Online research in philosophy

Neurochemistry is a powerful discipline of modern neuroscience based on a description of neuronal function in terms of molecular reaction and interaction. This study aims at a neurochemical approach to the "hard" philosophical mind-body problem: the search for the neuronal correlate of consciousness. The scattered pattern of remote areas in the human brain simultaneously busy with the computation of single perceptions has left us with the unanswered questions why, where, and how the neuronal activity gives rise to a unified conscious observation of the outer world in a space inside of the human brain. In this study, conscious perception of temporally and spatially distinct events by an inner observer, the self, is treated as a topological problem demanding for a correlation of the self with a particular orchestration of neuronal or neurochemical activity triggered by action potentials. According to a novel concept of "topological neurochemistry" it is assumed that three features of the human brain are necessary in order to generate consciousness: 1) A network of neurons with dendritic branching structure and re-entry signaling of action potentials. 2)A macromolecular lattice structure as part of the neuron which is excitable or modulated by action potentials. 3) A spatial superposition of action potentials which underlies conscious perception but reveals not necessarily the same topology as the space perceived in consciousness. Several molecular models for the generation of consciousness and the self will be discussed, and a new concept, the "fractal approach", will be introduced. Mathematical theory and experimental methods for investigation of human consciousness will be presented.

Chaos in nervous system is a fascinating but controversial field of investigation. To approach the role of chaos in the real brain, we theoretically and numerically investigate the occurrence of chaos inartificial neural networks. Most of the time, recurrent networks (with feedbacks) are fully connected. This architecture being not biologically plausible, the occurrence of chaos is studied here for a randomly diluted architecture. By normalizing the variance of synaptic weights, we produce a bifurcation parameter, dependent on this variance and on the slope of the transfer function, that allows a sustained activity and the occurrence of chaos when reaching a critical value. Even for weak connectivity and small size, we find numerical results in accordance with the theoretical ones previously established for fully connected infinite sized networks. The route towards chaos is numerically checked to be a quasi-periodic one, whatever the type of the first bifurcation is. Our results suggest that such high-dimensional networks behave like low-dimensional dynamical systems.

There is a gap between two different modes of computation: the symbolic mode and the subsymbolic (neuron-like) mode. The aim of this paper is to overcome this gap by viewing symbolism as a high-level description of the properties of (a class of) neural networks. Combining methods of algebraic semantics and non-monotonic logic, the possibility of integrating both modes of viewing cognition is demonstrated. The main results are (a) that certain activities of connectionist networks can be interpreted as non-monotonic inferences, and (b) that there is a strict correspondence between the coding of knowledge in Hopfield networks and the knowledge representation in weight-annotated Poole systems. These results show the usefulness of non-monotonic logic as a descriptive and analytic tool for analyzing emerging properties of connectionist networks. Assuming an exponential development of the weight function, the present account relates to optimality theory – a general framework that aims to integrate insights from symbolism and connectionism. The paper concludes with some speculations about extending the present ideas.

This article provides a retrospective, current and prospective overview on developments in brain research and neuroscience. Both theoretical and empirical studies are considered, with emphasis in the concept of multivariability and metastability in the brain. In this new view on the human brain, the potential multivariability of the neuronal networks appears to be far from continuous in time, but confined by the dynamics of short-term local and global metastable brain states. The article closes by suggesting some of the implications of this view in future multidisciplinary brain research.

Quartz & Sejnowski (Q&S) disregard evidence that suggests that their view of dendrites is inadequate and they ignore recent results concerning the role of neurotrophic factors in synaptic remodelling. They misrepresent neuronal selectionism and thus erect a straw-man argument. Finally, the results discussed in section 4.2 require neuronal proliferation, but this does not occur during the period of neuronal development of relevance here. Footnotes1 Address correspondence to TE at te@proteus.psyc.nott.ac.uk.

