Related papers: A faster, high precision algorithm for calculating…
This document describes some special cases in which the stransverse mass, MT2, may be calculated by non-iterative algorithms. The most notable special case is that in which the visible particles and the hypothesised invisible particles are…
An MT2 calculation algorithm is described. It is shown to achieve better precision than the fastest and most popular existing bisection-based methods. Most importantly, it is also the first algorithm to be able to reliably calculate…
Although numerical methods are required to evaluate the stransverse mass, MT2, for general input momenta, non-numerical methods have been proposed for some special clases of input momenta. One special case, considered in this note, is the…
The MT2 or "s-transverse mass" statistic was developed to associate a parent mass scale to a missing transverse energy signature, given that escaping particles are generally expected in pairs, while collider experiments are sensitive to…
The $M_2$ variables are devised to extend $M_{T2}$ by promoting transverse masses to Lorentz-invariant ones and making explicit use of on-shell mass relations. Unlike simple kinematic variables such as the invariant mass of visible…
In this article we provide a fast computational method in order to calculate the Moore-Penrose inverse of singular square matrices and of rectangular matrices. The proposed method proves to be much faster and has significantly better…
We propose an inclusive analysis of a stransverse mass (m_{T2}) using a hemisphere method for supersymmetry studies at the LHC . The hemisphere method is an algorithm to group collinear and high p_T particles and jets, assuming that there…
We present new algorithms for $M$-estimators of multivariate scatter and location and for symmetrized $M$-estimators of multivariate scatter. The new algorithms are considerably faster than currently used fixed-point and related algorithms.…
We study the problem of estimating precision matrices in Gaussian distributions that are multivariate totally positive of order two ($\mathrm{MTP}_2$). The precision matrix in such a distribution is an M-matrix. This problem can be…
This paper describes novel and fast, simple and robust algorithm with O(N) expected complexity which enables to decrease run-time needed to find an exact maximum distance of two points in E2. The proposed algorithm has been evaluated…
The stransverse mass variable $M_{T2}$ was originally proposed for the study of hadron collider events in which $N=2$ parent particles are produced and then decay semi-invisibly. Here we consider the generalization to the case of $N\ge 3$…
In this paper, two accelerated divide-and-conquer algorithms are proposed for the symmetric tridiagonal eigenvalue problem, which cost $O(N^2r)$ {flops} in the worst case, where $N$ is the dimension of the matrix and $r$ is a modest number…
We present improved algorithms for fast calculation of the inverse square root for single-precision floating-point numbers. The algorithms are much more accurate than the famous fast inverse square root algorithm and have the same or…
A cumbersome operation in numerical analysis and linear algebra, optimization, machine learning and engineering algorithms; is inverting large full-rank matrices which appears in various processes and applications. This has both numerical…
We examine the relative performance of algorithms for the calculation of curvature in spacetime. The classical coordinate component method is compared to two distinct versions of the Newman-Penrose tetrad approach for a variety of…
We present the kinematic variable, m_T2, which is in some ways similar to the more familiar `transverse-mass', but which can be used in events where two or more particles have escaped detection. We define this variable and describe the…
This paper describes a novel and fast, simple and robust algorithm with O(N) expected complexity which enables to decrease run time needed to find the maximum distance of two points in E2. It can be easily modified for the E3 case in…
Implementations of two algorithms for the transverse Mercator projection are described; these achieve accuracies close to machine precision. One is based on the exact equations of Thompson and Lee and the other uses an extension of…
Cosmological perturbation theory is a powerful tool to predict the statistics of large-scale structure in the weakly non-linear regime, but even at 1-loop order it results in computationally expensive mode-coupling integrals. Here we…
The paper surveys recent progress in establishing uniqueness and developing inversion formulas and algorithms for the thermoacoustic tomography. In mathematical terms, one deals with a rather special inverse problem for the wave equation.…