cssi/SciSciGPT-SciSciNet huggingface dataset:
Sharp vanishing thresholds for cohomology of random flag complexes

For every k 1, the k-th cohomology group H k (X;Q) of the random ag complex X X(n;p) passes through two phase transitions: one where it appears and one where it vanishes. We describe the vanishing threshold and show that it is sharp. Using the same spectral methods, we also nd a sharp threshold for the fundamental group 1(X) to have Kazhdan’s property (T). Combining with earlier results, we obtain as a corollary that for every k 3, there is a regime in which the random ag complex is rationally homotopy equivalent to a bouquet of k-dimensional spheres.
Quartic surfaces with icosahedral symmetry

We study quartic surfaces that admit a group of projective automorphisms isomorphic to icosahedron group.
Sobolev Inequalities for $(0,q)$ forms on CR manifolds of finite type

We prove that odd Khovanov homology is mutation invariant over $\zz$, and therefore that Khovanov homology is mutation invariant over $\zzt$. We also establish mutation invariance for the entire Ozsv\'ath-Szab\'o spectral sequence from reduced Khovanov homology to the Heegaard Floer homology of the branched double-cover.
Know What You Don't Know: Unanswerable Questions for SQuAD

Extractive reading comprehension systems can often locate the correct answer to a question in a context document, but they also tend to make unreliable guesses on questions for which the correct answer is not stated in the context. Existing datasets either focus exclusively on answerable questions, or use automatically generated unanswerable questions that are easy to identify. To address these weaknesses, we present SQuADRUn, a new dataset that combines the existing Stanford Question Answering Dataset (SQuAD) with over 50,000 unanswerable questions written adversarially by crowdworkers to look similar to answerable ones. To do well on SQuADRUn, systems must not only answer questions when possible, but also determine when no answer is supported by the paragraph and abstain from answering. SQuADRUn is a challenging natural language understanding task for existing models: a strong neural system that gets 86% F1 on SQuAD achieves only 66% F1 on SQuADRUn. We release SQuADRUn to the community as the successor to SQuAD.
Learning to Bid Without Knowing your Value

We address online learning in complex auction settings, such as sponsored search auctions, where the value of the bidder is unknown to her, evolving in an arbitrary manner and observed only if the bidder wins an allocation. We leverage the structure of the utility of the bidder and the partial feedback that bidders typically receive in auctions, in order to provide algorithms with regret rates against the best fixed bid in hindsight, that are exponentially faster in convergence in terms of dependence on the action space, than what would have been derived by applying a generic bandit algorithm and almost equivalent to what would have been achieved in the full information setting. Our results are enabled by analyzing a new online learning setting with outcome-based feedback, which generalizes learning with feedback graphs. We provide an online learning algorithm for this setting, of independent interest, with regret that grows only logarithmically with the number of actions and linearly only in the number of potential outcomes (the latter being very small in most auction settings). Last but not least, we show that our algorithm outperforms the bandit approach experimentally and that this performance is robust to dropping some of our theoretical assumptions or introducing noise in the feedback that the bidder receives.
An excursion into geometric analysis

This is a guided tour through some selected topics in geometric analysis. We have chosen to illustrate many of the basic ideas as they apply to the theory of minimal surfaces. This is, in part, because minimal surfaces is, if not the oldest, then certainly one of the oldest areas of geometric analysis dating back to Euler's work in the 1740's and in fact many of the basic ideas in geometric analysis originated in the study of minimal surfaces. In any case, the ideas apply to a variety of different fields and we will mention some of these as we go along.
The defocusing energy-supercritical nonlinear wave equation in three space dimensions

We consider the defocusing nonlinear wave equation u tt ― Δu + |u| p u = 0 in the energy-supercritical regime p > 4. For even values of the power p, we show that blowup (or failure to scatter) must be accompanied by blowup of the critical Sobolev norm. An equivalent formulation is that solutions with bounded critical Sobolev norm are global and scatter. The impetus to consider this problem comes from recent work of Kenig and Merle who treated the case of spherically-symmetric solutions.
Recursion-theoretic ranking and compression

Abstract For which sets A does there exist a mapping, computed by a total or partial recursive function, such that the mapping, when its domain is restricted to A, is a 1-to-1, onto mapping to Σ ⁎ ? For which sets A does there exist such a mapping that respects the lexicographical ordering within A? Both cases are types of perfect, minimal hash functions. The complexity-theoretic versions of these notions are known as compression functions and ranking functions. This paper defines and studies the recursion-theoretic versions of compression and ranking functions, and in particular studies which sets have, or lack, such functions. Thus this is a case where, in contrast to the usual direction of notion transferal, notions from complexity theory are inspiring notions, and an investigation, in computability theory. We show that the rankable and compressible sets broadly populate the 1-truth-table degrees, and we prove that every nonempty coRE cylinder is recursively compressible.
Global sensitivity metrics from active subspaces

