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

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

Quantum statistical properties of some new classes of intelligent states associated with special quantum systems

Based on the {\it nonlinear coherent states} method, a general and simple algebraic formalism for the construction of \textit{`$f$-deformed intelligent states'} has been introduced. The structure has the potentiality to apply to systems with a known discrete spectrum as well as the generalized coherent states with known nonlinearity function $f (n)$. As some physical appearance of the proposed formalism, a few new classes of intelligent states associated with \textit{`center of-mass motion of a trapped ion'}, \textit{`harmonious states'} and \textit{`hydrogen-like spectrum'} have been realized. Finally, the nonclassicality of the obtained states has been investigated. To achieve this purpose the quantum statistical properties using the Mandel parameter and the squeezing of the quadratures of the radiation field corresponding to the introduced states have been established numerically.Comment: 13page

Effects of carbohydrate restricted diets on low density lipoprotein-cholesterol levels in overweight and obese adults: a systematic review and meta-analysis of large randomised controlled trials of at least 6 months

Context: Carbohydrate restricted diets may increase low density lipoprotein-cholesterol and thereby cardiovascular risk. Objective: A systematic review and meta-analyses was conducted to compare the effects of very low, low and moderate carbohydrate higher fat diets versus high-carbohydrate low-fat diets on low density lipoprotein-cholesterol and other lipid markers in overweight/obese adults. Data Sources: Medline, PubMed, Cochrane Central, and CINAHL Plus were searched to identify large randomised controlled trials (n > 100) with duration ≥ 6 months. Data Extraction: Eight randomised controlled trials (n = 1633, 818 carbohydrate restricted, 815 low fat diet) were included. Data Analysis: Quality assessment and risk of bias, a random effects model, sensitivity and subgroup analysis based on the degree of carbohydrate restriction were performed using Cochrane Review Manager. Results were reported according to ‘Preferred Reporting Items for Systematic Reviews and Meta-Analysis Protocol’. Results: Carbohydrate restricted diets showed a none significant difference in low density lipoprotein cholesterol after 6, 12, and 24 months. While an overall pooled analysis statistically favoured low-fat diets [0.07 mmol/L; 95% CI 0.02, 0.13; p = 0.009] this was clinically insignificant. High density lipoprotein-cholesterol and plasma triglycerides at 6 and 12 months, favoured carbohydrate restricted diets [0.08 mmol/L, 95% CI 0.06, 0.11; p < 1x10-5 37 and -0.13 mmol/L, 95% CI -0.19, -0.08; p < 1x10-5] respectively. These favourable changes were more marked in the subgroup with very-low carbohydrate content (< 50 g/day) [0.12 mmol/L, 95% CI 0.10, 0.14; p < 1x10-5 40 and -0.19 mmol/L, 95% CI -0.26, -0.12, p = 0.02] respectively. Conclusions: Large randomised controlled trials of at least 6 months duration with carbohydrate restriction appear superior in improving lipid markers when compared to low-fat diets. Dietary guidelines should consider carbohydrate restriction as an alternative dietary strategy for the prevention/management of dyslipidaemia for populations with cardiometabolic risk

Representations of Coherent and Squeezed States in a ff-deformed Fock Space

We establish some of the properties of the states interpolating between number and coherent states denoted by $| n >_{\lambda}$; among them are the reproducing of these states by the action of an operator-valued function on $| n>$ (the standard Fock space) and the fact that they can be regarded as $f$-deformed coherent bound states. In this paper we use them, as the basis of our new Fock space which in this case are not orthogonal but normalized. Then by some special superposition of them we obtain new representations for coherent and squeezed states in the new basis. Finally the statistical properties of these states are studied in detail.Comment: 13 pages, 4 Figure

Real-world outcomes of sipuleucel-T treatment in PROCEED, a prospective registry of men with metastatic castration-resistant prostate cancer.

