Quaderni di Dipartimento
Collezione dei preprint del Dipartimento di Matematica.
La presenza del full-text è lacunosa per i prodotti antecedenti maggio 2006.
Trovati 866 prodotti
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QDD217 - 26/11/2015
Bertacchi, D.; Zucca, F.
A generating function approach to branching random walks | Abstract | | It is well known that the behaviour of a branching process is completely described by the generating function of the o ffspring law and its fi xed points. Branching random walks are a natural generalization of branching processes: a branching process can be seen as a one-dimensional
branching random walk. We defi ne a multidimensional generating function associated to a given branching random walk. The present paper investigates the similarities and the di fferences of the generating functions, their fi xed points and the implications on the underlying stochastic process,
between the one-dimensional (branching process) and the multidimensional case (branching random walk). In particular, we show that the generating function of a branching random walk can
have uncountably many fixed points and a fixed point may not be an extinction probability, even in the irreducible case (extinction probabilities are always fixed points). Moreover, the generating
function might not be a convex function. We also study how the behaviour of a branching random walk is aff ected by local modi cations of the process. As a corollary, we describe a general procedure by which we can modify a continuous-time branching random walk which has a weak
phase and turn it into a continuous-time branching random walk which has strong local survival for large or small values of the parameter and non-strong local survival for intermediate values of the parameter. |
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QDD216 - 11/11/2015
Bramanti, M.; Fanciullo, M. S.
The local sharp maximal function and BMO on locally homogeneous spaces | Abstract | | We prove a local version of Fefferman-Stein inequality for the local sharp maximal function, and a local version of John-Nirenberg inequality for locally BMO functions, in the framework of locally homogeneous spaces, in the sense of Bramanti-Zhu [Manuscripta Math. 138 (2012), no. 3-4, 477-528]. |
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QDD215 - 11/11/2015
Bramanti, M.; Toschi, M.
The sharp maximal function approach to L^p estimates for operators structured on Hörmander's vector fields | Abstract | | We consider a nonvariational degenerate elliptic operator structured on a system of left invariant, 1-homogeneous, Hörmander's vector fields on a Carnot group in R^n, where the matrix of coefficients is symmetric, uniformly positive on a bounded domain of R^n and the coefficients are bounded, measurable and locally VMO in the domain. We give a new proof of the interior L^p estimates on the second order derivatives with respect to the vector fields, first proved by Bramanti-Brandolini in [Rend. Sem. Mat. dell'Univ. e del Politec. di Torino, Vol. 58, 4 (2000), 389-433], extending to this context Krylov' technique, introduced in [Comm. in P.D.E.s, 32 (2007), 453-475], consisting in estimating the sharp maximal function of the second order derivatives. |
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QDD214 - 14/10/2015
Dulio, P.; Finotelli, P.
A Graph Theoretical Approach to Neurobiological Databases Comparison | Abstract | | Music is one of the best tools to evoke emotions and feelings in
people. Generally, people like classical music, hip hop, house,
disco, underground or other kinds of music. People choose songs
basing on their preferences. For example, a subject while performing
an action such as running, studying or relaxing tends to listen to songs that give her or him a pleasant feeling. Interesting issues emerge: First,
collecting the brain reactions when the brain is stimulated by songs
(classified as pleasant). Second, comparing them with the resting
state condition, and third representing the neural network changes in
terms of emergent subgraphs.
We propose a general methodology concerning phase transitions
analysis of an arbitrary number of conditions.
We also apply such a methodology to real acoustic data and, though
our findings generally seem to agree with others available in the
literature, they also point out the existence of functional connectivity
between pairs of cerebral areas, usually not immediately associated
to an acoustical task.
Our results may explain why people when listening to pleasant music
activated emotional cerebral areas in spite of the fact that the
music they classify as pleasant is different for each subject.
Possible applications to Neuropsychiatry are discussed.
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QDD213 - 28/08/2015
Alpay, D.; Sabadini, I.