Abstract Predictions from science and engineering models depend on several input parameters. Global sensitivity analysis quantifies the importance of each input parameter, which can lead to insight into the model and reduced computational cost; commonly used sensitivity metrics include Sobol' total sensitivity indices and derivative-based global sensitivity measures. Active subspaces are part of an emerging set of tools for identifying important directions in a model's input parameter space; these directions can be exploited to reduce the model's dimension enabling otherwise infeasible parameter studies. In this paper, we develop global sensitivity metrics called activity scores from the active subspace, which yield insight into the important model parameters. We mathematically relate the activity scores to established sensitivity metrics, and we discuss computational methods to estimate the activity scores. We show two numerical examples with algebraic functions taken from simplified engineering models. For each model, we analyze the active subspace and discuss how to exploit the low-dimensional structure. We then show that input rankings produced by the activity scores are consistent with rankings produced by the standard metrics.
Capacity of cellular networks with femtocache

The capacity of next generation of cellular networks using femtocaches is studied when multihop communications and decentralized cache placement are considered. We show that the storage capability of future network User Terminals (UT) can be effectively used to increase the capacity in random decentralized uncoded caching. We further propose a random decentralized coded caching scheme which achieves higher capacity results than the random decentralized uncoded caching. The result shows that coded caching which is suitable for systems with limited storage capabilities can improve the capacity of cellular networks by a factor of log(n) where n is the number of nodes served by the femtocache.
Functional Limit Theorems for Toeplitz Quadratic Functionals of Continuous time Gaussian Stationary Processes

Abstract The paper establishes weak convergence in C [ 0 , 1 ] of normalized stochastic processes, generated by Toeplitz type quadratic functionals of a continuous time Gaussian stationary process, exhibiting long-range dependence. Both central and non-central functional limit theorems are obtained.
Marginal false discovery rate control for likelihood‐based penalized regression models

The popularity of penalized regression in high-dimensional data analysis has led to a demand for new inferential tools for these models. False discovery rate control is widely used in high-dimensional hypothesis testing, but has only recently been considered in the context of penalized regression. Almost all of this work, however, has focused on lasso-penalized linear regression. In this paper, we derive a general method for controlling the marginal false discovery rate that can be applied to any penalized likelihood-based model, such as logistic regression and Cox regression. Our approach is fast, flexible and can be used with a variety of penalty functions including lasso, elastic net, MCP, and MNet. We derive theoretical results under which the proposed method is valid, and use simulation studies to demonstrate that the approach is reasonably robust, albeit slightly conservative, when these assumptions are violated. Despite being conservative, we show that our method often offers more power to select causally important features than existing approaches. Finally, the practical utility of the method is demonstrated on gene expression datasets with binary and time-to-event outcomes.
UTD-CRSS submission for MGB-3 Arabic dialect identification: Front-end and back-end advancements on broadcast speech

This study presents systems submitted by the University of Texas at Dallas, Center for Robust Speech Systems (UTD-CRSS) to the MGB-3 Arabic Dialect Identification (ADI) subtask. This task is defined to discriminate between five dialects of Arabic, including Egyptian, Gulf, Levantine, North African, and Modern Standard Arabic. We develop multiple single systems with different front-end representations and back-end classifiers. At the front-end level, feature extraction methods such as Mel-frequency cepstral coefficients (MFCCs) and two types of bottleneck features (BNF) are studied for an i-Vector framework. As for the back-end level, Gaussian back-end (GB), and Generative Adversarial Networks (GANs) classifiers are applied alternately. The best submission (contrastive) is achieved for the ADI subtask with an accuracy of 76.94% by augmenting the randomly chosen part of the development dataset. Further, with a post evaluation correction in the submitted system, final accuracy is increased to 79.76%, which represents the best performance achieved so far for the challenge on the test dataset.
A nearly-quadratic gap between adaptive and non-adaptive property testers

We show that for all integers t ≥ 8 and arbitrarily small e > 0, there exists a graph property Π (which depends on e) such that e-testing Π has non-adaptive query complexity \(Q=\tilde\Theta(q^{2-2/t})\), where \(q=\tilde\Theta(\epsilon^{-1})\) is the adaptive query complexity. This resolves the question of how beneficial adaptivity is, in the context of proximity-dependent properties. This also gives evidence that the canonical transformation of Goldreich and Trevisan is essentially optimal when converting an adaptive property tester to a non-adaptive property tester.
Active discovery of network roles for predicting the classes of network nodes

