In this work, we study dynamic properties of classical solutions to a homogenous Neumann initial-boundary value problem (IBVP) for a two-species and two-stimuli chemotaxis model with/without chemical signalling loop in a 2D bounded and smooth domain. We successfully detect the product of two species masses as a feature to determine boundedness, gradient estimates, blow-up and $W^{j,infty}(1leq jleq 3)$-exponential convergence of classical solutions for the corresponding IBVP. More specifically, we first show generally a smallness on the product of both species masses, thus allowing one species mass to be suitably large, is sufficient to guarantee global boundedness, higher order gradient estimates and $W^{j,infty}$-convergence with rates of convergence to constant equilibria; and then, in a special case, we detect a straight line of masses on which blow-up occurs for large product of masses. Our findings provide new understandings about the underlying model, and thus, improve and extend greatly the existing knowledge relevant to this model.

In a multitype branching process, it is assumed that immigrants arrive according to a nonhomogeneous Poisson or a generalized Polya process (both processes are formulated as a nonhomogeneous birth process with an appropriate choice of transition intensities). We show that the renormalized numbers of objects of the various types alive at time $t$ for supercritical, critical, and subcritical cases jointly converge in distribution under those two different arrival processes. Furthermore, some transient moment analysis when there are only two types of particles is provided. AMS 2000 subject classifications: Primary 60J80, 60J85; secondary 60K10, 60K25, 90B15.

This paper is devoted to the study of the singularity phenomenon of timelike extremal hypersurfaces in Minkowski spacetime $mathbb{R}^{1+3}$. We find that there are two explicit lightlike self-similar solutions to a graph representation of timelike extremal hypersurfaces in Minkowski spacetime $mathbb{R}^{1+3}$, the geometry of them are two spheres. The linear mode unstable of those lightlike self-similar solutions for the radially symmetric membranes equation is given. After that, we show those self-similar solutions of the radially symmetric membranes equation are nonlinearly stable inside a strictly proper subset of the backward lightcone. This means that the dynamical behavior of those two spheres is as attractors. Meanwhile, we overcome the double roots case (the theorem of Poincar'{e} can't be used) in solving the difference equation by construction of a Newton's polygon when we carry out the analysis of spectrum for the linear operator.

In this paper we study the following set[A={p(n)+2^nd mod 1: ngeq 1}subset [0.1],] where $p$ is a polynomial with at least one irrational coefficient on non constant terms, $d$ is any real number and for $ain [0,infty)$, $a mod 1$ is the fractional part of $a$. By a Bernoulli decomposition method, we show that the closure of $A$ must have full Hausdorff dimension.

Tree balance plays an important role in different research areas like theoretical computer science and mathematical phylogenetics. For example, it has long been known that under the Yule model, a pure birth process, imbalanced trees are more likely than balanced ones. Therefore, different methods to measure the balance of trees were introduced. The Sackin index is one of the most frequently used measures for this purpose. In many contexts, statements about the minimal and maximal values of this index have been discussed, but formal proofs have never been provided. Moreover, while the number of trees with maximal Sackin index as well as the number of trees with minimal Sackin index when the number of leaves is a power of 2 are relatively easy to understand, the number of trees with minimal Sackin index for all other numbers of leaves was completely unknown. In this manuscript, we fully characterize trees with minimal and maximal Sackin index and also provide formulas to explicitly calculate the number of such trees.

In this review paper, we survey Hardy type inequalities from the point of view of Folland and Stein's homogeneous groups. Particular attention is paid to Hardy type inequalities on stratified groups which give a special class of homogeneous groups. In this environment, the theory of Hardy type inequalities becomes intricately intertwined with the properties of sub-Laplacians and more general subelliptic partial differential equations. Particularly, we discuss the Badiale-Tarantello conjecture and a conjecture on the geometric Hardy inequality in a half-space of the Heisenberg group with a sharp constant.

Let $Gamma subset operatorname{PU}(1,n)$ be a lattice, and $S_Gamma$ the associated ball quotient. We prove that, if $S_Gamma$ contains infinitely many maximal totally geodesic subvarieties, then $Gamma$ is arithmetic. We also prove an Ax-Schanuel Conjecture for $S_Gamma$, similar to the one recently proven by Mok, Pila and Tsimerman. One of the main ingredients in the proofs is to realise $S_Gamma$ inside a period domain for polarised integral variations of Hodge structures and interpret totally geodesic subvarieties as unlikely intersections.

