• arXiv.cs.RO Pub Date : 2020-01-15
Andreas Kamilaris; Nicolo Botteghi

As the Internet of Things (IoT) penetrates different domains and application areas, it has recently entered also the world of robotics. Robotics constitutes a modern and fast-evolving technology, increasingly being used in industrial, commercial and domestic settings. IoT, together with the Web of Things (WoT) could provide many benefits to robotic systems. Some of the benefits of IoT in robotics have been discussed in related work. This paper moves one step further, studying the actual current use of IoT in robotics, through various real-world examples encountered through a bibliographic research. The paper also examines the potential ofWoT, together with robotic systems, investigating which concepts, characteristics, architectures, hardware, software and communication methods of IoT are used in existing robotic systems, which sensors and actions are incorporated in IoT-based robots, as well as in which application areas. Finally, the current application of WoT in robotics is examined and discussed.

更新日期：2020-01-17
• arXiv.cs.RO Pub Date : 2020-01-16
Takuya Ohashi; Yosuke Ikegami; Yoshihiko Nakamura

Although many studies have been made on markerless motion capture, it has not been applied to real sports or concerts. In this paper, we propose a markerless motion capture method with spatiotemporal accuracy and smoothness from multiple cameras, even in wide and multi-person environments. The key idea is predicting each person's 3D pose and determining the bounding box of multi-camera images small enough. This prediction and spatiotemporal filtering based on human skeletal structure eases 3D reconstruction of the person and yields accuracy. The accurate 3D reconstruction is then used to predict the bounding box of each camera image in the next frame. This is a feedback from 3D motion to 2D pose, and provides a synergetic effect to the total performance of video motion capture. We demonstrate the method using various datasets and a real sports field. The experimental results show the mean per joint position error was 31.6mm and the percentage of correct parts was 99.3% under five people moving dynamically, with satisfying the range of motion. Video demonstration, datasets, and additional materials are posted on our project page.

更新日期：2020-01-17
• arXiv.cs.RO Pub Date : 2020-01-16
Jesse Haviland; Feras Dayoub; Peter Corke

In this paper we consider the problem of the final approach stage of closed-loop grasping where RGB-D cameras are no longer able to provide valid depth information. This is essential for grasping non-stationary objects; a situation where current robotic grasping controllers fail. We predict the image-plane coordinates of observed image features at the final grasp pose and use image-based visual servoing to guide the robot to that pose. Image-based visual servoing is a well established control technique that moves a camera in 3D space so as to drive the image-plane feature configuration to some goal state. In previous works the goal feature configuration is assumed to be known but for some applications this may not be feasible, if for example the motion is being performed for the first time with respect to a scene. Our proposed method provides robustness with respect to scene motion during the final phase of grasping as well as to errors in the robot kinematic control. We provide experimental results in the context of dynamic closed-loop grasping.

更新日期：2020-01-17
• arXiv.cs.RO Pub Date : 2020-01-16
Hsu-kuang Chiu; Antonio Prioletti; Jie Li; Jeannette Bohg

3D multi-object tracking is a key module in autonomous driving applications that provides a reliable dynamic representation of the world to the planning module. In this paper, we present our on-line tracking method, which made the first place in the NuScenes Tracking Challenge, held at the AI Driving Olympics Workshop at NeurIPS 2019. Our method estimates the object states by adopting a Kalman Filter. We initialize the state covariance as well as the process and observation noise covariance with statistics from the training set. We also use the stochastic information from the Kalman Filter in the data association step by measuring the Mahalanobis distance between the predicted object states and current object detections. Our experimental results on the NuScenes validation and test set show that our method outperforms the AB3DMOT baseline method by a large margin in the Average Multi-Object Tracking Accuracy (AMOTA) metric.

更新日期：2020-01-17
• arXiv.cs.RO Pub Date : 2020-01-16
Linh Kästner; Daniel Dimitrov; Jens Lambrecht

Augmented Reality has been subject to various integration efforts within industries due to its ability to enhance human machine interaction and understanding. Neural networks have achieved remarkable results in areas of computer vision, which bear great potential to assist and facilitate an enhanced Augmented Reality experience. However, most neural networks are computationally intensive and demand huge processing power thus, are not suitable for deployment on Augmented Reality devices. In this work we propose a method to deploy state of the art neural networks for real time 3D object localization on augmented reality devices. As a result, we provide a more automated method of calibrating the AR devices with mobile robotic systems. To accelerate the calibration process and enhance user experience, we focus on fast 2D detection approaches which are extracting the 3D pose of the object fast and accurately by using only 2D input. The results are implemented into an Augmented Reality application for intuitive robot control and sensor data visualization. For the 6D annotation of 2D images, we developed an annotation tool, which is, to our knowledge, the first open source tool to be available. We achieve feasible results which are generally applicable to any AR device thus making this work promising for further research in combining high demanding neural networks with Internet of Things devices.

更新日期：2020-01-17
• arXiv.cs.RO Pub Date : 2020-01-16

Probabilistic 3D map has been applied to object segmentation with multiple camera viewpoints, however, conventional methods lack of real-time efficiency and functionality of multilabel object mapping. In this paper, we propose a method to generate three-dimensional map with multilabel occupancy in real-time. Extending our previous work in which only target label occupancy is mapped, we achieve multilabel object segmentation in a single looking around action. We evaluate our method by testing segmentation accuracy with 39 different objects, and applying it to a manipulation task of multiple objects in the experiments. Our mapping-based method outperforms the conventional projection-based method by 40 - 96\% relative (12.6 mean $IU_{3d}$), and robot successfully recognizes (86.9\%) and manipulates multiple objects (60.7\%) in an environment with heavy occlusions.

更新日期：2020-01-17
• arXiv.cs.RO Pub Date : 2020-01-04
German I. Parisi

The robust recognition and assessment of human actions are crucial in human-robot interaction (HRI) domains. While state-of-the-art models of action perception show remarkable results in large-scale action datasets, they mostly lack the flexibility, robustness, and scalability needed to operate in natural HRI scenarios which require the continuous acquisition of sensory information as well as the classification or assessment of human body patterns in real time. In this chapter, I introduce a set of hierarchical models for the learning and recognition of actions from depth maps and RGB images through the use of neural network self-organization. A particularity of these models is the use of growing self-organizing networks that quickly adapt to non-stationary distributions and implement dedicated mechanisms for continual learning from temporally correlated input.

更新日期：2020-01-17
• arXiv.cs.RO Pub Date : 2019-12-28
Cansu Sancaktar; Pablo Lanillos

We present a pixel-based deep Active Inference algorithm (PixelAI) inspired in human body perception and successfully validated in robot body perception and action as a use case. Our algorithm combines the free energy principle from neuroscience, rooted in variational inference, with deep convolutional decoders to scale the algorithm to directly deal with images input and provide online adaptive inference. The approach enables the robot to perform 1) dynamical body estimation of arm using only raw monocular camera images and 2) autonomous reaching to "imagined" arm poses in the visual space. We statistically analyzed the algorithm performance in a simulated and a real Nao robot. Results show how the same algorithm deals with both perception an action, modelled as an inference optimization problem.

