cssi/SciSciGPT-SciSciNet huggingface dataset:
Propagating Cosmic Rays with exact Solution of Fokker-Planck Equation

Abstract Shortfalls in cosmic ray (CR) propagation models obscure the CR sources and acceleration mechanisms. This problem became particularly obvious after the Fermi, Pamela, and AMS-02 have discovered the electron/positron and p/He spectral anomalies. Most of the CR models use diffusive propagation that is inaccurate for weakly scattered energetic particles. So, some parts of the spectra affected by the heliospheric modulation, for example, cannot be interpreted. I discuss and adopt an exact solution of the Fokker-Planck equation [M. A. Malkov, Exact solution of the Fokker-Planck equation for isotropic scattering arXiv:1610.01584 , doi: https://doi.org/10.1103/PhysRevD.95.023007(2017) ], which gives a complete description of a ballistic, diffusive and transdiffusive (intermediate between the first two) propagation regimes. I derive a simplified version of an exact Fokker-Planck propagator that can easily be employed in place of the Gaussian propagator, currently used in major Solar modulation and other CR transport models.
Discriminant-stability in p-adic Lie towers of number fields

Abstract In this paper we consider a tower of number fields ⋯ ⊇ K ( 1 ) ⊇ K ( 0 ) ⊇ K arising naturally from a continuous p-adic representation of Gal ( Q ¯ / K ) , referred to as a p-adic Lie tower over K. A recent conjecture of Daqing Wan hypothesizes, for certain p-adic Lie towers of curves over F p , a stable (polynomial) growth formula for the genus. Here we prove the analogous result in characteristic zero, namely: the p-adic valuation of the discriminant of the extension K ( i ) / K is given by a polynomial in i , p i for i sufficiently large. This generalizes a previously known result on discriminant-growth in Z p -towers of local fields of characteristic zero.
Large Subgraphs in Rainbow‐Triangle Free Colorings

Fox–Grinshpun–Pach showed that every 3-coloring of the complete graph on n vertices without a rainbow triangle contains a clique of size Ω(n1/3log2n) that uses at most two colors, and this bound is tight up to the constant factor. We show that if instead of looking for large cliques one only tries to find subgraphs of large chromatic number, one can do much better. We show that every such coloring contains a 2-colored subgraph with chromatic number at least n2/3, and this is best possible. We further show that for fixed positive integers s,r with s≤r, every r-coloring of the edges of the complete graph on n vertices without a rainbow triangle contains a subgraph that uses at most s colors and has chromatic number at least ns/r, and this is best possible. Fox–Grinshpun–Pach previously showed a clique version of this result. As a direct corollary of our result we obtain a generalization of the celebrated theorem of Erdős-Szekeres, which states that any sequence of n numbers contains a monotone subsequence of length at least n. We prove that if an r-coloring of the edges of an n-vertex tournament does not contain a rainbow triangle then there is an s-colored directed path on ns/r vertices, which is best possible. This gives a partial answer to a question of Loh.
Cauchy problem for ultrasound-modulated EIT

Ultrasound modulation of electrical or optical properties of materials offers the possibility of devising hybrid imaging techniques that combine the high electrical or optical contrast observed in many settings of interest with the high resolution of ultrasound. Mathematically, these modalities require that we reconstruct a diffusion coefficient. x/ for x2 X, a bounded domain in R n , from knowledge of. x/jruj 2 .x/ for x2 X , where u is the solution to the elliptic equationr ruD 0 in X with uD f on@ X . This inverse problem may be recast as a nonlinear equation, which formally takes the form of a 0-Laplacian. Whereas p-Laplacians with p> 1 are well-studied variational elliptic nonlinear equations, pD 1 is a limiting case with a convex but not strictly convex functional, and the case p < 1 admits a variational formulation with a functional that is not convex. In this paper, we augment the equation for the 0-Laplacian with Cauchy data at the domain’s boundary, which results in a formally overdetermined, nonlinear hyperbolic equation. This paper presents existence, uniqueness, and stability results for the Cauchy problem of the 0Laplacian. In general, the diffusion coefficient . x/ can be stably reconstructed only on a subset of X described as the domain of influence of the space-like part of the boundary @ X for an appropriate Lorentzian metric. Global reconstructions for specific geometries or based on the construction of appropriate complex geometric optics solutions are also analyzed.
Molecular Hypergraph Grammar with Its Application to Molecular Optimization

Molecular optimization aims to discover novel molecules with desirable properties. Two fundamental challenges are: (i) it is not trivial to generate valid molecules in a controllable way due to hard chemical constraints such as the valency conditions, and (ii) it is often costly to evaluate a property of a novel molecule, and therefore, the number of property evaluations is limited. These challenges are to some extent alleviated by a combination of a variational autoencoder (VAE) and Bayesian optimization (BO). VAE converts a molecule into/from its latent continuous vector, and BO optimizes a latent continuous vector (and its corresponding molecule) within a limited number of property evaluations. While the most recent work, for the first time, achieved 100% validity, its architecture is rather complex due to auxiliary neural networks other than VAE, making it difficult to train. This paper presents a molecular hypergraph grammar variational autoencoder (MHG-VAE), which uses a single VAE to achieve 100% validity. Our idea is to develop a graph grammar encoding the hard chemical constraints, called molecular hypergraph grammar (MHG), which guides VAE to always generate valid molecules. We also present an algorithm to construct MHG from a set of molecules.
Smoothing Brascamp-Lieb inequalities and strong converses for common randomness generation

