cssi/SciSciGPT-SciSciNet huggingface dataset:
Continuous closure, axes closure, and natural closure

Let $R$ be a reduced affine $\mathbb C$-algebra, with corresponding affine algebraic set $X$. Let $\mathcal C(X)$ be the ring of continuous (Euclidean topology) $\mathbb C$-valued functions on $X$. Brenner defined the \emph{continuous closure} $I^{\rm cont}$ of an ideal $I$ as $I\mathcal C(X) \cap R$. He also introduced an algebraic notion of \emph{axes closure} $I^{\rm ax}$ that always contains $I^{\rm cont}$, and asked whether they coincide. We extend the notion of axes closure to general Noetherian rings, defining $f \in I^{\rm ax}$ if its image is in $IS$ for every homomorphism $R \to S$, where $S$ is a one-dimensional complete seminormal local ring. We also introduce the \emph{natural closure} $I^\natural$ of $I$. One of many characterizations is $I^\natural = I + \{f \in R: \exists n >0 \text{ with } f^n \in I^{n+1}\}$. We show that $I^\natural \subseteq I^{\rm ax}$, and that when continuous closure is defined, $I^\natural \subseteq I^{\rm cont }\subseteq I^{\rm ax}$. Under mild hypotheses on the ring, we show that $I^\natural= I^{\rm ax}$ when $I$ is primary to a maximal ideal, and that if $I$ has no embedded primes, then $I = I^\natural$ if and only if $I = I^{\rm ax}$, so that $I^{\rm cont}$ agrees as well. We deduce that in the polynomial ring $\mathbb C[x_1, \ldots, x_n]$, if $f = 0$ at all points where all of the ${\partial f \over \partial x_i}$ are 0, then $f \in ( {\partial f \over \partial x_1}, \, \ldots, \, {\partial f \over \partial x_n})R$. We characterize $I^{\rm cont}$ for monomial ideals in polynomial rings over $\mathbb C$, but we show that the inequalities $I^\natural \subset I^{\rm cont}$ and $I^{\rm cont} \subset I^{\rm ax}$ can be strict for monomial ideals even in dimension 3. Thus, $I^{\rm cont}$ and $I^{\rm ax}$ need not agree, although we prove they are equal in $\mathbb C[x_1, x_2]$.
An ensemble framework for detecting community changes in dynamic networks

Dynamic networks, especially those representing social networks, undergo constant evolution of their community structure over time. Nodes can migrate between different communities, communities can split into multiple new communities, communities can merge together, etc. In order to represent dynamic networks with evolving communities it is essential to use a dynamic model rather than a static one. Here we use a dynamic stochastic block model where the underlying block model is different at different times. In order to represent the structural changes expressed by this dynamic model the network will be split into discrete time segments and a clustering algorithm will assign block memberships for each segment. In this paper we show that using an ensemble of clustering assignments accommodates for the variance in scalable clustering algorithms and produces superior results in terms of pairwise-precision and pairwise-recall. We also demonstrate that the dynamic clustering produced by the ensemble can be visualized as a flowchart which encapsulates the community evolution succinctly.
Spectrum Sensing in Cognitive Radio Networks: Performance Evaluation and Optimization

Abstract This paper studies cooperative spectrum sensing in cognitive radio networks where secondary users collect local energy statistics and report their findings to a secondary base station, i.e., a fusion center. First, the average error probability is quantitively analyzed to capture the dynamic nature of both observation and fusion channels, assuming fixed amplifier gains for relaying local statistics to the fusion center. Second, the system level overhead of cooperative spectrum sensing is addressed by considering both the local processing cost and the transmission cost. Local processing cost incorporates the overhead of sample collection and energy calculation that must be conducted by each secondary user; the transmission cost accounts for the overhead of forwarding the energy statistic computed at each secondary user to the fusion center. Results show that when jointly designing the number of collected energy samples and transmission amplifier gains, only one secondary user needs to be actively engaged in spectrum sensing. Furthermore, when the number of energy samples or amplifier gains are fixed, closed form expressions for optimal solutions are derived and a generalized water-filling algorithm is provided.
Cutset sampling with likelihood weighting

The paper extends the principle of cutset sampling over Bayesian networks, presented previously for Gibbs sampling, to likelihood weighting (LW). Cutset sampling is motivated by the Rao-Blackwell theorem which implies that sampling over a subset of variables requires fewer samples for convergence due to the reduction in sampling variance. The scheme exploits the network structure in selecting cutsets that allow efficient computation of the sampling distributions. In particular, as we show empirically, likelihood weighting over a loop-cutset (abbreviated LWLC), is time-wise cost-effective. We also provide an effective way for caching the probabilities of the generated samples which improves the performance of the overall scheme. We compare LWLC against regular liklihood-weighting and against Gibbs-based cutset sampling.
EULER CHARACTERISTIC OF SPRINGER FIBERS

