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We consider the supermarket model in the usual Markovian setting where jobs arrive at rate $n \lambda_n$ for some $\lambda_n > 0$, with $n$ parallel servers each processing jobs in its queue at rate 1. An arriving job joins the shortest among $d_n \le n$ randomly selected service queues. We show that when $d_n \to \infty$ and $\lambda_n \to \lambda \in (0, \infty)$, under natural conditions on the initial queues, the state occupancy process converges in probability, in a suitable path space, to the unique solution of an infinite system of constrained ordinary differential equations parametrized by $\lambda$. Our main interest is in the study of fluctuations of the state process about its near equilibrium state in the critical regime, namely when $\lambda_n \to 1$. Previous papers have considered the regime $\frac{d_n}{\sqrt{n}\log n} \to \infty$ while the objective of the current work is to develop diffusion approximations for the state occupancy process that allow for all possible rates of growth of $d_n$. In particular we consider the three canonical regimes (a) ${d_n}/{\sqrt{n}} \to 0$; (b) ${d_n}/{\sqrt{n}} \to c\in (0,\infty)$ and, (c) ${d_n}/{\sqrt{n}} \to \infty$. In all three regimes we show, by establishing suitable functional limit theorems, that (under conditions on $\lambda_n$) fluctuations of the state process about its near equilibrium are of order $n^{-1/2}$ and are governed asymptotically by a one dimensional Brownian motion. The forms of the limit processes in the three regimes are quite different; in the first case we get a linear diffusion; in the second case we get a diffusion with an exponential drift; and in the third case we obtain a reflected diffusion in a half space. In the special case ${d_n}/({\sqrt{n}\log n}) \to \infty$ our work gives alternative proofs for the universality results established by Mukherjee et al in 2018., Comment: 45 pages with a 4 page Appendix

Language technologies contribute to promoting multilingualism and linguistic diversity around the world. However, only a very small number of the over 7000 languages of the world are represented in the rapidly evolving language technologies and applications. In this paper we look at the relation between the types of languages, resources, and their representation in NLP conferences to understand the trajectory that different languages have followed over time. Our quantitative investigation underlines the disparity between languages, especially in terms of their resources, and calls into question the "language agnostic" status of current models and systems. Through this paper, we attempt to convince the ACL community to prioritise the resolution of the predicaments highlighted here, so that no language is left behind., Comment: Accepted at ACL 2020 (10 pages + 2 pages Appendix). P.J., S.S. and A.B. contributed equally

We prove a large deviation principle (LDP) and a fluctuation theorem (FT) for the entropy production rate (EPR) of the following $d$ dimensional stochastic differential equation \begin{equation*} d X_{t}=AX_{t} d t+\sqrt{Q} d B_{t} \end{equation*} where $A$ is a real normal stable matrix, $Q$ is positive definite, and the matrices $A$ and $Q$ commute. The rate function for the EPR takes the following explicit form: \begin{equation*} I(x)=\left\{ \begin{array}{ll} x\frac{\sqrt{1+\ell_0(x)}-1}{2}+\frac 12\sum\limits_{k=1}^{d} \left(\sqrt{\alpha_k^2- \beta_k^2\ell_0(x)}+\alpha_k\right) , & x\ge 0 , \\ -x\frac{\sqrt{1+\ell_0(x)}+1}{2} +\frac 12\sum\limits_{k=1}^{d} \left(\sqrt{\alpha_k^2- \beta_k^2\ell_0(x)}+\alpha_k\right) , &x<0, \end{array} \right. \end{equation*} where $\alpha_{k}\pm {\rm i} \beta_{k}$ are the eigenvalues of $A$, and $\ell_0(x)$ is the unique solution of the equation: \begin{align*} |x|={\sqrt{1+\ell}} \times \sum_{k=1}^{d} \frac{\beta_k^2}{\sqrt{\alpha_k^2 -\ell\beta_k^2} },\qquad -1 \le \ell< \min_{k=1,...,d}\{\frac{\alpha_k^2}{\beta_k^2}\}. \end{align*} Simple closed form formulas for rate functions are rare and our work identifies an important class of large deviation problems where such formulas are available. The logarithmic moment generating function (the fluctuation function) $\Lambda$ associated with the LDP has a closed form (see it in the paper). The functions $\Lambda(\lambda)$ and $ I(x)$ satisfy the Cohen-Gallavotti symmetry properties. In particular, the functions $I$ and $\Lambda$ do not depend on the diffusion matrix $Q$, and are determined completely by the real and imaginary parts of the eigenvalues of $A$. Formally, the deterministic system with $Q=0$ has zero EPR and thus the model exhibits a phase transition in that the EPR changes discontinuously at $Q = 0$., Comment: There are two reasons for replace the papers: 1. the title of the paper makes others misunderstand that the work is just a straightforward generalization of our work before; 2. the content in introduction is not comprehensive and does not indicate our main contributions, we have to make some big revisions to make this paper more readable

