cssi/SciSciGPT-SciSciNet huggingface dataset:
Timely-Throughput Optimal Coded Computing over Cloud Networks

In modern distributed computing systems, unpredictable and unreliable infrastructures result in high variability of computing resources. Meanwhile, there is significantly increasing demand for timely and event-driven services with deadline constraints. Motivated by measurements over Amazon EC2 clusters, we consider a two-state Markov model for variability of computing speed in cloud networks. In this model, each worker can be either in a good state or a bad state in terms of the computation speed, and the transition between these states is modeled as a Markov chain which is unknown to the scheduler. We then consider a Coded Computing framework, in which the data is possibly encoded and stored at the worker nodes in order to provide robustness against nodes that may be in a bad state. With timely computation requests submitted to the system with computation deadlines, our goal is to design the optimal computation-load allocation scheme and the optimal data encoding scheme that maximize the timely computation throughput (i.e, the average number of computation tasks that are accomplished before their deadline). Our main result is the development of a dynamic computation strategy called Lagrange Estimate-and-Allocate (LEA) strategy, which achieves the optimal timely computation throughput. It is shown that compared to the static allocation strategy, LEA improves the timely computation throughput by 1.4x ~ 17.5x in various scenarios via simulations and by 1.27x ~ 6.5x in experiments over Amazon EC2 clusters.
Exponential growth of the vorticity gradient for the Euler equation on the torus

Abstract We prove that there are solutions to the Euler equation on the torus with C 1 , α vorticity and smooth except at one point such that the vorticity gradient grows in L ∞ at least exponentially as t → ∞ . The same result is shown to hold for the vorticity Hessian and smooth solutions. Our proofs use a version of a recent result by Kiselev and Sverak [6] .
Full first-principles theory of spin relaxation in group-IV materials.

We present a generally applicable parameter-free first-principles method to determine electronic spin relaxation times and apply it to the technologically important group-IV materials silicon, diamond, and graphite. We concentrate on the Elliott-Yafet mechanism, where spin relaxation is induced by momentum scattering off phonons and impurities. In silicon, we find a $\ensuremath{\sim}{T}^{\ensuremath{-}3}$ temperature dependence of the phonon-limited spin relaxation time ${T}_{1}$ and a value of 4.3 ns at room temperature, in agreement with experiments. For the phonon-dominated regime in diamond and graphite, we predict a stronger $\ensuremath{\sim}{T}^{\ensuremath{-}5}$ and $\ensuremath{\sim}{T}^{\ensuremath{-}4.5}$ dependence that limits ${T}_{1}$ (300 K) to 180 and 5.8 ns, respectively. A key aspect of this Letter is that the parameter-free nature of our approach provides a method to study the effect of any type of impurity or defect on spin transport. Furthermore we find that the spin-mix amplitude in silicon does not follow the ${E}_{g}^{\ensuremath{-}2}$ band gap dependence usually assigned to III-V semiconductors but follows a much weaker and opposite ${E}_{g}^{0.67}$ dependence. This dependence should be taken into account when constructing silicon spin transport models.
Sensing Matrix Design via Capacity Maximization for Block Compressive Sensing Applications

It is well-established in the compressive sensing (CS) literature that sensing matrices whose elements are drawn from independent random distributions exhibit enhanced reconstruction capabilities. In many CS applications, such as electromagnetic imaging, practical limitations on the measurement system prevent one from generating sensing matrices in this fashion. Although one can usually randomize the measurements to some degree, these sensing matrices do not achieve the same reconstruction performance as the aforementioned truly random sensing matrices. This paper presents a novel method, based upon capacity maximization, for designing sensing matrices with enhanced block-sparse signal reconstruction capabilities. Additionally, several numerical examples are also included to show how the proposed method enhances reconstruction performance.
Neural Models for Sequence Chunking

Many natural language understanding (NLU) tasks, such as shallow parsing (i.e., text chunking) and semantic slot filling, require the assignment of representative labels to the meaningful chunks in a sentence. Most of the current deep neural network (DNN) based methods consider these tasks as a sequence labeling problem, in which a word, rather than a chunk, is treated as the basic unit for labeling. These chunks are then inferred by the standard IOB (Inside-Outside- Beginning) labels. In this paper, we propose an alternative approach by investigating the use of DNN for sequence chunking, and propose three neural models so that each chunk can be treated as a complete unit for labeling. Experimental results show that the proposed neural sequence chunking models can achieve start-of-the-art performance on both the text chunking and slot filling tasks.
Asymptotic Linear Stability of Solitary Water Waves

