Efficient Computation of Squarefree Separator Polynomials

Given a finite set of distinct points, a separator family is a set of polynomials, each one corresponding to a point of the given set, such that each of them takes value one at the corresponding point, whereas it vanishes at any other point of the set. Separator polynomials are fundamental building blocks for polynomial interpolation and they can be employed in several practical applications. Ceria and Mora recently developed a new algorithm for squarefree separator polynomials. The algorithm employs as a tool the point trie structure, first defined by Felszeghy-R\ue1th-R\uf3nyai in their Lex game algorithm, which gives a compact representation of the relations among the points\u2019 coordinates. In this paper, we propose a fast implementation in C of the aforementioned algorithm, based on an efficient storing and visiting of the point trie. We complete the implementation with tests on some sets of points, giving different configurations of the corresponding tries

The vanishing ideal of a finite set of points with multiplicity structures

Given a finite set of arbitrarily distributed points in affine space with arbitrary multiplicity structures, we present an algorithm to compute the reduced Groebner basis of the vanishing ideal under the lexicographic ordering. Our method discloses the essential geometric connection between the relative position of the points with multiplicity structures and the quotient basis of the vanishing ideal, so we will explicitly know the set of leading terms of elements of I. We split the problem into several smaller ones which can be solved by induction over variables and then use our new algorithm for intersection of ideals to compute the result of the original problem. The new algorithm for intersection of ideals is mainly based on the Extended Euclidean Algorithm.Comment: 12 pages,12 figures,ASCM 201

Algorithms for zero-dimensional ideals using linear recurrent sequences

Inspired by Faug\`ere and Mou's sparse FGLM algorithm, we show how using linear recurrent multi-dimensional sequences can allow one to perform operations such as the primary decomposition of an ideal, by computing the annihilator of one or several such sequences.Comment: LNCS, Computer Algebra in Scientific Computing CASC 201

Testing a global standard for quantifying species recovery and assessing conservation impact

Recognizing the imperative to evaluate species recovery and conservation impact, in 2012 the International Union for Conservation of Nature (IUCN) called for development of a “Green List of Species” (now the IUCN Green Status of Species). A draft Green Status framework for assessing species’ progress toward recovery, published in 2018, proposed 2 separate but interlinked components: a standardized method (i.e., measurement against benchmarks of species’ viability, functionality, and preimpact distribution) to determine current species recovery status (herein species recovery score) and application of that method to estimate past and potential future impacts of conservation based on 4 metrics (conservation legacy, conservation dependence, conservation gain, and recovery potential). We tested the framework with 181 species representing diverse taxa, life histories, biomes, and IUCN Red List categories (extinction risk). Based on the observed distribution of species’ recovery scores, we propose the following species recovery categories: fully recovered, slightly depleted, moderately depleted, largely depleted, critically depleted, extinct in the wild, and indeterminate. Fifty-nine percent of tested species were considered largely or critically depleted. Although there was a negative relationship between extinction risk and species recovery score, variation was considerable. Some species in lower risk categories were assessed as farther from recovery than those at higher risk. This emphasizes that species recovery is conceptually different from extinction risk and reinforces the utility of the IUCN Green Status of Species to more fully understand species conservation status. Although extinction risk did not predict conservation legacy, conservation dependence, or conservation gain, it was positively correlated with recovery potential. Only 1.7% of tested species were categorized as zero across all 4 of these conservation impact metrics, indicating that conservation has, or will, play a role in improving or maintaining species status for the vast majority of these species. Based on our results, we devised an updated assessment framework that introduces the option of using a dynamic baseline to assess future impacts of conservation over the short term to avoid misleading results which were generated in a small number of cases, and redefines short term as 10 years to better align with conservation planning. These changes are reflected in the IUCN Green Status of Species Standard

Herpes simplex virus disrupts NF-kappa B regulation by blocking its recruitment on the I kappa B alpha promoter and directing the factor on viral genes.

Herpes simplex viruses (HSVs) are able to hijack the host-cell I kappa B kinase (IKK)/NF-kappa B pathway, which regulates critical cell functions from apoptosis to inflammatory responses; however, the molecular mechanisms involved and the outcome of the signaling dysregulation on the host-virus interaction are mostly unknown. Here we show that in human keratinocytes HSV-1 attains a sophisticated control of the IKK/NF-kappa B pathway, inducing two distinct temporally controlled waves of IKK activity and disrupting the NF-kappa B autoregulatory mechanism. Using chromatin immunoprecipitation we demonstrate that dysregulation of the NF-kappa B-response is mediated by a virus-induced block of NF-kappa B recruitment to the promoter of the I kappa B alpha gene, encoding the main NF-kappa B-inhibitor. We also show that HSV-1 redirects NF-kappa B recruitment to the promoter of ICP0, an immediate-early viral gene with a key role in promoting virus replication. The results reveal a new level of control of cellular functions by invading viruses and suggest that persistent NF-kappa B activation in HSV-1-infected cells, rather than being a host response to the virus, may play a positive role in promoting efficient viral replication

How sleep affects the developmental learning of bird song

Sleep affects learning and development in humans and other animals, but the role of sleep in developmental learning has never been examined. Here we show the effects of night-sleep on song development in the zebra finch by recording and analysing the entire song ontogeny. During periods of rapid learning we observed a pronounced deterioration in song structure after night-sleep. The song regained structure after intense morning singing. Daily improvement in similarity to the tutored song occurred during the late phase of this morning recovery; little further improvement occurred thereafter. Furthermore, birds that showed stronger post-sleep deterioration during development achieved a better final imitation. The effect diminished with age. Our experiments showed that these oscillations were not a result of sleep inertia or lack of practice, indicating the possible involvement of an active process, perhaps neural song-replay during sleep. We suggest that these oscillations correspond to competing demands of plasticity and consolidation during learning, creating repeated opportunities to reshape previously learned motor skills