589 research outputs found
Solution of the Fokker-Planck equation with a logarithmic potential and mixed eigenvalue spectrum
Motivated by a problem in climate dynamics, we investigate the solution of a
Bessel-like process with negative constant drift, described by a Fokker-Planck
equation with a potential V(x) = - [b \ln(x) + a\, x], for b>0 and a<0. The
problem belongs to a family of Fokker-Planck equations with logarithmic
potentials closely related to the Bessel process, that has been extensively
studied for its applications in physics, biology and finance. The Bessel-like
process we consider can be solved by seeking solutions through an expansion
into a complete set of eigenfunctions. The associated imaginary-time
Schroedinger equation exhibits a mix of discrete and continuous eigenvalue
spectra, corresponding to the quantum Coulomb potential describing the bound
states of the hydrogen atom. We present a technique to evaluate the
normalization factor of the continuous spectrum of eigenfunctions that relies
solely upon their asymptotic behavior. We demonstrate the technique by solving
the Brownian motion problem and the Bessel process both with a negative
constant drift. We conclude with a comparison with other analytical methods and
with numerical solutions.Comment: 21 pages, 8 figure
Who acquires infection from whom and how? Disentangling multi-host and multi-mode transmission dynamics in the 'elimination' era
Multi-host infectious agents challenge our abilities to understand, predict and manage disease dynamics. Within this, many infectious agents are also able to use, simultaneously or sequentially, multiple modes of transmission. Furthermore, the relative importance of different host species and modes can itself be dynamic, with potential for switches and shifts in host range and/ or transmission mode in response to changing selective pressures, such as those imposed by disease control interventions. The epidemiology of such multi-host, multi-mode infectious agents thereby can involve a multi-faceted community of definitive and intermediate/secondary hosts or vectors, often together with infectious stages in the environment, all of which may represent potential targets, as well as specific challenges, particularly where disease elimination is proposed. Here, we explore, focusing on examples fromboth human and animal pathogen systems, why and how we should aim to disentangle and quantify the relative importance of multi-host multi-mode infectious agent transmission dynamics under contrasting conditions, and ultimately, how this can be used to help achieve efficient and effective disease control.
This article is part of the themed issue 'Opening the black box: re-examining the ecology and evolution of parasite transmission'
Large deviations for clocks of self-similar processes
The Lamperti correspondence gives a prominent role to two random time
changes: the exponential functional of a L\'evy process drifting to
and its inverse, the clock of the corresponding positive self-similar process.
We describe here asymptotical properties of these clocks in large time,
extending the results of Yor and Zani
Distribution of the time at which the deviation of a Brownian motion is maximum before its first-passage time
We calculate analytically the probability density of the time
at which a continuous-time Brownian motion (with and without drift) attains its
maximum before passing through the origin for the first time. We also compute
the joint probability density of the maximum and . In the
driftless case, we find that has power-law tails: for large and for small . In
presence of a drift towards the origin, decays exponentially for large
. The results from numerical simulations are in excellent agreement with
our analytical predictions.Comment: 13 pages, 5 figures. Published in Journal of Statistical Mechanics:
Theory and Experiment (J. Stat. Mech. (2007) P10008,
doi:10.1088/1742-5468/2007/10/P10008
On arbitrages arising from honest times
In the context of a general continuous financial market model, we study
whether the additional information associated with an honest time gives rise to
arbitrage profits. By relying on the theory of progressive enlargement of
filtrations, we explicitly show that no kind of arbitrage profit can ever be
realised strictly before an honest time, while classical arbitrage
opportunities can be realised exactly at an honest time as well as after an
honest time. Moreover, stronger arbitrages of the first kind can only be
obtained by trading as soon as an honest time occurs. We carefully study the
behavior of local martingale deflators and consider no-arbitrage-type
conditions weaker than NFLVR.Comment: 25 pages, revised versio
Gold/Silica biochips: applications to Surface Plasmon Resonance and fluorescence quenching
We report Gold/Silica biochips for low cost biosensor devices. Firstly, the
study of biochemical interactions on silica by means of Surface Plasmon
Resonance (SPR) is presented. Secondly, Gold/Silica biochips are employed to
reduce the strong quenching that occurs when a fluorophore is close to the gold
surface. Furthermore, the control of the Silica-like thickness allows
optimizing the distance between the metallic surface and the fluorophore in
order to enhance the fluorescent signal. These results represent the first
steps towards highly sensitive, specific and low cost biosensors based, for
example, on Surface Plasmon Coupled Emission (SPCE) techniques
New early Triassic Lingulidae (Brachiopoda) genera and species from South China
Two new genera, Sinolingularia gen. nov. and Sinoglottidia gen. nov., together with three new species, Sinolingularia huananensis gen. et sp. nov., Sinolingularia yini gen. et sp. nov. and Sinoglottidia archboldi gen. et sp. nov., are described on the basis of a large collection of well-preserved specimens from several sections straddling the Permian - Triassic boundary in South China. <br /
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