Large aluminium convex mirror for the cryo-optical test of the Planck primary reflector

NASA Astrophysics Data System (ADS)

Gloesener, P.; Flébus, C.; Cola, M.; Roose, S.; Stockman, Y.; de Chambure, D.

2017-11-01

In the frame of the PLANCK mission telescope development, it is requested to measure the reflector changes of the surface figure error (SFE) with respect to the best ellipsoid, between 293 K and 50 K, with 1 μm RMS accuracy. To achieve this, Infra Red interferometry has been selected and a dedicated thermo mechanical set-up has been constructed. In order to realise the test set-up for this reflector, a large aluminium convex mirror with radius of 19500 mm has been manufactured. The mirror has to operate in a cryogenic environment lower than 30 K, and has a contribution to the RMS WFE with less than 1 μm between room temperature and cryogenic temperature. This paper summarises the design, manufacturing and characterisation of this mirror, showing it has fulfilled its requirements.

Coupling of high power laser diode optical power.

PubMed

Landry, M J; Rupert, J W; Mittas, A

1991-06-20

This paper describes the characteristics of optical couplers with high power laser diodes as sources. The couplers investigated include gradient-index (GRIN) lenses manufactured by Nippon Sheet Glass, a plano-convex lens, a prism, optical fibers manufactured by Ensign-Bickford and Nippon Sheet Glass, and fiber optic stub manufacture by Spec Tran. The characteristics measured included: (1) GRIN lens transmission of up to 97%, fiber transmission of up to 90%, plano-convex lens transmission of up to 92%; (2) intensity distribution contours and profiles of the beam transmitted through GRIN lenses and optical fibers; (3) the beam dimensions of a collimating system; and (4) the divergence of optical fibers of varying lengths. Spectra Diode Laboratory and McDonnell Astronautics Company/Opto Electronics Center manufactured the laser diodes sources that emitted up to 3.6 W.

Phase conjugate Twyman-Green interferometer for testing spherical surfaces and lenses and for measuring refractive indices of liquids or solid transparent materials

NASA Technical Reports Server (NTRS)

Shukla, R. P.; Dokhanian, Mostafa; Venkateswarlu, Putcha; George, M. C.

1990-01-01

The present paper describes an application of a phase conjugate Twyman-Green interferometer using barium titanate as a self-pumping mirror for testing optical components like concave and convex spherical mirrors and lenses. The aberrations introduced by the beam splitter while testing concave or convex spherical mirrors of large aperture are automatically eliminated due to self-focussing property of the phase conjugate mirror. There is no necessity for a good spherical surface as a reference surface unlike in classical Twyman-Green interferometer or Williams interferometer. The phase conjugate Twyman Green interferometer with a divergent illumination can be used as a test plate for checking spherical surfaces. A nondestructive technique for measuring the refractive indices of a Fabry Perot etalon by using a phase conjugate interferometer is also suggested. The interferometer is found to be useful for measuring the refractive indices of liquids and solid transparent materials with an accuracy of the order of + or - 0.0004.

High numerical aperture projection system for extreme ultraviolet projection lithography

DOEpatents

Hudyma, Russell M.

2000-01-01

An optical system is described that is compatible with extreme ultraviolet radiation and comprises five reflective elements for projecting a mask image onto a substrate. The five optical elements are characterized in order from object to image as concave, convex, concave, convex, and concave mirrors. The optical system is particularly suited for ring field, step and scan lithography methods. The invention uses aspheric mirrors to minimize static distortion and balance the static distortion across the ring field width which effectively minimizes dynamic distortion. The present invention allows for higher device density because the optical system has improved resolution that results from the high numerical aperture, which is at least 0.14.

Laser micromachining of optical devices

NASA Astrophysics Data System (ADS)

Kopitkovas, Giedrius; Lippert, Thomas; David, Christian; Sulcas, Rokas; Hobley, Jonathan; Wokaun, Alexander J.; Gobrecht, Jens

2004-10-01

The combination of a gray tone phase mask with a laser assisted wet etching process was applied to fabricate complex microstructures in UV transparent dielectric materials. This one-step method allows the generation of arrays of plano-convex and Fresnel micro-lenses using a conventional XeCl excimer laser and an absorbing liquid, which is in contact with the UV transparent material. An array of plano-convex micro-lenses was tested as beam homogenizer for a high power XeCl excimer and ps Nd:YAG laser. The roughness of the etched features varies from several μm to 10 nm, depending on the laser fluence and concentration of the dye in the organic liquid. The etching process can be divided into several etching mechanisms which vary with laser fluence.

Optical calibration and test of the VLT Deformable Secondary Mirror

NASA Astrophysics Data System (ADS)

Briguglio, Runa; Xompero, Marco; Riccardi, Armando; Andrighettoni, Mario; Pescoller, Dietrich; Biasi, Roberto; Gallieni, Daniele; Vernet, Elise; Kolb, Johann; Arsenault, Robin; Madec, Pierre-Yves

2013-12-01

The Deformable Secondary Mirror (DSM) for the VLT (ESO) represents the state-of-art of the large-format deformable mirror technology with its 1170 voice-coil actuators and its internal metrology based on actuator co-located capacitive sensors to control the shape of the 1.12m-diameter 2mm-thick convex shell. The present paper reports the results of the optical characterization of the mirror unit with the ASSIST facility located at ESO-Garching and executed in a collaborative effort by ESO, INAF-Osservatorio Astrofisico di Arcetri and the DSM manufacturing companies (Microgate s.r.l. and A.D.S. International s.r.l.). The main purposes of the tests are the optical characterization of the shell flattening residuals, the corresponding calibration of flattening commands, the optical calibration of the capacitive sensors and the optical calibration of the mirror influence functions. The results are used for the optical acceptance of the DSM and to allow the next test phase coupling the DSM with the wave-front sensor modules of the new Adaptive Optics Facility (AOF) of ESO.

Nanoantennas for enhancing and confining the magnetic optical field

NASA Astrophysics Data System (ADS)

Grosjean, Thierry; Mivelle, Mathieu; Baida, Fadi I.; Burr, Geoffrey W.; Fischer, Ulrich C.

2011-05-01

We propose different optical antenna structures for enhancing and confining the magnetic optical field. A common feature of these structures are concave corners in thin metal films as locations of the enhanced magnetic field. This proposal is inspired by Babinet's principle as the concave edges are the complementary structures to convex metal corners, which are known to be locations of a strongly enhanced electric field. Bowtie antennas and the bowtie apertures of appropriate size were shown to exhibit resonances in the infrared frequency range with an especially strong enhancement of the electrical field in the gap between 2 convex metal corners. We show by numerical calculations, that the complementary structures, the complementary bowtie aperture - the diabolo antenna - and the complementary bow tie antenna - two closely spaced triangular apertures in a metal film with a narrow gap between two opposing concave corners - exhibit resonances with a strongly enhanced magnetic field at the narrow metal constriction between the concave corners. We suggest sub-wavelength circuits of concave and convex corners as building blocks of planar metamaterials.

Laser-based study of geometrical optics at school level

NASA Astrophysics Data System (ADS)

Garg, Amit; Dhingra, Vishal; Sharma, Reena; Mittal, Ankit; Tiwadi, Raman; Chakravarty, Pratik

2011-10-01

Students at the school level from grade 7 to 12 are taught various concepts of geometrical optics but with little hands-on activities. Light propagation through different media, image formation using lenses and mirrors under different conditions and application of basic principles to characterization of lenses, mirrors and other instruments has been a subject which although fascinates students but due to lack of suitable demonstrating setups, students find difficulty in understanding these concepts and hence unable to appreciate the importance of such concepts in various useful scientific apparatus, day to day life, instruments and devices. Therefore, students tend to cram various concepts related to geometrical optics instead of understanding them. As part of the extension activity in the University Grants Commission major research project "Investigating science hands-on to promote innovation and research at undergraduate level" and University of Delhi at Acharya Narendra Dev College SPIE student chapter, students working under this optics outreach programme have demonstrated various experiments on geometrical optics using a five beam laser ray box and various optical components like different types of mirrors, lenses, prisms, optical fibers etc. The various hands-on activities includes demonstrations on laws of reflection, image formation using plane, concave and convex mirrors, mirror formula, total internal reflection, light propagation in an optical fiber, laws of refraction, image formation using concave and convex lenses and combination of these lenses, lens formula, light propagation through prisms, dispersion in prism, defects in eye- Myopia and hypermetropia. Subjects have been evaluated through pre and post tests in order to measure the improvement in their level of understanding.

Optical metrology at the Optical Sciences Center: an historical review

NASA Astrophysics Data System (ADS)

Creath, Katherine; Parks, Robert E.

2014-10-01

The Optical Sciences Center (OSC) begun as a graduate-level applied optics teaching institution to support the US space effort. The making of optics representative of those used in other space programs was deemed essential. This led to the need for optical metrology: at first Hartmann tests, but almost immediately to interferometric tests using the newly invented HeNe laser. Not only were new types of interferometers needed, but the whole infrastructure that went with testing, fringe location methods, aberration removal software and contour map generation to aid the opticians during polishing needed to be developed. Over the last half century more rapid and precise methods of interferogram data reduction, surface roughness measurement, and methods of instrument calibration to separate errors from those in the optic have been pioneered at OSC. Other areas of research included null lens design and the writing of lens design software that led into the design of computer generated holograms for asphere testing. More recently work has been done on the reduction of speckle noise in interferograms, methods to test large convex aspheres, and a return to slope measuring tests to increase the dynamic range of the types of aspheric surfaces amenable to optical testing including free-form surfaces. This paper documents the history of the development of optical testing projects at OSC and highlights the contributions some of the individuals associated with new methods of testing and the infrastructure needed to support the testing. We conclude with comments about the future trends optical metrology.

A 'range test' for determining scatterers with unknown physical properties

NASA Astrophysics Data System (ADS)

Potthast, Roland; Sylvester, John; Kusiak, Steven

2003-06-01

We describe a new scheme for determining the convex scattering support of an unknown scatterer when the physical properties of the scatterers are not known. The convex scattering support is a subset of the scatterer and provides information about its location and estimates for its shape. For convex polygonal scatterers the scattering support coincides with the scatterer and we obtain full shape reconstructions. The method will be formulated for the reconstruction of the scatterers from the far field pattern for one or a few incident waves. The method is non-iterative in nature and belongs to the type of recently derived generalized sampling schemes such as the 'no response test' of Luke-Potthast. The range test operates by testing whether it is possible to analytically continue a far field to the exterior of any test domain Omegatest. By intersecting the convex hulls of various test domains we can produce a minimal convex set, the convex scattering support of which must be contained in the convex hull of the support of any scatterer which produces that far field. The convex scattering support is calculated by testing the range of special integral operators for a sampling set of test domains. The numerical results can be used as an approximation for the support of the unknown scatterer. We prove convergence and regularity of the scheme and show numerical examples for sound-soft, sound-hard and medium scatterers. We can apply the range test to non-convex scatterers as well. We can conclude that an Omegatest which passes the range test has a non-empty intersection with the infinity-support (the complement of the unbounded component of the complement of the support) of the true scatterer, but cannot find a minimal set which must be contained therein.

Cryogenic optical testing results of JWST aspheric test plate lens

NASA Astrophysics Data System (ADS)

Smith, Koby Z.; Towell, Timothy C.

2011-09-01

The James Webb Space Telescope (JWST) Secondary Mirror Assembly (SMA) is a circular 740mm diameter beryllium convex hyperboloid that has a 23.5nm-RMS (λ/27 RMS) on-orbit surface figure error requirement. The radius of curvature of the SMA is 1778.913mm+/-0.45mm and has a conic constant of -1.6598+/-0.0005. The on-orbit operating temperature of the JWST SMA is 22.5K. Ball Aerospace & Technologies Corp. (BATC) is under contract to Northrop Grumman Aerospace Systems (NGAS) to fabricate, assemble, and test the JWST SMA to its on-orbit requirements including the optical testing of the SMA at its cryogenic operating temperature. BATC has fabricated and tested an Aspheric Test Plate Lens (ATPL) that is an 870mm diameter fused silica lens used as the Fizeau optical reference in the ambient and cryogenic optical testing of the JWST Secondary Mirror Assembly (SMA). As the optical reference for the SMA optical test, the concave optical surface of the ATPL is required to be verified at the same 20K temperature range required for the SMA. In order to meet this objective, a state-of-the-art helium cryogenic testing facility was developed to support the optical testing requirements of a number of the JWST optical testing needs, including the ATPL and SMA. With the implementation of this cryogenic testing facility, the ATPL was successfully cryogenically tested and performed to less than 10nm-RMS (λ/63 RMS) surface figure uncertainty levels for proper reference backout during the SMA optical testing program.

The deformable secondary mirror of VLT: final electro-mechanical and optical acceptance test results

NASA Astrophysics Data System (ADS)

Briguglio, Runa; Biasi, Roberto; Xompero, Marco; Riccardi, Armando; Andrighettoni, Mario; Pescoller, Dietrich; Angerer, Gerald; Gallieni, Daniele; Vernet, Elise; Kolb, Johann; Arsenault, Robin; Madec, Pierre-Yves

2014-07-01

The Deformable Secondary Mirror (DSM) for the VLT ended the stand-alone electro-mechanical and optical acceptance process, entering the test phase as part of the Adaptive Optics Facility (AOF) at the ESO Headquarter (Garching). The VLT-DSM currently represents the most advanced already-built large-format deformable mirror with its 1170 voice-coil actuators and its internal metrology based on co-located capacitive sensors to control the shape of the 1.12m-diameter 2mm-thick convex shell. The present paper reports the final results of the electro-mechanical and optical characterization of the DSM executed in a collaborative effort by the DSM manufacturing companies (Microgate s.r.l. and A.D.S. International s.r.l.), INAF-Osservatorio Astrofisico di Arcetri and ESO. The electro-mechanical acceptance tests have been performed in the company premises and their main purpose was the dynamical characterization of the internal control loop response and the calibration of the system data that are needed for its optimization. The optical acceptance tests have been performed at ESO (Garching) using the ASSIST optical test facility. The main purpose of the tests are the characterization of the optical shell flattening residuals, the corresponding calibration of flattening commands, the optical calibration of the capacitive sensors and the optical calibration of the mirror influence functions.

Convex set and linear mixing model

NASA Technical Reports Server (NTRS)

Xu, P.; Greeley, R.

1993-01-01

A major goal of optical remote sensing is to determine surface compositions of the earth and other planetary objects. For assessment of composition, single pixels in multi-spectral images usually record a mixture of the signals from various materials within the corresponding surface area. In this report, we introduce a closed and bounded convex set as a mathematical model for linear mixing. This model has a clear geometric implication because the closed and bounded convex set is a natural generalization of a triangle in n-space. The endmembers are extreme points of the convex set. Every point in the convex closure of the endmembers is a linear mixture of those endmembers, which is exactly how linear mixing is defined. With this model, some general criteria for selecting endmembers could be described. This model can lead to a better understanding of linear mixing models.

High numerical aperture ring field projection system for extreme ultraviolet lithography

DOEpatents

Hudyma, Russell; Shafer, David R.

2001-01-01

An all-reflective optical system for a projection photolithography camera has a source of EUV radiation, a wafer and a mask to be imaged on the wafer. The optical system includes a first convex mirror, a second mirror, a third convex mirror, a fourth concave mirror, a fifth convex mirror and a sixth concave mirror. The system is configured such that five of the six mirrors receive a chief ray at an incidence angle of less than substantially 9.degree., and each of the six mirrors receives a chief ray at an incidence angle of less than substantially 14.degree.. Four of the six reflecting surfaces have an aspheric departure of less than substantially 12 .mu.m. Five of the six reflecting surfaces have an aspheric departure of less than substantially 12 .mu.m. Each of the six reflecting surfaces has an aspheric departure of less than substantially 16 .mu.m.

High numerical aperture ring field projection system for extreme ultraviolet lithography

DOEpatents

Hudyma, Russell; Shafer, David

2001-01-01

An all-reflective optical system for a projection photolithography camera has a source of EUV radiation, a wafer and a mask to be imaged on the wafer. The optical system includes a first convex mirror, a second mirror, a third convex mirror, a fourth concave mirror, a fifth convex mirror and a sixth concave mirror. The system is configured such that five of the six mirrors receives a chief ray at an incidence angle of less than substantially 9.degree., and each of the six mirrors receives a chief ray at an incidence angle of less than substantially 14.degree.. Four of the six reflecting surfaces have an aspheric departure of less than substantially 12 .mu.m. Five of the six reflecting surfaces have an aspheric departure of less than substantially 12 .mu.m. Each of the six reflecting surfaces has an aspheric departure of less than substantially 16 .mu.m.

Four-mirror extreme ultraviolet (EUV) lithography projection system

DOEpatents

Cohen, Simon J; Jeong, Hwan J; Shafer, David R

2000-01-01

The invention is directed to a four-mirror catoptric projection system for extreme ultraviolet (EUV) lithography to transfer a pattern from a reflective reticle to a wafer substrate. In order along the light path followed by light from the reticle to the wafer substrate, the system includes a dominantly hyperbolic convex mirror, a dominantly elliptical concave mirror, spherical convex mirror, and spherical concave mirror. The reticle and wafer substrate are positioned along the system's optical axis on opposite sides of the mirrors. The hyperbolic and elliptical mirrors are positioned on the same side of the system's optical axis as the reticle, and are relatively large in diameter as they are positioned on the high magnification side of the system. The hyperbolic and elliptical mirrors are relatively far off the optical axis and hence they have significant aspherical components in their curvatures. The convex spherical mirror is positioned on the optical axis, and has a substantially or perfectly spherical shape. The spherical concave mirror is positioned substantially on the opposite side of the optical axis from the hyperbolic and elliptical mirrors. Because it is positioned off-axis to a degree, the spherical concave mirror has some asphericity to counter aberrations. The spherical concave mirror forms a relatively large, uniform field on the wafer substrate. The mirrors can be tilted or decentered slightly to achieve further increase in the field size.

Optical performance of random anti-reflection structured surfaces (rARSS) on spherical lenses

NASA Astrophysics Data System (ADS)

Taylor, Courtney D.

