cssi/SciSciGPT-SciSciNet huggingface dataset:
SiAl alloy feedhorn arrays: material properties, feedhorn design, and astrophysical applications

We present here a study of the use of the SiAl alloy CE7 for the packaging of silicon devices at cryogenic temperatures. We report on the development of baseplates and feedhorn arrays for millimeter wave bolometric detectors for astrophysics. Existing interfaces to such detectors are typically made either of metals, which are easy to machine but mismatched to the thermal contraction profile of Si devices, or of silicon, which avoids the mismatch but is difficult to directly machine. CE7 exhibits properties of both Si and Al, which makes it uniquely well suited for this application. We measure CE7 to a) superconduct below a critical transition temperature, T (sub c), 1.2 K, b) have a thermal contraction profile much closer to Si than metals, which enables simple mating, and c) have a low thermal conductivity which can be improved by Au-plating. Our investigations also demonstrate that CE7 can be machined well enough to fabricate small structures, such as #0-80 threaded holes, to tight tolerances (approximately 25 microns) in contrast with pure silicon and similar substrates. We have fabricated CE7 baseplates being deployed in the 93 gigahertz polarimetric focal planes used in the Cosmology Large Angular Scale Surveyor (CLASS). We also report on the development of smooth-walled feedhorn arrays made of CE7 that will be used in a focal plane of dichroic 150/220 gigahertz detectors for the CLASS High-Frequency camera.
The case for black hole thermodynamics part II: Statistical mechanics

Abstract I present in detail the case for regarding black hole thermodynamics as having a statistical-mechanical explanation in exact parallel with the statistical-mechanical explanation believed to underlie the thermodynamics of other systems. (Here I presume that black holes are indeed thermodynamic systems in the fullest sense; I review the evidence for that conclusion in the prequel to this paper.) I focus on three lines of argument: (i) zero-loop and one-loop calculations in quantum general relativity understood as a quantum field theory, using the path-integral formalism; (ii) calculations in string theory of the leading-order terms, higher-derivative corrections, and quantum corrections, in the black hole entropy formula for extremal and near-extremal black holes; (iii) recovery of the qualitative and (in some cases) quantitative structure of black hole statistical mechanics via the AdS/CFT correspondence. In each case I briefly review the content of, and arguments for, the form of quantum gravity being used (effective field theory; string theory; AdS/CFT) at a (relatively) introductory level: the paper is aimed at readers with some familiarity with thermodynamics, quantum mechanics and general relativity but does not presume advanced knowledge of quantum gravity. My conclusion is that the evidence for black hole statistical mechanics is as solid as we could reasonably expect it to be in the absence of a directly-empirically-verified theory of quantum gravity.
Improved SVRG for non-strongly-convex or sum-of-non-convex objectives

Many classical algorithms are found until several years later to outlive the confines in which they were conceived, and continue to be relevant in unforeseen settings. In this paper, we show that SVRG is one such method: being originally designed for strongly convex objectives, it is also very robust in non-strongly convex or sum-of-nonconvex settings. More precisely, we provide new analysis to improve the state-of-the-art running times in both settings by either applying SVRG or its novel variant. Since non-strongly convex objectives include important examples such as Lasso or logistic regression, and sum-of-non-convex objectives include famous examples such as stochastic PCA and is even believed to be related to training deep neural nets, our results also imply better performances in these applications.
Modeling morphology evolution during solvent-based fabrication of organic solar cells

Abstract Solvent-based thin-film deposition constitutes a popular class of fabrication strategies for manufacturing organic electronic devices like organic solar cells. All such solvent-based techniques usually involve preparing dilute blends of electron-donor and electron-acceptor materials dissolved in a volatile solvent. After some form of coating onto a substrate to form a thin film, the solvent evaporates. An initially homogeneous mixture separates into electron-acceptor rich and electron-donor rich regions as the solvent evaporates. Depending on the specifics of the blend, processing conditions, and substrate characteristics different morphologies are typically formed. Experimental evidence consistently confirms that the resultant morphology critically affects device performance. A computational framework that can predict morphology evolution can significantly augment experimental analysis. Such a framework will also allow high throughput analysis of the large phase space of processing parameters, thus yielding considerable insight into the process–structure–property relationships governing organic solar cell behavior. In this paper, we formulate a computational framework to predict evolution of morphology during solvent-based fabrication of organic thin films. This is accomplished by developing a phase field-based model of evaporation-induced and substrate-induced phase-separation in ternary systems . This formulation allows most of the important physical phenomena affecting morphology evolution during fabrication to be naturally incorporated. We discuss the various numerical and computational challenges associated with a three dimensional, finite-element based, massively parallel implementation of this framework. This formulation allows, for the first time, to model three-dimensional nanomorphology evolution over large time spans on device scale domains. We illustrate this framework by investigating and quantifying the effect of various process and system variables on morphology evolution. We explore ways to control the morphology evolution by investigating different evaporation rates, blend ratios and interaction parameters between components.
Relations among conditional probabilities

