cssi/SciSciGPT-SciSciNet huggingface dataset:
Information Bottleneck Methods for Distributed Learning

We study a distributed learning problem in which Alice sends a compressed distillation of a set of training data to Bob, who uses the distilled version to best solve an associated learning problem. We formalize this as a rate-distortion problem in which the training set is the source and Bob’s cross-entropy loss is the distortion measure. We consider this problem for un- supervised learning for batch and sequential data. In the batch data, this problem is equivalent to the information bottleneck (IB), and we show that reduced-complexity versions of standard IB methods solve the associated rate-distortion problem. For the streaming data, we present a new algorithm, which may be of independent interest, that solves the rate-distortion problem for Gaussian sources. Furthermore, to improve the results of the iterative algorithm for sequential data we introduce a two-pass version of this algorithm. Finally, we show the dependency of the rate on the number of samples k required for Gaussian sources to ensure cross-entropy loss that scales optimally with the growth of the training set.
Exchange-Correlation Energy Functional Based on the Airy-Gas Reference System

In recent work, generalized gradient approximations (GGAs) have been constructed from the energy density of the Airy gas for exchange but not for correlation. We report the random-phase approximation (RPA) conventional correlation energy density of the Airy gas, the simplest edge electron gas, in which the auxiliary noninteracting electrons experience a linear potential. By fitting the Airy-gas RPA exchange-correlation energy density and making an accurate short-range correction to RPA, we propose a simple beyond RPA GGA density functional (``$\text{ARPA}+$'') for the exchange-correlation energy. Our functional, tested for jellium surfaces, atoms, molecules, and solids, improves mildly over the local spin-density approximation for atomization energies and lattice constants without much worsening the already good surface exchange-correlation energies.
Prediction of Turbulent Shear Stresses through Dysfunctional Bileaflet Mechanical Heart Valves using Computational Fluid Dynamics

There are more than 300,000 heart valves implanted annually worldwide with about 50% of them being mechanical valves. The heart valve replacement is often a common treatment for severe valvular disease. However, valves may dysfunction leading to adverse hemodynamic conditions. The current computational study investigated the flow around a bileaflet mechanical heart valve at different leaflet dysfunction levels of 0%, 50%, and 100%, and documented the relevant flow characteristics such as vortical structures and turbulent shear stresses. Studying the flow characteristics through these valves during their normal operation and dysfunction can lead to better understanding of their performance, possibly improved designs, and help identify conditions that may increase the potential risk of blood cell damage. Results suggested that maximum flow velocities increased with dysfunction from 2.05 to 4.49 ms-1 which were accompanied by growing eddies and velocity fluctuations. These fluctuations led to higher turbulent shear stresses from 90 to 800 N.m-2 as dysfunctionality increased. These stress values exceeded the thresholds corresponding to elevated risk of hemolysis and platelet activation. The regions of elevated stresses were concentrated around and downstream of the functional leaflet where high jet velocity and stronger helical structures existed.
Existence and convergence of solutions of the boundary value problem in atomistic and continuum nonlinear elasticity theory

We show existence of solutions for the equations of static atomistic nonlinear elasticity theory on a bounded domain with prescribed boundary values. We also show their convergence to the solutions of continuum nonlinear elasticity theory, with energy density given by the Cauchy–Born rule, as the interatomic distances tend to zero. These results hold for small data close to a stable lattice for general finite range interaction potentials. We also discuss the notion of stability in detail.
Word Ordering Without Syntax

Recent work on word ordering has argued that syntactic structure is important, or even required, for effectively recovering the order of a sentence. We find that, in fact, an n-gram language model with a simple heuristic gives strong results on this task. Furthermore, we show that a long short-term memory (LSTM) language model is even more effective at recovering order, with our basic model outperforming a state-of-the-art syntactic model by 11.5 BLEU points. Additional data and larger beams yield further gains, at the expense of training and search time.
Derandomizing Restricted Isometries via the Legendre Symbol

The restricted isometry property (RIP) is an important matrix condition in compressed sensing, but the best matrix constructions to date use randomness. This paper leverages pseudorandom properties of the Legendre symbol to reduce the number of random bits in an RIP matrix with Bernoulli entries. In this regard, the Legendre symbol is not special—our main result naturally generalizes to any small-bias sample space. We also conjecture that no random bits are necessary for our Legendre symbol-based construction.
Non-transversal intersection of the free and fixed boundary in the mean-field theory of superconductivity

Non-transversal intersection of the free and fixed boundary is shown to hold and a classification of blow-up solutions is given for obstacle problems generated by fully nonlinear uniformly elliptic operators in two dimensions which appear in the mean-field theory of superconducting vortices.
Radon transforms over lower-dimensional horospheres in real hyperbolic space

We study horospherical Radon transforms that integrate functions on the $n$-dimensional real hyperbolic space over horospheres of arbitrary fixed dimension $1\le d\le n-1$. Exact existence conditions and new explicit inversion formulas are obtained for these transforms acting on smooth functions and functions belonging to $L^p$. The case $d=n-1$ agrees with the well-known Gelfand-Graev transform.
Controlled information fusion with risk-averse CVaR social sensors

