Spectral transform simulations of finite amplitude double-diffusive instabilities in two dimensions

Simulations of double-diffusion with a two-dimensional, vertical plane spectral transform model reveal details of finite amplitude behavior in salt finger, interleaving and diffusive instabilities. Within the range of fluid parameters studied (3 \u3c σ \u3c 10, .1 \u3c r \u3c .5), infinite, fastest-growing fingers are unstable to Holyer\u27s (1984) nonoscillatory instability and are completely disrupted by it. Finite fingers localized on density steps are also disrupted. Initialized density steps are eroded (the gradients reduced). Fluxes and other diagnostic quantities were determined for salt finger fields at statistical stationarity. These fields contain transitory, irregular finger structures. Fluxes decline steeply as Rfp increases. A single point of comparison of buoyancy flux with ocean measurement yielded good agreement. The dependence of flux ratio on the stability parameter is similar to the linear theory prediction for fastest-growing, infinite fingers and does not increase as Rfp approaches 1, in contrast to laboratory measurements. Holyer\u27s (1984) Floquet theory is extended to the case of nonzero, density compensating, horizontal gradients, and, together with the simulation results, encourages the interpretation of the interleaving instability as being sloping salt fingers. A few preliminary simulations of the diffusive regime indicate very complex behavior. A growing oscillatory perturbation can lead to subcritical convective instability. Such motions sharpen initialized density steps. In the presence of a step, unstable motions are supported even when the fluid is linearly stable to both convection and the diffusive mode

Parameterized Complexity of Maximum Edge Colorable Subgraph

A graph $H$ is {\em $p$-edge colorable} if there is a coloring $\psi: E(H) \rightarrow \{1,2,\dots,p\}$, such that for distinct $uv, vw \in E(H)$, we have $\psi(uv) \neq \psi(vw)$. The {\sc Maximum Edge-Colorable Subgraph} problem takes as input a graph $G$ and integers $l$ and $p$, and the objective is to find a subgraph $H$ of $G$ and a $p$-edge-coloring of $H$, such that $|E(H)| \geq l$. We study the above problem from the viewpoint of Parameterized Complexity. We obtain \FPT\ algorithms when parameterized by: $(1)$ the vertex cover number of $G$, by using {\sc Integer Linear Programming}, and $(2)$ $l$, a randomized algorithm via a reduction to \textsc{Rainbow Matching}, and a deterministic algorithm by using color coding, and divide and color. With respect to the parameters $p+k$, where $k$ is one of the following: $(1)$ the solution size, $l$, $(2)$ the vertex cover number of $G$, and $(3)$ l - {\mm}(G), where {\mm}(G) is the size of a maximum matching in $G$; we show that the (decision version of the) problem admits a kernel with $\mathcal{O}(k \cdot p)$ vertices. Furthermore, we show that there is no kernel of size $\mathcal{O}(k^{1-\epsilon} \cdot f(p))$, for any $\epsilon > 0$ and computable function $f$, unless \NP \subseteq \CONPpoly

When Patrolmen Become Corrupted: Monitoring a Graph using Faulty Mobile Robots

International audienceA team of k mobile robots is deployed on a weighted graph whose edge weights represent distances. The robots perpetually move along the domain, represented by all points belonging to the graph edges, not exceeding their maximal speed. The robots need to patrol the graph by regularly visiting all points of the domain. In this paper, we consider a team of robots (patrolmen), at most f of which may be unreliable, i.e. they fail to comply with their patrolling duties. What algorithm should be followed so as to minimize the maximum time between successive visits of every edge point by a reliable patrolmen? The corresponding measure of efficiency of patrolling called idleness has been widely accepted in the robotics literature. We extend it to the case of untrusted patrolmen; we denote by Ifk (G) the maximum time that a point of the domain may remain unvisited by reliable patrolmen. The objective is to find patrolling strategies minimizing Ifk (G). We investigate this problem for various classes of graphs. We design optimal algorithms for line segments, which turn out to be surprisingly different from strategies for related patrolling problems proposed in the literature. We then use these results to study the case of general graphs. For Eulerian graphs G, we give an optimal patrolling strategy with idleness Ifk (G) = (f + 1)|E|/k, where |E| is the sum of the lengths of the edges of G. Further, we show the hardness of the problem of computing the idle time for three robots, at most one of which is faulty, by reduction from 3-edge-coloring of cubic graphs — a known NP-hard problem. A byproduct of our proof is the investigation of classes of graphs minimizing idle time (with respect to the total length of edges); an example of such a class is known in the literature under the name of Kotzig graphs

The complexity of counting edge colorings and a dichotomy for some higher domain Holant problems