We describe a universal Grobner basis of relations among conditional probabilities in a discrete probability space, with any set of conditioned-upon events. They may be specialized to the partially-observed random variable case, the purely conditional case, and other special cases. We also investigate the connection to generalized permutohedra and describe a ''conditional probability simplex'' which is the image of a multigraded moment map.
Genetic Exponentially Fitted Method for Solving Multi-dimensional Drift-diffusion Equations

A general approach was proposed in this article to develop high-order exponentially fitted basis functions for finite element approximations of multi-dimensional drift-diusion equations for modeling biomolecular electrodiusion processes. Such methods are highly desirable for achieving numerical stability and eciency. We found that by utilizing the one-to-one correspondence between the continuous piecewise polynomial space of degree k + 1 and the divergencefree vector space of degree k, one can construct high-order two-dimensional exponentially fitted basis functions that are strictly interpolative at a selected node set but are discontinuous on edges in general, spanning nonconforming finite element spaces. First order convergence was proved for the methods constructed from divergence-free Raviart-Thomas space RT 0 0 at two dierent node sets.
Hodge theory on transversely symplectic foliations

In this paper, we develop symplectic Hodge theory on transversely symplectic foliations. In particular, we establish the symplectic $d\delta$-lemma for any such foliations with the (transverse) $s$-Lefschetz property. As transversely symplectic foliations include many geometric structures, such as contact manifolds, co-symplectic manifolds, symplectic orbifolds, and symplectic quasi-folds as special examples, our work provides a unifying treatment of symplectic Hodge theory in these geometries. As an application, we show that on compact $K$-contact manifolds, the $s$-Lefschetz property implies a general result on the vanishing of cup products, and that the cup length of a $2n+1$ dimensional compact $K$-contact manifold with the (transverse) $s$-Lefschetz property is at most $2n-s$. For any even integer $s\geq 2$, we also apply our main result to produce examples of $K$-contact manifolds that are $s$-Lefschetz but not $(s+1)$-Lefschetz.
Predicted bulk photovoltaic effect in hydrogenated Zintl compounds

The bulk photovoltaic effect (BPVE) is a phenomenon that creates a net electrical current from sunlight in a polar noncentrosymmetric material possessing a moderate band gap. This effect is being explored as an alternative to traditional p–n junction solar cells to convert solar energy into electricity. This paper assesses the possibility that hydrogenated Zintl-phase compounds, consisting only of metal, metalloid, and hydrogen atoms, may be able to provide a BPVE response. Towards this end, the magnitude of the BPVE shift current is calculated for each of the compounds AeTrTtH (Ae = Ca, Sr, and Ba; Tr = Al and Ga; and Tt = Si, Ge, and Sn). For this family of hydogenated Zintl compounds, maximum shift current responses are predicted to be up to eight times greater than that calculated for BiFeO3, and have a significant response down to much lower photon energies than BiFeO3 as well. With band gaps below 1 eV, and with some members of this family of compounds exhibiting stability in air up to 770 K, some of these compounds may find use in photovoltaic devices.
Logarithmically spiraling helicoids

We construct helicoid-like embedded minimal disks with axes along self-similar curves modeled on logarithmic spirals. The surfaces have a self-similarity inherited from the curves and the nature of the construction. Moreover, inside of a "logarithmic cone", the surfaces are embedded.
Proximal quasi-Newton methods for regularized convex optimization with linear and accelerated sublinear convergence rates

A general, inexact, efficient proximal quasi-Newton algorithm for composite optimization problems has been proposed by Scheinberg and Tang (Math Program 160:495–529, 2016) and a sublinear global convergence rate has been established. In this paper, we analyze the global convergence rate of this method, in the both exact and inexact settings, in the case when the objective function is strongly convex. We also investigate a practical variant of this method by establishing a simple stopping criterion for the subproblem optimization. Furthermore, we consider an accelerated variant, based on FISTA of Beck and Teboulle (SIAM 2:183–202, 2009), to the proximal quasi-Newton algorithm. Jiang et al. (SIAM 22:1042–1064, 2012) considered a similar accelerated method, where the convergence rate analysis relies on very strong impractical assumptions on Hessian estimates. We present a modified analysis while relaxing these assumptions and perform a numerical comparison of the accelerated proximal quasi-Newton algorithm and the regular one. Our analysis and computational results show that acceleration may not bring any benefit in the quasi-Newton setting.
Layering Data Structures over Skip Graphs for Increased NUMA Locality

We present a lock-free, linearizable, and NUMA-aware data structure that implements sets, maps, and priority queue abstract data types (ADTs), based on using thread-local, sequential maps that are used to "jump" to suitable positions in a lock-free, linearizable variant of a skip graph. Our skip graph is suitably constrained in height and subjected to a data partition scheme that reduces contention and increases NUMA locality. We developed an additional skip graph variant, which we call sparse skip graph, that causes our thread-local maps as well as our shared structure to become more sparse. Compared to using regular skip graphs, sparse skip graphs show increased performance in workloads dominated by "insert" or "remove" operations, and comparable performance in workloads dominated by "contains" operations.
On the Structure and Interpolation Properties of Quasi Shift-invariant Spaces

