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Modal array signal processing, as treated in this book, comprises waveform estimation tasks, i.e. beamforming, as well as parameter estimation tasks, i.e. source localization and the estimation of the number of active sources. Modal array signal processing has important applications in the areas of teleconferencing, surveillance, and seamless acoustic human-machine interfaces. [ABSTRACT FROM AUTHOR]

This chapter describes a practical real-time capable system designed to verify the claim developed throughout the previous chapters that acoustic scene analysis tasks can be tackled by wavefield decomposition methods using microphone arrays. In this chapter and in Appendix F, it will be shown that a circular microphone array mounted into a rigid cylindrical baffle is capable of performing waveform estimation and parameter estimation in the sense of Chapter 5 in real acoustic environments. The remainder of this chapter is organized as follows. Section 6.1 discusses hardware, software, and algorithmic details utilized throughout the evaluation process. The measurements to be presented in Section 6.2 were performed in a real room allowing for varying degrees of reverberation. [ABSTRACT FROM AUTHOR]

In this chapter, the path of classical acoustics, illuminated by the previous two chapters, is abandoned for introducing the concepts of the second pillar necessary for understanding the fruitful combination of classical acoustics with classical array signal processing to be presented in Chapter 5. Array signal processing is the science of signal processing where more than one sensor is used to obtain an additional dimension of freedom for the solution of signal processing tasks. In most cases, this additional dimension is the spatial dimension. Since this book deals with acoustic wavefields propagating in air, the sensors utilized are microphones. However, most techniques developed here are also applicable to array signal processing in the fields of radar (antennas), sonar (hydrophones), and seismic imaging (accelerometers). Indeed, most of the techniques presented in this chapter have been originally developed in the radar and sonar community. As a tribute to this development, the more general term ‘sensor' is used in most of the following discussions. [ABSTRACT FROM AUTHOR]

In this chapter, the concepts of classical acoustics and wavefield decomposition as derived in Chapters 2 and 3 on the one hand, and classical array signal processing, as discussed in Chapter 4, on the other hand, are combined to yield novel solutions for sensor array signal processing tasks. As before, the signal processing tasks considered are beamforming, i.e. waveform estimation (WE), and the localization of possibly multiple acoustic sources, i.e. parameter estimation (PE). In addition, the problem of how to determine the number of active sources in a wavefield is addressed. One of the central observations to be made here, which makes the combination of the two paradigms possible, is that the individual circular or spherical harmonics resulting from the wavefield decomposition step can be regarded as individual sensors in the classical sensor array processing framework. In the following, the circular and spherical harmonics are jointly denoted as eigenbeams, a concept first applied to acoustic signal processing by Elko et al. in [EKM03] and [ME04]. [ABSTRACT FROM AUTHOR]

This chapter deals with wavefield decomposition making extensive use of the theoretical foundations of acoustic wavefields laid out in Chapter 2. Wavefield decomposition (WFD), as treated in this book, is a technique that decomposes a wavefield into spatially orthogonal eigen-solutions of the acoustic wave equation in a coordinate system that best suits the geometry of the aperture under consideration. Here, apertures are spatially distributed observation devices for analyzing the characteristics of the spatio-temporal nature exhibited by wavefields. This aperture may be a continuous processor in threedimensional space. Alternatively, this continuous aperture may be sampled by discrete points in space. The resulting processor is called an array. [ABSTRACT FROM AUTHOR]

This chapter is concerned with acoustic radiators and scatterers of cylindrical and spherical shape which forms the basis for the discussion of wavefield decomposition to be detailed in Chapter 3. Acoustic wavefields in cylindrical and spherical coordinate systems are considered that travel through a fluid, most notably air, and that interact with objects and structures resulting in scattering phenomena. In order to arrive at tractable mathematical descriptions of problems related to acoustic radiation and scattering a few basic assumptions are introduced here [JF93]: 1.All fluids and materials considered are assumed to obey linear equations. This restriction limits the following discussions to small-signal disturbances of the transmitting medium.2.The media the acoustic wavefields interact with are assumed to be homogeneous.3.Steady-state conditions are assumed which means that initial transient effects can be neglected.4.For scattering problems, only local interactions between a wavefield propagating in a homogeneous medium and bodies within this medium are assumed. It should be noted that all of the above assumptions are reasonably standard in many textbooks on linear acoustics, such as [MI68], [JF93], [Wil99] and [Bla00]. [ABSTRACT FROM AUTHOR]

