The signed total domination number of a graph is a certain variant of the domination number. If $v$ is a vertex of a graph $G$, then $N(v)$ is its oper neighbourhood, i.e. the set of all vertices adjacent to $v$ in $G$. A mapping $f: V(G) \rightarrow \lbrace -1, 1\rbrace $, where $V(G)$ is the vertex set of $G$, is called a signed total dominating function (STDF) on $G$, if $\sum _{x \in N(v)} f(x) \ge 1$ for each $v \in V(G)$. The minimum of values $\sum _{x \in V(G)} f(x)$, taken over all STDF’s of $G$, is called the signed total domination number of $G$ and denoted by $\gamma _{\mathrm st}(G)$. A theorem stating lower bounds for $\gamma _{\mathrm st}(G)$ is stated for the case of regular graphs. The values of this number are found for complete graphs, circuits, complete bipartite graphs and graphs on $n$-side prisms. At the end it is proved that $\gamma _{\mathrm st}(G)$ is not bounded from below in general.
This paper analyses rent-based determinants of earthquake damage from an urban planning perspective with the data gathered from Adapazari, Turkey, after the disaster in 1999 Eastern Marmara Earthquake (EME). The study employs linear regression, log-linear regression, and artificial neural networks (ANN) methods for cross-verification of results and for finding out the significant urban rent attribute(s) responsible for the damage. All models used are equally capable of predicting the earthquake damage and converge to similar results even if the data are limited. Of the rent variables, the physical density is proved to be especially significant in predicting earthquake damage, while the land value contributes to building resistance. Thus, urban rent can be the primary tool for planners to help reduce the fatalities in preventive planning studies.
Modern biology is interested in better understanding mechanisms within cells. For this purpose, products of cells like metabolites, peptides, proteins or mRNA are measured and compared under different conditions, for instance healthy cells vs. infected cells. Such experiments usually yield regulation or expression values - the abundance or absence of a cell product in one condition compared to another one - for a large number of cell products, but with only a few replicates. In order to distinguish random fluctuations and noise from true regulations, suitable significance tests are needed. Here we propose a simple model which is based on the assumption that the regulation factors follow normal distributions with different expected values, but with the same standard deviation. Before suitable significance tests can be derived from this model, a reliable estimation for the standard deviation in the context of many small samples is needed. We therefore also include a discussion on the properties of the sample MAD ({\bf M}edian {\bf A}bsolute {\bf D}eviation from the median) and the sample standard deviation for small samples sizes.
By a ternary system we mean an ordered pair $(W, R)$, where $W$ is a finite nonempty set and $R \subseteq W \times W \times W$. By a signpost system we mean a ternary system $(W, R)$ satisfying the following conditions for all $x, y, z \in W$: if $(x, y, z) \in R$, then $(y, x, x) \in R$ and $(y, x, z) \notin R$; if $x \ne y$, then there exists $t \in W$ such that $(x, t, y) \in R$. In this paper, a signpost system is used as a common description of a connected graph and a spanning tree of the graph. By a ct-pair we mean an ordered pair $(G, T)$, where $G$ is a connected graph and $T$ is a spanning tree of $G$. If $(G, T)$ is a ct-pair, then by the guide to $(G,T)$ we mean the ternary system $(W, R)$, where $W = V(G)$ and the following condition holds for all $u, v, w \in W$: $(u, v, w) \in R$ if and only if $uv \in E(G)$ and $v$ belongs to the $u-w$ path in $T$. By Proposition 1, the guide to a ct-pair is a signpost system. We say that a signpost system is tree-controlled if it satisfies a certain set of four axioms (these axioms could be formulated in a language of the first-order logic). Consider the mapping $\phi $ from the class of all ct-pairs into the class of all signpost systems such that $\phi ((G, T))$ is the guide to $(G, T)$ for every ct-pair $(G, T)$. It is proved in this paper that $\phi $ is a bijective mapping from the class of all ct-pairs onto the class of all tree-controlled signpost systems.
A number of clinical neurological pathologies are associated with increased permeability of the blood brain barrier (BBB). Induced changes of the homeostatic mechanisms in the brain microenvironment lead among others to cellular changes in the CNS. The question was whether some of these changes can be induced by osmotic opening of BBB in an in vivo experiment and whether they can be detected in cerebrospinal fluid (CSF). CSF was taken via the suboccipital puncture from 10 healthy rats and six rats after the osmotic opening of the BBB. In all 16 animals, concentration of myelin basic protein (MBP ng/ml), Neuron-specific enolase (NSE ng/ml) and Tau-protein (Tau pg/ml) were determined in CSF by ELISA. Values in both groups were statistically evaluated. Significant difference between the control and experimental group was revealed only for the concentration of myelin basic protein (p<0.01). The presented results indicate that osmotic opening of the BBB in vivo experiment without the presence of other pathological conditions of the brain leads to a damage of myelin, without impairment of neurons or their axons., P. Kozler, O. Sobek, J. Pokorný., and Obsahuje bibliografii
Recenzent představuje vzpomínkovou knihu ekonoma Miloše Picka, jejímž jádrem je líčení strastiplných poměrů a prožitků v koncentračních táborech Terezín, Osvětim a Buchenwald, kam byl autor jako Žid okupační mocí uvržen, a při pochodu smrti na konci války. Kromě sugestivní síly této výpovědi je dle recenzenta cenné vystižení „obyčejného života“ židovské středostavovské rodiny ve východočeském maloměstě před válkou, informace o levicovém odbojovém hnutí v terezínském ghettu i o pomoci pražských odbojářů tamním vězňům a také autorovy reflexe vlastních poválečných iluzí o demokratickém socialismu i angažmá v reformním hnutí pražského jara 1968, po němž následovalo vyloučení z komunistické strany a ztráta možnosti odborného uplatnění. and The book under review, whose title translates as ‘I Don’t Know How to Give Up Hope’‚ is a memoir-like work by the economist Miloš Pick (b. 1926). The core of the book is a depiction of the dreadful experiences of people interned in Theresienstadt, Auschwitz, and Buchenwald, where Pick, a Jew, had been deported by the Nazi régime. He also describes his experience of a death march at the end of the war. Of particular value, apart from the moving power of his testimony, is the depiction of the ‘ordinary life’ of a middle-class Jewish family in a small east Bohemian town before the war, the information about the leftwing resistance movement in Theresienstadt, and the help provided by Prague members of the resistance to Theresienstadt inmates. Equally interesting are Pick’s reflections on his own post-war illusions about democratic socialism and his involvement in the reform movement of the Prague Spring of 1968, after which he was thrown out of the Czechoslovak Communist Party and was prevented from working in his field.