Abstract The structure of certain types of quasi shift-invariant spaces, which take the form V ( ψ , X ) : = span ‾ L 2 { ψ ( ⋅ − x j ) : j ∈ Z } for an infinite discrete set X = ( x j ) ⊂ R is investigated. Additionally, the relation is explored between pairs ( ψ , X ) and ( ϕ , Y ) such that interpolation of functions in V ( ψ , X ) via interpolants in V ( ϕ , Y ) solely from the samples of the original function is possible and stable. Some conditions are given for which the sampling problem is stable, and for which recovery of functions from their interpolants from a family of spaces V ( ϕ α , Y ) is possible.
Hilbert’s fifth problem for local groups

We solve Hilbert's fifth problem for local groups: every locally euclidean local group is locally isomorphic to a Lie group. Jacoby claimed a proof of this in 1957, but this proof is seriously flawed. We use methods from nonstandard analysis and model our solution after a treatment of Hilbert's fifth problem for global groups by Hirschfeld.
The MegaFace Benchmark: 1 Million Faces for Recognition at Scale

Recent face recognition experiments on a major benchmark (LFW [15]) show stunning performance–a number of algorithms achieve near to perfect score, surpassing human recognition rates. In this paper, we advocate evaluations at the million scale (LFW includes only 13K photos of 5K people). To this end, we have assembled the MegaFace dataset and created the first MegaFace challenge. Our dataset includes One Million photos that capture more than 690K different individuals. The challenge evaluates performance of algorithms with increasing numbers of "distractors" (going from 10 to 1M) in the gallery set. We present both identification and verification performance, evaluate performance with respect to pose and a persons age, and compare as a function of training data size (#photos and #people). We report results of state of the art and baseline algorithms. The MegaFace dataset, baseline code, and evaluation scripts, are all publicly released for further experimentations1.
Improved asymmetric locality sensitive hashing (ALSH) for Maximum Inner Product Search (MIPS)

Recently we showed that the problem of Maximum Inner Product Search (MIPS) is efficient and it admits provably sub-linear hashing algorithms. In [23], we used asymmetric transformations to convert the problem of approximate MIPS into the problem of approximate near neighbor search which can be efficiently solved using L2-LSH. In this paper, we revisit the problem of MIPS and argue that the quantizations used in L2-LSH is suboptimal for MIPS compared to signed random projections (SRP) which is another popular hashing scheme for cosine similarity (or correlations). Based on this observation, we provide different asymmetric transformations which convert the problem of approximate MIPS into the problem amenable to SRP instead of L2-LSH. An additional advantage of our scheme is that we also obtain LSH type space partitioning which is not possible with the existing scheme. Our theoretical analysis shows that the new scheme is significantly better than the original scheme for MIPS. Experimental evaluations strongly support the theoretical findings. In addition, we also provide the first empirical comparison that shows the superiority of hashing over tree based methods [21] for MIPS.
Earth Matter Effect on Democratic Neutrinos

Abstract The neutrino propagation through the Earth is investigated in the framework of the democratic neutrino theory. In this theory the neutrino mixing angle θ13 is approximately determined, which allows one to make a well defined neutrino oscillogram driven by the 1-3 mixing in the matter of the Earth. Significant differences in this oscillogram from the case of models with relatively small θ13 are discussed.
Solitons, the Korteweg-de Vries equation with step boundary values, and pseudo-embedded eigenvalues

The Korteweg-deVries (KdV) equation with step boundary conditions is considered, with an emphasis on soliton dynamics. When one or more initial solitons are of sufficient size, they can propagate through the step; in this case, the phase shift is calculated via the inverse scattering transform. On the other hand, when the amplitude is too small, they become trapped. In the trapped case, the transmission coefficient of the associated linear Schrodinger equation can become large at a point exponentially close to the continuous spectrum. This point is referred to as a pseudo-embedded eigenvalue. Employing the inverse problem, it is shown that the continuous spectrum associated with a branch cut in the neighborhood of the pseudo-embedded eigenvalue plays the role of discrete spectra, which in turn leads to a trapped soliton in the KdV equation.The Korteweg-deVries (KdV) equation with step boundary conditions is considered, with an emphasis on soliton dynamics. When one or more initial solitons are of sufficient size, they can propagate through the step; in this case, the phase shift is calculated via the inverse scattering transform. On the other hand, when the amplitude is too small, they become trapped. In the trapped case, the transmission coefficient of the associated linear Schrodinger equation can become large at a point exponentially close to the continuous spectrum. This point is referred to as a pseudo-embedded eigenvalue. Employing the inverse problem, it is shown that the continuous spectrum associated with a branch cut in the neighborhood of the pseudo-embedded eigenvalue plays the role of discrete spectra, which in turn leads to a trapped soliton in the KdV equation.
An upper bound on the Abbes–Saito filtration for finite flat group schemes and applications

