Stability of linear difference and differential inclusions

Any given n X n matrix A is shown to be a restriction, to the A-invariant subspace, of a nonnegative N x N matrix B of spectral radius p(B) arbitrarily close to p(A). A difference inclusion x(k+1) is an element of Ax(k), where A is a compact set of matrices, is asymptotically stable if and only if A can be extended to a set B of nonnegative matrices B with \ \B \ \ (1) < 1 or \ \B \ \ (infinity) < 1. Similar results are derived for differential inclusions.

The impact of an expert's gender on jurors' decisions

This study uses a simulated civil trial to examine the effect of a male expert's testimony in a male-dominated industry as compared to a female expert's testimony in a traditionally female-dominated industry. ... As noted by Cooper et al., research on persuasion has reliably demonstrated that, under conditions of message complexity, people rely on heuristic cues rather than the content of the message when judging its validity. ... Similarly, Swenson, Nash, and Roos determined that a female expert witness in a child custody dispute was perceived as possessing greater expertise than a male expert, although this difference was only marginally significant. Findings from an unpublished dissertation, which investigated the influence of expert gender in a case involving child sexual abuse, also found some support, in terms of whether or not jurors reached a verdict in a specified period of time or remained hung, for the hypothesis that a female expert would be more influential than her male counterpart. ... Within each of these trial domains (construction, women's clothing), the second experimental variable was manipulated by varying the gender of the plaintiff's expert witness, with half of the participants receiving testimony from a female expert (Dr. Elizabeth Pinder) and half of the participants receiving testimony from a male expert (Dr. Michael Pinder).

Towards a definition of "difference" in osteoarthritis

To assess existing information regarding detectable differences in osteoarthritis (OA), a systematic literature search was conducted up to December 1999. Thirty-three articles were considered methodologically relevant to the definition and categorization of detectable differences in OA. It was determined that the musculoskeletal literature contains a wealth of information that relates to observed changes, much of which is derived from the clinical trials literature, but there have been relatively few methodological studies that have systematically evaluated the nature, categorization, and relevance of the change. Furthermore, most of those that have been published take the perspective of an individual or groups of experts other than that of the patient. This summary of the current literature reveals that the diverse sources of information go part way towards developing an understanding of detectable differences and their importance in the area of OA research and clinical practice. Stakeholders' interests as well as factors that modulate perceptions of importance need to be taken under consideration. In particular, the patient's perspective of the importance of change at an individual level requires further evaluation. This area of clinical research is relatively underdeveloped, but there is considerable opportunity for progress.

Regulation of male sexual development by Sry and Sox9

Sry, a gene from the Y chromosome, is known to initiate testis formation and subsequent male differentiation in mammals. A related gene, Sox9, also plays a critical role in testis determination, possibly in all vertebrates. A number of models have been presented regarding the molecular modes of action of these two genes. However, details regarding their regulation, regulatory target genes, and interacting protein factors and co-factors have not been established with any certainty. In this review, we examine new evidence and re-examine existing evidence bearing on these issues, in an effort to build up an integrative model of the network of gene activity centred around Sry and Sox9. J. Exp. Zool. 290:463-474, 2001. (C) 2001 Wiley-Liss, Inc.

Interaction between natural and sexual selection during the evolution of mate recognition

The interaction between natural and sexual selection is central to many theories of how mate choice and reproductive isolation evolve, but their joint effect on the evolution of mate recognition has not, to my knowledge, been investigated in an evolutionary experiment. Natural and sexual selection were manipulated in interspecific hybrid populations of Drosophila to determine their effects on the evolution of a mate recognition system comprised of cuticular hydrocarbons (CHCs). The effect of natural selection in isolation indicated that CHCs were costly for males and females to produce. The effect of sexual selection in isolation indicated that females preferred males with a particular CHC composition. However, the interaction between natural and sexual selection had a greater effect on the evolution of the mate recognition system than either process in isolation. When natural and sexual selection were permitted to operate in combination, male CHCs became exaggerated to a greater extent than in the presence of sexual selection alone, and female CHCs evolved against the direction of natural selection. This experiment demonstrated that the interaction between natural and sexual selection is critical in determining the direction and magnitude of the evolutionary response of the mate recognition system.

Boundary value problems for systems of difference equations associated with systems of second-order ordinary differential equations

We study difference equations which arise as discrete approximations to two-point boundary value problems for systems of second-order ordinary differential equations. We formulate conditions which guarantee a priori bounds on first differences of solutions to the discretized problem. We establish existence results for solutions to the discretized boundary value problems subject to nonlinear boundary conditions. We apply our results to show that solutions to the discrete problem converge to solutions of the continuous problem in an aggregate sense. (C) 2002 Elsevier Science Ltd. All rights reserved.

Difference equations associated with fully nonlinear boundary value problems for second order ordinary differential equations

We study the continuous problem y"=f(x,y,y'), xc[0,1], 0=G((y(0),y(1)),(y'(0), y'(1))), and its discrete approximation (y(k+1)-2y(k)+y(k-1))/h(2) =f(t(k), y(k), v(k)), k = 1,..., n-1, 0 = G((y(0), y(n)), (v(1), v(n))), where f and G = (g(0), g(1)) are continuous and fully nonlinear, h = 1/n, v(k) = (y(k) - y(k-1))/h, for k =1,..., n, and t(k) = kh, for k = 0,...,n. We assume there exist strict lower and strict upper solutions and impose additional conditions on f and G which are known to yield a priori bounds on, and to guarantee the existence of solutions of the continuous problem. We show that the discrete approximation also has solutions which approximate solutions of the continuous problem and converge to the solution of the continuous problem when it is unique, as the grid size goes to 0. Homotopy methods can be used to compute the solution of the discrete approximation. Our results were motivated by those of Gaines.

Body mass index-related human adipocyte agouti expression is sex-specific but not depot-specific

Objective: To determine if human adipocyte agouti signal protein (ASIP) mRNA expression is associated with obesity and is gender and/or depot specific. Research Methods and Procedures: Subjects included 8 men (64 +/- 3 years) and 14 women (56 +/- 15 years) undergoing elective abdominal surgery. ASIP mRNA levels in isolated omental and subcutaneous abdominal adipocytes were measured by quantitative reverse transcription polymerase chain reaction. Results: No significant depot difference was observed between genders; ASIP mRNA levels of omental and subcutaneous abdominal adipocytes were pooled for this analysis. BMI and ASIP gene expression were negatively correlated in men (p = -0.70; p < 0.05), whereas a positive relationship was observed in women (p = 0.48; p < 0.05). No significant difference was observed in age, body weight, body mass index (BMI), and waist circumference between groups. Hip circumference was significantly higher in women than in men (p < 0.05). Also, no significant difference in ASIP mRNA expression was observed between men and women, regardless of the fat depot. Discussion: These results show that men and women of similar age and BMI present similar ASIP mRNA levels in omental and subcutaneous abdominal adipocytes. However, a sexual dimorphism exists in the relationship between ASIP expression and BMI. If ASIP is involved in appetite regulation or energy homeostasis in humans, this observation may contribute to the recognized differences in these parameters between men and women.