Many problems arising in science and engineering aim to find a function which is the optimal value of a specified functional. Some examples include optimal control, inverse analysis and optimal shape design. Only some of these, regarded as variational problems, can be solved analytically, and the only general technique is to approximate the solution using direct methods. Unfortunately, variational problems are very difficult to solve, and it becomes necessary to innovate in the field of numerical methods in order to overcome the difficulties. The objective of this PhD Thesis is to develop a conceptual theory of neural networks from the perspective of functional analysis and variational calculus. Within this formulation, learning means to solve a variational problem by minimizing an objective functional associated to the neural network. The choice of the objective functional depends on the particular application. On the other side, its evaluation might need the integration of functions, ordinary differential equations or partial differential equations. As it will be shown, neural networks are able to deal with a wide range of applications in mathematics and physics.

Predicting the throughput of large TCP transfers is important for a broad class of applications. This paper focuses on the design, empirical evaluation and analysis of TCP throughput predictors. We first classify TCP throughput prediction techniques into two categories: Formula-Based and History-Based. Within each class, we develop representative prediction algorithms, which we then evaluate empirically over the RON testbed. FB prediction relies on mathematical models that express the TCP throughput as a function of the characteristics of the underlying network path. It does not rely on previous TCP transfers in the given path and it can be performed with non intrusive network measurements. We show that the FB method is accurate only if the TCP transfer is window-limited to the point that it does not saturate the underlying path, and explain the main causes of the prediction errors. HB techniques predict the throughput of TCP flows from a time series of previous TCP throughput measurements on the same path, when such a history is available. We show that even simple HB predictors, like Moving Average and Holt-Winters, using a history of few and sporadic samples can be quite accurate