A model employing separate dose-dependent response functions for proliferation and differentiation of idiotypically interacting $B$ cell clones is presented. For each clone the population dynamics of proliferating $B$ cells, non-proliferating $B$ cells and free antibodies are considered. An...

We present explicit formulae for one-step evolution of the overlaps in a clock neural network for the parallel dynamics. These formulae constitute recursion relations for the exact dynamics in the case of extreme dilution. The fixed point equation for this exactly soluble model is investigated...

We have considered a classical system, consisting of particles with centre-of-mass coordinates x∈Rd and equipped with a one-component spin σx∈R1; their pairwise additive interaction potential is defined by W(x,σx,y,σy)=Φ(∥x−y∥)−J(∥x−y∥)σxσy, where Φ(∥x−y∥) contains...

We consider dependence of the critical fluctuation operators on the rate of interaction decay for an exactly soluble model of the quantum anharmonic crystal of ferroelectric type. The critical exponents for the abnormal behavior of the displacement and momentum fluctuation operators on the...