Nodes in real world networks often have class labels, or underlying attributes, that are related to the way in which they connect to other nodes. Sometimes this relationship is simple, for instance nodes of the same class are may be more likely to be connected. In other cases, however, this is not true, and the way that nodes link in a network exhibits a different, more complex relationship to their attributes. Here, we consider networks in which we know how the nodes are connected, but we do not know the class labels of the nodes or how class labels relate to the network links. We wish to identify the best subset of nodes to label in order to learn this relationship between node attributes and network links. We can then use this discovered relationship to accurately predict the class labels of the rest of the network nodes. We present a model that identifies groups of nodes with similar link patterns, which we call network roles, using a generative blockmodel. The model then predicts labels by learning the mapping from network roles to class labels using a maximum margin classifier. We choose a subset of nodes to label according to an iterative margin-based active learning strategy. By integrating the discovery of network roles with the classifier optimisation, the active learning process can adapt the network roles to better represent the network for node classification. We demonstrate the model by exploring a selection of real world networks, including a marine food web and a network of English words. We show that, in contrast to other network classifiers, this model achieves good classification accuracy for a range of networks with different relationships between class labels and network links.
Finite Orbits in Random Subshifts of Finite Type

For each \(n, d \in {{\mathbb {N}}}\) and \(0 0\) such that for \(\alpha < \alpha _0\) and with probability tending to 1 as \(n \rightarrow \infty \), this random subshift will contain only finitely many elements. In the case \(d = 1\), we obtain the best possible such \(\alpha _0, 1/|{\mathcal {A}}|\).
The Subset Assignment Problem for Data Placement in Caches

We introduce the subset assignment problem in which items of varying sizes are placed in a set of bins with limited capacity. Items can be replicated and placed in any subset of the bins. Each (item, subset) pair has an associated cost. Not assigning an item to any of the bins is not free in general and can potentially be the most expensive option. The goal is to minimize the total cost of assigning items to subsets without exceeding the bin capacities. The subset assignment problem models the problem of managing a cache composed of banks of memory with varying cost/performance specifications. The ability to replicate a data item in more than one memory bank can benefit the overall performance of the system with a faster recovery time in the event of a memory failure. For this setting, the number n of data objects (items) is very large and the number d of memory banks (bins) is a small constant (on the order of 3 or 4). Therefore, the goal is to determine an optimal assignment in time that minimizes dependence on n. The integral version of this problem is NP-hard since it is a generalization of the knapsack problem. We focus on an efficient solution to the LP relaxation as the number of fractionally assigned items will be at most d. If the data objects are small with respect to the size of the memory banks, the effect of excluding the fractionally assigned data items from the cache will be small. We give an algorithm that solves the LP relaxation and runs in time $$O(\left( {\begin{array}{c}3^d\\ d+1\end{array}}\right) {\text {poly}}(d) n \log (n) \log (nC) \log (Z))$$ , where Z is the maximum item size and C the maximum storage cost.
Generalized geometry, T-duality, and renormalization group flow

Abstract We interpret the physical B -field renormalization group flow in the language of Courant algebroids, clarifying the sense in which this flow is the natural “Ricci flow” for generalized geometry. Next we show that the B -field renormalization group flow preserves T -duality in a natural sense. As corollaries we obtain new long time existence results for the B -field renormalization group flow.
Mean estimation from adaptive one-bit measurements

We consider the problem of estimating the mean of a normal distribution under the following constraint: the estimator can access only a single bit from each sample from this distribution. We study the squared error risk in this estimation as a function of the number of samples and one-bit measurements n. We consider an adaptive estimation setting where the single-bit sent at step n is a function of both the new sample and the previous n − 1 acquired bits. For this setting, we show that no estimator can attain asymptotic mean squared error smaller than π/(2n)+ O(n−2) times the variance. In other words, one-bit restriction increases the number of samples required for a prescribed accuracy of estimation by a factor of at least π /2 compared to the unrestricted case. In addition, we provide an explicit estimator that attains this asymptotic error, showing that, rather surprisingly, only π /2 times more samples are required in order to attain estimation performance equivalent to the unrestricted case.
The Cost of Uncertainty in Curing Epidemics

Epidemic models are used across biological and social sciences, engineering, and computer science, and have had important impact in the study of the dynamics of human disease and computer viruses, but also trends rumors, viral videos, and most recently the spread of fake news on social networks. In this paper, we focus on epidemics propagating on a graph, as introduced by the seminal paper [5]. In particular, we consider so-called SI models (see below for a precise definition) where an infected node can only propagate the infection to its non-infected neighbor, as opposed to the fully mixed models considered in the early literature. This graph-based approach provides a more realistic model, in which the spread of the epidemic is determined by the connectivity of the graph, and accordingly some nodes may play a larger role than others in the spread of the infection.
Backprop without Learning Rates Through Coin Betting

