cssi/SciSciGPT-SciSciNet huggingface dataset:
Randomized estimation of spectral densities of large matrices made accurate

For a large Hermitian matrix $$A\in \mathbb {C}^{N\times N}$$AźCN?N, it is often the case that the only affordable operation is matrix---vector multiplication. In such case, randomized method is a powerful way to estimate the spectral density (or density of states) of A. However, randomized methods developed so far for estimating spectral densities only extract information from different random vectors independently, and the accuracy is therefore inherently limited to $$\mathcal {O}(1/\sqrt{N_{v}})$$O(1/Nv) where $$N_{v}$$Nv is the number of random vectors. In this paper we demonstrate that the "$$\mathcal {O}(1/\sqrt{N_{v}})$$O(1/Nv) barrier" can be overcome by taking advantage of the correlated information of random vectors when properly filtered by polynomials of A. Our method uses the fact that the estimation of the spectral density essentially requires the computation of the trace of a series of matrix functions that are numerically low rank. By repeatedly applying A to the same set of random vectors and taking different linear combination of the results, we can sweep through the entire spectrum of A by building such low rank decomposition at different parts of the spectrum. Under some assumptions, we demonstrate that a robust and efficient implementation of such spectrum sweeping method can compute the spectral density accurately with $$\mathcal {O}(N^2)$$O(N2) computational cost and $$\mathcal {O}(N)$$O(N) memory cost. Numerical results indicate that the new method can significantly outperform existing randomized methods in terms of accuracy. As an application, we demonstrate a way to accurately compute a trace of a smooth matrix function, by carefully balancing the smoothness of the integrand and the regularized density of states using a deconvolution procedure.
Critical Properties of Complex Fitness Landscapes

Evolutionary adaptation is the process that increases the fit of a population to the fitness landscape it inhabits. As a consequence, evolutionary dynamics is shaped, constrained, and channeled, by that fitness landscape. Much work has been expended to understand the evolutionary dynamics of adapting populations, but much less is known about the structure of the landscapes. Here, we study the global and local structure of complex fitness landscapes of interacting loci that describe protein folds or sets of interacting genes forming pathways or modules. We find that in these landscapes, high peaks are more likely to be found near other high peaks, corroborating Kauffman’s “Massif Central” hypothesis. We study the clusters of peaks as a function of the ruggedness of the landscape and find that this clustering allows peaks to form interconnected networks. These networks undergo a percolation phase transition as a function of minimum peak height, which indicates that evolutionary trajectories that take no more than two mutations to shift from peak to peak can span the entire genetic space. These networks have implications for evolution in rugged landscapes, allowing adaptation to proceed after a local fitness peak has been ascended.
On integers $n$ for which $X^n-1$ has a divisor of every degree

A positive integer $n$ is called $\varphi$-practical if the polynomial $X^n-1$ has a divisor in $\mathbb{Z}[X]$ of every degree up to $n$. In this paper, we show that the count of $\varphi$-practical numbers in $[1, x]$ is asymptotic to $C x/\log x$ for some positive constant $C$ as $x \rightarrow \infty$.
A Direct Method for the Transient Stability Analysis of Transmission Switching Events

In this paper, we propose an energy-based method for the transient stability analysis of a power system transmission switching event. In this method the exit point of pseudo-fault trajectory is used to determine a relevant controlling unstable equilibrium point (CUEP) for a switching event, the stability of the switching event is then assessed based on the energy margin between the computed relevant CUEP and the post-switching initial point. The effectiveness of the method is demonstrated on switching events in the structure-preserving models of a heavily loaded version of the WSCC 9-bus 3-machine system, and the base case IEEE 145-bus 50-machine system. A scheme for the detailed analysis of power system switching events is then proposed.
Cooperative jamming for wireless physical layer security

Cooperative jamming is an approach that has been recently proposed for improving physical layer based security for wireless networks in the presence of an eavesdropper. While the source transmits its message to its destination, a relay node transmits a jamming signal to create interference at the eavesdropper. In this paper, a scenario in which the relay is equipped with multiple antennas is considered. A novel system design is proposed for determining the antenna weights and transmit power of source and relay, so that the system secrecy rate is maximized subject to a total transmit power constraint, or, the transmit power is minimized subject to a secrecy rate constraint. Since the optimal solutions to these problems are difficult to obtain, suboptimal closed-form solutions are proposed that introduce an additional constraint, i.e., the complete nulling of jamming signal at the destination.
Stochastic homogenization of interfaces moving with changing sign velocity

Abstract We are interested in the averaging behavior of interfaces moving in stationary ergodic environments with oscillatory normal velocity which changes sign. The problem can be reformulated as the homogenization of a Hamilton–Jacobi equation with a positively homogeneous of degree one non-coercive Hamiltonian. The periodic setting was studied earlier by Cardaliaguet, Lions and Souganidis (2009) [16] . Here we concentrate in the random media and show that the solutions of the oscillatory Hamilton–Jacobi equation converge in L ∞ -weak ⋆ to a linear combination of the initial datum and the solutions of several initial value problems with deterministic effective Hamiltonian(s), determined by the properties of the random media.
Adiabatic approach for natural gas pipeline computations