We study the infimum of the best constant in a functional inequality, the Brascamp-Lieb-like inequality, over auxiliary measures within a neighborhood of a product distribution. In the finite alphabet and the Gaussian cases, such an infimum converges to the best constant in a mutual information inequality. Implications for strong converse properties of two common randomness (CR) generation problems are discussed. In particular, we prove the strong converse property of the rate region for the omniscient helper CR generation problem in the discrete and the Gaussian cases. The latter case is a rare instance of a strong converse for a continuous source when the rate region involves auxiliary random variables.
On Randomly Projected Hierarchical Clustering with Guarantees.

Hierarchical clustering (HC) algorithms are generally limited to small data instances due to their runtime costs. Here we mitigate this shortcoming and explore fast HC algorithms based on random projections for single (SLC) and average (ALC) linkage clustering as well as for the minimum spanning tree problem (MST). We present a thorough adaptive analysis of our algorithms that improve prior work from $O(N^2)$ by up to a factor of $N/(\log N)^2$ for a dataset of $N$ points in Euclidean space. The algorithms maintain, with arbitrary high probability, the outcome of hierarchical clustering as well as the worst-case running-time guarantees. We also present parameter-free instances of our algorithms.
An Implicit Boundary Integral Method for Interfaces Evolving by Mullins-Sekerka Dynamics

We present an algorithm for computing the nonlinear interface dynamics of the Mullins-Sekerka model for interfaces that are defined implicitly (e.g. by a level set function) using integral equations. The computation of the dynamics involves solving Laplace’s equation with Dirichlet boundary conditions on multiply connected and unbounded domains and propagating the interface using a normal velocity obtained from the solution of the PDE at each time step. Our method is based on a simple formulation for implicit interfaces, which rewrites boundary integrals as volume integrals over the entire space. The resulting algorithm thus inherits the benefits of both level set methods and boundary integral methods to simulate the nonlocal front propagation problem with possible topological changes. We present numerical results in both two and three dimensions to demonstrate the effectiveness of the algorithm.
Characterization of Lee-Yang polynomials

The Lee-Yang circle theorem describes complex polynomials of degree n in z with all their zeros on the unit circle jzj D 1. These polynomials are obtained by taking z1 D D zn D z in certain multiaffine polynomials ‰.z1; : : : ; zn/ which we call Lee-Yang polynomials (they do not vanish when jz1j; : : : ; jznj 1). We characterize the Lee-Yang polynomials ‰ in nC1 variables in terms of polynomials ˆ in n variables (those such that ˆ.z1; : : : ; zn/¤ 0 when jz1j; : : : ; jznj 1 (including jzi j D 1 in a sense to be made precise later). Our current understanding of Lee-Yang polynomials is based on the concept of Asano contraction [1]. We shall define an inner radius associated with a multiaffine polynomial ˆ, and see that it behaves supermultiplicatively with respect to Asano contraction (Proposition 2). Using the properties of the inner radius, we shall characterize the ‰ 2 LYnC1 (nC 1 variables) in terms of polynomials ˆ in n variables such that ˆ.z1; : : : ; zn/¤ 0 when jz1j; : : : ; jznj < 1 (Theorem 3). This characterization will give us a good understanding of LYnC1 (Proposition 5), and allow us to exhibit elements of LYnC1 outside of the (pair interaction) class originally considered by Lee and Yang (see in particular Example 7(d)). The original
The highest dimensional stochastic blockmodel with a regularized estimator

This paper advances the high dimensional frontier for network clustering. In the high dimensional Stochastic Blockmodel for a random network, the number of clusters (or blocks) K grows with the number of nodes N . Previous authors have studied the statistical estimation performance of spectral clustering and the maximum likelihood estimator under the high dimensional model. These authors do not allow K to grow faster than N1/2. We study a model where, ignoring log terms, K can grow proportionally to N . Since the number of clusters must be smaller than the number of nodes, no reasonable model allows K to grow faster; thus, our asymptotic results are the “highest” dimensional. To push the asymptotic setting to this extreme, we make additional assumptions that are motivated from empirical observations in physical anthropology [1], and an in depth study of massive empirical networks[2]. Furthermore, we develop a regularized maximum likelihood estimator that performs well in the highest dimensional model. We prove that, under certain conditions, the proportion of nodes that the regularized estimator misclusters converges to zero. This is the first paper to explicitly introduce and demonstrate the advantages of statistical regularization in a parametric form for network analysis.
Boundary effect of Ricci curvature

On a compact Riemannian manifold with boundary, we study how Ricci curvature of the interior affects the geometry of the boundary. First, we establish integral inequalities for functions defined solely on the boundary and apply them to obtain geometric inequalities involving the total mean curvature. Then, we discuss related rigidity questions and prove Ricci curvature rigidity results for manifolds with boundary.
Influence of Multiplicative Stochastic Variation on Translational Elongation Rates

