The directed 2-linkage problem with length constraints

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Parameterized Complexity of Directed Spanner Problems

We initiate the parameterized complexity study of minimum t-spanner problems on directed graphs. For a positive integer t, a multiplicative t-spanner of a (directed) graph G is a spanning subgraph H such that the distance between any two vertices in H is at most t times the distance between these vertices in G, that is, H keeps the distances in G up to the distortion (or stretch) factor t. An additive t-spanner is defined as a spanning subgraph that keeps the distances up to the additive distortion parameter t, that is, the distances in H and G differ by at most t. The task of Directed Multiplicative Spanner is, given a directed graph G with m arcs and positive integers t and k, decide whether G has a multiplicative t-spanner with at most m-k arcs. Similarly, Directed Additive Spanner asks whether G has an additive t-spanner with at most m-k arcs. We show that - Directed Multiplicative Spanner admits a polynomial kernel of size ?(k?t?) and can be solved in randomized (4t)^k? n^?(1) time, - Directed Additive Spanner is W[1]-hard when parameterized by k even if t = 1 and the input graphs are restricted to be directed acyclic graphs. The latter claim contrasts with the recent result of Kobayashi from STACS 2020 that the problem for undirected graphs is FPT when parameterized by t and k

Detours in Directed Graphs

We study two "above guarantee" versions of the classical Longest Path problem on undirected and directed graphs and obtain the following results. In the first variant of Longest Path that we study, called Longest Detour, the task is to decide whether a graph has an (s,t)-path of length at least dist_G(s,t)+k (where dist_G(s,t) denotes the length of a shortest path from s to t). Bezáková et al. [Ivona Bezáková et al., 2019] proved that on undirected graphs the problem is fixed-parameter tractable (FPT) by providing an algorithm of running time 2^{O(k)}⋅ n. Further, they left the parameterized complexity of the problem on directed graphs open. Our first main result establishes a connection between Longest Detour on directed graphs and 3-Disjoint Paths on directed graphs. Using these new insights, we design a 2^{O (k)}· n^{O(1)} time algorithm for the problem on directed planar graphs. Further, the new approach yields a significantly faster FPT algorithm on undirected graphs. In the second variant of Longest Path, namely Longest Path above Diameter, the task is to decide whether the graph has a path of length at least diam(G)+k(diam(G)denotes the length of a longest shortest path in a graph G). We obtain dichotomy results about Longest Path above Diameter on undirected and directed graphs. For (un)directed graphs, Longest Path above Diameter is NP-complete even for k=1. However, if the input undirected graph is 2-connected, then the problem is FPT. On the other hand, for 2-connected directed graphs, we show that Longest Path above Diameter is solvable in polynomial time for each k ∈ {1,..., 4} and is NP-complete for every k ≥ 5. The parameterized complexity of Longest Detour on general directed graphs remains an interesting open problem.publishedVersio

The great melting pot. Common sole population connectivity assessed by otolith and water fingerprints

Quantifying the scale and importance of individual dispersion between populations and life stages is a key challenge in marine ecology. The common sole (Solea solea), an important commercial flatfish in the North Sea, Atlantic Ocean and the Mediterranean Sea, has a marine pelagic larval stage, a benthic juvenile stage in coastal nurseries (lagoons, estuaries or shallow marine areas) and a benthic adult stage in deeper marine waters on the continental shelf. To date, the ecological connectivity among these life stages has been little assessed in the Mediterranean. Here, such an assessment is provided for the first time for the Gulf of Lions, NW Mediterranean, based on a dataset on otolith microchemistry and stable isotopic composition as indicators of the water masses inhabited by individual fish. Specifically, otolith Ba/Ca and Sr/Ca profiles, and delta C-13 and delta O-18 values of adults collected in four areas of the Gulf of Lions were compared with those of young-of-the-year collected in different coastal nurseries. Results showed that a high proportion of adults (>46%) were influenced by river inputs during their larval stage. Furthermore Sr/Ca ratios and the otolith length at one year of age revealed that most adults (similar to 70%) spent their juvenile stage in nurseries with high salinity, whereas the remainder used brackish environments. In total, data were consistent with the use of six nursery types, three with high salinity (marine areas and two types of highly saline lagoons) and three brackish (coastal areas near river mouths, and two types of brackish environments), all of which contributed to the replenishment of adult populations. These finding implicated panmixia in sole population in the Gulf of Lions and claimed for a habitat integrated management of fisherie

No evident association between efavirenz use and suicidality was identified from a disproportionality analysis using the FAERS database

