Refined energy inequality with application to well-posedness for the fourth order nonlinear Schrodinger type equation on torus

We consider the time local and global well-posedness for the fourth order nonlinear Schrodinger type equation (4NLS) on the torus. The nonlinear term of (4NLS) contains the derivatives of unknown function and this prevents us to apply the classical energy method. To overcome this difficulty, we introduce the modified energy and derive an a priori estimate for the solution to (4NLS)

Operators for transforming kernels into quasi-local kernels that improve SVM accuracy

Motivated by the crucial role that locality plays in various learning approaches, we present, in the framework of kernel machines for classification, a novel family of operators on kernels able to integrate local information into any kernel obtaining quasi-local kernels. The quasi-local kernels maintain the possibly global properties of the input kernel and they increase the kernel value as the points get closer in the feature space of the input kernel, mixing the effect of the input kernel with a kernel which is local in the feature space of the input one. If applied on a local kernel the operators introduce an additional level of locality equivalent to use a local kernel with non-stationary kernel width. The operators accept two parameters that regulate the width of the exponential influence of points in the locality-dependent component and the balancing between the feature-space local component and the input kernel. We address the choice of these parameters with a data-dependent strategy. Experiments carried out with SVM applying the operators on traditional kernel functions on a total of 43 datasets with di®erent characteristics and application domains, achieve very good results supported by statistical significance

Models and Performance of VANET based Emergency Braking

The network research community is working in the field of automotive to provide VANET based safety applications to reduce the number of accidents, deaths, injuries and loss of money. Several approaches are proposed and investigated in VANET literature, but in a completely network-oriented fashion. Most of them do not take into account application requirements and no one considers the dynamics of the vehicles. Moreover, message repropagation schemes are widely proposed without investigating their benefits and using very complicated approaches. This technical report, which is derived from the Master Thesis of Michele Segata, focuses on the Emergency Electronic Brake Lights (EEBL) safety application, meant to send warning messages in the case of an emergency brake, in particular performing a joint analysis of network requirements and provided application level benefits. The EEBL application is integrated within a Collaborative Adaptive Cruise Control (CACC) which uses network-provided information to automatically brake the car if the driver does not react to the warning. Moreover, an information aggregation scheme is proposed to analyze the benefits of repropagation together with the consequent increase of network load. This protocol is compared to a protocol without repropagation and to a rebroadcast protocol found in the literature (namely the weighted p-persistent rebroadcast). The scenario is a highway stretch in which a platoon of vehicles brake down to a complete stop. Simulations are performed using the NS_3 network simulation in which two mobility models have been embedded. The first one, which is called Intelligent Driver Model (IDM) emulates the behavior of a driver trying to reach a desired speed and braking when approaching vehicles in front. The second one (Minimizing Overall Braking Induced by Lane change (MOBIL)), instead, decides when a vehicle has to change lane in order to perform an overtake or optimize its path. The original simulator has been modified by - introducing real physical limits to naturally reproduce real crashes; - implementing a CACC; - implementing the driver reaction when a warning is received; - implementing different network protocols. The tests are performed in different situations, such as different number of lanes (one to five), different average speeds, different network protocols and different market penetration rates and they show that: - the adoption of this technology considerably decreases car accidents since the overall average maximum deceleration is reduced; - network load depends on application-level details, such as the implementation of the CACC; - VANET safety application can improve safety even with a partial market penetration rate; - message repropagation is important to reduce the risk of accidents when not all vehicles are equipped; - benefits are gained not only by equipped vehicles but also by unequipped ones