arXiv subjects

Masaki Ogura

Publications and source records attributed to Masaki Ogura.

At least 55 records · Page 3Linked to original sources

arXiv2018

Kronecker weights for instability analysis of Markov jump linear systems

In this paper, we analyze the instability of continuous-time Markov jump linear systems. Although there exist several effective criteria for the stability of Markov jump linear systems, there is a lack of methodologies for verifying their instability. In this paper, we present a novel criterion for the exponential mean instability of Markov jump linear systems. The main tool of our analysis is an auxiliary Markov jump linear system, which results from taking the Kronecker products of the given system matrices and a set of appropriate matrix weights. We furthermore show that the problem of finding matrix weights for tighter instability analysis can be transformed to the spectral optimization of an affine matrix family, which can be efficiently performed by gradient-based non-smooth optimization algorithms. We confirm the effectiveness of the proposed methods by numerical examples.

math.OC↗

arXiv2018

Model predictive control for energy-efficient operation of data centers with cold aisle containments

In this paper, we study a problem of controlling cooling facilities and computational equipments for energy-efficient operations of data centers. Although a plethora of approaches have been proposed in previous literatures, there is a lack of rigorous methodologies for effectively addressing the problem. To bridge this gap, we propose MPC frameworks for jointly and optimally tuning the Computer Room Air Conditioner (CRAC) supplying air temperature as well as the number of active servers for minimizing the overall energy consumption. We specifically find that, when a standard model of data centers with contained cold aisles and cooling facilities are used, the optimization problems arising from the MPC framework can be transformed to convex optimization problems that can be solved efficiently. We present several numerical simulations to illustrate the effectiveness of our theoretical results.

math.OC↗

arXiv2018

LQ-optimal Sample-data Control under Stochastic Delays: Gridding Approach for Stabilizability and Detectability

We solve a linear quadratic optimal control problem for sampled-data systems with stochastic delays. The delays are stochastically determined by the last few delays. The proposed optimal controller can be efficiently computed by iteratively solving a Riccati difference equation, provided that a discrete-time Markov jump system equivalent to the sampled-data system is stochastic stabilizable and detectable. Sufficient conditions for these notions are provided in the form of linear matrix inequalities, from which stabilizing controllers and state observers can be constructed.

math.OC↗

arXiv2018

Optimal Containment of Epidemics over Temporal Activity-Driven Networks

In this paper, we study the dynamics of epidemic processes taking place in temporal and adaptive networks. Building on the activity-driven network model, we propose an adaptive model of epidemic processes, where the network topology dynamically changes due to both exogenous factors independent of the epidemic dynamics as well as endogenous preventive measures adopted by individuals in response to the state of the infection. A direct analysis of the model using Markov processes involves the spectral analysis of a transition probability matrix whose size grows exponentially with the number of nodes. To overcome this limitation, we derive an upper-bound on the decay rate of the number of infected nodes in terms of the eigenvalues of a $2 \times 2$ matrix. Using this upper bound, we propose an efficient algorithm to tune the parameters describing the endogenous preventive measures in order to contain epidemics over time. We confirm our theoretical results via numerical simulations.

cs.SI↗

arXiv2018

Resource Allocation for Containing Epidemics from Temporal Network Data

We study the problem of containing epidemic spreading processes in temporal networks. We specifically focus on the problem of finding a resource allocation to suppress epidemic infection, provided that an empirical time-series data of connectivities between nodes is available. Although this problem is of practical relevance, it has not been clear how an empirical time-series data can inform our strategy of resource allocations, due to the computational complexity of the problem. In this direction, we present a computationally efficient framework for finding a resource allocation that satisfies a given budget constraint and achieves a given control performance. The framework is based on convex programming and, moreover, allows the performance measure to be described by a wide class of functionals called posynomials with nonnegative exponents. We illustrate our theoretical results using a data of temporal interaction networks within a primary school.

cs.SI↗

arXiv2018

Distributed Agreement on Activity Driven Networks

In this paper, we investigate asymptotic properties of a consensus protocol taking place in a class of temporal (i.e., time-varying) networks called the activity driven network. We first show that a standard methodology provides us with an estimate of the convergence rate toward the consensus, in terms of the eigenvalues of a matrix whose computational cost grows exponentially fast in the number of nodes in the network. To overcome this difficulty, we then derive alternative bounds involving the eigenvalues of a matrix that is easy to compute. Our analysis covers the regimes of 1) sparse networks and 2) fast-switching networks. We numerically confirm our theoretical results by numerical simulations.

cs.SI↗

arXiv2017

Second-Order Moment-Closure for Tighter Epidemic Thresholds

In this paper, we study the dynamics of contagious spreading processes taking place in complex contact networks. We specifically present a lower-bound on the decay rate of the number of nodes infected by a susceptible-infected-susceptible (SIS) stochastic spreading process. A precise quantification of this decay rate is crucial for designing efficient strategies to contain epidemic outbreaks. However, existing lower-bounds on the decay rate based on first-order mean-field approximations are often accompanied by a large error resulting in inefficient containment strategies. To overcome this deficiency, we derive a lower-bound based on a second-order moment-closure of the stochastic SIS processes. The proposed second-order bound is theoretically guaranteed to be tighter than existing first-order bounds. We also present various numerical simulations to illustrate how our lower-bound drastically improves the performance of existing first-order lower-bounds in practical scenarios, resulting in more efficient strategies for epidemic containment.

