Almost periodic solutions of periodic linear partial functional differential equations

We study conditions for the abstract periodic linear functional differential equation $\dot{x}=Ax+F(t)x_t+f(t)$ to have almost periodic with the same structure of frequencies as $f$. The main conditions are stated in terms of the spectrum of the monodromy operator associated with the equation and the frequencies of the forcing term $f$. The obtained results extend recent results on the subject. A discussion on how the results could be extended to the case when $A$ depends on $t$ is given.Comment: 17 page

On regular and singular points of the minimum time function

In this thesis, we study the regularity of the minimum time function Τ for both linear and nonlinear control systems in Euclidean space. We first consider nonlinear problems satisfying Petrov condition. In this case, Τ is locally Lipschitz and then is differentiable almost everywhere. In general, Τ fails to be differentiable at points where there are multiple time optimal trajectories and its differentiability at a point does not guarantee continuous differentiability around this point. We show that, under some regularity assumptions, the non-emptiness of proximal subdifferential of the minimum time function at a point x implies its continuous differentiability on a neighborhood of Υ. The technique consists of deriving sensitivity relations for the proximal subdifferential of the minimum time function and excluding the presence of conjugate points when the proximal subdifferential is nonempty. We then study the regularity the minimum time function Τ to reach the origin under controllability conditions which do not imply the Lipschitz continuity of Τ. Basing on the analysis of zeros of the switching function, we find out singular sets (e.g., non - Lipschitz set, non - differentiable set) and establish rectifiability properties for them. The results imply further regularity properties of Τ such as the SBV regularity, the differentiability and the analyticity. The results are mainly for linear control problems

Efficient HEVC-based video adaptation using transcoding

In a video transmission system, it is important to take into account the great diversity of the network/end-user constraints. On the one hand, video content is typically streamed over a network that is characterized by different bandwidth capacities. In many cases, the bandwidth is insufficient to transfer the video at its original quality. On the other hand, a single video is often played by multiple devices like PCs, laptops, and cell phones. Obviously, a single video would not satisfy their different constraints. These diversities of the network and devices capacity lead to the need for video adaptation techniques, e.g., a reduction of the bit rate or spatial resolution. Video transcoding, which modifies a property of the video without the change of the coding format, has been well-known as an efficient adaptation solution. However, this approach comes along with a high computational complexity, resulting in huge energy consumption in the network and possibly network latency. This presentation provides several optimization strategies for the transcoding process of HEVC (the latest High Efficiency Video Coding standard) video streams. First, the computational complexity of a bit rate transcoder (transrater) is reduced. We proposed several techniques to speed-up the encoder of a transrater, notably a machine-learning-based approach and a novel coding-mode evaluation strategy have been proposed. Moreover, the motion estimation process of the encoder has been optimized with the use of decision theory and the proposed fast search patterns. Second, the issues and challenges of a spatial transcoder have been solved by using machine-learning algorithms. Thanks to their great performance, the proposed techniques are expected to significantly help HEVC gain popularity in a wide range of modern multimedia applications

Indoor assistance for visually impaired people using a RGB-D camera

In this paper a navigational aid for visually impaired people is presented. The system uses a RGB-D camera to perceive the environment and implements self-localization, obstacle detection and obstacle classification. The novelty of this work is threefold. First, self-localization is performed by means of a novel camera tracking approach that uses both depth and color information. Second, to provide the user with semantic information, obstacles are classified as walls, doors, steps and a residual class that covers isolated objects and bumpy parts on the floor. Third, in order to guarantee real time performance, the system is accelerated by offloading parallel operations to the GPU. Experiments demonstrate that the whole system is running at 9 Hz