For Weyl groups of classical types, we present formulas to calculate the restriction of Springer representations to a maximal parabolic subgroup of the same type. As a result, we give recursive formulas for Euler characteristics of Springer fibers for classical types. We also give tables of those for exceptional types.
Unsupervised Learning with Truncated Gaussian Graphical Models

Gaussian graphical models (GGMs) are widely used for statistical modeling, because of ease of inference and the ubiquitous use of the normal distribution in practical approximations. However, they are also known for their limited modeling abilities, due to the Gaussian assumption. In this paper, we introduce a novel variant of GGMs, which relaxes the Gaussian restriction and yet admits efficient inference. Specifically, we impose a bipartite structure on the GGM and govern the hidden variables by truncated normal distributions. The nonlinearity of the model is revealed by its connection to rectified linear unit (ReLU) neural networks. Meanwhile, thanks to the bipartite structure and appealing properties of truncated normals, we are able to train the models efficiently using contrastive divergence. We consider three output constructs, accounting for real-valued, binary and count data. We further extend the model to deep constructions and show that deep models can be used for unsupervised pre-training of rectifier neural networks. Extensive experimental results are provided to validate the proposed models and demonstrate their superiority over competing models.
Complete branching rules for Specht modules

Abstract We give a combinatorial description for when the Specht module of an arbitrary diagram admits a (complete) branching rule. This description, given in terms of the maximal rectangles of the diagram, generalizes all previously known branching rules for Specht modules, such as those given by Reiner and Shimozono for northwest diagrams and by the present author for forest diagrams.
On the cycle structure of the product of random maximal cycles.

The subject of this paper is the cycle structure of the random permutation $\sigma$ of $[N]$, which is the product of $k$ independent random cycles of maximal length $N$. We use the character-based Fourier transform to study the number of cycles of $\sigma$ and also the distribution of the elements of the subset $[\ell]$ among the cycles of $\sigma$.
Distributed estimation of graph spectrum

In this paper, we develop a two-stage distributed algorithm that enables nodes in a graph to cooperatively estimate the spectrum of a matrix W associated with the graph, which includes the adjacency and Laplacian matrices as special cases. In the first stage, the algorithm uses a discrete-time linear iteration and the Cayley-Hamilton theorem to convert the problem into one of solving a set of linear equations, where each equation is known to a node. In the second stage, if the nodes happen to know that W is cyclic, the algorithm uses a Lyapunov approach to asymptotically solve the equations with an exponential rate of convergence. If they do not know whether W is cyclic, the algorithm uses a random perturbation approach and a structural controllability result to approximately solve the equations with an error that can be made small. Finally, we provide simulation results that illustrate the algorithm.
RASMUSSEN INVARIANT, SLICE-BENNEQUIN INEQUALITY, AND SLICENESS OF KNOTS

We use recently introduced Rasmussen invariant to find knots that are topologically locally-flatly slice but not smoothly slice. We note that this invariant can be used to give a combinatorial proof of the slice-Bennequin inequality. Finally, we compute the Rasmussen invariant for quasipositive knots and show that most of our examples of non-slice knots are not quasipositive and, to the best of our knowledge, were previously unknown.
prDeep: Robust phase retrieval with a flexible deep network

Phase retrieval algorithms have become an important component in many modern computational imaging systems. For instance, in the context of ptychography and speckle correlation imaging, they enable imaging past the diffraction limit and through scattering media, respectively. Unfortunately, traditional phase retrieval algorithms struggle in the presence of noise. Progress has been made recently on more robust algorithms using signal priors, but at the expense of limiting the range of supported measurement models (e.g., to Gaussian or coded diffraction patterns). In this work we leverage the regularization-by-denoising framework and a convolutional neural network denoiser to create prDeep, a new phase retrieval algorithm that is both robust and broadly applicable. We test and validate prDeep in simulation to demonstrate that it is robust to noise and can handle a variety of system models. A MatConvNet implementation of prDeep is available at this https URL.
Automatic Classification of Roof Shapes for Multicopter Emergency Landing Site Selection

Geographic information systems (GIS) now provide accurate maps of terrain, roads, waterways, and building footprints and heights. Aircraft, particularly small unmanned aircraft systems, can exploit additional information such as building roof structure to improve navigation accuracy and safety particularly in urban regions. This paper proposes a method to automatically label building roof shape types. Satellite imagery and LIDAR data from Witten, Germany are fed to convolutional neural networks (CNN) to extract salient feature vectors. Supervised training sets are automatically generated from pre-labeled buildings contained in the OpenStreetMap database. Multiple CNN architectures are trained and tested, with the best performing networks providing a condensed feature set for support vector machine and decision tree classifiers. Satellite and LIDAR data fusion is shown to provide greater classification accuracy than through use of either data type individually.
Diffuse scattering on graphs

