cssi/SciSciGPT-SciSciNet huggingface dataset:
Ringel duality for perverse sheaves on hypertoric varieties

Abstract Motivated by the polynomial representation theory of the general linear group and the theory of symplectic singularities, we study a category of perverse sheaves with coefficients in a field k on any affine unimodular hypertoric variety M . Our main result is that this is a highest weight category whose Ringel dual is the corresponding category for the Gale dual hypertoric variety M ! . On the way to proving our main result, we confirm a conjecture of Finkelberg–Kubrak in the case of hypertoric varieties. We also show that our category is equivalent to representations of a combinatorially-defined algebra, recently introduced in a related paper.
Generalizing the Minkowski question mark function to a family of multidimensional continued fractions

The Minkowski question mark function ? : [0, 1] → [0, 1] is a continuous, strictly increasing, one-to-one and onto function that has derivative zero almost everywhere. Key to these facts are the ba...
A Method to Solve the Diophantine Equation

Here, we show that: if the equation has an integer solution and a b is not a perfect square, then has an infinitude of integer solutions.
Solutions to the Reifenberg Plateau problem with cohomological spanning conditions

We prove existence and regularity of minimizers for Holder densities over general surfaces of arbitrary dimension and codimension in \( \mathbb {R}^n \), satisfying a cohomological boundary condition, providing a natural dual to Reifenberg’s Plateau problem. We generalize and extend methods of Reifenberg, Besicovitch, and Adams; in particular we generalize a particular type of minimizing sequence used by Reifenberg (whose limits have nice properties, including lower bounds on lower density and finite Hausdorff measure), prove such minimizing sequences exist, and develop cohomological spanning conditions which generalize spanning conditions using linking numbers and have better properties than homological spanning conditions. Our cohomology lemmas are dual versions of the homology lemmas in the celebrated appendix by Adams found in Reifenberg’s 1960 paper.
Ultra-Low-Energy Electric Field-Induced Magnetization Switching in Multiferroic Heterostructures

Electric field-induced magnetization switching in multiferroics is intriguing for both fundamental studies and potential technological applications. Here, we review the recent developments on electric field-induced magnetization switching in multiferroic heterostructures. Particularly, we study the dynamics of magnetization switching between the two stable states in a shape-anisotropic single-domain nanomagnet using stochastic Landau–Lifshitz–Gilbert (LLG) equation in the presence of thermal fluctuations. For magnetostrictive nanomagnets in strain-coupled multiferroic composites, such study of magnetization dynamics, contrary to steady-state scenario, revealed intriguing new phenomena on binary switching mechanism. While the traditional method of binary switching requires to tilt the potential profile to the desired state of switching, we show that no such tilting is necessary to switch successfully since the magnetization’s excursion out of magnet’s plane can generate a built-in asymmetry during switching. We also study the switching dynamics in multiferroic heterostructures having magnetoelectric coupling at the interface and magnetic exchange coupling that can facilitate to maintain the direction of switching with the polarity of the applied electric field. We calculate the performance metrics like switching delay and energy dissipation during switching while simulating LLG dynamics. The performance metrics turn out to be very encouraging for potential technological applications.
Exploiting the Natural Dynamics of Series Elastic Robots by Actuator-Centered Sequential Linear Programming

Series elastic robots are best able to follow trajectories which obey the limitations of their actuators, since they cannot instantly change their joint forces. In fact, the performance of series elastic actuators can surpass that of ideal force source actuators by storing and releasing energy. In this paper, we formulate the trajectory optimization problem for series elastic robots in a novel way based on sequential linear programming. Our framework is unique in the separation of the actuator dynamics from the rest of the dynamics, and in the use of a tunable pseudo-mass parameter that improves the discretization accuracy of our approach. The actuator dynamics are truly linear, which allows them to be excluded from trust-region mechanics. This causes our algorithm to have similar run times with and without the actuator dynamics. We demonstrate our optimization algorithm by tuning high performance behaviors for a single-leg robot in simulation and on hardware for a single degree-of-freedom actuator testbed. The results show that compliance allows for faster motions and takes a similar amount of computation time.
The radial defocusing energy-supercritical nonlinear wave equation in all space dimensions

We consider the defocusing nonlinear wave equation u tt ― Δu + |u| p u = 0 with spherically-symmetric initial data in the regime 4 d―2 7, but for a smaller range of p > 4 d―2. The principal result is that blowup (or failure to scatter) must be accompanied by blowup of the critical Sobolev norm. An equivalent formulation is that maximal-lifespan solutions with bounded critical Sobolev norm are global and scatter.
Singular values of large non-central random matrices

We study largest singular values of large random matrices, each with mean of a fixed rank K. Our main result is a limit theorem as the number of rows and columns approach infinity, while their rati...
Beyond Disagreement-Based Agnostic Active Learning

