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We give a definition of higher dimensional iterated integrals based on integration over membranes. We prove basic properties of this definition and formulate a conjecture which extends Chen's de Rham Theorem for iterated integrals to the…
In this paper a new restarting method for Krylov subspace matrix exponential evaluations is proposed. Since our restarting technique essentially employs the residual, some convergence results for the residual are given. We also discuss how…
Bayesian model comparison (BMC) offers a principled approach for assessing the relative merits of competing computational models and propagating uncertainty into model selection decisions. However, BMC is often intractable for the popular…
This is a revised version of NT0505521, a translation of our Japanese expository article that was published under the title `{\it An overview of sieve methods}' in the second issue of the 52nd volume of Sugaku, the Mathematical Society of…
We consider the possibility of using the hierarchical approximation to understand the continuum limit of a reformulation of the 3D Ising model initiated by Polyakov. We introduce several new formulations of the hierarchical model using dual…
This paper was prepared by the HEP Software Foundation (HSF) PyHEP Working Group as input to the second phase of the LHCC review of High-Luminosity LHC (HL-LHC) computing, which took place in November, 2021. It describes the adoption of…
Online evaluation of machine learning models is typically conducted through A/B experiments. Sequential statistical tests are valuable tools for analysing these experiments, as they enable researchers to stop data collection early without…
The full causal ladder of spacetimes is constructed, and their updated main properties are developed. Old concepts and alternative definitions of each level of the ladder are revisited, with emphasis in minimum hypotheses. The implications…
Eigenspaces of covariance matrices play an important role in statistical machine learning, arising in variety of modern algorithms. Quantitatively, it is convenient to describe the eigenspaces in terms of spectral projectors. This work…
Bayesian optimization has emerged as a strong candidate tool for global optimization of functions with expensive evaluation costs. However, due to the dynamic nature of research in Bayesian approaches, and the evolution of computing…
In this paper, we will review the process of evidence accumulation in the PSEIKI system for expectation-driven interpretation of images of 3-D scenes. Expectations are presented to PSEIKI as a geometrical hierarchy of abstractions. PSEIKI's…
This paper presents an iteration method for solving linear particle transport problems in binary stochastic mixtures. It is based on nonlinear projection approach. The method is defined by a hierarchy of equations consisting of the…
We investigate the second time scale of the metastable behavior of the reversible inclusion process in an extension of the study by [Bianchi, Dommers, and Giardin\`a, Electronic Journal of Probability, 22: 1-34, 2017], which presented the…
An integro-differential equation of hyperbolic type, with mixed boundary conditions, is considered. A continuous space-time finite element method of degree one is formulated. A posteriori error representations based on space-time cells is…
The described works have been carried out in the framework of a mid-term study initiated by the Centre Electronique de l'Armement, then by an advanced study launched by the Direction de la Recherche et des Etudes Technologiques in France in…
A parallelizable iterative procedure based on domain decomposition is presented and analyzed for weak Galerkin finite element methods for second order elliptic equations. The convergence analysis is established for the decomposition of the…
Incremental learning from non-stationary data poses special challenges to the field of machine learning. Although new algorithms have been developed for this, assessment of results and comparison of behaviors are still open problems, mainly…
In this paper a novel hybrid approach for compensating the distortion of any interpolation has been proposed. In this hybrid method, a modular approach was incorporated in an iterative fashion. By using this approach we can get drastic…
Starting with the recursive extended Euclid's algorithm, we apply a systematic approach using matrix notation to transform it into an iterative algorithm. The partial correctness proof derived from the transformation turns out to be very…
In a randomised clinical trial, when the result of the primary endpoint shows a significant benefit, the secondary endpoints are scrutinised to identify additional effects of the treatment. However, this approach entails a risk of…