HH-product and HH-threshold graphs

This paper is the continuation of the research of the author and his colleagues of the {\it canonical} decomposition of graphs. The idea of the canonical decomposition is to define the binary operation on the set of graphs and to represent the graph under study as a product of prime elements with respect to this operation. We consider the graph together with the arbitrary partition of its vertex set into $n$ subsets ($n$-partitioned graph). On the set of $n$-partitioned graphs distinguished up to isomorphism we consider the binary algebraic operation $\circ_H$ ($H$-product of graphs), determined by the digraph $H$. It is proved, that every operation $\circ_H$ defines the unique factorization as a product of prime factors. We define $H$-threshold graphs as graphs, which could be represented as the product $\circ_{H}$ of one-vertex factors, and the threshold-width of the graph $G$ as the minimum size of $H$ such, that $G$ is $H$-threshold. $H$-threshold graphs generalize the classes of threshold graphs and difference graphs and extend their properties. We show, that the threshold-width is defined for all graphs, and give the characterization of graphs with fixed threshold-width. We study in detail the graphs with threshold-widths 1 and 2

On 2-switches and isomorphism classes

A 2-switch is an edge addition/deletion operation that changes adjacencies in the graph while preserving the degree of each vertex. A well known result states that graphs with the same degree sequence may be changed into each other via sequences of 2-switches. We show that if a 2-switch changes the isomorphism class of a graph, then it must take place in one of four configurations. We also present a sufficient condition for a 2-switch to change the isomorphism class of a graph. As consequences, we give a new characterization of matrogenic graphs and determine the largest hereditary graph family whose members are all the unique realizations (up to isomorphism) of their respective degree sequences.Comment: 11 pages, 6 figure

The Analysis of Links between the Characteristics of Active Regions on the Sun and X-flares Classes M and X on the GOES Scale

AbstractThe analysis of links between speed and size of squares change of visible active regions at the Sun and their classification index with the generation of powerful solar flares of classes M and X according to Space Weather Prediction Center NOAA data is carried out. Measurements in 23 and 24 cycles of solar activity were processed. Results of the analysis and offer on algorithm for control by the biaxial targeting platform on the service module “Zvezda” of the Russian Segment of the International Space Station, where the GRIS device detectors unit is placed, are given

Modulace nociceptivního synaptického přenosu na míšní úrovni

Chronic pain phenomenon is an important problem in modern medicine. Occurring of this phenomenon is tightly connected with nociceptive transmission and modulation of nociceptive signal on the spinal cord level. Under the pathological conditions such as injury or inflammation this modulation is affected by different types of endogenous molecules with pain enhancing attributes. Important group of these molecules are chemokines, immune system substances, also responsible for immune cells recruitments. However, in pathological states chemokines show ability to modulate nociceptive signal and induce chronic pain. CCL2, in particular, has a significant role in modulation of these processes in the spinal cord. Investigation of the mechanisms by which CCL2 influences the spinal cord and dorsal root ganglion may be an important part for preventing the development of chronic pain. Key words: nociception, pain, spinal cord, chemokines, CCL2Fenomén chronické bolesti je významným problémem současné medicíny. Vznik tohoto fenoménu těsně spojen s nociceptivním přenosem a modulací nociceptivního signálu na míšní úrovni. Za patologických podmínek jako je úraz nebo zánět je tato modulace ovlivněna působením různých endogenních molekul s bolest zesilujícími účinky. Důležitou skupinou mezi těmito molekulami jsou chemokiny - látky produkované imunitním systémem, které jsou mimo jiné zodpovědné za atrakci imunitních buněk. Nicméně, u patologických stavů mají chemokiny schopnost modulace nociceptivního signálu a indukce chronické bolesti. CCL2, zejména, má významnou roli v modulačních procesech na míšní úrovni. Zkoumaní mechanismů působení CCL2 na úrovní míchy a ganglii může být jedním s klíčů pro prevenci vývoje chronické bolesti. Klíčová slova: nocicepce, bolest, mícha, chemokiny, CCL2Department of PhysiologyKatedra fyziologieFaculty of SciencePřírodovědecká fakult

