We report on our recent studies of the large N renormalization group (RG) method which clariies phase structure of random matrix models. We derive an exact RG equation which enables us to obtain the exact locations of xed points and their scaling exponents. The classiication of phases is given by this analysis. A linear approximation visualizes the RG ow of crossover phenomena including several...

Xia’s algorithm consists of a reduction algorithm and a translation procedure both originally used to tackle the xed point property for ordered sets. We present results that show that the translation procedure allows access to a much wider range of problems and results showing that the algorithm is very e cient when applied to the xed point property in ordered sets or for order=graph isomorphis...

We report numerical and analytical studies of the nite size time scales in a system with microscopic stochastic dynamics which in the bulk limit corresponds to an evolution equation with an accumulation point of critical xed points. Our results suggest that the nite size behavior is dominated not by uctuations but by the bottleneck statistical weights at near-xed-point conditions in a nite-size...

Associative recall and completion of information is one of the astonishing abilities of intelligent living beings. The search for mechanisms which produce this ability of associative memory yielded a class of computational systems composed of many neuron-like, non-linear units. The neural units are connected to artiicial neural networks. The basic principle of associative information recall is ...

This paper provides a systematic solvability analysis for (generalized) variational inequalities on separable Hilbert lattices. By contrast to a large part of the existing literature, our approach is lattice-theoretic, and is not based on topological …xed point theory. This allows us to establish the solvability of certain types of (generalized) variational inequalities without requiring the in...

The complex-logarithmic number system (CLNS), which represents each complex point in log/polar coordinates, may be practical to implement the Fast Fourier Transform (FFT). The roots of unity needed by the FFT have exact representations in CLNS and do not require a ROM. We present an error analysis and simulation results for a radix-two FFT that compares a rectangular xed-point representation of...

Synopsis. We introduce a domain-theoretic foundation for disjunctive logic programming. This foundation is built on clausal logic, a representation of the Smyth powerdomain of a coherent algebraic dcpo. The robustness of this approach comes from the agreement bewteen the declarative semantics and the xed-point semantics, as well as the agreement between the xed-point semantics and the semantics...

We investigate circuit complexity under the additional assumption of full combinatorial symmetry with respect to permutations of the input representation. With this approach we derive a very natural and simple characterization of rst-order logic and its innnitary variant with bounded numbers of variables over nite structures. Extending these results to not necessarily acyclic boolean networks, ...

In this paper we summarize a dual-time scale formulation of dynamic user equilibrium with demand growth due to Friesz et al (2008). This formulation belongs to the problem class that Pang and Stewart (2008) refer to as di¤erential variational inequalities. We also present a …xed point algorithm for computing solutions to the dual time-scale model without calculating derivatives, along with a nu...

A dynamic antigen response of the immune network is discussed, based on shape-space modelling. The present model extends the shape-space modelling by introducing the evolution of speci"city of idiotypes. When the amount of external antigen increases, a measure of stability of the immune network is lost and thus the network can respond to the antigen. It is shown that speci"c and non-speci"c res...