Asymptotic divergences and strong dichotomy

The Schnorr-Stimm dichotomy theorem [31] concerns finite-state gamblers that bet on infinite sequences of symbols taken from a finite alphabet S. The theorem asserts that, for any such sequence S, the following two things are true. (1) If S is not normal in the sense of Borel (meaning that every two strings of equal length appear with equal asymptotic frequency in S), then there is a finite-state gambler that wins money at an infinitely-often exponential rate betting on S. (2) If S is normal, then any finite-state gambler betting on S loses money at an exponential rate betting on S. In this paper we use the Kullback-Leibler divergence to formulate the lower asymptotic divergence div(S||a) of a probability measure a on S from a sequence S over S and the upper asymptotic divergence Div(S||a) of a from S in such a way that a sequence S is a-normal (meaning that every string w has asymptotic frequency a(w) in S) if and only if Div(S||a) = 0. We also use the Kullback-Leibler divergence to quantify the total risk RiskG(w) that a finite-state gambler G takes when betting along a prefix w of S. Our main theorem is a strong dichotomy theorem that uses the above notions to quantify the exponential rates of winning and losing on the two sides of the Schnorr-Stimm dichotomy theorem (with the latter routinely extended from normality to a-normality). Modulo asymptotic caveats in the paper, our strong dichotomy theorem says that the following two things hold for prefixes w of S. (10) The infinitely-often exponential rate of winning in 1 is 2Div(S||a)|w| . (20) The exponential rate of loss in 2 is 2-RiskG(w) . We also use (10) to show that 1 - Div(S||a)/c, where c = log(1/mina¿S a(a)), is an upper bound on the finite-state a-dimension of S and prove the dual fact that 1 - div(S||a)/c is an upper bound on the finite-state strong a-dimension of S

Dimension Spectra of Lines

This paper investigates the algorithmic dimension spectra of lines in the Euclidean plane. Given any line L with slope a and vertical intercept b, the dimension spectrum sp(L) is the set of all effective Hausdorff dimensions of individual points on L. We draw on Kolmogorov complexity and geometrical arguments to show that if the effective Hausdorff dimension dim(a, b) is equal to the effective packing dimension Dim(a, b), then sp(L) contains a unit interval. We also show that, if the dimension dim(a, b) is at least one, then sp(L) is infinite. Together with previous work, this implies that the dimension spectrum of any line is infinite

Nerve growth factor is expressed by postmitotic avian retinal horizontal cells and supports their survival during development in an autocrine mode of action.

Cell death in the developing retina is regulated, but so far little is known about what factors regulate the cell death. Several neurotrophic factors and receptors, including the neurotrophins and Trk receptors, are expressed during the critical time. We have studied the developing avian retina with respect to the role of nerve growth factor (NGF) in these processes. Our starting point for the work was that NGF and its receptor TrkA are expressed in a partially overlapping pattern in the inner nuclear layer of the developing retina. Our results show that TrkA and NGF-expressing cells are postmitotic. The first NGF-expressing cells were found on the vitreal side of the central region of E5.5–E6 retina. This pattern changed and NGF-expressing cells identified as horizontal cells were later confined to the external inner nuclear layer. We show that these horizontal cells co-express TrkA and NGF, unlike a subpopulation of amacrine cells that only expresses TrkA. In contrast to the horizontal cells, which survive, the majority of the TrkA-expressing amacrine cells die during a period of cell death in the inner nuclear layer. Intraocular injections of NGF protein rescued the dying amacrine cells and injection of antisense oligonucleotides for NGF that block its synthesis, caused death among the TrkA-expressing horizontal cells, which normally would survive. Our results suggest that NGF supports the survival of TrkA expressing avian horizontal cells in an autocrine mode of action in the retina of E10-E12 chicks. The cells co-express TrkA and NGF and the role for NGF is to maintain the TrkA-expressing horizontal cells. The TrkA-expressing amacrine cells are not supported by NGF and subsequently die. In addition to the effect on survival, our results suggest that NGF plays a role in horizontal cell plasticity

Evaluación continua y ayuda al aprendizaje. Análisis de una experiencia de innovación en educación superior con apoyo de las TIC

En este artículo se presenta y discute un sistema integrado de evaluación continua (SIEC) en la educación superior diseñado con el fin de obtener múltiples evidencias de los conocimientos y habilidades de los estudiantes y facilitar el seguimiento y apoyo de sus procesos de aprendizaje. Inspirado en un enfoque socio-constructivista que postula una relación estrecha entre enseñanza, aprendizaje y evaluación, este sistema combina diferentes tipos de actividades organizadas en torno a bloques temáticos amplios y dirigidas a obtener informaciones relativas tanto a la comprensión de los contenidos como a su aplicación y uso funcional en contextos auténticos. La experiencia de innovación en cuyo marco se ha elaborado y aplicado este sistema ha tenido lugar durante el curso 2005-06 y se ha llevado a cabo en tres grupos de "Psicología de la Educación", una asignatura troncal de la Licenciatura de Psicología diseñada en créditos ECTS (European Credit Transfer System) con una metodología de la enseñanza centrada en el estudiante y apoyo de las tecnologías de la información y la comunicación (TIC). La experiencia ha sido planificada y desarrollada por el grupo consolidado de innovación docente en psicología de la educación (GIDPE) de la Universidad de Barcelona. Los resultados obtenidos sustentan una valoración positiva tanto del rendimiento académico de los estudiantes como de su satisfacción con la participación en la experiencia. Dos conclusiones merecen ser destacadas. La primera es que el SIEC utilizado ha mostrado ser un instrumento potente y útil para la obtención de evidencias de los procesos de aprendizaje y para la administración y gestión de ayudas educativas diversas a los estudiantes en estos procesos. Y la segunda, que la potencia y utilidad del SIEC reside en el conjunto de opciones y criterios que lo integran más que en la aplicación de uno u otro criterio u opción aisladamente considerados