We prove an asymptotic stability result for the water wave equations linearized around small solitary waves. The equations we consider govern irrotational flow of a fluid with constant density bounded below by a rigid horizontal bottom and above by a free surface under the influence of gravity neglecting surface tension. For sufficiently small amplitude waves, with waveform well-approximated by the well-known sech-squared shape of the KdV soliton, solutions of the linearized equations decay at an exponential rate in an energy norm with exponential weight translated with the wave profile. This holds for all solutions with no component in (that is, symplectically orthogonal to) the two-dimensional neutral-mode space arising from infinitesimal translational and wave-speed variation of solitary waves. We also obtain spectral stability in an unweighted energy norm.
Uniform Convergence of Gradients for Non-Convex Learning and Optimization

We investigate 1) the rate at which refined properties of the empirical risk---in particular, gradients---converge to their population counterparts in standard non-convex learning tasks, and 2) the consequences of this convergence for optimization. Our analysis follows the tradition of norm-based capacity control. We propose vector-valued Rademacher complexities as a simple, composable, and user-friendly tool to derive dimension-free uniform convergence bounds for gradients in non-convex learning problems. As an application of our techniques, we give a new analysis of batch gradient descent methods for non-convex generalized linear models and non-convex robust regression, showing how to use any algorithm that finds approximate stationary points to obtain optimal sample complexity, even when dimension is high or possibly infinite and multiple passes over the dataset are allowed. Moving to non-smooth models we show----in contrast to the smooth case---that even for a single ReLU it is not possible to obtain dimension-independent convergence rates for gradients in the worst case. On the positive side, it is still possible to obtain dimension-independent rates under a new type of distributional assumption.
Variations of Hodge structure and orbits in flag varieties

Abstract Period domains, the classifying spaces for (pure, polarized) Hodge structures, and more generally Mumford–Tate domains, arise as open G R -orbits in flag varieties G / P . We investigate Hodge-theoretic aspects of the geometry and representation theory associated with these flag varieties. In particular, we relate the Griffiths–Yukawa coupling to the variety of lines on G / P (under a minimal homogeneous embedding), construct a large class of polarized G R -orbits in G / P , and compute the associated Hodge-theoretic boundary components. An emphasis is placed throughout on adjoint flag varieties and the corresponding families of Hodge structures of levels two and four.
On the Consistency of Quick Shift

Quick Shift is a popular mode-seeking and clustering algorithm. We present finite sample statistical consistency guarantees for Quick Shift on mode and cluster recovery under mild distributional assumptions. We then apply our results to construct a consistent modal regression algorithm.
Bessel models for GSp(4): Siegel vectors of square-free level

Abstract We determine test vectors and explicit formulas for all Bessel models for those Iwahori-spherical representations of GSp 4 over a p-adic field that have non-zero vectors fixed under the Siegel congruence subgroup.
Bootstrapping for multivariate linear regression models

Abstract The multivariate linear regression model is an important tool for investigating relationships between several response variables and several predictor variables. The primary interest is in inference about the unknown regression coefficient matrix. We propose multivariate bootstrap techniques as a means for making inferences about the unknown regression coefficient matrix. These bootstrapping techniques are extensions of those developed in Freedman (1981), which are only appropriate for univariate responses. Extensions to the multivariate linear regression model are made without proof. We formalize this extension and prove its validity. A real data example and two simulated data examples which offer some finite sample verification of our theoretical results are provided.
DUALITY STRUCTURES AND DISCRETE CONFORMAL VARIATIONS OF PIECEWISE CONSTANT CURVATURE SURFACES

Abstract A piecewise constant curvature manifold is a triangulated manifold that is assigned a geometry by specifying lengths of edges and stipulating the simplex has an isometric embedding into a constant curvature background geometry (Euclidean, hyperbolic, or spherical) with the specified edge lengths. Additional geometric structure leads to a notion of discrete conformal structure, generalizing circle packings and their generalizations as studied by Thurston and others. We analyze discrete conformal variations of piecewise constant curvature 2-manifolds, giving particular attention to the variation of angles. Formulas are derived for the derivatives of angles in each background geometry, which yield formulas for the derivatives of curvatures and to curvature functionals. Finally, we provide a complete classification of possible definitions of discrete conformal structures in each of the background geometries.
Characterization of intersecting families of maximum size in PSL(2,q)

Abstract We consider the action of the 2-dimensional projective special linear group P S L ( 2 , q ) on the projective line P G ( 1 , q ) over the finite field F q , where q is an odd prime power. A subset S of P S L ( 2 , q ) is said to be an intersecting family if for any g 1 , g 2 ∈ S , there exists an element x ∈ P G ( 1 , q ) such that x g 1 = x g 2 . It is known that the maximum size of an intersecting family in P S L ( 2 , q ) is q ( q − 1 ) / 2 . We prove that all intersecting families of maximum size are cosets of point stabilizers for all odd prime powers q > 3 .
Gaussians rarely extremize adjoint Fourier restriction inequalities for paraboloids

