Discrete uniform limit law for additive functions on shifted primes

The sufficient and necessary conditions for a weak convergence of distributions of a set of strongly additive functions fx , x ⩾ 2, the arguments of which run through shifted primes, to the discrete uniform law are obtained. The case when fx (p) ∈ {0, 1} for every prime pis considered

Paskaitų tvarkaraščiai ir Monte Karlo metodas

In this paper the problem of the construction of schedule of lectures is considered. The Markov chain Monte Carlo method is used. A particular program based on simulated annealing algorithm was created.  Straipsnyje nagrinėjamas paskaitų tvarkaraščių konstravimo uždavinys naudojant Monte Karlo metodą. Sukurta tvarkaraščio optimizavimo programa remiasi vėsinimo (annealing) algoritmu. &nbsp

Correlations of multiplicative functions and applications

We give an asymptotic formula for correlations $$\sum_{n\le x}f_1(P_1(n))f_2(P_2(n))\cdot \dots \cdot f_m(P_m(n))$$ where $f\dots,f_m$ are bounded "pretentious" multiplicative functions, under certain natural hypotheses. We then deduce several desirable consequences:\ First, we characterize all multiplicative functions $f:\mathbb{N}\to\{-1,+1\}$ with bounded partial sums. This answers a question of Erd\H{o}s from $1957$ in the form conjectured by Tao. Second, we show that if the average of the first divided difference of multiplicative function is zero, then either $f(n)=n^s$ for $\operatorname{Re}(s)<1$ or $|f(n)|$ is small on average. This settles an old conjecture of K\'atai. Third, we apply our theorem to count the number of representations of $n=a+b$ where $a,b$ belong to some multiplicative subsets of $\mathbb{N}.$ This gives a new "circle method-free" proof of the result of Br\"udern

Hidden diversity in honey bee gut symbionts detected by single-cell genomics.

Microbial communities in animal guts are composed of diverse, specialized bacterial species, but little is known about how gut bacteria diversify to produce genetically and ecologically distinct entities. The gut microbiota of the honey bee, Apis mellifera, presents a useful model, because it consists of a small number of characteristic bacterial species, each showing signs of diversification. Here, we used single-cell genomics to study the variation within two species of the bee gut microbiota: Gilliamella apicola and Snodgrassella alvi. For both species, our analyses revealed extensive variation in intraspecific divergence of protein-coding genes but uniformly high levels of 16S rRNA similarity. In both species, the divergence of 16S rRNA loci appears to have been curtailed by frequent recombination within populations, while other genomic regions have continuously diverged. Furthermore, gene repertoires differ markedly among strains in both species, implying distinct metabolic capabilities. Our results show that, despite minimal divergence at 16S rRNA genes, in situ diversification occurs within gut communities and generates bacterial lineages with distinct ecological niches. Therefore, important dimensions of microbial diversity are not evident from analyses of 16S rRNA, and single cell genomics has potential to elucidate processes of bacterial diversification

De novo synthesis and functional analysis of the phosphatase-encoding gene acI-B of uncultured Actinobacteria from Lake Stechlin (NE Germany)

The National Center for Biotechnology Information [http://www.ncbi.nlm.nih.gov/guide/taxonomy/] database enlists more than 15,500 bacterial species. But this also includes a plethora of uncultured bacterial representations. Owing to their metabolism, they directly influence biogeochemical cycles, which underscores the the important status of bacteria on our planet. To study the function of a gene from an uncultured bacterium, we have undertaken a de novo gene synthesis approach. Actinobacteria of the acI-B subcluster are important but yet uncultured members of the bacterioplankton in temperate lakes of the northern hemisphere such as oligotrophic Lake Stechlin (NE Germany). This lake is relatively poor in phosphate (P) and harbors on average ~1.3 x 106 bacterial cells/ml, whereby Actinobacteria of the ac-I lineage can contribute to almost half of the entire bacterial community depending on seasonal variability. Single cell genome analysis of Actinobacterium SCGC AB141-P03, a member of the acI-B tribe in Lake Stechlin has revealed several phosphate-metabolizing genes. The genome of acI-B Actinobacteria indicates potential to degrade polyphosphate compound. To test for this genetic potential, we targeted the exoP-annotated gene potentially encoding polyphosphatase and synthesized it artificially to examine its biochemical role. Heterologous overexpression of the gene in Escherichia coli and protein purification revealed phosphatase activity. Comparative genome analysis suggested that homologs of this gene should be also present in other Actinobacteria of the acI lineages. This strategic retention of specialized genes in their genome provides a metabolic advantage over other members of the aquatic food web in a P-limited ecosystem. [Int Microbiol 2016; 19(1):39-47]Keywords: acI-B in Actinobacteria &middot; phosphatases &middot; single cell genomics &middot; phosphate limitation &middot; Lake Stechlin, NE German

De novo synthesis and functional analysis of the phosphatase-encoding gene acI-B of uncultured Actinobacteria from Lake Stechlin (NE Germany)

The National Center for Biotechnology Information [http://www.ncbi.nlm.nih.gov/guide/taxonomy/] database enlists more than 15,500 bacterial species. But this also includes a plethora of uncultured bacterial representations. Owing to their metabolism, they directly influence biogeochemical cycles, which underscores the the important status of bacteria on our planet. To study the function of a gene from an uncultured bacterium, we have undertaken a de novo gene synthesis approach. Actinobacteria of the acI-B subcluster are important but yet uncultured members of the bacterioplankton in temperate lakes of the northern hemisphere such as oligotrophic Lake Stechlin (NE Germany). This lake is relatively poor in phosphate (P) and harbors on average ~1.3 x 106 bacterial cells/ml, whereby Actinobacteria of the ac-I lineage can contribute to almost half of the entire bacterial community depending on seasonal variability. Single cell genome analysis of Actinobacterium SCGC AB141-P03, a member of the acI-B tribe in Lake Stechlin has revealed several phosphate-metabolizing genes. The genome of acI-B Actinobacteria indicates potential to degrade polyphosphate compound. To test for this genetic potential, we targeted the exoP-annotated gene potentially encoding polyphosphatase and synthesized it artificially to examine its biochemical role. Heterologous overexpression of the gene in Escherichia coli and protein purification revealed phosphatase activity. Comparative genome analysis suggested that homologs of this gene should be also present in other Actinobacteria of the acI lineages. This strategic retention of specialized genes in their genome provides a metabolic advantage over other members of the aquatic food web in a P-limited ecosystem. [Int Microbiol 2016; 19(1):39-47]Keywords: acI-B in Actinobacteria &middot; phosphatases &middot; single cell genomics &middot; phosphate limitation &middot; Lake Stechlin, NE German

Poisson distribution for a sum of additive functions on shifted primes

This excellent, well-written article argues that, for all his admiration for the lands of the East, and especially Iran, Jean Chardin saw eastern societies as corrupt and craven, debilitated by luxury and sensuality. Focusing on Chardin’s depiction of the Safavid harem as the center of languid lassitude, the author describes how the French Huguenot portrayed a hothouse of intrigue and cruelty, where growth through fertility was curbed through forced abortions and infanticide, thus providing a..

Kai kurie polivalentinių sistemų modeliavimo geometriniai aspektai

In this paper we consider the interaction of ligands and receptors on the plane and in the space.Šiame darbe nagrinėjami kai kurie polivalentinių sistemų modeliavimo geometriniai aspektai: ligandų ir receptorių sąveikos plokštumoje ir erdvėje