Abstract We formulate and analyze difference equations on graphs analogous to time-independent diffusion equations arising in the study of diffuse scattering in continuous media. Moreover, we show how to construct solutions in the presence of weak scatterers from the solution to the homogeneous (background problem) using Born series, providing necessary conditions for convergence and demonstrating the process through numerous examples. In addition, we outline a method for finding Green's functions for Cayley graphs for both abelian and non-abelian groups. Finally, we conclude with a discussion of the effects of sparsity on our method and results, outlining the simplifications that can be made provided that the scatterers are weak and well-separated.
Tight Lower Bounds for Data-Dependent Locality-Sensitive Hashing

We prove a tight lower bound for the exponent rho for data-dependent Locality-Sensitive Hashing schemes, recently used to design efficient solutions for the c-approximate nearest neighbor search. In particular, our lower bound matches the bound of rho<= 1/(2c-1)+o(1) for the l_1 space, obtained via the recent algorithm from [Andoni-Razenshteyn, STOC'15]. In recent years it emerged that data-dependent hashing is strictly superior to the classical Locality-Sensitive Hashing, when the hash function is data-independent. In the latter setting, the best exponent has been already known: for the l_1 space, the tight bound is rho=1/c, with the upper bound from [Indyk-Motwani,STOC'98] and the matching lower bound from [O'Donnell-Wu-Zhou,ITCS'11]. We prove that, even if the hashing is data-dependent, it must hold that rho>=1/(2c-1)-o(1). To prove the result, we need to formalize the exact notion of data-dependent hashing that also captures the complexity of the hash functions (in addition to their collision properties). Without restricting such complexity, we would allow for obviously infeasible solutions such as the Voronoi diagram of a dataset. To preclude such solutions, we require our hash functions to be succinct. This condition is satisfied by all the known algorithmic results.
Subsampled Rényi Differential Privacy and Analytical Moments Accountant

We study the problem of subsampling in differential privacy (DP), a question that is the centerpiece behind many successful differentially private machine learning algorithms. Specifically, we provide a tight upper bound on the Renyi Differential Privacy (RDP) [Mironov 2017] parameters for algorithms that: (1) subsample the dataset, and then (2) applies a randomized mechanism M to the subsample, in terms of the RDP parameters of M and the subsampling probability parameter. Our results generalize the moments accounting technique, developed by [Abadi et al. 2016] for the Gaussian mechanism, to any subsampled RDP mechanism.
Lattice-integrality of certain group-invariant integral forms in vertex operator algebras

Abstract Certain vertex operator algebras have integral forms (integral spans of bases which are closed under the countable set of products). It is unclear when they (or integral multiples of them) are integral as lattices under the natural bilinear form on the VOA. We show that lattice-integrality may be arranged under some hypotheses, including cases of integral forms invariant by finite groups. In particular, there exists a lattice-integral Monster-invariant integral form in the Moonshine VOA.
On the syntax of logic and set theory

We introduce an extension of the propositional calculus to include abstracts of predicates and quantifiers, employing a single rule along with a novel comprehension schema and a principle of extensionality, which are substituted for the Bernays postulates for quantifiers and the comprehension schemata of ZF and other set theories. We prove that it is consistent in any finite Boolean subset lattice. We investigate the antinomies of Russell, Cantor, Burali-Forti, and others, and discuss the relationship of the system to other set-theoretic systems ZF, NBG, and NF. We discuss two methods of axiomatizing higher order quantification and abstraction, and then very briefly discuss the application of one of these methods to areas of mathematics outside of logic.
Two-component marangoni-contracted droplets: friction and shape

When a mixture of propylene glycol and water is deposited on a clean glass slide, it forms a droplet of a given apparent contact angle rather than spreading as one would expect on such a high-energy surface. The droplet is stabilized by a Marangoni flow due to the non-uniformity of the components' concentrations between the border and the apex of the droplet, itself a result of evaporation. These self-contracting droplets have unusual properties such as absence of pinning and the ability to move under an external humidity gradient. The droplets' apparent contact angles are a function of their concentration and the external humidity. Here we study the motion of such droplets sliding down slopes and compare the results to normal non-volatile droplets. We precisely control the external humidity and explore the influence of the volume, viscosity, surface tension, and contact angle. We find that the droplets suffer a negligible pinning force so that for small velocities the capillary number (Ca) is directly proportional to the Bond number (Bo): Ca = Bo sin α with α the angle of the slope. Lastly we study the successive shapes the droplets take when sliding at larger and larger velocities.
Canonical Sectors and Evolution of Firms in the US Stock Markets

Unsupervised machine learning can provide an objective and comprehensive broad-level sector decomposition of stocks
Estimating scaled treatment effects with multiple outcomes