It was proved independently by Foschi and Hundertmark, Zharnitsky that Gaussians extremize the adjoint Fourier restriction inequality for L^2 functions on the paraboloid in the two lowest-dimesional cases. Here we prove that Gaussians are critical points for the L^p to L^q adjoint Fourier restriction inequalities if and only if p=2. Also, Gaussians are critial points for the L^2 to L^r_t L^q_x Strichartz inequalities for all admissible pairs (r,q) in (1,infinity)^2.
Implicit/inverse function theorems for free noncommutative functions

Abstract We prove an implicit function theorem and an inverse function theorem for free noncommutative functions over operator spaces and on the set of nilpotent matrices. We apply these results to study dependence of the solution of the initial value problem for ODEs in noncommutative spaces on the initial data and to extremal problems with noncommutative constraints.
Kakeya configurations in Lie groups and homogeneous spaces

Abstract In this paper, we study continuous Kakeya line and needle configurations, of both the oriented and unoriented varieties, in connected Lie groups and some associated homogenous spaces. These are the analogs of Kakeya line (needle) sets (subsets of R n where it is possible to turn a line (respectively an interval of unit length) through all directions continuously , without repeating a “ direction ”). We show under some general assumptions that any such continuous Kakeya line configuration set in a connected Lie group must contain an open neighborhood of the identity, and hence must have positive Haar measure. In connected nilpotent Lie groups G , the only subspace of G that contains such an unoriented line configuration is shown to be G itself. Finally some similar questions in homogeneous spaces are addressed. These questions were motivated by work of Z. Dvir in the finite field setting.
Diameters, distortion, and eigenvalues

We study the relation between the diameter, the first positive eigenvalue of the discrete p -Laplacian, and the ? p -distortion of a finite graph. We prove an inequality relating these three quantities, and apply it to families of Cayley and Schreier graphs. We also show that the ? p -distortion of Pascal graphs, approximating the Sierpinski gasket, is bounded, which allows one to obtain estimates for the convergence to zero of the spectral gap as an application of the main result.
MUSIC for single-snapshot spectral estimation: Stability and super-resolution

Abstract This paper studies the problem of line spectral estimation in the continuum of a bounded interval with one snapshot of array measurement. The single-snapshot measurement data are turned into a Hankel data matrix which admits the Vandermonde decomposition and is suitable for the MUSIC algorithm. The MUSIC algorithm amounts to finding the null space (the noise space) of the adjoint of the Hankel matrix, forming the noise-space correlation function and identifying the s smallest local minima of the noise-space correlation as the frequency set. In the noise-free case exact reconstruction is guaranteed for any arbitrary set of frequencies as long as the number of measurement data is at least twice the number of distinct frequencies to be recovered. In the presence of noise the stability analysis shows that the perturbation of the noise-space correlation is proportional to the spectral norm of the noise matrix as long as the latter is smaller than the smallest (nonzero) singular value of the noiseless Hankel data matrix. Under the assumption that the true frequencies are separated by at least twice the Rayleigh Length (RL), the stability of the noise-space correlation is proved by means of novel discrete Ingham inequalities which provide bounds on the largest and smallest nonzero singular values of the noiseless Hankel data matrix. The numerical performance of MUSIC is tested in comparison with other algorithms such as BLO-OMP and SDP (TV-min). While BLO-OMP is the stablest algorithm for frequencies separated above 4 RL, MUSIC becomes the best performing one for frequencies separated between 2 RL and 3 RL. Also, MUSIC is more efficient than other methods. MUSIC truly shines when the frequency separation drops to 1 RL or below when all other methods fail. Indeed, the resolution length of MUSIC decreases to zero as noise decreases to zero as a power law with an exponent smaller than an upper bound established by Donoho.
Characterizing the Language of Online Communities and its Relation to Community Reception

This work investigates style and topic aspects of language in online communities: looking at both utility as an identifier of the community and correlation with community reception of content. Style is characterized using a hybrid word and part-of-speech tag n-gram language model, while topic is represented using Latent Dirichlet Allocation. Experiments with several Reddit forums show that style is a better indicator of community identity than topic, even for communities organized around specific topics. Further, there is a positive correlation between the community reception to a contribution and the style similarity to that community, but not so for topic similarity.
Optimizing age of information in wireless networks with perfect channel state information

Age of information (AoI), defined as the time elapsed since the last received update was generated, is a newly proposed metric to measure the timeliness of information updates in a network. We consider AoI minimization problem for a network with general interference constraints, and time varying channels. We propose two policies, namely, virtual-queue based policy and age-based policy when the channel state is available to the network scheduler at each time step. We prove that the virtual-queue based policy is nearly optimal, up to a constant additive factor, and the age-based policy is at-most factor 4 away from optimality. Comparison with previous work, which derived age optimal policies when channel state information is not available to the scheduler, demonstrates a 4 fold improvement in age due to the availability of channel state information.
An Expectation Conditional Maximization Approach for Gaussian Graphical Models