Experimental data indicate that stochastic effects exerted at the level of translation contribute substantially to the variation in abundance of proteins expressed at moderate to high levels. This study analyzes the theoretical consequences of fluctuations in residue-specific elongation rates during translation. A simple analytical framework shows that rate variation during elongation gives rise to protein production rates that consist of sums of products of random variables. Simulations show that because the contribution to total variation of products of random variables greatly exceeds that of sums of random variables, the overall distribution exhibits approximately log-normal behavior. Empirical fits of the data can be satisfied by either sums of log-normal distributions, or sums of log-normal and log-logistic distributions. Elongation rate stochastic variation offers an accounting for a major component of biological variation. The analysis provided here highlights a probability distribution that is a natural extension of the Poisson and has broad applicability to many types of multiplicative noise processes.
Adaptive stimulus selection in ERP-based brain-computer interfaces by maximizing expected discrimination gain

Brain-computer interfaces (BCIs) can provide an alternative means of communication for individuals with severe neuromuscular limitations. The P300-based BCI speller relies on eliciting and detecting transient event-related potentials (ERPs) in electroencephalography (EEG) data, in response to a user attending to rarely occurring target stimuli amongst a series of non-target stimuli. However, in most P300 speller implementations, the stimuli to be presented are randomly selected from a limited set of options and stimulus selection and presentation are not optimized based on previous user data. In this work, we propose a data-driven method for stimulus selection based on the expected discrimination gain metric. The data-driven approach selects stimuli based on previously observed stimulus responses, with the aim of choosing a set of stimuli that will provide the most information about the user's intended target character. Our approach incorporates knowledge of physiological and system constraints imposed due to real-time BCI implementation. Simulations were performed to compare our stimulus selection approach to the row-column paradigm, the conventional stimulus selection method for P300 spellers. Results from the simulations demonstrated that our adaptive stimulus selection approach has the potential to significantly improve performance from the conventional method: up to 34% improvement in accuracy and 43% reduction in the mean number of stimulus presentations required to spell a character in a 72-character grid. In addition, our greedy approach to stimulus selection provides the flexibility to accommodate design constraints.
Potentially semi-stable deformations of specified Hodge-Tate type and Galois type

Abstract Let k be a perfect field of characteristic p > 2 , and let K be a finite totally ramified extension of W ( k ) [ 1 p ] . We prove that the locus of potentially semi-stable Gal ( K ¯ / K ) -representations of a given Hodge–Tate type and Galois type is a closed subspace of the universal deformation ring, generalizing the result of Kisin (2007) [Kis07] where k is assumed to be finite.
Domain Adaptation of Recurrent Neural Networks for Natural Language Understanding.

The goal of this paper is to use multi-task learning to efficiently scale slot filling models for natural language understanding to handle multiple target tasks or domains. The key to scalability is reducing the amount of training data needed to learn a model for a new task. The proposed multi-task model delivers better performance with less data by leveraging patterns that it learns from the other tasks. The approach supports an open vocabulary, which allows the models to generalize to unseen words, which is particularly important when very little training data is used. A newly collected crowd-sourced data set, covering four different domains, is used to demonstrate the effectiveness of the domain adaptation and open vocabulary techniques.
A NOTE ON QUANTUM 3-MANIFOLD INVARIANTS AND HYPERBOLIC VOLUME

For a closed oriented 3-manifold M and an integer r > 0, let τr(M) denote the SU(2) Reshetikhin–Turaev–Witten invariant of M at level r. We show that for every n > 0, and for r1,…, rn > 0 sufficiently large integers, there exist infinitely many non-homeomorphic hyperbolic 3-manifolds M, all of which have different hyperbolic volume, such that τri(M) = 1, for i = 1,…, n.
Deforming Calabi-Yau threefolds

This paper first generalises the Bogomolov-Tian-Todorov unobstructedness theorem to the case of Calabi-Yau threefolds with canonical singularities. The deformation space of such a Calabi-Yau threefold is no longer smooth, but the general principle is that the obstructions to deforming such a threefold are precisely the obstructions to deforming the singularities of the threefold. Secondly, these results are applied to smoothing singular Calabi-Yau threefolds with crepant resolutions. Any such Calabi-Yau threefold with isolated complete intersection singularities which are not ordinary double points is smoothable. A Calabi-Yau threefold with non-complete intersection isolated singularities is proved to be smoothable under much stronger hypotheses.
Embedding optimal transports in statistical manifolds

We consider Monge-Kantorovich optimal transport problems on ℝ d , d ≥ 1, with a convex cost function given by the cumulant generating function of a probability measure. Examples include theWasserstein-2 transport whose cost function is the square of the Euclidean distance and corresponds to the cumulant generating function of the multivariate standard normal distribution. The optimal coupling is usually described via an extended notion of convex/concave functions and their gradient maps. These extended notions are nonintuitive and do not satisfy useful inequalities such as Jensen’s inequality. Under mild regularity conditions, we show that all such extended gradient maps can be recovered as the usual supergradients of a nonnegative concave function on the space of probability distributions. This embedding provides a universal geometry for all such optimal transports and an unexpected connection with information geometry of exponential families of distributions.
On the Brauer–Picard group of a finite symmetric tensor category