We study agnostic active learning, where the goal is to learn a classifier in a pre-specified hypothesis class interactively with as few label queries as possible, while making no assumptions on the true function generating the labels. The main algorithm for this problem is disagreement-based active learning, which has a high label requirement. Thus a major challenge is to find an algorithm which achieves better label complexity, is consistent in an agnostic setting, and applies to general classification problems. In this paper, we provide such an algorithm. Our solution is based on two novel contributions; first, a reduction from consistent active learning to confidence-rated prediction with guaranteed error, and second, a novel confidence-rated predictor.
Black-box optimization with a politician

We propose a new framework for black-box convex optimization which is well-suited for situations where gradient computations are expensive. We derive a new method for this framework which leverages several concepts from convex optimization, from standard first-order methods (e.g. gradient descent or quasi-Newton methods) to analytical centers (i.e. minimizers of self-concordant barriers). We demonstrate empirically that our new technique compares favorably with state of the art algorithms (such as BFGS).
End-To-End Source Separation With Adaptive Front-Ends

Source separation and other audio applications have traditionally relied on the use of short-time Fourier transforms as a front-end frequency domain representation step. The unavailability of a neural network equivalent to forward and inverse transforms hinders the implementation of end-to-end learning systems for these applications. We develop an auto-encoder neural network that can act as an equivalent to short-time front-end transforms. We demonstrate the ability of the network to learn optimal, real-valued basis functions directly from the raw waveform of a signal and further show how it can be used as an adaptive front-end for supervised source separation. In terms of separation performance, these transforms significantly outperform their Fourier counterparts. Finally, we also propose and interpret a novel source to distortion ratio based cost function for end-to-end source separation.
An Improved Discrete Least-Squares/Reduced-Basis Method for Parameterized Elliptic PDEs

It is shown that the computational efficiency of the discrete least-squares (DLS) approximation of solutions of stochastic elliptic PDEs is improved by incorporating a reduced-basis method into the DLS framework. In particular, we consider stochastic elliptic PDEs with an affine dependence on the random variable. The goal is to recover the entire solution map from the parameter space to the finite element space. To this end, first, a reduced-basis solution using a weak greedy algorithm is constructed, then a DLS approximation is determined by evaluating the reduced-basis approximation instead of the full finite element approximation. The main advantage of the new approach is that one only need apply the DLS operator to the coefficients of the reduced-basis expansion, resulting in huge savings in both the storage of the DLS coefficients and the online cost of evaluating the DLS approximation. In addition, the recently developed quasi-optimal polynomial space is also adopted in the new approach, resulting in superior convergence rates for a wider class of problems than previous analyzed. Numerical experiments are provided that illustrate the theoretical results.
Asymptotic decay for a one-dimensional nonlinear wave equation

We consider the asymptotic behaviour of finite energy solutions to the one-dimensional defocusing nonlinear wave equation $-u_{tt} + u_{xx} = |u|^{p-1} u$, where $p > 1$. Standard energy methods guarantee global existence, but do not directly say much about the behaviour of $u(t)$ as $t \to \infty$. Note that in contrast to higher-dimensional settings, solutions to the linear equation $-u_{tt} + u_{xx} = 0$ do not exhibit decay, thus apparently ruling out perturbative methods for understanding such solutions. Nevertheless, we will show that solutions for the nonlinear equation behave differently from the linear equation, and more specifically that we have the average $L^\infty$ decay $\lim_{T \to +\infty} \frac{1}{T} \int_0^T \|u(t)\|_{L^\infty_x(\R)}\ dt = 0$, in sharp contrast to the linear case. An unusual ingredient in our arguments is the classical Radamacher differentiation theorem that asserts that Lipschitz functions are almost everywhere differentiable.
The Multiplicity of Eigenvalues of the Hodge Laplacian on 5-Dimensional Compact Manifolds

We study the multiplicity of the eigenvalues of the Hodge Laplacian on smooth, compact Riemannian manifolds of dimension five for generic families of metrics. We prove that generically the Hodge Laplacian, restricted to the subspace of co-exact two-forms, has nonzero eigenvalues of multiplicity two. The proof is based on the fact that the Hodge Laplacian restricted to the subspace of co-exact two-forms is minus the square of the Beltrami operator, a first-order operator. We prove that for generic metrics the spectrum of the Beltrami operator is simple. Because the Beltrami operator in this setting is a skew-adjoint operator, this implies the main result for the Hodge Laplacian.
Robust Bayesian Inference via Coarsening

The standard approach to Bayesian inference is based on the assumption that the distribution of the data belongs to the chosen model class. However, even a small violation of this assumption can ha...
Affect Intensity Estimation Using Multiple Modalities

One of the challenges in affect recognition is accurate estimation of the emotion intensity level. This research proposes development of an affect intensity estimation model based on a weighted sum of classification confidence levels, displacement of feature points and speed of feature point motion. The parameters of the model were calculated from data captured using multiple modalities such as face, body posture, hand movement and speech. A preliminary study was conducted to compare the accuracy of the model with the annotated intensity levels. An emotion intensity scale ranging from 0 to 1 along the arousal dimension in the emotion space was used. Results indicated speech and hand modality significantly contributed in improving accuracy in emotion intensity estimation using the proposed model.
Location Name Extraction from Targeted Text Streams using Gazetteer-based Statistical Language Models

