cssi/SciSciGPT-SciSciNet huggingface dataset:
C-BERST: defining subnuclear proteomic landscapes at genomic elements with dCas9–APEX2

Mapping proteomic composition at distinct genomic loci in living cells has been a long-standing challenge. Here we report that dCas9-APEX2 biotinylation at genomic elements by restricted spatial tagging (C-BERST) allows the rapid, unbiased mapping of proteomes near defined genomic loci, as demonstrated for telomeres and centromeres. C-BERST enables the high-throughput identification of proteins associated with specific sequences, thereby facilitating annotation of these factors and their roles.
Multimodal sensorimotor system in unicellular zoospores of a fungus

ABSTRACT Complex sensory systems often underlie critical behaviors, including avoiding predators and locating prey, mates and shelter. Multisensory systems that control motor behavior even appear in unicellular eukaryotes, such as Chlamydomonas, which are important laboratory models for sensory biology. However, we know of no unicellular opisthokonts that control motor behavior using a multimodal sensory system. Therefore, existing single-celled models for multimodal sensorimotor integration are very distantly related to animals. Here, we describe a multisensory system that controls the motor function of unicellular fungal zoospores. We found that zoospores of Allomyces arbusculus exhibit both phototaxis and chemotaxis. Furthermore, we report that closely related Allomyces species respond to either the chemical or the light stimuli presented in this study, not both, and likely do not share this multisensory system. This diversity of sensory systems within Allomyces provides a rare example of a comparative framework that can be used to examine the evolution of sensory systems following the gain/loss of available sensory modalities. The tractability of Allomyces and related fungi as laboratory organisms will facilitate detailed mechanistic investigations into the genetic underpinnings of novel photosensory systems, and how multisensory systems may have functioned in early opisthokonts before multicellularity allowed for the evolution of specialized cell types.
o-Quinone Methides from 4-Allenylcyclobutenones: Synthesis and Chemistry

Selected 4-allenylcyclobutenones ring expand to the corresponding o-quinone methides upon thermolysis in refluxing toluene or benzene. These reactive intermediates were not isolated but trapped to give stable products. The reaction has synthetic potential as a route to highly-substituted phenols, benzofurans, and aryl analogs of hexahydrocannabinol. In addition, a unique rearrangement involving a methyl migration from silicon to carbon of selected 4-[3,3-bis(trimethylsilyl)-1,2-propadienyl]cyclobutenones to give 1,2-benzoxasilols is described. Finally, data are presented that show rapid rotation around the alkylidene bond of o-quinone methides at 30 °C and that 2-(1-methylethenyl)phenols are in equilibrium with the corresponding o-quinone methides.
Nanopore long-read RNAseq reveals widespread transcriptional variation among the surface receptors of individual B cells

Understanding gene regulation and function requires a genome-wide method capable of capturing both gene expression levels and isoform diversity at the single-cell level. Short-read RNAseq is limited in its ability to resolve complex isoforms because it fails to sequence full-length cDNA copies of RNA molecules. Here, we investigate whether RNAseq using the long-read single-molecule Oxford Nanopore MinION sequencer is able to identify and quantify complex isoforms without sacrificing accurate gene expression quantification. After benchmarking our approach, we analyse individual murine B1a cells using a custom multiplexing strategy. We identify thousands of unannotated transcription start and end sites, as well as hundreds of alternative splicing events in these B1a cells. We also identify hundreds of genes expressed across B1a cells that display multiple complex isoforms, including several B cell-specific surface receptors. Our results show that we can identify and quantify complex isoforms at the single cell level.
Optical Recording of Action Potential Initiation and Propagation in Mouse Skeletal Muscle Fibers

Abstract Skeletal muscle fibers have been used to examine a variety of cellular functions and pathologies. Among other parameters, skeletal muscle action potential (AP) propagation has been measured to assess the integrity and function of skeletal muscle. In this work, we utilize 1-(3-sulfonatopropyl)-4[β[2-(Di-n-octylamino)-6-naphtyl]vinyl]pyridinium betaine, a potentiometric dye, and mag-fluo-4, a low-affinity intracellular Ca2+indicator, to noninvasively and reliably measure AP conduction velocity in skeletal muscle. We used remote extracellular bipolar electrodes to generate an alternating polarity electric field that initiates an AP at either end of the fiber. Using enzymatically dissociated flexor digitorum brevis (FDB) fibers and high-speed line scans, we determine the conduction velocity to be ∼0.4 m/s. We applied these methodologies to FDB fibers under elevated extracellular potassium conditions and confirmed that the conduction velocity is significantly reduced in elevated [K+]o. Because our recorded velocities for FDB fibers were much slower than previously reported for other muscle groups, we compared the conduction velocity in FDB fibers to that of extensor digitorum longus (EDL) fibers and measured a significantly faster velocity in EDL fibers than FDB fibers. As a basis for this difference in conduction velocity, we found a similarly higher level of expression of Na+ channels in EDL than in FDB fibers. In addition to measuring the conduction velocity, we can also measure the passive electrotonic potentials elicited by pulses by applying tetrodotoxin and have constructed a circuit model of a skeletal muscle fiber to predict passive polarization of the fiber by the field stimuli. Our predictions from the model fiber closely resemble the recordings acquired from in vitro assays. With these techniques, we can examine how various pathologies and mutations affect skeletal muscle AP propagation. Our work demonstrates the utility of using 1-(3-sulfonatopropyl)-4[β[2-(Di-n-octylamino)-6-naphtyl]vinyl]pyridinium betaine or mag-fluo-4 to noninvasively measure AP initiation and conduction.
Neutron Scattering Studies of Antiferromagnetic Correlations in Cuprates

