cssi/SciSciGPT-SciSciNet huggingface dataset:
On the stochastic homogenization of fully nonlinear uniformly parabolic equations in stationary ergodic spatio-temporal media

Abstract We study homogenization for fully nonlinear uniformly parabolic equations in stationary ergodic spatio-temporal media from the qualitative and quantitative perspectives. Under suitable hypotheses, solutions to fully nonlinear uniformly parabolic equations in spatio-temporal media homogenize almost surely. In addition, we obtain a logarithmic rate of convergence for this homogenization in measure, assuming that the environment is strongly mixing with a prescribed logarithmic rate. A general methodology to study the stochastic homogenization and rates of convergence for stochastic homogenization of uniformly elliptic equations was introduced by Caffarelli, Souganidis, and Wang [1] , and Caffarelli and Souganidis [2] . We extend their approach to fully nonlinear uniformly parabolic equations, developing a number of new arguments to handle the parabolic structure of the problem.
Implementing an Automatic Differentiator in ACL2

The foundational theory of differentiation was developed as part of the original release of ACL2(r). In work reported at the last ACL2 Workshop, we presented theorems justifying the usual differentiation rules, including the chain rule and the derivative of inverse functions. However, the process of applying these theorems to formalize the derivative of a particular function is completely manual. More recently, we developed a macro and supporting functions that can automate this process. This macro uses the ACL2 table facility to keep track of functions and their derivatives, and it also interacts with the macro that introduces inverse functions in ACL2(r), so that their derivatives can also be automated. In this paper, we present the implementation of this macro and related functions.
Uncertainty quantification under group sparsity

SummaryQuantifying the uncertainty in penalized regression under group sparsity is an important open question. We establish, under a high-dimensional scaling, the asymptotic validity of a modified parametric bootstrap method for the group lasso, assuming a Gaussian error model and mild conditions on the design matrix and the true coefficients. Simulation of bootstrap samples provides simultaneous inferences on large groups of coefficients. Through extensive numerical comparisons, we demonstrate that our bootstrap method performs much better than popular competitors, highlighting its practical utility. The theoretical results generalize to other block norm penalization and sub-Gaussian errors, which further broadens the potential applications.
Sobolev Stability of Plane Wave Solutions to the Nonlinear Schrödinger Equation

This article explores the questions of long time orbital stability in high order Sobolev norms of plane wave solutions to the NLSE in the defocusing case.
Bäcklund transformations for Darboux integrable differential systems: Examples and applications

Abstract In this article we demonstrate a new symmetry based method for constructing Backlund transformations by finding explicit Backlund transformations between Darboux integrable systems. This results in a number of new examples of Backlund transformations which are quite different in character than those typically found in the literature. The relation between the intermediate integrals for Darboux integrable systems and the differential invariants of the Vessiot group is also illustrated. We then show that a well known class of Backlund transformations between a Darboux integrable Monge–Ampere system and the wave equation always arises by this method. The results of this paper build upon the presentation of Darboux integrable systems as quotients of differential systems by symmetry groups.
Provable Bayesian Inference via Particle Mirror Descent

Bayesian methods are appealing in their flexibility in modeling complex data and ability in capturing uncertainty in parameters. However, when Bayes' rule does not result in tractable closed-form, most approximate inference algorithms lack either scalability or rigorous guarantees. To tackle this challenge, we propose a simple yet provable algorithm, \emph{Particle Mirror Descent} (PMD), to iteratively approximate the posterior density. PMD is inspired by stochastic functional mirror descent where one descends in the density space using a small batch of data points at each iteration, and by particle filtering where one uses samples to approximate a function. We prove result of the first kind that, with $m$ particles, PMD provides a posterior density estimator that converges in terms of $KL$-divergence to the true posterior in rate $O(1/\sqrt{m})$. We demonstrate competitive empirical performances of PMD compared to several approximate inference algorithms in mixture models, logistic regression, sparse Gaussian processes and latent Dirichlet allocation on large scale datasets.
Thin one-phase almost minimizers

Abstract We consider almost minimizers to the thin-one phase energy functional and we prove optimal regularity of the solution and partial regularity of the free boundary. We recover the theory for energy minimizers developed in De Silva and Roquejoffre (2012) and De Silva and Savin (2015). Our methods are based on a noninfinitesimal notion of viscosity solutions we introduced in De Silva and Savin (2018).
Exponential concentration of cover times

We prove an exponential concentration bound for cover times of general graphs in terms of the Gaussian free field, extending the work of Ding, Lee, and Peres [8] and Ding [7]. The estimate is asymptotically sharp as the ratio of hitting time to cover time goes to zero. The bounds are obtained by showing a stochastic domination in the generalized second Ray-Knight theorem, which was shown to imply exponential concentration of cover times by Ding in [7]. This stochastic domination result appeared earlier in a preprint of Lupu [22], but the connection to cover times was not mentioned.
Best-of-K-bandits

