Related papers: Melnikov-Arnold integrals and optimal normal forms
In this paper we present an approach towards the comprehensive analysis of the non-integrability of differential equations in the form $\ddot x=f(x,t)$ which is analogous to Hamiltonian systems with 1+1/2 degree of freedom. In particular,…
Mean motion resonances [MMRs] play an important role in the formation and evolution of planetary systems and have significantly influenced the orbital properties and distribution of planets and minor planets in the solar system as well as…
We show that various formulations (e.g., dual and Kullback-Csiszar iterations) of estimation of maximum entropy (ME) models can be transformed to solving systems of polynomial equations in several variables for which one can use celebrated…
We present the integrand reduction via multivariate polynomial division as a natural technique to encode the unitarity conditions of Feynman amplitudes. We derive a recursive formula for the integrand reduction, valid for arbitrary…
In this paper, we derive a model from Maxwell equations for the magnetic resonance of split-ring resonators. Using this model we revisit the scaling of split-ring resonators. Inspired by our model, we propose a new type of split-hybrid…
In this work, the estimation of the multivariate normal mean by different classes of shrinkage estimators is investigated. The risk associated with the balanced loss function is used to compare two estimators. We start by considering…
We propose a second-order accurate method to estimate the eigenvectors of extremely large matrices thereby addressing a problem of relevance to statisticians working in the analysis of very large datasets. More specifically, we show that…
Adaptive Multilevel Splitting (AMS for short) is a generic Monte Carlo method for Markov processes that simulates rare events and estimates associated probabilities. Despite its practical efficiency, there are almost no theoretical results…
Magnetic Particle Imaging (MPI) is a recent imaging modality where superparamagnetic nanoparticles are employed as tracers. The reconstruction task is to obtain the spatial particle distribution from a voltage signal induced by the…
We propose a first implementation of the integrand-reduction method for two-loop scattering amplitudes. We show that the residues of the amplitudes on multi-particle cuts are polynomials in the irreducible scalar products involving the loop…
In this paper we study the performance of a symplectic numerical integrator based on the splitting method. This method is applied to a subtle problem i.e. higher order resonance of the elastic pendulum. In order to numerically study the…
Second-order superintegrable systems in dimensions two and three are essentially classified. With increasing dimension, however, the non-linear partial differential equations employed in current methods become unmanageable. Here we propose…
Imaging with multiple modalities or multiple channels is becoming increasingly important for our modern society. A key tool for understanding and early diagnosis of cancer and dementia is PET-MR, a combined positron emission tomography and…
Detecting out of distribution (OOD) samples is of paramount importance in all Machine Learning applications. Deep generative modeling has emerged as a dominant paradigm to model complex data distributions without labels. However, prior work…
In this paper, we propose new operator-splitting algorithms for the total variation regularized infimal convolution (TV-IC) model [4] in order to remove mixed Poisson-Gaussian(MPG) noise. In the existing splitting algorithm for TV-IC, an…
The most general form of a marginal extended perturbation in a two-dimensional system is deduced from scaling considerations. It includes as particular cases extended perturbations decaying either from a surface, a line or a point for which…
M.Levitin and E.Shargorodsky purposed in a recent article, [math.SP/0212087], the use of the so called ``second order relative spectrum'', to find eigenvalues of self-adjoint operators in gaps of the essential spectrum. Let $M$ be a…
Developing a versatile deep neural network to model music audio is crucial in MIR. This task is challenging due to the intricate spectral variations inherent in music signals, which convey melody, harmonics, and timbres of diverse…
Regular chains and triangular decompositions are fundamental and well-developed tools for describing the complex solutions of polynomial systems. This paper proposes adaptations of these tools focusing on solutions of the real analogue:…
The paper deals with the problem of existence of a convergent "strong" normal form in the neighbourhood of an equilibrium, for a finite dimensional system of differential equations with analytic and time-dependent non-linear term. The…