Width and serialization of classical planning problems

We introduce a width parameter that bounds the complexity of classical planning problems and domains, along with a simple but effective blind-search procedure that runs in time that is exponential in the problem width. We show that many benchmark domains have a bounded and small width provided thatgoals are restricted to single atoms, and hence that such problems are provably solvable in low polynomial time. We then focus on the practical value of these ideas over the existing benchmarks which feature conjunctive goals. We show that the blind-search procedure can be used for both serializing the goal into subgoals and for solving the resulting problems, resulting in a ‘blind’ planner that competes well with a best-first search planner guided by state-of-the-art heuristics. In addition, ideas like helpful actions and landmarks can be integrated as well, producing a planner with state-of-the-art performance.

Computational problems in perfect phylogeny haplotyping: Typing without calling the allele

A haplotype is an m-long binary vector. The XOR-genotype of two haplotypes is the m-vector of their coordinate-wise XOR. We study the following problem: Given a set of XOR-genotypes, reconstruct their haplotypes so that the set of resulting haplotypes can be mapped onto a perfect phylogeny (PP) tree. The question is motivated by studying population evolution in human genetics and is a variant of the PP haplotyping problem that has received intensive attention recently. Unlike the latter problem, in which the input is '' full '' genotypes, here, we assume less informative input and so may be more economical to obtain experimentally. Building on ideas of Gusfield, we show how to solve the problem in polynomial time by a reduction to the graph realization problem. The actual haplotypes are not uniquely determined by the tree they map onto and the tree itself may or may not be unique. We show that tree uniqueness implies uniquely determined haplotypes, up to inherent degrees of freedom, and give a sufficient condition for the uniqueness. To actually determine the haplotypes given the tree, additional information is necessary. We show that two or three full genotypes suffice to reconstruct all the haplotypes and present a linear algorithm for identifying those genotypes.

Parametric Approach to Blind Deconvolution of Nonlinear Channels

A parametric procedure for the blind inversion of nonlinear channels is proposed, based on a recent method of blind source separation in nonlinear mixtures. Experiments show that the proposed algorithms perform efficiently, even in the presence of hard distortion. The method, based on the minimization of the output mutual information, needs the knowledge of log-derivative of input distribution (the so-called score function). Each algorithm consists of three adaptive blocks: one devoted to adaptive estimation of the score function, and two other blocks estimating the inverses of the linear and nonlinear parts of the channel, (quasi-)optimally adapted using the estimated score functions. This paper is mainly concerned by the nonlinear part, for which we propose two parametric models, the first based on a polynomial model and the second on a neural network, while [14, 15] proposed non-parametric approaches.

Generation of symmetric periodic orbits by a heteroclinic loop formed by two singular points and their invariant manifolds of dimension 1 and 2 in R3

In this paper we will find a continuous of periodic orbits passing near infinity for a class of polynomial vector fields in R3. We consider polynomial vector fields that are invariant under a symmetry with respect to a plane and that possess a “generalized heteroclinic loop” formed by two singular points e+ and e− at infinity and their invariant manifolds � and . � is an invariant manifold of dimension 1 formed by an orbit going from e− to e+, � is contained in R3 and is transversal to . is an invariant manifold of dimension 2 at infinity. In fact, is the 2–dimensional sphere at infinity in the Poincar´e compactification minus the singular points e+ and e−. The main tool for proving the existence of such periodic orbits is the construction of a Poincar´e map along the generalized heteroclinic loop together with the symmetry with respect to .

Symmetric periodic orbits near a heteroclinic loop in R3 formed by two singular points, a semistable periodic orbit and their invariant manifolds

In this paper we consider C1 vector fields X in R3 having a “generalized heteroclinic loop” L which is topologically homeomorphic to the union of a 2–dimensional sphere S2 and a diameter connecting the north with the south pole. The north pole is an attractor on S2 and a repeller on . The equator of the sphere is a periodic orbit unstable in the north hemisphere and stable in the south one. The full space is topologically homeomorphic to the closed ball having as boundary the sphere S2. We also assume that the flow of X is invariant under a topological straight line symmetry on the equator plane of the ball. For each n ∈ N, by means of a convenient Poincar´e map, we prove the existence of infinitely many symmetric periodic orbits of X near L that gives n turns around L in a period. We also exhibit a class of polynomial vector fields of degree 4 in R3 satisfying this dynamics.