We consider slowly evolving, i.e. ADIABATIC, operational regime within a transmission level (continental scale) natural gas pipeline system. This allows us to introduce a set of nodal equations of reduced complexity describing gas transients in injection/consumption UNBALANCED (so-called line-pack) cases. We discuss, in details, construction of the UNBALANCED ADIABATIC (UA) approximation on the basic example of a single pipe. The UA approximation is expected to play a significant “model reduction” role in solving control, optimization and planning problems relevant for flawless functioning of modern natural gas networks.
Universal countable Borel quasi-orders

In recent years, much work in descriptive set theory has been focused on the Borel complexity of naturally occurring classification problems, in particular, the study of countable Borel equivalence relations and their structure under the quasi-order of Borel reducibility. Following the approach of Louveau and Rosendal for the study of analytic equivalence relations, we study countable Borel quasi-orders. In this paper we are concerned with universal countable Borel quasi-orders, i.e., countable Borel quasi-orders above all other countable Borel quasi-orders with regard to Borel reducibility. We first establish that there is a universal countable Borel quasi-order, and then establish that several countable Borel quasi-orders are universal. An important example is an embeddability relation on descriptive set theoretic trees. Our main result states that embeddability of finitely generated groups is a universal countable Borel quasi-order, answering a question of Louveau and Rosendal. This immediately implies that biembeddability of finitely generated groups is a universal countable Borel equivalence relation. The same techniques are also used to show that embeddability of countable groups is a universal analytic quasi-order. Finally, we show that, up to Borel bireducibility, there are 2^(X)0 distinct countable Borel quasi-orders, which symmetrize to a universal countable Borel equivalence relation.
On Gevrey regularity of the supercritical SQG equation in critical Besov spaces

Abstract In this paper, we show that the solution of the supercritical surface quasi-geostrophic (SQG) equation, with initial data in a critical Besov space, belongs to a subanalytic Gevrey class. In order to prove this, a suitable estimate on the nonlinear term, in the form of a commutator, is required. We express the commutator as a bilinear multiplier operator and obtain single-scale estimates for its symbol. In particular, we show that the localized symbol is of Marcinkiewicz type, and show that due to the localizations inherited from working in the Besov spaces, this condition implies the requisite boundedness of the corresponding operator. This result strengthens previous ones which showed that solutions starting from initial data in critical Besov spaces are classical. As a direct consequence of our method, decay estimates of higher-order derivatives are easily deduced.
A local curvature estimate for the Ricci flow

Abstract We show that the norm of the Riemann curvature tensor of any smooth solution to the Ricci flow can be explicitly estimated in terms of its initial values on a given ball, a local uniform bound on the Ricci tensor, and the elapsed time. This provides a new, direct proof of a result of Sesǔm, which asserts that the curvature of a solution on a compact manifold cannot blow up while the Ricci curvature remains bounded, and extends its conclusions to the noncompact setting. We also prove that the Ricci curvature must blow up at least linearly along a subsequence at a finite time singularity.
A BRACKET POLYNOMIAL FOR GRAPHS, IV: UNDIRECTED EULER CIRCUITS, GRAPH-LINKS AND MULTIPLY MARKED GRAPHS

In earlier work we introduced the graph bracket polynomial of graphs with marked vertices, motivated by the fact that the Kauffman bracket of a link diagram D is determined by a looped, marked version of the interlacement graph associated to a directed Euler system of the universe graph of D. Here we extend the graph bracket to graphs whose vertices may carry different kinds of marks, and we show how multiply marked graphs encode interlacement with respect to arbitrary (undirected) Euler systems. The extended machinery brings together the earlier version and the graph-links of Ilyutko and Manturov [J. Knot Theory Ramifications18 (2009) 791–823]. The greater flexibility of the extended bracket also allows for a recursive description much simpler than that of the earlier version.
Approximate Green’s function for the conductivity equation with conormal coefficient

We construct an approximate Green’s function for \(L_{\gamma }:={\nabla } \cdot \gamma (x) {\nabla } u(x)\), which belongs to a class of Fourier integral operators (FIOs) associated to two canonical relations. This leads to analysis of the composition of two FIOs, associated to a canonical relation with a zero section problem. The resulting composition is a sum of two FIOs, each associated to two intersecting canonical relations.
CONSECUTIVE PRIMES IN TUPLES

In a stunning new advance towards the Prime k-tuple Conjecture, Maynard and Tao have shown that if k is sufficiently large in terms ofm, then for any admissible k-tuple H(x) = {gjx + hj} k=1 of linear forms in Z(x) the set H(n) = {gjn + hj} k=1 contains at least m primes for infinitely many n ∈ N. In this short note, we show how the Maynard-Tao theorem may be used to produce m-tuples H(x) for which the m primes that occur in H(n) are consecutive. We answer an old question of Erdýos and Turan by producing strings of m + 1 consecutive primes whose successive gaps �1,...,�m form an increasing (resp. decreasing) sequence. We also show that such strings exist for whichj 1 | �j for 2 6 j 6 m. For any coprime integers a and D > 1 we find strings of consecutive primes of arbitrary length in the congruence class a mod D.
Revisiting Summarization Evaluation for Scientific Articles.

