Crystallization of random trigonometric polynomials

We give a precise measure of the rate at which repeated differentiation of a random trigonometric polynomial causes the roots of the function to approach equal spacing. This can be viewed as a toy model of crystallization in one dimension. In particular we determine the asymptotics of the distribution of the roots around the crystalline configuration and find that the distribution is not Gaussian.Comment: 10 pages, 3 figure

Individuals living with lupus: findings from the LUPUS UK Members Survey 2014

Systemic lupus erythematosus (SLE) is a complex and unpredictable disease which varies greatly among patients and has a significant impact on an individual’s daily living and quality of life. A better understanding of the patients’ experiences with the disease is vital to the effective management of the disease. LUPUS UK, a national UK-registered charity supporting people with systemic and discoid lupus, conducted a UK-wide survey of individuals living with lupus in order to provide foundation information to support and identify gaps needing further research. An anonymous survey was sent to 5660 LUPUS UK members in order to obtain demographic, diagnosis, symptom and treatment information. A total of 2527 surveys were returned by 2371 females (mean age 56.9 years, SD 13.6) and 156 males, (mean age 60.9 years, SD 15.7). Individuals reported a mean (SD) time to diagnosis from the first symptom of 6.4 (9.5) years, with 47% (n ¼ 1186) initially being given a different diagnosis prior to lupus. Fatigue/weakness (91%, n ¼ 2299) and joint pain/swelling (77.4%, n ¼ 1957) were the most common symptoms that interfere with daily activities, while 73% (n ¼ 1836) noted having some problems that make them unable to carry out their usual daily activities. Thirty-two per cent (n ¼ 806) were also seeking support beyond traditional pharmacological treatments, such as acupuncture and massage. This study highlights the range and frequency of symptoms difficult to live with on a daily basis and support areas needing further research to improve patients’ well-being

Randomly incomplete spectra and intermediate statistics

By randomly removing a fraction of levels from a given spectrum a model is constructed that describes a crossover from this spectrum to a Poisson spectrum. The formalism is applied to the transitions towards Poisson from random matrix theory (RMT) spectra and picket fence spectra. It is shown that the Fredholm determinant formalism of RMT extends naturally to describe incomplete RMT spectra.Comment: 9 pages, 2 figures. To appear in Physical Review

Random polynomials, random matrices, and LL-functions

We show that the Circular Orthogonal Ensemble of random matrices arises naturally from a family of random polynomials. This sheds light on the appearance of random matrix statistics in the zeros of the Riemann zeta-function.Comment: Added background material. Final version. To appear in Nonlinearit

Quantum Chaotic Dynamics and Random Polynomials

We investigate the distribution of roots of polynomials of high degree with random coefficients which, among others, appear naturally in the context of "quantum chaotic dynamics". It is shown that under quite general conditions their roots tend to concentrate near the unit circle in the complex plane. In order to further increase this tendency, we study in detail the particular case of self-inversive random polynomials and show that for them a finite portion of all roots lies exactly on the unit circle. Correlation functions of these roots are also computed analytically, and compared to the correlations of eigenvalues of random matrices. The problem of ergodicity of chaotic wave-functions is also considered. For that purpose we introduce a family of random polynomials whose roots spread uniformly over phase space. While these results are consistent with random matrix theory predictions, they provide a new and different insight into the problem of quantum ergodicity. Special attention is devoted all over the paper to the role of symmetries in the distribution of roots of random polynomials.Comment: 33 pages, Latex, 6 Figures not included (a copy of them can be requested at [email protected]); to appear in Journal of Statistical Physic

An improvement of the Berry--Esseen inequality with applications to Poisson and mixed Poisson random sums

