Transitioning from military to civilian life can take time and can be tricky. Adam talks about how student veteran groups on college campuses can help vets reintegrate socially in their own way and  time.

For many veterans’ spouses, we’ve watched our partners struggle not only with post-traumatic stress disorder (PTSD) but with other mental health conditions, as well. Around 80 percent of people with PTSD wrestle with at least one other co-occurring mental health condition in their lifetime.What many people don’t see is the impact PTSD and comorbidity have on vets’ spouses.

A federal watchdog is recommending that ousted vaccine expert Rick Bright be reinstated while it investigates whether the Trump administration retaliated against his whistleblower complaints when it removed him from a key post overseeing the coronavirus response, Bright's lawyers said Friday.

In these strange times when everything is connected, it’s too easy to feel lonely and detached. Yes, everybody is just one message away, but there is always something in the way — deadlines to meet, Slack messages to reply, or urgent PRs to review. Connections need time and space to grow, just like learning, and conferences are a great way to find that time and that space. In fact, with SmashingConfs, we’ve always been trying to create such friendly and inclusive spaces.

The Godox SL series LED lights have proven to be extremely popular due to their low cost. Two of the models in that range, the SL150 and SL200 have seen a Mark II update today, according to an email that Godox has been sending out today. One of the features of the new SL150II and […]

The post Godox’s new SL150/SL200 Mark II LED lights offer fanless “silent mode” operation appeared first on DIY Photography.

In this article, we characterize nearly invariant subspaces of finite defect for the backward shift operator acting on the vector-valued Hardy space which is a vectorial generalization of a result of Chalendar-Gallardo-Partington (C-G-P). Using this characterization of nearly invariant subspace under the backward shift we completely describe the almost invariant subspaces for the shift and its adjoint acting on the vector valued Hardy space.

An inverse spectral problem for the Sturm-Liouville operator with a singular potential from the class $W_2^{-1}$ is solved by the method of spectral mappings. We prove the uniqueness theorem, develop a constructive algorithm for solution, and obtain necessary and sufficient conditions of solvability for the inverse problem in the self-adjoint and the non-self-adjoint cases

Applying the equivariant moving frames method, we construct convergent normal forms for real-analytic 5-dimensional totally nondegenerate CR submanifolds of C^4. These CR manifolds are divided into several biholomorphically inequivalent subclasses, each of which has its own complete normal form. Moreover it is shown that, biholomorphically, Beloshapka's cubic model is the unique member of this class with the maximum possible dimension seven of the corresponding algebra of infinitesimal CR automorphisms. Our results are also useful in the study of biholomorphic equivalence problem between CR manifolds, in question.

In this article, we prove that the completeness of the Hamilton flow and essential self-dajointness are equivalent for real principal type operators on the circle. Moreover, we study spectral properties of these operators.

We show weak-strong uniqueness and stability results for the motion of a two or three dimensional fluid governed by the Navier-Stokes equation interacting with a flexible, elastic plate of Koiter type. The plate is situated at the top of the fluid and as such determines the variable part of a time changing domain (that is hence a part of the solution) containing the fluid. The uniqueness result is a consequence of a stability estimate where the difference of two solutions is estimated by the distance of the initial values and outer forces. For that we introduce a methodology that overcomes the problem that the two (variable in time) domains of the fluid velocities and pressures are not the same. The estimate holds under the assumption that one of the two weak solutions possesses some additional higher regularity. The additional regularity is exclusively requested for the velocity of one of the solutions resembling the celebrated Ladyzhenskaya-Prodi-Serrin conditions in the framework of variable domains.

Let $chi_{Delta}(mathbb{R}^{n})$ denote the minimum number of colors needed to color $mathbb{R}^{n}$ so that there will not be a monochromatic equilateral triangle with side length $1$. Using the slice rank method, we reprove a result of Frankl and Rodl, and show that $chi_{Delta}left(mathbb{R}^{n} ight)$ grows exponentially with $n$. This technique substantially improves upon the best known quantitative lower bounds for $chi_{Delta}left(mathbb{R}^{n} ight)$, and we obtain [ chi_{Delta}left(mathbb{R}^{n} ight)>(1.01446+o(1))^{n}. ]

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.

We introduce primal and dual stochastic gradient oracle methods for decentralized convex optimization problems. Both for primal and dual oracles the proposed methods are optimal in terms of the number of communication steps. However, for all classes of the objective, the optimality in terms of the number of oracle calls per node in the class of methods with optimal number of communication steps takes place only up to a logarithmic factor and the notion of smoothness. By using mini-batching technique we show that all proposed methods with stochastic oracle can be additionally parallelized at each node.