更新日期：2020-01-17
• arXiv.cs.RO Pub Date : 2020-01-09
Siddhartha Vibhu Pharswan; Mohit Vohra; Ashish Kumar; Laxmidhar Behera

One of the main challenges in the vision-based grasping is the selection of feasible grasp regions while interacting with novel objects. Recent approaches exploit the power of the convolutional neural network (CNN) to achieve accurate grasping at the cost of high computational power and time. In this paper, we present a novel unsupervised learning based algorithm for the selection of feasible grasp regions. Unsupervised learning infers the pattern in data-set without any external labels. We apply k-means clustering on the image plane to identify the grasp regions, followed by an axis assignment method. We define a novel concept of Grasp Decide Index (GDI) to select the best grasp pose in image plane. We have conducted several experiments in clutter or isolated environment on standard objects of Amazon Robotics Challenge 2017 and Amazon Picking Challenge 2016. We compare the results with prior learning based approaches to validate the robustness and adaptive nature of our algorithm for a variety of novel objects in different domains.

更新日期：2020-01-17
• arXiv.cs.RO Pub Date : 2020-01-11
Richard Savery; Ryan Rose; Gil Weinberg

As human-robot collaboration opportunities continue to expand, trust becomes ever more important for full engagement and utilization of robots. Affective trust, built on emotional relationship and interpersonal bonds is particularly critical as it is more resilient to mistakes and increases the willingness to collaborate. In this paper we present a novel model built on music-driven emotional prosody and gestures that encourages the perception of a robotic identity, designed to avoid uncanny valley. Symbolic musical phrases were generated and tagged with emotional information by human musicians. These phrases controlled a synthesis engine playing back pre-rendered audio samples generated through interpolation of phonemes and electronic instruments. Gestures were also driven by the symbolic phrases, encoding the emotion from the musical phrase to low degree-of-freedom movements. Through a user study we showed that our system was able to accurately portray a range of emotions to the user. We also showed with a significant result that our non-linguistic audio generation achieved an 8% higher mean of average trust than using a state-of-the-art text-to-speech system.

更新日期：2020-01-17
• arXiv.cs.RO Pub Date : 2020-01-16
Mycal Tucker; Yilun Zhou; Julie Shah

Robotic agents must adopt existing social conventions in order to be effective teammates. These social conventions, such as driving on the right or left side of the road, are arbitrary choices among optimal policies, but all agents on a successful team must use the same convention. Prior work has identified a method of combining self-play with paired input-output data gathered from existing agents in order to learn their social convention without interacting with them. We build upon this work by introducing a technique called Adversarial Self-Play (ASP) that uses adversarial training to shape the space of possible learned policies and substantially improves learning efficiency. ASP only requires the addition of unpaired data: a dataset of outputs produced by the social convention without associated inputs. Theoretical analysis reveals how ASP shapes the policy space and the circumstances (when behaviors are clustered or exhibit some other structure) under which it offers the greatest benefits. Empirical results across three domains confirm ASP's advantages: it produces models that more closely match the desired social convention when given as few as two paired datapoints.

更新日期：2020-01-17
• arXiv.cs.RO Pub Date : 2019-09-10
Hung Pham; Quang-Cuong Pham

Controlling contacts is truly challenging, and this has been a major hurdle to deploying industrial robots into unstructured/human-centric environments. More specifically, the main challenges are: (i) how to ensure stability at all times; (ii) how to satisfy task-specific performance specifications; (iii) how to achieve (i) and (ii) under environment uncertainty, robot parameters uncertainty, sensor and actuator time delays, external perturbations, etc. Here, we propose a new approach -- Convex Controller Synthesis (CCS) -- to tackle the above challenges based on robust control theory and convex optimization. In two physical interaction tasks -- robot hand guiding and sliding on surfaces with different and unknown stiffnesses -- we show that CCS controllers outperform their classical counterparts in an essential way.

更新日期：2020-01-17
• arXiv.cs.RO Pub Date : 2019-11-20
Yuyao Shi; Mohan Rajesh Elara; Anh Vu Le; Veerajagadheswar Prabakaran; Kristin L. Wood

The research interest in mobile robots with independent steering wheels has been increasing over recent years due to their high mobility and better payload capacity over the systems using omnidirectional wheels. However, with more controllable degrees of freedom, almost all of the platforms include redundancy which is modeled using the instantaneous center of rotation (ICR). This paper deals with a Tetris inspired floor cleaning robot hTetro which consists of four interconnected differential-drive units, i.e., each module has a differential drive unit, which can steer individually. Differing from most other steerable wheeled mobile robots, the wheel arrangement of this robot changes because of its self-reconfigurability. In this paper, we proposed a robust path tracking controller that can handle discontinuous trajectories and sudden orientation changes. Singularity problems are resolved on both the mechanical aspect and control aspect. The controller is tested experimentally with the self-reconfigurable robotic platform hero, and results are discussed.

更新日期：2020-01-17
• arXiv.cs.NA Pub Date : 2020-01-15
Steffen Börm

Boundary element methods (BEM) reduce a partial differential equation in a domain to an integral equation on the domain's boundary. They are particularly attractive for solving problems on unbounded domains, but handling the dense matrices corresponding to the integral operators requires efficient algorithms. This article describes two approaches that allow us to solve boundary element equations on surface meshes consisting of several million of triangles while preserving the optimal convergence rates of the Galerkin discretization.

更新日期：2020-01-17
• arXiv.cs.NA Pub Date : 2020-01-15
Karl Erik Holter; Miroslav Kuchta; Kent-Andre Mardal

In many applications, one wants to model physical systems consisting of two different physical processes in two different domains that are coupled across a common interface. A crucial challenge is then that the solutions of the two different domains often depend critically on the interaction at the interface and therefore the problem cannot be easily decoupled into its subproblems. Here, we present a framework for finding robust preconditioners for a fairly general class of such problems by exploiting operators representing fractional and weighted Laplacians at the interface. Furthermore, we show feasibility of the framework for two common multiphysics problems; namely the Darcy-Stokes problem and a fluid--structure interaction problem. Numerical experiments that demonstrate the effectiveness of the approach are included.

更新日期：2020-01-17
• arXiv.cs.NA Pub Date : 2020-01-15
Karl Erik Holter; Miroslav Kuchta; Kent-Andre Mardal

The coupled Darcy-Stokes problem is widely used for modeling fluid transport in physical systems consisting of a porous part and a free part. In this work we consider preconditioners for monolitic solution algorithms of the coupled Darcy-Stokes problem, where the Darcy problem is in primal form. We employ the operator preconditioning framework and utilize a fractional solver at the interface between the problems to obtain order optimal schemes that are robust with respect to the material parameters, i.e. the permeability, viscosity and Beavers-Joseph-Saffman parameter. Our approach is similar to our earlier work, but since the Darcy problem is in primal form, the mass conservation at the interface introduces some challenges. These challenges will be specifically addressed in this paper. Numerical experiments illustrating the performance are provided. The preconditioner is posed in non-standard Sobolev spaces which may be perceived as an obstacle for its use in applications. However, we detail the implementational aspects and show that the preconditioner is quite feasible to realize in practice.

更新日期：2020-01-17
• arXiv.cs.NA Pub Date : 2020-01-15

The study of greedy approximation in the context of convex optimization is becoming a promising research direction as greedy algorithms are actively being employed to construct sparse minimizers for convex functions with respect to given sets of elements. In this paper we propose a unified way of analyzing a certain kind of greedy-type algorithms for the minimization of convex functions on Banach spaces. Specifically, we define the class of Weak Biorthogonal Greedy Algorithms for convex optimization that contains a wide range of greedy algorithms. We analyze the introduced class of algorithms and establish the properties of convergence, rate of convergence, and numerical stability, which is understood in the sense that the steps of the algorithm are allowed to be performed not precisely but with controlled computational inaccuracies. We show that the following well-known algorithms for convex optimization --- the Weak Chebyshev Greedy Algorithm (co) and the Weak Greedy Algorithm with Free Relaxation (co) --- belong to this class, and introduce a new algorithm --- the Rescaled Weak Relaxed Greedy Algorithm (co). Presented numerical experiments demonstrate the practical performance of the aforementioned greedy algorithms in the setting of convex minimization as compared to optimization with regularization, which is the conventional approach of constructing sparse minimizers.

