cssi/SciSciGPT-SciSciNet huggingface dataset:
Precise Error Analysis of Regularized $M$ -Estimators in High Dimensions

A popular approach for estimating an unknown signal $ \mathbf {x}_{0}\in \mathbb {R} ^{n}$ from noisy, linear measurements $ \mathbf {y}= \mathbf {A} \mathbf {x} _{0}+ \mathbf {z}\in \mathbb {R}^{m}$ is via solving a so called regularized $M$ -estimator: $\hat{\mathbf {x}} :=\arg \min _ \mathbf {x} \mathcal {L} (\mathbf {y}- \mathbf {A} \mathbf {x})+\lambda f(\mathbf {x})$ . Here, $ \mathcal {L}$ is a convex loss function, $f$ is a convex (typically, non-smooth) regularizer, and $\lambda > 0$ is a regularizer parameter. We analyze the squared error performance $\|\hat{\mathbf {x}} - \mathbf {x}_{0}\|_{2}^{2}$ of such estimators in the high-dimensional proportional regime where $m,n\rightarrow \infty $ and $m/n\rightarrow \delta $ . The design matrix $ \mathbf {A}$ is assumed to have entries iid Gaussian; only minimal and rather mild regularity conditions are imposed on the loss function, the regularizer, and on the noise and signal distributions. We show that the squared error converges in probability to a nontrivial limit that is given as the solution to a minimax convex-concave optimization problem on four scalar optimization variables. We identify a new summary parameter, termed the expected Moreau envelope to play a central role in the error characterization. The precise nature of the results permits an accurate performance comparison between different instances of regularized $M$ -estimators and allows to optimally tune the involved parameters (such as the regularizer parameter and the number of measurements). The key ingredient of our proof is the convex Gaussian min-max theorem which is a tight and strengthened version of a classical Gaussian comparison inequality that was proved by Gordon in 1988.
Multi-Stage Holomorphic Embedding Method for Calculating the Power-Voltage Curve

The recently proposed non-iterative load flow method, called the holomorphic embedding method, may encounter the precision issue, i.e., the nontrivial round-off errors caused by the limited digits used in computing the power-voltage (P-V) curve for a heavily loaded power system. This letter proposes a multi-stage scheme to solve such a precision issue and calculate an accurate P-V curve. The scheme is verified on the New England 39-bus power system and benchmarked with the result from the traditional continuation power flow method.
Generalized coherent states, reproducing kernels, and quantum support vector machines

The support vector machine (SVM) is a popular machine learning classification method which produces a nonlinear decision boundary in a feature space by constructing linear boundaries in a transformed Hilbert space. It is well known that these algorithms when executed on a classical computer do not scale well with the size of the feature space both in terms of data points and dimensionality. One of the most significant limitations of classical algorithms using non-linear kernels is that the kernel function has to be evaluated for all pairs of input feature vectors which themselves may be of substantially high dimension. This can lead to computationally excessive times during training and during the prediction process for a new data point. Here, we propose using both canonical and generalized coherent states to calculate specific nonlinear kernel functions. The key link will be the reproducing kernel Hilbert space (RKHS) property for SVMs that naturally arise from canonical and generalized coherent states. Specffically, we discuss the evaluation of radial kernels through a positive operator valued measure (POVM) on a quantum optical system based on canonical coherent states. A similar procedure may also lead to calculations of kernels not usually used in classical algorithms such as those arising from generalized coherent states.
Length-scale cascade and spread rate of atomizing planar liquid jets

Abstract The primary breakup of a planar liquid jet is explored via direct numerical simulation (DNS) of the incompressible Navier–Stokes equation with level-set and volume-of-fluid interface capturing methods. PDFs of the local radius of curvature and the local cross-flow displacement of the liquid-gas interface are evaluated over wide ranges of the Reynolds number (Re), Weber number (We), density ratio and viscosity ratio. The temporal cascade of liquid-structure length scales and the spread rate of the liquid jet during primary atomization are analyzed. The formation rate of different surface structures, e.g. lobes, ligaments and droplets, are compared for different flow conditions and are explained in terms of the vortex dynamics in each atomization domain that we identified recently. With increasing We, the average radius of curvature of the surface decreases, the number of small droplets increases, and the cascade and the surface area growth occur at faster rates. The spray angle is mainly affected by Re and density ratio, and is larger at higher We, at higher density ratios, and also at lower Re. The change in the spray spread rate versus Re is attributed to the angle of ligaments stretching from the jet core, which increases as Re decreases. Gas viscosity has negligible effect on both the droplet-size distribution and the spray angle. Increasing the wavelength-to-sheet-thickness ratio, however, increases the spray angle and the structure cascade rate, while decreasing the droplet size. The smallest length scale is determined more by surface tension and liquid inertia than by the liquid viscosity, while gas inertia and liquid surface tension are the key parameters in determining the spray angle.
GROUPS OF MORLEY RANK 4

