202 research outputs found

    The maximum of the local time of a diffusion process in a drifted Brownian potential

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    We consider a one-dimensional diffusion process XX in a (κ/2)(-\kappa/2)-drifted Brownian potential for κ0\kappa\neq 0. We are interested in the maximum of its local time, and study its almost sure asymptotic behaviour, which is proved to be different from the behaviour of the maximum local time of the transient random walk in random environment. We also obtain the convergence in law of the maximum local time of XX under the annealed law after suitable renormalization when κ1\kappa \geq 1. Moreover, we characterize all the upper and lower classes for the hitting times of XX, in the sense of Paul L\'evy, and provide laws of the iterated logarithm for the diffusion XX itself. To this aim, we use annealed technics.Comment: 38 pages, new version, merged with hal-00013040 (arXiv:math/0511053), with some additional result

    Directed polymer in a random medium of dimension 1+1 and 1+3: weights statistics in the low-temperature phase

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    We consider the low-temperature T<TcT<T_c disorder-dominated phase of the directed polymer in a random potentiel in dimension 1+1 (where Tc=T_c=\infty) and 1+3 (where Tc<T_c<\infty). To characterize the localization properties of the polymer of length LL, we analyse the statistics of the weights wL(r)w_L(\vec r) of the last monomer as follows. We numerically compute the probability distributions P1(w)P_1(w) of the maximal weight wLmax=maxr[wL(r)]w_L^{max}= max_{\vec r} [w_L(\vec r)], the probability distribution Π(Y2)\Pi(Y_2) of the parameter Y2(L)=rwL2(r)Y_2(L)= \sum_{\vec r} w_L^2(\vec r) as well as the average values of the higher order moments Yk(L)=rwLk(r)Y_k(L)= \sum_{\vec r} w_L^k(\vec r). We find that there exists a temperature Tgap<TcT_{gap}<T_c such that (i) for T<TgapT<T_{gap}, the distributions P1(w)P_1(w) and Π(Y2)\Pi(Y_2) present the characteristic Derrida-Flyvbjerg singularities at w=1/nw=1/n and Y2=1/nY_2=1/n for n=1,2..n=1,2... In particular, there exists a temperature-dependent exponent μ(T)\mu(T) that governs the main singularities P1(w)(1w)μ(T)1P_1(w) \sim (1-w)^{\mu(T)-1} and Π(Y2)(1Y2)μ(T)1\Pi(Y_2) \sim (1-Y_2)^{\mu(T)-1} as well as the power-law decay of the moments Yk(i)ˉ1/kμ(T) \bar{Y_k(i)} \sim 1/k^{\mu(T)}. The exponent μ(T)\mu(T) grows from the value μ(T=0)=0\mu(T=0)=0 up to μ(Tgap)2\mu(T_{gap}) \sim 2. (ii) for Tgap<T<TcT_{gap}<T<T_c, the distribution P1(w)P_1(w) vanishes at some value w0(T)<1w_0(T)<1, and accordingly the moments Yk(i)ˉ\bar{Y_k(i)} decay exponentially as (w0(T))k(w_0(T))^k in kk. The histograms of spatial correlations also display Derrida-Flyvbjerg singularities for T<TgapT<T_{gap}. Both below and above TgapT_{gap}, the study of typical and averaged correlations is in full agreement with the droplet scaling theory.Comment: 13 pages, 29 figure

    Magnetoresistance of a two-dimensional electron gas with spatially periodic lateral modulations: Exact consequences of Boltzmann's equation

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    On the basis of Boltzmann's equation, and including anisotropic scattering in the collision operator, we investigate the effect of one-dimensional superlattices on two-dimensional electron systems. In addition to superlattices defined by static electric and magnetic fields, we consider mobility superlattices describing a spatially modulated density of scattering centers. We prove that magnetic and electric superlattices in xx-direction affect only the resistivity component ρxx\rho_{xx} if the mobility is homogeneous, whereas a mobility lattice in xx-direction in the absence of electric and magnetic modulations affects only ρyy\rho_{yy}. Solving Boltzmann's equation numerically, we calculate the positive magnetoresistance in weak magnetic fields and the Weiss oscillations in stronger fields within a unified approach.Comment: submitted to PR

