cssi/SciSciGPT-SciSciNet huggingface dataset:
Equivariant fixed-point theory

We reexamine equivariant generalizations of the Lefschetz number and Reidemeister trace using categorical traces. This gives simple, conceptual descriptions of the invariants as well as direct comparisons to previously defined generalizations. These comparisons are illuminating applications of the additivity and multiplicativity of the categorical trace.
The Geometry of Points on Quantum Projectivizations

Abstract Suppose S is an affine, noetherian scheme, X is a separated, noetherian S-scheme, E is a coherent O X-bimodule, and I ⊂ T( E ) is a graded ideal. We study the geometry of the functor Γn of flat families of truncated B = T( E )/ I -point modules of length n + 1. We then use the results of our study to show that if Proj B is a quantum ruled surface, the point modules over B are parameterized by the closed points of P X2( E ). When X = P 1, we construct, for any B -point module, a graded O X − B -bimodule resolution.
Coresets for Scalable Bayesian Logistic Regression

The use of Bayesian methods in large-scale data settings is attractive because of the rich hierarchical models, uncertainty quantification, and prior specification they provide. Standard Bayesian inference algorithms are computationally expensive, however, making their direct application to large datasets difficult or infeasible. Recent work on scaling Bayesian inference has focused on modifying the underlying algorithms to, for example, use only a random data subsample at each iteration. We leverage the insight that data is often redundant to instead obtain a weighted subset of the data (called a coreset) that is much smaller than the original dataset. We can then use this small coreset in any number of existing posterior inference algorithms without modification. In this paper, we develop an efficient coreset construction algorithm for Bayesian logistic regression models. We provide theoretical guarantees on the size and approximation quality of the coreset -- both for fixed, known datasets, and in expectation for a wide class of data generative models. Crucially, the proposed approach also permits efficient construction of the coreset in both streaming and parallel settings, with minimal additional effort. We demonstrate the efficacy of our approach on a number of synthetic and real-world datasets, and find that, in practice, the size of the coreset is independent of the original dataset size. Furthermore, constructing the coreset takes a negligible amount of time compared to that required to run MCMC on it.
Enhanced Cellular Coverage and Throughput Using Rateless Codes

Rateless codes have been shown to provide robust error correction over a wide range of binary and noisy channels. Using a stochastic geometry model, this paper studies the performance of rateless codes in the cellular downlink and compares it with the performance of fixed-rate codes. For the case of Rayleigh fading, an accurate approximation is proposed for the distribution of the packet transmission time of $K$ -bit information packets using rateless codes. The two types of channel coding schemes are compared by evaluating the typical user and per-user success probability and the rate. Based on both the analytical results and simulations, the paper shows that rateless coding provides a significant throughput gain relative to fixed-rate coding. Moreover, the benefit is not restricted to the typical user but applies to all users in the cellular network.
A moving target approach for identifying malicious sensors in control systems

In this paper, we consider the problem of attack identification in cyber-physical systems (CPS). Attack identification is often critical for the recovery and performance of a CPS that is targeted by malicious entities, allowing defenders to construct algorithms which bypass harmful nodes. Previous work has characterized limitations in the perfect identification of adversarial attacks on deterministic LTI systems. For instance, a system must remain observable after removing any 2q sensors to only identify q attacks. However, the ability for an attacker to create an unidentifiable attack requires knowledge of the system model. In this paper, we aim to limit the adversary's knowledge of the system model with the goal of accurately identifying all sensor attacks. Such a scheme will allow systems to withstand larger attacks or system operators to allocate fewer sensing devices to a control system while maintaining security. We explore how changing the dynamics of the system as a function of time allows us to actively identify malicious/faulty sensors in a control system. We discuss the design of time varying system matrices to meet this goal and evaluate performance in deterministic and stochastic systems.
Systemic measures for performance and robustness of large-scale interconnected dynamical networks

In this paper, we develop a novel unified methodology for performance and robustness analysis of linear dynamical networks. We introduce the notion of systemic measures for the class of first-order linear consensus networks. We classify two important types of performance and robustness measures according to their functional properties: convex systemic measures and Schur-convex systemic measures. It is shown that a viable systemic measure should satisfy several fundamental properties such as homogeneity, monotonicity, convexity, and orthogonal invariance. In order to support our proposed unified framework, we verify functional properties of several existing performance and robustness measures from the literature and show that they all belong to the class of systemic measures. Moreover, we introduce new classes of systemic measures based on (a version of) the well-known Riemann zeta function, input-output system norms, and etc. Then, it is shown that for a given linear dynamical network one can take several different strategies to optimize a given performance and robustness systemic measure via convex optimization. Finally, we characterized an interesting fundamental limit on the best achievable value of a given systemic measure after adding some certain number of new weighted edges to the underlying graph of the network.
Stochastic blockmodel approximation of a graphon: Theory and consistent estimation