Let Cn denote the representation category of finite supergroup ∧kn⋊Z/2Z. We compute the Brauer–Picard group BrPic(Cn) of Cn. This is done by identifying BrPic(Cn) with the group of braided tensor autoequivalences of the Drinfeld center of Cn and studying the action of the latter group on the categorical Lagrangian Grassmannian of Cn. We show that this action corresponds to the action of a projective symplectic group on a classical Lagrangian Grassmannian.
Multi-space Variational Encoder-Decoders for Semi-supervised Labeled Sequence Transduction

Labeled sequence transduction is a task of transforming one sequence into another sequence that satisfies desiderata specified by a set of labels. In this paper we propose multi-space variational encoder-decoders, a new model for labeled sequence transduction with semi-supervised learning. The generative model can use neural networks to handle both discrete and continuous latent variables to exploit various features of data. Experiments show that our model provides not only a powerful supervised framework but also can effectively take advantage of the unlabeled data. On the SIGMORPHON morphological inflection benchmark, our model outperforms single-model state-of-art results by a large margin for the majority of languages.
A Uniform Proof of the Macdonald-Mehta-Opdam Identity for Finite Coxeter Groups

In this note we give a new proof of the Macdonald-Mehta-Opdam integral identity for finite Coxeter groups (in the equal parameter case). This identity was conjectured by Macdonald and proved by Opdam in \cite{O1,O2} using the theory of multivariable Bessel functions, but in non-crystallographic cases the proof relied on a computer calculation by F. Garvan. Our proof is somewhat more elementary (in particular, it does not use multivariable Bessel functions), and uniform (does not refer to the classification of finite Coxeter groups). \footnote{We expect that this proof can be generalized to the case of non-equal parameters. Indeed, many of the steps of our proof, including key Proposition \ref{l2}, generalize without effort to this setting.
Score Function Features for Discriminative Learning

Author(s): Janzamin, Majid; Sedghi, Hanie; Anandkumar, Anima | Editor(s): Bengio, Yoshua; LeCun, Yann | Abstract: Feature learning forms the cornerstone for tackling challenging learning problems in domains such as speech, computer vision and natural language processing. In this paper, we consider a novel class of matrix and tensor-valued features, which can be pre-trained using unlabeled samples. We present efficient algorithms for extracting discriminative information, given these pre-trained features and labeled samples for any related task. Our class of features are based on higher-order score functions, which capture local variations in the probability density function of the input. We establish a theoretical framework to characterize the nature of discriminative information that can be extracted from score-function features, when used in conjunction with labeled samples. We employ efficient spectral decomposition algorithms (on matrices and tensors) for extracting discriminative components. The advantage of employing tensor-valued features is that we can extract richer discriminative information in the form of an overcomplete representations. Thus, we present a novel framework for employing generative models of the input for discriminative learning.
Brittleness of Bayesian inference and new Selberg formulas

The incorporation of priors in the Optimal Uncertainty Quantification (OUQ) framework reveals brittleness in Bayesian inference; a model may share an arbitrarily large number of finite-dimensional marginals with, or be arbitrarily close (in Prokhorov or total variation metrics) to, the data-generating distribution and still make the largest possible prediction error after conditioning on an arbitrarily large number of samples. The initial purpose of this paper is to unwrap this brittleness mechanism by providing (i) a quantitative version of the Brittleness Theorem of and (ii) a detailed and comprehensive analysis of its application to the revealing example of estimating the mean of a random variable on the unit interval [0, 1] using priors that exactly capture the distribution of an arbitrarily large number of Hausdorff moments. However, in doing so, we discovered that the free parameter associated with Markov and Kreĩn’s canonical representations of truncated Hausdorff moments generates reproducing kernel identities corresponding to reproducing kernel Hilbert spaces of polynomials. Furthermore, these reproducing identities lead to biorthogonal systems of Selberg integral formulas. This process of discovery appears to be generic: whereas Karlin and Shapley used Selberg’s integral formula to first compute the volume of the Hausdorff moment space (the polytope defined by the first n moments of a probability measure on the interval [0, 1]), we observe that the computation of that volume along with higher order moments of the uniform measure on the moment space, using different finite-dimensional representations of subsets of the infinite-dimensional set of probability measures on [0, 1] representing the first n moments, leads to families of equalities corresponding to classical and new Selberg identities.
INFORMATION RANKING AND POWER LAWS ON TREES

In this paper we consider the stochastic analysis of information ranking algorithms of large interconnected data sets, e.g. Google’s PageRank algorithm for ranking pages on the World Wide Web. The stochastic formulation of the problem results in an equation of the form R d = Q + � N=1 Ci Ri , where N,Q, {Ri }i≥1, and {C, Ci }i≥1 are independent nonnegative random variables, the {C, Ci }i≥1 are identically distributed, and the {Ri }i≥1 are independent copies of R ;‘ d =’ stands for equality in distribution. We study the asymptotic properties of the distribution of R that, in the context of PageRank, represents the frequencies of highly ranked pages. The preceding equation is interesting in its own right since it belongs to a more general class of weighted branching processes that have been found to be useful in the analysis of many other algorithms. Our first main result shows that if E N E[C α ]= 1 ,α >0, and Q, N satisfy additional moment conditions, then R has a power law distribution of index α. This result is obtained using a new approach based on an extension of Goldie’s (1991) implicit renewal theorem. Furthermore, when N is regularly varying of index α> 1, E N E[C α ] < 1, and Q, C have higher moments than α, then the distributions of R and N are tail equivalent. The latter result is derived via a novel sample path large deviation method for recursive random sums. Similarly, we characterize the situation when the distribution of R is determined by the tail of Q. The preceding approaches may be of independent interest, as they can be used for analyzing other functionals on trees. We also briefly discuss the engineering implications of our results.
A Characterization of Toric Varieties in Characteristic p

If X is a smooth toric variety over an algebraically closed field of positive characteristic and L is an invertible sheaf on X, then F∗L, the pushforward of L along the Frobenius morphism of X, splits into a direct sum of invertible sheaves [Tho00], [Bog98]. We show that this property characterizes smooth projective toric varieties. INTRODUCTION If X is a smooth toric variety over an algebraically closed field of positive characteristic and L is an invertible sheaf on X, then F∗L, the push-forward of L along the Frobenius morphism of X, splits into a direct sum of invertible sheaves [Tho00], [Bog98]. In this article, we show that this property in fact characterizes smooth projective toric varieties. Theorem 1. Let X be a projective connected scheme over an algebraically closed field k of characteristic p > 0. ThenX is a smooth toric variety if and only if, for every invertible sheaf L on X, F∗L is a direct sum of invertible sheaves. Although the “only if” part of this result has been known already, we include a short proof for completeness (Theorem 2). The proof of the “if” part (Theorem 4) is a bit more involved: we first reduce to the case when the Picard group of X is free abelian and look at the Cox ring R of X. The assumption on X means that R is flat over R, so R is regular by Kunz’s criterion. It follows that R has to be a polynomial ring, so X is a toric variety. We may expect Theorem 1 to hold more generally for X proper. However, we use the characterization of toric varieties in terms of their Cox rings in the form stated in [KW11] which requires X to be projective. It is worth noting that similar characterizations have been obtained [BH07, Corollary 4.4] for X satisfying the A2 condition: every two points have a common affine neighborhood. These theorems, depending on various results on group actions, have been stated only in characteristic zero, therefore we have to be very careful applying them to actions of tori in positive characteristic. 1. PROOF OF THE “ONLY IF” PART We provide an a bit shorter and more explicit proof of Thomsen’s result [Tho00]. The proof gives a very short computation even for projective spaces (in which case one can use the Horrocks splitting criterion and the projection formula to prove that the direct image is a direct sum of invertible sheaves). The key point of our approach is to consider Frobenius push-forwards of all invertible sheaves at once. 1
Representing meaning with a combination of logical and distributional models

NLP tasks differ in the semantic information they require, and at this time no single semantic representation fulfills all requirements. Logic-based representations characterize sentence structure, but do not capture the graded aspect of meaning. Distributional models give graded similarity ratings for words and phrases, but do not capture sentence structure in the same detail as logic-based approaches. It has therefore been argued that the two are complementary. We adopt a hybrid approach that combines logical and distributional semantics using probabilistic logic, specifically Markov Logic Networks. In this article, we focus on the three components of a practical system:1 1 Logical representation focuses on representing the input problems in probabilistic logic; 2 knowledge base construction creates weighted inference rules by integrating distributional information with other sources; and 3 probabilistic inference involves solving the resulting MLN inference problems efficiently. To evaluate our approach, we use the task of textual entailment, which can utilize the strengths of both logic-based and distributional representations. In particular we focus on the SICK data set, where we achieve state-of-the-art results. We also release a lexical entailment data set of 10,213 rules extracted from the SICK data set, which is a valuable resource for evaluating lexical entailment systems.2
Learning to Represent Edits.

We introduce the problem of learning distributed representations of edits. By combining a “neural editor” with an “edit encoder”, our models learn to represent the salient information of an edit and can be used to apply edits to new inputs. We experiment on natural language and source code edit data. Our evaluation yields promising results that suggest that our neural network models learn to capture the structure and semantics of edits. We hope that this interesting task and data source will inspire other researchers to work further on this problem.
Analysis of a one-dimensional prescribed mean curvature equation with singular nonlinearity

Abstract In this paper, the classical solution set ( λ , u ) of the one-dimensional prescribed mean curvature equation ( ⋆ ) − ( u ′ 1 + ( u ′ ) 2 ) ′ = λ ( 1 − u ) 2 , − L x L ; u ( − L ) = u ( L ) = 0 , for λ > 0 and L > 0 , is analyzed via a time map. It is shown that the solution set depends on both parameters λ and L and undergoes two bifurcations. The first is a standard saddle node bifurcation, which happens for all L at λ = λ ∗ ( L ) . The second is a splitting bifurcation, namely, there exists a value L ∗ such that as L transitions from greater than or equal to L ∗ to less than L ∗ the upper branch of the bifurcation diagram of problem ( ⋆ ) splits into two parts. In contrast, the solution set of the semilinear version of problem ( ⋆ ) is independent of L and exhibits only a saddle node bifurcation. Therefore, as this analysis suggests, the splitting bifurcation is a byproduct of the mean curvature operator coupled with the singular forcing.
Global Existence for the 2D Incompressible Isotropic Elastodynamics for Small Initial Data

We establish the global existence and the asymptotic behavior for the 2D incompressible isotropic elastodynamics for sufficiently small, smooth initial data in the Eulerian coordinates formulation. The main tools used to derive the main results are, on the one hand, a modified energy method to derive the energy estimate and, on the other hand, a Fourier transform method with a suitable choice of Z-norm to derive the sharp $$L^\infty $$ -estimate. We mention that the global existence of the same system but in the Lagrangian coordinates formulation was recently obtained by Lei (Global well-posedness of incompressible Elastodynamics in 2D, 2014). Our goal is to improve the understanding of the behavior of solutions. Also, we present a different approach to study 2D nonlinear wave equations from the point of view in frequency space.
Unique Rectification in $d$-Complete Posets: Towards the $K$-Theory of Kac-Moody Flag Varieties

The jeu-de-taquin-based Littlewood-Richardson rule of H. Thomas and A. Yong (2009) for minuscule varieties has been extended in two orthogonal directions, either enriching the cohomology theory or else expanding the family of varieties considered. In one direction, A. Buch and M. Samuel (2016) developed a combinatorial theory of 'unique rectification targets' in minuscule posets to extend the Thomas-Yong rule from ordinary cohomology to $K$-theory. Separately, P.-E. Chaput and N. Perrin (2012) used the combinatorics of R. Proctor's '$d$-complete posets' to extend the Thomas-Yong rule from minuscule varieties to a broader class of Kac-Moody structure constants. We begin to address the unification of these theories. Our main result is the existence of unique rectification targets in a large class of $d$-complete posets. From this result, we obtain conjectural positive combinatorial formulas for certain $K$-theoretic Schubert structure constants in the Kac-Moody setting.
Lower Bounds for Enumerative Counts of Positive-Genus Real Curves

Abstract We transform the positive-genus real Gromov–Witten invariants of many real-orientable symplectic threefolds into signed counts of curves. These integer invariants provide lower bounds for counts of real curves of a given genus that pass through conjugate pairs of constraints. We conclude with some implications and related conjectures for Hodge integrals.
On the Banach-Mazur distance to cross-polytope

Abstract Let n ≥ 3 , and let B 1 n be the standard n-dimensional cross-polytope (i.e. the convex hull of standard coordinate vectors and their negatives). We show that there exists a symmetric convex body G m in R n such that the Banach–Mazur distance d BM ( B 1 n , G m ) satisfies d BM ( B 1 n , G m ) ≥ n 5 / 9 log − C ⁡ n , where C > 0 is a universal constant. The body G m is obtained as a typical realization of a random polytope in R n with 2 m : = 2 n 3 vertices. The result improves upon an earlier estimate of S. Szarek which gives d BM ( B 1 n , G m ) ≥ c n 1 / 2 log ⁡ n (with a different choice of m). This shows in a strong sense that the cross-polytope (or the cube [ − 1 , 1 ] n ) cannot be an “approximate” center of the Minkowski compactum.
Vertex-algebraic structure of the principal subspaces of level one modules for the untwisted affine Lie algebras of types A,D,E

Abstract Generalizing some of our earlier work, we prove natural presentations of the principal subspaces of the level one standard modules for the untwisted affine Lie algebras of types A , D and E , and also of certain related spaces. As a consequence, we obtain a canonical complete set of recursions ( q -difference equations) for the (multi-)graded dimensions of these spaces, and we derive their graded dimensions. Our methods are based on intertwining operators in vertex operator algebra theory.
Transformation formulas in quantum cohomology

We discuss a natural action of the center of G on the Gromov–Witten numbers of G / B 's and G / P 's. This action is suggested by some problems in representation theory. The quantum Schubert calculus of Grassmannians is an easy consequence of this action. We also strengthen a theorem of Fulton and Woodward, in the case of Grasmannians.
The classification of 231-avoiding permutations by descents and maximum drop

We study the number of 231-avoiding permutations with $j$-descents and maximum drop is less than or equal to $k$ which we denote by $a_{n,231,j}^{(k)}$. We show that $a_{n,231,j}^{(k)}$ also counts the number of Dyck paths of length $2n$ with $n-j$ peaks and height $\leq k+1$, and the number of ordered trees with $n$ edges, $j+1$ internal nodes, and of height $\leq k+1$. We show that the generating functions for the $a_{n,231,j}^{(k)}$s with $k$ fixed satisfy a simple recursion. We also use the combinatorics of ordered trees to prove new explicit formulas for $a_{n,231,j}^{(k)}$ as a function of $n$ in a number of special values of $j$ and $k$ and prove a simple recursion for the $a_{n,231,j}^{(k)}$s.
Time Series Classification to Improve Poultry Welfare

Poultry farms are an important contributor to the human food chain. Worldwide, humankind keeps an enormous number of domesticated birds (e.g. chickens) for their eggs and their meat, providing rich sources of low-fat protein. However, around the world, there have been growing concerns about the quality of life for the livestock in poultry farms; and increasingly vocal demands for improved standards of animal welfare. Recent advances in sensing technologies and machine learning allow the possibility of automatically assessing the health of some individual birds, and employing the lessons learned to improve the welfare for all birds. This task superficially appears to be easy, given the dramatic progress in recent years in classifying human behaviors, and given that human behaviors are presumably more complex. However, as we shall demonstrate, classifying chicken behaviors poses several unique challenges, chief among which is creating a generalizable "dictionary" of behaviors from sparse and noisy data. In this work we introduce a novel time series dictionary learning algorithm that can robustly learn from weakly labeled data sources.
Quantitative version of the Oppenheim conjecture for inhomogeneous quadratic forms

We prove a quantitative version of the Oppenheim conjecture for inhomogeneous quadratic forms. We also give an application to eigenvalue spacing on flat 2-tori with Aharonov-Bohm flux.
On the global stability of the wave-map equation in Kerr spaces with small angular momentum

This paper is motivated by the problem of the nonlinear stability of the Kerr solution for axially symmetric perturbations. We consider a model problem concerning the axially symmetric perturbations of a wave map $$\Phi $$ defined from a fixed Kerr solution $${\mathcal K}(M,a)$$ , $$0\le a \le M $$ , with values in the two dimensional hyperbolic space $${\mathbb H}^2$$ . A particular such wave map is given by the complex Ernst potential associated to the axial Killing vector-field $$\mathbf{Z}$$ of $${\mathcal K}(M,a)$$ . We conjecture that this stationary solution is stable, under small axially symmetric perturbations, in the domain of outer communication (DOC) of $${\mathcal K}(M,a)$$ , for all $$0\le a<M$$ and we provide preliminary support for its validity, by deriving convincing stability estimates for the linearized system.
Rise in mortality involving poisoning by medicaments other than narcotics, including poisoning by psychotropic drugs in different age/racial groups in the US.

Background Increase in mortality involving poisoning, particularly by narcotics, is known to have been one of the factors that affected life expectancy in the US during the last two decades, especially for white Americans and Native Americans. However, the contribution of medicaments other than narcotics to mortality in different racial/age groups is less studied. Methods We regressed annual rates of mortality involving poisoning by medicaments but not narcotics/psychodysleptics (ICD-10 codes T36-39.xx or T41-50.8 but not T40.xx present as either underlying or contributing causes of death), as well as annual rates of mortality for certain subcategories of the above, including mortality involving poisoning by psychotropic drugs but not narcotics/psychodysleptics (ICD-10 codes T43.xx but not T40.xx present as either underlying or contributing causes of death) in different age/racial groups for both the 2000–2011 period and the 2011–2017 period against calendar year. Results Annual numbers of deaths involving poisoning by medicaments but not narcotics/psychodysleptics grew from 4,332 between 2000–2001 to 11,401 between 2016–2017, with the growth in the rates of those deaths being higher for the 2011–2017 period compared to the 2000–2011 period. The largest increases in the rates of mortality involving poisoning by medicaments but not narcotics/psychodysleptics were in non-elderly Non-Hispanic Native Americans, followed by Non-Hispanic whites. Most of those increases came from increases in the rates of mortality involving poisoning by psychotropic medications; the latter rates grew for the period of 2015–2017 vs. 2000–2002 by factors ranging from 2.75 for ages 35-44y to 5.37 for ages 55-64y. Conclusions There were major increases in mortality involving poisoning by non-narcotic, particularly psychotropic medicaments, especially in non-elderly non-Hispanic whites and Native Americans. Our results support the need for a comprehensive evaluation of the effect of psychotropic medications on health-related outcomes, including mortality for causes other than poisoning, and the impact of medication misuse.
Can evolution paths be explained by chance alone

We propose a purely probabilistic model to explain the evolution path of a population maximum fitness. We show that after n births in the population there are about ln n upwards jumps. This is true for any mutation probability and any fitness distribution and therefore suggests a general law for the number of upwards jumps. Simulations of our model show that a typical evolution path has first a steep rise followed by long plateaux. Moreover, independent runs show parallel paths. This is consistent with what was observed by Lenski and Travisano (1994) in their bacteria experiments.
Inverting the Furstenberg correspondence

Given a sequence of sets $A_n \subseteq \{0,\ldots,n-1\}$, the Furstenberg correspondence principle provides a shift-invariant measure on $2^N$ that encodes combinatorial information about infinitely many of the $A_n$'s. Here it is shown that this process can be inverted, so that for any such measure, ergodic or not, there are finite sets whose combinatorial properties approximate it arbitarily well. The finite approximations are obtained from the measure by an explicit construction, with an explicit upper bound on how large $n$ has to be to yield a sufficiently good approximation. We draw conclusions for computable measure theory, and show, in particular, that given any computable shift-invariant measure on $2^N$, there is a computable element of $2^N$ that is generic for the measure. We also consider a generalization of the correspondence principle to countable discrete amenable groups, and once again provide an effective inverse.
Quantifying residual finiteness of linear groups

