k-Trails: Recognition, Complexity, and Approximations

The notion of degree-constrained spanning hierarchies, also called k-trails, was recently introduced in the context of network routing problems. They describe graphs that are homomorphic images of connected graphs of degree at most k. First results highlight several interesting advantages of k-trails compared to previous routing approaches. However, so far, only little is known regarding computational aspects of k-trails. In this work we aim to fill this gap by presenting how k-trails can be analyzed using techniques from algorithmic matroid theory. Exploiting this connection, we resolve several open questions about k-trails. In particular, we show that one can recognize efficiently whether a graph is a k-trail. Furthermore, we show that deciding whether a graph contains a k-trail is NP-complete; however, every graph that contains a k-trail is a (k+1)-trail. Moreover, further leveraging the connection to matroids, we consider the problem of finding a minimum weight k-trail contained in a graph G. We show that one can efficiently find a (2k-1)-trail contained in G whose weight is no more than the cheapest k-trail contained in G, even when allowing negative weights. The above results settle several open questions raised by Molnar, Newman, and Sebo

Distribution and morphological variation of Eleutherodactylus mercedesae Lynch & McDiarmid, 1987 (Amphibia, Anura, Leptodactylidae) with first record for Peru

Accepted by S. Carranza: 19 May 2006; published: 3 Aug. 2006 49[EN] We report new distributional information for Eleutherodactylus mercedesae in Bolivia, and provide the first record for Peru based on an adult female. This species, previously endemic to Bolivia, now ranges across about 1000 km in cloud forests on the Amazonian slopes of the Andes from southern Peru to central Bolivia. We provide the first morphological description of females based on two specimens, compare them with the male type and paratype, add some observations to the original description, and comment on variation in the species.[ES] Aportamos información novedosa sobre la distribución de Eleutherodactylus mercedesae en Bolivia y la primera cita para Perú, basada en una hembra adulta. Esta especie se consideraba hasta ahora endémica para Bolivia. Su rango conocido de distribución comprende actualmente unos 1000 km de los bosques nublados de las laderas amazónicas de los Andes, desde el sur de Perú al centro de Bolivia. Se describe por primera vez la hembra de esta especie en base a dos ejemplares, que son comparados con el holotipo y el paratipo. Añadimos algunas observaciones sobre la descripción original y la variación morfológica de la especie.This work was partially funded by projects REN/GLO 2001-1046 and CGL2005-03156 of the Spanish Ministry of Education and Science (I. De la Riva, Principal Investigator).Peer reviewe

Assigning channels via the meet-in-the-middle approach

We study the complexity of the Channel Assignment problem. By applying the meet-in-the-middle approach we get an algorithm for the $\ell$-bounded Channel Assignment (when the edge weights are bounded by $\ell$) running in time $O^*((2\sqrt{\ell+1})^n)$. This is the first algorithm which breaks the $(O(\ell))^n$ barrier. We extend this algorithm to the counting variant, at the cost of slightly higher polynomial factor. A major open problem asks whether Channel Assignment admits a $O(c^n)$-time algorithm, for a constant $c$ independent of $\ell$. We consider a similar question for Generalized T-Coloring, a CSP problem that generalizes \CA. We show that Generalized T-Coloring does not admit a $2^{2^{o\left(\sqrt{n}\right)}} {\rm poly}(r)$-time algorithm, where $r$ is the size of the instance.Comment: SWAT 2014: 282-29

A study of omega bands and Ps6 pulsations on the ground, at low altitude and at geostationary orbit

We investigate the electrodynamic coupling between auroral omega bands and the inner magnetosphere. The goal of this study is to determine the features to which omega bands map in the magnetosphere. To establish the auroral-magnetosphere connection, we appeal to the case study analysis of the data rich event of September 26, 1989. At 6 magnetic local time (MLT), two trains of Ps6 pulsations (ground magnetic signatures of omega bands) were observed to drift over the Canadian Auroral Network For the OPEN Program Unified Study (CANOPUS) chain. At the same time periodic ionospheric flow patterns moved through the collocated Bistatic Auroral Radar System (BARS) field of view. Similar coincident magnetic variations were observed by GOES 6, GOES 7 and SCATHA, all of which had magnetic foot points near the CANOPUS/BARS stations. SCATHA, which was located at 6 MLT, 0.5 RE earthward of GOES 7 observed the 10 min period pulsations, whereas GOES 7 did not. In addition, DMSP F6 and F8 were over-flying the region and observed characteristic precipitation and flow signatures. From this fortunate constellation of ground and space observations, we conclude that auroral omega bands are the electrodynamic signature of a corrugated current sheet (or some similar spatially localized magnetic structure) in the near-Earth geostationary magnetosphere