This paper studies the Best-of-K Bandit game: At each time the player chooses a subset S among all N-choose-K possible options and observes reward max(X(i) : i in S) where X is a random vector drawn from a joint distribution. The objective is to identify the subset that achieves the highest expected reward with high probability using as few queries as possible. We present distributiondependent lower bounds based on a particular construction which force a learner to consider all N-choose-K subsets, and match naive extensions of known upper bounds in the bandit setting obtained by treating each subset as a separate arm. Nevertheless, we present evidence that exhaustive search may be avoided for certain, favorable distributions because the influence of high-order order correlations may be dominated by lower order statistics. Finally, we present an algorithm and analysis for independent arms, which mitigates the surprising non-trivial information occlusion that occurs due to only observing the max in the subset. This may inform strategies for more general dependent measures, and we complement these result with independent-arm lower bounds.
Achievable Rates and Optimal Resource Allocation for Imperfectly-Known Fading Relay Channels

In this paper, achievable rates and optimal resource allocation strategies for imperfectly-known fading relay channels are studied. It is assumed that communication starts with the network training phase in which the receivers estimate the fading coefficients of their respective channels. In the data transmission phase, amplify-and-forward and decode-and-forward relaying schemes with different degrees of cooperation are considered, and the corresponding achievable rate expressions are obtained. Three resource allocation problems are addressed: 1) power allocation between data and training symbols; 2) time/bandwidth allocation to the relay; 3) power allocation between the source and relay in the presence of total power constraints. The achievable rate expressions are employed to identify the optimal resource allocation strategies. Finally, energy efficiency is investigated by studying the bit energy requirements in the low-SNR regime.
Hyperbolic groups with boundary an n-dimensional Sierpinski space

For n ≥ 7, we show that if G is a torsion-free hyperbolic group whose visual boundary ∂∞G ≃&#x1d4ae;n−2 is an (n − 2)-dimensional Sierpinski space, then G = π1(W) for some aspherical n-manifold W with non-empty boundary. Concerning the converse, we construct, for each n ≥ 4, examples of aspherical manifolds with boundary, whose fundamental group G is hyperbolic, but with visual boundary ∂∞G not homeomorphic to &#x1d4ae;n−2. Our examples even support (metric) negative curvature, and have totally geodesic boundary.
Divergent series and Serre's intersection formula for graded rings

Abstract On a smooth variety, Serre's intersection formula computes intersection multiplicities via an alternating sum of the lengths of Tor groups. When the variety is singular, the corresponding sum can be a divergent series. But there are alternate geometric approaches for assigning (often fractional) intersection multiplicities in some singular settings. Our motivating question comes from Fulton, who asks whether an analytic continuation of the divergent series from Serre's formula can be related to these fractional multiplicities. We apply work of Avramov and Buchweitz to answer Fulton's question in the context of graded rings.
The formation of astrophysical Mg-rich silicate dust

Abstract We present new results for ground-state candidate energies of Mg-rich olivine (MRO) clusters and use the binding energies of these clusters to determine their nucleation rates in stellar outflows, with particular interest in the environments of core-collapse supernovae (CCSNe). Low-lying structures of clusters (Mg 2 SiO 4 ) n 2 ≤ n ≤ 13 are determined from a modified minima hopping algorithm using an empirical silicate potential in the Buckingham form. These configurations are further refined and optimized using the density functional theory code Quantum Espresso. Utilizing atomistic nucleation theory, we determine the critical size and nucleation rates of these clusters. We find that configurations and binding energies in this regime are very dissimilar from those of the bulk lattice. Clusters grow with SiO 4 –MgO layering and exhibit only global, rather than local, symmetries. When compared to classical nucleation theory we find suppressed nucleation rates at most temperatures and pressures, with enhanced nucleation rates at very large pressures. This implies a slower progression of silicate dust formation in stellar environments than previously assumed.
Linear Laurent Phenomenon Algebras

In [LP] we introduced Laurent phenomenon algebras, a generalization of cluster algebras. Here we give an explicit description of Laurent phenomenon algebras with a linear initial seed arising from a graph. In particular, any graph associahedron is shown to be the dual cluster complex for some Laurent phenomenon algebra.
Effective Prime Uniqueness

Assuming the obvious definitions (see paper) we show the a decidable model that is effectively prime is also effectively atomic. This implies that two effectively prime (decidable) models are computably isomorphic. This is in contrast to the theorem that there are two atomic decidable models which are not computably isomorphic. The implications of this work in reverse mathematics is that "effectively prime implies effectively atomic" holds in topped models. But due to an observation of David Belanger, "effectively prime implies effectively atomic" fails for some Scott sets. The reserve mathematical strength of "Prime Uniqueness" remains open.
Q-DeckRec: A Fast Deck Recommendation System for Collectible Card Games