Bayesian graphical models are a useful tool for understanding dependence relationships among many variables, particularly in situations with external prior information. In high-dimensional settings, the space of possible graphs becomes enormous, rendering even state-of-the-art Bayesian stochastic search computationally infeasible. We propose a deterministic alternative to estimate Gaussian and Gaussian copula graphical models using an Expectation Conditional Maximization (ECM) algorithm, extending the EM approach from Bayesian variable selection to graphical model estimation. We show that the ECM approach enables fast posterior exploration under a sequence of mixture priors, and can incorporate multiple sources of information.
Autonomous Tracking of Intermittent RF Source Using a UAV Swarm

The localization of a radio-frequency transmitter with intermittent transmissions is considered via a group of unmanned aerial vehicles (UAVs) equipped with omnidirectional received signal strength sensors. This group embarks on an autonomous patrol to localize and track the target with a specified accuracy, as quickly as possible. The challenge can be decomposed into two stages: 1) estimation of the target position given previous measurements (localization) and 2) planning the future trajectory of the tracking UAVs to get lower expected localization error given current estimation (path planning). For each stage, we compare two algorithms in terms of performance and computational load. For the localization stage, we compare a detection-based extended Kalman filter (EKF) and a recursive Bayesian estimator. For the path planning stage, we compare a steepest descent posterior Cramer–Rao lower bound path planning and a bioinspired heuristic path planning. Our results show that the steepest descent path planning outperforms the bioinspired path planning by an order of magnitude, and recursive Bayesian estimator narrowly outperforms detection-based EKF.
Sequential analysis in high-dimensional multiple testing and sparse recovery

This paper studies the problem of high-dimensional multiple testing and sparse recovery from the perspective of sequential analysis. In this setting, the probability of error is a function of the dimension of the problem. A simple sequential testing procedure is proposed. We derive necessary conditions for reliable recovery in the non-sequential setting and contrast them with sufficient conditions for reliable recovery using the proposed sequential testing procedure. Applications of the main results to several commonly encountered models show that sequential testing can be exponentially more sensitive to the difference between the null and alternative distributions (in terms of the dependence on dimension), implying that subtle cases can be much more reliably determined using sequential methods.
On Generalizations of Separating and Splitting Families

Starting from the well-established notion of a separating family (or separating system) and the refinement known as a splitting family, we define and study generalizations called $n$-separating and $n$-splitting families, obtaining lower and upper bounds on their minimum sizes. For $n$-separating families our bounds are asymptotically tight within a linear factor, while for $n$-splitting families we provide partial results and open questions.
Towards an “In-the-Wild” Emotion Dataset Using a Game-Based Framework

In order to create an "in-the-wild" dataset of facial emotions with large number of balanced samples, this paper proposes a game-based data collection framework. The framework mainly include three components: a game engine, a game interface, and a data collection and evaluation module. We use a deep learning approach to build an emotion classifier as the game engine. Then a emotion web game to allow gamers to enjoy the games, while the data collection module obtains automatically-labelled emotion images. Using our game, we have collected more than 15,000 images within a month of the test run and built an emotion dataset "GaMo". To evaluate the dataset, we compared the performance of two deep learning models trained on both GaMo and CIFE. The results of our experiments show that because of being large and balanced, GaMo can be used to build a more robust emotion detector than the emotion detector trained on CIFE, which was used in the game engine to collect the face images.
Properties of Dust in Giant Elliptical Galaxies: The rôle of the Environment

The properties of dust in giant elliptical galaxies are reviewed, with particular emphasis on the influence of the environment. After normalizing by the optical luminosities, a strong anticorrelation between the masses of dust and hot gas in X-ray bright ellipticals is found. Furthermore, large-scale, regularly-shaped dust lanes (which are symmetric with respect to the galaxy nucleus) are only found to be present in ellipticals with the lowest ratios of the mass of hot gas to the blue luminosity ( M hot / L B ≲ 0.04 in solar units). This can be explained by the short time scale for the destruction of dust grains within the hot, X-ray- emitting gas compared to the formation timescale of such dust lanes in early-type galaxies. Dust within ellipticals in “loose” environments (i.e. in the field or in loose groups) is typically characterized by small values of R V ≡ A V / E B − V (i-e. small characteristic grain sizes), and distributed in dust lanes with a smooth, relaxed morphology. On the other hand, dust in ellipticals that are in or near the center of dense groups or clusters is typically much more irregularly distributed, and characterized by R V values that are close to the Galactic one. I predict that ellipticals containing “relaxed” dust lanes with typical dust masses of 10 6 − 10 7 M ⊙ do not contain hot, X-ray-emitting gas.
The van Dommelen and Shen singularity in the Prandtl equations

Abstract In 1980, van Dommelen and Shen provided a numerical simulation that predicted the spontaneous generation of a singularity in the Prandtl boundary layer equations from a smooth initial datum, for a nontrivial Euler background. In this paper we prove this numerical conjecture by rigorously establishing the finite time blowup of the boundary layer thickness.
Optimized Regression Discontinuity Designs