Extracting location names from informal and unstructured social media data requires the identification of referent boundaries and partitioning compound names. Variability, particularly systematic variability in location names (Carroll, 1983), challenges the identification task. Some of this variability can be anticipated as operations within a statistical language model, in this case drawn from gazetteers such as OpenStreetMap (OSM), Geonames, and DBpedia. This permits evaluation of an observed n-gram in Twitter targeted text as a legitimate location name variant from the same location-context. Using n-gram statistics and location-related dictionaries, our Location Name Extraction tool (LNEx) handles abbreviations and automatically filters and augments the location names in gazetteers (handling name contractions and auxiliary contents) to help detect the boundaries of multi-word location names and thereby delimit them in texts. We evaluated our approach on 4,500 event-specific tweets from three targeted streams to compare the performance of LNEx against that of ten state-of-the-art taggers that rely on standard semantic, syntactic and/or orthographic features. LNEx improved the average F-Score by 33-179%, outperforming all taggers. Further, LNEx is capable of stream processing.
How Do You Fix an Oval Track Puzzle

The oval track group, $OT_{n,k}$, is the subgroup of the symmetric group, $S_n$, generated by the basic moves available in a generalized oval track puzzle with $n$ tiles and a turntable of size $k$. In this paper we completely describe the oval track group for all possible $n$ and $k$ and use this information to answer the following question: If the tiles are removed from an oval track puzzle, how must they be returned in order to ensure that the puzzle is still solvable? As part of this discussion we introduce the parity subgroup of $S_n$ in the case when $n$ is even.
Poisson percolation on the oriented square lattice

Abstract In Poisson percolation each edge becomes open after an independent exponentially distributed time with rate that decreases in the distance from the origin. As a sequel to our work on the square lattice, we describe the limiting shape of the component containing the origin in the oriented case. We show that the density of occupied sites at height y in the cluster is close to the percolation probability in the corresponding homogeneous percolation process, and we study the fluctuations of the boundary.
Sub-Linear Time Support Recovery for Compressed Sensing Using Sparse-Graph Codes

We study the support recovery problem for compressed sensing, where the goal is to reconstruct the sparsity pattern of a high-dimensional $K$ -sparse signal $\mathrm {x}\in \mathbb {R}^{N}$ , as well as the corresponding sparse coefficients, from low-dimensional linear measurements with and without noise. Our key contribution is a new compressed sensing framework through a new family of carefully designed sparse measurement matrices associated with minimal measurement costs and a low-complexity recovery algorithm. Specifically, the measurement matrix in our framework is designed based on the well-crafted sparsification through capacity-approaching sparse-graph codes , where the sparse coefficients can be recovered efficiently in a few iterations by performing simple error decoding over the observations. We formally connect this general recovery problem with sparse-graph decoding in packet communication systems and analyze our framework in terms of the measurement cost, computational complexity, and recovery performance. Specifically, we show that in the noiseless setting, our framework can recover any arbitrary $K$ -sparse signal in $O(K)$ time using $2K$ measurements asymptotically with a vanishing error probability . In the noisy setting, when the sparse coefficients take values in a finite and quantized alphabet, our framework can achieve the same goal in time $O(K\log (N/K))$ using $O(K\log (N/K))$ measurements obtained from measurement matrix with elements {−1, 0, 1}. When the sparsity $K$ is sub-linear in the signal dimension $K=O(N^\delta )$ for some $0 , our results are order-optimal in terms of measurement costs and run-time, both of which are sub-linear in the signal dimension $N$ . The sub-linear measurement cost and run-time can also be achieved with continuous-valued sparse coefficients, with a slight increment in the logarithmic factors. More specifically, in the continuous alphabet setting, when $K=O(N^\delta )$ and the magnitudes of all the sparse coefficients are bounded below by a positive constant, our algorithm can recover an arbitrarily large $(1-p)$ -fraction of the support of the sparse signal using $O(K\log (N/K)\log \log (N/K))$ measurements, and $O(K\log ^{1+r}(N/K))$ run-time, where $r$ is an arbitrarily small constant. For each recovered sparse coefficient, we can achieve $O(\epsilon )$ error for an arbitrarily small constant $\epsilon $ . In addition, if the magnitudes of all the sparse coefficients are upper bounded by $O(K^{c})$ for some constant $c , then we are able to provide a strong $\ell _{1}$ recovery guarantee for the estimated signal $\widehat { \mathrm {x}}$ : $\|\widehat { \mathrm {x}} - \mathrm {x}\|_{1} \le \kappa \| \mathrm {x}\|_{1}$ , where the constant $\kappa $ can be arbitrarily small. This offers the desired scalability of our framework that can potentially enable real-time or near-real-time processing for massive datasets featuring sparsity, which are relevant to a multitude of practical applications.
Stackable vs autonomous cars for shared mobility systems: A preliminary performance evaluation

