Sparse polynomial space approach to dissipative quantum systems: Application to the sub-ohmic spin-boson model

We propose a general numerical approach to open quantum systems with a coupling to bath degrees of freedom. The technique combines the methodology of polynomial expansions of spectral functions with the sparse grid concept from interpolation theory. Thereby we construct a Hilbert space of moderate dimension to represent the bath degrees of freedom, which allows us to perform highly accurate and efficient calculations of static, spectral and dynamic quantities using standard exact diagonalization algorithms. The strength of the approach is demonstrated for the phase transition, critical behaviour, and dissipative spin dynamics in the spin boson modelComment: 4 pages, 4 figures, revised version accepted for publication in PR

Simultaneous measurement of the trace elements Al, As, B, Be, Cd, Co, Cu, Fe, Li, Mn, Mo, Ni, Rb, Se, Sr, and Zn in human serum and their reference ranges by ICP-MS

The goal of this article was to establish reference ranges of the concentration of trace elements in human serum and to compare these results with those reported by other authors. We describe the sample preparation and measurement conditions that allow the rapid, precise, and accurate determination of Al, As, B, Be, Cd, Co, Cu, Fe, Li, Mn, Mo, Ni, Rb, Se, Sr, and Zn in human serum samples (n=110) by inductively coupled plasma-mass spectrometry (ICP-MS). Accuracy and precision were determined by analyzing three reconstituted reference serum samples by comparison with other methods and by the standard addition procedure. The advantages of the ICP-MS method include short time of analysis of the elements mentioned, low detection limit, high precision, and high accuracy. Disadventages include a high risk of contamination due to the presence of some of the elements of interest in the environment, the relatively delicate sample handling, and the high cost of the equipmen

Asymptotic and exact series representations for the incomplete Gamma function

Using a variational approach, two new series representations for the incomplete Gamma function are derived: the first is an asymptotic series, which contains and improves over the standard asymptotic expansion; the second is a uniformly convergent series, completely analytical, which can be used to obtain arbitrarily accurate estimates of $\Gamma(a,x)$ for any value of $a$ or $x$. Applications of these formulas are discussed.Comment: 8 pages, 4 figure

Concentration of 17 trace elements in serum and whole blood of plains viscachas (Lagostomus maximus) by ICP-MS, their reference ranges, and their relation to cataract

The reference ranges of the trace elements Al, As, Be, B, Cd, Co, Cu, Fe, Mn, Mo, Ni, Pb, Li, Rb, Se, Sr, and Zn were determined by inductively coupled plasma-mass spectrometry (ICP-MS) in sera of a group of free-ranging plains viscachas of the pampa grasslands of Argentina. The values were compared with those of a small group of captive plains viscachas of the Zurich Zoo with diabetes and bilateral cataracts. In addition, a method for digestion of whole-blood samples is described for the trace element determination. Significant differences in the concentration of trace elements in the two groups of animals are discussed. No correlation was found between the levels of selenium and of other trace elements compared to the formation of cataract

Thyroid hormones, blood plasma metabolites and haematological parameters in relationship to milk yield in dairy cows

To study their relationship to milk yield, the concentrations, in jugular venous blood, of thyroxine iodine (T4I), thyroxine (T4), 3,5,3'-tri-iodothyronine (T3), glucose, non-esterified fatty acids (NEFA), triglycerides, phospholipids, cholesterol, total protein, albumin, urea, haemoglobin and packed cell volume (PCV) have been measured in 36 cows (Simmental, Swiss Brown, Holstein and Simmental × Holstein) of different ages during a full lactation, pregnancy, dry period, parturition and 150 days of the ensuing lactation. Thyroid hormones and triglycerides were negatively, and total protein, globulin, cholesterol and phospholipids were positively, correlated with uncorrected or corrected milk yield during several periods of lactation, whereas glucose, NEFA, albumin, urea, haemoglobin and packed cell volume were not correlated with milk yield. The 10 animals with the highest milk yield (18·9 to 23·5 kg/day) exhibited significantly lower values of T4I, T4, T3 and glucose, significantly higher levels of total protein and globulin and tended to have higher levels of NEFA than the 10 cows with the lowest milk yield (10·9 to 14·3 kg/day) throughout or during certain periods of lactation, whereas concentrations of triglycerides, phospholipids, cholesterol, albumin, haemoglobin and PCV did not differ. Changes in T4I, T4, T3, glucose and total protein during lactation were also influenced by age, presumably associated with an increase in milk production with age. T3 was consistently lowest and cholesterol and phospholipids, during later stages of lactation, were highest in Holsteins, which had the highest milk yields of all breeds. Changes of blood parameters were mainly caused by shifts in energy and protein metabolism in association with level of milk productio