更新日期：2020-01-17
• arXiv.cs.NA Pub Date : 2020-01-15
G. Deligiannidis; S. Maurer; M. V. Tretyakov

We consider stochastic differential equations driven by a general L\'evy processes (SDEs) with infinite activity and the related, via the Feynman-Kac formula, Dirichlet problem for parabolic integro-differential equation (PIDE). We approximate the solution of PIDE using a numerical method for the SDEs. The method is based on three ingredients: (i) we approximate small jumps by a diffusion; (ii) we use restricted jump-adaptive time-stepping; and (iii) between the jumps we exploit a weak Euler approximation. We prove weak convergence of the considered algorithm and present an in-depth analysis of how its error and computational cost depend on the jump activity level. Results of some numerical experiments, including pricing of barrier basket currency options, are presented.

更新日期：2020-01-17
• arXiv.cs.NA Pub Date : 2020-01-15
Assyr Abdulle; Doghonay Arjmand; Edoardo Paganoni

This paper aims at an accurate and efficient computation of effective quantities, e.g., the homogenized coefficients for approximating the solutions to partial differential equations with oscillatory coefficients. Typical multiscale methods are based on a micro-macro coupling, where the macro model describes the coarse scale behaviour, and the micro model is solved only locally to upscale the effective quantities, which are missing in the macro model. The fact that the micro problems are solved over small domains within the entire macroscopic domain, implies imposing artificial boundary conditions on the boundary of the microscopic domains. A naive treatment of these artificial boundary conditions leads to a first order error in $\varepsilon/\delta$, where $\varepsilon < \delta$ represents the characteristic length of the small scale oscillations and $\delta^d$ is the size of micro domain. This error dominates all other errors originating from the discretization of the macro and the micro problems, and its reduction is a main issue in today's engineering multiscale computations. The objective of the present work is to analyze a parabolic approach, first announced in [A. Abdulle, D. Arjmand, E. Paganoni, C. R. Acad. Sci. Paris, Ser. I, 2019], for computing the homogenized coefficients with arbitrarily high convergence rates in $\varepsilon/\delta$. The analysis covers the setting of periodic micro structure, and numerical simulations are provided to verify the theoretical findings for more general settings, e.g. random stationary micro structures.

更新日期：2020-01-17
• arXiv.cs.NA Pub Date : 2020-01-16
Dai Taguchi

Avikainen provided a sharp upper bound of the difference $\mathbb{E}[|g(X)-g(\widehat{X})|^{q}]$ by the moments of $|X-\widehat{X}|$ for any one-dimensional random variables $X$ with bounded density and $\widehat{X}$, and function of bounded variation $g$. In this article, we generalize this estimate to any one-dimensional random variable $X$ with H\"older continuous distribution function. As applications, we provide the rate of convergence for numerical schemes for solutions of one-dimensional stochastic differential equations (SDEs) driven by Brownian motion and symmetric $\alpha$-stable with $\alpha \in (1,2)$, fractional Brownian motion with drift and Hurst parameter $H \in (0,1/2)$, and stochastic heat equations (SHEs) with Dirichlet boundary conditions driven by space--time white noise, with irregular coefficients. We also consider a numerical scheme for maximum and integral type functionals of SDEs driven by Brownian motion with irregular coefficients and payoffs which are related to multilevel Monte Carlo method.

更新日期：2020-01-17
• arXiv.cs.NA Pub Date : 2020-01-16
Florent Renac

This work concerns the numerical approximation of the multicomponent compressible Euler system for a mixture of immiscible fluids in multiple space dimensions and its contribution is twofold. We first derive an entropy stable, positive and accurate three-point finite volume scheme using relaxation-based approximate Riemann solvers from Bouchut [Nonlinear stability of finite volume methods for hyperbolic conservation laws and well-balanced schemes for sources, Frontiers in Mathematics, Birkhauser, 2004] and Coquel and Perthame [SIAM J. Numer. Anal., 35 (1998)]. Then, we extend these results to the high-order discontinuous Galerkin spectral element method (DGSEM) based on collocation of quadrature and interpolation points [Kopriva and Gassner, J. Sci. Comput., 44 (2010)]. The method relies on the framework introduced by Fisher and Carpenter [J. Comput. Phys., 252 (2013)] and Gassner [SIAM J. Sci. Comput., 35 (2013),] where we replace the physical fluxes by entropy conservative numerical fluxes [Tadmor, Math. Comput., 49 (1987)] in the integral over discretization cells, while entropy stable numerical fluxes are used at cell interfaces. Time discretization is performed with a strong-stability preserving Runge-Kutta scheme. We design two-point numerical fluxes satisfying the Tadmor's entropy conservation condition and use the numerical flux from the three-point scheme as entropy stable flux. We derive conditions on the numerical parameters to guaranty a semi-discrete entropy inequality and positivity of the fully discrete DGSEM scheme at any approximation order. The scheme is also accurate in the sense that the solution at interpolation points is exact for stationary contact waves. Numerical experiments in one and two space dimensions on flows with discontinuous solutions support the conclusions of our analysis and highlight stability, robustness and high resolution of the scheme.

更新日期：2020-01-17
• arXiv.cs.NA Pub Date : 2020-01-16
Peter Kritzer; Friedrich Pillichshammer; G. W. Wasilkowski

In the present paper we study quasi-Monte Carlo rules for approximating integrals over the $d$-dimensional unit cube for functions from weighted Sobolev spaces of regularity one. While the properties of these rules are well understood for anchored Sobolev spaces, this is not the case for the ANOVA spaces, which are another very important type of reference spaces for quasi-Monte Carlo rules. Using a direct approach we provide a formula for the worst case error of quasi-Monte Carlo rules for functions from weighted ANOVA spaces. As a consequence we bound the worst case error from above in terms of weighted discrepancy of the employed integration nodes. On the other hand we also obtain a general lower bound in terms of the number $n$ of used integration nodes. For the one-dimensional case our results lead to the optimal integration rule and also in the two-dimensional case we provide rules yielding optimal convergence rates.

更新日期：2020-01-17
• arXiv.cs.NA Pub Date : 2020-01-16
Alexander Katsevich

Let $f(x)$, $x\in\mathbb R^2$, be a piecewise smooth function with a jump discontinuity across a smooth surface $\mathcal S$. Let $f_{\Lambda\epsilon}$ denote the Lambda tomography (LT) reconstruction of $f$ from its discrete Radon data $\hat f(\alpha_k,p_j)$. The sampling rate along each variable is $\sim\epsilon$. First, we compute the limit $f_0(\check x)=\lim_{\epsilon\to0}\epsilon f_{\Lambda\epsilon}(x_0+\epsilon\check x)$ for a generic $x_0\in\mathcal S$. Once the limiting function $f_0(\check x)$ is known (which we call the discrete transition behavior, or DTB for short), the resolution of reconstruction can be easily found. Next, we show that straight segments of $\mathcal S$ lead to non-local artifacts in $f_{\Lambda\epsilon}$, and that these artifacts are of the same strength as the useful singularities of $f_{\Lambda\epsilon}$. We also show that $f_{\Lambda\epsilon}(x)$ does not converge to its continuous analogue $f_\Lambda=(-\Delta)^{1/2}f$ as $\epsilon\to0$ even if $x\not\in\mathcal S$. Results of numerical experiments presented in the paper confirm these conclusions. We also consider a class of Fourier integral operators $\mathcal{B}$ with the same canonical relation as the classical Radon transform adjoint, and conormal distributions $g\in\mathcal{E}'(Z_n)$, $Z_n:=S^{n-1}\times\mathbb R$, and obtain easy to use formulas for the DTB when $\mathcal{B} g$ is computed from discrete data $g(\alpha_{\vec k},p_j)$. Exact and LT reconstructions are particlular cases of this more general theory.