Deep learning methods achieve state-of-the-art performance in many application scenarios. Yet, these methods require a significant amount of hyperparameters tuning in order to achieve the best results. In particular, tuning the learning rates in the stochastic optimization process is still one of the main bottlenecks. In this paper, we propose a new stochastic gradient descent procedure for deep networks that does not require any learning rate setting. Contrary to previous methods, we do not adapt the learning rates nor we make use of the assumed curvature of the objective function. Instead, we reduce the optimization process to a game of betting on a coin and propose a learning rate free optimal algorithm for this scenario. Theoretical convergence is proven for convex and quasi-convex functions and empirical evidences show the advantage of our algorithm over popular stochastic gradient algorithms.
Deep RNN-Oriented Paradigm Shift through BOCANet: Broken Obfuscated Circuit Attack

Logic encryption obfuscation has been used for thwarting counterfeiting, overproduction, and reverse engineering but vulnerable to attacks. However, it was recently shown that satisfiability - checking (SAT) can potentially compromise hardware obfuscation circuits. In this paper, we develop a novel attack called BOCANet that can be beneficial from deep learning architecture to compromise hardware obfuscation circuits's key. Our approach involves exploiting deep recurrent neural network (D-RNN) model, and developing attack model to compromise the obfuscated hardware at least an order-of magnitude more efficiently and under resource-constrained scenarios. In our experiments, the BOCANet approach achieves an average success rate of 100% for 32 bit key size, 93.4% for 64 bit key size, 92.2% and 91.7% for 128 and 256 bit key size, respectively.
Alternating distances of knots and links

Abstract An alternating distance is a link invariant that measures how far away a link is from alternating. We study several alternating distances and demonstrate that there exist families of links for which the difference between certain alternating distances is arbitrarily large. We also show that two alternating distances, the alternation number and the alternating genus, are not comparable.
A Practical Algorithm for Distributed Clustering and Outlier Detection

We study the classic k-means/median clustering, which are fundamental problems in unsupervised learning, in the setting where data are partitioned across multiple sites, and where we are allowed to discard a small portion of the data by labeling them as outliers. We propose a simple approach based on constructing small summary for the original dataset. The proposed method is time and communication efficient, has good approximation guarantees, and can identify the global outliers effectively. To the best of our knowledge, this is the first practical algorithm with theoretical guarantees for distributed clustering with outliers. Our experiments on both real and synthetic data have demonstrated the clear superiority of our algorithm against all the baseline algorithms in almost all metrics.
Heat kernel analysis on infinite-dimensional Heisenberg groups

Abstract We introduce a class of non-commutative Heisenberg-like infinite-dimensional Lie groups based on an abstract Wiener space. The Ricci curvature tensor for these groups is computed and shown to be bounded. Brownian motion and the corresponding heat kernel measures, { ν t } t > 0 , are also studied. We show that these heat kernel measures admit: (1) Gaussian like upper bounds, (2) Cameron–Martin type quasi-invariance results, (3) good L p -bounds on the corresponding Radon–Nikodym derivatives, (4) integration by parts formulas, and (5) logarithmic Sobolev inequalities. The last three results heavily rely on the boundedness of the Ricci tensor.
Correlations in disordered quantum harmonic oscillator systems: The effects of excitations and quantum quenches

We prove spatial decay estimates on disorder-averaged position-momentum correlations in a gapless class of random oscillator models. First, we prove a decay estimate on dynamic correlations for general eigenstates with a bound that depends on the magnitude of the maximally excited mode. Then, we consider the situation of a quantum quench. We prove that the full time-evolution of an initially chosen (uncorrelated) product state has disorder-averaged correlations which decay exponentially in space, uniformly in time.
Derived Functors Related to Wall-Crossing

The setting is the representation theory of a simply connected, semisimple algebraic group over a field of positive characteristic. There is a natural transformation from the wall-crossing functor to the identity functor. The kernel of this transformation is a left exact functor. This functor and its first derived functor are evaluated on the global sections of a line bundle on the flag variety. It is conjectured that the derived functors of order greater than one annihilate the global sections. Also, the principal indecomposable modules for the Frobenius subgroups are shown to be acyclic.
A refinement of Koblitz's conjecture

Let E be an elliptic curve over the rationals. In 1988, Koblitz conjectured an asymptotic for the number of primes p for which the cardinality of the group of &#x1d53d;p-points of E is prime. However, the constant occurring in his asymptotic does not take into account that the distributions of the |E(&#x1d53d;p)| need not be independent modulo distinct primes. We shall describe a corrected constant. We also take the opportunity to extend the scope of the original conjecture to ask how often |E(&#x1d53d;p)|/t is an integer and prime for a fixed positive integer t, and to consider elliptic curves over arbitrary number fields. Several worked out examples are provided to supply numerical evidence for the new conjecture.
h*-Polynomials with Roots on the Unit Circle

For an n-dimensional lattice simplex Δ(1,q) with vertices given by the standard basis vectors and −q where q has positive entries, we investigate when the Ehrhart h*-polynomial for Δ(1,q) factors a...
The Weil representation in characteristic two

