The main goal of this paper is to achieve a parametrization of the solution set of the truncated matricial Hausdorff moment problem in the non-degenerate and degenerate situation. We treat the even and the odd cases simultaneously. Our approach is based on Schur analysis methods. More precisely, we use two interrelated versions of Schur-type algorithms, namely an algebraic one and a function-theoretic one. The algebraic version, worked out in our former paper arXiv:1908.05115, is an algorithm which is applied to finite or infinite sequences of complex matrices. The construction and discussion of the function-theoretic version is a central theme of this paper. This leads us to a complete description via Stieltjes transform of the solution set of the moment problem under consideration. Furthermore, we discuss special solutions in detail.

We derive sufficient conditions for exponential decay of solutions of the delay negative feedback equation with distributed delay. The conditions are written in terms of exponential moments of the distribution. Our method only uses elementary tools of calculus and is robust towards possible extensions to more complex settings, in particular, systems of delay differential equations. We illustrate the applicability of the method to particular distributions - Dirac delta, Gamma distribution, uniform and truncated normal distributions.

Finite metric spaces are the object of study in many data analysis problems. We examine the concept of weak isometry between finite metric spaces, in order to analyse properties of the spaces that are invariant under strictly increasing rescaling of the distance functions. In this paper, we analyse some of the possible complete and incomplete invariants for weak isometry and we introduce a dissimilarity measure that asses how far two spaces are from being weakly isometric. Furthermore, we compare these ideas with the theory of persistent homology, to study how the two are related.

ErdH{o}s and Hajnal constructed a 4-coloring of the triples of an $N$-element set such that every $n$-element subset contains 2 triples with distinct colors, and $N$ is double exponential in $n$. Conlon, Fox and R"odl asked whether there is some integer $qge 3$ and a $q$-coloring of the triples of an $N$-element set such that every $n$-element subset has 3 triples with distinct colors, and $N$ is double exponential in $n$. We make the first nontrivial progress on this problem by providing a $q$-coloring with this property for all $qgeq 9$, where $N$ is exponential in $n^{2+cq}$ and $c>0$ is an absolute constant.

In this paper we study manifolds $M_{Sigma}$ with fibered singularities, more specifically, a relevant space $Riem^{psc}(X_{Sigma})$ of Riemannian metrics with positive scalar curvature. Our main goal is to prove that the space $Riem^{psc}(X_{Sigma})$ is homotopy invariant under certain surgeries on $M_{Sigma}$.

A graph $G=(V,E)$ is $delta$-hyperbolic if for any four vertices $u,v,w,x$, the two larger of the three distance sums $d(u,v)+d(w,x)$, $d(u,w)+d(v,x)$, and $d(u,x)+d(v,w)$ differ by at most $2delta geq 0$. Recent work shows that many real-world graphs have small hyperbolicity $delta$. This paper describes the eccentricity terrain of a $delta$-hyperbolic graph. The eccentricity function $e_G(v)=max{d(v,u) : u in V}$ partitions the vertex set of $G$ into eccentricity layers $C_{k}(G) = {v in V : e(v)=rad(G)+k}$, $k in mathbb{N}$, where $rad(G)=min{e_G(v): vin V}$ is the radius of $G$. The paper studies the eccentricity layers of vertices along shortest paths, identifying such terrain features as hills, plains, valleys, terraces, and plateaus. It introduces the notion of $eta$-pseudoconvexity, which implies Gromov's $epsilon$-quasiconvexity, and illustrates the abundance of pseudoconvex sets in $delta$-hyperbolic graphs. In particular, it shows that all sets $C_{leq k}(G)={vin V : e_G(v) leq rad(G) + k}$, $kin mathbb{N}$, are $(2delta-1)$-pseudoconvex. Additionally, several bounds on the eccentricity of a vertex are obtained which yield a few approaches to efficiently approximating all eccentricities. An $O(delta |E|)$ time eccentricity approximation $hat{e}(v)$, for all $vin V$, is presented that uses distances to two mutually distant vertices and satisfies $e_G(v)-2delta leq hat{e}(v) leq {e_G}(v)$. It also shows existence of two eccentricity approximating spanning trees $T$, one constructible in $O(delta |E|)$ time and the other in $O(|E|)$ time, which satisfy ${e}_G(v) leq e_T(v) leq {e}_G(v)+4delta+1$ and ${e}_G(v) leq e_T(v) leq {e}_G(v)+6delta$, respectively. Thus, the eccentricity terrain of a tree gives a good approximation (up-to an additive error $O(delta))$ of the eccentricity terrain of a $delta$-hyperbolic graph.

