A recursive process related to a partisan variation of Wythoff

Wythoff Queens is a classical combinatorial game related to very interesting mathematical results. An amazing one is the fact that the P-positions are given by (⌊├ φn⌋┤┤,├ ├ ⌊φ┤^2 n⌋) and (⌊├ φ^2 n⌋┤┤,├ ├ ⌊φ┤n⌋) where φ=(1+√5)/2. In this paper, we analyze a different version where one player (Left) plays with a chess bishop and the other (Right) plays with a chess knight. The new game (call it Chessfights) lacks a Beatty sequence structure in the P-positions as in Wythoff Queens. However, it is possible to formulate and prove some general results of a general recursive law which is a particular case of a Partizan Subtraction game.

Seasonal variation of total particulate matter and children respiratory diseases at Lisbon primary schools using passive methods

In this work, 14 primary schools of Lisbon city, Portugal, followed a questionnaire of the ISAAC - International Study of Asthma and Allergies in Childhood Program, in 2009/2010. The questionnaire contained questions to identify children with respiratory diseases (wheeze, asthma and rhinitis). Total particulate matter (TPM) was passively collected inside two classrooms of each of 14 primary schools. Two types of filter matrices were used to collect TPM: Millipore (IsoporeTM) polycarbonate and quartz. Three campaigns were selected for the measurement of TPM: Spring, Autumn and Winter. The highest difference between the two types of filters is that the mass of collected particles was higher in quartz filters than in polycarbonate filters, even if their correlation is excellent. The highest TPM depositions occurred between October 2009 and March 2010, when related with rhinitis proportion. Rhinitis was found to be related to TPM when the data were grouped seasonally and averaged for all the schools. For the data of 2006/2007, the seasonal variation was found to be related to outdoor particle deposition (below 10 μm).

Variation of magnetic properties in sedimentary rocks hosting the Foum Zguid dyke (southern Morocco): Combined effects of re-crystallization and Fe-metasomatism

The effects of dyke intrusion on the magnetic properties of host sedimentary rocks are still poorly understood. Therefore, we have evaluated bulk magnetic parameters of standard palaeomagnetic samples collected along several sections across the sediments hosting the Foum Zguid dyke in southern Morocco. The study has been completed with the evaluation of the magnetic fabric after laboratory application of sequential heating experiments. The present study shows that: (1) close to Fourn Zguid dykes, the variations of the bulk magnetic parameters and of the magnetic fabric is strongly related with re-crystallization and Fe-metasomatism intensity. (2) The thermal experiments on AMS of samples collected farther from the dyke and, thus, less affected by heating during dyke emplacement, indicate that 300-400 degrees C is the minimum experimental temperature necessary to trigger appreciable transformations of the pre-existing magnetic fabrics. For temperatures higher than ca. 580 degrees C, the magnetic fabric transformations are fully realized, with complete transposition of the initial fabric to a fabric similar to that of samples collected close to the dyke. Therefore, measured variations of the magnetic fabric can be used to evaluate re-crystallization temperatures experienced by the host sedimentary rock during dyke emplacement. The distinct magnetic behaviour observed along the cross-sections strongly suggests that samples collected farther from the dyke margins did not experience thermal episodes with temperatures higher than 300 degrees C after dyke emplacement. (3) AMS data shows a gradual variation of the magnetic fabric with distance from the dyke margin, from sub-horizontal K-3 away from the dyke to vertical K3 close to the dyke. Experimental heating shows that heat alone can be responsible for this strong variation. Therefore, such orientation changes should not be unequivocally interpreted as the result of a stress field (resulting from the emplacement of the dyke, for instance). (4) Magnetic studies prove to be a very sensitive tool to assess rock magnetic transformations, thermally and chemically induced by dyke intrusion in hosting sediments.