The article is devoted to the expansion of iterated Stratonovich stochastic integrals of arbitrary multiplicity $k$ $(kinmathbb{N})$ based on the generalized iterated Fourier series. The case of Fourier-Legendre series as well as the case of trigonotemric Fourier series are considered in details. The obtained expansion provides a possibility to represent the iterated Stratonovich stochastic integral in the form of iterated series of products of standard Gaussian random variables. Convergence in the mean of degree $2n$ $(nin mathbb{N})$ of the expansion is proved. Some modifications of the mentioned expansion were derived for the case $k=2$. One of them is based of multiple trigonomentric Fourier series converging almost everywhere in the square $[t, T]^2$. The results of the article can be applied to the numerical solution of Ito stochastic differential equations.

Axial algebras are non-associative algebras generated by semisimple idempotents whose adjoint actions obey a fusion law. Axial algebras that are generated by two such idempotents play a crucial role in the theory. We classify all primitive 2-generated axial algebras whose fusion laws have two eigenvalues and all graded primitive 2-generated axial algebras whose fusion laws have three eigenvalues. This represents a significant broadening in our understanding of axial algebras.

Among all dissipative solutions of the multi-dimensional isentropic Euler equations there exists at least one that minimizes the acceleration, which implies that the solution is as close to being a weak solution as possible. The argument is based on a suitable selection procedure.

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.

In this article, we prove that if $R$ is a finitely generated ring over $mathbb{Z}$ of dimension $d, dgeq2, frac{1}{d!}in R$, then any unimodular row over $R[X]$ of length $d+1$ can be mapped to a factorial row by elementary transformations.

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.

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.

This is the second of two papers in which we construct formal power series solutions in external parameters to the vacuum Einstein equations, implementing one bounce for the Belinskii-Khalatnikov-Lifshitz (BKL) proposal for spatially inhomogeneous spacetimes. Here we show that spatially inhomogeneous perturbations of spatially homogeneous elements are unobstructed. A spectral sequence for a filtered complex, and a homological contraction based on gauge-fixing, are used to do this.

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 information theory, the so-called log-sum inequality is fundamental and a kind of generalization of the non-nagativity for the relative entropy. In this paper, we show the generalized log-sum inequality for two functions defined for scalars. We also give a new result for commutative matrices. In addition, we demonstrate further results for general non-commutative positive semi-definite matrices.

The congruence subgroup problem for a finitely generated group $Gamma$ and $Gleq Aut(Gamma)$ asks whether the map $hat{G} o Aut(hat{Gamma})$ is injective, or more generally, what is its kernel $Cleft(G,Gamma ight)$? Here $hat{X}$ denotes the profinite completion of $X$. In the case $G=Aut(Gamma)$ we denote $Cleft(Gamma ight)=Cleft(Aut(Gamma),Gamma ight)$.

Let $Gamma$ be a finitely generated group, $ar{Gamma}=Gamma/[Gamma,Gamma]$, and $Gamma^{*}=ar{Gamma}/tor(ar{Gamma})congmathbb{Z}^{(d)}$. Denote $Aut^{*}(Gamma)= extrm{Im}(Aut(Gamma) o Aut(Gamma^{*}))leq GL_{d}(mathbb{Z})$. In this paper we show that when $Gamma$ is nilpotent, there is a canonical isomorphism $Cleft(Gamma ight)simeq C(Aut^{*}(Gamma),Gamma^{*})$. In other words, $Cleft(Gamma ight)$ is completely determined by the solution to the classical congruence subgroup problem for the arithmetic group $Aut^{*}(Gamma)$.

In particular, in the case where $Gamma=Psi_{n,c}$ is a finitely generated free nilpotent group of class $c$ on $n$ elements, we get that $C(Psi_{n,c})=C(mathbb{Z}^{(n)})={e}$ whenever $ngeq3$, and $C(Psi_{2,c})=C(mathbb{Z}^{(2)})=hat{F}_{omega}$ = the free profinite group on countable number of generators.

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 $nge 3.$

We introduce natural deformation classes of generalized K"ahler structures using the Courant symmetry group. We show that these yield natural extensions of the notions of K"ahler class and K"ahler cone to generalized K"ahler geometry. Lastly we show that the generalized K"ahler-Ricci flow preserves this generalized K"ahler cone, and the underlying real Poisson tensor.