In learning-to-rank for information retrieval, a ranking model is automatically learned from the data and then utilized to rank the sets of retrieved documents. Therefore, an ideal ranking model would be a mapping from a document set to a permutation on the set, and should satisfy two critical requirements: (1)~it should have the ability to model cross-document interactions so as to capture local context information in a query; (2)~it should be permutation-invariant, which means that any permutation of the inputted documents would not change the output ranking. Previous studies on learning-to-rank either design uni-variate scoring functions that score each document separately, and thus failed to model the cross-document interactions; or construct multivariate scoring functions that score documents sequentially, which inevitably sacrifice the permutation invariance requirement. In this paper, we propose a neural learning-to-rank model called SetRank which directly learns a permutation-invariant ranking model defined on document sets of any size. SetRank employs a stack of (induced) multi-head self attention blocks as its key component for learning the embeddings for all of the retrieved documents jointly. The self-attention mechanism not only helps SetRank to capture the local context information from cross-document interactions, but also to learn permutation-equivariant representations for the inputted documents, which therefore achieving a permutation-invariant ranking model. Experimental results on three large scale benchmarks showed that the SetRank significantly outperformed the baselines include the traditional learning-to-rank models and state-of-the-art Neural IR models.

When time-dependent partial differential equations (PDEs) are solved numerically in a domain with curved boundary or on a curved surface, mesh error and geometric approximation error caused by the inaccurate location of vertices and other interior grid points, respectively, could be the main source of the inaccuracy and instability of the numerical solutions of PDEs. The role of these geometric errors in deteriorating the stability and particularly the conservation properties are largely unknown, which seems to necessitate very fine meshes especially to remove geometric approximation error. This paper aims to investigate the effect of geometric approximation error by using a high-order mesh with negligible geometric approximation error, even for high order polynomial of order p. To achieve this goal, the high-order mesh generator from CAD geometry called NekMesh is adapted for surface mesh generation in comparison to traditional meshes with non-negligible geometric approximation error. Two types of numerical tests are considered. Firstly, the accuracy of differential operators is compared for various p on a curved element of the sphere. Secondly, by applying the method of moving frames, four different time-dependent PDEs on the sphere are numerically solved to investigate the impact of geometric approximation error on the accuracy and conservation properties of high-order numerical schemes for PDEs on the sphere.

The central importance of large scale eigenvalue problems in scientific computation necessitates the development of massively parallel algorithms for their solution. Recent advances in dense numerical linear algebra have enabled the routine treatment of eigenvalue problems with dimensions on the order of hundreds of thousands on the world's largest supercomputers. In cases where dense treatments are not feasible, Krylov subspace methods offer an attractive alternative due to the fact that they do not require storage of the problem matrices. However, demonstration of scalability of either of these classes of eigenvalue algorithms on computing architectures capable of expressing massive parallelism is non-trivial due to communication requirements and serial bottlenecks, respectively. In this work, we introduce the SISLICE method: a parallel shift-invert algorithm for the solution of the symmetric self-consistent field (SCF) eigenvalue problem. The SISLICE method drastically reduces the communication requirement of current parallel shift-invert eigenvalue algorithms through various shift selection and migration techniques based on density of states estimation and k-means clustering, respectively. This work demonstrates the robustness and parallel performance of the SISLICE method on a representative set of SCF eigenvalue problems and outlines research directions which will be explored in future work.

The objective of deep metric learning (DML) is to learn embeddings that can capture semantic similarity and dissimilarity information among data points. Existing pairwise or tripletwise loss functions used in DML are known to suffer from slow convergence due to a large proportion of trivial pairs or triplets as the model improves. To improve this, ranking-motivated structured losses are proposed recently to incorporate multiple examples and exploit the structured information among them. They converge faster and achieve state-of-the-art performance. In this work, we unveil two limitations of existing ranking-motivated structured losses and propose a novel ranked list loss to solve both of them. First, given a query, only a fraction of data points is incorporated to build the similarity structure. To address this, we propose to build a set-based similarity structure by exploiting all instances in the gallery. The learning setting can be interpreted as few-shot retrieval: given a mini-batch, every example is iteratively used as a query, and the rest ones compose the galley to search, i.e., the support set in few-shot setting. The rest examples are split into a positive set and a negative set. For every mini-batch, the learning objective of ranked list loss is to make the query closer to the positive set than to the negative set by a margin. Second, previous methods aim to pull positive pairs as close as possible in the embedding space. As a result, the intraclass data distribution tends to be extremely compressed. In contrast, we propose to learn a hypersphere for each class in order to preserve useful similarity structure inside it, which functions as regularisation. Extensive experiments demonstrate the superiority of our proposal by comparing with the state-of-the-art methods on the fine-grained image retrieval task.