We show that any simple group of Morley rank 4 must be a bad group with no proper definable subgroups of rank larger than 1. We also give an application to groups acting on sets of Morley rank 2.
An aggregation method for sparse logistic regression

L1 regularised logistic regression has now become a workhorse of data mining and bioinformatics: it is widely used for many classification problems, particularly ones with many features. However, L1 regularisation typically selects too many features and that so-called false positives are unavoidable. In this paper, we demonstrate and analyse an aggregation method for sparse logistic regression in high dimensions. This approach linearly combines the estimators from a suitable set of logistic models with different underlying sparsity patterns and can balance the predictive ability and model interpretability. Numerical performance of our proposed aggregation method is then investigated using simulation studies. We also analyse a published genome-wide case-control dataset to further evaluate the usefulness of the aggregation method in multi-locus association mapping.
A Randomized Greedy Algorithm for Near-Optimal Sensor Scheduling in Large-Scale Sensor Networks

We study the problem of scheduling sensors in a resource-constrained linear dynamical system, where the objective is to select a small subset of sensors from a large network to perform the state estimation task. We formulate this problem as the maximization of a monotone set function under a uniform matroid constraint. We propose a randomized greedy algorithm that is significantly faster than state-of-the-art methods. By introducing the notion of curvature which quantifies how close a function is to being submodular, we analyze the performance of the proposed algorithm and find a bound on the expected mean square error (MSE) of the estimator that uses the selected sensors in terms of the optimal MSE. Moreover, we derive a probabilistic bound on the curvature for the scenario where the measurements are i.i.d. random vectors with bounded $\ell_{2}$ -norm. Simulation results demonstrate efficacy of the randomized greedy algorithm in a comparison with greedy and semidefinite programming relaxation methods.
Dynamic Collaborative Filtering with Compound Poisson Factorization

Model-based collaborative filtering analyzes user-item interactions to infer latent factors that represent user preferences and item characteristics in order to predict future interactions. Most collaborative filtering algorithms assume that these latent factors are static, although it has been shown that user preferences and item perceptions drift over time. In this paper, we propose a conjugate and numerically stable dynamic matrix factorization (DCPF) based on compound Poisson matrix factorization that models the smoothly drifting latent factors using Gamma-Markov chains. We propose a numerically stable Gamma chain construction, and then present a stochastic variational inference approach to estimate the parameters of our model. We apply our model to time-stamped ratings data sets: Netflix, Yelp, and this http URL, where DCPF achieves a higher predictive accuracy than state-of-the-art static and dynamic factorization models.
Convolution of Probability Measures on Lie Groups and Homogenous Spaces

We study (weakly) continuous convolution semigroups of probability measures on a Lie group G or a homogeneous space G/K, where K is a compact subgroup. We show that such a convolution semigroup is the convolution product of its initial measure and a continuous convolution semigroup with initial measure at the identity of G or the origin of G/K. We will also obtain an extension of Dani-McCrudden’s result on embedding an infinitely divisible probability measure in a continuous convolution semigroup on a Lie group to a homogeneous space.
Anisotropic mesh adaptation for image representation

Triangular meshes have gained much interest in image representation and have been widely used in image processing. This paper introduces a framework of anisotropic mesh adaptation (AMA) methods to image representation and proposes a GPRAMA method that is based on AMA and greedy-point removal (GPR) scheme. Different than many other methods that triangulate sample points to form the mesh, the AMA methods start directly with a triangular mesh and then adapt the mesh based on a user-defined metric tensor to represent the image. The AMA methods have clear mathematical framework and provide flexibility for both image representation and image reconstruction. A mesh patching technique is developed for the implementation of the GPRAMA method, which leads to an improved version of the popular GPRFS-ED method. The GPRAMA method can achieve better quality than the GPRFS-ED method but with lower computational cost.
A Koopman Operator Approach for Computing and Balancing Gramians for Discrete Time Nonlinear Systems

In this paper, we consider the problem of quantifying controllability and observability of a nonlinear discrete time dynamical system. We introduce the Koopman operator as a canonical representation of the system and apply a lifting technique to compute gramians in the space of full-state observables. We illustrate the properties of these gramians and identify several relationships with canonical results on local controllability and observability. Once defined, we show that these gramians can be balanced through a change of coordinates on the observables space, which in turn allows for direct application of balanced truncation. Throughout the paper, we highlight the aspects of our approach with an example nonlinear system.
Optimization of a finite frequency-hopping ad hoc network in Nakagami fading