Deck building is a crucial component in playing Collectible Card Games (CCGs). The goal of deck building is to choose a fixed-sized subset of cards from a large card pool, so that they work well together in-game against specific opponents. Existing methods either lack flexibility to adapt to different opponents or require large computational resources, still making them unsuitable for any real-time or large-scale application. We propose a new deck recommendation system, named Q-DeckRec, which learns a deck search policy during a training phase and uses it to solve deck building problem instances. Our experimental results demonstrate Q-DeckRec requires less computational resources to build winning-effective decks after a training phase compared to several baseline methods.
One-Shot Adaptation of Supervised Deep Convolutional Models

Dataset bias remains a significant barrier towards solving real world computer vision tasks. Though deep convolutional networks have proven to be a competitive approach for image classification, a question remains: have these models have solved the dataset bias problem? In general, training or fine-tuning a state-of-the-art deep model on a new domain requires a significant amount of data, which for many applications is simply not available. Transfer of models directly to new domains without adaptation has historically led to poor recognition performance. In this paper, we pose the following question: is a single image dataset, much larger than previously explored for adaptation, comprehensive enough to learn general deep models that may be effectively applied to new image domains? In other words, are deep CNNs trained on large amounts of labeled data as susceptible to dataset bias as previous methods have been shown to be? We show that a generic supervised deep CNN model trained on a large dataset reduces, but does not remove, dataset bias. Furthermore, we propose several methods for adaptation with deep models that are able to operate with little (one example per category) or no labeled domain specific data. Our experiments show that adaptation of deep models on benchmark visual domain adaptation datasets can provide a significant performance boost.
Approximation by Polynomials in Sobolev Spaces with Jacobi Weight

Polynomial approximation is studied in the Sobolev space $$W_p^r(w_{\alpha ,\beta })$$ that consists of functions whose r-th derivatives are in weighted $$L^p$$ space with the Jacobi weight function $$w_{\alpha ,\beta }$$ . This requires simultaneous approximation of a function and its consecutive derivatives up to s-th order with $$s \le r$$ . We provide sharp error estimates given in terms of $$E_n(f^{(r)})_{L^p(w_{\alpha ,\beta })}$$ , the error of best approximation to $$f^{(r)}$$ by polynomials in $$L^p(w_{\alpha ,\beta })$$ , and an explicit construction of the polynomials that approximate simultaneously with the sharp error estimates.
A Stackelberg game perspective on the conflict between machine learning and data obfuscation

Data is the new oil; this refrain is repeated extensively in the age of internet tracking, machine learning, and data analytics. As data collection becomes more personal and pervasive, however, public pressure is mounting for privacy protection. In this atmosphere, developers have created applications to add noise to user attributes visible to tracking algorithms. This creates a strategic interaction between trackers and users when incentives to maintain privacy and improve accuracy are misaligned. In this paper, we conceptualize this conflict through an N + 1-player, augmented Stackelberg game. First a machine learner declares a privacy protection level, and then users respond by choosing their own perturbation amounts. We use the general frameworks of differential privacy and empirical risk minimization to quantify the utility components due to privacy and accuracy, respectively. In equilibrium, each user perturbs her data independently, which leads to a high net loss in accuracy. To remedy this scenario, we show that the learner improves his utility by proactively perturbing the data himself. While other work in this area has studied privacy markets and mechanism design for truthful reporting of user information, we take a different viewpoint by considering both user and learnerperturbation.
On the cofinality of the splitting number

Abstract The splitting number s can be singular. The key method is to construct a forcing poset with finite support matrix iterations of ccc posets introduced by Blass and Shelah (1989).
AdaPT: an interactive procedure for multiple testing with side information

We consider the problem of multiple hypothesis testing with generic side information: for each hypothesis $H_i$ we observe both a p-value $p_i$ and some predictor $x_i$ encoding contextual information about the hypothesis. For large-scale problems, adaptively focusing power on the more promising hypotheses (those more likely to yield discoveries) can lead to much more powerful multiple testing procedures. We propose a general iterative framework for this problem, called the Adaptive p-value Thresholding (AdaPT) procedure, which adaptively estimates a Bayes-optimal p-value rejection threshold and controls the false discovery rate (FDR) in finite samples. At each iteration of the procedure, the analyst proposes a rejection threshold and observes partially censored p-values, estimates the false discovery proportion (FDP) below the threshold, and either stops to reject or proposes another threshold, until the estimated FDP is below $\alpha$. Our procedure is adaptive in an unusually strong sense, permitting the analyst to use any statistical or machine learning method she chooses to estimate the optimal threshold, and to switch between different models at each iteration as information accrues. We demonstrate the favorable performance of AdaPT by comparing it to state-of-the-art methods in five real applications and two simulation studies.
The unconditional constants for Hilbert space frame expansions

