3,479 research outputs found
Dynamical Complexity, Intermittent Turbulence, Coarse-Grained Dissipation, Criticality and Multifractal Processes
The ideas of dynamical complexity induced intermittent turbulence by sporadic
localized interactions of coherent structures are discussed. In particular, we
address the phenomenon of magnetic reconfiguration due to coarse-grained
dissipation as well as the interwoven connection between criticality and
multifractal processes. Specific examples are provided.Comment: 6 pages, 2 figures, submitted to AIP Conference Proceedings for the
6th Annual International Astrophysics Conference, Honolulu, March 16-22, 200
Preferential Acceleration of Coherent Magnetic Structures and Bursty Bulk Flows in Earth's Magnetotail
Observations indicate that the magnetotail convection is turbulent and
bi-modal, consisting of fast bursty bulk flows (BBF) and a nearly stagnant
background. We demonstrate that this observed phenomenon may be understood in
terms of the intermittent interactions, dynamic mergings and preferential
accelerations of coherent magnetic structures under the influence of a
background magnetic field geometry that is consistent with the development of
an X-point mean-field structure.Comment: 12 pages, 5 Postscript figures, uses agums.st
A path-integral approach to Bayesian inference for inverse problems using the semiclassical approximation
We demonstrate how path integrals often used in problems of theoretical
physics can be adapted to provide a machinery for performing Bayesian inference
in function spaces. Such inference comes about naturally in the study of
inverse problems of recovering continuous (infinite dimensional) coefficient
functions from ordinary or partial differential equations (ODE, PDE), a problem
which is typically ill-posed. Regularization of these problems using
function spaces (Tikhonov regularization) is equivalent to Bayesian
probabilistic inference, using a Gaussian prior. The Bayesian interpretation of
inverse problem regularization is useful since it allows one to quantify and
characterize error and degree of precision in the solution of inverse problems,
as well as examine assumptions made in solving the problem -- namely whether
the subjective choice of regularization is compatible with prior knowledge.
Using path-integral formalism, Bayesian inference can be explored through
various perturbative techniques, such as the semiclassical approximation, which
we use in this manuscript. Perturbative path-integral approaches, while
offering alternatives to computational approaches like Markov-Chain-Monte-Carlo
(MCMC), also provide natural starting points for MCMC methods that can be used
to refine approximations.
In this manuscript, we illustrate a path-integral formulation for inverse
problems and demonstrate it on an inverse problem in membrane biophysics as
well as inverse problems in potential theories involving the Poisson equation.Comment: Fixed some spelling errors and the author affiliations. This is the
version accepted for publication by J Stat Phy
Bayesian field theoretic reconstruction of bond potential and bond mobility in single molecule force spectroscopy
Quantifying the forces between and within macromolecules is a necessary first
step in understanding the mechanics of molecular structure, protein folding,
and enzyme function and performance. In such macromolecular settings, dynamic
single-molecule force spectroscopy (DFS) has been used to distort bonds. The
resulting responses, in the form of rupture forces, work applied, and
trajectories of displacements, have been used to reconstruct bond potentials.
Such approaches often rely on simple parameterizations of one-dimensional bond
potentials, assumptions on equilibrium starting states, and/or large amounts of
trajectory data. Parametric approaches typically fail at inferring
complex-shaped bond potentials with multiple minima, while piecewise estimation
may not guarantee smooth results with the appropriate behavior at large
distances. Existing techniques, particularly those based on work theorems, also
do not address spatial variations in the diffusivity that may arise from
spatially inhomogeneous coupling to other degrees of freedom in the
macromolecule, thereby presenting an incomplete picture of the overall bond
dynamics. To solve these challenges, we have developed a comprehensive
empirical Bayesian approach that incorporates data and regularization terms
directly into a path integral. All experiemental and statistical parameters in
our method are estimated empirically directly from the data. Upon testing our
method on simulated data, our regularized approach requires fewer data and
allows simultaneous inference of both complex bond potentials and diffusivity
profiles.Comment: In review - Python source code available on github. Abridged abstract
on arXi
Horn formula minimization
Horn formulas make up an important subclass of Boolean formulas that exhibits interesting and useful computational properties. They have been widely studied due to the fact that the satisfiability problem for Horn formulas is solvable in linear time. Also resulting from this, Horn formulas play an important role in the field of artificial intelligence. The minimization problem of Horn formulas is to reduce the size of a given Horn formula to find a shortest equivalent representation. Many knowledge bases in propositional expert systems are represented as Horn formulas. Therefore the minimization of Horn formulas can be used to reduce the size of these knowledge bases, thereby increasing the efficiency of queries. The goal of this project is to study the properties of Horn formulas and the minimization of Horn formulas. Topics discussed include The satisfiability problem for Horn formulas. NP-completeness of Horn formula minimization. Subclasses of Horn formulas for which the minimization problem is solvable in polynomial time. Approximation algorithms for Horn formula minimization
Pathways to Higher Education
Presents case studies from Ford's initiative to support efforts to transform universities abroad to enable poor, minority, and otherwise underrepresented students to obtain a university degree. Outlines selected best practices from grantees
Rank-ordered Multifractal Spectrum for Intermittent Fluctuations
We describe a new method that is both physically explicable and
quantitatively accurate in describing the multifractal characteristics of
intermittent events based on groupings of rank-ordered fluctuations. The
generic nature of such rank-ordered spectrum leads it to a natural connection
with the concept of one-parameter scaling for monofractals. We demonstrate this
technique using results obtained from a 2D MHD simulation. The calculated
spectrum suggests a crossover from the near Gaussian characteristics of small
amplitude fluctuations to the extreme intermittent state of large rare events.Comment: 4 pages, 5 figure
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