This paper considers the analysis and optimization of a frequency-hopping ad hoc network with a finite number of mobiles and finite spatial extent. The mobiles communicate using coded continuous-phase frequency-shift keying (CPFSK) modulation. The performance of the system is a function of the number of hopping channels, the rate of the error-correction code, and the modulation index used by the CPFSK modulation. For a given channel model and density of mobiles, these parameters are jointly optimized by maximizing the (modulation-constrained) transmission capacity, which is a measure of the spatial spectral efficiency of the system. The transmission capacity of the finite network is found by using a recent expression for the spatially averaged outage probability in the presence of Nakagami fading, which is found in closed form in the absence of shadowing and can be solved using numerical integration in the presence of shadowing.
Classes on the moduli space of Riemann surfaces through a noncommutative Batalin–Vilkovisky formalism

Abstract Using the machinery of the Batalin–Vilkovisky formalism, we construct cohomology classes on compactifications of the moduli space of Riemann surfaces from the data of a contractible differential graded Frobenius algebra. We describe how evaluating these cohomology classes upon a well-known construction producing homology classes in the moduli space can be expressed in terms of the Feynman diagram expansion of some functional integral. By computing these integrals for specific examples, we are able to demonstrate that this construction produces families of nontrivial classes.
The stability of the first Neumann Laplacian eigenfunction under domain deformations and applications

Abstract The robustness of manifold learning methods is often predicated on the stability of the Neumann Laplacian eigenfunctions under deformations of the assumed underlying domain. Indeed, many manifold learning methods are based on approximating the Neumann Laplacian eigenfunctions on a manifold that is assumed to underlie data, which is viewed through a source of distortion. In this paper, we study the stability of the first Neumann Laplacian eigenfunction with respect to deformations of a domain by a diffeomorphism. In particular, we are interested in the stability of the first eigenfunction on tall thin domains where, intuitively, the first Neumann Laplacian eigenfunction should only depend on the length along the domain. We prove a rigorous version of this statement and apply it to a machine learning problem in geophysical interpretation.
Varieties for modules of finite dimensional Hopf algebras

We survey variety theory for modules of finite dimensional Hopf algebras, recalling some definitions and basic properties of support and rank varieties where they are known. We focus specifically on properties known for classes of examples such as finite group algebras and finite group schemes. We list open questions about tensor products of modules and projectivity, where varieties may play a role in finding answers.
Linear independence of time frequency translates for special configurations

We prove that for any 4 points in the plane that belong to 2 parallel lines, there is no linear dependence between the associated time-frequency translates of any nontrivial Schwartz function. If mild Diophantine properties are satisfied, we also prove linear independence in the category of $L^2(\R)$ functions
Brain and cognitive reserve: Translation via network control theory.

Abstract Traditional approaches to understanding the brain’s resilience to neuropathology have identified neurophysiological variables, often described as brain or cognitive “reserve,” associated with better outcomes. However, mechanisms of function and resilience in large-scale brain networks remain poorly understood. Dynamic network theory may provide a basis for substantive advances in understanding functional resilience in the human brain. In this perspective, we describe recent theoretical approaches from network control theory as a framework for investigating network level mechanisms underlying cognitive function and the dynamics of neuroplasticity in the human brain. We describe the theoretical opportunities offered by the application of network control theory at the level of the human connectome to understand cognitive resilience and inform translational intervention.
Style Transfer from Non-Parallel Text by Cross-Alignment

This paper focuses on style transfer on the basis of non-parallel text. This is an instance of a broad family of problems including machine translation, decipherment, and sentiment modification. The key challenge is to separate the content from other aspects such as style. We assume a shared latent content distribution across different text corpora, and propose a method that leverages refined alignment of latent representations to perform style transfer. The transferred sentences from one style should match example sentences from the other style as a population. We demonstrate the effectiveness of this cross-alignment method on three tasks: sentiment modification, decipherment of word substitution ciphers, and recovery of word order.
VARIETIES OF ELEMENTARY SUBALGEBRAS OF MAXIMAL DIMENSION FOR MODULAR LIE ALGEBRAS

Motivated by questions in modular representation theory, Carlson, Friedlander, and the first author introduced the varieties \(\mathbb E(r, \mathfrak g)\) of r-dimensional abelian p-nilpotent subalgebras of a p-restricted Lie algebra \(\mathfrak g\) in [8]. In this paper, we identify the varieties \(\mathbb E(r, \mathfrak g)\) for a reductive restricted Lie algebra \(\mathfrak g\) and r the maximal dimension of an abelian p-nilpotent subalgebra of \(\mathfrak g\).
Automated game design learning

While general game playing is an active field of research, the learning of game design has tended to be either a secondary goal of such research or it has been solely the domain of humans. We propose a field of research. Automated Game Design Learning (AGDL), with the direct purpose of learning game designs directly through interaction with games in the mode that most people experience games: via play. We detail existing work that touches the edges of this field, describe current successful projects in AGDL and the theoretical foundations that enable them, point to promising apphcations enabled by AGDL, and discuss next steps for this exciting area of study. The key moves of AGDL are to use game programs as the ultimate source of truth about their own design, and to make these design properties available to other systems and avenues of inquiry.
Ensemble-based estimates of eigenvector error for empirical covariance matrices