Non-parametric approaches for analyzing network data based on exchangeable graph models (ExGM) have recently gained interest. The key object that defines an ExGM is often referred to as a graphon. This non-parametric perspective on network modeling poses challenging questions on how to make inference on the graphon underlying observed network data. In this paper, we propose a computationally efficient procedure to estimate a graphon from a set of observed networks generated from it. This procedure is based on a stochastic blockmodel approximation (SBA) of the graphon. We show that, by approximating the graphon with a stochastic block model, the graphon can be consistently estimated, that is, the estimation error vanishes as the size of the graph approaches infinity.
Split graphs and Nordhaus-Gaddum graphs

A graph G is an NG-graph if ź ( G ) + ź ( G ź ) = | V ( G ) | + 1 . We characterize NG-graphs solely from degree sequences leading to a linear-time recognition algorithm. We also explore the connections between NG-graphs and split graphs. There are three types of NG-graphs and split graphs can also be divided naturally into two categories, balanced and unbalanced. We characterize each of these five classes by degree sequence. We construct bijections between classes of NG-graphs and balanced and unbalanced split graphs which, together with the known formula for the number of split graphs on n vertices, allows us to compute the sizes of each of these classes. Finally, we provide a bijection between unbalanced split graphs on n vertices and split graphs on n - 1 or fewer vertices providing evidence for our conjecture that the rapid growth in the number of split graphs comes from the balanced split graphs.
Noncommutative Tsen's theorem in dimension one

Abstract Let k be a field. In this paper, we find necessary and sufficient conditions for a noncommutative curve of genus zero over k to be a noncommutative P 1 -bundle. This result can be considered a noncommutative, one-dimensional version of Tsen's theorem. By specializing this theorem, we show that every arithmetic noncommutative projective line is a noncommutative curve, and conversely we characterize exactly those noncommutative curves of genus zero which are arithmetic. We then use this characterization, together with results from [9] , to address some problems posed in [4] .
A new analysis of the DS-CDMA cellular downlink under spatial constraints

The direct-sequence code-division multiple access (DS-CDMA) cellular downlink is modeled by a constrained random spatial model involving a fixed number of base stations placed over a finite area with a minimum separation. The analysis is driven by a new closed-form expression for the conditional outage probability at each mobile, where the conditioning is with respect to the network realization. The analysis features a flexible channel model, accounting for path loss, Nakagami fading, and shadowing. By generating many random networks and applying a given resource allocation policy, the distribution of the rates provided to each user is obtained. In addition to determining the average rate, the analysis can determine the transmission capacity of the network and can characterize fairness in terms of the fraction of users that achieve a specified rate. The analysis is used to compare a rate-control policy against a power-control policy and investigate the influence of the minimum base-station separation.
Motivic stable homotopy and the stable 51 and 52 stems

Abstract We establish a differential d 2 ( D 1 ) = h 0 2 h 3 g 2 in the 51-stem of the Adams spectral sequence at the prime 2, which gives the first correct calculation of the stable 51 and 52 stems. This differential is remarkable since we know of no way to prove it without recourse to the motivic Adams spectral sequence. It is the last undetermined differential in the range of the first author's detailed calculations of the n-stems for n 60 [6] . This note advertises the use of the motivic Adams spectral sequence to obtain information about classical stable homotopy groups.
Shift-invariant and sampling spaces associated with the special affine Fourier transform

Abstract The Special Affine Fourier Transformation or the SAFT generalizes a number of well known unitary transformations as well as signal processing and optics related mathematical operations. Shift-invariant spaces also play an important role in sampling theory, multiresolution analysis, and many other areas of signal and image processing. Shannon's sampling theorem, which is at the heart of modern digital communications, is a special case of sampling in shift-invariant spaces. Furthermore, it is well known that the Poisson summation formula is equivalent to the sampling theorem and that the Zak transform is closely connected to the sampling theorem and the Poisson summation formula. These results have been known to hold in the Fourier transform domain for decades and were recently shown to hold in the Fractional Fourier transform domain by A. Bhandari and A. Zayed. The main goal of this article is to show that these results also hold true in the SAFT domain. We provide a short, self-contained proof of Shannon's theorem for functions bandlimited in the SAFT domain and then show that sampling in the SAFT domain is equivalent to orthogonal projection of functions onto a subspace of bandlimited basis associated with the SAFT domain. This interpretation of sampling leads to least-squares optimal sampling theorem. Furthermore, we show that this approximation procedure is linked with convolution and semi-discrete convolution operators that are associated with the SAFT domain. We conclude the article with an application of fractional delay filtering of SAFT bandlimited functions.
Identification and Estimation of Causal Effects with Outcomes Truncated by Death