更新日期：2020-01-17
• arXiv.cs.NA Pub Date : 2020-01-16
Cairong Chen; Dongmei Yu; Deren Han

The absolute value equations (AVE) $Ax - |x| - b = 0$ is of interest of the optimization community. Recently, the SOR-like iteration method has been developed (Ke and Ma [{\em Appl. Math. Comput.}, 311:195--202, 2017]) and shown to be efficient for numerically solving the AVE with $\nu=\|A^{-1}\|_2<1$ (Ke and Ma [{\em Appl. Math. Comput.}, 311:195--202, 2017]; Guo, Wu and Li [{\em Appl. Math. Lett.}, 97:107--113, 2019]). Since the SOR-like iteration method is one-parameter-dependent, it is an important problem to determine the optimal iteration parameter. In this paper, we revisit the convergence conditions of the SOR-like iteration method proposed by Ke and Ma ([{\em Appl. Math. Comput.}, 311:195--202, 2017]). Furthermore, we explore the optimal parameter which minimizes $\|T(\omega)\|_2$ and the approximate optimal parameter which minimizes $\eta=\max\{|1-\omega|,\nu\omega^2\}$. The optimal and approximate optimal parameters are iteration-independent. Numerical results demonstrate that the SOR-like iteration method with the optimal parameter is superior to that with the approximate optimal parameter proposed by Guo, Wu and Li ([{\em Appl. Math. Lett.}, 97:107--113, 2019]).

更新日期：2020-01-17
• arXiv.cs.NA Pub Date : 2020-01-16
M. A. Sbai; A. Larabi

Sparse iterative solvers preconditioned with the algebraic multigrid has been devised as an optimal technology to speed up the response of large linear systems. In this work, this technique was introduced into the framework of the dual delineation approach. This involves a single groundwater flow solution and a scalar advective transport solution with different right-hand sides. The method was compared with traditional preconditioned iterative methods and a direct sparse solver on several two- and three-dimensional benchmarks spanning homogeneous and heterogeneous formations. The algebraic multigrid preconditioning enabled speedups lying between one and two orders of magnitude for the groundwater flow problems. However, the sparse direct solver was the fastest for the pure advective transport processes such as the forward travel time simulations. This leads to conclude that the best sparse solver for the general advection-dispersion transport equation is P\'eclet number dependent. When equipped with the best solvers, the dual delineation technique was run on a took only a few seconds to solve multi-million grid cell problems paving the way for comprehensive sensitivity analysis. The paper gives practical hints on the strategies and conditions under which the algebraic multigrid preconditioning for nonlinear and/or transient problems would remain competitive.

更新日期：2020-01-17
• arXiv.cs.NA Pub Date : 2020-01-15
M. J. Piotrowska; K. Sakowski; A. Karch; H. Tahir; J. Horn; M. E. Kretzschmar; R. T. Mikolajczyk

A hybrid network--deterministic model for simulation of multiresistant pathogen spread in a healthcare system is presented. The model accounts for two paths of pathogen transmission between the healthcare facilities: inter-hospital patient transfers (direct transfers) and readmission of colonized patients (indirect transfers). In the latter case, the patients may be readmitted to the same facility or to a different one. Intra-hospital pathogen transmission is governed by a SIS model expressed by a system of ordinary differential equations. Using a network model created for a Lower Saxony region (Germany), we showed that the proposed model reproduces the basic properties of healthcare-associated pathogen spread. Moreover, it shows the important contribution of the readmission of colonized patients on the prevalence of individual hospitals as well as of overall healthcare system: it can increase the overall prevalence by the factor of 4 as compared to inter-hospital transfers only. The final prevalence in individual healthcare facilities was shown to depend on average length of stay by a non-linear concave function. Finally, we demonstrated that the network parameters of the model may be derived from administrative admission/discharge records. In particular, they are sufficient to obtain inter-hospital transfer probabilities, and to express the patients' transfer as a Markov process.

更新日期：2020-01-17
• arXiv.cs.NA Pub Date : 2020-01-16
Gang Bao; Mingming Zhang; Bin Hu; Peijun Li

This paper is concerned with a numerical solution of the acoustic scattering by a bounded impenetrable obstacle in three dimensions. The obstacle scattering problem is formulated as a boundary value problem in a bounded domain by using a Dirichlet-to-Neumann (DtN) operator. An a posteriori error estimate is derived for the finite element method with the truncated DtN operator. The a posteriori error estimate consists of the finite element approximation error and the truncation error of the DtN operator, where the latter is shown to decay exponentially with respect to the truncation parameter. Based on the a posteriori error estimate, an adaptive finite element method is developed for the obstacle scattering problem. The truncation parameter is determined by the truncation error of the DtN operator and the mesh elements for local refinement are marked through the finite element approximation error. Numerical experiments are presented to demonstrate the effectiveness of the proposed method.

更新日期：2020-01-17
• arXiv.cs.NA Pub Date : 2017-08-19
Qiya Hu

This paper is the first one of two serial articles, whose goal is to prove convergence of HX Preconditioner (proposed by Hiptmair and Xu 2007) for Maxwell's equations with jump coefficients. In this paper we establish various extensions of the regular Helmholtz decomposition for edge finite element functions defined in three dimensional domains. The functions defined by the regular Helmholtz decompositions can preserve the zero tangential complement on faces and edges of polyhedral domains and some non-Lipchitz domains, and possess stability estimates with only a $logarithm$ factor. These regular Helmholtz decompositions will be used to prove convergence of the HX preconditioner for Maxwell's equations with jump coefficients in another paper (Hu 2017).

更新日期：2020-01-17
• arXiv.cs.NA Pub Date : 2018-03-12
Mihály Kovács; Stig Larsson; Fardin Saedpanah

Motivated by fractional derivative models in viscoelasticity, a class of semilinear stochastic Volterra integro-differential equations, and their deterministic counterparts, are considered. A generalized exponential Euler method, named here as the Mittag-Leffler Euler integrator, is used for the temporal discretization, while the spatial discretization is performed by the spectral Galerkin method. The temporal rate of strong convergence is found to be (almost) twice compared to when the backward Euler method is used together with a convolution quadrature for time discretization. Numerical experiments that validate the theory are presented.

更新日期：2020-01-17
• arXiv.cs.NA Pub Date : 2019-01-15
Murat Uzunca; Ayşe Sarıaydın-Filibelioğlu

We apply a space adaptive interior penalty discontinuous Galerkin method for solving advective Allen-Cahn equation with expanding and contracting velocity fields. The advective Allen-Cahn equation is first discretized in time and the resulting semi-linear elliptic PDE is solved by an adaptive algorithm using a residual-based a posteriori error estimator. The a posteriori error estimator contains additional terms due to the non-divergence-free velocity field. Numerical examples demonstrate the effectiveness and accuracy of the adaptive approach by resolving the sharp layers accurately.

