Related papers: The Helicoidal Method
Equilibrium measures are special invariant measures of chaotic dynamical systems and iterated function systems, commonly studied as salient examples of fractal measures. While useful analytic expressions are rare, computational exploration…
We present and analyze a multiscale method for wave propagation problems, posed on spatial networks. By introducing a coarse scale, using a finite element space interpolated onto the network, we construct a discrete multiscale space using…
This article presents a generic hybrid numerical method to price a wide range of options on one or several assets, as well as assets with stochastic drift or volatility. In particular for equity and interest rate hybrid with local…
We present a method for studying the secular gravitational dynamics of hierarchical multiple systems consisting of nested binaries, which is valid for an arbitrary number of bodies and arbitrary hierarchical structure. We derive the…
The heterogeneous multi-scale method (HMM) is a general strategy for dealing with problems involving multi-scales, with multi-physics, using multi-grids. It not only unifies several existing multi-scale methods, but also provide a…
One popular method for dealing with large-scale data sets is sampling. For example, by using the empirical statistical leverage scores as an importance sampling distribution, the method of algorithmic leveraging samples and rescales…
This survey note describes a brief systemic view to approaches for evaluation of hierarchical composite (modular) systems. The list of considered issues involves the following: (i) basic assessment scales (quantitative scale, ordinal scale,…
A parameter estimation method is devised for a slow-fast stochastic dynamical system, where often only the slow component is observable. By using the observations only on the slow component, the system parameters are estimated by working on…
We consider a finite element method for elliptic equation with heterogeneous and possibly high-contrast coefficients based on primal hybrid formulation. A space decomposition as in FETI and BDCC allows a sequential computations of the…
Recent advances have made it feasible to apply the stochastic variational paradigm to a collapsed representation of latent Dirichlet allocation (LDA). While the stochastic variational paradigm has successfully been applied to an uncollapsed…
Conditional heteroscedastic (CH) models are routinely used to analyze financial datasets. The classical models such as ARCH-GARCH with time-invariant coefficients are often inadequate to describe frequent changes over time due to market…
Hamiltonian systems are known to conserve the Hamiltonian function, which describes the energy evolution over time. Obtaining a numerical spatio-temporal scheme that accurately preserves the discretized Hamiltonian function is often a…
In this paper, we are interested in investigating a weighted variant of Hermite-Hadamard type inequalities involving convex functionals. The approach undertaken makes it possible to refine and reverse certain inequalities already known in…
In this work, we apply the finite element heterogeneous multiscale method to a class of dispersive first-order time-dependent Maxwell systems. For this purpose, we use an analytic homogenization result, which shows that the effective system…
Multivariate time series classification is a task with increasing importance due to the proliferation of new problems in various fields (economy, health, energy, transport, crops, etc.) where a large number of information sources are…
We devise and evaluate numerically Hybrid High-Order (HHO) methods for hyperelastic materials undergoing finite deformations. The HHO methods use as discrete unknowns piecewise polynomials of order $k\ge1$ on the mesh skeleton, together…
An analytical method for investigation of the evolution of dynamical systems {\it with independent on time accuracy} is developed for perturbed Hamiltonian systems. The error-free estimation using of computer algebra enables the application…
In the present paper we consider the varying coefficient model which represents a useful tool for exploring dynamic patterns in many applications. Existing methods typically provide asymptotic evaluation of precision of estimation…
High dimensional Vector Autoregressions (VAR) have received a lot of interest recently due to novel applications in health, engineering, finance and the social sciences. Three issues arise when analyzing VAR's: (a) The high dimensional…
The paper is devoted to a systematic study and characterizations of notions of local maximal monotonicity and their strong counterparts for set-valued operators that appear in variational analysis, optimization, and their applications. We…