340,347 research outputs found
Theoretical Interpretations and Applications of Radial Basis Function Networks
Medical applications usually used Radial Basis Function Networks just as Artificial Neural Networks. However, RBFNs are Knowledge-Based Networks that can be interpreted in several way: Artificial Neural Networks, Regularization Networks, Support Vector Machines, Wavelet Networks, Fuzzy Controllers, Kernel Estimators, Instanced-Based Learners. A survey of their interpretations and of their corresponding learning algorithms is provided as well as a brief survey on dynamic learning algorithms. RBFNs' interpretations can suggest applications that are particularly interesting in medical domains
Correlation function algebra for inhomogeneous fluids
We consider variational (density functional) models of fluids confined in
parallel-plate geometries (with walls situated in the planes z=0 and z=L
respectively) and focus on the structure of the pair correlation function
G(r_1,r_2). We show that for local variational models there exist two
non-trivial identities relating both the transverse Fourier transform G(z_\mu,
z_\nu;q) and the zeroth moment G_0(z_\mu,z_\nu) at different positions z_1, z_2
and z_3. These relations form an algebra which severely restricts the possible
form of the function G_0(z_\mu,z_\nu). For the common situations in which the
equilibrium one-body (magnetization/number density) profile m_0(z) exhibits an
odd or even reflection symmetry in the z=L/2 plane the algebra simplifies
considerably and is used to relate the correlation function to the finite-size
excess free-energy \gamma(L). We rederive non-trivial scaling expressions for
the finite-size contribution to the free-energy at bulk criticality and for
systems where large scale interfacial fluctuations are present. Extensions to
non-planar geometries are also considered.Comment: 15 pages, RevTex, 4 eps figures. To appear in J.Phys.Condens.Matte
Divergent mathematical treatments in utility theory
In this paper I study how divergent mathematical treatments affect mathematical modelling, with a special focus on utility theory. In particular I examine recent work on the ranking of information states and the discounting of future utilities, in order to show how, by replacing the standard analytical treatment of the models involved with one based on the framework of Nonstandard Analysis, diametrically opposite results are obtained. In both cases, the choice between the standard and nonstandard treatment amounts to a selection of set-theoretical parameters that cannot be made on purely empirical grounds. The analysis of this phenomenon gives rise to a simple logical account of the relativity of impossibility theorems in economic theory, which concludes the paper
Nonparametric estimation of composite functions
We study the problem of nonparametric estimation of a multivariate function
that can be represented as a composition of two
unknown smooth functions and . We suppose that and belong to known smoothness classes of
functions, with smoothness and , respectively. We obtain the
full description of minimax rates of estimation of in terms of and
, and propose rate-optimal estimators for the sup-norm loss. For the
construction of such estimators, we first prove an approximation result for
composite functions that may have an independent interest, and then a result on
adaptation to the local structure. Interestingly, the construction of
rate-optimal estimators for composite functions (with given, fixed smoothness)
needs adaptation, but not in the traditional sense: it is now adaptation to the
local structure. We prove that composition models generate only two types of
local structures: the local single-index model and the local model with
roughness isolated to a single dimension (i.e., a model containing elements of
both additive and single-index structure). We also find the zones of (,
) where no local structure is generated, as well as the zones where the
composition modeling leads to faster rates, as compared to the classical
nonparametric rates that depend only to the overall smoothness of .Comment: Published in at http://dx.doi.org/10.1214/08-AOS611 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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