Covariance matrices are fundamental to the analysis and forecast of economic, physical and biological systems. Although the eigenvalues $\{\lambda_i\}$ and eigenvectors $\{{\bf u}_i\}$ of a covariance matrix are central to such endeavors, in practice one must inevitably approximate the covariance matrix based on data with finite sample size $n$ to obtain empirical eigenvalues $\{\tilde{\lambda}_i\}$ and eigenvectors $\{\tilde{\bf u}_i\}$, and therefore understanding the error so introduced is of central importance. We analyze eigenvector error $\|{\bf u}_i - \tilde{\bf u}_i \|^2$ while leveraging the assumption that the true covariance matrix having size $p$ is drawn from a matrix ensemble with known spectral properties---particularly, we assume the distribution of population eigenvalues weakly converges as $p\to\infty$ to a spectral density $\rho(\lambda)$ and that the spacing between population eigenvalues is similar to that for the Gaussian orthogonal ensemble. Our approach complements previous analyses of eigenvector error that require the full set of eigenvalues to be known, which can be computationally infeasible when $p$ is large. To provide a scalable approach for uncertainty quantification of eigenvector error, we consider a fixed eigenvalue $\lambda$ and approximate the distribution of the expected square error $r= \mathbb{E}\left[\| {\bf u}_i - \tilde{\bf u}_i \|^2\right]$ across the matrix ensemble for all ${\bf u}_i$ associated with $\lambda_i=\lambda$. We find, for example, that for sufficiently large matrix size $p$ and sample size $n>p$, the probability density of $r$ scales as $1/nr^2$. This power-law scaling implies that eigenvector error is extremely heterogeneous---even if $r$ is very small for most eigenvectors, it can be large for others with non-negligible probability. We support this and further results with numerical experiments.
Repairing multiple failures for scalar MDS codes

In distributed storage, erasure codes — like Reed-Solomon Codes — are often employed to provide reliability. In this setting, it is desirable to be able to repair one or more failed nodes while minimizing the repair bandwidth. In this work, motivated by Reed-Solomon codes, we study the problem of repairing multiple failed nodes in a scalar MDS code. We extend the framework of (Guruswami and Wootters, 2017) to give a framework for constructing repair schemes for multiple failures in general scalar MDS codes, in the centralized repair model. We then specialize our framework to Reed-Solomon codes, and extend and improve upon recent results of (Dau et al., 2017).
Counting the electrons in a multiphoton ionization by elastic scattering of microwaves

Multiphoton ionization (MPI) is a fundamental first step in high-energy laser-matter interaction and is important for understanding the mechanism of plasma formation. With the discovery of MPI more than 50 years ago, there were numerous attempts to determine the basic physical constants of this process in direct experiments, namely photoionization rates and cross-sections of the MPI; however, no reliable data was available until now, and the spread in the literature values often reaches 2–3 orders of magnitude. This is due to the inability to conduct absolute measurements of plasma electron numbers generated by MPI, which leads to uncertainties and, sometimes, contradictions between MPI cross-section values utilized by different researchers across the field. Here, we report the first direct measurement of absolute plasma electron numbers generated at MPI of air, and subsequently we precisely determine the ionization rate and cross-section of eight-photon ionization of oxygen molecule by 800 nm photons σ8 = (3.3 ± 0.3)×10−130 W−8m16s−1. The method, based on the absolute measurement of the electron number created by MPI using elastic scattering of microwaves off the plasma volume in Rayleigh regime, establishes a general approach to directly measure and tabulate basic constants of the MPI process for various gases and photon energies.
Practical Low-Dimensional Halfspace Range Space Sampling.

We develop, analyze, implement, and compare new algorithms for creating $\varepsilon$-samples of range spaces defined by halfspaces which have size sub-quadratic in $1/\varepsilon$, and have runtime linear in the input size and near-quadratic in $1/\varepsilon$. The key to our solution is an efficient construction of partition trees. Despite not requiring any techniques developed after the early 1990s, apparently such a result was not ever explicitly described. We demonstrate that our implementations, including new implementations of several variants of partition trees, do indeed run in time linear in the input, appear to run linear in output size, and observe smaller error for the same size sample compared to the ubiquitous random sample (which requires size quadratic in $1/\varepsilon$). This result has direct applications in speeding up discrepancy evaluation, approximate range counting, and spatial anomaly detection.
Digitally delicate primes

Abstract Tao has shown that in any fixed base, a positive proportion of prime numbers cannot have any digit changed and remain prime. In other words, most primes are “digitally delicate”. We strengthen this result in a manner suggested by Tao: A positive proportion of primes become composite under any change of a single digit and any insertion of a fixed number of arbitrary digits at the beginning or end.
Improving 6D Pose Estimation of Objects in Clutter Via Physics-Aware Monte Carlo Tree Search