Evaluation of text summarization approaches have been mostly based on metrics that measure similarities of system generated summaries with a set of human written gold-standard summaries. The most widely used metric in summarization evaluation has been the ROUGE family. ROUGE solely relies on lexical overlaps between the terms and phrases in the sentences; therefore, in cases of terminology variations and paraphrasing, ROUGE is not as effective. Scientific article summarization is one such case that is different from general domain summarization (e.g. newswire data). We provide an extensive analysis of ROUGE’s effectiveness as an evaluation metric for scientific summarization; we show that, contrary to the common belief, ROUGE is not much reliable in evaluating scientific summaries. We furthermore show how different variants of ROUGE result in very different correlations with the manual Pyramid scores. Finally, we propose an alternative metric for summarization evaluation which is based on the content relevance between a system generated summary and the corresponding human written summaries. We call our metric SERA (Summarization Evaluation by Relevance Analysis). Unlike ROUGE, SERA consistently achieves high correlations with manual scores which shows its effectiveness in evaluation of scientific article summarization.
A Catalog of 29 Open Clusters and Associations Observed by the Kepler and K2 Missions

Over the past nine years, the Kepler and K2 Missions have carried out high precision photometric monitoring of more than half a million stars. Among these targets are 29 clusters and associations, with ages from 1 Myr to over 11 Gyr. We have generated a catalog of Kepler/K2 clusters, including basic information about the observations as well as the degree of scientific attention paid to them thus far. We present the catalog and a discussion of current and future cluster science endeavors as a way to motivate the astronomical community to continue mining these exquisite datasets.
Symmetric drainage flow of a compressible fluid from a fracture: Analytical solution and slip-like flow rate

Abstract Symmetric drainage flow of a compressible fluid from a thin fracture modeled as a long narrow 2D channel is studied on the basis of linearized compressible Navier-Stokes equations with the no-slip condition. The Helmholtz decomposition theorem is used to decompose the velocity field into an irrotational part and a solenoidal part. The irrotational velocity is driven by the fluid's volumetric expansion; whilst the role of the solenoidal velocity is to enforce the no-slip condition for the overall velocity and it does not contribute to the mass flow rate. It is found that, at large times, this no-slip flow exhibits a time-dependent slip-like mass flow rate linearly proportional to the channel gap instead of the cubic power of the gap for the Poiseuille-type of flow. The drainage rate is also proportional to the kinematic viscosity, opposite to Poiseuille-type of flow, which produces a drainage rate proportional to the inverse of the kinematic viscosity. The same drainage rate formula also applies to drainage flow from a semi-sealed thin fracture.
Rigid Body Dynamic Simulation With Multiple Convex Contact Patches

We present a principled method for dynamic simulation of rigid bodies in intermittent contact with each other where the contact is assumed to be a non-convex contact patch that can be modeled as a union of convex patches. The prevalent assumption in simulating rigid bodies undergoing intermittent contact with each other is that the contact is a point contact. In recent work, we introduced an approach to simulate contacting rigid bodies with convex contact patches (line and surface contact). In this paper, for non-convex contact patches modeled as a union of convex patches, we formulate a discrete-time mixed complementarity problem where we solve the contact detection and integration of the equations of motion simultaneously. Thus, our method is a geometrically-implicit method and we prove that in our formulation, there is no artificial penetration between the contacting rigid bodies. We solve for the equivalent contact point (ECP) and contact impulse of each contact patch simultaneously along with the state, i.e., configuration and velocity of the objects. We provide empirical evidence to show that if the number of contact patches between two objects is less than or equal to three, the state evolution of the bodies is unique, although the contact impulses and ECP may not be unique. We also present simulation results showing that our method can seamlessly capture transition between different contact modes like non-convex patch to point (or line contact) and vice-versa during simulation.
Optimal local and remote controllers with unreliable communication

We consider a decentralized optimal control problem for a linear plant controlled by two controllers, a local controller and a remote controller. The local controller directly observes the state of the plant and can inform the remote controller of the plant state through a packet-drop channel. We assume that the remote controller is able to send acknowledgments to the local controller to signal the successful receipt of transmitted packets. The objective of the two controllers is to cooperatively minimize a quadratic performance cost. We provide a dynamic program for this decentralized control problem using the common information approach. Although our problem is not a partially nested LQG problem, we obtain explicit optimal strategies for the two controllers. In the optimal strategies, both controllers compute a common estimate of the plant state based on the common information. The remote controller's action is a linear function of the common state estimate, and the local controller's action is a linear function of both the actual state and the common state estimate.
Nielsen equivalence in mapping tori over the torus