We show that an effective version of Siegel’s Theorem on finiteness of integer solutions and an application of elementary Galois theory are key ingredients in a complexity classification of some Holant problems. These Holant problems, denoted by Holant(f), are defined by a symmetric ternary function f that is invariant under any permutation of the κ ≥ 3 domain elements. We prove that Holant(f) exhibits a complexity dichotomy. This dichotomy holds even when restricted to planar graphs. A special case of this result is that counting edge κ-colorings is #P-hard over planar 3-regular graphs for κ ≥ 3. In fact, we prove that counting edge κ-colorings is #P-hard over planar r-regular graphs for all κ ≥ r ≥ 3. The problem is polynomial-time computable in all other parameter settings. The proof of the dichotomy theorem for Holant(f) depends on the fact that a specific polynomial p(x, y) has an explicitly listed finite set of integer solutions, and the determination of the Galois groups of some specific polynomials. In the process, we also encounter the Tutte polynomial, medial graphs, Eulerian partitions, Puiseux series, and a certain lattice condition on the (logarithm of) the roots of polynomials.

Evolution through segmental duplications and losses : A Super-Reconciliation approach

The classical gene and species tree reconciliation, used to infer the history of gene gain and loss explaining the evolution of gene families, assumes an independent evolution for each family. While this assumption is reasonable for genes that are far apart in the genome, it is not appropriate for genes grouped into syntenic blocks, which are more plausibly the result of a concerted evolution. Here, we introduce the Super-Reconciliation problem which consists in inferring a history of segmental duplication and loss events (involving a set of neighboring genes) leading to a set of present-day syntenies from a single ancestral one. In other words, we extend the traditional Duplication-Loss reconciliation problem of a single gene tree, to a set of trees, accounting for segmental duplications and losses. Existency of a Super-Reconciliation depends on individual gene tree consistency. In addition, ignoring rearrangements implies that existency also depends on gene order consistency. We first show that the problem of reconstructing a most parsimonious Super-Reconciliation, if any, is NP-hard and give an exact exponential-time algorithm to solve it. Alternatively, we show that accounting for rearrangements in the evolutionary model, but still only minimizing segmental duplication and loss events, leads to an exact polynomial-time algorithm. We finally assess time efficiency of the former exponential time algorithm for the Duplication-Loss model on simulated datasets, and give a proof of concept on the opioid receptor genes

Justi?a fiscal e neutralidade fiscal : a quest?o do ICMS nas opera??es interestaduais

Made available in DSpace on 2015-04-14T14:33:25Z (GMT). No. of bitstreams: 1 383753.pdf: 1097271 bytes, checksum: ec852da20af3956be7b5c483d8986a3d (MD5) Previous issue date: 2006-06-14O presente trabalho objetiva analisar a tributa??o do ICMS nas opera??es interestaduais, buscando apontar as principais caracter?sticas que deve ter um sistema de tributa??o de opera??es interjurisdicionais capaz de atender aos princ?pios da justi?a fiscal e da neutralidade fiscal, tendo como resultado o fortalecimento da Federa??o brasileira. Estuda os princ?pios da justi?a fiscal e da neutralidade fiscal, abordando a capacidade contributiva e a extrafiscalidade. Resgata o hist?rico dos impostos sobre o valor agregado, do qual o ICMS ? esp?cie. Trata da Federa??o brasileira, mercado integrado, dotado de desequil?brios verticais e horizontais. Cuida da autonomia estadual, do papel exercido pelo ICMS e da competi??o fiscal danosa entre Estados, apontando as propostas de altera??o constitucional relativas a esse imposto. Apresenta os princ?pios de imposi??o na origem e no destino como elementos de conex?o nas opera??es interjurisdicionais. Tra?a paralelo com a experi?ncia vivida pela Uni?o Europ?ia, desde a entrada em vigor do mercado comum, quanto ? tributa??o do Imposto sobre o Valor Agregado nas opera??es intracomunit?rias, demonstrando as vantagens e desvantagens do sistema l? adotado. Discorre sobre o hist?rico de tributa??o de opera??es interestaduais na Federa??o brasileira. Apresenta o sistema misto previsto na Constitui??o Federal de 1988, de tributa??o na origem e compensa??o de receitas com o Estado de destino, atrav?s de al?quotas interestaduais diferenciadas, analisando os problemas resultantes dessa op??o, especialmente sob o prisma do princ?pio da justi?a fiscal e da neutralidade fiscal. A partir da preocupa??o em equacionar, na tributa??o das opera??es interestaduais, os princ?pios da justi?a fiscal e da neutralidade fiscal com o aprimoramento da Federa??o e redu??o de suas desigualdades, conclui pela necessidade de tributa??o no Estado de origem, pr?pria de um mercado integrado como a Federa??o brasileira, assim como de aloca??o da receita do tributo para o Estado de destino, conseq??ncia da natureza de imposto sobre o consumo do ICMS. Analisa, tamb?m, os modelos para mudan?a da tributa??o das opera??es interestaduais formalizados atrav?s de Propostas de Emenda Constitucional