Characterizing extremal digraphs for identifying codes and extremal cases of Bondy's theorem on induced subsets

An identifying code of a (di)graph $G$ is a dominating subset $C$ of the vertices of $G$ such that all distinct vertices of $G$ have distinct (in)neighbourhoods within $C$. In this paper, we classify all finite digraphs which only admit their whole vertex set in any identifying code. We also classify all such infinite oriented graphs. Furthermore, by relating this concept to a well known theorem of A. Bondy on set systems we classify the extremal cases for this theorem

An improved lower bound for (1,<=2)-identifying codes in the king grid

We call a subset $C$ of vertices of a graph $G$ a $(1,\leq \ell)$-identifying code if for all subsets $X$ of vertices with size at most $\ell$, the sets $\{c\in C |\exists u \in X, d(u,c)\leq 1\}$ are distinct. The concept of identifying codes was introduced in 1998 by Karpovsky, Chakrabarty and Levitin. Identifying codes have been studied in various grids. In particular, it has been shown that there exists a $(1,\leq 2)$-identifying code in the king grid with density 3/7 and that there are no such identifying codes with density smaller than 5/12. Using a suitable frame and a discharging procedure, we improve the lower bound by showing that any $(1,\leq 2)$-identifying code of the king grid has density at least 47/111

Generalized iterated wreath products of symmetric groups and generalized rooted trees correspondence

Consider the generalized iterated wreath product $S_{r_1}\wr \ldots \wr S_{r_k}$ of symmetric groups. We give a complete description of the traversal for the generalized iterated wreath product. We also prove an existence of a bijection between the equivalence classes of ordinary irreducible representations of the generalized iterated wreath product and orbits of labels on certain rooted trees. We find a recursion for the number of these labels and the degrees of irreducible representations of the generalized iterated wreath product. Finally, we give rough upper bound estimates for fast Fourier transforms.Comment: 18 pages, to appear in Advances in the Mathematical Sciences. arXiv admin note: text overlap with arXiv:1409.060

Вплив наносполук Феруму та Германію на вміст церулоплазміну в крові свиноматок і отриманих від них поросят

The work is devoted to establishing the degree and nature of the effect of the application of iron and germanium nano compounds on the content of ceruloplasmin in the blood plasma of sows and piglets obtained from them. For this, two groups of sows (control and experimental) were selected; the pigs of the experimental group were given a complex of nano compounds of trace elements iron and germanium, and the ceruloplasmin content in the blood was evaluated. A reliable effect of the application of iron and germanium nanocompounds on the content of ceruloplasmin in the blood of sows was established – F = 25.5 &gt; FU = 4.15; P &lt; 0.001, which is manifested only after farrowing – gh²ᵪ = 0.48–0.74 (P ≤ 0.05–0.01). Thus, after farrowing (on the first and third day), the content of the enzyme in the blood of these animals was significantly higher than that of sows of the control group (12.7–13.5 %; P ≤ 0.05). It was established that the ceruloplasmin content in the blood of piglets obtained from sows that were given the mentioned metal nanocompounds on the second (gh²ᵪ = 0.52; P ≤ 0.05) and seventh (gh²ᵪ = 0.70; P ≤ 0.01) days of life of animals depends on the application of iron and germanium nanocompounds. In these piglets, the enzyme content two and seven days after birth is 13.3–20.0 % (P ≤ 0.05) higher than piglets obtained from sows that were not given nanocompounds. It was experimentally proven that the content of ceruloplasmin in the blood plasma of piglets obtained from sows that were given nano compounds of metals is directly related to its content in the blood of sows, in particular, the content of the enzyme in the blood of two- and 7-day-old piglets correlates with the content of the enzyme in the blood of sows on the day of farrowing – r = 0.91–0.95 (P ≤ 0.001). Therefore, the conducted studies indicate the effectiveness of using ferrum and germanium nanoparticles to correct the ceruloplasmin content in the blood of both sows and suckling piglets.Роботу присвячено встановленню ступеня і характеру впливу наносполук Феруму та Германію на вміст церулоплазміну в плазмі крові свиноматок і отриманих від них поросят. Для цього було підібрано дві групи свиноматок (контрольна і дослідна), свиням дослідної групи задавали комплекс наносполук мікроелементів Феруму та Германію і оцінювали вміст церулоплазміну в крові. Встановлено достовірний вплив наносполук Феруму та Германію на вміст церулоплазміну в крові свиноматок – F= 25,5 &gt; FU = 4,15; Р &lt; 0,001, який проявляється лише після опоросу – ղ²ᵪ = 0,48–0,74 (P ≤ 0,05–0,01). Так, після опоросу (на першу і третю добу) вміст ензиму в крові цих тварин був достовірно більшим від такого у свиноматок контрольної групи (на 12,7–13,5 %; P ≤ 0,05). Встановлено, що у поросят отриманих від свиноматок, яким задавали згадані наносполуки металів вміст церулоплазміну в крові на другу (ղ²ᵪ = 0,52; P ≤ 0,05) та сьому (ղ²ᵪ = 0,70; P ≤ 0,01) добу життя залежить від задавання наносполук Феруму та Германію. У цих поросят вміст ензиму через дві та сім діб після народження більше на 13,3–20,0 % (P ≤ 0,05) від такого у поросят отриманих від свиноматок, яким наносполуки не задавали. Експериментально доведено, що вміст церулоплазміну в плазмі крові поросят отриманих від свиноматок, яким задавали наносполуки металів прямо пов’язаний з його вмістом в крові свиноматок, зокрема, вміст ензиму в крові дво- та 7-добових поросят корелює з вмістом ензиму в крові свиноматок в день опоросу – r = 0,91–0,95 (P ≤ 0,001). Отже, проведені дослідження вказують на ефективність застосування наночастинок Феруму та Германію для корекції вмісту церулоплазміну в крові як свиноматок, так і молочних поросят