In classical study designs, the aim is often to learn about the effects of a treatment or intervention on a single outcome; in many modern studies, however, data on multiple outcomes are collected and it is of interest to explore effects on multiple outcomes simultaneously. Such designs can be particularly useful in patient-centered research, where different outcomes might be more or less important to different patients. In this paper, we propose scaled effect measures (via potential outcomes) that translate effects on multiple outcomes to a common scale, using mean-variance and median-interquartile range based standardizations. We present efficient, nonparametric, doubly robust methods for estimating these scaled effects (and weighted average summary measures), and for testing the null hypothesis that treatment affects all outcomes equally. We also discuss methods for exploring how treatment effects depend on covariates (i.e., effect modification). In addition to describing efficiency theory for our estimands and the asymptotic behavior of our estimators, we illustrate the methods in a simulation study and a data analysis. Importantly, and in contrast to much of the literature concerning effects on multiple outcomes, our methods are nonparametric and can be used not only in randomized trials to yield increased efficiency, but also in observational studies with high-dimensional covariates to reduce confounding bias.
Robust large-scale non-negative matrix factorization using Proximal Point algorithm

A robust algorithm for non-negative matrix factorization (NMF) is presented in this paper with the purpose of dealing with large-scale data, where the separability assumption is satisfied. In particular, we modify the Linear Programming (LP) algorithm of [6] by introducing a reduced set of constraints for exact NMF. In contrast to the previous approaches, the proposed algorithm does not require the knowledge of factorization rank (extreme rays [3] or topics [5]). Furthermore, motivated by a similar problem arising in the context of metabolic network analysis [16], we consider an entirely different regime where the number of extreme rays or topics can be much larger than the dimension of the data vectors. The performance of the algorithm for different synthetic data sets is provided.
Shape optimization of wave energy converters for broadband directional incident waves

Abstract Here, through a systematic methodology and the use of high performance computing, we calculate the optimum shape for a wave energy converter under the action of incident waves of (i) monochromatic unidirectional, (ii) monochromatic directional, (iii) polychromatic unidirectional and (iv) polychromatic directional (with both directional symmetry and asymmetry). As a benchmark for our study, without loss of generality, we consider a submerged planar pressure differential wave energy converter, and use the Genetic Algorithm to search through a wide range of shapes. A new parametric description of absorber shape based on Fourier decomposition of geometrical shapes is introduced, and for each shape hydrodynamic coefficients are calculated, optimum power take-off parameters are obtained, and overall efficiency is determined. We show that an optimum geometry of the absorber plate can absorb significantly higher energy (in some cases few times higher) when compared to a circular shape of the same area. Specifically, for a unidirectional incident wave, the optimum shape, as expected, is obtained to be the most elongated shape. For directional incident waves, a butterfly-shape is the optimum geometry whose details depend on not only the amplitude and direction of incident wave components, but also the relative phases of those components. For the latter effect, we find an optimally averaged profile through a statistical analysis.
Revisiting Asynchronous Linear Solvers: Provable Convergence Rate through Randomization

Asynchronous methods for solving systems of linear equations have been researched since Chazan and Miranker's [1969] pioneering paper on chaotic relaxation. The underlying idea of asynchronous methods is to avoid processor idle time by allowing the processors to continue to make progress even if not all progress made by other processors has been communicated to them.Historically, the applicability of asynchronous methods for solving linear equations has been limited to certain restricted classes of matrices, such as diagonally dominant matrices. Furthermore, analysis of these methods focused on proving convergence in the limit. Comparison of the asynchronous convergence rate with its synchronous counterpart and its scaling with the number of processors have seldom been studied and are still not well understood.In this article, we propose a randomized shared-memory asynchronous method for general symmetric positive definite matrices. We rigorously analyze the convergence rate and prove that it is linear and is close to that of the method's synchronous counterpart if the processor count is not excessive relative to the size and sparsity of the matrix. We also present an algorithm for unsymmetric systems and overdetermined least-squares. Our work presents a significant improvement in the applicability of asynchronous linear solvers as well as in their convergence analysis, and suggests randomization as a key paradigm to serve as a foundation for asynchronous methods.
Schanuel's Conjecture and Algebraic Roots of Exponential Polynomials

In this article, I will prove that assuming Schanuel's conjecture, an exponential polynomial with algebraic coefficients can have only finitely many algebraic roots. Furthermore, this proof demonstrates that there are no unexpected algebraic roots of any such exponential polynomial. This implies a special case of Shapiro's conjecture: if p(x) and q(x) are two exponential polynomials with algebraic coefficients, each involving only one iteration of the exponential map, and they have common factors only of the form exp (g) for some exponential polynomial g, then p and q have only finitely many common zeros.
How fast can we multiply large integers on an actual computer

We provide two complexity measures that can be used to measure the running time of algorithms to compute multiplications of long integers. The random access machine with unit or logarithmic cost is not adequate for measuring the complexity of a task like multiplication of long integers. The Turing machine is more useful here, but fails to take into account the multiplication instruction for short integers, which is available on physical computing devices.
A Griffith–Euler–Bernoulli theory for thin brittle beams derived from nonlinear models in variational fracture mechanics