BackgroundThe large registry, PROVENGE Registry for the Observation, Collection, and Evaluation of Experience Data (PROCEED)(NCT01306890), evaluated sipuleucel-T immunotherapy for asymptomatic/minimally symptomatic metastatic castration-resistant prostate cancer (mCRPC).MethodsPROCEED enrolled patients with mCRPC receiving 3 biweekly sipuleucel-T infusions. Assessments included overall survival (OS), serious adverse events (SAEs), cerebrovascular events (CVEs), and anticancer interventions (ACIs). Follow-up was for ≥3&nbsp;years or until death or study withdrawal.ResultsIn 2011-2017, 1976 patients were followed for 46.6&nbsp;months (median). The median age was 72&nbsp;years, and the baseline median prostate-specific antigen level was 15.0&nbsp;ng/mL; 86.7% were white, and 11.6% were African American. Among the patients, 1902 had 1 or more sipuleucel-T infusions. The median OS was 30.7&nbsp;months (95% confidence interval [CI], 28.6-32.2&nbsp;months). Known prognostic factors were independently associated with OS in a multivariable analysis. Among the 1255 patients who died, 964 (76.8%) died of prostate cancer (PC) progression. The median time from the first infusion to PC death was 42.7&nbsp;months (95% CI, 39.4-46.2&nbsp;months). The incidence of sipuleucel-T-related SAEs was 3.9%. The incidence of CVEs was 2.8%, and the rate per 100 person-years was 1.2 (95% CI, 0.9-1.6). The CVE incidence among 11,972 patients with mCRPC from the Surveillance, Epidemiology, and End Results-Medicare database was 2.8%; the rate per 100 person-years was 1.5 (95% CI, 1.4-1.7). One or more ACIs (abiraterone, enzalutamide, docetaxel, cabazitaxel, or radium 223) were received by 77.1% of the patients after sipuleucel-T; 32.5% and 17.4% of the patients experienced 1- and 2-year treatment-free intervals, respectively.ConclusionsPROCEED provides contemporary survival data for sipuleucel-T-treated men in a real-world setting of new life-prolonging agents, which will be useful in discussing treatment options with patients and in powering future trials with sipuleucel-T. The safety and tolerability of sipuleucel-T in PROCEED were consistent with previous findings

A phase I study of the safety and pharmacokinetics of the histone deacetylase inhibitor belinostat administered in combination with carboplatin and/or paclitaxel in patients with solid tumours

BACKGROUND: This phase I study assessed the maximum tolerated dose, dose-limiting toxicity (DLT) and pharmacokinetics of belinostat with carboplatin and paclitaxel and the anti-tumour activity of the combination in solid tumours. METHODS: Cohorts of three to six patients were treated with escalating doses of belinostat administered intravenously once daily, days 1-5 q21 days; on day 3, carboplatin (area under the curve (AUC) 5) and/or paclitaxel (175 mgm(-2)) were administered 2-3 h after the end of the belinostat infusion. RESULTS: In all 23 patients received 600-1000 mgm(-2) per day of belinostat with carboplatin and/or paclitaxel. No DLT was observed. The maximal administered dose of belinostat was 1000 mgm(-2) per day for days 1-5, with paclitaxel (175 mgm-2) and carboplatin AUC 5 administered on day 3. Grade III/IV adverse events were (n; %): leucopenia (5; 22%), neutropenia (7; 30%), thrombocytopenia (3; 13%) anaemia (1; 4%), peripheral sensory neuropathy (2; 9%), fatigue (1; 4%), vomiting (1; 4%) and myalgia (1; 4%). The pharmacokinetics of belinostat, paclitaxel and carboplatin were unaltered by the concurrent administration. There were two partial responses (one rectal cancer and one pancreatic cancer). A third patient (mixed mullerian tumour of ovarian origin) showed a complete CA-125 response. In addition, six patients showed a stable disease lasting >= 6 months. CONCLUSION: The combination was well tolerated, with no evidence of pharmacokinetic interaction. Further evaluation of anti-tumour activity is warranted. British Journal of Cancer (2010) 103, 12-17. doi:10.1038/sj.bjc.6605726 www.bjcancer.com Published online 15 June 2010 (C) 2010 Cancer Research U