We investigate sparse matrix bipartitioning -- a problem where we minimize the communication volume in parallel sparse matrix-vector multiplication. We prove, by reduction from graph bisection, that this problem is $mathcal{NP}$-complete in the case where each side of the bipartitioning must contain a linear fraction of the nonzeros.

We present an improved exact branch-and-bound algorithm which finds the minimum communication volume for a given matrix and maximum allowed imbalance. The algorithm is based on a maximum-flow bound and a packing bound, which extend previous matching and packing bounds.

We implemented the algorithm in a new program called MP (Matrix Partitioner), which solved 839 matrices from the SuiteSparse collection to optimality, each within 24 hours of CPU-time. Furthermore, MP solved the difficult problem of the matrix cage6 in about 3 days. The new program is on average more than ten times faster than the previous program MondriaanOpt.

Benchmark results using the set of 839 optimally solved matrices show that combining the medium-grain/iterative refinement methods of the Mondriaan package with the hypergraph bipartitioner of the PaToH package produces sparse matrix bipartitionings on average within 10% of the optimal solution.

This work deals with the efficient numerical solution of the time-fractional heat equation discretized on non-uniform temporal meshes. Non-uniform grids are essential to capture the singularities of "typical" solutions of time-fractional problems. We propose an efficient space-time multigrid method based on the waveform relaxation technique, which accounts for the nonlocal character of the fractional differential operator. To maintain an optimal complexity, which can be obtained for the case of uniform grids, we approximate the coefficient matrix corresponding to the temporal discretization by its hierarchical matrix (${cal H}$-matrix) representation. In particular, the proposed method has a computational cost of ${cal O}(k N M log(M))$, where $M$ is the number of time steps, $N$ is the number of spatial grid points, and $k$ is a parameter which controls the accuracy of the ${cal H}$-matrix approximation. The efficiency and the good convergence of the algorithm, which can be theoretically justified by a semi-algebraic mode analysis, are demonstrated through numerical experiments in both one- and two-dimensional spaces.

Dense kernel matrices $Theta in mathbb{R}^{N imes N}$ obtained from point evaluations of a covariance function $G$ at locations ${ x_{i} }_{1 leq i leq N} subset mathbb{R}^{d}$ arise in statistics, machine learning, and numerical analysis. For covariance functions that are Green's functions of elliptic boundary value problems and homogeneously-distributed sampling points, we show how to identify a subset $S subset { 1 , dots , N }^2$, with $# S = O ( N log (N) log^{d} ( N /epsilon ) )$, such that the zero fill-in incomplete Cholesky factorisation of the sparse matrix $Theta_{ij} 1_{( i, j ) in S}$ is an $epsilon$-approximation of $Theta$. This factorisation can provably be obtained in complexity $O ( N log( N ) log^{d}( N /epsilon) )$ in space and $O ( N log^{2}( N ) log^{2d}( N /epsilon) )$ in time, improving upon the state of the art for general elliptic operators; we further present numerical evidence that $d$ can be taken to be the intrinsic dimension of the data set rather than that of the ambient space. The algorithm only needs to know the spatial configuration of the $x_{i}$ and does not require an analytic representation of $G$. Furthermore, this factorization straightforwardly provides an approximate sparse PCA with optimal rate of convergence in the operator norm. Hence, by using only subsampling and the incomplete Cholesky factorization, we obtain, at nearly linear complexity, the compression, inversion and approximate PCA of a large class of covariance matrices. By inverting the order of the Cholesky factorization we also obtain a solver for elliptic PDE with complexity $O ( N log^{d}( N /epsilon) )$ in space and $O ( N log^{2d}( N /epsilon) )$ in time, improving upon the state of the art for general elliptic operators.

In ASPIC-style structured argumentation an argument can rebut another argument by attacking its conclusion. Two ways of formalizing rebuttal have been proposed: In restricted rebuttal, the attacked conclusion must have been arrived at with a defeasible rule, whereas in unrestricted rebuttal, it may have been arrived at with a strict rule, as long as at least one of the antecedents of this strict rule was already defeasible. One systematic way of choosing between various possible definitions of a framework for structured argumentation is to study what rationality postulates are satisfied by which definition, for example whether the closure postulate holds, i.e. whether the accepted conclusions are closed under strict rules. While having some benefits, the proposal to use unrestricted rebuttal faces the problem that the closure postulate only holds for the grounded semantics but fails when other argumentation semantics are applied, whereas with restricted rebuttal the closure postulate always holds. In this paper we propose that ASPIC-style argumentation can benefit from keeping track not only of the attack relation between arguments, but also the relation of deductive joint support that holds between a set of arguments and an argument that was constructed from that set using a strict rule. By taking this deductive joint support relation into account while determining the extensions, the closure postulate holds with unrestricted rebuttal under all admissibility-based semantics. We define the semantics of deductive joint support through the flattening method.