Car sharing is one of the key elements of a Mobility-on-Demand system, but it still suffers from several shortcomings, the most significant of which is the fleet unbalance during the day. What is typically observed in car sharing systems, in fact, is a vehicle shortage in so-called hot spots (i.e., areas with high demand) and vehicle accumulation in cold spots, due to the patterns in people flows during the day. In this work, we overview the main approaches to vehicle redistribution based on the type of vehicles the car sharing fleet is composed of, and we evaluate their performance using a realistic car sharing demand derived for a suburban area around Lyon, France. The main result of this paper is that stackable vehicles can achieve a relocation performance close to that of autonomous vehicles, significantly improving over the no-relocation approach and over traditional relocation with standard cars.
Mining container image repositories for software configuration and beyond

This paper introduces the idea of mining container image repositories for configuration and other deployment information of software systems. Unlike traditional software repositories (e.g., source code repositories and app stores), image repositories encapsulate the entire execution ecosystem for running target software, including its configurations, dependent libraries and components, and OS-level utilities, which contributes to a wealth of data and information. We showcase the opportunities based on concrete software engineering tasks that can benefit from mining image repositories. To facilitate future mining efforts, we summarize the challenges of analyzing image repositories and the approaches that can address these challenges. We hope that this paper will stimulate exciting research agenda of mining this emerging type of software repositories.
How to round subspaces: a new spectral clustering algorithm

A basic problem in spectral clustering is the following. If a solution obtained from the spectral relaxation is close to an integral solution, is it possible to find this integral solution even though they might be in completely different basis? In this paper, we propose a new spectral clustering algorithm. It can recover a k-partition such that the subspace corresponding to the span of its indicator vectors is O([EQUATION]) close to the original subspace in spectral norm with OPT being the minimum possible (OPT ≤ 1 always). Moreover our algorithm does not impose any restriction on the cluster sizes. Previously, no algorithm was known which could find a k-partition closer than o(k · OPT).We present two applications for our algorithm. First one finds a disjoint union of bounded degree expanders which approximate a given graph in spectral norm. The second one is for approximating the sparsest k-partition in a graph where each cluster have expansion at most φk provided φk ≤ O(λk+1) where λk+1 is the (k + 1)st eigenvalue of Laplacian matrix. This significantly improves upon the previous algorithms, which required φk ≤ O(λk+1/k).
Variable Bandwidth Diffusion Kernels

Abstract Practical applications of kernel methods often use variable bandwidth kernels, also known as self-tuning kernels, however much of the current theory of kernel based techniques is only applicable to fixed bandwidth kernels. In this paper, we derive the asymptotic expansion of these variable bandwidth kernels for arbitrary bandwidth functions; generalizing the theory of Diffusion Maps and Laplacian Eigenmaps. We also derive pointwise error estimates for the corresponding discrete operators which are based on finite data sets; generalizing a result of Singer which was restricted to fixed bandwidth kernels. Our analysis reveals how areas of small sampling density lead to large errors, particularly for fixed bandwidth kernels. We explain the limitation of the existing theory to data sampled from compact manifolds by showing that when the sampling density is not bounded away from zero (which implies that the data lies on an open set) the error estimates for fixed bandwidth kernels will be unbounded. We show that this limitation can be overcome by choosing a bandwidth function inversely proportional to the sampling density (which can be estimated from data) which allows us to control the error estimates uniformly over a non-compact manifold. We numerically verify these results on non-compact manifolds by constructing the generator of the Ornstein–Uhlenbeck process on a real line and a two-dimensional plane using data sampled independently from the respective invariant measures. We also verify our results on compact manifolds by constructing the Laplacian on the unit circle and the unit sphere and we show that the variable bandwidth kernels exhibit reduced sensitivity to bandwidth selection and give better results for an automatic bandwidth selection algorithm.
A Secret Key Generation Scheme for Internet of Things using Ternary-States ReRAM-based Physical Unclonable Functions

Some of the main challenges towards utilizing conventional cryptographic techniques in Internet of Things (IoT) include the need for generating secret keys for such a large-scale network, distributing the generated keys to all the devices, key storage as well as the vulnerability to security attacks when an adversary gets physical access to the devices. In this paper, a novel secret key generation method is proposed for IoTs that utilize the intrinsic randomness embedded in the devices’ memories introduced in the manufacturing process. A fuzzy extractor structure using serially concatenated BCHPolar codes is proposed to generate reproducible keys from a ReRAM-based ternary-state Physical Unclonable Functions (PUFs) for device authentication and secret key generation. The main concern in deploying PUF-based key generation methods is the leakage of information about the secret keys from the publicly available helper data. The fuzzy extractor proposed in this paper ensures much less mutual information between the generated keys and the helper data. The experimental results show that our proposed scheme is capable of generating notably stronger keys compared to existing techniques, while utilizing a significantly lower number of helper data bits. The failure probability when a low complex Successive Cancellation decoder is implemented in the proposed fuzzy extractor structure is $10 ^{-8\, }$which was further increased to $10 ^{-10\, }$ when a complex iterative belief propagation decoder was used.11This project is partially supported by Arizona Board of Regents under Grant # 1003330.
Ultra-high-Q phononic resonators on-chip at cryogenic temperatures

