Computing with rational symmetric functions and applications to invariant theory and PI-algebras

Let the formal power series f in d variables with coefficients in an arbitrary field be a symmetric function decomposed as a series of Schur functions, and let f be a rational function whose denominator is a product of binomials of the form (1 - monomial). We use a classical combinatorial method of Elliott of 1903 further developed in the Partition Analysis of MacMahon in 1916 to compute the generating function of the multiplicities (i.e., the coefficients) of the Schur functions in the expression of f. It is a rational function with denominator of a similar form as f. We apply the method to several problems on symmetric algebras, as well as problems in classical invariant theory, algebras with polynomial identities, and noncommutative invariant theory.Comment: 37 page

EFFECTIVENESS OF DIABETIC KETOACIDOSIS TREATMENT WITH LOW-DOSIS VENOUS INSULIN INFUSIONS

No abstrac

Isolation and primary identification of shiga toxin producing Escherichia coli O157 in dairy cattle

During the last years, the significance of diseases associated etiologically to Shiga-toxin producing Escherichia coli (STEC) is continuously increasing at a global scale, while the O157 serotype is con-sidered as one of the most important pathogens of animal origin. Large ruminants play a key role in the epidemiology of E. coli diseases among men. Bovine faeces are a primary source of contamina-tion of the environment and foods with this agent. The purpose of this study was to test a specific, microbiological algorithm for primary identification of STEC isolates from bovine faeces using sorbi-tol McConkey agar supplemented with cefixime and tellurite. The attempts were focused not only on increasing the sensitivity and specificity of serotype identification, but also on optimisation of labour and analysis costs. From May 2013 to October 2014, a total number of 1104 faecal swab samples from calves 3 to 6 months of age were collected from 19 farms in different administrative and geo-graphical regions of Bulgaria. Thirty six sorbitol-negative E. coli isolates (3.26%) were detected as belonging to the O157 serotype after slide agglutination test

IMMUNE RESPONSE IN MALIGNANT GLIOMA

Objective: Malignant gliomas are primary brain tumors with excessive mortality and high resistance to chemotherapy and radiotherapy. The survival time for glioblastoma multi­forme is about 6-12 months. As key pathogenetic mechanisms are recognized the massive necrosis, angiogenesis and hypoxia within the tumor, as well as the resistance to apoptosis. It is also suspected that altered immune response might contribute to the fatal clinical outcome.The aim of the present study was to determine the immune status of patients with malignant gliomas.Material and methods: Peripheral blood lymphocytes were collected preoperatively from 9 patients (aged 57-76) diagnosed as anaplastic astrocytoma grade III (n=4) and glioblastoma multiforme (n=5). The following lymphocyte populations were analyzed by flow cytometry: CD19+, CD3+, CD3+CD4+, CD3+CD8+, CD3-CD56+, CD3+CD56+, CD3+CD25+, CD8-CD11b+, CD8+CD11b+, CD8+CD11b-. The results obtained were compared to reference values for each cell population.Results: No significant alterations were detected in CD19+, CD3+, CD3+CD4+, CD3+CD8+ cells, but the CD4/CD8 ratio was below the reference range in some cases. No obvious decrease in (CD3-CD56+) NK cells and (CD3-CD56+) NKT cells was observed in most patients. A reproducible phenomenon of increased CD8+CD11b+ and decreased CD8+CD11b- cells was noticed. These preliminary results suggest that the immune response in patients with malignant glioma is seriously disregulated. The rapid clinical deterioration, relapses and high mortality could be at least partially explained with the suppressed activity of NK-cells which are the major cytotoxic antitumoral cells. The increase in the population of activated suppressor-effector cells also contributes to the unfavourable outcome in malignant brain tumors.Conclusion: This pilot study reveals the presence of altered immune response in malignant gliomas and opens possibilities for prospective investigations concerning immune status and clinical outcome

Eigenvalue distributions for some correlated complex sample covariance matrices

The distributions of the smallest and largest eigenvalues for the matrix product $Z^\dagger Z$, where $Z$ is an $n \times m$ complex Gaussian matrix with correlations both along rows and down columns, are expressed as $m \times m$ determinants. In the case of correlation along rows, these expressions are computationally more efficient than those involving sums over partitions and Schur polynomials reported recently for the same distributions.Comment: 11 page

Asymptotics for products of characteristic polynomials in classical β\beta-Ensembles

We study the local properties of eigenvalues for the Hermite (Gaussian), Laguerre (Chiral) and Jacobi $\beta$-ensembles of $N\times N$ random matrices. More specifically, we calculate scaling limits of the expectation value of products of characteristic polynomials as $N\to\infty$. In the bulk of the spectrum of each $\beta$-ensemble, the same scaling limit is found to be $e^{p_{1}}{}_1F_{1}$ whose exact expansion in terms of Jack polynomials is well known. The scaling limit at the soft edge of the spectrum for the Hermite and Laguerre $\beta$-ensembles is shown to be a multivariate Airy function, which is defined as a generalized Kontsevich integral. As corollaries, when $\beta$ is even, scaling limits of the $k$-point correlation functions for the three ensembles are obtained. The asymptotics of the multivariate Airy function for large and small arguments is also given. All the asymptotic results rely on a generalization of Watson's lemma and the steepest descent method for integrals of Selberg type.Comment: [v3] 35 pages; this is a revised and enlarged version of the article with new references, simplified demonstations, and improved presentation. To be published in Constructive Approximation 37 (2013

A natural mutation in Pisum sativum L. (pea) alters starch assembly and improves glucose homeostasis in humans

Elevated postprandial glucose (PPG) is a significant risk factor for non-communicable diseases globally. Currently, there is a limited understanding of how starch structures within a carbohydrate-rich food matrix interact with the gut luminal environment to control PPG. Here, we use pea seeds (Pisum sativum) and pea flour, derived from two near-identical pea genotypes (BC1/19RR and BC1/19rr) differing primarily in the type of starch accumulated, to explore the contribution of starch structure, food matrix and intestinal environment to PPG. Using stable isotope 13C-labelled pea seeds, coupled with synchronous gastric, duodenal and plasma sampling in vivo, we demonstrate that maintenance of cell structure and changes in starch morphology are closely related to lower glucose availability in the small intestine, resulting in acutely lower PPG and promotion of changes in the gut bacterial composition associated with long-term metabolic health improvements

Eco-biological charactEristics of mEdicinal plants in thE rEsErvE gorna topchiya (rivEr tundzha hilly vallEy)

abstract Koev, K., S. GeorGiev and A. TAShev, 2014. eco-biological characteristics of medicinal plants in the reserve Gorna Topchiya (river Tundzha hilly valley). Bulg. J. Agric. Sci., over a period of 3 years, medicinal plants were investigated in the reserve Gorna Topchiya, situated in the middle course of the river Toundzha near the village of Konevets, Yambol, Municipality Tundzha (Tundzha hilly valley). vegetation seasons included the period from February to october, which guarantees the traceability of growing cycles of both annual and perennial species, as well as ephemeral and ephemeral-like species. in the present study we did eco-biological characteristics of these plants, as the species are divided into biological groups according to their life forms, floral elements and flowering time. Medicinal plants are also classified according to their relation to water, light and heat. We have made conclusions about the influence of hydrodynamics on the change of floristic composition and the changes that occur in cenosis characteristics of the protected area