    Stochastic evolution equations driven by Liouville fractional Brownian motion

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    Let H be a Hilbert space and E a Banach space. We set up a theory of stochastic integration of L(H,E)-valued functions with respect to H-cylindrical Liouville fractional Brownian motions (fBm) with arbitrary Hurst parameter in the interval (0,1). For Hurst parameters in (0,1/2) we show that a function F:(0,T)\to L(H,E) is stochastically integrable with respect to an H-cylindrical Liouville fBm if and only if it is stochastically integrable with respect to an H-cylindrical fBm with the same Hurst parameter. As an application we show that second-order parabolic SPDEs on bounded domains in \mathbb{R}^d, driven by space-time noise which is white in space and Liouville fractional in time with Hurst parameter in (d/4,1) admit mild solution which are H\"older continuous both and space.Comment: To appear in Czech. Math.

    Random walks and polymers in the presence of quenched disorder

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    After a general introduction to the field, we describe some recent results concerning disorder effects on both `random walk models', where the random walk is a dynamical process generated by local transition rules, and on `polymer models', where each random walk trajectory representing the configuration of a polymer chain is associated to a global Boltzmann weight. For random walk models, we explain, on the specific examples of the Sinai model and of the trap model, how disorder induces anomalous diffusion, aging behaviours and Golosov localization, and how these properties can be understood via a strong disorder renormalization approach. For polymer models, we discuss the critical properties of various delocalization transitions involving random polymers. We first summarize some recent progresses in the general theory of random critical points : thermodynamic observables are not self-averaging at criticality whenever disorder is relevant, and this lack of self-averaging is directly related to the probability distribution of pseudo-critical temperatures Tc(i,L)T_c(i,L) over the ensemble of samples (i)(i) of size LL. We describe the results of this analysis for the bidimensional wetting and for the Poland-Scheraga model of DNA denaturation.Comment: 17 pages, Conference Proceedings "Mathematics and Physics", I.H.E.S., France, November 200

    Critical structure factors of bilinear fields in O(N)-vector models

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    We compute the two-point correlation functions of general quadratic operators in the high-temperature phase of the three-dimensional O(N) vector model by using field-theoretical methods. In particular, we study the small- and large-momentum behavior of the corresponding scaling functions, and give general interpolation formulae based on a dispersive approach. Moreover, we determine the crossover exponent ϕT\phi_T associated with the traceless tensorial quadratic field, by computing and analyzing its six-loop perturbative expansion in fixed dimension. We find: ϕT=1.184(12)\phi_T=1.184(12), ϕT=1.271(21)\phi_T=1.271(21), and ϕT=1.40(4)\phi_T=1.40(4) for N=2,3,5N=2,3,5 respectively.Comment: 27 page

    Upregulation of miR-31* Is Negatively Associated with Recurrent/Newly Formed Oral Leukoplakia

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    BACKGROUND: Oral leukoplakia (OLK) is a potentially malignant disorder of the oral cavity. However, the underlying mechanism of OLK is still unclear. In this study, we explore possible miRNAs involved in OLK. METHODOLOGY/PRINCIPAL FINDINGS: Using miRNA microarrays, we profiled miRNA expression in OLK and malignantly transformed OLK (mtOLK) tissue samples. The upregulation of miR-31*, miR-142-5p, miR-33a, miR-1259, miR-146b-5p, miR-886-3p, miR-886-5p, miR-519d, and miR-301a along with the downregulation of miR-572, miR-611, miR-602, miR-675, miR-585, miR-623, miR-637, and miR-1184 in mtOLK were new observations. Fluorescence in situ hybridization (FISH) analyses confirmed that miR-31* is highly expressed in mtOLK. There was a significant difference between the FISH score (p<0.05) in patients with or without recurrent/newly formed OLK. Functional analyses demonstrated that a miR-31* inhibitor decreased apoptosis in the Leuk-1, which is an immortalized oral epithelial cell line spontaneously derived from an oral leukoplakia lesion. miR-31* regulated apoptosis, cell proliferation, migration, and invasion in the HOIEC, which is a HPV E6/E7-immortalized oral epithelial cell line. Furthermore, miR-31* modulated the biological functions of apoptosis, cell proliferation, cell cycle, migration, and invasion in the oral squamous cell carcinoma cell line, Cal-27. Using bioinformatic analyses and dual luciferase reporter assays, we determined that the 3' untranslated region of fibroblast growth factor 3 (FGF3) is the target of miR-31*. Expression of FGF3 was downregulated or upregulated in the presence of a miR-31* mimic or inhibitor, respectively. CONCLUSIONS/SIGNIFICANCE: Upregulation of miR-31* is negatively associated with recurrent/newly formed OLK. MiR-31* may exert similar but distinguishable effects on biological function in oral cells with different malignant potential. FGF3 is the target of miR-31*. miR-31* may play an important role during OLK progression through regulating FGF3. MiRNA* strands may also have prominent roles in oral carcinogenesis

