Abstract:
Formation factors of Belarus settlement system are analyzed in the article. Spatial and temporal trends in urban and rural settlement system of Belarus for the period of 1979-2009 years are characterized. Spatial and temporal shifts in the distribution of urban and rural population and the structure of urban and rural settlements are detected. The types of rural settlement of Belarus are presented. The features of distribution and demographic development of new Belarusian rural settlements form– agrotowns - are developed.

The development of small molecule nerve
growth factor (NGF) mimetics is a promising approach to overcome limitations in
the use of the neurotrophin as a drug, which are poor pharmacokinetics and
undesirable side effects. We designed dimeric dipeptide called GK-2
(bis(N-succinyl-L-glutamyl-L-lysine)hexametylendiamide) on the base of
beta-turn sequence of NGF loop4 which most exposed to solvent and hence can
play the major role in the interaction of NGF with the receptor. It was shown,
that GK-2 stimulates phosphorylation of TrkA receptor, selectively activates
PI3K/Akt signaling cascade that is important for cell survival, and does not
activate MAPK/Erk pathway, associated not only with cell survival but also with
cell differentiation. According to these data, GK-2 in vitro prevented H_{2}O_{2}- or MPTP- or
glutamate-induced neuronal cell deathat
nanomolar concentrations, but did not provoke neurite outgrowth in PC12 cells. In vivo GK-2 exhibits therapeutic
effects in models of Parkinson’s disease, Alzheimer’s disease, brain ischemia
and diabetes mellitus. GK-2 shows activity in doses 0.01 - 5 mg/kg
intraperitoneally and retains the activity
after oral administration in dose 10 mg/kg. GK-2 has no side effects
accompanying NGF treatment namely hyperalgesia and weight loss. Thus,
the designed dimeric substituted dipeptide provides promising drug candidate
and a molecular tool for investigating the possibility of divergence in NGF
therapeutic and adverse effects.

Abstract:
High throughput screening of small-molecule libraries is a well-established and highly productive tool for the identification of chemical compounds targeting a specific protein function of interest. Traditionally, the high-throughput screening for modulators of molecular pathways involves cell-free biochemical assays, or in some cases, highly specialized cell-based phenotypic assays [1]. However, in many cases the optimal target for therapeutic intervention is not known, or the development of a suitable phenotypic read-out is not technically feasible. For example, it is becoming increasingly of interest to modulate the activity of particular signal transduction pathways, but the components of such pathways are in many cases only partially known. It would therefore be of interest to develop a screening approach that could identify inhibitors of such pathways without first defining the biochemical target of candidate small molecules. Here we demonstrate that it is possible to use mRNA expression levels as a read-out to infer activity of a signal transduction pathway, thus establishing a general approach to screening for modulators of signal transduction pathways.Endogenous mRNA expression has been previously successfully used as a surrogate of cellular states in high-throughput screening for compounds inducing differentiation of acute myeloid leukemia cells, and for identifying inhibitors of androgen receptor-mediated transcriptional activation in prostate cancer [2-5]. It is not obvious, however, that gene expression signatures could be used to identify inhibitors of signal transduction pathways that are regulated at the level of post-translational modification (phosphorylation), as opposed to transcriptional regulation.To test the feasibility of using gene expression-based high-throughput screening (GE-HTS) to identify inhibitors of a signaling pathway, we chose platelet derived growth factor receptor (PDGFR) signaling for a proof-of-concept study, with particular e

Abstract:
The methodology has been tested on a dataset comprising 317 Affymetrix HuGeneFL GeneChips. The performance of the original and reduced probe sets was compared in four cancer-classification problems. The results of these comparisons show that reduction of the probe set by 95% does not dramatically affect performance, and thus illustrate the feasibility of substantially reducing probe numbers without significantly compromising sensitivity and specificity of detection.The strategy described here is potentially useful for designing small, limited-probe genome-wide arrays for screening applications.DNA microarrays have become commonplace for the genome-wide measurement of mRNA expression levels. The first described microarray for this purpose, the cDNA microarray, involves the mechanical deposition of cDNA clones on glass slides [1]. Although this strategy has proved highly effective, it has two limitations: cross-hybridization can occur between mRNAs and non-unique or repetitive portions of the cDNA clone; and the maintenance and quality control of large, arrayed cDNA libraries can be challenging. For these reasons, oligonucleotide microarrays have at least theoretical advantages. Short probes (25 nucleotides or longer) can be selected on the basis of their sequence specificity, and either synthesized in situ (by photolithography or inkjet technology) on a solid surface or conventionally synthesized and then robotically deposited.The first oligonucleotide microarrays contained hundreds of distinct probes per gene in order to maximize sensitivity and specificity of detection [2]. Over the past few years, the number of probes per gene has decreased as increasing amounts of sequence information have become available, probe-selection algorithms have improved, feature sizes have decreased and researchers have wanted to maximize the number of genes assayable on a single microarray. Nevertheless, no single array representing the entire human genome has been described. Furtherm