We use the geometry of the Farey graph to give an alternative proof of the fact that if $A \in GL_2\mathbb Z$ and $G_A=\mathbb Z^2 \rtimes_A \mathbb Z$ is generated by two elements, there is a single Nielsen equivalence class of $2$-element generating sets for $G_A$ unless $A$ is conjugate to $\pm \left(\begin {smallmatrix} 2 & 1 \\ 1 & 1 \end {smallmatrix}\right )$, in which case there are two.
Crystals and D-modules

The goal of this paper is to develop the notion of crystal in the context of derived algebraic geometry, and to connect crystals to more classical objects such as D-modules.
Multilayer Spectral Graph Clustering via Convex Layer Aggregation: Theory and Algorithms

Multilayer graphs are commonly used for representing different relations between entities and handling heterogeneous data processing tasks. Nonstandard multilayer graph clustering methods are needed for assigning clusters to a common multilayer node set and for combining information from each layer. This paper presents a multilayer spectral graph clustering (SGC) framework that performs convex layer aggregation. Under a multilayer signal-plus-noise model, we provide a phase transition analysis of clustering reliability. Moreover, we use the phase transition criterion to propose a multilayer iterative model order selection algorithm (MIMOSA) for multilayer SGC, which features automated cluster assignment and layer weight adaptation, and provides statistical clustering reliability guarantees. Numerical simulations on synthetic multilayer graphs verify the phase transition analysis, and experiments on real-world multilayer graphs show that MIMOSA is competitive or better than other clustering methods.
ALOHA-NOMA for Massive Machine-to-Machine IoT Communication

This paper proposes a new medium access control (MAC) protocol for Internet of Things (IoT) applications incorporating pure ALOHA with power domain non-orthogonal multiple access (NOMA) in which the number of transmitters are not known as a priori information and estimated with multihypothesis testing. The proposed protocol referred to as ALOHA-NOMA is not only scalable, energy efficient and matched to the low complexity requirements of IoT devices, but it also significantly increases the throughput. Specifically, throughput is increased to 1.27 with ALOHA-NOMA when 5 users can be separated via a SIC (Successive Interference Cancellation) receiver in comparison to the classical result of 0.18 in pure ALOHA. The results further show that there is a greater than linear increase in throughput as the number of active IoT devices increases.
Integrable orbit equivalence rigidity for free groups

It is shown that every accessible group which is integrable orbit equivalent to a free group is virtually free. Moreover, we also show that any integrable orbit-equivalence between finitely generated groups extends to their end compactifications.
An introduction to large deviations for random graphs

This article gives an overview of the emerging literature on large deviations for random graphs. Written for the general mathematical audience, the article begins with a short introduction to the theory of large deviations. This is followed by a description of some large deviation questions about random graphs, and an outline of the recent progress on this topic. A more elaborate discussion follows, with a brief account of graph limit theory and its application in constructing a large deviation theory for dense random graphs. The role of Szemer\'edi's regularity lemma is explained, together with a sketch of the proof of the main large deviation result and some examples. Applications to exponential random graph models are briefly touched upon. The remainder of the paper is devoted to large deviations for sparse graphs. Since the regularity lemma is not applicable in the sparse regime, new tools are needed. Fortunately, there have been several new breakthroughs that managed to achieve the goal by an indirect method. These are discussed, together with an exposition of the underlying theory. The last section contains a list of open problems.
Improving Multilingual Sentence Embedding using Bi-directional Dual Encoder with Additive Margin Softmax.

In this paper, we present an approach to learn multilingual sentence embeddings using a bi-directional dual-encoder with additive margin softmax. The embeddings are able to achieve state-of-the-art results on the United Nations (UN) parallel corpus retrieval task. In all the languages tested, the system achieves P@1 of 86% or higher. We use pairs retrieved by our approach to train NMT models that achieve similar performance to models trained on gold pairs. We explore simple document-level embeddings constructed by averaging our sentence embeddings. On the UN document-level retrieval task, document embeddings achieve around 97% on P@1 for all experimented language pairs. Lastly, we evaluate the proposed model on the BUCC mining task. The learned embeddings with raw cosine similarity scores achieve competitive results compared to current state-of-the-art models, and with a second-stage scorer we achieve a new state-of-the-art level on this task.
Learning Two Layer Rectified Neural Networks in Polynomial Time.