The increasing popularity of regression discontinuity methods for causal inference in observational studies has led to a proliferation of different estimating strategies, most of which involve firs...
Relating games of Menger, countable fan tightness, and selective separability

Abstract By adapting techniques of Arkhangel'skiĭ, Barman, and Dow, we may equate the existence of perfect-information, Markov, and tactical strategies between two interesting selection games. These results shed some light on Gruenhage's question asking whether all strategically selectively separable spaces are Markov selectively separable.
Improving Agreement and Disagreement Identification in Online Discussions with A Socially-Tuned Sentiment Lexicon

We study the problem of agreement and disagreement detection in online discussions. An isotonic Conditional Random Fields (isotonic CRF) based sequential model is proposed to make predictions on sentence- or segment-level. We automatically construct a socially-tuned lexicon that is bootstrapped from existing general-purpose sentiment lexicons to further improve the performance. We evaluate our agreement and disagreement tagging model on two disparate online discussion corpora ‐ Wikipedia Talk pages and online debates. Our model is shown to outperform the state-of-the-art approaches in both datasets. For example, the isotonic CRF model achieves F1 scores of 0.74 and 0.67 for agreement and disagreement detection, when a linear chain CRF obtains 0.58 and 0.56 for the discussions on Wikipedia Talk pages.
Dynamic Wavelength-Tunable Photodetector Using Subwavelength Graphene Field-Effect Transistors

Dynamic wavelength tunability has long been the holy grail of photodetector technology. Because of its atomic thickness and unique properties, graphene opens up new paradigms to realize this concept, but so far this has been elusive experimentally. Here we employ detailed quantum transport modeling of photocurrent in graphene field-effect transistors (including realistic electromagnetic fields) to show that wavelength tunability is possible by dynamically changing the gate voltage. We reveal the phenomena that govern the behavior of this type of device and show significant departure from the simple expectations based on vertical transitions. We find strong focusing of the electromagnetic fields at the contact edges over the same length scale as the band-bending. Both of these spatially-varying potentials lead to an enhancement of non-vertical optical transitions, which dominate even in the absence of phonon or impurity scattering. We also show that the vanishing density of states near the Dirac point leads to contact blocking and a gate-dependent modulation of the photocurrent. Several of the effects discussed here should be applicable to a broad range of one- and two-dimensional materials and devices.
Compactness of the complex Green operator

Let $\Omega\subset\C^n$ be a bounded smooth pseudoconvex domain. We show that compactness of the complex Green operator $G_{q}$ on $(0,q)$-forms on $b\Omega$ implies compactness of the $\dbar$-Neumann operator $N_{q}$ on $\Omega$. We prove that if $1 \leq q \leq n-2$ and $b\Omega$ satisfies $(P_q)$ and $(P_{n-q-1})$, then $G_{q}$ is a compact operator (and so is $G_{n-1-q}$). Our method relies on a jump type formula to represent forms on the boundary, and we prove an auxiliary compactness result for an `annulus' between two pseudoconvex domains. Our results, combined with the known characterization of compactness in the $\overline{\partial}$-Neumann problem on locally convexifiable domains, yield the corresponding characterization of compactness of the complex Green operator(s) on these domains.
Porous medium flow with both a fractional potential pressure and fractional time derivative

The authors study a porous medium equation with a right-hand side. The operator has nonlocal diffusion effects given by an inverse fractional Laplacian operator. The derivative in time is also fractional and is of Caputo-type, which takes into account “memory”. The precise model is $$D_t^\alpha u - div\left( {u - {{\left( { - \Delta } \right)}^{ - \sigma }}u} \right) = f,0 < \sigma < \frac{1}{2}.$$ This paper poses the problem over {t ∈ R+, x ∈ R n } with nonnegative initial data u(0, x) ≥ 0 as well as the right-hand side f ≥ 0. The existence for weak solutions when f, u(0, x) have exponential decay at infinity is proved. The main result is Holder continuity for such weak solutions.
The extremal functions for triangle-free graphs with excluded minors

Abstract We prove two results: 1. A graph G on at least seven vertices with a vertex v such that G − v is planar and t triangles satisfies | E ( G ) | ≤ 3 | V ( G ) | − 9 + t ∕ 3 . 2. For p = 2 , 3 , … , 9 , a triangle-free graph G on at least 2 p − 5 vertices with no K p -minor satisfies | E ( G ) | ≤ ( p − 2 ) | V ( G ) | − ( p − 2 ) 2 .
Risk Prediction of a Multiple Sclerosis Diagnosis