Inclusion of L-DOPA,
the standard Parkinson’s disease medication, into polymeric particles (PLGA)
results in optimization the drug metabolism and increasing its bioavailability,
significantly increases of physical endurance, better coordination and lower
anxiety in Wistar rats, when chronically administered nasally.

Abstract:
The author considers conceptual issues, characterizing Russian art as an element of spiritual and ethic system of personality development, the result of European and Russian cultural systems co-integration; methods of Russian art actualization in modern youth environment have been specified.

Abstract:
This paper is devoted to the computation of the number of ordered factorizations of a long cycle in the symmetric group where the number of factors is arbitrary and the cycle structure of the factors is given. Jackson (1988) derived the first closed form expression for the generating series of these numbers using the theory of the irreducible characters of the symmetric group. Thanks to a direct bijection we compute a similar formula and provide the first purely combinatorial evaluation of these generating series.

Abstract:
This paper is devoted to the distribution of the eigenvalues of $XUYU^t$ where $X$ and $Y$ are given symmetric matrices and $U$ is a random real valued square matrix of standard normal distribution. More specifically we look at its moments, i.e. the mathematical expectation of the trace of $(XUYU^t)^n$ for arbitrary integer $n$. Hanlon, Stanley, Stembridge (1992) showed that this quantity can be expressed in terms of some generating series for the connection coefficients of the double cosets of the hyperoctahedral group with the eigenvalues of $X$ and $Y$ as indeterminate. We provide an explicit evaluation of these series in terms of monomial symmetric functions. Our development relies on an interpretation of the connection coefficients in terms of locally orientable hypermaps and a new bijective construction between partitioned locally orientable hypermaps and some decorated forests. As a corollary we provide a simple explicit evaluation of the moments of $XUYU^*$ when $U$ is complex valued and $X$ and $Y$ are given hermitian matrices.

Abstract:
This article is devoted to the computation of Jack connection coefficients, a generalization of the connection coefficients of two classical commutative subalgebras of the group algebra of the symmetric group: the class algebra and the double coset algebra. The connection coefficients of these two algebraic structures are of significant interest in the study of Schur and zonal polynomials as well as the irreducible characters of the symmetric group and the zonal spherical functions. Furthermore they play an important role in combinatorics as they give the number of factorizations of a permutation into a product of permutations with given cyclic properties. Usually studied separately, these two families of coefficients share strong similar properties. First (partially) introduced by Goulden and Jackson in 1996, Jack connection coefficients provide a natural unified approach closely related to the theory of Jack polynomials, a family of bases in the ring of symmetric functions indexed by a parameter \alpha that generalizes both Schur (case \alpha = 1) and zonal polynomials (case \alpha = 2). Jack connection coefficients are also directly linked to Jack characters, a general view of the characters of the symmetric group and the zonal spherical functions. Goulden and Jackson conjectured that these coefficients are polynomials in \alpha with nice combinatorial properties, the so-called Matchings-Jack conjecture. In this paper, we use the theory of Jack symmetric functions and the Laplace Beltrami operator to show the polynomial properties of Jack connection coefficients in some important cases. We also provide explicit formulations including notably a generalization of a classical formula of D\'enes for the number of minimal factorizations of a permutation into transpositions.

Abstract:
This paper is devoted to the explicit computation of generating series for the connection coefficients of two commutative subalgebras of the group algebra of the symmetric group, the class algebra and the double coset algebra. As shown by Hanlon, Stanley and Stembridge (1992), these series gives the spectral distribution of some random matrices that are of interest to statisticians. Morales and Vassilieva (2009, 2011) found explicit formulas for these generating series in terms of monomial symmetric functions by introducing a bijection between partitioned hypermaps on (locally) orientable surfaces and some decorated forests and trees. Thanks to purely algebraic means, we recover the formula for the class algebra and provide a new simpler formula for the double coset algebra. As a salient ingredient, we derive a new explicit expression for zonal polynomials indexed by partitions of type [a,b,1^(n-a-b)].