High-order filtered schemes for time-dependent second order HJB equations

In this paper, we present and analyse a class of "filtered" numerical schemes for second order Hamilton-Jacobi-Bellman equations. Our approach follows the ideas introduced in B.D. Froese and A.M. Oberman, Convergent filtered schemes for the Monge-Amp\`ere partial differential equation, SIAM J. Numer. Anal., 51(1):423--444, 2013, and more recently applied by other authors to stationary or time-dependent first order Hamilton-Jacobi equations. For high order approximation schemes (where "high" stands for greater than one), the inevitable loss of monotonicity prevents the use of the classical theoretical results for convergence to viscosity solutions. The work introduces a suitable local modification of these schemes by "filtering" them with a monotone scheme, such that they can be proven convergent and still show an overall high order behaviour for smooth enough solutions. We give theoretical proofs of these claims and illustrate the behaviour with numerical tests from mathematical finance, focussing also on the use of backward difference formulae (BDF) for constructing the high order schemes.Comment: 27 pages, 16 figures, 4 table

Pretty Private Group Management

Group management is a fundamental building block of today's Internet applications. Mailing lists, chat systems, collaborative document edition but also online social networks such as Facebook and Twitter use group management systems. In many cases, group security is required in the sense that access to data is restricted to group members only. Some applications also require privacy by keeping group members anonymous and unlinkable. Group management systems routinely rely on a central authority that manages and controls the infrastructure and data of the system. Personal user data related to groups then becomes de facto accessible to the central authority. In this paper, we propose a completely distributed approach for group management based on distributed hash tables. As there is no enrollment to a central authority, the created groups can be leveraged by various applications. Following this paradigm we describe a protocol for such a system. We consider security and privacy issues inherently introduced by removing the central authority and provide a formal validation of security properties of the system using AVISPA. We demonstrate the feasibility of this protocol by implementing a prototype running on top of Vuze's DHT

Сучасна наука та раціональність

У статті на основі аналізу сучасної науки розглядається поняття раціональності і її видів. Підкреслюється обмежений характер наукової раціональності, її історичний характер. Проводиться думка про те, що тільки в єдності з соціальною та гуманітарною раціональністю, використовуванням інших форм духовного досвіду наука здібна відобразити цілісність оточуючого світу.In the article notion of rationality and its aspects are considered on the basis of analysis of the modern science. The limited character of scientific rationality and its historical character is stressed there. The idea is following only in the unity of social and humanitarian rationality and use of other forms of spiritual experience, science can reflect integrity of the surrounding world

Stability and convergence of second order backward differentiation schemes for parabolic Hamilton-Jacobi-Bellman equations

We study a second order BDF (Backward Differentiation Formula) scheme for the numerical approximation of parabolic HJB (Hamilton-Jacobi-Bellman) equations. The scheme under consideration is implicit, non-monotone, and second order accurate in time and space. The lack of monotonicity prevents the use of well-known convergence results for solutions in the viscosity sense. In this work, we establish rigorous stability results in a general nonlinear setting as well as convergence results for some particular cases with additional regularity assumptions. While most results are presented for one-dimensional, linear parabolic and non-linear HJB equations, some results are also extended to multiple dimensions and to Isaacs equations. Numerical tests are included to validate the method

Formation of Giant Planets- An Attempt in Matching Observational Constraints

We present models of giant planet formation, taking into account migration and disk viscous evolution. We show that migration can significantly reduce the formation timescale bringing it in good agreement with typical observed disk lifetimes. We then present a model that produces a planet whose current location, core mass and total mass are comparable with the one of Jupiter. For this model, we calculate the enrichments in volatiles and compare them with the one measured by the Galileo probe. We show that our models can reproduce both the measured atmosphere enrichments and the constraints derived by Guillot et al. (2004), if we assume the accretion of planetesimals with ices/rocks ratio equal to 4, and that a substantial amount of CO2 was present in vapor phase in the solar nebula, in agreement with ISM measurement

Renormalization of effective interactions in a negative charge-transfer insulator

We compute from first principles the effective interaction parameters appropriate for a low-energy description of the rare-earth nickelate LuNiO$_{3}$ involving the partially occupied $e_g$ states only. The calculation uses the constrained random-phase approximation and reveals that the effective on-site Coulomb repulsion is strongly reduced by screening effects involving the oxygen-$p$ and nickel-$t_{2g}$ states. The long-range component of the effective low-energy interaction is also found to be sizeable. As a result, the effective on-site interaction between parallel-spin electrons is reduced down to a small negative value. This validates effective low-energy theories of these materials proposed earlier. Electronic structure methods combined with dynamical mean-field theory are used to construct and solve an appropriate low-energy model and explore its phase diagram as a function of the on-site repulsion and Hund's coupling. For the calculated values of these effective interactions we find, in agreement with experiments, that LuNiO$_{3}$ is a metal without disproportionation of the $e_g$ occupancy when considered in its orthorhombic structure, while the monoclinic phase is a disproportionated insulator.Comment: 10 pages, 4 figure

Effect of Experimental Parameters on Water Splitting Using a Hematite Photoanode: FH-HES

Many studies designate hematite as a promising material for direct water splitting into hydrogen and oxygen. For a real outdoor application, it is important to consider hourly and seasonal conditions like temperature and sunlight intensity. The performance of an undoped hematite thin-film photoanode was tested in a photoelectrochemical cell under varying conditions of temperature and light intensity. Both parameters show a positive effect on performance under outdoor conditions