Subexponential estimations in Shirshov's height theorem (in English)

In 1993 E. I. Zelmanov asked the following question in Dniester Notebook: "Suppose that F_{2, m} is a 2-generated associative ring with the identity x^m=0. Is it true, that the nilpotency degree of F_{2, m} has exponential growth?" We show that the nilpotency degree of l-generated associative algebra with the identity x^d=0 is smaller than Psi(d,d,l), where Psi(n,d,l)=2^{18} l (nd)^{3 log_3 (nd)+13}d^2. We give the definitive answer to E. I. Zelmanov by this result. It is the consequence of one fact, which is based on combinatorics of words. Let l, n and d>n be positive integers. Then all the words over alphabet of cardinality l which length is greater than Psi(n,d,l) are either n-divided or contain d-th power of subword, where a word W is n-divided, if it can be represented in the following form W=W_0 W_1...W_n such that W_1 >' W_2>'...>'W_n. The symbol >' means lexicographical order here. A. I. Shirshov proved that the set of non n-divided words over alphabet of cardinality l has bounded height h over the set Y consisting of all the words of degree <n. Original Shirshov's estimation was just recursive, in 1982 double exponent was obtained by A.G.Kolotov and in 1993 A.Ya.Belov obtained exponential estimation. We show, that h<Phi(n,l), where Phi(n,l) = 2^{87} n^{12 log_3 n + 48} l. Our proof uses Latyshev idea of Dilworth theorem application.Comment: 21 pages, Russian version of the article is located at the link arXiv:1101.4909; Sbornik: Mathematics, 203:4 (2012), 534 -- 55

Asymmetric and symmetric fission of excited nuclei of 180,190Hg and 184,192,202Pb formed in the reactions with 36Ar and 40,48Ca ions

Background: Observation of asymmetric fission of 180Hg has led to intensive theoretical and experimental studies of fission of neutron-deficient nuclei in the lead region. Purpose: The study of asymmetric and symmetric fission modes of 180,190Hg and 184,192,202Pb nuclei. Methods: Mass-energy distributions of fission fragments of 180,190Hg and 184Pb formed in the 36Ar+144,154Sm and 40Ca+144Sm reactions, respectively, at energies near the Coulomb barrier have been measured using the double-arm time-of-flight spectrometer CORSET and compared with previously measured 192,202Pb isotopes produced in the 48Ca+144,154Sm reactions. The mass distributions for 180,190Hg and 184,192,202Pb together with old data for 187Ir, 195Au, 198Hg, 201Tl, 205,207Bi, 210Po, and 213At [J. Nucl. Phys. 53, 1225 (1991)] have been decomposed into symmetric and asymmetric fission modes. The total kinetic-energy distributions for different fission fragment mass regions have been analyzed for 180,190Hg and 184Pb. Results: The stabilization role of proton numbers at Z≈36, 38, Z≈45, 46, and Z=28/50 in asymmetric fission of excited preactinide nuclei has been observed. The high (≈145−MeV) and the low (≈128−MeV) energy components have been found in the total kinetic-energy distributions of 180,190Hg fission fragments corresponding to the fragments with proton numbers near Z≈46 and Z≈36, respectively. In the case of fission of 184Pb only the low-energy component (≈135MeV) for the fragments with masses corresponding to the proton numbers Z≈36 and 46 has been found. Conclusions: The studied properties of asymmetric fission of 180,190Hg and 184,192,202Pb nuclei point out the existence of well deformed proton shell at Z≈36 and less deformed proton shell at Z≈46.peerReviewe

S-layer protein 2 of 'Lactobacillus crispatus' 2029, its structural and immunomodulatory characteristics and roles in protective potential of the whole bacteria against foodborne pathogens

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

Mapping H4K20me3 onto the chromatin landscape of senescent cells indicates a function in control of cell senescence and tumor suppression through preservation of genetic and epigenetic stability

Background: Histone modification H4K20me3 and its methyltransferase SUV420H2 have been implicated in suppression of tumorigenesis. The underlying mechanism is unclear, although H4K20me3 abundance increases during cellular senescence, a stable proliferation arrest and tumor suppressor process, triggered by diverse molecular cues, including activated oncogenes. Here, we investigate the function of H4K20me3 in senescence and tumor suppression. Results: Using immunofluorescence and ChIP-seq we determine the distribution of H4K20me3 in proliferating and senescent human cells. Altered H4K20me3 in senescence is coupled to H4K16ac and DNA methylation changes in senescence. In senescent cells, H4K20me3 is especially enriched at DNA sequences contained within specialized domains of senescence-associated heterochromatin foci (SAHF), as well as specific families of non-genic and genic repeats. Altered H4K20me3 does not correlate strongly with changes in gene expression between proliferating and senescent cells; however, in senescent cells, but not proliferating cells, H4K20me3 enrichment at gene bodies correlates inversely with gene expression, reflecting de novo accumulation of H4K20me3 at repressed genes in senescent cells, including at genes also repressed in proliferating cells. Although elevated SUV420H2 upregulates H4K20me3, this does not accelerate senescence of primary human cells. However, elevated SUV420H2/H4K20me3 reinforces oncogene-induced senescence-associated proliferation arrest and slows tumorigenesis in vivo. Conclusions: These results corroborate a role for chromatin in underpinning the senescence phenotype but do not support a major role for H4K20me3 in initiation of senescence. Rather, we speculate that H4K20me3 plays a role in heterochromatinization and stabilization of the epigenome and genome of pre-malignant, oncogene-expressing senescent cells, thereby suppressing epigenetic and genetic instability and contributing to long-term senescence-mediated tumor suppression

PHARMACOEPIDEMIOLOGICAL PARAMETERS OF USE OF POTENT OPIOIDS IN SAINT PETERSBURG (in the light of differences in approaches to using the drugs of this group in Russia and in the world)

The paper considers the pharmacoepidemiological parameters of the use of potent opioids in Saint-Petersburg in 2000-2009. These parameters are compared with those in a number of countries of the world, particularly in the Scandinavian countries that are close to Saint Petersburg in population. The reasons for the differences in the use of potent analgesics are analyzed. Approaches to prescribing the drugs of this group for non-cancer pain caused by neurological diseases in particular are also analyzed