cs.SI↗

arXiv2017

Delayed Bet-Hedging Resilience Strategies Under Environmental Fluctuations

Many biological populations, such as bacterial colonies, have developed through evolution a protection mechanism, called bet-hedging, to increase their probability of survival under stressful environmental fluctutation. In this context, the concept of preadaptation refers to a common type of bet-hedging protection strategy in which a relatively small number of individuals in a population stochastically switch their phenotypes to a `dormant' metabolic state in which they increase their probability of survival against potential environmental shocks. Hence, if an environmental shock took place at some point in time, preadapted organisms would be better adapted to survive and proliferate once the shock is over. In many biological populations, the mechanisms of preadaptation and proliferation present delays whose influence in the fitness of the population are not well-understood. In this paper, we propose a rigorous mathematical framework to analyze the role of delays in both preadaptation and proliferation mechanisms in the survival of biological populations, with an emphasis on bacterial colonies. Our theoretical framework allows us to analytically quantify the average growth rate of a bet-hedging bacterial colony with stochastically delayed reactions with arbitrary precision. We verify the accuracy of the proposed method by numerical simulations and conclude that the growth rate of a bet-hedging population shows a non-trivial dependency on their preadaptation and proliferation delays. Contrary to the current belief, our results show that faster reactions do not, in general, increase the overall fitness of a biological population.

q-bio.PE↗

arXiv2016

Optimal Containment of Epidemics in Temporal and Adaptive Networks

In this chapter, we focus on the problem of containing the spread of diseases taking place in both temporal and adaptive networks (i.e., networks whose structure `adapts' to the state of the disease). We specifically focus on the problem of finding the optimal allocation of containment resources (e.g., vaccines, medical personnel, traffic control resources, etc.) to eradicate epidemic outbreaks over the following three models of temporal and adaptive networks: (i) Markovian temporal networks, (ii) aggregated-Markovian temporal networks, and (iii) stochastically adaptive models. For each model, we present a rigorous and tractable mathematical framework to efficiently find the optimal distribution of control resources to eliminate the disease. In contrast with other existing results, our results are not based on heuristic control strategies, but on a disciplined analysis using tools from dynamical systems and convex optimization.

cs.SI↗

arXiv2016

Bio-Inspired Framework for Allocation of Protection Resources in Cyber-Physical Networks

In this chapter, we consider the problem of designing protection strategies to contain spreading processes in complex cyber-physical networks. We illustrate our ideas using a family of bio-motivated spreading models originally proposed in the epidemiological literature, e.g., the Susceptible-Infected-Susceptible (SIS) model. We first introduce a framework in which we are allowed to distribute two types of resources in order to contain the spread, namely, (i) preventive resources able to reduce the spreading rate, and (ii) corrective resources able to increase the recovery rate of nodes in which the resources are allocated. In practice, these resources have an associated cost that depends on either the resiliency level achieved by the preventive resource, or the restoration efficiency of the corrective resource. We present a mathematical framework, based on dynamic systems theory and convex optimization, to find the cost-optimal distribution of protection resources in a network to contain the spread. We also present two extensions to this framework in which (i) we consider generalized epidemic models, beyond the simple SIS model, and (ii) we assume uncertainties in the contact network in which the spreading is taking place. We compare these protection strategies with common heuristics previously proposed in the literature and illustrate our results with numerical simulations using the air traffic network.

cs.SI↗

arXiv2016

Katz Centrality of Markovian Temporal Networks: Analysis and Optimization

Identifying important nodes in complex networks is a fundamental problem in network analysis. Although a plethora of measures has been proposed to identify important nodes in static (i.e., time-invariant) networks, there is a lack of tools in the context of temporal networks (i.e., networks whose connectivity dynamically changes over time). The aim of this paper is to propose a system-theoretic approach for identifying important nodes in temporal networks. In this direction, we first propose a generalization of the popular Katz centrality measure to the family of Markovian temporal networks using tools from the theory of Markov jump linear systems. We then show that Katz centrality in Markovian temporal networks can be efficiently computed using linear programming. Finally, we propose a convex program for optimizing the Katz centrality of a given node by tuning the weights of the temporal network in a cost-efficient manner. Numerical simulations illustrate the effectiveness of the obtained results.

physics.soc-ph↗

arXiv2016

Efficient Method for Computing Lower Bounds on the $p$-radius of Switched Linear Systems

This paper proposes lower bounds on a quantity called $L^p$-norm joint spectral radius, or in short, $p$-radius, of a finite set of matrices. Despite its wide range of applications to, for example, stability analysis of switched linear systems and the equilibrium analysis of switched linear economical models, algorithms for computing the $p$-radius are only available in a very limited number of particular cases. The proposed lower bounds are given as the spectral radius of an average of the given matrices weighted via Kronecker products and do not place any requirements on the set of matrices. We show that the proposed lower bounds theoretically extend and also can practically improve the existing lower bounds. A Markovian extension of the proposed lower bounds is also presented.

