On the center of mass of Ising vectors

We show that the center of mass of Ising vectors that obey some simple constraints, is again an Ising vector.Comment: 8 pages, 3 figures, LaTeX; Claims in connection with disordered systems have been withdrawn; More detailed description of the simulations; Inset added to figure

Mutual learning in a tree parity machine and its application to cryptography

Mutual learning of a pair of tree parity machines with continuous and discrete weight vectors is studied analytically. The analysis is based on a mapping procedure that maps the mutual learning in tree parity machines onto mutual learning in noisy perceptrons. The stationary solution of the mutual learning in the case of continuous tree parity machines depends on the learning rate where a phase transition from partial to full synchronization is observed. In the discrete case the learning process is based on a finite increment and a full synchronized state is achieved in a finite number of steps. The synchronization of discrete parity machines is introduced in order to construct an ephemeral key-exchange protocol. The dynamic learning of a third tree parity machine (an attacker) that tries to imitate one of the two machines while the two still update their weight vectors is also analyzed. In particular, the synchronization times of the naive attacker and the flipping attacker recently introduced in [1] are analyzed. All analytical results are found to be in good agreement with simulation results

Training a perceptron in a discrete weight space

On-line and batch learning of a perceptron in a discrete weight space, where each weight can take $2 L+1$ different values, are examined analytically and numerically. The learning algorithm is based on the training of the continuous perceptron and prediction following the clipped weights. The learning is described by a new set of order parameters, composed of the overlaps between the teacher and the continuous/clipped students. Different scenarios are examined among them on-line learning with discrete/continuous transfer functions and off-line Hebb learning. The generalization error of the clipped weights decays asymptotically as $exp(-K \alpha^2)$/$exp(-e^{|\lambda| \alpha})$ in the case of on-line learning with binary/continuous activation functions, respectively, where $\alpha$ is the number of examples divided by N, the size of the input vector and $K$ is a positive constant that decays linearly with 1/L. For finite $N$ and $L$, a perfect agreement between the discrete student and the teacher is obtained for $\alpha \propto \sqrt{L \ln(NL)}$. A crossover to the generalization error $\propto 1/\alpha$, characterized continuous weights with binary output, is obtained for synaptic depth $L > O(\sqrt{N})$.Comment: 10 pages, 5 figs., submitted to PR

Pectin-bioactive glass self-gelling, injectable composites with high antibacterial activity

The present work focuses on the development of novel injectable, self-gelling composite hydrogels based on two types of low esterified amidated pectins from citrus peels and apple pomace. Sol-gelderived, calcium-rich bioactive glass (BG) fillers in a particle form are applied as delivery vehicles for the release of Ca2+ ions to induce internal gelation of pectins. Composites were prepared by a relatively simple mixing technique, using 20% w/v BG particles of two different sizes (2.5 and <45 µm). Smaller particles accelerated pectin gelation slightly faster than bigger ones, which appears to result from the higher rate of Ca2+ ion release. µCT showed inhomogeneous distribution of the BG particles within the hydrogels. All composite hydrogels exhibited strong antibacterial activity against methicilin-resistant Staphylococcus aureus. The mineralization process of pectin-BG composite hydrogels occurred upon incubation in simulated body fluid for 28 days. In vitro studies demonstrated cytocompatibility of composite hydrogels with MC3T3-E1 osteoblastic cells

Van Strydonck (Guillaume)

info:eu-repo/semantics/publishe