We develop a distributional framework for the shearlet transform $mathcal{S}_{psi}colonmathcal{S}_0(mathbb{R}^2) omathcal{S}(mathbb{S})$ and the shearlet synthesis operator $mathcal{S}^t_{psi}colonmathcal{S}(mathbb{S}) omathcal{S}_0(mathbb{R}^2)$, where $mathcal{S}_0(mathbb{R}^2)$ is the Lizorkin test function space and $mathcal{S}(mathbb{S})$ is the space of highly localized test functions on the standard shearlet group $mathbb{S}$. These spaces and their duals $mathcal{S}_0^prime (mathbb R^2),, mathcal{S}^prime (mathbb{S})$ are called Lizorkin type spaces of test functions and distributions. We analyze the continuity properties of these transforms when the admissible vector $psi$ belongs to $mathcal{S}_0(mathbb{R}^2)$. Then, we define the shearlet transform and the shearlet synthesis operator of Lizorkin type distributions as transpose mappings of the shearlet synthesis operator and the shearlet transform, respectively. They yield continuous mappings from $mathcal{S}_0^prime (mathbb R^2)$ to $mathcal{S}^prime (mathbb{S})$ and from $mathcal{S}^prime (mathbb S)$ to $mathcal{S}_0^prime (mathbb{R}^2)$. Furthermore, we show the consistency of our definition with the shearlet transform defined by direct evaluation of a distribution on the shearlets. The same can be done for the shearlet synthesis operator. Finally, we give a reconstruction formula for Lizorkin type distributions, from which follows that the action of such generalized functions can be written as an absolutely convergent integral over the standard shearlet group.

A reaction-diffusion model was developed describing the spread of the COVID-19 virus considering the mean daily movement of susceptible, exposed and asymptomatic individuals. The model was calibrated using data on the confirmed infection and death from France as well as their initial spatial distribution. First, the system of partial differential equations is studied, then the basic reproduction number, R0 is derived. Second, numerical simulations, based on a combination of level-set and finite differences, shown the spatial spread of COVID-19 from March 16 to June 16. Finally, scenarios of unlockdown are compared according to variation of distancing, or partially spatial lockdown.

In cite{S 2017}, Suh gave a non-existence theorem for Hopf real hypersurfaces in the complex quadric with parallel normal Jacobi operator. Motivated by this result, in this paper, we introduce some generalized conditions named $mathcal C$-parallel or Reeb parallel normal Jacobi operators. By using such weaker parallelisms of normal Jacobi operator, first we can assert a non-existence theorem of Hopf real hypersurfaces with $mathcal C$-parallel normal Jacobi operator in the complex quadric $Q^{m}$, $m geq 3$. Next, we prove that a Hopf real hypersurface has Reeb parallel normal Jacobi operator if and only if it has an $mathfrak A$-isotropic singular normal vector field.

Given spherically symmetric characteristic initial data for the Einstein-scalar field system with a positive cosmological constant, we provide a criterion, in terms of the dimensionless size and dimensionless renormalized mass content of an annular region of the data, for the formation of a future trapped surface. This corresponds to an extension of Christodoulou's classical criterion by the inclusion of the cosmological term.

Classical studies on aspiration-based dynamics suggest that a dissatisfied individual changes strategy without taking into account the success of others. This promotes defection spreading. The imitation-based dynamics allow individuals to imitate successful strategies without taking into account their own-satisfactions. In this article, we propose to study a dynamic based on aspiration which takes into account imitation of successful strategies for dissatisfied individuals. This helps cooperative members to resist. Individuals compare their success to their desired satisfaction level before making a decision to update their strategies. This mechanism helps individuals with a minimum of self-satisfaction to maintain their strategies. If an individual is dissatisfied, it will learn from others by choosing successful strategies. We derive an exact expression of the fixation probability in well-mixed populations as in structured populations in networks. As a result, we show that selection may favor cooperation more than defection in well-mixed populations as in populations ranged over a regular graph. We show that the best scenario is a graph with small connectivity.

We study a 1-cocycle on the fatgraph complex of a punctured surface introduced by Penner. We present an explicit cobounding cochain for this cocycle, whose formula involves a summation over trivalent vertices of a trivalent fatgraph spine. In a similar fashion, we express the symplectic form of the underlying surface of a given fatgraph spine.

