Search results for "Functional analysis"
showing 10 items of 1059 documents
Some Remarks on Automata Minimality
2011
It is well known that the minimization problem of deterministic finite automata (DFAs) is related to the indistinguishability notion of states (cf. [HMU00]). Indeed, a well known technique to minimize a DFA, essentially, consists in finding pairs of states that are equivalent (or indistinguishable), namely pairs of states (p,q) such that it is impossible to assert the difference between p and q only by starting in each of the two states and asking whether or not a given input string leads to a final state. Since, in the testing states equivalence, the notion of initial state is irrelevant, some of the main techniques for the minimization of automata, such as Moore’s algorithm [Moo56] and Ho…
Input-output finite-time stability of positive switched linear systems with state delays
2013
This paper is concerned with the problem of input-output finite-time stability (IO-FTS) for a class of discrete-time positive switched systems with time-varying delays. Two sufficient conditions for the existence of IO-FTS of such systems with respect to two different input signals are presented, respectively. All the results obtained are formulated in a set of linear inequalities. Two numerical examples are given to illustrate the effectiveness of the proposed results.
Algebrability of the set of hypercyclic vectors for backward shift operators
2020
Abstract We study the existence of algebras of hypercyclic vectors for weighted backward shifts on Frechet sequence spaces that are algebras when endowed with coordinatewise multiplication or with the Cauchy product. As a particular case, we obtain that the sets of hypercyclic vectors for Rolewicz's and MacLane's operators are algebrable.
Induced &#x2113;<inf>2</inf> control of discrete-time Takagi-Sugeno fuzzy systems with time-varying delays via dynamic output feedback
2012
This paper is concerned with analyzing a novel model transformation of discrete-time Takagi-Sugeno (T-S) fuzzy systems with time-varying delays and applying it to dynamic output feedback (DOF) controller design. A new auxiliary model is proposed by employing a new approximation for time-varying delay state, and then delay partitioning method is used to analyze the scaled small gain of this auxiliary model. A sufficient condition on discrete-time T-S fuzzy systems with time-varying delays, which guarantees the corresponding closed-loop system to be asymptotically stable and has an induced l 2 disturbance attenuation performance, is derived by employing the scaled small gain theorem. Then the…
Universal freezing of quantum correlations within the geometric approach
2015
Quantum correlations in a composite system can be measured by resorting to a geometric approach, according to which the distance from the state of the system to a suitable set of classically correlated states is considered. Here we show that all distance functions, which respect natural assumptions of invariance under transposition, convexity, and contractivity under quantum channels, give rise to geometric quantifiers of quantum correlations which exhibit the peculiar freezing phenomenon, i.e., remain constant during the evolution of a paradigmatic class of states of two qubits each independently interacting with a non-dissipative decohering environment. Our results demonstrate from first …
METABOLIC NETWORKS ROBUSTNESS: THEORY, SIMULATIONS AND RESULTS
2011
Metabolic networks are composed of several functional modules, reproducing metabolic pathways and describing the entire cellular metabolism of an organism. In the last decade, an enormous interest has grown for the study of tolerance to errors and attacks in metabolic networks. Studies on their robustness have suggested that metabolic networks are tolerant to errors, but very vulnerable to targeted attacks against highly connected nodes. However, many findings on metabolic networks suggest that the above classification is too simple and imprecise, since hub node attacks can be by-passed if alternative metabolic paths can be exploited. On the contrary, non-hub nodes attacks can affect cell …
Design for invention: a framework for identifying emerging design–prior art conflict
2018
The increasing complexity of patented mechanical designs means that their novelty and inventive steps increasingly rely on interacting geometric features and how they contribute to device functions. These features and interactions are normally incorporated in patents through clear patent claims. However, patents can be difficult to interpret and understand for designers due to their legal terminologies. This suggests there is a need for greater awareness of relevant prior art amongst designers in terms of avoiding potential conflict. This paper presents a framework that helps designers obtain insight on relevant prior art and enables emerging design–prior art comparison. The framework mainl…
Topological Information, Flux Balance Analysis, and Extreme Pathways Extraction for Metabolic Networks Behaviour Investigation
2011
In recent years biological processes modeling and simulation have become two key issues in analyzing complex cellular systems. Information about metabolic networks is often incomplete, since a large portion of available data is ignored by its probabilistic nature. The main objective of this work is to investigate metabolic networks behavior in terms of their fault tolerance capabilities as random removal of network nodes and high-connectivity-degree node deletion aimed at compromising or modifying network activity. This paper proposes a software framework, namely CEllDataLaB, containing three tasks to perform the structural and functional analysis: topological analysis, flux balance analysi…
Normalised compression distance and evolutionary distance of genomic sequences: comparison of clustering results
2009
Genomic sequences are usually compared using evolutionary distance, a procedure that implies the alignment of the sequences. Alignment of long sequences is a time consuming procedure and the obtained dissimilarity results is not a metric. Recently, the normalised compression distance was introduced as a method to calculate the distance between two generic digital objects and it seems a suitable way to compare genomic strings. In this paper, the clustering and the non-linear mapping obtained using the evolutionary distance and the compression distance are compared, in order to understand if the two distances sets are similar.
Incoherent dispersive shocks in the spectral evolution of random waves
2013
We predict theoretically and numerically the existence of incoherent dispersive shock waves. They manifest themselves as an unstable singular behavior of the spectrum of incoherent waves that evolve in a noninstantaneous nonlinear environment. This phenomenon of "spectral wave breaking" develops in the weakly nonlinear regime of the random wave. We elaborate a general theoretical formulation of these incoherent objects on the basis of a weakly nonlinear statistical approach: a family of singular integro-differential kinetic equations is derived, which provides a detailed deterministic description of the incoherent dispersive shock wave phenomenon.