    Rheological properties of magnetic biogels

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    We report an experimental and theoretical study of the rheological properties of magnetic biogels consisting of fibrin polymer networks with embedded magnetite nanoparticles, swollen by aqueous solutions. We studied two types of magnetic biogels, differenced by the presence or absence of an applied magnetic field during the initial steps of cross-linking. The experiments demonstrated very strong dependence of the elastic modulus of the magnetic biogels on the concentration of the magnetic particles. We finally developed some theoretical models that explain the observed strong concentration effects.This study was supported by projects FIS2013-41821-R (Plan Nacional de Investigación Científica, Desarrollo e Innovación Tecnológica, MINECO, Spain, co-funded by ERDF, European Union) and FIS2017-85954-R (Ministerio de Economía, Industria y Competitividad, MINECO, andAgencia Estatal de Investigación, AEI, Spain, co-funded by Fondo Europeo de Desarrollo Regional, FEDER, European Union). A.Z. is grateful to the program of the Ministry of Education and Science of the Russian Federation, projects 02.A03.21.0006, 3.1438.2017/4.6, and 3.5214.2017/6.7, as well as to the Russian Fund of Basic Researches, project 18-08-00178

    RAD21 Cooperates with Pluripotency Transcription Factors in the Maintenance of Embryonic Stem Cell Identity

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    For self-renewal, embryonic stem cells (ESCs) require the expression of specific transcription factors accompanied by a particular chromosome organization to maintain a balance between pluripotency and the capacity for rapid differentiation. However, how transcriptional regulation is linked to chromosome organization in ESCs is not well understood. Here we show that the cohesin component RAD21 exhibits a functional role in maintaining ESC identity through association with the pluripotency transcriptional network. ChIP-seq analyses of RAD21 reveal an ESC specific cohesin binding pattern that is characterized by CTCF independent co-localization of cohesin with pluripotency related transcription factors Oct4, Nanog, Sox2, Esrrb and Klf4. Upon ESC differentiation, most of these binding sites disappear and instead new CTCF independent RAD21 binding sites emerge, which are enriched for binding sites of transcription factors implicated in early differentiation. Furthermore, knock-down of RAD21 causes expression changes that are similar to expression changes after Nanog depletion, demonstrating the functional relevance of the RAD21 - pluripotency transcriptional network association. Finally, we show that Nanog physically interacts with the cohesin or cohesin interacting proteins STAG1 and WAPL further substantiating this association. Based on these findings we propose that a dynamic placement of cohesin by pluripotency transcription factors contributes to a chromosome organization supporting the ESC expression program

    RNAi for Treating Hepatitis B Viral Infection

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    Chronic hepatitis B virus (HBV) infection is one of the leading causes of liver cirrhosis and hepatocellular carcinoma (HCC). Current treatment strategies of HBV infection including the use of interferon (IFN)-α and nucleotide analogues such as lamivudine and adefovir have met with only partial success. Therefore, it is necessary to develop more effective antiviral therapies that can clear HBV infection with fewer side effects. RNA interference (RNAi), by which a small interfering RNA (siRNA) induces the gene silence at a post-transcriptional level, has the potential of treating HBV infection. The successful use of chemically synthesized siRNA, endogenous expression of small hairpin RNA (shRNA) or microRNA (miRNA) to silence the target gene make this technology towards a potentially rational therapeutics for HBV infection. However, several challenges including poor siRNA stability, inefficient cellular uptake, widespread biodistribution and non-specific effects need to be overcome. In this review, we discuss several strategies for improving the anti-HBV therapeutic efficacy of siRNAs, while avoiding their off-target effects and immunostimulation. There is an in-depth discussion on the (1) mechanisms of RNAi, (2) methods for siRNA/shRNA production, (3) barriers to RNAi-based therapies, and (4) delivery strategies of siRNA for treating HBV infection
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