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Minimax theorems for finite blocklength lossy joint source-channel coding over an AVC

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arXiv 2019年

作者： Vora, Anuj S. Kulkarni, Ankur A. Systems and Control Engineering group Indian Institute of Technology Bombay Mumbai400076 India

Motivated by applications in the security of cyber-physical systems, we pose the finite blocklength communication problem in the presence of a jammer as a zero-sum game between the encoder-decoder team and the jammer, by allowing the communicating team as well as the jammer only locally randomized strategies. The communicating team’s problem is non-convex under locally randomized codes, and hence, in general, a minimax theorem need not hold for this game. However, we show that approximate minimax theorems hold in the sense that the minimax and maximin values of the game approach each other asymptotically. In particular, for rates strictly below a critical threshold, both the minimax and maximin values approach zero, and for rates strictly above it, they both approach unity. We then show a second order minimax theorem, i.e., for rates exactly approaching the threshold with along a specific scaling, the minimax and maximin values approach the same constant value, that is neither zero nor one. Critical to these results is our derivation of finite blocklength bounds on the minimax and maximin values of the game and our derivation of second order dispersion-based *** Codes 94A15, 91A99 Copyright © 2019, The Authors. All rights reserved.

关键词： Embedded systems

DICTIONARY LEARNING WITH ALMOST SURE ERROR CONSTRAINTS

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arXiv 2019年

作者： Sheriff, Mohammed Rayyan Chatterjee, Debasish Systems & Control Engineering Indian Institute of Technology Bombay Powai Mumbai400076 India

A dictionary is a database of standard vectors, so that other vectors / signals are expressed as linear combinations of dictionary vectors, and the task of learning a dictionary for a given data is to find a good dictionary so that the representation of data points has desirable features. Dictionary learning and the related matrix factorization methods have gained significant prominence recently due to their applications in Wide variety of fields like machine learning, signal processing, statistics etc. In this article we study the dictionary learning problem for achieving desirable features in the representation of a given data with almost sure recovery constraints. We impose the constraint that every sample is reconstructed properly to within a predefined threshold. This problem formulation is more challenging than the conventional dictionary learning, which is done by minimizing a regularised cost function. We make use of the duality results for linear inverse problems to obtain an equivalent reformulation in the form of a convex-concave min-max problem. The resulting min-max problem is then solved using gradient descent-ascent like algorithms. Copyright © 2019, The Authors. All rights reserved.

关键词： Gradient methods

ON CONVEX DUALITY IN LINEAR INVERSE PROBLEMS

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arXiv 2019年

作者： Sheriff, Mohammed Rayyan Chatterjee, Debasish Systems and Control Engineering Indian Institute of Technology Bombay Powai Mumbai400076 India

In this article we expose the convex geometry of the class of coding problems that includes the likes of Basis Pursuit Denoising. We propose a novel reformulation of the coding problem as a convex-concave min-max problem. This particular reformulation not only provides a nontrivial method to update the dictionary in order to obtain better sparse representations with hard error constraints, but also gives further insights into the underlying geometry of the coding problem. Our results shed provide pointers to new ascent-descent type algorithms that could be used to solve the coding problem. Copyright © 2019, The Authors. All rights reserved.

关键词： Inverse problems

Stochastic predictive control under intermittent observations and unreliable actions

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arXiv 2019年

作者： Mishra, Prabhat K. Chatterjee, Debasish Quevedo, Daniel E. Systems & Control Engineering Indian Institute of Technology Bombay India Paderborn University Germany

We propose a provably stabilizing and tractable approach for control of constrained linear systems under intermittent observations and unreliable transmissions of control commands. A smart sensor equipped with a Kalman filter is employed for the estimation of the states from incomplete and corrupt measurements, and an estimator at the controller side optimally feeds the intermittently received sensor data to the controller. The remote controller iteratively solves constrained stochastic optimal control problems and transmits the control commands according to a carefully designed transmission protocol through an unreliable channel. We present a (globally) recursively feasible quadratic program, which is solved online to yield a stabilizing controller for Lyapunov stable linear time invariant systems under any positive bound on control values and any non-zero transmission probabilities of Bernoulli channels. Copyright © 2019, The Authors. All rights reserved.

关键词： Kalman filters

Price-coupling games and the generation expansion planning problem

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arXiv 2019年

作者： Abraham, Mathew P. Kulkarni, Ankur A. Systems and Control Engineering Group Indian Institute of Technology Bombay Mumbai400076 India

In this paper, we introduce and study a class of games called price-coupling games that arise in many scenarios, especially in the electricity industry. In a price-coupling game, there is a part of the objective function of a player which has an identical form for all players and there is coupling in the cost functions of players through a price which is determined uniformly for all players by an independent entity called the price-determining player (e.g. independent system operator (ISO) in an electricity market). This price appears in the objective function only in the part which is identical for all players. We study the existence of equilibria in such games under two broad categories, namely price-anticipative and price-taking formulations. In the price-anticipative formulation, the players anticipate the price and make their decisions while in the price-taking formulation, the players make their decisions considering the price as a given parameter. We model the price-anticipative case as a leader-follower formulation where the players (leaders) conjecture the price (follower's decision) and make their decision. The price-taking formulation is modelled as an N + 1 player game with the additional player as the price-determining player. The existence of an equilibrium in such games are not easy mainly because of the coupled-constraint structure of the game and the non-convexity of the action set. We give conditions for the existence of equilibria in both formulations. We apply our results to analyze the existence of an equilibrium in the generation expansion planning problem using the above results.91A99, 78M50 Copyright © 2019, The Authors. All rights reserved.

