Mean--field limit of a particle approximation of the one-dimensional parabolic--parabolic Keller-Segel model without smoothing

In this work, we prove the well--posedness of a singularly interacting stochastic particle system and we establish propagation of chaos result towards the one-dimensional parabolic-parabolic Keller-Segel model

NON INVASIVE INVESTIGATION OF SENSORIMOTOR CONTROL FOR FUTURE DEVELOPMENT OF BRAIN-MACHINE-INTERFACE (BMI)

My thesis focuses on describing novel functional connectivity properties of the sensorimotor system that are of potential interest in the field of brain-machine interface. In particular, I have investigated how the connectivity changes as a consequence of either pathologic conditions or spontaneous fluctuations of the brain's internal state. An ad-hoc electronic device has been developed to implement the appropriate experimental settings. First, the functional communication among sensorimotor primary nodes was investigated in multiple sclerosis patients afflicted by persistent fatigue. I selected this condition, for which there is no effective pharmacological treatment, since existing literature links this type of fatigue to the motor control system. In this study, electroencephalographic (EEG) and electromyographic (EMG) traces were acquired together with the pressure exerted on a bulb during an isometric hand grip. The results showed a higher frequency connection between central and peripheral nervous systems (CMC) and an overcorrection of the exerted movement in fatigued multiple sclerosis patients. In fact, even though any fatigue-dependent brain and muscular oscillatory activity alterations were absent, their connectivity worked at higher frequencies as fatigue increased, explaining 67% of the fatigue scale (MFIS) variance (p=.002). In other terms, the functional communication within the central-peripheral nervous systems, namely involving primary sensorimotor areas, was sensitive to tiny alterations in neural connectivity leading to fatigue, well before the appearance of impairments in single nodes of the network. The second study was about connectivity intended as propagation of information and studied in dependence on spontaneous fluctuations of the sensorimotor system triggered by an external stimulus. Knowledge of the propagation mechanisms and of their changes is essential to extract significant information from single trials. The EEG traces were acquired during transcranial magnetic stimulation (TMS) to yield to a deeper knowledge about the response to an external stimulation while the cortico-spinal system passes through different states. The results showed that spontaneous increases of the excitation of the node originating the transmission within the hand control network gave rise to dynamic recruitment patterns with opposite behaviors, weaker in homotopic and parietal circuits, stronger in frontal ones. As probed by TMS, this behavior indicates that the effective connectivity within bilateral circuits orchestrating hand control are dynamically modulated in time even in resting state. The third investigation assessed the plastic changes in the sensorimotor system after stroke induced by 3 months of robotic rehabilitation in chronic phase. A functional source extraction procedure was applied on the acquired EEG data, enabling the investigation of the functional connectivity between homologous areas in the resting state. The most significant result was that the clinical ameliorations were associated to a ‘normalization’ of the functional connectivity between homologous areas. In fact, the brain connectivity did not necessarily increase or decrease, but it settled within a ‘physiological’ range of connectivity. These studies strengthen our knowledge about the behavioral role of the functional connectivity among neuronal networks’ nodes, which will be essential in future developments of enhanced rehabilitative interventions, including brain-machine interfaces. The presented research also moves the definition of new indices of clinical state evaluation relevant for compensating interventions, a step forward

Blow-up for a Stochastic Model of Chemotaxis Driven by Conservative Noise on R2\mathbb{R}^2

We establish criteria on the chemotactic sensitivity $\chi$ for the non-existence of global weak solutions (i.e. \textit{blow-up} in finite time) to a stochastic Keller--Segel model with spatially inhomogeneous, conservative noise on $\mathbb{R}^2$. We show that if $\chi$ is sufficiently large then \emph{blow-up} occurs with probability $1$. In this regime our criterion agrees with that of a deterministic Keller--Segel model with increased viscosity. However, for $\chi$ in an intermediate regime, determined by the variance of the initial data and the spatial correlation of the noise, we show that \emph{blow-up} occurs with positive probability.Comment: Example of conservative noise edited and issue with uniqueness of weak solutions addressed; 25 page

Quantitative approximation of the Keller-Segel and Burgers equations by moderately interacting particles

In this work we derive the rate of convergence for the empirical measure of a moderately interacting stochastic particle system towards the Keller-Segel and Burgers equations. In the case of the Keller-Segel equation on a $d$-dimensional torus, we obtain almost sure convergence of the mollified empirical measure to the solution of the PDE in some $L^1\cap L^p$ spaces with a rate of order $N^{-\frac{1}{2d+1}}$. The same holds for the genuine empirical measure in Wasserstein distance. The result holds in both subcritical and supercritical cases for the sensitivity parameter $\chi$ of the equation up to the maximal existence time of the PDE. This extends our previous work to moderately interacting particle systems without cutoff in the drift term. Then, we extend our method to Burgers equation in $\mathbb{R}$ and obtain a rate of convergence of the order $N^{-1/8}$.Comment: This is a preliminary version of the pape

The sensory quality of meat, game, poultry, seafood and meat products as affected by intense light pulses: A systematic review

The effect of intense light pulses (ILP) on sensory quality of 16 different varieties of meat, meat products, game, poultry and seafood are reviewed. Changes induced by ILP are animal species, type of meat product and fluences applied dependent. ILP significantly deteriorates sensory quality of cooked meat products. It causes less change in the sensory properties of dry cured than cooked meat products while fermented sausage is least affected. The higher fluence applied significantly changes the instrumental color values of meat, poultry, game and meat products. The use of ILP on seafood regarding its influence on sensory quality is promising

Quantum Information Bound on the Energy

According to the classical Penrose inequality, the mass at spatial infinity is bounded from below by a function of the area of certain trapped surfaces. We exhibit quantum field theory states that violate this relation at the semiclassical level. We formulate a Quantum Penrose Inequality, by replacing the area with the generalized entropy of the lightsheet of an appropriate quantum trapped surface. We perform a number of nontrivial tests of our proposal, and we consider and rule out alternative formulations. We also discuss the relation to weak cosmic censorhip.Comment: 47 pages, 10 figure