Fast Dynamic Graph Algorithms for Parameterized Problems

Fully dynamic graph is a data structure that (1) supports edge insertions and deletions and (2) answers problem specific queries. The time complexity of (1) and (2) are referred to as the update time and the query time respectively. There are many researches on dynamic graphs whose update time and query time are $o(|G|)$, that is, sublinear in the graph size. However, almost all such researches are for problems in P. In this paper, we investigate dynamic graphs for NP-hard problems exploiting the notion of fixed parameter tractability (FPT). We give dynamic graphs for Vertex Cover and Cluster Vertex Deletion parameterized by the solution size $k$. These dynamic graphs achieve almost the best possible update time $O(\mathrm{poly}(k)\log n)$ and the query time $O(f(\mathrm{poly}(k),k))$, where $f(n,k)$ is the time complexity of any static graph algorithm for the problems. We obtain these results by dynamically maintaining an approximate solution which can be used to construct a small problem kernel. Exploiting the dynamic graph for Cluster Vertex Deletion, as a corollary, we obtain a quasilinear-time (polynomial) kernelization algorithm for Cluster Vertex Deletion. Until now, only quadratic time kernelization algorithms are known for this problem. We also give a dynamic graph for Chromatic Number parameterized by the solution size of Cluster Vertex Deletion, and a dynamic graph for bounded-degree Feedback Vertex Set parameterized by the solution size. Assuming the parameter is a constant, each dynamic graph can be updated in $O(\log n)$ time and can compute a solution in $O(1)$ time. These results are obtained by another approach.Comment: SWAT 2014 to appea

The expression of epidermal growth factor and transforming growth factor-α mRNA in the small intestine of suckling rats: organ culture study

AbstractEpidermal growth factor (EGF) and transforming growth factor-α (TGF-α) are associated with regulation of various gastrointestinal functions. In order to better understand their role in developing small intestine EGF, TGF-α and EGF-R steady-state mRNA levels and transcript stability were determined. Reverse transcription (RT) competitive-polymerase chain reaction (PCR) revealed that intestinal TGF-α mRNA levels were 10-fold higher in comparison with EGF mRNA. The primary intestinal culture technique was used to evaluate mRNA stability. The stability of TGF-α mRNA was remarkably lower than the stability of EGF mRNA. High levels of TGF-α mRNA accompanied by high degradation rate of this mRNA suggested a rapid turnover of intestinal TGF-α mRNA

Some Diptera families from beer traps in the Volga region (Russia)

We have studied the material of some Diptera families collected with beer traps from middle part of the Volga River region (central part of European Russia: Nizhny Novgorod and Ulyanovsk regions, and southeastern part of European Russia: Saratov Region). Thirty species from 10 Diptera families are reported: Culicidae (2 spp.), Dryomyzidae (2 spp.), Lauxaniidae (7 spp.), Limoniidae (3 spp.), Pallopteridae (4 spp.), Periscelididae (1 sp.), Platystomatidae (2 spp.), Sciomyzidae (2 spp.), Tabanidae (1 sp.), Ulidiidae (6 spp.). Two species, Peplomyza intermedia Remm, 1979 (Lauxaniidae) and Periscelis annulipes Loew, 1858 (Periscelididae) are recorded from Russia for the first tim

Potential new genes for resistance to Mycosphaerella graminicola identified in Triticum aestivum x Lophopyrum elongatum disomic substitution lines.