Consider a multi-agent network comprised of risk-averse social sensors and a controller that jointly seek to estimate an unknown state of nature, given noisy measurements. The network of social sensors perform Bayesian social learning — each sensor fuses the information revealed by previous social sensors along with its private valuation using Bayes' rule — to optimize a local cost function. The controller sequentially modifies the cost function of the sensors by discriminatory pricing (control inputs) to realize long term global objectives. We formulate the stochastic control problem faced by the controller as a Partially Observed Markov Decision Process (POMDP) and derive structural results for the optimal control policy as a function of the risk-aversion factor in the Conditional Value-at-Risk (CVaR) cost function of the sensors. We show that the optimal price sequence when the sensors are risk-averse is a super-martingale; i.e, it decreases on average over time.
A LIFTED SQUARE FORMULATION FOR CERTIFIABLE SCHUBERT CALCULUS

Abstract Formulating a Schubert problem as the solutions to a system of equations in either Plucker space or in the local coordinates of a Schubert cell usually involves more equations than variables. Using reduction to the diagonal, we previously gave a primal–dual formulation for Schubert problems that involved the same number of variables as equations (a square formulation). Here, we give a different square formulation by lifting incidence conditions which typically involves fewer equations and variables. Our motivation is certification of numerical computation using Smale's α -theory.
Factoring in the Chicken McNugget Monoid

People just want more of it.—Ray Kroc [9]Every day, 34 million Chicken McNuggets are sold worldwide [4]. At most McDonalds locations in the United States today, Chicken McNuggets are sold in packs ...
Sequential low-rank change detection

Detecting emergence of a low-rank signal from high-dimensional data is an important problem arising from many applications such as camera surveillance and swarm monitoring using sensors. We consider a procedure based on the largest eigenvalue of the sample covariance matrix over a sliding window to detect the change. To achieve dimensionality reduction, we present a sketching-based approach for rank change detection using the low-dimensional linear sketches of the original high-dimensional observations. The premise is that when the sketching matrix is a random Gaussian matrix, and the dimension of the sketching vector is sufficiently large, the rank of sample covariance matrix for these sketches equals the rank of the original sample covariance matrix with high probability. Hence, we may be able to detect the low-rank change using sample covariance matrices of the sketches without having to recover the original covariance matrix. We character the performance of the largest eigenvalue statistic in terms of the false-alarm-rate and the expected detection delay, and present an efficient online implementation via subspace tracking.
A Leray regularized ensemble-proper orthogonal decomposition method for parameterized convection-dominated flows

Partial differential equations (PDEs) are often dependent on input quantities which are inherently uncertain. To quantify this uncertainty, these PDEs must be solved over a large ensemble of parameters. Even for a single realization this can a computationally intensive process. In the case of flows governed by the Navier-Stokes equations, an efficient method has been devised for computing an ensemble of solutions. To further reduce the computational cost of this method, an ensemble proper orthogonal decomposition (POD) method was recently proposed. The main contribution of this work is the introduction of POD spatial filtering for ensemble-POD methods. The POD spatial filter makes possible the construction of the Leray ensemble-POD model, which is a regularized reduced order model for the numerical simulation of convection-dominated flows. The Leray ensemble-POD model employs the POD spatial filter to smooth (regularize) the convection term in the Navier-Stokes equations and greatly diminishes the numerical inaccuracies produced by the ensemble-POD method in the numerical simulation of convection-dominated flows. Specifically, for the numerical simulation of a convection-dominated two-dimensional flow between two offset cylinders, we show that the Leray ensemble-POD method yields accurate results, whereas the ensemble-POD is highly inaccurate. The second contribution of this work is a new numerical discretization of the variable viscosity ensemble algorithm in which the average viscosity is replaced with the maximum viscosity. It is shown that this new numerical discretization is significantly more stable than those in current use. Furthermore, error estimates for the novel Leray ensemble-POD algorithm with this new numerical discretization are also proven.
Robust Convergence of Power Flow Using TX Stepping Method with Equivalent Circuit Formulation

Robust solving of critical large power flow cases (with 50k or greater buses) forms the backbone of planning and operation of any large connected power grid. At present, reliable convergence with applications of existing power flow tools to large power systems is contingent upon a good initial guess for the system state. To enable robust convergence for large scale systems starting with an arbitrary initial guess, we extend our equivalent circuit formulation for power flow analysis to include a novel continuation method based on transmission line (‘Tx’) stepping. While various continuation methods have been proposed for use with the traditional ‘PQV’ power flow formulation, these methods have either failed to completely solve the problem or have resulted in convergence to a low voltage solution. The proposed “Tx Stepping” method in this paper demonstrates robust convergence to the high voltage solution from an arbitrary initial guess. Example systems, including 75k+ bus test cases representing different loading and operating conditions for Eastern Interconnection of the U.S. power grid, are solved from arbitrary initial guesses.
Spectral decomposition of fractional operators and a reflected stable semigroup

