Multiple G-It\^{o} integral in the G-expectation space

In this paper, motivated by mathematic finance we introduce the multiple G-It\^{o} integral in the G-expectation space, then investigate how to calculate. We get the the relationship between Hermite polynomials and multiple G-It\^{o} integrals which is a natural extension of the classical result obtained by It\^{o} in 1951.Comment: 9 page

There is no Nontrivial Hedging Portfolio for Option Pricing with Transaction Costs

Conventional wisdom holds that since continuous-time, Black-Scholes hedging is infinitely expensive in a model with proportional transaction costs, there is no continuous-time strategy which hedges a European call option perfectly. Of course, if one is attempting to dominate the European call rather than replicate it, then one can use the trivial strategy of buying one share of the underlying stock and holding to maturity. In this paper we prove that this is, in fact, the least expensive method of dominating a European call in a Black-Scholes model with proportional transaction costs

On the existence and uniqueness of solutions to stochastic differential equations driven by G-Brownian motion with integral-Lipschitz coefficients

In this paper, we study the existence and uniqueness of solutions to stochastic differential equations driven by G-Brownian motion (GSDEs) with integral-Lipschitz conditions on their coefficients

An overview of Viscosity Solutions of Path-Dependent PDEs

This paper provides an overview of the recently developed notion of viscosity solutions of path-dependent partial di erential equations. We start by a quick review of the Crandall- Ishii notion of viscosity solutions, so as to motivate the relevance of our de nition in the path-dependent case. We focus on the wellposedness theory of such equations. In partic- ular, we provide a simple presentation of the current existence and uniqueness arguments in the semilinear case. We also review the stability property of this notion of solutions, in- cluding the adaptation of the Barles-Souganidis monotonic scheme approximation method. Our results rely crucially on the theory of optimal stopping under nonlinear expectation. In the dominated case, we provide a self-contained presentation of all required results. The fully nonlinear case is more involved and is addressed in [12]

Vortex density models for superconductivity and superfluidity

We study some functionals that describe the density of vortex lines in superconductors subject to an applied magnetic field, and in Bose-Einstein condensates subject to rotational forcing, in quite general domains in 3 dimensions. These functionals are derived from more basic models via Gamma-convergence, here and in a companion paper. In our main results, we use these functionals to obtain descriptions of the critical applied magnetic field (for superconductors) and forcing (for Bose-Einstein), above which ground states exhibit nontrivial vorticity, as well as a characterization of the vortex density in terms of a non local vector-valued generalization of the classical obstacle problem.Comment: 34 page

Some flows in shape optimization

Geometric flows related to shape optimization problems of Bernoulli type are investigated. The evolution law is the sum of a curvature term and a nonlocal term of Hele-Shaw type. We introduce generalized set solutions, the definition of which is widely inspired by viscosity solutions. The main result is an inclusion preservation principle for generalized solutions. As a consequence, we obtain existence, uniqueness and stability of solutions. Asymptotic behavior for the flow is discussed: we prove that the solutions converge to a generalized Bernoulli exterior free boundary problem

Convergence of Ginzburg-Landau functionals in 3-d superconductivity

In this paper we consider the asymptotic behavior of the Ginzburg- Landau model for superconductivity in 3-d, in various energy regimes. We rigorously derive, through an analysis via {\Gamma}-convergence, a reduced model for the vortex density, and we deduce a curvature equation for the vortex lines. In a companion paper, we describe further applications to superconductivity and superfluidity, such as general expressions for the first critical magnetic field H_{c1}, and the critical angular velocity of rotating Bose-Einstein condensates.Comment: 45 page

CD38/cADPR Signaling Pathway in Airway Disease: Regulatory Mechanisms

Asthma is an inflammatory disease in which proinflammatory cytokines have a role in inducing abnormalities of airway smooth muscle function and in the development of airway hyperresponsiveness. Inflammatory cytokines alter calcium (Ca2+) signaling and contractility of airway smooth muscle, which results in nonspecific airway hyperresponsiveness to agonists. In this context, Ca2+ regulatory mechanisms in airway smooth muscle and changes in these regulatory mechanisms encompass a major component of airway hyperresponsiveness. Although dynamic Ca2+ regulation is complex, phospholipase C/inositol tris-phosphate (PLC/IP3) and CD38-cyclic ADP-ribose (CD38/cADPR) are two major pathways mediating agonist-induced Ca2+ regulation in airway smooth muscle. Altered CD38 expression or enhanced cyclic ADP-ribosyl cyclase activity associated with CD38 contributes to human pathologies such as asthma, neoplasia, and neuroimmune diseases. This review is focused on investigations on the role of CD38-cyclic ADP-ribose signaling in airway smooth muscle in the context of transcriptional and posttranscriptional regulation of CD38 expression. The specific roles of transcription factors NF-kB and AP-1 in the transcriptional regulation of CD38 expression and of miRNAs miR-140-3p and miR-708 in the posttranscriptional regulation and the underlying mechanisms of such regulation are discussed

Robustness of Massively Parallel Sequencing Platforms

The improvements in high throughput sequencing technologies (HTS) made clinical sequencing projects such as ClinSeq and Genomics England feasible. Although there are significant improvements in accuracy and reproducibility of HTS based analyses, the usability of these types of data for diagnostic and prognostic applications necessitates a near perfect data generation. To assess the usability of a widely used HTS platform for accurate and reproducible clinical applications in terms of robustness, we generated whole genome shotgun (WGS) sequence data from the genomes of two human individuals in two different genome sequencing centers. After analyzing the data to characterize SNPs and indels using the same tools (BWA, SAMtools, and GATK), we observed significant number of discrepancies in the call sets. As expected, the most of the disagreements between the call sets were found within genomic regions containing common repeats and segmental duplications, albeit only a small fraction of the discordant variants were within the exons and other functionally relevant regions such as promoters. We conclude that although HTS platforms are sufficiently powerful for providing data for first-pass clinical tests, the variant predictions still need to be confirmed using orthogonal methods before using in clinical applications

Repeated games for eikonal equations, integral curvature flows and non-linear parabolic integro-differential equations

The main purpose of this paper is to approximate several non-local evolution equations by zero-sum repeated games in the spirit of the previous works of Kohn and the second author (2006 and 2009): general fully non-linear parabolic integro-differential equations on the one hand, and the integral curvature flow of an interface (Imbert, 2008) on the other hand. In order to do so, we start by constructing such a game for eikonal equations whose speed has a non-constant sign. This provides a (discrete) deterministic control interpretation of these evolution equations. In all our games, two players choose positions successively, and their final payoff is determined by their positions and additional parameters of choice. Because of the non-locality of the problems approximated, by contrast with local problems, their choices have to "collect" information far from their current position. For integral curvature flows, players choose hypersurfaces in the whole space and positions on these hypersurfaces. For parabolic integro-differential equations, players choose smooth functions on the whole space