DFAs and PFAs with Long Shortest Synchronizing Word Length

It was conjectured by \v{C}ern\'y in 1964, that a synchronizing DFA on $n$ states always has a shortest synchronizing word of length at most $(n-1)^2$, and he gave a sequence of DFAs for which this bound is reached. Until now a full analysis of all DFAs reaching this bound was only given for $n \leq 4$, and with bounds on the number of symbols for $n \leq 10$. Here we give the full analysis for $n \leq 6$, without bounds on the number of symbols. For PFAs the bound is much higher. For $n \leq 6$ we do a similar analysis as for DFAs and find the maximal shortest synchronizing word lengths, exceeding $(n-1)^2$ for $n =4,5,6$. For arbitrary n we give a construction of a PFA on three symbols with exponential shortest synchronizing word length, giving significantly better bounds than earlier exponential constructions. We give a transformation of this PFA to a PFA on two symbols keeping exponential shortest synchronizing word length, yielding a better bound than applying a similar known transformation.Comment: 16 pages, 2 figures source code adde

On the Number of Synchronizing Colorings of Digraphs

We deal with $k$-out-regular directed multigraphs with loops (called simply \emph{digraphs}). The edges of such a digraph can be colored by elements of some fixed $k$-element set in such a way that outgoing edges of every vertex have different colors. Such a coloring corresponds naturally to an automaton. The road coloring theorem states that every primitive digraph has a synchronizing coloring. In the present paper we study how many synchronizing colorings can exist for a digraph with $n$ vertices. We performed an extensive experimental investigation of digraphs with small number of vertices. This was done by using our dedicated algorithm exhaustively enumerating all small digraphs. We also present a series of digraphs whose fraction of synchronizing colorings is equal to $1-1/k^d$, for every $d \ge 1$ and the number of vertices large enough. On the basis of our results we state several conjectures and open problems. In particular, we conjecture that $1-1/k$ is the smallest possible fraction of synchronizing colorings, except for a single exceptional example on 6 vertices for $k=2$.Comment: CIAA 2015. The final publication is available at http://link.springer.com/chapter/10.1007/978-3-319-22360-5_1

Nomenclature of Cambrian lithostratigraphy of the Skryje-Týřovice Basin

Ecuador Debate es una publicación periódica electrónica dependiente del Centro Andino de Acción Popular (CAAP), que cubre diversos temas de la actualidad local y Latinoamericana. Centrada especialmente en asuntos económicos y políticos del Ecuador, la publicación también incluye importantes secciones dedicadas a la cultura (crítica literaria), el mundo agrario, social-urbano, y los temas de conflictividad social. Estos últimos son analizados desde un punto de vista de sociológico y cuantitat..

Synchronization Problems in Automata without Non-trivial Cycles

We study the computational complexity of various problems related to synchronization of weakly acyclic automata, a subclass of widely studied aperiodic automata. We provide upper and lower bounds on the length of a shortest word synchronizing a weakly acyclic automaton or, more generally, a subset of its states, and show that the problem of approximating this length is hard. We investigate the complexity of finding a synchronizing set of states of maximum size. We also show inapproximability of the problem of computing the rank of a subset of states in a binary weakly acyclic automaton and prove that several problems related to recognizing a synchronizing subset of states in such automata are NP-complete.Comment: Extended and corrected version, including arXiv:1608.00889. Conference version was published at CIAA 2017, LNCS vol. 10329, pages 188-200, 201

Gene Expression in Human Hippocampus from Cocaine Abusers Identifies Genes which Regulate Extracellular Matrix Remodeling

The chronic effects of cocaine abuse on brain structure and function are blamed for the inability of most addicts to remain abstinent. Part of the difficulty in preventing relapse is the persisting memory of the intense euphoria or cocaine “rush”. Most abused drugs and alcohol induce neuroplastic changes in brain pathways subserving emotion and cognition. Such changes may account for the consolidation and structural reconfiguration of synaptic connections with exposure to cocaine. Adaptive hippocampal plasticity could be related to specific patterns of gene expression with chronic cocaine abuse. Here, we compare gene expression profiles in the human hippocampus from cocaine addicts and age-matched drug-free control subjects. Cocaine abusers had 151 gene transcripts upregulated, while 91 gene transcripts were downregulated. Topping the list of cocaine-regulated transcripts was RECK in the human hippocampus (FC = 2.0; p<0.05). RECK is a membrane-anchored MMP inhibitor that is implicated in the coordinated regulation of extracellular matrix integrity and angiogenesis. In keeping with elevated RECK expression, active MMP9 protein levels were decreased in the hippocampus from cocaine abusers. Pathway analysis identified other genes regulated by cocaine that code for proteins involved in the remodeling of the cytomatrix and synaptic connections and the inhibition of blood vessel proliferation (PCDH8, LAMB1, ITGB6, CTGF and EphB4). The observed microarray phenotype in the human hippocampus identified RECK and other region-specific genes that may promote long-lasting structural changes with repeated cocaine abuse. Extracellular matrix remodeling in the hippocampus may be a persisting effect of chronic abuse that contributes to the compulsive and relapsing nature of cocaine addiction

Analýza problematiky krajinného rázu v ČR

V rámci úkolu byly vyhodnoceny a editorsky zpracovány metodické materiály. CD-ROM obsahuje tyto texty sborníku "Hodnocení navrhovaných staveb a využití území z hlediska zásahu do krajinného rázu": Krajinný ráz v odborné a správní praxi správ chráněných krajinných oblastí (Petr Moucha), Posuzování vlivů na životní prostředí (EIA) a aspekty krajinného rázu při tomto řízení (Libor Dvořák), Formy účasti veřejnosti při ochraně krajinného rázu (Milan Doucha), Přírodní podmínky území a jejich význam pro krajinný ráz (Martin Culek), Struktura venkovského osídlení (Miroslav Baše), Hodnocení vlivu liniových staveb s koridorovým efektem na krajinný ráz – příklady dálnice D8 a plavebních stupňů na Labi (Ivan Vorel)

Posouzení vlivu navrhované stavby‚ činnosti nebo změny využití území na krajinný ráz (metodický postup případového hodnocení konkrétních záměrů)

Cílem metodického postupu je stanovení způsobu, principů a jednotlivých fází posouzení vlivu navrhovaného záměru (staveb, činnosti nebo využití území) na krajinný ráz na základě definice pojmů § 12 zákona č. 114/1992 Sb., o ochraně přírody a krajiny v platném znění. Jedná se o odborný nástroj, prakticky využitelný v rozhodovací činnosti orgánů ochrany přírody a aplikovatelný ve většině běžných případů. Metodický postup případového hodnocení bude využit k jednotnému a standardizovanému posuzování navrhovaných záměrů na krajinný ráz. Posouzení zpracované podle tohoto metodického postupu představuje objektivizovaný podklad pro rozhodování dle § 12 zákona, ohraničující možnosti neadekvátního užívání subjektivních pohledů na hodnocení