Random anti-reflection structured surfaces (rARSS) have been reported to improve transmittance of optical-grade fused silica planar substrates to values greater than 99%. These textures are fabricated directly on the substrates using reactive-ion/inductively-coupled plasma etching (RIE/ICP) techniques, and often result in transmitted spectra with no measurable interference effects (fringes) for a wide range of wavelengths. The RIE/ICP processes used in the fabrication process to etch the rARSS is anisotropic and thus well suited for planar components. The improvement in spectral transmission has been found to be independent of optical incidence angles for values from 0° to +/-30°. Qualifying and quantifying the rARSS performance on curved substrates, such as convex lenses, is required to optimize the fabrication of the desired AR effect on optical-power elements. In this work, rARSS was fabricated on fused silica plano-convex (PCX) and plano-concave (PCV) lenses using a planar-substrate optimized RIE process to maximize optical transmission in the range from 500 to 1100 nm. An additional set of lenses were etched in a non-optimized ICP process to provide additional comparisons. Results are presented from optical transmission and beam propagation tests (optimized lenses only) of rARSS lenses for both TE and TM incident polarizations at a wavelength of 633 nm and over a 70° full field of view in both singlet and doublet configurations. These results suggest optimization of the fabrication process is not required, mainly due to the wide angle-of-incidence AR tolerance performance of the rARSS lenses. Non-optimized recipe lenses showed low transmission enhancement, and confirmed the need to optimized etch recipes prior to process transfer of PCX/PCV lenses. Beam propagation tests indicated no major beam degradation through the optimized lens elements. Scanning electron microscopy (SEM) images confirmed different structure between optimized and non-optimized samples. SEM images also indicated isotropically-oriented surface structures on both types of lenses.

Large-stroke convex micromirror actuated by electromagnetic force for optical power control.

PubMed

Hossain, Md Mahabub; Bin, Wu; Kong, Seong Ho

2015-11-02

This paper contributes a novel design and the corresponding fabrication process to research on the unique topic of micro-electro-mechanical systems (MEMS) deformable convex micromirror used for focusing-power control. In this design, the shape of a thin planar metal-coated polymer-membrane mirror is controlled electromagnetically by using the repulsive force between two magnets, a permanent magnet and a coil solenoid, installed in an actuator system. The 5 mm effective aperture of a large-stroke micromirror showed a maximum center displacement of 30.08 µm, which enabled control of optical power across a wide range that could extend up to around 20 diopters. Specifically, utilizing the maximum optical power of 20 diopter by applying a maximum controlling current of 0.8 A yielded consumption of at most 2 W of electrical power. It was also demonstrated that this micromirror could easily be integrated in miniature tunable optical imaging systems.

Compact high-efficiency 100-W-level diode-side-pumped Nd:YAG laser with linearly polarized TEM00 mode output.

PubMed

Xu, Yi-Ting; Xu, Jia-Lin; Guo, Ya-Ding; Yang, Feng-Tu; Chen, Yan-Zhong; Xu, Jian; Xie, Shi-Yong; Bo, Yong; Peng, Qin-Jun; Cui, Dafu; Xu, Zu-Yan

2010-08-20

We present a compact high-efficiency and high-average-power diode-side-pumped Nd:YAG rod laser oscillator operated with a linearly polarized fundamental mode. The oscillator resonator is based on an L-shaped convex-convex cavity with an improved module and a dual-rod configuration for birefringence compensation. Under a pump power of 344 W, a linearly polarized average output power of 101.4 W at 1064 nm is obtained, which corresponds to an optical-to-optical conversion efficiency of 29.4%. The laser is operated at a repetition rate of 400 Hz with a beam quality factor of M(2)=1.14. To the best of our knowledge, this is the highest optical-to-optical efficiency for a side-pumped TEM(00) Nd:YAG rod laser oscillator with a 100-W-level output ever reported.

Optical design of a LED searchlight system

NASA Astrophysics Data System (ADS)

Gong, Chen; Xu, Haiping; Liang, Jinhua; Liu, Yunfei; Yuan, Zengquan

2018-01-01

A 1200m visible searchlight system is designed based on photometry and application of geometric optics. To generate intensity distribution of this relatively powerful light beam we propose to use a high power LED and several refractive optical elements, which are composed of two plane-convex lenses and a conventional Fresnel lens. Two plane-convex lenses enable refraction of the side rays from the LED to the front direction which incident on the Fresnel lens. Fresnel lens, in its turn, concentrate the light flux and provide a nearly collimated beam to meet the requirement of forming a well-illuminated area across the road in the far field. Simulation data shows that this searchlight allow generating an appropriate illumination distribution for the long range requirements. A proof-of-concept prototype producing acceptable illuminance is developed.

Tackling misconceptions in geometrical optics

NASA Astrophysics Data System (ADS)

Ceuppens, S.; Deprez, J.; Dehaene, W.; De Cock, M.

2018-07-01

To improve the teaching and learning materials for a curriculum it is important to incorporate the findings from educational research. In light of this, we present creative exercises and experiments to elicit, confront and resolve misconceptions in geometrical optics. Since ray diagrams can be both the cause and the solution for many misconceptions we focus strongly on improving understanding of this tool to solve and understand optical phenomena. Through a combination of a conceptual understanding programme (CUP) and provocative exercises with ray diagrams we aim to elicit conceptual or cognitive conflict and exploit this to tackle misconceptions and increase students’ conceptual understanding through inquiry. We describe exercises for image formation by a plane mirror, image formation by a convex lens and indirect and direct observation of a real image formed by a convex lens as examples of our approach.

Fabricating small-scale, curved, polymeric structures with convex and concave menisci through interfacial free energy equilibrium.

PubMed

Cheng, Chao-Min; Matsuura, Koji; Wang, I-Jan; Kuroda, Yuka; LeDuc, Philip R; Naruse, Keiji

2009-11-21

Polymeric curved structures are widely used in imaging systems including optical fibers and microfluidic channels. Here, we demonstrate that small-scale, poly(dimethylsiloxane) (PDMS)-based, curved structures can be fabricated through controlling interfacial free energy equilibrium. Resultant structures have a smooth, symmetric, curved surface, and may be convex or concave in form based on surface tension balance. Their curvatures are controlled by surface characteristics (i.e., hydrophobicity and hydrophilicity) of the molds and semi-liquid PDMS. In addition, these structures are shown to be biocompatible for cell culture. Our system provides a simple, efficient and economical method for generating integrateable optical components without costly fabrication facilities.

Ion beam figuring of Φ520mm convex hyperbolic secondary mirror

NASA Astrophysics Data System (ADS)

Meng, Xiaohui; Wang, Yonggang; Li, Ang; Li, Wenqing

2016-10-01

The convex hyperbolic secondary mirror is a Φ520-mm Zerodur lightweight hyperbolic convex mirror. Typically conventional methods like CCOS, stressed-lap polishing are used to manufacture this secondary mirror. Nevertheless, the required surface accuracy cannot be achieved through the use of conventional polishing methods because of the unpredictable behavior of the polishing tools, which leads to an unstable removal rate. Ion beam figuring is an optical fabrication method that provides highly controlled error of previously polished surfaces using a directed, inert and neutralized ion beam to physically sputter material from the optic surface. Several iterations with different ion beam size are selected and optimized to fit different stages of surface figure error and spatial frequency components. Before ion beam figuring, surface figure error of the secondary mirror is 2.5λ p-v, 0.23λ rms, and is improved to 0.12λ p-v, 0.014λ rms in several process iterations. The demonstration clearly shows that ion beam figuring can not only be used to the final correction of aspheric, but also be suitable for polishing the coarse surface of large, complex mirror.

Fabrication of embedded microball lens in PMMA with high repetition rate femtosecond fiber laser.

PubMed

Zheng, Chong; Hu, Anming; Li, Ruozhou; Bridges, Denzel; Chen, Tao

2015-06-29

Embedded microball lenses with superior optical properties function as convex microball lens (VMBL) and concave microball lens (CMBL) were fabricated inside a PMMA substrate with a high repetition rate femtosecond fiber laser. The VMBL was created by femtosecond laser-induced refractive index change, while the CMBL was fabricated due to the heat accumulation effect of the successive laser pulses irradiation at a high repetition rate. The processing window for both types of the lenses was studied and optimized, and the optical properties were also tested by imaging a remote object with an inverted microscope. In order to obtain the microball lenses with adjustable focal lengths and suppressed optical aberration, a shape control method was thus proposed and examined with experiments and ZEMAX® simulations. Applying the optimized fabrication conditions, two types of the embedded microball lenses arrays were fabricated and then tested with imaging experiments. This technology allows the direct fabrication of microlens inside transparent bulk polymer material which has great application potential in multi-function integrated microfluidic devices.

Laser Resonator

NASA Technical Reports Server (NTRS)

Harper, L. L. (Inventor)

1983-01-01

An optical resonator cavity configuration has a unitary mirror with oppositely directed convex and concave reflective surfaces disposed into one fold and concertedly reversing both ends of a beam propagating from a laser rod disposed between two total internal reflection prisms. The optical components are rigidly positioned with perpendicularly crossed virtual rooflines by a compact optical bed. The rooflines of the internal reflection prisms, are arranged perpendicularly to the axis of the laser beam and to the optical axes of the optical resonator components.

Fréchet derivative with respect to the shape of a strongly convex nonscattering region in optical tomography

NASA Astrophysics Data System (ADS)

Hyvönen, Nuutti

2007-10-01

The aim of optical tomography is to reconstruct the optical properties inside a physical body, e.g. a neonatal head, by illuminating it with near-infrared light and measuring the outward flux of photons on the object boundary. Because a brain consists of strongly scattering tissue with imbedded cavities filled by weakly scattering cerebrospinal fluid, propagation of near-infrared photons in the human head can be treated by combining the diffusion approximation of the radiative transfer equation with geometrical optics to obtain the radiosity-diffusion forward model of optical tomography. At the moment, a disadvantage with the radiosity-diffusion model is that the locations of the transparent cavities must be known in advance in order to be able to reconstruct the physiologically interesting quantities, i.e., the absorption and the scatter in the strongly scattering brain tissue. In this work we show that the boundary measurement map of optical tomography is Fréchet differentiable with respect to the shape of a strongly convex nonscattering region. Using this result, we introduce a numerical algorithm for approximating an unknown nonscattering cavity by a ball if the background diffuse optical properties of the object are known. The functionality of the method is demonstrated through two-dimensional numerical experiments.

Metrology of Large Parts. Chapter 5

NASA Technical Reports Server (NTRS)

Stahl, H. Philip

2012-01-01

As discussed in the first chapter of this book, there are many different methods to measure a part using optical technology. Chapter 2 discussed the use of machine vision to measure macroscopic features such as length and position, which was extended to the use of interferometry as a linear measurement tool in chapter 3, and laser or other trackers to find the relation of key points on large parts in chapter 4. This chapter looks at measuring large parts to optical tolerances in the sub-micron range using interferometry, ranging, and optical tools discussed in the previous chapters. The purpose of this chapter is not to discuss specific metrology tools (such as interferometers or gauges), but to describe a systems engineering approach to testing large parts. Issues such as material warpage and temperature drifts that may be insignificant when measuring a part to micron levels under a microscope, as will be discussed in later chapters, can prove to be very important when making the same measurement over a larger part. In this chapter, we will define a set of guiding principles for successfully overcoming these challenges and illustrate the application of these principles with real world examples. While these examples are drawn from specific large optical testing applications, they inform the problems associated with testing any large part to optical tolerances. Manufacturing today relies on micrometer level part performance. Fields such as energy and transportation are demanding higher tolerances to provide increased efficiencies and fuel savings. By looking at how the optics industry approaches sub-micrometer metrology, one can gain a better understanding of the metrology challenges for any larger part specified to micrometer tolerances. Testing large parts, whether optical components or precision structures, to optical tolerances is just like testing small parts, only harder. Identical with what one does for small parts, a metrologist tests large parts and optics in particular to quantify their mechanical properties (such as dimensions, mass, etc); their optical prescription or design (i.e. radius of curvature, conic constant, vertex location, size); and their full part shape. And, just as with small parts, a metrologist accomplishes these tests using distance measuring instruments such as tape measures, inside micrometers, coordinate measuring machines, distance measuring interferometers; angle measuring instruments such as theodolites, autocollimators; and surface measuring instruments including interferometers, stylus profilers, interference microscopes, photogrammetric cameras, or other tools. However, while the methodology may be similar, it is more difficult to test a large object for the simple reason that most metrologists do not have the necessary intuition. The skills used to test small parts or optics in a laboratory do not extrapolate to testing large parts in an industrial setting any more than a backyard gardener might successfully operate a farm. But first, what is a large part? A simple definition might be the part's size or diameter. For optics and diffuse surface parts alike, the driving constraint is ability to illuminate the part's surface. For reflective convex mirrors, large is typically anything greater than 1 meter. But, for refractive optics, flats or convex mirrors, large is typically greater than 0.5 meter. While a size definition is simple, it may be less than universal. A more nuanced definition might be that a large part is any component which cannot be easily tested in a standard laboratory environment, on a standard vibration isolated table using standard laboratory infrastructure. A micro-switch or a precision lens might be easily measured to nanometer levels under a microscope in a lab, but a power turbine spline or a larger telescope mirror will not fit under that microscope and may not even fit on the table.

A new phenomenon?

NASA Astrophysics Data System (ADS)

Ganci, S.

2017-03-01

This letter describes an interesting optical phenomenon engaging the reflected images of a new tube LED lamp (an array of high luminosity LEDs substituting the old fluorescent lamps) on any convex glossy black surface.

Physical-geometric optics method for large size faceted particles.

PubMed

Sun, Bingqiang; Yang, Ping; Kattawar, George W; Zhang, Xiaodong

2017-10-02

A new physical-geometric optics method is developed to compute the single-scattering properties of faceted particles. It incorporates a general absorption vector to accurately account for inhomogeneous wave effects, and subsequently yields the relevant analytical formulas effective and computationally efficient for absorptive scattering particles. A bundle of rays incident on a certain facet can be traced as a single beam. For a beam incident on multiple facets, a systematic beam-splitting technique based on computer graphics is used to split the original beam into several sub-beams so that each sub-beam is incident only on an individual facet. The new beam-splitting technique significantly reduces the computational burden. The present physical-geometric optics method can be generalized to arbitrary faceted particles with either convex or concave shapes and with a homogeneous or an inhomogeneous (e.g., a particle with a core) composition. The single-scattering properties of irregular convex homogeneous and inhomogeneous hexahedra are simulated and compared to their counterparts from two other methods including a numerically rigorous method.

Acoustic Models of Optical Mirrors

ERIC Educational Resources Information Center

Mayer, V. V.; Varaksina, E. I.

2014-01-01

Students form a more exact idea of the action of optical mirrors if they can observe the wave field being formed during reflection. For this purpose it is possible to organize model experiments with flexural waves propagating in thin elastic plates. The direct and round edges of the plates are used as models of plane, convex and concave mirrors.…

Experimental method for testing diffraction properties of reflection waveguide holograms.

PubMed

Xie, Yi; Kang, Ming-Wu; Wang, Bao-Ping

2014-07-01

Waveguide holograms' diffraction properties include peak wavelength and diffraction efficiency, which play an important role in determining their display performance. Based on the record and reconstruction theory of reflection waveguide holograms, a novel experimental method for testing diffraction properties is introduced and analyzed in this paper, which uses a plano-convex lens optically contacted to the surface of the substrate plate of the waveguide hologram, so that the diffracted light beam can be easily detected. Then an experiment is implemented. The designed reconstruction wavelength of the test sample is 530 nm, and its diffraction efficiency is 100%. The experimental results are a peak wavelength of 527.7 nm and a diffraction efficiency of 94.1%. It is shown that the tested value corresponds well with the designed value.

[Design method of convex master gratings for replicating flat-field concave gratings].

PubMed

Zhou, Qian; Li, Li-Feng

2009-08-01

Flat-field concave diffraction grating is the key device of a portable grating spectrometer with the advantage of integrating dispersion, focusing and flat-field in a single device. It directly determines the quality of a spectrometer. The most important two performances determining the quality of the spectrometer are spectral image quality and diffraction efficiency. The diffraction efficiency of a grating depends mainly on its groove shape. But it has long been a problem to get a uniform predetermined groove shape across the whole concave grating area, because the incident angle of the ion beam is restricted by the curvature of the concave substrate, and this severely limits the diffraction efficiency and restricts the application of concave gratings. The authors present a two-step method for designing convex gratings, which are made holographically with two exposure point sources placed behind a plano-convex transparent glass substrate, to solve this problem. The convex gratings are intended to be used as the master gratings for making aberration-corrected flat-field concave gratings. To achieve high spectral image quality for the replicated concave gratings, the refraction effect at the planar back surface and the extra optical path lengths through the substrate thickness experienced by the two divergent recording beams are considered during optimization. This two-step method combines the optical-path-length function method and the ZEMAX software to complete the optimization with a high success rate and high efficiency. In the first step, the optical-path-length function method is used without considering the refraction effect to get an approximate optimization result. In the second step, the approximate result of the first step is used as the initial value for ZEMAX to complete the optimization including the refraction effect. An example of design problem was considered. The simulation results of ZEMAX proved that the spectral image quality of a replicated concave grating is comparable with that of a directly recorded concave grating.

Ray Tracing with Virtual Objects.

ERIC Educational Resources Information Center

Leinoff, Stuart

1991-01-01

Introduces the method of ray tracing to analyze the refraction or reflection of real or virtual images from multiple optical devices. Discusses ray-tracing techniques for locating images using convex and concave lenses or mirrors. (MDH)

Inspection and characterization of flexo-printing plates

NASA Astrophysics Data System (ADS)

Hahlweg, Cornelius; Pescoller, Lukas; Zhao, Wenjing

2013-09-01

In continuation of last year's paper on distorting optics for inspection of 2 1/2D surfaces with convex or elevated elements - like braille paper and other special printing products - the present paper is dedicated to the quality control and characterization of flexo-printing plates. The need for high optical resolution contradicts the need for depth of field. A rugged optical system for gathering a series of microscopic images at various planes of focus is discussed.

Point-in-convex polygon and point-in-convex polyhedron algorithms with O(1) complexity using space subdivision

NASA Astrophysics Data System (ADS)

Skala, Vaclav

2016-06-01

There are many space subdivision and space partitioning techniques used in many algorithms to speed up computations. They mostly rely on orthogonal space subdivision, resp. using hierarchical data structures, e.g. BSP trees, quadtrees, octrees, kd-trees, bounding volume hierarchies etc. However in some applications a non-orthogonal space subdivision can offer new ways for actual speed up. In the case of convex polygon in E2 a simple Point-in-Polygon test is of the O(N) complexity and the optimal algorithm is of O(log N) computational complexity. In the E3 case, the complexity is O(N) even for the convex polyhedron as no ordering is defined. New Point-in-Convex Polygon and Point-in-Convex Polyhedron algorithms are presented based on space subdivision in the preprocessing stage resulting to O(1) run-time complexity. The presented approach is simple to implement. Due to the principle of duality, dual problems, e.g. line-convex polygon, line clipping, can be solved in a similarly.

