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We consider distributed stochastic optimization problems that are solved with master/workers computation architecture. Statistical arguments allow to exploit statistical similarity and approximate this problem by a finite-sum problem, for…
We introduce a machine learning model designed to rapidly and accurately predict the time domain gravitational wave emission of non-precessing binary black hole coalescences, incorporating the effects of higher order modes of the multipole…
Quantum neural networks (QNNs) provide expressive probabilistic models by leveraging quantum superposition and entanglement, yet their practical training remains challenging due to highly oscillatory loss landscapes and noise inherent to…
The reciprocal square root is an important computation for which many sophisticated algorithms exist (see for example \cite{Moroz,863046,863031} and the references therein). A common theme is the use of Newton's method to refine the…
We propose a new efficient iterative method for generating random correlated binary sequences with prescribed correlation function. The method is based on consecutive linear modulations of initially uncorrelated sequence into a correlated…
In this paper, an exact algorithm in polynomial time is developed to solve unrestricted binary quadratic programs. The computational complexity is $O\left( n^{\frac{15}{2}}\right) $, although very conservative, it is sufficient to prove…
We construct an efficient frequency domain waveform for generic circular compact object binaries that include neutron stars. The orbital precession is solved on the radiation reaction timescale (and then transformed to the frequency…
Planets and satellites orbiting a binary system exist in the solar system and extrasolar planetary systems. Their orbits can be significantly different from Keplerian orbits, if they are close to the binary and the secondary-to-primary mass…
Using a method of H. Davenport and W. M. Schmidt, we show that, for each positive integer n, the ratio 2/n is the optimal exponent of simultaneous approximation to real irrational numbers 1) by all conjugates of algebraic numbers of degree…
We construct pseudorandom generators of seed length $\tilde{O}(\log(n)\cdot \log(1/\epsilon))$ that $\epsilon$-fool ordered read-once branching programs (ROBPs) of width $3$ and length $n$. For unordered ROBPs, we construct pseudorandom…
We present a fast method for obtaining fully analytical approximations for gravitational waveforms produced by merging of neutron stars and/or black holes for the earliest stages of the merger process. The obtained analytical formula is…
Building initial conditions for generic binary black-hole evolutions without initial spurious eccentricity remains a challenge for numerical-relativity simulations. This problem can be overcome by applying an eccentricity-removal procedure…
The starting point of any general relativistic numerical simulation is a solution of the Hamiltonian and momentum constraints that (ideally) represents an astrophysically realistic scenario. We present a new method to produce initial data…
Modeling of large populations of binary stellar systems is an intergral part of a many areas of astrophysics, from radio pulsars and supernovae to X-ray binaries, gamma-ray bursts, and gravitational-wave mergers. Binary population synthesis…
Finite precision computations using digital computers involve the following inherent errors: (1) Round-off error of finite precision computations (2) Binary computer arithmetic precludes exact number representation of traditional decimal…
Several theoretical waveform models have been developed over the years to capture the gravitational wave emission from the dynamical evolution of compact binary systems of neutron stars and black holes. As ground-based detectors improve…
We introduce an effective algorithmic method for the computation of a lower bound for uniform expansion in one-dimensional dynamics. The approach employs interval arithmetic and thus provides a rigorous numerical result (computer-assisted…
In this paper we study a class of dynamical systems generated by iterations of multivariate polynomials and estimate the degreegrowth of these iterations. We use these estimates to bound exponential sums along the orbits of these dynamical…
The Fast Reciprocal Square Root Algorithm is a well-established approximation technique consisting of two stages: first, a coarse approximation is obtained by manipulating the bit pattern of the floating point argument using integer…
Mounting evidence indicates that some of the gravitational wave signals observed by the LIGO/Virgo/KAGRA observatories might arise from eccentric compact object binaries, increasing the urgency for accurate waveform models for such systems.…