关键词： Cost functions

Linear Quadratic Formulation based Station-Keeping in Halo Orbit

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Linear Quadratic Formulation based Station-Keeping in Halo O...

control Conference (ICC), 2019 Sixth indian

作者： Ramteke Vivek Haribhau Shashi Ranjan Kumar Department of Aerospace Engineering Indian Institute of Technology Bombay Powai India Intelligent Systems & Control Laboratory Indian Institute of Technology Bombay Powai India

ISBN: (数字)9781728138602

ISBN: (纸本)9781728138619

A three body problem is an interesting problem in the classical mechanics and dynamical systems theory. When formulated and simplified, for certain cases, interesting trajectories can be obtained around the equilibrium points of the system. This paper deals with such trajectory tracking problem for halo orbit around the L 1 point of the SunEarth system. The proposed tracking controllers are obtained using the linear quadratic formulation for a given reference trajectory. Two different approaches for such formulation are considered. The first one is based on linearized equations of motion about its operating points. The linearization of dynamics may lead to loss of the system characteristics, when it is far from the operating point, and consequently the controller may not perform satisfactory. To avoid such difficulties, a suboptimal controller using state dependent Riccati equation is also proposed. The efficacy of proposed controllers in the stations keeping is vindicated through numerical simulations, for the orbit insertion errors.

关键词： Halo orbit station keeping trajectory tracking linear quadratic formulation

Nonlinear rheology of cellular networks

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arXiv 2021年

作者： Duclut, Charlie Paijmans, Joris Inamdar, Mandar M. Modes, Carl D. Julicher, Frank Max Planck Institute for Physics of Complex Systems Nothnitzer Str. 8 Dresden01187 Germany Department of Civil Engineering Indian Institute of Technology Bombay Powai Mumbai400076 India Dresden01307 Germany Center for Systems Biology Dresden Pfotenhauerstrasse 108 Dresden01307 Germany Cluster of Excellence Physics of Life Tu Dresden Dresden01307 Germany

Morphogenesis depends crucially on the complex rheological properties of cell tissues and on their ability to maintain mechanical integrity while rearranging at long times. In this paper, we study the rheology of polygonal cellular networks described by a vertex model in the presence of fluctuations. We use a triangulation method to decompose shear into cell shape changes and cell rearrangements. Considering the steady-state stress under constant shear, we observe nonlinear shear-thinning behavior at all magnitudes of the fluctuations, and an even stronger nonlinear regime at lower values of the fluctuations. We successfully capture this nonlinear rheology by a mean-field model that describes the tissue in terms of cell elongation and cell rearrangements. We furthermore introduce anisotropic active stresses in the vertex model and analyze their effect on rheology. We include this anisotropy in the mean-field model and show that it recapitulates the behavior observed in the simulations. Our work clarifies how tissue rheology is related to stochastic cell rearrangements and provides a simple biophysical model to describe biological tissues. Further, it highlights the importance of nonlinearities when discussing tissue mechanics. © 2021, CC BY-NC-ND.

关键词： Cells

Aggregate Play and Welfare in Strategic Interaction on Networks

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arXiv 2019年

作者： Chadha, Karan N. Kulkarni, Ankur A. Electrical Engineering Department at the Indian Institute of Technology Bombay Mumbai400076 India Systems and Control Engineering group at the Indian Institute of Technology Bombay Mumbai400076 India

In recent work by Bramoullé and Kranton [2], a model for the provision of public goods on a network was presented and relations between equilibria of such a game and properties of the network were established. This model was further extended to include games with imperfect substitutability in Bramoullé et al. [3]. The vast multiplicity of equilibria in such games along with the drastic changes in equilibria with small changes in network structure, makes it challenging for a system planner to estimate the maximum social welfare of such a game or to devise interventions that enhance this welfare. Our main results address this challenge by providing close approximations to the maximum social welfare and the maximum aggregate play in terms of only network characteristics such as the maximum degree and independence number. For the special case when the underlying network is a tree, we derive formulae which use only the number of nodes and their degrees. These results allow a system planner to assess aggregate outcomes and design interventions for the game, directly from the underlying graph structure, without enumerating all equilibria of the game, thereby significantly simplifying the planner’s problem. A part of our results can be viewed as a logical extension of [7] where the maximum weighted aggregate effort of the model in [2] was characterized as the weighted independence number of the graph.91A43, 05C57, 05C35 Copyright © 2019, The Authors. All rights reserved.

关键词： Aggregates

Active T1 transitions in cellular networks

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arXiv 2021年

作者： Duclut, Charlie Paijmans, Joris Inamdar, Mandar M. Modes, Carl D. Jülicher, Frank Max Planck Institute for the Physics of Complex Systems Nöthnitzer Str. 8 Dresden01187 Germany Department of Civil Engineering Indian Institute of Technology Bombay Powai Mumbai400076 India Dresden01307 Germany Center for Systems Biology Dresden Pfotenhauerstrasse 108 Dresden01307 Germany Cluster of Excellence Physics of Life TU Dresden Dresden01307 Germany

In amorphous solids as in tissues, neighbor exchanges can relax local stresses and allow the material to flow. In this paper, we use an anisotropic vertex model to study T1 rearrangements in polygonal cellular networks. We consider two different physical realizations of the active anisotropic stresses: (i) anisotropic bond tension and (ii) anisotropic cell stress. Interestingly, the two types of active stress lead to patterns of relative orientation of T1 transitions and cell elongation that are different. Our work suggests that these two realizations of anisotropic active stresses can be observed in vivo. We describe and explain these results through the lens of a continuum description of the tissue as an anisotropic active material. We furthermore discuss the energetics of the dynamic tissue and express the energy balance in terms of internal elastic energy, mechanical work, chemical work and heat. This allows us to define active T1 transitions that can perform mechanical work while consuming chemical energy. © 2021, CC BY.

关键词： Anisotropy