The term ‘acoustic scene analysis' (ASA) describes the task of extracting information contained in an acoustic wavefield, such as the waveform itself or parameter describing the source of the wavefield. Since acoustic wavefields are processes spread-out in space and time it follows quite naturally that ASA is predominantly performed by evaluating the signals captured by a number of spatially distinct microphones, i.e. microphone arrays. A standard and widely applied vehicle for evaluating the microphone array signals is built upon classical array signal processing techniques [JD93, Tre02]. In this context, the term ‘classical' is used to denote signal processing algorithms, to be introduced below, that are applied directly to the individual microphones comprising the array. In contrast, the algorithms to be derived in this book are applied to signals that are obtained by transforming the microphone signals into a domain defined by the eigen-solutions of the acoustic wave equation in two- and three spatial dimensions. [ABSTRACT FROM AUTHOR]

In this chapter we deal with the discrete-time linear uncertain system in the form [ABSTRACT FROM AUTHOR]

In this section we consider an uncertain system in the form [ABSTRACT FROM AUTHOR]

As stated in Theorem 3.1, quadratic stability of system (3.1) guarantees exponential stability for all time behaviors of parameters which are of interest in the practise (see also Remark 3.2); in particular, exponential stability is guaranteed for discontinuous parameters which exhibit an unbounded rate of variation at the discontinuity points. [ABSTRACT FROM AUTHOR]

Most part of this chapter deals with the Lyapunov stability analysis of a linear system subject to parametric uncertainties as given by [ABSTRACT FROM AUTHOR]

In this chapter we consider the qualitative behavior of solutions of the system of linear differential equations [ABSTRACT FROM AUTHOR]

According to the celebrated paper [68], linear systems uncertainties can be divided into two big families: dynamical input-output uncertainties and state space uncertainties. [ABSTRACT FROM AUTHOR]

We model the behaviour of a surfer who makes a walk on the webgraph favouring webpages with a high ranking. [ABSTRACT FROM AUTHOR]

This paper presents new results to verify the robust absolute stability property of the Lur'e systems. As it is known, to solve the problem of robust absolute stability, the strict positive realness property (SPR) of a ficticious transfer function needs to be verified. Therefore, the aim of this work is determine sufficient conditions to verify the robust absolute stability property of Lur'e systems using a sign decomposition technique that guarantees the positivity of multivariable polynomials. [ABSTRACT FROM AUTHOR]

Iterated means of neighbourhoods are used to define finite condensing systems of particles in euclidean N-space. Synchronized systems are proved to converge. Necessary and sufficient conditions are discussed for the limit to be a singleton (consensus). [ABSTRACT FROM AUTHOR]

Some systems display repetitive crisis which perturb their periodic evolution. Several examples are demonstrated in such diverse fields as social sciences, physiology, population dynamics, ecology and economics. For instance, the so-called resilience property, which has received much interest from specialists of complex systems (see [3]), has some connection with such repetitive crisis. In this article, we address the question to describe and explain this type of behaviour for a tritrophic slow-fast system. Of course, such a system should incorporate two different time scales: one for the normal periodic state and another for the periodic crisis. The crucial point consists in understanding the "matching" between slow and fast motions. Thus, we focus on the analysis of bifurcations of the fast dynamics. The first part of this article introduces the system which extends Lotka-Volterra dynamics (see [6]) by adding a superpredator. Second part shows the analysis of singular points and bifurcations undergone by fast dynamics. Third part is devoted to the analysis of the various behaviours of the full system depending on the parameters. Fourth part is concerned with the main results relating to the existence and unicity of periodic bursting orbit in those different cases. [ABSTRACT FROM AUTHOR]

System reduction is applied to a mathematical model of glycolysis in yeast and to a chain network without and with feedback. The method of system reduction used is linearization of a rational positive system at a steady state, balancing of the local linear system, and truncation of the balanced linear system. For a model of glycolysis in yeast with glucose as input and pyruvate as output, it is shown that a third order linear system locally approximates well the original thirteenth order nonlinear system. [ABSTRACT FROM AUTHOR]

This paper deals with global convergence to equilibria, and in particular Hirsch's generic convergence theorem for strongly monotone systems, for singular perturbations of monotone systems. [ABSTRACT FROM AUTHOR]

In this paper, the positive invariance of sets defined by nonlinear inequalities with respect to nonlinear maps from a partially ordered set into itself is investigated. The results of this paper extend former results relative to the positive invariance of polyhedral sets with respect to linear systems defined in ordered semirings as well as former results relative to nonlinear dynamical systems defined in the real n-space. The v-monotonicity of nonlinear maps is also been investigated. It is shown that, opposite to the case of linear maps, the v-monotonicity of a nonlinear map is not a necessary condition for a set defined by nonlinear inequalities to be positively invariant. [ABSTRACT FROM AUTHOR]