Extreme Value Theory versus traditional GARCH approaches applied to financial data: a comparative evaluation

Although stock prices fluctuate, the variations are relatively small and are frequently assumed to be normal distributed on a large time scale. But sometimes these fluctuations can become determinant, especially when unforeseen large drops in asset prices are observed that could result in huge losses or even in market crashes. The evidence shows that these events happen far more often than would be expected under the generalized assumption of normal distributed financial returns. Thus it is crucial to properly model the distribution tails so as to be able to predict the frequency and magnitude of extreme stock price returns. In this paper we follow the approach suggested by McNeil and Frey (2000) and combine the GARCH-type models with the Extreme Value Theory (EVT) to estimate the tails of three financial index returns DJI,FTSE 100 and NIKKEI 225 representing three important financial areas in the world. Our results indicate that EVT-based conditional quantile estimates are much more accurate than those from conventional AR-GARCH models assuming normal or Student’s t-distribution innovations when doing out-of-sample estimation (within the insample estimation, this is so for the right tail of the distribution of returns).

Convex Total Variation Denoising of Poisson Fluorescence Confocal Images With Anisotropic Filtering

Fluorescence confocal microscopy (FCM) is now one of the most important tools in biomedicine research. In fact, it makes it possible to accurately study the dynamic processes occurring inside the cell and its nucleus by following the motion of fluorescent molecules over time. Due to the small amount of acquired radiation and the huge optical and electronics amplification, the FCM images are usually corrupted by a severe type of Poisson noise. This noise may be even more damaging when very low intensity incident radiation is used to avoid phototoxicity. In this paper, a Bayesian algorithm is proposed to remove the Poisson intensity dependent noise corrupting the FCM image sequences. The observations are organized in a 3-D tensor where each plane is one of the images acquired along the time of a cell nucleus using the fluorescence loss in photobleaching (FLIP) technique. The method removes simultaneously the noise by considering different spatial and temporal correlations. This is accomplished by using an anisotropic 3-D filter that may be separately tuned in space and in time dimensions. Tests using synthetic and real data are described and presented to illustrate the application of the algorithm. A comparison with several state-of-the-art algorithms is also presented.

Role of malnutrition and parasite infections in the spatial variation in children’s anaemia risk in Northern Angola

Anaemia has a significant impact on child development and mortality and is a severe public health problem in most countries in sub-Saharan Africa. Nutritional and infectious causes of anaemia are geographically variable and anaemia maps based on information on the major aetiologies of anaemia are important for identifying communities most in need and the relative contribution of major causes. We investigated the consistency between ecological and individual-level approaches to anaemia mapping, by building spatial anaemia models for children aged ≤15 years using different modeling approaches. We aimed to a) quantify the role of malnutrition, malaria, Schistosoma haematobium and soil-transmitted helminths (STH) for anaemia endemicity in children aged ≤15 years and b) develop a high resolution predictive risk map of anaemia for the municipality of Dande in Northern Angola. We used parasitological survey data on children aged ≤15 years to build Bayesian geostatistical models of malaria (PfPR≤15), S. haematobium, Ascaris lumbricoides and Trichuris trichiura and predict small-scale spatial variation in these infections. The predictions and their associated uncertainty were used as inputs for a model of anemia prevalence to predict small-scale spatial variation of anaemia. Stunting, PfPR≤15, and S. haematobium infections were significantly associated with anaemia risk. An estimated 12.5%, 15.6%, and 9.8%, of anaemia cases could be averted by treating malnutrition, malaria, S. haematobium, respectively. Spatial clusters of high risk of anaemia (>86%) were identified. Using an individual-level approach to anaemia mapping at a small spatial scale, we found that anaemia in children aged ≤15 years is highly heterogeneous and that malnutrition and parasitic infections are important contributors to the spatial variation in anemia risk. The results presented in this study can help inform the integration of the current provincial malaria control program with ancillary micronutrient supplementation and control of neglected tropical diseases, such as urogenital schistosomiasis and STH infection.

