), similar to existing drift-plus-penalty based algorithms. This raises important open questions regarding optimal adaptation.
Weight design of distributed approximate Newton algorithms for constrained optimization

This paper presents a distributed algorithm to solve an economic dispatch problem, which takes the form of a linearly-constrained resource allocation problem. Distributed gradient-based methods are commonly used to solve problems of this form, which inherit slow convergence. The Newton method is a centralized alternative which uses second-order information to provide faster convergence. However, computing a Newton step is difficult in distributed settings and typically requires all-to-all agent communication. In this paper, we propose the distributed approx-Newton algorithm to approximate the Newton step with only distributed communication. The convergence of this algorithm is discussed and rigorously analyzed. In addition, we aim to address the problem of designing communication topologies and weightings that are optimal for second-order methods. To this end, we propose an effective approximation which is loosely based on completing the square to address the NP-hard bilinear optimization involved in the design. Simulations demonstrate that our proposed weight design applied to the distributed approx-Newton algorithm has a superior convergence property compared to existing gradient-inspired weight design applied to the Distributed Gradient Descent method.
Class 2 quotients of solvable linear groups

Abstract Let G be a finite group, and let V be a completely reducible faithful G-module. By a result of Glauberman it has been known for a long time that if G is nilpotent of class 2, then | G | | V | . In this paper we generalize this result as follows. Assuming G to be solvable, we show that the order of the maximal class 2 quotient of G is strictly bounded above by | V | .
Comparing volumes by concurrent cross-sections of complex lines: a Busemann–Petty type problem

We consider the problem of comparing the volumes of two star bodies in an even-dimensional Euclidean space $${\mathbb {R}}^{2n} = {\mathbb {C}}^n$$ by comparing their cross sectional areas along complex lines (special 2-dimensional real planes) through the origin. Under mild symmetry conditions on one of the bodies a Busemann–Petty type theorem holds. Quaternionic and octonionic analogs also hold. The argument relies on integration in polar coordinates coupled with Jensen’s inequality. Along the way we provide a criterion that detects which centered bodies are circular. i.e., stabilized by multiplication by complex numbers of unit modulus. Our goal is to present a Busemann–Petty type result with a minimum of required background (in the spirit of L. K. Hua’s book on the classical domains) and, in addition, to suggest characterizations of classes of star bodies by means of integral geometric inequalities.
Matrix completion with noisy entries and outliers

This paper considers the problem of matrix completion when the observed entries are noisy and contain outliers. It begins with introducing a new optimization criterion for which the recovered matrix is defined as its solution. This criterion uses the celebrated Huber function from the robust statistics literature to downweigh the effects of outliers. A practical algorithm is developed to solve the optimization involved. This algorithm is fast, straightforward to implement, and monotonic convergent. Furthermore, the proposed methodology is theoretically shown to be stable in a well defined sense. Its promising empirical performance is demonstrated via a sequence of simulation experiments, including image inpainting.
Weighted Fourier Frames on Self-Affine Measures

Abstract Continuing the ideas from our previous paper [6] , we construct Parseval frames of weighted exponential functions for self-affine measures.
Minimal Surfaces in the Round Three‐Sphere by Doubling the Equatorial Two‐Sphere, II

We construct closed embedded minimal surfaces in the round three-sphere, resembling two parallel copies of the equatorial two-sphere, joined by small catenoidal bridges symmetrically arranged either along two parallel circles of the equator, or along the equatorial circle and the poles. To carry out these constructions we refine and reorganize the doubling methodology in ways which we expect to apply also to further constructions. In particular we introduce what we call linearized doubling, which is an intermediate step where singular solutions to the linearized equation are constructed subject to appropriate linear and nonlinear conditions. Linearized doubling provides a systematic approach for dealing with the obstructions involved and also understanding in detail the regions further away from the catenoidal bridges.
A Bayesian approach to calibrating hydrogen flame kinetics using many experiments and parameters