Neutron scattering studies have provided important information about the momentum and energy dependence of magnetic excitations in cuprate superconductors. Of particular interest are the recent indications of a universal magnetic excitation spectrum in hole-doped cuprates. That starting point provides motivation for reviewing the antiferromagnetic state of the parent insulators, and the destruction of the ordered state by hole doping. The nature of spin correlations in stripe-ordered phases is discussed, followed by a description of the doping and temperature dependence of magnetic correlations in superconducting cuprates. After describing the impact on the magnetic correlations of perturbations such as an applied magnetic field or impurity substitution, a brief summary of work on electron-doped cuprates is given. The chapter concludes with a summary of experimental trends and a discussion of theoretical perspectives.
Multiple large-scale gene and genome duplications during the evolution of hexapods

Polyploidy or whole genome duplication (WGD) is a major contributor to genome evolution and diversity. Although polyploidy is recognized as an important component of plant evolution, it is generally considered to play a relatively minor role in animal evolution. Ancient polyploidy is found in the ancestry of some animals, especially fishes, but there is little evidence for ancient WGDs in other metazoan lineages. Here we use recently published transcriptomes and genomes from more than 150 species across the insect phylogeny to investigate whether ancient WGDs occurred during the evolution of Hexapoda, the most diverse clade of animals. Using gene age distributions and phylogenomics, we found evidence for 18 ancient WGDs and six other large-scale bursts of gene duplication during insect evolution. These bursts of gene duplication occurred in the history of lineages such as the Lepidoptera, Trichoptera, and Odonata. To further corroborate the nature of these duplications, we evaluated the pattern of gene retention from putative WGDs observed in the gene age distributions. We found a relatively strong signal of convergent gene retention across many of the putative insect WGDs. Considering the phylogenetic breadth and depth of the insect phylogeny, this observation is consistent with polyploidy as we expect dosage balance to drive the parallel retention of genes. Together with recent research on plant evolution, our hexapod results suggest that genome duplications contributed to the evolution of two of the most diverse lineages of eukaryotes on Earth.
Synthesis and [4 + 2]-annulation of enantioenriched (z)-crotylsilanes: preparation of the C1-C13 fragment of bistramide A.

New chiral crotylsilanes that bear a (Z)-olefin geometry were synthesized in high enantiopurity. The reagents participate in [4 + 2]-annulations with aldehydes to give stereochemically complementary pyrans (relative to (E)-crotylsilanes) bearing 2,6-cis-5,6-cis and 2,6-trans-5,6-cis relationships of peripheral functionalities. A stereoselective synthesis of the C1−C13 fragment of bistramide A is also described highlighting this annulation strategy.
Chemical Aspects of Polymeric Electroluminescent Devices

Electroluminescence (EL) from organic materials was first observed in the early 1960s, during what might be considered a “golden age” of the physical chemistry of organic materials: the foundations of our current knowledge of electronic excitations, energy transport, and photochemistry were all laid in that era.1,2 The potential of these materials for commercial application was quickly recognized, and a great deal of work has been expended over the years in attempts to develop such products as solar cells, photochromic or holographic memories, nonlinear optical devices, displays, and transistors. Until recently, however, the only significant success story was in xerography: essentially all photocopiers today use organic photoconductors.3 Today a second contender has finally entered the arena: Pioneer Electronics now markets a 64 × 256 pixel organic EL (OEL) monochrome display for automobiles. Although they are first to market with a product, other companies are in close contention: Philips and Uniax have both built production facilities and are prepared to supply prototype samples of OEL displays, and the list of companies and universities with RD hence, external quantum efficiency, which is the quantity of practical interest, is much lower than internal quantum efficiency). By using two organic layers, having an interface with energy level offsets, the majority charge carriers can be slowed and prevented from flowing through the device without recombination, thus increasing quantum efficiency at the expense of higher bias. The appearance of organic electroluminescence as a practical display technology traces its origins to Tang and VanSlyke,4 who introduced the double-layer concept in 1987: this was the first publication that combined modern thin film deposition techniques with suitable materials and structure to give a moderately low bias voltage, attractive efficiency, and encouraging lifetimes. Their devices were made by subliming molecules of a triarylamine as hole transporter, followed by aluminatotris(8hydroxyquinolate) (Alq3) for electron injection and emission, and a magnesium-silver alloy cathode. In 1991 Burroughes et al.,5 at Cambridge University, reported a similar single-layer device made with a polymeric meJames R. Sheats received his B.S. in chemistry from Colorado State University in 1974, and his Ph.D. in physical chemistry in 1978 at Stanford University (under H. M. McConnell), with a thesis on molecular motion in lipid membranes. After postdoctoral work in nonlinear chemical dynamics at the Massachusetts Institute of Technology and Stanford, he joined HP Laboratories in 1982 where he has contributed to a wide range of applications of chemistry in electronics, including photolithography, high-temperature superconductors, and organic electroluminescence, described in 40 journal articles and several patents. While remaining active in the development of organic materials for electronics, he currently manages a program to analyze and develop technology opportunities motivated by environmental sustainability.
The Effect of the Community Eligibility Provision on the Ability of Free and Reduced-Price Meal Data to Identify Disadvantaged Students

