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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QDD63 - 03/25/2010
Zucca, F.
Survival, extinction and approximation of discrete-time branching random walks | Abstract | | We consider a general discrete-time branching random walk on a countable set X. We relate local and global survival with suitable inequalities involving the first-moment matrix M of the process. In particular we prove that, while the local behavior is characterized by M, the global
behavior cannot be completely described in terms of properties involving M alone. Moreover we show that locally surviving branching random walks can be approximated by sequences of spatially confined and stochastically dominated branching random walks which eventually survive locally if the (possibly finite) state space is large enough. An analogous result can be achieved by
approximating a branching random walk by a sequence of multitype contact processes and allowing a sufficiently large number of particles per site. We compare these results with the ones obtained in the continuous-time case and we give some examples and counterexamples. |
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QDD62 - 03/01/2010
Brera, M. ; Jerome, J.W. ; Mori, Y. ; Sacco, R.
A Conservative and Monotone Mixed-Hybridized Finite Element Approximation of Transport Problems in Heterogeneous Domains | Abstract | | In this article, we discuss the numerical approximation of transport phenomena occurring at material interfaces between physical subdomains with heterogenous properties. The model in each subdomain consists of a partial differential equation with diffusive, convective and reactive terms, the coupling between each subdomain being realized through an interface transmission condition of Robin type. The numerical approximation of the problem in the two-dimensional case is carried out through a dual mixed-hybridized finite element method with numerical quadrature of the mass flux matrix.
The resulting method is a conservative finite volume scheme over triangular grids, for which a discrete maximum principle is proved under the assumption that the mesh is of Delaunay type in the interior of the domain and of weakly acute type along the domain external boundary and internal interface. The stability, accuracy and robustness of the proposed method are validated on several numerical examples motivated by applications in Biology, Electrophysiology and Neuroelectronics.
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QDD61 - 02/04/2010
C.D. Pagani; D. Pierotti
Multiple variational solutions to nonlinear Steklov problems | Abstract | | We consider the problem of finding a harmonic function in a bounded domain, satisfying a nonlinear Steklov boundary condition with indefinite weight functions. The non linear term is represented by a continuously differentiable odd function with superlinear and subcritical growth at infinity. By using variants of the mountain pass lemma based on index theory, we discuss existence and multiplicity of non trivial solutions to the problem. |
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QDD60 - 12/11/2009
CARRIERO, M.; LEACI, A.; TOMARELLI, F.
Uniform density estimates for Blake & Zisserman functional | Abstract | | We prove density estimates and elimination properties for minimizing triplets of functionals which are related to contour detection in image segmentation and depend on free discontinuities, free gradient discontinuities and second order derivatives. All the estimates concern optimal segmentation under Dirichlet boundary conditions and are uniform in the image domain up to the boundary. |
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QDD59 - 11/26/2009
Citterio, M.; Pavani, R.
About k-digit rational approximations | Abstract | | We focus on the computation of best k-digit rational bounds for a given irrational number. We present new results, which allow to implement a reliable
very fast algorithm whose computational time increases at most linearly with k. Several numerical examples are reported. |
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QDD57 - 11/19/2009
Bertacchi, D.; Lanchier, N.; Zucca, F.
Contact and voter processes on the infinite percolation cluster as models of host-symbiont interactions | Abstract | | We introduce spatially explicit stochastic processes to model multispecies hostsymbiont interactions. The host environment is static, modeled by the infinite percolation cluster of site percolation. Symbionts evolve on the infinite cluster through contact or voter type interactions, where each host may be infected by a colony of symbionts. In the presence of a single symbiont species, the condition for invasion as a function of the density of the habitat of hosts and the maximal size of the colonies is investigated in details. In the presence of multiple symbiont species, it is proved that the community of symbionts clusters in two dimensions whereas symbiont species may coexist in higher dimensions. |
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QDD58 - 11/19/2009
Belhadji, L.; Bertacchi, D.; Zucca, F.
A self-regulating and patch subdivided population | Abstract | | We consider an interacting particle system on a graph which, from a macroscopic point of view,
looks like ${ mathbb Z}^d$ and, at a microscopic level, is a complete graph of degree $N$ (called a patch).
There are two birth rates: an inter-patch one $ lambda$ and an intra-patch one $ phi$. Once a
site is occupied, there is no breeding from outside the patch and the probability $c(i)$ of success of an intra-patch breeding decreases with the size $i$ of the population in the site. We prove the existence of a critical value $ lambda_{cr}( phi, c, N)$ and a critical value $ phi_{cr}( lambda, c, N)$.
We consider a sequence of processes generated by the families of control functions $ {c_i }_{i in N}$ and degrees $ {N_i }_{i in { mathbb N}}$; we prove, under mild assumptions, the existence of a critical value $i_{cr}( lambda, phi,c)$. Roughly speaking we show that, in the limit, these processes behave as the branching random walk on ${ mathbb Z}^d$ with intra-neighbor birth rate $ lambda$ and on-site birth rate $ phi$.
Some examples of models that can be seen as particular cases are given. |
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QDD54 - 11/06/2009
Berchio, E ; Gazzola, F.
Positive solutions to a linearly perturbed critical growth biharmonic problem | Abstract | | Existence and nonexistence results for positive solutions to a linearly perturbed critical growth biharmonic problem under Steklov boundary conditions, are determined. Furthermore, by investigating the critical dimensions for this problem, a Sobolev inequality with remainder terms, of both interior and boundary type, is deduced. |
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