We study a planar thin brittle beam subject to elastic deformations and cracks described in terms of a nonlinear Griffith energy functional acting on SBV deformations of the beam. In particular, we consider the case in which elastic bulk contributions due to finite bending of the beam are comparable to the surface energy which is necessary to completely break the beam into several large pieces. In the limit of vanishing aspect ratio we rigorously derive an effective Griffith–Euler–Bernoulli functional which acts on piecewise W2,2 regular curves representing the midline of the beam. The elastic part of this functional is the classical Euler–Bernoulli functional for thin beams in the bending dominated regime in terms of the curve’s curvature. In addition there also emerges a fracture term proportional to the number of discontinuities of the curve and its first derivative.
Mesoscopic Perturbations of Large Random Matrices

We consider the eigenvalues and eigenvectors of small rank perturbations of random N × N matrices. We allow the rank of perturbation M to increase with N, and the only assumption is M = o(N). The spiked population model, proposed by Johnstone [On the distribution of the largest eigenvalue in principal components analysis, Ann. Statist. 29(2) (2001) 295–327], is of this kind, in which all the population eigenvalues are 1’s except for a few fixed eigenvalues. Our model is more general since we allow the number of non-unit population eigenvalues to grow with the population size. In both additive and multiplicative perturbation models, we study the nonasymptotic relation between the extreme eigenvalues of the perturbed random matrix and those of the perturbation. As N goes to infinity, we derive the empirical distribution of the extreme eigenvalues of the perturbed random matrix. We also compute the appropriate projection of eigenvectors corresponding to the extreme eigenvalues of the perturbed random matrix....
Ma–Schlenker c -Octahedra in the 2-Sphere

We present constructions inspired by the Ma–Schlenker example of “Non-rigidity of spherical inversive distance circle packings” (Discrete Comput Geom 47(3):610–617, 2012). In contrast to the use in Ma and Schlenker (2012) of an infinitesimally flexible Euclidean polyhedron, embeddings in de Sitter space, and Pogorelov maps, our elementary constructions use only the inversive geometry of the 2-sphere.
The distribution of Fst and other genetic statistics for a class of population structure models.

We examine genetic statistics used in the study of structured populations. In a 1999 paper, Wakeley observed that the coalescent process associated with the finite island model can be decomposed into a scattering phase and a collecting phase. This decomposition becomes exact in the large population limit with the coalescent at the end of the scattering phase converging to the Ewens sampling formula and the coalescent during the collecting phase converging to the Kingman coalescent. In this paper we introduce a class of limiting models, which we refer to as G/KC models, that generalize Wakeley’s decomposition. G in G/KC represents a completely general limit for the scattering phase, while KC represents a Kingman coalescent limit for the collecting phase. We show that both the island and two-dimensional stepping stone models converge to G/KC models in the large population limit. We then derive the distribution of the statistic F st for all G/KC models under a large sample limit for the cases of strong or weak mutation, thereby deriving the large population, large sample limiting distribution of F st for the island and two-dimensional stepping stone models as a special case of a general formula. Our methods allow us to take the large population and large sample limits simultaneously. In the context of large population, large sample limits, we show that the variance of F st in the presence of weak mutation collapses as $${O(\frac{1}{\log d})}$$ where d is the number of demes sampled. Further, we show that this $${O(\frac{1}{\log d})}$$ is caused by a heavy tail in the distribution of F st . Our analysis of F st can be extended to an entire class of genetic statistics, and we use our approach to examine homozygosity measures. Our analysis uses coalescent based methods.
Explicit resilient functions matching ajtai-linial

A Boolean function on n variables is q-resilient if for any subset of at most q variables, the function is very likely to be determined by a uniformly random assignment to the remaining n − q variables; in other words, no coalition of at most q variables has significant influence on the function. Resilient functions have been extensively studied with a variety of applications in cryptography, distributed computing, and pseudorandomness. The best known resilient function on n variables due to Ajtai and Linial [AL93] has the property that only sets of size Ω(n/(log2n)) can have influence bounded away from zero. However, the construction of Ajtai and Linial is by the probabilistic method and does not give an efficiently computable function.We construct an explicit monotone depth three almost-balanced Boolean function on n bits that is Ω(n/(log2n))-resilient matching the bounds of Ajtai and Linial. The best previous explicit constructions of Meka [Mek09] (which only gives a logarithmic depth function), and Chattopadhyay and Zuckerman [CZ15] were only (n1−β)-resilient for any constant 0
Learning compact recurrent neural networks