The Community Eligibility Provision (CEP) is a policy change to the federally administered National School Lunch Program that allows schools serving low-income populations to classify all students ...
Learning to Design From Humans: Imitating Human Designers Through Deep Learning

Humans as designers have quite versatile problem-solving strategies. Computer agents on the other hand can access large scale computational resources to solve certain design problems. Hence, if agents can learn from human behavior, a synergetic human-agent problem solving team can be created. This paper presents an approach to extract human design strategies and implicit rules, purely from historical human data, and use that for design generation. A two-step framework that learns to imitate human design strategies from observation is proposed and implemented. This framework makes use of deep learning constructs to learn to generate designs without any explicit information about objective and performance metrics. The framework is designed to interact with the problem through a visual interface as humans did when solving the problem. It is trained to imitate a set of human designers by observing their design state sequences without inducing problem-specific modelling bias or extra information about the problem. Furthermore, an end-to-end agent is developed that uses this deep learning framework as its core in conjunction with image processing to map pixel-to-design moves as a mechanism to generate designs. Finally, the designs generated by a computational team of these agents are then compared to actual human data for teams solving a truss design problem. Results demonstrates that these agents are able to create feasible and efficient truss designs without guidance, showing that this methodology allows agents to learn effective design strategies.
On the Construction of Substitutes

Gross substitutability is a central concept in economics and is connected to important notions in discrete convex analysis, number theory, and the analysis of greedy algorithms in computer science....
An abstract characterization of noncommutative projective lines

Let $k$ be a field. We describe necessary and sufficient conditions for a $k$-linear abelian category to be a noncommutative projective line, i.e. a noncommutative $\mathbb{P}^{1}$-bundle over a pair of division rings over $k$. As an application, we prove that $\mathbb{P}^{1}_{n}$, Piontkovski's $n$th noncommutative projective line, is the noncommutative projectivization of an $n$-dimensional vector space.
High-performance FPGA implementation of equivariant adaptive separation via independence algorithm for Independent Component Analysis

Independent Component Analysis (ICA) is a dimensionality reduction technique that can boost efficiency of machine learning models that deal with probability density functions, e.g. Bayesian neural networks. Algorithms that implement adaptive ICA converge slower than their nonadaptive counterparts, however, they are capable of tracking changes in underlying distributions of input features. This intrinsically slow convergence of adaptive methods combined with existing hardware implementations that operate at very low clock frequencies necessitate fundamental improvements in both algorithm and hardware design. This paper presents an algorithm that allows efficient hardware implementation of ICA. Compared to previous work, our FPGA implementation of adaptive ICA improves clock frequency by at least one order of magnitude and throughput by at least two orders of magnitude. Our proposed algorithm is not limited to ICA and can be used in various machine learning problems that use stochastic gradient descent optimization.
Proximity Variational Inference

Variational inference is a powerful approach for approximate posterior inference. However, it is sensitive to initialization and can be subject to poor local optima. In this paper, we develop proximity variational inference (PVI). PVI is a new method for optimizing the variational objective that constrains subsequent iterates of the variational parameters to robustify the optimization path. Consequently, PVI is less sensitive to initialization and optimization quirks and finds better local optima. We demonstrate our method on three proximity statistics. We study PVI on a Bernoulli factor model and sigmoid belief network with both real and synthetic data and compare to deterministic annealing (Katahira et al., 2008). We highlight the flexibility of PVI by designing a proximity statistic for Bayesian deep learning models such as the variational autoencoder (Kingma and Welling, 2014; Rezende et al., 2014). Empirically, we show that PVI consistently finds better local optima and gives better predictive performance.
Challenges for Emergent Gravity

Abstract The idea of gravity as an “emergent” phenomenon has gained popularity in recent years. I discuss some of the obstacles that any such model must overcome in order to agree with the observational underpinnings of general relativity.
The infinite topology of the hyperelliptic locus in Torelli space

