A graph $G$ is stratified if its vertex set is partitioned into classes, called strata. If there are $k$ strata, then $G$ is $k$-stratified. These graphs were introduced to study problems in VLSI design. The strata in a stratified graph are also referred to as color classes. For a color $X$ in a stratified graph $G$, the $X$-eccentricity $e_X(v)$ of a vertex $v$ of $G$ is the distance between $v$ and an $X$-colored vertex furthest from $v$. The minimum $X$-eccentricity among the vertices of $G$ is the $X$-radius $\mathop {\mathrm rad}\nolimits _XG$ of $G$ and the maximum $X$-eccentricity is the $X$-diameter $\mathop {\mathrm diam}\nolimits _XG$. It is shown that for every three positive integers $a, b$ and $k$ with $a \le b$, there exist a $k$-stratified graph $G$ with $\mathop {\mathrm rad}\nolimits _XG=a$ and $\mathop {\mathrm diam}\nolimits _XG=b$. The number $s_X$ denotes the minimum $X$-eccetricity among the $X$-colored vertices of $G$. It is shown that for every integer $t$ with $\mathop {\mathrm rad}\nolimits _XG \le t \le \mathop {\mathrm diam}\nolimits _XG$, there exist at least one vertex $v$ with $e_X(v)=t$; while if $\mathop {\mathrm rad}\nolimits _XG \le t \le s_X$, then there are at least two such vertices. The $X$-center $C_X(G)$ is the subgraph induced by those vertices $v$ with $e_X(v)=\mathop {\mathrm rad}\nolimits _XG$ and the $X$-periphery $P_X(G)$ is the subgraph induced by those vertices $v$ with $e_X(G)=\mathop {\mathrm diam}\nolimits _XG$. It is shown that for $k$-stratified graphs $H_1, H_2, \dots , H_k$ with colors $X_1, X_2, \dots , X_k$ and a positive integer $n$, there exists a $k$-stratified graph $G$ such that $C_{X_i}(G) \cong H_i \ (1 \le i \le k)$ and $d(C_{X_i}(G), C_{X_j}(G)) \ge n \text{for} i \ne j$. Those $k$-stratified graphs that are peripheries of $k$-stratified graphs are characterized. Other distance-related topics in stratified graphs are also discussed.
Let p′ and q′ be points in \Rn. Write p′∼q′ if p′−q′ is a multiple of (1,…,1). Two different points p and q in \Rn/∼ uniquely determine a tropical line L(p,q) passing through them and stable under small perturbations. This line is a balanced unrooted semi-labeled tree on n leaves. It is also a metric graph. If some representatives p′ and q′ of p and q are the first and second columns of some real normal idempotent order n matrix A, we prove that the tree L(p,q) is described by a matrix F, easily obtained from A. We also prove that L(p,q) is caterpillar. We prove that every vertex in L(p,q) belongs to the tropical linear segment joining p and q. A vertex, denoted pq, closest (w.r.t tropical distance) to p exists in L(p,q). Same for q. The distances between pairs of adjacent vertices in L(p,q) and the distances \dd(p,pq), \dd(qp,q) and \dd(p,q) are certain entries of the matrix |F|. In addition, if p and q are generic, then the tree L(p,q) is trivalent. The entries of F are differences (i. e., sum of principal diagonal minus sum of secondary diagonal) of order 2 minors of the first two columns of A.
Our studies in hypertensive Ren-2 transgenic rats (TGR) demonstrated that chronic administration of atrasentan (ETA receptor antagonist) decreased blood pressure by reduced Ca2+ influx through L-type voltage-dependent calcium channels (L-VDCC) and attenuated angiotensin II-dependent vasoconstriction. We were interested whether bosentan (nonselective ETA/ETB receptor antagonist) would have similar effects. Young 4-week-old (preventive study) and adult 8-weekold (therapeutic study) heterozygous TGR and their normotensive Hannover Sprague-Dawley (HanSD) controls were fed normal-salt (NS, 0.6 % NaCl) or high-salt (HS, 2 % NaCl) diet for 8 weeks. An additional group of TGR fed HS was treated with bosentan (100 mg/kg/day). Bosentan had no effect on BP of TGR fed highsalt diet in both the preventive and therapeutic studies. There was no difference in the contribution of angiotensin II-dependent and sympathetic vasoconstriction in bosentan-treated TGR compared to untreated TGR under the condition of high-salt intake. However, bosentan significantly reduced NO-dependent vasodilation and nifedipine-sensitive BP component in TGR on HS diet. A highly important correlation of nifedipine-induced BP change and the BP after L-NAME administration was demonstrated. Although bosentan did not result in any blood pressure lowering effects, it substantially influenced NO-dependent vasodilation and calcium influx through L-VDCC in the heterozygous TGR fed HS diet. A significant correlation of nifedipine-induced BP change and the BP after L-NAME administration suggests an important role of nitric oxide in the closure of L-type voltage dependent calcium channels.
