Analytic approximation of solutions of parabolic partial differential equations with variable coefficients

A complete family of solutions for the one-dimensional reaction-diffusion equation $$u_{xx}(x,t)-q(x)u(x,t) = u_t(x,t)$$ with a coefficient $q$ depending on $x$ is constructed. The solutions represent the images of the heat polynomials under the action of a transmutation operator. Their use allows one to obtain an explicit solution of the noncharacteristic Cauchy problem for the considered equation with sufficiently regular Cauchy data as well as to solve numerically initial boundary value problems. In the paper the Dirichlet boundary conditions are considered however the proposed method can be easily extended onto other standard boundary conditions. The proposed numerical method is shown to reveal good accuracy.Comment: 8 pages, 1 figure. Minor updates to the tex

A new sequential covering strategy for inducing classification rules with ant colony algorithms

Ant colony optimization (ACO) algorithms have been successfully applied to discover a list of classification rules. In general, these algorithms follow a sequential covering strategy, where a single rule is discovered at each iteration of the algorithm in order to build a list of rules. The sequential covering strategy has the drawback of not coping with the problem of rule interaction, i.e., the outcome of a rule affects the rules that can be discovered subsequently since the search space is modified due to the removal of examples covered by previous rules. This paper proposes a new sequential covering strategy for ACO classification algorithms to mitigate the problem of rule interaction, where the order of the rules is implicitly encoded as pheromone values and the search is guided by the quality of a candidate list of rules. Our experiments using 18 publicly available data sets show that the predictive accuracy obtained by a new ACO classification algorithm implementing the proposed sequential covering strategy is statistically significantly higher than the predictive accuracy of state-of-the-art rule induction classification algorithms

Forelimb muscle and joint actions in Archosauria: insights from Crocodylus johnstoni (Pseudosuchia) and Mussaurus patagonicus (Sauropodomorpha)

Many of the major locomotor transitions during the evolution of Archosauria, the lineage including crocodiles and birds as well as extinct Dinosauria, were shifts from quadrupedalism to bipedalism (and vice versa). Those occurred within a continuum between more sprawling and erect modes of locomotion and involved drastic changes of limb anatomy and function in several lineages, including sauropodomorph dinosaurs. We present biomechanical computer models of two locomotor extremes within Archosauria in an analysis of joint ranges of motion and the moment arms of the major forelimb muscles in order to quantify biomechanical differences between more sprawling, pseudosuchian (represented the crocodile Crocodylus johnstoni) and more erect, dinosaurian (represented by the sauropodomorph Mussaurus patagonicus) modes of forelimb function. We compare these two locomotor extremes in terms of the reconstructed musculoskeletal anatomy, ranges of motion of the forelimb joints and the moment arm patterns of muscles across those ranges of joint motion. We reconstructed the three-dimensional paths of 30 muscles acting around the shoulder, elbow and wrist joints. We explicitly evaluate how forelimb joint mobility and muscle actions may have changed with postural and anatomical alterations from basal archosaurs to early sauropodomorphs. We thus evaluate in which ways forelimb posture was correlated with muscle leverage, and how such differences fit into a broader evolutionary context (i.e. transition from sprawling quadrupedalism to erect bipedalism and then shifting to graviportal quadrupedalism). Our analysis reveals major differences of muscle actions between the more sprawling and erect models at the shoulder joint. These differences are related not only to the articular surfaces but also to the orientation of the scapula, in which extension/flexion movements in Crocodylus (e.g. protraction of the humerus) correspond to elevation/depression in Mussaurus. Muscle action is highly influenced by limb posture, more so than morphology. Habitual quadrupedalism in Mussaurus is not supported by our analysis of joint range of motion, which indicates that glenohumeral protraction was severely restricted. Additionally, some active pronation of the manus may have been possible in Mussaurus, allowing semi-pronation by a rearranging of the whole antebrachium (not the radius against the ulna, as previously thought) via long-axis rotation at the elbow joint. However, the muscles acting around this joint to actively pronate it may have been too weak to drive or maintain such orientations as opposed to a neutral position in between pronation and supination. Regardless, the origin of quadrupedalism in Sauropoda is not only linked to manus pronation but also to multiple shifts of forelimb morphology, allowing greater flexion movements of the glenohumeral joint and a more columnar forelimb posture

Improving the Interpretability of Classification Rules Discovered by an Ant Colony Algorithm: Extended Results

The vast majority of Ant Colony Optimization (ACO) algorithms for inducing classification rules use an ACO-based procedure to create a rule in an one-at-a-time fashion. An improved search strategy has been proposed in the cAnt-MinerPB algorithm, where an ACO-based procedure is used to create a complete list of rules (ordered rules)-i.e., the ACO search is guided by the quality of a list of rules, instead of an individual rule. In this paper we propose an extension of the cAnt-MinerPB algorithm to discover a set of rules (unordered rules). The main motivations for this work are to improve the interpretation of individual rules by discovering a set of rules and to evaluate the impact on the predictive accuracy of the algorithm. We also propose a new measure to evaluate the interpretability of the discovered rules to mitigate the fact that the commonly-used model size measure ignores how the rules are used to make a class prediction. Comparisons with state-of-the-art rule induction algorithms, support vector machines and the cAnt-MinerPB producing ordered rules are also presented

Does the Badal optometer stimulate accommodation accurately?

Postprint (author's final draft

Evolving Recursive Programs using Non-recursive Scaffolding

Genetic programming has proven capable of evolving solutions to a wide variety of problems. However, the successes have largely been with programs without iteration or recursion; evolving recursive programs has turned out to be particularly challenging. The main obstacle to evolving recursive programs seems to be that they are particularly fragile to the application of search operators: a small change in a correct recursive program generally produces a completely wrong program. In this paper, we present a simple and general method that allows us to pass back and forth from a recursive program to an associated non-recursive program. Finding a recursive program can be reduced to evolving non-recursive programs followed by converting the optimum non-recursive program found to the associated optimum recursive program. This avoids the fragility problem above, as evolution does not search the space of recursive programs. We present promising experimental results on a test-bed of recursive problems

Avances que se deben consolidar

Si bien se registran lentos pero decididos avances de cara a la implementación efectiva de las leyes que se fundamentan en la doctrina de la protección integral, aún persisten focos reticentes a una perspectiva de derechos en áreas claves de la administración estatal. La prolongada crisis económica repercute más intensamente en la población infanto - juvenil

Systematic search for gamma-ray periodicity in active galactic nuclei detected by the Fermi Large Area Telescope

We use nine years of gamma-ray data provided by the Fermi Large Area Telescope (LAT) to systematically study the light curves of more than two thousand active galactic nuclei (AGN) included in recent Fermi-LAT catalogs. Ten different techniques are used, which are organized in an automatic periodicity-search pipeline, in order to search for evidence of periodic emission in gamma rays. Understanding the processes behind this puzzling phenomenon will provide a better view about the astrophysical nature of these extragalactic sources. However, the observation of temporal patterns in gamma-ray light curves of AGN is still challenging. Despite the fact that there have been efforts on characterizing the temporal emission of some individual sources, a systematic search for periodicities by means of a full likelihood analysis applied to large samples of sources was missing. Our analysis finds 11 AGN, of which 9 are identified for the first time, showing periodicity at more than 4sigma in at least four algorithms. These findings will help in solving questions related to the astrophysical origin of this periodic behavior.Comment: 16 pages, 5 figures, 4 tables. Accepted by Ap