Riesz potentials and nonlinear parabolic equations

The spatial gradient of solutions to nonlinear degenerate parabolic equations can be pointwise estimated by the caloric Riesz potential of the right hand side datum, exactly as in the case of the heat equation. Heat kernels type estimates persist in the nonlinear cas

Fluctuation superconductivity limited noise in a transition-edge sensor

In order to investigate the origin of the until now unaccounted excess noise and to minimize the uncontrollable phenomena at the transition in X-ray microcalorimeters we have developed superconducting transition-edge sensors into an edgeless geometry, the so-called Corbino disk (CorTES), with superconducting contacts in the centre and at the outer perimeter. The measured rms current noise and its spectral density can be modeled as resistance noise resulting from fluctuations near the equilibrium superconductor-normal metal boundaryComment: 9 pages, 4 figures.; Corrections to text and equations; replaced the affected figures. Added reference [12

Delocalization of ultracold atoms in a disordered potential due to light scattering

We numerically study the expansion dynamics of ultracold atoms in a one-dimensional disordered potential in the presence of a weak position measurement of the atoms. We specifically consider this position measurement to be realized by a combination of an external laser and a periodic array of optical microcavities along a waveguide. The position information is acquired through the scattering of a near-resonant laser photon into a specific eigenmode of one of the cavities. The time evolution of the atomic density in the presence of this light scattering mechanism is described within a Lindblad master equation approach, which is numerically implemented using the Monte Carlo wave function technique. We find that an arbitrarily weak rate of photon emission leads to a breakdown of Anderson localization of the atoms.Comment: 7 pages, 8 figure

The role of social networks in students’ learning experiences

The aim of this research is to investigate the role of social networks in computer science education. The Internet shows great potential for enhancing collaboration between people and the role of social software has become increasingly relevant in recent years. This research focuses on analyzing the role that social networks play in students’ learning experiences. The construction of students’ social networks, the evolution of these networks, and their effects on the students’ learning experience in a university environment are examined

Degradation of cognitive timing mechanisms in behavioural variant frontotemporal dementia.

The current study examined motor timing in frontotemporal dementia (FTD), which manifests as progressive deterioration in social, behavioural and cognitive functions. Twenty-patients fulfilling consensus clinical criteria for behavioural variant FTD (bvFTD), 11 patients fulfilling consensus clinical criteria for semantic-variant primary progressive aphasia (svPPA), four patients fulfilling criteria for nonfluent/agrammatic primary progressive aphasia (naPPA), eight patients fulfilling criteria for Alzheimer׳s disease (AD), and 31 controls were assessed on both an externally- and self-paced finger-tapping task requiring maintenance of a regular, 1500 ms beat over 50 taps. Grey and white matter correlates of deficits in motor timing were examined using voxel-based morphometry (VBM) and diffusion tensor imaging (DTI). bvFTD patients exhibited significant deficits in aspects of both externally- and self-paced tapping. Increased mean inter-response interval (faster than target tap time) in the self-paced task was associated with reduced grey matter volume in the cerebellum bilaterally, right middle temporal gyrus, and with increased axial diffusivity in the right superior longitudinal fasciculus, regions and tracts which have been suggested to be involved in a subcortical-cortical network of structures underlying timing abilities. This suggests that such structures can be affected in bvFTD, and that impaired motor timing may underlie some characteristics of the bvFTD phenotype

Regularity of maximal operators: recent progress and some open problems

This is an expository paper on the regularity theory of maximal operators, when these act on Sobolev and BV functions, with a special focus on some of the current open problems in the topic. Overall, a list of fifteen research problems is presented. It summarizes the contents of a talk delivered by the author at the CIMPA 2017 Research School - Harmonic Analysis, Geometric Measure Theory and Applications, in Buenos Aires, Argentina.Comment: 19 pages. Expository paper with the contents of a lecture given at the in the CIMPA 2017 Research School - Harmonic Analysis, Geometric Measure Theory and Applications, in Buenos Aires, Argentin