Symmetric periodic orbits near a heteroclinic loop formed by two singular points and their invariant manifolds of dimension 1 and 2

In this paper we consider vector fields in R3 that are invariant under a suitable symmetry and that posses a “generalized heteroclinic loop” L formed by two singular points (e+ and e −) and their invariant manifolds: one of dimension 2 (a sphere minus the points e+ and e −) and one of dimension 1 (the open diameter of the sphere having endpoints e+ and e −). In particular, we analyze the dynamics of the vector field near the heteroclinic loop L by means of a convenient Poincar´e map, and we prove the existence of infinitely many symmetric periodic orbits near L. We also study two families of vector fields satisfying this dynamics. The first one is a class of quadratic polynomial vector fields in R3, and the second one is the charged rhomboidal four body problem.

A(-infinity)-interpolation in the ball

We give a necessary and sufficient condition for a sequence [ak}k in the unit ball of C° to be interpolating for the class A~°° of holomorphic functions with polynomial growth. The condition, which goes along the lines of the ones given by Berenstein and Li for some weighted spaces of entire functions and by Amar for H°° functions in the ball, is given in terms of the derivatives of m > n functions F Fm e A~°° vanishing on {ak)k.

Global periodicity conditions for maps and recurrences via Normal Forms

We face the problem of characterizing the periodic cases in parametric families of (real or complex) rational diffeomorphisms having a fixed point. Our approach relies on the Normal Form Theory, to obtain necessary conditions for the existence of a formal linearization of the map, and on the introduction of a suitable rational parametrization of the parameters of the family. Using these tools we can find a finite set of values p for which the map can be p-periodic, reducing the problem of finding the parameters for which the periodic cases appear to simple computations. We apply our results to several two and three dimensional classes of polynomial or rational maps. In particular we find the global periodic cases for several Lyness type recurrences

J-shaped association between serum glucose and functional outcome in acute ischemic stroke.

BACKGROUND AND PURPOSE: Hyperglycemia after stroke is associated with larger infarct volume and poorer functional outcome. In an animal stroke model, the association between serum glucose and infarct volume is described by a U-shaped curve with a nadir ≈7 mmol/L. However, a similar curve in human studies was never reported. The objective of the present study is to investigate the association between serum glucose levels and functional outcome in patients with acute ischemic stroke. METHODS: We analyzed 1446 consecutive patients with acute ischemic stroke. Serum glucose was measured on admission at the emergency department together with multiple other metabolic, clinical, and radiological parameters. National Institutes of Health Stroke Scale (NIHSS) score was recorded at 24 hours, and Rankin score was recorded at 3 and 12 months. The association between serum glucose and favorable outcome (Rankin score ≤2) was explored in univariate and multivariate analysis. The model was further analyzed in a robust regression model based on fractional polynomial (-2-2) functions. RESULTS: Serum glucose is independently correlated with functional outcome at 12 months (OR, 1.15; P=0.01). Other predictors of outcome include admission NIHSS score (OR, 1.18; P<0001), age (OR, 1.06; P<0.001), prestroke Rankin score (OR, 20.8; P=0.004), and leukoaraiosis (OR, 2.21; P=0.016). Using these factors in multiple logistic regression analysis, the area under the receiver-operator characteristic curve is 0.869. The association between serum glucose and Rankin score at 12 months is described by a J-shaped curve with a nadir of 5 mmol/L. Glucose values between 3.7 and 7.3 mmol/L are associated with favorable outcome. A similar curve was generated for the association of glucose and 24-hour NIHSS score, for which glucose values between 4.0 and 7.2 mmol/L are associated with a NIHSS score <7. Discussion-Both hypoglycemia and hyperglycemia are dangerous in acute ischemic stroke as shown by a J-shaped association between serum glucose and 24-hour and 12-month outcome. Initial serum glucose values between 3.7 and 7.3 mmol/L are associated with favorable outcome.

Equidistribution of Fekete Points on the Sphere

Fekete points are the points that maximize a Vandermonde-type determinant that appears in the polynomial Lagrange interpolation formula. They are well suited points for interpolation formulas and numerical integration. We prove the asymptotic equidistribution of Fekete points in the sphere. The way we proceed is by showing their connection to other arrays of points, the so-called Marcinkiewicz-Zygmund arrays and interpolating arrays, that have been studied recently.