ObjectiveTo assess the potential association of selected antiretrovirals (ARVs), including efavirenz, with suicidality.DesignRetrospective analysis of the Food and Drug Administration Adverse Event Reporting System (FAERS), by performing a Multi-Item Gamma Poisson Shrinker (MGPS) disproportionality analysis.MethodsMGPS disproportionality analysis, a technique to identify associations between drugs and adverse events, was performed using cumulative data from the FAERS database collected up to August 2012. This method yields an Empirical Bayesian Geometric Mean score and corresponding 90% confidence interval (EB05, EB95). EB05 scores ≥2 were pre-defined as a signal for a potential drug-event association. The FAERS database includes spontaneous adverse-event reports from consumers and healthcare professionals. All FAERS reports of suicidality (including suicidal ideation, suicide attempt and completed suicide or a composite of these) in patients taking efavirenz (as single agent or in fixed-dose combination), atazanavir, darunavir, etravirine, nevirapine and raltegravir were identified. A number of parallel analyses were performed to assess the validity of the methodology: fluoxetine and sertraline, antidepressants with a known association with suicidality, and raltegravir, an ARV with rhabdomyolysis and myopathy listed as “uncommon” events in the US-prescribing information.ResultsA total of 29,856 adverse event reports were identified among patients receiving efavirenz, atazanavir, darunavir, etravirine, nevirapine and raltegravir, of which 457 were reports of suicidality events. EB05 scores observed for the composite suicidality term for efavirenz (EB05=0.796), and other ARVs (EB05=0.279–0.368), were below the pre-defined threshold. Fluoxetine and sertraline gave EB05 scores for suicidality >2. Raltegravir gave EB05 scores >2 for myopathy and rhabdomyolysis.ConclusionsThe pre-determined threshold for signals for suicidality, including suicidal ideation, suicide attempt, completed suicide and a composite suicidality endpoint, was not exceeded for efavirenz and other ARVs in this analysis. Efavirenz has been associated with suicidality in clinical trials. Further studies that adjust for confounding factors are needed to better understand any potential association with ARVs and suicidality

Population ecology of the sea lamprey (Petromyzon marinus) as an invasive species in the Laurentian Great Lakes and an imperiled species in Europe

The sea lamprey Petromyzon marinus (Linnaeus) is both an invasive non-native species in the Laurentian Great Lakes of North America and an imperiled species in much of its native range in North America and Europe. To compare and contrast how understanding of population ecology is useful for control programs in the Great Lakes and restoration programs in Europe, we review current understanding of the population ecology of the sea lamprey in its native and introduced range. Some attributes of sea lamprey population ecology are particularly useful for both control programs in the Great Lakes and restoration programs in the native range. First, traps within fish ladders are beneficial for removing sea lampreys in Great Lakes streams and passing sea lampreys in the native range. Second, attractants and repellants are suitable for luring sea lampreys into traps for control in the Great Lakes and guiding sea lamprey passage for conservation in the native range. Third, assessment methods used for targeting sea lamprey control in the Great Lakes are useful for targeting habitat protection in the native range. Last, assessment methods used to quantify numbers of all life stages of sea lampreys would be appropriate for measuring success of control in the Great Lakes and success of conservation in the native range

Variation de l'anisotropie optique moléculaire avec l'état physique (gaz, liquides et solutions, cristaux)

Les mesures de l'anisotropie optique à partir de l'intensité et de la polarisation de la lumière diffusée par les solutions de molécules anisotropes dans un solvant isotrope, traduisent les différentes formes d'associations ou d'orientations moléculaires que l'on peut prévoir dans les solutions concentrées et les liquides purs. La théorie du champ intermoléculaire de Raman et Krishnan, qui se proposait de calculer la variation de l'anisotropie quand on passe du gaz au liquide pur, explique seulement la diminution de l'anisotropie quand on passe du gaz à la solution étendue. La diminution considérable de l'anisotropie des ions NO- 3 et CO--3 quand on passe de la solution au cristal s'explique par la forte anisotropie du champ intermoléculaire lorsque ces ions plans sont parallèles

L'effet Raman et le pivotement des molécules dans les cristaux : étude des spectres de basses fréquences des composés dihalogénés du benzène

Les raies de basse fréquence des spectres Raman des cristaux organiques sont dues à des pivotements cohérents des molécules autour de leurs axes d'inertie. Cette hypothèse, qui nous avait permis d'interpréter les raies externes du naphtalène cristallisé, s'est montrée féconde dans le cas des dérivés dihalogénés du benzène dont la structure cristalline est assez bien connue grâce aux rayons X. Nous avons pu classer les fréquences des diiodobenzènes (méta et ortho) d'après la seule énumération des basses fréquences. Après avoir exposé notre étude expérimentale de la polarisation des raies externes des dérivés para (dichloro et dibromobenzène), nous montrons que notre théorie des pivotements rend bien compte encore ici des fréquences et du type de symétrie des oscillations. Mais, dans le cas général, sous la forme simplifiée où nous l'avons développée, elle ne peut ' donner l'intensité de la raie diffusée, qui est liée aux variations de réfractivités de la maille au cours de l'oscillation. Il est remarquable que, contrairement à ce qui a été observé avec d'autres cristaux (calcite par exemple), on ne trouve pas, dans les spectres de ces cristaux organiques, de raies dues à des « translations » des molécules, mais que l'on doive attribuer toutes les raies externes à des « pivotements »

Effet Raman dans les cristaux : symétrie des ions SO4 2- dans le gypse

La polarisation des raies Raman du gypse montre que, contrairement à ce qu'on observe dans les solutions de sulfates alcalins, les ions SO4 2- de ce cristal n'ont plus la symétrie du tétraèdre régulier; dans ces ions déformés, on ne trouve plus comme éléments de symétrie qu'un axe binaire parallèle à l'axe binaire de ce cristal monoclinique. Considérations théoriques et étude expérimentale