The accurate assembly of the system matrix is an important step in any code that solves partial differential equations on a mesh. We either explicitly set up a matrix, or we work in a matrix-free environment where we have to be able to quickly return matrix entries upon demand. Either way, the construction can become costly due to non-trivial material parameters entering the equations, multigrid codes requiring cascades of matrices that depend upon each other, or dynamic adaptive mesh refinement that necessitates the recomputation of matrix entries or the whole equation system throughout the solve. We propose that these constructions can be performed concurrently with the multigrid cycles. Initial geometric matrices and low accuracy integrations kickstart the multigrid, while improved assembly data is fed to the solver as and when it becomes available. The time to solution is improved as we eliminate an expensive preparation phase traditionally delaying the actual computation. We eliminate algorithmic latency. Furthermore, we desynchronise the assembly from the solution process. This anarchic increase of the concurrency level improves the scalability. Assembly routines are notoriously memory- and bandwidth-demanding. As we work with iteratively improving operator accuracies, we finally propose the use of a hierarchical, lossy compression scheme such that the memory footprint is brought down aggressively where the system matrix entries carry little information or are not yet available with high accuracy.

In recent years there has been a burgeoning interest in the use of computational methods to distinguish between elicited speech samples produced by patients with dementia, and those from healthy controls. The difference between perplexity estimates from two neural language models (LMs) - one trained on transcripts of speech produced by healthy participants and the other trained on transcripts from patients with dementia - as a single feature for diagnostic classification of unseen transcripts has been shown to produce state-of-the-art performance. However, little is known about why this approach is effective, and on account of the lack of case/control matching in the most widely-used evaluation set of transcripts (DementiaBank), it is unclear if these approaches are truly diagnostic, or are sensitive to other variables. In this paper, we interrogate neural LMs trained on participants with and without dementia using synthetic narratives previously developed to simulate progressive semantic dementia by manipulating lexical frequency. We find that perplexity of neural LMs is strongly and differentially associated with lexical frequency, and that a mixture model resulting from interpolating control and dementia LMs improves upon the current state-of-the-art for models trained on transcript text exclusively.

Deep learning-based object detection and instance segmentation have achieved unprecedented progress. In this paper, we propose Complete-IoU (CIoU) loss and Cluster-NMS for enhancing geometric factors in both bounding box regression and Non-Maximum Suppression (NMS), leading to notable gains of average precision (AP) and average recall (AR), without the sacrifice of inference efficiency. In particular, we consider three geometric factors, i.e., overlap area, normalized central point distance and aspect ratio, which are crucial for measuring bounding box regression in object detection and instance segmentation. The three geometric factors are then incorporated into CIoU loss for better distinguishing difficult regression cases. The training of deep models using CIoU loss results in consistent AP and AR improvements in comparison to widely adopted $ell_n$-norm loss and IoU-based loss. Furthermore, we propose Cluster-NMS, where NMS during inference is done by implicitly clustering detected boxes and usually requires less iterations. Cluster-NMS is very efficient due to its pure GPU implementation, , and geometric factors can be incorporated to improve both AP and AR. In the experiments, CIoU loss and Cluster-NMS have been applied to state-of-the-art instance segmentation (e.g., YOLACT), and object detection (e.g., YOLO v3, SSD and Faster R-CNN) models. Taking YOLACT on MS COCO as an example, our method achieves performance gains as +1.7 AP and +6.2 AR$_{100}$ for object detection, and +0.9 AP and +3.5 AR$_{100}$ for instance segmentation, with 27.1 FPS on one NVIDIA GTX 1080Ti GPU. All the source code and trained models are available at https://github.com/Zzh-tju/CIoU

In this paper, we present three distributed algorithms to solve a class of generalized Nash equilibrium (GNE) seeking problems in strongly monotone games. The first one (SD-GENO) is based on synchronous updates of the agents, while the second and the third (AD-GEED and AD-GENO) represent asynchronous solutions that are robust to communication delays. AD-GENO can be seen as a refinement of AD-GEED, since it only requires node auxiliary variables, enhancing the scalability of the algorithm. Our main contribution is to prove converge to a variational GNE of the game via an operator-theoretic approach. Finally, we apply the algorithms to network Cournot games and show how different activation sequences and delays affect convergence. We also compare the proposed algorithms to the only other in the literature (ADAGNES), and observe that AD-GENO outperforms the alternative.