We study a single server queue operating under the shortest remaining processing time (SRPT) scheduling policy; that is, the server preemptively serves the job with the shortest remaining processing time first. In this work we are interested in studying the asymptotic behavior of suitably scaled measure-valued state descriptors that describe the evolution of a sequence of SRPT queuing systems. Gromoll, Kruk, and Puha (2011) have studied this problem under diffusive scaling. In the setting where the processing time distributions have unbounded support, under suitable conditions, they show that the diffusion scaled measures converge in distribution to the process that is identically zero. In Puha (2015) for the setting where the processing time distributions have unbounded support and light tails, a non-standard scaling of the queue length process is shown to give rise to a form of state space collapse that results in a nonzero limit. In the current work we consider the case where processing time distributions have finite second moments and regularly varying tails. We show that the measure valued process, under a non-standard scaling, converges in distribution in the space of paths of measures. In sharp contrast with previous results, there is no state space collapse. Nevertheless, the description of the limit is simple and given explicitly in terms of a certain $\mathbb{R}_+$ valued random field which is determined from a single Brownian motion. Along the way we establish convergence of suitably scaled workload and queue length processes. We also show that as the tail of the distribution of job processing times becomes lighter in an appropriate fashion, the difference between the limiting queue length process and the limiting workload process converges to zero, thereby approaching the behavior of state space collapse., Comment: 64 pages, to appear in The Annals of Applied Probability

In this paper, we study the problem of recommendation system where the users and items to be recommended are rich data structures with multiple entity types and with multiple sources of side-information in the form of graphs. We provide a general formulation for the problem that captures the complexities of modern real-world recommendations and generalizes many existing formulations. In our formulation, each user/document that requires a recommendation and each item or tag that is to be recommended, both are modeled by a set of static entities and a dynamic component. The relationships between entities are captured by several weighted bipartite graphs. To effectively exploit these complex interactions and learn the recommendation model, we propose MEDRES- a multiple graph-CNN based novel deep-learning architecture. MEDRES uses AL-GCN, a novel graph convolution network block, that harnesses strong representative features from the underlying graphs. Moreover, in order to capture highly heterogeneous engagement of different users with the system and constraints on the number of items to be recommended, we propose a novel ranking metric pAp@k along with a method to optimize the metric directly. We demonstrate effectiveness of our method on two benchmarks: a) citation data, b) Flickr data. In addition, we present two real-world case studies of our formulation and the MEDRES architecture. We show how our technique can be used to naturally model the message recommendation problem and the teams recommendation problem in the Microsoft Teams (MSTeams) product and demonstrate that it is 5-6% points more accurate than the production-grade models., Comment: The first two authors contributed equally. 21 pages, 8 figures and 6 tables

This paper develops tools to obtain robust probabilistic estimates for queueing models at the large deviations (LD) scale. These tools are based on the recently introduced robust R\'enyi bounds, which provide LD estimates (and more generally risk-sensitive (RS) cost estimates) that hold uniformly over an uncertainty class of models, provided that the class is defined in terms of R\'enyi divergence with respect to a reference model and that estimates are available for the reference model. One very attractive quality of the approach is that the class to which the estimates apply may consist of hard models, such as highly non-Markovian models and ones for which the LD principle is not available. Our treatment provides exact expressions as well as bounds on the R\'enyi divergence rate on families of marked point processes, including as a special case renewal processes. Another contribution is a general result that translates robust RS control problems, where robustness is formulated via R\'enyi divergence, to finite dimensional convex optimization problems, when the control set is a finite dimensional convex set. The implications to queueing are vast, as they apply in great generality. This is demonstrated on two non-Markovian queueing models. One is the multiclass single-server queue considered as a RS control problem, with scheduling as the control process and exponential weighted queue length as cost. The second is the many-server queue with reneging, with the probability of atypically large reneging count as performance criterion. As far as LD analysis is concerned, no robust estimates or non-Markovian treatment were previously available for either of these models., Comment: 37 pages, 3 figures; Section of concluding remarks is added

