Search

The purpose of this paper is to state the correct formulation of a theorem proposed by M. Roitman and Z. Rubinstein on the characterization of linear recursions which imply a linear recursion with nonnegative coefficients. The authors present a counterexample to such a theorem and then state its correct formulation.

Large-scale "omics" data are often represented as networks of interacting components, but such representation is inherently static and, as such, cannot provide a realistic picture of the temporal dynamics of complex cellular functions. These difficulties suggest moving to a modeling strategy that explicitly takes into account both the wiring of the components and the task they perform. From an engineering perspective, this problem resembles that of "circuit analysis". In this paper, we focus on a limited but relevant biological circuit, the G1 to S transition in yeast cell cycle, and investigate both the network representation and the corresponding circuit described by a mathematical model, by means of a wide range of numerical simulation analysis. Reliable predictions of system-level properties are achieved and the parameters that mostly affect these properties are found out. © 2010 Elsevier Inc. All rights reserved.

The area of signal processing is very wide. In this review paper we will focus on how the theory of nonnegative matrices may arise in the field of digital filter design: an area in which the role of nonnegative matrices is increasingly relevant due to the development of new technologies in the field of optical components and charge coupling devices.

Compartmental systems are composed of a finite number of subsystems, called compartments, interacting by exchanging material. We propose a set of constraints ensuring compartmentality in an identification process.

Positive systems are systems in which the input/state/output variables are always positive since they represent quantities. We propose an identification procedure for a class of positive linear systems.

In this survey paper some recent results on the minimality problem for positive realizations are discussed. In particular, it is firstly shown, by means of two examples, that the minimal dimension of a positive realization of a given transfer function, may be much 'larger' than its McMillan degree. Then, necessary and sufficient conditions for the minimality of a given positive realization in terms of positive factorization of the Hankel matrix are given. Finally, necessary and sufficient conditions for a third order transfer function with distinct real positive poles to have a third order positive realization are provided.

In this paper, based on algebraic arguments, a new proof of the spectral characterization of those real matrices which leave a proper polyhedral cone invariant - see Tam and Schneider (1994) - is given. The proof is a constructive one, as it allows to explicitly obtain for every matrix A, which satisfies the aforementioned spectral requirements, an A-invariant proper polyhedral cone K . Some new results are also presented, concerning the way A acts on the cone K . In particular, K -irreducibility, K -primitivity and K -positivity are fully characterized. Connections between the afforded problem and the more general problem of constrained control of a linear state space model are later explored, by means of a significant example, in the concluding section.

The positive realization problem for linear systems is to find, for a given transfer function, all possible realizations with a state space of minimal dimension such that the resulting system is a positive system. In this paper, discrete-time positive linear systems having the nonnegative orthant reachable from the origin in a finite time interval with nonnegative inputs, are considered and the solution of the positive realization problem for this class of systems is given.

The positive realization problem for linear systems is to find conditions, for a given transfer function with nonnegative impulse response, to have a realization such that the resulting system is a positive system. Recently, it has been shown that, under a mild assumption on the long-term behaviour of the impulse response, this problem is related to the maximum modulus poles only. In this paper necessary and sufficient conditions for positive realizability of discrete-time systems are given. They show that also nondominant poles play a role in the most general case. Positive realizability conditions for the continuous-time case are also given.

A discrete-time positive linear system has the property that any nonnegative initial state and any nonnegative input produces a nonnegative trajectory in the state space and output for all time. Such systems are R n+ - reachable if every state of the nonnegative orthant R n+ is reachable from origin with a nonnegative input function, in a finite-time interval. A simple necessary and sufficient condition for R n+ - realizability , i.e. for the existence of a nonnegative realization that is also R n+ - reachable , is stated. The realization procedure is straightforward.