This work proposes a process for efficiently searching over combinations of individual object 6D pose hypotheses in cluttered scenes, especially in cases involving occlusions and objects resting on each other. The initial set of candidate object poses is generated from state-of-the-art object detection and global point cloud registration techniques. The best scored pose per object by using these techniques may not be accurate due to overlaps and occlusions. Nevertheless, experimental indications provided in this work show that object poses with lower ranks may be closer to the real poses than ones with high ranks according to registration techniques. This motivates a global optimization process for improving these poses by taking into account scene-level physical interactions between objects. It also implies that the Cartesian product of candidate poses for interacting objects must be searched so as to identify the best scene-level hypothesis. To perform the search efficiently, the candidate poses for each object are clustered so as to reduce their number but still keep a sufficient diversity. Then, searching over the combinations of candidate object poses is performed through a Monte Carlo Tree Search (MCTS) process that uses the similarity between the observed depth image of the scene and a rendering of the scene given the hypothesized pose as a score that guides the search procedure. MCTS handles in a principled way the tradeoff between fine-tuning the most promising poses and exploring new ones, by using the Upper Confidence Bound (UCB) technique. Experimental results indicate that this process is able to quickly identify in cluttered scenes physically-consistent object poses that are significantly closer to ground truth compared to poses found by point cloud registration methods.
Isometric embeddings of polyhedra into Euclidean space

In this paper we consider piecewise linear (pl) isometric embeddings of Euclidean polyhedra into Euclidean space. A Euclidean polyhedron is just a metric space which admits a triangulation such that each n-dimensional simplex of is affinely isometric to a simplex in &#x1d53c;n. We prove that any 1-Lipschitz map from an n-dimensional Euclidean polyhedron into &#x1d53c;3n is ϵ-close to a pl isometric embedding for any ϵ > 0. If we remove the condition that the map be pl, then any 1-Lipschitz map into &#x1d53c;2n + 1 can be approximated by a (continuous) isometric embedding. These results are extended to isometric embedding theorems of spherical and hyperbolic polyhedra into Euclidean space by the use of the Nash–Kuiper C1 isometric embedding theorem ([9] and [13]).
Building near-real-time processing pipelines with the spark-MPI platform

Advances in detectors and computational technologies provide new opportunities for applied research and the fundamental sciences. Concurrently, dramatic increases in the three V’s (Volume, Velocity, and Variety) of experimental data and the scale of computational tasks produced the demand for new real-time processing systems at experimental facilities. Recently, this demand was addressed by the Spark-MPI approach connecting the Spark data-intensive platform with the MPI high-performance framework. In contrast with existing data management and analytics systems, Spark introduced a new middleware based on resilient distributed datasets (RDDs), which decoupled various data sources from high-level processing algorithms. The RDD middleware significantly advanced the scope of data-intensive applications, spreading from SQL queries to machine learning to graph processing. Spark-MPI further extended the Spark ecosystem with the MPI applications using the Process Management Interface. The paper explores this integrated platform within the context of online ptychographic and tomographic reconstruction pipelines.
Direct probes of neutrino mass

Abstract The discovery of neutrino oscillations has shown that neutrinos, in contradiction to a prediction of the minimal standard model, have mass. Oscillations do not yield a value for the mass, but do set a lower limit of 0.02 eV on the average of the 3 known eigenmasses. Moreover, they make it possible to determine or limit all 3 masses from measurements of electron-flavor neutrinos in beta decay. The present upper limit from such measurements is 2 eV. We review the status of laboratory work toward closing the remaining window between 2 and 0.02 eV, and measuring the mass.
Torsion in kernels of induced maps on divisor class groups

We investigate torsion elements in the kernel of the map on divisor class groups of excellent local normal domains A and A/I, for an ideal I of finite projective dimension. The motivation for this work is a result of Griffith–Weston which applies when I is principal.
Two partition functions with congruences modulo 3, 5, 7, and 13

We introduce two new integer partition functions, both of which are the number of partition quadruples of n with certain size restrictions. We prove both functions satisfy Ramanujan-type congruences modulo 3, 5, 7, and 13 by use of generalized Lambert series identities and q-series techniques.
Robust routing in interdependent networks

We consider a model of two interdependent networks, where every node in one network depends on one or more supply nodes in the other network and a node fails if it loses all of its supply nodes. We develop algorithms to compute the failure probability of a path, and obtain the most reliable path between a pair of nodes in a network, under the condition that each supply node fails independently with a given probability. Our work generalizes the classical shared risk group model, by considering multiple risks associated with a node and letting a node fail if all the risks occur. Moreover, we study the diverse routing problem by considering two paths between a pair of nodes. We define two paths to be d-failure resilient if at least one path survives after removing d or fewer supply nodes, which generalizes the concept of disjoint paths in a single network, and risk-disjoint paths in a classical shared risk group model. We compute the probability that both paths fail, and develop algorithms to compute the most reliable pair of paths.
Modeling granular material segregation using a combined finite element method and advection–diffusion–segregation equation model

