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

Protein phosphatase 1-dependent bidirectional synaptic plasticity controls ischemic recovery in the adult brain

Protein kinases and phosphatases can alter the impact of excitotoxicity resulting from ischemia by concurrently modulating apoptotic/survival pathways. Here, we show that protein phosphatase 1 (PP1), known to constrain neuronal signaling and synaptic strength (Mansuy et al., 1998; Morishita et al., 2001), critically regulates neuroprotective pathways in the adult brain. When PP1 is inhibited pharmacologically or genetically, recovery from oxygen/glucose deprivation (OGD) in vitro, or ischemia in vivo is impaired. Furthermore, in vitro, inducing LTP shortly before OGD similarly impairs recovery, an effect that correlates with strong PP1 inhibition. Conversely, inducing LTD before OGD elicits full recovery by preserving PP1 activity, an effect that is abolished by PP1 inhibition. The mechanisms of action of PP1 appear to be coupled with several components of apoptotic pathways, in particular ERK1/2 (extracellular signal-regulated kinase 1/2) whose activation is increased by PP1 inhibition both in vitro and in vivo. Together, these results reveal that the mechanisms of recovery in the adult brain critically involve PP1, and highlight a novel physiological function for long-term potentiation and long-term depression in the control of brain damage and repair

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

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 $P(t_m)$ of the time $t_m$ 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 $P(M,t_m)$ of the maximum $M$ and $t_m$. In the driftless case, we find that $P(t_m)$ has power-law tails: $P(t_m)\sim t_m^{-3/2}$ for large $t_m$ and $P(t_m)\sim t_m^{-1/2}$ for small $t_m$. In presence of a drift towards the origin, $P(t_m)$ decays exponentially for large $t_m$. 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

Implication of sperm RNAs in transgenerational inheritance of the effects of early trauma in mice.

Small non-coding RNAs (sncRNAs) are potential vectors at the interface between genes and environment. We found that traumatic stress in early life altered mouse microRNA (miRNA) expression, and behavioral and metabolic responses in the progeny. Injection of sperm RNAs from traumatized males into fertilized wild-type oocytes reproduced the behavioral and metabolic alterations in the resulting offspring.We thank M. Rassoulzadegan and V. Grandjean for help with the sperm purification, F. Manuella and H. Hörster for assistance with the MSUS paradigm, H. Welzl for help with behavior, G. Vernaz for help with western blotting, R. Tweedie-Cullen and P. Nanni for help with mass spectrometry, A. Patrignani for advice on DNA and RNA quality assessment, and A. Chen and A. Brunner for constructive discussions. This work was supported by the Austrian Academy of Sciences, the University of Zürich, the Swiss Federal Institute of Technology, Roche, the Swiss National Science Foundation, and The National Center of Competence in Research “Neural Plasticity and Repair”. P.S. was supported by a Gonville and Caius College fellowship.This is the accepted manuscript. The final version is available in Nature Neuroscience 17, 667–669 (2014), doi:10.1038/nn.369

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 /

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

Mapping global forest cover of the year 2020 to support the EU regulation on deforestation-free supply chains

This document presents the input data, methodology and a preliminary assessment of the first version of the Global Forest Cover map for year 2020 at 10m spatial resolution (GFC 2020, version 1, dated 07 December 2023). GFC 2020 builds on several global data sets and provides a harmonized, globally consistent and spatially explicit representation of forest presence and absence for year 2020. The map aims to support the implementation of the EU Regulation on Deforestation-free supply chains. The primary access to GFC 2020 is via the EU Observatory on Deforestation and Forest Degradation