Recurrent neural networks (RNNs), including long short-term memory (LSTM) RNNs, have produced state-of-the-art results on a variety of speech recognition tasks. However, these models are often too large in size for deployment on mobile devices with memory and latency constraints. In this work, we study mechanisms for learning compact RNNs and LSTMs via low-rank factorizations and parameter sharing schemes. Our goal is to investigate redundancies in recurrent architectures where compression can be admitted without losing performance. A hybrid strategy of using structured matrices in the bottom layers and shared low-rank factors on the top layers is found to be particularly effective, reducing the parameters of a standard LSTM by 75%, at a small cost of 0.3% increase in WER, on a 2,000-hr English Voice Search task.
Loss Visibility Optimized Real-Time Video Transmission Over MIMO Systems

The structured nature of video data motivates introducing video-aware decisions that make use of this structure for improved video transmission over wireless networks . In this paper, we introduce an architecture for real-time video transmission over multiple-input multiple-output (MIMO) wireless communication systems using loss visibility side information . We quantify the perceptual importance of a packet through the packet loss visibility and use the loss visibility distribution to provide a notion of relative packet importance . To jointly achieve high video quality and low latency, we define the optimization objective function as the throughput weighted by the loss visibility of each packet, a proxy for the total perceptual value of successful packets per unit of time. We solve the problem of mapping video packets to MIMO subchannels and adapting per-stream rates to maximize the proposed objective . We show that the solution enables jointly reaping gains in terms of improved video quality and lower latency. Optimized packet-stream mapping enables transmission of more relevant packets over more reliable streams while unequal modulation opportunistically increases the transmission rate on the stronger streams to enable low latency delivery of high priority packets. Tested on H.264-encoded video sequences, for a $4 \times 4$ MIMO system with three spatial streams, the proposed architecture achieves 8 dB power reduction for the same video quality and supports $2.4\times $ higher throughput due to unequal modulation. Furthermore, the gains are achieved at the expense of few bits of cross-layer overhead rather than a complex cross-layer design.
On the analysis of a continuous-time bi-virus model

This paper studies a distributed continuous-time bi-virus model for a system of groups of individuals. An in-depth stability analysis is performed for the healthy and epidemic equilibria. Sensitivity properties of some nontrivial equilibria are also investigated.
On lattice points in large convex bodies

We consider a compact convex body $\mathcal{B}$ in $\mathbb{R}^d$ $(d\geqslant 3)$ with smooth boundary and nonzero Gaussian curvature and prove a new estimate of $P_{\mathcal{B}}(t)$, the remainder in the lattice point problem, which improves previously known best result.
A Smooth Transition from Wishart to GOE

It is well known that an $$n \times n$$ Wishart matrix with d degrees of freedom is close to the appropriately centered and scaled Gaussian orthogonal ensemble (GOE) if d is large enough. Recent work of Bubeck, Ding, Eldan, and Racz, and independently Jiang and Li, shows that the transition happens when $$d = \Theta ( n^{3} )$$ . Here we consider this critical window and explicitly compute the total variation distance between the Wishart and GOE matrices when $$d / n^{3} \rightarrow c \in (0, \infty )$$ . This shows, in particular, that the phase transition from Wishart to GOE is smooth.
The IBM Speaker Recognition System: Recent Advances and Error Analysis

We present the recent advances along with an error analysis of the IBM speaker recognition system for conversational speech. Some of the key advancements that contribute to our system include: a nearest-neighbor discriminant analysis (NDA) approach (as opposed to LDA) for intersession variability compensation in the i-vector space, the application of speaker and channel-adapted features derived from an automatic speech recognition (ASR) system for speaker recognition, and the use of a DNN acoustic model with a very large number of output units (similar to 10k senones) to compute the frame-level soft alignments required in the i-vector estimation process. We evaluate these techniques on the NIST 2010 SRE extended core conditions (C1-C9), as well as the 10sec-10sec condition. To our knowledge, results achieved by our system represent the best performances published to date on these conditions. For example, on the extended tel-tel condition (C5) the system achieves an EER of 0.59%. To garner further understanding of the remaining errors (on C5), we examine the recordings associated with the low scoring target trials, where various issues are identified for the problematic recordings/trials. Interestingly, it is observed that correcting the pathological recordings not only improves the scores for the target trials but also for the non target trials.
Restriction estimates using polynomial partitioning II

We improve the estimates in the restriction problem in dimension $n \geqslant 4$. To do so, we establish a weak version of a $k$-linear restriction estimate for any $k$. The exponents in this weak $k$-linear estimate are sharp for all $k$ and $n$.
Cellularity of diagram algebras as twisted semigroup algebras

Abstract The Temperley–Lieb and Brauer algebras and their cyclotomic analogues, as well as the partition algebra, are all examples of twisted semigroup algebras. We prove a general theorem about the cellularity of twisted semigroup algebras of regular semigroups, which allows us to easily reproduce the cellularity of these algebras. This theorem generalizes a result of East about the cellularity of semigroup algebras of inverse semigroups.
Observations of the Crab Nebula with Early HAWC Data