With the continued digitalization of societal processes, we are seeing an explosion in available data. This is referred to as big data. In a research setting, three aspects of the data are often viewed as the main sources of challenges when attempting to enable value creation from big data: volume, velocity and variety. Many studies address volume or velocity, while much fewer studies concern the variety. Metric space is ideal for addressing variety because it can accommodate any type of data as long as its associated distance notion satisfies the triangle inequality. To accelerate search in metric space, a collection of indexing techniques for metric data have been proposed. However, existing surveys each offers only a narrow coverage, and no comprehensive empirical study of those techniques exists. We offer a survey of all the existing metric indexes that can support exact similarity search, by i) summarizing all the existing partitioning, pruning and validation techniques used for metric indexes, ii) providing the time and storage complexity analysis on the index construction, and iii) report on a comprehensive empirical comparison of their similarity query processing performance. Here, empirical comparisons are used to evaluate the index performance during search as it is hard to see the complexity analysis differences on the similarity query processing and the query performance depends on the pruning and validation abilities related to the data distribution. This article aims at revealing different strengths and weaknesses of different indexing techniques in order to offer guidance on selecting an appropriate indexing technique for a given setting, and directing the future research for metric indexes.

We study the language universality problem for One-Counter Nets, also known as 1-dimensional Vector Addition Systems with States (1-VASS), parameterized either with an initial counter value, or with an upper bound on the allowed counter value during runs. The language accepted by an OCN (defined by reaching a final control state) is monotone in both parameters. This yields two natural questions: 1) Does there exist an initial counter value that makes the language universal? 2) Does there exist a sufficiently high ceiling so that the bounded language is universal? Despite the fact that unparameterized universality is Ackermann-complete and that these problems seem to reduce to checking basic structural properties of the underlying automaton, we show that in fact both problems are undecidable. We also look into the complexities of the problems for several decidable subclasses, namely for unambiguous, and deterministic systems, and for those over a single-letter alphabet.

Diagnosis of high impedance fault (HIF) is a challenge for nowadays distribution network protections. The fault current of a HIF is much lower than that of a normal load, and fault feature is significantly affected by fault scenarios. A detection and feeder identification algorithm for HIFs is proposed in this paper, based on the high-resolution and synchronous waveform data. In the algorithm, an interval slope is defined to describe the waveform distortions, which guarantees a uniform feature description under various HIF nonlinearities and noise interferences. For three typical types of network neutrals, i.e.,isolated neutral, resonant neutral, and low-resistor-earthed neutral, differences of the distorted components between the zero-sequence currents of healthy and faulty feeders are mathematically deduced, respectively. As a result, the proposed criterion, which is based on the distortion relationships between zero-sequence currents of feeders and the zero-sequence voltage at the substation, is theoretically supported. 28 HIFs grounded to various materials are tested in a 10kV distribution networkwith three neutral types, and are utilized to verify the effectiveness of the proposed algorithm.

Most currently available schemes for performance based ranking of Universities or Research organizations, such as, Quacarelli Symonds (QS), Times Higher Education (THE), Shanghai University based All Research of World Universities (ARWU) use a variety of criteria that include productivity, citations, awards, reputation, etc., while Leiden and Scimago use only bibliometric indicators. The research performance evaluation in the aforesaid cases is based on bibliometric data from Web of Science or Scopus, which are commercially available priced databases. The coverage includes peer reviewed journals and conference proceedings. Google Scholar (GS) on the other hand, provides a free and open alternative to obtaining citations of papers available on the net, (though it is not clear exactly which journals are covered.) Citations are collected automatically from the net and also added to self created individual author profiles under Google Scholar Citations (GSC). This data was used by Webometrics Lab, Spain to create a ranked list of 4000+ institutions in 2016, based on citations from only the top 10 individual GSC profiles in each organization. (GSC excludes the top paper for reasons explained in the text; the simple selection procedure makes the ranked list size-independent as claimed by the Cybermetrics Lab). Using this data (Transparent Ranking TR, 2016), we find the regional and country wise distribution of GS-TR Citations. The size independent ranked list is subdivided into deciles of 400 institutions each and the number of institutions and citations of each country obtained for each decile. We test for correlation between institutional ranks between GS TR and the other ranking schemes for the top 20 institutions.