In this paper, we derive a formula for the sums of powers of the first $n$ positive integers that involves the hyperharmonic numbers and the Stirling numbers of the second kind. Then, using an explicit representation for the hyperharmonic numbers, we generalize this formula to the sums of powers of an arbitrary arithmetic progression. Moreover, as a by-product, we express the Bernoulli polynomials in terms of the hyperharmonic polynomials and the Stirling numbers of the second kind.

We show that every 4-uniform hypergraph with $n$ vertices and minimum pair degree at least $(5/9+o(1))n^2/2$ contains a tight Hamiltonian cycle. This degree condition is asymptotically optimal.

We construct a 2-equivalence $mathfrak{CohTheory}^ ext{op} simeq mathfrak{TypeSpaceFunc}$. Here $mathfrak{CohTheory}$ is the 2-category of positive theories and $mathfrak{TypeSpaceFunc}$ is the 2-category of type space functors. We give a precise definition of interpretations for positive logic, which will be the 1-cells in $mathfrak{CohTheory}$. The 2-cells are definable homomorphisms. The 2-equivalence restricts to a duality of categories, making precise the philosophy that a theory is `the same' as the collection of its type spaces (i.e. its type space functor).

In characterising those functors that arise as type space functors, we find that they are specific instances of (coherent) hyperdoctrines. This connects two different schools of thought on the logical structure of a theory.

The key ingredient, the Deligne completeness theorem, arises from topos theory, where positive theories have been studied under the name of coherent theories.

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.

Let $Gamma$ be a discrete group acting properly discontinuously and isometrically on the three-dimensional anti-de Sitter space $mathrm{AdS}^{3}$, and $square$ the Laplacian which is a second-order hyperbolic differential operator. We study linear independence of a family of generalized Poincar'{e} series introduced by Kassel-Kobayashi [Adv. Math. 2016], which are defined by the $Gamma$-average of certain eigenfunctions on $mathrm{AdS}^{3}$. We prove that the multiplicities of $L^{2}$-eigenvalues of the hyperbolic Laplacian $square$ on $Gammaackslashmathrm{AdS}^{3}$ are unbounded when $Gamma$ is finitely generated. Moreover, we prove that the multiplicities of extit{stable $L^{2}$-eigenvalues} for compact anti-de Sitter $3$-manifolds are unbounded.

In this paper, we give a criterion of the Gorenstein property of the Ehrhart ring of the stable set polytope of an h-perfect graph: the Ehrhart ring of the stable set polytope of an h-perfect graph $G$ is Gorenstein if and only if (1) sizes of maximal cliques are constant (say $n$) and (2) (a) $n=1$, (b) $n=2$ and there is no odd cycle without chord and length at least 7 or (c) $ngeq 3$ and there is no odd cycle without chord and length at least 5.

We study a two-stage reneging queue with Poisson arrivals, exponential services, and two levels of exponential reneging behaviors, extending the popular Erlang A model that assumes a constant reneging rate. We derive approximate analytical formulas representing performance measures for the two-stage queue following the Markov chain decomposition approach. Our formulas not only give accurate results spanning the heavy-traffic to the light-traffic regimes, but also provide insight into capacity decisions.

The aim of this paper is to obtain a generalized CK-extension theorem in superspace for the bi-axial Dirac operator. In the classical commuting case, this result can be written as a power series of Bessel type of certain differential operators acting on a single initial function. In the superspace setting, novel structures appear in the cases of negative even superdimensions. In these cases, the CK-extension depends on two initial functions on which two power series of differential operators act. These series are not only of Bessel type but they give rise to an additional structure in terms of Appell polynomials. This pattern also is present in the structure of the Pizzetti formula, which describes integration over the supersphere in terms of differential operators. We make this relation explicit by studying the decomposition of the generalized CK-extension into plane waves integrated over the supersphere. Moreover, these results are applied to obtain a decomposition of the Cauchy kernel in superspace into monogenic plane waves, which shall be useful for inverting the super Radon transform.