The High Altitude Water Cherenkov (HAWC) Observatory is a TeV gamma-ray detector, completed in early 2015. HAWC started science operations in August 2013 with a third of the detector taking data. Several known gamma-ray sources have already been detected with the first HAWC data. Among these sources, the Crab Nebula, the brightest steady gamma-ray source at very high energies in our Galaxy, has been detected with high significance. In this contribution I will present the results of the observations of the Crab Nebula with HAWC, including time variability, and the detector performance based on early data.
Direct and Binary Direct Bases for One-Set Updates of a Closure System

We introduce a concept of a binary-direct implicational basis and show that the shortest binary-direct basis exists and it is known as the D-basis introduced in Adaricheva, Nation, Rand [4]. Using this concept we approach the algorithmic solution to the Singleton Horn Extension problem, as well as the one set removal problem, when the closure system is given by the canonical direct or binary-direct basis. In this problem, a new closed set is added to or removed from the closure system forcing the re-write of a given basis. Our goal is to obtain the same type of implicational basis for the new closure system as was given for original closure system and to make the basis update an optimal process.
Evaporation-driven ring and film deposition from colloidal droplets

Evaporating suspensions of colloidal particles lead to the formation of a variety of patterns, ranging from a left-over ring of a dried coffee drop to uniformly distributed solid pigments left behind wet paint. To characterize the transition between rings and uniform deposits, we investigate the dynamics of a drying droplet via a multiphase model of colloidal particles in a solvent. Our theory couples the inhomogeneous evaporation at the evolving droplet interface to the dynamics inside the drop. This includes the liquid flow, local variations of the particle concentration leading to a cross-over between dilute and dense suspensions, and the resulting propagation of the deposition front. A dimensionless parameter combining the capillary number and the droplet aspect ratio captures the formation conditions of different pattern types while correctly accounting for the transition from Stokes flow to Darcy flow at high solute concentrations.
Perceptions, People, and Places: Influences on Cycling for Latino Immigrants and Implications for Equity:

The recent growth in cycling in the United States has paralleled a growth in the diversity of cyclists, but what encourages people to bicycle is not the same across all demographic groups. This stu...
Pnictogen bonding with alkoxide cages: Which pnictogen is best?

Pnictogen bonding is beginning to emerge as a useful supramolecular interaction. The design strategies for these systems are still in the early stages of development and much attention has been focused on the lighter pnictogens. Pnictogen bond donors can have up to three independent sites for binding which can result in triple pnictogen bonding. This has been observed in the self-assembly of antimony alkoxide cages, but not with the lighter congeners. This work reports structural characterization of an analogous arsenic alkoxide cage that engages in a single pnictogen bond and synthetic explorations of the bismuth congener. DFT calculations are used to evaluate the differences between the structures. Ultimately the partial charge on the pnictogen and the energy of the pnictogen lone pair dictate the strength, orientation and number of pnictogen bonds that these cages form. Antimony cages strike the best balance between strength and directionality, allowing them to achieve triple pnictogen bonding where the other congeners do not.
Sparse inverse covariance estimation for high-throughput microRNA sequencing data in the Poisson log-normal graphical model

We introduce a one-step EM algorithm to estimate the graphical structure in a Poisson-Log-Normal graphical model. This procedure is equivalent to a normality transformation that makes the problem o...
DISCRETE METRIC SPACES: STRUCTURE, ENUMERATION, AND 0-1 LAWS

Fix an integer .Our work can be viewed as an extension of a long line of research in extremal combinatorics to the colored setting, as well as an addition to the collection of known structures that admit logical 0-1 laws.
Evolutionary characteristics of intergenic transcribed regions indicate rare novel genes and widespread noisy transcription in the Poaceae

Extensive transcriptional activity occurring in intergenic regions of genomes has raised the question whether intergenic transcription represents the activity of novel genes or noisy expression. To address this, we evaluated cross-species and post-duplication sequence and expression conservation of intergenic transcribed regions (ITRs) in four Poaceae species. Among 43,301 ITRs across the four species, 34,460 (80%) are species-specific. ITRs found across species tend to be more divergent in expression and have more recent duplicates compared to annotated genes. To assess if ITRs are functional (under selection), machine learning models were established in Oryza sativa (rice) that could accurately distinguish between phenotype genes and pseudogenes (area under curve-receiver operating characteristic = 0.94). Based on the models, 584 (8%) and 4391 (61%) rice ITRs are classified as likely functional and nonfunctional with high confidence, respectively. ITRs with conserved expression and ancient retained duplicates, features that were not part of the model, are frequently classified as likely-functional, suggesting these characteristics could serve as pragmatic rules of thumb for identifying candidate sequences likely to be under selection. This study also provides a framework to identify novel genes using comparative transcriptomic data to improve genome annotation that is fundamental for connecting genotype to phenotype in crop and model systems.
Low-Rank Bandit Methods for High-Dimensional Dynamic Pricing