Abstract First-principles Markov Chain Monte Carlo sampling is used to investigate uncertainty quantification and uncertainty propagation in parameters describing hydrogen kinetics. Specifically, we sample the posterior distribution for thirty-one parameters focusing on the H2O2 and HO2 reactions resulting from conditioning on ninety-one experiments. Established literature values are used for the remaining parameters in the mechanism as well as other thermodynamic and transport data needed to specify fluid properties. The samples are computed using an affine invariant sampler starting with broad, noninformative priors. Autocorrelation analysis shows that O(1M) samples are sufficient to obtain a reasonable sampling of the posterior. The resulting distribution identifies strong positive and negative correlations and several non-Gaussian characteristics. Using samples drawn from the posterior, we investigate the impact of parameter uncertainty on the prediction of two more complex flames: a 2D premixed flame kernel and the ignition of a hydrogen jet issuing into a heated chamber. The former represents a combustion regime similar to the target experiments used to calibrate the mechanism and the latter represents a different combustion regime. For the premixed flame, the net amount of product after a given time interval has a standard deviation of less than 2% whereas the standard deviation of the ignition time for the jet is more than 10%. The samples used for these studies are posted online. These results indicate the degree to which parameters consistent with the target experiments constrain predicted behavior in different combustion regimes. This process provides a framework for both identifying reactions for further study from candidate mechanisms as well as combining uncertainty quantification and propagation to, ultimately, tie uncertainty in laboratory flame experiments to uncertainty in end-use numerical predictions of more complicated scenarios.
Temporal magnification for streaked ultrafast electron diffraction and microscopy.

Abstract One of the frontiers of modern electron scattering instrumentation is improving temporal resolution in order to enable the observation of dynamical phenomena at their fundamental time-scales. We analyze how a radiofrequency cavity can be used as an electron longitudinal lens in order to produce a highly magnified temporal replica of an ultrafast process, and, in combination with a deflecting cavity, enable streaked electron images of optical-frequency phenomena. We present start-to-end simulations of an MeV electron beamline for two variations of this idea (a “magnifying-glass” and a “point-projection” configuration) showing the feasibility for an electron probe to achieve single shot 1.4 fs(rms) temporal resolution.
Dynamic ASEP, Duality, and Continuous q−1-Hermite Polynomials

We demonstrate a Markov duality between the dynamic ASEP and the standard ASEP. We then apply this to step initial data, as well as a half-stationary initial data (which we introduce). While investigating the duality for half-stationary initial data, we uncover and utilize connections to continuous $q^{-1}$-Hermite polynomials. Finally, we introduce a family of stationary initial data which are related to the indeterminate moment problem associated with these $q^{-1}$-Hermite polynomials.
Interference mitigation through limited receiver cooperation: Symmetric case

Interference is a major issue that limits the performance in wireless networks, and cooperation among receivers can help mitigate interference by forming distributed MIMO systems. The rate at which receivers cooperate, however, is limited in most scenarios. How much interference can one bit of receiver cooperation mitigate? In this paper, we study the two-user Gaussian interference channel with conferencing decoders to answer this question in a simple setting. We characterize the fundamental gain from cooperation: at high SNR, when INR is below 50% of SNR in dB scale, one-bit cooperation per direction buys roughly one-bit gain per user until full receiver cooperation performance is reached, while when INR is between 67% and 200% of SNR in dB scale, one-bit cooperation per direction buys roughly half-bit gain per user. The conclusion is drawn based on the approximate characterization of the symmetric capacity in the symmetric set-up. We propose strategies achieving the symmetric capacity universally to within 3 bits. The strategy consists of two parts: (1) the transmission scheme, where superposition encoding with a simple power split is employed, and (2) the cooperative protocol, where quantize-binning is used for relaying.
Transfer Topic Modeling with Ease and Scalability.

The increasing volume of short texts generated on social media sites, such as Twitter or Facebook, creates a great demand for effective and efficient topic modeling approaches. While latent Dirichlet allocation (LDA) can be applied, it is not optimal due to its weakness in handling short texts with fast-changing topics and scalability concerns. In this paper, we propose a transfer learning approach that utilizes abundant labeled documents from other domains (such as Yahoo! News or Wikipedia) to improve topic modeling, with better model fitting and result interpretation. Specifically, we develop Transfer Hierarchical LDA (thLDA) model, which incorporates the label information from other domains via informative priors. In addition, we develop a parallel implementation of our model for large-scale applications. We demonstrate the effectiveness of our thLDA model on both a microblogging dataset and standard text collections including AP and RCV1 datasets.
R.E. Axiomatization of Conditional Independence.

