Universal analytic properties of noise. Introducing the J-Matrix formalism

We propose a new method in the spectral analysis of noisy time-series data for damped oscillators. From the Jacobi three terms recursive relation for the denominators of the Pad\'e Approximations built on the well-known Z-transform of an infinite time-series, we build an Hilbert space operator, a J-Operator, where each bound state (inside the unit circle in the complex plane) is simply associated to one damped oscillator while the continuous spectrum of the J-Operator, which lies on the unit circle itself, is shown to represent the noise. Signal and noise are thus clearly separated in the complex plane. For a finite time series of length 2N, the J-operator is replaced by a finite order J-Matrix J_N, having N eigenvalues which are time reversal covariant. Different classes of input noise, such as blank (white and uniform), Gaussian and pink, are discussed in detail, the J-Matrix formalism allowing us to efficiently calculate hundreds of poles of the Z-transform. Evidence of a universal behaviour in the final statistical distribution of the associated poles and zeros of the Z-transform is shown. In particular the poles and zeros tend, when the length of the time series goes to infinity, to a uniform angular distribution on the unit circle. Therefore at finite order, the roots of unity in the complex plane appear to be noise attractors. We show that the Z-transform presents the exceptional feature of allowing lossless undersampling and how to make use of this property. A few basic examples are given to suggest the power of the proposed method.Comment: 14 pages, 8 figure

Semiclassical Quantization by Pade Approximant to Periodic Orbit Sums

Periodic orbit quantization requires an analytic continuation of non-convergent semiclassical trace formulae. We propose a method for semiclassical quantization based upon the Pade approximant to the periodic orbit sums. The Pade approximant allows the re-summation of the typically exponentially divergent periodic orbit terms. The technique does not depend on the existence of a symbolic dynamics and can be applied to both bound and open systems. Numerical results are presented for two different systems with chaotic and regular classical dynamics, viz. the three-disk scattering system and the circle billiard.Comment: 7 pages, 3 figures, submitted to Europhys. Let

Accelerating cycle expansions by dynamical conjugacy

Periodic orbit theory provides two important functions---the dynamical zeta function and the spectral determinant for the calculation of dynamical averages in a nonlinear system. Their cycle expansions converge rapidly when the system is uniformly hyperbolic but greatly slowed down in the presence of non-hyperbolicity. We find that the slow convergence can be associated with singularities in the natural measure. A properly designed coordinate transformation may remove these singularities and results in a dynamically conjugate system where fast convergence is restored. The technique is successfully demonstrated on several examples of one-dimensional maps and some remaining challenges are discussed

Post-Prior discrepancies in CDW-EIS calculations for ion impact ionization fully differential cross sections

In this work we present fully differential cross sections (FDCSs) calculations using post and prior version of CDW--EIS theory for helium single ionization by 100 MeV C$^{6+}$ amu$^{-1}$ and 3.6 MeV amu$^{-1}$ Au$^{24+}$ and Au$^{53+}$ ions. We performed our calculations for different momentum transfer and ejected electron energies. The influence of internuclear potential on the ejected electron spectra is taken into account in all cases. We compare our calculations with absolute experimental measurements. It is shown that prior version calculations give better agreement with experiments in almost all studied cases.Comment: 9 pages, 7 figure

A Self-Consistent Model for Positronium Formation from Helium Atoms

The differential and total cross sections for electron capture by positrons from helium atoms are calculated using a first-order distorted wave theory satisfying the Coulomb boundary conditions. In this formalism a parametric potential is used to describe the electron screening in a consistent and realistic manner. The present procedure is self consistent because (i) it satisfies the correct boundary conditions and post-prior symmetry, and (ii) the potential and the electron binding energies appearing in the transition amplitude are consistent with the wave functions describing the collision system. The results are compared with the other theories and with the available experimental measurements. At the considered range of collision energies, the results agree reasonably well with recent experiments and theories. [Note: This paper will be published on volume 42 of the Brazilian Journal of Physics

Psychosocial work factors, job stress and strain at the wheel: Validation of the Copenhagen Psychosocial Questionnaire (COPSOQ) in professional drivers