Scalar perturbations of higher dimensional rotating and ultra-spinning black holes

We investigate the stability of higher dimensional rotating black holes against scalar perturbations. In particular, we make a thorough numerical and analytical analysis of six-dimensional black holes, not only in the low rotation regime but in the high rotation regime as well. Our results suggest that higher dimensional Kerr black holes are stable against scalar perturbations, even in the ultra-spinning regime.Comment: 7 pages, ReVTeX

How Many Subpopulations is Too Many? Exponential Lower Bounds for Inferring Population Histories

Reconstruction of population histories is a central problem in population genetics. Existing coalescent-based methods, like the seminal work of Li and Durbin (Nature, 2011), attempt to solve this problem using sequence data but have no rigorous guarantees. Determining the amount of data needed to correctly reconstruct population histories is a major challenge. Using a variety of tools from information theory, the theory of extremal polynomials, and approximation theory, we prove new sharp information-theoretic lower bounds on the problem of reconstructing population structure -- the history of multiple subpopulations that merge, split and change sizes over time. Our lower bounds are exponential in the number of subpopulations, even when reconstructing recent histories. We demonstrate the sharpness of our lower bounds by providing algorithms for distinguishing and learning population histories with matching dependence on the number of subpopulations. Along the way and of independent interest, we essentially determine the optimal number of samples needed to learn an exponential mixture distribution information-theoretically, proving the upper bound by analyzing natural (and efficient) algorithms for this problem.Comment: 38 pages, Appeared in RECOMB 201

Direct and Inverse Computation of Jacobi Matrices of Infinite Homogeneous Affine I.F.S

We introduce a new set of algorithms to compute Jacobi matrices associated with measures generated by infinite systems of iterated functions. We demonstrate their relevance in the study of theoretical problems, such as the continuity of these measures and the logarithmic capacity of their support. Since our approach is based on a reversible transformation between pairs of Jacobi matrices, we also discuss its application to an inverse / approximation problem. Numerical experiments show that the proposed algorithms are stable and can reliably compute Jacobi matrices of large order.Comment: 20 pages 6 figure

CBR Anisotropy from Primordial Gravitational Waves in Two-Component Inflationary Cosmology

We examine stochastic temperature fluctuations of the cosmic background radiation (CBR) arising via the Sachs-Wolfe effect from gravitational wave perturbations produced in the early universe. We consider spatially flat, perturbed FRW models that begin with an inflationary phase, followed by a mixed phase containing both radiation and dust. The scale factor during the mixed phase takes the form $a(\eta)=c_1\eta^2+c_2\eta+c_3$, where $c_i$ are constants. During the mixed phase the universe smoothly transforms from being radiation to dust dominated. We find analytic expressions for the graviton mode function during the mixed phase in terms of spheroidal wave functions. This mode function is used to find an analytic expression for the multipole moments $\langle a_l^2\rangle$ of the two-point angular correlation function $C(\gamma)$ for the CBR anisotropy. The analytic expression for the multipole moments is written in terms of two integrals, which are evaluated numerically. The results are compared to multipoles calculated for models that are {\it completely} dust dominated at last-scattering. We find that the multipoles $\langle a_l^2\rangle$ of the CBR temperature perturbations for $l>10$ are significantly larger for a universe that contains both radiation and dust at last-scattering. We compare our results with recent, similar numerical work and find good agreement. The spheroidal wave functions may have applications to other problems of cosmological interest.Comment: 28 pgs + 6 postscript figures, RevTe