IFSM representation of Brownian motion with applications to simulation

Several methods are currently available to simulate paths of the Brownian motion. In particular, paths of the BM can be simulated using the properties of the increments of the process like in the Euler scheme, or as the limit of a random walk or via L2 decomposition like the Kac-Siegert/Karnounen-Loeve series. In this paper we first propose a IFSM (Iterated Function Systems with Maps) operator whose fixed point is the trajectory of the BM. We then use this representation of the process to simulate its trajectories. The resulting simulated trajectories are self-affine, continuous and fractal by construction. This fact produces more realistic trajectories than other schemes in the sense that their geometry is closer to the one of the true BM's trajectories. The IFSM trajectory of the BM can then be used to generate more realistic solutions of stochastic differential equations

Blazar Flaring Patterns (B-FlaP): Classifying Blazar Candidates of Uncertain type in the third Fermi-LAT catalog by Artificial Neural Networks

The Fermi Large Area Telescope (LAT) is currently the most important facility for investigating the GeV $\gamma$-ray sky. With Fermi LAT more than three thousand $\gamma$-ray sources have been discovered so far. 1144 ($\sim40\%$) of the sources are active galaxies of the blazar class, and 573 ($\sim20\%$) are listed as Blazar Candidate of Uncertain type (BCU), or sources without a conclusive classification. We use the Empirical Cumulative Distribution Functions (ECDF) and the Artificial Neural Networks (ANN) for a fast method of screening and classification for BCUs based on data collected at $\gamma$-ray energies only, when rigorous multiwavelength analysis is not available. Based on our method, we classify 342 BCUs as BL Lacs and 154 as FSRQs, while 77 objects remain uncertain. Moreover, radio analysis and direct observations in ground-based optical observatories are used as counterparts to the statistical classifications to validate the method. This approach is of interest because of the increasing number of unclassified sources in Fermi catalogs and because blazars and in particular their subclass High Synchrotron Peak (HSP) objects are the main targets of atmospheric Cherenkov telescopes.Comment: 18 pages, 17 figures, accepted for publication on MNRA

A Pedestrian Introduction to Gamow Vectors

The Gamow vector description of resonances is compared with the S-matrix and the Green function descriptions using the example of the square barrier potential. By imposing different boundary conditions on the time independent Schrodinger equation, we obtain either eigenvectors corresponding to real eigenvalues and the physical spectrum or eigenvectors corresponding to complex eigenvalues (Gamow vectors) and the resonance spectrum. We show that the poles of the S matrix are the same as the poles of the Green function and are the complex eigenvalues of the Schrodinger equation subject to a purely outgoing boundary condition. The intrinsic time asymmetry of the purely outgoing boundary condition is discussed. Finally, we show that the probability of detecting the decay within a shell around the origin of the decaying state follows an exponential law if the Gamow vector (resonance) contribution to this probability is the only contribution that is taken into account.Comment: 25 RevTex pages, 3 figure

Cosmology with two compactification scales

We consider a (4+d)-dimensional spacetime broken up into a (4-n)-dimensional Minkowski spacetime (where n goes from 1 to 3) and a compact (n+d)-dimensional manifold. At the present time the n compactification radii are of the order of the Universe size, while the other d compactification radii are of the order of the Planck length.Comment: 16 pages, Latex2e, 7 figure

Preserving Value in the Post-BAPCPA Era — An Empirical Study

Through the use of a multivariate regression model, this article studies the effect on debtor reorganization values of the shortened reorganization timeframe imposed by the Bankruptcy Abuse Prevention and Consumer Protection Act (“BAPCPA”). The study shows that BAPCPA is positively correlated at a statistically significant level with higher reorganization recoveries. This result is attributed to the increased proportion of prepackaged and prenegotiated bankruptcies observed in the post-2005 era, as these “fast-track” bankruptcy cases entail lower costs and better preserve the firm’s value

The synergistic effect between positivity, socio-demographic factors and smoking cessation: results of a cohort study

OBJECTIVE: To examine the extent to which a effect does exist between Positivity (POS), smoking and socio-demographic factors in determining quitting smoking in subjects participating in a Group Counselling Program (GCP) for smoking cessation.METHODS: 481 subjects were contacted through a telephone call. A logistic regression analysis was carried out. Possible interaction between sociodemographic variables and POS level was tested using the Synergism Index (SI).RESULTS: For individuals with a POS level over or equal to 3.4 the odds of being smoker was significantly higher among females (OR = 1.55), who smoked at home (OR = 2.16) and lower if there had children at home (OR = 0.53). For individuals with a POS level under 3.4, the only significant variable associated with smoking was beinga female (OR = 2.58). As far concerns the synergistic effect between the variables considered does exist between POS levels and having children at home (SI=1.13) and female gender (SI = 2.8).CONCLUSIONS: The synergistic effect between POS and sociodemographic factors adds evidence on the use of POS as possible determinants of individual happiness