Stability of the essential spectrum for 2D--transport models with Maxwell boundary conditions

We discuss the spectral properties of collisional semigroups associated to various models from transport theory by exploiting the links between the so-called resolvent approach and the semigroup approach. Precisely, we show that the essential spectrum of the full transport semigroup coincides with that of the collisionless transport semigroup in any $L^p$--spaces $(1 <p < \infty)$ for three 2D--transport models with Maxwell--boundary conditions.Comment: 23 page

Claw-free t-perfect graphs can be recognised in polynomial time

A graph is called t-perfect if its stable set polytope is defined by non-negativity, edge and odd-cycle inequalities. We show that it can be decided in polynomial time whether a given claw-free graph is t-perfect

Reconfiguring Independent Sets in Claw-Free Graphs

We present a polynomial-time algorithm that, given two independent sets in a claw-free graph $G$, decides whether one can be transformed into the other by a sequence of elementary steps. Each elementary step is to remove a vertex $v$ from the current independent set $S$ and to add a new vertex $w$ (not in $S$) such that the result is again an independent set. We also consider the more restricted model where $v$ and $w$ have to be adjacent

Changes in the composition and fatty acid profile of Najdi ewes’ milk before and after weaning

This trial aimed to study the changes in the yield, composition, and fatty acid (FA) profile of ewes’ milk during suckling and milking periods. Nineteen multiparous Najdi ewes were kept under identical management and feeding conditions during a 12-week trial that was divided into two periods. Milk samples were collected on each sampling day from the total yield during the suckling (3rd, 6th, and 9th week) and milking (12th week) periods. The milk yield and the total solids, fat, protein, and lactose contents of the milk remained constant throughout the suckling weeks, but the protein content increased and milk yield and lactose content decreased after weaning. There were no differences in milk saturated FA (SFA), unsaturated FA (UFA), and monounsaturated FA (MUFA) contents during the suckling and milking periods, whereas the polyunsaturated FA content increased during the milking period. There were no differences in the individual milk SFA during the weeks of suckling, but the contents of caproic acid (C6:0), caprylic acid (C8:0), margaric acid (C17:0), and stearic acid (C18:0) decreased. However, myristic acid (C14:0), lauric acid (C12:0), and isomers of pentadecanoic (C15:0) acid increased during the milking period. The percentage of vaccenic acid (C18:1△11t), rumenic acid (C18:2△9c,11t; conjugated linoleic acid (CLA)), ω-3 FA group, and the atherogenicity index did not differ during the suckling period, but increased after weaning in the 12th week of lactation. This study demonstrated that weaning lambs in Najdi ewes is probably a factor that strongly affects milk traits by changing yield, composition, and FA profile.Keywords: CLA, dairy ewes, milk fat, milk yield, stage of lactatio

Composición química, estabilidad oxidativa y actividad antiproliferativa del extracto de hexano de semilla de Anethum graveolens (eneldo)

This study aimed to evaluate the physicochemical properties, chemical composition, and anti­proliferative activity of the hexane extract of Anethum graveolens L. (dill) seeds using gas chromatography mass spectrometry (GC-MS). Two fractions, namely the lipid fraction (74%) and volatile fraction (26%), were detected. The extract content of the seeds was about 9.4% and the extract had a pleasant spicy aroma. Oleic acid (52%), cis-vaccenic acid (6.2%), linoleic acid (5.5%), and palmitic acid (3.3%) were the key fatty acids in the lipid fraction, while apiol (23%) and d-carvone (2.4%) were the major volatile components. Tocols (tocopherols and tocotrienols) were also detected in the A. Graveolens extract (155 mg/100 g) and b-tocopherol was identified as the major tocol (71%). Dill extract showed a high oxidative stability (induction time = 45.22 h). Furthermore, dill extract showed antiproliferative activity against breast cancer cell lines.Este estudio tuvo como objetivo evaluar las propiedades fisicoquí­micas, la composición química y la actividad antiproliferativa del extracto de hexano de semillas de Anethum graveolens L. (eneldo) mediante cromatografía de gases con espectrometría de masas (GC-MS). Se detectaron dos fracciones, la fracción lipídica (74%) y la fracción volátil (26%). El contenido del extracto de las semi­llas fue de aproximadamente 9,4% y el extracto tenía un agradable aroma picante. Los ácidos oleico (52%), cis-vaccénico (6,2%), linoleico (5,5%) y palmítico (3,3%) fueron los ácidos grasos clave en la fracción lipídica, mientras que el apiol (23%) y la d-carvona (2,4%) fueron los principales componentes volátiles. También se detectaron tocoles (tocoferoles y tocotrienoles) en el extracto de A. Graveolens (155 mg/100 g) y se identificó el β-tocoferol como el principal tocol (71%). El extracto de eneldo mostró una alta estabilidad oxidativa (tiempo de inducción = 45,22 h). Además, el extracto de eneldo mostró actividad antiproliferativa contra las líneas celulares de cáncer de mama

A note on anti-coordination and social interactions

This note confirms a conjecture of [Bramoull\'{e}, Anti-coordination and social interactions, Games and Economic Behavior, 58, 2007: 30-49]. The problem, which we name the maximum independent cut problem, is a restricted version of the MAX-CUT problem, requiring one side of the cut to be an independent set. We show that the maximum independent cut problem does not admit any polynomial time algorithm with approximation ratio better than $n^{1-\epsilon}$, where $n$ is the number of nodes, and $\epsilon$ arbitrarily small, unless P=NP. For the rather special case where each node has a degree of at most four, the problem is still MAXSNP-hard.Comment: 7 page

Independent Set Reconfiguration in Cographs

We study the following independent set reconfiguration problem, called TAR-Reachability: given two independent sets $I$ and $J$ of a graph $G$, both of size at least $k$, is it possible to transform $I$ into $J$ by adding and removing vertices one-by-one, while maintaining an independent set of size at least $k$ throughout? This problem is known to be PSPACE-hard in general. For the case that $G$ is a cograph (i.e. $P_4$-free graph) on $n$ vertices, we show that it can be solved in time $O(n^2)$, and that the length of a shortest reconfiguration sequence from $I$ to $J$ is bounded by $4n-2k$, if such a sequence exists. More generally, we show that if $X$ is a graph class for which (i) TAR-Reachability can be solved efficiently, (ii) maximum independent sets can be computed efficiently, and which satisfies a certain additional property, then the problem can be solved efficiently for any graph that can be obtained from a collection of graphs in $X$ using disjoint union and complete join operations. Chordal graphs are given as an example of such a class $X$

Vector Bin Packing with Multiple-Choice

We consider a variant of bin packing called multiple-choice vector bin packing. In this problem we are given a set of items, where each item can be selected in one of several $D$-dimensional incarnations. We are also given $T$ bin types, each with its own cost and $D$-dimensional size. Our goal is to pack the items in a set of bins of minimum overall cost. The problem is motivated by scheduling in networks with guaranteed quality of service (QoS), but due to its general formulation it has many other applications as well. We present an approximation algorithm that is guaranteed to produce a solution whose cost is about $\ln D$ times the optimum. For the running time to be polynomial we require $D=O(1)$ and $T=O(\log n)$. This extends previous results for vector bin packing, in which each item has a single incarnation and there is only one bin type. To obtain our result we also present a PTAS for the multiple-choice version of multidimensional knapsack, where we are given only one bin and the goal is to pack a maximum weight set of (incarnations of) items in that bin

Spectre multifractal : Applications aux images médicales

Dans cet article, nous proposons une méthode puissante pour la caractérisation et la segmentation des images médicales basée sur la géométrie fractale. Le principe de cette méthode en analyse d’images est justifié par l’auto-similarité d’une texture sur une résolution finie qui repose principalement sur l’estimation d’attributs fractals. Diverses méthodes ont été proposées pour estimer la dimension fractale. Dans ce travail nous développons une méthode basée sur le spectre multifractal de Hausdorff pour caractériser des images médicales CT-Scan. Les résultats obtenus démontrent l’intérêt de cette géométrie et son adaptabilité pour caractériser les altérations des textures osseuses saines et ostéoporotiques

Parameterized Inapproximability of Independent Set in HH-Free Graphs

We study the Independent Set (IS) problem in $H$-free graphs, i.e., graphs excluding some fixed graph $H$ as an induced subgraph. We prove several inapproximability results both for polynomial-time and parameterized algorithms. Halld\'orsson [SODA 1995] showed that for every $\delta>0$ IS has a polynomial-time $(\frac{d-1}{2}+\delta)$-approximation in $K_{1,d}$-free graphs. We extend this result by showing that $K_{a,b}$-free graphs admit a polynomial-time $O(\alpha(G)^{1-1/a})$-approximation, where $\alpha(G)$ is the size of a maximum independent set in $G$. Furthermore, we complement the result of Halld\'orsson by showing that for some $\gamma=\Theta(d/\log d),$ there is no polynomial-time $\gamma$-approximation for these graphs, unless NP = ZPP. Bonnet et al. [IPEC 2018] showed that IS parameterized by the size $k$ of the independent set is W[1]-hard on graphs which do not contain (1) a cycle of constant length at least $4$, (2) the star $K_{1,4}$, and (3) any tree with two vertices of degree at least $3$ at constant distance. We strengthen this result by proving three inapproximability results under different complexity assumptions for almost the same class of graphs (we weaken condition (2) that $G$ does not contain $K_{1,5}$). First, under the ETH, there is no $f(k)\cdot n^{o(k/\log k)}$ algorithm for any computable function $f$. Then, under the deterministic Gap-ETH, there is a constant $\delta>0$ such that no $\delta$-approximation can be computed in $f(k) \cdot n^{O(1)}$ time. Also, under the stronger randomized Gap-ETH there is no such approximation algorithm with runtime $f(k)\cdot n^{o(k)}$. Finally, we consider the parameterization by the excluded graph $H$, and show that under the ETH, IS has no $n^{o(\alpha(H))}$ algorithm in $H$-free graphs and under Gap-ETH there is no $d/k^{o(1)}$-approximation for $K_{1,d}$-free graphs with runtime $f(d,k) n^{O(1)}$.Comment: Preliminary version of the paper in WG 2020 proceeding