更新日期：2020-01-17
• arXiv.cs.NA Pub Date : 2019-02-04
Qiya Hu; Rongrong Song

In this paper we are concerned with numerical methods for nonhomogeneous Helmholtz equations in inhomogeneous media. We design a least squares method for discretization of the considered Helmholtz equations. In this method, an auxiliary unknown is introduced on the common interface of any two neighboring elements and a quadratic subject functional is defined by the jumps of the traces of the solutions of local Helmholtz equations across all the common interfaces, where the local Helmholtz equations are defined on elements and are imposed Robin-type boundary conditions given by the auxiliary unknowns. A minimization problem with the subject functional is proposed to determine the auxiliary unknowns. The resulting discrete system of the auxiliary unknowns is Hermitian positive definite and so it can be solved by the PCG method. Under some assumptions we show that the generated approximate solutions possess almost the optimal error estimates with little "wave number pollution". Moreover, we construct a substructuring preconditioner for the discrete system of the auxiliary unknowns. Numerical experiments show that the proposed methods are very effective for the tested Helmholtz equations with large wave numbers.

更新日期：2020-01-17
• arXiv.cs.NA Pub Date : 2019-04-27
Andrea Bonito; Ronald DeVore; Diane Guignard; Peter Jantsch; Guergana Petrova

Motivated by numerical methods for solving parametric partial differential equations, this paper studies the approximation of multivariate analytic functions by algebraic polynomials. We introduce various anisotropic model classes based on Taylor expansions, and study their approximation by finite dimensional polynomial spaces $\cal{P}_{\Lambda}$ described by lower sets $\Lambda$. Given a budget $n$ for the dimension of $\cal{P}_{\Lambda}$, we prove that certain lower sets $\Lambda_n$, with cardinality $n$, provide a certifiable approximation error that is in a certain sense optimal, and that these lower sets have a simple definition in terms of simplices. Our main goal is to obtain approximation results when the number of variables $d$ is large and even infinite, and so we concentrate almost exclusively on the case $d=\infty$. We also emphasize obtaining results which hold for the full range $n\ge 1$, rather than asymptotic results that only hold for $n$ sufficiently large. In applications, one typically wants $n$ small to comply with computational budgets.

更新日期：2020-01-17
• arXiv.cs.NA Pub Date : 2019-05-05
Andrea Bonito; Diane Guignard; Ashley R. Zhang