This work addresses the problem of traffic management at and near an isolated un-signalized intersection for autonomous and networked vehicles through coordinated optimization of their trajectories. We decompose the trajectory of each vehicle into two phases: the provisional phase and the coordinated phase. A vehicle, upon entering the region of interest, initially operates in the provisional phase, in which the vehicle is allowed to optimize its trajectory but is constrained to guarantee in-lane safety and to not enter the intersection. Periodically, all the vehicles in their provisional phase switch to their coordinated phase, which is obtained by coordinated optimization of the schedule of the vehicles' intersection usage as well as their trajectories. For the coordinated phase, we propose a data-driven solution, in which the intersection usage order is obtained through a data-driven online "classification" and the trajectories are computed sequentially. This approach is computationally very efficient and does not compromise much on optimality. Moreover, it also allows for incorporation of "macro" information such as traffic arrival rates into the solution. We also discuss a distributed implementation of this proposed data-driven sequential algorithm. Finally, we compare the proposed algorithm and its two variants against traditional methods of intersection management and against some existing results in the literature by micro-simulations.

Bernstein polynomials, long a staple of approximation theory and computational geometry, have also increasingly become of interest in finite element methods. Many fundamental problems in interpolation and approximation give rise to interesting linear algebra questions. When attempting to find a polynomial approximation of boundary or initial data, one encounters the Bernstein-Vandermonde matrix, which is found to be highly ill-conditioned. Previously, we used the relationship between monomial Bezout matrices and the inverse of Hankel matrices to obtain a decomposition of the inverse of the Bernstein mass matrix in terms of Hankel, Toeplitz, and diagonal matrices. In this paper, we use properties of the Bernstein-Bezout matrix to factor the inverse of the Bernstein-Vandermonde matrix into a difference of products of Hankel, Toeplitz, and diagonal matrices. We also use a nonstandard matrix norm to study the conditioning of the Bernstein-Vandermonde matrix, showing that the conditioning in this case is better than in the standard 2-norm. Additionally, we use properties of multivariate Bernstein polynomials to derive a block $LU$ decomposition of the Bernstein-Vandermonde matrix corresponding to equispaced nodes on the $d$-simplex.

This paper investigates the convergence of the randomized Kaczmarz algorithm for the problem of phase retrieval of complex-valued objects. While this algorithm has been studied for the real-valued case}, its generalization to the complex-valued case is nontrivial and has been left as a conjecture. This paper establishes the connection between the convergence of the algorithm and the convexity of an objective function. Based on the connection, it demonstrates that when the sensing vectors are sampled uniformly from a unit sphere and the number of sensing vectors $m$ satisfies $m>O(nlog n)$ as $n, m ightarrowinfty$, then this algorithm with a good initialization achieves linear convergence to the solution with high probability.

By using dissipativity approach, we establish the stability condition for the feedback connection of a deterministic dynamical system $Sigma$ and a stochastic memoryless map $Psi$. After that, we extend the result to the class of large scale systems in which: $Sigma$ consists of many sub-systems; and $Psi$ consists of many "stochastic actuators" and "probability controllers" that control the actuator's output events. We will demonstrate the proposed approach by showing the design procedures to globally stabilize the manufacturing systems while locally balance the stock levels in any production process.

We introduce a variant of PCPs, that we refer to as rectangular PCPs, wherein proofs are thought of as square matrices, and the random coins used by the verifier can be partitioned into two disjoint sets, one determining the row of each query and the other determining the *column*.

We construct PCPs that are efficient, short, smooth and (almost-)rectangular. As a key application, we show that proofs for hard languages in NTIME$(2^n)$, when viewed as matrices, are rigid infinitely often. This strengthens and considerably simplifies a recent result of Alman and Chen [FOCS, 2019] constructing explicit rigid matrices in FNP. Namely, we prove the following theorem: - There is a constant $delta in (0,1)$ such that there is an FNP-machine that, for infinitely many $N$, on input $1^N$ outputs $N imes N$ matrices with entries in $mathbb{F}_2$ that are $delta N^2$-far (in Hamming distance) from matrices of rank at most $2^{log N/Omega(log log N)}$.

Our construction of rectangular PCPs starts with an analysis of how randomness yields queries in the Reed--Muller-based outer PCP of Ben-Sasson, Goldreich, Harsha, Sudan and Vadhan [SICOMP, 2006; CCC, 2005]. We then show how to preserve rectangularity under PCP composition and a smoothness-inducing transformation. This warrants refined and stronger notions of rectangularity, which we prove for the outer PCP and its transforms.

