Combinatorial coherent states via normal ordering of bosons

We construct and analyze a family of coherent states built on sequences of integers originating from the solution of the boson normal ordering problem. These sequences generalize the conventional combinatorial Bell numbers and are shown to be moments of positive functions. Consequently, the resulting coherent states automatically satisfy the resolution of unity condition. In addition they display such non-classical fluctuation properties as super-Poissonian statistics and squeezing.Comment: 12 pages, 7 figures. 20 references. To be published in Letters in Mathematical Physic

Dobinski-type relations: Some properties and physical applications

We introduce a generalization of the Dobinski relation through which we define a family of Bell-type numbers and polynomials. For all these sequences we find the weight function of the moment problem and give their generating functions. We provide a physical motivation of this extension in the context of the boson normal ordering problem and its relation to an extension of the Kerr Hamiltonian.Comment: 7 pages, 1 figur

Combinatorial Physics, Normal Order and Model Feynman Graphs

The general normal ordering problem for boson strings is a combinatorial problem. In this note we restrict ourselves to single-mode boson monomials. This problem leads to elegant generalisations of well-known combinatorial numbers, such as Bell and Stirling numbers. We explicitly give the generating functions for some classes of these numbers. Finally we show that a graphical representation of these combinatorial numbers leads to sets of model field theories, for which the graphs may be interpreted as Feynman diagrams corresponding to the bosons of the theory. The generating functions are the generators of the classes of Feynman diagrams.Comment: 9 pages, 4 figures. 12 references. Presented at the Symposium 'Symmetries in Science XIII', Bregenz, Austria, 200

Association between telomere length and complete blood count in US adults

Introduction: Telomere length (TL) is related to age-related health outcomes, but little is known about the relationship between TL and complete blood count (CBC) parameters. We aimed to determine the relationship between TL and CBC in a sample of healthy US adults. Material and methods: Participants in the National Health and Nutrition Examination Survey (NHANES) recruited between 1999 and 2002 who had essential data on total CBC and TL were studied. We computed age- and race-adjusted mean values for total CBC using analysis of covariance (ANCOVA). All statistical analyses accounted for the survey design and sample weights by using SPSS Complex Samples v22.0 (IBM Corp, Armonk, NY). Results: Of the 8892 eligible participants, 47.8% (n = 4123) were men. The mean age was 41.8 years overall, 41.0 years in men and 42.6 in women (p = 0.238). The sex-stratified ANCOVA showed no significant difference in the total CBC across TL quartiles (all p > 0.05) in both sexes. In the adjusted model, there was a significant negative relationship with monocyte count ( = –0.051, 95% CI: –0.422; –0.142), mean cell hemoglobin ( = –0.051, 95% CI: –0.038; –0.011) and red cell distribution width ( = –0.031, 95% CI: –0.054; –0.003), while there was a significant positive relationship with basophil ratio ( = 0.046, 95% CI: 0.049–0.171). Conclusions: These results support the possibility that telomere attrition may be a marker for reduced proliferative reserve in hematopoietic progenitor cells

Hopf Algebras in General and in Combinatorial Physics: a practical introduction

This tutorial is intended to give an accessible introduction to Hopf algebras. The mathematical context is that of representation theory, and we also illustrate the structures with examples taken from combinatorics and quantum physics, showing that in this latter case the axioms of Hopf algebra arise naturally. The text contains many exercises, some taken from physics, aimed at expanding and exemplifying the concepts introduced

A product formula and combinatorial field theory

We treat the problem of normally ordering expressions involving the standard boson operators a, ay where [a; ay] = 1. We show that a simple product formula for formal power series | essentially an extension of the Taylor expansion | leads to a double exponential formula which enables a powerful graphical description of the generating functions of the combinatorial sequences associated with such functions | in essence, a combinatorial eld theory. We apply these techniques to some examples related to specic physical Hamiltonians

LDL-C: Lower is Better for Longer - Even at Low Risk

Background: Low-density lipoprotein cholesterol (LDL-C) causes atherosclerotic disease, as demonstrated in experimental and epidemiological cohorts, randomised controlled trials, and Mendelian randomisation studies. Main text: There is considerable inconsistency between existing guidelines as to how to effectively manage patients at low overall risk of cardiovascular disease (CVD) who have persistently elevated levels of LDL-C. We propose a step-by-step practical approach for the management of cardiovascular risks in individuals with low ( 140 mg/dL, 3.6 mmol/L) LDL-C. The strategy proposed is based on the level of adherence to lifestyle interventions (LSI), and in case of non-adherence, stepwise practical management, including lipid-lowering therapy, is recommended to achieve a target LDL-C levels (< 115 mg/dL, 3.0 mmol/L). Conclusions: Further studies are necessary to answer the questions on the long-term efficacy, safety, and cost-effectiveness of the suggested approach. This is critical, considering the ever-increasing numbers of such low-risk patients seen in clinical practice

Hierarchical Dobinski-type relations via substitution and the moment problem

We consider the transformation properties of integer sequences arising from the normal ordering of exponentiated boson ([a,a*]=1) monomials of the form exp(x (a*)^r a), r=1,2,..., under the composition of their exponential generating functions (egf). They turn out to be of Sheffer-type. We demonstrate that two key properties of these sequences remain preserved under substitutional composition: (a)the property of being the solution of the Stieltjes moment problem; and (b) the representation of these sequences through infinite series (Dobinski-type relations). We present a number of examples of such composition satisfying properties (a) and (b). We obtain new Dobinski-type formulas and solve the associated moment problem for several hierarchically defined combinatorial families of sequences.Comment: 14 pages, 31 reference