Thin Shell Manufacturing for large Wavefront correctors

NASA Astrophysics Data System (ADS)

Ruch, Eric; Poutriquet, Florence

2011-09-01

One of the major key elements in large adaptive optical systems is the thin shell, used as a deformable mirror. Although the optical prescriptions are relaxed with respect to a passive mirror, especially in the low spatial frequency domain, other requirements, such as the cosmetic defects (scratch & dig), the tight control of the thickness uniformity and of course the fragility of the piece having an aspect ratio up to 1000:1, generate new problems during the manufacturing, testing and handling of such optics. Moreover, the optical surface has to be tested in two different ways: a classical optical test bench allows us to create a surface map of the mirror. This map is then computed to determine the force required by the actuators to flatten the mirror and this becomes also a specification for polishing and implies a good interaction with the voice coil manufacturer. More than twenty years ago Sagem - Reosc developed the first meter class thin shell for early adaptive optics experiments. Since then, large thin shell have been used as the optical part in composite mirrors and more recently the aspheric shell for the VLT Deformable Secondary Mirror has been polished and prototypes, up to scale 1, of the E-ELT M4 Adaptive Mirror have been delivered to ESO in 2010. This paper will present some recent results in the manufacturing and testing technologies of large this shell, especially focusing on the development of the 1,1 meter convex aspherical shell for the VLT M2 mirror and on the results obtained on the largest thin shell produced so far (2,5 meter in diameter) developed as a demonstrator for the future E-ELT M4.

Imaging spectrometer/camera having convex grating

NASA Technical Reports Server (NTRS)

Reininger, Francis M. (Inventor)

2000-01-01

An imaging spectrometer has fore-optics coupled to a spectral resolving system with an entrance slit extending in a first direction at an imaging location of the fore-optics for receiving the image, a convex diffraction grating for separating the image into a plurality of spectra of predetermined wavelength ranges; a spectrometer array for detecting the spectra; and at least one concave sperical mirror concentric with the diffraction grating for relaying the image from the entrance slit to the diffraction grating and from the diffraction grating to the spectrometer array. In one embodiment, the spectrometer is configured in a lateral mode in which the entrance slit and the spectrometer array are displaced laterally on opposite sides of the diffraction grating in a second direction substantially perpendicular to the first direction. In another embodiment, the spectrometer is combined with a polychromatic imaging camera array disposed adjacent said entrance slit for recording said image.

High numerical aperture ring field projection system for extreme ultraviolet lithography

DOEpatents

Hudyma, Russell

2001-01-01

An all-reflective optical system for a projection photolithography camera has a source of EUV radiation, a wafer and a mask to be imaged on the wafer. The optical system includes a first concave mirror, a second mirror, a third convex mirror, a fourth concave mirror, a fifth convex mirror and a sixth concave mirror. The system is configured such that five of the six mirrors receives a chief ray at an incidence angle of less than substantially 12.degree., and each of the six mirrors receives a chief ray at an incidence angle of less than substantially 15.degree.. Four of the six reflecting surfaces have an aspheric departure of less than substantially 7 .mu.m. Five of the six reflecting surfaces have an aspheric departure of less than substantially 14 .mu.m. Each of the six reflecting surfaces has an aspheric departure of less than 16.0 .mu.m.

High numerical aperture ring field projection system for extreme ultraviolet lithography

DOEpatents

Hudyma, Russell

2000-01-01

An all-refelctive optical system for a projection photolithography camera has a source of EUV radiation, a wafer and a mask to be imaged on the wafer. The optical system includes a first concave mirror, a second mirror, a third convex mirror, a fourth concave mirror, a fifth convex mirror and a sixth concave mirror. The system is configured such that five of the six mirrors receives a chief ray at an incidence angle less than substantially 12.degree., and each of the six mirrors receives a chief ray at an incidence angle of less than substantially 15.degree.. Four of the six reflecting surfaces have an aspheric departure of less than substantially 7 .mu.m. Five of the six reflecting surfaces have an aspheric departure of less than substantially 14 .mu.m. Each of the six refelecting surfaces has an aspheric departure of less than 16.0 .mu.m.

Thick lens chromatic effective focal length variation versus bending

NASA Astrophysics Data System (ADS)

Sparrold, Scott

2017-11-01

Longitudinal chromatic aberration (LCA) can limit the optical performance in refractive optical systems. Understanding a singlet's chromatic change of effective focal leads to insights and methods to control LCA. Long established, first order theory, shows the chromatic change in focal length for a zero thickness lens is proportional to it's focal length divided by the lens V number or inverse dispersion. This work presents the derivation of an equation for a thick singlet's chromatic change in effective focal length as a function of center thickness, t, dispersion, V, index of refraction, n, and the Coddington shape factor, K. A plot of bending versus chromatic focal length variation is presented. Lens thickness does not influence chromatic variation of effective focal length for a convex plano or plano convex lens. A lens's center thickness'influence on chromatic focal length variation is more pronounced for lower indices of refraction.

Usefulness of the convexity apparent hyperperfusion sign in 123I-iodoamphetamine brain perfusion SPECT for the diagnosis of idiopathic normal pressure hydrocephalus.

PubMed

Ohmichi, Takuma; Kondo, Masaki; Itsukage, Masahiro; Koizumi, Hidetaka; Matsushima, Shigenori; Kuriyama, Nagato; Ishii, Kazunari; Mori, Etsuro; Yamada, Kei; Mizuno, Toshiki; Tokuda, Takahiko

2018-03-16

OBJECTIVE The gold standard for the diagnosis of idiopathic normal pressure hydrocephalus (iNPH) is the CSF removal test. For elderly patients, however, a less invasive diagnostic method is required. On MRI, high-convexity tightness was reported to be an important finding for the diagnosis of iNPH. On SPECT, patients with iNPH often show hyperperfusion of the high-convexity area. The authors tested 2 hypotheses regarding the SPECT finding: 1) it is relative hyperperfusion reflecting the increased gray matter density of the convexity, and 2) it is useful for the diagnosis of iNPH. The authors termed the SPECT finding the convexity apparent hyperperfusion (CAPPAH) sign. METHODS Two clinical studies were conducted. In study 1, SPECT was performed for 20 patients suspected of having iNPH, and regional cerebral blood flow (rCBF) of the high-convexity area was examined using quantitative analysis. Clinical differences between patients with the CAPPAH sign (CAP) and those without it (NCAP) were also compared. In study 2, the CAPPAH sign was retrospectively assessed in 30 patients with iNPH and 19 healthy controls using SPECT images and 3D stereotactic surface projection. RESULTS In study 1, rCBF of the high-convexity area of the CAP group was calculated as 35.2-43.7 ml/min/100 g, which is not higher than normal values of rCBF determined by SPECT. The NCAP group showed lower cognitive function and weaker responses to the removal of CSF than the CAP group. In study 2, the CAPPAH sign was positive only in patients with iNPH (24/30) and not in controls (sensitivity 80%, specificity 100%). The coincidence rate between tight high convexity on MRI and the CAPPAH sign was very high (28/30). CONCLUSIONS Patients with iNPH showed hyperperfusion of the high-convexity area on SPECT; however, the presence of the CAPPAH sign did not indicate real hyperperfusion of rCBF in the high-convexity area. The authors speculated that patients with iNPH without the CAPPAH sign, despite showing tight high convexity on MRI, might have comorbidities such as Alzheimer's disease.

A Bayesian observer replicates convexity context effects in figure-ground perception.

PubMed

Goldreich, Daniel; Peterson, Mary A

2012-01-01

Peterson and Salvagio (2008) demonstrated convexity context effects in figure-ground perception. Subjects shown displays consisting of unfamiliar alternating convex and concave regions identified the convex regions as foreground objects progressively more frequently as the number of regions increased; this occurred only when the concave regions were homogeneously colored. The origins of these effects have been unclear. Here, we present a two-free-parameter Bayesian observer that replicates convexity context effects. The Bayesian observer incorporates two plausible expectations regarding three-dimensional scenes: (1) objects tend to be convex rather than concave, and (2) backgrounds tend (more than foreground objects) to be homogeneously colored. The Bayesian observer estimates the probability that a depicted scene is three-dimensional, and that the convex regions are figures. It responds stochastically by sampling from its posterior distributions. Like human observers, the Bayesian observer shows convexity context effects only for images with homogeneously colored concave regions. With optimal parameter settings, it performs similarly to the average human subject on the four display types tested. We propose that object convexity and background color homogeneity are environmental regularities exploited by human visual perception; vision achieves figure-ground perception by interpreting ambiguous images in light of these and other expected regularities in natural scenes.

In-situ spectrophotometric probe

DOEpatents

Prather, William S.

1992-01-01

A spectrophotometric probe for in situ absorption spectra measurements comprising a first optical fiber carrying light from a remote light source, a second optical fiber carrying light to a remote spectrophotometer, the proximal ends of the first and second optical fibers parallel and coterminal, a planoconvex lens to collimate light from the first optical fiber, a reflecting grid positioned a short distance from the lens to reflect the collimated light back to the lens for focussing on the second optical fiber. The lens is positioned with the convex side toward the optical fibers. A substrate for absorbing analyte or an analyte and reagent mixture may be positioned between the lens and the reflecting grid.

Application of identifying transmission spheres for spherical surface testing

NASA Astrophysics Data System (ADS)

Han, Christopher B.; Ye, Xin; Li, Xueyuan; Wang, Quanzhao; Tang, Shouhong; Han, Sen

2017-06-01

We developed a new application on Microsoft Foundation Classes (MFC) to identify correct transmission spheres (TS) for Spherical Surface Testing (SST). Spherical surfaces are important optical surfaces, and the wide application and high production rate of spherical surfaces necessitates an accurate and highly reliable measuring device. A Fizeau Interferometer is an appropriate tool for SST due to its subnanometer accuracy. It measures the contour of a spherical surface using a common path, which is insensitive to the surrounding circumstances. The Fizeau Interferometer transmits a wide laser beam, creating interference fringes from re-converging light from the transmission sphere and the test surface. To make a successful measurement, the application calculates and determines the appropriate transmission sphere for the test surface. There are 3 main inputs from the test surfaces that are utilized to determine the optimal sizes and F-numbers of the transmission spheres: (1) the curvatures (concave or convex), (2) the Radii of Curvature (ROC), and (3) the aperture sizes. The application will firstly calculate the F-numbers (i.e. ROC divided by aperture) of the test surface, secondly determine the correct aperture size of a convex surface, thirdly verify that the ROC of the test surface must be shorter than the reference surface's ROC of the transmission sphere, and lastly calculate the percentage of area that the test surface will be measured. However, the amount of interferometers and transmission spheres should be optimized when measuring large spherical surfaces to avoid requiring a large amount of interferometers and transmission spheres for each test surface. Current measuring practices involve tedious and potentially inaccurate calculations. This smart application eliminates human calculation errors, optimizes the selection of transmission spheres (including the least number required) and interferometer sizes, and increases efficiency.

Fabrication of ф 160 mm convex hyperbolic mirror for remote sensing instrument

NASA Astrophysics Data System (ADS)

Kuo, Ching-Hsiang; Yu, Zong-Ru; Ho, Cheng-Fang; Hsu, Wei-Yao; Chen, Fong-Zhi

2012-10-01

In this study, efficient polishing processes with inspection procedures for a large convex hyperbolic mirror of Cassegrain optical system are presented. The polishing process combines the techniques of conventional lapping and CNC polishing. We apply the conventional spherical lapping process to quickly remove the sub-surface damage (SSD) layer caused by grinding process and to get the accurate radius of best-fit sphere (BFS) of aspheric surface with fine surface texture simultaneously. Thus the removed material for aspherization process can be minimized and the polishing time for SSD removal can also be reduced substantially. The inspection procedure was carried out by using phase shift interferometer with CGH and stitching technique. To acquire the real surface form error of each sub aperture, the wavefront errors of the reference flat and CGH flat due to gravity effect of the vertical setup are calibrated in advance. Subsequently, we stitch 10 calibrated sub-aperture surface form errors to establish the whole irregularity of the mirror in 160 mm diameter for correction polishing. The final result of the In this study, efficient polishing processes with inspection procedures for a large convex hyperbolic mirror of Cassegrain optical system are presented. The polishing process combines the techniques of conventional lapping and CNC polishing. We apply the conventional spherical lapping process to quickly remove the sub-surface damage (SSD) layer caused by grinding process and to get the accurate radius of best-fit sphere (BFS) of aspheric surface with fine surface texture simultaneously. Thus the removed material for aspherization process can be minimized and the polishing time for SSD removal can also be reduced substantially. The inspection procedure was carried out by using phase shift interferometer with CGH and stitching technique. To acquire the real surface form error of each sub aperture, the wavefront errors of the reference flat and CGH flat due to gravity effect of the vertical setup are calibrated in advance. Subsequently, we stitch 10 calibrated sub-aperture surface form errors to establish the whole irregularity of the mirror in 160 mm diameter for correction polishing. The final result of the Fabrication of ф160 mm Convex Hyperbolic Mirror for Remote Sensing Instrument160 mm convex hyperbolic mirror is 0.15 μm PV and 17.9 nm RMS.160 mm convex hyperbolic mirror is 0.15 μm PV and 17.9 nm RMS.

On the convexity of ROC curves estimated from radiological test results

PubMed Central

Pesce, Lorenzo L.; Metz, Charles E.; Berbaum, Kevin S.

2010-01-01

Rationale and Objectives Although an ideal observer’s receiver operating characteristic (ROC) curve must be convex — i.e., its slope must decrease monotonically — published fits to empirical data often display “hooks.” Such fits sometimes are accepted on the basis of an argument that experiments are done with real, rather than ideal, observers. However, the fact that ideal observers must produce convex curves does not imply that convex curves describe only ideal observers. This paper aims to identify the practical implications of non-convex ROC curves and the conditions that can lead to empirical and/or fitted ROC curves that are not convex. Materials and Methods This paper views non-convex ROC curves from historical, theoretical and statistical perspectives, which we describe briefly. We then consider population ROC curves with various shapes and analyze the types of medical decisions that they imply. Finally, we describe how sampling variability and curve-fitting algorithms can produce ROC curve estimates that include hooks. Results We show that hooks in population ROC curves imply the use of an irrational decision strategy, even when the curve doesn’t cross the chance line, and therefore usually are untenable in medical settings. Moreover, we sketch a simple approach to improve any non-convex ROC curve by adding statistical variation to the decision process. Finally, we sketch how to test whether hooks present in ROC data are likely to have been caused by chance alone and how some hooked ROCs found in the literature can be easily explained as fitting artifacts or modeling issues. Conclusion In general, ROC curve fits that show hooks should be looked upon with suspicion unless other arguments justify their presence. PMID:20599155

Effect of dental arch convexity and type of archwire on frictional forces.

PubMed

Fourie, Zacharias; Ozcan, Mutlu; Sandham, Andrew

2009-07-01

Friction measurements in orthodontics are often derived from models by using brackets placed on flat models with various straight wires. Dental arches are convex in some areas. The objectives of this study were to compare the frictional forces generated in conventional flat and convex dental arch setups, and to evaluate the effect of different archwires on friction in both dental arch models. Two stainless steel models were designed and manufactured simulating flat and convex maxillary right buccal dental arches. Five stainless steel brackets from the maxillary incisor to the second premolar (slot size, 0.22 in, Victory, 3M Unitek, Monrovia, Calif) and a first molar tube were aligned and clamped on the metal model at equal distances of 6 mm. Four kinds of orthodontic wires were tested: (1) A. J. Wilcock Australian wire (0.016 in, G&H Wire, Hannover, Germany); and (2) 0.016 x 0.022 in, (3) 0.018 x 0.022 in, and (4) 0.019 x 0.025 in (3M Unitek GmbH, Seefeld, Germany). Gray elastomeric modules (Power O 110, Ormco, Glendora, Calif) were used for ligation. Friction tests were performed in the wet state with artificial saliva lubrication and by pulling 5 mm of the whole length of the archwire. Six measurements were made from each bracket-wire combination, and each test was performed with new combinations of materials for both arch setups (n = 48, 6 per group) in a universal testing machine (crosshead speed: 20 mm/min). Significant effects of arch model (P = 0.0000) and wire types (P = 0.0000) were found. The interaction term between the tested factors was not significant (P = 0.1581) (2-way ANOVA and Tukey test). Convex models resulted in significantly higher frictional forces (1015-1653 g) than flat models (680-1270 g) (P <0.05). In the flat model, significantly lower frictional forces were obtained with wire types 1 (679 g) and 3 (1010 g) than with types 2 (1146 g) and 4 (1270 g) (P <0.05). In the convex model, the lowest friction was obtained with wire types 1 (1015 g) and 3 (1142 g) (P >0.05). Type 1 wire tended to create the least overall friction in both flat and convex dental arch simulation models.

Design and simulation of MEMS-actuated adjustable optical wedge for laser beam scanners

NASA Astrophysics Data System (ADS)

Bahgat, Ahmed S.; Zaki, Ahmed H.; Abdo Mohamed, Mohamed; El Sherif, Ashraf Fathy

2018-01-01

This paper introduces both optical and mechanical design and simulation of large static deflection MOEMS actuator. The designed device is in the form of an adjustable optical wedge (AOW) laser scanner. The AOW is formed of 1.5-mm-diameter plano-convex lens separated by air gap from plano-concave fixed lens. The convex lens is actuated by staggered vertical comb drive and suspended by rectangular cross-section torsion beam. An optical analysis and simulation of air separated AOW as well as detailed design, analysis, and static simulation of comb -drive are introduced. The dynamic step response of the full system is also introduced. The analytical solution showed a good agreement with the simulation results. A general global minimum optimization algorithm is applied to the comb-drive design to minimize driving voltage. A maximum comb-drive mechanical deflection angle of 12 deg in each direction was obtained under DC actuation voltage of 32 V with a settling time of 90 ms, leading to 1-mm one-dimensional (1-D) steering of laser beam with continuous optical scan angle of 5 deg in each direction. This optimization process provided a design of larger deflection actuator with smaller driving voltage compared with other conventional devices. This enhancement could lead to better performance of MOEMS-based laser beam scanners for imaging and low-speed applications.

Exploring the imaging properties of thin lenses for cryogenic infrared cameras

NASA Astrophysics Data System (ADS)

Druart, Guillaume; Verdet, Sebastien; Guerineau, Nicolas; Magli, Serge; Chambon, Mathieu; Grulois, Tatiana; Matallah, Noura

2016-05-01

Designing a cryogenic camera is a good strategy to miniaturize and simplify an infrared camera using a cooled detector. Indeed, the integration of optics inside the cold shield allows to simply athermalize the design, guarantees a cold pupil and releases the constraint on having a high back focal length for small focal length systems. By this way, cameras made of a single lens or two lenses are viable systems with good optical features and a good stability in image correction. However it involves a relatively significant additional optical mass inside the dewar and thus increases the cool down time of the camera. ONERA is currently exploring a minimalist strategy consisting in giving an imaging function to thin optical plates that are found in conventional dewars. By this way, we could make a cryogenic camera that has the same cool down time as a traditional dewar without an imagery function. Two examples will be presented: the first one is a camera using a dual-band infrared detector made of a lens outside the dewar and a lens inside the cold shield, the later having the main optical power of the system. We were able to design a cold plano-convex lens with a thickness lower than 1mm. The second example is an evolution of a former cryogenic camera called SOIE. We replaced the cold meniscus by a plano-convex Fresnel lens with a decrease of the optical thermal mass of 66%. The performances of both cameras will be compared.

In-situ spectrophotometric probe

DOEpatents

Prather, W.S.