Much work in the study of large deviations for random graph models is focused on the dense regime where the theory of graphons has emerged as a principal tool. These tools do not give a good approach to large deviation problems for random graph models in the sparse regime. The aim of this paper is to study an approach for large deviation problems in this regime by establishing Large Deviation Principles (LDP) on suitable path spaces for certain exploration processes of the associated random graph sequence. Our work focuses on the study of one particular class of random graph models, namely the configuration model; however the general approach of using exploration processes for studying large deviation properties of sparse random graph models has broader applicability. The goal is to study asymptotics of probabilities of non-typical behavior in the large network limit. The first key step for this is to establish a LDP for an exploration process associated with the configuration model. A suitable exploration process here turns out to be an infinite dimensional Markov process with transition probability rates that diminish to zero in certain parts of the state space. Large deviation properties of such Markovian models is challenging due to poor regularity behavior of the associated local rate functions. Next, using the rate function in the LDP for the exploration process we formulate a calculus of variations problem associated with the asymptotics of component degree distributions. The second key ingredient in our study is a careful analysis of the infinite dimensional Euler-Lagrange equations associated with this calculus of variations problem. Exact solutions are identified which then provide explicit formulas for decay rates of probabilities of non-typical component degree distributions and related quantities. Please see the paper for the complete abstract., Comment: 62 pages. arXiv admin note: substantial text overlap with arXiv:1708.01832

We consider a collection of Markov chains that model the evolution of multitype biological populations. The state space of the chains is the positive orthant, and the boundary of the orthant is absorbing representing the extinction states of different population types. We are interested in the long-term behavior of the Markov chain away from extinction, under a small noise scaling. Under this scaling, the trajectory of the Markov process over any compact interval converges in distribution to the solution of an ordinary differential equation (ODE) evolving in the positive orthant. We study the asymptotic behavior of the quasi-stationary distributions (QSD) in this scaling regime. Our main result shows that the limit points of the QSD are supported on the union of interior attractors of the flow determined by the ODE. We also give lower bounds on expected extinction times which scale exponentially with the system size. Results of this type when the deterministic dynamical system obtained under the scaling limit is given by a discrete time evolution equation and the dynamics are essentially in a compact space (namely, the one step map is a bounded function) have been studied by Faure and Schreiber (2014). Our results extend these to a setting of an unbounded state space and continuous time dynamics. The proofs rely on uniform large deviation results for small noise stochastic dynamical systems and methods from the theory of dynamical systems. In general QSD for Markov chains with absorbing states and unbounded state spaces may not exist. We study one basic family of Binomial-Poisson models in the positive orthant where one can use Lyapunov function methods to establish existence of QSD and also to argue the tightness of the QSD of the scaled sequence of Markov chains. The results from the first part are then used to characterize the support of limit points of this sequence of QSD., Comment: 39 pages

We introduce Crocoddyl (Contact RObot COntrol by Differential DYnamic Library), an open-source framework tailored for efficient multi-contact optimal control. Crocoddyl efficiently computes the state trajectory and the control policy for a given predefined sequence of contacts. Its efficiency is due to the use of sparse analytical derivatives, exploitation of the problem structure, and data sharing. It employs differential geometry to properly describe the state of any geometrical system, e.g. floating-base systems. Additionally, we propose a novel optimal control algorithm called Feasibility-driven Differential Dynamic Programming (FDDP). Our method does not add extra decision variables which often increases the computation time per iteration due to factorization. FDDP shows a greater globalization strategy compared to classical Differential Dynamic Programming (DDP) algorithms. Concretely, we propose two modifications to the classical DDP algorithm. First, the backward pass accepts infeasible state-control trajectories. Second, the rollout keeps the gaps open during the early "exploratory" iterations (as expected in multiple-shooting methods with only equality constraints). We showcase the performance of our framework using different tasks. With our method, we can compute highly-dynamic maneuvers (e.g. jumping, front-flip) within few milliseconds., Comment: 6 pages, ICRA-20

Consider a collection of particles whose state evolution is described through a system of interacting diffusions in which each particle is driven by an independent individual source of noise and also by a small amount of noise that is common to all particles. The interaction between the particles is due to the common noise and also through the drift and diffusion coefficients that depend on the state empirical measure. We study large deviation behavior of the empirical measure process which is governed by two types of scaling, one corresponding to mean field asymptotics and the other to the Freidlin-Wentzell small noise asymptotics. Different levels of intensity of the small common noise lead to different types of large deviation behavior, and we provide a precise characterization of the various regimes. We also study large deviation behavior of interacting particle systems approximating various types of Feynman-Kac functionals. Proofs are based on stochastic control representations for exponential functionals of Brownian motions and on uniqueness results for weak solutions of stochastic differential equations associated with controlled nonlinear Markov processes.