Abstract A two-dimensional, transient, multi-scale modeling approach is presented for predicting the magnitude and rate of percolation segregation for binary mixtures of granular material in a rotating drum and conical hopper. The model utilizes finite element method simulations to determine the bulk-level granular velocity field, which is then combined with particle-level diffusion and segregation correlations using the advection-diffusion-segregation equation. The utility of this modeling approach is demonstrated by predicting segregation patterns in a rotating drum and during the discharge of conical hoppers with different geometries. The model exhibits good quantitative accuracy in predicting DEM and experimental segregation data reported in the literature for cohesionless granular materials. Moreover, since the numerical approach does not directly model individual particles, it is expected to scale well to systems of industrial scale.
An analytic model for eddy current separation

Abstract Eddy current separation (ECS) is a process used throughout the scrap recycling industry for separating nonferrous metals from nonmetallic fluff. To date, however, the physical theory of ECS has generally been limited to empirical approximations and numerical simulations. We therefore introduce a simplified, two-dimensional model for ECS based on a cylindrical array of permanent, alternating magnets. The result is a Fourier-series expansion that describes the total magnetic field profile over all space. If the magnets are then rotated with constant angular velocity, the magnetic fields vary as a discrete series of sinusoidal harmonics, thereby inducing electrical eddy currents in nearby conductive particles. Force and torque calculations can then be used to predict the corresponding kinematic trajectories.
Electronic Metamaterials with Tunable Second-order Optical Nonlinearities.

The ability to engineer metamaterials with tunable nonlinear optical properties is crucial for nonlinear optics. Traditionally, metals have been employed to enhance nonlinear optical interactions through field localization. Here, inspired by the electronic properties of materials, we introduce and demonstrate experimentally an asymmetric metal-semiconductor-metal (MSM) metamaterial that exhibits a large and electronically tunable effective second-order optical susceptibility (χ(2)). The induced χ(2) originates from the interaction between the third-order optical susceptibility of the semiconductor (χ(3)) with the engineered internal electric field resulting from the two metals possessing dissimilar work function at its interfaces. We demonstrate a five times larger second-harmonic intensity from the MSM metamaterial, compared to contributions from its constituents with electrically tunable nonlinear coefficient ranging from 2.8 to 15.6 pm/V. Spatial patterning of one of the metals on the semiconductor demonstrates tunable nonlinear diffraction, paving the way for all-optical spatial signal processing with space-invariant and -variant nonlinear impulse response.
A note on the almost-one-half holomorphic pinching

Abstract Motivated by a previous work by Zheng and the second-named author, we study pinching constants of compact Kahler manifolds with positive holomorphic sectional curvature. In particular, we prove a gap theorem on Kahler manifolds with almost-one-half pinched holomophic sectional curvature. The proof is motivated by the work of Petersen and Tao on Riemannian manifolds with almost-quarter-pinched sectional curvature.
On a class number formula for real quadratic number fields

For an even Dirichlet character psi, we obtain a formula for L(1,psi) in terms of a sum of Dirichlet L-series evaluated at s=2 and s=3 and a rapidly convergent numerical series involving the central binomial coefficients. We then derive a class number formula for real quadratic number fields by taking L(s,psi) to be the quadratic L-series associated with these fields.
The spectral norm of random inner-product kernel matrices

We study an “inner-product kernel” random matrix model, whose empirical spectral distribution was shown by Xiuyuan Cheng and Amit Singer to converge to a deterministic measure in the large n and p limit. We provide an interpretation of this limit measure as the additive free convolution of a semicircle law and a Marchenko–Pastur law. By comparing the tracial moments of this matrix to an additive deformation of a Wigner matrix, we establish that for odd kernel functions, the spectral norm of this matrix converges almost surely to the edge of the limiting spectrum. Our study is motivated by the analysis of a covariance thresholding procedure for the statistical detection and estimation of sparse principal components, and our results characterize the limit of the largest eigenvalue of the thresholded sample covariance matrix in the null setting.
Skew Clifford algebras

Abstract We introduce a generalization, called a skew Clifford algebra , of a Clifford algebra, and relate these new algebras to the notion of graded skew Clifford algebra that was defined in 2010. In particular, we examine homogenizations of skew Clifford algebras, and determine which skew Clifford algebras can be homogenized to create Artin-Schelter regular algebras. Just as (classical) Clifford algebras are the Poincare-Birkhoff-Witt (PBW) deformations of exterior algebras , skew Clifford algebras are the Z 2 -graded PBW deformations of quantum exterior algebras. We also determine the possible dimensions of skew Clifford algebras and provide several examples.
Decoupled limbs yield differentiable trajectory outcomes through intermittent contact in locomotion and manipulation

When limbs are decoupled, we find that trajectory outcomes in mechanical systems subject to unilateral constraints vary differentiably with respect to initial conditions, even as the contact mode sequence varies.
Statistical Learning for DC Optimal Power Flow

