Umbral Calculus, Discretization, and Quantum Mechanics on a Lattice

`Umbral calculus' deals with representations of the canonical commutation relations. We present a short exposition of it and discuss how this calculus can be used to discretize continuum models and to construct representations of Lie algebras on a lattice. Related ideas appeared in recent publications and we show that the examples treated there are special cases of umbral calculus. This observation then suggests various generalizations of these examples. A special umbral representation of the canonical commutation relations given in terms of the position and momentum operator on a lattice is investigated in detail.Comment: 19 pages, Late

Composition-Diamond lemma for λ\lambda-differential associative algebras with multiple operators

In this paper, we establish the Composition-Diamond lemma for $\lambda$-differential associative algebras over a field $K$ with multiple operators. As applications, we obtain Gr\"{o}bner-Shirshov bases of free $\lambda$-differential Rota-Baxter algebras. In particular, linear bases of free $\lambda$-differential Rota-Baxter algebras are obtained and consequently, the free $\lambda$-differential Rota-Baxter algebras are constructed by words

Role of body condition score and adiponectin expression in the progression of canine mammary carcinomas

Obesity has been identified as a risk factor for developing breast cancer in post-menopausal period in humans and has been suspected to be associated with a worse prognosis also in the bitch. The aims of this study were to investigate the association between body condition score (BCS) and the prognosis of canine mammary carcinomas (CMCs) and the relationships between adiponectin expression and tumour behaviour. Seventy-three bitches with tubular, tubulopapillary, solid or complex carcinomas were included in the present study. For each dog, evaluation of BCS was conducted using a nine-point BCS system and the study population was divided into normal weight (4–5/9 points; n = 42), overweight (6–7/9 points; n = 19) and obese (8–9/9 points; n = 12). Type of diet (commercial, homemade or mixed) was recorded. After surgical excision, histological type, tumour size and nodal status were assessed and adiponectin expression was determined and quantified by immunohistochemistry and morphometric analysis. CMC histotype was not correlated with BCS, while a positive correlation between BCS and histological grade (p <.01) was observed. Overweight and obese bitches combined showed a shorter cancer-specific survival than normal weighted bitches (p <.01). Bitches fed with a homemade diet had a higher BCS than dogs fed with a commercial one, although no relationship was observed between diet and cancer-specific survival. Thirty-six CMCs scored positive for adiponectin expression (49%), but no correlation was found between the hormone expression and either CMC characteristics or prognosis. In conclusion, a higher BCS seems to be related with a higher prevalence of more aggressive CMCs and negatively affects the survival time in bitches with these mammary tumours

Dynamic Regulation of Vascular Myosin Light Chain (MYL9) with Injury and Aging

Aging-associated changes in the cardiovascular system increase the risk for disease development and lead to profound alterations in vascular reactivity and stiffness. Elucidating the molecular response of arteries to injury and age will help understand the exaggerated remodeling of aging vessels.We studied the gene expression profile in a model of mechanical vascular injury in the iliac artery of aging (22 months old) and young rats (4 months old). We investigated aging-related variations in gene expression at 30 min, 3 d and 7 d post injury. We found that the Myosin Light Chain gene (MYL9) was the only gene differentially expressed in the aged versus young injured arteries at all time points studied, peaking at day 3 after injury (4.6 fold upregulation (p<0.05) in the smooth muscle cell layers. We confirmed this finding on an aging aortic microarray experiment available through NCBI's GEO database. We found that Myl9 was consistently upregulated with age in healthy rat aortas. To determine the arterial localization of Myl9 with age and injury, we performed immunohistochemistry for Myl9 in rat iliac arteries and found that in healthy and injured (30 days post injury) arteries, Myl9 expression increased with age in the endothelial layers.The consistent upregulation of the myosin light chain protein (Myl9) with age and injury in arterial tissue draws attention to the increased vascular permeability and to the age-caused predisposition to arterial constriction after balloon angioplasty

naevoid basal cell carcinoma syndrome in a 22 month old child presenting with multiple basal cell carcinomas and a fetal rhabdomyoma

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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

Objective assessment of walking impairments in myotonic dystrophy by means of a wearable technology and a novel severity index

Myotonic dystrophy type 1 (DM1) is a genetic inherited autosomal dominant disease characterized by multisystem involvement, including muscle, heart, brain, eye, and endocrine system. Although several methods are available to evaluate muscle strength, endurance, and dexterity, there are no validated outcome measures aimed at objectively evaluating qualitative and quantitative gait alterations. Advantageously, wearable sensing technology has been successfully adopted in objectifying the assessment of motor disabilities in different medical occurrences, so that here we consider the adoption of such technology specifically for DM1. In particular, we measured motor tasks through inertial measurement units on a cohort of 13 DM1 patients and 11 healthy control counterparts. The motor tasks consisted of 16 meters of walking both at a comfortable speed and fast pace. Measured data consisted of plantar-flexion and dorsi-flexion angles assumed by both ankles, so to objectively evidence the footdrop behavior of the DM1 disease, and to define a novel severity index, termed SI-Norm2, to rate the grade of walking impairments. According to the obtained results, our approach could be useful for a more precise stratification of DM1 patients, providing a new tool for a personalized rehabilitation approach

Cardiopulmonary exercise testing in a combined screening approach to individuate pulmonary arterial hypertension in systemic sclerosis

Objectives The DETECT algorithm has been developed to identify SSc patients at risk for pulmonary arterial hypertension (PAH) yielding high sensitivity but low specificity, and positive predictive value. We tested whether cardiopulmonary exercise testing (CPET) could improve the performance of the DETECT screening strategy. Methods Consecutive SSc patients over a 30-month period were screened with the DETECT algorithm and positive subjects were referred for CPET before the execution of right-heart catheterization. The predictive performance of CPET on top of DETECT was evaluated and internally validated via bootstrap replicates. Results Out of 314 patients, 96 satisfied the DETECT application criteria and 54 were positive. PAH was ascertained in 17 (31.5%) and pre-capillary pulmonary hypertension in 23 (42.6%) patients. Within CPET variables, the slope of the minute ventilation to carbon dioxide production relationship (VE/VCO2 slope) had the best performance to predict PAH at right-heart catheterization [median (interquartile range) of specificity 0.778 (0.714\u20130.846), positive predictive value 0.636 (0.556\u20130.750)]; exploratory analysis on pre-capillary yielded a specificity of 0.714 (0.636\u20130.8) and positive predictive value of 0.714 (0.636\u20130.8). Conclusion In association with the DETECT algorithm, CPET may be considered as a useful tool in the workup of SSc-related pulmonary hypertension. The sequential determination of the VE/VCO2 slope in DETECT-positive subjects may reduce the number of unnecessary invasive procedures without any loss in the capability to capture PAH. This strategy had also a remarkable performance in highlighting the presence of pre-capillary pulmonary hypertension