We present results for two different kinds of high order connections between neurons acting as corrections to the Hopfield model. Equilibrium properties are analyzed using the replica mean-field theory and compared with numerical simulations. An optimal learning algorithm for fourth order connections is given that improves the storage capacity without increasing the weight of the higher order t...

Using the Dirac constraint method we show that the pure fourth-order PaisUhlenbeck oscillator model is free of observable negative norm states. Even though such ghosts do appear when the fourth order theory is coupled to a second order one, the limit in which the second order action is switched off is found to be a highly singular one in which these states move off shell. Given this result, con...

A topic of present interest is the application of experimentally observed quantum mechanical levels of ultra-cold neutrons in the earth’s gravitational field for searching short-range modifications to gravity. A constraint on new forces in the nanometer-range published by Nesvizhevsky and Protasov follows from inadequate modelling of the interaction potential of a neutron with a mirror wall. Li...

This paper deals with the existence of traveling fronts for the reaction-diffusion equation: ∂u ∂t −∆u = h(u, y) t ∈ R, x = (x1, y) ∈ R . We first consider the case h(u, y) = f(u) − αg(y)u where f is of KPP or bistable type and lim|y|→+∞ g(y) = +∞. This equation comes from a model in population dynamics in which there is spatial spreading as well as genetic mutation of a quantitative genetic tr...

Triterpene saponins are a diverse group of biologically functional products in plants. Saponins usually are glycosylated, which gives rise to a wide diversity of structures and functions. In the group A saponins of soybean (Glycine max), differences in the terminal sugar species located on the C-22 sugar chain of an aglycone core, soyasapogenol A, were observed to be under genetic control. Furt...

Since there are some important systems which have constraints not contained in their field algebras, we develop here in a C*-context the algebraic structures of these. The constraints are defined as a group G acting as outer automorphisms on the field algebra J^, α:Gι-> Aut $F, αG φ Inn J^, and we find that the selection of G-invariant states on 3F is the same as the selection of states ω on M(...

We show that small solids in low mass, turbulent protoplanetary disks collect into self-gravitating rings. Growth is faster than disk lifetimes and radial drift times for moderately strong turbulence, characterized by dimensionless diffusivities, αg . 10 —10 when particles are mm-sized. This range reflects a strong dependance on disk models. Growth is faster for higher particle surface densitie...

Interleukin-1 receptor-associated kinases (IRAKs) are Ser/Thr protein kinases that play an important role as signaling mediators in the signal transduction facilitated by the Toll-like receptor (TLR) and interleukin-1 receptor families. Among IRAK family members, IRAK4 is one of the drug targets for diseases related to the TLR and IL-1R signaling pathways. Experimental evidence suggests that th...

Given a finite group G acting as automorphisms on a ring A, the skew group ring A∗G is an important tool for studying the structure of G-stable ideals of A. The ring A∗G is G-graded, i.e.G coacts on A∗G. The Cohen-Montgomery duality says that the smash product A ∗ G#k[G]∗ of A ∗ G with the dual group ring k[G]∗ is isomorphic to the full matrix ring Mn(A) over A, where n is the order of G. In th...

New upper bounds on codes are presented. The bounds are obtained by linear and semidefinite programming. INTRODUCTION One of the central problems in coding theory is to find upper bounds on maximum size Aq(n, d) of a code of word length n and minimum Hamming distance at least d over the alphabet Q of q ≥ 2 letters. Let us provide Q with the structure of an Abelian group, in an arbitrary way. In...