Coordinating the operation of combined heat and power plants (CHPs) and heat pumps (HPs) at the interface between heat and power systems is essential to achieve a cost-effective and efficient operation of the overall energy system. Indeed, in the current sequential market practice, the heat market has no insight into the impacts of heat dispatch on the electricity market. While preserving this sequential practice, this paper introduces an electricity-aware heat unit commitment model. Coordination is achieved through bid validity constraints, which embed the techno-economic linkage between heat and electricity outputs and costs of CHPs and HPs. This approach constitutes a novel market mechanism for the coordination of heat and power systems, defining heat bids conditionally on electricity market prices. The resulting model is a trilevel optimization problem, which we recast as a mixed-integer linear program using a lexicographic function. We use a realistic case study based on the Danish power and heat system, and show that the proposed model yields a 4.5% reduction in total operating cost of heat and power systems compared to a traditional decoupled unit commitment model, while reducing the financial losses of each CHP and HP due to invalid bids by up-to 20.3 million euros.

PRINCE Raoden of Arelon awoke early that morning, completely unaware that he had been damned for all eternity. What a way to start a novel. As a reader, I don’t think about the first words of a book when…

Sam Mendes' 1917, which took Best Picture and Best Director awards at the Golden Globes earlier this week, looks like a standard period piece.…

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By Michael D. Shear and Sarah Mervosh WASHINGTON — President Donald Trump on Friday openly encouraged right-wing protests of social distancing restrictions in states with stay-at-home orders, a day after announcing guidelines for how the nation’s governors should carry out an orderly reopening of their communities on their own timetables.…

Provided are an anti-static and anti-microbial surface treatment agent including a quaternary ammonium salt compound as an active ingredient and a method of preventing a polymer fiber from developing static electricity by using the surface treatment agent. The quaternary ammonium salt compound has excellent anti-static and anti-microbial effects for the prevention or improvement of static electricity in a polymer fiber. Accordingly, the quaternary ammonium salt compound is suitable for use as a fabric softener, or an anti-static agent, and also, provides anti-microbial effects to a polymer fiber.

The present invention relates to an improved process for fractionating triglyceride oil. The process according to the present invention attains a reproducible crystallization by introducing a controlled temperature profile and ensuing crystal development that reduce the amount of entrapped olein inside the crystals or crystal aggregates. The process of the present invention may be used to fractionate vegetable oils such as palm oil or its blends with other palm oil products or edible vegetable oils.

A method for producing a high viscosity, low volatiles blown stripped oil blend is provided. The method may include the steps of: (i) obtaining an oil blend of corn stillage oil and soybean oil having a weight ratio of corn stillage oil to soybean oil of from about 1:2 to 3:1; (ii) heating the oil blend to at least 90° C.; (iii) passing air through the heated oil blend to produce a blown oil having a viscosity of at least 50 cSt at 40° C.; and (iv) stripping the blown oil from step (iii) to reduce an acid value of the blown oil to less than 5.0 mg KOH/gram.

The present invention relates to a method for removing phosphorus-containing compounds from triglyceride-containing compositions.

Bioassays for detecting the ability of one sample of a food substance, nutritional supplement, therapeutic agent and/or disease preventive agent relative to that of a second sample of such a substance, supplement and/or agent to inhibit, upregulate or otherwise modulate translation initiation, and thereby demonstrate a disease curative and/or preventive effect in a human and/or animal that consumes a such substance, supplement and/or agent or to whom a such substance, supplement and/or agent is administered are provided.

This invention relates to an improved process for the preparation of green fatty acid methyl esters (FAME; commonly called as biodiesel) from different triglyceride oils using mixed metal oxides derived from layered double hydroxides (referred here as LDHs) as reusable solid heterogeneous base catalysts. This process uses very low alcohohoil molar ratio and catalyst and/or products are easily separable after the reaction through simple physical processes. The properties of thus obtained biodiesel meet the standard biodiesel values and can directly be used as transport fuel.

Disclosed is a process for reducing the amount of sterol in a sterol-containing microbial oil composition, including distilling, under short path distillation conditions, a sterol-containing microbial oil wherein said distillation produces a distillate fraction containing the sterol and a triacylglycerol-containing fraction having a reduced amount of the sterol when compared to the amount of sterol in the sterol-containing microbial oil composition that has not been subjected to short path distillation.

Provided are triazine compounds for inhibiting of Syk kinase, intermediates used in making such compounds, methods for their preparation, pharmaceutical compositions thereof, methods for inhibiting Syk kinase activity, and methods for treating conditions mediated at least in part by Syk kinase activity.

A process for the preparation of a chiral compound, in particular posaconazole, wherein the process comprises mixing and reacting the compounds of formula (I) Y3—NH2; of formula (IIa) 0=C═N—Y0 and/or of formula (IIb) and of formula (III) in a solvent in any order to obtain a reaction mixture containing a chiral compound of formula (IV) and/or formula (V).

