One-to-many node-disjoint paths in (n,k)-star graphs

We present an algorithm which given a source node and a set of n−1 target nodes in the (n,k)-star graph Sn,k, where all nodes are distinct, builds a collection of n−1 node-disjoint paths, one from each target node to the source. The collection of paths output from the algorithm is such that each path has length at most 6k−7, and the algorithm has time complexity O(k2n2)

Metasurfaces: Beyond Diffractive and Refractive Optics

Optical metasurfaces are a category of thin diffractive optical elements, fabricated using the standard micro- and nano-fabrication techniques. They provide new ways of controlling the flow of light based on various properties such as polarization, wavelength, and propagation direction. In addition, their compatibility with standard micro-fabrication techniques and compact form factor allows for the development of several novel platforms for the design and implementation of various complicated optical elements and systems. In this thesis, I first give a short overview and a brief history of the works on optical metasurfaces. Then I discuss the capabilities of metasurfaces in controlling the polarization and phase of light, and showcase their potential applications through the cases of polarimetric imaging and vectorial holography. Then, a discussion of the chromatic dispersion in optical metasurfaces is given, followed by three methods that can be utilized to design metasurfaces working at multiple discrete wavelengths. As a potential application of such metasurfaces, I present results of using them as objective lenses in two-photon microscopy. In addition, I discuss how metasurfaces enable the at-will control of chromatic dispersion in diffractive optical elements, demonstrate metasurfaces with controlled dispersion, and provide a discussion of their limitations. Integration of multiple metasurfaces into metasystems allows for implementation of complicated optical functions such as imaging and spectrometry. In this regard, I present several examples of how such metasystems can be designed, fabricated, and utilized to provide wide field of view imaging and projection, microelectromechanically tunable lenses, optical spectrometers, and retroreflectors. I conclude with an outlook on where metasurfaces can be most useful, and what limitations should be overcome before they can find wide-spread application.</p

Redshift-independent Distances in the NASA/IPAC Extragalactic Database: Methodology, Content, and Use of NED-D

Estimates of galaxy distances based on indicators that are independent of cosmological redshift are fundamental to astrophysics. Researchers use them to establish the extragalactic distance scale, to underpin estimates of the Hubble constant, and to study peculiar velocities induced by gravitational attractions that perturb the motions of galaxies with respect to the "Hubble flow" of universal expansion. In 2006 the NASA/IPAC Extragalactic Database (NED) began making available a comprehensive compilation of redshift-independent extragalactic distance estimates. A decade later, this compendium of distances (NED-D) now contains more than 100,000 individual estimates based on primary and secondary indicators, available for more than 28,000 galaxies, and compiled from over 2000 references in the refereed astronomical literature. This paper describes the methodology, content, and use of NED-D, and addresses challenges to be overcome in compiling such distances. Currently, 75 different distance indicators are in use. We include a figure that facilitates comparison of the indicators with significant numbers of estimates in terms of the minimum, 25th percentile, median, 75th percentile, and maximum distances spanned. Brief descriptions of the indicators, including examples of their use in the database, are given in an appendix

Protein Concentration Elevations in Mouse Lungs Following Sudden Transient Cephalad (+Gz) Acceleration

Laboratory and feral lineages of mice were subjected to cephalad (+GZ) accelerations, for 1.8 seconds, aboard a solid fuel rocket. Spectrophotometric analysis of bronchoalveolar lavage retrieved post launch revealed significant (p \u3c .001) elevations of protein in the lungs of experimental mice. Sudden transient imposition of a mean +GZ acceleration of 6.22 ± .47 (SD) G, at lift-off, may have induced hypervolemia of basilar pulmonary microvasculature with concomitant migration of fluid and protein from intravascular to juxta-alveolar perivascular compartments. Exudates may have entered bronchiolar airways subsequently gravitating toward alveoli