Let OK be a complete discrete valuation ring of residue characteristic p > 0, and G be a finite flat group scheme over OK of order a power of p. We prove in this paper that the Abbes-Saito filtration of G is bounded by a linear function of the degree of G. Assume OK has generic characteristic 0 and the residue field of OK is perfect. Fargues constructed the higher level canonical subgroups for a "not too supersingular" Barsotti- Tate group G over OK. As an application of our bound, we prove that the canonical subgroup of G of level n � 2 constructed by Fargues appears in the Abbes-Saito filtration of the p n -torsion subgroup of G. Let OK be a complete discrete valuation ring with residue field k of characteristic p > 0 and fraction field K. We denote by vthe valuation on K normalized by v�(K × ) = Z. Let G be a finite and flat group scheme over OK of order a power of p such that G K is etale. We denote by (G a ;a 2 Q�0) the Abbes-Saito filtration of G. This is a decreasing and separated filtration of G by finite and flat closed subgroup schemes. We refer the readers to (AS02, AS03, AM04) for a full discussion, and to section 1 for a brief review of this filtration. Let !G be the module of invariant differentials of G. The generic etaleness of G implies that !G is a torsion OK-module of finite type. There exist thus nonzero elements a1;���;ad 2 O K such that !G ' d
Motion Planning for a UAV with a Straight or Kinked Tether

This paper develops and compares two motion planning algorithms for a tethered UAV with and without the possibility of the tether contacting the confined and cluttered environment. Tethered aerial vehicles have been studied due to their advantages such as power duration, stability, and safety. However, the disadvantages brought in by the extra tether have not been well investigated by the robotic locomotion community, especially when the tethered agent is locomoting in a non-free space occupied with obstacles. In this work, we propose two motion planning frameworks that (1) reduce the reachable configuration space by taking into account the tether and (2) deliberately plan (and relax) the contact point(s) of the tether with the environment and enable an equivalent reachable configuration space as the non-tethered counterpart would have. Both methods are tested on a physical robot, Fotokite Pro. With our approaches, tethered aerial vehicles could find their applications in confined and cluttered environments with obstacles as opposed to ideal free space, while still maintaining the advantages from the usage of a tether. The motion planning strategies are particularly suitable for marsupial heterogeneous robotic teams, such as visual servoing/assisting for another mobile, tele-operated primary robot.
Generalized cross entropy loss for training deep neural networks with noisy labels

Deep neural networks (DNNs) have achieved tremendous success in a variety of applications across many disciplines. Yet, their superior performance comes with the expensive cost of requiring correctly annotated large-scale datasets. Moreover, due to DNNs' rich capacity, errors in training labels can hamper performance. To combat this problem, mean absolute error (MAE) has recently been proposed as a noise-robust alternative to the commonly-used categorical cross entropy (CCE) loss. However, as we show in this paper, MAE can perform poorly with DNNs and challenging datasets. Here, we present a theoretically grounded set of noise-robust loss functions that can be seen as a generalization of MAE and CCE. Proposed loss functions can be readily applied with any existing DNN architecture and algorithm, while yielding good performance in a wide range of noisy label scenarios. We report results from experiments conducted with CIFAR-10, CIFAR-100 and FASHION-MNIST datasets and synthetically generated noisy labels.
Conformal bootstrap at large charge

We consider unitary CFTs with continuous global symmetries in d > 2. We consider a state created by the lightest operator of large charge Q ≫ 1 and analyze the correlator of two light charged operators in this state. We assume that the correlator admits a well-defined large Q expansion and, relatedly, that the macroscopic (thermodynamic) limit of the correlator exists. We find that the crossing equations admit a consistent truncation, where only a finite number N of Regge trajectories contribute to the correlator at leading nontrivial order. We classify all such truncated solutions to the crossing. For one Regge trajectory N = 1, the solution is unique and given by the effective field theory of a Goldstone mode. For two or more Regge trajectories N ≥ 2, the solutions are encoded in roots of a certain degree N polynomial. Some of the solutions admit a simple weakly coupled EFT description, whereas others do not. In the weakly coupled case, each Regge trajectory corresponds to a field in the effective Lagrangian.
Learning Deep Mean Field Games for Modeling Large Population Behavior.