1992-12-15

A spectrophotometric probe is described for in situ absorption spectra measurements comprising a first optical fiber carrying light from a remote light source, a second optical fiber carrying light to a remote spectrophotometer, the proximal ends of the first and second optical fibers parallel and co-terminal, a planoconvex lens to collimate light from the first optical fiber, a reflecting grid positioned a short distance from the lens to reflect the collimated light back to the lens for focusing on the second optical fiber. The lens is positioned with the convex side toward the optical fibers. A substrate for absorbing analyte or an analyte and reagent mixture may be positioned between the lens and the reflecting grid. 5 figs.

The role of convexity in perception of symmetry and in visual short-term memory.

PubMed

Bertamini, Marco; Helmy, Mai Salah; Hulleman, Johan

2013-01-01

Visual perception of shape is affected by coding of local convexities and concavities. For instance, a recent study reported that deviations from symmetry carried by convexities were easier to detect than deviations carried by concavities. We removed some confounds and extended this work from a detection of reflection of a contour (i.e., bilateral symmetry), to a detection of repetition of a contour (i.e., translational symmetry). We tested whether any convexity advantage is specific to bilateral symmetry in a two-interval (Experiment 1) and a single-interval (Experiment 2) detection task. In both, we found a convexity advantage only for repetition. When we removed the need to choose which region of the contour to monitor (Experiment 3) the effect disappeared. In a second series of studies, we again used shapes with multiple convex or concave features. Participants performed a change detection task in which only one of the features could change. We did not find any evidence that convexities are special in visual short-term memory, when the to-be-remembered features only changed shape (Experiment 4), when they changed shape and changed from concave to convex and vice versa (Experiment 5), or when these conditions were mixed (Experiment 6). We did find a small advantage for coding convexity as well as concavity over an isolated (and thus ambiguous) contour. The latter is consistent with the known effect of closure on processing of shape. We conclude that convexity plays a role in many perceptual tasks but that it does not have a basic encoding advantage over concavity.

Detection of longitudinal ulcer using roughness value for computer aided diagnosis of Crohn's disease

NASA Astrophysics Data System (ADS)

Oda, Masahiro; Kitasaka, Takayuki; Furukawa, Kazuhiro; Watanabe, Osamu; Ando, Takafumi; Goto, Hidemi; Mori, Kensaku

2011-03-01

The purpose of this paper is to present a new method to detect ulcers, which is one of the symptoms of Crohn's disease, from CT images. Crohn's disease is an inflammatory disease of the digestive tract. Crohn's disease commonly affects the small intestine. An optical or a capsule endoscope is used for small intestine examinations. However, these endoscopes cannot pass through intestinal stenosis parts in some cases. A CT image based diagnosis allows a physician to observe whole intestine even if intestinal stenosis exists. However, because of the complicated shape of the small and large intestines, understanding of shapes of the intestines and lesion positions are difficult in the CT image based diagnosis. Computer-aided diagnosis system for Crohn's disease having automated lesion detection is required for efficient diagnosis. We propose an automated method to detect ulcers from CT images. Longitudinal ulcers make rough surface of the small and large intestinal wall. The rough surface consists of combination of convex and concave parts on the intestinal wall. We detect convex and concave parts on the intestinal wall by a blob and an inverse-blob structure enhancement filters. A lot of convex and concave parts concentrate on roughed parts. We introduce a roughness value to differentiate convex and concave parts concentrated on the roughed parts from the other on the intestinal wall. The roughness value effectively reduces false positives of ulcer detection. Experimental results showed that the proposed method can detect convex and concave parts on the ulcers.

EEG Dynamics Reflect the Distinct Cognitive Process of Optic Problem Solving

PubMed Central

She, Hsiao-Ching; Jung, Tzyy-Ping; Chou, Wen-Chi; Huang, Li-Yu; Wang, Chia-Yu; Lin, Guan-Yu

2012-01-01

This study explores the changes in electroencephalographic (EEG) activity associated with the performance of solving an optics maze problem. College students (N = 37) were instructed to construct three solutions to the optical maze in a Web-based learning environment, which required some knowledge of physics. The subjects put forth their best effort to minimize the number of convexes and mirrors needed to guide the image of an object from the entrance to the exit of the maze. This study examines EEG changes in different frequency bands accompanying varying demands on the cognitive process of providing solutions. Results showed that the mean power of θ, α1, α2, and β1 significantly increased as the number of convexes and mirrors used by the students decreased from solution 1 to 3. Moreover, the mean power of θ and α1 significantly increased when the participants constructed their personal optimal solution (the least total number of mirrors and lens used by students) compared to their non-personal optimal solution. In conclusion, the spectral power of frontal, frontal midline and posterior theta, posterior alpha, and temporal beta increased predominantly as the task demands and task performance increased. PMID:22815800

Extended surface parallel coating inspection method

DOEpatents

Naulleau, Patrick P.

2006-03-21

Techniques for rapidly characterizing reflective surfaces and especially multi-layer EUV reflective surfaces of optical components involve illuminating the entire reflective surface instantaneously and detecting the image far field. The technique provides a mapping of points on the reflective surface to corresponding points on a detector, e.g., CCD. This obviates the need to scan a probe over the entire surface of the optical component. The reflective surface can be flat, convex, or concave.

Fabrication of large diffractive optical elements in thick film on a concave lens surface.

PubMed

Xie, Yongjun; Lu, Zhenwu; Li, Fengyou

2003-05-05

We demonstrate experimentally the technique of fabricating large diffractive optical elements (DOEs) in thick film on a concave lens surface (mirrors) with precise alignment by using the strategy of double exposure. We adopt the method of double exposure to overcome the difficulty of processing thick photoresist on a large curved substrate. A uniform thick film with arbitrary thickness on a concave lens can be obtained with this technique. We fabricate a large concentric circular grating with a 10-ìm period on a concave lens surface in film with a thickness of 2.0 ìm after development. It is believed that this technique can also be used to fabricate larger DOEs in thicker film on the concave or convex lens surface with precise alignment. There are other potential applications of this technique, such as fabrication of micro-optoelectromechanical systems (MOEMS) or microelectromechanical systems (MEMS) and fabrication of microlens arrays on a large concave lens surface or convex lens surface with precise alignment.

Measurement of aspheric mirror segments using Fizeau interferometry with CGH correction

NASA Astrophysics Data System (ADS)

Burge, James H.; Zhao, Chunyu; Dubin, Matt

2010-07-01

Large aspheric primary mirrors are proposed that use hundreds segments that all must be aligned and phased to approximate the desired continuous mirror. We present a method of measuring these concave segments with a Fizeau interferometer where a spherical convex reference surface is held a few millimeters from the aspheric segment. The aspheric shape is accommodated by a small computer generated hologram (CGH). Different segments are measured by replacing the CGH. As a Fizeau test, nearly all of the optical elements and air spaces are common to both the measurement and reference wavefront, so the sensitivities are not tight. Also, since the reference surface of the test plate is common to all tests, this system achieves excellent control for the radius of curvature variation from one part to another. This paper describes the test system design and analysis for such a test, and presents data from a similar 1.4-m test performed at the University of Arizona.

Optically-initiated silicon carbide high voltage switch with contoured-profile electrode interfaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sullivan, James S.; Hawkins, Steven A.

An improved photoconductive switch having a SiC or other wide band gap substrate material with opposing contoured profile cavities which have a contoured profile selected from one of Rogowski, Bruce, Chang, Harrison, and Ernst profiles, and two electrodes with matching contoured-profile convex interface surfaces.

A trait-based test for habitat filtering: Convex hull volume

USGS Publications Warehouse

Cornwell, W.K.; Schwilk, D.W.; Ackerly, D.D.

2006-01-01

Community assembly theory suggests that two processes affect the distribution of trait values within communities: competition and habitat filtering. Within a local community, competition leads to ecological differentiation of coexisting species, while habitat filtering reduces the spread of trait values, reflecting shared ecological tolerances. Many statistical tests for the effects of competition exist in the literature, but measures of habitat filtering are less well-developed. Here, we present convex hull volume, a construct from computational geometry, which provides an n-dimensional measure of the volume of trait space occupied by species in a community. Combined with ecological null models, this measure offers a useful test for habitat filtering. We use convex hull volume and a null model to analyze California woody-plant trait and community data. Our results show that observed plant communities occupy less trait space than expected from random assembly, a result consistent with habitat filtering. ?? 2006 by the Ecological Society of America.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Skala, Vaclav

There are many space subdivision and space partitioning techniques used in many algorithms to speed up computations. They mostly rely on orthogonal space subdivision, resp. using hierarchical data structures, e.g. BSP trees, quadtrees, octrees, kd-trees, bounding volume hierarchies etc. However in some applications a non-orthogonal space subdivision can offer new ways for actual speed up. In the case of convex polygon in E{sup 2} a simple Point-in-Polygon test is of the O(N) complexity and the optimal algorithm is of O(log N) computational complexity. In the E{sup 3} case, the complexity is O(N) even for the convex polyhedron as no orderingmore » is defined. New Point-in-Convex Polygon and Point-in-Convex Polyhedron algorithms are presented based on space subdivision in the preprocessing stage resulting to O(1) run-time complexity. The presented approach is simple to implement. Due to the principle of duality, dual problems, e.g. line-convex polygon, line clipping, can be solved in a similarly.« less

Polymeric PLC-type thermo-optic optical attenuator fabricated by UV imprint technique

NASA Astrophysics Data System (ADS)

Kim, Jin Tae; Choi, Choon-Gi

2006-01-01

A planar lightwave circuit-type polymer thermo-optic optical attenuator was fabricated via a UV imprint technique. In order to reduce the step for filling of cores and minimize the detrimental residual slab waveguide, convex ridge-type micro cores for guidance of light were defined with an accuracy of ±0.5 μm on the under-clad by a single step of imprinting. The voltage-controlled polymer optical attenuator showed 30-dB attenuation with 80-mW electrical input power at a wavelength of 1.55 μm. The rise and fall times are less than 5 ms. It displays about 0.2- and 1-dB polarization dependence at 0- and 10-dB attenuations, respectively.

The effect of optical system design for laser micro-hole drilling process

NASA Astrophysics Data System (ADS)

Ding, Chien-Fang; Lan, Yin-Te; Chien, Yu-Lun; Young, Hong-Tsu

2017-08-01

Lasers are a promising high accuracy tool to make small holes in composite or hard material. They offer advantages over the conventional machining process, which is time consuming and has scaling limitations. However, the major downfall in laser material processing is the relatively large heat affect zone or number of molten burrs it generates, even when using nanosecond lasers over high-cost ultrafast lasers. In this paper, we constructed a nanosecond laser processing system with a 532 nm wavelength laser source. In order to enhance precision and minimize the effect of heat generation with the laser drilling process, we investigated the geometric shape of optical elements and analyzed the images using the modulation transfer function (MTF) and encircled energy (EE) by using optical software Zemax. We discuss commercial spherical lenses, including plano-convex lenses, bi-convex lenses, plano-concave lenses, bi-concave lenses, best-form lenses, and meniscus lenses. Furthermore, we determined the best lens configuration by image evaluation, and then verified the results experimentally by carrying out the laser drilling process on multilayer flexible copper clad laminate (FCCL). The paper presents the drilling results obtained with different lens configurations and found the best configuration had a small heat affect zone and a clean edge along laser-drilled holes.

The Backscattering Phase Function for a Sphere with a Two-Scale Relief of Rough Surface

NASA Astrophysics Data System (ADS)

Klass, E. V.

2017-12-01

The backscattering of light from spherical surfaces characterized by one and two-scale roughness reliefs has been investigated. The analysis is performed using the three-dimensional Monte-Carlo program POKS-RG (geometrical-optics approximation), which makes it possible to take into account the roughness of objects under study by introducing local geometries of different levels. The geometric module of the program is aimed at describing objects by equations of second-order surfaces. One-scale roughness is set as an ensemble of geometric figures (convex or concave halves of ellipsoids or cones). The two-scale roughness is modeled by convex halves of ellipsoids, with surface containing ellipsoidal pores. It is shown that a spherical surface with one-scale convex inhomogeneities has a flatter backscattering phase function than a surface with concave inhomogeneities (pores). For a sphere with two-scale roughness, the dependence of the backscattering intensity is found to be determined mostly by the lower-level inhomogeneities. The influence of roughness on the dependence of the backscattering from different spatial regions of spherical surface is analyzed.

Implementation of light extraction improvements of GaN-based light-emitting diodes with specific textured sidewalls

NASA Astrophysics Data System (ADS)

Chen, Chun-Yen; Chen, Wei-Cheng; Chang, Ching-Hong; Lee, Yu-Lin; Liu, Wen-Chau

2018-05-01

Textured-sidewall GaN-based light-emitting diodes (LEDs) with various sidewall angles (15-90°) and convex or concave sidewalls prepared using an inductively-coupled-plasma approach are comprehensively fabricated and studied. The device with 45° sidewalls (Device F) and that with convex sidewalls (Device B) show significant improvements in optical properties. Experiments show that, at an injection current of 350 mA, the light output power, external quantum efficiency, wall-plug efficiency, and luminous flux of Device F (Device B) are greatly improved by 18.3% (18.2%), 18.2% (18.2%), 17.3% (19.8%), and 16.6% (18.4%), respectively, compared to those of a conventional LED with flat sidewalls. In addition, negligible degradation in electrical properties is found. The enhanced optical performance is mainly attributed to increased light extraction in the horizontal direction due to a significant reduction in total internal reflection at the textured sidewalls. Therefore, the reported specific textured-sidewall structures (Devices B and F) are promising for high-power GaN-based LED applications.

Three-dimensional integration of microoptical components buried inside photosensitive glass by femtosecond laser direct writing

NASA Astrophysics Data System (ADS)

Wang, Zhongke; Sugioka, Koji; Midorikawa, Katsumi

2007-12-01

We report the three-dimensional (3D) integration of microoptical components such as microlenses, micromirrors and optical waveguides in a single glass chip by femtosecond (fs) laser direct writing. First, two types of microoptical lenses were fabricated inside photosensitive Foturan glass by forming hollow microstructures using fs laser direct writing followed by thermal treatment, successive wet etching and additional annealing. One type of lens is the cylindrical microlens with a curvature radius R of 1.0 mm, and the other is the plano-convex microlens with radius R of 0.75 mm. Subsequently, by the continuous procedure of hollow microstructure fabrication, a micromirror was integrated with the plano-convex microlens in the single glass chip. Further integration of waveguides was performed by internal refractive index modification using fs laser direct writing after the hollow structure fabrication of the microlens and the micromirror. A demonstration of the laser beam transmission in the integrated optical microdevice shows that the 3D integration of waveguides with a micromirror and a microoptical lens in a single glass chip is highly effective for light beam guiding and focusing.

Fabrication and evaluation of variable focus and large deformation plano-convex microlens based on non-ionic poly(vinyl chloride)/dibutyl adipate gels

NASA Astrophysics Data System (ADS)

Kim, Sang-Youn; Yeo, Myoung; Shin, Eun-Jae; Park, Won-Hyeong; Jang, Jong-Seok; Nam, Byeong-Uk; Bae, Jin Woo

2015-11-01

In this paper, we propose a variable focus microlens module based on a transparent, electroactive, and non-ionic PVC/DBA gel. A non-ionic PVC/DBA (nPVC) gel on an ITO glass was confined beneath a rigid annular electrode, and applied pressure squeezed a bulge of the nPVC gel into the annular electrode, resulting in a hemispherical plano-convex nPVC gel microlens. The proposed nPVC gel microlens was analyzed and optimized. When voltage is applied to the circular perimeter (the annular electrode) of this fabricated microlens, electrically induced creep deformation of the nPVC gel occurs, changing its optical focal length. The focal length remarkably increases from 3.8 mm up to 14.3 mm with increasing applied voltages from 300 V to 800 V. Due to its compact, transparent, and electroactive characteristics, the proposed nPVC gel microlens can be easily inserted into small consumer electronic devices, such as digital cameras, camcorders, cell phones, and other portable optical devices.

Security hologram foil labels with a design facilitating authenticity testing: effects of mechanical bending of substrates with the glued on holograms

NASA Astrophysics Data System (ADS)

Aubrecht, Ivo

2015-05-01

Optimal design of security holograms or diffractive optically variable image devices (DOVIDs) that would be complex enough to deter counterfeiters from attempts of mimicking but contains features readily recognizable by laymen has been addressed by many experts. This paper tries to discuss effects of mechanical bending of a flexible substrate to visual appearance of a glued-on foil DOVID. Initially plane, the DOVID is deformed to a convex- or concave-shaped curved surface. Theoretical analyses and experimental results assume the surface to be a cylindrical segment and concern rainbow-type surface-relief holograms that are recorded piecewise in a photoresist material, coated on planar and non-planar substrates.

Turbulent boundary layers subjected to multiple curvatures and pressure gradients

NASA Technical Reports Server (NTRS)

Bandyopadhyay, Promode R.; Ahmed, Anwar

1993-01-01

The effects of abruptly applied cycles of curvatures and pressure gradients on turbulent boundary layers are examined experimentally. Two two-dimensional curved test surfaces are considered: one has a sequence of concave and convex longitudinal surface curvatures and the other has a sequence of convex and concave curvatures. The choice of the curvature sequences were motivated by a desire to study the asymmetric response of turbulent boundary layers to convex and concave curvatures. The relaxation of a boundary layer from the effects of these two opposite sequences has been compared. The effect of the accompaying sequences of pressure gradient has also been examined but the effect of curvature dominates. The growth of internal layers at the curvature junctions have been studied. Measurements of the Gortler and corner vortex systems have been made. The boundary layer recovering from the sequence of concave to convex curvature has a sustained lower skin friction level than in that recovering from the sequence of convex to concave curvature. The amplification and suppression of turbulence due to the curvature sequences have also been studied.

Optical integration of Pancharatnam-Berry phase lens and dynamical phase lens

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ke, Yougang; Liu, Yachao; Zhou, Junxiao

In the optical system, most elements such as lens, prism, and optical fiber are made of silica glass. Therefore, integrating Pancharatnam-Berry phase elements into silica glass has potential applications in the optical system. In this paper, we take a lens, for example, which integrates a Pancharatnam-Berry phase lens into a conventional plano-convex lens. The spin states and positions of focal points can be modulated by controlling the polarization states of the incident beam. The proposed lens has a high transmission efficiency, and thereby acts as a simple and powerful tool to manipulate spin photons. Furthermore, the method can be convenientlymore » extended to the optical fiber and laser cavity, and may provide a route to the design of the spin-photonic devices.« less

Some Tours Are More Equal than Others: The Convex-Hull Model Revisited with Lessons for Testing Models of the Traveling Salesperson Problem

ERIC Educational Resources Information Center

Tak, Susanne; Plaisier, Marco; van Rooij, Iris

2008-01-01

To explain human performance on the "Traveling Salesperson" problem (TSP), MacGregor, Ormerod, and Chronicle (2000) proposed that humans construct solutions according to the steps described by their convex-hull algorithm. Focusing on tour length as the dependent variable, and using only random or semirandom point sets, the authors…

Wide field of view telescope

DOEpatents

Ackermann, Mark R [Albuquerque, NM; McGraw, John T [Placitas, NM; Zimmer, Peter C [Albuquerque, NM

2008-01-15

A wide field of view telescope having two concave and two convex reflective surfaces, each with an aspheric surface contour, has a flat focal plane array. Each of the primary, secondary, tertiary, and quaternary reflective surfaces are rotationally symmetric about the optical axis. The combination of the reflective surfaces results in a wide field of view in the range of approximately 3.8.degree. to approximately 6.5.degree.. The length of the telescope along the optical axis is approximately equal to or less than the diameter of the largest of the reflective surfaces.

