Related papers: Exact renormalisation for patch frequencies in inf…
We show that, for the purpose of pricing Swaptions, the Swap rate and the corresponding Forward rates can be considered lognormal under a single martingale measure. Swaptions can then be priced as options on a basket of lognormal assets and…
For finite volume field theories with discrete translational invariance, conserved currents can be additively renormalized by infrared effects. We demonstrate this for pions using chiral perturbation theory coupled to electromagnetism in a…
Recently there have been differing viewpoints on how to evaluate the curvature power spectrum generated during inflation. In a series of papers by some authors it has been argued that the renormalization scheme adopted for the inflaton…
We consider the method of self-similar renormalization for calculating critical temperatures and critical indices. A new optimized variant of the method for an effective summation of asymptotic series is suggested and illustrated by several…
A new family of inflation models is introduced and studied. The models are characterised by a scalar potential which, far from the origin, approximates an inflationary plateau, while near the origin becomes monomial, as in chaotic…
We present non-standard optical Ramsey schemes that use pulses individually tailored in duration, phase, and frequency to cancel spurious frequency shifts related to the excitation itself. In particular, the field shifts and their…
Parametric resonance or preheating is a plausible mechanism for bringing about the transition between the inflationary phase and a hot, radiation dominated universe. This epoch results in the rapid production of heavy particles far from…
Formulae are derived for the spectra of scalar curvature perturbations and gravitational waves produced during inflation, special cases of which include power law inflation, natural inflation in the small angle approximation and inflation…
We present a finite-order system of recurrence relations for a permanent of circulant matrices containing a band of k any-value diagonals on top of a uniform matrix (for k = 1, 2, and 3) as well as the method for deriving such recurrence…
This paper considers the model problem of reconstructing an object from incomplete frequency samples. Consider a discrete-time signal $f \in \C^N$ and a randomly chosen set of frequencies $\Omega$ of mean size $\tau N$. Is it possible to…
The possibility that quantum corrections break the conservation of superhorizon adiabatic perturbations in single field inflation is examined. I consider the lowest order corrections from massless matter fields in the Hamiltonian formalism.…
The problem of calculating the frequencies of network motifs on three and four nodes in large networks is considered. Telecommunications networks, cell molecular networks are investigated. The sizes of the investigated networks are hundreds…
Equation-free macroscale modelling is a systematic and rigorous computational methodology for efficiently predicting the dynamics of a microscale system at a desired macroscale system level. In this scheme, the given microscale model is…
Classical studies of the Fibonacci sequence focus on its periodicity modulo $m$ (the Pisano periods) with canonical initialization. We investigate instead the complete periodic structure arising from all $m^2$ possible initializations in…
In this paper we build a geometric model for the renormalisation of irrationally indifferent fixed points. The geometric model incorporates the fine arithmetic properties of the rotation number at the fixed point. Using this model for the…
The study of nonlinear phenomena in systems with many degrees of freedom often relies on complex numerical simulations. In trying to model realistic situations, these systems may be coupled to an external environment which drives their…
We describe how monomial chaotic inflation becomes compatible with the latest CMB data thanks to radiative corrections producing a plateau. The interactions of the inflation with other fields, required for reheating, can flatten the…
Understanding complex systems which exhibit desynchronization as an emergent property should have important implications, particularly in treating neurological disorders and designing efficient communication networks. Here were demonstrate…
In this article, we consider a simple representation for real numbers and propose top-down procedures to approximate various algebraic and transcendental operations with arbitrary precision. Detailed algorithms and proofs are provided to…
Probabilistic graphical models are a key tool in machine learning applications. Computing the partition function, i.e., normalizing constant, is a fundamental task of statistical inference but it is generally computationally intractable,…