Scientific Reports
The preprint collection of the Department of Mathematics.
Full-text generally not available for preprints prior to may 2006.
Found 866 products
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QDD225 - 03/20/2017
Bertacchi D.; Coletti C.F.; Zucca F.
Global survival of branching random walks and tree-like branching random walks | Abstract | | The local critical parameter $lambda_s$ of continuous-time branching random walks is completely understood and can be computed as a function of the reproduction rates. On the other hand, only for some classes of branching random walks it is known that the global critical parameter $lambda_w$ is a certain function of the reproduction rates, which we denote by $ 1/K_w$. We provide here new sufficient conditions which guarantee that the global critical parameter equals $ 1/K_w$. This result extends previously known results for branching random walks on multigraphs and general branching random walks.
We show that these sufficient conditions are satisfied by periodic tree-like branching random walks.
We also discuss the critical parameter and the critical behaviour of continuous-time branching processes in varying environment.
So far, only examples where $lambda_w=1/K_w$ were known; here we
provide an example where $lambda_w>1/K_w$. |
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QDD224 - 11/10/2016
Zucca F.; Bertacchi D.; Rodriguez P.M.
Galton-Watson processes in varying environment and accessibility percolation | Abstract | | This paper deals with branching processes in varying environment, namely, whose offspring distributions depend on the
generations. We provide sufficient conditions for survival or extinction which rely only on the first and second moments of the
offspring distributions. These results are then applied
to branching processes in varying environment with selection where every particle has a real-valued label and labels can only increase along
genealogical lineages;
we obtain analogous conditions for survival or extinction. These last results can be interpreted in terms of
accessibility percolation on Galton-Watson trees, which represents a relevant tool for modeling the evolution of biological populations. |
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QDD223 - 08/27/2016
Pellacci, B.; Verzinii, G.
Optimization of the positive principal eigenvalue for indefinite fractional Neumann problems | Abstract | | We study the positive principal eigenvalue of a weighted problem associated with the Neumann spectral fractional Laplacian. This analysis is related to the investigation of the survival threshold in population dynamic. Our main result concerns the optimization of such eigenvalue with respect to the fractional order s in (0,1], the case s = 1 corresponding to the standard Neumann Laplacian: when the habitat is not too hostile in average, the principal positive eigenvalue can not have local minima for 0 < s < 1. As a consequence, the best strategy for survival is either following the diffusion with the lowest possible s, or with s = 1, depending on the size of the domain. In addition, we show that analogous results hold for the standard fractional Laplacian in the whole space , in periodic environments. |
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QDD221 - 07/16/2016
Cipriani, F.
Noncommutative PotentialTheory: a survay | Abstract | | The aim of these notes is to provide an introduction to Noncommutative Potential Theory as given at I.N.D.A.M.-C.N.R.S. "Noncommutative Geometry and Applications" Lectures, Villa Mondragone-Frascati June 2014. |
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QDD222 - 07/16/2016
Pierotti, D.; Verzini, G.
Normalized bound states for the nonlinear Schrödinger equation in bounded domains | Abstract | | We investigate the standing wave solutions with prescribed mass (or charge) of the nonlinear Schrödinger equation with power nonlinearity, in a bounded domain of dimension N and with Dirichlet boundary condition. Assuming that the exponent p>1 of the nonlinear term is Sobolev-subcritical, it follows by the Gagliardo-Nirenberg inequality that there are solutions of any positive mass whenever p is less than the critical value 1+4/N. If p is equal or larger than 1+4/N, we prove that there are solutions having Morse index bounded above (by some positive integer k) only for sufficiently small masses. Lower bounds on these intervals of allowed masses are then obtained, by suitable variational principles, in terms of the Dirichlet eigenvalues of the Laplacian. |
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QDD220 - 03/21/2016
Lember, J.; Matzinger, H., Sova, J.; Zucca, F.
Lower bounds for moments of global scores of pairwise Markov chains | Abstract | | Let us consider two random sequences such
that every random variable takes values in a finite set. We consider a global similarity score that measures the homology
(relatedness) of words obtained by the random sequences. A
typical example of such score is the length of the longest common
subsequence. We study the order of central absolute r-moment of the score
in the case where the two-dimensional joint process represented by the two random sequences is a Markov chain. This is a very general model involving independent
Markov chains, hidden Markov models, Markov switching models and
many more. Our main result establishes a general condition which allows to
obtain an explicit asymptotic value of the central absolute r-moment of the score. We also perform simulations indicating the validity of the condition. |
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QDD219 - 12/10/2015
Cipriani, F.; Sauvageot, J.-L.
Negative definite functions on groups with polynomial growth | Abstract | | The aim of this work is to show that on a locally compact, second countable, compactly generated group G with polynomial growth and homogeneous dimension $d_h$, there exist a continuous, proper, negative definite function $ell$ with polynomial growth dimension $d_ell$ arbitrary close to $d_h$. |
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QDD218 - 11/30/2015
Cirant, M.; Verzini, G.
Bifurcation and segregation in quadratic two-populations Mean Field Games systems | Abstract | | We consider a two-populations ergodic Mean Field Games system, which describes Nash equilibria in differential games with identical players. In these models, each population consists of a very large number of indistinguishable rational agents, aiming at minimizing some long-time average criterion. Via the Hopf-Cole transformation, such system reduces to a semilinear elliptic one, for normalized densities. Firstly, we discuss existence of nontrivial solutions; secondly, for selected families of nontrivial solutions, we address the appearing of segregation in the vanishing viscosity limit. |
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