1,246 research outputs found
Entropic Approach to Multiscale Clustering Analysis
(iii) not biased against the null hypothesis. Applications to the physics of ultra-high energy cosmic rays, as a cosmological probe, are presented and discussed
Statistical mechanics characterization of spatio-compositional inhomogeneity
On the basis of a model system of pillars built of unit cubes, a
two-component entropic measure for the multiscale analysis of
spatio-compositional inhomogeneity is proposed. It quantifies the statistical
dissimilarity per cell of the actual configurational macrostate and the
theoretical reference one that maximizes entropy. Two kinds of disorder
compete: i) the spatial one connected with possible positions of pillars inside
a cell (the first component of the measure), ii) the compositional one linked
to compositions of each local sum of their integer heights into a number of
pillars occupying the cell (the second component). As both the number of
pillars and sum of their heights are conserved, the upper limit for a pillar
height hmax occurs. If due to a further constraint there is the more demanding
limit h <= h* < hmax, the exact number of restricted compositions can be then
obtained only through the generating function. However, at least for systems
with exclusively composition degrees of freedom, we show that the neglecting of
the h* is not destructive yet for a nice correlation of the h*-constrained
entropic measure and its less demanding counterpart, which is much easier to
compute. Given examples illustrate a broad applicability of the measure and its
ability to quantify some of the subtleties of a fractional Brownian motion,
time evolution of a quasipattern [28,29] and reconstruction of a laser-speckle
pattern [2], which are hardly to discern or even missed.Comment: 17 pages, 5 figure
A Smoothed Dual Approach for Variational Wasserstein Problems
Variational problems that involve Wasserstein distances have been recently
proposed to summarize and learn from probability measures. Despite being
conceptually simple, such problems are computationally challenging because they
involve minimizing over quantities (Wasserstein distances) that are themselves
hard to compute. We show that the dual formulation of Wasserstein variational
problems introduced recently by Carlier et al. (2014) can be regularized using
an entropic smoothing, which leads to smooth, differentiable, convex
optimization problems that are simpler to implement and numerically more
stable. We illustrate the versatility of this approach by applying it to the
computation of Wasserstein barycenters and gradient flows of spacial
regularization functionals
Variational Methods for Biomolecular Modeling
Structure, function and dynamics of many biomolecular systems can be
characterized by the energetic variational principle and the corresponding
systems of partial differential equations (PDEs). This principle allows us to
focus on the identification of essential energetic components, the optimal
parametrization of energies, and the efficient computational implementation of
energy variation or minimization. Given the fact that complex biomolecular
systems are structurally non-uniform and their interactions occur through
contact interfaces, their free energies are associated with various interfaces
as well, such as solute-solvent interface, molecular binding interface, lipid
domain interface, and membrane surfaces. This fact motivates the inclusion of
interface geometry, particular its curvatures, to the parametrization of free
energies. Applications of such interface geometry based energetic variational
principles are illustrated through three concrete topics: the multiscale
modeling of biomolecular electrostatics and solvation that includes the
curvature energy of the molecular surface, the formation of microdomains on
lipid membrane due to the geometric and molecular mechanics at the lipid
interface, and the mean curvature driven protein localization on membrane
surfaces. By further implicitly representing the interface using a phase field
function over the entire domain, one can simulate the dynamics of the interface
and the corresponding energy variation by evolving the phase field function,
achieving significant reduction of the number of degrees of freedom and
computational complexity. Strategies for improving the efficiency of
computational implementations and for extending applications to coarse-graining
or multiscale molecular simulations are outlined.Comment: 36 page
Self-Assembly of Nanocomponents into Composite Structures: Derivation and Simulation of Langevin Equations
The kinetics of the self-assembly of nanocomponents into a virus,
nanocapsule, or other composite structure is analyzed via a multiscale
approach. The objective is to achieve predictability and to preserve key
atomic-scale features that underlie the formation and stability of the
composite structures. We start with an all-atom description, the Liouville
equation, and the order parameters characterizing nanoscale features of the
system. An equation of Smoluchowski type for the stochastic dynamics of the
order parameters is derived from the Liouville equation via a multiscale
perturbation technique. The self-assembly of composite structures from
nanocomponents with internal atomic structure is analyzed and growth rates are
derived. Applications include the assembly of a viral capsid from capsomers, a
ribosome from its major subunits, and composite materials from fibers and
nanoparticles. Our approach overcomes errors in other coarse-graining methods
which neglect the influence of the nanoscale configuration on the atomistic
fluctuations. We account for the effect of order parameters on the statistics
of the atomistic fluctuations which contribute to the entropic and average
forces driving order parameter evolution. This approach enables an efficient
algorithm for computer simulation of self-assembly, whereas other methods
severely limit the timestep due to the separation of diffusional and complexing
characteristic times. Given that our approach does not require recalibration
with each new application, it provides a way to estimate assembly rates and
thereby facilitate the discovery of self-assembly pathways and kinetic dead-end
structures.Comment: 34 pages, 11 figure
Generating realistic scaled complex networks
Research on generative models is a central project in the emerging field of
network science, and it studies how statistical patterns found in real networks
could be generated by formal rules. Output from these generative models is then
the basis for designing and evaluating computational methods on networks, and
for verification and simulation studies. During the last two decades, a variety
of models has been proposed with an ultimate goal of achieving comprehensive
realism for the generated networks. In this study, we (a) introduce a new
generator, termed ReCoN; (b) explore how ReCoN and some existing models can be
fitted to an original network to produce a structurally similar replica, (c)
use ReCoN to produce networks much larger than the original exemplar, and
finally (d) discuss open problems and promising research directions. In a
comparative experimental study, we find that ReCoN is often superior to many
other state-of-the-art network generation methods. We argue that ReCoN is a
scalable and effective tool for modeling a given network while preserving
important properties at both micro- and macroscopic scales, and for scaling the
exemplar data by orders of magnitude in size.Comment: 26 pages, 13 figures, extended version, a preliminary version of the
paper was presented at the 5th International Workshop on Complex Networks and
their Application
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