A common strategy today to generate efficient locomotion movements is to split the problem into two consecutive steps: the first one generates the contact sequence together with the centroidal trajectory, while the second one computes the whole-body trajectory that follows the centroidal pattern. Yet the second step is generally handled by a simple program such as an inverse kinematics solver. In contrast, we propose to compute the whole-body trajectory by using a local optimal control solver, namely Differential Dynamic Programming (DDP). Our method produces more efficient motions, with lower forces and smaller impacts, by exploiting the Angular Momentum (AM). With this aim, we propose an original DDP formulation exploiting the Karush-Kuhn-Tucker constraint of the rigid contact model. We experimentally show the importance of this approach by executing large steps walking on the real HRP-2 robot, and by solving the problem of attitude control under the absence of external forces., Comment: 6 pages, IEEE RAS International Conference on Humanoid Robots

The Join-the-Shortest-Queue routing policy is studied in an asymptotic regime where the number of processors $n$ scales with the arrival rate. A large deviation principle (LDP) for the occupancy process is established, as $n\to \infty$, in a suitable infinite-dimensional path space. Model features that present technical challenges include, Markovian dynamics with discontinuous statistics, a diminishing rate property of the transition probability rates, and an infinite-dimensional state space. The difficulty is in the proof of the Laplace lower bound which requires establishing the uniqueness of solutions of certain infinite-dimensional systems of controlled ordinary differential equations. The LDP gives information on the rate of decay of probabilities of various types of rare events associated with the system. We illustrate this by establishing explicit exponential decay rates for probabilities of long queues. In particular, denoting by $E_j^n(T)$ the event that there is at least one queue with $j$ or more jobs at some time instant over $[0,T]$, we show that, in the critical case, for large $n$ and $T$, $\mathbb{P}(E^n_j(T)) \approx \exp\left [-\frac{n (j-2)^2}{4T}\right].$, Comment: 48 pages, 2 figures

For the M/M/1+M model at the law-of-large-numbers scale, the long run reneging count per unit time does not depend on the individual (i.e., per customer) reneging rate. This paradoxical statement has a simple proof. Less obvious is a large deviations analogue of this fact, stated as follows: The decay rate of the probability that the long run reneging count per unit time is atypically large or atypically small does not depend on the individual reneging rate. In this paper, the sample path large deviations principle for the model is proved and the rate function is computed. Next, large time asymptotics for the reneging rate are studied for the case when the arrival rate exceeds the service rate. The key ingredient is a calculus of variations analysis of the variational problem associated with atypical reneging. A characterization of the aforementioned decay rate, given explicitly in terms of the arrival and service rate parameters of the model, is provided yielding a precise mathematical description of this paradoxical behavior., Comment: 37 pages

We consider the problem of choosing design parameters to minimize the probability of an undesired rare event that is described through the average of $n$ iid random variables. Since the probability of interest for near optimal design parameters is very small, one needs to develop suitable accelerated Monte-Carlo methods for estimating the objective function of interest. One of the challenges in the study is that simulating from exponential twists of the laws of the summands may be computationally demanding since these transformed laws may be non-standard and intractable. We consider a setting where the summands are given as a nonlinear functional of random variables that are more tractable for importance sampling in that the exponential twists of their distributions take a simpler form (than that for the original summands). We also study the closely related problem of estimating buffered probability of exceedance and provide the first rigorous results that relate the asymptotics of buffered probability and that of the ordinary probability under a large deviation scaling. The analogous minimization problem for buffered probability, under conditions, can be formulated as a convex optimization problem which makes it more tractable than the original optimization problem. We show that, under conditions, changes of measures that are asymptotically efficient (under the large deviation scaling) for estimating ordinary probability are also asymptotically efficient for estimating the buffered probability of exceedance. We embed the constructed importance sampling scheme in suitable gradient descent/ascent algorithms for solving the optimization problems of interest. Implementation of schemes for some examples is illustrated through computational experiments.

We obtain rates of convergence to stationarity in L^1-Wasserstein distance for a d-dimensional reflected Brownian motion (RBM) in the nonnegative orthant that are explicit in the dimension and the system parameters. The results are then applied to a class of RBMs considered in Blanchet-Chen (2016) and to rank-based diffusions including the Atlas model. In both cases, we obtain explicit rates and bounds on relaxation times. In the first case we improve the relaxation time estimates of O(d^4(log d)^2) obtained in Blanchet-Chen (2016) to O((log d)^2). In the latter case, we give the first results on explicit parameter and dimension dependent rates under the Wasserstein distance. The proofs do not require an explicit form for the stationary measure or reversibility of the process with respect to this measure, and cover settings where these properties are not available. In the special case of the standard Atlas model, we obtain a bound on the relaxation time of O(d^6(log d)^2)., Comment: 24 pages. To appear in Ann. Appl. Prob