Význam cholinergní signalizace ve striatu pro řízení chování a kognitivní flexibility

Cognitive flexibility is an important mechanism enabling organisms to adapt to their changing environment. Different brain structures are involved in this complex process. It has been repeatedly shown that the striatum is one of the key structures controlling cognitive flexibility. Striatum receives rich input from different brain regions while its output is rather uniform. Striatal functions and signalling are greatly modulated by dopamine and acetylcholine. A number of studies have shown involvement of striatal acetylcholine and its receptors in the control of cognitive flexibility but very little is known about the role of M4 muscarinic acetylcholine receptors. These receptors are inhibitory, and they have been shown to induce long-term depression in striatal medium spiny neurons, therefore opposing the action of the dopamine D1 receptors. We hypothesize that the inhibitory effect of M4 muscarinic acetylcholine receptors may supress spiny projection neurons coding for outdated and no longer effective behavioural strategy and thus they may be necessary for the flexible change of behaviour. In the present thesis, I investigated the effects of pharmacological antagonism of M4 receptors on cognitive flexibility of mice tested in a simple reversal learning paradigm. Key words: striatum; cholinergic...Kognitivní flexibilita je důležitým mechanismem umožňujícím organismům adaptovat se na neustále se měnící prostředí. Jednou z klíčových částí mozku podílejících se na řízení kognitivní flexibility je striatum. Striatum přijímá projekce neuronů z různých mozkových oblastí, zatímco jeho vlastní projekce jsou poměrně uniformní a podílejí se na výběru vhodných motorických odpovědí organismu. Signalizace ve striatu je modulována především dopaminem a acetylcholinem. Řada studií ukázala na význam acetylcholinu a jeho receptorů ve striatu pro správnou funkci kognitivní flexibility, ale konkrétně role M4 muskarinových receptorů v tomto kontextu je stále nejasná. M4 inhibiční receptory jsou schopné indukovat dlouhodobou depresi (LTD) na projekčních neuronech striata a působí tak proti účinku D1 dopaminových receptorů. Podle naší hypotézy může inhibiční účinek M4 receptorů potlačovat projekční neurony kódující již zastaralou a neefektivní behaviorální strategii, a tím přispívat ke flexibilní změně chování. Cílem této práce bylo otestovat účinek farmakologické inhibice M4 receptorů na kognitivní flexibilitu myší vystavených jednoduchému testu reverzního učení v operantním boxu. Klicová slova: striatum; cholinergní systém; myš; behaviorální experimentyDepartment of PhysiologyKatedra fyziologieFaculty of SciencePřírodovědecká fakult

Canonical horizontal visibility graphs are uniquely determined by their degree sequence

Horizontal visibility graphs (HVGs) are graphs constructed in correspondence with number sequences that have been introduced and explored recently in the context of graph-theoretical time series analysis. In most of the cases simple measures based on the degree sequence (or functionals of these such as entropies over degree and joint degree distributions) appear to be highly informative features for automatic classification and provide nontrivial information on the associated dynam- ical process, working even better than more sophisticated topological metrics. It is thus an open question why these seemingly simple measures capture so much information. Here we prove that, under suitable conditions, there exist a bijection between the adjacency matrix of an HVG and its degree sequence, and we give an explicit construction of such bijection. As a consequence, under these conditions HVGs are unigraphs and the degree sequence fully encapsulates all the information of these graphs, thereby giving a plausible reason for its apparently unreasonable effectiveness

RT-2 Detection of Quasi-Periodic Pulsations in the 2009 July 5 Solar Hard X-ray Flare

We present the results of an analysis of hard X-ray observations of the C2.7 solar flare detected by the RT-2 Experiment onboard the Coronas - Photon satellite. We detect hard X-ray pulsations at periods of ~12 s and ~15 s. We find a marginal evidence for a decrease in period with time. We have augmented these results using the publicly available data from the RHESSI satellite. We present a spectral analysis and measure the spectral parameters.Comment: 12 pages, 8 figures and 3 tables, accepted for publication in The Astrophysical Journa