Genus g Torelli space is the moduli space of genus g curves of compact type equipped with a homology framing. The hyperelliptic locus is a closed analytic subvariety consisting of finitely many mutually isomorphic components. We use properties of the hyperelliptic Torelli group to show that when \(g\ge 3\) these components do not have the homotopy type of a finite CW complex. Specifically, we show that the second rational homology of each component is infinite-dimensional. We give a more detailed description of the topological features of these components when \(g=3\) using properties of genus 3 theta functions.
Auslander-Reiten Sequences for Gorenstein Rings of Dimension One

Let R be a complete local Gorenstein ring of dimension one, with maximal ideal $\mathfrak {m}$. We show that if M is a Cohen-Macaulay R-module which begins an AR-sequence, then this sequence is produced by a particular endomorphism of $\mathfrak {m}$ corresponding to a minimal prime ideal of R. We apply this result to determining the shape of some components of stable Auslander-Reiten quivers, which in the considered examples are shown to be tubes.
Weighted anisotropic product Hardy spaces and boundedness of sublinear operators

Let A1 and A2 be expansive dilations, respectively, on ℝn and ℝm. Let A ≡ (A1, A2) and p(A) be the class of product Muckenhoupt weights on ℝn × ℝm for p ∈ (1, ∞]. When p ∈ (1, ∞) and w ∈ p(A), the authors characterize the weighted Lebesgue space Lpw(ℝn × ℝm) via the anisotropic Lusin-area function associated with A. When p ∈ (0, 1], w ∈ ∞(A), the authors introduce the weighted anisotropic product Hardy space Hp w (ℝn × ℝm; A) via the anisotropic Lusin-area function and establish its atomic decomposition. Moreover, the authors prove that finite atomic norm on a dense subspace of Hpw (ℝn×ℝm; A) is equivalent with the standard infinite atomic decomposition norm. As an application, the authors prove that if T is a sublinear operator and maps all atoms into uniformly bounded elements of a quasi-Banach space ℬ, then T uniquely extends to a bounded sublinear operator from Hp w (ℝn × ℝm; A) to ℬ. The results of this paper improve the existing results for weighted product Hardy spaces and are new even in the unweighted anisotropic setting (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
Multiaccuracy: Black-Box Post-Processing for Fairness in Classification

Prediction systems are successfully deployed in applications ranging from disease diagnosis, to predicting credit worthiness, to image recognition. Even when the overall accuracy is high, these systems may exhibit systematic biases that harm specific subpopulations; such biases may arise inadvertently due to underrepresentation in the data used to train a machine-learning model, or as the result of intentional malicious discrimination. We develop a rigorous framework of *multiaccuracy* auditing and post-processing to ensure accurate predictions across *identifiable subgroups*. Our algorithm, MULTIACCURACY-BOOST, works in any setting where we have black-box access to a predictor and a relatively small set of labeled data for auditing; importantly, this black-box framework allows for improved fairness and accountability of predictions, even when the predictor is minimally transparent. We prove that MULTIACCURACY-BOOST converges efficiently and show that if the initial model is accurate on an identifiable subgroup, then the post-processed model will be also. We experimentally demonstrate the effectiveness of the approach to improve the accuracy among minority subgroups in diverse applications (image classification, finance, population health). Interestingly, MULTIACCURACY-BOOST can improve subpopulation accuracy (e.g. for "black women") even when the sensitive features (e.g. "race", "gender") are not given to the algorithm explicitly.
Faster principal component regression and stable matrix Chebyshev approximation

We solve principal component regression (PCR), up to a multiplicative accuracy 1 + γ, by reducing the problem to O(γ-1) black-box calls of ridge regression. Therefore, our algorithm does not require any explicit construction of the top principal components, and is suitable for large-scale PCR instances. In contrast, previous result requires O(γ-2) such black-box calls. We obtain this result by developing a general stable recurrence formula for matrix Chebyshev polynomials, and a degree-optimal polynomial approximation to the matrix sign function. Our techniques may be of independent interests, especially when designing iterative methods.
A note on efficient performance evaluation of the Cumulative Sum chart and the Sequential Probability Ratio Test

We establish a simple connection between certain in-control characteristics of the Cumulative Sum CUSUM Run Length and their out-of-control counterparts. The connection is in the form of paired integral renewal equations. The derivation exploits Wald's likelihood ratio identity and the well-known fact that the CUSUM chart is equivalent to repetitive application of Wald's Sequential Probability Ratio Test SPRT. The characteristics considered include the entire Run Length distribution and all of the corresponding moments, starting from the zero-state average run length. A particular practical benefit of our result is that it enables the in-control and out-of-control characteristics of the CUSUM Run Length to be computed concurrently. Moreover, owing to the equivalence of the CUSUM chart to a sequence of SPRTs, the Average Sample Number and Operating Characteristic functions of an SPRT under the null and under the alternative can all be computed simultaneously as well. This would double up the efficiency of any numerical method that one may choose to devise to carry out the actual computations. Copyright © 2016 John Wiley & Sons, Ltd.
Codes with unequal locality

In many practical settings, there is a need to design distributed storage codes with certain locality constraints. For a code C, its i-th symbol is said to have locality r if it can be recovered by accessing some other r symbols of C. Locally repairable codes (LRCs) are the family of codes such that every symbol has small locality.
Counting Perron numbers by absolute value

