Birational Mappings and Matrix Sub-algebra from the Chiral Potts Model

We study birational transformations of the projective space originating from lattice statistical mechanics, specifically from various chiral Potts models. Associating these models to \emph{stable patterns} and \emph{signed-patterns}, we give general results which allow us to find \emph{all} chiral $q$-state spin-edge Potts models when the number of states $q$ is a prime or the square of a prime, as well as several $q$-dependent family of models. We also prove the absence of monocolor stable signed-pattern with more than four states. This demonstrates a conjecture about cyclic Hadamard matrices in a particular case. The birational transformations associated to these lattice spin-edge models show complexity reduction. In particular we recover a one-parameter family of integrable transformations, for which we give a matrix representationComment: 22 pages 0 figure The paper has been reorganized, splitting the results into two sections : results pertaining to Physics and results pertaining to Mathematic

The random field ising model: algorithmic complexity and phase transition

The random field Ising model (RFIM) is investigated from the complexity point of view. We prove that finding a ground state of the ferromagnetic RFIM is a polynomial (P) optimization problem in any dimension d. A new rigidity algorithm for the search of the ground state morphology is also given. In contrast, the problem associated to the antiferromagnetic RFIM is shown to be an NP-complete optimization problem. The absence of any sensivity to d contrasts sharply with the known results previously obtained for the frustration model of spin glasses. Our results show, in particular, the absence of a simple one to one correspondence between finite Tc phase transition and NP-completeness properties in statistical mechanics models with competing interactions

The random field Ising model : algorithmic complexity and phase transition

The random field Ising model (RFIM) is investigated from the complexity point of view. We prove that finding a ground state of the ferromagnetic RFIM is a polynomial (P) optimization problem in any dimension d. A new rigidity algorithm for the search of the ground state morphology is also given. In contrast, the problem associated to the antiferromagnetic RFIM is shown to be an NP-complete optimization problem. The absence of any sensivity to d contrasts sharply with the known results previously obtained for the frustration model of spin glasses. Our results show, in particular, the absence of a simple one to one correspondence between finite Tc phase transition and NP-completeness properties in statistical mechanics models with competing interactions.Le modèle d'Ising en champ aléatoire (RFIM) est étudié du point de vue de la complexité algorithmique. On montre que le problème d'optimisation de la recherche d'un état de base du modèle ferromagnétique est polynomial (P) en toutes dimensions. Un nouvel algorithme de rigidité pour l'étude de la morphologie des états de base est aussi donné. Par opposition, le problème associé au modèle antiferromagnétique est démontré être NP-complet. L'absence d'une dépendance explicite de la complexité du RFIM avec la dimensionnalité contraste avec les résultats connus pour le modèle de frustration des verres de spins. Nos résultats montrent en particulier l'absence d'une correspondance simple entre les propriétés : NP-complet et existence d'une transition de phase a Tc fini dans les modèles de mécanique statistique avec des interactions en compétition

Increased postsynaptic density protein-95 expression in the frontal cortex of aged cognitively impaired rats

In the present work we studied synaptic protein concentrations in relation to behavioral performance. Long-Evans rats, aged 22-23 months, were classified for individual expression of place memory in the Morris water maze, in reference to young adults. Two main subgroups of aged rats were established: the Aged cognitively Unimpaired (AU) had search accuracy within the range (percent of time in training sector within mean ± 2 SEM) of young rats and the Aged cognitively Impaired (AI) rats had search accuracy below this range. Samples from the hippocampus and frontal cortex of all the AI, AU and young rats were analyzed for the expression of postsynaptic protein PSD-95 by Image J analysis of immunohistochemical data and by Western blots. PSD-95 expression was unchanged in the hippocampus, but, together with synaptophysin, was significantly increased in the frontal cortex of the AI rats. A significant correlation between individual accuracy (time spent in the training zone) and PSD-95 expression was observed in the aged group. No significant effect of age or PSD-95 expression was observed in the learning of a new position. All together, these data suggest that increased expression of PSD-95 in the frontal cortex of aged rats co-occurs with cognitive impairment that might be linked to functional alterations extending over frontal networks

Verkehr und Umwelt in Nordrhein-Westfalen. T. 1 Tausalz

TIB Hannover: FR 504 (1) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman