Determinantal Processes and Independence

We give a probabilistic introduction to determinantal and permanental point processes. Determinantal processes arise in physics (fermions, eigenvalues of random matrices) and in combinatorics (nonintersecting paths, random spanning trees). They have the striking property that the number of points in a region $D$ is a sum of independent Bernoulli random variables, with parameters which are eigenvalues of the relevant operator on $L^2(D)$. Moreover, any determinantal process can be represented as a mixture of determinantal projection processes. We give a simple explanation for these known facts, and establish analogous representations for permanental processes, with geometric variables replacing the Bernoulli variables. These representations lead to simple proofs of existence criteria and central limit theorems, and unify known results on the distribution of absolute values in certain processes with radially symmetric distributions.Comment: Published at http://dx.doi.org/10.1214/154957806000000078 in the Probability Surveys (http://www.i-journals.org/ps/) by the Institute of Mathematical Statistics (http://www.imstat.org

Eigenvalue variance bounds for Wigner and covariance random matrices

This work is concerned with finite range bounds on the variance of individual eigenvalues of Wigner random matrices, in the bulk and at the edge of the spectrum, as well as for some intermediate eigenvalues. Relying on the GUE example, which needs to be investigated first, the main bounds are extended to families of Hermitian Wigner matrices by means of the Tao and Vu Four Moment Theorem and recent localization results by Erd\"os, Yau and Yin. The case of real Wigner matrices is obtained from interlacing formulas. As an application, bounds on the expected 2-Wasserstein distance between the empirical spectral measure and the semicircle law are derived. Similar results are available for random covariance matrices

Obeying the rules of the road: Procedural justice, social identity and normative compliance

Why do people comply with traffic laws and regulations? Road traffic policing tends to be premised on the idea that people comply when they are presented with a credible risk of sanction in the event of non-compliance. Such an instrumental model of compliance contrasts with the normative account offered by procedural justice theory, in which compliance is encouraged by legitimate legal authorities. Comparing these two accounts, we find evidence that both instrumental and normative factors explain variance in motorists’ self-reported propensity to offend. Extending the standard procedural justice account, we also find that it is social identity – not legitimacy – that forms the ‘bridge’ linking procedural fairness and compliance, at least according to a definition of legitimacy that combines felt obligation and moral endorsement. Fair treatment at the hands of police officers seems to enhance identification with the social group the police represent, and in turn, identification seems to motivate adherence to rules (laws) governing social behavior. These findings have implications not only for understandings of legal compliance, but also our understanding of why procedural justice motivates compliance, and the role of procedural justice in promoting social cohesion

Hematopoietic Stem Cell Transplantation Resolves the Immune Deficit Associated with STAT3-Dominant-Negative Hyper-IgE Syndrome.

To access publisher's full text version of this article, please click on the hyperlink in Additional Links field or click on the hyperlink at the top of the page marked DownloadAutosomal dominant hyper-IgE syndrome caused by dominant-negative loss-of-function mutations in signal transducer and activator of transcription factor 3 (STAT3) (STAT3-HIES) is a rare primary immunodeficiency with multisystem pathology. The quality of life in patients with STAT3-HIES is determined by not only the progressive, life-limiting pulmonary disease, but also significant skin disease including recurrent infections and abscesses requiring surgery. Our early report indicated that hematopoietic stem cell transplantation might not be effective in patients with STAT3-HIES, although a few subsequent reports have reported successful outcomes. We update on progress of our patient now with over 18 years of follow-up and report on an additional seven cases, all of whom have survived despite demonstrating significant disease-related pathology prior to transplant. We conclude that effective cure of the immunological aspects of the disease and stabilization of even severe lung involvement may be achieved by allogeneic hematopoietic stem cell transplantation. Recurrent skin infections and abscesses may be abolished. Donor TH17 cells may produce comparable levels of IL17A to healthy controls. The future challenge will be to determine which patients should best be offered this treatment and at what point in their disease history.Job Research Foundation Welsh Clinical Academic Training (WCAT) programme German Research Foundation (DFG) German Research Foundation (DFG) Federal Ministry of Education & Research (BMBF) Center for Chronic Immunodeficiency (CCI), Freiburg Center for Rare Diseases (FZSE

A model for the bus system in Cuernavaca (Mexico)

The bus system in Cuernavaca, Mexico and its connections to random matrix distributions have been the subject of an interesting recent study by M Krbálek and P Šeba in [15, 16]. In this paper we introduce and analyse a microscopic model for the bus system. We show that introducing a natural repulsion does produce random matrix distributions in natural double scaling regimes. The techniques employed include non-intersecting paths, logarithmic potential theory, determinantal point processes, and asymptotic analysis of several orthogonal polynomial ensembles. In addition, we introduce a circular bus model and include various calculations of non-crossing probabilities.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/48795/2/a6_28_s11.pd

Enhancing public trust and police legitimacy during road traffic encounters:Results from a randomised controlled trial in Scotland

Objectives This paper reports results from the Scottish Community Engagement Trial (ScotCET), devised to replicate the Queensland Community Trial (QCET). ScotCET was an RCT that tested the effects of ‘procedurally just’ policing on public trust and police legitimacy Methods A block-randomized (matched pairs) design, with pretest and posttest measures, was implemented in the context of road policing in Scotland. Participants were drivers stopped by police in December and January 2013/14 as part of Police Scotland’s ‘Festive Road Safety Campaign’. The experimental intervention comprised a checklist of key messages to include in routine roadside vehicle stops, and a leaflet for officers to give to drivers. Analysis proceeds via random effects regression models predicting latent variable measures of trust, satisfaction and legitimacy Results Contrary to expectations the intervention did not improve trust and legitimacy; rather, trust in the officers who made the stop, and satisfaction with their conduct fell in the test sites, relative to the controls, after implementation of the intervention. The intervention had no significant effect on general trust in the police, or on police legitimacy. Conclusions Results demonstrate the difficulty in translating experimental interventions across policing contexts, and challenge the notion that public perceptions may be improved through a simple, additive approach to the delivery and communication of procedural justice.</p