We consider the numerical approximation of the spectral fractional diffusion problem based on the so called Balakrishnan representation. The latter consists of an improper integral approximated via quadratures. At each quadrature point, a reaction-diffusion problem must be approximated and is the method bottle neck. In this work, we propose to reduce the computational cost using a reduced basis strategy allowing for a fast evaluation of the reaction-diffusion problems. The reduced basis does not depend on the fractional power $s$ for $0 更新日期：2020-01-17 • arXiv.cs.NA Pub Date : 2019-06-19 Ben Snowball; Sheehan Olver Sparse spectral methods for solving partial differential equations have been derived in recent years using hierarchies of classical orthogonal polynomials on intervals, disks, and triangles. In this work we extend this methodology to a hierarchy of non-classical orthogonal polynomials on disk slices (e.g. a half-disk) and trapeziums. This builds on the observation that sparsity is guaranteed due to the boundary being defined by an algebraic curve, and that the entries of partial differential operators can be determined using formulae in terms of (non-classical) univariate orthogonal polynomials. We apply the framework to solving the Poisson, variable coefficient Helmholtz, and Biharmonic equations. 更新日期：2020-01-17 • arXiv.cs.NA Pub Date : 2019-07-08 Bazyli Klockiewicz; Eric Darve When solving linear systems arising from PDE discretizations, iterative methods (such as Conjugate Gradient, GMRES, or MINRES) are often the only practical choice. To converge in a small number of iterations, however, they have to be coupled with an efficient preconditioner. The efficiency of the preconditioner depends largely on its accuracy on the eigenvectors corresponding to small eigenvalues, and unfortunately, black-box methods typically cannot guarantee sufficient accuracy on these eigenvectors. Thus, constructing the preconditioner becomes a problem-dependent task. However, for a large class of problems, including many elliptic equations, the eigenvectors corresponding to small eigenvalues are smooth functions of the PDE grid. In this paper, we describe a hierarchical approximate factorization approach which focuses on improving accuracy on the smooth eigenvectors. The improved accuracy is achieved by preserving the action of the factorized matrix on piecewise polynomial functions of the grid. Based on the factorization, we propose a family of sparse preconditioners with$O(n)$or$O(n \log{n})$construction complexities. Our methods exhibit the optimal$O(n)$solution times in benchmarks run on large elliptic problems of different types, arising for example in flow or mechanical simulations. In the case of the linear elasticity equation the preconditioners are exact on the near-kernel rigid body modes. 更新日期：2020-01-17 • arXiv.cs.NA Pub Date : 2019-12-17 Ruifeng Yuan; Sha Liu; Chengwen Zhong In this paper, authors focus effort on improving the conventional discrete velocity method (DVM) into a multiscale scheme in finite volume framework for gas flow in all flow regimes. Unlike the typical multiscale kinetic methods unified gas-kinetic scheme (UGKS) and discrete unified gas-kinetic scheme (DUGKS), which concentrate on the evolution of the distribution function at the cell interface, in the present scheme the flux for macroscopic variables is split into the equilibrium part and the nonequilibrium part, and the nonequilibrium flux is calculated by integrating the discrete distribution function at the cell center, which overcomes the excess numerical dissipation of the conventional DVM in the continuum flow regime. Afterwards, the macroscopic variables are finally updated by simply integrating the discrete distribution function at the cell center, or by a blend of the increments based on the macroscopic and the microscopic systems, and the multiscale property is achieved. Several test cases, involving unsteady, steady, high speed, low speed gas flows in all flow regimes, have been performed, demonstrating the good performance of the multiscale DVM from free molecule to continuum Navier-Stokes solutions and the multiscale property of the scheme is proved. 更新日期：2020-01-17 • arXiv.cs.NA Pub Date : 2019-12-19 Jonas Kusch; Jannick Wolters; Martin Frank Methods for quantifying the effects of uncertainties in hyperbolic problems can be divided into intrusive and non-intrusive techniques. Non-intrusive methods allow the usage of a given deterministic solver in a black-box manner, while being embarrassingly parallel. However, avoiding intrusive modifications of a given solver takes away the ability to use several inherently intrusive numerical acceleration tools. Moreover, intrusive methods are expected to reach a given accuracy with a smaller number of unknowns compared to non-intrusive techniques. This effect is amplified in settings with high dimensional uncertainty. A downside of intrusive methods is however the need to guarantee hyperbolicity of the resulting moment system. In contrast to stochastic-Galerkin (SG), the Intrusive Polynomial Moment (IPM) method is able to maintain hyperbolicity at the cost of solving an optimization problem in every spatial cell and every time step. In this work, we propose several acceleration techniques for intrusive methods and study their advantages and shortcomings compared to the non-intrusive Stochastic Collocation method. When solving steady problems with IPM, the numerical costs arising from repeatedly solving the IPM optimization problem can be reduced by using concepts from PDE-constrained optimization. Additionally, we propose an adaptive implementation and efficient parallelization strategy of the IPM method. The effectiveness of the proposed adaptations is demonstrated for multi-dimensional uncertainties in fluid dynamics applications, resulting in the observation of requiring a smaller number of unknowns to achieve a given accuracy when using intrusive methods. Furthermore, using the proposed acceleration techniques, our implementation reaches a given accuracy faster than Stochastic Collocation. 更新日期：2020-01-17 • arXiv.cs.NA Pub Date : 2019-12-21 Miranda Holmes-Cerfon Many problems in materials science and biology involve particles interacting with strong, short-ranged bonds, that can break and form on experimental timescales. Treating such bonds as constraints can significantly speed up sampling their equilibrium distribution, and there are several methods to sample subject to fixed constraints. We introduce a Monte Carlo method to handle the case when constraints can break and form. Abstractly, the method samples a probability distribution on a stratification: a collection of manifolds of different dimensions, where the lower-dimensional manifolds lie on the boundaries of the higher-dimensional manifolds. We show several applications of the method in polymer physics, self-assembly of colloids, and volume calculation in high dimensions. 更新日期：2020-01-17 • arXiv.cs.NA Pub Date : 2017-12-19 Dimitrios Loukrezis; Ulrich Römer; Herbert De Gersem We consider the problem of quantifying uncertainty regarding the output of an electromagnetic field problem in the presence of a large number of uncertain input parameters. In order to reduce the growth in complexity with the number of dimensions, we employ a dimension-adaptive stochastic collocation method based on nested univariate nodes. We examine the accuracy and performance of collocation schemes based on Clenshaw-Curtis and Leja rules, for the cases of uniform and bounded, non-uniform random inputs, respectively. Based on numerical experiments with an academic electromagnetic field model, we compare the two rules in both the univariate and multivariate case and for both quadrature and interpolation purposes. Results for a real-world electromagnetic field application featuring high-dimensional input uncertainty are also presented. 更新日期：2020-01-17 • arXiv.cs.IT Pub Date : 2020-01-15 Rafael G. L. D'Oliveira; Salim El Rouayheb; Daniel Heinlein; David Karpuk We consider the problem of secure distributed matrix multiplication in which a user wishes to compute the product of two matrices with the assistance of honest but curious servers. We show that if the user is only concerned in optimizing the download rate, a common assumption in the literature, then the problem can be converted into a simple private information retrieval problem by means of a scheme we call Private Oracle Querying. However, this comes at large upload and computational costs for both the user and the servers. In contrast, we show that for the right choice of parameters, polynomial codes can lower the computational time of the system, e.g. if the computational time complexity of an operation in$\mathbb{F}_q$is at most$\mathcal{Z}_q$and the computational time complexity of multiplying two$n\times n$matrices is$\mathcal{O}(n^\omega \mathcal{Z}_q)$then the user together with the servers can compute the multiplication in$\mathcal{O}(n^{4-\frac{6}{\omega+1}} \mathcal{Z}_q)$time. 更新日期：2020-01-17 • arXiv.cs.IT Pub Date : 2020-01-15 Omer Sabary; Eitan Yaakobi; Alexander Yucovich This paper studies the problem of reconstructing a word given several of its noisy copies. This setup is motivated by several applications, among them is reconstructing strands in DNA-based storage systems. Under this paradigm, a word is transmitted over some fixed number of identical independent channels and the goal of the decoder is to output the transmitted word or some close approximation. The main focus of this paper is the case of two deletion channels and studying the error probability of the maximum-likelihood (ML) decoder under this setup. First, it is discussed how the ML decoder operates. Then, we observe that the dominant error patterns are deletions in the same run or errors resulting from alternating sequences. Based on these observations, it is derived that the error probability of the ML decoder is roughly$\frac{3q-1}{q-1}p^2$, when the transmitted word is any$q$-ary sequence and$pis the channel's deletion probability. We also study the cases when the transmitted word belongs to the Varshamov Tenengolts (VT) code or the shifted VT code. Lastly, the insertion channel is studied as well. These theoretical results are verified by corresponding simulations. 