By a modification of the method that was applied in (Korolev and Shevtsova, 2009), here the inequalities $$\rho(F_n,\Phi)\le\frac{0.335789(\beta^3+0.425)}{\sqrt{n}}$$ and $$\rho(F_n,\Phi)\le \frac{0.3051(\beta^3+1)}{\sqrt{n}}$$ are proved for the uniform distance $\rho(F_n,\Phi)$ between the standard normal distribution function $\Phi$ and the distribution function $F_n$ of the normalized sum of an arbitrary number $n\ge1$ of independent identically distributed random variables with zero mean, unit variance and finite third absolute moment $\beta^3$. The first of these inequalities sharpens the best known version of the classical Berry--Esseen inequality since $0.335789(\beta^3+0.425)\le0.335789(1+0.425)\beta^3<0.4785\beta^3$ by virtue of the condition $\beta^3\ge1$, and 0.4785 is the best known upper estimate of the absolute constant in the classical Berry--Esseen inequality. The second inequality is applied to lowering the upper estimate of the absolute constant in the analog of the Berry--Esseen inequality for Poisson random sums to 0.3051 which is strictly less than the least possible value of the absolute constant in the classical Berry--Esseen inequality. As a corollary, the estimates of the rate of convergence in limit theorems for compound mixed Poisson distributions are refined.Comment: 33 page

"Psychic Degenerate": Why G. Was Interned

Abstract This chapter explains how homosexuality was pathologised: to do this, it traces the origins of the "effeminate male" stereotype, explaining how the socio-cultural concept of degeneration was extended to include "sexual inversion". Through the doctors' words, G.'s biography starts to take shape and it becomes clear how it matched the "degenerate" and "effeminate pederast" stereotypical description

Valuing Health Gain from Composite Response Endpoints for Multisystem Diseases

Objectives: This study aimed to demonstrate how to estimate the value of health gain after patients with a multisystem disease achieve a condition-specific composite response endpoint. Methods: Data from patients treated in routine practice with an exemplar multisystem disease (systemic lupus erythematosus) were extracted from a national register (British Isles Lupus Assessment Group Biologics Register). Two bespoke composite response endpoints (Major Clinical Response and Improvement) were developed in advance of this study. Difference-in-differences regression compared health utility values (3-level version of EQ-5D; UK tariff) over 6 months for responders and nonresponders. Bootstrapped regression estimated the incremental quality-adjusted life-years (QALYs), probability of QALY gain after achieving the response criteria, and population monetary benefit of response. Results: Within the sample (n = 171), 18.2% achieved Major Clinical Response and 49.1% achieved Improvement at 6 months. Incremental health utility values were 0.0923 for Major Clinical Response and 0.0454 for Improvement. Expected incremental QALY gain at 6 months was 0.020 for Major Clinical Response and 0.012 for Improvement. Probability of QALY gain after achieving the response criteria was 77.6% for Major Clinical Response and 72.7% for Improvement. Population monetary benefit of response was £1 106 458 for Major Clinical Response and £649 134 for Improvement. Conclusions: Bespoke composite response endpoints are becoming more common to measure treatment response for multisystem diseases in trials and observational studies. Health technology assessment agencies face a growing challenge to establish whether these endpoints correspond with improved health gain. Health utility values can generate this evidence to enhance the usefulness of composite response endpoints for health technology assessment, decision making, and economic evaluation

Building Ideological Bridges and Inventing Institutional Traditions: Festivities and Commemorative Rituals in the Fascist and Nazi Police

This article analyses the employment of rituals of celebration and commemoration to ideologically and culturally bind police forces to the fascist and Nazi dictatorships. It considers public festivities such as ?police day? (Festa della Polizia/Tag der deutschen Polizei) as instruments for demonstrating the professional and political integration of the police into the fascist/Nazi regimes, in the broader context of the staging by these regimes of highly aestheticized rituals to reinforce the national community. Police rituals, notably those involving the commemoration of ?martyrs?, were also employed with the intention of bringing together policemen and fascists/Nazis, by claiming that they shared common values and formative experience. While the ideological success of these rituals is questioned, the article argues that police institutions often willingly participated in them to ensure their occupation of public space and high standing in the eyes of their political masters. The article illustrates the importance of bringing cultural approaches to the study of police history and underlines the need for a more thorough comparison between the police forces of fascist Italy and Nazi Germany