We count various classes of algebraic integers of fixed degree by their largest absolute value. The classes of integers considered include all algebraic integers, Perron numbers, totally real integers, and totally complex integers. We give qualitative and quantitative results concerning the distribution of Perron numbers, answering in part a question of W. Thurston.
Classifying Voronoi graphs of hex spheres

Abstract A hex sphere is a singular Euclidean sphere with four cones points whose cone angles are (integer) multiples of 2 π 3 but less than 2π. Given a hex sphere M, we consider its Voronoi decomposition centered at the two cone points with greatest cone angles. In this paper we use elementary Euclidean geometry to describe the Voronoi regions of hex spheres and classify the Voronoi graphs of hex spheres (up to graph isomorphism).
Closed minimal surfaces in cusped hyperbolic three-manifolds

Motivated by classical theorems on minimal surface theory in compact hyperbolic 3-manifolds, we investigate the questions of existence and deformations for least area minimal surfaces in complete noncompact hyperbolic 3-manifold of finite volume. We prove any closed immersed incompressible surface can be deformed to a closed immersed least area surface within its homotopy class in any cusped hyperbolic 3-manifold. Our techniques highlight how special structures of these cusped hyperbolic 3-manifolds prevent any least area minimal surface going too deep into the cusped region.
Poset edge densities, nearly reduced words, and barely set-valued tableaux

Abstract In certain finite posets, the expected down-degree of their elements is the same whether computed with respect to either the uniform distribution or the distribution weighting an element by the number of maximal chains passing through it. We show that this coincidence of expectations holds for Cartesian products of chains, connected minuscule posets, weak Bruhat orders on finite Coxeter groups, certain lower intervals in Young's lattice, and certain lower intervals in the weak Bruhat order below dominant permutations. Our tools involve formulas for counting nearly reduced factorizations in 0-Hecke algebras; that is, factorizations that are one letter longer than the Coxeter group length.
Clusters of Driving Behavior From Observational Smartphone Data

Understanding driving behaviors is essential for improving safety and mobility of our transportation systems. Data is usually collected via simulator-based studies or naturalistic driving studies. Those techniques allow for understanding relations between demographics, road conditions and safety. On the other hand, they are very costly and time consuming. Thanks to the ubiquity of smartphones, we have an opportunity to substantially complement more traditional data collection techniques with data extracted from phone sensors, such as GPS, accelerometer gyroscope and camera. We developed statistical models that provided insight into driver behavior in the San Francisco metro area based on tens of thousands of driver logs. We used novel data sources to support our work. We used cell phone sensor data drawn from five hundred drivers in San Francisco to understand the speed of traffic across the city as well as the maneuvers of drivers in different areas. Specifically, we clustered drivers based on their driving behavior. We looked at driver norms by street and flagged driving behaviors that deviated from the norm.
On bodies with congruent sections or projections

Abstract In this paper, we construct two convex bodies K and L in R n , n ≥ 3 , such that their projections K | H , L | H onto every subspace H are congruent, but nevertheless, K and L do not coincide up to a translation or a reflection in the origin. This gives a negative answer to an old conjecture posed by Nakajima and Suss.
Note on the rank of quadratic twists of Mordell equations

Abstract Let E be the elliptic curve given by a Mordell equation y 2 = x 3 − A where A ∈ Z . Michael Stoll found a precise formula for the size of a Selmer group of E for certain values of A. For D ∈ Z , let E D denote the quadratic twist D y 2 = x 3 − A . We use Stoll's formula to show that for a positive square-free integer A ≡ 1 or 25 mod 36 and for a nonnegative integer k, we can compute a lower bound for the proportion of square-free integers D up to X such that rank E D ( Q ) ⩽ 2 k . We also compute an upper bound for a certain average rank of quadratic twists of E.
Cup products in surface bundles, higher Johnson invariants, and MMM classes

In this paper we prove a family of results connecting the problem of computing cup products in surface bundles to various other objects that appear in the theory of the cohomology of the mapping class group $${\text {Mod}}_g$$ and the Torelli group $$\mathcal {I}_g$$ . We show that Kawazumi’s twisted MMM class $$m_{0,k}$$ can be used to compute k-fold cup products in surface bundles, and that $$m_{0,k}$$ provides an extension of the higher Johnson invariant $$\tau _{k-2}$$ to $$H^{k-2}({\text {Mod}}_{g,*}, \wedge ^k H_1)$$ . These results are used to show that the behavior of the restriction of the even MMM classes $$e_{2i}$$ to $$H^{4i}(\mathcal {I}_g^1)$$ is completely determined by $${\text {im}}(\tau _{4i}) \le \wedge ^{4i+2}H_1$$ , and to give a partial answer to a question of D. Johnson. We also use these ideas to show that all surface bundles with monodromy in the Johnson kernel $$\mathcal K_{g,*}$$ have cohomology rings isomorphic to that of a trivial bundle, implying the vanishing of all $$\tau _i$$ when restricted to $$\mathcal K_{g,*}$$ .
Rate-Distortion Auto-Encoders