We consider the problem of representing collective behavior of large populations and predicting the evolution of a population distribution over a discrete state space. A discrete time mean field game (MFG) is motivated as an interpretable model founded on game theory for understanding the aggregate effect of individual actions and predicting the temporal evolution of population distributions. We achieve a synthesis of MFG and Markov decision processes (MDP) by showing that a special MFG is reducible to an MDP. This enables us to broaden the scope of mean field game theory and infer MFG models of large real-world systems via deep inverse reinforcement learning. Our method learns both the reward function and forward dynamics of an MFG from real data, and we report the first empirical test of a mean field game model of a real-world social media population.
Sharp Weighted Korn and Korn-Like Inequalities and an Application to Washers

In this paper we prove asymptotically sharp weighted “first-and-a-half” $2D$ Korn and Korn-like inequalities with a singular weight occurring from Cartesian to cylindrical change of variables. We prove some Hardy and the so-called “harmonic function gradient separation” inequalities with the same singular weight. Then we apply the obtained $2D$ inequalities to prove similar inequalities for washers with thickness $h$ subject to vanishing Dirichlet boundary conditions on the inner and outer thin faces of the washer. A washer can be regarded in two ways: As the limit case of a conical shell when the slope goes to zero, or as a very short hollow cylinder. While the optimal Korn constant in the first Korn inequality for a conical shell with thickness $h$ and with a positive slope scales like $h^{1.5}$ , e.g., (Grabovsky and Harutyunyan in arXiv:1602.03601 , 2016), the optimal Korn constant in the first Korn inequality for a washer scales like $h^{2}$ and depends only on the outer radius of the washer as we show in the present work. The Korn constant in the first and a half inequality scales like $h$ and depends only on $h$ . The optimal Korn constant is realized by a Kirchhoff Ansatz. This results can be applied to calculate the critical buckling load of a washer under in plane loads, e.g., (Antman and Stepanov in J. Elast. 124(2):243–278, 2016).
Adoption as a social marker: Innovation diffusion with outgroup aversion

ABSTRACTSocial identities are among the key factors driving behavior in complex societies. Signals of social identity are known to influence individual behaviors in the adoption of innovations. Yet the population-level consequences of identity signaling on the diffusion of innovations are largely unknown. Here we use both analytical and agent-based modeling to consider the spread of a beneficial innovation in a structured population in which there exist two groups who are averse to being mistaken for each other. We investigate the dynamics of adoption and consider the role of structural factors such as demographic skew and communication scale on population-level outcomes. We find that outgroup aversion can lead to adoption being delayed or suppressed in one group, and that population-wide underadoption is common. Comparing the two models, we find that differential adoption can arise due to structural constraints on information flow even in the absence of intrinsic between-group differences in adoption rat...
Symmetric Gini covariance and correlation

Standard Gini covariance and Gini correlation play important roles in measuring the dependence of random variables with heavy tails. However, the asymmetry brings a substantial difficulty in interpretation. In this paper, we propose a symmetric Gini-type covariance and a symmetric Gini correlation ($\rho_g$) based on the joint rank function. The proposed correlation $\rho_g$ is more robust than the Pearson correlation but less robust than the Kendall's $\tau$ correlation. We establish the relationship between $\rho_g$ and the linear correlation $\rho$ for a class of random vectors in the family of elliptical distributions, which allows us to estimate $\rho$ based on estimation of $\rho_g$. The asymptotic normality of the resulting estimators of $\rho$ are studied through two approaches: one from influence function and the other from U-statistics and the delta method. We compare asymptotic efficiencies of linear correlation estimators based on the symmetric Gini, regular Gini, Pearson and Kendall's $\tau$ under various distributions. In addition to reasonably balancing between robustness and efficiency, the proposed measure $\rho_g$ demonstrates superior finite sample performance, which makes it attractive in applications.
The Ghirlanda-Guerra identities for mixed p-spin model

Abstract We show that, under the conditions known to imply the validity of the Parisi formula, if the generic Sherrington–Kirkpatrick Hamiltonian contains a p-spin term then the Ghirlanda–Guerra identities for the pth power of the overlap hold in a strong sense without averaging. This implies strong version of the extended Ghirlanda–Guerra identities for mixed p-spin models than contain terms for all even p ⩾ 2 and p = 1 .
Virtually geometric words and Whitehead's algorithm

Motivated by a question of Gordon and Wilton, we consider the question of which collections of words are "virtually geometric". In particular, we prove that some words (e.g. bbaaccabc) are not virtually geometric.
Modular Bootstrap Revisited

We constrain the spectrum of two-dimensional unitary, compact conformal field theories with central charge c > 1 using modular bootstrap. Upper bounds on the gap in the dimension of primary operators of any spin, as well as in the dimension of scalar primaries, are computed numerically as functions of the central charge using semi-definite programming. Our bounds refine those of Hellerman and Friedan-Keller, and are in some cases saturated by known CFTs. In particular, we show that unitary CFTs with c < 8 must admit relevant deformations, and that a nontrivial bound on the gap of scalar primaries exists for c < 25. We also study bounds on the dimension gap in the presence of twist gaps, bounds on the degeneracy of operators, and demonstrate how “extremal spectra” which maximize the degeneracy at the gap can be determined numerically.
Persistent Topology of Syntax