Multiple sclerosis (MS) is a chronic autoimmune disease that affects the central nervous system. The progression and severity of MS varies by individual, but it is generally a disabling disease. Although medications have been developed to slow the disease progression and help manage symptoms, MS research has yet to result in a cure. Early diagnosis and treatment of the disease have been shown to be effective at slowing the development of disabilities. However, early MS diagnosis is difficult because symptoms are intermittent and shared with other diseases. Thus most previous works have focused on uncovering the risk factors associated with MS and predicting the progression of disease after a diagnosis rather than disease prediction. This paper investigates the use of data available in electronic medical records (EMRs) to create a risk prediction model, thereby helping clinicians perform the difficult task of diagnosing an MS patient. Our results demonstrate that even given a limited time window of patient data, one can achieve reasonable classification with an area under the receiver operating characteristic curve of 0.724. By restricting our features to common EMR components, the developed models also generalize to other healthcare systems.
Controller synthesis for bisimulation equivalence

The objective of this paper is to solve the controller synthesis problem for bisimulation equivalence in a wide variety of scenarios including discrete-event systems, nonlinear control systems, behavioral systems, hybrid systems and many others. This will be accomplished by showing that the arguments underlying proofs of existence and the methods for the construction of controllers are extraneous to the particular class of systems being considered and thus can be presented in greater generality.
Schur–Agler and Herglotz–Agler classes of functions: Positive-kernel decompositions and transfer-function realizations

Abstract We discuss transfer-function realization for multivariable holomorphic functions mapping the unit polydisk or the right polyhalfplane into the operator analogue of either the unit disk or the right halfplane (Schur/Herglotz functions over either the unit polydisk or the right polyhalfplane) which satisfy the appropriate stronger contractive/positive real part condition for the values of these functions on commutative tuples of strict contractions/strictly accretive operators (Schur–Agler/Herglotz–Agler functions over either the unit polydisk or the right polyhalfplane). As originally shown by Agler, the first case (polydisk to disk) can be solved via unitary extensions of a partially defined isometry constructed in a canonical way from a kernel decomposition for the function (the lurking-isometry method ). We show how a geometric reformulation of the lurking-isometry method (embedding of a given isotropic subspace of a Kreĭn space into a Lagrangian subspace—the lurking-isotropic-subspace method ) can be used to handle the second two cases (polydisk to halfplane and polyhalfplane to disk), as well as the last case (polyhalfplane to halfplane) if an additional growth condition at ∞ is imposed. For the general fourth case, we show how a linear-fractional-transformation change of variable can be used to arrive at the appropriate symmetrized nonhomogeneous Bessmertnyĭ long-resolvent realization. We also indicate how this last result recovers the classical integral representation formula for scalar-valued holomorphic functions mapping the right halfplane into itself.
Mechanistic, empirical and numerical perspectives on wind-waves interaction

Abstract A mechanistic theory of wind-wave interaction must rely on verifiable assumptions and offer reproducible observable predictions. For decades, the limited mechanistic grasp on the problem has motivated RANS and LES modeling and has driven a vast empirical effort to describe the interaction in terms of wave-induced modifications of standard statistical characteristics of the wind, such as wind profile, kinetic energy balance or exchange coefficients. Because the mechanistic, empirical and numerical approaches are all concerned with the same phenomenon occurring in the same media, consistency here requires that the assumptions on which the approaches rest and the predictions they generate are compatible with each other and supported by measurements. Recent findings from theoretical analysis and field experiments advanced the understanding of the statistical and dynamic patterns of the wave-coherent flow, which is at the core of the mechanistic description of the wind-wave exchange. The progress prompts reexamining of earlier concepts, efforts and findings to evaluate their suitability, validity and usefulness. For the purpose, this survey traces the development of ideas, methods and results in the study of the wind wave generation.
Provable Estimation of the Number of Blocks in Block Models

Community detection is a fundamental unsupervised learning problem for unlabeled networks which has a broad range of applications. Many community detection algorithms assume that the number of clusters $r$ is known apriori. In this paper, we propose an approach based on semi-definite relaxations, which does not require prior knowledge of model parameters like many existing convex relaxation methods and recovers the number of clusters and the clustering matrix exactly under a broad parameter regime, with probability tending to one. On a variety of simulated and real data experiments, we show that the proposed method often outperforms state-of-the-art techniques for estimating the number of clusters.
A Reliable Uplink Control Channel Design with Complementary Sequences

In this study, we propose two schemes for uplink control channels based on non-contiguous complementary sequences (CSs) where the peak-to-average-power ratio (PAPR) of the resulting orthogonal frequency division multiplexing (OFDM) signal is always less than or equal to 3 dB. To obtain the proposed schemes, we extend Golay's concatenation and interleaving methods by considering extra upsampling and shifting parameters. The proposed schemes enable a flexible non-contiguous resource allocation in frequency, e.g., an arbitrary number of null symbols between the occupied resource blocks (RBs). The first scheme separates the PAPR minimization and the inter-cell interference minimization problems. While the former is solved by spreading the sequences in a Golay complementary pair (GCP) with the sequences in another GCP, the latter is managed by designing a set of GCPs with low cross-correlation. The second scheme generates reference symbols (RSs) and data symbols on each RB as parts of an encoded CS. Therefore, it enables coherent detection at the receiver side. The numerical results show that the proposed schemes offer significantly improved PAPR and cubic metric (CM) results in case of non-contiguous resource allocation as compared to the sequences defined in 3GPP New Radio (NR) and Zadoff-Chu (ZC) sequences.
Patent Citation Dynamics Modeling via Multi-Attention Recurrent Networks.