Consider the following fundamental learning problem: given input examples $x \in \mathbb{R}^d$ and their vector-valued labels, as defined by an underlying generative neural network, recover the weight matrices of this network. We consider two-layer networks, mapping $\mathbb{R}^d$ to $\mathbb{R}^m$, with $k$ non-linear activation units $f(\cdot)$, where $f(x) = \max \{x , 0\}$ is the ReLU. Such a network is specified by two weight matrices, $\mathbf{U}^* \in \mathbb{R}^{m \times k}, \mathbf{V}^* \in \mathbb{R}^{k \times d}$, such that the label of an example $x \in \mathbb{R}^{d}$ is given by $\mathbf{U}^* f(\mathbf{V}^* x)$, where $f(\cdot)$ is applied coordinate-wise. Given $n$ samples as a matrix $\mathbf{X} \in \mathbb{R}^{d \times n}$ and the (possibly noisy) labels $\mathbf{U}^* f(\mathbf{V}^* \mathbf{X}) + \mathbf{E}$ of the network on these samples, where $\mathbf{E}$ is a noise matrix, our goal is to recover the weight matrices $\mathbf{U}^*$ and $\mathbf{V}^*$. In this work, we develop algorithms and hardness results under varying assumptions on the input and noise. Although the problem is NP-hard even for $k=2$, by assuming Gaussian marginals over the input $\mathbf{X}$ we are able to develop polynomial time algorithms for the approximate recovery of $\mathbf{U}^*$ and $\mathbf{V}^*$. Perhaps surprisingly, in the noiseless case our algorithms recover $\mathbf{U}^*,\mathbf{V}^*$ exactly, i.e., with no error. To the best of the our knowledge, this is the first algorithm to accomplish exact recovery. For the noisy case, we give the first polynomial time algorithm that approximately recovers the weights in the presence of mean-zero noise $\mathbf{E}$. Our algorithms generalize to a larger class of rectified activation functions, $f(x) = 0$ when $x\leq 0$, and $f(x) > 0$ otherwise.
People, Inc.? Law, Economic Enterprise, and the Development of Inequality in China

This Article tells the story of two Chinas and of different forms of public enterprise associated with each: state-owned enterprises (SOEs) in urban China and township-and-village enterprises (TVEs) in rural China. Historically SOEs have constituted the dominant form of socialist enterprise in China. However, China’s unprecedented economic growth began with the rise of rural industry in the 1980s, and the bulk of rural growth was generated by a new type of entity known as TVEs. While legal scholars have mostly ignored TVEs, economists have devoted a great deal of theoretical attention to them: How were TVEs able to succeed in the absence of legally protected property rights, in defiance of standard economic theory? Remarkably, they operated without a formal legal basis. This Article argues that long before the enactment of the PRC’s first Company Law in 1993, in TVEs local government law performed the core functions of corporation law—a phenomenon this Article characterizes as “Village, Inc.” It was this law of local governance, and the formal and informal institutions supporting it, that propelled China’s phenomenal growth for nearly two decades while helping close the historic welfare gap between city and country. The Article next compares TVEs’ record of success with that of SOEs. The Company Law promulgated in 1993 marked a reorientation from rural reforms to restructuring urban SOEs. Despite its apparent novelty, in many respects the Company Law simply codified institutional arrangements pioneered by TVEs. Even after SOEs were “corporatized” in order to attract outside capital, the state remained a controlling shareholder—a configuration this Article describes as “People, Inc.” However, despite the benefit of a formally promulgated corporate statute, as a group corporatized SOEs have not been able to replicate TVEs’ extraordinary success. Beyond the Company Law’s formal structures, there has been no informal “local law” of SOEs to regulate them, equivalent to the relatively egalitarian village institutions that governed the operation of TVEs. Significantly, however, the corporatization of SOEs has not only restructured the state’s relationship to capital. The final part of the Article considers how it has also fundamentally altered the relationship between capital and labor. The enactment of the Company Law was accompanied by the promulgation of a new Labor Law in 1994, mandating that all employees be provided with employment contracts. Since then, the revolutionary political subject of Maoism—“the people”—has been atomized into independent economic subjects responsible for their own welfare outside of work. This, in turn, has resulted in tectonic shifts in the boundaries among the state, the market, and the family. Moreover, with the contractualization of all labor, even urban workers no longer enjoy a guaranteed share of the benefits of economic development. Today, an earlier state-enforced inequality between city and country is increasingly overwhelmed by a society-wide gulf between the rich and the poor, without a necessary geographical correlate.
Searching for Humanitarian Discretion in Immigration Enforcement: Reflections on a Year as an Immigration Attorney in the Trump Era

This article describes one of the most striking features of the Trump Administration’s immigration policy: the shift in the way discretion operates in the legal immigration system. Unlike other high-profile immigration policies that have been the focus of class action lawsuits and public outcry, the changes to the role of discretion have attracted little attention, in part because they are implemented through low-visibility individualized decisions that are difficult to identify, let alone challenge systemically. After providing historical context regarding the role of discretion in the immigration system before the Trump Administration, I offer four case studies from my immigration practice in Arizona that illustrate discretion’s new role. The cases highlight three key trends that result from the way discretion currently operates in the immigration system: (1) the ever-widening enforcement net; (2) the emboldening of front-line bureaucrats; and (3) the changing bureaucratic culture within United States Citizenship and Immigration Services, an agency that previously had seen its mission as one of integration, but has now shifted to an aggressive enforcement orientation. I close with a final section reflecting on the important role that individual direct representation can play in fighting against this new enforcement regime.
Functional Horseshoe Priors for Subspace Shrinkage.