Lophopyrum species carry many desirable agronomic traits, including disease resistance, which can be transferred towheat by interspecific hybridization. To identify potentially new genes for disease and insect resistance carried by individual Lophopyrum chromosomes, 19 of 21 possible wheat cultivar Chinese Spring 9 Lophopyrum elongatum disomic substitution lines were tested for resistance to barley yellow dwarf virus (BYDV), cereal yellow dwarf virus (CYDV), the Hessian fly Mayetiola destructor, and the fungal pathogens Blumeria graminis and Mycosphaerella graminicola (asexual stage: Septoria tritici). Low resistance to BYDV occurred in some of the disomic substitution lines, but viral titers were significantly higher than those of two Lophopyrum species tested. This suggested that genes on more than one Lophopyrum chromosome are required for complete resistance to this virus. A potentially new gene for resistance to CYDV was detected on wheatgrass chromosome 3E. All of the substitution lines were susceptible to Mayetiola destructor and one strain of B. graminis. Disomic substitution lines containing wheatgrass chromosomes 1E and 6E were significantly more resistant to M. graminicola compared to Chinese Spring. Although neither chromosome by itself conferred resistance as high as that in the wheatgrass parent, they do appear to contain potentially new genes for resistance against this pathogen that could be useful for future plant-improvement programs

Triangle-Free Penny Graphs: Degeneracy, Choosability, and Edge Count

We show that triangle-free penny graphs have degeneracy at most two, list coloring number (choosability) at most three, diameter $D=\Omega(\sqrt n)$, and at most $\min\bigl(2n-\Omega(\sqrt n),2n-D-2\bigr)$ edges.Comment: 10 pages, 2 figures. To appear at the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017

Self-avoiding walks and connective constants

The connective constant $\mu(G)$ of a quasi-transitive graph $G$ is the asymptotic growth rate of the number of self-avoiding walks (SAWs) on $G$ from a given starting vertex. We survey several aspects of the relationship between the connective constant and the underlying graph $G$. $\bullet$ We present upper and lower bounds for $\mu$ in terms of the vertex-degree and girth of a transitive graph. $\bullet$ We discuss the question of whether $\mu\ge\phi$ for transitive cubic graphs (where $\phi$ denotes the golden mean), and we introduce the Fisher transformation for SAWs (that is, the replacement of vertices by triangles). $\bullet$ We present strict inequalities for the connective constants $\mu(G)$ of transitive graphs $G$, as $G$ varies. $\bullet$ As a consequence of the last, the connective constant of a Cayley graph of a finitely generated group decreases strictly when a new relator is added, and increases strictly when a non-trivial group element is declared to be a further generator. $\bullet$ We describe so-called graph height functions within an account of "bridges" for quasi-transitive graphs, and indicate that the bridge constant equals the connective constant when the graph has a unimodular graph height function. $\bullet$ A partial answer is given to the question of the locality of connective constants, based around the existence of unimodular graph height functions. $\bullet$ Examples are presented of Cayley graphs of finitely presented groups that possess graph height functions (that are, in addition, harmonic and unimodular), and that do not. $\bullet$ The review closes with a brief account of the "speed" of SAW.Comment: Accepted version. arXiv admin note: substantial text overlap with arXiv:1304.721

Lattice models and Landau theory for type II incommensurate crystals

Ground state properties and phonon dispersion curves of a classical linear chain model describing a crystal with an incommensurate phase are studied. This model is the DIFFOUR (discrete frustrated phi4) model with an extra fourth-order term added to it. The incommensurability in these models may arise if there is frustration between nearest-neighbor and next-nearest-neighbor interactions. We discuss the effect of the additional term on the phonon branches and phase diagram of the DIFFOUR model. We find some features not present in the DIFFOUR model such as the renormalization of the nearest-neighbor coupling. Furthermore the ratio between the slopes of the soft phonon mode in the ferroelectric and paraelectric phase can take on values different from -2. Temperature dependences of the parameters in the model are different above and below the paraelectric transition, in contrast with the assumptions made in Landau theory. In the continuum limit this model reduces to the Landau free energy expansion for type II incommensurate crystals and it can be seen as the lowest-order generalization of the simplest Lifshitz-point model. Part of the numerical calculations have been done by an adaption of the Effective Potential Method, orginally used for models with nearest-neighbor interaction, to models with also next-nearest-neighbor interactions.Comment: 33 pages, 7 figures, RevTex, submitted to Phys. Rev.

A systematic review of potential long-term effects of sport-related concussion

Systematic review of possible long-term effects of sports-related concussion in retired athletes