Critical values of Gaussian SU(2) random polynomials

In this note, we will get the estimate of the expected distribution of critical values of Gaussian SU(2) random polynomials as the degree large enough. The result is a direct application of the Kac-Rice formula. The critical values will accumulate at infinity, we further study the rate of this convergence and its rescaling limit as $n\to\infty$.Comment: the growth of critical values is further studied, the rescaling limit of the density is added, some typos are fixed, to appear in Proceeding of AM

Measurement of differential cross sections for top quark pair production using the lepton plus jets final state in proton-proton collisions at 13 TeV

National Science Foundation (U.S.

Optimasi Portofolio Resiko Menggunakan Model Markowitz MVO Dikaitkan dengan Keterbatasan Manusia dalam Memprediksi Masa Depan dalam Perspektif Al-Qur`an

Risk portfolio on modern finance has become increasingly technical, requiring the use of sophisticated mathematical tools in both research and practice. Since companies cannot insure themselves completely against risk, as human incompetence in predicting the future precisely that written in Al-Quran surah Luqman verse 34, they have to manage it to yield an optimal portfolio. The objective here is to minimize the variance among all portfolios, or alternatively, to maximize expected return among all portfolios that has at least a certain expected return. Furthermore, this study focuses on optimizing risk portfolio so called Markowitz MVO (Mean-Variance Optimization). Some theoretical frameworks for analysis are arithmetic mean, geometric mean, variance, covariance, linear programming, and quadratic programming. Moreover, finding a minimum variance portfolio produces a convex quadratic programming, that is minimizing the objective function ðð¥with constraintsð ð 𥠥 ðandð´ð¥ = ð. The outcome of this research is the solution of optimal risk portofolio in some investments that could be finished smoothly using MATLAB R2007b software together with its graphic analysis

Measurement of t(t)over-bar normalised multi-differential cross sections in pp collisions at root s=13 TeV, and simultaneous determination of the strong coupling strength, top quark pole mass, and parton distribution functions

Peer reviewe

An embedding technique to determine ττ backgrounds in proton-proton collision data

An embedding technique is presented to estimate standard model tau tau backgrounds from data with minimal simulation input. In the data, the muons are removed from reconstructed mu mu events and replaced with simulated tau leptons with the same kinematic properties. In this way, a set of hybrid events is obtained that does not rely on simulation except for the decay of the tau leptons. The challenges in describing the underlying event or the production of associated jets in the simulation are avoided. The technique described in this paper was developed for CMS. Its validation and the inherent uncertainties are also discussed. The demonstration of the performance of the technique is based on a sample of proton-proton collisions collected by CMS in 2017 at root s = 13 TeV corresponding to an integrated luminosity of 41.5 fb(-1).Peer reviewe