To study 3D nuclear distributions of epigenetic hist one modifications such as H3(K9) acetylation, H3(K4) dimethylation, H3(K9) dimethylation, and H3(K27) trimethylation, and of histone methyltransferase Suv39H1, we used advanced image analysis methods, comb ined with Nipkow disk confocal microscopy. Total fluorescence intensity and distributions of fluorescently labelled proteins were analyzed in formaldehyde-fixed interphase nuclei. Our data showed reduced fluorescent signals of H3(K9) acetylation and H3(K4) dimethylation (di-me) at the nuclear periphery, while di-meH3(K9) was also abundant in chromatin regions closely associated with the nuclear envelope. Little overlapping (intermingling) was observed for di-meH3(K4) and H3(K27) trimethylation (tri-me), and for di-meH3(K9) and Suv39H1. The histone modifications studied were absent in the nucleolar compartment with the exception of H3(K9) dimethylation that was closely associated with perinucleolar regions which are formed by centromeres of acrocentric chromosomes. Using immunocytochemistry, no di-meH3(K4) but only dense di-meH3(K9) was found for the human acrocentric chromosomes 14 and 22. The active X chromosome was observed to be partially acetylated, while the inactive X was more condensed, located in a very peripheral part of the interphase nuclei, and lacked H3(K9) acetylation. Our results confirmed specific interphase patterns of histone modifications within the interphase nuclei as well as within their chromosome territories., M. Skalníková, E. Bártová, V. Ulman, P. Matula, D. Svoboda, A. Harničarová, M. Kozubek, S. Kozubek., and Obsahuje bibliografii a bibliografické odkazy
Gestational diabetes mellitus (GDM) and polycystic ovary syndrome (PCOS) are distinct pathologies with impaired insulin sensitivity as a common feature. The aim of this study was to evaluate the response of fat tissue adipokines and gastrointestinal incretins to glucose load in patients diagnosed with one of the two disorders and to compare it with healthy controls. Oral glucose tolerance test (oGTT) was performed in 77 lean young women: 22 had positive history of GDM, 19 were PCOS patients, and 36 were healthy controls. Hormones were evaluated in fasting and in 60 min intervals during the 3 h oGTT using Bio-Plex ProHuman Diabetes 10-Plex Assay for C-peptide, ghrelin, GIP, GLP1, glucagon, insulin, leptin, total PAI1, resistin, visfatin and Bio-Plex ProHuman Diabetes Adipsin and Adiponectin Assays (Bio-Rad). Despite lean body composition, both PCOS and GDM women were more insulin resistant than controls. Significant postchallenge differences between the GDM and PCOS groups were observed in secretion of adipsin, leptin, glucagon, visfatin, ghrelin, GIP, and also GLP1 with higher levels in GDM. Conversely, PCOS was associated with the highest resistin, C-peptide, and PAI1 levels. Our data suggest that decreased insulin sensitivity observed in lean women with GDM and PCOS is associated with distinct hormonal response of fat and gastrointestinal tissue to glucose load., D. Vejrazkova, O. Lischkova, M. Vankova, S. Stanicka, J. Vrbikova, P. Lukasova, J. Vcelak, G. Vacinova, B. Bendlova., and Obsahuje bibliografii
The distinguished completion $E(G)$ of a lattice ordered group $G$ was investigated by Ball [1], [2], [3]. An analogous notion for $MV$-algebras was dealt with by the author [7]. In the present paper we prove that if a lattice ordered group $G$ is a direct product of lattice ordered groups $G_i$ $(i\in I)$, then $E(G)$ is a direct product of the lattice ordered groups $E(G_i)$. From this we obtain a generalization of a result of Ball [3].
In this paper, we focus on an aggregative optimization problem under the communication bottleneck. The aggregative optimization is to minimize the sum of local cost functions. Each cost function depends on not only local state variables but also the sum of functions of global state variables. The goal is to solve the aggregative optimization problem through distributed computation and local efficient communication over a network of agents without a central coordinator. Using the variable tracking method to seek the global state variables and the quantization scheme to reduce the communication cost spent in the optimization process, we develop a novel distributed quantized algorithm, called D-QAGT, to track the optimal variables with finite bits communication. Although quantization may lose transmitting information, our algorithm can still achieve the exact optimal solution with linear convergence rate. Simulation experiments on an optimal placement problem is carried out to verify the correctness of the theoretical results.
One of the problems during a great disaster is the breakdown of communication infra structure. One of the solutions is the use of mobile ad-hoc networks (MANET). In this paper, we consider the situation in a building after a big fire, explosion or earthquake. Rescue workers equipped with PDAs, which are wireless connected, explore the dynamically changing world. Each individual builds up a local world map based on their local exploration and observation. The local maps are fused via the MANET structure and provide an up to date map of the dynamically changing world. Such maps can be used for mitigation, escape or rescue work.
In this paper, we investigate multi-agent consensus problem with discrete-time linear dynamics under directed interaction topology. By assumption that all agents can only access the measured outputs of its neighbor agents and itself, a kind of distributed reduced-order observer-based protocols are proposed to solve the consensus problem. A multi-step algorithm is provided to construct the gain matrices involved in the protocols. By using of graph theory, modified discrete-time algebraic Riccati equation and Lyapunov method, the proposed protocols can be proved to solve the discrete-time consensus problem. Furthermore, the proposed protocol is generalized to solve the model-reference consensus problem. Finally, a simulation example is given to illustrate the effectiveness of our obtained results.