Abstract The most fundamental notion in frame theory is the frame expansion of a vector. Although it is well known that these expansions are unconditionally convergent series, no characterizations of the unconditional constant were known. This has made it impossible to get accurate quantitative estimates for problems which require using subsequences of a frame. We will prove some new results in frame theory by showing that the unconditional constants of the frame expansion of a vector in a Hilbert space are bounded by B A , where A , B are the frame bounds of the frame. Tight frames thus have unconditional constant one, which we then generalize by showing that Bessel sequences have frame expansions with unconditional constant one if and only if the sequence is an orthogonal sum of tight frames. We give further results concerning frame expansions, in which we examine when B A is actually attained or not. We end by discussing the connections of this work to frame multipliers. These results hold in both real and complex Hilbert spaces.
Quantum intermittency for sparse CMV matrices with an application to quantum walks on the half-line

We study the dynamics given by the iteration of a (half-line) CMV matrix with sparse, high barriers. Using an approach of Tcheremchantsev, we are able to explicitly compute the transport exponents for this model in terms of the given parameters. In light of the connection between CMV matrices and quantum walks on the half-line due to Cantero-Grunbaum-Moral-Velazquez, our result also allows us to compute transport exponents corresponding to a quantum walk which is sparsely populated with strong reflectors. To the best of our knowledge, this provides the first rigorous example of a quantum walk that exhibits quantum intermittency, i.e., nonconstancy of the transport exponents. When combined with the CMV version of the Jitomirskaya-Last theory of subordinacy and the general discrete-time dynamical bounds from Damanik-Fillman-Vance, we are able to exactly compute the Hausdorff dimension of the associated spectral measure.
Dissipation and plastic deformation in collisions between metallic nanoparticles

Abstract Collisions between amorphous Fe nanoparticles were studied using molecular-dynamics simulation. For head-on collisions of nanoparticles with radii R = 1.4 nm , R = 5.2 nm , and R = 11 nm , sticking was observed at all simulated velocities. The results were compared to the description provided by the JKR model. It was found that strong disagreement exists between the predictions of JKR and the results of the molecular-dynamics simulation due to the presence of additional dissipative processes which strengthen sticking behavior. First, it is demonstrated that very strong dissipation into atomic vibrations occurs during the collision. The dissipation is strong enough to prevent significant rebound of the nanoparticles. Additionally, the morphology of the adhered nanoparticles includes a “neck” that increases in radius with increasing collision velocity which results in amplified irreversibility and adhesion. Approximate calculation of the stress during the collision indicates that stress levels are well above typical yield stress values even for low velocity collisions, consistent with the observation of plastic deformation. Furthermore, it is shown that for nanoparticles with R ⩽ 11 nm , the dominance of surface attraction results in large effective collision velocities and plastic deformation. By obtaining scaling relations for computed quantities, predictions are made for larger nanoparticles up to R ∼ 1 μ m . This work provides a new perspective on collisional dissipation and adhesion with an important connection to the modern understanding of tribology and friction.
Strong Orientational Coupling of Block Copolymer Microdomains to Smectic Layering Revealed by Magnetic Field Alignment

We elucidate the roles of the isotropic–nematic (I–N) and nematic–smectic A (N–SmA) transitions in the magnetic field directed self-assembly of a liquid crystalline block copolymer (BCP), using in situ X-ray scattering. Cooling into the nematic from the disordered melt yields poorly ordered and weakly aligned BCP microdomains. Continued cooling into the SmA, however, results in an abrupt increase in BCP orientational order with microdomain alignment tightly coupled to the translational order parameter of the smectic layers. These results underscore the significance of the N–SmA transition in generating highly aligned states under magnetic fields in these hierarchically ordered materials.
Mapping to Declarative Knowledge for Word Problem Solving

Math word problems form a natural abstraction to a range of quantitative reasoning problems, such as understanding financial news, sports results, and casualties of war. Solving such problems requi...
The More, the Merrier: the Blessing of Dimensionality for Learning Large Gaussian Mixtures

In this paper we show that very large mixtures of Gaussians are efficiently learnable in high dimension. More precisely, we prove that a mixture with known identical covariance matrices whose number of components is a polynomial of any fixed degree in the dimension n is polynomially learnable as long as a certain non-degeneracy condition on the means is satisfied. It turns out that this condition is generic in the sense of smoothed complexity, as soon as the dimensionality of the space is high enough. Moreover, we prove that no such condition can possibly exist in low dimension and the problem of learning the parameters is generically hard. In contrast, much of the existing work on Gaussian Mixtures relies on low-dimensional projections and thus hits an artificial barrier. Our main result on mixture recovery relies on a new “Poissonization”-based technique, which transforms a mixture of Gaussians to a linear map of a product distribution. The problem of learning this map can be efficiently solved using some recent results on tensor decompositions and Independent Component Analysis (ICA), thus giving an algorithm for recovering the mixture. In addition, we combine our low-dimensional hardness results for Gaussian mixtures with Poissonization to show how to embed difficult instances of low-dimensional Gaussian mixtures into the ICA setting, thus establishing exponential information-theoretic lower bounds for underdetermined ICA in low dimension. To the best of our knowledge, this is the first such result in the literature. In addition to contributing to the problem of Gaussian mixture learning, we believe that this work is among the first steps toward better understanding the rare phenomenon of the “blessing of dimensionality” in the computational aspects of statistical inference.
Syzygies of Curves Beyond Green’s Conjecture