Psychosocial work environment has been related to many negative health outcomes in different workforces. However, evidence in this regard is still limited in the case of transport workers, and most of the tools used in research, often excessively generic, do not fully consider the specific key stressors, and adverse issues present in the psychosocial environment of professional driving. Objective: Thus, the purpose of this study was to obtain a complete description of the validation of measurement applied to psychosocial factors at work in professional drivers, using the Enterprise version (2018) of COPSOQ-III. Methods: The data was collected from 726 Spanish professional drivers, and the analyses were conducted using the competitive Confirmatory Factor Analysis or CFA, obtaining basic psychometric properties and an optimized structure for the instrument applied to active transport workers. Results: The results suggest a clear factorial structure, high factorial weights, internal consistency, and an improved adjustment to the psychosocial conditions of this group, excluding a set of items with low psychometrical adjustment and keeping the five-factor structure of the questionnaire: demands, influence and development, interpersonal relationships and leadership, job insecurity, and strain-effects and outcomes. Conclusion: Overall, what was found in this study supports the hypothesis that the validated version of COPSOQ in professional drivers, together with complementary information sources specific for their work environment, may have a relevant research value and some important practical implications for the improvement of the occupational safety, and health within the typically vulnerable industry of transportatio

Which health professionals are most at risk for cardiovascular disease? Or do not be a manager

Objectives: Health care workers constitute a high-risk occupational category owing to the character of their work that includes high-risk environment, shift work and mental as well as physical stress. In occupational medicine, caring for their health condition should be a priority and include measures aimed at preventing cardiovascular diseases. The study aimed at determining the prevalence of cardiovascular disease (CVD) risk factors in employees of a large hospital and assessing their effect on the incidence of cardiovascular events. Materials and Methods: The group comprised 3124 employees with a mean age of 36.1 years (SD = 11.4), out of whom 562 were males (mean age of 37.1 years, range: 18-72; SD = 12.26) and 2562 were females (mean age of 35.9 years, range: 18-68; SD = 11.24). At their initial examination, the employees filled in a questionnaire on basic CVD risk factors (according to valid recommendations). This was supplemented with objective data to determine the risk of CVD using valid charts. From this group, a subset of persons at a high or intermediate risk was selected, comprising 247 individuals with a mean age of 54.1 years (SD = 5.73). After 5-9 years (mean 7.24±1.38 years), they either underwent another examination or their health status was ascertained by phone or in a computer database. The end point was the incidence of cardiovascular events (sudden death, acute myocardial infarction, unstable angina pectoris, percutaneous coronary intervention, cardiac failure, stroke or transient ischemic attack). Results: The end point was noted in a total of 15 males (6.07%) and 6 females (2.42%), being statistically significantly present in managers (males p < 0.00007, females p < 0.00001), male physicians/surgeons (p < 0.025), tertiary-educated males (p < 0.0095), female smokers (p < 0.015), male ex-smokers (p < 0.007), overweight or obese males (p < 0.02) and those with the waist-to-hip ratio above 1.0 (p < 0.005). Conclusions: Cardiovascular events are most likely to occur in obese male physicians/surgeons holding managerial positions and in female managers

Mathematical Properties of a New Levin-Type Sequence Transformation Introduced by \v{C}\'{\i}\v{z}ek, Zamastil, and Sk\'{a}la. I. Algebraic Theory

\v{C}\'{\i}\v{z}ek, Zamastil, and Sk\'{a}la [J. Math. Phys. \textbf{44}, 962 - 968 (2003)] introduced in connection with the summation of the divergent perturbation expansion of the hydrogen atom in an external magnetic field a new sequence transformation which uses as input data not only the elements of a sequence $\{s_n \}_{n=0}^{\infty}$ of partial sums, but also explicit estimates $\{\omega_n \}_{n=0}^{\infty}$ for the truncation errors. The explicit incorporation of the information contained in the truncation error estimates makes this and related transformations potentially much more powerful than for instance Pad\'{e} approximants. Special cases of the new transformation are sequence transformations introduced by Levin [Int. J. Comput. Math. B \textbf{3}, 371 - 388 (1973)] and Weniger [Comput. Phys. Rep. \textbf{10}, 189 - 371 (1989), Sections 7 -9; Numer. Algor. \textbf{3}, 477 - 486 (1992)] and also a variant of Richardson extrapolation [Phil. Trans. Roy. Soc. London A \textbf{226}, 299 - 349 (1927)]. The algebraic theory of these transformations - explicit expressions, recurrence formulas, explicit expressions in the case of special remainder estimates, and asymptotic order estimates satisfied by rational approximants to power series - is formulated in terms of hitherto unknown mathematical properties of the new transformation introduced by \v{C}\'{\i}\v{z}ek, Zamastil, and Sk\'{a}la. This leads to a considerable formal simplification and unification.Comment: 41 + ii pages, LaTeX2e, 0 figures. Submitted to Journal of Mathematical Physic