The relative energy of homogeneous and isotropic universes from variational principles

We calculate the relative conserved currents, superpotentials and conserved quantities between two homogeneous and isotropic universes. In particular we prove that their relative "energy" (defined as the conserved quantity associated to cosmic time coordinate translations for a comoving observer) is vanishing and so are the other conserved quantities related to a Lie subalgebra of vector fields isomorphic to the Poincar\'e algebra. These quantities are also conserved in time. We also find a relative conserved quantity for such a kind of solutions which is conserved in time though non-vanishing. This example provides at least two insights in the theory of conserved quantities in General Relativity. First, the contribution of the cosmological matter fluid to the conserved quantities is carefully studied and proved to be vanishing. Second, we explicitly show that our superpotential (that happens to coincide with the so-called KBL potential although it is generated differently) provides strong conservation laws under much weaker hypotheses than the ones usually required. In particular, the symmetry generator is not needed to be Killing (nor Killing of the background, nor asymptotically Killing), the prescription is quasi-local and it works fine in a finite region too and no matching condition on the boundary is required.Comment: Corrected typos and improved forma

Stochastic Chemical Kinetics. Theory and (Mostly) Systems Biological Applications, P. Erdi, G. Lente. Springer (2014)

Book review of Stochastic Chemical Kinetics. Theory and (Mostly) Systems Biological Applications, P. Erdi, G. Lente. Springer (2014

Chetaev vs. vakonomic prescriptions in constrained field theories with parametrized variational calculus

Starting from a characterization of admissible Cheataev and vakonomic variations in a field theory with constraints we show how the so called parametrized variational calculus can help to derive the vakonomic and the non-holonomic field equations. We present an example in field theory where the non-holonomic method proved to be unphysical

A copula-based method to build diffusion models with prescribed marginal and serial dependence

This paper investigates the probabilistic properties that determine the existence of space-time transformations between diffusion processes. We prove that two diffusions are related by a monotone space-time transformation if and only if they share the same serial dependence. The serial dependence of a diffusion process is studied by means of its copula density and the effect of monotone and non-monotone space-time transformations on the copula density is discussed. This provides us a methodology to build diffusion models by freely combining prescribed marginal behaviors and temporal dependence structures. Explicit expressions of copula densities are provided for tractable models. A possible application in neuroscience is sketched as a proof of concept

Estimation in discretely observed diffusions killed at a threshold

Parameter estimation in diffusion processes from discrete observations up to a first-hitting time is clearly of practical relevance, but does not seem to have been studied so far. In neuroscience, many models for the membrane potential evolution involve the presence of an upper threshold. Data are modeled as discretely observed diffusions which are killed when the threshold is reached. Statistical inference is often based on the misspecified likelihood ignoring the presence of the threshold causing severe bias, e.g. the bias incurred in the drift parameters of the Ornstein-Uhlenbeck model for biological relevant parameters can be up to 25-100%. We calculate or approximate the likelihood function of the killed process. When estimating from a single trajectory, considerable bias may still be present, and the distribution of the estimates can be heavily skewed and with a huge variance. Parametric bootstrap is effective in correcting the bias. Standard asymptotic results do not apply, but consistency and asymptotic normality may be recovered when multiple trajectories are observed, if the mean first-passage time through the threshold is finite. Numerical examples illustrate the results and an experimental data set of intracellular recordings of the membrane potential of a motoneuron is analyzed.Comment: 29 pages, 5 figure

Analyzing RNA data with scVelo: identifiability issues and a Bayesian implementation

The analysis of RNA data plays a crucial role in understanding cellular differentiation. One widely-used methodology for analyzing RNA data is scVelo. However, in this paper, we show that, among other issues of scVelo, the current model formalization suffers from identifiability problems. We propose a Bayesian version of scVelo with modifications that address these issues