BSP-fields: An Exact Representation of Polygonal Objects by Differentiable Scalar Fields Based on Binary Space Partitioning

The problem considered in this work is to find a dimension independent algorithm for the generation of signed scalar fields exactly representing polygonal objects and satisfying the following requirements: the defining real function takes zero value exactly at the polygonal object boundary; no extra zero-value isosurfaces should be generated; C1 continuity of the function in the entire domain. The proposed algorithms are based on the binary space partitioning (BSP) of the object by the planes passing through the polygonal faces and are independent of the object genus, the number of disjoint components, and holes in the initial polygonal mesh. Several extensions to the basic algorithm are proposed to satisfy the selected optimization criteria. The generated BSP-fields allow for applying techniques of the function-based modeling to already existing legacy objects from CAD and computer animation areas, which is illustrated by several examples

Relaxation oscillations in a class of delay-differential equations.

We study a class of delay differential equations which have been used to model hematological stem cell regulation and dynamics. Under certain circumstances the model exhibits self-sustained oscillations, with periods which can be significantly longer than the basic cell cycle time. We show that the long periods in the oscillations occur when the cell generation rate is small, and we provide an asymptotic analysis of the model in this case. This analysis bears a close resemblance to the analysis of relaxation oscillators (such as the Van der Pol oscillator), except that in our case the slow manifold is infinite dimensional. Despite this, a fairly complete analysis of the problem is possible

An evolutionary approach to the extraction of object construction trees from 3D point clouds

In order to extract a construction tree from a finite set of points sampled on the surface of an object, we present an evolutionary algorithm that evolves set-theoretic expressions made of primitives fitted to the input point-set and modeling operations. To keep relatively simple trees, we use a penalty term in the objective function optimized by the evolutionary algorithm. We show with experiments successes but also limitations of this approach

Addressing Integration Error for Polygonal Finite Elements Through Polynomial Projections: A Patch Test Connection

Polygonal finite elements generally do not pass the patch test as a result of quadrature error in the evaluation of weak form integrals. In this work, we examine the consequences of lack of polynomial consistency and show that it can lead to a deterioration of convergence of the finite element solutions. We propose a general remedy, inspired by techniques in the recent literature of mimetic finite differences, for restoring consistency and thereby ensuring the satisfaction of the patch test and recovering optimal rates of convergence. The proposed approach, based on polynomial projections of the basis functions, allows for the use of moderate number of integration points and brings the computational cost of polygonal finite elements closer to that of the commonly used linear triangles and bilinear quadrilaterals. Numerical studies of a two-dimensional scalar diffusion problem accompany the theoretical considerations

Self-directedness, integration and higher cognition

In this paper I discuss connections between self-directedness, integration and higher cognition. I present a model of self-directedness as a basis for approaching higher cognition from a situated cognition perspective. According to this model increases in sensorimotor complexity create pressure for integrative higher order control and learning processes for acquiring information about the context in which action occurs. This generates complex articulated abstractive information processing, which forms the major basis for higher cognition. I present evidence that indicates that the same integrative characteristics found in lower cognitive process such as motor adaptation are present in a range of higher cognitive process, including conceptual learning. This account helps explain situated cognition phenomena in humans because the integrative processes by which the brain adapts to control interaction are relatively agnostic concerning the source of the structure participating in the process. Thus, from the perspective of the motor control system using a tool is not fundamentally different to simply controlling an arm

Geometría, Estructura y Forma. Centro George Ponpidou

Geometría, Estructura y Forma. Centro George Ponpidou. Jornadas Internacionales de Investigación en Construcción, ?Hitos Estructurales de la Arquitectura y la Ingeniería, Instituto de Ciencias de la Construcción Eduardo Torroja, Consejo Superior de Investigaciones Científicas, Universidad Politécnica de Madrid, Ministerio de Ciencia e Innovación, Madrid, noviembre 2011

On random tomography with unobservable projection angles

We formulate and investigate a statistical inverse problem of a random tomographic nature, where a probability density function on $\mathbb{R}^3$ is to be recovered from observation of finitely many of its two-dimensional projections in random and unobservable directions. Such a problem is distinct from the classic problem of tomography where both the projections and the unit vectors normal to the projection plane are observable. The problem arises in single particle electron microscopy, a powerful method that biophysicists employ to learn the structure of biological macromolecules. Strictly speaking, the problem is unidentifiable and an appropriate reformulation is suggested hinging on ideas from Kendall's theory of shape. Within this setup, we demonstrate that a consistent solution to the problem may be derived, without attempting to estimate the unknown angles, if the density is assumed to admit a mixture representation.Comment: Published in at http://dx.doi.org/10.1214/08-AOS673 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Tangible user interfaces : past, present and future directions

In the last two decades, Tangible User Interfaces (TUIs) have emerged as a new interface type that interlinks the digital and physical worlds. Drawing upon users' knowledge and skills of interaction with the real non-digital world, TUIs show a potential to enhance the way in which people interact with and leverage digital information. However, TUI research is still in its infancy and extensive research is required in or- der to fully understand the implications of tangible user interfaces, to develop technologies that further bridge the digital and the physical, and to guide TUI design with empirical knowledge. This paper examines the existing body of work on Tangible User In- terfaces. We start by sketching the history of tangible user interfaces, examining the intellectual origins of this field. We then present TUIs in a broader context, survey application domains, and review frame- works and taxonomies. We also discuss conceptual foundations of TUIs including perspectives from cognitive sciences, phycology, and philoso- phy. Methods and technologies for designing, building, and evaluating TUIs are also addressed. Finally, we discuss the strengths and limita- tions of TUIs and chart directions for future research

Precis of neuroconstructivism: how the brain constructs cognition

Neuroconstructivism: How the Brain Constructs Cognition proposes a unifying framework for the study of cognitive development that brings together (1) constructivism (which views development as the progressive elaboration of increasingly complex structures), (2) cognitive neuroscience (which aims to understand the neural mechanisms underlying behavior), and (3) computational modeling (which proposes formal and explicit specifications of information processing). The guiding principle of our approach is context dependence, within and (in contrast to Marr [1982]) between levels of organization. We propose that three mechanisms guide the emergence of representations: competition, cooperation, and chronotopy; which themselves allow for two central processes: proactivity and progressive specialization. We suggest that the main outcome of development is partial representations, distributed across distinct functional circuits. This framework is derived by examining development at the level of single neurons, brain systems, and whole organisms. We use the terms encellment, embrainment, and embodiment to describe the higher-level contextual influences that act at each of these levels of organization. To illustrate these mechanisms in operation we provide case studies in early visual perception, infant habituation, phonological development, and object representations in infancy. Three further case studies are concerned with interactions between levels of explanation: social development, atypical development and within that, developmental dyslexia. We conclude that cognitive development arises from a dynamic, contextual change in embodied neural structures leading to partial representations across multiple brain regions and timescales, in response to proactively specified physical and social environment