54 research outputs found
Cooling down Levy flights
Let L(t) be a Levy flights process with a stability index \alpha\in(0,2), and
U be an external multi-well potential. A jump-diffusion Z satisfying a
stochastic differential equation dZ(t)=-U'(Z(t-))dt+\sigma(t)dL(t) describes an
evolution of a Levy particle of an `instant temperature' \sigma(t) in an
external force field. The temperature is supposed to decrease polynomially
fast, i.e. \sigma(t)\approx t^{-\theta} for some \theta>0. We discover two
different cooling regimes. If \theta<1/\alpha (slow cooling), the jump
diffusion Z(t) has a non-trivial limiting distribution as t\to \infty, which is
concentrated at the potential's local minima. If \theta>1/\alpha (fast cooling)
the Levy particle gets trapped in one of the potential wells
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
Multi-level Dynamical Systems: Connecting the Ruelle Response Theory and the Mori-Zwanzig Approach
In this paper we consider the problem of deriving approximate autonomous
dynamics for a number of variables of a dynamical system, which are weakly
coupled to the remaining variables. In a previous paper we have used the Ruelle
response theory on such a weakly coupled system to construct a surrogate
dynamics, such that the expectation value of any observable agrees, up to
second order in the coupling strength, to its expectation evaluated on the full
dynamics. We show here that such surrogate dynamics agree up to second order to
an expansion of the Mori-Zwanzig projected dynamics. This implies that the
parametrizations of unresolved processes suited for prediction and for the
representation of long term statistical properties are closely related, if one
takes into account, in addition to the widely adopted stochastic forcing, the
often neglected memory effects.Comment: 14 pages, 1 figur
Time separation as a hidden variable to the Copenhagen school of quantum mechanics
The Bohr radius is a space-like separation between the proton and electron in
the hydrogen atom. According to the Copenhagen school of quantum mechanics, the
proton is sitting in the absolute Lorentz frame. If this hydrogen atom is
observed from a different Lorentz frame, there is a time-like separation
linearly mixed with the Bohr radius. Indeed, the time-separation is one of the
essential variables in high-energy hadronic physics where the hadron is a bound
state of the quarks, while thoroughly hidden in the present form of quantum
mechanics. It will be concluded that this variable is hidden in Feynman's rest
of the universe. It is noted first that Feynman's Lorentz-invariant
differential equation for the bound-state quarks has a set of solutions which
describe all essential features of hadronic physics. These solutions explicitly
depend on the time separation between the quarks. This set also forms the
mathematical basis for two-mode squeezed states in quantum optics, where both
photons are observable, but one of them can be treated a variable hidden in the
rest of the universe. The physics of this two-mode state can then be translated
into the time-separation variable in the quark model. As in the case of the
un-observed photon, the hidden time-separation variable manifests itself as an
increase in entropy and uncertainty.Comment: LaTex 10 pages with 5 figure. Invited paper presented at the
Conference on Advances in Quantum Theory (Vaxjo, Sweden, June 2010), to be
published in one of the AIP Conference Proceedings serie
Mechanics and thermodynamics of a new minimal model of the atmosphere
The understanding of the fundamental properties of the climate system has long benefitted from the use of simple numerical models able to parsimoniously represent the essential ingredients of its processes. Here, we introduce a new model for the atmosphere that is constructed by supplementing the now-classic Lorenz ’96 one-dimensional lattice model with temperature-like variables. The model features an energy cycle that allows for energy to be converted between the kinetic form and the potential form and for introducing a notion of efficiency. The model’s evolution is controlled by two contributions—a quasi-symplectic and a gradient one, which resemble (yet not conforming to) a metriplectic structure. After investigating the linear stability of the symmetric fixed point, we perform a systematic parametric investigation that allows us to define regions in the parameters space where at steady-state stationary, quasi-periodic, and chaotic motions are realised, and study how the terms responsible for defining the energy budget of the system depend on the external forcing injecting energy in the kinetic and in the potential energy reservoirs. Finally, we find preliminary evidence that the model features extensive chaos. We also introduce a more complex version of the model that is able to accommodate for multiscale dynamics and that features an energy cycle that more closely mimics the one of the Earth’s atmosphere
sciReptor: analysis of single-cell level immunoglobulin repertoires
BACKGROUND: The sequencing of immunoglobulin (Ig) transcripts from single B cells yields essential information about Ig heavy:light chain pairing, which is lost in conventional bulk sequencing experiments. The previously limited throughput of single-cell approaches has recently been overcome by the introduction of multiple next-generation sequencing (NGS)-based platforms. Furthermore, single-cell techniques allow the assignment of additional data types (e.g. cell surface marker expression), which are crucial for biological interpretation. However, the currently available computational tools are not designed to handle single-cell data and do not provide integral solutions for linking of sequence data to other biological data. RESULTS: Here we introduce sciReptor, a flexible toolkit for the processing and analysis of antigen receptor repertoire sequencing data at single-cell level. The software combines bioinformatics tools for immunoglobulin sequence annotation with a relational database, where raw data and analysis results are stored and linked. sciReptor supports attribution of additional data categories such as cell surface marker expression or immunological metadata. Furthermore, it comprises a quality control module as well as basic repertoire visualization tools. CONCLUSION: sciReptor is a flexible framework for standardized sequence analysis of antigen receptor repertoires on single-cell level. The relational database allows easy data sharing and downstream analyses as well as immediate comparisons between different data sets
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