Modeling and forecasting forward citations to a patent is a central task for the discovery of emerging technologies and for measuring the pulse of inventive progress. Conventional methods for forecasting these forward citations cast the problem as analysis of temporal point processes which rely on the conditional intensity of previously received citations. Recent approaches model the conditional intensity as a chain of recurrent neural networks to capture memory dependency in hopes of reducing the restrictions of the parametric form of the intensity function. For the problem of patent citations, we observe that forecasting a patent's chain of citations benefits from not only the patent's history itself but also from the historical citations of assignees and inventors associated with that patent. In this paper, we propose a sequence-to-sequence model which employs an attention-of-attention mechanism to capture the dependencies of these multiple time sequences. Furthermore, the proposed model is able to forecast both the timestamp and the category of a patent's next citation. Extensive experiments on a large patent citation dataset collected from USPTO demonstrate that the proposed model outperforms state-of-the-art models at forward citation forecasting.
Convergence of recent GWAS data for suicidality with previous blood biomarkers: independent reproducibility using independent methodologies in independent cohorts.

Recent genetic studies for suicidality, including four independent GWAS, have not reproduced each other’s top implicated genes. While arguments of heterogeneity, methodology, and sample sizes can be invoked, heterogeneity is a feature, not a “bug” (as is well understood in biology and in personalized medicine). A comprehensive body of work on blood biomarkers for suicidality has previously been published by our group. We examine the issue of reproducibility using these different approaches, and provide reassuring evidence for convergence of findings, as well as some generalizable insights.
ADDIS: an adaptive discarding algorithm for online FDR control with conservative nulls

Major internet companies routinely perform tens of thousands of A/B tests each year. Such large-scale sequential experimentation has resulted in a recent spurt of new algorithms that can provably control the false discovery rate (FDR) in a fully online fashion. However, current state-of-the-art adaptive algorithms can suffer from a significant loss in power if null p-values are conservative (stochastically larger than the uniform distribution), a situation that occurs frequently in practice. In this work, we introduce a new adaptive discarding method called ADDIS that provably controls the FDR and achieves the best of both worlds: it enjoys appreciable power increase over all existing methods if nulls are conservative (the practical case), and rarely loses power if nulls are exactly uniformly distributed (the ideal case). We provide several practical insights on robust choices of tuning parameters, and extend the idea to asynchronous and offline settings as well.
Odd order obstructions to the Hasse principle on general K3 surfaces

We show that odd order transcendental elements of the Brauer group of a K3 surface can obstruct the Hasse principle. We exhibit a general K3 surface $Y$ of degree 2 over $\mathbb{Q}$ together with a three torsion Brauer class $\alpha$ that is unramified at all primes except for 3, but ramifies at all 3-adic points of $Y$. Motivated by Hodge theory, the pair $(Y, \alpha)$ is constructed from a cubic fourfold $X$ of discriminant 18 birational to a fibration into sextic del Pezzo surfaces over the projective plane. Notably, our construction does not rely on the presence of a central simple algebra representative for $\alpha$. Instead, we prove that a sufficient condition for such a Brauer class to obstruct the Hasse principle is insolubility of the fourfold $X$ (and hence the fibers) over $\mathbb{Q}_3$ and local solubility at all other primes.
Overwriting and Under-Deciding: Addressing the Roberts Court's Shrinking Docket

This article critiques the Roberts Court’s tendency to overwrite and underdecide. Despite Chief Justice Roberts’s Senate testimony asserting that the Supreme Court should take more cases, the Roberts Court has fallen below the previous recorded lows of the Rehnquist Court. Returning to Chief Justice Roberts’s goal for the Court to be more productive, this article offers two solutions: the Court should stop publishing (1) signed opinions and (2) separate opinions. At a time when government feels strained, if not broken, the Supreme Court’s reluctance to decide actual controversies—but allowing each Justice to publish their separate ideas on each decision—merits serious discussion. Should the average number of dissents (56) rival the average number of signed majority decisions (67)? And what are the opportunity costs of a Court that averages 31 more separate opinions each Term (98 total, comprised of 56 dissenting opinions and 43 concurring opinions) than decisional opinions? Ironically, Chief Justice Roberts has spoken on his Court’s tendencies to individualize the law. In a 2007 interview, Chief Justice Roberts admonished that “every justice should be worried about the Court acting as a Court and functioning as a Court, and they should all be worried, when they’re writing separately, about the effect on the Court as an institution.” Looking at the numbers, it truly is time to worry. It is also time for the Justices to return to the Court’s primary duty—the duty to decide.
Informational benefits of managerial myopia

