Observations of Ion Density and Temperature around the International Space Station During two Geomagnetic Storms

The International Space Station (ISS) is a low Earth orbit research facility and host to an international crew. Geomagnetic storms cause changes in the Earth’s magnetic field and affect the ion density and temperature in the ionosphere which could pose a hazard to ISS crew. This hazard is measured by the Floating Potential Measurement Unit (FPMU) which measures ion density, ion temperature, and the charge differential of the ISS relative to its surrounding environment. I analyzed data collected by Narrow Sweep Langmuir Probe for two storms in 2015. Ion density and temperature were affected by geomagnetic storms, but the effects were less than those found due to normal orbital conditions

Replica Treatment of the Calogero-Sutherland Model

Employing Forrester-Ha method of Jack polynomials, we derive an integral identity connecting certain N-fold coordinate average of the Calogero-Sutherland model with the n-fold replica integral. Subsequent analytical continuation to non-integer n leads to asymptotic expressions for the (static and dynamic) density-density correlation function of the model as well as the Green's function for an arbitrary coupling constant $\lambda$.Comment: 15 pages, 3 figures, revised version, section 5 corrected, submitted to Nucl.Phys.

Conceptualising rural-urban dynamics

This paper revisits the work of Richard Cantillon and Francois Quesnay in order to conceptualise the dynamics between rural and urban areas in an economy. Concepts of social surplus and economy as a circular flow are presented in order to highlight the interrelationship between the growth processes in the rural as well as urban areas. The paper concludes by pointing out the significance of the works of Cantillon and Quesnay.Economic growth; Cantillon; Quesnay; Urban; Rural

On symmetric continuum opinion dynamics

This paper investigates the asymptotic behavior of some common opinion dynamic models in a continuum of agents. We show that as long as the interactions among the agents are symmetric, the distribution of the agents' opinion converges. We also investigate whether convergence occurs in a stronger sense than merely in distribution, namely, whether the opinion of almost every agent converges. We show that while this is not the case in general, it becomes true under plausible assumptions on inter-agent interactions, namely that agents with similar opinions exert a non-negligible pull on each other, or that the interactions are entirely determined by their opinions via a smooth function.Comment: 28 pages, 2 figures, 3 file

A Depth-Optimal Canonical Form for Single-qubit Quantum Circuits

Given an arbitrary single-qubit operation, an important task is to efficiently decompose this operation into an (exact or approximate) sequence of fault-tolerant quantum operations. We derive a depth-optimal canonical form for single-qubit quantum circuits, and the corresponding rules for exactly reducing an arbitrary single-qubit circuit to this canonical form. We focus on the single-qubit universal H,T basis due to its role in fault-tolerant quantum computing, and show how our formalism might be extended to other universal bases. We then extend our canonical representation to the family of Solovay-Kitaev decomposition algorithms, in order to find an \epsilon-approximation to the single-qubit circuit in polylogarithmic time. For a given single-qubit operation, we find significantly lower-depth \epsilon-approximation circuits than previous state-of-the-art implementations. In addition, the implementation of our algorithm requires significantly fewer resources, in terms of computation memory, than previous approaches.Comment: 10 pages, 3 figure

Subspace Least Squares Multidimensional Scaling

Multidimensional Scaling (MDS) is one of the most popular methods for dimensionality reduction and visualization of high dimensional data. Apart from these tasks, it also found applications in the field of geometry processing for the analysis and reconstruction of non-rigid shapes. In this regard, MDS can be thought of as a \textit{shape from metric} algorithm, consisting of finding a configuration of points in the Euclidean space that realize, as isometrically as possible, some given distance structure. In the present work we cast the least squares variant of MDS (LS-MDS) in the spectral domain. This uncovers a multiresolution property of distance scaling which speeds up the optimization by a significant amount, while producing comparable, and sometimes even better, embeddings.Comment: Scale Space and Variational Methods in Computer Vision: 6th International Conference, SSVM 2017, Kolding, Denmark, June 4-8, 201