Scientific Reports
The preprint collection of the Department of Mathematics.
Full-text generally not available for preprints prior to may 2006.
Found 868 products
-
QDD121 - 04/02/2012
Baraldo, S.; Ieva, F.; Mainardi, L.; Paganoni, A. M.
Estimation approaches for the Apparent Diffusion Coefficient in Rice-distributed MR signals | Abstract | | The Apparent Diffusion Coefficient (ADC) is often considered in the differential diagnosis of tumors, since the analysis of a field of ADCs on a particular region of the body allows to identify regional necrosis. This quantity can be estimated from magnitude signals obtained in diffusion
Magnetic Resonance (MR), but in some situations, like total body MRs, it is possible to repeat only few measurements on the same patient, thus providing a limited amount of data for the estimation of ADCs. In this work we consider a Rician distributed magnitude signal with an exponential
dependence on the so-called b-value. Different pixelwise estimators for the ADC, both frequentist and Bayesian, are proposed and compared by a simulation study, focusing on issues caused by low signal-to-noise ratios and small sample sizes. |
-
QDD120 - 02/10/2012
Barchielli, A.; Gregoratti, M.
Entanglement Protection and Generation Under Continuous Monitoring | Abstract | | Entanglement between two quantum systems is a resource in quantum information, but dissipation usually destroys it. In this article we consider two qubits without direct interaction and we show that, even in cases where the open system dynamics destroys any initial entanglement, the mere monitoring of the environment can preserve or create the entanglement, by filtering the state of the qubits. While the systems we study are very simple, we can show examples with entanglement protection or entanglement birth, death, rebirth due to monitoring. |
-
QDD116 - 01/31/2012
Bertacchi D.; Machado F.P.; Zucca F.
Local and global survival for nonhomogeneous random walk systems on Z | Abstract | | We study an interacting random walk system on Z where at time 0 there is an
active particle at 0 and one inactive particle on each site $n ge1$. Particles
become active when hit by another active particle. Once activated
they perform an asymmetric nearest neighbour random walk which depends
only on the starting location of the particle. We give conditions for global survival,
local survival and infinite activation both in the case where all particles are
immortal and in the case where particles have geometrically distributed lifespan
(with parameter depending on the starting location of the particle).
In particular, in the immortal case, we prove a 0-1 law for the probability of local
survival when all particles drift to the right. Besides that, we give sufficient conditions
for local survival or local extinction when all particles drift to the left.
In the mortal case, we provide sufficient conditions for global survival, local
survival and local extinction. Analysis of explicit examples is provided. |
-
QDD117 - 01/31/2012
Fragalà, I.; Gazzola, F.; Lamboley, J.
Sharp bounds for the p-torsion of convex planar domains | Abstract | | We obtain some sharp estimates for the p-torsion of convex planar domains in terms of their area,
perimeter, and inradius. The approach we adopt relies on the use of web functions (i.e. functions depending only on the distance from the boundary), and on the behaviour of the inner parallel sets of convex polygons. As an application of our isoperimetric inequalities, we consider the shape optimization problem which
consists in maximizing the p-torsion among polygons having a given number of vertices and a given area. A long-standing conjecture by P´olya-Szeg¨o states that the solution is the regular polygon. We show that such conjecture is true within the subclass of polygons for which a suitable notion of “asymmetry measure” exceeds a critical threshold. |
-
QDD118 - 01/31/2012
Cipriani, F.; Guido, D.; Isola, T.; Sauvageot J.L.
Differential 1-forms, their integrals ans Potential Theory on the Sierpinski gasket | Abstract | | We provide a de finition of diff erential 1-forms on the Sierpinski gasket K and their integrals on paths. We show how these tools can be used to build up a Potential Theory on K. In particular, we prove: i) a de Rham re-construction of a 1-form from its periods
around lacunas in K; ii) a Hodge decomposition of 1-forms with respect to the Hilbertian energy norm; iii) the existence of potentials of elementary 1-forms on suitable covering spaces of K. We then apply this framework to the topology of the fractal K, showing that each element of the dual of the first Cech homology group is represented by a suitable
harmonic 1-form. |
-
QDD119 - 01/31/2012
Cipriani, F.; Guido, D. Isola, T. Sauvageot J.L.
Spectral Triples for the Sierpinski gasket | Abstract | | We construct a 2-parameter family of spectral triples for the Sierpinski Gasket K. We determine their associated Connes distances in terms of suitable roots of the plane Euclidean metric and their dimensional spectra, and show that the pairing of the associated Fredholm module with (odd) K-theory is non-trivial. We recover the Hausdorff measure of
K in terms of the residue of a functional at its abscissa of convergence d, which coincides with the Hausdorff dimension of the fractal. We recover also the unique,
standard Dirichlet form on K, as the residue of another functional at its abscissa of convergence d , which we call the energy dimension. The fact that the volume dimension diff ers from the energy dimension
reflects the fact that on K energy and volume are distributed singularly. |
-
QDD115 - 01/12/2012
Berchio, E.
On the second solution to a critical growth Robin problem | Abstract | | We investigate the existence of the second mountain-pass solution to a Robin problem, where
the equation is at critical growth and depends on a positive parameter $ë$. More precisely, we
determine existence and nonexistence regions for this type of solutions, depending both on $ë$ and
on the parameter in the boundary conditions. |
-
QDD114 - 12/14/2011
Noris, B.; Verzini, G.
A remark on natural constraints in variational methods and an application to superlinear Schrödinger systems | Abstract | | For a regular functional J defined on a Hilbert space X, we consider the set N of points x of X such that the projection of the gradient of J at x onto a closed linear subspace V(x) of X vanishes. We study sufficient conditions for a constrained critical point of J restricted to N to be a free critical point of J, providing a unified approach to different natural constraints known in the literature, such as the Birkhoff-Hestenes natural isoperimetric conditions and the Nehari manifold. As an application, we prove multiplicity of solutions to a class of superlinear Schrödinger systems on singularly perturbed domains.
|
|
