A random journey through the math of gambling

The laws of chance are often subtle and deceptive. This is why games of chance work. People are convinced that they obey seemingly intuitive laws, while the underlying mathematical structure reveals a different and more complex reality. This article is a brief and rigorous journey through the implications that the mathematical laws governing stochastic processes have on gambling. It addresses a specific process, the random walk, and analyze some instances of fair and unfair games by highlighting the fallacy of many of our intuitions and beliefs. The paper gradually moves from the analysis of the random walk properties to a comprehensive description of the ruin problem. The introduction of the idea of transient and persistent states concludes the discussion. Much emphasis is placed on concrete examples and on the numerical values, in particular of the involved probabilities, and the interpretation of the results is always more central than the demonstrative technical details, which are nevertheless available to the reader

The Augmented Lagrange Multiplier Method for Exact Recovery of Corrupted Low-Rank Matrices

This paper proposes scalable and fast algorithms for solving the Robust PCA problem, namely recovering a low-rank matrix with an unknown fraction of its entries being arbitrarily corrupted. This problem arises in many applications, such as image processing, web data ranking, and bioinformatic data analysis. It was recently shown that under surprisingly broad conditions, the Robust PCA problem can be exactly solved via convex optimization that minimizes a combination of the nuclear norm and the $\ell^1$-norm . In this paper, we apply the method of augmented Lagrange multipliers (ALM) to solve this convex program. As the objective function is non-smooth, we show how to extend the classical analysis of ALM to such new objective functions and prove the optimality of the proposed algorithms and characterize their convergence rate. Empirically, the proposed new algorithms can be more than five times faster than the previous state-of-the-art algorithms for Robust PCA, such as the accelerated proximal gradient (APG) algorithm. Moreover, the new algorithms achieve higher precision, yet being less storage/memory demanding. We also show that the ALM technique can be used to solve the (related but somewhat simpler) matrix completion problem and obtain rather promising results too. We further prove the necessary and sufficient condition for the inexact ALM to converge globally. Matlab code of all algorithms discussed are available at http://perception.csl.illinois.edu/matrix-rank/home.htmlComment: Please cite "Zhouchen Lin, Risheng Liu, and Zhixun Su, Linearized Alternating Direction Method with Adaptive Penalty for Low Rank Representation, NIPS 2011." (available at arXiv:1109.0367) instead for a more general method called Linearized Alternating Direction Method This manuscript first appeared as University of Illinois at Urbana-Champaign technical report #UILU-ENG-09-2215 in October 2009 Zhouchen Lin, Risheng Liu, and Zhixun Su, Linearized Alternating Direction Method with Adaptive Penalty for Low Rank Representation, NIPS 2011. (available at http://arxiv.org/abs/1109.0367

The Challenging Pathway of Treatment for Neurogenesis Impairment in Down Syndrome: Achievements and Perspectives

Down syndrome (DS), also known as trisomy 21, is a genetic disorder caused by triplication of Chromosome 21. Gene triplication may compromise different body functions but invariably impairs intellectual abilities starting from infancy. Moreover, after the fourth decade of life people with DS are likely to develop Alzheimer's disease. Neurogenesis impairment during fetal life stages and dendritic pathology emerging in early infancy are thought to be key determinants of alterations in brain functioning in DS. Although the progressive improvement in medical care has led to a notable increase in life expectancy for people with DS, there are currently no treatments for intellectual disability. Increasing evidence in mouse models of DS reveals that pharmacological interventions in the embryonic and neonatal periods may greatly benefit brain development and cognitive performance. The most striking results have been obtained with pharmacotherapies during embryonic life stages, indicating that it is possible to pharmacologically rescue the severe neurodevelopmental defects linked to the trisomic condition. These findings provide hope that similar benefits may be possible for people with DS. This review summarizes current knowledge regarding (i) the scope and timeline of neurogenesis (and dendritic) alterations in DS, in order to delineate suitable windows for treatment; (ii) the role of triplicated genes that are most likely to be the key determinants of these alterations, in order to highlight possible therapeutic targets; and (iii) prenatal and neonatal treatments that have proved to be effective in mouse models, in order to rationalize the choice of treatment for human application. Based on this body of evidence we will discuss prospects and challenges for fetal therapy in individuals with DS as a potential means of drastically counteracting the deleterious effects of gene triplication