Abstract In this paper, we provide the spectral decomposition in Hilbert space of the C 0 -semigroup P and its adjoint P ˆ having as generator, respectively, the Caputo and the right-sided Riemann–Liouville fractional derivatives of index 1 α 2 . These linear operators, which are non-local and non-self-adjoint, appear in many recent studies in applied mathematics and also arise as the infinitesimal generators of some substantial processes such as the reflected spectrally negative α-stable process. Our approach relies on intertwining relations that we establish between these semigroups and the semigroup of a Bessel type process whose generator is a self-adjoint second order differential operator. In particular, from this commutation relation, we characterize the positive real axis as the continuous point spectrum of P and provide a power series representation of the corresponding eigenfunctions. We also identify the positive real axis as the residual spectrum of the adjoint operator P ˆ and elucidate its role in the spectral decomposition of these operators. By resorting to the concept of continuous frames, we proceed by investigating the domain of the spectral operators and derive two representations for the heat kernels of these semigroups. As a by-product, we also obtain regularity properties for these latter and also for the solution of the associated Cauchy problem.
Up-to-constants bounds on the two-point Green's function for SLE curves *

The Green's function for the chordal Schramm-Loewner evolution $SLE_\kappa$for $0 < \kappa < 8$, gives the normalizedprobability of getting near points. We give up-to-constant bounds for the two-point Green's function.
Temporally-Biased Sampling for Online Model Management.

To maintain the accuracy of supervised learning models in the presence of evolving data streams, we provide temporally-biased sampling schemes that weight recent data most heavily, with inclusion probabilities for a given data item decaying exponentially over time. We then periodically retrain the models on the current sample. This approach speeds up the training process relative to training on all of the data. Moreover, time-biasing lets the models adapt to recent changes in the data while -- unlike in a sliding-window approach -- still keeping some old data to ensure robustness in the face of temporary fluctuations and periodicities in the data values. In addition, the sampling-based approach allows existing analytic algorithms for static data to be applied to dynamic streaming data essentially without change. We provide and analyze both a simple sampling scheme (T-TBS) that probabilistically maintains a target sample size and a novel reservoir-based scheme (R-TBS) that is the first to provide both complete control over the decay rate and a guaranteed upper bound on the sample size, while maximizing both expected sample size and sample-size stability. The latter scheme rests on the notion of a "fractional sample" and, unlike T-TBS, allows for data arrival rates that are unknown and time varying. R-TBS and T-TBS are of independent interest, extending the known set of unequal-probability sampling schemes. We discuss distributed implementation strategies; experiments in Spark illuminate the performance and scalability of the algorithms, and show that our approach can increase machine learning robustness in the face of evolving data.
Late Ordovician geographic patterns of extinction compared with simulations of astrophysical ionizing radiation damage

Terrestrial mass extinctions have been attributed to a wide range of causes. Some of them are external to Earth, such as bolide impacts (as widely discussed for the K/T boundary) and radiation events. Among radiation events, there are possible large solar flares, nearby supernovae, gamma-ray bursts (GRBs), and others. These have variable intensity, duration, and probability of occurrence, although some generalizations are possible in understanding their effects (Ejzak et al. 2007). Here we focus on gamma-ray bursts (Thorsett 1995; Scalo and Wheeler 2002), a proposed causal agent for the end-Ordovician extinction. These are the most remote and infrequent of events, but by virtue of their power, a threat approximately competitive with, for example, that of nearby supernovae. A GRB of the most powerful type (Woosley and Bloom 2006) is thought to result from a supernova at the end of stellar evolution for very massive stars with high rotational speed. Much of their energy is channeled into beams, or jets, which include very high energy electromagnetic energy, i.e., gamma-rays and X-rays. It is a testament to the power of these events, far across the observable universe, that they were first detected in the 1969–1970 results from monitoring satellites designed to detect nuclear explosions on Earth's surface. It was not until the 1990s, when the distance to the events became known, that their power became apparent. Several such events occur every day in the observable universe. Other kinds of events are also potentially damaging, such as so-called short bursts and solar flares, but rate information is only now beginning to clarify how much threat is likely from such sources. From the rate of these events in the universe as a whole, it is possible to estimate the rate and distribution of likely distances to events that irradiate Earth (Scalo and Wheeler …
Sample-based population observers

Abstract In this paper, a first sample-based formulation of the recently considered population observers, or ensemble observers, which estimate the state distribution of dynamic populations from measurements of the output distribution is established. The results presented in this paper yield readily applicable computational procedures that provide novel avenues to circumvent issues regarding the curse of dimensionality, which all previously developed techniques employing a kernel-based approach are inherently suffering from. The novel insights that eventually pave the way for all different kinds of sample-based considerations are in fact deeply rooted in the basic probabilistic framework underlying the problem, bridging optimal mass transport problems defined on the level of distributions with actual randomized strategies operating on the level of individual points. The conceptual insights established in this paper not only yield insight into the underlying mechanisms of sample-based ensemble observers but significantly advance our understanding of estimation and tracking problems for the class of ensembles of dynamical systems in general.
Optimal open-locating-dominating sets in infinite triangular grids

