Polynomial-Time Amoeba Neighborhood Membership and Faster Localized Solving

We derive efficient algorithms for coarse approximation of algebraic hypersurfaces, useful for estimating the distance between an input polynomial zero set and a given query point. Our methods work best on sparse polynomials of high degree (in any number of variables) but are nevertheless completely general. The underlying ideas, which we take the time to describe in an elementary way, come from tropical geometry. We thus reduce a hard algebraic problem to high-precision linear optimization, proving new upper and lower complexity estimates along the way.Comment: 15 pages, 9 figures. Submitted to a conference proceeding

Acceleration of Relativistic Protons during the 20 January 2005 Flare and CME

The origin of relativistic solar protons during large flare/CME events has not been uniquely identified so far.We perform a detailed comparative analysis of the time profiles of relativistic protons detected by the worldwide network of neutron monitors at Earth with electromagnetic signatures of particle acceleration in the solar corona during the large particle event of 20 January 2005. The intensity-time profile of the relativistic protons derived from the neutron monitor data indicates two successive peaks. We show that microwave, hard X-ray and gamma-ray emissions display several episodes of particle acceleration within the impulsive flare phase. The first relativistic protons detected at Earth are accelerated together with relativistic electrons and with protons that produce pion decay gamma-rays during the second episode. The second peak in the relativistic proton profile at Earth is accompanied by new signatures of particle acceleration in the corona within approximatively 1 solar radius above the photosphere, revealed by hard X-ray and microwave emissions of low intensity, and by the renewed radio emission of electron beams and of a coronal shock wave. We discuss the observations in terms of different scenarios of particle acceleration in the corona.Comment: 22 pages, 5 figure

Astronomical Distance Determination in the Space Age: Secondary Distance Indicators

The formal division of the distance indicators into primary and secondary leads to difficulties in description of methods which can actually be used in two ways: with, and without the support of the other methods for scaling. Thus instead of concentrating on the scaling requirement we concentrate on all methods of distance determination to extragalactic sources which are designated, at least formally, to use for individual sources. Among those, the Supernovae Ia is clearly the leader due to its enormous success in determination of the expansion rate of the Universe. However, new methods are rapidly developing, and there is also a progress in more traditional methods. We give a general overview of the methods but we mostly concentrate on the most recent developments in each field, and future expectations. © 2018, The Author(s)

Structured Coculture of Mesenchymal Stem Cells and Disc Cells Enhances Differentiation and Proliferation

PURPOSE: During in vivo stem cell differentiation, mature cells often induce the differentiation of nearby stem cells. Accordingly, prior studies indicate that a randomly mixed coculture can help transform mesenchymal stem cells (MSC) into Nucleus Pulposus cells (NPC). However, because in vivo signaling typically occurs heterotopically between adjacent cell layers, we hypothesized that a structurally organized coculture between MSC and NPC will result in greater cell differentiation and proliferation over single cell type controls and cocultures with random organization. METHODS: We developed a novel bilaminar cell pellet (BCP) system where a sphere of MSC is enclosed in a shell of NPC by successive centrifugation. Controls were made using single-cell type pellets and coculture pellets with random organization. The pellets were evaluated for DNA content, gene expression, and histology. RESULTS: A bilaminar 3D organization enhanced cell proliferation and differentiation. BCP showed significantly more cell proliferation than pellets with one cell type and those with random organization. Enhanced differentiation of MSC within the BCP pellet relative to single cell type pellets was demonstrated by quantitative RT-PCR, histology, and in situ hybridization. CONCLUSIONS: The BCP culture system increases MSC proliferation and differentiation as compared to single-cell type or randomly mixed co-culture controls