We study the persistent homology of a data set of syntactic parameters of world languages. We show that, while homology generators behave erratically over the whole data set, non-trivial persistent homology appears when one restricts to specific language families. Different families exhibit different persistent homology. We focus on the cases of the Indo-European and the Niger–Congo families, for which we compare persistent homology over different cluster filtering values. The persistent components appear to correspond to linguistic subfamilies, while the meaning, in historical linguistic terms, of the presence of persistent generators of the first homology is more mysterious. We investigate the possible significance of the persistent first homology generator that we find in the Indo-European family. We show that it is not due to the Anglo-Norman bridge (which is a lexical, not syntactic phenomenon), but is related instead to the position of Ancient Greek and the Hellenic branch within the Indo-European phylogenetic network.
Hierarchical distributed framework for EV charging scheduling using exchange problem

Abstract In this paper, a distributed trilayer multi-agent framework is proposed for optimal electric vehicle charging scheduling (EVCS). The framework reduces the negative effects of electric vehicle charging demand on the electrical grids. To solve the scheduling problem, a novel hierarchical distributed EV charging scheduling (HDEVCS) is developed as the exchange problem, where the agents are clustered based on their coupling constraints. According to the separability of the agents’ objectives and the clusters’ coupled constraints, HDEVCS is solved efficiently in a distributed manner by the alternating direction method of multipliers (ADMM). Comparing to the exiting trilayer methods, HDEVCS reduces the convergence time and the iteration numbers since its structure allows the agents to update their primal optimization variable simultaneously. The performance of HDEVCS is evaluated by numerical simulation of two small- and large- scale case studies consisting of 306 and 9051 agents, respectively. The results verify the scalability and efficiency of the proposed method, as it reduces the convergence time and iteration numbers by 60 % compared to the state-of-the-art methods, flattens the load profile and decreases the charging cost considerably without violating the grid feeders’ capacity. The significant outcome of our method is the accommodation of a large EV population without investment in grid expansion.
On Asymptotic Normality of the Local Polynomial Regression Estimator with Stochastic Bandwidths

Nonparametric density and regression estimators commonly depend on a bandwidth. The asymptotic properties of these estimators have been widely studied when bandwidths are non stochastic. In practice, however, in order to improve finite sample performance of these estimators, bandwidths are selected by data driven methods, such as cross-validation or plug-in procedures. As a result, nonparametric estimators are usually constructed using stochastic bandwidths. In this article, we establish the asymptotic equivalence in probability of local polynomial regression estimators under stochastic and nonstochastic bandwidths. Our result extends previous work by Boente and Fraiman (1995) and Ziegler (2004).
A sum-of-squares approach to the stability and control of interconnected systems using vector Lyapunov functions

Stability analysis tools are essential to understanding and controlling any engineering system. Recently, sum-of-squares (SOS) based methods have been used to compute Lyapunov based estimates for the region-of-attraction (ROA) of polynomial dynamical systems. But for a real-life large scale dynamical system this method becomes inapplicable because of growing computational burden. In such a case, it is important to develop a subsystem based stability analysis approach which is the focus of the work presented here. A parallel and scalable algorithm is used to infer stability of an interconnected system, with the help of the subsystem Lyapunov functions. Locally computable control laws are proposed to guarantee asymptotic stability under a given disturbance.
Feature-Budgeted Random Forest

We seek decision rules for prediction-time cost reduction, where complete data is available for training, but during prediction-time, each feature can only be acquired for an additional cost. We propose a novel random forest algorithm to minimize prediction error for a user-specified average feature acquisition budget. While random forests yield strong generalization performance, they do not explicitly account for feature costs and furthermore require low correlation among trees, which amplifies costs. Our random forest grows trees with low acquisition cost and high strength based on greedy minimax cost-weighted-impurity splits. Theoretically, we establish near-optimal acquisition cost guarantees for our algorithm. Empirically, on a number of benchmark datasets we demonstrate competitive accuracy-cost curves against state-of-the-art prediction-time algorithms.
Nonlinear stability of the ensemble Kalman filter with adaptive covariance inflation

The Ensemble Kalman filter and Ensemble square root filters are data assimilation methods used to combine high dimensional nonlinear models with observed data. These methods have proved to be indispensable tools in science and engineering as they allow computationally cheap, low dimensional ensemble state approximation for extremely high dimensional turbulent forecast models. From a theoretical perspective, these methods are poorly understood, with the exception of a recently established but still incomplete nonlinear stability theory. Moreover, recent numerical and theoretical studies of catastrophic filter divergence have indicated that stability is a genuine mathematical concern and can not be taken for granted in implementation. In this article we propose a simple modification of ensemble based methods which resolves these stability issues entirely. The method involves a new type of adaptive covariance inflation, which comes with minimal additional cost. We develop a complete nonlinear stability theory for the adaptive method, yielding Lyapunov functions and geometric ergodicity under weak assumptions. We present numerical evidence which suggests the adaptive methods have improved accuracy over standard methods and completely eliminate catastrophic filter divergence. This enhanced stability allows for the use of extremely cheap, unstable forecast integrators, which would otherwise lead to widespread filter malfunction.
Moments of averages of generalized Ramanujan sums

