Pathwise optimal transport bounds between a one-dimensional diffusion and its Euler scheme

In the present paper, we prove that the Wasserstein distance on the space of continuous sample-paths equipped with the supremum norm between the laws of a uniformly elliptic one-dimensional diffusion process and its Euler discretization with $N$ steps is smaller than $O(N^{-2/3+\varepsilon})$ where $\varepsilon$ is an arbitrary positive constant. This rate is intermediate between the strong error estimation in $O(N^{-1/2})$ obtained when coupling the stochastic differential equation and the Euler scheme with the same Brownian motion and the weak error estimation $O(N^{-1})$ obtained when comparing the expectations of the same function of the diffusion and of the Euler scheme at the terminal time $T$. We also check that the supremum over $t\in[0,T]$ of the Wasserstein distance on the space of probability measures on the real line between the laws of the diffusion at time $t$ and the Euler scheme at time $t$ behaves like $O(\sqrt{\log(N)}N^{-1})$.Comment: Published in at http://dx.doi.org/10.1214/13-AAP941 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Drift dependence of optimal trade execution strategies under transient price impact

We give a complete solution to the problem of minimizing the expected liquidity costs in presence of a general drift when the underlying market impact model has linear transient price impact with exponential resilience. It turns out that this problem is well-posed only if the drift is absolutely continuous. Optimal strategies often do not exist, and when they do, they depend strongly on the derivative of the drift. Our approach uses elements from singular stochastic control, even though the problem is essentially non-Markovian due to the transience of price impact and the lack in Markovian structure of the underlying price process. As a corollary, we give a complete solution to the minimization of a certain cost-risk criterion in our setting

Hot Zero and Full Power Validation of PHISICS RELAP-5 Coupling

PHISICS is a reactor analysis toolkit developed over the last 3 years at the Idaho National Laboratory. It has been coupled with the reactor safety analysis code RELAP5-3D. PHISICS is aimed at providing an optimal trade off between needed computational resources (in the range of 10~100 computer processors) and accuracy. In fact, this range has been identified as the next 5 to 10 years average computational capability available to nuclear reactor design and optimization nuclear reactor cores. Detailed information about the individual modules of PHISICS can be found in [1]. An overview of the modules used in this study is given in the next subsection. Lately, the Idaho National Laboratory gained access plant data for the first cycle of a PWR, including Hot Zero Power (HZP) and Hot Full Power (HFP). This data provides the opportunity to validate the transport solver, the interpolation capability for mixed macro and micro cross section and the criticality search option of the PHISICS pack

Lymphogranuloma venerum

This issue of eMedRef provides information to clinicians on the pathophysiology, diagnosis, and therapeutics of lymphogranuloma venerum

Geomagnetism and Aeronomy activities in Italy during IGY, 1957/58

In 2007 several events were organized to celebrate the fiftieth anniversary of the International Geophysical Year (IGY, 1957-1958). The celebrations will last until 2009 and are taking place within different contexts: the International Polar Year (IPY), the International Heliophysical Year (IHY), the electronic Geophysical Year (eGY) and the International Year of Planet Earth (IYPE). IGY offered a very appropriate and timely occasion to undertake a series of coordinated observations of various geophysical phenomena all over the globe. Italy took part in the broad international effort stimulated by IGY. In fact, Italy participated in observations and studies in many of the proposed scientific areas, in particular Geomagnetism and Aeronomy. The Istituto Nazionale di Geofisica (ING) started the installation of observatories, and updated and ensured continuous recording of geophysical observations. Geomagnetism, ionospheric physics, seismology, and other geophysical disciplines, were advanced. Although much of the work was undertaken in Italy, some attention was also devoted to other areas of the world, in particular Antarctica, where Italy participated in seismological observations. This paper gives a summary of the Geomagnetism and Ionospheric Physics activities within IGY. Furthermore, we highlight the importance of this historical event and its outcomes for the improvement of geophysical observations and the post-IGY growth of scientific investigations in Italy

Geomagnetism and Aeronomy activities in Italy during IGY, 1957/58

In 2007 several events were organized to celebrate the fiftieth anniversary of the International Geophysical Year (IGY, 1957-1958). The celebrations will last until 2009 and are taking place within different contexts: the International Polar Year (IPY), the International Heliophysical Year (IHY), the electronic Geophysical Year (eGY) and the International Year of Planet Earth (IYPE). IGY offered a very appropriate and timely occasion to undertake a series of coordinated observations of various geophysical phenomena all over the globe. Italy took part in the broad international effort stimulated by IGY. In fact, Italy participated in observations and studies in many of the proposed scientific areas, in particular Geomagnetism and Aeronomy. The Istituto Nazionale di Geofisica (ING) started the installation of observatories, and updated and ensured continuous recording of geophysical observations. Geomagnetism, ionospheric physics, seismology, and other geophysical disciplines, were advanced. Although much of the work was undertaken in Italy, some attention was also devoted to other areas of the world, in particular Antarctica, where Italy participated in seismological observations. This paper gives a summary of the Geomagnetism and Ionospheric Physics activities within IGY. Furthermore, we highlight the importance of this historical event and its outcomes for the improvement of geophysical observations and the post-IGY growth of scientific investigations in Italy