Abstract An open-locating-dominating set (OLD-set) is a subset of vertices of a graph such that every vertex in the graph has at least one neighbor in the set and no two vertices in the graph have the same set of neighbors in the set. This is an analogue to the well-studied identifying code in the literature. In this paper, we prove that the optimal density of an OLD-set for the infinite triangular grid is 4 / 13 .
Electroid varieties and a compactification of the space of electrical networks

Abstract We construct a compactification of the space of circular planar electrical networks studied by Curtis–Ingerman–Morrow [4] and Colin de Verdiere–Gitler–Vertigan [3] , using cactus networks. We embed this compactification as a linear slice of the totally nonnegative Grassmannian, and relate Kenyon and Wilson's grove measurements to Postnikov's boundary measurements. Intersections of the slice with the positroid stratification leads to a class of electroid varieties, indexed by matchings. The uncrossing partial order on matchings arising from electrical networks is shown to be dual to a subposet of affine Bruhat order. The analogues of matroids in this setting are certain distinguished collections of non-crossing partitions.
Tin–Selenium Compounds at Ambient and High Pressures

SnxSey crystalline compounds consisting of Sn and Se atoms of varying compositions are systematically investigated at pressures from 0 to 100 GPa using the first-principles evolutionary crystal structure search method based on density functional theory. All known experimental phases of SnSe and SnSe2 are found without any prior input. A second-order polymorphic phase transition from SnSe-Pnma phase to SnSe-Cmcm phase is predicted at 2.5 GPa. Initially being semiconducting, this phase becomes metallic at 7.3 GPa. Upon further increase of pressure up to 36.6 GPa, SnSe-Cmcm phase is transformed to CsCl-type SnSe-Pm3m phase, which remains stable at even higher pressures. A metallic compound with different stoichiometry, Sn3Se4-I43d, is found to be thermodynamically stable from 18 to 70 GPa. Known semiconductor tin diselenide SnSe2-P3m1 phase is found to be thermodynamically stable from ambient pressure up to 18 GPa. Initially being semiconducting, it experiences metallization at pressures above 8 GPa.
Poisson–de Rham homology of hypertoric varieties and nilpotent cones

We prove a conjecture of Etingof and the second author for hypertoric varieties that the Poisson–de Rham homology of a unimodular hypertoric cone is isomorphic to the de Rham cohomology of its hypertoric resolution. More generally, we prove that this conjecture holds for an arbitrary conical variety admitting a symplectic resolution if and only if it holds in degree zero for all normal slices to symplectic leaves. The Poisson–de Rham homology of a Poisson cone inherits a second grading. In the hypertoric case, we compute the resulting 2-variable Poisson–de Rham–Poincare polynomial and prove that it is equal to a specialization of an enrichment of the Tutte polynomial of a matroid that was introduced by Denham (J Algebra 242(1):160–175, 2001). We also compute this polynomial for S3-varieties of type A in terms of Kostka polynomials, modulo a previous conjecture of the first author, and we give a conjectural answer for nilpotent cones in arbitrary type, which we prove in rank less than or equal to 2.
A uniform version of a finiteness conjecture for CM elliptic curves

Let A be an abelian variety defined over a number field F. For a prime number $\ell$, we consider the field extension of F generated by the $\ell$-powered torsion points of A. According to a conjecture made by Rasmussen and Tamagawa, if we require these fields to be both a pro-$\ell$ extension of $F(\mu_{\ell^{\infty}})$ and unramified away from $\ell$, examples are quite rare. Indeed, it is expected that for a fixed dimension and field of definition, there exists such an abelian variety for only a finite number of primes. We prove a uniform version of the conjecture in the case where the abelian varieties are elliptic curves with complex multiplication. In addition, we provide explicit bounds in cases where the number field has degree less than or equal to 100.
A $q$-Robinson-Schensted-Knuth Algorithm and a $q$-Polymer

In Matveev-Petrov (2017) a $q$-deformed Robinson-Schensted-Knuth algorithm ($q$RSK) was introduced.In this article we give reformulations of this algorithm in terms of the Noumi-Yamada description, growth diagrams and local moves. We show that the algorithm is symmetric, namely the output tableaux pairs are swapped in a sense of distribution when the input matrix is transposed. We also formulate a $q$-polymer model based on the $q$RSK, prove the corresponding Burke property, which we use to show a strong law of large numbers for the partition function given stationary boundary conditions and $q$-geometric weights.We use the $q$-local moves to define a generalisation of the $q$RSK taking a Young diagram-shape of array as the input. We write down the joint distribution of partition functions in the space-like direction of the $q$-polymer in $q$-geometric environment, formulate a $q$-version of the multilayer polynuclear growth model ($q$PNG) and write down the joint distribution of the $q$-polymer partition functions at a fixed time.
Generative models for network neuroscience: prospects and promise.

