Long-range interactions in Sznajd consensus model

The traditional Sznajd model, as well as its Ochrombel simplification, for opinion spreading are modified to have a convincing strength proportional to a negative power of the spatial distance. We find the usual phase transition in the full Sznajd model, but not in the Ochrombel simplification. We also mix the two rules, which favours a phase transition.Comment: Not ye4t submittted, waiting for your comments; 6 page

Using polyhedral models to automatically sketch idealized geometry for structural analysis

Simplification of polyhedral models, which may incorporate large numbers of faces and nodes, is often required to reduce their amount of data, to allow their efficient manipulation, and to speed up computation. Such a simplification process must be adapted to the use of the resulting polyhedral model. Several applications require simplified shapes which have the same topology as the original model (e.g. reverse engineering, medical applications, etc.). Nevertheless, in the fields of structural analysis and computer visualization, for example, several adaptations and idealizations of the initial geometry are often necessary. To this end, within this paper a new approach is proposed to simplify an initial manifold or non-manifold polyhedral model with respect to bounded errors specified by the user, or set up, for example, from a preliminary F.E. analysis. The topological changes which may occur during a simplification because of the bounded error (or tolerance) values specified are performed using specific curvature and topological criteria and operators. Moreover, topological changes, whether or not they kept the manifold of the object, are managed simultaneously with the geometric operations of the simplification process

Region-specific dendritic simplification induced by Aβ, mediated by tau via dysregulation of microtubule dynamics: a mechanistic distinct event from other neurodegenerative processes.

BackgroundDendritic simplification, a key feature of the neurodegenerative triad of Alzheimer's disease (AD) in addition to spine changes and neuron loss, occurs in a region-specific manner. However, it is unknown how changes in dendritic complexity are mediated and how they relate to spine changes and neuron loss.ResultsTo investigate the mechanisms of dendritic simplification in an authentic CNS environment we employed an ex vivo model, based on targeted expression of enhanced green fluorescent protein (EGFP)-tagged constructs in organotypic hippocampal slices of mice. Algorithm-based 3D reconstruction of whole neuron morphology in different hippocampal regions was performed on slices from APPSDL-transgenic and control animals. We demonstrate that induction of dendritic simplification requires the combined action of amyloid beta (Aβ) and human tau. Simplification is restricted to principal neurons of the CA1 region, recapitulating the region specificity in AD patients, and occurs at sites of Schaffer collateral input. We report that γ-secretase inhibition and treatment with the NMDA-receptor antagonist, CPP, counteract dendritic simplification. The microtubule-stabilizing drug epothilone D (EpoD) induces simplification in control cultures per se. Similar morphological changes were induced by a phosphoblocking tau construct, which also increases microtubule stability. In fact, low nanomolar concentrations of naturally secreted Aβ decreased phosphorylation at S262 in a cellular model, a site which is known to directly modulate tau-microtubule interactions.ConclusionsThe data provide evidence that dendritic simplification is mechanistically distinct from other neurodegenerative events and involves microtubule stabilization by dendritic tau, which becomes dephosphorylated at certain sites. They imply that treatments leading to an overall decrease of tau phosphorylation might have a negative impact on neuronal connectivity