The optimal power flow problem plays an important role in the market clearing and operation of electric power systems. However, with increasing uncertainty from renewable energy operation, the optimal operating point of the system changes more significantly in real-time. In this paper, we aim at developing control policies that are able to track the optimal set-point with high probability. The approach is based on the observation that the OPF solution corresponding to a certain uncertainty realization is a basic feasible solution, which provides an affine control policy. The optimality of this basis policy is restricted to uncertainty realizations that share the same set of active constraints. We propose an ensemble control policy that combines several basis policies to improve performance. Although the number of possible bases is exponential in the size of the system, we show that only a few of them are relevant to system operation. We adopt a statistical learning approach to learn these important bases, and provide theoretical results that validate our observations. For most systems, we observe that efficient ensemble policies constructed using as few as ten bases, are able to obtain optimal solutions with high probability.
Online Alternating Direction Method

Online optimization has emerged as powerful tool in large scale optimization. In this paper, we introduce efficient online algorithms based on the alternating directions method (ADM). We introduce a new proof technique for ADM in the batch setting, which yields the O(1/T) convergence rate of ADM and forms the basis of regret analysis in the online setting. We consider two scenarios in the online setting, based on whether the solution needs to lie in the feasible set or not. In both settings, we establish regret bounds for both the objective function as well as constraint violation for general and strongly convex functions. Preliminary results are presented to illustrate the performance of the proposed algorithms.
Algorithmic constructions of relative train track maps and CTs

Every rotationless outer automorphism of a finite rank free group is represented by a particularly useful relative train track map called a CT. The main result of this paper is that the constructions of CTs can be made algorithmic. A key step in our argument is proving that it is algorithmic to check if an inclusion of one invariant free factor system in another is reduced. Several applications are included, as well as algorithmic constructions for relative train track maps in the general case.
Multiagent Soft Q-Learning

Policy gradient methods are often applied to reinforcement learning in continuous multiagent games. These methods perform local search in the joint-action space, and as we show, they are susceptable to a game-theoretic pathology known as relative overgeneralization. To resolve this issue, we propose Multiagent Soft Q-learning, which can be seen as the analogue of applying Q-learning to continuous controls. We compare our method to MADDPG, a state-of-the-art approach, and show that our method achieves better coordination in multiagent cooperative tasks, converging to better local optima in the joint action space.
Commensurability, jamming, and dynamics for vortices in funnel geometries

With advances in fabrication technologies it is now possible to create precisely controlled geometries and pinning landscapes for vortex matter in type-II superconductors. Here we use numerical simulations to examine vortex states and dynamics in periodic funnel geometries where a drive is applied in the easy-flow direction. We show that this system exhibits a number of different commensurability effects when the vortex configurations match to both the periodicity of the array and the geometry of the funnels. The vortex configurations in this system are generally different from those observed for single isolated triangular superconducting samples due to the coupling of vortices in adjacent funnels. At certain matching fields, peaks in the critical current are absent due to the particular vortex configurations that occur at these fields. We find that the overall depinning force increases with increasing vortex density as a result of the enhanced vortex-vortex interactions caused by a crowding effect at the funnel tips. When a system becomes less mobile as a result of increased particle interactions, it is said to exhibit a jamming behavior. Under an applied drive we observe a series of elastic and plastic vortex flow phases which produce pronounced features such as jumps or dips in the transport curves. In all of the flow phases, only one vortex can pass through the funnel tip at a time due to the vortex-vortex repulsion forces. As a consequence of this constraint, we observe the remarkable result that the sum of the vortex velocities at a fixed drive remains nearly constant with increasing magnetic field $B$ rather than increasing linearly. This result is similar to the behavior of sand in an hourglass. We also show how noise fluctuations can be used to distinguish the different flow phases. Our results should be readily generalizable to other systems of particles flowing in periodic funnel geometries, such as colloids or Wigner crystals.
DA-RNN: Semantic Mapping with Data Associated Recurrent Neural Networks

3D scene understanding is important for robots to interact with the 3D world in a meaningful way. Most previous works on 3D scene understanding focus on recognizing geometrical or semantic properties of the scene independently. In this work, we introduce Data Associated Recurrent Neural Networks (DA-RNNs), a novel framework for joint 3D scene mapping and semantic labeling. DA-RNNs use a new recurrent neural network architecture for semantic labeling on RGB-D videos. The output of the network is integrated with mapping techniques such as KinectFusion in order to inject semantic information into the reconstructed 3D scene. Experiments conducted on a real world dataset and a synthetic dataset with RGB-D videos demonstrate the ability of our method in semantic 3D scene mapping.
Design of black phosphorus 2D nanomechanical resonators by exploiting the intrinsic mechanical anisotropy

