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.

Reinforcement Learning Based on the Bayesian Theorem for Electricity Markets Decision Support

This paper presents the applicability of a reinforcement learning algorithm based on the application of the Bayesian theorem of probability. The proposed reinforcement learning algorithm is an advantageous and indispensable tool for ALBidS (Adaptive Learning strategic Bidding System), a multi-agent system that has the purpose of providing decision support to electricity market negotiating players. ALBidS uses a set of different strategies for providing decision support to market players. These strategies are used accordingly to their probability of success for each different context. The approach proposed in this paper uses a Bayesian network for deciding the most probably successful action at each time, depending on past events. The performance of the proposed methodology is tested using electricity market simulations in MASCEM (Multi-Agent Simulator of Competitive Electricity Markets). MASCEM provides the means for simulating a real electricity market environment, based on real data from real electricity market operators.

Understanding Cardiac Myxoma Recurrence: A Case Report

Recurrence of cardiac myxoma is a rare condition, observed in about 3% of patients in sporadic cases, although it is more frequent in familial ones. Several mechanisms have been proposed to explain such recurrence, and the importance of increased vascularization as a facilitating feature is the subject of debate. The authors report the case of a non-familial right atrial myxoma, unusual for both its histopathology and recurrence.

Recurrence After Operative Management of Intrahepatic Cholangiocarcinoma

INTRODUCTION: Data on recurrence after operation for intrahepatic cholangiocarcinoma (ICC) are limited. We sought to investigate rates and patterns of recurrence in patients after operative intervention for ICC. METHODS: We identified 301 patients who underwent operation for ICC between 1990 and 2011 from an international, multi-institutional database. Clinicopathologic data, recurrence patterns, and recurrence-free survival (RFS) were analyzed. RESULTS: During the median follow up duration of 31 months (range 1-208), 53.5% developed a recurrence. Median RFS was 20.2 months and 5-year actuarial disease-free survival, 32.1%. The most common site for initial recurrence after operation of ICC was intrahepatic (n = 98; 60.9%), followed by simultaneous intra- and extrahepatic disease (n = 30; 18.6%); 33 (21.0%) patients developed extrahepatic recurrence only as the first site of recurrence. Macrovascular invasion (hazard ratio [HR], 2.08; 95% confidence interval [CI], 1.34-3.21; P < .001), nodal metastasis (HR, 1.55; 95% CI, 1.01-2.45; P = .04), unknown nodal status (HR, 1.57; 95% CI, 1.10-2.25; P = .04), and tumor size ≥5 cm (HR, 1.84; 95% CI, 1.28-2.65; P < .001) were independently associated with increased risk of recurrence. Patients were assigned a clinical score from 0 to 3 according to the presence of these risk factors. The 5-year RFS for patients with scores of 0, 1, 2, and 3 was 61.8%, 36.2%, 19.5%, and 9.6%, respectively. CONCLUSION: Recurrence after operative intervention for ICC was common. Disease recurred both at intra- and extrahepatic sites with roughly the same frequency. Factors such as lymph node metastasis, tumor size, and vascular invasion predict highest risk of recurrence.

Long-Term Evaluation of Recurrence after Photodynamic Therapy with Topical Methyl Aminolevulinate for Non-Melanoma Skin Cancer: a Hospital-Based Study

Introduction & Objectives: Several factors may influence the decision to pursue nonsurgical modalities for the treatment of non-melanoma skin cancer. Topical photodynamic therapy (PDT) is a non-invasive alternative treatment reported to have a high efficacy when using standardized protocols in Bowen’s disease (BD), superficial basal cell carcinoma (BCC) and in thin nodular BCC. However, long-term recurrence studies are lacking. The aim of this study was to evaluate the long-term efficacy of PDT with topical methylaminolevulinate (MAL) for the treatment of BD and BCC in a dermato-oncology department. Materials & Methods: All patients with the diagnosis of BD or BCC, treated with MAL-PDT from the years 2004 to 2008, were enrolled. Treatment protocol included two MAL-PDT sessions one week apart repeated at three months when incomplete response, using a red light dose of 37-40 J/cm2 and an exposure time of 8’20’’. Clinical records were retrospectively reviewed, and data regarding age, sex, tumour location, size, treatment outcomes and recurrence were registered. Descriptive analysis was performed using chi square tests, followed by survival analysis with the Kaplan-Meier and Cox regression models. Results: Sixty-eight patients (median age 71.0 years, P25;P75=30;92) with a total of 78 tumours (31 BD, 45 superficial BCC, 2 nodular BCC) and a median tumour size of 5 cm2 were treated. Overall, the median follow-up period was 43.5 months (P25;P75=0;100), and a total recurrence rate of 33.8% was observed (24.4 % for BCC vs. 45.2% for BD). Estimated recurrence rates for BCC and BD were 5.0% vs. 7.4% at 6 months, 23.4% vs. 27.9% at 12 months, and 30.0% vs. 72.4% at 60 months. Both age and diagnosis were independent prognostic factors for recurrence, with significantly higher estimated recurrence rates in patients with BD (p=0.0036) or younger than 58 years old (p=0.039). The risk of recurrence (hazard ratio) was 2.4 times higher in patients with BD compared to superficial BCC (95% CI:1.1-5.3; p=0.033), and 2.8 times higher in patients younger than 58 years old (95% CI:1.2-6.5; p=0.02). Conclusions: In the studied population, estimated recurrence rates are higher than those expected from available literature, possibly due to a longer follow-up period. To the authors’ knowledge there is only one other study with a similar follow-up period, regarding BCC solely. BD, as an in situ squamous cell carcinoma, has a higher tendency to recur than superficial BCC. Despite greater cosmesis, PDT might no be the best treatment option for young patients considering their higher risk of recurrence.