In this paper several recent results concerning the dynamics of order preserving (sub)homogeneous maps on polyhedral cones are reviewed. These results were obtained by the author in collaboration with Marianne Akian, Stéphane Gaubert, Roger Nussbaum, Michael Scheutzow and Colin Sparrow in [2], [13] and [15], and are new nonlinear extensions of the Perron-Frobenius theory. [ABSTRACT FROM AUTHOR]

P-temporal Petri Nets are convenient tools to model manufacturing systems whose activities times are included between a minimum and a maximum value. The typical feature of these nets is that a control of the firing dates of the transitions is required for the controlled system to behave as close as possible to the specified outputs and to ensure the liveness of tokens, when possible. This paper aims at designing a control law which is obtained by using residuated and dual residuated mappings. An example is given to illustrate the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper we deal with the problem of controlling timed continuous Petri nets in order to reach a final (steady state) configuration while minimizing a quadratic performance index. The formulation of a discrete-time linear positive model with dynamic (or state-based) constraints on the control input, enables us to design a state-feedback control law based on explicit model predictive control (eMPC). The eMPC partitions the state space into polytopes: an affine state-feedback control law is uniquely associated to each polytope, while the on-line phase of the approach consists in evaluating the current region and consequently the optimal control law. [ABSTRACT FROM AUTHOR]

Networks can support Quality of Service (QoS) architectures for a wide variety of applications. The Network Calculus (NC) appeared as a set of rules and results for computing bounds for QoS parameters. The goal of this paper is to improve the systematic use of the Max-Plus algebra in the formulation and derivation of NC results. To illustrate the presented methodology, we analyze the problem of optimizing the playback delay and the buffer size of an optimal video decoder with some look-ahead. [ABSTRACT FROM AUTHOR]

Biologists are increasingly conscious of the critical role that noise plays in cellular functions such as genetic regulation, often in connection with fluctuations in small numbers of key regulatory molecules. This has inspired the development of models that capture this fundamentally discrete and stochastic nature of cellular biology — most notably the Gillespie stochastic simulation algorithm (SSA). The SSA simulates a temporally homogeneous, discrete-state, continuous-time Markov process, and of course the corresponding probabilities and numbers of each molecular species must all remain positive. While accurately serving this purpose, the SSA can be computationally inefficient due to very small time stepping so faster approximations such as the Poisson and Binomial τ-leap methods have been suggested. This work places these leap methods in the context of numerical methods for the solution of stochastic differential equations (SDEs) driven by Poisson noise. This allows analogues of Euler-Maruyuma, Milstein and even higher order methods to be developed through the Itô-Taylor expansions as well as similar derivative-free Runge-Kutta approaches. Numerical results demonstrate that these novel methods compare favourably with existing techniques for simulating biochemical reactions by more accurately capturing crucial properties such as the mean and variance than existing methods. [ABSTRACT FROM AUTHOR]

In this paper we consider a finite state Markov chain with two outputs, an observed output and a to-be-estimated output, and derive a recursive estimator for the to-be-estimated output from an observed output string. The main point of this article is to illustrate that for this kind of filtering problem, it is not needed to have a positive hidden Markov realization of the joint process, but it suffices to have a quasi-realization. We also present an approximate quasi-realization algorithm. We perform a simulation comparing the behavior of the exact, experimental and approximate quasi-realizations and checking the performance of the estimator. [ABSTRACT FROM AUTHOR]

A direct adaptive control framework for stochastic nonnegative and compartmental dynamical systems is developed. In the face of stochastic variations of system coefficients, we present analysis and adaptive control methodology that guarantees global ultimate boundedness of the second moment of the nonlinear stochastic nonnegative systems. [ABSTRACT FROM AUTHOR]

This paper investigates the relation between the spectrum of the system matrix of a positive linear system and the existence of positive linear observers. We only consider single output case. It is shown that a positive linear system admits a Luenberger type positive linear observer only if the number of nonnegative real eigenvalues of the system matrix is at most one. Moreover, we provide a necessary condition on the existence of positive linear observers which employ a coordinates transformation and whose system matrices are diagonal. [ABSTRACT FROM AUTHOR]

