Boundary-Induced Pattern Formation from Temporal Oscillation: Spatial Map Analysis

Boundary-induced pattern formation from a spatially uniform state is investigated using one-dimensional reaction-diffusion equations. The temporal oscillation is successively transformed into a spatially periodic pattern, triggered by diffusion from the fixed boundary. We introduced a spatial map, whose temporal sequence, under selection criteria from multiple stationary solutions, can completely reproduce the emergent pattern, by replacing the time with space. The relationship of the pattern wavelength with the period of oscillation is also obtained. The generality of the pattern selection process and algorithm is discussed with possible relevance to biological morphogenesis.Comment: 17page

A Neural Model of How The Brain Represents and Compares Numbers

Many psychophysical experiments have shown that the representation of numbers and numerical quantities in humans and animals is related to number magnitude. A neural network model is proposed to quantitatively simulate error rates in quantification and numerical comparison tasks, and reaction times for number priming and numerical assessment and comparison tasks. Transient responses to inputs arc integrated before they activate an ordered spatial map that selectively responds to the number of events in a sequence. The dynamics of numerical comparison are encoded in activity pattern changes within this spatial map. Such changes cause a "directional comparison wave" whose properties mimic data about numerical comparison. These model mechanisms are variants of neural mechanisms that have elsewhere been used to explain data about motion perception, attention shifts, and target tracking. Thus, the present model suggests how numerical representations may have emerged as specializations of more primitive mechanisms in the cortical Where processing stream.National Science Foundation (IRI-97-20333); Defense Advanced research Projects Agency and the Office of Naval Research (N00014-95-1-0409); National Institute of Health (1-R29-DC02952-01

Periodic Coherence Peak Height Modulations in Superconducting BSCCO

In this paper we analyze, using scanning tunneling spectroscopy (STS), the local density of electronic states (LDOS) in nearly optimally doped BSCCO in zero field. We see both dispersive and non-dispersive spatial LDOS modulations as a function of energy in our samples. Moreover, a spatial map of the superconducting coherence peak heights shows the same structure as the low energy LDOS. This suggests that these non-dispersive LDOS modulations originate from an underlying charge-density modulation which interacts with superconductivity.Comment: 8 pages, 5 figures with 15 total eps file

A What-and-Where Neural Network for Invariant Image Preprocessing

A feedforward neural network for invariant image preprocessing is proposed that represents the position1 orientation and size of an image figure (where it is) in a multiplexed spatial map. This map is used to generate an invariant representation of the figure that is insensitive to position1 orientation, and size for purposes of pattern recognition (what it is). A multiscale array of oriented filters followed by competition between orientations and scales is used to define the Where filter.British Petroleum (89-A-1024); Defense Advanced Research Projects Agency (90-0083); National Science Foundation (IRI 90-00530); Office of Naval Research (N0014-91-J-4100); Air Force Office of Scientific Research (90-0175); NSF Graduate Fellowshi