Abstract We show that managerial myopia has an informational benefit that has been overlooked in the prior research. Compared with managers who care sufficiently about the long-term, a moderately myopic manager incentivizes the proponent of a risky long-term project to produce more information about the project, leading to more informed decision making and higher firm value.
A Blended Human-Robot Shared Control Framework to Handle Drift and Latency

Maximizing the utility of human-robot teams in disaster response and search and rescue (SAR) missions remains to be a challenging problem. This is mainly due to the dynamic, uncertain nature of the environment and the variability in cognitive performance of the human operators. By having an autonomous agent share control with the operator, we can achieve near-optimal performance by augmenting the operator's input and compensate for the factors resulting in degraded performance. What this solution does not consider though is the latency in human input and errors caused by potential hardware failures that can occur during task completion with safety, security and rescue robots. In this paper, we propose the use of blended shared control (BSC) architecture to address these issues and investigate the architecture's performance in constrained, dynamic environments with a differential drive robot that has input latency and drift caused by erroneous odometry feedback. We conduct a validation study (n=12) for our control architecture and then a user study (n=14) in 2 different environments that are unknown to both the human operator and the autonomous agent. The results demonstrate that the BSC architecture prevents collisions and enhance team performance without the need of a complete transfer of control between the human operator and autonomous agent.
Group contests with private information and the “Weakest Link”

Abstract We study weakest-link group contests with private information. We characterize all pure-strategy Bayes-Nash equilibria: various degrees of coordination are possible, from every cost type choosing a distinct effort level to all cost types coordinating on a single effort level. Such coordination may not enhance welfare. If groups are symmetric except for group size, players in the smaller group bid more aggressively than those in the larger group, but when asymmetries regard multiple dimensions, no clear-cut conclusions are evident. As an additional avenue for cooperation, we investigate cheap-talk sharing of private information among teammates, who then coordinate on the effort level most preferred by the player with the largest announced cost. A single group sharing information does better. But, with respect to the equilibrium in which all types choose a distinct effort, when players of both groups cooperate in this fashion all within-group gains are lost to increased competition between groups.
Winding of a Brownian particle around a point vortex

We derive the asymptotic winding law for a Brownian particle in the plane subjected to a tangential drift due to a point vortex. For winding around a point, the normalized winding angle converges t...
State-specific gating of salient cues by midbrain dopaminergic input to basal amygdala

Basal amygdala (BA) neurons guide associative learning via acquisition of responses to stimuli that predict salient appetitive or aversive outcomes. We examined the learning- and state-dependent dynamics of BA neurons and ventral tegmental area (VTA) dopamine (DA) axons that innervate BA (VTADA→BA) using two-photon imaging and photometry in behaving mice. BA neurons did not respond to arbitrary visual stimuli, but acquired responses to stimuli that predicted either rewards or punishments. Most VTADA→BA axons were activated by both rewards and punishments, and they acquired responses to cues predicting these outcomes during learning. Responses to cues predicting food rewards in VTADA→BA axons and BA neurons in hungry mice were strongly attenuated following satiation, while responses to cues predicting unavoidable punishments persisted or increased. Therefore, VTADA→BA axons may provide a reinforcement signal of motivational salience that invigorates adaptive behaviors by promoting learned responses to appetitive or aversive cues in distinct, intermingled sets of BA excitatory neurons.
Universal Feedback Controllers and Inverse Optimality for Nonlinear Stochastic Systems

In this paper, we develop a constructive finite time stabilizing feedback control law for stochastic dynamical systems driven by Wiener processes based on the existence of a stochastic control Lyapunov function. In addition, we present necessary and sufficient conditions for continuity of such controllers. Moreover, using stochastic control Lyapunov functions, we construct a universal inverse optimal feedback control law for nonlinear stochastic dynamical systems that possesses guaranteed gain and sector margins. An illustrative numerical example involving the control of thermoacoustic instabilities in combustion processes is presented to demonstrate the efficacy of the proposed framework.
Interference Management and Capacity Analysis for mm-Wave Picocells in Urban Canyons

Millimeter (mm) wave picocellular networks are a promising approach for delivering the 1000-fold capacity increase required to keep up with projected demand for wireless data: the available bandwidth is orders of magnitude larger than that in existing cellular systems, and the small carrier wavelength enables the realization of highly directive antenna arrays in compact form factors, thus drastically increasing spatial reuse. In this paper, we carry out an interference analysis for mm-wave picocells in an urban canyon with a dense deployment of base stations. Each base station sector can serve multiple simultaneous users, which implies that both intra- and inter-cell interference must be managed. We propose a cross-layer approach to interference management based on (i) suppressing interference at the physical layer and (ii) managing the residual interference at the medium access control layer. We provide an estimate of network capacity, and establish that 1000-fold increase relative to conventional LTE cellular networks is indeed feasible.