We study the problem of tracking multiple moving targets using a team of mobile robots. Each robot has a set of motion primitives to choose from in order to collectively maximize the number of targets tracked or the total quality of tracking. Our focus is on scenarios where communication is limited and the robots have limited time to share information with their neighbors. As a result, we seek distributed algorithms that can find solutions in bounded amount of time. We present two algorithms: (1) a greedy algorithm that is guaranteed finds a $2$-approximation to the optimal (centralized) solution albeit requiring $|R|$ communication rounds in the worst-case, where $|R|$ denotes the number of robots; and (2) a local algorithm that finds a $\mathcal{O}\left((1+\epsilon)(1+1/h)\right)$-approximation algorithm in $\mathcal{O}(h\log 1/\epsilon)$ communication rounds. Here, $h$ and $\epsilon$ are parameters that allow the user to trade-off the solution quality with communication time. In addition to theoretical results, we present empirical evaluation including comparisons with centralized optimal solutions., Comment: 18 pages, 17 figures, Published in Autonomous Robots. arXiv admin note: text overlap with arXiv:1706.02245

We consider a multi-pair two-way amplify-and-forward massive multi-input multi-output (MIMO) hybrid relay with MIMO user-pairs. A hybrid relay has lesser number of radio frequency (RF) chains than the antennas, which significantly reduces the implementation cost. We employ block-diagonalization-based baseband processing at the hybrid relay to cancel the inter user-pair interference and equal-gain-combining-based RF processing to maximize the beamforming gain. We also use an algebraic norm maximizing relay transmit strategy to maximize the spectral efficiency (SE) of each user-pair. We numerically show that the proposed hybrid relay has only marginally inferior SE than a full RF-chain relay., Comment: Accepted for publication in IEEE SPCOM'18

As the Portable Document Format (PDF) file format increases in popularity, research in analysing its structure for text extraction and analysis is necessary. Detecting headings can be a crucial component of classifying and extracting meaningful data. This research involves training a supervised learning model to detect headings with features carefully selected through recursive feature elimination. The best performing classifier had an accuracy of 96.95%, sensitivity of 0.986 and a specificity of 0.953. This research into heading detection contributes to the field of PDF based text extraction and can be applied to the automation of large scale PDF text analysis in a variety of professional and policy based contexts.

The course description provided by instructors is an important piece of information as it defines what is expected from the instructor and what he/she is going to deliver during a particular course. One of the key components of a course description is the Learning Outcomes section. The contents of this section are used by program managers who are tasked to compare and match two different courses during the development of Transfer Agreements between different institutions. This research introduces the development of visual tools for understanding the two different courses and making comparisons. We designed methods to extract the text from a course description document, developed an algorithm to perform semantic analysis, and displayed the results in a web interface. We are able to achieve the intermediate results of the research which includes extracting, analyzing and visualizing the data.

We give a new proof of the large deviation principle from the hydrodynamic limit for the Ginzberg-Landau model studied in Donsker and Varadhan (1989) using techniques from the theory of stochastic control and weak convergence methods. The proof is based on characterizing subsequential hydrodynamic limits of controlled diffusions with nearest neighbor interaction that arise from a variational representation of certain Laplace functionals. The approach taken here does not require superexponential probability estimates, estimation of exponential moments, or an analysis of eigenvalue problems, that are central ingredients in previous proofs. Instead, proof techniques are very similar to those used for the law of large number analysis, namely in the proof of convergence to the hydrodynamic limit (cf. Guo, Papanicolaou and Varadhan (1988)). Specifically, the key step in the proof is establishing suitable bounds on relative entropies and Dirichlet forms associated with certain controlled laws. This general approach has the promise to be applicable to other interacting particle systems as well and to the case of non-equilibrium starting configurations, and to infinite volume systems., Comment: 48 pages

We prove a large deviation principle (LDP) for a general class of Banach space valued stochastic differential equations (SDE) that is uniform with respect to initial conditions in bounded subsets of the Banach space. A key step in the proof is showing that a uniform large deviation principle over compact sets is implied by a uniform over compact sets Laplace principle. Because bounded subsets of infinite dimensional Banach spaces are in general not relatively compact in the norm topology, we embed the Banach space into its double dual and utilize the weak-$\star $ compactness of closed bounded sets in the double dual space. We prove that a modified version of our stochastic differential equation satisfies a uniform Laplace principle over weak-$\star $ compact sets and consequently a uniform over bounded sets large deviation principle. We then transfer this result back to the original equation using a contraction principle. The main motivation for this uniform LDP is to generalize results of Freidlin and Wentzell concerning the behavior of finite dimensional SDEs. Here we apply the uniform LDP to study the asymptotics of exit times from bounded sets of Banach space valued small noise SDE, including reaction diffusion equations with multiplicative noise and $2$-dimensional stochastic Navier-Stokes equations with multiplicative noise.

