Efficient learning of decomposable models with a bounded clique size

The learning of probability distributions from data is a ubiquitous problem in the fields of Statistics and Artificial Intelligence. During the last decades several learning algorithms have been proposed to learn probability distributions based on decomposable models due to their advantageous theoretical properties. Some of these algorithms can be used to search for a maximum likelihood decomposable model with a given maximum clique size, k, which controls the complexity of the model. Unfortunately, the problem of learning a maximum likelihood decomposable model given a maximum clique size is NP-hard for k > 2. In this work, we propose a family of algorithms which approximates this problem with a computational complexity of O(k · n^2 log n) in the worst case, where n is the number of implied random variables. The structures of the decomposable models that solve the maximum likelihood problem are called maximal k-order decomposable graphs. Our proposals, called fractal trees, construct a sequence of maximal i-order decomposable graphs, for i = 2, ..., k, in k − 1 steps. At each step, the algorithms follow a divide-and-conquer strategy based on the particular features of this type of structures. Additionally, we propose a prune-and-graft procedure which transforms a maximal k-order decomposable graph into another one, increasing its likelihood. We have implemented two particular fractal tree algorithms called parallel fractal tree and sequential fractal tree. These algorithms can be considered a natural extension of Chow and Liu’s algorithm, from k = 2 to arbitrary values of k. Both algorithms have been compared against other efficient approaches in artificial and real domains, and they have shown a competitive behavior to deal with the maximum likelihood problem. Due to their low computational complexity they are especially recommended to deal with high dimensional domains.

Number of prior episodes and the presence of depressive symptoms are associated with longer length of stay for patients with acute manic episodes

Background: Few studies have analyzed predictors of length of stay (LOS) in patients admitted due to acute bipolar manic episodes. The purpose of the present study was to estimate LOS and to determine the potential sociodemographic and clinical risk factors associated with a longer hospitalization. Such information could be useful to identify those patients at high risk for long LOS and to allocate them to special treatments, with the aim of optimizing their hospital management. Methods: This was a cross-sectional study recruiting adult patients with a diagnosis of bipolar disorder (Diagnostic and Statistical Manual of Mental Disorders, 4th edition, text revision (DSM-IV-TR) criteria) who had been hospitalized due to an acute manic episode with a Young Mania Rating Scale total score greater than 20. Bivariate correlational and multiple linear regression analyses were performed to identify independent predictors of LOS. Results: A total of 235 patients from 44 centers were included in the study. The only factors that were significantly associated to LOS in the regression model were the number of previous episodes and the Montgomery-Åsberg Depression Rating Scale (MADRS) total score at admission (P < 0.05). Conclusions: Patients with a high number of previous episodes and those with depressive symptoms during mania are more likely to stay longer in hospital. Patients with severe depressive symptoms may have a more severe or treatment-resistant course of the acute bipolar manic episode.

Accuracy in Copy Number Calling by qPCR and PRT : A Matter of DNA

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Number of Players and Relative Pitch Area per Player: Comparing Their Influence on Heart Rate and Physical Demands in Under-12 and Under-13 Football Players

The aim of the present study is to analyse the influence of different large-sided games (LSGs) on the physical and physiological variables in under-12s (U12) and -13s (U13) soccer players. The effects of the combination of different number of players per team, 7, 9, and 11 (P7, P9, and P11, respectively) with three relative pitch areas, 100, 200, and 300 m(2) (A100, A200, and A300, respectively), were analysed in this study. The variables analysed were: 1) global indicator such as total distance (TD); work:rest ratio (W:R); player-load (PL) and maximal speed (V-max); 2) heart rate (HR) mean and time spent in different intensity zones of HR (<75%, 75-84%, 84-90% and >90%), and; 3) five absolute (<8, 8-13, 13-16 and >16 Km h(-1)) and three relative speed categories (<40%, 40-60% and >60% V-max). The results support the theory that a change in format (player number and pitch dimensions) affects no similarly in the two players categories. Although it can seem that U13 players are more demanded in this kind of LSG, when the work load is assessed from a relative point of view, great pitch dimensions and/or high number of player per team are involved in the training task to the U12 players. The results of this study could alert to the coaches to avoid some types of LSGs for the U12 players such as:P11 played in A100, A200 or A300, P9 played in A200 or A300 and P7 played in A300 due to that U13>U12 in several physical and physiological variables (W:R, time spent in 84-90% HRmax, distance in 8-13 and 13-16 Km h(-1) and time spent in 40-60% V-max). These results may help youth soccer coaches to plan the progressive introduction of LSGs so that task demands are adapted to the physiological and physical development of participants.