Long-lived, high-frequency phonons are valuable for applications ranging from optomechanics to emerging quantum systems. For scientific as well as technological impact, we seek high-performance oscillators that offer a path toward chip-scale integration. Confocal bulk acoustic wave resonators have demonstrated an immense potential to support long-lived phonon modes in crystalline media at cryogenic temperatures. So far, these devices have been macroscopic with cm-scale dimensions. However, as we push these oscillators to high frequencies, we have an opportunity to radically reduce the footprint as a basis for classical and emerging quantum technologies. In this paper, we present novel design principles and simple microfabrication techniques to create high performance chip-scale confocal bulk acoustic wave resonators in a wide array of crystalline materials. We tailor the acoustic modes of such resonators to efficiently couple to light, permitting us to perform a non-invasive laser-based phonon spectroscopy. Using this technique, we demonstrate an acoustic Q-factor of 2.8 × 107 (6.5 × 106) for chip-scale resonators operating at 12.7 GHz (37.8 GHz) in crystalline z-cut quartz (x-cut silicon) at cryogenic temperatures.
Sampling and multilevel coarsening algorithms for fast matrix approximations

This paper addresses matrix approximation problems for matrices that are large, sparse and/or that are representations of large graphs. To tackle these problems, we consider algorithms that are based primarily on coarsening techniques, possibly combined with random sampling. A multilevel coarsening technique is proposed which utilizes a hypergraph associated with the data matrix and a graph coarsening strategy based on column matching. Theoretical results are established that characterize the quality of the dimension reduction achieved by a coarsening step, when a proper column matching strategy is employed. We consider a number of standard applications of this technique as well as a few new ones. Among the standard applications we first consider the problem of computing the partial SVD for which a combination of sampling and coarsening yields significantly improved SVD results relative to sampling alone. We also consider the Column subset selection problem, a popular low rank approximation method used in data related applications, and show how multilevel coarsening can be adapted for this problem. Similarly, we consider the problem of graph sparsification and show how coarsening techniques can be employed to solve it. Numerical experiments illustrate the performances of the methods in various applications.
High‐Efficiency Thin‐Film Superlattice Thermoelectric Cooler Modules Enabled by Low Resistivity Contacts

V-telluride superlattice thin films have shown promising performance for on-chip cooling devices. Recent experimental studies have indicated that device performance is limited by the metal/semiconductor electrical contacts. One challenge in realizing a low resistivity contacts is the absence of fundamental knowledge of the physical and chemical properties of interfaces between metal and V-telluride materials. Here we present a combination of experimental and theoretical efforts to understand, design and harness low resistivity contacts to V-tellurides. Ab initio calculations are used to explore the effects of interfacial structure and chemical compositions on the electrical contacts, and an ab initio based macroscopic model is employed to predict the fundamental limit of contact resistivity as a function of both carrier concentration and temperature. Under the guidance of theoretical studies, we develop an experimental approach to fabricate low resistivity metal contacts to V-telluride thin film superlattices, achieving a 100-fold reduction compared to previous work. Interfacial characterization and analysis using both scanning transmission electron microscopy and energy-dispersive x-ray spectroscopy show the unusual interfacial morphology and the potential for further improvement in contact resistivity. Finally, we harness the improved contacts to realize an improved high-performance thermoelectric cooling module.
Engineered nanomaterials in the context of global element cycles

Environmental nanomaterials researchers are challenged to discern relevant use and release scenarios of engineered nanomaterials (ENMs). Here, we evaluated ENMs within the framework of global anthropogenic element cycles. To provide a bird's-eye view of the status and scale of nanotechnologies, we constructed a multifaceted framework to discern industrial relevance by employing metrics, such as technology readiness level, annual production volumes, synthetic efficiencies, and projected annual market growth rates across twenty-five ENMs. For eight detailed element cycles (Ce, Ag, Zn, Al, Co, Cu, Ni, and Fe), ENMs had a minor influence on anthropogenic element cycling (2 × 10−6 to 2% of total extracted ore), while nSiO2 represents 3–25% of Si metal mined. Production volumes represent only a portion of the material mined for nanomaterial synthesis; synthetic yields for metal, metalloid, and metal oxide nanomaterials were high (typically greater than 90%), while carbon-based nanomaterials have dramatically lower synthetic efficiencies (8–33%). Finally, technology readiness levels indicated that carbon-based nanomaterials have a diverse suite of current applications, whereas metal and metalloid-oxide applications are more limited in number. Several markets continue to grow, particularly quantum dots (58% projected annual growth from 2015–2025). Probing the vast nanomaterial space en masse serves to focus environmental health and safety efforts on materials that are most industrially relevant to biogeochemical processes, and this article is first to consider ENMs within the framework of anthropogenic element cycling of bulk materials at the global level.
Fourier duality of quantum curves