We consider a variation of the supermarket model in which the servers can communicate with their neighbors and where the neighborhood relationships are described in terms of a suitable graph. Tasks with unit-exponential service time distributions arrive at each vertex as independent Poisson processes with rate $\lambda$, and each task is irrevocably assigned to the shortest queue among the one it first appears and its $d-1$ randomly selected neighbors. This model has been extensively studied when the underlying graph is a clique in which case it reduces to the well known power-of-$d$ scheme. In particular, results of Mitzenmacher (1996) and Vvedenskaya et al. (1996) show that as the size of the clique gets large, the occupancy process associated with the queue-lengths at the various servers converges to a deterministic limit described by an infinite system of ordinary differential equations (ODE). In this work, we consider settings where the underlying graph need not be a clique and is allowed to be suitably sparse. We show that if the minimum degree approaches infinity (however slowly) as the number of servers $N$ approaches infinity, and the ratio between the maximum degree and the minimum degree in each connected component approaches 1 uniformly, the occupancy process converges to the same system of ODE as the classical supermarket model. In particular, the asymptotic behavior of the occupancy process is insensitive to the precise network topology. We also study the case where the graph sequence is random, with the $N$-th graph given as an Erd\H{o}s-R\'enyi random graph on $N$ vertices with average degree $c(N)$. Annealed convergence of the occupancy process to the same deterministic limit is established under the condition $c(N)\to\infty$, and under a stronger condition $c(N)/\ln N\to\infty$, convergence (in probability) is shown for almost every realization of the random graph., Comment: 32 pages

We consider resource sharing networks of the form introduced in the work of Massouli\'{e} and Roberts(2000) as models for Internet flows. The goal is to study the open problem, formulated in Harrison et al. (2014), of constructing simple form rate allocation policies for broad families of resource sharing networks with associated costs converging to the Hierarchical Greedy Ideal performance in the heavy traffic limit. We consider two types of cost criteria, an infinite horizon discounted cost, and a long time average cost per unit time. We introduce a sequence of rate allocation control policies that are determined in terms of certain thresholds for the scaled queue length processes and prove that, under conditions, both type of costs associated with these policies converge in the heavy traffic limit to the corresponding HGI performance. The conditions needed for these results are satisfied by all the examples considered in Harrison et al. (2014).

Users of Virtual Reality (VR) systems often experience vection, the perception of self-motion in the absence of any physical movement. While vection helps to improve presence in VR, it often leads to a form of motion sickness called cybersickness. Cybersickness is a major deterrent to large scale adoption of VR. Prior work has discovered that changing vection (changing the perceived speed or moving direction) causes more severe cybersickness than steady vection (walking at a constant speed or in a constant direction). Based on this idea, we try to reduce the cybersickness caused by character movements in a First Person Shooter (FPS) game in VR. We propose Rotation Blurring (RB), uniformly blurring the screen during rotational movements to reduce cybersickness. We performed a user study to evaluate the impact of RB in reducing cybersickness. We found that the blurring technique led to an overall reduction in sickness levels of the participants and delayed its onset. Participants who experienced acute levels of cybersickness benefited significantly from this technique.

We consider two-way amplify and forward relaying, where multiple full-duplex user pairs exchange information via a shared full-duplex massive multiple-input multiple-output (MIMO) relay. We derive closed-form lower bound for the spectral efficiency with zero-forcing processing at the relay, by using minimum mean squared error channel estimation. The zero-forcing lower bound for the system model considered herein, which is valid for arbitrary number of antennas, is not yet derived in the massive MIMO relaying literature. We numerically demonstrate the accuracy of the derived lower bound and the performance improvement achieved using zero-forcing processing. We also numerically demonstrate the spectral gains achieved by a full-duplex system over a half-duplex one for various antenna regimes., Comment: Conference paper, 6 pages

We use the Markov chain approximation method to construct approximations for the solution of the mean field game (MFG) with reflecting barriers studied in Bayraktar, Budhiraja, and Cohen (2017). The MFG is formulated in terms of a controlled reflected diffusion with a cost function that depends on the reflection terms in addition to the standard variables: state, control, and the mean field term. This MFG arises from the asymptotic analysis of an $N$-player game for single server queues with strategic servers. By showing that our scheme is an almost contraction, we establish the convergence of this numerical scheme over a small time interval., Comment: arXiv admin note: text overlap with arXiv:1605.09010

