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Recent experimental results on the static or quasistatic response of granular materials have been interpreted to suggest the inapplicability of the traditional engineering approaches, which are based on elasto-plastic models (which are…
In models of oceanic and atmospheric flows, thermodynamic functions and conservative variables may be defined up to a certain degree of arbitrariness, in the sense that, for a given set of observable quantities such as pressure and…
The current Universe is composed by a mixture of relativistic species, baryonic matter, dark matter and dark energy which evolve in a non-trivial way at perturbative level. An advanced description of the cosmological dynamics should include…
There is a persistent confusion about determinism and predictability. In spite of the opinions of some eminent philosophers (e.g., Popper), it is possible to understand that the two concepts are completely unrelated. In few words we can say…
We present a simple, nearly model-independent estimate that yields the predictions of the simplest inflationary and ekpyrotic/cyclic models for the spectral tilt of the primordial density inhomogeneities. Remarkably, we find that the…
Big bang nucleosynthesis constraints on baryon isocurvature perturbations are determined. A simple model ignoring the effects of the scale of the perturbations is first reviewed. This model is then extended to test the claim that large…
The conventional cosmological perturbation theory has been performed under the assumption that we know the whole spatial region of the universe with infinite volume. This is, however, not the case in the actual observations because…
Many, if not most, inflationary models predict the power-law index of the spectrum of density perturbations is close to one, though not precisely equal to one, |n-1| \sim O(0.1), implying that the spectrum of density perturbations is…
In recent work we analyzed the evolution of primordial perturbations satisfying Planck-scale-modified dispersion relations and showed that there is no cosmological "squeezing" in the critical model that produces perturbations with a scale…
Quantifying model uncertainty is critical for understanding prediction reliability, yet distinguishing between aleatoric and epistemic uncertainty remains challenging. We extend recent work from classification to regression to provide a…
In this paper we provide a conceptual overview of latent variable models within a probabilistic modeling framework, an overview that emphasizes the compositional nature and the interconnectedness of the seemingly disparate models commonly…
Models of dark energy in which neutrinos interact with the scalar field supposed to be responsible for the acceleration of the universe usually imply a variation of the neutrino masses on cosmological time scales. In this work we propose a…
Intensity minima and maxima of speckle patterns obtained behind a diffuser are experimentally interchanged by applying a spiral phase delay of charge $\pm 1$ to the impinging coherent beam. This transform arises from the intuitive…
The preferred shape for the primordial spectrum of curvature perturbations is determined by performing a Bayesian model selection analysis of cosmological observations. We first reconstruct the spectrum modelled as piecewise linear in \log…
Macroscopic models for spatially extended systems under random influences are often described by stochastic partial differential equations (SPDEs). Some techniques for understanding solutions of such equations, such as estimating…
The details of reheating energy scale $\rho_{reh}$ is largely uncertain today, independent of inflation models. This would induce uncertainty in predicting primordial spectrum. Such uncertainty could be very large, especially for spectra…
The general relationship between an arbitrary frequency distribution and the expectation value of the frequency distributions of its samples is discussed. A wide set of measurable quantities ("invariant moments") whose expectation value…
We study small perturbations of diffusion processes in $\mathbb{R}^d$ that leave invariant a finite collection of hypersurfaces. Each surface is assumed to be repelling for the unperturbed process, and the unperturbed motion on each of the…
Recent theoretical ideas and observational claims suggest that the fine structure constant alpha may be variable. We examine a spectrum of models in which alpha is a function of a scalar field. Specifically, we consider three scenarios:…
A particular class of flat Emergent Universe scenario is studied in light of recent observational data. Observationally permissible ranges of values are obtained for the model parameters. The class of model studied here can accommodate…