Resolution of Nested Neuronal Representations Can Be Exponential in the Number of Neurons

Collective computation is typically polynomial in the number of computational elements, such as transistors or neurons, whether one considers the storage capacity of a memory device or the number of floating-point operations per second of a CPU. However, we show here that the capacity of a computational network to resolve real-valued signals of arbitrary dimensions can be exponential in N, even if the individual elements are noisy and unreliable. Nested, modular codes that achieve such high resolutions mirror the properties of grid cells in vertebrates, which underlie spatial navigation

Solvable model of a phase oscillator network on a circle with infinite-range Mexican-hat-type interaction

We describe a solvable model of a phase oscillator network on a circle with infinite-range Mexican-hat-type interaction. We derive self-consistent equations of the order parameters and obtain three non-trivial solutions characterized by the rotation number. We also derive relevant characteristics such as the location-dependent distributions of the resultant frequencies of desynchronized oscillators. Simulation results closely agree with the theoretical ones

Symmetry considerations and development of pinwheels in visual maps

Neurons in the visual cortex respond best to rod-like stimuli of given orientation. While the preferred orientation varies continuously across most of the cortex, there are prominent pinwheel centers around which all orientations a re present. Oriented segments abound in natural images, and tend to be collinear}; neurons are also more likely to be connected if their preferred orientations are aligned to their topographic separation. These are indications of a reduced symmetry requiring joint rotations of both orientation preference and the underl ying topography. We verify that this requirement extends to cortical maps of mo nkey and cat by direct statistical analysis. Furthermore, analytical arguments and numerical studies indicate that pinwheels are generically stable in evolving field models which couple orientation and topography

On Multifractal Structure in Non-Representational Art

Multifractal analysis techniques are applied to patterns in several abstract expressionist artworks, paintined by various artists. The analysis is carried out on two distinct types of structures: the physical patterns formed by a specific color (``blobs''), as well as patterns formed by the luminance gradient between adjacent colors (``edges''). It is found that the analysis method applied to ``blobs'' cannot distinguish between artists of the same movement, yielding a multifractal spectrum of dimensions between about 1.5-1.8. The method can distinguish between different types of images, however, as demonstrated by studying a radically different type of art. The data suggests that the ``edge'' method can distinguish between artists in the same movement, and is proposed to represent a toy model of visual discrimination. A ``fractal reconstruction'' analysis technique is also applied to the images, in order to determine whether or not a specific signature can be extracted which might serve as a type of fingerprint for the movement. However, these results are vague and no direct conclusions may be drawn.Comment: 53 pp LaTeX, 10 figures (ps/eps

Universal properties of correlation transfer in integrate-and-fire neurons

One of the fundamental characteristics of a nonlinear system is how it transfers correlations in its inputs to correlations in its outputs. This is particularly important in the nervous system, where correlations between spiking neurons are prominent. Using linear response and asymptotic methods for pairs of unconnected integrate-and-fire (IF) neurons receiving white noise inputs, we show that this correlation transfer depends on the output spike firing rate in a strong, stereotyped manner, and is, surprisingly, almost independent of the interspike variance. For cells receiving heterogeneous inputs, we further show that correlation increases with the geometric mean spiking rate in the same stereotyped manner, greatly extending the generality of this relationship. We present an immediate consequence of this relationship for population coding via tuning curves

DMSO-free methods of preserving mesenchymal stem cells (MSCs) that retain high levels of post thaw function

A novel, biologically-inspired strategy was developed to improve the preservation of mesenchymal stem cells (MSCs). MSCs are being investigated for the treatment of cardiovascular disorders, diabetes, connective tissue disorders, acute lung injury, amyotrophic lateral sclerosis, kidney diseases and more. To date, over 300 clinical trials involve the use of MSCs, with well over 2000 patients safely treated.Current methods of preserving MSCs are inadequate/ suboptimal. Concerns over poor post thaw function have become so pervasive that it is now common for MSCs to be cultured for 24-72 h prior to administration. These MSCs have a short shelf life (\u3c 24 hours), require special FDA permission, and the process increases cost and reduces access. The research described here utilizes an evolutionary algorithm to identify combinations of naturally occurring osmolytes that yield high cell recovery post thaw and optimize the composition of a DMSO-free, protein-free medium for cryopreservation of the cells. Additionally, we demonstrate that these novel solutions maintain MSC functionality when evaluated using surface markers, attachment, proliferation, actin alignment, RNA expression, and DNA hydroxymethlyation. Please click Additional Files below to see the full abstract

