Scientific Reports
The preprint collection of the Department of Mathematics.
Full-text generally not available for preprints prior to may 2006.
Found 868 products
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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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QDD217 - 11/26/2015
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 - 10/14/2015
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 - 08/28/2015
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 - 07/01/2015
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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