Network neuroscience is the emerging discipline concerned with investigating the complex patterns of interconnections found in neural systems, and identifying principles with which to understand th...
Guard zones and the near-far problem in DS-CDMA ad hoc networks

The central issue in direct-sequence code-division multiple-access (DS-CDMA) ad hoc networks is the prevention of a near-far problem. This paper considers two types of guard zones that may be used to control the near-far problem: a fundamental exclusion zone and an additional CSMA guard zone that may be established by the carrier-sense multiple-access (CSMA) protocol. In the exclusion zone, no mobiles are physically present, modeling the minimum physical separation among mobiles that is always present in actual networks. Potentially interfering mobiles beyond a transmitting mobile's exclusion zone, but within its CSMA guard zone, are deactivated by the protocol. This paper provides an analysis of DS-CSMA networks with either or both types of guard zones. A network of finite extent with a finite number of mobiles is modeled as a uniform clustering process. The analysis uses a closed-form expression for the outage probability in the presence of Nakagami fading, conditioned on the network geometry. By using the analysis developed in this paper, the tradeoffs between exclusion zones and CSMA guard zones are explored for DS-CDMA and unspread networks.
Counterexample-Guided Data Augmentation.

Author(s): Dreossi, Tommaso; Ghosh, Shromona; Yue, Xiangyu; Keutzer, Kurt; Sangiovanni-Vincentelli, Alberto L; Seshia, Sanjit A | Editor(s): Lang, Jerome
Algebraic subgroups of acylindrically hyperbolic groups

Abstract A subgroup of a group G is called algebraic if it can be expressed as a finite union of solution sets to systems of equations. We prove that a non-elementary subgroup H of an acylindrically hyperbolic group G is algebraic if and only if there exists a finite subgroup K of G such that C G ( K ) ≤ H ≤ N G ( K ) . We provide some applications of this result to free products, torsion-free relatively hyperbolic groups, and ascending chains of algebraic subgroups in acylindrically hyperbolic groups.
Parallel accelerated Custom Correlation Coefficient calculations for genomics applications

Abstract The massive quantities of genomic data being made available through gene sequencing techniques are enabling breakthroughs in genomic science in many areas such as medical advances in the diagnosis and treatment of diseases. Analyzing this data, however, is a computational challenge insofar as the computational costs of the relevant algorithms can grow with quadratic, cubic or higher complexity—leading to the need for leadership scale computing. In this paper we describe a new approach to calculations of the Custom Correlation Coefficient (CCC) between Single Nucleotide Polymorphisms (SNPs) across a population, suitable for parallel systems equipped with graphics processing units (GPUs) or Intel Xeon Phi processors. We describe the mapping of the algorithms to accelerated processors, techniques used for eliminating redundant calculations due to symmetries, and strategies for efficient mapping of the calculations to many-node parallel systems. Results are presented demonstrating high per-node performance and near-ideal parallel scalability with rates of more than nine quadrillion (9 × 1015) elementwise comparisons achieved per second with the latest optimized code on the ORNL Titan system, this being orders of magnitude faster than rates achieved using other codes and platforms as reported in the literature. Also it is estimated that as many as 90 quadrillion (90 × 1015) comparisons per second may be achievable on the upcoming ORNL Summit system, an additional 10X performance increase. In a companion paper we describe corresponding techniques applied to calculations of the Proportional Similarity metric for comparative genomics applications.
Local moment matching: A unified methodology for symmetric functional estimation and distribution estimation under Wasserstein distance

We present \emph{Local Moment Matching (LMM)}, a unified methodology for symmetric functional estimation and distribution estimation under Wasserstein distance. We construct an efficiently computable estimator that achieves the minimax rates in estimating the distribution up to permutation, and show that the plug-in approach of our unlabeled distribution estimator is "universal" in estimating symmetric functionals of discrete distributions. Instead of doing best polynomial approximation explicitly as in existing literature of functional estimation, the plug-in approach conducts polynomial approximation implicitly and attains the optimal sample complexity for the entropy, power sum and support size functionals.
RECONSTRUCTION OF FRACTIONAL QUANTUM HALL EDGES

Edge reconstruction has been a well-known effect for integer quantum Hall liquids in the presence of both electron interactions and a confining potential generated by charged background. At more generic fractional fillings, we point out that confined two-dimensional interacting electrons can exhibit the similar reconstruction effect. Our exact diagonalization results show that, in a fractional quantum Hall system with a sharp cleaved edge potential, the electron density oscillation near the edge increases with the distance between the electron gas and the background charge layer. As a results, the outermost hump can detach from the bulk beyond certain point. We suggest that the edge reconstruction effect is relevant to the recent edge tunneling experiments,1 as well as the microwave absorption experiment on two-dimensional electrons in an antidot array.2 Calculating the finite-temperature density profiles, we estimate the temperature above which the edge reconstruction disappears to further discuss the relevance to the microwave absorption experiment.
Domains of attraction for positive and discrete tempered stable distributions

