About the Algebraic Solutions of Smallest Enclosing Cylinders Problems

Given n points in Euclidean space E^d, we propose an algebraic algorithm to compute the best fitting (d-1)-cylinder. This algorithm computes the unknown direction of the axis of the cylinder. The location of the axis and the radius of the cylinder are deduced analytically from this direction. Special attention is paid to the case d=3 when n=4 and n=5. For the former, the minimal radius enclosing cylinder is computed algebrically from constrained minimization of a quartic form of the unknown direction of the axis. For the latter, an analytical condition of existence of the circumscribed cylinder is given, and the algorithm reduces to find the zeroes of an one unknown polynomial of degree at most 6. In both cases, the other parameters of the cylinder are deduced analytically. The minimal radius enclosing cylinder is computed analytically for the regular tetrahedron and for a trigonal bipyramids family with a symmetry axis of order 3.Comment: 13 pages, 0 figure; revised version submitted to publication (previous version is a copy of the original one of 2010

Life Beyond the Solar System: Space Weather and Its Impact on Habitable Worlds

The search of life in the Universe is a fundamental problem of astrobiology and a major priority for NASA. A key area of major progress since the NASA Astrobiology Strategy 2015 (NAS15) has been a shift from the exoplanet discovery phase to a phase of characterization and modeling of the physics and chemistry of exoplanetary atmospheres, and the development of observational strategies for the search for life in the Universe by combining expertise from four NASA science disciplines including heliophysics, astrophysics, planetary science and Earth science. The NASA Nexus for Exoplanetary System Science (NExSS) has provided an efficient environment for such interdisciplinary studies. Solar flares, coronal mass ejections and solar energetic particles produce disturbances in interplanetary space collectively referred to as space weather, which interacts with the Earth upper atmosphere and causes dramatic impact on space and ground-based technological systems. Exoplanets within close in habitable zones around M dwarfs and other active stars are exposed to extreme ionizing radiation fluxes, thus making exoplanetary space weather (ESW) effects a crucial factor of habitability. In this paper, we describe the recent developments and provide recommendations in this interdisciplinary effort with the focus on the impacts of ESW on habitability, and the prospects for future progress in searching for signs of life in the Universe as the outcome of the NExSS workshop held in Nov 29 - Dec 2, 2016, New Orleans, LA. This is one of five Life Beyond the Solar System white papers submitted by NExSS to the National Academy of Sciences in support of the Astrobiology Science Strategy for the Search for Life in the Universe.Comment: 5 pages, the white paper was submitted to the National Academy of Sciences in support of the Astrobiology Science Strategy for the Search for Life in the Univers

Definitions and methodology for the grayscale and radiofrequency intravascular ultrasound and coronary angiographic analyses

Objectives: In a prospective study of the natural history of coronary atherosclerosis using angiography and grayscale and radio

Bounding Helly numbers via Betti numbers

We show that very weak topological assumptions are enough to ensure the existence of a Helly-type theorem. More precisely, we show that for any non-negative integers $b$ and $d$ there exists an integer $h(b,d)$ such that the following holds. If $\mathcal F$ is a finite family of subsets of $\mathbb R^d$ such that $\tilde\beta_i\left(\bigcap\mathcal G\right) \le b$ for any $\mathcal G \subsetneq \mathcal F$ and every $0 \le i \le \lceil d/2 \rceil-1$ then $\mathcal F$ has Helly number at most $h(b,d)$. Here $\tilde\beta_i$ denotes the reduced $\mathbb Z_2$-Betti numbers (with singular homology). These topological conditions are sharp: not controlling any of these $\lceil d/2 \rceil$ first Betti numbers allow for families with unbounded Helly number. Our proofs combine homological non-embeddability results with a Ramsey-based approach to build, given an arbitrary simplicial complex $K$, some well-behaved chain map $C_*(K) \to C_*(\mathbb R^d)$.Comment: 29 pages, 8 figure