We present new results on decomposing the transfer function t(z) of a linear, asymptotically stable, discrete-time SISO system as a difference t(z) = t1(z) − t2(z) of two positive linear systems. We extend the results of [4] to a class of transfer functions t(z) with multiple poles. One of the appearing positive systems is always 1-dimensional, while the other has dimension corresponding to the location and order of the poles of t(z). Recently, in [11], a universal approach was found, providing a decomposition for any asymptotically stable t(z). Our approach here gives lower dimensions than [11] in certain cases but, unfortunately, at present it can only be applied to a relatively small class of transfer functions, and it does not yield a general algorithm. [ABSTRACT FROM AUTHOR]

In this paper, the conditions are discussed for the third-order systems with the complex poles to have third-order positive realizations. These systems are divided into two classes by the distribution of the complex poles. For one class, a sufficient condition is presented, and for the other one, a necessary and sufficient condition is presented. Finally some examples are given to show the contribution and limitation of these results. [ABSTRACT FROM AUTHOR]

A non-linear model for the description of packet-switched communication networks is presented. This model is combined with a model of an additive increase, multiplicative decrease end-to-end controller to obtain a global description of a controlled packet switched network with buffering delays. The global stability of this general model is then analysed using singular perturbation analysis. It is shown that under sufficiently small propagation delays, this general model is globally and exponentially stable. [ABSTRACT FROM AUTHOR]

We deal with problems of maximizing the norm of the transfer matrix function of linear dynamical systems. It is shown that if a linear system is positive and (exponentially) asymptotically stable then the norm of its transfer matrix function attains the maximum at a specific point on the boundary of the stable region. For sake of space, exposure is kept to minimum in this paper. Two examples are given to illustrate the obtained results. [ABSTRACT FROM AUTHOR]

In this paper a global stabilizing control law for a PVTOL aircraft is developed. It considers the positiveness of the thrust and the boundedness of the control inputs. The performance of the proposed controller is compared with other existing approaches. [ABSTRACT FROM AUTHOR]

Sufficient conditions are reported for the existence of a solution to the positive linear quadratic (LQ) problem. These conditions are established by using a Newton-type iterative scheme converging to the unique stabilizing positive semidefinite solution of the algebraic Riccati equation. These results are obtained for stable and detectable linear continuous time-invariant positive systems. [ABSTRACT FROM AUTHOR]

In the paper we give sufficient conditions for the controllability of nonlinear control systems to the arbitrary point of a given interval Q contained in ℝn. [ABSTRACT FROM AUTHOR]

An approach that uses tools from systems and control theory is presented. Such technique enables the determination of the essential interactions in the autoregulatory process that describes the cell cycle of Xenopus frog eggs. The results make possible an assessment of the effect of each protein on the biochemical network stability. The proposed method is based on bifurcation diagram and linearization near the operating point of interest. A perturbation analysis makes possible the determination of the critical proteins responsible for complex behavior in the system, emphasizing how system theory can play an essential role in the study of these systems. [ABSTRACT FROM AUTHOR]

In this paper, the optimal drug injection problem arising in cancer treatment by cell-cycle-specific chemotherapy is investigated. It is shown that this problem can be approximately solved up to any desired precision by using an indexed family of state-unconstrained optimal control problems. The existence of solutions is proved and the resulting approximation is characterized by appropriate two-sides inequalities. Simulations are provided to show the efficiency and relevance of the proposed formulation. [ABSTRACT FROM AUTHOR]

In the course of his work on the analysis of genetic regulatory networks represented by signed directed graphs, R. Thomas has proposed that the occurrence of a positive regulatory circuit is a necessary condition for the existence of multiple stable states, whereas a negative circuit is necessary to generate stable oscillations. Here, we formulate and prove a theorem establishing these rules in a multilevel discrete framework. [ABSTRACT FROM AUTHOR]

In this paper, a nonuniform Space-Time Conservation Element-Solution Element (CE-SE) method is developed in order to improve the relation accuracy-computational cost in the study of unsteady flow with chemical transport. We analyze this improvement by means of an illustrative example. [ABSTRACT FROM AUTHOR]

This papers analyzes a class of non-linear additive-increase multiplicative-decrease (AIMD) protocols that are widely deployed in communication networks. It is demonstrated that the use of these protocols guarantee that the system has a unique stable outcome to which it converges geometrically under all starting points. The development is based on a contraction argument and the derivation of explicit bounds on the contraction coefficient of corresponding operators in terms of the network parameters. In particular, bounds on the corresponding rate of convergence are obtained, improving upon known bounds for standard (linear) AIMD networks. [ABSTRACT FROM AUTHOR]

We introduce the definition of Social Leader that gives a local centrality measure for each node in a graph. A node u is a Social Leader if the number of cycles of length 3 passing through u is greater than the corresponding number for its neighbors. This concept is used to visualize large graphs, identify influent agents in social networks (word of mouth effect) and find communities. [ABSTRACT FROM AUTHOR]