更新日期：2020-01-17 • arXiv.cs.IT Pub Date : 2020-01-15 Xiaoshen Song; Giuseppe Caire Millimeter wave (mmWave) bands are considered a powerful key enabler for next generation (5G) mobile networks by providing multi-Gbps data rates. However, their severe pathloss and sensitivity to blockage present challenges in practical implementation. One effective way to mitigate these effects and to increase communication range is beamforming in combination with relaying. In this paper, we focus on two typical mmWave relay networks and for each network, we propose three beam scheduling methods to approach the network information theoretic capacity. The proposed beam scheduling methods include the deterministic horizontal continuous edge coloring (HC-EC) scheduler, the adaptive back pressure (BP) scheduler and the adaptive low-delay new back pressure (newBP) scheduler. With the aid of computer simulations, we show that within the network capacity range, the proposed schedulers provide good guarantees for the network stability, meanwhile achieve very low packet end-to-end delay. 更新日期：2020-01-17 • arXiv.cs.IT Pub Date : 2020-01-16 Chong Xiao Wang; Yang Song; Wee Peng Tay Each agent in a network makes a local observation that is linearly related to a set of public and private parameters. The agents send their observations to a fusion center to allow it to estimate the public parameters. To prevent leakage of the private parameters, each agent first sanitizes its local observation using a local privacy mechanism before transmitting it to the fusion center. We investigate the utility-privacy trade-off in terms of the Cram\'er-Rao lower bounds for estimating the public and private parameters. We study the class of privacy mechanisms given by linear compression and noise perturbation, and derive necessary and sufficient conditions for achieving arbitrarily strong utility-privacy trade-off in a decentralized agent network for both the cases where prior information is available and unavailable, respectively. We also provide a method to find the maximum estimation privacy achievable without compromising the utility and propose an alternating algorithm to optimize the utility-privacy trade-off in the case where arbitrarily strong utility-privacy trade-off is not achievable. 更新日期：2020-01-17 • arXiv.cs.IT Pub Date : 2020-01-16 Sergey Tridenski; Anelia Somekh-Baruch; Ram Zamir For a discrete memoryless channel with finite input and output alphabets, we prove convergence of iterative computation of the optimal correct-decoding exponent as a function of communication rate, for a fixed rate and for a fixed slope. 更新日期：2020-01-17 • arXiv.cs.IT Pub Date : 2020-01-16 Guangxu Zhu; Yuqing Du; Deniz Gunduz; Kaibin Huang Federated edge learning (FEEL) is a popular framework for model training at an edge server using data distributed at edge devices (e.g., smart-phones and sensors) without compromising their privacy. In the FEEL framework, edge devices periodically transmit high-dimensional stochastic gradients to the edge server, where these gradients are aggregated and used to update a global model. When the edge devices share the same communication medium, the multiple access channel from the devices to the edge server induces a communication bottleneck. To overcome this bottleneck, an efficient broadband analog transmission scheme has been recently proposed, featuring the aggregation of analog modulated gradients (or local models) via the waveform-superposition property of the wireless medium. However, the assumed linear analog modulation makes it difficult to deploy this technique in modern wireless systems that exclusively use digital modulation. To address this issue, we propose in this work a novel digital version of broadband over-the-air aggregation, called one-bit broadband digital aggregation (OBDA). The new scheme features one-bit gradient quantization followed by digital modulation at the edge devices and a majority-voting based decoding at the edge server. We develop a comprehensive analysis framework for quantifying the effects of wireless channel hostilities (channel noise, fading, and channel estimation errors) on the convergence rate. The analysis shows that the hostilities slow down the convergence of the learning process by introducing a scaling factor and a bias term into the gradient norm. However, we show that all the negative effects vanish as the number of participating devices grows, but at a different rate for each type of channel hostility. 更新日期：2020-01-17 • arXiv.cs.IT Pub Date : 2020-01-16 Holger Boche; Minglai Cai; Christian Deppe; Roberto Ferrara; Moritz Wiese We determine the semantic security capacity for quantum wiretap channels. We extend methods for classical channels to quantum channels to demonstrate that a strongly secure code guarantees a semantically secure code with the same secrecy rate. Furthermore, we show how to transform a non-secure code into a semantically secure code by means of biregular irreducible functions (BRI functions). We analyze semantic security for classical quantum channels and for quantum channels. 更新日期：2020-01-17 • arXiv.cs.IT Pub Date : 2020-01-16 Keke Ying; Zhen Gao; Shanxiang Lyu; Yongpeng Wu; Hua Wang; Mohamed-Slim Alouini Reconfigurable intelligent surface (RIS) is considered to be an energy-efficient approach to reshape the wireless environment for improved throughput. Its passive feature greatly reduces the energy consumption, which makes RIS a promising technique for enabling the future smart city. Existing beamforming designs for RIS mainly focus on optimizing the spectral efficiency for single carrier systems. To avoid the complicated bit allocation on different spatial domain subchannels in MIMO systems, in this paper, we propose a geometric mean decomposition-based beamforming for RIS-assisted millimeter wave (mmWave) hybrid MIMO systems so that multiple parallel data streams in the spatial domain can be considered to have the same channel gain. Specifically, by exploiting the common angular-domain sparsity of mmWave massive MIMO channels over different subcarriers, a simultaneous orthogonal match pursuit algorithm is utilized to obtain the optimal multiple beams from an oversampling 2D-DFT codebook. Moreover, by only leveraging the angle of arrival and angle of departure associated with the line of sight (LoS) channels, we further design the phase shifters for RIS by maximizing the array gain for LoS channel. Simulation results show that the proposed scheme can achieve better BER performance than conventional approaches. Our work is an initial attempt to discuss the broadband hybrid beamforming for RIS-assisted mmWave hybrid MIMO systems. 更新日期：2020-01-17 • arXiv.cs.IT Pub Date : 2020-01-16 Mozhgan Bayat; Kai Wan; Mingyue Ji; Giuseppe Caire Coded caching is an information theoretic scheme to reduce high peak hours traffic by partially prefetching files in the users local storage during low peak hours. This paper considers heterogeneous decentralized caching systems where cache of users and content library files may have distinct sizes. The server communicates with the users through a Gaussian broadcast channel. The main contribution of this paper is a novel modulation strategy to map the multicast messages generated in the coded caching delivery phase to the symbols of a signal constellation, such that users can leverage their cached content to demodulate the desired symbols with higher reliability. For the sake of simplicity, in this paper we focus only on uncoded modulation and symbol-by-symbol error probability. However, our scheme in conjunction with multilevel coded modulation can be extended to channel coding over a larger block lengths. 更新日期：2020-01-17 • arXiv.cs.IT Pub Date : 2020-01-16 Takayuki Nozaki This paper investigates the extended weight enumerators for the number-theoretic insertion/deletion correcting codes. As a special case, this paper provides the Hamming weight enumerators and cardinalities of the non-binary VT codes. 更新日期：2020-01-17 • arXiv.cs.IT Pub Date : 2020-01-16 Junho Cho; Ori Shental We use prefix-free code distribution matching (PCDM) for rate matching (RM) in some 5G New Radio (NR) deployment scenarios, realizing a wide range of information rates from 1.4 to 6.0 bit/symbol in fine granularity of 0.2 bit/symbol. We study the performance and implementation of the PCDM-based RM, in comparison with the low-density parity-check (LDPC)-based RM, as defined in the 5G NR standard. Simulations in the additive white Gaussian noise channel show that up to 2.16 dB gain in the signal-to-noise ratio can be obtained with the PCDM-based RM at a block error rate of 10-2 when compared to LDPC-based RM in the tested scenarios, potentially at a smaller hardware cost. 更新日期：2020-01-17 • arXiv.cs.IT Pub Date : 2020-01-16 Matteo Allaix; Lukas Holzbaur; Tefjol Pllaha; Camilla Hollanti In the classical private information retrieval (PIR) setup, a user wants to retrieve a file from a database or a distributed storage system (DSS) without revealing the file identity to the servers holding the data. In the quantum PIR (QPIR) setting, a user privately retrieves a classical file by downloading quantum systems from the servers. The QPIR problem has been treated by Song \emph{et al.} in the case of replicated servers, both without collusion and with all but one servers colluding. In this paper, the QPIR setting is extended to account for MDS-coded servers. The proposed protocol works for any [n,k]-MDS code and t-collusion with t = n - k. Similarly to the previous cases, the rates achieved are better than those known or conjectured in the classical counterparts. 更新日期：2020-01-17 • arXiv.cs.IT Pub Date : 2020-01-16 Vincent Corlay; Joseph J. Boutros; Philippe Ciblat; Loïc Brunel We present new efficient recursive decoders for the Barnes-Wall lattices based on their squaring construction. The analysis of the new decoders reveals a quasi-quadratic complexity in the lattice dimension. The error rate is shown to be close to the universal lower bound in dimensions 64 and 128. 更新日期：2020-01-17 • arXiv.cs.IT Pub Date : 2020-01-16 Hamdi Joudeh; Giuseppe Caire In this work, we study the generalized degrees-of-freedom (GDoF) of downlink and uplink cellular networks, modeled as Gaussian interfering broadcast channels (IBC) and Gaussian interfering multiple access channels (IMAC), respectively. We focus on regimes of low inter-cell interference, where single-cell transmission with power control and treating inter-cell interference as noise (mc-TIN) is GDoF optimal. Recent works have identified two relevant regimes in this context: one in which the GDoF region achieved through mc-TIN for both the IBC and IMAC is a convex polyhedron without the need for time-sharing (mc-CTIN regime), and a smaller (sub)regime where mc-TIN is GDoF optimal for both the IBC and IMAC (mc-TIN regime). In this work, we extend the mc-TIN framework to cellular scenarios where channel state information at the transmitters (CSIT) is limited to finite precision. We show that in this case, the GDoF optimality of mc-TIN extends to the entire mc-CTIN regime, where GDoF benefits due to interference alignment (IA) are lost. Our result constitutes yet another successful application of robust outer bounds based on the aligned images (AI) approach. 