Informational Aesthetics Measures

The Birkhoff aesthetic measure of an object is the ratio between order and complexity. Informational aesthetics describes the interpretation of this measure from an information-theoretic perspective. From these ideas, the authors define a set of ratios based on information theory and Kolmogorov complexity that can help to quantify the aesthetic experience

Estimating cell diffusivity and cell proliferation rate by interpreting IncuCyte ZOOM™ assay data using the Fisher-Kolmogorov model

Background: Standard methods for quantifying IncuCyte ZOOM™ assays involve measurements that quantify how rapidly the initially-vacant area becomes re-colonised with cells as a function of time. Unfortunately, these measurements give no insight into the details of the cellular-level mechanisms acting to close the initially-vacant area. We provide an alternative method enabling us to quantify the role of cell motility and cell proliferation separately. To achieve this we calibrate standard data available from IncuCyte ZOOM™ images to the solution of the Fisher-Kolmogorov model. Results: The Fisher-Kolmogorov model is a reaction-diffusion equation that has been used to describe collective cell spreading driven by cell migration, characterised by a cell diffusivity, D, and carrying capacity limited proliferation with proliferation rate, λ, and carrying capacity density, K. By analysing temporal changes in cell density in several subregions located well-behind the initial position of the leading edge we estimate λ and K. Given these estimates, we then apply automatic leading edge detection algorithms to the images produced by the IncuCyte ZOOM™ assay and match this data with a numerical solution of the Fisher-Kolmogorov equation to provide an estimate of D. We demonstrate this method by applying it to interpret a suite of IncuCyte ZOOM™ assays using PC-3 prostate cancer cells and obtain estimates of D, λ and K. Comparing estimates of D, λ and K for a control assay with estimates of D, λ and K for assays where epidermal growth factor (EGF) is applied in varying concentrations confirms that EGF enhances the rate of scratch closure and that this stimulation is driven by an increase in D and λ, whereas K is relatively unaffected by EGF. Conclusions: Our approach for estimating D, λ and K from an IncuCyte ZOOM™ assay provides more detail about cellular-level behaviour than standard methods for analysing these assays. In particular, our approach can be used to quantify the balance of cell migration and cell proliferation and, as we demonstrate, allow us to quantify how the addition of growth factors affects these processes individually.

A fully discrete C-0 interior penalty Galerkin approximation of the extended Fisher-Kolmogorov equation

A fully discrete C-0 interior penalty finite element method is proposed and analyzed for the Extended Fisher-Kolmogorov (EFK) equation u(t) + gamma Delta(2)u - Delta u + u(3) - u = 0 with appropriate initial and boundary conditions, where gamma is a positive constant. We derive a regularity estimate for the solution u of the EFK equation that is explicit in gamma and as a consequence we derive a priori error estimates that are robust in gamma. (C) 2013 Elsevier B.V. All rights reserved.

Generalizations and extensions of the Fokker-Planck-Kolmogorov equations

The problem of determining probability density functions of general transformations of random processes is considered in this thesis. A method of solution is developed in which partial differential equations satisfied by the unknown density function are derived. These partial differential equations are interpreted as generalized forms of the classical Fokker-Planck-Kolmogorov equations and are shown to imply the classical equations for certain classes of Markov processes. Extensions of the generalized equations which overcome degeneracy occurring in the steady-state case are also obtained.

The equations of Darling and Siegert are derived as special cases of the generalized equations thereby providing unity to two previously existing theories. A technique for treating non-Markov processes by studying closely related Markov processes is proposed and is seen to yield the Darling and Siegert equations directly from the classical Fokker-Planck-Kolmogorov equations.

As illustrations of their applicability, the generalized Fokker-Planck-Kolmogorov equations are presented for certain joint probability density functions associated with the linear filter. These equations are solved for the density of the output of an arbitrary linear filter excited by Markov Gaussian noise and for the density of the output of an RC filter excited by the Poisson square wave. This latter density is also found by using the extensions of the generalized equations mentioned above. Finally, some new approaches for finding the output probability density function of an RC filter-limiter-RC filter system driven by white Gaussian noise are included. The results in this case exhibit the data required for complete solution and clearly illustrate some of the mathematical difficulties inherent to the use of the generalized equations.

Biological controls on resuspension and the relationship between particle size and the Kolmogorov length scale in a shallow coastal sea

Measurements of suspended particle matter (SPM) and turbulence have been obtained over five tidal surveys during spring and summer 2010 at station L4 (5025 degrees N 04.22 degrees W, depth 50 m), in the Western English Channel. The relationship between turbulence intensity and bed stress is explored, with an in-line holographic imaging system evaluating the extent to which material is resuspended. Image analysis allows for the identification of SPM above a size threshold of 200 pm, capturing particle variability across tidal cycles and the two seasons. Dissipation of turbulent kinetic energy, which exceeds 10(-5) W kg(-1), yields maximum values of bed stress of between 0.17 and 0.20 N m(-2), frequently resulting in the resuspension of material from the bed. Resuspension is shown to promote aggregation of SPM into flocs, where the size of such particles is theoretically determined by the Kolmogorov microscale, l(k). During the spring surveys, flocs of a size larger than lk were observed, though this was not repeated during summer. It is proposed that the presence of gelatinous, biological material in spring allows flocculated particles to exceed l(k). This suggests that under specific circumstances, the limiting factor on the growth of flocculated SPM is not only turbulence, as previously thought, but the presence or absence of certain types of biological particle.

Statistic Complexity: Combining Kolmogorov Complexity with an Ensemble Approach

Background: The evaluation of the complexity of an observed object is an old but outstanding problem. In this paper we are tying on this problem introducing a measure called statistic complexity.

Tirant del cabdell de la complexitat ecològica amb l'educació ambiental. 'Tirando del ovillo de la complejidad ecológica con la educación ambiental'.

Resumen tomado de la revista

Aproximar-se al coneixement del medi des de la complexitat. 'Aproximarse al conocimiento del medio desde la complejidad'.

Resumen de la revista en catalán

La complexitat de l'ensenyament inicial de l'escriptura. 'La complejidad de la ense??anza inicial de la escritura'

Exploraci??n de las perspectivas que la autora ha considerado esenciales para ense??ar a escribir. La reflexi??n se realiza en base a la idea de dejar participar a los ni??os en estas mismas actividades.

La complexitat. 'La complejidad'

Se parte de la idea de que la incertidumbre ocupa un lugar cada vez m??s significativo en la sociedad. Ante este hecho, se considera que la escuela tiene un doble reto. Por un lado ayudar al alumnado a convivir en esta realidad y por el otro comprender qu?? comporta el paradigma de la complejidad. Los autores creen que esto implica un salto cualitativo en todos los ??mbitos escolares, como la gesti??n del aula o los procesos de ense??anza-aprendizaje.

Educar des de la complexitat de l'art. 'Educar desde la complejidad del arte'.

Resumen basado en el de la publicación. Monográfico con el título: 'L'art, una oportunitat per aprendre'