Optimal execution strategies in limit order books with general shape functions

We consider optimal execution strategies for block market orders placed in a limit order book (LOB). We build on the resilience model proposed by Obizhaeva and Wang (2005) but allow for a general shape of the LOB defined via a given density function. Thus, we can allow for empirically observed LOB shapes and obtain a nonlinear price impact of market orders. We distinguish two possibilities for modeling the resilience of the LOB after a large market order: the exponential recovery of the number of limit orders, i.e., of the volume of the LOB, or the exponential recovery of the bid-ask spread. We consider both of these resilience modes and, in each case, derive explicit optimal execution strategies in discrete time. Applying our results to a block-shaped LOB, we obtain a new closed-form representation for the optimal strategy, which explicitly solves the recursive scheme given in Obizhaeva and Wang (2005). We also provide some evidence for the robustness of optimal strategies with respect to the choice of the shape function and the resilience-type

Higher current algebras, homotopy Manin triples, and a rectilinear adelic complex

The notion of a Manin triple of Lie algebras admits a generalization, to dg Lie algebras, in which various properties are required to hold only up to homotopy. This paper introduces two classes of examples of such homotopy Manin triples. These examples are associated to analogs in complex dimension two of, respectively, the punctured formal 1-disc, and the complex plane with multiple punctures. The dg Lie algebras which appear include certain higher current algebras in the sense of Faonte, Hennion and Kapranov arXiv:1701.01368. We work in a ringed space we call rectilinear space, and one of the tools we introduce is a model of the derived sections of its structure sheaf, whose construction is in the spirit of the adelic complexes for schemes due to Parshin and Beilinson.Comment: 60 page

Towards non-perturbative BV-theory via derived differential cohesive geometry

We propose a global geometric framework which allows one to encode a natural non-perturbative generalisation of usual Batalin-Vilkovisky (BV-)theory. Namely, we construct a concrete model of derived differential cohesive geometry, whose geometric objects are formal derived smooth stacks, i.e. stacks on formal derived smooth manifolds, together with a notion of differential geometry on them. This provides a working language to study generalised geometric spaces that are smooth, infinite-dimensional, higher and derived at the same time. Such a formalism is obtained by combining Schreiber's differential cohesion with the machinery of T\"oen-Vezzosi's homotopical algebraic geometry applied to the theory of derived manifolds of Spivak and Carchedi-Steffens. We investigate two classes of examples of non-perturbative classical BV-theories in the context of derived differential cohesion: scalar field theory and Yang-Mills theory.Comment: 106 pages, 11 figure

Flow Resistance in Open Channel Due to Vegetation at Reach Scale: A Review

Vegetation on the banks and flooding areas of watercourses significantly affects energy losses. To take the latter into account, computational models make use of resistance coefficients based on the evaluation of bed and walls roughness besides the resistance to flow offered by vegetation. This paper, after summarizing the classical approaches based on descriptions and pictures, considers the recent advancements related to the analytical methods relative both to rigid and flexible vegetation. In particular, emergent rigid vegetation is first analyzed by focusing on the methods for determining the drag coefficient, then submerged rigid vegetation is analyzed, highlighting briefly the principles on which the different models are based and recalling the comparisons made in the literature. Then, the models used in the case of both emergent and submerged rigid vegetation are highlighted. As to flexible vegetation, the paper reminds first the flow conditions that cause the vegetation to lay on the channel bed, and then the classical resistance laws that were developed for the design of irrigation canals. The most recent developments in the case of submerged and emergent flexible vegetation are then presented. Since turbulence studies should be considered as the basis of flow resistance, even though the path toward practical use is still long, the new developments in the field of 3D numerical methods are briefly reviewed, presently used to assess the characteristics of turbulence and the transport of sediments and pollutants. The use of remote sensing to map riparian vegetation and estimating biomechanical parameters is briefly analyzed. Finally, some applications are presented, aimed at highlighting, in real cases, the influence exerted by vegetation on water depth and maintenance interventions