Search results for "parable"

Estimating the geometric median in Hilbert spaces with stochastic gradient algorithms: Lp and almost sure rates of convergence

2016

The geometric median, also called L 1 -median, is often used in robust statistics. Moreover, it is more and more usual to deal with large samples taking values in high dimensional spaces. In this context, a fast recursive estimator has been introduced by Cardot et?al. (2013). This work aims at studying more precisely the asymptotic behavior of the estimators of the geometric median based on such non linear stochastic gradient algorithms. The L p rates of convergence as well as almost sure rates of convergence of these estimators are derived in general separable Hilbert spaces. Moreover, the optimal rates of convergence in quadratic mean of the averaged algorithm are also given.

Mean-field games and two-point boundary value problems

2014

A large population of agents seeking to regulate their state to values characterized by a low density is considered. The problem is posed as a mean-field game, for which solutions depend on two partial differential equations, namely the Hamilton-Jacobi-Bellman equation and the Fokker-Plank-Kolmogorov equation. The case in which the distribution of agents is a sum of polynomials and the value function is quadratic is considered. It is shown that a set of ordinary differential equations, with two-point boundary value conditions, can be solved in place of the more complicated partial differential equations associated with the problem. The theory is illustrated by a numerical example.

Global integrability of the gradients of solutions to partial differential equations

1994

On ordinary differential equations with interface conditions

1968

On solving separable block tridiagonal linear systems using a GPU implementation of radix-4 PSCR method

2018

Partial solution variant of the cyclic reduction (PSCR) method is a direct solver that can be applied to certain types of separable block tridiagonal linear systems. Such linear systems arise, e.g., from the Poisson and the Helmholtz equations discretized with bilinear finite-elements. Furthermore, the separability of the linear system entails that the discretization domain has to be rectangular and the discretization mesh orthogonal. A generalized graphics processing unit (GPU) implementation of the PSCR method is presented. The numerical results indicate up to 24-fold speedups when compared to an equivalent CPU implementation that utilizes a single CPU core. Attained floating point perfor…

Physical oceanography, sea-bed photographs and videos of benthos from the Weddell Sea taken with remote operated vehicle CHEROKEE during POLARSTERN c…

2010

The marine ecosystem on the eastern shelf of the Antarctic Peninsula was surveyed 5 and 12 years after the climate-induced collapse of the Larsen A and B ice shelves. An impoverished benthic fauna was discovered, that included deep-sea species presumed to be remnants from ice-covered conditions. The current structure of various ecosystem components appears to result from extremely different response rates to the change from an oligotrophic sub-ice-shelf ecosystem to a productive shelf ecosystem. Meiobenthic communities remained impoverished only inside the embayments. On local scales, macro- and mega-epibenthic diversity was generally low, with pioneer species and typical Antarctic megabent…

Almost square Banach spaces

2014

We single out and study a natural class of Banach spaces -- almost square Banach spaces. In an almost square space we can find, given a finite set $x_1,x_2,\ldots,x_N$ in the unit sphere, a unit vector $y$ such that $\|x_i-y\|$ is almost one. These spaces have duals that are octahedral and finite convex combinations of slices of the unit ball of an almost square space have diameter 2. We provide several examples and characterizations of almost square spaces. We prove that non-reflexive spaces which are M-ideals in their biduals are almost square. We show that every separable space containing a copy of $c_0$ can be renormed to be almost square. A local and a weak version of almost square spa…

On GPU-accelerated fast direct solvers and their applications in image denoising

2015

Does self-efficacy influence academic results? A separable-effect mediation analysis

2021

In causal mediation analysis, natural effects are identified only under strict assumptions involving cross-world counterfactuals. An alternative approach recently developed, called separable, allows for identification of mediational effects in a wide range of models, since it relies on weaker assumptions than those required by natural effects. In this paper, the separable-effect approach is revised and an application to data is presented.

Advanced spatio-temporal point processes for the Sicily seismicity analysis

2018

Due to the complexity of the generator process of seismic events, we study under several aspects the interaction structure between earthquake events using recently developed spatio-temporal statistical techniques and models. Using these advanced statistical tools, we aim to characterise the global and local scale cluster behaviour of the Easter Sicily seismicity considering the catalogue data since 2006, when the Italian National Seismic Network was upgraded and earthquake location was sensibly improved. Firstly, we characterise the global complex spatiotemporal interaction structure with the space-time ETAS model where background seismicity is estimated non-parametrically, while triggered …