Data-driven modelling of biological multi-scale processes

Biological processes involve a variety of spatial and temporal scales. A holistic understanding of many biological processes therefore requires multi-scale models which capture the relevant properties on all these scales. In this manuscript we review mathematical modelling approaches used to describe the individual spatial scales and how they are integrated into holistic models. We discuss the relation between spatial and temporal scales and the implication of that on multi-scale modelling. Based upon this overview over state-of-the-art modelling approaches, we formulate key challenges in mathematical and computational modelling of biological multi-scale and multi-physics processes. In particular, we considered the availability of analysis tools for multi-scale models and model-based multi-scale data integration. We provide a compact review of methods for model-based data integration and model-based hypothesis testing. Furthermore, novel approaches and recent trends are discussed, including computation time reduction using reduced order and surrogate models, which contribute to the solution of inference problems. We conclude the manuscript by providing a few ideas for the development of tailored multi-scale inference methods.Comment: This manuscript will appear in the Journal of Coupled Systems and Multiscale Dynamics (American Scientific Publishers

On analog networks and mixed-domain spatio-temporal frequency response

Published versio

The What-And-Where Filter: A Spatial Mapping Neural Network for Object Recognition and Image Understanding

The What-and-Where filter forms part of a neural network architecture for spatial mapping, object recognition, and image understanding. The Where fllter responds to an image figure that has been separated from its background. It generates a spatial map whose cell activations simultaneously represent the position, orientation, ancl size of all tbe figures in a scene (where they are). This spatial map may he used to direct spatially localized attention to these image features. A multiscale array of oriented detectors, followed by competitve and interpolative interactions between position, orientation, and size scales, is used to define the Where filter. This analysis discloses several issues that need to be dealt with by a spatial mapping system that is based upon oriented filters, such as the role of cliff filters with and without normalization, the double peak problem of maximum orientation across size scale, and the different self-similar interpolation properties across orientation than across size scale. Several computationally efficient Where filters are proposed. The Where filter rnay be used for parallel transformation of multiple image figures into invariant representations that are insensitive to the figures' original position, orientation, and size. These invariant figural representations form part of a system devoted to attentive object learning and recognition (what it is). Unlike some alternative models where serial search for a target occurs, a What and Where representation can he used to rapidly search in parallel for a desired target in a scene. Such a representation can also be used to learn multidimensional representations of objects and their spatial relationships for purposes of image understanding. The What-and-Where filter is inspired by neurobiological data showing that a Where processing stream in the cerebral cortex is used for attentive spatial localization and orientation, whereas a What processing stream is used for attentive object learning and recognition.Advanced Research Projects Agency (ONR-N00014-92-J-4015, AFOSR 90-0083); British Petroleum (89-A-1204); National Science Foundation (IRI-90-00530, Graduate Fellowship); Office of Naval Research (N00014-91-J-4100, N00014-95-1-0409, N00014-95-1-0657); Air Force Office of Scientific Research (F49620-92-J-0499, F49620-92-J-0334

Visual motion processing and human tracking behavior

The accurate visual tracking of a moving object is a human fundamental skill that allows to reduce the relative slip and instability of the object's image on the retina, thus granting a stable, high-quality vision. In order to optimize tracking performance across time, a quick estimate of the object's global motion properties needs to be fed to the oculomotor system and dynamically updated. Concurrently, performance can be greatly improved in terms of latency and accuracy by taking into account predictive cues, especially under variable conditions of visibility and in presence of ambiguous retinal information. Here, we review several recent studies focusing on the integration of retinal and extra-retinal information for the control of human smooth pursuit.By dynamically probing the tracking performance with well established paradigms in the visual perception and oculomotor literature we provide the basis to test theoretical hypotheses within the framework of dynamic probabilistic inference. We will in particular present the applications of these results in light of state-of-the-art computer vision algorithms

Cellular neural networks, Navier-Stokes equation and microarray image reconstruction

Copyright @ 2011 IEEE.Although the last decade has witnessed a great deal of improvements achieved for the microarray technology, many major developments in all the main stages of this technology, including image processing, are still needed. Some hardware implementations of microarray image processing have been proposed in the literature and proved to be promising alternatives to the currently available software systems. However, the main drawback of those proposed approaches is the unsuitable addressing of the quantification of the gene spot in a realistic way without any assumption about the image surface. Our aim in this paper is to present a new image-reconstruction algorithm using the cellular neural network that solves the Navier–Stokes equation. This algorithm offers a robust method for estimating the background signal within the gene-spot region. The MATCNN toolbox for Matlab is used to test the proposed method. Quantitative comparisons are carried out, i.e., in terms of objective criteria, between our approach and some other available methods. It is shown that the proposed algorithm gives highly accurate and realistic measurements in a fully automated manner within a remarkably efficient time