Priors Stabilizers and Basis Functions: From Regularization to Radial, Tensor and Additive Splines

We had previously shown that regularization principles lead to approximation schemes, as Radial Basis Functions, which are equivalent to networks with one layer of hidden units, called Regularization Networks. In this paper we show that regularization networks encompass a much broader range of approximation schemes, including many of the popular general additive models, Breiman's hinge functions and some forms of Projection Pursuit Regression. In the probabilistic interpretation of regularization, the different classes of basis functions correspond to different classes of prior probabilities on the approximating function spaces, and therefore to different types of smoothness assumptions. In the final part of the paper, we also show a relation between activation functions of the Gaussian and sigmoidal type.

On the Noise Model of Support Vector Machine Regression

Support Vector Machines Regression (SVMR) is a regression technique which has been recently introduced by V. Vapnik and his collaborators (Vapnik, 1995; Vapnik, Golowich and Smola, 1996). In SVMR the goodness of fit is measured not by the usual quadratic loss function (the mean square error), but by a different loss function called Vapnik"s $epsilon$- insensitive loss function, which is similar to the "robust" loss functions introduced by Huber (Huber, 1981). The quadratic loss function is well justified under the assumption of Gaussian additive noise. However, the noise model underlying the choice of Vapnik's loss function is less clear. In this paper the use of Vapnik's loss function is shown to be equivalent to a model of additive and Gaussian noise, where the variance and mean of the Gaussian are random variables. The probability distributions for the variance and mean will be stated explicitly. While this work is presented in the framework of SVMR, it can be extended to justify non-quadratic loss functions in any Maximum Likelihood or Maximum A Posteriori approach. It applies not only to Vapnik's loss function, but to a much broader class of loss functions.

Hilbert space on probability density functions with Aitchison geometry

Compositional data analysis motivated the introduction of a complete Euclidean structure in the simplex of D parts. This was based on the early work of J. Aitchison (1986) and completed recently when Aitchinson distance in the simplex was associated with an inner product and orthonormal bases were identified (Aitchison and others, 2002; Egozcue and others, 2003). A partition of the support of a random variable generates a composition by assigning the probability of each interval to a part of the composition. One can imagine that the partition can be refined and the probability density would represent a kind of continuous composition of probabilities in a simplex of infinitely many parts. This intuitive idea would lead to a Hilbert-space of probability densities by generalizing the Aitchison geometry for compositions in the simplex into the set probability densities

Scoring Methods for Ordinal Multidimensional Forced-Choice Items

In most psychological tests and questionnaires, a test score is obtained by taking the sum of the item scores. In virtually all cases where the test or questionnaire contains multidimensional forced-choice items, this traditional scoring method is also applied. We argue that the summation of scores obtained with multidimensional forced-choice items produces uninterpretable test scores. Therefore, we propose three alternative scoring methods: a weak and a strict rank preserving scoring method, which both allow an ordinal interpretation of test scores; and a ratio preserving scoring method, which allows a proportional interpretation of test scores. Each proposed scoring method yields an index for each respondent indicating the degree to which the response pattern is inconsistent. Analysis of real data showed that with respect to rank preservation, the weak and strict rank preserving method resulted in lower inconsistency indices than the traditional scoring method; with respect to ratio preservation, the ratio preserving scoring method resulted in lower inconsistency indices than the traditional scoring method

Comparing methods for dimensionality reduction when data are density functions

Functional Data Analysis (FDA) deals with samples where a whole function is observed for each individual. A particular case of FDA is when the observed functions are density functions, that are also an example of infinite dimensional compositional data. In this work we compare several methods for dimensionality reduction for this particular type of data: functional principal components analysis (PCA) with or without a previous data transformation and multidimensional scaling (MDS) for diferent inter-densities distances, one of them taking into account the compositional nature of density functions. The difeerent methods are applied to both artificial and real data (households income distributions)

Evaluation of five guidelines for option development in multiple-choice item-writing. 'Evaluaci??n de cinco directrices para la construcci??n de opciones en ??tems de elecci??n m??ltiple'

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Special Functions

Exam questions and solutions in LaTex

Special Functions pdf

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Vector functions and curves

Exercises and solutions about vector functions and curves.