We survey three results on syzygies of curves beyond Green’s conjecture, with a particular emphasis on drawing connections between the study of syzygies and other topics in moduli theory.
A Geometric Perspective on the MSTD Question

A more sums than differences (MSTD) set A is a subset of $$\mathbb {Z}$$ for which $$|A+A| > |A-A|$$ . Martin and O’Bryant used probabilistic techniques to prove that a non-vanishing proportion of subsets of $$\{1, \dots , n\}$$ are MSTD as $$n \rightarrow \infty $$ . However, to date only a handful of explicit constructions of MSTD sets are known. We study finite collections of disjoint intervals on the real line, $$\mathbb {I}$$ , and explore the MSTD question for such sets, as well as the relation between such sets and MSTD subsets of $$\mathbb {Z}$$ . In particular we show that every finite subset of $$\mathbb {Z}$$ can be transformed into an element of $$\mathbb {I}$$ with the same additive behavior. Using tools from discrete geometry, we show that there are no MSTD sets in $$\mathbb {I}$$ consisting of three or fewer intervals, but there are MSTD sets for four or more intervals. Furthermore, we show how to obtain an infinite parametrized family of MSTD subsets of $$\mathbb {Z}$$ from a single such set A; these sets are parametrized by lattice points satisfying simple congruence relations contained in a polyhedral cone associated to A.
A new proof of the New Intersection Theorem

Abstract In 1987 Roberts completed the proof of the New Intersection Theorem (NIT) by settling the mixed characteristic case using local Chern characters, as developed by Fulton and also by Roberts. His proof has been the only one recorded of the NIT in mixed characteristic. This paper gives a new proof of this theorem, one which mostly parallels Roberts' original proof, but avoids the use of local Chern characters. Instead, the proof here uses Adams operations on K-theory with supports as developed by Gillet and Soule.
Guided-Processing Outperforms Duty-Cycling for Energy-Efficient Systems

Energy efficiency is highly desirable for sensing systems in the Internet of Things. A common approach to achieve low-power systems is duty cycling, where components in a system are turned OFF periodically to meet an energy budget. However, this paper shows that such an approach is not necessarily optimal in energy efficiency, and proposes guided processing as a fundamentally better alternative. The proposed approach offers: 1) explicit modeling of performance uncertainties in system internals; 2) a realistic resource consumption model; and 3) a key insight into the superiority of guided processing over duty cycling. Generalization from the cascade structure to the more general graph-based one is also presented. Once applied to optimize a large-scale audio sensing system with a practical detection application, empirical results show that the proposed approach significantly improves the detection performance (up to 1.7 times and 4 times reduction in false alarm and miss rate, respectively) for the same energy consumption, when compared with the duty-cycling approach.
Deformations of the braid arrangement and Trees

Abstract We establish general counting formulas and bijections for deformations of the braid arrangement. Precisely, we consider real hyperplane arrangements such that all the hyperplanes are of the form x i − x j = s for some integer s. Classical examples include the braid, Catalan, Shi, semiorder and Linial arrangements, as well as graphical arrangements. We express the number of regions of any such arrangement as a signed count of decorated plane trees. The characteristic and coboundary polynomials of these arrangements also have simple expressions in terms of these trees. We then focus on certain “well-behaved” deformations of the braid arrangement that we call transitive. This includes the Catalan, Shi, semiorder and Linial arrangements, as well as many other arrangements appearing in the literature. For any transitive deformation of the braid arrangement we establish a simple bijection between regions of the arrangement and a set of labeled plane trees defined by local conditions. This answers a question of Gessel.
Phases in large combinatorial systems

This is a status report on a companion subject to extremal combinatorics, obtained by replacing extremality properties with emergent structure, `phases'. We discuss phases, and phase transitions, in large graphs and large permutations, motivating and using the asymptotic formalisms of graphons for graphs and permutons for permutations. Phase structure is shown to emerge using entropy and large deviation techniques.
Sup norms of Cauchy data of eigenfunctions on manifolds with concave boundary

ABSTRACTWe prove that the Cauchy data of Dirichlet or Neumann Δ- eigenfunctions of Riemannian manifolds with concave (diffractive) boundary can only achieve maximal sup norm bounds if there exists a self-focal point on the boundary, i.e., a point at which a positive measure of geodesics leaving the point return to the point. In the case of real analytic Riemannian manifolds with real analytic boundary, maximal sup norm bounds on boundary traces of eigenfunctions can only be achieved if there exists a point on the boundary at which all geodesics loop back. As an application, the Dirichlet or Neumann eigenfunctions of Riemannian manifolds with concave boundary and non-positive curvature never have eigenfunctions whose boundary traces achieve maximal sup norm bounds. The key new ingredient is the Melrose–Taylor diffractive parametrix and Melrose’s analysis of the Weyl law.
A Hitting Time Formula for the Discrete Green's Function