Normal residual finiteness growth measures how well a finitely generated residually finite group is approximated by its finite quotients. We show that any finitely generated linear group Γ≤GLd(K)Γ≤GLd(K) has normal residual finiteness growth asymptotically bounded above by (nlog⁡n)d2−1(nlog⁡n)d2−1; notably this bound depends only on the degree of linearity of Γ. If char K=0K=0 or K is a purely transcendental extension of a finite field, then this bound can be improved to nd2−1nd2−1. We also give lower bounds on the normal residual finiteness growth of Γ in the case that Γ is a finite index subgroup of G(Z)G(Z) or G(Fp[t])G(Fp[t]), where G is Chevalley group of rank at least 2. These lower bounds agree with the computed upper bounds, providing exact asymptotics on the normal residual finiteness growth. In particular, finite index subgroups of G(Z)G(Z) and G(Fp[t])G(Fp[t]) have normal residual finiteness growth ndim⁡(G)ndim⁡(G). We also compute the non-normal residual finiteness growth in the above cases; for the lower bounds the exponent dim⁡(G)dim⁡(G) is replaced by the minimal codimension of a maximal parabolic subgroup of G.
Fuzzi: a three-level logic for differential privacy

Curators of sensitive datasets sometimes need to know whether queries against the data are differentially private. Two sorts of logics have been proposed for checking this property: (1) type systems and other static analyses, which fully automate straightforward reasoning with concepts like “program sensitivity” and “privacy loss,” and (2) full-blown program logics such as apRHL (an approximate, probabilistic, relational Hoare logic), which support more flexible reasoning about subtle privacy-preserving algorithmic techniques but offer only minimal automation. We propose a three-level logic for differential privacy in an imperative setting and present a prototype implementation called Fuzzi. Fuzzi’s lowest level is a general-purpose logic; its middle level is apRHL; and its top level is a novel sensitivity logic adapted from the linear-logic-inspired type system of Fuzz, a differentially private functional language. The key novelty is a high degree of integration between the sensitivity logic and the two lower-level logics: the judgments and proofs of the sensitivity logic can be easily translated into apRHL; conversely, privacy properties of key algorithmic building blocks can be proved manually in apRHL and the base logic, then packaged up as typing rules that can be applied by a checker for the sensitivity logic to automatically construct privacy proofs for composite programs of arbitrary size. We demonstrate Fuzzi’s utility by implementing four different private machine-learning algorithms and showing that Fuzzi’s checker is able to derive tight sensitivity bounds.
Multidimensional Capacitive Sensing for Robot-Assisted Dressing and Bathing

Robotic assistance presents an opportunity to benefit the lives of many people with physical disabilities, yet accurately sensing the human body and tracking human motion remain difficult for robots. We present a multidimensional capacitive sensing technique that estimates the local pose of a human limb in real time. A key benefit of this sensing method is that it can sense the limb through opaque materials, including fabrics and wet cloth. Our method uses a multielectrode capacitive sensor mounted to a robot’s end effector. A neural network model estimates the position of the closest point on a person’s limb and the orientation of the limb’s central axis relative to the sensor’s frame of reference. These pose estimates enable the robot to move its end effector with respect to the limb using feedback control. We demonstrate that a PR2 robot can use this approach with a custom six electrode capacitive sensor to assist with two activities of daily living— dressing and bathing. The robot pulled the sleeve of a hospital gown onto able-bodied participants’ right arms, while tracking human motion. When assisting with bathing, the robot moved a soft wet washcloth to follow the contours of able-bodied participants’ limbs, cleaning their surfaces. Overall, we found that multidimensional capacitive sensing presents a promising approach for robots to sense and track the human body during assistive tasks that require physical human-robot interaction.
PHLPP1 counter-regulates STAT1-mediated inflammatory signaling

Inflammation is an essential aspect of innate immunity but also contributes to diverse human diseases. Although much is known about the kinases that control inflammatory signaling, less is known about the opposing phosphatases. Here we report that deletion of the gene encoding PH domain Leucine-rich repeat Protein Phosphatase 1 (PHLPP1) protects mice from lethal lipopolysaccharide (LPS) challenge and live Escherichia coli infection. Investigation of PHLPP1 function in macrophages reveals that it controls the magnitude and duration of inflammatory signaling by dephosphorylating the transcription factor STAT1 on Ser727 to inhibit its activity, reduce its promoter residency, and reduce the expression of target genes involved in innate immunity and cytokine signaling. This previously undescribed function of PHLPP1 depends on a bipartite nuclear localization signal in its unique N-terminal extension. Our data support a model in which nuclear PHLPP1 dephosphorylates STAT1 to control the magnitude and duration of inflammatory signaling in macrophages.
Blockchain in global supply chains and cross border trade: a critical synthesis of the state-of-the-art, challenges and opportunities

Blockchain possesses the potential of transforming global supply chain management. Gartner predicts that blockchain could be able to track $2 T of goods and services in their movement across the gl...