We consider dynamic pricing with many products under an evolving but low-dimensional demand model. Assuming the temporal variation in cross-elasticities exhibits low-rank structure based on fixed (latent) features of the products, we show that the revenue maximization problem reduces to an online bandit convex optimization with side information given by the observed demands. We design dynamic pricing algorithms whose revenue approaches that of the best fixed price vector in hindsight, at a rate that only depends on the intrinsic rank of the demand model and not the number of products. Our approach applies a bandit convex optimization algorithm in a projected low-dimensional space spanned by the latent product features, while simultaneously learning this span via online singular value decomposition of a carefully-crafted matrix containing the observed demands.
Remarks on generic stability in independent theories

Abstract In NIP theories, generically stable Keisler measures can be characterized in several ways. We analyze these various forms of “generic stability” in arbitrary theories. Among other things, we show that the standard definition of generic stability for types coincides with the notion of a frequency interpretation measure. We also give combinatorial examples of types in NSOP theories that are finitely approximated but not generically stable, as well as ϕ-types in simple theories that are definable and finitely satisfiable in a small model, but not finitely approximated. Our proofs demonstrate interesting connections to classical results from Ramsey theory for finite graphs and hypergraphs.
Interleukin-13 Is Unlucky for Allergy Sufferers.

Anaphylaxis, a life-threatening allergic reaction, is dependent on high affinity allergen-specific IgE. Gowthaman et al. now show that a new interleukin (IL)-13-expressing T helper cell subset specifically promotes high-affinity IgE responses. The discovery of T follicular helper (Tfh)13 cells defines potential new targets for allergy therapies.
Efficient global monitoring statistics for high‐dimensional data

Global monitoring statistics play an important role for developing efficient monitoring schemes for high-dimensional data streams. A number of global monitoring statistics have been proposed in the literature. However, most of them only work for certain types of abnormal scenarios under specific model assumptions. How to develop global monitoring statistics that are powerful for any abnormal scenarios under flexible model assumptions is a long-standing problem in the statistical process monitoring field. To provide a potential solution to this problem, we propose a novel class of global monitoring statistics by making use of the quantile information in the underlying distribution of the local monitoring statistic. Our proposed global monitoring statistics are easy to calculate and can work under flexible model assumptions since they can be built on any local monitoring statistic that is suitable for monitoring a single data stream. Our simulation studies show that the proposed global monitoring statistics perform well across a broad range of settings, and compare favorably with existing methods.
Adaptive control - A departure from the certainty-equivalence paradigm

A fundamental study of indirect adaptive control addressed towards a class of uncertain mechanical and aerospace systems is the subject of this paper. We utilize and build upon certain recent techniques within adaptive control that permit nonlinear parameterization of uncertainty, thereby amounting to a significant shift from the classical certainty equivalence methodology. Instead of the more popular direct adaptive control formulations, our focus is restricted to the indirect methods because imposing prior information on properties of physically meaningful plant parameters is convenient within this framework. For two different types of uncertainty parameterizations, namely scalar parameters and proper orthogonal matrix parameters, we present smooth, non-overparameterized (lower order), and stable adaptive control algorithms that provide improved transient performance while at the same time utilize all the available prior information on the unknown parameters. In the particular case when there exists a single scalar uncertain parameter, the most novel attribute of the proposed controller is that adaptation gets automatically frozen once the parameter estimate reaches the corresponding true value, a highly desirable feature that is clearly missing within all existing certainty equivalence adaptive control schemes. Through both analysis and simulations, we have been able to confirm that this “nice” feature amounts to having a proportional term within the parameter update law; and is in fact enabled by a crucial role played by the introduction of certain design functions that are embedded within the new controller. All technical descriptions will be further elaborated by illustrative physical examples as well as numerical simulations of the resulting closed-loop dynamics to demonstrate the potential advantages of this new approach.
Machine learning to predict final fire size at the time of ignition

Fires in boreal forests of Alaska are changing, threatening human health and ecosystems. Given expected increases in fire activity with climate warming, insight into the controls on fire size from the time of ignition is necessary. Such insight may be increasingly useful for fire management, especially in cases where many ignitions occur in a short time period. Here we investigated the controls and predictability of final fire size at the time of ignition. Using decision trees, we show that ignitions can be classified as leading to small, medium or large fires with 50.4 ± 5.2% accuracy. This was accomplished using two variables: vapour pressure deficit and the fraction of spruce cover near the ignition point. The model predicted that 40% of ignitions would lead to large fires, and those ultimately accounted for 75% of the total burned area. Other machine learning classification algorithms, including random forests and multi-layer perceptrons, were tested but did not outperform the simpler decision tree model. Applying the model to areas with intensive human management resulted in overprediction of large fires, as expected. This type of simple classification system could offer insight into optimal resource allocation, helping to maintain a historical fire regime and protect Alaskan ecosystems.