7,442 research outputs found
Geometric Path Integrals. A Language for Multiscale Biology and Systems Robustness
In this paper we suggest that, under suitable conditions, supervised learning
can provide the basis to formulate at the microscopic level quantitative
questions on the phenotype structure of multicellular organisms. The problem of
explaining the robustness of the phenotype structure is rephrased as a real
geometrical problem on a fixed domain. We further suggest a generalization of
path integrals that reduces the problem of deciding whether a given molecular
network can generate specific phenotypes to a numerical property of a
robustness function with complex output, for which we give heuristic
justification. Finally, we use our formalism to interpret a pointedly
quantitative developmental biology problem on the allowed number of pairs of
legs in centipedes
Multiple phases in stochastic dynamics: geometry and probabilities
Stochastic dynamics is generated by a matrix of transition probabilities.
Certain eigenvectors of this matrix provide observables, and when these are
plotted in the appropriate multi-dimensional space the phases (in the sense of
phase transitions) of the underlying system become manifest as extremal points.
This geometrical construction, which we call an
\textit{observable-representation of state space}, can allow hierarchical
structure to be observed. It also provides a method for the calculation of the
probability that an initial points ends in one or another asymptotic state
Image processing as state reconstruction in optics
The image reconstruction of partially coherent light is interpreted as the
quantum state reconstruction. The efficient method based on maximum-likelihood
estimation is proposed to acquire information from registered intensity
measurements affected by noise. The connection with totally incoherent image
restoration is pointed out. The feasibility of the method is demonstrated
numerically. Spatial and correlation details significantly smaller than the
diffraction limit are revealed in the reconstructed pattern.Comment: 10 pages, 5 figure
Extreme-Value Copulas
Being the limits of copulas of componentwise maxima in independent random
samples, extreme-value copulas can be considered to provide appropriate models
for the dependence structure between rare events. Extreme-value copulas not
only arise naturally in the domain of extreme-value theory, they can also be a
convenient choice to model general positive dependence structures. The aim of
this survey is to present the reader with the state-of-the-art in dependence
modeling via extreme-value copulas. Both probabilistic and statistical issues
are reviewed, in a nonparametric as well as a parametric context.Comment: 20 pages, 3 figures. Minor revision, typos corrected. To appear in F.
Durante, W. Haerdle, P. Jaworski, and T. Rychlik (editors) "Workshop on
Copula Theory and its Applications", Lecture Notes in Statistics --
Proceedings, Springer 201
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