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73
Consensus Problems in Networks of Agents with Switching Topology and TimeDelays
, 2003
"... In this paper, we discuss consensus problems for a network of dynamic agents with fixed and switching topologies. We analyze three cases: i) networks with switching topology and no timedelays, ii) networks with fixed topology and communication timedelays, and iii) maxconsensus problems (or leader ..."
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Cited by 516 (15 self)
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In this paper, we discuss consensus problems for a network of dynamic agents with fixed and switching topologies. We analyze three cases: i) networks with switching topology and no timedelays, ii) networks with fixed topology and communication timedelays, and iii) maxconsensus problems (or leader determination) for groups of discretetime agents. In each case, we introduce a linear/nonlinear consensus protocol and provide convergence analysis for the proposed distributed algorithm. Moreover, we establish a connection between the Fiedler eigenvalue of the information flow in a network (i.e. algebraic connectivity of the network) and the negotiation speed (or performance) of the corresponding agreement protocol. It turns out that balanced digraphs play an important role in addressing averageconsensus problems. We introduce disagreement functions that play the role of Lyapunov functions in convergence analysis of consensus protocols. A distinctive feature of this work is to address consensus problems for networks with directed information flow. We provide analytical tools that rely on algebraic graph theory, matrix theory, and control theory. Simulations are provided that demonstrate the effectiveness of our theoretical results.
Guaranteed Passive Balancing Transformations for Model Order Reduction
, 2002
"... The major concerns in stateoftheart model reduction algorithms are: achieving accurate models of sufficiently small size, numerically stable and efficient generation of the models, and preservation of system properties such as passivity. Algorithms such as PRIMA generate guaranteedpassive models ..."
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Cited by 46 (6 self)
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The major concerns in stateoftheart model reduction algorithms are: achieving accurate models of sufficiently small size, numerically stable and efficient generation of the models, and preservation of system properties such as passivity. Algorithms such as PRIMA generate guaranteedpassive models, for systems with special internal structure, using numerically stable and efficient Krylovsubspace iterations. Truncated Balanced Realization (TBR) algorithms, as used to date in the design automation community, can achieve smaller models with better error control, but do not necessarily preserve passivity. In this paper we show how to construct TBRlike methods that guarantee passive reduced models and in addition are applicable to statespace systems with arbitrary internal structure.
What Matters in Neuronal Locking?
"... Present and permanent address: PhysikDepartment der TU Munchen Exploiting local stability we show what neuronal characteristics are essential to ensure that coherent oscillations are asymptotically stable in a spatially homogeneous network of spiking neurons. Under standard conditions, a necessa ..."
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Cited by 45 (10 self)
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Present and permanent address: PhysikDepartment der TU Munchen Exploiting local stability we show what neuronal characteristics are essential to ensure that coherent oscillations are asymptotically stable in a spatially homogeneous network of spiking neurons. Under standard conditions, a necessary and in the limit of a large number of interacting neighbors also sufficient condition is that the postsynaptic potential is increasing in time as the neurons fire. If the postsynaptic potential is decreasing, oscillations are bound to be unstable. This is a kind of locking theorem and boils down to a subtle interplay of axonal delays, postsynaptic potentials, and refractory behavior. The theorem also allows for mixtures of excitatory and inhibitory interactions. On the basis of the locking theorem we present a simple geometric method to verify existence and local stability of a coherent oscillation. 2 1
Worstcase complexity bounds on algorithms for computing the canonical structure of finite abelian groups and the Hermite and Smith normal forms of an integer matrix
 SIAM J. Comput
, 1989
"... Abstract. An O(s5M($2)) algorithm for computing the canonical structure of a finite Abelian group represented by an integer matrix of size (this is the Smith normal form of the matrix) is presented. Moreover, an O(s3M(s2)) algorithm for computing the Hermite normal form of an integer matrix of size ..."