The main purpose of this paper is to study and characterize the existing of general asymptotic regional gradient observer which observe the current gradient state of the original system in connection with gradient strategic sensors. Thus, we give an approach based to Luenberger observer theory of linear distributed parameter systems which is enabled to determinate asymptotically regional gradient estimator of current gradient system state. More precisely, under which condition the notion of asymptotic regional gradient observability can be achieved. Furthermore, we show that the measurement structures allows the existence of general asymptotic regional gradient observer and we give a sufficient condition for such asymptotic regional gradient observer in general case. We also show that, there exists a dynamical system for the considered system is not general asymptotic gradient observer in the usual sense, but it may be general asymptotic regional gradient observer. Then, for this purpose we present various results related to different types of sensor structures, domains and boundary conditions in two dimensional distributed diffusion systems

We show that a random puncturing of a code with good distance is list recoverable beyond the Johnson bound. In particular, this implies that there are Reed-Solomon codes that are list recoverable beyond the Johnson bound. It was previously known that there are Reed-Solomon codes that do not have this property. As an immediate corollary to our main theorem, we obtain better degree bounds on unbalanced expanders that come from Reed-Solomon codes.

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.

Image analysis in the field of digital pathology has recently gained increased popularity. The use of high-quality whole slide scanners enables the fast acquisition of large amounts of image data, showing extensive context and microscopic detail at the same time. Simultaneously, novel machine learning algorithms have boosted the performance of image analysis approaches. In this paper, we focus on a particularly powerful class of architectures, called Generative Adversarial Networks (GANs), applied to histological image data. Besides improving performance, GANs also enable application scenarios in this field, which were previously intractable. However, GANs could exhibit a potential for introducing bias. Hereby, we summarize the recent state-of-the-art developments in a generalizing notation, present the main applications of GANs and give an outlook of some chosen promising approaches and their possible future applications. In addition, we identify currently unavailable methods with potential for future applications.

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.

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.

How to generate testing scenario libraries for connected and automated vehicles (CAVs) is a major challenge faced by the industry. In previous studies, to evaluate maneuver challenge of a scenario, surrogate models (SMs) are often used without explicit knowledge of the CAV under test. However, performance dissimilarities between the SM and the CAV under test usually exist, and it can lead to the generation of suboptimal scenario libraries. In this paper, an adaptive testing scenario library generation (ATSLG) method is proposed to solve this problem. A customized testing scenario library for a specific CAV model is generated through an adaptive process. To compensate the performance dissimilarities and leverage each test of the CAV, Bayesian optimization techniques are applied with classification-based Gaussian Process Regression and a new-designed acquisition function. Comparing with a pre-determined library, a CAV can be tested and evaluated in a more efficient manner with the customized library. To validate the proposed method, a cut-in case study was performed and the results demonstrate that the proposed method can further accelerate the evaluation process by a few orders of magnitude.

We live and cooperate in networks. However, links in networks only allow for pairwise interactions, thus making the framework suitable for dyadic games, but not for games that are played in groups of more than two players. To remedy this, we introduce higher-order interactions, where a link can connect more than two individuals, and study their evolutionary dynamics. We first consider a public goods game on a uniform hypergraph, showing that it corresponds to the replicator dynamics in the well-mixed limit, and providing an exact theoretical foundation to study cooperation in networked groups. We also extend the analysis to heterogeneous hypergraphs that describe interactions of groups of different sizes and characterize the evolution of cooperation in such cases. Finally, we apply our new formulation to study the nature of group dynamics in real systems, showing how to extract the actual dependence of the synergy factor on the size of a group from real-world collaboration data in science and technology. Our work is a first step towards the implementation of new actions to boost cooperation in social groups.

Interaction languages such as MSC are often associated with formal semantics by means of translations into distinct behavioral formalisms such as automatas or Petri nets. In contrast to translational approaches we propose an operational approach. Its principle is to identify which elementary communication actions can be immediately executed, and then to compute, for every such action, a new interaction representing the possible continuations to its execution. We also define an algorithm for checking the validity of execution traces (i.e. whether or not they belong to an interaction's semantics). Algorithms for semantic computation and trace validity are analyzed by means of experiments.

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.

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.

Generative feature matching network (GFMN) is an approach for training implicit generative models for images by performing moment matching on features from pre-trained neural networks. In this paper, we present new GFMN formulations that are effective for sequential data. Our experimental results show the effectiveness of the proposed method, SeqGFMN, for three distinct generation tasks in English: unconditional text generation, class-conditional text generation, and unsupervised text style transfer. SeqGFMN is stable to train and outperforms various adversarial approaches for text generation and text style transfer.

