Canalizing Kauffman networks: non-ergodicity and its effect on their critical behavior

Boolean Networks have been used to study numerous phenomena, including gene regulation, neural networks, social interactions, and biological evolution. Here, we propose a general method for determining the critical behavior of Boolean systems built from arbitrary ensembles of Boolean functions. In particular, we solve the critical condition for systems of units operating according to canalizing functions and present strong numerical evidence that our approach correctly predicts the phase transition from order to chaos in such systems.Comment: to be published in PR

Classification of minimal actions of a compact Kac algebra with amenable dual

We show the uniqueness of minimal actions of a compact Kac algebra with amenable dual on the AFD factor of type II$_1$. This particularly implies the uniqueness of minimal actions of a compact group. Our main tools are a Rohlin type theorem, the 2-cohomology vanishing theorem, and the Evans-Kishimoto type intertwining argument.Comment: 68 pages, Introduction rewritten; minor correction

Extracting the Groupwise Core Structural Connectivity Network: Bridging Statistical and Graph-Theoretical Approaches

Finding the common structural brain connectivity network for a given population is an open problem, crucial for current neuro-science. Recent evidence suggests there's a tightly connected network shared between humans. Obtaining this network will, among many advantages , allow us to focus cognitive and clinical analyses on common connections, thus increasing their statistical power. In turn, knowledge about the common network will facilitate novel analyses to understand the structure-function relationship in the brain. In this work, we present a new algorithm for computing the core structural connectivity network of a subject sample combining graph theory and statistics. Our algorithm works in accordance with novel evidence on brain topology. We analyze the problem theoretically and prove its complexity. Using 309 subjects, we show its advantages when used as a feature selection for connectivity analysis on populations, outperforming the current approaches

Ground state representations of loop algebras

Let g be a simple Lie algebra, Lg be the loop algebra of g. Fixing a point in S^1 and identifying the real line with the punctured circle, we consider the subalgebra Sg of Lg of rapidly decreasing elements on R. We classify the translation-invariant 2-cocycles on Sg. We show that the ground state representation of Sg is unique for each cocycle. These ground states correspond precisely to the vacuum representations of Lg.Comment: 22 pages, no figur

MySQL extension automatic porting to PDO for PHP migration and security improvement

In software management, the upgrade of programming languages may introduce critical issues. This is the case of PHP, the fifth version of which is going towards the end of the support. The new release improves on different aspects, but removes the old deprecated MySQL extensions, and supports only the newer library of functions for the connection to the databases. The software systems already in place need to be renewed to be compliant with respect to the new language version. The conversion of the source code, to be safe against injection attacks, should involve also the transformation of the query code. The purpose of this work is the design of specific tool that automatically applies the required transformation yielding to a precise and efficient conversion procedure. The tool has been applied to different projects to provide evidence of its effectiveness

Lattice dynamics and structural stability of ordered Fe3Ni, Fe3Pd and Fe3Pt alloys

We investigate the binding surface along the Bain path and phonon dispersion relations for the cubic phase of the ferromagnetic binary alloys Fe3X (X = Ni, Pd, Pt) for L12 and DO22 ordered phases from first principles by means of density functional theory. The phonon dispersion relations exhibit a softening of the transverse acoustic mode at the M-point in the L12-phase in accordance with experiments for ordered Fe3Pt. This instability can be associated with a rotational movement of the Fe-atoms around the Ni-group element in the neighboring layers and is accompanied by an extensive reconstruction of the Fermi surface. In addition, we find an incomplete softening in [111] direction which is strongest for Fe3 Ni. We conclude that besides the valence electron density also the specific Fe-content and the masses of the alloying partners should be considered as parameters for the design of Fe-based functional magnetic materials.Comment: Revised version, accepted for publication in Physical Review

Twisted duality of the CAR-Algebra

We give a complete proof of the twisted duality property M(q)'= Z M(q^\perp) Z* of the (self-dual) CAR-Algebra in any Fock representation. The proof is based on the natural Halmos decomposition of the (reference) Hilbert space when two suitable closed subspaces have been distinguished. We use modular theory and techniques developed by Kato concerning pairs of projections in some essential steps of the proof. As a byproduct of the proof we obtain an explicit and simple formula for the graph of the modular operator. This formula can be also applied to fermionic free nets, hence giving a formula of the modular operator for any double cone.Comment: 32 pages, Latex2e, to appear in Journal of Mathematical Physic

Singularities of equidistants and global centre symmetry sets of Lagrangian submanifolds

We define the Global Centre Symmetry set (GCS) of a smooth closed m-dimensional submanifold M of R^n, $n \leq 2m$, which is an affinely invariant generalization of the centre of a k-sphere in R^{k+1}. The GCS includes both the centre symmetry set defined by Janeczko and the Wigner caustic defined by Berry. We develop a new method for studying generic singularities of the GCS which is suited to the case when M is lagrangian in R^{2m} with canonical symplectic form. The definition of the GCS, which slightly generalizes one by Giblin and Zakalyukin, is based on the notion of affine equidistants, so, we first study singularities of affine equidistants of Lagrangian submanifolds, classifying all the stable ones. Then, we classify the affine-Lagrangian stable singularities of the GCS of Lagrangian submanifolds and show that, already for smooth closed convex curves in R^2, many singularities of the GCS which are affine stable are not affine-Lagrangian stable.Comment: 26 pages, 2 figure