Let $G=(V,E)$ be a finite graph and $M_G$ be the centered Hardy-Littlewood maximal operator defined there. We found the optimal value $C_{G,p}$ such that the inequality $$Var_{p}(M_{G}f)le C_{G,p}Var_{p}(f)$$ holds for every every $f:V o mathbb{R},$ where $Var_p$ stands for the $p$-variation, when: (i)$G=K_n$ (complete graph) and $pin [frac{ln(4)}{ln(6)},infty)$ or $G=K_4$ and $pin (0,infty)$;(ii) $G=S_n$(star graph) and $1ge pge frac{1}{2}$; $pin (0,frac{1}{2})$ and $nge C(p)<infty$ or $G=S_3$ and $pin (1,infty).$ We also found the optimal value $L_{G,2}$ such that the inequality $$|M_{G}f|_2le L_{G,2}|f|_2$$ holds for every $f:V o mathbb{R}$, when: (i)$G=K_n$ and $nge 3$;(ii)$G=S_n$ and $nge 3.$

For an odd prime $p$, we determined the Brown-Peterson cohomology of $BPU_n$ in dimensions $-(2p-2)leq ileq 2p+2$, where $BPU_n$ is the classifying space of the projective unitary group $PU_n$. We construct a family of $p$-torsion classes $eta_{p,k}in BP^{2p^{k+1}+2}(BPU_n)$ for $p|n$ and $kgeq 0$ and identify their images under the Thom map with well understood cohomology classes in $H^*(BPU_n;mathbb{Z}_{(p)})$.

High-performance implementations of graph algorithms are challenging to implement on new parallel hardware such as GPUs, because of three challenges: (1) difficulty of coming up with graph building blocks, (2) load imbalance on parallel hardware, and (3) graph problems having low arithmetic intensity. To address these challenges, GraphBLAS is an innovative, on-going effort by the graph analytics community to propose building blocks based in sparse linear algebra, which will allow graph algorithms to be expressed in a performant, succinct, composable and portable manner. In this paper, we examine the performance challenges of a linear algebra-based approach to building graph frameworks and describe new design principles for overcoming these bottlenecks. Among the new design principles is exploiting input sparsity, which allows users to write graph algorithms without specifying push and pull direction. Exploiting output sparsity allows users to tell the backend which values of the output in a single vectorized computation they do not want computed. Load-balancing is an important feature for balancing work amongst parallel workers. We describe the important load-balancing features for handling graphs with different characteristics. The design principles described in this paper have been implemented in "GraphBLAST", the first open-source linear algebra-based graph framework on GPU targeting high-performance computing. The results show that on a single GPU, GraphBLAST has on average at least an order of magnitude speedup over previous GraphBLAS implementations SuiteSparse and GBTL, comparable performance to the fastest GPU hardwired primitives and shared-memory graph frameworks Ligra and Gunrock, and better performance than any other GPU graph framework, while offering a simpler and more concise programming model.

Temporal event segmentation of a long video into coherent events requires a high level understanding of activities' temporal features. The event segmentation problem has been tackled by researchers in an offline training scheme, either by providing full, or weak, supervision through manually annotated labels or by self-supervised epoch based training. In this work, we present a continual learning perceptual prediction framework (influenced by cognitive psychology) capable of temporal event segmentation through understanding of the underlying representation of objects within individual frames. Our framework also outputs attention maps which effectively localize and track events-causing objects in each frame. The model is tested on a wildlife monitoring dataset in a continual training manner resulting in $80\%$ recall rate at $20\%$ false positive rate for frame level segmentation. Activity level testing has yielded $80\%$ activity recall rate for one false activity detection every 50 minutes.

Large-scale pretrained language models are the major driving force behind recent improvements in performance on the Winograd Schema Challenge, a widely employed test of common sense reasoning ability. We show, however, with a new diagnostic dataset, that these models are sensitive to linguistic perturbations of the Winograd examples that minimally affect human understanding. Our results highlight interesting differences between humans and language models: language models are more sensitive to number or gender alternations and synonym replacements than humans, and humans are more stable and consistent in their predictions, maintain a much higher absolute performance, and perform better on non-associative instances than associative ones. Overall, humans are correct more often than out-of-the-box models, and the models are sometimes right for the wrong reasons. Finally, we show that fine-tuning on a large, task-specific dataset can offer a solution to these issues.

