We consider a random walk in
Z
2
and establish a number of results for the distributions and expectations of the number of usual (undirected) and specifically defined in the paper directed ...state-crossings and different sets of states crossings. As well, we extend the results to
d
-dimensional random walks,
d
≥
2
, in bounded areas.
We provide a simple proof for the extended Bertrand-De Morgan test that was earlier studied in Ďuriš, F., (2009). Infinite series: Convergence tests. Bachelor thesis, Univerzita Komenského, ...Bratislava, Slovakia and Tabatabai Adnani, A. A., Reza, A., Morovati, M. (2013). J. Lin. Topol. Algebra. 2(3): 141-147 and demonstrate an application of that test to the theory of birth-and-death processes.
In the present paper, we define conservative and semiconservative random walks in
Z
d
and study various families of random walks. The family of symmetric random walks is one of the families of ...conservative random walks, and simple (Pólya) random walks are their representatives. The classification of random walks given in the present paper enables us to provide a new approach to random walks in
Z
d
by reduction to birth-and-death processes. We construct nontrivial examples of recurrent random walks in
Z
d
for any
d
≥
3
and transient random walks in
Z
2
.
This paper studies a discrete model of a large dam where the difference between lower and upper levels, L, is assumed to be large. Passage across the levels leads to damage, and the damage costs of ...crossing the lower or upper level are proportional to the large parameter L. Input stream of water is described by compound Poisson process, and the water cost depends upon current level of water in the dam. The aim of the paper is to choose the parameters of output stream (specifically defined in the paper) minimizing the long-run expenses that include the damage costs and water costs. The present paper addresses the important question: How does the structure of water costs affect the optimal solution? We prove the existence and uniqueness of a solution. A special attention is attracted to the case of linear structure of the costs. As well, the paper contributes to the theory of state-dependent queueing systems. The inter-relations between important characteristics of a state-dependent queueing system are established, and their asymptotic analysis that involves analytic techniques of Tauberian theory and heavy traffic approximations is provided.
Cationic copolymers based on 2-(N,
-dimethylamino)ethyl methacrylate and polyethylene glycol monomethyl ether (pDMAEMA-co-PEO) with different molecular weights have been synthesized. Their ...physicochemical properties were studied by NMR spectroscopy, sedimentation, and potentiometric titration. According to the data of potentiometric titration for the synthesized pegylated cationic copolymers, the apparent dissociation constants were determined in the pH range from 4.5 to 8.5. The physicochemical properties of interpolyelectrolyte complexes of these polycations with circular DNA (IPEC DNA) were also studied by dynamic light scattering, electrophoretic mobility, and TEM methods. It has been established that the diameter and electrokinetic potential (ζ-potential) of interpolyelectrolyte complexes can be varied over a wide range (from 200 nm to 1.5 μm and from -25 mV to +30 mV) by changing the ratio of oppositely charged ionizable groups in pegylated cationic copolymers and DNA, as well as by regulating medium pH. The resistance of the IPEC DNA/polycation complex to the action of nucleases was studied by electrophoresis in agarose gel; the cytotoxic effect of the polymers in vitro, and the efficiency of penetration (transfection) of IPEC DNA with PDMAEMA-co-PEO-polycations into eukaryotic cells of a cell line derived from human embryonic kidneys HEK 293 in vitro.