In this paper we construct a new variant of the Weil representation, associated with a symplectic vector space (V, ω) defined over a finite field of characteristic two. Our variant is a representation ρ : AM p (V ) → G L (H), where the group AM p (V ) is the fourth cover of a group ASp (V ) which is a non-trivial extension of the symplectic group Sp (V ) by the dual group V ∗ . In particular, the group ASp (V ) contains Weil’s pseudo-symplectic group as a strict subgroup. Along the way, we develop the formalism of canonical vector spaces which enables us to realize the group AM p (V ) and the Weil representation ρ in a transparent manner and also yields a conceptual explanation for these important objects of representation theory. c
A higher-order Godunov method for radiation hydrodynamics: Radiation subsystem

A higher order Godunov method for the radiation subsystem of radiation hydrodynamics is presented. A key ingredient of the method is the direct coupling of stiff source term effects to the hyperbolic structure of the system of conservation laws; it is composed of a predictor step that is based on Duhamel's principle and a corrector step that is based on Picard iteration. The method is second order accurate in both time and space, unsplit, asymptotically preserving, and uniformly well behaved from the photon free streaming (hyperbolic) limit through the weak equilibrium diffusion (parabolic) limit and to the strong equilibrium diffusion (hyperbolic) limit. Numerical tests demonstrate second order convergence across various parameter regimes.
On suprema of autoconvolutions with an application to Sidon sets

Let $f$ be a nonnegative function supported on $(-1/4, 1/4)$. We show $$ \sup_{x \in \mathbb{R}}{\int_{\mathbb{R}}{f(t)f(x-t)dt}} \geq 1.28\left(\int_{-1/4}^{1/4}{f(x)dx} \right)^2,$$ where 1.28 improves on a series of earlier results. The inequality arises naturally in additive combinatorics in the study of Sidon sets. We derive a relaxation of the problem that reduces to a finite number of cases and yields slightly stronger results. Our approach should be able to prove lower bounds that are arbitrary close to the sharp result. Currently, the bottleneck in our approach is runtime: new ideas might be able to significantly speed up the computation.
Gaussian Process Subset Scanning for Anomalous Pattern Detection in Non-iid Data

Identifying anomalous patterns in real-world data is essential for understanding where, when, and how systems deviate from their expected dynamics. Yet methods that separately consider the anomalousness of each individual data point have low detection power for subtle, emerging irregularities. Additionally, recent detection techniques based on subset scanning make strong independence assumptions and suffer degraded performance in correlated data. We introduce methods for identifying anomalous patterns in non-iid data by combining Gaussian processes with novel log-likelihood ratio statistic and subset scanning techniques. Our approaches are powerful, interpretable, and can integrate information across multiple data streams. We illustrate their performance on numeric simulations and three open source spatiotemporal datasets of opioid overdose deaths, 311 calls, and storm reports.
Polynomial multiple recurrence over rings of integers

We generalize the polynomial Szemeredi theorem to intersective polynomials over the ring of integers of an algebraic number field, by which we mean polynomials having a common root modulo every ideal. This leads to the existence of new polynomial configurations in positive-density subsets of and strengthens and extends recent results of Bergelson, Leibman and Lesigne [Intersective polynomials and the polynomial Szemeredi theorem. Adv. Math. 219(1) (2008), 369–388] on polynomials over the integers.
Risk Mitigation for Dynamic State Estimation Against Cyber Attacks and Unknown Inputs

Phasor measurement units (PMUs) can be effectively utilized for the monitoring and control of the power grid. As the cyber-world becomes increasingly embedded into power grids, the risks of this inevitable evolution become serious. In this paper, we present a risk mitigation strategy, based on dynamic state estimation, to eliminate threat levels from the grid’s unknown inputs and potential cyber-attacks. The strategy requires: 1) the potentially incomplete knowledge of power system models and parameters and 2) real-time PMU measurements. First, we utilize a dynamic state estimator for higher order depictions of power system dynamics for simultaneous state and unknown inputs estimation. Second, estimates of cyber-attacks are obtained through an attack detection algorithm. Third, the estimation and detection components are seamlessly utilized in an optimization framework to determine the most impacted PMU measurements. Finally, a risk mitigation strategy is proposed to guarantee the elimination of threats from attacks, ensuring the observability of the power system through available, safe measurements. Case studies are included to validate the proposed approach. Insightful suggestions, extensions, and open problems are also posed.
On the waring rank of binary forms

Abstract The K-rank of a binary form f in K [ x , y ] , K ⊆ C , is the smallest number of d-th powers of linear forms over K of which f is a K-linear combination. We provide lower bounds for the C -rank (Waring rank) and for the R -rank (real Waring rank) of binary forms depending on their factorization. We study binary forms with unique C -minimal representation.
A Deterministic Nonsmooth Frank Wolfe Algorithm with Coreset Guarantees

We present a new Frank Wolfe type algorithm that is applicable to minimization problems with a nonsmooth convex objective. We provide convergence bounds and show that the scheme yields so-called co...
On the matrix square root via geometric optimization