Event-related potential (ERP) speller can be utilized in device control and communication for locked-in or severely injured patients. However, problems such as inter-subject performance instability and ERP-illiteracy are still unresolved. Therefore, it is necessary to predict classification performance before performing an ERP speller in order to use it efficiently. In this study, we investigated the correlations with ERP speller performance using a resting-state before an ERP speller. In specific, we used spectral power and functional connectivity according to four brain regions and five frequency bands. As a result, the delta power in the frontal region and functional connectivity in the delta, alpha, gamma bands are significantly correlated with the ERP speller performance. Also, we predicted the ERP speller performance using EEG features in the resting-state. These findings may contribute to investigating the ERP-illiteracy and considering the appropriate alternatives for each user.

The quantum Fourier transform brings efficiency in many respects, especially usage of resource, for most operations on quantum computers. In this study, the existing QFT-based and non-QFT-based quantum arithmetic operations are examined. The capabilities of QFT-based addition and multiplication are improved with some modifications. The proposed operations are compared with the nearest quantum arithmetic operations. Furthermore, novel QFT-based subtraction and division operations are presented. The proposed arithmetic operations can perform non-modular operations on all signed numbers without any limitation by using less resources. In addition, novel quantum circuits of two's complement, absolute value and comparison operations are also presented by using the proposed QFT based addition and subtraction operations.

The connection between visual input and tactile sensing is critical for object manipulation tasks such as grasping and pushing. In this work, we introduce the challenging task of estimating a set of tactile physical properties from visual information. We aim to build a model that learns the complex mapping between visual information and tactile physical properties. We construct a first of its kind image-tactile dataset with over 400 multiview image sequences and the corresponding tactile properties. A total of fifteen tactile physical properties across categories including friction, compliance, adhesion, texture, and thermal conductance are measured and then estimated by our models. We develop a cross-modal framework comprised of an adversarial objective and a novel visuo-tactile joint classification loss. Additionally, we develop a neural architecture search framework capable of selecting optimal combinations of viewing angles for estimating a given physical property.

We consider a fair division setting where indivisible items are allocated to agents. Each agent in the setting has strictly negative, zero or strictly positive utility for each item. We, thus, make a distinction between items that are good for some agents and bad for other agents (i.e. mixed), good for everyone (i.e. goods) or bad for everyone (i.e. bads). For this model, we study axiomatic concepts of allocations such as jealousy-freeness up to one item, envy-freeness up to one item and Pareto-optimality. We obtain many new possibility and impossibility results in regard to combinations of these properties. We also investigate new computational tasks related to such combinations. Thus, we advance the state-of-the-art in fair division of mixed manna.

Representation learning is a critical ingredient for natural language processing systems. Recent Transformer language models like BERT learn powerful textual representations, but these models are targeted towards token- and sentence-level training objectives and do not leverage information on inter-document relatedness, which limits their document-level representation power. For applications on scientific documents, such as classification and recommendation, the embeddings power strong performance on end tasks. We propose SPECTER, a new method to generate document-level embedding of scientific documents based on pretraining a Transformer language model on a powerful signal of document-level relatedness: the citation graph. Unlike existing pretrained language models, SPECTER can be easily applied to downstream applications without task-specific fine-tuning. Additionally, to encourage further research on document-level models, we introduce SciDocs, a new evaluation benchmark consisting of seven document-level tasks ranging from citation prediction, to document classification and recommendation. We show that SPECTER outperforms a variety of competitive baselines on the benchmark.

Recent advances in deep learning have facilitated the design of speaker verification systems that directly input raw waveforms. For example, RawNet extracts speaker embeddings from raw waveforms, which simplifies the process pipeline and demonstrates competitive performance. In this study, we improve RawNet by scaling feature maps using various methods. The proposed mechanism utilizes a scale vector that adopts a sigmoid non-linear function. It refers to a vector with dimensionality equal to the number of filters in a given feature map. Using a scale vector, we propose to scale the feature map multiplicatively, additively, or both. In addition, we investigate replacing the first convolution layer with the sinc-convolution layer of SincNet. Experiments performed on the VoxCeleb1 evaluation dataset demonstrate the effectiveness of the proposed methods, and the best performing system reduces the equal error rate by half compared to the original RawNet. Expanded evaluation results obtained using the VoxCeleb1-E and VoxCeleb-H protocols marginally outperform existing state-of-the-art systems.

Existing patient data analytics platforms fail to incorporate information that has context, is personal, and topical to patients. For a recommendation system to give a suitable response to a query or to derive meaningful insights from patient data, it should consider personal information about the patient's health history, including but not limited to their preferences, locations, and life choices that are currently applicable to them. In this review paper, we critique existing literature in this space and also discuss the various research challenges that come with designing, building, and operationalizing a personal health knowledge graph (PHKG) for patients.