A rekindled the interest in auto-encoder algorithms has been spurred by recent work on deep learning. Current efforts have been directed towards effective training of auto-encoder architectures with a large number of coding units. Here, we propose a learning algorithm for auto-encoders based on a rate-distortion objective that minimizes the mutual information between the inputs and the outputs of the auto-encoder subject to a fidelity constraint. The goal is to learn a representation that is minimally committed to the input data, but that is rich enough to reconstruct the inputs up to certain level of distortion. Minimizing the mutual information acts as a regularization term whereas the fidelity constraint can be understood as a risk functional in the conventional statistical learning setting. The proposed algorithm uses a recently introduced measure of entropy based on infinitely divisible matrices that avoids the plug in estimation of densities. Experiments using over-complete bases show that the rate-distortion auto-encoders can learn a regularized input-output mapping in an implicit manner.
Irreducibles and Primes in Computable Integral Domains

A computable ring is a ring equipped with a mechanical procedure to add and multiply elements. In most natural computable integral domains, there is a computational procedure to determine if a given element is prime/irreducible. However, there do exist computable UFDs (in fact, polynomial rings over computable fields) where the set of prime/irreducible elements is not computable. Outside of the class of UFDs, the notions of irreducible and prime may not coincide. We demonstrate how different these concepts can be by constructing computable integral domains where the set of irreducible elements is computable while the set of prime elements is not, and vice versa. Along the way, we will generalize Kronecker’s method for computing irreducibles and factorizations in \(\mathbb {Z}[x]\).
On the rigidity of rank gradient in a group of intermediate growth

We introduce and investigate a rigidity property of rank gradient for an example of a group $$ \mathcal{G} $$ of intermediate growth constructed by the first author in [R. I. Grigorchuk, Funkts.. Anal. Prilozh., 14 No. 1, 53–54 (1980)]. It is shown that $$ \mathcal{G} $$ is normally (f, g)-RG rigid, where f(n) = log(n) and g(n) = log(log(n)).
Estimation of Poisson Arrival Processes Under Linear Models

In this paper, we consider the problem of estimating the parameters of a Poisson arrival process, where the intensity function is assumed to lie in the span of a known basis. Our goal is to estimate the basis expansions coefficients given a realization of this process. We establish novel guarantees concerning the accuracy achieved by the maximum likelihood estimate. Our initial result is near-optimal, with the exception of an undesirable dependence on the dynamic range of the intensity function. We then show how to remove this dependence through a process of “noise regularization,” which results in an improved bound under our analysis. We conjecture that a similar guarantee should be possible when using a more direct (deterministic) regularization scheme. We conclude with a discussion of practical applications and an empirical examination of the proposed regularization schemes.
CHERN-WEIL FORMS AND ABSTRACT HOMOTOPY THEORY

We prove that Chern-Weil forms are the only natural differential forms associated to a connection on a principal G-bundle. We use the homotopy theory of simplicial sheaves on smooth manifolds to formulate the theorem and set up the proof. Other arguments come from classical invariant theory. We identify the Weil algebra as the de Rham complex of a specific simplicial sheaf, and similarly give a new interpretation of the Weil model in equivariant de Rham theory. There is an appendix proving a general theorem about set-theoretic transformations of polynomial functors.
Network Interdiction Using Adversarial Traffic Flows

Traditional network interdiction refers to the problem of an interdictor trying to reduce the throughput of network users by removing network edges. In this paper, we propose a new paradigm for network interdiction that models scenarios, such as stealth DoS attack, where the interdiction is performed through injecting adversarial traffic flows. Under this paradigm, we first study the deterministic flow interdiction problem, where the interdictor has perfect knowledge of the operation of network users. We show that the problem is highly inapproximable on general networks and is NP-hard even when the network is acyclic. We then propose an algorithm that achieves a logarithmic approximation ratio and quasi-polynomial time complexity for acyclic networks through harnessing the submodularity of the problem. Next, we investigate the robust flow interdiction problem, which adopts the robust optimization framework to capture the case where definitive knowledge of the operation of network users is not available. We design an approximation framework that integrates the aforementioned algorithm, yielding a quasi-polynomial time procedure with poly-logarithmic approximation ratio for the more challenging robust flow interdiction. Finally, we evaluate the performance of the proposed algorithms through simulations, showing that they can be efficiently implemented and yield near-optimal solutions.
Fast and Guaranteed Blind Multichannel Deconvolution Under a Bilinear System Model

