Level Crossing in Random Matrices: I. Random perturbation of a fixed matrix

We consider level crossing in a matrix family $H=H_0+\lambda V$ where $H_0$ is a fixed $N\times N$ matrix and $V$ belongs to one of the standard Gaussian random matrix ensembles. We study the probability distribution of level crossing points in the complex plane of $\lambda$, for which we obtain a number of exact, asymptotic and approximate formulas.Comment: 35 pages, 16 figures; v2: Introduction and sec. 3.3 expanded, refs. adde

Sentencing Reform for Nonviolent Offenses: Benefits and Estimated Savings for Illinois

Commissioned by the Developing Justice Coalition, this report examines alternatives to incarceration for nonviolent drug offenses. The report discusses the potential cost savings and the social benefits of sentencing nonviolent drug offenders to mandated substance abuse treatment and intensive community supervision instead of prison

Community Organizing in Three South Side Chicago Communities: Leadership, Activities, and Prospects

This study identifies barriers facing groups and leaders in communities on the South Side of Chicago that limit not only their capacity for organizing but also their ability to attract resources for their work. The findings also provide key data on current activities at the grassroots level, with particular attention to groups and leaders that have the potential to expand the scope of their efforts to larger, community-based initiatives

Mechanisms in Adaptive Feedback Control: Photoisomerization in a Liquid

The underlying mechanism for Adaptive Feedback Control in the experimental photoisomerization of NK88 in methanol is exposed theoretically. With given laboratory limitations on laser output, the complicated electric fields are shown to achieve their targets in qualitatively simple ways. Further, control over the cis population without laser limitations reveals an incoherent pump-dump scenario as the optimal isomerization strategy. In neither case are there substantial contributions from quantum multiple-path interference or from nuclear wavepacket coherence. Environmentally induced decoherence is shown to justify the use of a simplified theoretical model.Comment: 10 pages, 3 figures, to be published in Phys. Rev. Let

Pulsed Adiabatic Photoassociation via Scattering Resonances

We develop the theory for the Adiabatic Raman Photoassociation (ARPA) of ultracold atoms to form ultracold molecules in the presence of scattering resonances. Based on a computational method in which we replace the continuum with a discrete set of "effective modes", we show that the existence of resonances greatly aids in the formation of deeply bound molecular states. We illustrate our general theory by computationally studying the formation of $^{85}$Rb$_2$ molecules from pairs of colliding ultracold $^{85}$Rb atoms. The single-event transfer yield is shown to have a near-unity value for wide resonances, while the ensemble-averaged transfer yield is shown to be higher for narrow resonances. The ARPA yields are compared with that of (the experimentally measured) "Feshbach molecule" magneto-association. Our findings suggest that an experimental investigation of ARPA at sub-$\mu$K temperatures is warranted.Comment: 20 pages, 11 figure

Computational Evolutionary Embryogeny

Evolutionary and developmental processes are used to evolve the configurations of 3-D structures in silico to achieve desired performances. Natural systems utilize the combination of both evolution and development processes to produce remarkable performance and diversity. However, this approach has not yet been applied extensively to the design of continuous 3-D load-supporting structures. Beginning with a single artificial cell containing information analogous to a DNA sequence, a structure is grown according to the rules encoded in the sequence. Each artificial cell in the structure contains the same sequence of growth and development rules, and each artificial cell is an element in a finite element mesh representing the structure of the mature individual. Rule sequences are evolved over many generations through selection and survival of individuals in a population. Modularity and symmetry are visible in nearly every natural and engineered structure. An understanding of the evolution and expression of symmetry and modularity is emerging from recent biological research. Initial evidence of these attributes is present in the phenotypes that are developed from the artificial evolution, although neither characteristic is imposed nor selected-for directly. The computational evolutionary development approach presented here shows promise for synthesizing novel configurations of high-performance systems. The approach may advance the system design to a new paradigm, where current design strategies have difficulty producing useful solutions

Performance analysis of low-flux least-squares single-pixel imaging

A single-pixel camera is able to computationally form spatially resolved images using one photodetector and a spatial light modulator. The images it produces in low-light-level operation are imperfect, even when the number of measurements exceeds the number of pixels, because its photodetection measurements are corrupted by Poisson noise. Conventional performance analysis for single-pixel imaging generates estimates of mean-square error (MSE) from Monte Carlo simulations, which require long computational times. In this letter, we use random matrix theory to develop a closed-form approximation to the MSE of the widely used least-squares inversion method for Poisson noise-limited single-pixel imaging. We present numerical experiments that validate our approximation and a motivating example showing how our framework can be used to answer practical optical design questions for a single-pixel camera.This work was supported in part by the Samsung Scholarship and in part by the US National Science Foundation under Grant 1422034. (Samsung Scholarship; 1422034 - US National Science Foundation)Accepted manuscrip

An evaluation of staff engagement programmes in four National Health Service Acute Trusts

Purpose – The purpose of this paper is to report the findings from an evaluation project conducted to investigate the impact of two staff engagement programmes introduced to four National Health Service (NHS) hospital Trusts in England. It seeks to examine this development in the context of current policy initiatives aimed at increasing the level of staff involvement in decision-making, and the related literature. \ud \ud Design/methodology/approach – A mixed-methods approach incorporating document analysis, interviews, a survey and appreciative inquiry, informed by the principles of impact evaluation design, was used. \ud \ud Findings – The main finding to emerge was that leadership was crucial if widespread staff engagement was to be achieved. Indeed, in some of the trusts the staff engagement programmes were seen as mechanisms for developing leadership capability. The programmes had greater impact when they were “championed” by the Chief Executive. Effective communication throughout the organisations was reported to be a prerequisite for staff engagement. Problems were identified at the level of middle management where the lack of confidence in engaging with staff was a barrier to implementation. \ud \ud Practical implications – The nature of the particular organisational context is crucial to the success of efforts to increase levels of staff engagement. The measures that were found to work in the trusts would need to be adapted and applied to best meet the needs of other organisations. \ud \ud Originality/value – Many health care organisations in England will need to harness the efforts of their workforce if they are to meet the significant challenges of dealing with financial restraint and increasing patient demand. This paper provides some insights on how this can be done