It is common in medical studies that the outcome of interest is truncated by death, meaning that a subject has died before the outcome could be measured. In this case, restricted analysis among survivors may be subject to selection bias. Hence, it is of interest to estimate the survivor average causal effect, defined as the average causal effect among the subgroup consisting of subjects who would survive under either exposure. In this paper, we consider the identification and estimation problems of the survivor average causal effect. We propose to use a substitution variable in place of the latent membership in the always-survivor group. The identification conditions required for a substitution variable are conceptually similar to conditions for a conditional instrumental variable, and may apply to both randomized and observational studies. We show that the survivor average causal effect is identifiable with use of such a substitution variable, and propose novel model parameterizations for estimation of the survivor average causal effect under our identification assumptions. Our approaches are illustrated via simulation studies and a data analysis.
Janossy Pooling: Learning Deep Permutation-Invariant Functions for Variable-Size Inputs

We consider a simple and overarching representation for permutation-invariant functions of sequences (or multiset functions). Our approach, which we call Janossy pooling, expresses a permutation-invariant function as the average of a permutation-sensitive function applied to all reorderings of the input sequence. This allows us to leverage the rich and mature literature on permutation-sensitive functions to construct novel and flexible permutation-invariant functions. If carried out naively, Janossy pooling can be computationally prohibitive. To allow computational tractability, we consider three kinds of approximations: canonical orderings of sequences, functions with $k$-order interactions, and stochastic optimization algorithms with random permutations. Our framework unifies a variety of existing work in the literature, and suggests possible modeling and algorithmic extensions. We explore a few in our experiments, which demonstrate improved performance over current state-of-the-art methods.
Spectral measures generated by arbitrary and random convolutions

Abstract We study spectral measures generated by infinite convolution products of discrete measures generated by Hadamard triples, and we present sufficient conditions for the measures to be spectral, generalizing a criterion by Strichartz. We then study the spectral measures generated by random convolutions of finite atomic measures and rescaling, where the digits are chosen from a finite collection of digit sets. We show that in dimension one, or in higher dimensions under certain conditions, “almost all” such measures generate spectral measures, or, in the case of complete digit sets, translational tiles. Our proofs are based on the study of self-affine spectral measures and tiles generated by Hadamard triples in quasi-product form.
Toward a Theory of Markov Influence Systems and their Renormalization

Nonlinear Markov chains are probabilistic models commonly used in physics, biology, and the social sciences. In "Markov influence systems" (MIS), the transition probabilities of the chains change as a function of the current state distribution. This work introduces a renormalization framework for analyzing the dynamics of MIS. It comes in two independent parts: first, we generalize the standard classification of Markov chain states to the dynamic case by showing how to "parse" graph sequences. We then use this framework to carry out the bifurcation analysis of a few important MIS families. In particular, we show that irreducible MIS are almost always asymptotically periodic. We also give an example of "hyper-torpid" mixing, where a stationary distribution is reached in super-exponential time, a timescale that cannot be achieved by any Markov chain.
Distributed Synthesis Using Accelerated ADMM

We propose a convex distributed optimization algorithm for synthesizing robust controllers for large-scale continuous time systems subject to exogenous disturbances. Given a large scale system, instead of solving the larger centralized synthesis task, we decompose the problem into a set of smaller synthesis problems for the local subsystems with a given interconnection topology. Hence, the synthesis problem is constrained to the sparsity pattern dictated by the interconnection topology. To this end, for each subsystem, we solve a local dissipation inequality and then check a small-gain like condition for the overall system. To minimize the effect of disturbances, we consider the H∞ synthesis problems. We instantiate the distributed synthesis method using accelerated alternating direction method of multipliers (ADMM) with convergence rate $O(\frac{1}{k^{2}})$ with $k$ being the number of iterations.
Exact Bounds on the Inverse Mills Ratio and Its Derivatives

The inverse Mills ratio is $$R:=\varphi /\Psi $$ , where $$\varphi $$ and $$\Psi $$ are, respectively, the probability density function and the tail function of the standard normal distribution. Exact bounds on R(z) for complex z with $$\mathfrak {R}z\geqslant 0$$ are obtained, which then yield logarithmically exact upper bounds on high-order derivatives of R. These results complement the many known bounds on the (inverse) Mills ratio of the real argument. The main idea of the proof is a non-asymptotic version of the so-called stationary-phase method. This study was prompted by a recently discovered alternative to the Euler–Maclaurin formula.
Edge Based Grid Super-Imposition for Crowd Emotion Recognition

Numerous automatic continuous emotion detection system studies have examined mostly use of videos and images containing individual person expressing emotions. This study examines the detection of spontaneous emotions in a group and crowd settings. Edge detection was used with a grid of lines superimposition to extract the features. The feature movement in terms of movement from the reference point was used to track across sequences of images from the color channel. Additionally the video data capturing was done on spontaneous emotions invoked by watching sports events from group of participants. The method was view and occlusion independent and the results were not affected by presence of multiple people chaotically expressing various emotions. The edge thresholds of 0.2 and grid thresholds of 20 showed the best accuracy results. The overall accuracy of the group emotion classifier was 70.9%.
Fast Geometrically-Perturbed Adversarial Faces

