91,414 research outputs found
Fractal geometry, information growth and nonextensive thermodynamics
This is a study of the information evolution of complex systems by
geometrical consideration. We look at chaotic systems evolving in fractal phase
space. The entropy change in time due to the fractal geometry is assimilated to
the information growth through the scale refinement. Due to the incompleteness
of the state number counting at any scale on fractal support, the incomplete
normalization is applied throughout the paper, where is the
fractal dimension divided by the dimension of the smooth Euclidean space in
which the fractal structure of the phase space is embedded. It is shown that
the information growth is nonadditive and is proportional to the trace-form
which can be connected to several nonadditive
entropies. This information growth can be extremized to give power law
distributions for these non-equilibrium systems. It can also be used for the
study of the thermodynamics derived from Tsallis entropy for nonadditive
systems which contain subsystems each having its own . It is argued that,
within this thermodynamics, the Stefan-Boltzmann law of blackbody radiation can
be preserved.Comment: Final version, 10 pages, no figures, Invited talk at the
international conference NEXT2003, 21-28 september 2003, Villasimius
(Cagliari), Ital
Estimating Semiparametric Panel Data Models by Marginal Integration
We propose a new methodology for estimating semiparametric panel data models, with a primary focus on the nonparametric component. We eliminate individual effects using first differencing transformation and estimate the unknown function by marginal integration. We extend our methodology to treat panel data models with both individual and time effects. And we characterize the asymptotic behavior of our estimators. Monte Carlo simulations show that our estimator behaves well in finite samples in both random effects and fixed effects settings.Semiparametric Panel Data Model, Partially Linear, First Differencing, Marginal Integration
Sketch-based 3D Shape Retrieval using Convolutional Neural Networks
Retrieving 3D models from 2D human sketches has received considerable
attention in the areas of graphics, image retrieval, and computer vision.
Almost always in state of the art approaches a large amount of "best views" are
computed for 3D models, with the hope that the query sketch matches one of
these 2D projections of 3D models using predefined features.
We argue that this two stage approach (view selection -- matching) is
pragmatic but also problematic because the "best views" are subjective and
ambiguous, which makes the matching inputs obscure. This imprecise nature of
matching further makes it challenging to choose features manually. Instead of
relying on the elusive concept of "best views" and the hand-crafted features,
we propose to define our views using a minimalism approach and learn features
for both sketches and views. Specifically, we drastically reduce the number of
views to only two predefined directions for the whole dataset. Then, we learn
two Siamese Convolutional Neural Networks (CNNs), one for the views and one for
the sketches. The loss function is defined on the within-domain as well as the
cross-domain similarities. Our experiments on three benchmark datasets
demonstrate that our method is significantly better than state of the art
approaches, and outperforms them in all conventional metrics.Comment: CVPR 201
Measuring information growth in fractal phase space
We look at chaotic systems evolving in fractal phase space. The entropy
change in time due to the fractal geometry is assimilated to the information
growth through the scale refinement. Due to the incompleteness, at any scale,
of the information calculation in fractal support, the incomplete normalization
is applied throughout the paper. It is shown that the
information growth is nonadditive and is proportional to the trace-form
so that it can be connected to several nonadditive
entropies. This information growth can be extremized to give, for
non-equilibrium systems, power law distributions of evolving stationary state
which may be called ``maximum entropic evolution''.Comment: 10 pages, 1 eps figure, TeX. Chaos, Solitons & Fractals (2004), in
pres
Spontaneous Formation of Stable Capillary Bridges for Firming Compact Colloidal Microstructures in Phase Separating Liquids: A Computational Study
Computer modeling and simulations are performed to investigate capillary
bridges spontaneously formed between closely packed colloidal particles in
phase separating liquids. The simulations reveal a self-stabilization mechanism
that operates through diffusive equilibrium of two-phase liquid morphologies.
Such mechanism renders desired microstructural stability and uniformity to the
capillary bridges that are spontaneously formed during liquid solution phase
separation. This self-stabilization behavior is in contrast to conventional
coarsening processes during phase separation. The volume fraction limit of the
separated liquid phases as well as the adhesion strength and thermodynamic
stability of the capillary bridges are discussed. Capillary bridge formations
in various compact colloid assemblies are considered. The study sheds light on
a promising route to in-situ (in-liquid) firming of fragile colloidal crystals
and other compact colloidal microstructures via capillary bridges
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