Performance of juveniles of Pseudoplatystoma fasciatum fed graded levels of corn gluten meal

The objective of this work was to evaluate corn gluten meal (CGM) as a substitute for fish meal in diets for striped catfish (Pseudoplatystoma fasciatum) juveniles. Eight isonitrogenous (46% crude protein) and isoenergetic (3,450 kcal kg-1 digestible energy) diets, with increasing levels of CGM - 0, 6, 12, 18, 24, 30, 36, and 42% -, were fed to juvenile striped catfish (113.56±5.10 g) for seven weeks. Maximum values for weight gain, specific growth rate, protein efficiency ratio and feed conversion ratio, evaluated by polynomial quadratic regression, were observed with 10.4, 11.4, 15.4 and 15% of CGM inclusion, respectively. Feed intake decreased significantly from 0.8% CGM. Mesenteric fat index and body gross energy decreased linearly with increasing levels of CGM; minimum body protein contents were observed with 34.1% CGM. Yellow pigmentation of fillets significantly increased until 26.5% CGM, and decreased from this point forth. Both plasma glucose and protein concentrations decreased with increased CGM levels. The inclusion of 10-15% CGM promotes optimum of striped catfish juveniles depending on the parameter evaluated. Yellow coloration in fillets produced by CGM diets can have marketing implications.

Aplicaciones de la Teoría de Matrices en Matemática Discreta

Se describen algunas aplicaciones de la teoría de matrices a diversos temas pertenecientes alámbito de la matem\'atica discreta.

Random regression models to estimate genetic parameters for milk production of Guzerat cows using orthogonal Legendre polynomials

The objective of this work was to compare random regression models for the estimation of genetic parameters for Guzerat milk production, using orthogonal Legendre polynomials. Records (20,524) of test-day milk yield (TDMY) from 2,816 first-lactation Guzerat cows were used. TDMY grouped into 10-monthly classes were analyzed for additive genetic effect and for environmental and residual permanent effects (random effects), whereas the contemporary group, calving age (linear and quadratic effects) and mean lactation curve were analized as fixed effects. Trajectories for the additive genetic and permanent environmental effects were modeled by means of a covariance function employing orthogonal Legendre polynomials ranging from the second to the fifth order. Residual variances were considered in one, four, six, or ten variance classes. The best model had six residual variance classes. The heritability estimates for the TDMY records varied from 0.19 to 0.32. The random regression model that used a second-order Legendre polynomial for the additive genetic effect, and a fifth-order polynomial for the permanent environmental effect is adequate for comparison by the main employed criteria. The model with a second-order Legendre polynomial for the additive genetic effect, and that with a fourth-order for the permanent environmental effect could also be employed in these analyses.

Expanding view of phenotype and oxidative stress in Friedreich's ataxia patients with and without idebenone

Summary: Friedreich's ataxia (FRDA), the most common autosomal recessive ataxia, is characterised by progressive ataxia with dysarthria of speech, loss of deep-tendon reflexes, impaired vibratory and proprioceptive sensations and corticospinal weakness with a Babinski's sign. Patients eventually also develop kyphoscoliosis, cardiomyopathy and diabetes mellitus. The disease is a GAA repeat disorder resulting in severely reduced levels of frataxin, with secondary increased sensitivity to oxidative stress. The anti-oxidative drug, idebenone, is effective against FRDA-associated cardiomyopathy. We provide detailed clinical, electrophysiological and biochemical data from 20 genetically confirmed FRDA patients and have analysed the relation-ship between phenotype, genotype and malondialdehyde (MDA), which is a marker of superoxide formation. We assessed the effects of idebenone biochemically by measuring blood M DA and clinically by serial measurements of the International Cooperative Ataxia Rating Scale (ICARS). The GAA repeat length influenced the age at onset (p <0.001), the severity of ataxia (p= 0.02), the presence of cardiomyopathy (p =0.04) and of low-frequency hearing loss (p = 0.009). Multilinear regression analysis showed (p = 0.006) that ICARS was dependent on the two variables of disease duration (p = 0.01) and size of the GAA expansion (p = 0.02). We found no correlation to bilateral palpebral ptosis visual impairment, diabetes mellitus or skeletal deformities, all of which appear to be signs of disease progression rather than severity. We discuss more thoroughly two underrecognised clinical findings: palpebral ptosis and GAA length-dependent low-frequency hearing loss. The average ICARS remained unchanged in 10 patients for whom follow-up on treatment was available (mean 2.9 years), whereas most patients treated with idebenone reported an improvement in dysarthria (63%), hand dexterity (.58%) and fatigue (47%) after taking the drug for several weeks or months. Oxidative stress analysis showed an unexpected increase in blood MDA levels in patients on idebenone (p = 0.04), and we discuss the putative underlying mechanism for this result, which could then explain the unique efficacy of idebenone in treating the FRDA-associated cardiomyopathy, as opposed to other antioxidative drugs. Indeed, idebenone is not only a powerful stimulator of complexes II and III of the respiratory chain, but also an inhibitor of complex I activity, then promoting superoxide formation. Our preliminary clinical observations are the first to date supporting an effect of idebenone in delaying neurological worsening. Our MDA results point to the dual effect of idebenone on oxidative stress and to the need for controlled studies to assess its potential toxicity at high doses on the one hand, and to revisit the exact mechanisms underlying the .physiopathology of Friedreich's ataxia on the other hand, while recent reports suggest non-oxidative pathophysiology of the disease.