math.OC↗

arXiv2016

Epidemic Processes over Adaptive State-Dependent Networks

In this paper, we study the dynamics of epidemic processes taking place in adaptive networks of arbitrary topology. We focus our study on the adaptive susceptible-infected-susceptible (ASIS) model, where healthy individuals are allowed to temporarily cut edges connecting them to infected nodes in order to prevent the spread of the infection. In this paper, we derive a closed-form expression for a lower bound on the epidemic threshold of the ASIS model in arbitrary networks with heterogeneous node and edge dynamics. For networks with homogeneous node and edge dynamics, we show that the resulting \blue{lower bound} is proportional to the epidemic threshold of the standard SIS model over static networks, with a proportionality constant that depends on the adaptation rates. Furthermore, based on our results, we propose an efficient algorithm to optimally tune the adaptation rates in order to eradicate epidemic outbreaks in arbitrary networks. We confirm the tightness of the proposed lower bounds with several numerical simulations and compare our optimal adaptation rates with popular centrality measures.

cs.SI↗

arXiv2016

Dynamic Analysis of Bet-Hedging Strategies as a Protection Mechanism against Environmental Fluctuations

In order to increase their robustness against environmental fluctuations, many biological populations have developed bet-hedging mechanisms in which the population `bets' against the presence of prolonged favorable environmental conditions by having a few individual behaving as if they sensed a threatening or stressful environment. As a result, the population (as a whole) increases its chances of surviving environmental fluctuations in the long term, while sacrificing short-term performance. In this paper, we propose a theoretical framework, based on Markov jump linear systems, to model and evaluate the performance of bet-hedging strategies in the presence of stochastic fluctuations. We illustrate our results using numerical simulations.

q-bio.PE↗

arXiv2015

Stability of Markov regenerative switched linear systems

In this paper, we give a necessary and sufficient condition for mean stability of switched linear systems having a Markov regenerative process as its switching signal. This class of switched linear systems, which we call Markov regenerative switched linear systems, contains Markov jump linear systems and semi-Markov jump linear systems as special cases. We show that a Markov regenerative switched linear system is $m$th mean stable if and only if a particular matrix is Schur stable, under the assumption that either $m$ is even or the system is positive.

eess.SY↗

arXiv2015

Stability of Spreading Processes over Time-Varying Large-Scale Networks

In this paper, we analyze the dynamics of spreading processes taking place over time-varying networks. A common approach to model time-varying networks is via Markovian random graph processes. This modeling approach presents the following limitation: Markovian random graphs can only replicate switching patterns with exponential inter-switching times, while in real applications these times are usually far from exponential. In this paper, we introduce a flexible and tractable extended family of processes able to replicate, with arbitrary accuracy, any distribution of inter-switching times. We then study the stability of spreading processes in this extended family. We first show that a direct analysis based on Itô's formula provides stability conditions in terms of the eigenvalues of a matrix whose size grows exponentially with the number of edges. To overcome this limitation, we derive alternative stability conditions involving the eigenvalues of a matrix whose size grows linearly with the number of nodes. Based on our results, we also show that heuristics based on aggregated static networks approximate the epidemic threshold more accurately as the number of nodes grows, or the temporal volatility of the random graph process is reduced. Finally, we illustrate our findings via numerical simulations.

cs.SI↗

arXiv2015

Optimal Design of Networks of Positive Linear Systems under Stochastic Uncertainty

In this paper, we study networks of positive linear systems subject to time-invariant and random uncertainties. We present linear matrix inequalities for checking the stability of the whole network around the origin with prescribed probability and decay rate. Based on this condition, we then give an efficient method, based on geometric programming, to find the optimal parameters of the probability distribution describing the uncertainty. We illustrate our results by analyzing the stability of a viral spreading process in the presence of random uncertainties.

math.OC↗

arXiv2015

Spreading Processes over Socio-Technical Networks with Phase-Type Transmissions

Most theoretical tools available for the analysis of spreading processes over networks assume exponentially distributed transmission and recovery times. In practice, the empirical distribution of transmission times for many real spreading processes, such as the spread of web content through the Internet, are far from exponential. To bridge this gap between theory and practice, we propose a methodology to model and analyze spreading processes with arbitrary transmission times using phase-type distributions. Phase-type distributions are a family of distributions that is dense in the set of positive-valued distributions and can be used to approximate any given distributions. To illustrate our methodology, we focus on a popular model of spreading over networks: the susceptible-infected-susceptible (SIS) networked model. In the standard version of this model, individuals informed about a piece of information transmit this piece to its neighbors at an exponential rate. In this paper, we extend this model to the case of transmission rates following a phase-type distribution. Using this extended model, we analyze the dynamics of the spread based on a vectorial representations of phase-type distributions. We illustrate our results by analyzing spreading processes over networks with transmission and recovery rates following a Weibull distribution.

cs.SI↗