Let $$\beta $$ be a positive integer. A generalization of the Ramanujan sum due to Cohen is given by $$\begin{aligned} c_{q,\beta }(n) := \sum \limits _{{{(h,{q^\beta })}_\beta } = 1} {{e^{2\pi inh/{q^\beta }}}}, \end{aligned}$$ where h ranges over the non-negative integers less than $$q^{\beta }$$ such that h and $$q^{\beta }$$ have no common $$\beta $$ -th power divisors other than 1. The distribution of the average value of the Ramanujan sum is a subject of extensive research. In this paper, we study the distribution of the average value of $$c_{q,\beta }(n)$$ by computing the k-th moments of the average value of $$c_{q,\beta }(n)$$ . In particular we have provided the first and second moments with improved error terms. We give more accurate results for the main terms than our predecessors. We also provide an asymptotic result for an extension of a divisor problem and for an extension of Ramanujan’s formula.
Direct numerical simulations of turbulent channel flow under transcritical conditions

Turbulent flows under transcritical conditions are present in regenerative cooling systems of rocker engines and extraction processes in chemical engineering. The turbulent flows and the corresponding heat transfer phenomena in these complex processes are still not well understood experimentally and numerically. The objective of this work is to investigate the turbulent flows under transcritical conditions using DNS of turbulent channel flows. A fully compressible solver is used in conjunction with a Peng-Robinson real-fluid equation of state to describe the transcritical flows. A channel flow with two isothermal walls is simulated with one heated and one cooled boundary layers. The grid resolution adopted in this study is slightly finer than that required for DNS of incompressible channel flows. The simulations are conducted using both fully (FC) and quasi-conservative (QC) schemes to assess their performance for transcritical wall-bounded flows. The instantaneous flows and the statistics are analyzed and compared with the canonical theories. It is found that results from both FC and QC schemes qualitatively agree well with noticeable difference near the top heated wall, where spurious oscillations in velocity can be observed. Using the DNS data, we then examine the usefulness of Townsend attached eddy hypothesis in the context of flows at transcritical conditions. It is shown that the streamwise energy spectrum exhibits the inverse wavenumber scaling and that the streamwise velocity structure function follows a logarithmic scaling, thus providing support to the attached eddy model at transcritical conditions.
Safe platooning of unmanned aerial vehicles via reachability

Recently, there has been immense interest in using unmanned aerial vehicles (UAVs) for civilian operations such as package delivery, firefighting, and fast disaster response. As a result, UAV traffic management systems are needed to support potentially thousands of UAVs flying simultaneously in the airspace, in order to ensure their liveness and safety requirements are met. Hamilton-Jacobi (HJ) reachability is a powerful framework for providing conditions under which these requirements can be met, and for synthesizing the optimal controller for meeting them. However, due to the curse of dimensionality, HJ reachability is only tractable for a small number of vehicles if their set of maneuvers is unrestricted. In this paper, we define a platoon to be a group of UAVs in a single-file formation. We model each vehicle as a hybrid system with modes corresponding to its role in the platoon, and specify the set of allowed maneuvers in each mode to make the analysis tractable. We propose several liveness controllers based on HJ reachability, and wrap a safety controller, also based on HJ reachability, around the liveness controllers. For a single altitude range, our approach guarantees safety for one safety breach; in the unlikely event of multiple safety breaches, safety can be guaranteed over multiple altitude ranges. We demonstrate the satisfaction of liveness and safety requirements through simulations of three common scenarios.
An Online Learning Approach to Model Predictive Control

Model predictive control (MPC) is a powerful technique for solving dynamic control tasks. In this paper, we show that there exists a close connection between MPC and online learning, an abstract theoretical framework for analyzing online decision making in the optimization literature. This new perspective provides a foundation for leveraging powerful online learning algorithms to design MPC algorithms. Specifically, we propose a new algorithm based on dynamic mirror descent (DMD), an online learning algorithm that is designed for non-stationary setups. Our algorithm, Dynamic Mirror Descent Model Predictive Control (DMD-MPC), represents a general family of MPC algorithms that includes many existing techniques as special instances. DMD-MPC also provides a fresh perspective on previous heuristics used in MPC and suggests a principled way to design new MPC algorithms. In the experimental section of this paper, we demonstrate the flexibility of DMD-MPC, presenting a set of new MPC algorithms on a simple simulated cartpole and a simulated and real-world aggressive driving task. Videos of the real-world experiments can be found at this https URL and this https URL.
The diffractive wave trace on manifolds with conic singularities

Abstract Let ( X , g ) be a compact manifold with conic singularities. Taking Δ g to be the Friedrichs extension of the Laplace–Beltrami operator, we examine the singularities of the trace of the half-wave group e − i t Δ g arising from strictly diffractive closed geodesics. Under a generic nonconjugacy assumption, we compute the principal amplitude of these singularities in terms of invariants associated to the geodesic and data from the cone point. This generalizes the classical theorem of Duistermaat–Guillemin on smooth manifolds and a theorem of Hillairet on flat surfaces with cone points.
Sequential Monte Carlo for fractional stochastic volatility models