The discrete Green's function (without boundary) is a pseudo-inverse of the combinatorial Laplace operator of a graph G = (V, E). We reveal the intimate connection between Green's function and the theory of exact stopping rules for random walks on graphs. We give an elementary formula for Green's function in terms of state-to-state hitting times of the underlying graph. Namely, where π i is the stationary distribution at vertex i, H(i, j) is the expected hitting time for a random walk starting from vertex i to first reach vertex j, and H(π, j) = ∑ k∈V π k H(k, j). This formula also holds for the digraph Laplace operator. The most important characteristics of a stopping rule are its exit frequencies, which are the expected number of exits of a given vertex before the rule halts the walk. We show that Green's function is, in fact, a matrix of exit frequencies plus a rank one matrix. In the undirected case, we derive spectral formulas for Green's function and for some mixing measures arising from stopping rules. Finally, we further explore the exit frequency matrix point of view, and discuss a natural generalization of Green's function for any distribution τ defined on the vertex set of the graph.
Adiabatic dynamics of edge waves in photonic graphene

The propagation of localized edge modes in photonic honeycomb lattices, formed from an array of adiabatically varying periodic helical waveguides, is considered. Asymptotic analysis leads to an explicit description of the underlying dynamics. Depending on parameters, edge states can exist over an entire period or only part of a period; in the latter case an edge mode can effectively disintegrate and scatter into the bulk. In the presence of nonlinearity, a 'time'-dependent one-dimensional nonlinear Schrodinger (NLS) equation describes the envelope dynamics of edge modes. When the average of the 'time varying' coefficients yields a focusing NLS equation, soliton propagation is exhibited. For both linear and nonlinear systems, certain long lived traveling modes with minimal backscattering are found; they exhibit properties of topologically protected states.
Forced to Learn: Discovering Disentangled Representations Without Exhaustive Labels.

Learning a better representation with neural networks is a challenging problem, which was tackled extensively from different prospectives in the past few years. In this work, we focus on learning a representation that could be used for a clustering task and introduce two novel loss components that substantially improve the quality of produced clusters, are simple to apply to an arbitrary model and cost function, and do not require a complicated training procedure. We evaluate them on two most common types of models, Recurrent Neural Networks and Convolutional Neural Networks, showing that the approach we propose consistently improves the quality of KMeans clustering in terms of Adjusted Mutual Information score and outperforms previously proposed methods.
Improving the Thresholds of Sparse Recovery: An Analysis of a Two-Step Reweighted Basis Pursuit Algorithm

It is well known that $\ell _{1}$ minimization can be used to recover sufficiently sparse unknown signals from compressed linear measurements. Exact thresholds on the sparsity, as a function of the ratio between the system dimensions, so that with high probability almost all sparse signals can be recovered from independent identically distributed (i.i.d.) Gaussian measurements, have been computed and are referred to as weak thresholds. In this paper, we introduce a reweighted $\ell _{1}$ recovery algorithm composed of two steps: 1) a standard $\ell _{1}$ minimization step to identify a set of entries where the signal is likely to reside and 2) a weighted $\ell _{1}$ minimization step where entries outside this set are penalized. For signals where the non-sparse component entries are independent and identically drawn from certain classes of distributions, (including most well-known continuous distributions), we prove a strict improvement in the weak recovery threshold. Our analysis suggests that the level of improvement in the weak threshold depends on the behavior of the distribution at the origin. Numerical simulations verify the distribution dependence of the threshold improvement very well, and suggest that in the case of i.i.d. Gaussian nonzero entries, the improvement can be quite impressive—over 20% in the example we consider.
DRESS: Dynamic RESource-Reservation Scheme for Congested Data-Intensive Computing Platforms

In the past few years, we have envisioned an increasing number of businesses start driving by big data analytics, such as Amazon recommendations and Google Advertisements. At the back-end side, the businesses are powered by big data processing platforms to quickly extract information and make decisions. Running on top of a computing cluster, those platforms utilize scheduling algorithms to allocate resources. An efficient scheduler is crucial to the system performance due to limited resources, e.g. CPU and Memory, and a large number of user demands. However, besides requests from clients and current status of the system, it has limited knowledge about execution length of the running jobs, and incoming jobs' resource demands, which make assigning resources a challenging task. If most of the resources are occupied by a long-running job, other jobs will have to keep waiting until it releases them. This paper presents a new scheduling strategy, named DRESS that particularly aims to optimize the allocation among jobs with various demands. Specifically, it classifies the jobs into two categories based on their requests, reserves a portion of resources for each of category, and dynamically adjusts the reserved ratio by monitoring the pending requests and estimating release patterns of running jobs. The results demonstrate DRESS significantly reduces the completion time for one category, up to 76.1% in our experiments, and in the meanwhile, maintains a stable overall system performance.
The local distribution of the number of small prime factors: variation of the classical theme