We consider the multichannel blind deconvolution problem where we observe the output of multiple channels that are all excited with the same unknown input. From these observations, we wish to estimate the impulse responses of each of the channels. We show that this problem is well-posed if the channels follow a bilinear model where the ensemble of channel responses is modeled as lying in a low-dimensional subspace but with each channel modulated by an independent gain. Under this model, we show how the channel estimates can be found by minimizing a quadratic function over a non-convex set. We analyze two methods for solving this non-convex program, and provide performance guarantees for each. The first is a method of alternating eigenvectors that breaks the program down into a series of eigenvalue problems. The second is a truncated power iteration, which can roughly be interpreted as a method for finding the largest eigenvector of a symmetric matrix with the additional constraint that it adheres to our bilinear model. As with most non-convex optimization algorithms, the performance of both of these algorithms is highly dependent on having a good starting point. We show how such a starting point can be constructed from the channel measurements. Our performance guarantees are non-asymptotic, and provide a sufficient condition on the number of samples observed per channel in order to guarantee channel estimates of certain accuracy. Our analysis uses a model with a “generic” subspace that is drawn at random, and we show the performance bounds hold with high probability. Mathematically, the key estimates are derived by quantifying how well the eigenvectors of certain random matrices approximate the eigenvectors of their mean. We also present a series of numerical results demonstrating that the empirical performance is consistent with the presented theory.
Recovering the spacetime metric from a holographic dual

We review our recent proposal to use certain spatial cross-sections of the boundary at infinity -- light-cone cuts -- to recover the conformal metric in the bulk. We discuss some extensions of this work, including how to obtain the conformal metric near the horizon of a collapsing black hole. We also show how to obtain the conformal factor under certain conditions.
A Bound Strengthening Method for Optimal Transmission Switching in Power Systems

This paper studies the optimal transmission switching (OTS) problem for power systems, where certain lines are fixed (uncontrollable) and the remaining ones are controllable via on / off switches. The goal is to identify a topology of the power grid that minimizes the cost of the system operation while satisfying the physical and operational constraints. Most of the existing methods for the problem are based on first converting the OTS into a mixed-integer linear program (MILP) or mixed-integer quadratic program (MIQP), and then iteratively solving a series of its convex relaxations. The performance of these methods depends heavily on the strength of the MILP or MIQP formulations. In this paper, it is shown that finding the strongest variable upper and lower bounds to be used in an MILP or MIQP formulation of the OTS based on the big- $M$ or McCormick inequalities is NP-hard. Furthermore, it is proven that unless $P=NP$ , there is no constant-factor approximation algorithm for constructing these variable bounds. Despite the inherent difficulty of obtaining the strongest bounds in general, a simple bound strengthening method is presented to strengthen the convex relaxation of the problem when there exists a connected spanning subnetwork of the system with fixed lines. With the proposed bound strengthening method, remarkable improvements in the runtime of the mixed-integer solvers and the optimality gaps of the solutions are achieved for medium- and large-scale real-world systems.
The Mori–Zwanzig formalism for the derivation of a fluctuating heat conduction model from molecular dynamics

Energy transport equations are derived directly from full molecular dynamics models as coarse-grained description. With the local energy chosen as the coarse-grained variables, we apply the Mori-Zwanzig formalism to derive a reduced model, in the form of a generalized Langevin equation. A Markovian embedding technique is then introduced to eliminate the history dependence. In sharp contrast to conventional energy transport models, this derivation yields {\it stochastic} dynamics models for the spatially averaged energy. We discuss the approximation of the random force using both additive and multiplicative noises, to ensure the correct statistics of the solution.
A Bayesian perspective on Residential Demand Response using smart meter data

The widespread deployment of Advanced Metering Infrastructure has made granular data of residential electricity consumption available on a large scale. One field of research that relies on such granular consumption data is Residential Demand Response, where individual users are incentivized to temporarily reduce their consumption during periods of high marginal cost of electricity. To quantify the economic potential of Residential Demand Response, it is important to estimate the reductions during Demand Response hours, taking into account the heterogeneity of electricity users. In this paper, we incorporate latent variables representing behavioral archetypes of electricity users into the process of short-term load forecasting with Machine Learning methods, thereby differentiating between varying levels of energy consumption. The latent variables are constructed by fitting Conditional Mixture Models of Linear Regressions and Hidden Markov Models on smart meter data of a Residential Demand Response program in the western United States. We observe a notable increase in the accuracy of short-term load forecasts compared to the case without latent variables. We estimate the reductions during Demand Response events conditional on the latent variables and discover a higher DR reduction among users with automated smart home devices compared to those without.
Community Extraction in Multilayer Networks with Heterogeneous Community Structure

Multilayer networks are a useful way to capture and model multiple, binary or weighted relationships among a fixed group of objects. While community detection has proven to be a useful exploratory technique for the analysis of single-layer networks, the development of community detection methods for multilayer networks is still in its infancy. We propose and investigate a procedure, called Multilayer Extraction, that identifies densely connected vertex-layer sets in multilayer networks. Multilayer Extraction makes use of a significance based score that quantifies the connectivity of an observed vertex-layer set through comparison with a fixed degree random graph model. Multilayer Extraction directly handles networks with heterogeneous layers where community structure may be different from layer to layer. The procedure can capture overlapping communities, as well as background vertex-layer pairs that do not belong to any community. We establish consistency of the vertex-layer set optimizer of our proposed multilayer score under the multilayer stochastic block model. We investigate the performance of Multilayer Extraction on three applications and a test bed of simulations. Our theoretical and numerical evaluations suggest that Multilayer Extraction is an effective exploratory tool for analyzing complex multilayer networks. Publicly available code is available at https://github.com/jdwilson4/MultilayerExtraction.
From behavior to sparse graphical games: Efficient recovery of equilibria

