Gershgorin disks for multiple eigenvalues of non-negative matrices

Gershgorin's famous circle theorem states that all eigenvalues of a square matrix lie in disks (called Gershgorin disks) around the diagonal elements. Here we show that if the matrix entries are non-negative and an eigenvalue has geometric multiplicity at least two, then this eigenvalue lies in a smaller disk. The proof uses geometric rearrangement inequalities on sums of higher dimensional real vectors which is another new result of this paper

Encoding dynamics for multiscale community detection: Markov time sweeping for the Map equation

The detection of community structure in networks is intimately related to finding a concise description of the network in terms of its modules. This notion has been recently exploited by the Map equation formalism (M. Rosvall and C.T. Bergstrom, PNAS, 105(4), pp.1118--1123, 2008) through an information-theoretic description of the process of coding inter- and intra-community transitions of a random walker in the network at stationarity. However, a thorough study of the relationship between the full Markov dynamics and the coding mechanism is still lacking. We show here that the original Map coding scheme, which is both block-averaged and one-step, neglects the internal structure of the communities and introduces an upper scale, the `field-of-view' limit, in the communities it can detect. As a consequence, Map is well tuned to detect clique-like communities but can lead to undesirable overpartitioning when communities are far from clique-like. We show that a signature of this behavior is a large compression gap: the Map description length is far from its ideal limit. To address this issue, we propose a simple dynamic approach that introduces time explicitly into the Map coding through the analysis of the weighted adjacency matrix of the time-dependent multistep transition matrix of the Markov process. The resulting Markov time sweeping induces a dynamical zooming across scales that can reveal (potentially multiscale) community structure above the field-of-view limit, with the relevant partitions indicated by a small compression gap.Comment: 10 pages, 6 figure

A measure of centrality based on the spectrum of the Laplacian

We introduce a family of new centralities, the k-spectral centralities. k-Spectral centrality is a measurement of importance with respect to the deformation of the graph Laplacian associated with the graph. Due to this connection, k-spectral centralities have various interpretations in terms of spectrally determined information. We explore this centrality in the context of several examples. While for sparse unweighted networks 1-spectral centrality behaves similarly to other standard centralities, for dense weighted networks they show different properties. In summary, the k-spectral centralities provide a novel and useful measurement of relevance (for single network elements as well as whole subnetworks) distinct from other known measures.Comment: 12 pages, 6 figures, 2 table

Electric field representation of pulsar intensity spectra

Pulsar dynamic spectra exhibit high visibility fringes arising from interference between scattered radio waves. These fringes may be random or highly ordered patterns, depending on the nature of the scattering or refraction. Here we consider the possibility of decomposing pulsar dynamic spectra -- which are intensity measurements -- into their constituent scattered waves, i.e. electric field components. We describe an iterative method of achieving this decomposition and show how the algorithm performs on data from the pulsar B0834+06. The match between model and observations is good, although not formally acceptable as a representation of the data. Scattered wave components derived in this way are immediately useful for qualitative insights into the scattering geometry. With some further development this approach can be put to a variety of uses, including: imaging the scattering and refracting structures in the interstellar medium; interstellar interferometric imaging of pulsars at very high angular resolution; and mitigating pulse arrival time fluctuations due to interstellar scattering.Comment: 7 Pages, 2 Figures, revised version, accepted by MNRA

Static Dielectric Constant of β-Ga2O3 Perpendicular to the Principal Planes (100), (010), and (001)

The relative static dielectric constant ℇr of β-Ga2O3 perpendicular to the planes (100), (010), and (001) is determined in the temperature range from 25 K to 500 K by measuring the AC capacitance of correspondingly oriented plate capacitor structures using test frequencies of up to 1 MHz. This allows a direct quantification of the static dielectric constant and a unique direction assignment of the obtained values. At room temperature, ℇr perpendicular to the planes (100), (010), and (001) amounts to 10.2 ± 0.2, 10.87 ± 0.08, and 12.4 ± 0.4, respectively, which clearly evidence the anisotropy expected for β-Ga2O3 due to its monoclinic crystal structure. An increase of ℇr by about 0.5 with increasing temperature from 25 K to 450 K was found for all orientations. Our ℇr data resolve the inconsistencies in the previously available literature data with regard to absolute values and their directional assignment and therefore provide a reliable basis for the simulation and design of devices. © The Author(s) 2019

Human Performance in Extreme Environments

Even on a bad day, looking down from orbit is a powerful and enjoyable experience, enhanced by the knowledge that time in orbit represents only a tiny fraction of one's life. You look down at Earth and you feel a sense of peace and solidarity. You look at the stars, and because they are not obscured by atmosphere, they are far more abundant than you realized, and they shine very bright. Later on you will reflect on this as one of life's greatest moments. Today astronauts and a few wealthy space tourists have been able to experience staying on the International Space Station. As representatives of humankind in space, astronauts have to get out there and tell people what it's like, and to encourage successive generations of children to consider careers in space. Perhaps the more people who can experience this view, the nicer we will all be to one another. Astronauts must speak authoritatively, without arrogance or a lack of humility. Each astronaut is an emissary who can share his or her experiences and educate people who will not have the opportunity to fly in space. This chapter is a part of that communication process

A Cosmic Ray Measurement Facility for ATLAS Muon Chambers

Monitored Drift Tube (MDT) chambers will constitute the large majority of precision detectors in the Muon Spectrometer of the ATLAS experiment at the Large Hadron Collider at CERN. For commissioning and calibration of MDT chambers, a Cosmic Ray Measurement Facility is in operation at Munich University. The objectives of this facility are to test the chambers and on-chamber electronics, to map the positions of the anode wires within the chambers with the precision needed for standalone muon momentum measurement in ATLAS, and to gain experience in the operation of the chambers and on-line calibration procedures. Until the start of muon chamber installation in ATLAS, 88 chambers built at the Max Planck Institute for Physics in Munich have to be commissioned and calibrated. With a data taking period of one day individual wire positions can be measured with an accuracy of 8.3 micrometers in the chamber plane and 27 micrometers in the direction perpendicular to that plane.Comment: 14+1 pages, 11 figures, contributed paper to the EPS2003 conference, Aache