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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
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