The state-of-the-art performance of deep learning algorithms has led to a considerable increase in the utilization of machine learning in security-sensitive and critical applications. However, it has recently been shown that a small and carefully crafted perturbation in the input space can completely fool a deep model. In this study, we explore the extent to which face recognition systems are vulnerable to geometrically-perturbed adversarial faces. We propose a fast landmark manipulation method for generating adversarial faces, which is approximately 200 times faster than the previous geometric attacks and obtains 99.86% success rate on the state-of-the-art face recognition models. To further force the generated samples to be natural, we introduce a second attack constrained on the semantic structure of the face which has the half speed of the first attack with the success rate of 99.96%. Both attacks are extremely robust against the state-of-the-art defense methods with the success rate of equal or greater than 53.59%. Code is available at https://github.com/alldbi/FLM
Compressed Representations of Conjunctive Query Results

Relational queries, and in particular join queries, often generate large output results when executed over a huge dataset. In such cases, it is often infeasible to store the whole materialized output if we plan to reuse it further down a data processing pipeline. Motivated by this problem, we study the construction of space-efficient compressed representations of the output of conjunctive queries, with the goal of supporting the efficient access of the intermediate compressed result for a given access pattern. In particular, we initiate the study of an important tradeoff: minimizing the space necessary to store the compressed result, versus minimizing the answer time and delay for an access request over the result. Our main contribution is a novel parameterized data structure, which can be tuned to trade off space for answer time. The tradeoff allows us to control the space requirement of the data structure precisely, and depends both on the structure of the query and the access pattern. We show how we can use the data structure in conjunction with query decomposition techniques in order to efficiently represent the outputs for several classes of conjunctive queries.
A decade of fast radio bursts

Modern astrophysics is undergoing a revolution. As detector technology has advanced, and astronomers have been able to study the sky with finer temporal detail, a rich diversity of sources that vary on timescales from years down to a few nanoseconds has been found. Among these are fast radio bursts, which exhibit pulses of millisecond duration and anomalously high dispersion compared to Galactic pulsars, first seen a decade ago. Since then, a new research community has been actively working on a variety of experiments and developing models to explain this new phenomenon, and devising ways to use them as astrophysical tools. In this Perspective, I describe how astronomers have reached this point, review the highlights from the first decade of research in this field, give some current breaking news, and look ahead to what might be expected in the next few years. The first fast radio burst (FRB) was discovered in 2007, and in the following decade ~25 more were detected. Now the field stands on the brink of an explosion of detections, largely driven by the availability of new radio facilities. One of the founders of the field, Duncan Lorimer, reviews the early years of FRB science.
On the distribution of distances in homogeneous compact metric spaces

Abstract We provide a simple proof that in any homogeneous, compact metric space of diameter D, if one finds the average distance A achieved in X with respect to some isometry invariant Borel probability measure, then D 2 ≤ A ≤ D . This result applies equally to vertex-transitive graphs and to compact, connected, homogeneous Riemannian manifolds.
Exotic Bailey-Slater spt-functions III: Bailey pairs from groups B, F, G, and J

We continue to investigate spt-type functions that arise from Bailey pairs. In this third paper on the subject, we proceed to introduce additional spt-type functions. We prove simple Ramanujan type congruences for these functions which can be explained by a spt-crank-type function. The spt-crank-type functions are actually defined first, with the spt-type functions coming from setting $z=1$ in the spt-crank-type functions. We find some of the spt-crank-type functions to have interesting representations as single series, some of which reduce to infinite products. Additionally we find dissections of the other spt-crank-type functions when $z$ is a certain root of unity. Both methods are used to explain congruences for the spt-type functions. Our series formulas require Bailey's Lemma and conjugate Bailey pairs. Our dissection formulas follow from Bailey's Lemma and dissections of known ranks and cranks.
Learning dominant wave directions for plane wave methods for high-frequency Helmholtz equations

We present a ray-based finite element method for the high-frequency Helmholtz equation in smooth media, whose basis is learned adaptively from the medium and source. The method requires a fixed number of grid points per wavelength to represent the wave field; moreover, it achieves an asymptotic convergence rate of $$\mathcal {O}(\omega ^{-\frac{1}{2}})$$ O ( ω - 1 2 ) , where $$\omega $$ ω is the frequency parameter in the Helmholtz equation. The local basis is motivated by the geometric optics ansatz and is composed of polynomials modulated by plane waves propagating in a few dominant ray directions. The ray directions are learned by processing a low-frequency wave field that probes the medium with the same source. Once the local ray directions are extracted, they are incorporated into the local basis to solve the high-frequency Helmholtz equation. This process can be continued to further improve the approximations for both local ray directions and high-frequency wave fields iteratively. Finally, a fast solver is developed for solving the resulting linear system with an empirical complexity $$\mathcal {O}(\omega ^d)$$ O ( ω d ) up to a poly-logarithmic factor. Numerical examples in 2D are presented to corroborate the claims.
Congruences for Andrews' Smallest Parts Partition Function and New Congruences for Dyson's Rank