Beurling-Lax type theorems in the complex and quaternionic setting: the half-space case | Abstract | | We give a generalization of the Beurling-Lax theorem both in the complex and quaternionic settings. We consider in the first case
functions meromorphic in the right complex half-plane, and functions slice hypermeromorphic in the right quaternionic half-space in the second case. In both settings we also discuss a unified framework, which includes both the disk and the half-plane for the complex case and the
open unit ball and the half-space in the quaternionic setting.
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QDD212 - 01/07/2015
Barchielli, A.
Quantum stochastic equations for an opto-mechanical oscillator with radiation pressure interaction and non-Markovian effects | Abstract | | The quantum stochastic Schroedinger equation or Hudson-Parthasareathy (HP) equation is a powerful tool to construct unitary dilations of quantum dynamical semigroups and to develop the theory of measurements in continuous time via the construction of output fields. An important feature of such an equation is that it allows to treat not only absorption and emission of quanta, but also scattering processes, which however had very few applications in physical modelling. Moreover, recent developments have shown that also some non-Markovian dynamics can be generated by suitable choices of the state of the quantum noises involved in the HP-equation. This paper is devoted to an application involving these two features, non-Markovianity and scattering process. We consider a micro-mirror mounted on a vibrating structure and reflecting a laser beam, a process giving rise to a radiation-pressure force on the mirror. We show that this process needs the scattering part of the HP-equation to be described. On the other side, non-Markovianity is introduced by the dissipation due to the interaction with some thermal environment which we represent by a phonon field, with a nearly arbitrary excitation spectrum, and by the introduction of phase noise in the laser beam. Finally, we study the full power spectrum of the reflected light and we show how the laser beam can be used as a temperature probe. |
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QDD211 - 04/06/2015
Pagani,C.D.; Pierotti, D.; Pistoia, A.; Vaira, G.
Concentration along geodesics for a nonlinear Steklov problem arising in corrosion modelling | Abstract | | We consider the problem of finding pairs (lambda; u), with lambda > 0 and u a harmonic function in a three dimensional torus-like domain D, satisfying the nonlinear boundary condition partial_n u = sinh u on partial D. This type of boundary condition arises in corrosion modelling (Butler Volmer condition). We prove existence of solutions
which concentrate along some geodesics of the boundary as the parameter lambda goes to zero. |
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QDD210 - 05/05/2015
Bertacchi, D; Zucca, F; Ambrosini, R.
The timing of life history events in presence of soft disturbances | Abstract | | We study a model for the evolutionarily stable strategy (ESS) used by biological populations for choosing the time
of life-history events, such as migration and breeding. In our model
we accounted for both intra-species competition (early individuals have a competitive advantage) and a disturbance
which strikes at a random time, killing a fraction 1-p of the population.
Disturbances include spells of bad weather, such as freezing or heavily raining days
It has been shown by Iwasa and Levin (1995), that when p=0, then
the ESS is a mixed strategy, where individuals wait for a certain time and afterwards
start arriving (or breeding) every day. We remove the constraint $p=0$ and show that if 0
then the ESS still implies a mixed choice of times, but strong competition may lead to a massive arrival
at the earliest time possible of a fraction of the population, while the rest
will arrive throughout the whole period during which the disturbance may occur.
More precisely, given "p", there is a threshold for the competition
parameter "a", above which massive arrivals occur and below which there is a behaviour as in Iwasa and Levin (1995). We study the behaviour of the ESS and of the average fitness of the population, depending on the parameters
involved. We also discuss how the population may be affected by climate change, in two respects:
first, how the ESS should change under the new climate and whether this change implies
an increase of the average fitness; second, which is the impact of the new climate on a population
that still follows the old strategy. We show that, at least under some conditions, extreme weather
events imply a temporary decrease of the average fitness (thus an increasing mortality).
If the population adapts to the new climate, the survivors may have a larger fitness. |
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