Squatter settlements as social catalysts towards a sustainable urban development: a positive look at the case of Villa El Salvador, Lima-Perú

Se ha estimado que más de 900 millones de personas viven actualmente en asentamientos marginales en países en vías de desarrollo (Montgomery 2005); fenómeno que se originó a partir de un acelerado proceso de urbanización desencadenado por una masiva migración urbana (Johansson et al. 2011). El propósito de este documento es determinar e identificar aquellos atributos, factores, estrategias y políticas necesarias para aumentar la capacidad de auto-mejora de estos asentamientos para lograr convertirlos en lugares menos vulnerables, más resistentes y ambientalmente más responsables. El Caso de estudio de Villa El Salvador, ubicado en Lima-Perú, es analizado como evidencia de que las organizaciones de base y el modelo de ‘Auto-ayuda’ liderados por la propia comunidad son efectivos para un desarrollo urbano sustentable. Este análisis hace hincapié en la necesidad de cambiar la actitud hacia los ‘Pueblos Jóvenes’, descubriendo sus potencialidades para proveer vivienda asequible y desarrollo socio-económico para los más pobres. Las conclusiones intentan lograr un mejor entendimiento de esta problemática desde una perspectiva mucho más humana y positiva, con la esperanza de contribuir en el proceso de acrecentamiento e integración urbana de comunidades segregadas; una visión que demanda la incorporación de los pobladores como los catalizadores sociales necesarios para lograr un futuro más equitativo y sustentable.).It is estimated that more than 900 million of the total population of developing countries is living in squatter settlements (Montgomery 2005); phenomenon originated from the accelerated process of urbanisation unleashed by the massive migration of the poorer from rural to urban areas (Johansson et al. 2011). The purpose of this paper is to determine and identify those attributes, factors, strategies and policies necessary for boosting the upgrading capacity of slums in order to turn them into less vulnerable, more resilient and environmentally-oriented places. The case study of Villa El Salvador, a slum located in Lima-Peru, is analysed as a supporting evidence of effective grass-roots management and as an exemplary self-help model led by residents and community organisations. This analysis emphasizes the necessity to change the attitude towards squatter settlements, by unveiling their potential to provide affordable housing and socio-economic development to the poorer. Conclusions are intended to gain a better understanding of this problematic from a more positive and humanitarian perspective, with the hope of contributing with the accretion process and urban integration of segregated communities; a vision that demands the incorporation of dwellers as the social catalyst needed to achieve a more sustainable and equitable future.Eje 4: Construir las nuevas agendas socio-ambientales. Orientar y gestionar las transiciones y transformaciones urbanas.Facultad de Arquitectura y Urbanism

Squatter settlements as social catalysts towards a sustainable urban development: a positive look at the case of Villa El Salvador, Lima-Perú