Endothelial cells, when cultured on gelled basement membrane matrix exert forces of tension through which they deform the matrix and at the same time they aggregate into clusters. The cells eventually form a network of cord-like structures connecting cell aggregates. In this network, almost all of the matrix has been pulled underneath the cell cords and cell clusters. This phenomenon has been proposed as a possible model for the growth and development of planar vascular systems in vitro. Our hypothesis is that the matrix is reorganized and the cellular networks form as a result of traction forces exerted by the cells on the matrix and the latter's elasticity. We construct and analyze a mathematical model based on this hypothesis and examine conditions necessary for the formation of the pattern. We show cell migration is not necessary for pattern formation and that isotropic, strain-stimulated traction is sufficient to form the observed patterns.

A categorical, higher dimensional algebra and generalized topos framework for Łukasiewicz–Moisil Algebraic–Logic models of non-linear dynamics in complex functional genomes and cell interactomes is proposed. Łukasiewicz–Moisil Algebraic–Logic models of neural, genetic and neoplastic cell networks, as well as signaling pathways in cells are formulated in terms of non-linear dynamic systems with n-state components that allow for the generalization of previous logical models of both genetic activities and neural networks. An algebraic formulation of variable ‘next-state functions’ is extended to a Łukasiewicz–Moisil Topos with an n-valued Łukasiewicz–Moisil Algebraic Logic subobject classifier description that represents non-random and non-linear network activities as well as their transformations in developmental processes and carcinogenesis. The unification of the theories of organismic sets, molecular sets and Robert Rosen’s (M,R)-systems is also considered here in terms of natural transformations of organismal structures which generate higher dimensional algebras based on consistent axioms, thus avoiding well known logical paradoxes occurring with sets. Quantum bionetworks, such as quantum neural nets and quantum genetic networks, are also discussed and their underlying, non-commutative quantum logics are considered in the context of an emerging Quantum Relational Biology.

Cognition or higher brain activity is sometimes seen as a phenomenon greater than the sum of its parts. This viewpoint however is largely dependent on the state of the art of experimental techniques that endeavor to characterize morphology and its association to function. Retinal ganglion cells are readily accessible for this work and we discuss recent advances in computational techniques in identifying novel parameters that describe structural attributes possibly associated with specific function. These parameters are based on calculating wavelet gradients from cell images followed by the extraction of meaningful measures including 2nd wavelet moment, entropy of orientation, and curvature. For the three cell types analyzed, the mean 2nd wavelet moment, which relates to the field of influence of the dendritic-tree segments was significantly different. cells had the highest mean 2nd wavelet moment, followed by the and cells (134 ± 22, 93 ± 19 and 63 ± 12, respectively). There was no significant difference between cells for entropy of orientation, indicating no class with a preferential orientation of their dendritic tree. Curvature provided similar results to the 2nd wavelet moment with cells having the highest curvature followed by and the cells (mean ± SD: 161 ± 15; 134 ± 22; 121 ± 15). Our feature space analysis also indicated a difference between these cell types. No difference was found between the and cell types and their physiological counterparts the Y and X cells based on wavelet analysis. Both the X and Y cells can be divided into two subtypes, the ON- and OFF-center cells based on the stratification level of the dendritic tree within the retina. Using 2nd wavelet moment, a difference in their morphological attributes, not reported previously, was noted for these subtypes. The 2nd wavelet moment and curvature are further discussed with respect to explaining regularity of spacing and coverage associated with retinal ganglion cell mosaics.

This paper reports on the investigation of the effects of neuronal shape, at both individual cell and network level, on the behavior of neuronal systems. More specifically, two-dimensional biologically realistic neuronal networks are obtained that take explicity into account the position and morphology of neuronal cells, with the respective behavior for associative recall being simulated through a diluted version of Hopfield's model. While a specific probability density function is used for the placement of the cell bodies, images of real neuronal cells (namely alpha and beta ganglion cells from the cat retina) are used to obtain biologically realistic models. Several morphological measures – including fractal dimension, the excluded volume, and integral geometry functionals–are estimated for the considered cells, and their values are correlated with the potential of the network for associative recall, which is quantified in terms of the overlap between distorted version of the trained patterns and their original version. Such an approach allows the quantitative and objective characterization of the relationship between neuronal shape and function, an important issue in neuroscience. The obtained results substantiate interesting relationships between the neural morphology and function as determined by the performance of the network.