Universal Behavior in Large-scale Aggregation of Independent Noisy Observations

Aggregation of noisy observations involves a difficult tradeoff between observation quality, which can be increased by increasing the number of observations, and aggregation quality which decreases if the number of observations is too large. We clarify this behavior for a protypical system in which arbitrarily large numbers of observations exceeding the system capacity can be aggregated using lossy data compression. We show the existence of a scaling relation between the collective error and the system capacity, and show that large scale lossy aggregation can outperform lossless aggregation above a critical level of observation noise. Further, we show that universal results for scaling and critical value of noise which are independent of system capacity can be obtained by considering asymptotic behavior when the system capacity increases toward infinity.Comment: 10 pages, 3 figure

Understanding of BRCA VUS genetic results by breast cancer specialists.

BACKGROUND: Mainstreaming genetic medicine, increased media coverage and clinical trials for BRCA mutation carriers are leading oncologists into more patient discussions about BRCA genetic testing. BRCA variants of uncertain significance (VUS) occur in 10-20% of tests. VUS detection introduces additional uncertainty for patient and potentially clinician. We aimed to explore the ability of breast cancer specialists (BCS) in the UK to correctly respond to a VUS report. METHODS: A survey sent to 800 UK BCS collected demographics data, VUS general knowledge and interpretation and communication based on two genetics reports. A separate survey of UK clinical geneticists collected demographics data, laboratory reporting practice and methods used to clarify VUS pathogenicity including classification systems. RESULTS: Of the 155 BCS (22.5%) who completed the survey, 12% reported no genetics training. Ninety five percent referred patients for BRCA genetic tests, 71% felt unsure about the clinical implications of the test reports presented here. A VUS report from a patient with a positive family history was interpreted and theoretically communicated correctly by 94% but when presented with a different VUS report with no management guidance and negative family history, 39% did not know how to communicate this result to the patient. Geneticists reported multiple VUS classification systems; the most commonly used was word-based in 32%. CONCLUSIONS: A consistent and standardised format to report particularly VUS results across all diagnostic laboratories plus additional training of UK BCS will be necessary for effective mainstreaming of BRCA testing to the oncology clinic

Initial state maximizing the nonexponentially decaying survival probability for unstable multilevel systems

The long-time behavior of the survival probability for unstable multilevel systems that follows the power-decay law is studied based on the N-level Friedrichs model, and is shown to depend on the initial population in unstable states. A special initial state maximizing the asymptote of the survival probability at long times is found and examined by considering the spontaneous emission process for the hydrogen atom interacting with the electromagnetic field.Comment: 5 pages, 1 table. Accepted for publication in Phys. Rev.

Initial wave packets and the various power-law decreases of scattered wave packets at long times

The long time behavior of scattered wave packets $\psi (x,t)$ from a finite-range potential is investigated, by assuming $\psi (x,t)$ to be initially located outside the potential. It is then shown that $\psi (x,t)$ can asymptotically decrease in the various power laws at long time, according to its initial characteristics at small momentum. As an application, we consider the square-barrier potential system and demonstrate that $\psi (x,t)$ exhibits the asymptotic behavior $t^{-3/2}$, while another behavior like $t^{-5/2}$ can also appear for another $\psi (x,t)$.Comment: 5 pages, 1 figur

Electrostatics in a Schwarzschild black hole pierced by a cosmic string

We explicitly determine the expression of the electrostatic potential generated by a point charge at rest in the Schwarzschild black hole pierced by a cosmic string. We can then calculate the electrostatic self-energy. From this, we find again the upper entropy bound for a charged object by employing thermodynamics of the black hole.Comment: Latex, 8 pages, 1 figure in late

Continuous-time quantum walk on integer lattices and homogeneous trees

This paper is concerned with the continuous-time quantum walk on Z, Z^d, and infinite homogeneous trees. By using the generating function method, we compute the limit of the average probability distribution for the general isotropic walk on Z, and for nearest-neighbor walks on Z^d and infinite homogeneous trees. In addition, we compute the asymptotic approximation for the probability of the return to zero at time t in all these cases.Comment: The journal version (save for formatting); 19 page

The Nystrom plus Correction Method for Solving Bound State Equations in Momentum Space

A new method is presented for solving the momentum-space Schrodinger equation with a linear potential. The Lande-subtracted momentum space integral equation can be transformed into a matrix equation by the Nystrom method. The method produces only approximate eigenvalues in the cases of singular potentials such as the linear potential. The eigenvalues generated by the Nystrom method can be improved by calculating the numerical errors and adding the appropriate corrections. The end results are more accurate eigenvalues than those generated by the basis function method. The method is also shown to work for a relativistic equation such as the Thompson equation.Comment: Revtex, 21 pages, 4 tables, to be published in Physical Review

Takagi-Taupin Description of X-ray Dynamical Diffraction from Diffractive Optics with Large Numerical Aperture

We present a formalism of x-ray dynamical diffraction from volume diffractive optics with large numerical aperture and high aspect ratio, in an analogy to the Takagi-Taupin equations for strained single crystals. We derive a set of basic equations for dynamical diffraction from volume diffractive optics, which enable us to study the focusing property of these optics with various grating profiles. We study volume diffractive optics that satisfy the Bragg condition to various degrees, namely flat, tilted and wedged geometries, and derive the curved geometries required for ultimate focusing. We show that the curved geometries satisfy the Bragg condition everywhere and phase requirement for point focusing, and effectively focus hard x-rays to a scale close to the wavelength.Comment: 18 pages, 12 figure

Electrostatic boundary value problems in the Schwarzschild background

The electrostatic potential of any test charge distribution in Schwarzschild space with boundary values is derived. We calculate the Green's function, generalize the second Green's identity for p-forms and find the general solution. Boundary value problems are solved. With a multipole expansion the asymptotic property for the field of any charge distribution is derived. It is shown that one produces a Reissner--Nordstrom black hole if one lowers a test charge distribution slowly toward the horizon. The symmetry of the distribution is not important. All the multipole moments fade away except the monopole. A calculation of the gravitationally induced electrostatic self-force on a pointlike test charge distribution held stationary outside the black hole is presented.Comment: 18 pages, no figures, uses iopart.st

Applications of the Mellin-Barnes integral representation

We apply the Mellin-Barnes integral representation to several situations of interest in mathematical-physics. At the purely mathematical level, we derive useful asymptotic expansions of different zeta-functions and partition functions. These results are then employed in different topics of quantum field theory, which include the high-temperature expansion of the free energy of a scalar field in ultrastatic curved spacetime, the asymptotics of the $p$-brane density of states, and an explicit approach to the asymptotics of the determinants that appear in string theory.Comment: 20 pages, LaTe