Interconnection networks for parallel and distributed computing

Parallel computers are generally either shared-memory machines or distributed- memory machines. There are currently technological limitations on shared-memory architectures and so parallel computers utilizing a large number of processors tend tube distributed-memory machines. We are concerned solely with distributed-memory multiprocessors. In such machines, the dominant factor inhibiting faster global computations is inter-processor communication. Communication is dependent upon the topology of the interconnection network, the routing mechanism, the flow control policy, and the method of switching. We are concerned with issues relating to the topology of the interconnection network. The choice of how we connect processors in a distributed-memory multiprocessor is a fundamental design decision. There are numerous, often conflicting, considerations to bear in mind. However, there does not exist an interconnection network that is optimal on all counts and trade-offs have to be made. A multitude of interconnection networks have been proposed with each of these networks having some good (topological) properties and some not so good. Existing noteworthy networks include trees, fat-trees, meshes, cube-connected cycles, butterflies, Möbius cubes, hypercubes, augmented cubes, k-ary n-cubes, twisted cubes, n-star graphs, (n, k)-star graphs, alternating group graphs, de Bruijn networks, and bubble-sort graphs, to name but a few. We will mainly focus on k-ary n-cubes and (n, k)-star graphs in this thesis. Meanwhile, we propose a new interconnection network called augmented k-ary n- cubes. The following results are given in the thesis.1. Let k ≥ 4 be even and let n ≥ 2. Consider a faulty k-ary n-cube Q(^k_n) in which the number of node faults f(_n) and the number of link faults f(_e) are such that f(_n) + f(_e) ≤ 2n - 2. We prove that given any two healthy nodes s and e of Q(^k_n), there is a path from s to e of length at least k(^n) - 2f(_n) - 1 (resp. k(^n) - 2f(_n) - 2) if the nodes s and e have different (resp. the same) parities (the parity of a node Q(^k_n) in is the sum modulo 2 of the elements in the n-tuple over 0, 1, ∙∙∙ , k - 1 representing the node). Our result is optimal in the sense that there are pairs of nodes and fault configurations for which these bounds cannot be improved, and it answers questions recently posed by Yang, Tan and Hsu, and by Fu. Furthermore, we extend known results, obtained by Kim and Park, for the case when n = 2.2. We give precise solutions to problems posed by Wang, An, Pan, Wang and Qu and by Hsieh, Lin and Huang. In particular, we show that Q(^k_n) is bi-panconnected and edge-bipancyclic, when k ≥ 3 and n ≥ 2, and we also show that when k is odd, Q(^k_n) is m-panconnected, for m = (^n(k - 1) + 2k - 6’ / ‘_2), and (k -1) pancyclic (these bounds are optimal). We introduce a path-shortening technique, called progressive shortening, and strengthen existing results, showing that when paths are formed using progressive shortening then these paths can be efficiently constructed and used to solve a problem relating to the distributed simulation of linear arrays and cycles in a parallel machine whose interconnection network is Q(^k_n) even in the presence of a faulty processor.3. We define an interconnection network AQ(^k_n) which we call the augmented k-ary n-cube by extending a k-ary n-cube in a manner analogous to the existing extension of an n-dimensional hypercube to an n-dimensional augmented cube. We prove that the augmented k-ary n-cube Q(^k_n) has a number of attractive properties (in the context of parallel computing). For example, we show that the augmented k-ary n-cube Q(^k_n) - is a Cayley graph (and so is vertex-symmetric); has connectivity 4n - 2, and is such that we can build a set of 4n - 2 mutually disjoint paths joining any two distinct vertices so that the path of maximal length has length at most max{{n- l)k- (n-2), k + 7}; has diameter [(^k) / (_3)] + [(^k - 1) /( _3)], when n = 2; and has diameter at most (^k) / (_4) (n+ 1), for n ≥ 3 and k even, and at most [(^k)/ (_4) (n + 1) + (^n) / (_4), for n ^, for n ≥ 3 and k odd.4. We present an algorithm which given a source node and a set of n - 1 target nodes in the (n, k)-star graph S(_n,k) where all nodes are distinct, builds a collection of n - 1 node-disjoint paths, one from each target node to the source. The collection of paths output from the algorithm is such that each path has length at most 6k - 7, and the algorithm has time complexity O(k(^3)n(^4))

The James Webb Space Telescope

The James Webb Space Telescope (JWST) is a large (6.6m), cold (50K), infrared-optimized space observatory that will be launched early in the next decade. The observatory will have four instruments: a near-infrared camera, a near-infrared multi-object spectrograph, and a tunable filter imager will cover the wavelength range, 0.6 to 5.0 microns, while the mid-infrared instrument will do both imaging and spectroscopy from 5.0 to 29 microns. The JWST science goals are divided into four themes. The End of the Dark Ages: First Light and Reionization theme seeks to identify the first luminous sources to form and to determine the ionization history of the early universe. The Assembly of Galaxies theme seeks to determine how galaxies and the dark matter, gas, stars, metals, morphological structures, and active nuclei within them evolved from the epoch of reionization to the present day. The Birth of Stars and Protoplanetary Systems theme seeks to unravel the birth and early evolution of stars, from infall on to dust-enshrouded protostars to the genesis of planetary systems. The Planetary Systems and the Origins of Life theme seeks to determine the physical and chemical properties of planetary systems including our own, and investigate the potential for the origins of life in those systems. To enable these observations, JWST consists of a telescope, an instrument package, a spacecraft and a sunshield. The telescope consists of 18 beryllium segments, some of which are deployed. The segments will be brought into optical alignment on-orbit through a process of periodic wavefront sensing and control. The JWST operations plan is based on that used for previous space observatories, and the majority of JWST observing time will be allocated to the international astronomical community through annual peer-reviewed proposal opportunities.Comment: 96 pages, including 48 figures and 15 tables, accepted by Space Science Review

Redshift-independent Distances in the NASA/IPAC Extragalactic Database: Methodology, Content, and Use of NED-D

Estimates of galaxy distances based on indicators that are independent of cosmological redshift are fundamental to astrophysics. Researchers use them to establish the extragalactic distance scale, to underpin estimates of the Hubble constant, and to study peculiar velocities induced by gravitational attractions that perturb the motions of galaxies with respect to the "Hubble flow" of universal expansion. In 2006 the NASA/IPAC Extragalactic Database (NED) began making available a comprehensive compilation of redshift-independent extragalactic distance estimates. A decade later, this compendium of distances (NED-D) now contains more than 100,000 individual estimates based on primary and secondary indicators, available for more than 28,000 galaxies, and compiled from over 2000 references in the refereed astronomical literature. This paper describes the methodology, content, and use of NED-D, and addresses challenges to be overcome in compiling such distances. Currently, 75 different distance indicators are in use. We include a figure that facilitates comparison of the indicators with significant numbers of estimates in terms of the minimum, 25th percentile, median, 75th percentile, and maximum distances spanned. Brief descriptions of the indicators, including examples of their use in the database, are given in an appendix