The Octree Encoding Method for Efficient Solid Modeling.

DTIC Science & Technology

1982-08-01

vertex point of a test obel is interior or exterior to the object. If the object is a convex polyhedron , the surface is described by a L 55 yp Test Obel...values can be generated by adding an offset from a pre-computed table. For a convex polyhedron , if a point is in the positive . .half-space of all face...planes, then it is interior to the polyhedron . If it is in the negative half-plane of any face plane, then it is exterior to the object. Otherwise, the

Physical properties of asteroids derived from a novel approach to modeling of optical lightcurves and WISE thermalinfrared data

NASA Astrophysics Data System (ADS)

Durech, Josef; Hanus, Josef; Delbo, Marco; Ali-Lagoa, Victor; Carry, Benoit

2014-11-01

Convex shape models and spin vectors of asteroids are now routinely derived from their disk-integrated lightcurves by the lightcurve inversion method of Kaasalainen et al. (2001, Icarus 153, 37). These shape models can be then used in combination with thermal infrared data and a thermophysical model to derive other physical parameters - size, albedo, macroscopic roughness and thermal inertia of the surface. In this classical two-step approach, the shape and spin parameters are kept fixed during the thermophysical modeling when the emitted thermal flux is computed from the surface temperature, which is computed by solving a 1-D heat diffusion equation in sub-surface layers. A novel method of simultaneous inversion of optical and infrared data was presented by Durech et al. (2012, LPI Contribution No. 1667, id.6118). The new algorithm uses the same convex shape representation as the lightcurve inversion but optimizes all relevant physical parameters simultaneously (including the shape, size, rotation vector, thermal inertia, albedo, surface roughness, etc.), which leads to a better fit to the thermal data and a reliable estimation of model uncertainties. We applied this method to selected asteroids using their optical lightcurves from archives and thermal infrared data observed by the Wide-field Infrared Survey Explorer (WISE) satellite. We will (i) show several examples of how well our model fits both optical and infrared data, (ii) discuss the uncertainty of derived parameters (namely the thermal inertia), (iii) compare results obtained with the two-step approach with those obtained by our method, (iv) discuss the advantages of this simultaneous approach with respect to the classical two-step approach, and (v) advertise the possibility to use this approach to tens of thousands asteroids for which enough WISE and optical data exist.

Needle tip visualization by bevel-point ultrasound generator and prototype photoacoustic imaging system

NASA Astrophysics Data System (ADS)

Irisawa, Kaku; Murakoshi, Dai; Hashimoto, Atsushi; Yamamoto, Katsuya; Hayakawa, Toshiro

2017-03-01

Visualization of the tip of medical devices like needles or catheters under ultrasound imaging has been a continuous topic since the early 1980's. In this study, a needle tip visualization system utilizing photoacoustic effects is proposed. In order to visualize the needle tip, an optical fiber was inserted into a needle. The optical fiber tip is placed on the needle bevel and affixed with black glue. The pulsed laser light from laser diode was transferred to the optical fiber and converted to ultrasound due to laser light absorption of the black glue and the subsequent photoacoustic effect. The ultrasound is detected by transducer array and reconstructed into photoacoustic images in the ultrasound unit. The photoacoustic image is displayed with a superposed ultrasound B-mode image. As a system evaluation, the needle is punctured into bovine meat and the needle tip is observed with commercialized conventional linear transducers or convex transducers. The needle tip is visualized clearly at 7 and 12 cm depths with linear and convex probes, respectively, even with a steep needle puncture angle of around 90 degrees. Laser and acoustic outputs, and thermal rise at the needle tip, were measured and were well below the limits of the safety standards. Compared with existing needle tip visualization technologies, the photoacoustic needle tip visualization system has potential distinguishable features for clinical procedures related with needle puncture and injection.

Study of foldable elastic tubes for large space structure applications, phase 1

NASA Technical Reports Server (NTRS)

Jones, I. W.; Boateng, C.; Williams, C. D.

1980-01-01

Structural members that might be suitable for strain energy deployable structures, are discussed with emphasis on a thin-walled cylindrical tube with a cross-section that is called 'bi-convex'. The design of bi-convex tube test specimens and their fabrication are described as well as the design and construction of a special purpose testing machine to determine the deployment characteristics. The results of the first series of tests were quite mixed, but clearly revealed that since most of the specimens failed to deploy completely, due to a buckling problem, this type of tube requires some modification in order to be viable.

Optical lenses design and experimental investigations of a dynamic focusing unit for a CO2 laser scanning system

NASA Astrophysics Data System (ADS)

Chen, Wei; Xu, Yue; Zhang, Huaxin; Liu, Peng; Jiao, Guohua

2016-09-01

Laser scanners are critical components in material processing systems, such as welding, cutting, and drilling. To achieve high-accuracy processing, the laser spot size should be small and uniform in the entire objective flat field. However, traditional static focusing method using F-theta objective lens is limited by the narrow flat field. To overcome these limitations, a dynamic focusing unit consisting of two lenses is presented in this paper. The dual-lens system has a movable plano-concave lens and a fixed convex lens. As the location of the movable optical elements is changed, the focal length is shifted to keep a small focus spot in a broad flat processing filed. The optical parameters of the two elements are theoretical analyzed. The spot size is calculated to obtain the relationship between the moving length of first lens and the shift focus length of the system. Also, the Zemax model of the optical system is built up to verify the theoretical design and optimize the optical parameter. The proposed lenses are manufactured and a test system is built up to investigate their performances. The experimental results show the spot size is smaller than 450um in all the 500*500mm 2 filed with CO2 laser. Compared with the other dynamic focusing units, this design has fewer lenses and no focusing spot in the optical path. In addition, the focal length minimal changes with the shit of incident laser beam.

Micro-optical design of a three-dimensional microlens scanner for vertically integrated micro-opto-electro-mechanical systems.

PubMed

Baranski, Maciej; Bargiel, Sylwester; Passilly, Nicolas; Gorecki, Christophe; Jia, Chenping; Frömel, Jörg; Wiemer, Maik

2015-08-01

This paper presents the optical design of a miniature 3D scanning system, which is fully compatible with the vertical integration technology of micro-opto-electro-mechanical systems (MOEMS). The constraints related to this integration strategy are considered, resulting in a simple three-element micro-optical setup based on an afocal scanning microlens doublet and a focusing microlens, which is tolerant to axial position inaccuracy. The 3D scanning is achieved by axial and lateral displacement of microlenses of the scanning doublet, realized by micro-electro-mechanical systems microactuators (the transmission scanning approach). Optical scanning performance of the system is determined analytically by use of the extended ray transfer matrix method, leading to two different optical configurations, relying either on a ball lens or plano-convex microlenses. The presented system is aimed to be a core component of miniature MOEMS-based optical devices, which require a 3D optical scanning function, e.g., miniature imaging systems (confocal or optical coherence microscopes) or optical tweezers.

Lensless imaging for wide field of view

NASA Astrophysics Data System (ADS)

Nagahara, Hajime; Yagi, Yasushi

2015-02-01

It is desirable to engineer a small camera with a wide field of view (FOV) because of current developments in the field of wearable cameras and computing products, such as action cameras and Google Glass. However, typical approaches for achieving wide FOV, such as attaching a fisheye lens and convex mirrors, require a trade-off between optics size and the FOV. We propose camera optics that achieve a wide FOV, and are at the same time small and lightweight. The proposed optics are a completely lensless and catoptric design. They contain four mirrors, two for wide viewing, and two for focusing the image on the camera sensor. The proposed optics are simple and can be simply miniaturized, since we use only mirrors for the proposed optics and the optics are not susceptible to chromatic aberration. We have implemented the prototype optics of our lensless concept. We have attached the optics to commercial charge-coupled device/complementary metal oxide semiconductor cameras and conducted experiments to evaluate the feasibility of our proposed optics.

Integration of a UV curable polymer lens and MUMPs structures on a SOI optical bench

NASA Astrophysics Data System (ADS)

Hsieh, Jerwei; Hsiao, Sheng-Yi; Lai, Chun-Feng; Fang, Weileun

2007-08-01

This work presents the design concept of integrating a polymer lens, poly-Si MUMPs and single-crystal-silicon HARM structures on a SOI wafer to form a silicon optical bench. This approach enables the monolithic integration of various optical components on the wafer so as to improve the design flexibility of the silicon optical bench. Fabrication processes, including surface and bulk micromachining on the SOI wafer, have been established to realize bi-convex spherical polymer lenses with in-plane as well as out-of-plane optical axes. In addition, a micro device consisting of an in-plane polymer lens, a thick fiber holder and a mechanical shutter driven by an electrothermal actuator is also demonstrated using the present approach. In summary, this study significantly improves the design flexibility as well as the functions of SiOBs.

A new convexity measure for polygons.

PubMed

Zunic, Jovisa; Rosin, Paul L

2004-07-01

Abstract-Convexity estimators are commonly used in the analysis of shape. In this paper, we define and evaluate a new convexity measure for planar regions bounded by polygons. The new convexity measure can be understood as a "boundary-based" measure and in accordance with this it is more sensitive to measured boundary defects than the so called "area-based" convexity measures. When compared with the convexity measure defined as the ratio between the Euclidean perimeter of the convex hull of the measured shape and the Euclidean perimeter of the measured shape then the new convexity measure also shows some advantages-particularly for shapes with holes. The new convexity measure has the following desirable properties: 1) the estimated convexity is always a number from (0, 1], 2) the estimated convexity is 1 if and only if the measured shape is convex, 3) there are shapes whose estimated convexity is arbitrarily close to 0, 4) the new convexity measure is invariant under similarity transformations, and 5) there is a simple and fast procedure for computing the new convexity measure.

Perspective and potential of smart optical materials

NASA Astrophysics Data System (ADS)

Choi, Sang H.; Duzik, Adam J.; Kim, Hyun-Jung; Park, Yeonjoon; Kim, Jaehwan; Ko, Hyun-U.; Kim, Hyun-Chan; Yun, Sungryul; Kyung, Ki-Uk

2017-09-01

The increasing requirements of hyperspectral imaging optics, electro/photo-chromic materials, negative refractive index metamaterial optics, and miniaturized optical components from micro-scale to quantum-scale optics have all contributed to new features and advancements in optics technology. Development of multifunctional capable optics has pushed the boundaries of optics into new fields that require new disciplines and materials to maximize the potential benefits. The purpose of this study is to understand and show the fundamental materials and fabrication technology for field-controlled spectrally active optics (referred to as smart optics) that are essential for future industrial, scientific, military, and space applications, such as membrane optics, filters, windows for sensors and probes, telescopes, spectroscopes, cameras, light valves, light switches, and flat-panel displays. The proposed smart optics are based on the Stark and Zeeman effects in materials tailored with quantum dot arrays and thin films made from readily polarizable materials via ferroelectricity or ferromagnetism. Bound excitonic states of organic crystals are also capable of optical adaptability, tunability, and reconfigurability. To show the benefits of smart optics, this paper reviews spectral characteristics of smart optical materials and device technology. Experiments testing the quantum-confined Stark effect, arising from rare earth element doping effects in semiconductors, and applied electric field effects on spectral and refractive index are discussed. Other bulk and dopant materials were also discovered to have the same aspect of shifts in spectrum and refractive index. Other efforts focus on materials for creating field-controlled spectrally smart active optics on a selected spectral range. Surface plasmon polariton transmission of light through apertures is also discussed, along with potential applications. New breakthroughs in micro scale multiple zone plate optics as a micro convex lens are reviewed, along with the newly discovered pseudo-focal point not predicted with conventional optics modeling. Micron-sized solid state beam scanner chips for laser waveguides are reviewed as well.

Transparent and flexible capacitors based on nanolaminate Al2O3/TiO2/Al2O3.

PubMed

Zhang, Guozhen; Wu, Hao; Chen, Chao; Wang, Ti; Yue, Jin; Liu, Chang

2015-01-01

Transparent and flexible capacitors based on nanolaminate Al2O3/TiO2/Al2O3 dielectrics have been fabricated on indium tin oxide-coated polyethylene naphthalate substrates by atomic layer deposition. A capacitance density of 7.8 fF/μm(2) at 10 KHz was obtained, corresponding to a dielectric constant of 26.3. Moreover, a low leakage current density of 3.9 × 10(-8) A/cm(2) at 1 V has been realized. Bending test shows that the capacitors have better performances in concave conditions than in convex conditions. The capacitors exhibit an average optical transmittance of about 70% in visible range and thus open the door for applications in transparent and flexible integrated circuits.

Shaping asteroid models using genetic evolution (SAGE)

NASA Astrophysics Data System (ADS)

Bartczak, P.; Dudziński, G.

2018-02-01

In this work, we present SAGE (shaping asteroid models using genetic evolution), an asteroid modelling algorithm based solely on photometric lightcurve data. It produces non-convex shapes, orientations of the rotation axes and rotational periods of asteroids. The main concept behind a genetic evolution algorithm is to produce random populations of shapes and spin-axis orientations by mutating a seed shape and iterating the process until it converges to a stable global minimum. We tested SAGE on five artificial shapes. We also modelled asteroids 433 Eros and 9 Metis, since ground truth observations for them exist, allowing us to validate the models. We compared the derived shape of Eros with the NEAR Shoemaker model and that of Metis with adaptive optics and stellar occultation observations since other models from various inversion methods were available for Metis.

Testing predictions of the quantum landscape multiverse 2: the exponential inflationary potential

NASA Astrophysics Data System (ADS)

Di Valentino, Eleonora; Mersini-Houghton, Laura

2017-03-01

The 2015 Planck data release tightened the region of the allowed inflationary models. Inflationary models with convex potentials have now been ruled out since they produce a large tensor to scalar ratio. Meanwhile the same data offers interesting hints on possible deviations from the standard picture of CMB perturbations. Here we revisit the predictions of the theory of the origin of the universe from the landscape multiverse for the case of exponential inflation, for two reasons: firstly to check the status of the anomalies associated with this theory, in the light of the recent Planck data; secondly, to search for a counterexample whereby new physics modifications may bring convex inflationary potentials, thought to have been ruled out, back into the region of potentials allowed by data. Using the exponential inflation as an example of convex potentials, we find that the answer to both tests is positive: modifications to the perturbation spectrum and to the Newtonian potential of the universe originating from the quantum entanglement, bring the exponential potential, back within the allowed region of current data; and, the series of anomalies previously predicted in this theory, is still in good agreement with current data. Hence our finding for this convex potential comes at the price of allowing for additional thermal relic particles, equivalently dark radiation, in the early universe.

Being "Secondary" is Important for a Webb Telescope Mirror

NASA Image and Video Library

2017-12-08

NASA release July 19, 2011 Click here to learn about the James Webb Space Telescope The secondary mirror (shown here) was polished at the L3 Integrated Optical Systems - Tinsley in Richmond, Calif. to accuracies of less than one millionth of an inch. That accuracy is important for forming the sharpest images when the mirrors cool to -400°F (-240°C) in the cold of space. The Webb's secondary mirror was recently completed, following polishing and gold-coating. "Secondary" may not sound as important as "primary" but when it comes to the next-generation James Webb Space Telescope a secondary mirror plays a critical role in ensuring the telescope gathers information from the cosmos. The Webb's secondary mirror was recently completed, following polishing and gold-coating. There are four different types of mirrors that will fly on the James Webb Space Telescope, and all are made of a light metal called beryllium. It is very strong for its weight and holds its shape across a range of temperatures. There are primary mirror segments (18 total that combined make the large primary mirror providing a collecting area of 25 meters squared/269.1 square feet), the secondary mirror, tertiary mirror and the fine steering mirror. Unlike the primary mirror, which is molded into the shape of a hexagon, the secondary mirror is perfectly rounded. The mirror is also convex, so the reflective surface bulges toward a light source. It looks much like a curved mirror that you'll see on the wall near the exit of a parking garage that lets motorists see around a corner. This mirror is coated with a microscopic layer of gold to enable it to efficiently reflect infrared light (which is what the Webb telescope's cameras see). The quality of the secondary mirror surface is so good that the final convex surface at cold temperatures does not deviate from the design by more than a few millionths of a millimeter - or about one ten thousandth the diameter of a human hair. "As the only convex mirror on the Webb telescope, the secondary mirror has always been recognized to be the hardest of all of the mirrors to polish and test, so we are delighted that its performance meets all specifications," said Lee Feinberg, Webb Optical Telescope manager at NASA's Goddard Space Flight Center in Greenbelt, Md. Convex mirrors are particularly hard to test because light that strikes them diverges away from the mirror. Feinberg noted, "The Webb telescope convex secondary mirror is approximately the size of the Spitzer Space Telescope's primary mirror and is by far the largest convex cryogenic mirror ever built for a NASA program." It was data from the Spitzer's mirrors that helped make the decision to use beryllium for the Webb telescope mirrors. Spitzer's mirrors were also made of beryllium. So why is this mirror so critical? Because the secondary mirror captures light from the 18 primary mirror segments and relays those distant images of the cosmos to the telescope's science cameras. The secondary mirror is mounted on folding "arms" that position it in front of the 18 primary mirror segments. The secondary mirror will soon come to NASA's Goddard Space Flight Center in Greenbelt, Md. where it will be installed on the telescope structure. Then, as a complete unit, the telescope structure and mirrors will undergo acoustic and vibration testing. The secondary mirror was developed at Ball Aerospace & Technology Corp. of Boulder, Colo. and the mirror recently completed polishing at the L3–IOS-Tinsley facility in Richmond, Calif. Northrop Grumman space Systems is the prime contractor on the Webb telescope program. The James Webb Space Telescope is the world’s next-generation space observatory and successor to the Hubble Space Telescope. The most powerful space telescope ever built, Webb will observe the most distant objects in the universe, provide images of the very first galaxies ever formed and see unexplored planets around distant stars. The Webb Telescope is a joint project of NASA, the European Space Agency and the Canadian Space Agency. Credit:NASA/Ball Aerospace/Tinsley NASA Goddard Space Flight Center enables NASA’s mission through four scientific endeavors: Earth Science, Heliophysics, Solar System Exploration, and Astrophysics. Goddard plays a leading role in NASA’s accomplishments by contributing compelling scientific knowledge to advance the Agency’s mission. Follow us on Twitter Like us on Facebook Find us on Instagram

Diffractive optical elements on non-flat substrates using electron beam lithography

NASA Technical Reports Server (NTRS)

Maker, Paul D. (Inventor); Muller, Richard E. (Inventor); Wilson, Daniel W. (Inventor)

2002-01-01

The present disclosure describes a technique for creating diffraction gratings on curved surfaces with electron beam lithography. The curved surface can act as an optical element to produce flat and aberration-free images in imaging spectrometers. In addition, the fabrication technique can modify the power structure of the grating orders so that there is more energy in the first order than for a typical grating. The inventors noticed that by using electron-beam lithography techniques, a variety of convex gratings that are well-suited to the requirements of imaging spectrometers can be manufactured.