The paper investigates properties of the conditional independence relation between pieces of information. This relation is also known in the database theory as embedded multivalued dependency. In 1980, Parker and Parsaye-Ghomi established that the properties of this relation can not be described by a finite system of inference rules. In 1995, Herrmann proved that the propositional theory of this relation is undecidable. The main result of this paper is a complete recursively enumerable axiomatization of this theory.
A Deeper Look into Dependency-Based Word Embeddings

We investigate the effect of various dependency-based word embeddings on distinguishing between functional and domain similarity, word similarity rankings, and two downstream tasks in English. Variations include word embeddings trained using context windows from Stanford and Universal dependencies at several levels of enhancement (ranging from unlabeled, to Enhanced++ dependencies). Results are compared to basic linear contexts and evaluated on several datasets. We found that embeddings trained with Universal and Stanford dependency contexts excel at different tasks, and that enhanced dependencies often improve performance.
Propagation of initially excited states in time-dependent density-functional theory

Many recent applications of time-dependent density functional theory begin in an initially excited state and propagate it using an adiabatic approximation for the exchange-correlation potential. This, however, inserts the excited-state density into a ground-state approximation. By studying a series of model calculations, we highlight the relevance of initial-state dependence of the exact functional when starting in an excited state, discuss different valid choices of the initial Kohn-Sham state, and explore the errors inherent in the adiabatic approximation that neglects this dependence.
On the necessity of Reidemeister move 2 for simplifying immersed planar curves

In 2001, Oestlund conjectured that Reidemeister moves 1 and 3 are sufficient to describe a homotopy from any generic immersion from the circle into the plane to the standard embedding of the circle. We show that this conjecture is false.
Which compacta are noncommutative ARs

Abstract We give a short answer to the question in the title: dendrits. Precisely we show that the C * -algebra C ( X ) of all complex-valued continuous functions on a compactum X is projective in the category C 1 of all (not necessarily commutative) unital C * -algebras if and only if X is an absolute retract of dimension dim X ⩽ 1 or, equivalently, that X is a dendrit.
A non-crossing standard monomial theory

Abstract The second author has introduced non-crossing tableaux, objects whose non-nesting analogues are semi-standard Young tableaux. We relate non-crossing tableaux to Gelfand–Tsetlin patterns and develop the non-crossing analogue of standard monomial theory. Leclerc and Zelevinsky's weakly separated sets are special cases of non-crossing tableaux, and we suggest that non-crossing tableaux may help illuminate the theory of weakly separated sets.
Fast Real-Time Time-Dependent Density Functional Theory Calculations with the Parallel Transport Gauge.

Real-time time-dependent density functional theory (RT-TDDFT) is known to be hindered by the very small time step (attosecond or smaller) needed in the numerical simulation, because of the fast oscillation of electron wave functions, which significantly limits its range of applicability for the study of ultrafast dynamics. In this paper, we demonstrate that such oscillation can be considerably reduced by optimizing the gauge choice using the parallel transport formalism. RT-TDDFT calculations can thus be significantly accelerated using a combination of the parallel transport gauge and implicit integrators, and the resulting scheme can be used to accelerate any electronic structure software that uses a Schrodinger representation. Using absorption spectrum, ultrashort laser pulse, and Ehrenfest dynamics calculations for example, we show that the new method can utilize a time step that is on the order of 10-100 attoseconds using a planewave basis set. Thanks to the significant increase of the size of the time step, we also demonstrate that the new method is more than 10 times faster, in terms of the wall clock time, when compared to the standard explicit fourth-order Runge-Kutta time integrator for silicon systems ranging from 32 to 1024 atoms.
Absolute vs. Relative Gromov-Witten Invariants

We compare the absolute and relative Gromov-Witten invariants of compact symplectic manifolds when the symplectic hypersurface contains no relevant holomorphic curves. We show that these invariants are then the same, except in a narrow range of dimensions of the target and genera of the domains, and provide examples when they fail to be the same.
Pruning Random Forests for Prediction on a Budget

We propose to prune a random forest (RF) for resource-constrained prediction. We first construct a RF and then prune it to optimize expected feature cost & accuracy. We pose pruning RFs as a novel 0-1 integer program with linear constraints that encourages feature re-use. We establish total unimodularity of the constraint set to prove that the corresponding LP relaxation solves the original integer program. We then exploit connections to combinatorial optimization and develop an efficient primal-dual algorithm, scalable to large datasets. In contrast to our bottom-up approach, which benefits from good RF initialization, conventional methods are top-down acquiring features based on their utility value and is generally intractable, requiring heuristics. Empirically, our pruning algorithm outperforms existing state-of-the-art resource-constrained algorithms.