The present invention pertains generally to the field of therapeutic compounds. More specifically the present invention pertains to certain pyridyl-amino-pyrazine carbonitrile compounds that, inter alia, inhibit Checkpoint Kinase 1 (CHK1) kinase function. The present invention also pertains to pharmaceutical compositions comprising such compounds, and the use of such compounds and compositions, both in vitro and in vivo, to inhibit CHK1 kinase function, and in the treatment of diseases and conditions that are mediated by CHK1, that are ameliorated by the inhibition of CHK1 kinase function, etc., including proliferative conditions such as cancer, etc., optionally in combination with another agent, for example, (a) a DNA topoisomerase I or II inhibitor; (b) a DNA damaging agent; (c) an antimetabolite or thymidylate synthase (TS) inhibitor; (d) a microtubule targeted agent; and (e) ionizing radiation.

The present invention provides a compound of formula I: a method for manufacturing the compounds of the invention, and its therapeutic uses. The present invention further provides a combination of pharmacologically active agents and a pharmaceutical composition.

This invention relates to novel 5-[(hydroxymethyl)aryl]-substituted pyrrolo[2,1-f][1,2,4]triazin-4-amines of formula (I), to processes for the preparation of such compounds, to pharmaceutical compositions containing such compounds, and to the use of such compounds or compositions for treating angiogenesis-related disorders, in particular angiogenesis-related ocular disorders.

Formulations comprising an isosorbide-modified unsaturated polyester comprising maleic acid, fumaric acid, itaconic acid or maleic anhydride and isosorbide and one or more low profile additives. The formulations exhibit better shrink control in molding compound formulations with standard low profile additives than their non-isosorbide-modified analogues. These isosorbide-modified unsaturated polyester resins may be applied in molding compounds like sheet molding compounds or bulk molding compounds and may be components of fiber reinforced composites or other composite materials.

A rubber composition for manufacturing tyres is based on one or more diene elastomers, one or more reinforcing fillers, and a vulcanization system. The vulcanization system includes one or more 1,2,4-triazine compounds chosen from compounds of formula I and compounds of formula II: Certain specific 1,2,4-triazine derivatives are described.

A metal complex having a β-diketonate represented by the following formula (1): wherein M represents a metal atom of the VIII group, R1, R2 and R3 represent a group or an atom selected from the group consisting of an alkyl group, an aryl group, a hydroxyl group, an amino group, an alkoxy group, a hydrogen atom and a halogen atom; X−1 represents an ion selected from a halogen, nitric acid, sulfonic acid, fluoroboric acid, fluorophosphoric acid, or perchloric acid ion; L1 or L2 represents a 2,2'-bipyridine or 1,10-phenanthroline group where these groups may be substituted with a group or an atom selected from an alkyl group, a carboxyl group, a sulfonic acid group, a phosphonic acid group, a hydroxyl group, an amino group, a hydrogen atom and a halogen atom. A photoelectric conversion element and a photochemical cell using the above-mentioned metal complex.

The invention relates to a process for preparing triethyl phosphate by reacting phosphorus oxychloride with a greater than stoichiometric quantity of ethanol under reduced pressure at temperatures of from 0 to 50° C. in a reaction vessel, wherein a) the volatile components resulting from the reaction are predominantly condensed by means of a reflux condenser and the remaining volatile components are passed into a scrubber filled with water,b) after the end of the reaction, the reaction mixture is separated distillatively in an outgassing column into a top product and a bottom product which predominantly comprises triethyl phosphate,c) the top product of the outgassing column is combined with the contents of the scrubber andd) the contents of the scrubber are separated distillatively in an azeotropic distillation to obtain water and ethanol as top product and the ethanol, preferably after dewatering, is preferably returned to the reaction.

There are provided a dielectric ceramic having a high Qf value in a relative permittivity ∈r range of 35 to 45, and a small absolute value of a temperature coefficient τf which indicates change of the resonant frequency in a wide temperature range from a low temperature range to a high temperature range, and a dielectric filter having the dielectric ceramic. A dielectric ceramic includes: a main component, molar ratios α, β, and γ satisfying expressions of 0.240≦α≦0.470, 0.040≦β≦0.200, 0.400≦γ≦0.650, and α+β+γ=1 when a composition formula of the main component is represented as αZrO2.βSnO2.γTiO2; and Mn, a content of Mn in terms of MnO2 being greater than or equal to 0.01% by mass and less than 0.1% by mass with respect to 100% by mass of the main component.