Matrix Analysis

Horn, Roger A.; Johnson, Charles R.

doi:10.1017/cbo9780511810817

Cited by 10,300 publications

(2,478 citation statements)

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“…For constant environments (i.e. S consists of a single environmental state), this assumption corresponds to a matrix being primitive (Horn & Johnson 1990, Caswell 2001). …”

Section: The Population Dynamicsmentioning

confidence: 99%

Persistence of structured populations in random environments

Benaı̈m

Schreiber

2009

Theoretical Population Biology

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“…For constant environments (i.e. S consists of a single environmental state), this assumption corresponds to a matrix being primitive (Horn & Johnson 1990, Caswell 2001). …”

Section: The Population Dynamicsmentioning

confidence: 99%

Persistence of structured populations in random environments

Benaı̈m

Schreiber

2009

Theoretical Population Biology

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“…Under this assumption, according to Horn and Johnson [37], the product of R S ⊗ B -1 and R H c , denoted by R SC , is positive semidefinite, i.e.,…”

Section: A Joint Optimization With the Weighted Norm Constraintmentioning

confidence: 99%

Joint optimization of MIMO radar waveform and biased estimator with prior information in the presence of clutter

Wang

Liao

Liu

et al. 2011

EURASIP J. Adv. Signal Process.

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In this article, we consider the problem of joint optimization of multi-input multi-output (MIMO) radar waveform and biased estimator with prior information on targets of interest in the presence of signal-dependent noise. A novel constrained biased Cramer-Rao bound (CRB) based method is proposed to optimize the waveform covariance matrix (WCM) and biased estimator such that the performance of parameter estimation can be improved. Under a simplifying assumption, the resultant nonlinear optimization problem is solved resorting to a convex relaxation that belongs to the semidefinite programming (SDP) class. An optimal solution of the initial problem is then constructed through a suitable approximation to an optimal solution of the relaxed one (in a least squares (LS) sense). Numerical results show that the performance of parameter estimation can be improved considerably by the proposed method compared to uncorrelated waveforms.

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“…That is, a necessary and sufficient condition for the strict diagonal dominance of A is that JL > 2 max (ri)· Observing further that all the diagonal elements of A are negative, and applying the Levy-Desplanques Theorem [7], we see that a sufficient condition for the zero solution to be stable is that JL > 2 max (ri)· This is simply a condition of mortality outpacing reproduction, and does not depend on pair formation rates at all. j,F'rom this analysis, we see that in systems where the recruitment rates can be written solely in terms of the aggregates Mi, Fi, i = 1, ... , N, i.e.…”

Section: Xjk = C(kj)mentioning

confidence: 99%

A pair formation approach to modeling inheritance of social traits

Lubkin¹,

Castillo‐Chavez²

1996

World Congress of Nonlinear Analysts '92

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Abstract. Transmission of cultural traits behaves superficially like genetic transmission, but is substantially more complicated, since transmission is influenced by the population at large, as is disease transmission. We present a framework for modeling cultural transmission by a system of ordinary differential equations, with nonlinearities both in the transmission and in the formation of pairs. The framework is illustrated with a simple example.

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Matrix Analysis

Cited by 10,300 publications

References 0 publications

Persistence of structured populations in random environments

Persistence of structured populations in random environments

Joint optimization of MIMO radar waveform and biased estimator with prior information in the presence of clutter

A pair formation approach to modeling inheritance of social traits

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