An Efficient Rank Based Approach for Closest String and Closest Substring

This paper aims to present a new genetic approach that uses rank distance for solving two known NP-hard problems, and to compare rank distance with other distance measures for strings. The two NP-hard problems we are trying to solve are closest string and closest substring. For each problem we build a genetic algorithm and we describe the genetic operations involved. Both genetic algorithms use a fitness function based on rank distance. We compare our algorithms with other genetic algorithms that use different distance measures, such as Hamming distance or Levenshtein distance, on real DNA sequences. Our experiments show that the genetic algorithms based on rank distance have the best results

Sequential Metric Dimension

International audienceSeager introduced the following game in 2013. An invisible and immobile target is hidden at some vertex of a graph $G$. Every step, one vertex $v$ of $G$ can be probed which results in the knowledge of the distance between $v$ and the target. The objective of the game is to minimize the number of steps needed to locate the target, wherever it is. We address the generalization of this game where $k ≥ 1$ vertices can be probed at every step. Our game also generalizes the notion of the metric dimension of a graph. Precisely, given a graph $G$ and two integers $k, ≥ 1$, the Localization Problem asks whether there exists a strategy to locate a target hidden in $G$ in at most steps by probing at most $k$ vertices per step. We show this problem is NP-complete when $k$ (resp.,) is a fixed parameter. Our main results are for the class of trees where we prove this problem is NP-complete when $k$ and are part of the input but, despite this, we design a polynomial-time (+1)-approximation algorithm in trees which gives a solution using at most one more step than the optimal one. It follows that the Localization Problem is polynomial-time solvable in trees if $k$ is fixed

Spin-dependent scattering in weakly coupled nickel films

We report the spin-dependent magneto-transport in chemically homogeneous weakly coupled nickel films above their conductance percolation threshold. This is a new type of GMR system free of a non-magnetic spacer where a sharp reversal of local magnetic moments is achieved by dimensional confinement. Magnetoresistance increases with the films resistivity in a remarkable similarity to the tunnel-type GMR systems

The tool simulated complex for study of molecular gears of homeostasis

For reception of integrated parameters of homeostasis and their evaluations the expensive technologies of researches are required. The tool complex for decision of this task at minimum possible costs is suggested