2,149 research outputs found
A New Class of Processes for Formalizing and Generalizing Individual-Based Models: The Semi-Semi-Markov Processes
2000 Mathematics Subject Classification: 60K15, 60K20, 60G20,60J75, 60J80, 60J85, 60-08,
90B15.Individual-based models are a \bottom-up" approach for calculating empirical distributions at the level of the population from simulated individual trajectories. We build a new class of stochastic processes for mathematically formalizing and generalizing these simulation models according to a \top-down" approach, when the individual state changes occur at countable random times. We allow individual population-dependent semi-Markovian transitions in a non closed population such as a branching population. These new processes are called Semi-Semi-Markov Processes (SSMP) and are generalizations of Semi-Markov processes. We calculate their kernel and their probability law, and we build a simulation algorithm from the kernel.This paper was supported by the program ECO-NET 2006 financed by the french foreign
office
A one-phase interior point method for nonconvex optimization
The work of Wachter and Biegler suggests that infeasible-start interior point
methods (IPMs) developed for linear programming cannot be adapted to nonlinear
optimization without significant modification, i.e., using a two-phase or
penalty method. We propose an IPM that, by careful initialization and updates
of the slack variables, is guaranteed to find a first-order certificate of
local infeasibility, local optimality or unboundedness of the (shifted)
feasible region. Our proposed algorithm differs from other IPM methods for
nonconvex programming because we reduce primal feasibility at the same rate as
the barrier parameter. This gives an algorithm with more robust convergence
properties and closely resembles successful algorithms from linear programming.
We implement the algorithm and compare with IPOPT on a subset of CUTEst
problems. Our algorithm requires a similar median number of iterations, but
fails on only 9% of the problems compared with 16% for IPOPT. Experiments on
infeasible variants of the CUTEst problems indicate superior performance for
detecting infeasibility.
The code for our implementation can be found at
https://github.com/ohinder/OnePhase .Comment: fixed typo in sign of dual multiplier in KKT syste
Noise and nonlinearities in high-throughput data
High-throughput data analyses are becoming common in biology, communications,
economics and sociology. The vast amounts of data are usually represented in
the form of matrices and can be considered as knowledge networks. Spectra-based
approaches have proved useful in extracting hidden information within such
networks and for estimating missing data, but these methods are based
essentially on linear assumptions. The physical models of matching, when
applicable, often suggest non-linear mechanisms, that may sometimes be
identified as noise. The use of non-linear models in data analysis, however,
may require the introduction of many parameters, which lowers the statistical
weight of the model. According to the quality of data, a simpler linear
analysis may be more convenient than more complex approaches.
In this paper, we show how a simple non-parametric Bayesian model may be used
to explore the role of non-linearities and noise in synthetic and experimental
data sets.Comment: 12 pages, 3 figure
Identification of nonlinear heat transfer laws from boundary observations
We consider the problem of identifying a nonlinear heat transfer law at the boundary, or of the temperature-dependent heat transfer coefficient in a parabolic equation from boundary observations. As a practical example, this model applies to the heat transfer coefficient that describes the intensity of heat exchange between a hot wire and the cooling water in which it is placed. We reformulate the inverse problem as a variational one which aims to minimize a misfit functional and prove that it has a solution. We provide a gradient formula for the misfit functional and then use some iterative methods for solving the variational problem. Thorough investigations are made with respect to several initial guesses and amounts of noise in the input data. Numerical results show that the methods are robust, stable and accurate
Non-Abelian Monopole and Dyon Solutions in a Modified Einstein-Yang-Mills-Higgs System
We have studied a modified Yang-Mills-Higgs system coupled to Einstein
gravity. The modification of the Einstein-Hilbert action involves a direct
coupling of the Higgs field to the scalar curvature. In this modified system we
are able to write a Bogomol'nyi type condition in curved space and demonstrate
that the positive static energy functional is bounded from below. We then
investigate non-Abelian sperically symmetric static solutions in a similar
fashion to the `t Hooft-Polyakov monopole. After reviewing previously studied
monopole solutions of this type, we extend the formalism to included electric
charge and we present dyon solutions.Comment: 18 pages LaTeX, 7 eps-figure
Effect of Peierls transition in armchair carbon nanotube on dynamical behaviour of encapsulated fullerene
The changes of dynamical behaviour of a single fullerene molecule inside an
armchair carbon nanotube caused by the structural Peierls transition in the
nanotube are considered. The structures of the smallest C20 and Fe@C20
fullerenes are computed using the spin-polarized density functional theory.
Significant changes of the barriers for motion along the nanotube axis and
rotation of these fullerenes inside the (8,8) nanotube are found at the Peierls
transition. It is shown that the coefficients of translational and rotational
diffusions of these fullerenes inside the nanotube change by several orders of
magnitude. The possibility of inverse orientational melting, i.e. with a
decrease of temperature, for the systems under consideration is predicted.Comment: 9 pages, 6 figures, 1 tabl
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