We have previously demonstrated that human vaginal Lactobacillus crispatus 2029 (LC2029) strain is highly adhesive to cervicovaginal epithelial cells, exhibits antagonistic activity against ...genitourinary pathogens and expresses surface-layer protein (Slp). The aims of the present study were elucidation of Slp structural and immunomodulatory characteristics and its roles in protective properties of the whole vaginal LC2029 bacteria against foodborne pathogens. Enteric Caco-2 and colon HT-29 cell lines were used as the in vitro models of the human intestinal epithelial layer. LC2029 strain has two homologous surface-layer (S-layer) genes, slp1 and slp2. Whilst we found no evidence for the expression of slp1 under the growth conditions used, a very high level of expression of the slp2 gene was detected. C-terminal part of the amino sequence of Slp2 protein was found to be highly similar to that of the conserved C-terminal region of SlpA protein of L. crispatus Zj001 isolated from pig intestines and CbsA protein of L. crispatus JCM5810 isolated from chicken intestines, and was substantially variable at the N-terminal and middle regions. The amino acid sequence identity between SlpA and CbsA was as high as 84%, whilst the identity levels of these sequences with that of Slp2 were only 49% and 50% (respectively). LC2029 strain was found to be both acid and bile tolerant. Survival in simulated gastric and intestinal juices of LC2029 cells unable to produce Slp2 was reduced by 2–3 logs. Vaginal L. crispatus 1385 (LC1385) strain not expressing Slp was also very sensitive to gastric and intestinal stresses. Slp2 was found to be non-covalently bound to the surface of the bacterium, acting as an adhesin and facilitating interaction of LC2029 lactobacilli with the host immature or fully differentiated Caco-2 cells, as well as HT-29 cells. No toxicity to or damage of Caco-2 or HT-29 epithelial cells were detected after 24 h of colonization by LC2029 lactobacilli. Both Slp2 protein and LC2029 cells induced NF-kB activation in Caco-2 and HT-29 cells, but did not induce expression of innate immunity mediators Il-8, Il-1β, and TNF-α. Slp2 and LC2029 inhibited Il-8 production in Caco-2 and HT-29 cells induced by MALP-2 and increased production of anti-inflammatory cytokine Il-6. Slp2 inhibited production of CXCL1 and RANTES by Caco-2 cells during differentiation and maturation process within 15 days. Culturing Caco-2 and HT-29 cells in the presence of Slp2 increased adhesion of bifidobacteria BLI-2780 to these enterocytes. Upon binding to Caco-2 and HT-29 cells, Slp2 protein and LC2029 lactobacilli were recognized by toll-like receptors (TLR) 2/6. It was shown that LC2029 strain is a strong co-aggregator of foodborne pathogens Campylobacter jejuni, Salmonella enteritidis, and Escherichia coli O157:H used in this study. The Slp2 was responsible for the ability of LC2029 to co-aggregate these enteropathogens. Slp2 and intact LC2029 lactobacilli inhibited foodborne pathogen-induced activation of caspase-9 and caspase-3 as apoptotic biomarkers in Caco-2 and HT-29 cells. In addition, Slp2 and Slp2-positive LC2029 strain reduced adhesion of tested pathogenic bacteria to Caco-2 and HT-29 cells. Slp2-positive LC2029 strain but not Slp2 alone provided bactericidal effect on foodborne pathogens. These results suggest a range of mechanisms involved in inhibition of growth, viability, and cell-adhesion properties of pathogenic Proteobacteria by the Slp2 producing LC2029, which may be useful in treatment of necrotizing enterocolitis (NEC) in newborns and foodborne infectious diseases in children and adults, increasing the colonization resistance and maintaining the intestinal homeostasis.
We have previously demonstrated the ability of the human vaginal strain Lactobacillus crispatus 2029 (LC2029) for strong adhesion to cervicovaginal epithelial cells, expression of the surface layer ...protein 2 (Slp2), and antagonistic activity against urogenital pathogens. Slp2 forms regular two-dimensional structure around the LC2029 cells,which is secreted into the medium and inhibits intestinal pathogen-induced activation of caspase-9 and caspase-3 in the human intestinal Caco-2 cells. Here, we elucidated the effects of soluble Slp2 on adhesion of proteobacteria pathogens inducing necrotizing enterocolitis (NEC), such as Escherichia coli ATCC E 2348/69, E. coli ATCC 31705, Salmonella Enteritidis ATCC 13076, Campylobacter jejuni ATCC 29428, and Pseudomonas aeruginosa ATCC 27853 to Caco-2 cells, as well as on growth promotion, differentiation, vascular endothelial growth factor (VEGF) production, and intestinal barrier function of Caco-2 cell monolayers. Slp2 acts as anti-adhesion agent for NEC-inducing proteobacteria, promotes growth of immature Caco-2 cells and their differentiation, and enhances expression and functional activity of sucrase, lactase, and alkaline phosphatase. Slp2 stimulates VEGF production, decreases paracellular permeability, and increases transepithelial electrical resistance, strengthening barrier function of Caco-2 cell monolayers. These data support the important role of Slp2 in the early postnatal development of the human small intestine enterocytes.
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