In this paper we study the problem of exact recovery of the pure-strategy Nash equilibria (PSNE) set of a graphical game from noisy observations of joint actions of the players alone. We consider sparse linear influence games — a parametric class of graphical games with linear payoffs, and represented by directed graphs of n nodes (players) and in-degree of at most k. We present an l 1 -regularized logistic regression based algorithm for recovering the PSNE set exactly, that is both computationally efficient — i.e. runs in polynomial time — and statistically efficient — i.e. has logarithmic sample complexity. Specifically, we show that the sufficient number of samples required for exact PSNE recovery scales as O(poly(k) log n). We also validate our theoretical results using synthetic experiments.
Localized LQR optimal control

This paper introduces a receding horizon like control scheme for localizable distributed systems, in which the effect of each local disturbance is limited spatially and temporally. We characterize such systems by a set of linear equality constraints, and show that the resulting feasibility test can be solved in a localized and distributed way. We also show that the solution of the local feasibility tests can be used to synthesize a receding horizon like controller that achieves the desired closed loop response in a localized manner as well. Finally, we formulate the Localized LQR (LLQR) optimal control problem and derive an analytic solution for the optimal controller. Through a numerical example, we show that the LLQR optimal controller, with its constraints on locality, settling time, and communication delay, can achieve similar performance as an unconstrained ℋ 2 optimal controller, but can be designed and implemented in a localized and distributed way.
Localized mirror functor constructed from a Lagrangian torus

Abstract Fixing a weakly unobstructed Lagrangian torus in a symplectic manifold X , we define a holomorphic function W known as the Floer potential. We construct a canonical A ∞ -functor from the Fukaya category of X to the category of matrix factorizations of W . It provides a unified way to construct matrix factorizations from Lagrangian Floer theory. The technique is applied to toric Fano manifolds to transform Lagrangian branes to matrix factorizations and prove homological mirror symmetry. Using the method, we also obtain an explicit expression of the matrix factorization mirror to the real locus of the complex projective space.
Existence of Broken Lefschetz Fibrations

We prove that every closed oriented smooth 4-manifold X admits a broken Lefschetz fibration (aka singular Lefschetz fibration) over the 2-sphere. Given any closed orientable surface F of square zero in X, we can choose the fibration so that F is a fiber component. Moreover, we can arrange it so that there is only one Lefschetz critical point when the Euler characteristic e(X) is odd, and none when e(X) is even. We make use of topological modifications of smooth maps with fold and cusp singularities due to Saeki and Levine, and thus, we get alternative proofs of previous existence results. Also shown is the existence of broken Lefschetz pencils with connected fibers on any near-symplectic 4-manifold.
Collaborative Platooning of Automated Vehicles Using Variable Time-Gaps

Connected automated vehicles (CAVs) could potentially be coordinated to safely attain the maximum traffic flow on roadways under dynamic traffic patterns, such as those engendered by the merger of two strings of vehicles due a lane drop. Strings of vehicles have to be shaped correctly in terms of the inter-vehicular time-gap and velocity to ensure that such operation is feasible. However, controllers that can achieve such traffic shaping over the multiple dimensions of target time-gap and velocity over a region of space are unknown. The objective of this work is to design such a controller, and to show that we can design candidate time-gap and velocity profiles such that it can stabilize the string of vehicles in attaining the target profiles. Our analysis is based on studying the system in the spacial rather than the time domain, which enables us to study stability as in terms of minimizing errors from the target profile and across vehicles as a function of location. Finally, we conduct numeral simulations in the context of shaping two platoons for merger, which we use to illustrate how to select time-gap and velocity profiles for maximizing flow and maintaining safety.
The Whittaker–Shintani Functions for Symplectic Groups

In this note, we give a formula for the Whittaker-Shintani functions for the p-adic symplectic groups, which is a generalization of the Zonal spherical functions and Whittaker functions. We then use the formula to give an alternative proof of a conjecture given by T.Shintani on the unramified calculation of L-function for $Sp_{2n}\times GL_{1}$.
Synchronization in Networks of Identical Systems via Pinning: Application to Distributed Secondary Control of Microgrids

Motivated by the need for the fast synchronized operation of power microgrids, we analyze the problem of single and multiple pinning in networked systems. We derive lower and upper bounds on the algebraic connectivity of the network with respect to the reference signal. These bounds are utilized to devise a suboptimal algorithm with polynomial complexity to find a suitable set of nodes to pin the network effectively and efficiently. The results are applied to secondary voltage pinning control design for a microgrid in islanded operation mode. Comparisons with existing single and multiple pinning strategies clearly demonstrate the efficacy of the obtained results.