There are two different ways to deform a quantum curve along the flows of the KP hierarchy. We clarify the relation between the two KP orbits: In the framework of suitable connections attached to the quantum curve they are related by a local Fourier duality. As an application we give a conceptual proof of duality results in 2D quantum gravity.
The hidden symmetry of the heterotic string

We propose that Borcherds' Fake Monster Lie algebra is a broken symmetry of heterotic string theory compactified on $T^7 \times T^2$. As evidence, we study the fully flavored counting function for BPS instantons contributing to a certain loop amplitude. The result is controlled by $\Phi_{12}$, an automorphic form for $O(2, 26, \mathbb{Z})$. The degeneracies it encodes in its Fourier coefficients are graded dimensions of a second-quantized Fock space for this large symmetry algebra. This construction provides a concrete realization of Harvey and Moore's proposed relationship between Generalized Kac-Moody symmetries and supersymmetric string vacua.
Status updates through multicast networks

Using age of information as the freshness metric, we examine a multicast network in which real-time status updates are generated by the source and sent to a group of n interested receivers. We show that in order to keep the information freshness at each receiver, the source should terminate the transmission of the current update and start sending a new update packet as soon as it receives the acknowledgements back from any k out of n nodes. As the source stopping threshold k increases, a node is more likely to get the latest generated update, but the age of the most recent update is more likely to become outdated. We derive the age minimized stopping threshold k that balances the likelihood of getting the latest update and the freshness of the latest update for shifted exponential link delay. Through numerical evaluations for different stopping strategies, we find that waiting for the acknowledgements from the earliest k out of n nodes leads to lower average age than waiting for a pre-selected group of k nodes. We also observe that a properly chosen threshold k can prevent information staleness for increasing number of nodes n in the multicast network.
Complacency at the gates

A field report on the non-impact of the ASA Statement on Statistical Significance and P-Values on the broader research community. This article discusses the implications of a premier accounting journal’s dismissive response to a systematic application of the 2016 ASA Statement principles to its published content for the ASA statement’s likely success in achieving its objective of improving statistical practice.
Recovering True Classifier Performance in Positive-Unlabeled Learning

A common approach in positive-unlabeled learning is to train a classification model between labeled and unlabeled data. This strategy is in fact known to give an optimal classifier under mild conditions; however, it results in biased empirical estimates of the classifier performance. In this work, we show that the typically used performance measures such as the receiver operating characteristic curve, or the precision recall curve obtained on such data can be corrected with the knowledge of class priors; i.e., the proportions of the positive and negative examples in the unlabeled data. We extend the results to a noisy setting where some of the examples labeled positive are in fact negative and show that the correction also requires the knowledge of the proportion of noisy examples in the labeled positives. Using state-of-the-art algorithms to estimate the positive class prior and the proportion of noise, we experimentally evaluate two correction approaches and demonstrate their efficacy on real-life data.
Sequential Deliberation for Social Choice

Social choice is a normative study of designing protocols for collective decision making. However, in instances where the underlying decision space is too large or complex for ordinal voting, standard voting methods may be impractical. How then can we design a protocol - preferably decentralized, simple, scalable, and not requiring any special knowledge of the decision space - to reach consensus? We propose sequential deliberation as a natural solution to this problem. In this iterative method, successive pairs of agents bargain over the decision space using the previous decision as a disagreement alternative. We show that sequential deliberation finds a 1.208-approximation to the optimal social cost when the space of preferences define a median graph, coming very close to this value with only a small constant number of agents sampled from the population. We also give lower bounds on simpler classes of mechanisms to justify our design choices. We further show that sequential deliberation is ex-post Pareto efficient and has truthful reporting as an equilibrium of the induced extensive form game. Finally, we prove that for general metric spaces, the first and second moment of the distribution of social cost of the outcomes produced by sequential deliberation are also bounded by constants.
Detecting Fourier Subspaces

Let G be a finite abelian group. We examine the discrepancy between subspaces of \(l^2(G)\) which are diagonalized in the standard basis and subspaces which are diagonalized in the dual Fourier basis. The general principle is that a Fourier subspace whose dimension is small compared to \(|G| = \mathrm{dim}\left( l^2(G)\right) \) tends to be far away from standard subspaces. In particular, the recent positive solution of the Kadison–Singer problem shows that from within any Fourier subspace whose dimension is small compared to |G| there is a standard subspace which is essentially indistinguishable from its orthogonal complement.
Multiplicative approximation by the Weil height

