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Symmetric Case (symmetric + case)

Distribution by Scientific Domains
Mathematics and Statistics40%

Selected Abstracts

MULTILOCUS GENETICS AND THE COEVOLUTION OF QUANTITATIVE TRAITS

EVOLUTION, Issue 7 2006
Michael Kopp
Abstract We develop and analyze an explicit multilocus genetic model of coevolution. We assume that interactions between two species (mutualists, competitors, or victim and exploiter) are mediated by a pair of additive quantitative traits that are also subject to direct stabilizing selection toward intermediate optima. Using a weak-selection approximation, we derive analytical results for a symmetric case with equal locus effects and no mutation, and we complement these results by numerical simulations of more general cases. We show that mutualistic and competitive interactions always result in coevolution toward a stable equilibrium with no more than one polymorphic locus per species. Victimexploiter interactions can lead to different dynamic regimes including evolution toward stable equilibria, cycles, and chaos. At equilibrium, the victim is often characterized by a very large genetic variance, whereas the exploiter is polymorphic in no more than one locus. Compared to related one-locus or quantitative genetic models, the multilocus model exhibits two major new properties. First, the equilibrium structure is considerably more complex. We derive detailed conditions for the existence and stability of various classes of equilibria and demonstrate the possibility of multiple simultaneously stable states. Second, the genetic variances change dynamically, which in turn significantly affects the dynamics of the mean trait values. In particular, the dynamics tend to be destabilized by an increase in the number of loci. [source]

The effect of parameter mismatches on the output waveform of an LC -VCO

INTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS, Issue 5 2010
Antonio Buonomo
Abstract The effect of parameter mismatches on the output waveforms of a popular voltage-controlled oscillator is investigated, schematizing the circuit as a system of two mutually coupled oscillators, whose describing equations are derived in a perturbation form. The circuit is studied using the method of two time-scales showing the existence of synchronization phenomena leading in presence of mismatches to a locking frequency, which significantly differs from the natural frequencies of the tanks, and to an oscillation amplitude different from that of the symmetric case. We also show that in-phase and quadrature oscillations at the drain nodes can be generated with a proper parameter setting. Circuit simulations confirm the presence of a synchronized oscillation, which is consistent with the prediction of the presented analysis. Copyright © 2009 John Wiley & Sons, Ltd. [source]

AGGLOMERATION VERSUS PRODUCT VARIETY: IMPLICATIONS FOR REGIONAL INEQUALITIES,

JOURNAL OF REGIONAL SCIENCE, Issue 5 2006
Kristian Behrens
ABSTRACT We investigate how cross-country differences in firms' fixed set-up costs affect the trade-off between global efficiency and spatial equity. Our analysis reveals that the standard assumption of symmetry in set-up costs masks the existence of an interesting effect: the range of available varieties depends on the spatial distribution of firms. In such a setting, where the market outcome leads to excessive agglomeration in the symmetric case, a planner may opt for asymmetric set-up costs and even more agglomeration. We show that the planner will always favor lower set-up costs in the large country with more agglomeration when the consumer's marginal preference for variety is high, or with less agglomeration when the consumer's marginal preference for variety is low. [source]

Asymptotic analysis and estimates of blow-up time for the radial symmetric semilinear heat equation in the open-spectrum case

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 13 2007
N. I. Kavallaris
Abstract We estimate the blow-up time for the reaction diffusion equation ut=,u+ ,f(u), for the radial symmetric case, where f is a positive, increasing and convex function growing fast enough at infinity. Here ,>,*, where ,* is the ,extremal' (critical) value for ,, such that there exists an ,extremal' weak but not a classical steady-state solution at ,=,* with ,w(,, ,),,,, as 0<,,,*,. Estimates of the blow-up time are obtained by using comparison methods. Also an asymptotic analysis is applied when f(s)=es, for ,,,*,1, regarding the form of the solution during blow-up and an asymptotic estimate of blow-up time is obtained. Finally, some numerical results are also presented. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Small confidence sets for the mean of a spherically symmetric distribution

JOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 3 2005
Richard Samworth
Summary., Suppose that X has a k -variate spherically symmetric distribution with mean vector , and identity covariance matrix. We present two spherical confidence sets for ,, both centred at a positive part Stein estimator . In the first, we obtain the radius by approximating the upper , -point of the sampling distribution of by the first two non-zero terms of its Taylor series about the origin. We can analyse some of the properties of this confidence set and see that it performs well in terms of coverage probability, volume and conditional behaviour. In the second method, we find the radius by using a parametric bootstrap procedure. Here, even greater improvement in terms of volume over the usual confidence set is possible, at the expense of having a less explicit radius function. A real data example is provided, and extensions to the unknown covariance matrix and elliptically symmetric cases are discussed. [source]