This paper is triggered by the preprint (P. Jain, C. Jin, S.M. Kakade, and P. Netra- palli. Computing matrix squareroot via non convex local search. Preprint, arXiv:1507.05854, 2015.), which analyzes gradient-descent for computing the square root of a positive definite matrix. Contrary to claims of Jain et al., the author's experiments reveal that Newton-like methods compute matrix square roots rapidly and reliably, even for highly ill-conditioned matrices and without requiring com- mutativity. The author observes that gradient-descent converges very slowly primarily due to tiny step-sizes and ill-conditioning. The paper derives an alternative first-order method based on geodesic convexity; this method admits a transparent convergence analysis (< 1 page), attains linear rate, and displays reliable convergence even for rank deficient problems. Though superior to gradient-descent, ultimately this method is also outperformed by a well-known scaled Newton method. Nevertheless, the primary value of the paper is conceptual: it shows that for deriving gradient based methods for the matrix square root, the manifold geometric view of positive definite matrices can be much more advantageous than the Euclidean view.
A fast distributed proximal-gradient method

We present a distributed proximal-gradient method for optimizing the average of convex functions, each of which is the private local objective of an agent in a network with time-varying topology. The local objectives have distinct differentiable components, but they share a common nondifferentiable component, which has a favorable structure suitable for effective computation of the proximal operator. In our method, each agent iteratively updates its estimate of the global minimum by optimizing its local objective function, and exchanging estimates with others via communication in the network. Using Nesterov-type acceleration techniques and multiple communication steps per iteration, we show that this method converges at the rate 1/k (where k is the number of communication rounds between the agents), which is faster than the convergence rate of the existing distributed methods for solving this problem. The superior convergence rate of our method is also verified by numerical experiments.
Variational and linearly implicit integrators, with applications

We show that symplectic and linearly implicit integrators proposed by Zhang & Skeel (1997, Cheap implicit symplectic integrators. Appl. Numer. Math., 25, 297–302) are variational linearizations of Newmark methods. When used in conjunction with penalty methods (i.e., methods that replace constraints by stiff potentials), these integrators permit coarse time-stepping of holonomically constrained mechanical systems and bypass the resolution of nonlinear systems. Although penalty methods are widely employed, an explicit link to Lagrange multiplier approaches appears to be lacking; such a link is now provided (in the context of two-scale flow convergence (Tao, M., Owhadi, H. & Marsden, J. E. (2010) Nonintrusive and structure-preserving multiscale integration of stiff ODEs, SDEs and Hamiltonian systems with hidden slow dynamics via flow averaging. Multiscale Model. Simul., 8, 1269–1324). The variational formulation also allows efficient simulations of mechanical systems on Lie groups.
Non-abelian Hodge theory for algebraic curves in characteristic p

Let G be a reductive group over an algebraically closed field of positive characteristic. Let C be a smooth projective curve over k. We give a description of the moduli space of flat G-bundles in terms of the moduli space of G-Higgs bundles over the Frobenius twist C′ of C. This description can be regarded as the non-abelian Hodge theory for curves in positive characteristic.
Mean-field theory of two-layers neural networks: dimension-free bounds and kernel limit

We consider learning two layer neural networks using stochastic gradient descent. The mean-field description of this learning dynamics approximates the evolution of the network weights by an evolution in the space of probability distributions in $R^D$ (where $D$ is the number of parameters associated to each neuron). This evolution can be defined through a partial differential equation or, equivalently, as the gradient flow in the Wasserstein space of probability distributions. Earlier work shows that (under some regularity assumptions), the mean field description is accurate as soon as the number of hidden units is much larger than the dimension $D$. In this paper we establish stronger and more general approximation guarantees. First of all, we show that the number of hidden units only needs to be larger than a quantity dependent on the regularity properties of the data, and independent of the dimensions. Next, we generalize this analysis to the case of unbounded activation functions, which was not covered by earlier bounds. We extend our results to noisy stochastic gradient descent. Finally, we show that kernel ridge regression can be recovered as a special limit of the mean field analysis.
Jacob's Ladder: The User Implications of Leveraging Graph Pivots

This paper reports on a simple visual technique that boils extracting a subgraph down to two operations—pivots and filters—that is agnostic to both the data abstraction, and its visual complexity scales independent of the size of the graph. The system's design, as well as its qualitative evaluation with users, clarifies exactly when and how the user's intent in a series of pivots is ambiguous—and, more usefully, when it is not. Reflections on our results show how, in the event of an ambiguous case, this innately practical operation could be further extended into "smart pivots" that anticipate the user's intent beyond the current step. They also reveal ways that a series of graph pivots can expose the semantics of the data from the user's perspective, and how this information could be leveraged to create adaptive data abstractions that do not rely as heavily on a system designer to create a comprehensive abstraction that anticipates all the user's tasks.
Improved Safe Real-Time Heuristic Search.

