Principles of calculating the dynamical response of misaligned complex resonant optical interferometers

In the long-baseline laser interferometers for measuring gravitational waves that are now under construction, understanding the dynamical response to small distortions such as angular alignment fluctuations presents a unique challenge. These interferometers comprise multiple coupled optical resonators with light storage times approaching 100 m. We present a basic formalism to calculate the frequency dependence of periodic variations in angular alignment and longitudinal displacement of the resonator mirrors. The electromagnetic field is decomposed into a superposition of higher-order spatial modes, Fourier frequency components, and polarization states. Alignment fluctuations and length variations of free-space propagation are represented by matrix operators that act on the multicomponent state vectors of the field

Taking advantage of multiplet structure for lineshape analysis in Fourier space

Lineshape analysis is a recurrent and often computationally intensive task in optics, even more so for multiple peaks in the presence of noise. We demonstrate an algorithm which takes advantage of peak multiplicity (N) to retrieve line shape information. The method is exemplified via analysis of Lorentzian and Gaussian contributions to individual lineshapes for a practical spectroscopic measurement and benefits from a linear increase in sensitivity with the number N. The robustness of the method and its benefits in terms of noise reduction and order of magnitude improvement in run-time performance are discussed.Comment: 12 pages, 6 figure

Journal of African Christian Biography: v. 1, no. 7

A publication of the Dictionary of African Christian Biography with U.S. offices located at the Center for Global Christianity and Mission at Boston University. This issue focuses on: 1. Rainisoalambo, Ravelonjanahary, and Volahavana Germaine (Nenilava): Revival Leaders of Madagascar. 2. Rainisoalambo. 3. Ravelonjanahary. 4. Volahavana Germaine (Nenilava). 5. Recent Print and Digital Resourcews Related to Christianity in Africa

Experimental test of an alignment-sensing scheme for a gravitational-wave interferometer

An alignment-sensing scheme for all significant angular degrees of freedom of a power-recycled Michelson interferometer with Fabry Perot cavities in the arms was tested on a tabletop interferometer. The response to misalignment of all degrees of freedom was measured at each sensor, and good agreement was found between measured and theoretical values

Learning Dictionaries with Bounded Self-Coherence

Sparse coding in learned dictionaries has been established as a successful approach for signal denoising, source separation and solving inverse problems in general. A dictionary learning method adapts an initial dictionary to a particular signal class by iteratively computing an approximate factorization of a training data matrix into a dictionary and a sparse coding matrix. The learned dictionary is characterized by two properties: the coherence of the dictionary to observations of the signal class, and the self-coherence of the dictionary atoms. A high coherence to the signal class enables the sparse coding of signal observations with a small approximation error, while a low self-coherence of the atoms guarantees atom recovery and a more rapid residual error decay rate for the sparse coding algorithm. The two goals of high signal coherence and low self-coherence are typically in conflict, therefore one seeks a trade-off between them, depending on the application. We present a dictionary learning method with an effective control over the self-coherence of the trained dictionary, enabling a trade-off between maximizing the sparsity of codings and approximating an equiangular tight frame.Comment: 4 pages, 2 figures; IEEE Signal Processing Letters, vol. 19, no. 12, 201

A note on OEIS sequence A111384

$A111384(n)$ is an upper bound for the number of primes that can be written as a sum of three distinct primes selected from a set of $n$ primes. Is this bound sharp

The advanced LIGO detectors in the era of first discoveries

Following a major upgrade, the two advanced detectors of the Laser Interferometer Gravitational-wave Ob- servatory (LIGO) held their first observation run between September 2015 and January 2016. The product of observable volume and measurement time exceeded that of all previous runs within the first 16 days of coincident observation. On September 14th, 2015 the Advanced LIGO detectors observed the transient gravitational-wave signal GW150914, determined to be the coalescence of two black holes, launching the era of gravitational-wave astronomy. We present the main features of the detectors that enabled this observation. At its core Advanced LIGO is a multi-kilometer long Michelson interferometer employing optical resonators to enhance its sensitivity. Four very pure and homogeneous fused silica optics with excellent figure quality serve as the test masses. The displacement produced by the event GW150914 was one 200th of a proton radius. It was observed with a combined signal-to-noise ratio of 24 in coincidence by the two detectors. At full sensitivity, the Advanced LIGO detectors are designed to deliver another factor of three improvement in the signal-to-noise ratio for binary black hole systems similar in masses to GW150914

Youth Evangelism, Link2Llife, A Strategy To Reach Postmodern Youth In Germany And Switzerland

Problem In terms of cross-cultural mission youth are the most crucial group of people to be reached with the Gospel. From a theological, a sociological as well as a psychological point of view adolescence can be seen as the most receptive phase of life regarding the adoption and integration of faith, a coherent value system and a meaningful life narrative. The process of individuation in the adolescent years offers the biggest potential for both conversion and apostasy. Despite a professionalized youth ministry youth evangelism has never been high on the missional agenda of the Christian Church. Method The youth ministries department of the Seventh-day Adventist Church in Germany and Switzerland initiated and conducted an international youth evangelism broadcast through satellite to reach postmodern youth within and outside the church with the Gospel of Jesus Christ in the years 2002 and 2004. Results In 2002 as well as in 2004 about 200 local congregations and youth clubs in Germany and Switzerland were part of the Link2Life initiative. Link2Life reached not only churched youth with the biblical message of Jesus Christ but also to a high percentage their unchurched friends. The Link2Life evangelism increased the identification with the Gospel message and the Adventist church among young people and lead to an increased number of baptisms. Conclusions Link2Life was an effective approach in the context of event or mass evangelism and a rare example of a missional attempt of the Seventh-day Adventist church in Germany and Switzerland to reach young people. Youth evangelistic events need the systemic context of an intergenerational and authentic community of faith. Youth evangelism, however, calls for an incamational and contextual approach that values authentic relationships