We introduce a new shrinkage prior on function spaces, called the functional horseshoe (fHS) prior, that encourages shrinkage toward parametric classes of functions. Unlike other shrinkage priors f...
Iteration complexity of inexact augmented Lagrangian methods for constrained convex programming

Augmented Lagrangian method (ALM) has been popularly used for solving constrained optimization problems. Practically, subproblems for updating primal variables in the framework of ALM usually can only be solved inexactly. The convergence and local convergence speed of ALM have been extensively studied. However, the global convergence rate of the inexact ALM is still open for problems with nonlinear inequality constraints. In this paper, we work on general convex programs with both equality and inequality constraints. For these problems, we establish the global convergence rate of the inexact ALM and estimate its iteration complexity in terms of the number of gradient evaluations to produce a primal and/or primal-dual solution with a specified accuracy. We first establish an ergodic convergence rate result of the inexact ALM that uses constant penalty parameters or geometrically increasing penalty parameters. Based on the convergence rate result, we then apply Nesterov’s optimal first-order method on each primal subproblem and estimate the iteration complexity of the inexact ALM. We show that if the objective is convex, then $$O(\varepsilon ^{-1})$$ gradient evaluations are sufficient to guarantee a primal $$\varepsilon $$ -solution in terms of both primal objective and feasibility violation. If the objective is strongly convex, the result can be improved to $$O(\varepsilon ^{-\frac{1}{2}}|\log \varepsilon |)$$ . To produce a primal-dual $$\varepsilon $$ -solution, more gradient evaluations are needed for convex case, and the number is $$O(\varepsilon ^{-\frac{4}{3}})$$ , while for strongly convex case, the number is still $$O(\varepsilon ^{-\frac{1}{2}}|\log \varepsilon |)$$ . Finally, we establish a nonergodic convergence rate result of the inexact ALM that uses geometrically increasing penalty parameters. This result is established only for the primal problem. We show that the nonergodic iteration complexity result is in the same order as that for the ergodic result. Numerical experiments on quadratically constrained quadratic programming are conducted to compare the performance of the inexact ALM with different settings.
Visual inspection of metal surfaces

The majority of applications of automatic visual inspection have been the case in which a high contrast image can be obtained. This will result from object silhouettes 1 and high contrast reflectivity changes as in printed text. In these cases, the image can usually be successfully segmented by a threshold operation 2 , 3 leading to a two-level or binary image.
Differentially Private Bayesian Linear Regression

Linear regression is an important tool across many fields that work with sensitive human-sourced data. Significant prior work has focused on producing differentially private point estimates, which provide a privacy guarantee to individuals while still allowing modelers to draw insights from data by estimating regression coefficients. We investigate the problem of Bayesian linear regression, with the goal of computing posterior distributions that correctly quantify uncertainty given privately released statistics. We show that a naive approach that ignores the noise injected by the privacy mechanism does a poor job in realistic data settings. We then develop noise-aware methods that perform inference over the privacy mechanism and produce correct posteriors across a wide range of scenarios.
Strong Stability Preserving Integrating Factor Two-Step Runge–Kutta Methods

Problems with components that feature significantly different time scales, where the stiff time-step restriction comes from a linear component, implicit-explicit (IMEX) methods alleviate this restriction if the concern is linear stability. However, when nonlinear non-inner-product stability properties are of interest, such as in the evolution of hyperbolic partial differential equations with shocks or sharp gradients, linear inner-product stability is no longer sufficient for convergence, and so strong stability preserving (SSP) methods are often needed. Where the SSP property is needed, IMEX SSP Runge–Kutta (SSP-IMEX) methods have very restrictive time-steps. An alternative to SSP-IMEX schemes is to adopt an integrating factor approach to handle the linear component exactly and step the transformed problem forward using some time-evolution method. The strong stability properties of integrating factor Runge–Kutta methods were established in Isherwood et al. (SIAM J Numer Anal 56(6):3276–3307, 2018), where it was shown that it is possible to define explicit integrating factor Runge–Kutta methods that preserve strong stability properties satisfied by each of the two components when coupled with forward Euler time-stepping. It was proved that the solution will be SSP if the transformed problem is stepped forward with an explicit SSP Runge–Kutta method that has non-decreasing abscissas. However, explicit SSP Runge–Kutta methods have an order barrier of $$p=4$$, and sometimes higher order is desired. In this work we consider explicit SSP two-step Runge–Kutta integrating factor methods to raise the order. We show that strong stability is ensured if the two-step Runge–Kutta method used to evolve the transformed problem is SSP and has non-decreasing abscissas. We find such methods up to eighth order and present their SSP coefficients. Adding a step allows us to break the fourth order barrier on explicit SSP Runge–Kutta methods; furthermore, our explicit SSP two-step Runge–Kutta methods with non-decreasing abscissas typically have larger SSP coefficients than the corresponding one-step methods. A selection of our methods are tested for convergence and demonstrate the design order. We also show, for selected methods, that the SSP time-step predicted by the theory is a lower bound of the allowable time-step for linear and nonlinear problems that satisfy the total variation diminishing (TVD) condition. We compare some of the non-decreasing abscissa SSP two-step Runge–Kutta methods to previously found methods that do not satisfy this criterion on linear and nonlinear TVD test cases to show that this non-decreasing abscissa condition is indeed necessary in practice as well as theory. We also compare these results to our SSP integrating factor Runge–Kutta methods designed in Isherwood et al. (2018).
Positive Grassmannian and polyhedral subdivisions