Understanding visual map formation through vortex dynamics of spin Hamiltonian models

The pattern formation in orientation and ocular dominance columns is one of the most investigated problems in the brain. From a known cortical structure, we build spin-like Hamiltonian models with long-range interactions of the Mexican hat type. These Hamiltonian models allow a coherent interpretation of the diverse phenomena in the visual map formation with the help of relaxation dynamics of spin systems. In particular, we explain various phenomena of self-organization in orientation and ocular dominance map formation including the pinwheel annihilation and its dependency on the columnar wave vector and boundary conditions.Comment: 4 pages, 15 figure

The scaling or ontogeny of human gait kinetics and walk-run transition: The implications of work vs. peak power minimization

A simple model is developed to find vertical force profiles and stance durations that minimize either limb mechanical work or peak power demands during bipedal locomotion. The model predicts that work minimization is achieved with a symmetrical vertical force profile, consistent with previous models and observations of adult humans, and data for 487 participants (predominantly 11–18 years old) required to walk at a range of speeds at a Science Fair. Work minimization also predicts the discrete walk-run transition, familiar for adult humans. In contrast, modeled peak limb mechanical power demands are minimized with an early skew in vertical ground reaction force that increases with speed, and stance durations that decrease steadily with speed across the work minimizing walk-run transition speed. The peak power minimization model therefore predicts a continuous walk-run gait transition that is quantitatively consistent with measurements of younger children (1.1–4.7 years) required to locomote at a range of speeds but free to select their own gaits

Founding quantum theory on the basis of consciousness

In the present work, quantum theory is founded on the framework of consciousness, in contrast to earlier suggestions that consciousness might be understood starting from quantum theory. The notion of streams of consciousness, usually restricted to conscious beings, is extended to the notion of a Universal/Global stream of conscious flow of ordered events. The streams of conscious events which we experience constitute sub-streams of the Universal stream. Our postulated ontological character of consciousness also consists of an operator which acts on a state of potential consciousness to create or modify the likelihoods for later events to occur and become part of the Universal conscious flow. A generalized process of measurement-perception is introduced, where the operation of consciousness brings into existence, from a state of potentiality, the event in consciousness. This is mathematically represented by (a) an operator acting on the state of potential-consciousness before an actual event arises in consciousness and (b) the reflecting of the result of this operation back onto the state of potential-consciousness for comparison in order for the event to arise in consciousness. Beginning from our postulated ontology that consciousness is primary and from the most elementary conscious contents, such as perception of periodic change and motion, quantum theory follows naturally as the description of the conscious experience.Comment: 41 pages, 3 figures. To be published in Foundations of Physics, Vol 36 (6) (June 2006), published online at http://dx.doi.org/10.1007/s10701-006-9049-

Handwritten digit recognition by bio-inspired hierarchical networks

The human brain processes information showing learning and prediction abilities but the underlying neuronal mechanisms still remain unknown. Recently, many studies prove that neuronal networks are able of both generalizations and associations of sensory inputs. In this paper, following a set of neurophysiological evidences, we propose a learning framework with a strong biological plausibility that mimics prominent functions of cortical circuitries. We developed the Inductive Conceptual Network (ICN), that is a hierarchical bio-inspired network, able to learn invariant patterns by Variable-order Markov Models implemented in its nodes. The outputs of the top-most node of ICN hierarchy, representing the highest input generalization, allow for automatic classification of inputs. We found that the ICN clusterized MNIST images with an error of 5.73% and USPS images with an error of 12.56%