更新日期：2020-01-17 • arXiv.cs.IT Pub Date : 2020-01-16 Keyvan Ramezanpour; Paul Ampadu; William Diehl Existing power analysis techniques rely on strong adversary models with prior knowledge of the leakage or training data. We introduce side-channel analysis with unsupervised learning (SCAUL) that can recover the secret key without requiring prior knowledge or profiling (training). We employ an LSTM auto-encoder to extract features from power traces with high mutual information with the data-dependent samples of the measurements. We demonstrate that by replacing the raw measurements with the auto-encoder features in a classical DPA attack, the efficiency, in terms of required number of measurements for key recovery, improves by 10X. Further, we employ these features to identify a leakage model with sensitivity analysis and multi-layer perceptron (MLP) networks. SCAUL uses the auto-encoder features and the leakage model, obtained in an unsupervised approach, to find the correct key. On a lightweight implementation of AES on Artix-7 FPGA, we show that SCAUL is able to recover the correct key with 3700 power measurements with random plaintexts, while a DPA attack requires at least 17400 measurements. Using misaligned traces, with an uncertainty equal to 20\% of the hardware clock cycle, SCAUL is able to recover the secret key with 12300 measurements while the DPA attack fails to detect the key. 更新日期：2020-01-17 • arXiv.cs.IT Pub Date : 2020-01-16 Shahab Asoodeh; Jiachun Liao; Flavio P. Calmon; Oliver Kosut; Lalitha Sankar We derive the optimal differential privacy (DP) parameters of a mechanism that satisfies a given level of R\'enyi differential privacy (RDP). Our result is based on the joint range of twof$-divergences that underlie the approximate and the R\'enyi variations of differential privacy. We apply our result to the moments accountant framework for characterizing privacy guarantees of stochastic gradient descent. When compared to the state-of-the-art, our bounds may lead to about 100 more stochastic gradient descent iterations for training deep learning models for the same privacy budget. 更新日期：2020-01-17 • arXiv.cs.IT Pub Date : 2020-01-16 Islam Samy; Mohamed A. Attia; Ravi Tandon; Loukas Lazos In many applications, content accessed by users (movies, videos, news articles, etc.) can leak sensitive latent attributes, such as religious and political views, sexual orientation, ethnicity, gender, and others. To prevent such information leakage, the goal of classical PIR is to hide the identity of the content/message being accessed, which subsequently also hides the latent attributes. This solution, while private, can be too costly, particularly, when perfect (information-theoretic) privacy constraints are imposed. For instance, for a single database holding$K$messages, privately retrieving one message is possible if and only if the user downloads the entire database of$K$messages. Retrieving content privately, however, may not be necessary to perfectly hide the latent attributes. Motivated by the above, we formulate and study the problem of latent-variable private information retrieval (LV-PIR), which aims at allowing the user efficiently retrieve one out of$K$messages (indexed by$\theta$) without revealing any information about the latent variable (modeled by$S$). We focus on the practically relevant setting of a single database and show that one can significantly reduce the download cost of LV-PIR (compared to the classical PIR) based on the correlation between$\theta$and$S$. We present a general scheme for LV-PIR as a function of the statistical relationship between$\theta$and$S$, and also provide new results on the capacity/download cost of LV-PIR. Several open problems and new directions are also discussed. 更新日期：2020-01-17 • arXiv.cs.IT Pub Date : 2019-11-12 Andrea Pizzo; Thomas L. Marzetta; Luca Sanguinetti Imagine an array with a massive (possibly uncountably infinite) number of antennas in a compact space. We refer to a system of this sort as Holographic MIMO. Given the impressive properties of Massive MIMO, one might expect a holographic array to realize extreme spatial resolution, incredible energy efficiency, and unprecedented spectral efficiency. At present, however, its fundamental limits have not been conclusively established. A major challenge for the analysis and understanding of such a paradigm shift is the lack of mathematically tractable and numerically reproducible channel models that retain some semblance to the physical reality. Detailed physical models are, in general, too complex for tractable analysis. This paper aims to take a closer look at this interdisciplinary challenge. Particularly, we consider the small-scale fading in the far-field, and we model it as a zero-mean, spatially-stationary, and correlated Gaussian scalar random field. Physically-meaningful correlation is obtained by requiring that the random field be consistent with the scalar Helmholtz equation. This formulation leads directly to a rather simple and exact description of the three-dimensional small-scale fading as a Fourier plane-wave spectral representation. Suitably discretized, this leads to a discrete representation for the field as a Fourier plane-wave series expansion, from which a computationally efficient way to generate samples of the small-scale fading over spatially-constrained compact spaces is developed. The connections with the conventional tools of linear systems theory and Fourier transform are thoroughly discussed. 更新日期：2020-01-17 • arXiv.cs.IT Pub Date : 2019-12-03 Xingran Chen; Konstantinos Gatsis; Hamed Hassani; Shirin Saeedi Bidokhti In applications of remote sensing, estimation, and control, timely communication is not always ensured by high-rate communication. This work proposes distributed age-efficient transmission policies for random access channels with$M$transmitters. In the first part of this work, we analyze the age performance of stationary randomized policies by relating the problem of finding age to the absorption time of a related Markov chain. In the second part of this work, we propose the notion of \emph{age-gain} of a packet to quantify how much the packet will reduce the instantaneous age of information at the receiver side upon successful delivery. We then utilize this notion to propose a transmission policy in which transmitters act in a distributed manner based on the age-gain of their available packets. In particular, each transmitter sends its latest packet only if its corresponding age-gain is beyond a certain threshold which could be computed adaptively using the collision feedback or found as a fixed value analytically in advance. Both methods improve age of information significantly compared to the state of the art. In the limit of large$M$, we prove that when the arrival rate is small (below$\frac{1}{eM}$), slotted ALOHA-type algorithms are asymptotically optimal. As the arrival rate increases beyond$\frac{1}{eM}$, while age increases under slotted ALOHA, it decreases significantly under the proposed age-based policies. For arrival rates$\theta$,$\theta=\frac{1}{o(M)}$, the proposed algorithms provide a multiplicative factor of at least two compared to the minimum age under slotted ALOHA (minimum over all arrival rates). We conclude that, as opposed to the common practice, it is beneficial to increase the sampling rate (and hence the arrival rate) and transmit packets selectively based on their age-gain. 更新日期：2020-01-17 • arXiv.cs.DS Pub Date : 2020-01-16 Kohei Yamada; Yuto Nakashima; Shunsuke Inenaga; Hideo Bannai; Masayuki Takeda The longest common subsequence (LCS) problem is a central problem in stringology that finds the longest common subsequence of given two strings$A$and$B$. More recently, a set of four constrained LCS problems (called generalized constrained LCS problem) were proposed by Chen and Chao [J. Comb. Optim, 2011]. In this paper, we consider the substring-excluding constrained LCS (STR-EC-LCS) problem. A string$Z$is said to be an STR-EC-LCS of two given strings$A$and$B$excluding$P$if,$Z$is one of the longest common subsequences of$A$and$B$that does not contain$P$as a substring. Wang et al. proposed a dynamic programming solution which computes an STR-EC-LCS in$O(mnr)$time and space where$m = |A|, n = |B|, r = |P|$[Inf. Process. Lett., 2013]. In this paper, we show a new solution for the STR-EC-LCS problem. Our algorithm computes an STR-EC-LCS in$O(n|\Sigma| + (L+1)(m-L+1)r)$time where$|\Sigma| \leq \min\{m, n\}$denotes the set of distinct characters occurring in both$A$and$B$, and$L$is the length of the STR-EC-LCS. This algorithm is faster than the$O(mnr)$-time algorithm for short/long STR-EC-LCS (namely,$L \in O(1)$or$m-L \in O(1)$), and is at least as efficient as the$O(mnr)$-time algorithm for all cases. 更新日期：2020-01-17 • arXiv.cs.DS Pub Date : 2020-01-16 Marc Hellmuth; Carsten R. Seemann; Peter F. Stadler Binary relations derived from labeled rooted trees play an import role in mathematical biology as formal models of evolutionary relationships. The (symmetrized) Fitch relation formalizes xenology as the pairs of genes separated by at least one horizontal transfer event. As a natural generalization, we consider symmetrized Fitch maps, that is, symmetric maps$\varepsilon$that assign a subset of colors to each pair of vertices in$X$and that can be explained by a tree$T$with edges that are labeled with subsets of colors in the sense that the color$m$appears in$\varepsilon(x,y)$if and only if$m$appears in a label along the unique path between$x$and$y$in$T$. We first give an alternative characterization of the monochromatic case and then give a characterization of symmetrized Fitch maps in terms of compatibility of a certain set of quartets. We show that recognition of symmetrized Fitch maps is NP-complete but FPT in general. In the restricted case where$|\varepsilon(x,y)|\leq 1\$ the problem becomes polynomial, since such maps coincide with class of monochromatic Fitch maps whose graph-representations form precisely the class of complete multi-partite graphs.

更新日期：2020-01-17
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