Black phosphorus (P), a layered material that can be isolated down to individual 2D crystalline sheets, exhibits highly anisotropic mechanical properties due to its corrugated crystal structure in each atomic layer, which are intriguing for two-dimensional (2D) nanomechanical devices. Here we lay the framework for describing the mechanical resonant responses in free-standing black P structures, by using a combination of analytical modeling and numerical simulation. We find that thicker devices (>100 nm) operating in the elastic plate regime exhibit pronounced signatures of mechanical anisotropy, and can lead to new multimode resonant characteristics in terms of mode sequences, shapes, and orientational preferences that are unavailable in nanomechanical resonators made of isotropic materials. In addition, through investigating devices with different geometries, we identify the resonant responses' dependence on crystal orientation in asymmetric devices, and evaluate the effects from the degree of anisotropy. The results suggest a pathway towards harnessing the mechanical anisotropy in black P for building novel 2D nanomechanical devices and resonant transducers with engineerable multimode functions.
Comparison of canonical and microcanonical definitions of entropy

Abstract For more than 100 years, one of the central concepts in statistical mechanics has been the microcanonical ensemble, which provides a way of calculating the thermodynamic entropy for a specified energy. A controversy has recently emerged between two distinct definitions of the entropy based on the microcanonical ensemble: (1) The Boltzmann entropy, defined by the density of states at a specified energy, and (2) The Gibbs entropy, defined by the sum or integral of the density of states below a specified energy. A critical difference between the consequences of these definitions pertains to the concept of negative temperatures, which by the Gibbs definition cannot exist. In this paper, we call into question the fundamental assumption that the microcanonical ensemble should be used to define the entropy. We base our analysis on a recently proposed canonical definition of the entropy as a function of energy. We investigate the predictions of the Boltzmann, Gibbs, and canonical definitions for a variety of classical and quantum models. Our results support the validity of the concept of negative temperature, but not for all models with a decreasing density of states. We find that only the canonical entropy consistently predicts the correct thermodynamic properties, while microcanonical definitions of entropy, including those of Boltzmann and Gibbs, are correct only for a limited set of models. For models which exhibit a first-order phase transition, we show that the use of the thermodynamic limit, as usually interpreted, can conceal the essential physics.
Hofer geometry and cotangent fibers

For a class of Riemannian manifolds that include products of arbitrary compact manifolds with manifolds of nonpositive sectional curvature on the one hand, or with certain positivecurvature examples such as spheres of dimension at least 3 and compact semisimple Lie groups on the other, we show that the Hamiltonian diffeomorphism group of the cotangent bundle contains as subgroups infinite-dimensional normed vector spaces that are bi-Lipschitz embedded with respect to Hofer’s metric; moreover these subgroups can be taken to consist of diffeomorphisms supported in an arbitrary neighborhood of the zero section. In fact, the orbit of a fiber of the cotangent bundle with respect to any of these subgroups is quasi-isometrically embedded with respect to the induced Hofer metric on the orbit of the fiber under the whole group. The diffeomorphisms in these subgroups are obtained from reparametrizations of the geodesic flow. Our proofs involve a study of the Hamiltonian-perturbed Floer complex of a pair of cotangent fibers (or, more generally, of a conormal bundle together with a cotangent fiber). Although the homology of this complex vanishes, an analysis of its boundary depth yields the lower bounds on the Lagrangian Hofer metric required for our main results.
Hyperbolicity of the complex of free factors

Abstract We develop the geometry of folding paths in Outer space and, as an application, prove that the complex of free factors of a free group of finite rank is hyperbolic.
A cospectral family of graphs for the normalized Laplacian found by toggling

Abstract We give a construction of a family of (weighted) graphs that are pairwise cospectral with respect to the normalized Laplacian matrix, or equivalently, probability transition matrix. This construction can be used to form pairs of cospectral graphs with different number of edges, including situations where one graph is a subgraph of the other. The method used to demonstrate cospectrality is by showing the characteristic polynomials are equal.
A study on smart online frame forging attacks against video surveillance system

Video Surveillance Systems (VSS) have become an essential infrastructural element of smart cities by increasing public safety and countering criminal activities. A VSS is normally deployed in a secure network to prevent the access from unauthorized personnel. Compared to traditional systems that continuously record video regardless of the actions in the frame, a smart VSS has the capability of capturing video data upon motion detection or object detection, and then extracts essential information and send to users. This increasing design complexity of the surveillance system, however, also introduces new security vulnerabilities. In this work, a smart, real-time frame duplication attack is investigated. We show the feasibility of forging the video streams in real-time as the camera’s surroundings change. The generated frames are compared constantly and instantly to identify changes in the pixel values that could represent motion detection or changes in light intensities outdoors. An attacker (intruder) can remotely trigger the replay of some previously duplicated video streams manually or automatically, via a special quick response (QR) code or when the face of an intruder appear in the camera field of view. A detection technique is proposed by leveraging the real-time electrical network frequency (ENF) reference database to match with the power grid frequency.