The stability of solitons in biomembranes and nerves.

We examine the stability of a class of solitons, obtained from a generalization of the Boussinesq equation, which have been proposed to be relevant for pulse propagation in biomembranes and nerves. These solitons are found to be stable with respect to small-amplitude fluctuations. They emerge naturally from non-solitonic initial excitations and are robust in the presence of dissipation. Solitary waves pass through each other with only minor dissipation when their amplitude is small. Large-amplitude solitons fall apart into several pulses and small-amplitude noise upon collision when the maximum density of the membrane is limited by the density of the solid phase membrane.

Citation networks in high energy physics.

The citation network constituted by the SPIRES database is investigated empirically. The probability that a given paper in the SPIRES database has k citations is well described by simple power laws, P(k) proportional to k(-alpha), with alpha approximately 1.2 for k less than 50 citations and alpha approximately 2.3 for 50 or more citations. A consideration of citation distribution by subfield shows that the citation patterns of high energy physics form a remarkably homogeneous network. Further, we utilize the knowledge of the citation distributions to demonstrate the extreme improbability that the citation records of selected individuals and institutions have been obtained by a random draw on the resulting distribution.

Anatomy of a bathtub vortex.

We present experiments and theory for the "bathtub vortex," which forms when a fluid drains out of a rotating cylindrical container through a small drain hole. The fast down-flow is found to be confined to a narrow and rapidly rotating "drainpipe" from the free surface down to the drain hole. Surrounding this drainpipe is a region with slow upward flow generated by the Ekman layer at the bottom of the container. This flow structure leads us to a theoretical model similar to one obtained earlier by Lundgren [J. Fluid Mech. 155, 381 (1985)]], but here including surface tension and Ekman upwelling, comparing favorably with our measurements. At the tip of the needlelike surface depression, we observe a bubble-forming instability at high rotation rates.

Products of random matrices.

We derive analytic expressions for infinite products of random 2 x 2 matrices. The determinant of the target matrix is log-normally distributed, whereas the remainder is a surprisingly complicated function of a parameter characterizing the norm of the matrix and a parameter characterizing its skewness. The distribution may have importance as an uncommitted prior in statistical image analysis.

Nonlinear backpropagation: doing backpropagation without derivatives of the activation function.

The conventional linear backpropagation algorithm is replaced by a nonlinear version, which avoids the necessity for calculating the derivative of the activation function. This may be exploited in hardware realizations of neural processors. In this paper we derive the nonlinear backpropagation algorithms in the framework of recurrent backpropagation and present some numerical simulations of feedforward networks on the NetTalk problem. A discussion of implementation in analog very large scale integration (VLSI) electronics concludes the paper.

Universal distribution of saliencies for pruning in layered neural networks.

A better understanding of pruning methods based on a ranking of weights according to their saliency in a trained network requires further information on the statistical properties of such saliencies. We focus on two-layer networks with either a linear or nonlinear output unit, and obtain analytic expressions for the distribution of saliencies and their logarithms. Our results reveal unexpected universal properties of the log-saliency distribution and suggest a novel algorithm for saliency-based weight ranking that avoids the numerical cost of second derivative evaluations.

Protein structures from distance inequalities.

A computer method for folding protein backbones from distance inequalities is presented. It involves an algorithm that uses a novel approach for handling inequalities through the minimization of a continuous energy function. Tests of the folding algorithm have been carried out on a small protein, the 6PTI (bovine pancreatic trypsin inhibitor) with 56 amino acid residues, and on a medium-size protein, the 1TRM (rat trypsin) with 223 amino acid residues. Reconstructions based on a real-valued distance matrix led to folded three-dimensional structures with root-mean-square values of 0.04 A when compared with the crystallographic data. The obtained root-mean-square measures were of the order of 1 A, when distance inequalities were used for the reconstruction. Subsequently, the folding approach has been applied to distance inequalities predicted by neural network techniques that use the amino acid sequence as the only input. The inaccuracy in the inequalities predicted by the neural network was the reason for the root-mean-square value of 5.2 A. An error analysis of the method for reconstruction was performed and showed that no more than 3% inaccurate distance inequalities could be corrected for. Finally, a simple technique for root-mean-square comparisons of different protein structures is discussed.

Analysis of the secondary structure of the human immunodeficiency virus (HIV) proteins p17, gp120, and gp41 by computer modeling based on neural network methods.

A neural network computer program, trained to predict secondary structure of proteins by exposing it to matching sets of primary and secondary structures from a database, was used to analyze the human immunodeficiency virus (HIV) proteins p17, gp120, and gp41 from their amino acid sequences. The results are compared to those obtained by the Chou-Fasman analysis. Two alpha-helical sequences corresponding to the putative fusigenic domain and to the transmembrane domain of gp41 could be predicted, as well as a possible binding site between p17 and gp41. On the basis of the secondary structure predictions, a three-dimensional model of p17 was constructed. This model was found to represent a stable conformation by an analysis using an energy-minimization program. The model predicts that p17 is attached to the membrane only by the acylated N-terminus, in analogy with the N-terminus of the gag protein of other retroviruses and also with the src oncogene protein p60src. The intracellular C-terminal part of gp41 may act as a receptor by electrostatic interaction with p17.

A novel approach to prediction of the 3-dimensional structures of protein backbones by neural networks.

Three-dimensional structures of protein backbones have been predicted using neural networks. A feed forward neural network was trained on a class of functionally, but not structurally, homologous proteins, using backpropagation learning. The network generated tertiary structure information in the form of binary distance constraints for the C(alpha) atoms in the protein backbone. The binary distance between two C(alpha) atoms was 0 if the distance between them was less than a certain threshold distance, and 1 otherwise. The distance constraints predicted by the trained neural network were utilized to generate a folded conformation of the protein backbone, using a steepest descent minimization approach.

Protein secondary structure and homology by neural networks. The alpha-helices in rhodopsin.

Neural networks provide a basis for semiempirical studies of pattern matching between the primary and secondary structures of proteins. Networks of the perceptron class have been trained to classify the amino-acid residues into two categories for each of three types of secondary feature: alpha-helix or not, beta-sheet or not, and random coil or not. The explicit prediction for the helices in rhodopsin is compared with both electron microscopy results and those of the Chou-Fasman method. A new measure of homology between proteins is provided by the network approach, which thereby leads to quantification of the differences between the primary structures of proteins.