We obtain uniform estimates for $$N_k(x,y)$$, the number of positive integers n up to x for which $$\omega _y(n)=k$$, where $$\omega _y(n)$$ is the number of distinct prime factors of n which are $$ 0$$ by the Buchstab–de Bruijn method. We also utilize a certain recent result of Tenenbaum to complete our asymptotic analysis.
Spectral Limitations of Quadrature Rules and Generalized Spherical Designs

We study manifolds $M$ equipped with a quadrature rule $$ \int_{M}{\phi(x) dx} \simeq \sum_{i=1}^{n}{a_i \phi(x_i)}.$$ We show that $n-$point quadrature rules with nonnegative weights on a compact $d-$dimensional manifold cannot integrate more than at most the first $c_{d}n + o(n)$ Laplacian eigenfunctions exactly. The constants $c_d$ are explicitly computed and $c_2 = 4$. The result is new even on $\mathbb{S}^2$ where it generalizes results on spherical designs.
Replication of the Keyword Extraction part of the paper "'Without the Clutter of Unimportant Words': Descriptive Keyphrases for Text Visualization"

"Keyword Extraction" refers to the task of automatically identifying the most relevant and informative phrases in natural language text. As we are deluged with large amounts of text data in many different forms and content - emails, blogs, tweets, Facebook posts, academic papers, news articles - the task of "making sense" of all this text by somehow summarizing them into a coherent structure assumes paramount importance. Keyword extraction - a well-established problem in Natural Language Processing - can help us here. In this report, we construct and test three different hypotheses (all related to the task of keyword extraction) that take us one step closer to understanding how to meaningfully identify and extract "descriptive" keyphrases. The work reported here was done as part of replicating the study by Chuang et al. [3].
Revisiting the Spectral and Timing Properties of NGC 4151

NGC 4151 is the brightest Seyfert 1 nucleus in X-rays. It was the first object to show short time delays in the Fe K band, which were attributed to relativistic reverberation, providing a new tool for probing regions at the black hole scale. Here, we report the results of a large XMM-Newton campaign in 2015 to study these short delays further. Analyzing high quality data that span time scales between hours and decades, we find that neutral and ionized absorption contribute significantly to the spectral shape. Accounting for their effects, we find no evidence for a relativistic reflection component, contrary to early work. Energy-dependent lags are significantly measured in the new data, but with an energy profile that does not resemble a broad iron line, in contrast to the old data. The complex lag-energy spectra, along with the lack of strong evidence for a relativistic spectral component, suggest that the energy-dependent lags are produced by absorption effects. The long term spectral variations provide new details on the variability of the narrow Fe Kα line. We find that its variations are correlated with, and delayed with respect to, the primary X-ray continuum. We measure a delay of τ=3.3-0.7+1.8 days, implying an origin in the inner broad line region (BLR). The delay is half the Hβ line delay, suggesting a geometry that differs slightly from the optical BLR.
Interrogating Mutant Allele Expression via Customized Reference Genomes to Define Influential Cancer Mutations

Genetic alterations are essential for cancer initiation and progression. However, differentiating mutations that drive the tumor phenotype from mutations that do not affect tumor fitness remains a fundamental challenge in cancer biology. To better understand the impact of a given mutation within cancer, RNA-sequencing data was used to categorize mutations based on their allelic expression. For this purpose, we developed the MAXX (Mutation Allelic Expression Extractor) software, which is highly effective at delineating the allelic expression of both single nucleotide variants and small insertions and deletions. Results from MAXX demonstrated that mutations can be separated into three groups based on their expression of the mutant allele, lack of expression from both alleles, or expression of only the wild-type allele. By taking into consideration the allelic expression patterns of genes that are mutated in PDAC, it was possible to increase the sensitivity of widely used driver mutation detection methods, as well as identify subtypes that have prognostic significance and are associated with sensitivity to select classes of therapeutic agents in cell culture. Thus, differentiating mutations based on their mutant allele expression via MAXX represents a means to parse somatic variants in tumor genomes, helping to elucidate a gene's respective role in cancer.
Toward A Deep Understanding of What Makes a Scientific Visualization Memorable

We report results from a preliminary study exploring the memorability of spatial scientific visualizations, the goal of which is to understand the visual features that contribute to memorability. The evaluation metrics include three objective measures (entropy, feature congestion, the number of edges), four subjective ratings (clutter, the number of distinct colors, familiarity, and realism), and two sentiment ratings (interestingness and happiness). We curate 1142 scientific visualization (SciVis) images from the original 2231 images in published IEEE SciVis papers from 2008 to 2017 and compute memorability scores of 228 SciVis images from data collected on Amazon Mechanical Turk (MTurk). Results showed that the memorability of SciVis images is mostly correlated with clutter and the number of distinct colors. We further investigate the differences between scientific visualization and infographics as a means to understand memorability differences by data attributes.
Decentralized optimal control of Connected Automated Vehicles at signal-free intersections including comfort-constrained turns and safety guarantees