The configuration model is a sequence of random graphs constructed such that in the large network limit the degree distribution converges to a pre-specified probability distribution. The component structure of such random graphs can be obtained from an infinite dimensional Markov chain referred to as the exploration process. We establish a large deviation principle for the exploration process associated with the configuration model. Proofs rely on a representation of the exploration process as a system of stochastic differential equations driven by Poisson random measures and variational formulas for moments of nonnegative functionals of Poisson random measures. Uniqueness results for certain controlled systems of deterministic equations play a key role in the analysis. Applications of the large deviation results, for studying asymptotic behavior of the degree sequence in large components of the random graphs, are discussed., Comment: 36 pages; this submission has now been replaced with new url arXiv:1912.04714 with new results

In large storage systems, files are often coded across several servers to improve reliability and retrieval speed. We study load balancing under the Batch Sampling routing scheme for a network of $n$ servers storing a set of files using the Maximum Distance Separable (MDS) code (cf. Li, Ramamoorthy, and Srikant (2016)). Specifically, each file is stored in equally sized pieces across $L$ servers such that any $k$ pieces can reconstruct the original file. When a request for a file is received, the dispatcher routes the job into the $k$-shortest queues among the $L$ for which the corresponding server contains a piece of the file being requested. We establish a law of large numbers and a central limit theorem as the system becomes large (i.e. $n\to\infty$). For the central limit theorem, the limit process take values in $\mathbf{\ell}_2$, the space of square summable sequences. Due to the large size of such systems, a direct analysis of the $n$-server system is frequently intractable. The law of large numbers and diffusion approximations established in this work provide practical tools with which to perform such analysis. The Power-of-$d$ routing scheme, also known as the supermarket model, is a special case of the model considered here., Comment: 40 pages

We study a multi-robot assignment problem for multi-target tracking. The proposed problem can be viewed as the mixed packing and covering problem. To deal with a limitation on both sensing and communication ranges, a distributed approach is taken into consideration. A local algorithm gives theoretical bounds on both the running time and approximation ratio to an optimal solution. We employ a local algorithm of max-min linear programs to solve the proposed task. Simulation result shows that a local algorithm is an effective solution to the multi-robot task allocation., Comment: 6 pages, 9 figures, Published in IEEE International Conference on Robotics and Automation (ICRA), 2018

We consider two-way amplify and forward relaying, where multiple full-duplex user pairs exchange information via a shared full-duplex massive multiple-input multiple-output (MIMO) relay. Most of the previous massive MIMO relaying works maximize the spectral efficiency (SE). By contrast, we maximize the non-convex energy efficiency (EE) metric by approximating it as a pseudo-concave problem, which is then solved using the classic Dinkelbach approach. We also maximize the EE of the least energy-efficient user {relying} on the max-min approach. For solving these optimization problems, we derive closed-form lower bounds for the ergodic achievable rate both for maximal-ratio combining and zero-forcing processing at the relay, by using minimum mean squared error channel estimation. We numerically characterize the accuracy of the lower bounds derived. We also compare the SE and EE of the proposed design to those of the existing full-duplex systems and quantify the significant improvement achieved by the proposed algorithm. We also compare the EE of the proposed full-duplex system to that of its half-duplex counterparts, and characterize the self-loop and inter-user interference regimes, for which the proposed full-duplex system succeeds in outperforming the half-duplex ones., Comment: 30 pages, Updated paper

A large deviation principle is established for a two-scale stochastic system in which the slow component is a continuous process given by a small noise finite dimensional It\^{o} stochastic differential equation, and the fast component is a finite state pure jump process. Previous works have considered settings where the coupling between the components is weak in a certain sense. In the current work we study a fully coupled system in which the drift and diffusion coefficient of the slow component and the jump intensity function and jump distribution of the fast process depend on the states of both components. In addition, the diffusion can be degenerate. Our proofs use certain stochastic control representations for expectations of exponential functionals of finite dimensional Brownian motions and Poisson random measures together with weak convergence arguments. A key challenge is in the proof of the large deviation lower bound where, due to the interplay between the degeneracy of the diffusion and the full dependence of the coefficients on the two components, the associated local rate function has poor regularity properties., Comment: 42 pages