Let $K/\mathbb{Q}$ be an algebraic extension of fields, and let $\alpha \not= 0$ be contained in an algebraic closure of $K$. If $\alpha$ can be approximated by roots of numbers in $K^{\times}$ with respect to the Weil height, we prove that some nonzero integer power of $\alpha$ must belong to $K^{\times}$. More generally, let $K_1, K_2, \dots , K_N$, be algebraic extensions of $\mathb{Q}$ such that each pair of extensions includes one which is a (possibly infinite) Galois extension of a common subfield. If $\alpha \not= 0$ can be approximated by a product of roots of numbers from each $K_n$ with respect to the Weil height, we prove that some nonzero integer power of $\alpha$ must belong to the multiplicative group $K_1^{\times} K_2^{\times} \cdots K_N^{\times}$. Our proof of the more general result uses methods from functional analysis.
Dictionary Learning and Sparse Coding-Based Denoising for High-Resolution Task Functional Connectivity MRI Analysis

We propose a novel denoising framework for task functional Magnetic Resonance Imaging (tfMRI) data to delineate the high-resolution spatial pattern of the brain functional connectivity via dictionary learning and sparse coding (DLSC). In order to address the limitations of the unsupervised DLSC-based fMRI studies, we utilize the prior knowledge of task paradigm in the learning step to train a data-driven dictionary and to model the sparse representation. We apply the proposed DLSC-based method to Human Connectome Project (HCP) motor tfMRI dataset. Studies on the functional connectivity of cerebrocerebellar circuits in somatomotor networks show that the DLSC-based denoising framework can significantly improve the prominent connectivity patterns, in comparison to the temporal non-local means (tNLM)-based denoising method as well as the case without denoising, which is consistent and neuroscientifically meaningful within motor area. The promising results show that the proposed method can provide an important foundation for the high-resolution functional connectivity analysis, and provide a better approach for fMRI preprocessing.
Positive mass theorem on manifolds admitting corners along a hypersurface

We study a class of non-smooth asymptotically flat manifolds on which metrics fails to be $C^1$ across a hypersurface $\Sigma$. We first give an approximation scheme to mollify the metric, then we prove that the Positive Mass Theorem still holds on these manifolds if a geometric boundary condition is satisfied by metrics separated by $\Sigma$.
Stochastic least-action principle for the incompressible Navier–Stokes equation

Abstract We formulate a stochastic least-action principle for solutions of the incompressible Navier–Stokes equation, which formally reduces to Hamilton’s principle for the incompressible Euler solutions in the case of zero viscosity. We use this principle to give a new derivation of a stochastic Kelvin Theorem for the Navier–Stokes equation, recently established by Constantin and Iyer, which shows that this stochastic conservation law arises from particle-relabelling symmetry of the action. We discuss issues of irreversibility, energy dissipation, and the inviscid limit of Navier–Stokes solutions in the framework of the stochastic variational principle. In particular, we discuss the connection of the stochastic Kelvin Theorem with our previous “martingale hypothesis” for fluid circulations in turbulent solutions of the incompressible Euler equations.
An “ad-hoc” modified Likelihood Function Applied to Optimization of Data Analysis in Atomic Spectroscopy

Abstract In this paper we propose an “ad-hoc” construction of the Likelihood Function, in order to develop a data analysis procedure, to be applied in atomic and nuclear spectral analysis. The classical Likelihood Function was modified taking into account the underlying statistics of the phenomena studied, by the inspection of the residues of the fitting, which should behave with specific statistical properties. This new formulation was analytically developed, but the sought parameter should be evaluated numerically, since it cannot be obtained as a function of each one of the independent variables. For this simple numerical evaluation, along with the acquired data, we also should process many sets of external data, with specific properties — This new random data should be uncorrelated with the acquired signal. The statistical method developed was evaluated over computer simulated spectra and over an experimental example. The numerical evaluations of the calculated parameter applying this method, indicate an improvement in one order of magnitude over accuracy compared with those produced by least squares approaches. In the experimental application of this method, over the quantification of Mn in a spectrum of a IAEA’s sample (Proficiency Ring Test, PTXRFIAEA12), we found an improvement over the precision of the results. We still have to evaluate the improvement produced by this method over Detection and Quantitation Limits, in TXRF spectral analysis.
Transfer Learning for Image-Based Malware Classification

In this paper, we consider the problem of malware detection and classification based on image analysis. We convert executable files to images and apply image recognition using deep learning (DL) models. To train these models, we employ transfer learning based on existing DL models that have been pre-trained on massive image datasets. We carry out various experiments with this technique and compare its performance to that of an extremely simple machine learning technique, namely, k-nearest neighbors (k-NN). For our k-NN experiments, we use features extracted directly from executables, rather than image analysis. While our image-based DL technique performs well in the experiments, surprisingly, it is outperformed by k-NN. We show that DL models are better able to generalize the data, in the sense that they outperform k-NN in simulated zero-day experiments.
When Not to Classify: Detection of Reverse Engineering Attacks on DNN Image Classifiers

