Eigenvalue Attraction

We prove that the complex conjugate (c.c.) eigenvalues of a smoothly varying real matrix attract (Eq. 15). We offer a dynamical perspective on the motion and interaction of the eigenvalues in the complex plane, derive their governing equations and discuss applications. C.c. pairs closest to the real axis, or those that are ill-conditioned, attract most strongly and can collide to become exactly real. As an application we consider random perturbations of a fixed matrix $M$. If $M$ is Normal, the total expected force on any eigenvalue is shown to be only the attraction of its c.c. (Eq. 24) and when $M$ is circulant the strength of interaction can be related to the power spectrum of white noise. We extend this by calculating the expected force (Eq. 41) for real stochastic processes with zero-mean and independent intervals. To quantify the dominance of the c.c. attraction, we calculate the variance of other forces. We apply the results to the Hatano-Nelson model and provide other numerical illustrations. It is our hope that the simple dynamical perspective herein might help better understanding of the aggregation and low density of the eigenvalues of real random matrices on and near the real line respectively. In the appendix we provide a Matlab code for plotting the trajectories of the eigenvalues.Comment: v1:15 pages, 12 figures, 1 Matlab code. v2: very minor changes, fixed a reference. v3: 25 pages, 17 figures and one Matlab code. The results have been extended and generalized in various ways v4: 26 pages, 10 figures and a Matlab Code. Journal Reference Added. http://link.springer.com/article/10.1007%2Fs10955-015-1424-

Sexual Attraction Toward Clients, Use of Supervision, and Prior Training: A Qualitative Study of Predoctoral Psychology Interns

Interviews were conducted with 13 predoctoral psychology interns about an experience of sexual attraction toward a client, use of supervision to address the sexual attraction, and prior training regarding sexual attraction. Results indicated that sexual attraction to clients consisted of physical and interpersonal aspects. Therapists believed they were more invested and attentive than usual to clients to whom they were sexually attracted, and they indicated that sexual attraction created distance, distraction, and loss of objectivity. In terms of supervision, only half of the participants disclosed their sexual attraction to supervisors, and supervisors seldom initiated the discussion. Furthermore, trainees found it helpful when supervisors normalized the sexual attraction and provided the opportunity to explore feelings in supervision. Finally, trainees believed their training programs did not adequately address therapist sexual attraction

Applicant Attraction Strategies: An Organizational Perspective

Developing labor shortages are expected to increase the importance of applicant attraction into the next century. Unfonunately, previous research has provided little in the way of unified theory or operational guidelines for organizations confronted with attraction difficulties. In part, this is because much research has been framed from the applicant\u27s, rather than the organization\u27s, perspective. In addition, attraction-related theories and research are scattered across a variety of literatures, and often identified primarily with topics other than attraction per se (e.g., wage, motivation, or discrimination theories). The present paper draws on multiple literatures to develop a model of applicant attraction from the organization\u27s perspective. In it, we (1) outline three general strategies for enhancing applicant attraction, (2) propose broad categories of contingency factors expected to affect the choice (and potential effectiveness) of alternative strategies, (3) suggest probable interrelationships among the strategies, (4) link applicant attraction strategies to other human resource practices, (5) outline various dimensions of attraction outcomes (e.g. qualitative and quantitative, attitudinal and behavioral, temporal), and (6) discuss implications for future attraction research

Criteria for strong and weak random attractors

The theory of random attractors has different notions of attraction, amongst them pullback attraction and weak attraction. We investigate necessary and sufficient conditions for the existence of pullback attractors as well as of weak attractors

A new concept of invariance for saturated systems

In this paper, a new concept of invariance for saturated linear systems is presented. This new notion of invariance, denoted SNS-invariance, has a number of geometrical properties that makes its use suitable for the estimation of the domain of attraction of saturated systems. The notion of SNS-domain of attraction, that serves as an estimation of the domain of attraction of a saturated system, is introduced. It is shown that, in case of single input saturated systems, any contractive set is contained in the SNS-domain of attraction. A simple algorithm that converges to the SNS-domain of attraction is presented. Some illustrative examples are given

Nonlinear rheology of dense colloidal systems with short-ranged attraction: A mode-coupling theory analysis

The nonlinear rheology of glass-forming colloidal suspensions with short-ranged attractions is discussed within the integration-through transients framework combined with the mode-coupling theory of the glass transition (ITT-MCT). Calculations are based on the square-well system (SWS), as a model for colloid-polymer mixtures. The high-density regime featuring reentrant melting of the glass upon increasing the attraction strength, and the crossover from repulsive glasses formed at weak attraction to attractive glasses formed at strong attraction, are discussed. Flow curves are found in qualitative agreement with experimental data, featuring a strong increase in the yield stress, and, for suitable interaction parameters, the crossover between two yield stresses. The yield strain, defined as the position of the stress overshoot under startup flow, is found to be proportional to the attraction range for strong attraction. At weak and intermediate attraction strength, the combined effects of hard-core caging and attraction-driven bonding result in a richer dependence on the parameters. The first normal-stress difference exhibits a weaker dependence on short-ranged attractions as the shear stress, since the latter is more sensitive the short-wavelength features of the static structure.Comment: 14 pages, 12 figure