Entropy and Energy in Characterizing the Organization of Concept Maps in Learning Science

The coherence and connectivity of such knowledge representations is known to be closely related to knowledge production, acquisition and processing. In this study we use network theory in making the clustering and cohesion of concept maps measurable, and show how the distribution of these properties can be interpreted through the Maximum Entropy (MaxEnt) method. This approach allows to introduce new concepts of the “energy of cognitive load” and the “entropy of knowledge organization” to describe the organization of knowledge in the concept mapsPeer reviewe

Infotropism as the underlying principle of perceptual organization

Whether perceptual organization favors the simplest or most likely interpretation of a distal stimulus has long been debated. An unbridgeable gulf has seemed to separate these, the Gestalt and Helmholtzian viewpoints. But in recent decades, the proposal that likelihood and simplicity are two sides of the same coin has been gaining ground, to the extent that their equivalence is now widely assumed. What then arises is a desire to know whether the two principles can be reduced to one. Applying Occam's Razor in this way is particularly desirable given that, as things stand, an account referencing one principle alone cannot be completely satisfactory. The present paper argues that unification of the two principles is possible, and that it can be achieved in terms of an incremental notion of `information seeking' (infotropism). Perceptual processing that is infotropic can be shown to target both simplicity and likelihood. The ability to see perceptual organization as governed by either objective can then be explained in terms of it being an infotropic process. Infotropism can be identified as the principle which underlies, and thus generalizes the principles of likelihood and simplicity

Toward a multilevel representation of protein molecules: comparative approaches to the aggregation/folding propensity problem

This paper builds upon the fundamental work of Niwa et al. [34], which provides the unique possibility to analyze the relative aggregation/folding propensity of the elements of the entire Escherichia coli (E. coli) proteome in a cell-free standardized microenvironment. The hardness of the problem comes from the superposition between the driving forces of intra- and inter-molecule interactions and it is mirrored by the evidences of shift from folding to aggregation phenotypes by single-point mutations [10]. Here we apply several state-of-the-art classification methods coming from the field of structural pattern recognition, with the aim to compare different representations of the same proteins gathered from the Niwa et al. data base; such representations include sequences and labeled (contact) graphs enriched with chemico-physical attributes. By this comparison, we are able to identify also some interesting general properties of proteins. Notably, (i) we suggest a threshold around 250 residues discriminating "easily foldable" from "hardly foldable" molecules consistent with other independent experiments, and (ii) we highlight the relevance of contact graph spectra for folding behavior discrimination and characterization of the E. coli solubility data. The soundness of the experimental results presented in this paper is proved by the statistically relevant relationships discovered among the chemico-physical description of proteins and the developed cost matrix of substitution used in the various discrimination systems.Comment: 17 pages, 3 figures, 46 reference

Data-Driven Shape Analysis and Processing

Data-driven methods play an increasingly important role in discovering geometric, structural, and semantic relationships between 3D shapes in collections, and applying this analysis to support intelligent modeling, editing, and visualization of geometric data. In contrast to traditional approaches, a key feature of data-driven approaches is that they aggregate information from a collection of shapes to improve the analysis and processing of individual shapes. In addition, they are able to learn models that reason about properties and relationships of shapes without relying on hard-coded rules or explicitly programmed instructions. We provide an overview of the main concepts and components of these techniques, and discuss their application to shape classification, segmentation, matching, reconstruction, modeling and exploration, as well as scene analysis and synthesis, through reviewing the literature and relating the existing works with both qualitative and numerical comparisons. We conclude our report with ideas that can inspire future research in data-driven shape analysis and processing.Comment: 10 pages, 19 figure

The Origins of Computational Mechanics: A Brief Intellectual History and Several Clarifications

The principle goal of computational mechanics is to define pattern and structure so that the organization of complex systems can be detected and quantified. Computational mechanics developed from efforts in the 1970s and early 1980s to identify strange attractors as the mechanism driving weak fluid turbulence via the method of reconstructing attractor geometry from measurement time series and in the mid-1980s to estimate equations of motion directly from complex time series. In providing a mathematical and operational definition of structure it addressed weaknesses of these early approaches to discovering patterns in natural systems. Since then, computational mechanics has led to a range of results from theoretical physics and nonlinear mathematics to diverse applications---from closed-form analysis of Markov and non-Markov stochastic processes that are ergodic or nonergodic and their measures of information and intrinsic computation to complex materials and deterministic chaos and intelligence in Maxwellian demons to quantum compression of classical processes and the evolution of computation and language. This brief review clarifies several misunderstandings and addresses concerns recently raised regarding early works in the field (1980s). We show that misguided evaluations of the contributions of computational mechanics are groundless and stem from a lack of familiarity with its basic goals and from a failure to consider its historical context. For all practical purposes, its modern methods and results largely supersede the early works. This not only renders recent criticism moot and shows the solid ground on which computational mechanics stands but, most importantly, shows the significant progress achieved over three decades and points to the many intriguing and outstanding challenges in understanding the computational nature of complex dynamic systems.Comment: 11 pages, 123 citations; http://csc.ucdavis.edu/~cmg/compmech/pubs/cmr.ht