Eficacia de los inhibidores selectivos de recaptación de serotonina en síntomas no cognitivos del alzhéimer: revisión sistemática

Introducción: El Alzhéimer tiene una prevalencia de 1,6% en las personas mayores de 65 años. Se caracteriza por la pérdida de memoria y otras funciones cognoscitivas, pero más del 70% de los afectados presentan síntomas no cognitivos entre los que se encuentran alteraciones del afecto, comportamiento y psicosis. Estos síntomas están asociados a mayores tasas de institucionalización, morbilidad y mortalidad. Métodos: Revisión sistemática de la literatura de artículos que proporcionaron información sobre la eficacia de los inhibidores selectivos de recaptación de serotonina en síntomas no cognitivos del Alzhéimer. Resultados: La búsqueda inicial arrojó un total de 495 resultados, 64 artículos fueron preseleccionados y 7 se incluyeron en la revisión; éstos se clasificaron como nivel de evidencia Ib; citalopram mostró ser más eficaz que el placebo y similar a antipsicóticos para síntomas comportamentales y psicóticos asociados al Alzhéimer con un perfil de efectos adversos más tolerable; sertralina no mostró eficacia en depresión y sí una mayor incidencia de efectos adversos con respecto al placebo. Discusión: Se obtuvieron resultados favorables en síntomas comportamentales y psicóticos pero no en afectivos. Las diferencias metodológicas de los estudios le dan complejidad a la interpretación de los resultados. Conclusión: La evidencia sugiere que el tratamiento con citalopram es eficaz en síntomas comportamentales y psicóticos asociados al Alzhéimer; para el tratamiento de la depresión asociado a esta demencia aún no existe un antidepresivo que pueda considerarse de elección.

Should rituximab be considered as the first-choice treatment for severe autoimmune rheumatic diseases?

The present study aimed to assess the tolerance and efficacy of rituximab (RTX), a chimeric IgG1 monoclonal antibody directed against the CD20 receptor present in B lymphocytes, in patients with autoimmune rheumatic diseases (AIRD). For this purpose, patients treated with RTX and their respective clinical charts were comprehensively examined. Indications for treatment were a refractory character of the disease, inefficacy or intolerance of other immunosuppressors. Activity indexes (SLEDAI, DAS28, and specific clinical manifestations) were used to evaluate efficacy. Serious side effects were also recorded. Seventy-four patients were included. Forty-three patients had systemic lupus erythematosus (SLE), 21 had rheumatoid arthritis (RA), 8 had Sjögren’s syndrome (SS), and 2 had Takayasu’s arteritis (TA). RTX was well-tolerated in 66 (89%) patients. In 8 patients (SLE = 3, SS = 3, RA = 2), serious side effects lead to discontinuation. The mean follow-up period was 12 ± 7.8 (2–35) months. The efficacy of RTX was registered in 58/66 (87%) patients, of whom 36 (83%) had SLE, 18/21 (85%) had RA, 3/8 (37%) had SS, and 1 had TA. The mean time of efficacy was 6.3 ± 5.1 weeks. A significant steroid-sparing effect was noticed in half of the patients. These results add further evidence for the use of RTX in AIRD. Based on its risk–benefit ratio, RTX might be used as the first-choice treatment for patients with severe AIRD.

Estudio de caso: análisis de la influencia del movimiento pro-choice estadounidense en la promoción de los derechos sexuales y reproductivos en Colombia en el periodo de 2001 – 2011.