Deep neural networks have exhibited promising performance in image super-resolution (SR). Most SR models follow a hierarchical architecture that contains both the cell-level design of computational blocks and the network-level design of the positions of upsampling blocks. However, designing SR models heavily relies on human expertise and is very labor-intensive. More critically, these SR models often contain a huge number of parameters and may not meet the requirements of computation resources in real-world applications. To address the above issues, we propose a Hierarchical Neural Architecture Search (HNAS) method to automatically design promising architectures with different requirements of computation cost. To this end, we design a hierarchical SR search space and propose a hierarchical controller for architecture search. Such a hierarchical controller is able to simultaneously find promising cell-level blocks and network-level positions of upsampling layers. Moreover, to design compact architectures with promising performance, we build a joint reward by considering both the performance and computation cost to guide the search process. Extensive experiments on five benchmark datasets demonstrate the superiority of our method over existing methods.

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.

This paper describes a dataset and protocols for evaluating continuous speech separation algorithms. Most prior studies on speech separation use pre-segmented signals of artificially mixed speech utterances which are mostly emph{fully} overlapped, and the algorithms are evaluated based on signal-to-distortion ratio or similar performance metrics. However, in natural conversations, a speech signal is continuous, containing both overlapped and overlap-free components. In addition, the signal-based metrics have very weak correlations with automatic speech recognition (ASR) accuracy. We think that not only does this make it hard to assess the practical relevance of the tested algorithms, it also hinders researchers from developing systems that can be readily applied to real scenarios. In this paper, we define continuous speech separation (CSS) as a task of generating a set of non-overlapped speech signals from a extit{continuous} audio stream that contains multiple utterances that are emph{partially} overlapped by a varying degree. A new real recorded dataset, called LibriCSS, is derived from LibriSpeech by concatenating the corpus utterances to simulate a conversation and capturing the audio replays with far-field microphones. A Kaldi-based ASR evaluation protocol is also established by using a well-trained multi-conditional acoustic model. By using this dataset, several aspects of a recently proposed speaker-independent CSS algorithm are investigated. The dataset and evaluation scripts are available to facilitate the research in this direction.

For decades, two-player (antagonistic) games on graphs have been a framework of choice for many important problems in theoretical computer science. A notorious one is controller synthesis, which can be rephrased through the game-theoretic metaphor as the quest for a winning strategy of the system in a game against its antagonistic environment. Depending on the specification, optimal strategies might be simple or quite complex, for example having to use (possibly infinite) memory. Hence, research strives to understand which settings allow for simple strategies.

In 2005, Gimbert and Zielonka provided a complete characterization of preference relations (a formal framework to model specifications and game objectives) that admit memoryless optimal strategies for both players. In the last fifteen years however, practical applications have driven the community toward games with complex or multiple objectives, where memory -- finite or infinite -- is almost always required. Despite much effort, the exact frontiers of the class of preference relations that admit finite-memory optimal strategies still elude us.

In this work, we establish a complete characterization of preference relations that admit optimal strategies using arena-independent finite memory, generalizing the work of Gimbert and Zielonka to the finite-memory case. We also prove an equivalent to their celebrated corollary of great practical interest: if both players have optimal (arena-independent-)finite-memory strategies in all one-player games, then it is also the case in all two-player games. Finally, we pinpoint the boundaries of our results with regard to the literature: our work completely covers the case of arena-independent memory (e.g., multiple parity objectives, lower- and upper-bounded energy objectives), and paves the way to the arena-dependent case (e.g., multiple lower-bounded energy objectives).

In this paper, we work on intra-variable handwriting, where the writing samples of an individual can vary significantly. Such within-writer variation throws a challenge for automatic writer inspection, where the state-of-the-art methods do not perform well. To deal with intra-variability, we analyze the idiosyncrasy in individual handwriting. We identify/verify the writer from highly idiosyncratic text-patches. Such patches are detected using a deep recurrent reinforcement learning-based architecture. An idiosyncratic score is assigned to every patch, which is predicted by employing deep regression analysis. For writer identification, we propose a deep neural architecture, which makes the final decision by the idiosyncratic score-induced weighted average of patch-based decisions. For writer verification, we propose two algorithms for patch-fed deep feature aggregation, which assist in authentication using a triplet network. The experiments were performed on two databases, where we obtained encouraging results.

