Search results for "gradient"
showing 10 items of 725 documents
Recursion at the crossroads of sequence modeling, random trees, stochastic algorithms and martingales
2013
This monograph synthesizes several studies spanning from dynamical systems in the statistical analysis of sequences, to analysis of algorithms in random trees and discrete stochastic processes. These works find applications in various fields ranging from biological sequences to linear regression models, branching processes, through functional statistics and estimates of risk indicators for insurances. All the established results use, in one way or another, the recursive property of the structure under study, by highlighting invariants such as martingales, which are at the heart of this monograph, as tools as well as objects of study.
Analyse numérique MIGS 1re Année
2021
Il s'agit d'un cours d'analyse numérique qui a été dispensé à l'Université de Bourgogne en Master MIGS 1re Année (en 2019-2020, et 2020-2021). Il traite principalement de la résolution itérative de systèmes linéaires symétriques par gradient conjugué, et aussi de la résolution de systèmes linéaires mal posés par moindres carrés. Il vient en complément aux cours d'analyse numérique et d'optimisation que les étudiants ont suivi auparavant.
Artificial Mosaics by Gradient Vector Flow
2008
Kvadrātiskās programmēšanas uzdevumu atrisināšanas metodes
2016
Bakalaura darbā tiek apskatītas kvadrātiskās programmēšanas uzdevumu atrisināšanas metodes. Kvadrātiskās programmēšana ir nelineārās programmēšanas nozare, kas pēta tādus uzdevumus, kuru mērķa funkcija ir otrās pakāpes funkcija, bet nosacījumu sistēma sastāv no lineārām nevienādībām. Darbā aplūkotas divas atrisināšanas metodes – gradienta metode un aktīvas kopas metode. Ilustrācijai aplūkoti piemēri un veikts metožu salīdzinājums.
CALIBRATION OF LÉVY PROCESSES USING OPTIMAL CONTROL OF KOLMOGOROV EQUATIONS WITH PERIODIC BOUNDARY CONDITIONS
2018
We present an optimal control approach to the problem of model calibration for L\'evy processes based on a non parametric estimation procedure. The calibration problem is of considerable interest in mathematical finance and beyond. Calibration of L\'evy processes is particularly challenging as the jump distribution is given by an arbitrary L\'evy measure, which form a infinite dimensional space. In this work, we follow an approach which is related to the maximum likelihood theory of sieves. The sampling of the L\'evy process is modelled as independent observations of the stochastic process at some terminal time $T$. We use a generic spline discretization of the L\'evy jump measure and selec…
Gradient and Lipschitz Estimates for Tug-of-War Type Games
2021
We define a random step size tug-of-war game and show that the gradient of a value function exists almost everywhere. We also prove that the gradients of value functions are uniformly bounded and converge weakly to the gradient of the corresponding $p$-harmonic function. Moreover, we establish an improved Lipschitz estimate when boundary values are close to a plane. Such estimates are known to play a key role in the higher regularity theory of partial differential equations. The proofs are based on cancellation and coupling methods as well as an improved version of the cylinder walk argument. peerReviewed
The Hajłasz Capacity Density Condition is Self-improving
2022
We prove a self-improvement property of a capacity density condition for a nonlocal Hajlasz gradient in complete geodesic spaces with a doubling measure. The proof relates the capacity density condition with boundary Poincare inequalities, adapts Keith-Zhong techniques for establishing local Hardy inequalities and applies Koskela-Zhong arguments for proving self-improvement properties of local Hardy inequalities. This leads to a characterization of the Hajlasz capacity density condition in terms of a strict upper bound on the upper Assouad codimension of the underlying set, which shows the self-improvement property of the Hajlasz capacity density condition. Open Access funding provided than…
On the second-order regularity of solutions to the parabolic p-Laplace equation
2022
AbstractIn this paper, we study the second-order Sobolev regularity of solutions to the parabolic p-Laplace equation. For any p-parabolic function u, we show that $$D(\left| Du\right| ^{\frac{p-2+s}{2}}Du)$$ D ( D u p - 2 + s 2 D u ) exists as a function and belongs to $$L^{2}_{\text {loc}}$$ L loc 2 with $$s>-1$$ s > - 1 and $$1<p<\infty $$ 1 < p < ∞ . The range of s is sharp.
A Continuous Pore Size Gradient PLLA Scaffold For Osteochondral Regeneration
2016
Osteochondral (OC) scaffold-based regenerative approaches in the joint are challenging since the scaffold must provide mechanical strength while also mimicking the local cartilage and bone microenvironments. Thermally Induced Phase Separation (TIPS) can produce scaffolds with a wide range of pore size morphologies/distributions. Here, we produced by TIPS a poly-L-lactide (PLL A) scaffold with a continuous pore size gradient along the sample thickness, from ~70μm diameter on one side to ~200 μm diameter on the opposite surface.
pH intramucoso gástrico (pHi) y gradiente sistémico-regional de CO2 en el paciente pediátrico crítico. Monitorización contínua de la perfusión tisula…
2016
INTRODUCCIÓN Las situaciones de shock compensado identificadas por la presencia de acidosis en la mucosa intestinal mediante la monitorización del pHi (pH intramucoso), son extremadamente frecuentes en el paciente crítico. Estos episodios de isquemia intestinal se relacionan con el síndrome de disfunción multiorgánica (SDMO). El pHi puede medirse de forma indirecta utilizando una modificación de la fórmula de Henderson-Hasselbach, mediante tonometría. Esta técnica se fundamenta en 2 asunciones: 1. La PCO2, medida tonométricamente se aproxima a la de la mucosa intestinal, 2. La concentración de bicarbonato en la mucosa intestinal está en equilibrio con la del lecho capilar intestinal, y ésta…