We introduce a large and flexible class of discrete tempered stable distributions, and analyze the domains of attraction for both this class and the related class of positive tempered stable distributions. Our results suggest that these are natural models for sums of independent and identically distributed random variables with tempered heavy tails, i.e. tails that appear to be heavy up to a point, but ultimately decay faster.
An explicit non-smoothable component of the compactified Jacobian

Abstract This paper studies the components of the moduli space of rank 1, torsion-free sheaves, or compactified Jacobian, of a non-Gorenstein curve. We exhibit a generically reduced component of dimension equal to the arithmetic genus and prove that it is the only non-smoothable component when the curve has a unique singularity that is of finite representation type. Analogous results are proven for the Hilbert scheme of points and the Quot scheme parameterizing quotients of the dualizing sheaf.
On the displacement of generators of free Fuchsian groups

We prove an inequality that must be satisfied by displacement of generators of free Fuchsian groups, which is the two-dimensional version of the $$\log (2k-1)$$ Theorem for Kleinian groups due to Anderson et al. (J Differ Geom 44:738–782, 1996). As applications, we obtain quantitative results on the geometry of hyperbolic surfaces such as the two-dimensional Margulis constant and lengths of a pair of based loops, which improves a result of Buser’s.
Mather–Jacobian singularities under generic linkage

In this paper, we prove that Mather-Jacobian (MJ) singularities are preserved under the process of generic linkage. More precisely, let $X$ be a variety with MJ-canonical (resp. MJ-log canonical) singularities. Then a generic link of $X$ is also MJ-canonical (resp. MJ-log canonical). This further leads us to a result on minimal log discrepancies under generic linkage.
Stochastic dynamics and combinatorial optimization

Natural dynamics is often dominated by sudden nonlinear processes such as neuroavalanches, gamma-ray bursts, solar flares, etc., that exhibit scale-free statistics much in the spirit of the logarithmic Ritcher scale for earthquake magnitudes. On phase diagrams, stochastic dynamical systems (DSs) exhibiting this type of dynamics belong to the finite-width phase (N-phase for brevity) that precedes ordinary chaotic behavior and that is known under such names as noise-induced chaos, self-organized criticality, dynamical complexity, etc. Within the recently proposed supersymmetric theory of stochastic dynamics, the N-phase can be roughly interpreted as the noise-induced “overlap” between integrable and chaotic deterministic dynamics. As a result, the N-phase dynamics inherits the properties of the both. Here, we analyze this unique set of properties and conclude that the N-phase DSs must naturally be the most efficient optimizers: on one hand, N-phase DSs have integrable flows with well-defined attractors that can be associated with candidate solutions and, on the other hand, the noise-induced attractor-to-attractor dynamics in the N-phase is effectively chaotic or aperiodic so that a DS must avoid revisiting solutions/attractors thus accelerating the search for the best solution. Based on this understanding, we propose a method for stochastic dynamical optimization using the N-phase DSs. This method can be viewed as a hybrid of the simulated and chaotic annealing methods. Our proposition can result in a new generation of hardware devices for efficient solution of various search and/or combinatorial optimization problems.
Detecting Backdoor Attacks on Deep Neural Networks by Activation Clustering.

While machine learning (ML) models are being increasingly trusted to make decisions in different and varying areas, the safety of systems using such models has become an increasing concern. In particular, ML models are often trained on data from potentially untrustworthy sources, providing adversaries with the opportunity to manipulate them by inserting carefully crafted samples into the training set. Recent work has shown that this type of attack, called a poisoning attack, allows adversaries to insert backdoors or trojans into the model, enabling malicious behavior with simple external backdoor triggers at inference time and only a blackbox perspective of the model itself. Detecting this type of attack is challenging because the unexpected behavior occurs only when a backdoor trigger, which is known only to the adversary, is present. Model users, either direct users of training data or users of pre-trained model from a catalog, may not guarantee the safe operation of their ML-based system. In this paper, we propose a novel approach to backdoor detection and removal for neural networks. Through extensive experimental results, we demonstrate its effectiveness for neural networks classifying text and images. To the best of our knowledge, this is the first methodology capable of detecting poisonous data crafted to insert backdoors and repairing the model that does not require a verified and trusted dataset.
Orthogonal Polynomials for Seminonparametric Instrumental Variables Model

