An Overview of Lifestyle in Communities During The Second Wave of Covid-19 Pandemic

Coronavirus 2019 (COVID-19) is a virus causing high mortality rates in variouscountries. So, the communities make preventive efforts with healthy lifestyle behaviors.The research aims to study lifestyle behaviors and community health conditions during the Covid 19 pandemic. This paper was a quantitative research design with a cross-sectional approach. In addition, the population was 170 respondents domiciled in Surabaya. Sampling techniques used simple random sampling. Data collection throughthe dissemination of questionnaires in google form circulated through WhatsApp group.Furthermore, the data were analyzed with a Linear Regression Test with  = 0.005. Theanalysis results gained public knowledge about the COVID-19 pandemic in the Lowcategory (13.94%). In addition, in public behavior variable showed that the communitydid not comply with health protocols during the COVID-19 pandemic (59.18%). Mostrespondents were in the category of low-risk cases. Linear statistic regression test resultsshowed lifestyle related to knowledge, healthy behavior, obedient protocol Health andhealth condition in individuals (= 0007). Public Health Condition is an indicator of thesuccessful assessment of the disconnection of the covid 19 spread chain. Future researchshould analyze awareness, compliance, and the willingness of the community to carryout health protocols.

Applications in random matrix theory of a PIII’ τ-function sequence from Okamoto’s Hamiltonian formulation

We consider the singular linear statistic of the Laguerre unitary ensemble (LUE) consisting of the sum of the reciprocal of the eigenvalues. It is observed that the exponential generating function for this statistic can be written as a Toeplitz determinant with entries given in terms of particular [Formula: see text] Bessel functions. Earlier studies have identified the same determinant, but with the [Formula: see text] Bessel functions replaced by [Formula: see text] Bessel functions, as relating to the hard edge scaling limit of a generalized gap probability for the LUE, in the case of non-negative integer Laguerre parameter. We show that the Toeplitz determinant formed from an arbitrary linear combination of these two Bessel functions occurs as a [Formula: see text]-function sequence in Okamoto’s Hamiltonian formulation of Painlevé III[Formula: see text], and consequently the logarithmic derivative of both Toeplitz determinants satisfies the same [Formula: see text]-form Painlevé III[Formula: see text] differential equation, giving an explanation of a fact which can be observed from earlier results. In addition, some insights into the relationship between this characterization of the generating function, and its characterization in the [Formula: see text] limit, both with the Laguerre parameter [Formula: see text] fixed, and with [Formula: see text] (this latter circumstance being relevant to an application to the distribution of the Wigner time delay statistic), are given.

Spectrum of SYK model III: Large deviations and concentration of measures

In [Spectrum of SYK model, preprint (2018), arXiv:1801.10073], we proved the almost sure convergence of eigenvalues of the SYK model, which can be viewed as a type of law of large numbers in probability theory; in [Spectrum of SYK model II: Central limit theorem, preprint (2018), arXiv:1806.05714], we proved that the linear statistic of eigenvalues satisfies the central limit theorem. In this paper, we continue to study another important theorem in probability theory — the concentration of measure theorem, especially for the Gaussian SYK model. We will prove a large deviation principle (LDP) for the normalized empirical measure of eigenvalues when [Formula: see text], in which case the eigenvalues can be expressed in terms of these of Gaussian random antisymmetric matrices. Such LDP result has its own independent interest in random matrix theory. For general [Formula: see text], we cannot prove the LDP, we will prove a concentration of measure theorem by estimating the Lipschitz norm of the Gaussian SYK model.

Circular(2)-linear regression analysis with iteration order manipulation

The selection of statistical analysis techniques to be used must be adjusted to the data. Data in the form of time cycle or point position to the angle of possibility is no longer suitable to be analyzed using classical linear statistic method because the direction and the angle influence the position between one data with other data. This paper aims to examine the comparison of Linear Regression Analysis with Circular Regression Analysis. The writing method used is literature review using simulation data. Simulation of data and analysis is done with the help of R program. The results showed that circular data is better in Circular Regression Analysis than Classical Linear Regression Analysis, so the conclusion is Selection of statistical analysis techniques to be used must be adjusted with the data that already held. Data in the form of time cycles or position of the point to the angle of probability is no longer suitable to be analyzed using classical linear statistic method because the direction and the angle influence the position between one data with other data.

ASYMPTOTICS OF SPACING DISTRIBUTIONS AT THE HARD EDGE FOR β-ENSEMBLES

In a previous work [J. Math. Phys.35 (1994) 2539–2551], generalized hypergeometric functions have been used to a give a rigorous derivation of the large s asymptotic form of the general β > 0 gap probability [Formula: see text], provided both βa/2 ∈ ℤ≥0 and 2/β ∈ ℤ+. It is shown how the details of this method can be extended to remove the requirement that 2/β ∈ ℤ+. Furthermore, a large deviation formula for the gap probability Eβ(n; (0, x); ME β, N(λaβ/2e-2βNλ)) is deduced by writing it in terms of the characteristic function of a certain linear statistic. By scaling x = s/(4N)2 and taking N → ∞, this is shown to reproduce a recent conjectured formula for [Formula: see text], βa/2 ∈ ℤ≥0, and moreover to give a prediction without the latter restriction. This extended formula, which for the constant term involves the Barnes double gamma function, is shown to satisfy an asymptotic functional equation relating the gap probability with parameters (β, n, a), to a gap probability with parameters (4/β, n′, a′), where n′ = β(n + 1)/2 - 1, a′ = β(a - 2)/2 + 2.