Role of malnutrition and parasite infections in the spatial variation in children’s anaemia risk in northern Angola

Anaemia is known to have an impact on child development and mortality and is a severe public health problem in most countries in sub-Saharan Africa. We investigated the consistency between ecological and individual-level approaches to anaemia mapping by building spatial anaemia models for children aged ≤15 years using different modelling approaches. We aimed to (i) quantify the role of malnutrition, malaria, Schistosoma haematobium and soil-transmitted helminths (STHs) in anaemia endemicity; and (ii) develop a high resolution predictive risk map of anaemia for the municipality of Dande in northern Angola. We used parasitological survey data for children aged ≤15 years to build Bayesian geostatistical models of malaria (PfPR≤15), S. haematobium, Ascaris lumbricoides and Trichuris trichiura and predict small-scale spatial variations in these infections. Malnutrition, PfPR≤15, and S. haematobium infections were significantly associated with anaemia risk. An estimated 12.5%, 15.6% and 9.8% of anaemia cases could be averted by treating malnutrition, malaria and S. haematobium, respectively. Spatial clusters of high risk of anaemia (>86%) were identified. Using an individual-level approach to anaemia mapping at a small spatial scale, we found that anaemia in children aged ≤15 years is highly heterogeneous and that malnutrition and parasitic infections are important contributors to the spatial variation in anaemia risk. The results presented in this study can help inform the integration of the current provincial malaria control programme with ancillary micronutrient supplementation and control of neglected tropical diseases such as urogenital schistosomiasis and STH infections.

Factors related with adiponectinemia in obese and normal-weight women and with its variation in weight loss programs

Objective: To assess different factors influencing adiponectinemia in obese and normal-weight women; to identify factors associated with the variation (Δ) in adiponectinemia in obese women following a 6-month weight loss program, according to surgical/non-surgical interventions. Methods: We studied 100 normal-weight women and 112 obese premenopausal women; none of them was on any medical treatment. Women were characterized for anthropometrics, daily macronutrient intake, smoking status, contraceptives use, adiponectin as well as IL-6 and TNF-α serum concentrations. Results: Adiponectinemia was lower in obese women (p < 0.001), revealing an inverse association with waist-to-hip ratio (p < 0.001; r = –0.335). Normal-weight women presented lower adiponectinemia among smokers (p = 0.041); body fat, waist-to-hip ratio, TNF-α levels, carbohydrate intake, and smoking all influence adiponectinemia (r 2 = 0.436). After weight loss interventions, a significant modification in macronutrient intake occurs followed by anthropometrics decrease (chiefly after bariatric procedures) and adiponectinemia increase (similar after surgical and non-surgical interventions). After bariatric intervention, Δ adiponectinemia was inversely correlated to Δ waist circumference and Δ carbohydrate intake (r 2 = 0.706). Conclusion: Anthropometrics, diet, smoking, and TNF-α levels all influence adiponectinemia in normal-weight women, although explaining less than 50% of it. In obese women, anthropometrics modestly explain adiponectinemia. Opposite to non-surgical interventions, after bariatric surgery adiponectinemia increase is largely explained by diet composition and anthropometric changes.

Dynamical analysis in growth models: Blumberg’s equation

We present a new dynamical approach to the Blumberg's equation, a family of unimodal maps. These maps are proportional to Beta(p, q) probability densities functions. Using the symmetry of the Beta(p, q) distribution and symbolic dynamics techniques, a new concept of mirror symmetry is defined for this family of maps. The kneading theory is used to analyze the effect of such symmetry in the presented models. The main result proves that two mirror symmetric unimodal maps have the same topological entropy. Different population dynamics regimes are identified, when the intrinsic growth rate is modified: extinctions, stabilities, bifurcations, chaos and Allee effect. To illustrate our results, we present a numerical analysis, where are demonstrated: monotonicity of the topological entropy with the variation of the intrinsic growth rate, existence of isentropic sets in the parameters space and mirror symmetry.