Long-Term Recurrence of Nonmelanoma Skin Cancer after Topical Methylaminolevulinate Photodynamic Therapy in a Dermato-Oncology Department

BACKGROUND: Most available studies on the efficacy of topical photodynamic therapy focus on short-to medium-term results. Long-term data are scarce. OBJECTIVE: To evaluate the long-term efficacy of photodynamic therapy with topical methylaminolevulinate to treat Bowen's disease and basal cell carcinoma in the clinical practice setting of a dermato-oncology department. METHODS: The study included patients diagnosed with Bowen's disease or basal cell carcinoma, and who received photodynamic therapy from 2004 to 2008. Treatment protocol and clinical follow-up were standardized. The primary endpoint was clinically observed recurrence in a previous photodynamic therapy-treated area. Descriptive and survival analyses were performed. RESULTS: A total of 31 Bowen's disease lesions and 44 superficial basal cell carcinoma were treated, with a median follow-up of 43.5 months. Recurrence was observed in 14 Bowen's disease lesions (53.8%) and in 11 superficial basal cell carcinoma (33.3%). Significantly higher estimates for recurrence rates were found in patients with Bowen's disease (p=0.0036) or those aged under 58 years (p=0.039). The risk of recurrence was higher in patients with Bowen's disease than in those with superficial basal cell carcinoma and younger patients. CONCLUSIONS: Recurrence should be considered when choosing to treat non-melanoma skin cancer with photodynamic therapy. Younger age and Bowen's disease were independent predictors for long-term recurrence, suggesting the need to establish an extended period of follow-up for this subset of patients.

Recurrence relations for Clifford algebra-valued orthogonal polynomials

The theory of orthogonal polynomials of one real or complex variable is well established as well as its generalization for the multidimensional case. Hypercomplex function theory (or Clifford analysis) provides an alternative approach to deal with higher dimensions. In this context, we study systems of orthogonal polynomials of a hypercomplex variable with values in a Clifford algebra and prove some of their properties.

Recurrence of atrial septal defect in three generations

Beginning with a patient presenting with an atrial septal defect (ASD) of the secundum type, the genealogy was identified in four affected individuals who belonged to three successive generations of the same family. The defects were visually confirmed in all individuals and were found to be anatomically similar. No other congenital malformations were present in these individuals. The genealogy was identified in 1972, when ASD recurred in two generations, and it was concluded that the mechanism of transmission was autosomal recessive. The fifth individual, identified 21 years later, and having an anomaly identical to that of the others, was the child of a couple who had no consaguinity and whose mother was a member of the previously studied genealogy. Considering the absence of phenotype in the parents and the rarity of the ASD gene in the general population, the occurrence of the uniparental disomy for this family nucleus, and the same autosomal recessive mechanism of transmission by this affected individual is possible. This study reports the familial occurrence of ASD by genetic mechanisms of transmission, emphasizing the necessity for genetic-clinical studies in members of the familial nucleus in order to detect new carriers, who usually are asymptomatic, thereby allowing for early and adequate treatment of individuals who may be affected.

Métodos para el análisis de programas probabilistas y no-deterministas utilizando probadores de teoremas. Methods for the analysis of probabilistic and nondeterministic programs using theorem provers.

