Defending the Structural Concept of Representation

The aim of this paper is to defend the structural concept of representation, as defined by homomorphisms, against its main objections, namely: logical objections, the objection from misrepresentation, the objection from failing necessity, and the copy theory objection. The logical objections can be met by reserving the relation ¿to be homomorphic to¿ for the explication of potential representation (or, of the representational content). Actual reference objects (¿targets¿) of representations are determined by (intentional or causal) representational mechanisms. Appealing to the independence of the dimensions of ¿content¿ and ¿target¿ also helps to see how the structural concept can cope with misrepresentation. Finally, I argue that homomorphic representations are not necessarily ¿copies¿ of their representanda, and thus can convey scientific insight

Coding of Melodic Gestalt in Human Auditory Cortex

The perception of a melody is invariant to the absolute properties of its constituting notes, but depends on the relation between them—the melody's relative pitch profile. In fact, a melody's "Gestalt” is recognized regardless of the instrument or key used to play it. Pitch processing in general is assumed to occur at the level of the auditory cortex. However, it is unknown whether early auditory regions are able to encode pitch sequences integrated over time (i.e., melodies) and whether the resulting representations are invariant to specific keys. Here, we presented participants different melodies composed of the same 4 harmonic pitches during functional magnetic resonance imaging recordings. Additionally, we played the same melodies transposed in different keys and on different instruments. We found that melodies were invariantly represented by their blood oxygen level-dependent activation patterns in primary and secondary auditory cortices across instruments, and also across keys. Our findings extend common hierarchical models of auditory processing by showing that melodies are encoded independent of absolute pitch and based on their relative pitch profile as early as the primary auditory corte

Multiscale resolution in the computation of crystalline microstructure

Summary.: This paper addresses the numerical approximation of microstructures in crystalline phase transitions without surface energy. It is shown that branching of different variants near interfaces of twinned martensite and austenite phases leads to reduced energies in finite element approximations. Such behavior of minimizing deformations is understood for an extended model that involves surface energies. Moreover, the closely related question of the role of different growth conditions of the employed bulk energy is discussed. By explicit construction of discrete deformations in lowest order finite element spaces we prove upper bounds for the energy and thereby clarify the question of the dependence of the convergence rate upon growth conditions and lamination orders. For first order laminates the estimates are optima

The modularity of processing and perception in the visual brain

Practical and theoretical approaches were applied to try to unravel the relationship of the anatomical processing sites to the relative timing of processing and perception. Psychophysical, imaging and theoretical studies led to the overall conclusion that simultaneously presented attributes that are perceived at the same time are processed at the same site, and ones that are perceived at different times are processed at different sites. This is referred to as to the theory of perceptual sites. Functional magnetic resonance imaging (fMRI) experiments charted the organisation of the human colour centre (the V4-complex), and found it to be more complex than previously believed. It has two subdivisions, V4 and V4α, of which V4 is retinotopically organised, while V4α is not. The extent and organisation of the colour centre revealed in this study may account for the variability and severity of the syndrome of achromatopsia (acquired cortical colour blindness). Application of an independent components analysis (ICA) to fMRI data showed that these two subdivisions are coactive and can be isolated together from the remaining brain activity. It was further shown that, because cortical areas enjoy substantial autonomy, they differ in their activation time courses, such that ICA can dissect the brain computationally into its functional units, creating what we call chronoarchitectonic maps. The above evidence, when viewed in context of previous experimental and clinical studies, leads us to propose the following: First, that the activity in different visual areas reaches conscious perceptual endpoints at different times; leading to the supposition that consciousness is not unitary but consists of many microconsciousnesses. Second, that since activity at each processing site can become perceptually explicit, there is no terminal perceptual stage in the visual brain; leading to the conclusion that activity at each site of the visual brain can be integrated with activity at any other site, and to the theory of multistage integration

Preparing the ground for an empirical theory of knowing-how : a reply to Ramiro Glauer

The commentary gives a clear and instructive summary of our main arguments against both, intellectualist and anti-intellectualist accounts of knowing-how. But the aim of our account is not correctly described as an attempt to give an explanation of certain cognitive capacities that are taken to be expressions of knowledge-how in terms of underlying mental representations. (Glauer this collection, p.10). What we aim at is not an empirical theory of knowing-how, but a framework that would be useful for cognitive scientific research on phenomena of knowing-how

Forces and effects in the privatisation process: an empirical study of telecommunications companies in Germany and Romania

Privatisation is supposed to lead to an increased efficiency and performance of a company. However, the internal and external environment of an enterprise is quite complex and many factors influence the organisation before and after the privatisation. The privatisation of a company (especially if it holds a natural monopoly) might be accompanied by a liberalisation of the market and the introduction of regulation. A model was developed which integrates all the major forces and effects with an influence on the performance of the company – incorporating also the peculiarities of transition economies. The model was verified on two telecommunications companies from Germany and Romania and shows inter alia that the effects “Laws and policies” and “Economic condition” may influence the overall performance of privatised companies in transition economies

A convergent and constraint-preserving finite element method for the p-harmonic flow into spheres

Published versio

Task-related edge density (TED) - a new method for revealing large-scale network formation in fMRI data of the human brain

The formation of transient networks in response to external stimuli or as a reflection of internal cognitive processes is a hallmark of human brain function. However, its identification in fMRI data of the human brain is notoriously difficult. Here we propose a new method of fMRI data analysis that tackles this problem by considering large-scale, task-related synchronisation networks. Networks consist of nodes and edges connecting them, where nodes correspond to voxels in fMRI data, and the weight of an edge is determined via task-related changes in dynamic synchronisation between their respective times series. Based on these definitions, we developed a new data analysis algorithm that identifies edges in a brain network that differentially respond in unison to a task onset and that occur in dense packs with similar characteristics. Hence, we call this approach "Task-related Edge Density" (TED). TED proved to be a very strong marker for dynamic network formation that easily lends itself to statistical analysis using large scale statistical inference. A major advantage of TED compared to other methods is that it does not depend on any specific hemodynamic response model, and it also does not require a presegmentation of the data for dimensionality reduction as it can handle large networks consisting of tens of thousands of voxels. We applied TED to fMRI data of a fingertapping task provided by the Human Connectome Project. TED revealed network-based involvement of a large number of brain areas that evaded detection using traditional GLM-based analysis. We show that our proposed method provides an entirely new window into the immense complexity of human brain function.Comment: 21 pages, 11 figure