Between theory and practice – teaching maths to elementary school students in Poland

The development of children's school achievements in mathematics is one of the most important aims of education in Poland. The results of research concerning monitoring of school achievements in maths is not optimistic. We can observe low levels of children’s understanding of the merits of maths, self-developed strategies in solving problems and practical usage of maths skills. This article frames the discussion of this problem in its psychological and didactic context and analyses the causes as they relate to school practice in teaching maths

Microscopic Theory of Anchoring Transitions at the Surfaces of Pure Liquid-Crystals and their Mixtures .1. The Fowler Approximation

We have generalized earlier work on anchoring of nematic liquid crystals by Sullivan, and Sluckin and Poniewierski, in order to study transitions which may occur in binary mixtures of nematic liquid crystals as a function of composition. Microscopic expressions have been obtained for the anchoring energy of (i) a liquid crystal in contact with a solid aligning surface; (ii) a liquid crystal in contact with an immiscible isotropic medium; (iii) a liquid crystal mixture in contact with a solid aligning surface. For (iii), possible phase diagrams of anchoring angle versus dopant concentration have been calculated using a simple liquid crystal model. These exhibit some interesting features including re-entrant conical anchoring, for what are believed to be realistic values of the molecular parameters. A way of relaxing the most drastic approximation implicit in the above approach is also briefly discussed.

Simulation and theory of hybrid aligned liquid crystal films

We present a study of the effects of nanoconfinement on a system of hard Gaussian overlap particles interacting with planar substrates through the hard-needle-wall potential, extending earlier work by two of us [D. J. Cleaver and P. I. C. Teixeira, Chem. Phys. Lett. 338, 1 (2001)]. Here, we consider the case of hybrid films, where one of the substrates induces strongly homeotropic anchoring, while the other favors either weakly homeotropic or planar anchoring. These systems are investigated using both Monte Carlo simulation and density-functional theory, the latter implemented at the level of Onsager's second-virial approximation with Parsons-Lee rescaling. The orientational structure is found to change either continuously or discontinuously depending on substrate separation, in agreement with earlier predictions by others. The theory is seen to perform well in spite of its simplicity, predicting the positional and orientational structure seen in simulations even for small particle elongations.

On lattices from combinatorial game theory modularity and a representation theorem: finite case

We show that a self-generated set of combinatorial games, S. may not be hereditarily closed but, strong self-generation and hereditary closure are equivalent in the universe of short games. In [13], the question "Is there a set which will give a non-distributive but modular lattice?" appears. A useful necessary condition for the existence of a finite non-distributive modular L(S) is proved. We show the existence of S such that L(S) is modular and not distributive, exhibiting the first known example. More, we prove a Representation Theorem with Games that allows the generation of all finite lattices in game context. Finally, a computational tool for drawing lattices of games is presented. (C) 2014 Elsevier B.V. All rights reserved.

A study on the modeling of sandwich functionally graded particulate composites

Dual-phase functionally graded materials are a particular type of composite materials whose properties are tailored to vary continuously, depending on its two constituent's composition distribution, and which use is increasing on the most diverse application fields. These materials are known to provide superior thermal and mechanical performances when compared to the traditional laminated composites, exactly because of this continuous properties variation characteristic, which enables among other advantages smoother stresses distribution profile. In this paper we study the influence of different homogenization schemes, namely the schemes due to Voigt, Hashin-Shtrikman and Mod-Tanaka, which can be used to obtain bounds estimates for the material properties of particulate composite structures. To achieve this goal we also use a set of finite element models based on higher order shear deformation theories and also on first order theory. From the studies carried out, on linear static analyses and on free vibration analyses, it is shown that the bounds estimates are as important as the deformation kinematics basis assumed to analyse these types of multifunctional structures. Concerning to the homogenization schemes studied, it is shown that Mori-Tanaka and Hashin-Shtrikman estimates lead to less conservative results when compared to Voigt rule of mixtures.