The nonnegative Grassmannian is a cell complex with rich geometric, algebraic, and combinatorial structures. Its study involves interesting combinatorial objects, such as positroids and plabic graphs. Remarkably, the same combinatorial structures appeared in many other areas of mathematics and physics, e.g., in the study of cluster algebras, scattering amplitudes, and solitons. We discuss new ways to think about these structures. In particular, we identify plabic graphs and more general Grassmannian graphs with polyhedral subdivisions induced by 2-dimensional projections of hypersimplices. This implies a close relationship between the positive Grassmannian and the theory of fiber polytopes and the generalized Baues problem. This suggests natural extensions of objects related to the positive Grassmannian.
CASPER: capacitive serendipitous power transfer for through-body charging of multiple wearable devices.

We present CASPER, a charging solution to enable a future of wearable devices that are much more distributed on the body. Instead of having to charge every device we want to adorn our bodies with, may it be distributed health sensors or digital jewelry, we can instead augment everyday objects such as beds, seats, and frequently worn clothing to provide convenient charging base stations that will charge devices on our body serendipitously as we go about our day. Our system works by treating the human body as a conductor and capacitively charging devices worn on the body whenever a well coupled electrical path is created during natural use of everyday objects. In this paper, we performed an extensive parameter characterization for through-body power transfer and based on our empirical findings, we present a design trade-off visualization to aid designers looking to integrate our system. Furthermore, we demonstrate how we utilized this design process in the development of our own smart bandage device and a LED adorned temporary tattoo that charges at hundreds of micro-watts using our system.
Nonequilibrium Oscillations, Probability Angular Momentum, and the Climate System

Though the Boltzmann–Gibbs framework of equilibrium statistical mechanics has been successful in many arenas, it is clearly inadequate for describing many interesting natural phenomena driven far from equilibrium. The simplest step towards that goal is a better understanding of nonequilibrium steady-states (NESS). Here we focus on one of the distinctive features of NESS—persistent probability currents—and their manifestations in our climate system. We consider the natural variability of the steady-state climate system, which can be approximated as a NESS. These currents must form closed loops, which are odd under time reversal, providing the crucial difference between systems in thermal equilibrium and NESS. Seeking manifestations of such current loops leads us naturally to the notion of “probability angular momentum” and oscillations in the space of observables. Specifically, we will relate this concept to the asymmetric part of certain time-dependent correlation functions. Applying this approach, we propose that these current loops give rise to preferred spatio-temporal patterns of natural climate variability that take the form of climate oscillations such as the El-Nino Southern Oscillation (ENSO) and the Madden–Julian Oscillation (MJO). In the space of climate indices, we observe persistent currents and define a new diagnostic for these currents: the probability angular momentum ( $$\mathscr {L}$$ ). Using the observed climatic time series of ENSO and MJO, we compute both the averages and the distributions of $$\mathscr {L}$$ . These results are in good agreement with the analysis from a linear Gaussian model. We propose that, in addition to being a new quantification of climate oscillations across models and observations, the probability angular momentum provides a meaningful characterization for all statistical systems in NESS.
Temperature Dependence of the Anomalous Hall Effect from Electron Interactions.

We consider the impact of electron-electron interactions on the temperature dependence of the anomalous Hall effect in disordered conductors. The microscopic analysis is carried out within the diagrammatic approach of the linear response Kubo-Streda formula with an account of both extrinsic skew-scattering and side-jump mechanisms of the anomalous Hall effect arising in the presence of spin-orbit coupling. We demonstrate the importance of electron interactions in the Cooper channel even for nominally non-superconducting materials and find that the corresponding low-temperature dependence of the anomalous Hall conductivity is asymptotically of the form $\sqrt{T}/\mathrm{ln}({T}_{0}/T)$ in three dimensions and $\mathrm{ln}[\mathrm{ln}({T}_{0}/T)]$ in two dimensions, where the scale of ${T}_{0}$ is parametrically of the order of Fermi energy. These results, in particular, may provide a possible explanation for the recently observed unconventional temperature dependence of the anomalous Hall effect in ${\mathrm{HgCr}}_{2}{\mathrm{Se}}_{4}$.
Trajectory Prediction by Coupling Scene-LSTM with Human Movement LSTM

We develop a novel human trajectory prediction system that incorporates the scene information (Scene-LSTM) as well as individual pedestrian movement (Pedestrian-LSTM) trained simultaneously within static crowded scenes. We superimpose a two-level grid structure (grid cells and subgrids) on the scene to encode spatial granularity plus common human movements. The Scene-LSTM captures the commonly traveled paths that can be used to significantly influence the accuracy of human trajectory prediction in local areas (i.e. grid cells). We further design scene data filters, consisting of a hard filter and a soft filter, to select the relevant scene information in a local region when necessary and combine it with Pedestrian-LSTM for forecasting a pedestrian’s future locations. The experimental results on several publicly available datasets demonstrate that our method outperforms related works and can produce more accurate predicted trajectories in different scene contexts.
Zonal Jet Creation from Secondary Instability of Drift Waves for Plasma Edge Turbulence

