Comment on "Emergence of prime numbers as the result of evolutionary strategy".
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Comment↗
Biomedical subjects
E Goles
Publications and source records attributed to E Goles.
Swirling granular solidlike clusters
Experiments and three-dimensional numerical simulations are presented to elucidate the dynamics of granular material in a cylindrical dish driven by a horizontal, periodic motion. The following phenomena are obtained both in the experiments and in the simulations: First, for large particle numbers N the particles describe hypocycloidal trajectories. In this state the particles are embedded in a solidlike cluster ("pancake") which counter-rotates with respect to the external driving (reptation). Self-organization within the cluster occurs such that the probability distribution of the particles consists of concentric rings. Second, the system undergoes phase transitions. These can be identified by changes of the quantity dE(kin)/dN (E(kin) is the mean kinetic energy) between zero (rotation), positive (reptation), and negative values (appearance of the totality of concentric rings).
Journal Article↗
Intermingled basins due to finite accuracy
We investigate numerically first a chaotic map interrupted by two small neighborhoods, each containing an attracting point, and secondly a periodically tilted box within which disorderly colliding disks can reach different attracting configurations, due to dissipation. For finite, arbitrarily small accuracy, both systems have basins of attraction that are indistinguishable from intermingled basins: any neighborhood of a point in phase space leading to one attractor contains points leading to the other attractor. A bifurcation destabilizing the fixed points or the disk configurations causes on-off intermittency; the disks then alternate between a "frozen" and a gaslike state.
Journal Article↗
Dynamical properties of min-max networks.
In this paper we study the dynamical behavior of a class of neural networks where the local transition rules are max or min functions. We prove that sequential updates define dynamics which reach the equilibrium in O(n2) steps, where n is the size of the network. For synchronous updates the equilibrium is reached in O(n) steps. It is shown that the number of fixed points of the sequential update is at most n. Moreover, given a set of p < or = n vectors, we show how to build a network of size n such that all these vectors are fixed points.
Mathematics↗
Shell structures with "magic numbers" of spheres in a swirled dish.
Molecular dynamic simulations of a low number N< or = 54 of spheres in a swirled dish yield solid-like shell structures with stable rings. In contrast to known granular media, solidification occurs only at singular values of N: 7, 8, 12, 14, 19, 21, 30, 37, 40. Otherwise, we obtain intermittent switching of particles between rings -- the average switching time scaling exponentially with a control parameter -- or fluid-like disorder. Stable shell structures can be classified by particular geometrical arrangements (one-centered hexagonal, one-centered "quasicircular," three centered, and four centered).
Journal Article↗
Dynamical and complexity results for high order neural networks.
We present dynamical results concerning neural networks with high order arguments. More precisely, we study the family of block-sequential iteration of neural networks with polynomial arguments. In this context, we prove that, under a symmetric hypothesis, the sequential iteration is the only one of this family to converge to fixed points. The other iteration modes present a highly complex dynamical behavior: non-bounded cycles and simulation of arbitrary non-symmetric linear neural network. We also study a high order memory iteration scheme which accepts an energy functional and bounded cycles in the size of the memory steps.
Computer Simulation↗