A fundamental concern in real-time planning is the presence of dead ends in the state space, from which no goal is reachable. Recently, the SafeRTS algorithm was proposed for searching in such spaces. SafeRTS exploits a user-provided predicate to identify safe states, from which a goal is likely reachable, and attempts to maintain a backup plan for reaching such a state at all times. In this paper, we study the SafeRTS approach, identify certain properties of its behavior, and design an improved framework for safe real-time search. We prove that the new approach performs at least as well as SafeRTS and present experimental results showing that its promise is fulfilled in practice.
Lexical Landscapes as large in silico data for examining advanced properties of fitness landscapes

In silico approaches have served a central role in the development of evolutionary theory for generations. This especially applies to the concept of the fitness landscape, one of the most important abstractions in evolutionary genetics, and one which has benefited from the presence of large empirical data sets only in the last decade or so. In this study, we propose a method that allows us to generate enormous data sets that walk the line between in silico and empirical: word usage frequencies as catalogued by the Google ngram corpora. These data can be codified or analogized in terms of a multidimensional empirical fitness landscape towards the examination of advanced concepts-adaptive landscape by environment interactions, clonal competition, higher-order epistasis and countless others. We argue that the greater Lexical Landscapes approach can serve as a platform that offers an astronomical number of fitness landscapes for exploration (at least) or theoretical formalism (potentially) in evolutionary biology.
Planning Online Advertising Using Gini Indices

Advertisers engaged in brand-building activities online often purchase significant volumes of impression-based online advertising (e.g., banner ads or video ads) from website publishers or their ad...
Sources of Manufacturing Productivity Growth in Africa

This paper investigates the sources of growth in manufacturing productivity in Cote D’Ivoire, Ethiopia and Tanzania in comparison with the case of Bangladesh. Based on the analysis of establishment census data since the mid-1990s, it finds that reallocation of market share between firms contributed substantially to productivity growth in each of the four countries, although to a varying extent. In Ethiopia, the impact of market share reallocations among survivors tended to be larger than those associated with increases in within-plant productivity. In addition, plant closure (or exit) boosted productivity more than new plant openings (or entry) did in the sense that the relative productivity of survivors (or continuing plants) was higher relative to that of closing plants (or exit cases) than it was relative to the productivity of newly opening plants (or new entrants). Reallocation of market share plays an important role in raising aggregate productivity in Cote d’Ivoire as well. But the pattern here is opposite to that in Ethiopia in that in Cote d’Ivoire entering (or newly opening) plants have larger impact on aggregate productivity growth than closing (or exiting) plants. Unlike the case with Cote D’Ivoire and of Ethiopia, the reallocation of market share among surviving plants is a smaller source of manufacturing productivity growth in Tanzania than the new plant openings and plant closure. The data suggest that the reallocation of market share among surviving plants and exiting plants has larger impact on productivity growth in Bangladesh than the productivity gap between new plants and survivors, as in the case of Ethiopia.
Graph Cover-Saturation

Graph G is F-saturated if G contains no copy of graph F but any edge added to G produces at least one copy of F. One common variant of saturation is to remove the former restriction: G is F-semi-saturated if any edge added to G produces at least one new copy of F. In this paper we take this idea one step further. Rather than just allowing edges of G to be in a copy of F, we require it: G is F-covered if every edge of G is in a copy of F. It turns out that there is smooth interaction between coverage and semi-saturation, which opens for investigation a natural analogue to saturation numbers. Therefore we present preliminary cover-saturation theory and structural bounds for the cover-saturation numbers of graphs. We also establish asymptotic cover-saturation densities for cliques and paths, and upper and lower bounds (with small gaps) for cycles and stars.
The Impact of Regularization on High-dimensional Logistic Regression

Logistic regression is commonly used for modeling dichotomous outcomes. In the classical setting, where the number of observations is much larger than the number of parameters, properties of the maximum likelihood estimator in logistic regression are well understood. Recently, Sur and Candes~\cite{sur2018modern} have studied logistic regression in the high-dimensional regime, where the number of observations and parameters are comparable, and show, among other things, that the maximum likelihood estimator is biased. In the high-dimensional regime the underlying parameter vector is often structured (sparse, block-sparse, finite-alphabet, etc.) and so in this paper we study regularized logistic regression (RLR), where a convex regularizer that encourages the desired structure is added to the negative of the log-likelihood function. An advantage of RLR is that it allows parameter recovery even for instances where the (unconstrained) maximum likelihood estimate does not exist. We provide a precise analysis of the performance of RLR via the solution of a system of six nonlinear equations, through which any performance metric of interest (mean, mean-squared error, probability of support recovery, etc.) can be explicitly computed. Our results generalize those of Sur and Candes and we provide a detailed study for the cases of $\ell_2^2$-RLR and sparse ($\ell_1$-regularized) logistic regression. In both cases, we obtain explicit expressions for various performance metrics and can find the values of the regularizer parameter that optimizes the desired performance. The theory is validated by extensive numerical simulations across a range of parameter values and problem instances.
Extensive ribosome and RF2 rearrangements during translation termination.

