17,236 research outputs found
Dynamical Properties of a Two-gene Network with Hysteresis
A mathematical model for a two-gene regulatory network is derived and several
of their properties analyzed. Due to the presence of mixed continuous/discrete
dynamics and hysteresis, we employ a hybrid systems model to capture the
dynamics of the system. The proposed model incorporates binary hysteresis with
different thresholds capturing the interaction between the genes. We analyze
properties of the solutions and asymptotic stability of equilibria in the
system as a function of its parameters. Our analysis reveals the presence of
limit cycles for a certain range of parameters, behavior that is associated
with hysteresis. The set of points defining the limit cycle is characterized
and its asymptotic stability properties are studied. Furthermore, the stability
property of the limit cycle is robust to small perturbations. Numerical
simulations are presented to illustrate the results.Comment: 55 pages, 31 figures.Expanded version of paper in Special Issue on
Hybrid Systems and Biology, Elsevier Information and Computation, 201
Renormalization of the EWCL and its Application to LEP2
We perform a systematic one-loop renormalization on the electroweak chiral
Lagrangian (EWCL) up to operators and construct the renormalization
group equations (RGE) for the anomalous couplings. We examine the impact of the
triple gauge coupling (TGC) measurement from LEP2 to the uncertainty of the
parameter at the , and find that the uncertainty in the
TGC measurements can shift at least .Comment: 4 pages, 1 eps figure, uses ws-ijmpa.cls. Paralell talk given at
"International Conference on QCD and hadronic Physics", Beijing, China, 16-20
June, 200
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Filtering for networked stochastic time-delay systems with sector nonlinearity
Copyright [2009] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.This paper is concerned with the filtering problem for a class of discrete-time stochastic nonlinear networked control systems with network-induced incomplete measurements. The incomplete measurements include both the multiple random communication delays and random packet losses, which are modeled by a unified stochastic expression in terms of a set of indicator functions that is dependent on certain stochastic variable. The nonlinear functions are assumed to satisfy the sector nonlinearities. The purpose of the addressed filtering problem is to design a linear filter such that the filtering-error dynamics is exponentially mean-square stable. By using the linear-matrix-inequality (LMI) method and delay-dependent technique, sufficient conditions are derived which are dependent on the occurrence probability of both the random communication delays and missing measurement. The filter gain is then characterized by the solution to a set of LMIs. A simulation example is exploited to demonstrate the effectiveness of the proposed design procedures
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On nonlinear H∞ filtering for discrete-time stochastic systems with missing measurements
Copyright [2008] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this paper, the H∞ filtering problem is investigated for a general class of nonlinear discrete-time stochastic systems with missing measurements. The system under study is not only corrupted by state-dependent white noises but also disturbed by exogenous inputs. The measurement output contains randomly missing data that is modeled by a Bernoulli distributed white sequence with a known conditional probability. A filter of very general form is first designed such that the filtering process is stochastically stable and the filtering error satisfies H infin performance constraint for all admissible missing observations and nonzero exogenous disturbances under the zero-initial condition. The existence conditions of the desired filter are described in terms of a second-order nonlinear inequality. Such an inequality can be decoupled into some auxiliary ones that can be solved independently by taking special form of the Lyapunov functionals. As a consequence, a linear time-invariant filter design problem is discussed for the benefit of practical applications, and some simplified conditions are obtained. Finally, two numerical simulation examples are given to illustrate the main results of this paper
Varieties of Mathematics in Economics- A Partial View
Real analysis, founded on the Zermelo-Fraenkel axioms, buttressed by the axiom of choice, is the dominant variety of mathematics utilized in the formalization of economic theory. The accident of history that led to this dominance is not inevitable, especially in an age when the digital computer seems to be ubiquitous in research, teaching and learning. At least three other varieties of mathematics, each underpinned by its own mathematical logic, have come to be used in the formalization of mathematics in more recent years. To set theory, model theory, proof theory and recursion theory correspond, roughly speaking, real analysis, non-standard analysis, constructive analysis and computable analysis. These other varieties, we claim, are more consistent with the intrinsic nature and ontology of economic concepts. In this paper we discuss aspects of the way real analysis dominates the mathematical formalization of economic theory and the prospects for overcoming this dominance.
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