Quadratic deformation of Minkowski space

We present a deformation of the Minkowski space as embedded into the conformal space (in the formalism of twistors) based in the quantum versions of the corresponding kinematic groups. We compute explicitly the star product, whose Poisson bracket is quadratic. We show that the star product although defined on the polynomials can be extended differentiably. Finally we compute the Eucliden and Minkowskian real forms of the deformation.Comment: Presented at XVII European Workshop on String Theory 2011. Padova (Italy) September 05-09; Fortschr. Phys. 1-7 (2012

Rigorous Bounds to Retarded Learning

We show that the lower bound to the critical fraction of data needed to infer (learn) the orientation of the anisotropy axis of a probability distribution, determined by Herschkowitz and Opper [Phys.Rev.Lett. 86, 2174 (2001)], is not always valid. If there is some structure in the data along the anisotropy axis, their analysis is incorrect, and learning is possible with much less data points.Comment: 1 page, 1 figure. Comment accepted for publication in Physical Review Letter

Stability of the replica symmetric solution for the information conveyed by by a neural network

The information that a pattern of firing in the output layer of a feedforward network of threshold-linear neurons conveys about the network's inputs is considered. A replica-symmetric solution is found to be stable for all but small amounts of noise. The region of instability depends on the contribution of the threshold and the sparseness: for distributed pattern distributions, the unstable region extends to higher noise variances than for very sparse distributions, for which it is almost nonexistant.Comment: 19 pages, LaTeX, 5 figures. Also available at http://www.mrc-bbc.ox.ac.uk/~schultz/papers.html . Submitted to Phys. Rev. E Minor change

The Index Distribution of Gaussian Random Matrices

We compute analytically, for large N, the probability distribution of the number of positive eigenvalues (the index N_{+}) of a random NxN matrix belonging to Gaussian orthogonal (\beta=1), unitary (\beta=2) or symplectic (\beta=4) ensembles. The distribution of the fraction of positive eigenvalues c=N_{+}/N scales, for large N, as Prob(c,N)\simeq\exp[-\beta N^2 \Phi(c)] where the rate function \Phi(c), symmetric around c=1/2 and universal (independent of $\beta$), is calculated exactly. The distribution has non-Gaussian tails, but even near its peak at c=1/2 it is not strictly Gaussian due to an unusual logarithmic singularity in the rate function.Comment: 4 pages Revtex, 4 .eps figures include

Topological Measure Locating the Effective Crossover between Segregation and Integration in a Modular Network

We introduce an easily computable topological measure which locates the effective crossover between segregation and integration in a modular network. Segregation corresponds to the degree of network modularity, while integration is expressed in terms of the algebraic connectivity of an associated hyper-graph. The rigorous treatment of the simplified case of cliques of equal size that are gradually rewired until they become completely merged, allows us to show that this topological crossover can be made to coincide with a dynamical crossover from cluster to global synchronization of a system of coupled phase oscillators. The dynamical crossover is signaled by a peak in the product of the measures of intra-cluster and global synchronization, which we propose as a dynamical measure of complexity. This quantity is much easier to compute than the entropy (of the average frequencies of the oscillators), and displays a behavior which closely mimics that of the dynamical complexity index based on the latter. The proposed toplogical measure simultaneously provides information on the dynamical behavior, sheds light on the interplay between modularity vs total integration and shows how this affects the capability of the network to perform both local and distributed dynamical tasks

Effective Free Energy for Individual Dynamics

Physics and economics are two disciplines that share the common challenge of linking microscopic and macroscopic behaviors. However, while physics is based on collective dynamics, economics is based on individual choices. This conceptual difference is one of the main obstacles one has to overcome in order to characterize analytically economic models. In this paper, we build both on statistical mechanics and the game theory notion of Potential Function to introduce a rigorous generalization of the physicist's free energy, which includes individual dynamics. Our approach paves the way to analytical treatments of a wide range of socio-economic models and might bring new insights into them. As first examples, we derive solutions for a congestion model and a residential segregation model.Comment: 8 pages, 2 figures, presented at the ECCS'10 conferenc

Prospective Survey of AntibioticUtilization in Pediatric Hospitalized Patients to IdentifyTargets for Improvement of Prescription

Abstract. : Background: : The rise in the use of antibiotics has resulted in increasing health care costs and the emergence of resistant bacteria. Little is known about the general misuse of antibiotics in hospitalized children. We evaluated the utilization of antibiotics in a pediatric teaching hospital aiming to identify targets for improvement of prescription. Patients and Methods: : Clinical, radiological, laboratory and treatment data of patients hospitalized in a pediatric medical and a pediatric surgery ward were prospectively collected during a 6-week period. A subsequent review of the collected data by a pediatric infectious diseases specialist, taking into consideration existing in-house treatment guidelines, was carried out. Results: : A total of 125 (36%) of 349 patients was prescribed 246 antibiotics. The median length of hospital stay for children prescribed antibiotics was 5 days (range, 2-30 days) and for those not prescribed 3 days (1-32 days; p < 0.001). Of 154 patients in the medical ward, 64 (42%) received antibiotics, compared to 61 (31%) of 195 patients in the surgical ward (p < 0.05). Empirical prescriptions were more frequent than prophylactic ones, which were more frequent than therapeutic prescriptions (136 [55%] vs 94 [38%] vs 16 [7%]; p < 0.001). Overall, 85% of the prescriptions were considered justified. The rates of inappropriate prescriptions were similar in the medical and surgical ward, and higher for therapeutic (19%) or prophylactic treatment (18%) than for empirical treatment (12%). Higher inappropriate prescription rates were noted for macrolides than for co-trimoxazole and β-lactams (50% vs 18% and 15%, respectively; p < 0.05). Conclusion: : Efforts need to be undertaken towards continuous education of medical staff on judicious antibiotic use, as well as ensuring compliance with existing guidelines. Improvement in the availability of rapid diagnostic methods to discern viral from bacterial infections may help reduce the numbers of empiric therapies in favor of pathogen-targeted therapeutic treatment

Lack of benefit of preoperative antimicrobial prophylaxis in children with acute appendicitis: a prospective cohort study

Background: Preoperative antimicrobial prophylaxis is widely used in pediatric patients undergoing appendectomy, but evidence showing a reduction of postoperative infectious complications is lacking. Methods: A prospective consecutive cohort study on changing from preoperative antimicrobial prophylaxis to no prophylaxis in children undergoing urgent appendectomy was undertaken. The impact of this change in management on postoperative infectious complications was evaluated by comparing the outcome in 100 patients receiving (group A) and a subsequent 100 patients not receiving prophylaxis (group B), which consisted of a preoperative single dose of intravenous metronidazole (10mg/kg body weight). Results: Histology confirmed acute appendicitis in 92 patients of group A and 95 patients of group B. In patients with histological simple appendicitis, postoperative infectious complications were noted in 2 (3.0%) of 69 patients from group A and in none of 70 patients from group B, and in patients with histological perforated appendicitis in 5 (22%) of 23 and 4 (16%) of 25 patients from groups A and B, respectively. Postoperative infectious complications were more frequent (p<0.05) in perforated than in simple appendicitis. These infectious complications included in simple appendicitis two wound infections in group A, and in perforated appendicitis four intraabdominal abscesses and one wound infection in group A and two intraabdominal abscesses and two wound infections in group B. Conclusion: Postoperative infectious complications were seen more often in patients with perforated appendicitis than in those with simple appendicitis. Preoperative antimicrobial prophylaxis with metronidazole did not reduce the rates of postoperative infectious complication