A Remark on Unified Error Exponents: Hypothesis Testing, Data Compression and Measure Concentration

Let A be finite set equipped with a probability distribution P, and let M be a “mass” function on A. A characterization is given for the most efficient way in which A n can be covered using spheres of a fixed radius. A covering is a subset C n of A n with the property that most of the elements of A n are within some fixed distance from at least one element of C n , and “most of the elements” means a set whose probability is exponentially close to one (with respect to the product distribution P n ). An efficient covering is one with small mass M n (C n ). With different choices for the geometry on A, this characterization gives various corollaries as special cases, including Marton’s error-exponents theorem in lossy data compression, Hoeffding’s optimal hypothesis testing exponents, and a new sharp converse to some measure concentration inequalities on discrete spaces

Executive functioning in preschool children: Performance on A-Not-B and other delayed response format tasks

The A-not-B (AB) task has been hypothesized to measure executive/frontal lobe function; however, the developmental and measurement characteristics of this task have not been investigated. The present study examined performance on AB and comparison tasks adapted from developmental and neuroscience literature in 117 1.9-5.5 yr old preschool children. Age significantly predicted performance on AB, Delayed Alternation, Spatial Reversal, Color Reversal, and Self-Control tasks. A 4-factor analytic model best fit task performance data. AB task indices loaded on 2 factors with measures from the Self-Control and Delayed Alternation tasks, respectively. AB indices did not load with those from the reversal tasks despite similarities in task administration and presumed cognitive demand (working memory). These results indicate that AB is sensitive to individual differences in age-related performance in preschool children and suggest that AB performance is related to both working memory and inhibition processes in this age range

Sexual coloration and sperm performance in the Australian painted dragon lizard, Ctenophorus pictus

Theory predicts trade-offs between pre- and post-copulatory sexually selected traits. This relationship may be mediated by the degree to which males are able to monopolize access to females, as this will place an upper limit on the strength of post-copulatory selection. Furthermore, traits that aid in mate monopolization may be costly to maintain and may limit investment in post-copulatory traits, such as sperm performance. Australian painted dragons are polymorphic for the presence or absence of a yellow gular patch (\u27bibs\u27), which may aid them to monopolize access to females. Previous work has shown that there are physiological costs of carrying this bib (greater loss of body condition in the wild). Here, we show that male painted dragons use this bright yellow bib as both an inter- and intrasexual signal, and we assess whether this signal is traded off against sperm performance within the same individuals. We found no relationship between aspects of bib colour and sperm swimming velocity or percentage of motile sperm and suggest that the bib polymorphism may be maintained by complex interactions between physiological or life-history traits including other sperm or ejaculate traits and environmental influences

A new species of arboreal toad (Anura: Bufonidae: Chaunus) from Madidi National Park, Bolivia

Accepted by M. Vences: 23 Jun 2006; published: 3 Aug. 2006A new arboreal species of the Chaunus veraguensis group is described for the humid montane forest of Madidi National Park, in northern Bolivia. The new species differs from other species in the group by the combination small size, long and slender extremities, webbed hands, conspicuous tympanic membrane, well developed parotoid glands, absence of large glands on dorsum and extremities, nuptial excrescences of males composed of pungent spines on dorsal surface of thumb, greenish-brown coloration on dorsum with red warts in life, and green iris. It is only known from two nearby localities in the Serranía Eslabón, Department La Paz. An operational key for species in the C. veraguensis group is provided.This work was partially funded by projects REN/GLO 2001-1046 and CGL2005-03156 of the Spanish Ministry of Education and Science (I. De la Riva, Principal Investigator) and by a project of the AECI (Spanish Agency of International Cooperation) (I. De la Riva, Principal Investigator) to inventory Madidi’s herpetofauna.Peer reviewe