Domain of mathematical logic in computers is dominated by automated theorem provers (ATP) and interactive theorem provers (ITP). Both of these are hard to access by AI from the human-imitation approach: ATPs often use human-unfriendly logical foundations while ITPs are meant for formalizing existing proofs rather than problem solving. We aim to create a simple human-friendly logical system for mathematical problem solving. We picked the case study of Euclidean geometry as it can be easily visualized, has simple logic, and yet potentially offers many high-school problems of various difficulty levels. To make the environment user friendly, we abandoned strict logic required by ITPs, allowing to infer topological facts from pictures. We present our system for Euclidean geometry, together with a graphical application GeoLogic, similar to GeoGebra, which allows users to interactively study and prove properties about the geometrical setup.

We consider the problem of efficiently simulating population protocols. In the population model, we are given a distributed system of $n$ agents modeled as identical finite-state machines. In each time step, a pair of agents is selected uniformly at random to interact. In an interaction, agents update their states according to a common transition function. We empirically and analytically analyze two classes of simulators for this model.

First, we consider sequential simulators executing one interaction after the other. Key to the performance of these simulators is the data structure storing the agents' states. For our analysis, we consider plain arrays, binary search trees, and a novel Dynamic Alias Table data structure.

Secondly, we consider batch processing to efficiently update the states of multiple independent agents in one step. For many protocols considered in literature, our simulator requires amortized sub-constant time per interaction and is fast in practice: given a fixed time budget, the implementation of our batched simulator is able to simulate population protocols several orders of magnitude larger compared to the sequential competitors, and can carry out $2^{50}$ interactions among the same number of agents in less than 400s.

We present a novel numerical scheme to approximate the solution map $smapsto u(s) := mathcal{L}^{-s}f$ to partial differential equations involving fractional elliptic operators. Reinterpreting $mathcal{L}^{-s}$ as interpolation operator allows us to derive an integral representation of $u(s)$ which includes solutions to parametrized reaction-diffusion problems. We propose a reduced basis strategy on top of a finite element method to approximate its integrand. Unlike prior works, we deduce the choice of snapshots for the reduced basis procedure analytically. Avoiding further discretization, the integral is interpreted in a spectral setting to evaluate the surrogate directly. Its computation boils down to a matrix approximation $L$ of the operator whose inverse is projected to a low-dimensional space, where explicit diagonalization is feasible. The universal character of the underlying $s$-independent reduced space allows the approximation of $(u(s))_{sin(0,1)}$ in its entirety. We prove exponential convergence rates and confirm the analysis with a variety of numerical examples.

Further improvements are proposed in the second part of this investigation to avoid inversion of $L$. Instead, we directly project the matrix to the reduced space, where its negative fractional power is evaluated. A numerical comparison with the predecessor highlights its competitive performance.

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.

We present a new mouse cursor designed to facilitate the use of the mouse by people with peripheral vision loss. The pointer consists of a collection of converging straight lines covering the whole screen and following the position of the mouse cursor. We measured its positive effects with a group of participants with peripheral vision loss of different kinds and we found that it can reduce by a factor of 7 the time required to complete a targeting task using the mouse. Using eye tracking, we show that this system makes it possible to initiate the movement towards the target without having to precisely locate the mouse pointer. Using Fitts' Law, we compare these performances with those of full visual field users in order to understand the relation between the accuracy of the estimated mouse cursor position and the index of performance obtained with our tool.

Image-based tracking of medical instruments is an integral part of many surgical data science applications. Previous research has addressed the tasks of detecting, segmenting and tracking medical instruments based on laparoscopic video data. However, the methods proposed still tend to fail when applied to challenging images and do not generalize well to data they have not been trained on. This paper introduces the Heidelberg Colorectal (HeiCo) data set - the first publicly available data set enabling comprehensive benchmarking of medical instrument detection and segmentation algorithms with a specific emphasis on robustness and generalization capabilities of the methods. Our data set comprises 30 laparoscopic videos and corresponding sensor data from medical devices in the operating room for three different types of laparoscopic surgery. Annotations include surgical phase labels for all frames in the videos as well as instance-wise segmentation masks for surgical instruments in more than 10,000 individual frames. The data has successfully been used to organize international competitions in the scope of the Endoscopic Vision Challenges (EndoVis) 2017 and 2019.