Tracking integration in concentrating photovoltaics using laterally moving optics.

PubMed

Duerr, Fabian; Meuret, Youri; Thienpont, Hugo

2011-05-09

In this work the concept of tracking-integrated concentrating photovoltaics is studied and its capabilities are quantitatively analyzed. The design strategy desists from ideal concentration performance to reduce the external mechanical solar tracking effort in favor of a compact installation, possibly resulting in lower overall cost. The proposed optical design is based on an extended Simultaneous Multiple Surface (SMS) algorithm and uses two laterally moving plano-convex lenses to achieve high concentration over a wide angular range of ±24°. It achieves 500× concentration, outperforming its conventional concentrating photovoltaic counterparts on a polar aligned single axis tracker.

Efficient Optical Energy Harvesting in Self-Accelerating Beams

PubMed Central

Bongiovanni, Domenico; Hu, Yi; Wetzel, Benjamin; Robles, Raul A.; Mendoza González, Gregorio; Marti-Panameño, Erwin A.; Chen, Zhigang; Morandotti, Roberto

2015-01-01

We report the experimental observation of energetically confined self-accelerating optical beams propagating along various convex trajectories. We show that, under an appropriate transverse compression of their spatial spectra, these self-accelerating beams can exhibit a dramatic enhancement of their peak intensity and a significant decrease of their transverse expansion, yet retaining both the expected acceleration profile and the intrinsic self-healing properties. We found our experimental results to be in excellent agreement with the numerical simulations. We expect further applications in such contexts where power budget and optimal spatial confinement can be important limiting factors. PMID:26299360

Wave-Based Algorithms and Bounds for Target Support Estimation

DTIC Science & Technology

2015-05-15

vector electromagnetic formalism in [5]. This theory leads to three main variants of the optical theorem detector, in particular, three alternative...further expands the applicability for transient pulse change detection of ar- bitrary nonlinear-media and time-varying targets [9]. This report... electromagnetic methods a new methodology to estimate the minimum convex source region and the (possibly nonconvex) support of a scattering target from knowledge of

Effect of polishing conditions on terminating optical connectors with spherical convex polished ends

NASA Astrophysics Data System (ADS)

Lin, Samuel I.-En

2002-01-01

Increased demand for fiber-optic technology has created significant growth in the sales of interconnection devices such as fiber-optic connectors, cable assemblies, and adapters. To ensure good connector performance during actual use, several process parameters related to geometric and optical characteristics of the connector must be thoroughly understood during the manufacturing stage. The experimental design has been used here to see the influence of applied pressure and time on the fiber end geometry as well as optical performance. The mathematical model is also applied to explain the phenomena of the present fiber undercut-reflectance relation. By a proper choice of polishing film grit size and processing conditions, it is possible to obtain fiber connectors with less fiber undercut and better return loss. Influences of film grit size and rubber-pad thickness on the reflectance and the fiber undercut are also presented.

Design and laboratory calibration of the compact pushbroom hyperspectral imaging system

NASA Astrophysics Data System (ADS)

Zhou, Jiankang; Ji, Yiqun; Chen, Yuheng; Chen, Xinhua; Shen, Weimin

2009-11-01

The designed hyperspectral imaging system is composed of three main parts, that is, optical subsystem, electronic subsystem and capturing subsystem. And a three-dimensional "image cube" can be obtained through push-broom. The fore-optics is commercial-off-the-shelf with high speed and three continuous zoom ratios. Since the dispersive imaging part is based on Offner relay configuration with an aberration-corrected convex grating, high power of light collection and variable view field are obtained. The holographic recording parameters of the convex grating are optimized, and the aberration of the Offner configuration dispersive system is balanced. The electronic system adopts module design, which can minimize size, mass, and power consumption. Frame transfer area-array CCD is chosen as the image sensor and the spectral line can be binned to achieve better SNR and sensitivity without any deterioration in spatial resolution. The capturing system based on the computer can set the capturing parameters, calibrate the spectrometer, process and display spectral imaging data. Laboratory calibrations are prerequisite for using precise spectral data. The spatial and spectral calibration minimize smile and keystone distortion caused by optical system, assembly and so on and fix positions of spatial and spectral line on the frame area-array CCD. Gases excitation lamp is used in smile calibration and the keystone calculation is carried out by different viewing field point source created by a series of narrow slit. The laboratory and field imaging results show that this pushbroom hyperspectral imaging system can acquire high quality spectral images.

A head-mounted compressive three-dimensional display system with polarization-dependent focus switching

NASA Astrophysics Data System (ADS)

Lee, Chang-Kun; Moon, Seokil; Lee, Byounghyo; Jeong, Youngmo; Lee, Byoungho

2016-10-01

A head-mounted compressive three-dimensional (3D) display system is proposed by combining polarization beam splitter (PBS), fast switching polarization rotator and micro display with high pixel density. According to the polarization state of the image controlled by polarization rotator, optical path of image in the PBS can be divided into transmitted and reflected components. Since optical paths of each image are spatially separated, it is possible to independently focus both images at different depth positions. Transmitted p-polarized and reflected s-polarized images can be focused by convex lens and mirror, respectively. When the focal lengths of the convex lens and mirror are properly determined, two image planes can be located in intended positions. The geometrical relationship is easily modulated by replacement of the components. The fast switching of polarization realizes the real-time operation of multi-focal image planes with a single display panel. Since it is possible to conserve the device characteristic of single panel, the high image quality, reliability and uniformity can be retained. For generating 3D images, layer images for compressive light field display between two image planes are calculated. Since the display panel with high pixel density is adopted, high quality 3D images are reconstructed. In addition, image degradation by diffraction between physically stacked display panels can be mitigated. Simple optical configuration of the proposed system is implemented and the feasibility of the proposed method is verified through experiments.

A path to asteroid bulk densities: Simultaneous size and shape optimization from optical lightcurves and Keck disk-resolved data

NASA Astrophysics Data System (ADS)

Hanus, Josef; Viikinkoski, Matti; Marchis, Franck; Durech, Josef

2015-11-01

A reliable bulk density of an asteroid can be determined from the knowledge of its volume and mass. This quantity provides hints on the internal structure of asteroids and their origin. We compute volume of several asteroids by scaling sizes of their 3D shape models to fit the disk-resolved images, which are available in the Keck Observatory Archive (KOA) and the Virtual Observatory Binary Asteroids Database (VOBAD). The size of an asteroid is optimized together with its shape by the All-Data Asteroid Modelling inversion algorithm (ADAM, Viikinkoski et al., 2015, A&A, 576, A8), while the spin state of the original convex shape model from the DAMIT database is only used as an initial guess for the modeling. Updated sets of optical lightcurves are usually employed. Thereafter, we combine obtained volume with mass estimates available in the literature and derive bulk densities for tens of asteroids with a typical accuracy of 20-50%.On top of that, we also provide a list of asteroids, for which (i) there are already mass estimates with reported uncertainties better than 20% or their masses will be most likely determined in the future from Gaia astrometric observations, and (ii) their 3D shape models are currently unknown. Additional optical lightcurves are necessary in order to determine convex shape models of these asteroids. Our web page (https://asteroid-obs.oca.eu/foswiki/bin/view/Main/Photometry) contains additional information about this observation campaign.

Transition operators in electromagnetic-wave diffraction theory. II - Applications to optics

NASA Technical Reports Server (NTRS)

Hahne, G. E.

1993-01-01

The theory developed by Hahne (1992) for the diffraction of time-harmonic electromagnetic waves from fixed obstacles is briefly summarized and extended. Applications of the theory are considered which comprise, first, a spherical harmonic expansion of the so-called radiation impedance operator in the theory, for a spherical surface, and second, a reconsideration of familiar short-wavelength approximation from the new standpoint, including a derivation of the so-called physical optics method on the basis of quasi-planar approximation to the radiation impedance operator, augmented by the method of stationary phase. The latter includes a rederivation of the geometrical optics approximation for the complete Green's function for the electromagnetic field in the presence of a smooth- and a convex-surfaced perfectly electrically conductive obstacle.

Organizing principles for dense packings of nonspherical hard particles: Not all shapes are created equal

NASA Astrophysics Data System (ADS)

Torquato, Salvatore; Jiao, Yang

2012-07-01

We have recently devised organizing principles to obtain maximally dense packings of the Platonic and Archimedean solids and certain smoothly shaped convex nonspherical particles [Torquato and Jiao, Phys. Rev. EPLEEE81539-375510.1103/PhysRevE.81.041310 81, 041310 (2010)]. Here we generalize them in order to guide one to ascertain the densest packings of other convex nonspherical particles as well as concave shapes. Our generalized organizing principles are explicitly stated as four distinct propositions. All of our organizing principles are applied to and tested against the most comprehensive set of both convex and concave particle shapes examined to date, including Catalan solids, prisms, antiprisms, cylinders, dimers of spheres, and various concave polyhedra. We demonstrate that all of the densest known packings associated with this wide spectrum of nonspherical particles are consistent with our propositions. Among other applications, our general organizing principles enable us to construct analytically the densest known packings of certain convex nonspherical particles, including spherocylinders, “lens-shaped” particles, square pyramids, and rhombic pyramids. Moreover, we show how to apply these principles to infer the high-density equilibrium crystalline phases of hard convex and concave particles. We also discuss the unique packing attributes of maximally random jammed packings of nonspherical particles.

On the convexity of ROC curves estimated from radiological test results.

PubMed

Pesce, Lorenzo L; Metz, Charles E; Berbaum, Kevin S

2010-08-01

Although an ideal observer's receiver operating characteristic (ROC) curve must be convex-ie, its slope must decrease monotonically-published fits to empirical data often display "hooks." Such fits sometimes are accepted on the basis of an argument that experiments are done with real, rather than ideal, observers. However, the fact that ideal observers must produce convex curves does not imply that convex curves describe only ideal observers. This article aims to identify the practical implications of nonconvex ROC curves and the conditions that can lead to empirical or fitted ROC curves that are not convex. This article views nonconvex ROC curves from historical, theoretical, and statistical perspectives, which we describe briefly. We then consider population ROC curves with various shapes and analyze the types of medical decisions that they imply. Finally, we describe how sampling variability and curve-fitting algorithms can produce ROC curve estimates that include hooks. We show that hooks in population ROC curves imply the use of an irrational decision strategy, even when the curve does not cross the chance line, and therefore usually are untenable in medical settings. Moreover, we sketch a simple approach to improve any nonconvex ROC curve by adding statistical variation to the decision process. Finally, we sketch how to test whether hooks present in ROC data are likely to have been caused by chance alone and how some hooked ROCs found in the literature can be easily explained as fitting artifacts or modeling issues. In general, ROC curve fits that show hooks should be looked on with suspicion unless other arguments justify their presence. 2010 AUR. Published by Elsevier Inc. All rights reserved.

Antireflective surface with a step in the taper: Numerical optimization and large-area fabrication

NASA Astrophysics Data System (ADS)

Shinotsuka, Kei; Hongo, Koki; Dai, Kotaro; Hirama, Satoru; Hatta, Yoshihisa

2017-02-01

In this study, we developed a practical method to improve the optical performance of subwavelength antireflective two-dimensional (2D) gratings. A numerical simulation of both convex and concave paraboloids suggested that surface reflectivity drastically decreases when a step is introduced in the taper. The optimum height and depth of a step provided average reflectances of 0.098% for convex protrusions and 0.040% for concave protrusions in the visible range. Furthermore, a stepped paraboloid was experimentally fabricated by dry etching of a Si substrate with SiO2 particle monolayer mask. A cyclo-olefin polymer (COP) reverse replica (concave) imprinted by the Si mold exhibited a measured reflectance of 0.077% on average in the visible range. It was also demonstrated that the antireflective structure was fabricated on the whole surface of a 6 in. Si wafer, which is a sufficient size for industrial utilization.

Deflectometric analysis of high volume injection molds for production of occupational eye wear.

PubMed

Speck, Alexis; Zelzer, Benedikt; Speich, Marco; Börret, Rainer; Langenbucher, Achim; Eppig, Timo

2013-12-01

Most of the protective eye wear devices currently on the market are manufactured on simple polycarbonate shields, produced by injection molding techniques. Despite high importance of optical quality, injection molds are rarely inspected for surface quality before or during the manufacturing process. Quality degradation is mainly monitored by optical testing of the molded parts. The purpose of this work was to validate a non-contact deflectometric measurement technique for surface and shape analysis of injection molds to facilitate deterministic surface quality control and to monitor minor conformity of the injection mold with the design data. The system is based on phase-measuring deflectometry with a operating measurement field of 80×80 mm(2) (±18° slope), a lateral resolution of 60μm and a local sensitivity of some nanometers. The calibration was tested with a calibration normal and a reference sphere. The results were crosschecked against a measurement of the same object with a tactile coordinate measuring machine. Eight injection molds for production of safety goggles with radii of +58mm (convex) and -60mm (concave) were measured in this study. The molds were separated into two groups (cavity 1 and 2 of the tool with different polishing techniques) and measured to test whether the measurement tool could extract differences. The analysis was performed on difference height between the measured surface and the spherical model. The device could derive the surface change due to polishing and discriminate between both polishing techniques, on the basis of the measured data. The concave nozzle sides of the first group (cavity 1) showed good shape conformity. In comparison, the nozzle sides of the second group (cavity 2) showed local deviations from design data up to 14.4μm. Local form variations of about 5μm occurred in the field of view. All convex ejector sides of both groups (cavity 1 and 2) showed rotational symmetric errors and the molds were measured in general flatter than design data. We applied a deflectometric system for measuring and evaluating specular reflective injection molding tools to optimize the production process of occupational eye wear. The surface quality could be inline monitored in the production processes for actual spectacle models. Copyright © 2013. Published by Elsevier GmbH.

Geometric approach to segmentation and protein localization in cell culture assays.

PubMed

Raman, S; Maxwell, C A; Barcellos-Hoff, M H; Parvin, B

2007-01-01

Cell-based fluorescence imaging assays are heterogeneous and require the collection of a large number of images for detailed quantitative analysis. Complexities arise as a result of variation in spatial nonuniformity, shape, overlapping compartments and scale (size). A new technique and methodology has been developed and tested for delineating subcellular morphology and partitioning overlapping compartments at multiple scales. This system is packaged as an integrated software platform for quantifying images that are obtained through fluorescence microscopy. Proposed methods are model based, leveraging geometric shape properties of subcellular compartments and corresponding protein localization. From the morphological perspective, convexity constraint is imposed to delineate and partition nuclear compartments. From the protein localization perspective, radial symmetry is imposed to localize punctate protein events at submicron resolution. Convexity constraint is imposed against boundary information, which are extracted through a combination of zero-crossing and gradient operator. If the convexity constraint fails for the boundary then positive curvature maxima are localized along the contour and the entire blob is partitioned into disjointed convex objects representing individual nuclear compartment, by enforcing geometric constraints. Nuclear compartments provide the context for protein localization, which may be diffuse or punctate. Punctate signal are localized through iterative voting and radial symmetries for improved reliability and robustness. The technique has been tested against 196 images that were generated to study centrosome abnormalities. Corresponding computed representations are compared against manual counts for validation.

Experimental Research on Air Propellers III

NASA Technical Reports Server (NTRS)

Durand, W F; Lesley, E P

1920-01-01

Report presents the results of wind tunnel tests of propellers that examined the influence of the following characteristics: (1) nominal pitch ratio 1.3 combined with a certain number of the more common or standard forms and proportions; (2) driving face slightly rounded or convex; (3) change in the location of the maximum thickness ordinate of the blade section; (4) pushing forward the leading edge of the blade, thus giving a rounded convex surface on the leading side of the driving face. (5) a series of values for the constant "angle of attack" in forming propellers with radially increasing pitch. In accordance with these purposes tests were carried out on 28 propellers.

String-averaging incremental subgradients for constrained convex optimization with applications to reconstruction of tomographic images

NASA Astrophysics Data System (ADS)

Massambone de Oliveira, Rafael; Salomão Helou, Elias; Fontoura Costa, Eduardo

2016-11-01

We present a method for non-smooth convex minimization which is based on subgradient directions and string-averaging techniques. In this approach, the set of available data is split into sequences (strings) and a given iterate is processed independently along each string, possibly in parallel, by an incremental subgradient method (ISM). The end-points of all strings are averaged to form the next iterate. The method is useful to solve sparse and large-scale non-smooth convex optimization problems, such as those arising in tomographic imaging. A convergence analysis is provided under realistic, standard conditions. Numerical tests are performed in a tomographic image reconstruction application, showing good performance for the convergence speed when measured as the decrease ratio of the objective function, in comparison to classical ISM.

Measuring large aspherics using a commercially available 3D-coordinate measuring machine

NASA Astrophysics Data System (ADS)

Otto, Wolfgang; Matthes, Axel; Schiehle, Heinz

2000-07-01

A CNC-controlled precision measuring machine is a very powerful tool in the optical shop not only to determine the surface figure, but also to qualify the radius of curvature and conic constant of aspherics. We used a commercially available 3D-coordinate measuring machine (CMM, ZEISS UPMC 850 CARAT S-ACC) to measure the shape of the GEMINI 1-m convex secondary mirrors at different lapping and polishing stages. To determine the measuring accuracy we compared the mechanical measurements with the results achieved by means of an interferometrical test setup. The data obtained in an early stage of polishing were evaluated in Zernike polynomials which show a very good agreement. The deviation concerning long wave rotational symmetrical errors was 20 nm rms, whereas the accuracy measuring of mid spatial frequency deviations was limited to about 100 nm rms.

Display-wide influences on figure-ground perception: the case of symmetry.

PubMed

Mojica, Andrew J; Peterson, Mary A

2014-05-01

Past research has demonstrated that convex regions are increasingly likely to be perceived as figures as the number of alternating convex and concave regions in test displays increases. This region-number effect depends on both a small preexisting preference for convex over concave objects and the presence of scene characteristics (i.e., uniform fill) that allow the integration of the concave regions into a background object/surface. These factors work together to enable the percept of convex objects in front of a background. We investigated whether region-number effects generalize to another property, symmetry, whose effectiveness as a figure property has been debated. Observers reported which regions they perceived as figures in black-and-white displays with alternating symmetric/asymmetric regions. In Experiments 1 and 2, the displays had articulated outer borders that preserved the symmetry/asymmetry of the outermost regions. Region-number effects were not observed, although symmetric regions were perceived as figures more often than chance. We hypothesized that the articulated outer borders prevented fitting a background interpretation to the asymmetric regions. In Experiment 3, we used straight-edge framelike outer borders and observed region-number effects for symmetry equivalent to those observed for convexity. These results (1) show that display-wide information affects figure assignment at a border, (2) extend the evidence indicating that the ability to fit background as well as foreground interpretations is critical in figure assignment, (3) reveal that symmetry and convexity are equally effective figure cues and, (4) demonstrate that symmetry serves as a figural property only when it is close to fixation.

