State complexity of the multiples of the Thue-Morse set

The Thue-Morse set is the set of those nonnegative integers whose binary expansions have an even number of $1$. We obtain an exact formula for the state complexity of the multiplication by a constant of the Thue-Morse set $\mathcal{T}$ with respect with any base $b$ which is a power of $2$. Our proof is constructive and we are able to explicitly provide the minimal automaton of the language of all $2^p$-expansions of the set of integers $m\mathcal{T}$ for any positive integers $m$ and $p$.Comment: 23 pages, 10 figure

A parallel second order Cartesian method for elliptic interface problems and its application to tumor growth model

This theses deals with a parallel Cartesian method to solve elliptic problems with complex interfaces and its application to elliptic irregular domain problems in the framework of a tumor growth model. This method is based on a finite differences scheme and is second order accurate in the whole domain. The originality of the method lies in the use of additional unknowns located on the interface, allowing to express the interface transmission conditions. The method is described and the details of its parallelization, performed with the PETSc library, are provided. Numerical validations of the method follow with comparisons to other related methods in literature. A numerical study of the parallelized method is also given. Then, the method is applied to solve elliptic irregular domain problems appearing in a three-dimensional continuous tumor growth model, the two-species Darcy model. The approach used in this application is based on the penalization of the interface transmission conditions, in order to impose homogeneous Neumann boundary conditions on the border of an irregular domain. The simulations of model are provided and they show the ability of the method to impose a good approximation of the considered boundary conditions

Device specialization in heterogeneous multi-GPU environments

In the last few years there have been many activities towards coupling CPUs and GPUs in order to get the most from CPU-GPU heterogeneous systems. One of the main problems that prevent these systems to be exploited in a device-aware manner is the CPU-GPU communication bottleneck, which often doesn\u27t allow to produce code more efficient than the GPU-only and the CPU-only counterparts. As a consequence, most of the heterogeneous scheduling systems treat CPUs and GPUs as homogeneous nodes, electing map-like data partitioning to employ both these processing resources. We propose to study how the radical change in the connection between GPU, CPU and memory characterizing the APUs (Accelerated Processing Units) affect the architecture of a compiler and if it is possible to use all these computing resources in a device-aware manner. We investigate on a methodology to analyze the devices that populate heterogeneous multi-GPU systems and to classify general purpose algorithms in order to perform near-optimal control flow and data partitioning

Modeling web applications infrastructure with ASMs

We describe via Abstract State Machines the major ingredients of contemporary web applications: a web browser running JavaScript programs and a web server dispatching requests to one of several modules, each one representing a class of established web application frameworks. The web browser model comes in four levels, namely transport, stream, context and browser level, and is focussed on the interaction with possibly multiple servers (which requires a concurrent computation model) and on script execution (which requires a dynamic assignment of agents to programs). The server model is focussed on the Request–Reply pattern, and specifies a delegation strategy where the handling of a request is entrusted to a module. We show how several major frameworks for web applications can be described as progressive refinements of a number of basic modules. Three modules are further detailed: static file transfer, CGI and generic scripting modules