Los procesos transnacionales han marcado un cambio en las relaciones entre los actores del sistema internacional, permitiendo el trabajo por diversas causas a través de las fronteras. Esto ha sido aprovechado por los movimientos sociales, para que su lucha no quede enmarcada simplemente en su país, sino que a partir de objetivos, problemáticas, valores y acciones similares se vea reflejado en diferentes Estados y se de una acción común y colectiva para generar un cambio. Este fenómeno ha sido tomado como referente el Movimiento Pro-choice para articularse transnacionalmente en Colombia para la promoción de los Derechos Sexuales y Reproductivos en el periodo de 2001 a 2011, alcanzando una serie de objetivos importantes que han permitido cambios legales al interior del país, generando también un cambio dentro de la sociedad colombiana. El estudio, análisis y comprensión de la articulación del movimiento prochoice a partir de una dinámica transnacional para la promoción de los derechos sexuales y reproductivos en Colombia, se perfila como un tema de importancia por su coyuntura actual en el mundo, puesto que ha estado latente en los últimos veinte años. Igualmente, la identificación de la acción de los MST como otros actores internacionales en la transformación de las sociedades tanto locales como internacionales, traducido como un fenómeno que se puede explicar dentro de las Relaciones Internacionales.

Mnesic performance and executive functions in patients with multiple sclerosis (MS)

The Episodic Memory (EM) and the Executive Functions (EF) are cognitive areas that are affected in patients with diagnosis of Multiple Sclerosis (MS). Nowadays there exists scarce works destined to explore the infl uence of the EF on measures of mnesic performance in MS. For this reason, we analyze the effect of the EF on the performance in a set of memory measures. We worked with a clinical group (n=36) and with a control group (n=36) compared by age and educational level. The results show that the clinical group obtained significantly low average values in all the mnesic indexes (with exception of recognition) and in all the executive measures. All the executive indexes showed significant associations with some of the indexes of mnesic performance. These findings suggest that the problems in the episodic memory in EM patients could be analyzed as the manifestation of a global disorder that could be similar to the one that involves the EF. 

Rehabilitation of executive functions: Implications and strategies

Executive Functions (EF) concern a range of abilitiesincluding problem-solving, planning, initiation, selfmonitoring,conscious attention, cope with new situationsand the ability to modify plans if necessary. It’s ahigh cognitive function that is crucial for a person to getengaged and maintain daily activities whilst keeping agood quality of life. Problems in the EF were formerlyknown as Dysexecutive Syndrome (DS). There are manymodels concerning DS, although the literature on thesubject still remains unclear. Several works appoint theeffects brought by elderly life, as well as abuse of drugsand some psychopathologies. These factors are knownto increase the distress of the frontal circuits and thatcould be associated to executive deficits. The effects ofDS would compromise individuals in day-to-day routine,academic, social and labor fields. There is a growingbody of studies trying to determine the causes, implications,associations and the best way to take care of theseeffects. This work intends to review DS, focusing on themost important fields related to this area, such as psychopathologyassociations, cognitive reserve, assessmentand cognitive rehabilitation programs.

Executive functions in school-aged children: age and socioeconomic status effects

Lately, the study of prefrontal executive functions in grade scholars has noticeably increased. The aim of this study is to investigate the influence of age and socioeconomic status (sEs) on executive tasks performance and to analyze those socioeconomic variables that predict a better execution. A sample of 254 children aged between 7 and 12 years from the city of santa Fe, Argentina and belonging to different socioeconomic status were tested. A bat- tery of executive functions sensitive to prefrontal function was used to obtain the results. These in- dicate a significant influence of age and SES on executive functions. The cognitive patterns follow a different path according to the development and sEs effect. Besides, it is revealed a pattern of low cognitive functioning in low-sEs children in all executive functions. Finally, from the variables included in this study, it was found that only the educational level of the mother and the housing conditions are associated to the children’s executive function. The results are discussed in terms of the influence of the cerebral maturation and the envi- ronmental variables in the executive functioning.