La verificación y el análisis de programas con características probabilistas es una tarea necesaria del quehacer científico y tecnológico actual. El éxito y su posterior masificación de las implementaciones de protocolos de comunicación a nivel hardware y soluciones probabilistas a problemas distribuidos hacen más que interesante el uso de agentes estocásticos como elementos de programación. En muchos de estos casos el uso de agentes aleatorios produce soluciones mejores y más eficientes; en otros proveen soluciones donde es imposible encontrarlas por métodos tradicionales. Estos algoritmos se encuentran generalmente embebidos en múltiples mecanismos de hardware, por lo que un error en los mismos puede llegar a producir una multiplicación no deseada de sus efectos nocivos.Actualmente el mayor esfuerzo en el análisis de programas probabilísticos se lleva a cabo en el estudio y desarrollo de herramientas denominadas chequeadores de modelos probabilísticos. Las mismas, dado un modelo finito del sistema estocástico, obtienen de forma automática varias medidas de performance del mismo. Aunque esto puede ser bastante útil a la hora de verificar programas, para sistemas de uso general se hace necesario poder chequear especificaciones más completas que hacen a la corrección del algoritmo. Incluso sería interesante poder obtener automáticamente las propiedades del sistema, en forma de invariantes y contraejemplos.En este proyecto se pretende abordar el problema de análisis estático de programas probabilísticos mediante el uso de herramientas deductivas como probadores de teoremas y SMT solvers. Las mismas han mostrado su madurez y eficacia en atacar problemas de la programación tradicional. Con el fin de no perder automaticidad en los métodos, trabajaremos dentro del marco de "Interpretación Abstracta" el cual nos brinda un delineamiento para nuestro desarrollo teórico. Al mismo tiempo pondremos en práctica estos fundamentos mediante implementaciones concretas que utilicen aquellas herramientas.

Non-classical error bounds in the central limit theorem

The classical central limit theorem states the uniform convergence of the distribution functions of the standardized sums of independent and identically distributed square integrable real-valued random variables to the standard normal distribution function. While first versions of the central limit theorem are already due to Moivre (1730) and Laplace (1812), a systematic study of this topic started at the beginning of the last century with the fundamental work of Lyapunov (1900, 1901). Meanwhile, extensions of the central limit theorem are available for a multitude of settings. This includes, e.g., Banach space valued random variables as well as substantial relaxations of the assumptions of independence and identical distributions. Furthermore, explicit error bounds are established and asymptotic expansions are employed to obtain better approximations. Classical error estimates like the famous bound of Berry and Esseen are stated in terms of absolute moments of the random summands and therefore do not reflect a potential closeness of the distributions of the single random summands to a normal distribution. Non-classical approaches take this issue into account by providing error estimates based on, e.g., pseudomoments. The latter field of investigation was initiated by work of Zolotarev in the 1960's and is still in its infancy compared to the development of the classical theory. For example, non-classical error bounds for asymptotic expansions seem not to be available up to now ...

Predictors of Atrial Fibrillation Recurrence in Hyperthyroid and Euthyroid Patients

Background: Atrial fibrillation (AF) is the most common arrhythmia in adults, and is encountered in 10-15% of the patients with hyperthyroidism. Unless euthyroidism is restored, pharmacological or electrical cardioversion is controversial in patients with AF who remain hyperthyroid. Objective: The aim of this study was to assess the efficacy of electrical cardioversion and predictors of AF recurrence in hyperthyroid and euthyroid patients. Methods: The study included 33 hyperthyroid (21 males) and 48 euthyroid (17 males) patients with persistent AF. The patients were sedated with intravenous midazolam before undergoing electrical cardioversion delivered by synchronized biphasic shocks. Rates of AF recurrence were recorded. Results: Mean follow-up was 23.63 ± 3.74 months in the hyperthyroid group and 22.78 ± 3.15 months in the euthyroid group (p = 0.51). AF recurred in 14 (43.8%) and 21 (44.7%) patients in each group, respectively (p = 0.93). Multivariate regression analysis in each group showed that AF duration was the only predictor of AF recurrence, with odds ratios of 1.38 (95% confidence interval [CI] = 1.05 - 1.82, p = 0.02) in the hyperthyroid group and 1.42 (95% CI = 1.05 - 1.91, p= 0.02) in the euthyroid group. Conclusion: Rates of long-term AF recurrence were similar in successfully cardioverted hyperthyroid and euthyroid patients. The only predictor of AF recurrence in both groups was AF duration.

Asymptotics of orthogonal polynomials via the Koosis theorem

The main aim of this short paper is to advertize the Koosis theorem in the mathematical community, especially among those who study orthogonal polynomials. We (try to) do this by proving a new theorem about asymptotics of orthogonal polynomi- als for which the Koosis theorem seems to be the most natural tool. Namely, we consider the case when a SzegÄo measure on the unit circumference is perturbed by an arbitrary measure inside the unit disk and an arbitrary Blaschke sequence of point masses outside the unit disk.

Diophantine approximation on projective varieties I: algebraic distance and metric Bézout theorem

"Vegeu el resum a l'inici del document del fitxer adjunt."

Shelah's singular compactness theorem

We present Shelah’s famous theorem in a version for modules, together with a self-contained proof and some examples. This exposition is based on lectures given at CRM in October 2006.