We study the problem of planning a tour for an energy-limited Unmanned Aerial Vehicle (UAV) to visit a set of sites in the least amount of time. We envision scenarios where the UAV can be recharged along the way either by landing on stationary recharging stations or on Unmanned Ground Vehicles (UGVs) acting as mobile recharging stations. This leads to a new variant of the Traveling Salesperson Problem (TSP) with mobile recharging stations. We present an algorithm that finds not only the order in which to visit the sites but also when and where to land on the charging stations to recharge. Our algorithm plans tours for the UGVs as well as determines best locations to place stationary charging stations. While the problems we study are NP-Hard, we present a practical solution using Generalized TSP that finds the optimal solution. If the UGVs are slower, the algorithm also finds the minimum number of UGVs required to support the UAV mission such that the UAV is not required to wait for the UGV. Our simulation results show that the running time is acceptable for reasonably sized instances in practice., Comment: 7 pages, 14 figures, ICRA2018 under review

We study the problem of planning paths for a team of robots for visually monitoring an environment. Our work is motivated by surveillance and persistent monitoring applications. We are given a set of target points in a polygonal environment that must be monitored using robots with cameras. The goal is to compute paths for all robots such that every target is visible from at least one path. In its general form, this problem is NP-hard as it generalizes the Art Gallery Problem and the Watchman Route Problem. We study two versions: (i) a geometric version in \emph{street polygons} for which we give a polynomial time $4$--approximation algorithm; and (ii) a general version for which we present a practical solution that finds the optimal solution in possibly exponential time. In addition to theoretical proofs, we also present results from simulation studies., Comment: 12 pages, 10 figures, submitted to IEEE Transactions on Robotics(TRO) and preliminary version of the paper was published in Intelligent Robots and Systems (IROS), 2015

We consider weakly interacting diffusions on time varying random graphs. The system consists of a large number of nodes in which the state of each node is governed by a diffusion process that is influenced by the neighboring nodes. The collection of neighbors of a given node changes dynamically over time and is determined through a time evolving random graph process. A law of large numbers and a propagation of chaos result is established for a multi-type population setting where at each instant the interaction between nodes is given by an inhomogeneous random graph which may change over time. This result covers the setting in which the edge probabilities between any two nodes is allowed to decay to $0$ as the size of the system grows. A central limit theorem is established for the single-type population case under stronger conditions on the edge probability function., Comment: 31 pages

Particle approximations for certain nonlinear and nonlocal reaction-diffusion equations are studied using a system of Brownian motions with killing. The system is described by a collection of i.i.d. Brownian particles where each particle is killed independently at a rate determined by the empirical sub-probability measure of the states of the particles alive. A large deviation principle (LDP) for such sub-probability measure-valued processes is established. Along the way a convenient variational representation, which is of independent interest, for expectations of nonnegative functionals of Brownian motions together with an i.i.d. sequence of random variables is established. Proof of the LDP relies on this variational representation and weak convergence arguments., Comment: v2: minor revisions, accepted by Journal of Theoretical Probability, 37 pages

We consider a large queueing system that consists of many strategic servers that are weakly interacting. Each server processes jobs from its unique critically loaded buffer and controls the rate of arrivals and departures associated with its queue to minimize its expected cost. The rates and the cost functions in addition to depending on the control action, can depend, in a symmetric fashion, on the size of the individual queue and the empirical measure of the states of all queues in the system. In order to determine an approximate Nash equilibrium for this finite player game we construct a Lasry-Lions type mean-field game (MFG) for certain reflected diffusions that governs the limiting behavior. Under conditions, we establish the convergence of the Nash-equilibrium value for the finite size queuing system to the value of the MFG., Comment: Keywords: Heavy traffic limits, queuing systems, strategic servers, mean-field games, rate control, reflected diffusions

We study a system of interacting diffusions that models chemotaxis of biological cells or microorganisms (referred to as particles) in a chemical field that is dynamically modified through the collective contributions from the particles. Such systems of reinforced diffusions have been widely studied and their hydrodynamic limits that are nonlinear non-local partial differential equations are usually referred to as Patlak-Keller-Segel (PKS) equations. Under the so-called "quasi-stationary hypothesis" on the chemical field the limit PDE is closely related to granular media equations that have been extensively studied probabilistically in recent years. Solutions of classical PKS solutions may blow up in finite time and much of the PDE literature has been focused on understanding this blow-up phenomenon. In this work we study a modified form of the PKS equation for which global existence and uniqueness of solutions holds. Our goal is to analyze the long-time behavior of the particle system approximating the equation. We establish, under suitable conditions, uniform in time convergence of the empirical measure of particle states to the solution of the PDE. We also provide uniform in time exponential concentration bounds for rate of the above convergence under additional integrability conditions. Finally, we introduce an Euler discretization scheme for the simulation of the interacting particle system and give error bounds that show that the scheme converges uniformly in time and in the size of the particle system as the discretization parameter approaches zero., Comment: 37 pages