An experimental investigation of turbulent boundary layers along curved surfaces

NASA Technical Reports Server (NTRS)

So, R. M. C.; Mellor, G. L.

1972-01-01

A curved wall tunnel was designed, and an equilibrium turbulent boundary layer was set up on the straight section preceding the curved test section. Turbulent boundary layer flows with uniform and adverse pressure distributions along convex and concave walls were investigated. Hot-wire measurements along the convex surface indicated that turbulent mixing between fluid layers was very much reduced. However, the law of the wall held and the skin friction, thus determined, correlated well with other measurements. Hot-wire measurements along the concave test wall revealed a system of longitudinal vortices inside the boundary layer and confirmed that concave curvature enhances mixing. A self-consistent set of turbulent boundary layer equations for flows along curved surfaces was derived together with a modified eddy viscosity. Solution of these equations together with the modified eddy viscosity gave results that correlated well with the present data on flows along the convex surface with arbitrary pressure distribution. However, it could only be used to predict the mean characteristics of the flow along concave walls because of the existence of the system of longitudinal vortices inside the boundary layer.

Transparent conductor-embedding nanocones for selective emitters: optical and electrical improvements of Si solar cells

PubMed Central

Kim, Joondong; Yun, Ju-Hyung; Kim, Hyunyub; Cho, Yunae; Park, Hyeong-Ho; Kumar, M. Melvin David; Yi, Junsin; Anderson, Wayne A.; Kim, Dong-Wook

2015-01-01

Periodical nanocone-arrays were employed in an emitter region for high efficient Si solar cells. Conventional wet-etching process was performed to form the nanocone-arrays for a large area, which spontaneously provides the graded doping features for a selective emitter. This enables to lower the electrical contact resistance and enhances the carrier collection due to the high electric field distribution through a nanocone. Optically, the convex-shaped nanocones efficiently reduce light-reflection and the incident light is effectively focused into Si via nanocone structure, resulting in an extremely improved the carrier collection performances. This nanocone-arrayed selective emitter simultaneously satisfies optical and electrical improvement. We report the record high efficiency of 16.3% for the periodically nanoscale patterned emitter Si solar cell. PMID:25787933

Transparent conductor-embedding nanocones for selective emitters: optical and electrical improvements of Si solar cells.

PubMed

Kim, Joondong; Yun, Ju-Hyung; Kim, Hyunyub; Cho, Yunae; Park, Hyeong-Ho; Kumar, M Melvin David; Yi, Junsin; Anderson, Wayne A; Kim, Dong-Wook

2015-03-19

Periodical nanocone-arrays were employed in an emitter region for high efficient Si solar cells. Conventional wet-etching process was performed to form the nanocone-arrays for a large area, which spontaneously provides the graded doping features for a selective emitter. This enables to lower the electrical contact resistance and enhances the carrier collection due to the high electric field distribution through a nanocone. Optically, the convex-shaped nanocones efficiently reduce light-reflection and the incident light is effectively focused into Si via nanocone structure, resulting in an extremely improved the carrier collection performances. This nanocone-arrayed selective emitter simultaneously satisfies optical and electrical improvement. We report the record high efficiency of 16.3% for the periodically nanoscale patterned emitter Si solar cell.

Optical devices combining an organic semiconductor crystal with a two-dimensional inorganic diffraction grating

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kitazawa, Takenori; Yamao, Takeshi, E-mail: yamao@kit.ac.jp; Hotta, Shu

2016-02-01

We have fabricated optical devices using an organic semiconductor crystal as an emission layer in combination with a two-dimensional (2D) inorganic diffraction grating used as an optical cavity. We formed the inorganic diffraction grating by wet etching of aluminum-doped zinc oxide (AZO) under a 2D cyclic olefin copolymer (COC) diffraction grating used as a mask. The COC diffraction grating was fabricated by nanoimprint lithography. The AZO diffraction grating was composed of convex prominences arranged in a triangular lattice. The organic crystal placed on the AZO diffraction grating indicated narrowed peaks in its emission spectrum under ultraviolet light excitation. These aremore » detected parallel to the crystal plane. The peaks were shifted by rotating the optical devices around the normal to the crystal plane, which reflected the rotational symmetries of the triangular lattice through 60°.« less

The investigation of flow instabilities on a rotating disk with curvature in the radial direction

NASA Technical Reports Server (NTRS)

Intemann, P. A.; Clarkson, M. H.

1982-01-01

The major objective is to explore any visible differences of the flow field with wall curvature of the test body, including possible interaction between Taylor-Gortler instabilities present along concave walls and the inflexional instabilities investigated here. An experimental study was conducted with emphasis placed on making visual observations and recording photographically the flow instabilities present under three different rotating bodies: a flat disk, a concave paraboloid, and a convex paraboloid. The data collected for the three test bodies lead to the conclusion that the wall curvature of the concave and convex paraboloids did not alter the observed flow field significantly from that observed on the flat disk.

OVERALL OPTICAL VIEWER

DOEpatents

Monk, G.S.

1959-02-24

An apparatus is described for viewing through a tube any desired internal portion of a reactor. A convex head mounted with a plurality or negative lenses with their axes substantially intersecting is fixed in the tube nearest the portion to be viewed. The interior of the tube is filled with a liquid transparent to light and opaque to neutrons and gamma rays. The lense may be made from polymerized methyl methacrylate and aqueous zinc chloride is a suitable transparent liquid.

Asteroid shape and spin statistics from convex models

NASA Astrophysics Data System (ADS)

Torppa, J.; Hentunen, V.-P.; Pääkkönen, P.; Kehusmaa, P.; Muinonen, K.

2008-11-01

We introduce techniques for characterizing convex shape models of asteroids with a small number of parameters, and apply these techniques to a set of 87 models from convex inversion. We present three different approaches for determining the overall dimensions of an asteroid. With the first technique, we measured the dimensions of the shapes in the direction of the rotation axis and in the equatorial plane and with the two other techniques, we derived the best-fit ellipsoid. We also computed the inertia matrix of the model shape to test how well it represents the target asteroid, i.e., to find indications of possible non-convex features or albedo variegation, which the convex shape model cannot reproduce. We used shape models for 87 asteroids to perform statistical analyses and to study dependencies between shape and rotation period, size, and taxonomic type. We detected correlations, but more data are required, especially on small and large objects, as well as slow and fast rotators, to reach a more thorough understanding about the dependencies. Results show, e.g., that convex models of asteroids are not that far from ellipsoids in root-mean-square sense, even though clearly irregular features are present. We also present new spin and shape solutions for Asteroids (31) Euphrosyne, (54) Alexandra, (79) Eurynome, (93) Minerva, (130) Elektra, (376) Geometria, (471) Papagena, and (776) Berbericia. We used a so-called semi-statistical approach to obtain a set of possible spin state solutions. The number of solutions depends on the abundancy of the data, which for Eurynome, Elektra, and Geometria was extensive enough for determining an unambiguous spin and shape solution. Data of Euphrosyne, on the other hand, provided a wide distribution of possible spin solutions, whereas the rest of the targets have two or three possible solutions.

Convex Lattice Polygons

ERIC Educational Resources Information Center

Scott, Paul

2006-01-01

A "convex" polygon is one with no re-entrant angles. Alternatively one can use the standard convexity definition, asserting that for any two points of the convex polygon, the line segment joining them is contained completely within the polygon. In this article, the author provides a solution to a problem involving convex lattice polygons.

[The eye, the optic system and its anomalies].

PubMed

Cohen, S Y

1993-09-15

The eye is a perceptive system with extremely complex physiology, although its optical properties can be assimilated to those of spherical diopters. Various approximations make it possible to reduce the eyeball to a single convex diopter. With a normal eye the image of an object situated ad infinitum focuses on the retina. The normal eye is called emmetropic. Otherwise, the eye is called ametropic. Several types of ametropy exist. When the image focuses in front of the retina the eye is said to be myopic. When the image focuses behind the retina the eye is called hypermetropic (or hyperopic). When the image of an object differs according to various focusing axes, the eye is said to be astigmatic.

Vertical viewing angle enhancement for the 360  degree integral-floating display using an anamorphic optic system.

PubMed

Erdenebat, Munkh-Uchral; Kwon, Ki-Chul; Yoo, Kwan-Hee; Baasantseren, Ganbat; Park, Jae-Hyeung; Kim, Eun-Soo; Kim, Nam

2014-04-15

We propose a 360 degree integral-floating display with an enhanced vertical viewing angle. The system projects two-dimensional elemental image arrays via a high-speed digital micromirror device projector and reconstructs them into 3D perspectives with a lens array. Double floating lenses relate initial 3D perspectives to the center of a vertically curved convex mirror. The anamorphic optic system tailors the initial 3D perspectives horizontally and vertically disperse light rays more widely. By the proposed method, the entire 3D image provides both monocular and binocular depth cues, a full-parallax demonstration with high-angular ray density and an enhanced vertical viewing angle.

Variation of telencephalon morphology of the threespine stickleback (Gasterosteus aculeatus) in relation to inferred ecology.

PubMed

Park, Peter J; Bell, M A

2010-06-01

We tested the hypothesis that increased telencephalon size has evolved in threespine stickleback fish (Gasterosteus aculeatus) from structurally complex habitats using field-caught samples from one sea-run (ancestral) and 18 ecologically diverse freshwater (descendant) populations. Freshwater habitats ranged from shallow, structurally complex lakes with benthic-foraging stickleback (benthics), to deeper, structurally simple lakes in which stickleback depend more heavily on plankton for prey (generalists). Contrary to our expectations, benthics had smaller telencephala than generalists, but the shape of the telencephalon of the sea-run and benthic populations were more convex laterally. Convex telencephalon shape may indicate enlargement of the dorsolateral region, which is homologous with the tetrapod hippocampus. Telencephalon morphology is also sexually dimorphic, with larger, less convex telencephala in males. Freshwater stickleback from structurally complex habitats have retained the ancestral telencephalon morphology, but populations that feed more in open habitats on plankton have evolved larger, laterally concave telencephala.

Turbulent boundary layer on a convex, curved surface

NASA Technical Reports Server (NTRS)

Gillis, J. C.; Johnston, J. P.; Kays, W. M.; Moffat, R. J.

1980-01-01

The effects of strong convex curvature on boundary layer turbulence were investigated. The data gathered on the behavior of Reynolds stress suggested the formulation of a simple turbulence model. Three sets of data were taken on two separate facilities. Both rigs had flow from a flat surface, over a convex surface with 90 deg of turning, and then onto a flat recovery surface. The geometry was adjusted so that, for both rigs, the pressure gradient along the test surface was zero - thus avoiding any effects of streamwise acceleration on the wall layers. Results show that after a sudden introduction of curvature, the shear stress in the outer part of the boundary layer is sharply diminished and is even slightly negative near the edge. The wall shear also drops off quickly downstream. In contrast, when the surface suddenly becomes flat again, the wall shear and shear stress profiles recover very slowly towards flat wall conditions.

Convex Clustering: An Attractive Alternative to Hierarchical Clustering

PubMed Central

Chen, Gary K.; Chi, Eric C.; Ranola, John Michael O.; Lange, Kenneth

2015-01-01

The primary goal in cluster analysis is to discover natural groupings of objects. The field of cluster analysis is crowded with diverse methods that make special assumptions about data and address different scientific aims. Despite its shortcomings in accuracy, hierarchical clustering is the dominant clustering method in bioinformatics. Biologists find the trees constructed by hierarchical clustering visually appealing and in tune with their evolutionary perspective. Hierarchical clustering operates on multiple scales simultaneously. This is essential, for instance, in transcriptome data, where one may be interested in making qualitative inferences about how lower-order relationships like gene modules lead to higher-order relationships like pathways or biological processes. The recently developed method of convex clustering preserves the visual appeal of hierarchical clustering while ameliorating its propensity to make false inferences in the presence of outliers and noise. The solution paths generated by convex clustering reveal relationships between clusters that are hidden by static methods such as k-means clustering. The current paper derives and tests a novel proximal distance algorithm for minimizing the objective function of convex clustering. The algorithm separates parameters, accommodates missing data, and supports prior information on relationships. Our program CONVEXCLUSTER incorporating the algorithm is implemented on ATI and nVidia graphics processing units (GPUs) for maximal speed. Several biological examples illustrate the strengths of convex clustering and the ability of the proximal distance algorithm to handle high-dimensional problems. CONVEXCLUSTER can be freely downloaded from the UCLA Human Genetics web site at http://www.genetics.ucla.edu/software/ PMID:25965340

Convex clustering: an attractive alternative to hierarchical clustering.

PubMed

Chen, Gary K; Chi, Eric C; Ranola, John Michael O; Lange, Kenneth

2015-05-01

The primary goal in cluster analysis is to discover natural groupings of objects. The field of cluster analysis is crowded with diverse methods that make special assumptions about data and address different scientific aims. Despite its shortcomings in accuracy, hierarchical clustering is the dominant clustering method in bioinformatics. Biologists find the trees constructed by hierarchical clustering visually appealing and in tune with their evolutionary perspective. Hierarchical clustering operates on multiple scales simultaneously. This is essential, for instance, in transcriptome data, where one may be interested in making qualitative inferences about how lower-order relationships like gene modules lead to higher-order relationships like pathways or biological processes. The recently developed method of convex clustering preserves the visual appeal of hierarchical clustering while ameliorating its propensity to make false inferences in the presence of outliers and noise. The solution paths generated by convex clustering reveal relationships between clusters that are hidden by static methods such as k-means clustering. The current paper derives and tests a novel proximal distance algorithm for minimizing the objective function of convex clustering. The algorithm separates parameters, accommodates missing data, and supports prior information on relationships. Our program CONVEXCLUSTER incorporating the algorithm is implemented on ATI and nVidia graphics processing units (GPUs) for maximal speed. Several biological examples illustrate the strengths of convex clustering and the ability of the proximal distance algorithm to handle high-dimensional problems. CONVEXCLUSTER can be freely downloaded from the UCLA Human Genetics web site at http://www.genetics.ucla.edu/software/.

Failure analysis of an aluminum alloy material framework component induced by casting defects

NASA Astrophysics Data System (ADS)

Li, Bo; Hu, Weiye

2017-09-01

Failure analysis on a fractured radome framework component was carried out through visual observations, metallographic examination using optical microscope, fractog-raphy inspections using scanning electron microscope and chemical composition analysis. The failed frame was made of casting Al-Si7-Mg0.4 aluminum alloy. It had suffered a former vi-bration performance tests. It was indicated that the fractures were attributed to fatigue cracks which were induced by casting porosities at the outer surfaces of frame. Failure analysis was carefully conducted for the semi-penetrating crack appearing on the framework. According to the fractography inspected by scanning electron microscope, it was indicated that numerous casting porosities at the outer surface of the framework played the role of multiple fracture sources due to some applied stresses. Optical microstructure observations suggested that the dendrite-shaped casting porosities largely contributed to the crack-initiation. The groove-shaped structure at roots of spatial convex-bodies on the edge of casting porosities supplied the preferred paths of the crack-propagation. Besides, the brittle silicon eutectic particles distrib-uting along grain boundaries induced the intergranular fracture mode in the region of the over-load final fracture surface.

Direct single-shot phase retrieval from the diffraction pattern of separated objects

DOE Office of Scientific and Technical Information (OSTI.GOV)

Leshem, Ben; Xu, Rui; Dallal, Yehonatan

The non-crystallographic phase problem arises in numerous scientific and technological fields. An important application is coherent diffractive imaging. Recent advances in X-ray free-electron lasers allow capturing of the diffraction pattern from a single nanoparticle before it disintegrates, in so-called ‘diffraction before destruction’ experiments. Presently, the phase is reconstructed by iterative algorithms, imposing a non-convex computational challenge, or by Fourier holography, requiring a well-characterized reference field. Here we present a convex scheme for single-shot phase retrieval for two (or more) sufficiently separated objects, demonstrated in two dimensions. In our approach, the objects serve as unknown references to one another, reducing themore » phase problem to a solvable set of linear equations. We establish our method numerically and experimentally in the optical domain and demonstrate a proof-of-principle single-shot coherent diffractive imaging using X-ray free-electron lasers pulses. Lastly, our scheme alleviates several limitations of current methods, offering a new pathway towards direct reconstruction of complex objects.« less

Direct single-shot phase retrieval from the diffraction pattern of separated objects

DOE PAGES

Leshem, Ben; Xu, Rui; Dallal, Yehonatan; ...

2016-02-22

The non-crystallographic phase problem arises in numerous scientific and technological fields. An important application is coherent diffractive imaging. Recent advances in X-ray free-electron lasers allow capturing of the diffraction pattern from a single nanoparticle before it disintegrates, in so-called ‘diffraction before destruction’ experiments. Presently, the phase is reconstructed by iterative algorithms, imposing a non-convex computational challenge, or by Fourier holography, requiring a well-characterized reference field. Here we present a convex scheme for single-shot phase retrieval for two (or more) sufficiently separated objects, demonstrated in two dimensions. In our approach, the objects serve as unknown references to one another, reducing themore » phase problem to a solvable set of linear equations. We establish our method numerically and experimentally in the optical domain and demonstrate a proof-of-principle single-shot coherent diffractive imaging using X-ray free-electron lasers pulses. Lastly, our scheme alleviates several limitations of current methods, offering a new pathway towards direct reconstruction of complex objects.« less

Uniform refraction in negative refractive index materials.

PubMed

Gutiérrez, Cristian E; Stachura, Eric

2015-11-01

We study the problem of constructing an optical surface separating two homogeneous, isotropic media, one of which has a negative refractive index. In doing so, we develop a vector form of Snell's law, which is used to study surfaces possessing a certain uniform refraction property, in both the near- and far-field cases. In the near-field problem, unlike the case when both materials have positive refractive indices, we show that the resulting surfaces can be neither convex nor concave.

A Novel Method of Aircraft Detection Based on High-Resolution Panchromatic Optical Remote Sensing Images.