We develop an approach that resolves a polynomial basis problem for a class of models with discrete endogenous covariate, and for a class of econometric models considered in the work of Newey and Powell [], where the endogenous covariate is continuous. Suppose X is a d -dimensional endogenous random variable, Z 1 and Z 2 are the instrumental variables (vectors), and . Now, assume that the conditional distributions of X given Z satisfy the conditions sufficient for solving the identification problem as in Newey and Powell [] or as in Proposition 1.1 of the current paper. That is, for a function π (z ) in the image space there is a.s. a unique function g (x, z 1 ) in the domain space such that \begin{eqnarray*} E[g(X,Z_1)~|~Z]=\pi(Z) \qquad Z-{\rm a.s.} \end{eqnarray*} E [ g ( X, Z 1 ) | Z ] = π ( Z ) Z − a . s . In this paper, for a class of conditional distributions X | Z , we produce an orthogonal polynomial basis { Q j (x, z 1 ) } j = 0, 1, ... such that for a.e. Z 1 = z 1 , and for all , and a certain μ (Z ), \begin{eqnarray*} P_j(\mu(Z))=E[Q_j(X, Z_1)~|~Z ], \end{eqnarray*} P j ( μ ( Z ) ) = E [ Q j ( X, Z 1 ) | Z ] , where P j is a polynomial of degree j . This is what we call solving the polynomial basis problem . Assuming the knowledge of X | Z and an inference of π (z ), our approach provides a natural way of estimating the structural function of interest g (x, z 1 ). Our polynomial basis approach is naturally extended to Pearson-like and Ord-like families of distributions.
Detection and Segmentation of Manufacturing Defects with Convolutional Neural Networks and Transfer Learning

Quality control is a fundamental component of many manufacturing processes, especially those involving casting or welding. However, manual quality control procedures are often time-consuming and error-prone. In order to meet the growing demand for high-quality products, the use of intelligent visual inspection systems is becoming essential in production lines. Recently, Convolutional Neural Networks (CNNs) have shown outstanding performance in both image classification and localization tasks. In this article, a system is proposed for the identification of casting defects in X-ray images, based on the Mask Region-based CNN architecture. The proposed defect detection system simultaneously performs defect detection and segmentation on input images, making it suitable for a range of defect detection tasks. It is shown that training the network to simultaneously perform defect detection and defect instance segmentation, results in a higher defect detection accuracy than training on defect detection alone. Transfer learning is leveraged to reduce the training data demands and increase the prediction accuracy of the trained model. More specifically, the model is first trained with two large openly-available image datasets before finetuning on a relatively small metal casting X-ray dataset. The accuracy of the trained model exceeds state-of-the art performance on the GRIMA database of X-ray images (GDXray) Castings dataset and is fast enough to be used in a production setting. The system also performs well on the GDXray Welds dataset. A number of in-depth studies are conducted to explore how transfer learning, multi-task learning, and multi-class learning influence the performance of the trained system.
Edge States in Honeycomb Structures

An edge state is a time-harmonic solution of a conservative wave system, e.g. Schrodinger, Maxwell, which is propagating (plane-wave-like) parallel to, and localized transverse to, a line-defect or “edge”. Topologically protected edge states are edge states which are stable against spatially localized (even strong) deformations of the edge. First studied in the context of the quantum Hall effect, protected edge states have attracted huge interest due to their role in the field of topological insulators. Theoretical understanding of topological protection has mainly come from discrete (tight-binding) models and direct numerical simulation. In this paper we consider a rich family of continuum PDE models for which we rigorously study regimes where topologically protected edge states exist. Our model is a class of Schrodinger operators on $${\mathbb {R}}^2$$ with a background two-dimensional honeycomb potential perturbed by an “edge-potential”. The edge potential is a domain-wall interpolation, transverse to a prescribed “rational” edge, between two distinct periodic structures. General conditions are given for the bifurcation of a branch of topologically protected edge states from Dirac points of the background honeycomb structure. The bifurcation is seeded by the zero mode of a one-dimensional effective Dirac operator. A key condition is a spectral no-fold condition for the prescribed edge. We then use this result to prove the existence of topologically protected edge states along zigzag edges of certain honeycomb structures. Our results are consistent with the physics literature and appear to be the first rigorous results on the existence of topologically protected edge states for continuum 2D PDE systems describing waves in a non-trivial periodic medium. We also show that the family of Hamiltonians we study contains cases where zigzag edge states exist, but which are not topologically protected.
Stick-breaking variational autoencoders

We extend Stochastic Gradient Variational Bayes to perform posterior inference for the weights of Stick-Breaking processes. This development allows us to define a Stick-Breaking Variational Autoencoder (SB-VAE), a Bayesian nonparametric version of the variational autoencoder that has a latent representation with stochastic dimensionality. We experimentally demonstrate that the SB-VAE, and a semi-supervised variant, learn highly discriminative latent representations that often outperform the Gaussian VAE's.
Cascading denial of service attacks on Wi-Fi networks

We unveil the existence of a vulnerability in Wi-Fi, which allows an adversary to remotely launch a Denial-of-Service (DoS) attack that propagates both in time and space. This vulnerability stems from a coupling effect induced by hidden nodes. Cascading DoS attacks can congest an entire network and do not require the adversary to violate any protocol. We demonstrate the feasibility of such attacks through experiments with real Wi-Fi cards, extensive ns-3 simulations, and theoretical analysis. The simulations show that the attack is effective both in networks operating under fixed and varying bit rates, as well as ad hoc and infrastructure modes. To gain insight into the root-causes of the attack, we model the network as a dynamical system and analyze its limiting behavior. The model predicts that a phase transition (and hence a cascading attack) is possible when the retry limit parameter of Wi-Fi is greater or equal to 7, and characterizes the phase transition region in terms of the system parameters.
Brownian motion with variable drift can be space filling