Let spt(n) denote the total number of appearances of smallest parts in the partitions of n. Recently, Andrews showed how spt(n) is related to the second rank moment, and proved some surprising Ramanujan-type congruences mod 5, 7 and 13. We prove a generalization of these congruences using known relations between rank and crank moments. We obtain explicit Ramanujan-type congruences for spt(n) mod l for l = 11, 17, 19, 29, 31 and 37. Recently, Bringmann and Ono proved that Dyson's rank function has infinitely many Ramanujan-type congruences. Their proof is non-constructive and utilizes the theory of weak Maass forms. We construct two explicit nontrivial examples mod 11 using elementary congruences between rank moments and half-integer weight Hecke eigenforms.
Bayesian State Estimation for Unobservable Distribution Systems via Deep Learning

The problem of state estimation for unobservable distribution systems is considered. A deep learning approach to Bayesian state estimation is proposed for real-time applications. The proposed technique consists of distribution learning of stochastic power injection, a Monte Carlo technique for the training of a deep neural network for state estimation, and a Bayesian bad-data detection and filtering algorithm. Structural characteristics of the deep neural networks are investigated. Simulations illustrate the accuracy of Bayesian state estimation for unobservable systems and demonstrate the benefit of employing a deep neural network. Numerical results show the robustness of Bayesian state estimation against modeling and estimation errors and the presence of bad and missing data. Comparing with pseudo-measurement techniques, direct Bayesian state estimation via deep learning neural network outperforms existing benchmarks.
Estimation procedures for robust sensor control

Many robotic sensor estimation problems can characterized in terms of nonlinear measurement systems. These systems are contaminated with noise and may be underdetermined from a single observation. In order to get reliable estimation results, the system must choose views which result in an overdetermined system. This is the sensor control problem. Accurate and reliable sensor control requires an estimation procedure which yields both estimates and measures of its own performance. In the case of nonlinear measurement systems, computationally simple closed-form estimation solutions may not exist. However, approximation techniques provide viable alternatives. In this paper, we evaluate three estimation techniques: the extended Kalman filter, a discrete Bayes approximation, and an iterative Bayes approximation. We present mathematical results and simulation statistics illustrating operating conditions where the extended Kalman filter is inappropriate for sensor control, and discuss issues in the use of the discrete Bayes approximation.
Technology Capacity Building Strategies for Increasing Participation & Persistence in the STEM Workforce

This research model uses an emancipatory approach to address challenges of equity in the science, technology, engineering, and math (STEM) workforce. Serious concerns about low minority participation callfor arigorous evaluation of new pedagogical methods that effectively prepares underrepresented groups for the increasingly digital world. The inability to achieve STEM workforce diversity goals is attributed to the failure of the academic pipeline to maintain a steady flow of underrepresented minority students. Formal curriculum frequently results in under-preparedness and a professional practices gap. Exacerbating lower performance are fragile communities where issues such as poverty, single-parent homes, incarceration, abuse, and homelessness disengage residents. Since data shows that more minorities have computing and engineering degrees than work in the field, this discussions explores how educational institutions can critically examine social and political realities that impede STEM diversity while capturing cultural cues that identify personal barriersamongst underrepresented groups.
Automatic tuning of interactive perception applications

Interactive applications incorporating high-data rate sensing and computer vision are becoming possible due to novel runtime systems and the use of parallel computation resources. To allow interactive use, such applications require careful tuning of multiple application parameters to meet required fidelity and latency bounds. This is a nontrivial task, often requiring expert knowledge, which becomes intractable as resources and application load characteristics change. This paper describes a method for automatic performance tuning that learns application characteristics and effects of tunable parameters online, and constructs models that are used to maximize fidelity for a given latency constraint. The paper shows that accurate latency models can be learned online, knowledge of application structure can be used to reduce the complexity of the learning task, and operating points can be found that achieve 90% of the optimal fidelity by exploring the parameter space only 3% of the time.
Local monomialization of analytic maps

Abstract In this paper local monomialization theorems are proven for morphisms of complex and real analytic spaces. This gives the generalization of the local monomialization theorem for morphisms of algebraic varieties over a field of characteristic zero proven in [16] and [18] to analytic spaces.
On the State of the Art of Evaluation in Neural Language Models

