Paradigms for Parameterized Enumeration

The aim of the paper is to examine the computational complexity and algorithmics of enumeration, the task to output all solutions of a given problem, from the point of view of parameterized complexity. First we define formally different notions of efficient enumeration in the context of parameterized complexity. Second we show how different algorithmic paradigms can be used in order to get parameter-efficient enumeration algorithms in a number of examples. These paradigms use well-known principles from the design of parameterized decision as well as enumeration techniques, like for instance kernelization and self-reducibility. The concept of kernelization, in particular, leads to a characterization of fixed-parameter tractable enumeration problems.Comment: Accepted for MFCS 2013; long version of the pape

Fixed-parameter tractability of multicut parameterized by the size of the cutset

Given an undirected graph $G$, a collection $\{(s_1,t_1),..., (s_k,t_k)\}$ of pairs of vertices, and an integer $p$, the Edge Multicut problem ask if there is a set $S$ of at most $p$ edges such that the removal of $S$ disconnects every $s_i$ from the corresponding $t_i$. Vertex Multicut is the analogous problem where $S$ is a set of at most $p$ vertices. Our main result is that both problems can be solved in time $2^{O(p^3)}... n^{O(1)}$, i.e., fixed-parameter tractable parameterized by the size $p$ of the cutset in the solution. By contrast, it is unlikely that an algorithm with running time of the form $f(p)... n^{O(1)}$ exists for the directed version of the problem, as we show it to be W[1]-hard parameterized by the size of the cutset

Time-reversible Born-Oppenheimer molecular dynamics

We present a time-reversible Born-Oppenheimer molecular dynamics scheme, based on self-consistent Hartree-Fock or density functional theory, where both the nuclear and the electronic degrees of freedom are propagated in time. We show how a time-reversible adiabatic propagation of the electronic degrees of freedom is possible despite the non-linearity and incompleteness of the self-consistent field procedure. Time-reversal symmetry excludes a systematic long-term energy drift for a microcanonical ensemble and the number of self-consistency cycles can be kept low (often only 2-4 cycles per nuclear time step) thanks to a good initial guess given by the adiabatic propagation of the electronic degrees of freedom. The time-reversible Born-Oppenheimer molecular dynamics scheme therefore combines a low computational cost with a physically correct time-reversible representation of the dynamics, which preserves a detailed balance between propagation forwards and backwards in time.Comment: 4 pages, 4 figure

Wavefunction extended Lagrangian Born-Oppenheimer molecular dynamics

Extended Lagrangian Born-Oppenheimer molecular dynamics [Niklasson, Phys. Rev. Lett. 100 123004 (2008)] has been generalized to the propagation of the electronic wavefunctions. The technique allows highly efficient first principles molecular dynamics simulations using plane wave pseudopotential electronic structure methods that are stable and energy conserving also under incomplete and approximate self-consistency convergence. An implementation of the method within the planewave basis set is presented and the accuracy and efficiency is demonstrated both for semi-conductor and metallic materials.Comment: 6 pages, 3 figure

Chromosomal locations of twelve isozyme loci in Pisum sativum

Approximate chromosomal locations of 12 loci specifying electrophoretic enzyme variants are described in the garden pea (Pisum sativum L.). The enzyme loci are distributed on five of the seven chromosomes. The position of the loci on chromosomes 2 and 3 are such that most of the known markers on these chromosomes will exhibit linkage with at least one of the isozyme loci. Several of the loci studied code for enzymes that have isozymic counterparts in other compartments of the cell. In order to distinguish among the genes coding these isozymes we have added a suffix to the locus designation corresponding to the intracellular location of its produc

Parameterized Inapproximability of Target Set Selection and Generalizations

In this paper, we consider the Target Set Selection problem: given a graph and a threshold value $thr(v)$ for any vertex $v$ of the graph, find a minimum size vertex-subset to "activate" s.t. all the vertices of the graph are activated at the end of the propagation process. A vertex $v$ is activated during the propagation process if at least $thr(v)$ of its neighbors are activated. This problem models several practical issues like faults in distributed networks or word-to-mouth recommendations in social networks. We show that for any functions $f$ and $\rho$ this problem cannot be approximated within a factor of $\rho(k)$ in $f(k) \cdot n^{O(1)}$ time, unless FPT = W[P], even for restricted thresholds (namely constant and majority thresholds). We also study the cardinality constraint maximization and minimization versions of the problem for which we prove similar hardness results

Comparison of effectiveness of heat and cold shocks applied in the induction of gynogenesis in Clarias gariepinus (Burchell)

An experiment was conducted to optimize the procedure of gynogenesis in African catfish, Clarias gariepinus by suppressing meiotic and mitotic cell divisions in fertilized eggs. Gynogensis was conducted by fertilizing normal eggs with UV-irradiated sperm followed by either heat or cold shocking Irradiation of spermatozoa was given for a duration of 1 min and the eggs were fertilized in vitro. Cold shock at a temperature of 3± 1°C for a duration of 30 and 60 min and heat shock at a temperature of 39± 1°C for a duration of 1 and 2 min was applied to induce diploidy. Higher percentage of hatching (68.66) was observed for meiotic gynogens at a shock temperature of 39± 1°C for a duration of 1 min, 5 min after fertilization (af). Higher percentage of mitotic gynogenetic induction (15.33) was observed at a temperature shock of 39± 1°C for a duration of 1 min, 30 min af

An isozyme marker for resistance to bean yellow mosaic virus in Pisum sativum

Linkage between Pgm-p, the locus specifying the plastid specific phosphoglucomutase, and Mo, the locus controlling resistance to bean yellow mosaic virus (BYMV), was investigated in the garden pea, Pisum sativum L. Both genes are known to be on chromosome 2 and exhibit linkage with two morphological marker loci, K and Wb. Our results indicate that the gene order is: Wb—K—Pgm-p—Mo. A map distance of approximately two recombinant units was determined for the Pgm-p—Mo linkage, suggesting that the enzyme locus can be used as a genetic marker for resistance to BYM