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.

Introduction of spectrum-sharing in 5G and subsequent generation networks demand base-station(s) with the capability to characterize the wideband spectrum spanned over licensed, shared and unlicensed non-contiguous frequency bands. Spectrum characterization involves the identification of vacant bands along with center frequency and parameters (energy, modulation, etc.) of occupied bands. Such characterization at Nyquist sampling is area and power-hungry due to the need for high-speed digitization. Though sub-Nyquist sampling (SNS) offers an excellent alternative when the spectrum is sparse, it suffers from poor performance at low signal to noise ratio (SNR) and demands careful design and integration of digital reconstruction, tunable channelizer and characterization algorithms. In this paper, we propose a novel deep-learning framework via a single unified pipeline to accomplish two tasks: 1)~Reconstruct the signal directly from sub-Nyquist samples, and 2)~Wideband spectrum characterization. The proposed approach eliminates the need for complex signal conditioning between reconstruction and characterization and does not need complex tunable channelizers. We extensively compare the performance of our framework for a wide range of modulation schemes, SNR and channel conditions. We show that the proposed framework outperforms existing SNS based approaches and characterization performance approaches to Nyquist sampling-based framework with an increase in SNR. Easy to design and integrate along with a single unified deep learning framework make the proposed architecture a good candidate for reconfigurable platforms.

Reading comprehension (RC) has been studied in a variety of datasets with the boosted performance brought by deep neural networks. However, the generalization capability of these models across different domains remains unclear. To alleviate this issue, we are going to investigate unsupervised domain adaptation on RC, wherein a model is trained on labeled source domain and to be applied to the target domain with only unlabeled samples. We first show that even with the powerful BERT contextual representation, the performance is still unsatisfactory when the model trained on one dataset is directly applied to another target dataset. To solve this, we provide a novel conditional adversarial self-training method (CASe). Specifically, our approach leverages a BERT model fine-tuned on the source dataset along with the confidence filtering to generate reliable pseudo-labeled samples in the target domain for self-training. On the other hand, it further reduces domain distribution discrepancy through conditional adversarial learning across domains. Extensive experiments show our approach achieves comparable accuracy to supervised models on multiple large-scale benchmark datasets.

Digital Twin technology is an emerging concept that has become the centre of attention for industry and, in more recent years, academia. The advancements in industry 4.0 concepts have facilitated its growth, particularly in the manufacturing industry. The Digital Twin is defined extensively but is best described as the effortless integration of data between a physical and virtual machine in either direction. The challenges, applications, and enabling technologies for Artificial Intelligence, Internet of Things (IoT) and Digital Twins are presented. A review of publications relating to Digital Twins is performed, producing a categorical review of recent papers. The review has categorised them by research areas: manufacturing, healthcare and smart cities, discussing a range of papers that reflect these areas and the current state of research. The paper provides an assessment of the enabling technologies, challenges and open research for Digital Twins.

Robots are required to operate autonomously in response to changing situations. Previously, imitation learning using 4ch-bilateral control was demonstrated to be suitable for imitation of object manipulation. However, cooperative work between humans and robots has not yet been verified in these studies. In this study, the task was expanded by cooperative work between a human and a robot. 4ch-bilateral control was used to collect training data for training robot motion. We focused on serving salad as a task in the home. The task was executed with a spoon and a fork fixed to robots. Adjustment of force was indispensable in manipulating indefinitely shaped objects such as salad. Results confirmed the effectiveness of the proposed method as demonstrated by the success of the task.

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.

Within the field of multilinear algebra, inverses and generalized inverses of tensors based on the Einstein product have been investigated over the past few years. In this paper, we explore the singular value decomposition and full-rank decomposition of arbitrary-order tensors using {it reshape} operation. Applying range and null space of tensors along with the reshape operation; we further study the Moore-Penrose inverse of tensors and their cancellation properties via the Einstein product. Then we discuss weighted Moore-Penrose inverses of arbitrary-order tensors using such product. Following a specific algebraic approach, a few characterizations and representations of these inverses are explored. In addition to this, we obtain a few necessary and sufficient conditions for the reverse-order law to hold for weighted Moore-Penrose inverses of arbitrary-order tensors.