One of the main open problems in the qualitative theory of real planar differential systems is the study of limit cycles. In this article, we present an algorithmic approach for detecting how many limit cycles can bifurcate from the periodic orbits of a given polynomial differential center when it is perturbed inside a class of polynomial differential systems via the averaging method. We propose four symbolic algorithms to implement the averaging method. The first algorithm is based on the change of polar coordinates that allows one to transform a considered differential system to the normal form of averaging. The second algorithm is used to derive the solutions of certain differential systems associated to the unperturbed term of the normal of averaging. The third algorithm exploits the partial Bell polynomials and allows one to compute the integral formula of the averaged functions at any order. The last algorithm is based on the aforementioned algorithms and determines the exact expressions of the averaged functions for the considered differential systems. The implementation of our algorithms is discussed and evaluated using several examples. The experimental results have extended the existing relevant results for certain classes of differential systems.

We empirically evaluate an undervolting technique, i.e., underscaling the circuit supply voltage below the nominal level, to improve the power-efficiency of Convolutional Neural Network (CNN) accelerators mapped to Field Programmable Gate Arrays (FPGAs). Undervolting below a safe voltage level can lead to timing faults due to excessive circuit latency increase. We evaluate the reliability-power trade-off for such accelerators. Specifically, we experimentally study the reduced-voltage operation of multiple components of real FPGAs, characterize the corresponding reliability behavior of CNN accelerators, propose techniques to minimize the drawbacks of reduced-voltage operation, and combine undervolting with architectural CNN optimization techniques, i.e., quantization and pruning. We investigate the effect of environmental temperature on the reliability-power trade-off of such accelerators. We perform experiments on three identical samples of modern Xilinx ZCU102 FPGA platforms with five state-of-the-art image classification CNN benchmarks. This approach allows us to study the effects of our undervolting technique for both software and hardware variability. We achieve more than 3X power-efficiency (GOPs/W) gain via undervolting. 2.6X of this gain is the result of eliminating the voltage guardband region, i.e., the safe voltage region below the nominal level that is set by FPGA vendor to ensure correct functionality in worst-case environmental and circuit conditions. 43% of the power-efficiency gain is due to further undervolting below the guardband, which comes at the cost of accuracy loss in the CNN accelerator. We evaluate an effective frequency underscaling technique that prevents this accuracy loss, and find that it reduces the power-efficiency gain from 43% to 25%.

Thin structures, such as wire-frame sculptures, fences, cables, power lines, and tree branches, are common in the real world.

It is extremely challenging to acquire their 3D digital models using traditional image-based or depth-based reconstruction methods because thin structures often lack distinct point features and have severe self-occlusion.

We propose the first approach that simultaneously estimates camera motion and reconstructs the geometry of complex 3D thin structures in high quality from a color video captured by a handheld camera.

Specifically, we present a new curve-based approach to estimate accurate camera poses by establishing correspondences between featureless thin objects in the foreground in consecutive video frames, without requiring visual texture in the background scene to lock on.

Enabled by this effective curve-based camera pose estimation strategy, we develop an iterative optimization method with tailored measures on geometry, topology as well as self-occlusion handling for reconstructing 3D thin structures.

Extensive validations on a variety of thin structures show that our method achieves accurate camera pose estimation and faithful reconstruction of 3D thin structures with complex shape and topology at a level that has not been attained by other existing reconstruction methods.

Despite recent progress on computer vision and natural language processing, developing video understanding intelligence is still hard to achieve due to the intrinsic difficulty of story in video. Moreover, there is not a theoretical metric for evaluating the degree of video understanding. In this paper, we propose a novel video question answering (Video QA) task, DramaQA, for a comprehensive understanding of the video story. The DramaQA focused on two perspectives: 1) hierarchical QAs as an evaluation metric based on the cognitive developmental stages of human intelligence. 2) character-centered video annotations to model local coherence of the story. Our dataset is built upon the TV drama "Another Miss Oh" and it contains 16,191 QA pairs from 23,928 various length video clips, with each QA pair belonging to one of four difficulty levels. We provide 217,308 annotated images with rich character-centered annotations, including visual bounding boxes, behaviors, and emotions of main characters, and coreference resolved scripts. Additionally, we provide analyses of the dataset as well as Dual Matching Multistream model which effectively learns character-centered representations of video to answer questions about the video. We are planning to release our dataset and model publicly for research purposes and expect that our work will provide a new perspective on video story understanding research.