Recently, a number of articles in scientific and popular journals dealt with the fact that there are losing gambling games which can be combined in a suitable stochastic or deterministic way to a winning game - the so-called Parrondo's paradox. Here we investigate a generalization of Parrondo's games introduced by E. Behrends in 2002 which can be analyzed by means of discrete Markov chains. We show that Behrends' requirements for such a chain's transition matrix can be weakened and give some new results concerning the behavior of combinations of these games. [ABSTRACT FROM AUTHOR]

The interaction of agents seeking an agreement or consensus is modeled in higher dimensional space as a time-dependent process of forming convex combinations. It is proved that convergence to a consensus is still possible provided the strength of communication does not fade away "too fast" and the structure of communication becomes not "too loose". The relationship to results obtained in [1] on the agreement algorithm, in [3] on opinion dynamics and in [4] on particle interaction will be discussed. [ABSTRACT FROM AUTHOR]

We present a convergence result for infinite products of stochastic matrices with positive diagonals. We regard infinity of the product to the left. Such a product converges partly to a fixed matrix if the minimal positive entry of each matrix does not converge too fast to zero and if either zero-entries are symmetric in each matrix or the length of subproducts which reach the maximal achievable connectivity is bounded. Variations of this result have been achieved independently in [1], [2] and [3]. We present briefly the opinion dynamics context, discuss the relations to infinite products where infinity is to the right (inhomogeneous Markov processes) and present a small improvement and sketch another. [ABSTRACT FROM AUTHOR]

For a class of positive matrices A + K with a stable positive nominal part A and a structured positive perturbation part K, we address the problem of finding the largest admissible perturbation such that the global matrix remains stable. Theoretical bounds on the size of this set are derived and an algorithm for constructing a set of admissible perturbation is presented. [ABSTRACT FROM AUTHOR]

In this paper, controllability and reachability properties of continuoustime positive switched systems are investigated. It is first shown that such systems are never controllable. On the other hand, monomial reachability, which represents a necessary condition for reachability, is fully characterized. Such a condition is also sufficient for reachability when dealing either with switched systems of size 2 or with positive (non-switched) systems. [ABSTRACT FROM AUTHOR]

It has been shown that a particular class of time-homogeneous Markov chains, called class C, possesses a closed form steady state solution. In this paper, we are interested in the transient analysis of this class of Markov chains. Unlike steady state analysis, transient analysis for continuous time (CTMC) and discrete time (DTMC) Markov chains have to be treated differently. First we show that transient distributions of class C Markov chains can be also computed through closed form solutions both for the cases of DTMC and CTMC. By means of the stochastic comparison approach, we construct bounding chains belonging to this class thus bounding transient distributions of the underlying Markov chain can be easily computed through the closed form solution. In this work we propose bounds both in the sense of the strong stochastic order, and the increasing convex stochastic order. [ABSTRACT FROM AUTHOR]

For the numerous applications of Markov chains (in particular MCMC methods), the problem of detecting an instant at which the convergence takes place is crucial. The ‘cut-off phenomenon', or abrupt convergence, provides an answer to this problem. When a sample of Markov chains, or more generally of exponentially converging processes, is simulated in parallel, it remains far from its stationary distribution until a deterministic instant, and approaches it exponentially fast afterwards. The cut-off instant is explicitly known, and can be detected algorithmically using appropriate stopping times. The technique is illustrated on the Ornstein-Uhlenbeck diffusion. [ABSTRACT FROM AUTHOR]

Deflection Routing is proposed for all optical core switches because of the lack of optical memory. In Shortest-path Deflection Routing, switches attempt to forward packets along a shortest hop path to their destinations. Each link can send a finite number of packets per time-slot (the link capacity). Incoming packets have to be sent immediately to their next switch along the path. If the number of packets which require a link is larger than the link capacity, only some of them will use the link they ask for and the other ones have to be misdirected or deflected. We build the Markov chain which models a packet routing in an odd torus. We prove that this matrix is ≼st-monotone. The proof is based on increasing sets as we consider a partial ordering on the state space based on the network topology. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the comparison of expected rewards for discrete-time reward Markov chains with different state spaces. Necessary and sufficient conditions for such a comparison are derived. Due to the special nature of the introduced binary relation, a criterion may be formulated in terms of an inclusion of polyhedral sets. Then, algebraic and geometric forms are easily obtained from Haar's Lemma. Our results allow us to discuss some earlier results on the stochastic comparison of functions of Markov chains. [ABSTRACT FROM AUTHOR]