In this paper, we consider a fractional stochastic volatility model, that is a model in which the volatility may exhibit a long-range dependent or a rough/antipersistent behaviour. We propose a dynamic sequential Monte Carlo methodology that is applicable to both long memory and antipersistent processes in order to estimate the volatility as well as the unknown parameters of the model. We establish a central limit theorem for the state and parameter filters and we study asymptotic properties (consistency and asymptotic normality) for the filter. We illustrate our results with a simulation study and we apply our method to estimate the volatility and the parameters of a long-range dependent model for S& P 500 data.
On Protocol and Physical Interference Models in Poisson Wireless Networks

This paper analyzes the connection between the protocol and physical interference models in the setting of Poisson wireless networks. A transmission is successful under the protocol model if there are no interferers within a parameterized guard zone around the receiver, while a transmission is successful under the physical model if the signal to interference plus noise ratio at the receiver is above a threshold. The parameterized protocol model forms a family of decision rules for predicting the success or failure of the same transmission attempt under the physical model. For Poisson wireless networks, we employ stochastic geometry to determine the prior, evidence, and posterior distributions associated with this estimation problem. With this in hand, we proceed to develop six sets of results: 1) the maximum correlation of protocol and physical model success indicators; 2) the minimum Bayes risk in estimating physical success from a protocol observation; 3) the receiver operating characteristic (ROC) of false rejection (Type I) and false acceptance (Type II) probabilities; 4) the impact of Rayleigh fading versus no fading on the correlation and ROC; 5) the impact of multiple prior protocol model observations in the setting of a wireless network with a fixed set of nodes in which the nodes employ the slotted Aloha protocol in each time slot; and 6) a numerical investigation of the effect of different pathloss models.
ExpSOS: Secure and Verifiable Outsourcing of Exponentiation Operations for Mobile Cloud Computing

Discrete exponential operation, such as modular exponentiation and scalar multiplication on elliptic curves, is a basic operation of many public-key cryptosystems. However, the exponential operations are considered prohibitively expensive for resource-constrained mobile devices. In this paper, we address the problem of secure outsourcing of exponentiation operations to one single untrusted server. Our proposed secure outsourcing scheme for general exponential (ExpSOS) only requires a very limited number of modular multiplications at local mobile environment, and thus it can achieve significant computational performance gain. ExpSOS also provides a secure verification scheme with probability approximately 1 to ensure that the mobile end users can always receive valid results. The comprehensive analysis as well as the simulation results in real mobile device demonstrates that our proposed ExpSOS can significantly improve the existing schemes in efficiency, security, and result verifiability. We apply ExpSOS to securely outsource several cryptographic protocols to show that ExpSOS can be widely applied to many computation-intensive applications and achieve significant performance improvement.
Sensitivity and Generalization in Neural Networks: an Empirical Study

In practice it is often found that large over-parameterized neural networks generalize better than their smaller counterparts, an observation that appears to conflict with classical notions of function complexity, which typically favor smaller models. In this work, we investigate this tension between complexity and generalization through an extensive empirical exploration of two natural metrics of complexity related to sensitivity to input perturbations. Our experiments survey thousands of models with various fully-connected architectures, optimizers, and other hyper-parameters, as well as four different image classification datasets. We find that trained neural networks are more robust to input perturbations in the vicinity of the training data manifold, as measured by the norm of the input-output Jacobian of the network, and that it correlates well with generalization. We further establish that factors associated with poor generalization $-$ such as full-batch training or using random labels $-$ correspond to lower robustness, while factors associated with good generalization $-$ such as data augmentation and ReLU non-linearities $-$ give rise to more robust functions. Finally, we demonstrate how the input-output Jacobian norm can be predictive of generalization at the level of individual test points.
Active Classification with Comparison Queries

We study an extension of active learning in which the learning algorithm may ask the annotator to compare the distances of two examples from the boundary of their label-class. For example, in a recommendation system application (say for restaurants), the annotator may be asked whether she liked or disliked a specific restaurant (a label query); or which one of two restaurants did she like more (a comparison query).We focus on the class of half spaces, and show that under natural assumptions, such as large margin or bounded bit-description of the input examples, it is possible to reveal all the labels of a sample of size n using approximately O(log n) queries. This implies an exponential improvement over classical active learning, where only label queries are allowed. We complement these results by showing that if any of these assumptions is removed then, in the worst case, &#x03A9;(n) queries are required.Our results follow from a new general framework of active learning with additional queries. We identify a combinatorial dimension, called the inference dimension, that captures the query complexity when each additional query is determined by O(1) examples (such as comparison queries, each of which is determined by the two compared examples). Our results for half spaces follow by bounding the inference dimension in the cases discussed above.
Conformal grafting and convergence of Fenchel-Nielsen twist coordinates

We cut a hyperbolic surface of finite area along some analytic simple closed curves, and glue in cylinders of varying moduli. We prove that as the moduli of the glued cylinders go to infinity, the Fenchel-Nielsen twist coordinates for the resulting surface around those cylinders converge.