Search results for "differential"
showing 10 items of 6566 documents
A posteriori error estimates for time-dependent reaction-diffusion problems based on the Payne-Weinberger inequality
2015
We consider evolutionary reaction-diffusion problem with mixed Dirichlet--Robin boundary conditions. For this class of problems, we derive two-sided estimates of the distance between any function in the admissible energy space and exact solution of the problem. The estimates (majorants and minorants) are explicitly computable and do not contain unknown functions or constants. Moreover, it is proved that the estimates are equivalent to the energy norm of the deviation from the exact solution.
Reduced Order Models for Pricing European and American Options under Stochastic Volatility and Jump-Diffusion Models
2017
Abstract European options can be priced by solving parabolic partial(-integro) differential equations under stochastic volatility and jump-diffusion models like the Heston, Merton, and Bates models. American option prices can be obtained by solving linear complementary problems (LCPs) with the same operators. A finite difference discretization leads to a so-called full order model (FOM). Reduced order models (ROMs) are derived employing proper orthogonal decomposition (POD). The early exercise constraint of American options is enforced by a penalty on subset of grid points. The presented numerical experiments demonstrate that pricing with ROMs can be orders of magnitude faster within a give…
Ensemble strategies in Compact Differential Evolution
2011
Differential Evolution is a population based stochastic algorithm with less number of parameters to tune. However, the performance of DE is sensitive to the mutation and crossover strategies and their associated parameters. To obtain optimal performance, DE requires time consuming trial and error parameter tuning. To overcome the computationally expensive parameter tuning different adaptive/self-adaptive techniques have been proposed. Recently the idea of ensemble strategies in DE has been proposed and favorably compared with some of the state-of-the-art self-adaptive techniques. Compact Differential Evolution (cDE) is modified version of DE algorithm which can be effectively used to solve …
Super-fit and population size reduction in compact Differential Evolution
2011
Although Differential Evolution is an efficient and versatile optimizer, it has a wide margin of improvement. During the latest years much effort of computer scientists studying Differential Evolution has been oriented towards the improvement of the algorithmic paradigm by adding and modifying components. In particular, two modifications lead to important improvements to the original algorithmic performance. The first is the super-fit mechanism, that is the injection at the beginning of the optimization process of a solution previously improved by another algorithm. The second is the progressive reduction of the population size during the evolution of the population. Recently, the algorithm…
Music, vibrotactile mediation and bodily sensations in anorexia nervosa : "It's like I can really feel my heart beating"
2020
This article presents the theoretical, scientific, and methodological foundations for the design and implementation of an innovative technological and clinical platform that combined sound, music, and vibrotactile mediation used in a therapeutic setting by adolescents suffering from anorexia nervosa. In 2019, we carried out a pilot experiment with a group of 8 adolescent patients hospitalized in the Eating Disorders Unit of the Department of Adolescent and Young Adult Psychiatry of the Institut Mutualiste Montsouris in Paris. Within this clinical framework, we aimed to create conditions suitable for patients to reinvest in their “disaffected” bodily zones and internal experiences through re…
Fractional viscoelastic transversally isotropic Timoshenko beam
2014
In this paper the viscoelastic behavior of pultruded beams has been examined. Pultruded beams are constituted by a polymer infilled with reinforcement in longitudinal direction, while in the orthogonal direction no fiber are present for technological reasons. As a consequence the material has two different behaviors in longitudinal and in orthogonal directions. It follows that pultruded beams are transversally isotropic, and the shear deformation may not be neglected. Based upon the previous observations and assuming for Creep and/or Relaxation test the power law, the constitutive equations are ruled by fractional operators. From constitutive laws, and assuming the Timoshenko beam theory to…
A survey on algebraic dilatations
2023
In this text, we wish to provide the reader with a short guide to recent works on the theory of dilatations in Commutative Algebra and Algebraic Geometry. These works fall naturally into two categories: one emphasises foundational and theoretical aspects and the other applications to existing theories.
Regularity for nonlinear stochastic games
2015
We establish regularity for functions satisfying a dynamic programming equation, which may arise for example from stochastic games or discretization schemes. Our results can also be utilized in obtaining regularity and existence results for the corresponding partial differential equations. peerReviewed
Remarks on regularity for p-Laplacian type equations in non-divergence form
2018
We study a singular or degenerate equation in non-divergence form modeled by the $p$-Laplacian, $$-|Du|^\gamma\left(\Delta u+(p-2)\Delta_\infty^N u\right)=f\ \ \ \ \text{in}\ \ \ \Omega.$$ We investigate local $C^{1,\alpha}$ regularity of viscosity solutions in the full range $\gamma>-1$ and $p>1$, and provide local $W^{2,2}$ estimates in the restricted cases where $p$ is close to 2 and $\gamma$ is close to 0.
Lidar detection of carbon dioxide in volcanic plumes
2015
Volcanic gases give information on magmatic processes. In particular, anomalous releases of carbon dioxide precede volcanic eruptions. Up to now, this gas has been measured in volcanic plumes with conventional measurements that imply the severe risks of local sampling and can last many hours. For these reasons and for the great advantages of laser sensing, the thorough development of volcanic lidar has been undertaken at the Diagnostics and Metrology Laboratory (UTAPRAD-DIM) of the Italian National Agency for New Technologies, Energy and Sustainable Economic Development (ENEA). In fact, lidar profiling allows one to scan remotely volcanic plumes in a fast and continuous way, and with high s…