This paper addresses detection of a reverse engineering (RE) attack targeting a deep neural network (DNN) image classifier; by querying, RE’s aim is to discover the classifier’s decision rule. RE can enable test-time evasion attacks, which require knowledge of the classifier. Recently, we proposed a quite effective approach (ADA) to detect test-time evasion attacks. In this paper, we extend ADA to detect RE attacks (ADA-RE). We demonstrate our method is successful in detecting "stealthy" RE attacks before they learn enough to launch effective test-time evasion attacks.
Reverse Mathematics of Matroids

Matroids generalize the familiar notion of linear dependence from linear algebra. Following a brief discussion of founding work in computability and matroids, we use the techniques of reverse mathematics to determine the logical strength of some basis theorems for matroids and enumerated matroids. Next, using Weihrauch reducibility, we relate the basis results to combinatorial choice principles and statements about vector spaces. Finally, we formalize some of the Weihrauch reductions to extract related reverse mathematics results. In particular, we show that the existence of bases for vector spaces of bounded dimension is equivalent to the induction scheme for \(\varSigma ^0_2\) formulas.
Quantitative uniqueness of solutions to second-order elliptic equations with singular lower order terms

In this article, we study some quantitative unique continuation properties of solutions to second-order elliptic equations with singular lower order terms. First, we quantify the strong unique cont...
Deep Bayesian Bandits Showdown: An Empirical Comparison of Bayesian Deep Networks for Thompson Sampling

Recent advances in deep reinforcement learning have made significant strides in performance on applications such as Go and Atari games. However, developing practical methods to balance exploration and exploitation in complex domains remains largely unsolved. Thompson Sampling and its extension to reinforcement learning provide an elegant approach to exploration that only requires access to posterior samples of the model. At the same time, advances in approximate Bayesian methods have made posterior approximation for flexible neural network models practical. Thus, it is attractive to consider approximate Bayesian neural networks in a Thompson Sampling framework. To understand the impact of using an approximate posterior on Thompson Sampling, we benchmark well-established and recently developed methods for approximate posterior sampling combined with Thompson Sampling over a series of contextual bandit problems. We found that many approaches that have been successful in the supervised learning setting underperformed in the sequential decision-making scenario. In particular, we highlight the challenge of adapting slowly converging uncertainty estimates to the online setting.
Helping a Student with Learning Disabilities Memorize Multiplication Facts

Abstract A sixth grade student’s ability to memorize multiplication facts was investigated. The overall goal of the work was to improve the student’s understanding and knowledge of basic multiplication facts (0-10) for the zeroes, to fives. There were 66 facts, for example 4 x 6 = 24. The student had been taught multiplication concepts in her elementary years and she did have a basic understand of the meaning of multiplication facts as shown on a pretest. She understood that 4 x 6 is a representation of four sets of six or 6 + 6 + 6 + 6 = 24. The student’s previous knowledge and history were used to develop an individualized education plan to help her have a better understanding of the concept and to memorize basic multiplication facts. The interventions were concrete, semi-concrete, and abstract models of instruction. A pretest was given prior to the sessions and a posttest was given after the sessions. The number of sessions was determined based on the student’s ability to learn the concepts. The student was successful at memorizing multiplication facts for the zeroes through fives. The next study will be to help the student achieve automaticity of the multiplication facts.
Primary Fascial Closure During Laparoscopic Ventral Hernia Repair Improves Patient Quality of Life: A Multicenter, Blinded Randomized Controlled Trial.

Background:Observational studies have reported conflicting results with primary fascial closure (PFC) versus bridged repair during laparoscopic ventral hernia repair (LVHR).Objective:The aim of the study was to determine whether when evaluated in a randomized controlled trial (RCT), PFC compared to
Faster width-dependent algorithm for mixed packing and covering LPs

In this paper, we give a faster width-dependent algorithm for mixed packing-covering LPs. Mixed packing-covering LPs are fundamental to combinatorial optimization in computer science and operations research. Our algorithm finds a $1+\eps$ approximate solution in time $O(Nw/ \varepsilon)$, where $N$ is number of nonzero entries in the constraint matrix, and $w$ is the maximum number of nonzeros in any constraint. This algorithm is faster than Nesterov's smoothing algorithm which requires $O(N\sqrt{n}w/ \eps)$ time, where $n$ is the dimension of the problem. Our work utilizes the framework of area convexity introduced in [Sherman-FOCS'17] to obtain the best dependence on $\varepsilon$ while breaking the infamous $\ell_{\infty}$ barrier to eliminate the factor of $\sqrt{n}$. The current best width-independent algorithm for this problem runs in time $O(N/\eps^2)$ [Young-arXiv-14] and hence has worse running time dependence on $\varepsilon$. Many real life instances of mixed packing-covering problems exhibit small width and for such cases, our algorithm can report higher precision results when compared to width-independent algorithms. As a special case of our result, we report a $1+\varepsilon$ approximation algorithm for the densest subgraph problem which runs in time $O(md/ \varepsilon)$, where $m$ is the number of edges in the graph and $d$ is the maximum graph degree.