Impact of Space Weather on Climate and Habitability of Terrestrial Type Exoplanets

The current progress in the detection of terrestrial type exoplanets has opened a new avenue in the characterization of exoplanetary atmospheres and in the search for biosignatures of life with the upcoming ground-based and space missions. To specify the conditions favorable for the origin, development and sustainment of life as we know it in other worlds, we need to understand the nature of astrospheric, atmospheric and surface environments of exoplanets in habitable zones around G-K-M dwarfs including our young Sun. Global environment is formed by propagated disturbances from the planet-hosting stars in the form of stellar flares, coronal mass ejections, energetic particles, and winds collectively known as astrospheric space weather. Its characterization will help in understanding how an exoplanetary ecosystem interacts with its host star, as well as in the specification of the physical, chemical and biochemical conditions that can create favorable and/or detrimental conditions for planetary climate and habitability along with evolution of planetary internal dynamics over geological timescales. A key linkage of (astro) physical, chemical, and geological processes can only be understood in the framework of interdisciplinary studies with the incorporation of progress in heliophysics, astrophysics, planetary and Earth sciences. The assessment of the impacts of host stars on the climate and habitability of terrestrial (exo)planets will significantly expand the current definition of the habitable zone to the biogenic zone and provide new observational strategies for searching for signatures of life. The major goal of this paper is to describe and discuss the current status and recent progress in this interdisciplinary field and to provide a new roadmap for the future development of the emerging field of exoplanetary science and astrobiology.Comment: 206 pages, 24 figures, 1 table; Review paper. International Journal of Astrobiology (2019

Discovery of a WZ Sge-Type Dwarf Nova, SDSS J102146.44+234926.3: Unprecedented Infrared Activity during a Rebrightening Phase

Several SU UMa-type dwarf novae, in particular, WZ Sge-type stars tend to exhibit rebrightenings after superoutbursts. The rebrightening phenomenon is problematic for the disk instability theory of dwarf novae since it requires a large amount of remnant matter in the disk even after superoutbursts. Here, we report our optical and infrared observations during the first-ever outburst of a new dwarf nova, SDSS J102146.44+234926.3. During the outburst, we detected superhumps with a period of 0.056281 +/- 0.000015 d, which is typical for superhump periods in WZ Sge stars. In conjunction with the appearance of a long-lived rebrightening, we conclude that the object is a new member of WZ Sge stars. Our observations, furthermore, revealed infrared behaviors for the first time in the rebrightening phase of WZ Sge stars. We discovered prominent infrared superhumps. We calculate the color temperature of the infrared superhump source to be 4600-6400 K. These temperatures are too low to be explained with a fully-ionized disk appearing during dwarf nova outbursts. We also found a Ks-band excess over the hot disk component. These unprecedented infrared activities provide evidence for the presence of mass reservoir at the outermost part of the accretion disk. We propose that a moderately high mass-accretion rate at this infrared active region leads to the long-lived rebrightening observed in SDSS J102146.44+234926.3.Comment: 11 pages, 10 figures. Accepted for publication in PAS

Gamma-Ray Emission Concurrent with the Nova in the Symbiotic Binary V407 Cygni

Novae are thermonuclear explosions on a white dwarf surface fueled by mass accreted from a companion star. Current physical models posit that shocked expanding gas from the nova shell can produce X-ray emission but emission at higher energies has not been widely expected. Here, we report the Fermi Large Area Telescope detection of variable gamma-ray (0.1-10 GeV) emission from the recently-detected optical nova of the symbiotic star V407 Cygni. We propose that the material of the nova shell interacts with the dense ambient medium of the red giant primary, and that particles can be accelerated effectively to produce pi0 decay gamma-rays from proton-proton interactions. Emission involving inverse Compton scattering of the red giant radiation is also considered and is not ruled out.Comment: 38 pages, includes Supplementary Online Material; corresponding authors: C.C. Cheung, A.B. Hill, P. Jean, S. Razzaque, K.S. Woo