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Cited by 45 (0 self)
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Abstract. An O(s5M($2)) algorithm for computing the canonical structure of a finite Abelian group represented by an integer matrix of size (this is the Smith normal form of the matrix) is presented. Moreover, an O(s3M(s2)) algorithm for computing the Hermite normal form of an integer matrix of size is given. The upper bounds derived on the computational complexity of the algorithms above improve the upper bounds given by Kannan and Bachem in [SIAM J. Comput., 8 (1979), pp. 499507] and Chou and Collins in [SIAM J. Comput., 11 (1982), pp. 687708]. Key words. Smith normal form, Hermite normal form, integer matrices, computational complexity
Canonical Correlation Analysis, Approximate Covariance Extension, and Identification of Stationary Time Series
 Automatica
, 1996
"... In this paper we analyze a class of statespace identification algorithms for timeseries, based on canonical correlation analysis, in the light of recent results on stochastic systems theory. In principle, these so called "subspace methods" can be described as covariance estimation follow ..."
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Cited by 36 (17 self)
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In this paper we analyze a class of statespace identification algorithms for timeseries, based on canonical correlation analysis, in the light of recent results on stochastic systems theory. In principle, these so called "subspace methods" can be described as covariance estimation followed by stochastic realization. The methods o#er the major advantage of converting the nonlinear parameter estimation phase in traditional ARMA models identification into the solution of a Riccati equation but introduce at the same time some nontrivial mathematical problems related to positivity. The reason for this is that an essential part of the problem is equivalent to the wellknown rational covariance extension problem. Therefore the usual deterministic arguments based on factorization of a Hankel matrix are not valid for generic data, something that is habitually overlooked in the literature. We demonstrate that there is no guarantee that several popular identification procedures based on the same principle will not fail to produce a positive extension, unless some rather stringent assumptions are made which, in general, are not explicitly reported. In this paper the statistical problem of stochastic modeling from estimated covariances is phrased in the geometric language of stochastic realization theory. We review the basic ideas of stochastic realization theory in the context of identification, discuss the concept of stochastic balancing and of stochastic model reduction by principal subsystem truncation. The model reduction method of Desai and Pal, based on truncated balanced stochastic realizations, is partially justified, showing that the reduced system structure has a positive covariance sequence but is in general not balanced. As a byproduct of this analysis we obtain a t...
Random incidence matrices: moments of the spectral density
 J. Stat. Phys
, 2001
"... We study numerically and analytically the spectrum of incidence matrices of random labeled graphs on N vertices: any pair of vertices is connected by an edge with probability p. We give two algorithms to compute the moments of the eigenvalue distribution as explicit polynomials in N and p. For large ..."
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Cited by 19 (4 self)
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We study numerically and analytically the spectrum of incidence matrices of random labeled graphs on N vertices: any pair of vertices is connected by an edge with probability p. We give two algorithms to compute the moments of the eigenvalue distribution as explicit polynomials in N and p. For large N and fixed p the spectrum contains a large eigenvalue at Np and a semicircle of “small ” eigenvalues. For large N and fixed average connectivity pN (dilute or sparse random matrices limit) we show that the spectrum always contains a discrete component. An anomaly in the spectrum near eigenvalue 0 for connectivity close to e is observed. We develop recursion relations to compute the moments as explicit polynomials in pN. Their growth is slow enough so that they determine the spectrum. The extension of our methods to the Laplacian matrix is given in Appendix.
On the Complexity of Finding Short Vector in Integer Lattices
, 1983
"... this paper we present a modified version of this algorithm n ..."
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Cited by 15 (1 self)
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this paper we present a modified version of this algorithm n
Random Heuristic Search
 Theoretical Computer Science
, 1999
"... There is a developing theory of growing power which, at its current stage of development (indeed, for a number of years now), speaks to qualitative and quantitative aspects of search strategies. Although it has been specialized and applied to genetic algorithms, it's implications and applicabil ..."
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Cited by 12 (1 self)
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There is a developing theory of growing power which, at its current stage of development (indeed, for a number of years now), speaks to qualitative and quantitative aspects of search strategies. Although it has been specialized and applied to genetic algorithms, it's implications and applicability are far more general. This paper deals with the broad outlines of the theory, introducing basic principles and results rather than analyzing or specializing to particular algorithms. A few specific examples are included for illustrative purposes, but the theory's basic structure, as opposed to applications, remains the focus. Key words: Random Heuristic Search, Modeling Evolutionary Algorithms, Degenerate Royal Road Functions. 1 Introduction Vose [20] introduced a rigorous dynamical system model for the binary representation genetic algorithm with proportional selection, mutation determined by a rate, and onepoint crossover, using the simplifying assumption of an infinite population. 1 ...