A classical problem in appointment scheduling, with applications in health care, concerns the determination of the patients' arrival times that minimize a cost function that is a weighted sum of mean waiting times and mean idle times. One aspect of this problem is the sequencing problem, which focuses on ordering the patients. We assess the performance of the smallest-variance-first (SVF) rule, which sequences patients in order of increasing variance of their service durations. While it was known that SVF is not always optimal, it has been widely observed that it performs well in practice and simulation. We provide a theoretical justification for this observation by proving, in various settings, quantitative worst-case bounds on the ratio between the cost incurred by the SVF rule and the minimum attainable cost. We also show that, in great generality, SVF is asymptotically optimal, i.e., the ratio approaches 1 as the number of patients grows large. While evaluating policies by considering an approximation ratio is a standard approach in many algorithmic settings, our results appear to be the first of this type in the appointment scheduling literature.

We design and implement the first private and anonymous decentralized crowdsourcing system ZebraLancer, and overcome two fundamental challenges of decentralizing crowdsourcing, i.e., data leakage and identity breach.

First, our outsource-then-prove methodology resolves the tension between the blockchain transparency and the data confidentiality to guarantee the basic utilities/fairness requirements of data crowdsourcing, thus ensuring: (i) a requester will not pay more than what data deserve, according to a policy announced when her task is published via the blockchain; (ii) each worker indeed gets a payment based on the policy, if he submits data to the blockchain; (iii) the above properties are realized not only without a central arbiter, but also without leaking the data to the open blockchain. Second, the transparency of blockchain allows one to infer private information about workers and requesters through their participation history. Simply enabling anonymity is seemingly attempting but will allow malicious workers to submit multiple times to reap rewards. ZebraLancer also overcomes this problem by allowing anonymous requests/submissions without sacrificing accountability. The idea behind is a subtle linkability: if a worker submits twice to a task, anyone can link the submissions, or else he stays anonymous and unlinkable across tasks. To realize this delicate linkability, we put forward a novel cryptographic concept, i.e., the common-prefix-linkable anonymous authentication. We remark the new anonymous authentication scheme might be of independent interest. Finally, we implement our protocol for a common image annotation task and deploy it in a test net of Ethereum. The experiment results show the applicability of our protocol atop the existing real-world blockchain.

A chordless cycle, or equivalently a hole, in a graph $G$ is an induced subgraph of $G$ which is a cycle of length at least $4$. We prove that the ErdH{o}s-P'osa property holds for chordless cycles, which resolves the major open question concerning the ErdH{o}s-P'osa property. Our proof for chordless cycles is constructive: in polynomial time, one can find either $k+1$ vertex-disjoint chordless cycles, or $c_1k^2 log k+c_2$ vertices hitting every chordless cycle for some constants $c_1$ and $c_2$. It immediately implies an approximation algorithm of factor $mathcal{O}(sf{opt}log {sf opt})$ for Chordal Vertex Deletion. We complement our main result by showing that chordless cycles of length at least $ell$ for any fixed $ellge 5$ do not have the ErdH{o}s-P'osa property.

We introduce $Psimathrm{ec}$, a local spectral exterior calculus for the two-sphere $S^2$. $Psimathrm{ec}$ provides a discretization of Cartan's exterior calculus on $S^2$ formed by spherical differential $r$-form wavelets. These are well localized in space and frequency and provide (Stevenson) frames for the homogeneous Sobolev spaces $dot{H}^{-r+1}( Omega_{ u}^{r} , S^2 )$ of differential $r$-forms. At the same time, they satisfy important properties of the exterior calculus, such as the de Rahm complex and the Hodge-Helmholtz decomposition. Through this, $Psimathrm{ec}$ is tailored towards structure preserving discretizations that can adapt to solutions with varying regularity. The construction of $Psimathrm{ec}$ is based on a novel spherical wavelet frame for $L_2(S^2)$ that we obtain by introducing scalable reproducing kernel frames. These extend scalable frames to weighted sampling expansions and provide an alternative to quadrature rules for the discretization of needlet-like scale-discrete wavelets. We verify the practicality of $Psimathrm{ec}$ for numerical computations using the rotating shallow water equations. Our numerical results demonstrate that a $Psimathrm{ec}$-based discretization of the equations attains accuracy comparable to those of spectral methods while using a representation that is well localized in space and frequency.

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.