Ongoing innovations in recurrent neural network architectures have provided a steady influx of apparently state-of-the-art results on language modelling benchmarks. However, these have been evaluated using differing code bases and limited computational resources, which represent uncontrolled sources of experimental variation. We reevaluate several popular architectures and regularisation methods with large-scale automatic black-box hyperparameter tuning and arrive at the somewhat surprising conclusion that standard LSTM architectures, when properly regularised, outperform more recent models. We establish a new state of the art on the Penn Treebank and Wikitext-2 corpora, as well as strong baselines on the Hutter Prize dataset.
Linear Time Computation of Moments in Sum-Product Networks

Bayesian online algorithms for Sum-Product Networks (SPNs) need to update their posterior distribution after seeing one single additional instance. To do so, they must compute moments of the model parameters under this distribution. The best existing method for computing such moments scales quadratically in the size of the SPN, although it scales linearly for trees. This unfortunate scaling makes Bayesian online algorithms prohibitively expensive, except for small or tree-structured SPNs. We propose an optimal linear-time algorithm that works even when the SPN is a general directed acyclic graph (DAG), which significantly broadens the applicability of Bayesian online algorithms for SPNs. There are three key ingredients in the design and analysis of our algorithm: 1). For each edge in the graph, we construct a linear time reduction from the moment computation problem to a joint inference problem in SPNs. 2). Using the property that each SPN computes a multilinear polynomial, we give an efficient procedure for polynomial evaluation by differentiation without expanding the network that may contain exponentially many monomials. 3). We propose a dynamic programming method to further reduce the computation of the moments of all the edges in the graph from quadratic to linear. We demonstrate the usefulness of our linear time algorithm by applying it to develop a linear time assume density filter (ADF) for SPNs.
Superconductivity in graphene-lithium

We present first-principles calculations on systems consisting of a few layers of graphene and lithium. In particular, we investigate the evolution of the electron?phonon coupling strength with increasing number of layers. We find that, for intercalated systems such as C6-Li-C6 or C6-Li-C6-Li-C6, the electron?phonon coupling is weak. However, for systems of equal number of graphene and lithium layers, such as C6-Li or C6-Li-C6-Li, the electron?phonon coupling is strong. We investigate the optimal configuration that yields the highest superconducting transition temperature.
Analysis of a Singular Boussinesq Model

Recently, a new singularity formation scenario for the 3D axi-symmetric Euler equation and the 2D inviscid Boussinesq system has been proposed by Hou and Luo (Multiscale Model Simul 12(4):1722–1776, 2014, PNAS 111(36):12968–12973, 2014) based on extensive numerical simulations. As the first step to understand the scenario, models with simplified sign-definite Biot–Savart law and forcing have recently been studied in Choi et al. (Commun Pure Appl Math 70(11):2218–2243, 2017, Commun Math Phys 334:1667–1679, 2015), Do et al. (J Nonlinear Sci, 2016. arXiv:1604.07118 ), Hoang et al. (J Differ Equ 264:7328–7356, 2018), Hou and Liu (Res Math Sci 2, 2015), Kiselev and Tan (Adv Math 325:34–55, 2018). In this paper, we aim to bring back one of the complications encountered in the original equation—the sign changing kernel in the Biot–Savart law. This makes analysis harder, as there are two competing terms in the fluid velocity integral whose balance determines the regularity properties of the solution. The equation we study here is based on the CKY model introduced in Choi et al. (2015). We prove that finite time blow up persists in a certain range of parameters.
Relating Metric Distortion and Fairness of Social Choice Rules

One way of evaluating social choice (voting) rules is through a utilitarian distortion framework. In this model, we assume that agents submit full rankings over the alternatives, and these rankings are generated from underlying, but unknown, quantitative costs. The \emph{distortion} of a social choice rule is then the ratio of the total social cost of the chosen alternative to the optimal social cost of any alternative; since the true costs are unknown, we consider the worst-case distortion over all possible underlying costs. Analogously, we can consider the worst-case \emph{fairness ratio} of a social choice rule by comparing a useful notion of fairness (based on approximate majorization) for the chosen alternative to that of the optimal alternative. With an additional metric assumption -- that the costs equal the agent-alternative distances in some metric space -- it is known that the Copeland rule achieves both a distortion and fairness ratio of at most 5. For other rules, only bounds on the distortion are known, e.g., the popular Single Transferable Vote (STV) rule has distortion $O(\log m)$, where $m$ is the number of alternatives. We prove that the distinct notions of distortion and fairness ratio are in fact closely linked -- within an additive factor of 2 for any voting rule -- and thus STV also achieves an $O(\log m)$ fairness ratio. We further extend the notions of distortion and fairness ratio to social choice rules choosing a \emph{set} of alternatives. By relating the distortion of single-winner rules to multiple-winner rules, we establish that Recursive Copeland achieves a distortion of 5 and a fairness ratio of at most 7 for choosing a set of alternatives.
Products in Hopf-cyclic cohomology