Abstract We extend earlier work for optimally controlling Connected Automated Vehicles (CAVs) crossing a signal-free intersection by including all possible turns taken so as to optimize a passenger comfort metric along with energy and travel time minimization. We show that it is possible to achieve this goal in a decentralized manner with each CAV solving an optimal control problem, and derive explicit solutions that guarantee collision avoidance and safe distance constraints within a control zone. We investigate the associated tradeoffs between minimizing energy and vehicle travel time, as well as the passenger comfort metric and include extensive simulations to illustrate this framework.
Safe U.S. Assets and U.S. Capital Flows

Abstract The “exorbitant privilege” of the U.S. – the ability of the U.S. to earn positive net income on its international portfolio even though it is a net debtor – may be linked to the “convenience yield” on U.S. government bonds. The convenience yield refers to the low pecuniary return on U.S. Treasuries associated with the non-pecuniary yield on those assets arising from their liquidity and safety. A simple model shows how the convenience yield can lead to current account deficits, an appreciated currency in real terms, and positive net factor income. Empirically, we find evidence associating the convenience yield with a strong dollar in real terms, and, in turn, evidence linking the real exchange rate to the U.S. current account. We calculate that this channel may account for approximately 40% of the U.S. current account deficit. We then discuss factors that might influence the convenience yield, and discuss possible drawbacks to the exorbitant privilege.
Remote Desktop Backdoor Implementation with Reverse TCP Payload using Open Source Tools for Instructional Use

In this paper, we present an implementation of remotely hacking into an older version of a popular operating system with reverse TCP payload using an open source tool. Reverse TCP opens a backdoor on the victim system which is remotely operated by the attacker without the victim's knowledge. The firewall, in this particular OS version, only scans the incoming traffic and doesn't examine the outgoing traffic which is the flaw that leads to the back door connection. The victim must initiate the connection in the reverse TCP payload. Armitage is an open source tool that provides a Graphical User Interface (GUI) to the Metasploit. The Metasploit framework is another open source framework which provides information about the vulnerabilities and aids in performing penetration testing. Metasploit contains an extensive database of exploits, payloads, and vulnerabilities that vary for different kind of systems. In the implemented attack, the attacker uploads the payload into a server, and the link to the payload is sent through an email which looks legitimate with the help of Social Engineering Toolkit. As soon as the victim executes the payload, the attacker can access the files, take a screenshot, monitor screen, sniff packets, and take pictures using the webcam. We demonstrate this attack which can be easily incorporated in a foundational cybersecurity course for enhanced learning.
G-graded irreducibility and the index of reducibility

Let R be a commutative Noetherian ring graded by a torsion-free abelian group G. We introduce the notion of G-graded irreducibility and prove that G-graded irreducibility is equivalent to irreducib...
SIM: A Slot-Independent Neural Model for Dialogue State Tracking.

Dialogue state tracking is an important component in task-oriented dialogue systems to identify users’ goals and requests as a dialogue proceeds. However, as most previous models are dependent on dialogue slots, the model complexity soars when the number of slots increases. In this paper, we put forward a slot-independent neural model (SIM) to track dialogue states while keeping the model complexity invariant to the number of dialogue slots. The model utilizes attention mechanisms between user utterance and system actions. SIM achieves state-of-the-art results on WoZ and DSTC2 tasks, with only 20% of the model size of previous models.
Optimization of quantum circuit mapping using gate transformation and commutation

Abstract This paper addresses quantum circuit mapping for Noisy Intermediate-Scale Quantum (NISQ) computers. Since NISQ computers constrain two-qubit operations to limited couplings, an input circuit must be transformed into an equivalent output circuit obeying the constraints. The transformation often requires additional gates that can affect the accuracy of running the circuit. On the basis of a previous work on quantum circuit mapping that leverages gate commutation rules, this paper presents algorithms that utilize both transformation and commutation rules. Results of experiments on a standard benchmark dataset demonstrate the algorithms with more rules can find even better circuit mappings than the previously known best algorithms.
Improving IT Support by Enhancing Incident Management Process with Multi-modal Analysis

IT support services industry is going through a major transformation with AI becoming commonplace. There has been a lot of effort in the direction of automation at every human touchpoint in the IT support processes. Incident management is one such process which has been a beacon process for AI based automation. The vision is to automate the process from the time an incident/ticket arrives till it is resolved and closed. While text is the primary mode of communicating the incidents, there has been a growing trend of using alternate modalities like image to communicate the problem. A large fraction of IT support tickets today contain attached image data in the form of screenshots, log messages, invoices and so on. These attachments help in better explanation of the problem which aids in faster resolution. Anybody who aspires to provide AI based IT support, it is essential to build systems which can handle multi-modal content.