49,216 research outputs found
A variational approach to moment-closure approximations for the kinetics of biomolecular reaction networks
Approximate solutions of the chemical master equation and the chemical
Fokker-Planck equation are an important tool in the analysis of biomolecular
reaction networks. Previous studies have highlighted a number of problems with
the moment-closure approach used to obtain such approximations, calling it an
ad-hoc method. In this article, we give a new variational derivation of
moment-closure equations which provides us with an intuitive understanding of
their properties and failure modes and allows us to correct some of these
problems. We use mixtures of product-Poisson distributions to obtain a flexible
parametric family which solves the commonly observed problem of divergences at
low system sizes. We also extend the recently introduced entropic matching
approach to arbitrary ansatz distributions and Markov processes, demonstrating
that it is a special case of variational moment closure. This provides us with
a particularly principled approximation method. Finally, we extend the above
approaches to cover the approximation of multi-time joint distributions,
resulting in a viable alternative to process-level approximations which are
often intractable.Comment: Minor changes and clarifications; corrected some typo
Acoustic characterization of crack damage evolution in sandstone deformed under conventional and true triaxial loading
We thank the Associate Editor, Michelle Cooke, and the reviewers, Ze'ev Reches and Yves Guéguen, for useful comments which helped to improve the manuscript. We thank J.G. Van Munster for providing access to the true triaxial apparatus at KSEPL and for technical support during the experimental program. We thank R. Pricci for assistance with technical drawings of the apparatus. This work was partly funded by NERC award NE/N002938/1 and by a NERC Doctoral Studentship, which we gratefully acknowledge. Supporting data are included in a supporting information file; any additional data may be obtained from J.B. (e-mail: [email protected]).Peer reviewedPublisher PD
The Effect of Plant Water Storage on Water Fluxes within the Coupled SoilâPlant System
In addition to buffering plants from water stress during severe droughts, plant water storage (PWS) alters many features of the spatio-temporal dynamics of water movement in the soilâplant system. How PWS impacts water dynamics and drought resilience is explored using a multi-layer porous media model
The Lundgren-Monin-Novikov Hierarchy: Kinetic Equations for Turbulence
We present an overview of recent works on the statistical description of
turbulent flows in terms of probability density functions (PDFs) in the
framework of the Lundgren-Monin-Novikov (LMN) hierarchy. Within this framework,
evolution equations for the PDFs are derived from the basic equations of fluid
motion. The closure problem arises either in terms of a coupling to multi-point
PDFs or in terms of conditional averages entering the evolution equations as
unknown functions. We mainly focus on the latter case and use data from direct
numerical simulations (DNS) to specify the unclosed terms. Apart from giving an
introduction into the basic analytical techniques, applications to
two-dimensional vorticity statistics, to the single-point velocity and
vorticity statistics of three-dimensional turbulence, to the temperature
statistics of Rayleigh-B\'enard convection and to Burgers turbulence are
discussed.Comment: Accepted for publication in C. R. Acad. Sc
Dynamical origins of the community structure of multi-layer societies
Social structures emerge as a result of individuals managing a variety of
different of social relationships. Societies can be represented as highly
structured dynamic multiplex networks. Here we study the dynamical origins of
the specific community structures of a large-scale social multiplex network of
a human society that interacts in a virtual world of a massive multiplayer
online game. There we find substantial differences in the community structures
of different social actions, represented by the various network layers in the
multiplex. Community size distributions are either similar to a power-law or
appear to be centered around a size of 50 individuals. To understand these
observations we propose a voter model that is built around the principle of
triadic closure. It explicitly models the co-evolution of node- and
link-dynamics across different layers of the multiplex. Depending on link- and
node fluctuation rates, the model exhibits an anomalous shattered fragmentation
transition, where one layer fragments from one large component into many small
components. The observed community size distributions are in good agreement
with the predicted fragmentation in the model. We show that the empirical
pairwise similarities of network layers, in terms of link overlap and degree
correlations, practically coincide with the model. This suggests that several
detailed features of the fragmentation in societies can be traced back to the
triadic closure processes.Comment: 8 pages, 6 figure
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