Se ha estimado que más de 900 millones de personas viven actualmente en asentamientos marginales en países en vías de desarrollo (Montgomery 2005); fenómeno que se originó a partir de un acelerado proceso de urbanización desencadenado por una masiva migración urbana (Johansson et al. 2011). El propósito de este documento es determinar e identificar aquellos atributos, factores, estrategias y políticas necesarias para aumentar la capacidad de auto-mejora de estos asentamientos para lograr convertirlos en lugares menos vulnerables, más resistentes y ambientalmente más responsables. El Caso de estudio de Villa El Salvador, ubicado en Lima-Perú, es analizado como evidencia de que las organizaciones de base y el modelo de ‘Auto-ayuda’ liderados por la propia comunidad son efectivos para un desarrollo urbano sustentable. Este análisis hace hincapié en la necesidad de cambiar la actitud hacia los ‘Pueblos Jóvenes’, descubriendo sus potencialidades para proveer vivienda asequible y desarrollo socio-económico para los más pobres. Las conclusiones intentan lograr un mejor entendimiento de esta problemática desde una perspectiva mucho más humana y positiva, con la esperanza de contribuir en el proceso de acrecentamiento e integración urbana de comunidades segregadas; una visión que demanda la incorporación de los pobladores como los catalizadores sociales necesarios para lograr un futuro más equitativo y sustentable.).It is estimated that more than 900 million of the total population of developing countries is living in squatter settlements (Montgomery 2005); phenomenon originated from the accelerated process of urbanisation unleashed by the massive migration of the poorer from rural to urban areas (Johansson et al. 2011). The purpose of this paper is to determine and identify those attributes, factors, strategies and policies necessary for boosting the upgrading capacity of slums in order to turn them into less vulnerable, more resilient and environmentally-oriented places. The case study of Villa El Salvador, a slum located in Lima-Peru, is analysed as a supporting evidence of effective grass-roots management and as an exemplary self-help model led by residents and community organisations. This analysis emphasizes the necessity to change the attitude towards squatter settlements, by unveiling their potential to provide affordable housing and socio-economic development to the poorer. Conclusions are intended to gain a better understanding of this problematic from a more positive and humanitarian perspective, with the hope of contributing with the accretion process and urban integration of segregated communities; a vision that demands the incorporation of dwellers as the social catalyst needed to achieve a more sustainable and equitable future.Eje 4: Construir las nuevas agendas socio-ambientales. Orientar y gestionar las transiciones y transformaciones urbanas.Facultad de Arquitectura y Urbanism

CPT groups for spinor field in de Sitter space

A group structure of the discrete transformations (parity, time reversal and charge conjugation) for spinor field in de Sitter space are studied in terms of extraspecial finite groups. Two $CPT$ groups are introduced, the first group from an analysis of the de Sitter-Dirac wave equation for spinor field, and the second group from a purely algebraic approach based on the automorphism set of Clifford algebras. It is shown that both groups are isomorphic to each other.Comment: 7 page

Inspiratory muscle training and its effect on indices of physiological and perceived stress during incremental walking exercise in normobaric hypoxia

This study evaluated the effects of inspiratory muscle training (IMT) on inspiratory muscle fatigue (IMF) and physiological and perceptual responses during trekking-specific exercise. An 8-week IMT program was completed by 21 males (age 32.4 ± 9.61 years, VO2peak 58.8 ± 6.75 mL/kg/min) randomised within matched pairs to either the IMT group (n = 11) or the placebo group [(P), n = 9]. Twice daily, participants completed 30 (IMT) or 60 (P) inspiratory efforts using a Powerbreathe initially set at a resistance of 50% (IMT) or used at 15% (P) of maximal inspiratory pressure (MIP) throughout. A loaded (12.5 kg) 39-minute incremental walking protocol (3–5 km/hour and 1–15% gradient) was completed in normobaric hypoxia (PIO2 = 110 mmHg, 3000 m) before and after training. MIP increased from 164 to 188 cmH2O (18%) and from 161 to 171 cmH2O (6%) in the IMT and P groups (P = 0.02). The 95% CI for IMT showed a significant improvement in MIP (5.21±43.33 cmH2O), but not for P. IMF during exercise (MIP) was*5%, showing no training effect for either IMT or P (P = 0.23). Rating of perceived exertion (RPE) was consistently reduced (*1) throughout exercise following training for IMT, but not for P (P = 0.03). The mean blood lactate concentration during exercise was significantly reduced by 0.26 and 0.15 mmol/L in IMT and P (P = 0.00), with no differences between groups (P = 0.34). Rating of dyspnoea during exercise decreased (*0.4) following IMT but increased (*0.3) following P (P = 0.01). IMT may attenuate the increased physiological and perceived exercise stress experienced during normobaric hypoxia, which may benefit moderate altitude expedition