For d ≥ 2 let B be standard d-dimensional Brownian motion. For any α d we construct an α-Holder continuous function f : [0, 1] → Rd so that the range of B − f covers an open set. This strengthens a result of Graversen (1982) and answers a question of Le Gall (1988).
Paths to Polarization: How Extreme Views, Miscommunication, and Random Chance Drive Opinion Dynamics

Understanding the social conditions that tend to increase or decrease polarization is important for many reasons. We study a network-structured agent-based model of opinion dynamics, extending a model previously introduced by Flache and Macy (2011), who found that polarization appeared to increase with the introduction of long-range ties but decrease with the number of salient opinions, which they called the population’s “cultural complexity.” We find the following. First, polarization is strongly path dependent and sensitive to stochastic variation. Second, polarization depends strongly on the initial distribution of opinions in the population. In the absence of extremists, polarization may be mitigated. Third, noisy communication can drive a population toward more extreme opinions and even cause acute polarization. Finally, the apparent reduction in polarization under increased “cultural complexity” arises via a particular property of the polarization measurement, under which a population containing a wider diversity of extreme views is deemed less polarized. This work has implications for understanding the population dynamics of beliefs, opinions, and polarization as well as broader implications for the analysis of agent-based models of social phenomena.
Extrema of graph eigenvalues

Abstract In 1993 Hong asked what are the best bounds on the k'th largest eigenvalue λ k ( G ) of a graph G of order n. This challenging question has never been tackled for any 2 k n . In the present paper tight bounds are obtained for all k > 2 , and even tighter bounds are obtained for the k'th largest singular value λ k ⁎ ( G ) . Some of these bounds are based on Taylor's strongly regular graphs, and others on a method of Kharaghani for constructing Hadamard matrices. The same kind of constructions are applied to other open problems, like Nordhaus–Gaddum problems of the kind: How large can λ k ( G ) + λ k ( G ¯ ) be? These constructions are successful also in another open question: How large can the Ky Fan norm λ 1 ⁎ ( G ) + ⋯ + λ k ⁎ ( G ) be? Ky Fan norms of graphs generalize the concept of graph energy, so this question generalizes the problem for maximum energy graphs. In the final section, several results and problems are restated for ( − 1 , 1 ) -matrices, which seem to provide a more natural ground for such research than graphs. Many of the results in the paper are paired with open questions and problems for further study.
Heartbeat Stars: Spectroscopic Orbital Solutions for Six Eccentric Binary Systems

We present multi-epoch spectroscopy of "heartbeat stars," eccentric binaries with dynamic tidal distortions and tidally induced pulsations originally discovered with the Kepler satellite. Optical spectra of six known heartbeat stars using the Wyoming Infrared Observatory 2.3 m telescope allow measurement of stellar effective temperatures and radial velocities from which we determine orbital parameters including the periods, eccentricities, approximate mass ratios, and component masses. These spectroscopic solutions confirm that the stars are members of eccentric binary systems with eccentricities e > 0.34 and periods P = 7–20 days, strengthening conclusions from prior works that utilized purely photometric methods. Heartbeat stars in this sample have A- or F-type primary components. Constraints on orbital inclinations indicate that four of the six systems have minimum mass ratios q = 0.3–0.5, implying that most secondaries are probable M dwarfs or earlier. One system is an eclipsing, double-lined spectroscopic binary with roughly equal-mass mid-A components (q = 0.95), while another shows double-lined behavior only near periastron, indicating that the F0V primary has a G1V secondary (q = 0.65). This work constitutes the first measurements of the masses of secondaries in a statistical sample of heartbeat stars. The good agreement between our spectroscopic orbital elements and those derived using a photometric model support the idea that photometric data are sufficient to derive reliable orbital parameters for heartbeat stars.
THE SHIMURA CURVE OF DISCRIMINANT 15 AND TOPOLOGICAL AUTOMORPHIC FORMS

We nd dening equations for the Shimura curve of discriminant 15 over Z[1=15]. We then determine the graded ring of automorphic forms over the 2-adic integers, as well as the higher cohomology. We apply this to calculate the homotopy groups of a spectrum of \topological automorphic forms" associated to this curve, as well as one associated to a quotient by an Atkin-Lehner involution.
MODELING AND CONTROL OF THERMOSTATICALLY CONTROLLED LOADS

As the penetration of intermittent energy sources grows substantially, loads will be required to play an increasingly important role in compensating the fast time- scale fluctuations in generated power. Recent numerical modeling of thermostatically controlled loads (TCLs) has demonstrated that such load following is feasible, but analyt- ical models that satisfactorily quantify the aggregate power consumption of a group of TCLs are desired to enable con- troller design. We develop such a model for the aggregate power response of a homogeneous population of TCLs to uni- form variation of all TCL setpoints. A linearized model of the response is derived, and a linear quadratic regulator (LQR) has been designed. Using the TCL setpoint as the control input, the LQR enables aggregate power to track reference signals that exhibit step, ramp and sinusoidal variations.