Protein synthesis ends when a ribosome reaches an mRNA stop codon. Release factors (RFs) decode the stop codon, hydrolyze peptidyl-tRNA to release the nascent protein, and then dissociate to allow ribosome recycling. To visualize termination by RF2, we resolved a cryo-EM ensemble of E. coli 70S•RF2 structures at up to 3.3 A in a single sample. Five structures suggest a highly dynamic termination pathway. Upon peptidyl-tRNA hydrolysis, the CCA end of deacyl-tRNA departs from the peptidyl transferase center. The catalytic GGQ loop of RF2 is rearranged into a long β-hairpin that plugs the peptide tunnel, biasing a nascent protein toward the ribosome exit. Ribosomal intersubunit rotation destabilizes the catalytic RF2 domain on the 50S subunit and disassembles the central intersubunit bridge B2a, resulting in RF2 departure. Our structures visualize how local rearrangements and spontaneous inter-subunit rotation poise the newly-made protein and RF2 to dissociate in preparation for ribosome recycling.
Directional Communication Enabled by Mobile Parasitic Elements

Mobile communications in complex environments such as mega-cities is a challenging problem that limits the ability to deploy autonomous agents in support of operations. Building on recent progress in low frequency networking that utilizes miniature antennas to provide persistent connectivity among agents, we consider the design and collaborative manipulation of a distributed robotic antenna array to provide directional communications that will enable enhanced networking, interference rejection, and collaborative control. The use of parasitic elements in a Yagi-Uda type array design avoids the need for synchronization and highly accurate position control among the agents. We utilize physics-based simulations to investigate the feasibility of using mobile agents equipped with an excited antenna element along with a set of support nodes having parasitic elements that adaptively configure to enhance radiation in a desired direction. We take into account mobile node pose uncertainty including element position and angular orientation, as well as ground scattering effects. We pursue an optimal design approach for different types of ground electromagnetic characteristics based on a hybrid full-wave propagation simulation and genetic algorithm optimization. We also present experiment with one mobile node and two static elements. The results demonstrate the ability to achieve directional low frequency communications that is robust to robotic pose error.
Echocardiographic Assessment of Pericardial Effusion Size: Time for a Quantitative Approach.

Guidelines for the echocardiographic assessment of pericardial effusion (PE) size rely on linear measurements of the largest width of the effusion. This approach is subjective and limited due to variations in heart size and the asymmetry of many effusions. We quantified PE volume using the method of
A mechanism for how Cdr1/Nim1 kinase promotes mitotic entry by inhibiting Wee1.

Cells require mechanisms to inhibit Wee1 for entry into mitosis. This study defines how fission yeast Cdr1/Nim1 inhibits Wee1 and demonstrates the in vivo relevance of this mechanism.
Thymically-derived Foxp3+ regulatory T cells are the primary regulators of type 1 diabetes in the non-obese diabetic mouse model.

Regulatory T cells (Tregs) are an immunosuppressive population that are identified based on the stable expression of the fate-determining transcription factor forkhead box P3 (Foxp3). Tregs can be divided into distinct subsets based on whether they developed in the thymus (tTregs) or in the periphery (pTregs). Whether there are unique functional roles that distinguish pTregs and tTregs remains largely unclear. To elucidate these functions, efforts have been made to specifically identify and modify individual Treg subsets. Deletion of the conserved non-coding sequence (CNS)1 in the Foxp3 locus leads to selective impairment of pTreg generation without disrupting tTreg generation in the C57BL/6J background. Using CRISPR-Cas9 genome editing technology, we removed the Foxp3 CNS1 region in the non-obese diabetic (NOD) mouse model of spontaneous type 1 diabetes mellitus (T1D) to determine if pTregs contribute to autoimmune regulation. Deletion of CNS1 impaired in vitro induction of Foxp3 in naive NOD CD4+ T cells, but it did not alter Tregs in most lymphoid and non-lymphoid tissues analyzed except for the large intestine lamina propria, where a small but significant decrease in RORγt+ Tregs and corresponding increase in Helios+ Tregs was observed in NOD CNS1-/- mice. CNS1 deletion also did not alter the development of T1D or glucose tolerance despite increased pancreatic insulitis in pre-diabetic female NOD CNS1-/- mice. Furthermore, the proportions of autoreactive Tregs and conventional T cells (Tconvs) within pancreatic islets were unchanged. These results suggest that pTregs dependent on the Foxp3 CNS1 region are not the dominant regulatory population controlling T1D in the NOD mouse model.