A new strategy is presented to explain the creation and persistence of zonal flows widely observed in plasma edge turbulence. The core physics in the edge regime of the magnetic-fusion tokamaks can be described qualitatively by the one-state modified Hasegawa-Mima (MHM for short) model, which creates enhanced zonal flows and more physically relevant features in comparison with the familiar Charney-Hasegawa-Mima (CHM for short) model for both plasma and geophysical flows. The generation mechanism of zonal jets is displayed from the secondary instability analysis via nonlinear interactions with a background base state. Strong exponential growth in the zonal modes is induced due to a non-zonal drift wave base state in the MHM model, while stabilizing damping effect is shown with a zonal flow base state. Together with the selective decay effect from the dissipation, the secondary instability offers a complete characterization of the convergence process to the purely zonal structure. Direct numerical simulations with and without dissipation are carried out to confirm the instability theory. It shows clearly the emergence of a dominant zonal flow from pure non-zonal drift waves with small perturbation in the initial configuration. In comparison, the CHM model does not create instability in the zonal modes and usually converges to homogeneous turbulence.
A homotopy training algorithm for fully connected neural networks.

In this paper, we present a homotopy training algorithm (HTA) to solve optimization problems arising from fully connected neural networks with complicated structures. The HTA dynamically builds the...
Modeling material stress using integrated Gaussian Markov random fields

The equations of a physical constitutive model for material stress within tantalum grains were solved numerically using a tetrahedrally meshed volume. The resulting output included a scalar vonMise...
Regularized calibrated estimation of propensity scores with model misspecification and high-dimensional data

Propensity score methods are widely used for estimating treatment effects from observational studies. A popular approach is to estimate propensity scores by maximum likelihood based on logistic regression, and then apply inverse probability weighted estimators or extensions to estimate treatment effects. However, a challenging issue is that such inverse probability weighting methods including doubly robust methods can perform poorly even when the logistic model appears adequate as examined by conventional techniques. In addition, there is increasing difficulty to appropriately estimate propensity scores when dealing with a large number of covariates. To address these issues, we study calibrated estimation as an alternative to maximum likelihood estimation for fitting logistic propensity score models. We show that, with possible model misspecification, minimizing the expected calibration loss underlying the calibrated estimators involves reducing both the expected likelihood loss and a measure of relative errors which controls the mean squared errors of inverse probability weighted estimators. Furthermore, we propose a regularized calibrated estimator by minimizing the calibration loss with a Lasso penalty. We develop a novel Fisher scoring descent algorithm for computing the proposed estimator, and provide a high-dimensional analysis of the resulting inverse probability weighted estimators of population means, leveraging the control of relative errors for calibrated estimation. We present a simulation study and an empirical application to demonstrate the advantages of the proposed methods compared with maximum likelihood and regularization.
Overlearning Reveals Sensitive Attributes

``"Overlearning'' means that a model trained for a seemingly simple objective implicitly learns to recognize attributes and concepts that are (1) not part of the learning objective, and (2) sensitive from a privacy or bias perspective. For example, a binary gender classifier of facial images also learns to recognize races, even races that are not represented in the training data, and identities. We demonstrate overlearning in several vision and NLP models and analyze its harmful consequences. First, inference-time representations of an overlearned model reveal sensitive attributes of the input, breaking privacy protections such as model partitioning. Second, an overlearned model can be "`re-purposed'' for a different, privacy-violating task even in the absence of the original training data. We show that overlearning is intrinsic for some tasks and cannot be prevented by censoring unwanted attributes. Finally, we investigate where, when, and why overlearning happens during model training.
Technological change in the production of new scientific knowledge: a second look

This paper presents and explains an approach for measuring technological change in the production of new scientific knowledge. The paper expands our previous work on this topic. Our approach is ill...
The Connectedness of Space Curve Invariants

In this paper we will give necessary conditions for a Borel-fixed monomial ideal to be the generic initial ideal of a reduced, irreducible, non-degenerate curve in P3.
Controllability-Gramian submatrices for a network consensus model

Abstract Principal submatrices of the controllability Gramian and their inverses are examined, for a network-consensus model with inputs at a subset of network nodes. Several properties of the Gramian submatrices and their inverses – including dominant eigenvalues and eigenvectors, diagonal entries, and sign patterns – are characterized by exploiting the special doubly-nonnegative structure of the matrices. In addition, majorizations for these properties are obtained in terms of cutsets in the network’s graph, based on the diffusive form of the model. The asymptotic (long time horizon) structure of the controllability Gramian is also analyzed. The results on the Gramian are used to study metrics for target control of the network-consensus model.