We construct several pairings in Hopf-cyclic cohomology of (co)module (co)algebras with arbitrary coefficients. The key ideas instrumental in constructing these pairings are the derived functor interpretation of Hopf-cyclic and equivariant cyclic (co)homology, and the Yoneda interpretation of Ext-groups. As a special case of one of these pairings, we recover the Connes-Moscovici characteristic map in Hopf-cyclic cohomology. We also prove that this particular pairing, along with few others, would stay the same if we replace the derived category of (co)cyclic modules with the homotopy category of (special) towers of $X$-complexes, or the derived category of mixed complexes.
Regularity criteria of the three-dimensional MHD system involving one velocity and one vorticity component

Abstract We obtain a regularity criteria of the solution to the three-dimensional magnetohydrodynamics system to remain smooth for all time involving only one velocity and one vorticity component. Moreover, the norm in space and time with which we impose our criteria for the vorticity component is at the scaling invariant level. The proof requires a new decomposition of the four non-linear terms making use of a new identity due to the divergence-free conditions of the velocity and the magnetic vector fields.
The revised and uniform fundamental groups and universal covers of geodesic spaces

Abstract Sormani and Wei proved in 2004 that a compact geodesic space has a categorical universal cover if and only if its covering/critical spectrum is finite. We add to this several equivalent conditions pertaining to the geometry and topology of the revised and uniform fundamental groups. We show that a compact geodesic space X has a universal cover if and only if the following hold: 1) its revised and uniform fundamental groups are finitely presented, or, more generally, countable; 2) its revised fundamental group is discrete as a quotient of the quasitopological fundamental group π 1 qtop ( X ) . In the process, we classify the topological singularities in X, and we show that the above conditions imply closed liftings of all sufficiently small path loops to all covers of X, generalizing the traditional semilocally simply connected property. A geodesic space X with this new property is called semilocally r-simply connected, and X has a universal cover if and only if it satisfies this condition. We then introduce the covering topology on π 1 ( X ) , which can be considered a geometrization of both Brazas–Fabelʼs shape topology and the topology induced by the more general Spanier groups. We establish several connections between properties of the covering topology, the existence of simply connected and universal covers, and geometries on the fundamental group.
On local holomorphic maps preserving invariant $(p, p)$-forms between bounded symmetric domains

Let $D, \Omega_1, ..., \Omega_m$ be irreducible bounded symmetric domains. We study local holomorphic maps from $D$ into $\Omega_1 \times... \Omega_m$ preserving the invariant $(p, p)$-forms induced from the normalized Bergman metrics up to conformal constants. We show that the local holomorphic maps extends to algebraic maps in the rank one case for any $p$ and in the rank at least two case for certain sufficiently large $p$. The total geodesy thus follows if $D=\mathbb{B}^n, \Omega_i = \mathbb{B}^{N_i}$ for any $p$ or if $D=\Omega_1 =...=\Omega_m$ with rank$(D)\geq 2$ and $p$ sufficiently large. As a consequence, the algebraic correspondence between quasi-projective varieties $D / \Gamma$ preserving invariant $(p, p)$-forms is modular, where $\Gamma$ is a torsion free, discrete, finite co-volume subgroup of Aut$(D)$. This solves partially a problem raised by Mok.
Parking Functions, Shi Arrangements, and Mixed Graphs

The Shi arrangement is the set of all hyperplanes in ℝn of the form xj − xk = 0 or 1 for 1 ≤ j < k ≤ n. Shi observed in 1986 that the number of regions (i.e., connected components of the complement...
Photoproduction prospects at the EIC

We discuss how photoproduction and electroproduction processes will provide a precise tool to study nuclear structure in the small- x region in the future Electron-Ion Collider. In particular, we emphasize how exclusive vector meson production at the EIC can be used to accurately map the gluonic density profile of nuclei, including its event-by-event fluctuations. In addition, we show how measurements of the total diffractive cross section will be sensitive to saturation effects.
Transfer Learning with Deep CNNs for Gender Recognition and Age Estimation

In this project, competition-winning deep neural networks with pretrained weights are used for image-based gender recognition and age estimation. Transfer learning is explored using both VGG19 and VGGFace pretrained models by testing the effects of changes in various design schemes and training parameters in order to improve prediction accuracy. Training techniques such as input standardization, data augmentation, and label distribution age encoding are compared. Finally, a hierarchy of deep CNNs is tested that first classifies subjects by gender, and then uses separate male and female age models to predict age. A gender recognition accuracy of 98.7% and an MAE of 4.1 years is achieved. This paper shows that, with proper training techniques, good results can be obtained by retasking existing convolutional filters towards a new purpose.
Improved coresets for kernel density estimates

