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Higher order correlation measurements involve multiple event averages which must run over unequal events to avoid statistical bias. We derive correction formulas for small event samples, where the bias is largest, and utilize the results to…
Phenomenological implications of neutrino oscillations implied by recent experimental data on pattern of neutrino mass matrix are disscussed. It is shown that it is possible to have a neutrino mass matrix which shows approximate flavor…
The dynamics of randomly crosslinked liquids is addressed via a Rouse- and a Zimm-type model with crosslink statistics taken either from bond percolation or Erdoes-Renyi random graphs. While the Rouse-type model isolates the effects of the…
Two properties are needed for a classical system to be chaotic: exponential stretching and mixing. Recently, out-of-time order correlators were proposed as a measure of chaos in a wide range of physical systems. While most of the attention…
For elliptic interface problems, this paper studies residual-based a posteriori error estimations for various finite element approximations. For the conforming and the Raviart-Thomas mixed elements in two-dimension and for the…
Quantum correlations reflect the quantumness of a system and are useful resources for quantum information and computational processes. The measures of quantum correlations do not have a classical analog and yet are influenced by the…
Fluctuation and correlation observables are often measured using multi-particle correlation methods and therefore mutually probe the origins of genuine correlations present in multi-particle distribution functions. We investigate the common…
We use high resolution direct numerical simulations to study the anisotropic contents of a turbulent, statistically homogeneous flow with random transitions among multiple energy containing states. We decompose the velocity correlation…
Multiscale correlation functions in high Reynolds number experimental turbulence, numerical simulations and synthetic signals are investigated. Fusion Rules predictions as they arise from multiplicative, almost uncorrelated, random…
Cross validation residuals are well known for the ordinary least squares model. Here leave-M-out cross validation is extended to generalised least squares. The relationship between cross validation residuals and Cook's distance is…
Recent work on improved efficiency of calculations for extreme mass ratio inspirals has produced the useful byproduct of comparisons of inspirals of comparable mass by particle perturbation (PP) methods and by numerical relativty (NR). Here…
Moment closure methods appear in myriad scientific disciplines in the modelling of complex systems. The goal is to achieve a closed form of a large, usually even infinite, set of coupled differential (or difference) equations. Each equation…
Recently Mayer et al. [Phys. Rev. E {\bf 68}, 016116 (2003)] proposed a new way to compute numerically the fluctuation-dissipation ratios in nonequilibrium critical systems. Using well-known facts of nonequilibrium critical dynamics I show…
In this short note we discuss recent observation of linear correlation on log-log scale between distribution of dark and visible mass in gravitationally bound systems. The coefficient of such correlation appears to be essentially the same…
Emergence of universal collective behaviour from interactions within a sufficiently large group of elementary constituents is a fundamental scientific paradigm. In physics, correlations in fluctuating microscopic observables can provide key…
Correlation mixtures of elliptical copulas arise when the correlation parameter is driven itself by a latent random process. For such copulas, both penultimate and asymptotic tail dependence are much larger than for ordinary elliptical…
When averages of different experimental determinations of the same quantity are computed, each with statistical and systematic error components, then frequently the statistical and systematic components of the combined error are quoted…
For slowly rotating fluids, we establish the existence of a critical point similar to the one found for non-rotating systems. As the fluid approaches the critical point, the effective inertial mass of any fluid element decreases, vanishing…
We develop the \textit{a posteriori} error analysis of three mixed finite element formulations for rotation-based equations in elasticity, poroelasticity, and interfacial elasticity-poroelasticity. The discretisations use $H^1$-conforming…
We describe an approach to improving model fitting and model generalization that considers the entropy of distributions of modelling residuals. We use simple simulations to demonstrate the observational signatures of overfitting on ordered…