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Collezione dei preprint del Dipartimento di Matematica.
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Trovati 868 prodotti
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QDD187 - 15/10/2014
Finotelli, P.; Dulio, P.
A Mathematical Proposal to Evaluate Functional Connectivity Strongness in Complex Brain Networks | Abstract | | The brain is a really complex organization of connectivity whose principal elements are neurons, synapses and brain regions. To date this connectivity is not fully understood. Graph Theory represents a powerful tool in the study of brain networks. Though the complex organization of connectivity in human and animal brain has found a great impulse by the use of Graph Theory, some points result to be not very clear and needed to be clarified, the weakness lies in the mismatching between the mathematical and neuroscientific approach. In this paper we focus, in particular, on two points: the concept of distance and a mathematical approach in treating functional and structural connectivity by means of the introduction of the parameter time. One of the most relevant remark we point out concerns the concept of graph in the inter-field crossing Mathematics and Neuroscience. In detail, when talking about Graph Theory in brain connectivity, it should be clear that we are considering two basic categories: one static, relative to the anatomical connectivity, and the other, dynamical, concerning the functional connectivity. We believe that in order to describe them it is fundamental to introduce the concept of time, which, at present, seems to be a lack in the theory of this area of research. For example, the static category regards the anatomical neural network in particular range of the life of human beings (and animals), i.e. the synaptic connections or directed anatomical pathways derived from neural tract tracing, can be retained static only in absence of injuries or cerebral illnesses, or far from the childhood and one’s old age. The dynamical approach is involved in the other cases, in particular it is linked to the functional connectivity, i.e. the temporal correlations between remote neurophysiological events as reaction to well specific external stimuli (e.g. social paradigms, social cognitive functions or other specific tasks), it interests cerebral areas not necessarily close each other (in the sense of Euclidean distance). Aside we emphasize that the functional connectivity is very distinctive from effective connectivity, i.e. the influence one neural system exerts over another [26]. The point is that these categories demand different kinds of graphs,except the case of resting state. The integration between these two different approaches is a topic of present interest. In this paper we formalize in a mathematical way this concept and we speculate the existence of a function which can give the weight of the edges composing the graph representing the functional connectivity. This function W(i, j, t) depends on the position of nodes i, j and on the time t at which a specific task is submitted to an health volunteer (and in prospective to a subject affected by a neurological disease). Interestingly this function, in particular cases, comes down to the probability of edge formation. Basically these particular cases are the resting state and when a particular task do not affect the cerebral region to which the nodes belong to. This second case is rare since when performing a task the region of interest, ROI, are well known. |
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QDD186 - 26/09/2014
Abu-Ghanem, K.; Alpay, D.; Colombo, F.; Sabadini, I.
Gleason’s Problem and Schur Multipliers in the Multivariable Quaternionic Setting | Abstract | | We define and study the counterparts of Gleason’s problem, of the Arveson’s space and of Schur multipliers when the unit ball of C^N is replaced by the unit ball of H^N . Schur multipliers are characterized in terms of coisometric operator matrices in quaternionic spaces. We define the counterpart of Blaschke factors in this setting.
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QDD185 - 08/07/2014
Barutello,V.; Boscaggin, A.; Verzini, G.
Positive solutions with a complex behavior for superlinear indefinite ODEs on the real line | Abstract | | We show the existence of infinitely many positive solutions, defined on the real line,for the nonlinear scalar ODE ....,where a is a periodic,
sign-changing function, and the parameter ? > 0 is large. Such solutions are characterized by the fact of being either small or large in each interval of positivity of a. In this way, we find periodic solutions, having minimal period arbitrarily large, and bounded non-periodic solutions, exhibiting a complex behavior. The proof is variational, exploiting suitable natural constraints of Nehari type.
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QDD183 - 10/06/2014
Gazzola, F.; Karageorgis, P.
Refined blow-up results for nonlinear fourth order differential equations | Abstract | | We study a class of nonlinear fourth order differential equations which arise as models of suspension bridges. When it comes to power-like nonlinearities, it is known that solutions may blow up in finite time, if the initial data satisfy some positivity assumption. We extend this result to more general nonlinearities allowing exponential growth and to a wider class of initial data. We also give some hints on how to prevent blow-up. |
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QDD184 - 10/06/2014
Cao, H.D.; Catino, G.; Chen, Q.; Mantegazza, C.; Mazzieri, L.
Bach-flat gradient steady Ricci solitons | Abstract | | Abstract. In this paper we prove that any n-dimensional (n ? 4) complete Bach-flat gradient steady Ricci soliton with positive Ricci curvature is isometric to the Bryant soliton. We also show that a three-dimensional gradient steady Ricci soliton with divergence-free Bach tensor is either flat or isometric to the Bryant soliton. In particular, these results improve the corresponding classification theorems for complete locally conformally flat gradient steady Ricci solitons in [8, 10].
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QDD182 - 22/05/2014
Noris, B.; Tavares, H.; Verzini, G.
Stable solitary waves with prescribed L2 mass for the cubic Schrodinger system with trapping potentials | Abstract | | For the cubic Schrodinger system with trapping potentials in RN, N <= 3, or in bounded domains, we investigate the existence and the orbital stability of standing waves having components with prescribed L2 mass provide a variational characterization of such solutions, which gives information on the stability through of a condition of Grillakis-Shatah-Strauss type. As an application, we show existence of conditionally orbitally stable solitary waves when: a) the masses are small, for almost every scattering lengths, and b) in the defocusing, weakly interacting case, for any masses. |
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QDD181 - 12/05/2014
Gazzola, F.; Jleli, M.; Samet, B.
On the Melan equation for suspension bridges | Abstract | | We ?rst recall how the classical Melan equation for suspension bridges is derived. We discuss the origin of its nonlinearity and the possible form of the nonlocal term: we show that some alternative forms may lead to fairly different responses. Then we prove several existence results through ?xed points theorems applied to suitable maps. The problem appears to be ill posed: we exhibit a counterexample to uniqueness. Finally, we implement a numerical procedure in order to try to approximate the solution; it turns out that the ?xed point may be quite unstable for actual suspension bridges. Several open problems are suggested. |
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QDD180 - 08/05/2014
Gregoratti, M.
The Hamiltonian generating Quantum Stochastic Evolutions in the limit from Repeated to Continuous Interactions | Abstract | | We consider a quantum stochastic evolution in continuous time defined by the quantum stochastic differential equation of Hudson and Parthasarathy. On one side, such an evolution can be defined also by a standard Schroedinger equation with a singular and unbounded Hamiltonian operator K. On the other side, such an evolution can be obtained also as a limit from Hamiltonian repeated interactions in discrete time. We study how the structure of the Hamiltonian K emerges in the limit from repeated to continuous interactions. We present results in the case of 1-dimensional multiplicity and system spaces, where calculations can be explicitly performed, and the proper formulation of the problem can be discussed. |
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