Estimating population size from multiple recapture experiments

AbstractThe size of a closed population is to be estimated using data from a multiple recapture study in either continuous or discrete time. Here the use of maximum likelihood raises computational problems. However, a family of martingale estimating functions related to the score function is shown to produce convenient simple estimators with good asymptotic efficiency relative to the maximum likelihood estimator

The Multidimensional Study of Viral Campaigns as Branching Processes

Viral campaigns on the Internet may follow variety of models, depending on the content, incentives, personal attitudes of sender and recipient to the content and other factors. Due to the fact that the knowledge of the campaign specifics is essential for the campaign managers, researchers are constantly evaluating models and real-world data. The goal of this article is to present the new knowledge obtained from studying two viral campaigns that took place in a virtual world which followed the branching process. The results show that it is possible to reduce the time needed to estimate the model parameters of the campaign and, moreover, some important aspects of time-generations relationship are presented.Comment: In proceedings of the 4th International Conference on Social Informatics, SocInfo 201

External Fluctuations in a Pattern-Forming Instability

The effect of external fluctuations on the formation of spatial patterns is analysed by means of a stochastic Swift-Hohenberg model with multiplicative space-correlated noise. Numerical simulations in two dimensions show a shift of the bifurcation point controlled by the intensity of the multiplicative noise. This shift takes place in the ordering direction (i.e. produces patterns), but its magnitude decreases with that of the noise correlation length. Analytical arguments are presented to explain these facts.Comment: 11 pages, Revtex, 10 Postscript figures added with psfig style (included). To appear in Physical Review

On Low-Energy Effective Actions in N = 2, 4 Superconformal Theories in Four Dimensions

We study some aspects of low-energy effective actions in 4-d superconformal gauge theories on the Coulomb branch. We describe superconformal invariants constructed in terms of N=2 abelian vector multiplet which play the role of building blocks for the N=2,4 supersymmetric low-energy effective actions. We compute the one-loop effective actions in constant N=2 field strength background in N=4 SYM theory and in N=2 SU(2) SYM theory with four hypermultiplets in fundamental representation. Using the classification of superconformal invariants we then find the manifestly N=2 superconformal form of these effective actions. While our explicit computations are done in the one-loop approximation, our conclusions about the structure of the effective actions in N=2 superconformal theories are general. We comment on some applications to supergravity - gauge theory duality in the description of D-brane interactions.Comment: 18 pages, latex, comments/reference adde

Coset Space Dimensional Reduction and Wilson Flux Breaking of Ten-Dimensional N=1, E(8) Gauge Theory

We consider a N=1 supersymmetric E(8) gauge theory, defined in ten dimensions and we determine all four-dimensional gauge theories resulting from the generalized dimensional reduction a la Forgacs-Manton over coset spaces, followed by a subsequent application of the Wilson flux spontaneous symmetry breaking mechanism. Our investigation is constrained only by the requirements that (i) the dimensional reduction leads to the potentially phenomenologically interesting, anomaly free, four-dimensional E(6), SO(10) and SU(5) GUTs and (ii) the Wilson flux mechanism makes use only of the freely acting discrete symmetries of all possible six-dimensional coset spaces.Comment: 45 pages, 2 figures, 10 tables, uses xy.sty, longtable.sty, ltxtable.sty, (a shorter version will be published in Eur. Phys. J. C

Recent results on multiplicative noise

Recent developments in the analysis of Langevin equations with multiplicative noise (MN) are reported. In particular, we: (i) present numerical simulations in three dimensions showing that the MN equation exhibits, like the Kardar-Parisi-Zhang (KPZ) equation both a weak coupling fixed point and a strong coupling phase, supporting the proposed relation between MN and KPZ; (ii) present dimensional, and mean field analysis of the MN equation to compute critical exponents; (iii) show that the phenomenon of the noise induced ordering transition associated with the MN equation appears only in the Stratonovich representation and not in the Ito one, and (iv) report the presence of a new first-order like phase transition at zero spatial coupling, supporting the fact that this is the minimum model for noise induced ordering transitions.Comment: Some improvements respect to the first versio

Stability and collapse of localized solutions of the controlled three-dimensional Gross-Pitaevskii equation

On the basis of recent investigations, a newly developed analytical procedure is used for constructing a wide class of localized solutions of the controlled three-dimensional (3D) Gross-Pitaevskii equation (GPE) that governs the dynamics of Bose-Einstein condensates (BECs). The controlled 3D GPE is decomposed into a two-dimensional (2D) linear Schr\"{o}dinger equation and a one-dimensional (1D) nonlinear Schr\"{o}dinger equation, constrained by a variational condition for the controlling potential. Then, the above class of localized solutions are constructed as the product of the solutions of the transverse and longitudinal equations. On the basis of these exact 3D analytical solutions, a stability analysis is carried out, focusing our attention on the physical conditions for having collapsing or non-collapsing solutions.Comment: 21 pages, 14 figure