We study the construction of coresets for kernel density estimates. That is we show how to approximate the kernel density estimate described by a large point set with another kernel density estimate with a much smaller point set. For characteristic kernels (including Gaussian and Laplace kernels), our approximation preserves the L∞ error between kernel density estimates within error ϵ, with coreset size 4/ϵ2, but no other aspects of the data, including the dimension, the diameter of the point set, or the bandwidth of the kernel common to other approximations. When the dimension is unrestricted, we show this bound is tight for these kernels as well as a much broader set. This work provides a careful analysis of the iterative Frank-Wolfe algorithm adapted to this context, an algorithm called kernel herding. This analysis unites a broad line of work that spans statistics, machine learning, and geometry. When the dimension d is constant, we demonstrate much tighter bounds on the size of the coreset specifically for Gaussian kernels, showing that it is bounded by the size of the coreset for axis-aligned rectangles. Currently the best known constructive bound is [EQUATION], and non-constructively, this can be improved by [EQUATION]. This improves the best constant dimension bounds polynomially for d ≥ 3.
Adaptive Coordination of Distributed Energy Resources in Lossy Power Distribution Systems

This paper is concerned with the problem of coordinating a set of distributed energy resources (DERs) in a lossy power distribution system to provide frequency regulation services to a bulk power grid with the explicit consideration of system losses. To this end, we formulate the problem as an optimization problem, the objective of which is to minimize some cost function subject to a set of constraints. The formulation requires knowledge of incremental total system losses, which we approximate using the so-called loss factors (LFs) that explicitly capture the impacts of both active and reactive power injections on system losses. The LFs are estimated recursively using power injection measurements; thus, they are adaptive to various phenomena that impact the power system operation. Numerical simulation on a 33-bus distribution test feeder validated the effectiveness of the proposed framework.
A spectral refinement of the Bergelson-Host-Kra decomposition and new multiple ergodic theorems

We investigate how spectral properties of a measure-preserving system . We also obtain a new refinement of Szemeredi’s theorem via Furstenberg’s correspondence principle.
A probabilistic approach towards exact-repair regeneration codes

Regeneration codes with exact-repair property for distributed storage systems is studied in this paper. For exact-repair problem, the achievable points of (α,β) tradeoff match with the outer bound only for minimum storage regenerating (MSR), minimum bandwidth regenerating (MBR), and some specific values of n, k, and d. Such tradeoff is characterized in this work for general (n, k, k), (i.e., k = d) for some range of per-node storage (α) and repair-bandwidth (β). Rather than explicit code construction, achievability of these tradeoff points is shown by proving existence of exact-repair regeneration codes for any (n, k, k). More precisely, it is shown that an (n, k, k) system can be extended by adding a new node, which is randomly picked from some ensemble, and it is proved that, with high probability, the existing nodes together with the newly added one maintain properties of exact-repair regeneration codes. The new achievable region improves upon the existing code constructions. In particular, this result provides a complete tradeoff characterization for an (n, 3, 3) distributed storage system for any value of n.
An algorithm for numerically inverting the modular j -function

The modular j-function is a bijective map from $$X_0(1) \setminus \{\infty \}$$ to $$\mathbb {C}$$ . A natural question is to describe the inverse map. Gauss offered a solution to the inverse problem in terms of the arithmetic–geometric mean. This method relies on an elliptic curve model and the Gaussian hypergeometric series. Here we use the theory of polar harmonic Maass forms to solve the inverse problem by directly examining the Fourier expansion of the weight 2 polar harmonic Maass form obtained by specializing the logarithmic derivative of the denominator formula for the Monster Lie algebra.
Kronecker sum decompositions of space-time data

In this paper we consider the use of the space vs. time Kronecker product decomposition in the estimation of covariance matrices for spatio-temporal data. This decomposition imposes lower dimensional structure on the estimated covariance matrix, thus reducing the number of samples required for estimation. To allow a smooth tradeoff between the reduction in the number of parameters (to reduce estimation variance) and the accuracy of the covariance approximation (affecting estimation bias), we introduce a diagonally loaded modification of the sum-of-kronecker products representation in [1].We derive an asymptotic Cramer-Rao bound (CRB) on the minimum attainable mean squared predictor coefficient estimation error for unbiased estimators of Kronecker structured covariance matrices. We illustrate the accuracy of the diagonally loaded Kronecker sum decomposition by applying it to the prediction of human activity video.
Universal geometric coefficients for the four-punctured sphere

We construct universal geometric coefficients for the cluster algebra associated to the four-punctured sphere and obtain, as a by-product, the g-vectors of cluster variables. We also construct the rational part of the mutation fan. These constructions rely on a classification of the allowable curves (the curves which can appear in quasi-laminations). The classification allows us to prove the Null Tangle Property for the four-punctured sphere, thus adding this surface to a short list of surfaces for which this property is known. The Null Tangle Property then implies that the shear coordinates of allowable curves are the universal coefficients. We compute shear coordinates explicitly to obtain universal geometric coefficients.
Representation theory of liftings of quantum planes

We determine the regular representations, Gabriel quivers and representation type of all liftings of two-dimensional quantum linear spaces.