Studies on integrating kinematic design method with mechanical systems simulation techniques

Theultimate goal of any research in the mechanism/kinematic/design area may be called predictive design, ie the optimisation of mechanism proportions in the design stage without requiring extensive life and wear testing. This is an ambitious goal and can be realised through development and refinement of numerical (computational) technology in order to facilitate the design analysis and optimisation of complex mechanisms, mechanical components and systems. As a part of the systematic design methodology this thesis concentrates on kinematic synthesis (kinematic design and analysis) methods in the mechanism synthesis process. The main task of kinematic design is to find all possible solutions in the form of structural parameters to accomplish the desired requirements of motion. Main formulations of kinematic design can be broadly divided to exact synthesis and approximate synthesis formulations. The exact synthesis formulation is based in solving n linear or nonlinear equations in n variables and the solutions for the problem areget by adopting closed form classical or modern algebraic solution methods or using numerical solution methods based on the polynomial continuation or homotopy. The approximate synthesis formulations is based on minimising the approximation error by direct optimisation The main drawbacks of exact synthesis formulationare: (ia) limitations of number of design specifications and (iia) failure in handling design constraints- especially inequality constraints. The main drawbacks of approximate synthesis formulations are: (ib) it is difficult to choose a proper initial linkage and (iib) it is hard to find more than one solution. Recentformulations in solving the approximate synthesis problem adopts polynomial continuation providing several solutions, but it can not handle inequality const-raints. Based on the practical design needs the mixed exact-approximate position synthesis with two exact and an unlimited number of approximate positions has also been developed. The solutions space is presented as a ground pivot map but thepole between the exact positions cannot be selected as a ground pivot. In this thesis the exact synthesis problem of planar mechanism is solved by generating all possible solutions for the optimisation process ¿ including solutions in positive dimensional solution sets - within inequality constraints of structural parameters. Through the literature research it is first shown that the algebraic and numerical solution methods ¿ used in the research area of computational kinematics ¿ are capable of solving non-parametric algebraic systems of n equations inn variables and cannot handle the singularities associated with positive-dimensional solution sets. In this thesis the problem of positive-dimensional solutionsets is solved adopting the main principles from mathematical research area of algebraic geometry in solving parametric ( in the mathematical sense that all parameter values are considered ¿ including the degenerate cases ¿ for which the system is solvable ) algebraic systems of n equations and at least n+1 variables.Adopting the developed solution method in solving the dyadic equations in direct polynomial form in two- to three-precision-points it has been algebraically proved and numerically demonstrated that the map of the ground pivots is ambiguousand that the singularities associated with positive-dimensional solution sets can be solved. The positive-dimensional solution sets associated with the poles might contain physically meaningful solutions in the form of optimal defectfree mechanisms. Traditionally the mechanism optimisation of hydraulically driven boommechanisms is done at early state of the design process. This will result in optimal component design rather than optimal system level design. Modern mechanismoptimisation at system level demands integration of kinematic design methods with mechanical system simulation techniques. In this thesis a new kinematic design method for hydraulically driven boom mechanism is developed and integrated in mechanical system simulation techniques. The developed kinematic design method is based on the combinations of two-precision-point formulation and on optimisation ( with mathematical programming techniques or adopting optimisation methods based on probability and statistics ) of substructures using calculated criteria from the system level response of multidegree-of-freedom mechanisms. Eg. by adopting the mixed exact-approximate position synthesis in direct optimisation (using mathematical programming techniques) with two exact positions and an unlimitednumber of approximate positions the drawbacks of (ia)-(iib) has been cancelled.The design principles of the developed method are based on the design-tree -approach of the mechanical systems and the design method ¿ in principle ¿ is capable of capturing the interrelationship between kinematic and dynamic synthesis simultaneously when the developed kinematic design method is integrated with the mechanical system simulation techniques.