PubMed

Wang, Wensheng; Nie, Ting; Fu, Tianjiao; Ren, Jianyue; Jin, Longxu

2017-05-06

In target detection of optical remote sensing images, two main obstacles for aircraft target detection are how to extract the candidates in complex gray-scale-multi background and how to confirm the targets in case the target shapes are deformed, irregular or asymmetric, such as that caused by natural conditions (low signal-to-noise ratio, illumination condition or swaying photographing) and occlusion by surrounding objects (boarding bridge, equipment). To solve these issues, an improved active contours algorithm, namely region-scalable fitting energy based threshold (TRSF), and a corner-convex hull based segmentation algorithm (CCHS) are proposed in this paper. Firstly, the maximal variance between-cluster algorithm (Otsu's algorithm) and region-scalable fitting energy (RSF) algorithm are combined to solve the difficulty of targets extraction in complex and gray-scale-multi backgrounds. Secondly, based on inherent shapes and prominent corners, aircrafts are divided into five fragments by utilizing convex hulls and Harris corner points. Furthermore, a series of new structure features, which describe the proportion of targets part in the fragment to the whole fragment and the proportion of fragment to the whole hull, are identified to judge whether the targets are true or not. Experimental results show that TRSF algorithm could improve extraction accuracy in complex background, and that it is faster than some traditional active contours algorithms. The CCHS is effective to suppress the detection difficulties caused by the irregular shape.

Ultrasonic transmission at solid-liquid interfaces

NASA Astrophysics Data System (ADS)

Wadley, Haydn N. G.; Queheillalt, Douglas T.; Lu, Yichi

1996-11-01

New non-invasive solid-liquid interface sensing technologies are a key element in the development of improved Bridman growth techniques for synthesizing single crystal semiconductor materials. Laser generated and optically detect ultrasonic techniques have the potential to satisfy this need. Using an anisotropic 3D ray tracing methodology combined with elastic constant data measured near the melting point, ultrasonic propagation in cylindrical single crystal bodies containing either a convex, flat, or concave solid-liquid interface has been simulated. Ray paths, wavefronts and the time-of-flight (TOF) of rays that travel from a source to an arbitrarily positioned receiver have all been calculated. Experimentally measured TOF data have been collected using laser generated, optically detected ultrasound on model systems with independently known interface shapes. Both numerically simulated and experimental data have shown that the solidification region can be easily identified from transmission TOF measurements because the velocity of the liquid is much smaller than that of the solid. Since convex and concave solid-liquid interfaces result in distinctively different TOF data profiles, the interface shape can also be readily determined from the TOF data. When TOF data collected in the diametral plane is used in conjunction with a nonlinear least squares algorithm, the interface geometry has been successfully reconstructed and ultrasonic velocities of both the solid and liquid obtained with reconstruction errors less than 5 percent.

Rainbow peacock spiders inspire miniature super-iridescent optics.

PubMed

Hsiung, Bor-Kai; Siddique, Radwanul Hasan; Stavenga, Doekele G; Otto, Jürgen C; Allen, Michael C; Liu, Ying; Lu, Yong-Feng; Deheyn, Dimitri D; Shawkey, Matthew D; Blackledge, Todd A

2017-12-22

Colour produced by wavelength-dependent light scattering is a key component of visual communication in nature and acts particularly strongly in visual signalling by structurally-coloured animals during courtship. Two miniature peacock spiders (Maratus robinsoni and M. chrysomelas) court females using tiny structured scales (~ 40 × 10 μm 2 ) that reflect the full visual spectrum. Using TEM and optical modelling, we show that the spiders' scales have 2D nanogratings on microscale 3D convex surfaces with at least twice the resolving power of a conventional 2D diffraction grating of the same period. Whereas the long optical path lengths required for light-dispersive components to resolve individual wavelengths constrain current spectrometers to bulky sizes, our nano-3D printed prototypes demonstrate that the design principle of the peacock spiders' scales could inspire novel, miniature light-dispersive components.

CONVEX mini manual

NASA Technical Reports Server (NTRS)

Tennille, Geoffrey M.; Howser, Lona M.

1993-01-01

The use of the CONVEX computers that are an integral part of the Supercomputing Network Subsystems (SNS) of the Central Scientific Computing Complex of LaRC is briefly described. Features of the CONVEX computers that are significantly different than the CRAY supercomputers are covered, including: FORTRAN, C, architecture of the CONVEX computers, the CONVEX environment, batch job submittal, debugging, performance analysis, utilities unique to CONVEX, and documentation. This revision reflects the addition of the Applications Compiler and X-based debugger, CXdb. The document id intended for all CONVEX users as a ready reference to frequently asked questions and to more detailed information contained with the vendor manuals. It is appropriate for both the novice and the experienced user.

Processing convexity and concavity along a 2-D contour: figure-ground, structural shape, and attention.

PubMed

Bertamini, Marco; Wagemans, Johan

2013-04-01

Interest in convexity has a long history in vision science. For smooth contours in an image, it is possible to code regions of positive (convex) and negative (concave) curvature, and this provides useful information about solid shape. We review a large body of evidence on the role of this information in perception of shape and in attention. This includes evidence from behavioral, neurophysiological, imaging, and developmental studies. A review is necessary to analyze the evidence on how convexity affects (1) separation between figure and ground, (2) part structure, and (3) attention allocation. Despite some broad agreement on the importance of convexity in these areas, there is a lack of consensus on the interpretation of specific claims--for example, on the contribution of convexity to metric depth and on the automatic directing of attention to convexities or to concavities. The focus is on convexity and concavity along a 2-D contour, not convexity and concavity in 3-D, but the important link between the two is discussed. We conclude that there is good evidence for the role of convexity information in figure-ground organization and in parsing, but other, more specific claims are not (yet) well supported.

A General Iterative Shrinkage and Thresholding Algorithm for Non-convex Regularized Optimization Problems.

PubMed

Gong, Pinghua; Zhang, Changshui; Lu, Zhaosong; Huang, Jianhua Z; Ye, Jieping

2013-01-01

Non-convex sparsity-inducing penalties have recently received considerable attentions in sparse learning. Recent theoretical investigations have demonstrated their superiority over the convex counterparts in several sparse learning settings. However, solving the non-convex optimization problems associated with non-convex penalties remains a big challenge. A commonly used approach is the Multi-Stage (MS) convex relaxation (or DC programming), which relaxes the original non-convex problem to a sequence of convex problems. This approach is usually not very practical for large-scale problems because its computational cost is a multiple of solving a single convex problem. In this paper, we propose a General Iterative Shrinkage and Thresholding (GIST) algorithm to solve the nonconvex optimization problem for a large class of non-convex penalties. The GIST algorithm iteratively solves a proximal operator problem, which in turn has a closed-form solution for many commonly used penalties. At each outer iteration of the algorithm, we use a line search initialized by the Barzilai-Borwein (BB) rule that allows finding an appropriate step size quickly. The paper also presents a detailed convergence analysis of the GIST algorithm. The efficiency of the proposed algorithm is demonstrated by extensive experiments on large-scale data sets.

Predictor-corrector framework for the sequential assembly of optical systems based on wavefront sensing.

PubMed

Schindlbeck, Christopher; Pape, Christian; Reithmeier, Eduard

2018-04-16

Alignment of optical components is crucial for the assembly of optical systems to ensure their full functionality. In this paper we present a novel predictor-corrector framework for the sequential assembly of serial optical systems. Therein, we use a hybrid optical simulation model that comprises virtual and identified component positions. The hybrid model is constantly adapted throughout the assembly process with the help of nonlinear identification techniques and wavefront measurements. This enables prediction of the future wavefront at the detector plane and therefore allows for taking corrective measures accordingly during the assembly process if a user-defined tolerance on the wavefront error is violated. We present a novel notation for the so-called hybrid model and outline the work flow of the presented predictor-corrector framework. A beam expander is assembled as demonstrator for experimental verification of the framework. The optical setup consists of a laser, two bi-convex spherical lenses each mounted to a five degree-of-freedom stage to misalign and correct components, and a Shack-Hartmann sensor for wavefront measurements.

Mathematical analysis on the cosets of subgroup in the group of E-convex sets

NASA Astrophysics Data System (ADS)

Abbas, Nada Mohammed; Ajeena, Ruma Kareem K.

2018-05-01

In this work, analyzing the cosets of the subgroup in the group of L – convex sets is presented as a new and powerful tool in the topics of the convex analysis and abstract algebra. On L – convex sets, the properties of these cosets are proved mathematically. Most important theorem on a finite group of L – convex sets theory which is the Lagrange’s Theorem has been proved. As well as, the mathematical proof of the quotient group of L – convex sets is presented.

Flexible top-emitting OLEDs for lighting: bending limits

NASA Astrophysics Data System (ADS)

Schwamb, Philipp; Reusch, Thilo C.; Brabec, Christoph J.

2013-09-01

Flexible OLED light sources have great appeal due to new design options, being unbreakable and their low weight. Top-emitting OLED device architectures offer the broadest choice of substrate materials including metals which are robust, impermeable to humidity, and good thermal conductors making them promising candidates for flexible OLED device substrates. In this study, we investigate the bending limits of flexible top-emitting OLED lighting devices with transparent metal electrode and thin film encapsulation on a variety of both metal and plastic foils. The samples were subjected to concave and convex bending and inspected by different testing methods for the onset of breakdown for example visible defects and encapsulation failures. The critical failure modes were identified as rupture of the transparent thin metal top electrode and encapsulation for convex bending and buckling of the transparent metal top electrode for concave bending. We investigated influences from substrate material and thickness and top coating thickness. The substrate thickness is found to dominate bending limits as expected by neutral layer modeling. Coating shows strong improvements for all substrates. Bending radii <15mm are achieved for both convex and concave testing without damage to devices including their encapsulation.

Design, Fabrication, Optical Testing, and Performance of Diamond Machined Aspheric Mirrors for Ground-Based Near-IR Astronomy

NASA Technical Reports Server (NTRS)

Ohl, Raymond G.; Mink, Ronald; Chambers, V. John; Connelly, Joseph A.; Mentzell, J. Eric; Tveekrem, June L.; Howard, Joseph M.; Preuss, Werner; Schroeder, Mechthild; Sohn, Alex;

Nash points, Ky Fan inequality and equilibria of abstract economies in Max-Plus and -convexity

NASA Astrophysics Data System (ADS)

Briec, Walter; Horvath, Charles

2008-05-01

-convexity was introduced in [W. Briec, C. Horvath, -convexity, Optimization 53 (2004) 103-127]. Separation and Hahn-Banach like theorems can be found in [G. Adilov, A.M. Rubinov, -convex sets and functions, Numer. Funct. Anal. Optim. 27 (2006) 237-257] and [W. Briec, C.D. Horvath, A. Rubinov, Separation in -convexity, Pacific J. Optim. 1 (2005) 13-30]. We show here that all the basic results related to fixed point theorems are available in -convexity. Ky Fan inequality, existence of Nash equilibria and existence of equilibria for abstract economies are established in the framework of -convexity. Monotone analysis, or analysis on Maslov semimodules [V.N. Kolokoltsov, V.P. Maslov, Idempotent Analysis and Its Applications, Math. Appl., volE 401, Kluwer Academic, 1997; V.P. Litvinov, V.P. Maslov, G.B. Shpitz, Idempotent functional analysis: An algebraic approach, Math. Notes 69 (2001) 696-729; V.P. Maslov, S.N. Samborski (Eds.), Idempotent Analysis, Advances in Soviet Mathematics, Amer. Math. Soc., Providence, RI, 1992], is the natural framework for these results. From this point of view Max-Plus convexity and -convexity are isomorphic Maslov semimodules structures over isomorphic semirings. Therefore all the results of this paper hold in the context of Max-Plus convexity.

Bypassing the Limits of Ll Regularization: Convex Sparse Signal Processing Using Non-Convex Regularization

NASA Astrophysics Data System (ADS)

Parekh, Ankit

Sparsity has become the basis of some important signal processing methods over the last ten years. Many signal processing problems (e.g., denoising, deconvolution, non-linear component analysis) can be expressed as inverse problems. Sparsity is invoked through the formulation of an inverse problem with suitably designed regularization terms. The regularization terms alone encode sparsity into the problem formulation. Often, the ℓ1 norm is used to induce sparsity, so much so that ℓ1 regularization is considered to be `modern least-squares'. The use of ℓ1 norm, as a sparsity-inducing regularizer, leads to a convex optimization problem, which has several benefits: the absence of extraneous local minima, well developed theory of globally convergent algorithms, even for large-scale problems. Convex regularization via the ℓ1 norm, however, tends to under-estimate the non-zero values of sparse signals. In order to estimate the non-zero values more accurately, non-convex regularization is often favored over convex regularization. However, non-convex regularization generally leads to non-convex optimization, which suffers from numerous issues: convergence may be guaranteed to only a stationary point, problem specific parameters may be difficult to set, and the solution is sensitive to the initialization of the algorithm. The first part of this thesis is aimed toward combining the benefits of non-convex regularization and convex optimization to estimate sparse signals more effectively. To this end, we propose to use parameterized non-convex regularizers with designated non-convexity and provide a range for the non-convex parameter so as to ensure that the objective function is strictly convex. By ensuring convexity of the objective function (sum of data-fidelity and non-convex regularizer), we can make use of a wide variety of convex optimization algorithms to obtain the unique global minimum reliably. The second part of this thesis proposes a non-linear signal decomposition technique for an important biomedical signal processing problem: the detection of sleep spindles and K-complexes in human sleep electroencephalography (EEG). We propose a non-linear model for the EEG consisting of three components: (1) a transient (sparse piecewise constant) component, (2) a low-frequency component, and (3) an oscillatory component. The oscillatory component admits a sparse time-frequency representation. Using a convex objective function, we propose a fast non-linear optimization algorithm to estimate the three components in the proposed signal model. The low-frequency and oscillatory components are then used to estimate the K-complexes and sleep spindles respectively. The proposed detection method is shown to outperform several state-of-the-art automated sleep spindles detection methods.

Scoliosis convexity and organ anatomy are related.

PubMed

Schlösser, Tom P C; Semple, Tom; Carr, Siobhán B; Padley, Simon; Loebinger, Michael R; Hogg, Claire; Castelein, René M

2017-06-01

Primary ciliary dyskinesia (PCD) is a respiratory syndrome in which 'random' organ orientation can occur; with approximately 46% of patients developing situs inversus totalis at organogenesis. The aim of this study was to explore the relationship between organ anatomy and curve convexity by studying the prevalence and convexity of idiopathic scoliosis in PCD patients with and without situs inversus. Chest radiographs of PCD patients were systematically screened for existence of significant lateral spinal deviation using the Cobb angle. Positive values represented right-sided convexity. Curve convexity and Cobb angles were compared between PCD patients with situs inversus and normal anatomy. A total of 198 PCD patients were screened. The prevalence of scoliosis (Cobb >10°) and significant spinal asymmetry (Cobb 5-10°) was 8 and 23%, respectively. Curve convexity and Cobb angle were significantly different within both groups between situs inversus patients and patients with normal anatomy (P ≤ 0.009). Moreover, curve convexity correlated significantly with organ orientation (P < 0.001; ϕ = 0.882): In 16 PCD patients with scoliosis (8 situs inversus and 8 normal anatomy), except for one case, matching of curve convexity and orientation of organ anatomy was observed: convexity of the curve was opposite to organ orientation. This study supports our hypothesis on the correlation between organ anatomy and curve convexity in scoliosis: the convexity of the thoracic curve is predominantly to the right in PCD patients that were 'randomized' to normal organ anatomy and to the left in patients with situs inversus totalis.

Use of Convexity in Ostomy Care

PubMed Central

Salvadalena, Ginger; Pridham, Sue; Droste, Werner; McNichol, Laurie; Gray, Mikel

2017-01-01

Ostomy skin barriers that incorporate a convexity feature have been available in the marketplace for decades, but limited resources are available to guide clinicians in selection and use of convex products. Given the widespread use of convexity, and the need to provide practical guidelines for appropriate use of pouching systems with convex features, an international consensus panel was convened to provide consensus-based guidance for this aspect of ostomy practice. Panelists were provided with a summary of relevant literature in advance of the meeting; these articles were used to generate and reach consensus on 26 statements during a 1-day meeting. Consensus was achieved when 80% of panelists agreed on a statement using an anonymous electronic response system. The 26 statements provide guidance for convex product characteristics, patient assessment, convexity use, and outcomes. PMID:28002174

Paraboloid-aspheric lenses free of spherical aberration

NASA Astrophysics Data System (ADS)

Lozano-Rincón, Ninfa del C.; Valencia-Estrada, Juan Camilo

2017-07-01

A method to design singlet paraboloid-aspheric lenses free of all orders of spherical aberration with maximum aperture is described. This work includes all parametric formulas to describe paraboloid-aspheric or aspheric-paraboloid lenses for any finite conjugated planes. It also includes the Schwarzchilds approximations (which can be used to calculate one rigorous propagation of light waves in physic optics) to design convex paraboloid-aspheric lenses for imaging an object at infinity, with explicit formulas to calculate thicknesses easily. The results were verified with software through ray tracing.

Generalised monogamy relation of convex-roof extended negativity in multi-level systems

NASA Astrophysics Data System (ADS)

Tian, Tian; Luo, Yu; Li, Yongming

2016-11-01

In this paper, we investigate the generalised monogamy inequalities of convex-roof extended negativity (CREN) in multi-level systems. The generalised monogamy inequalities provide the upper and lower bounds of bipartite entanglement, which are obtained by using CREN and the CREN of assistance (CRENOA). Furthermore, we show that the CREN of multi-qubit pure states satisfies some monogamy relations. Additionally, we test the generalised monogamy inequalities for qudits by considering the partially coherent superposition of a generalised W-class state in a vacuum and show that the generalised monogamy inequalities are satisfied in this case as well.

Generalised monogamy relation of convex-roof extended negativity in multi-level systems

PubMed Central

Tian, Tian; Luo, Yu; Li, Yongming

2016-01-01

In this paper, we investigate the generalised monogamy inequalities of convex-roof extended negativity (CREN) in multi-level systems. The generalised monogamy inequalities provide the upper and lower bounds of bipartite entanglement, which are obtained by using CREN and the CREN of assistance (CRENOA). Furthermore, we show that the CREN of multi-qubit pure states satisfies some monogamy relations. Additionally, we test the generalised monogamy inequalities for qudits by considering the partially coherent superposition of a generalised W-class state in a vacuum and show that the generalised monogamy inequalities are satisfied in this case as well. PMID:27857163

Generalised monogamy relation of convex-roof extended negativity in multi-level systems.

PubMed

Tian, Tian; Luo, Yu; Li, Yongming

2016-11-18

In this paper, we investigate the generalised monogamy inequalities of convex-roof extended negativity (CREN) in multi-level systems. The generalised monogamy inequalities provide the upper and lower bounds of bipartite entanglement, which are obtained by using CREN and the CREN of assistance (CRENOA). Furthermore, we show that the CREN of multi-qubit pure states satisfies some monogamy relations. Additionally, we test the generalised monogamy inequalities for qudits by considering the partially coherent superposition of a generalised W-class state in a vacuum and show that the generalised monogamy inequalities are satisfied in this case as well.

Geometric convex cone volume analysis

NASA Astrophysics Data System (ADS)

Li, Hsiao-Chi; Chang, Chein-I.

2016-05-01

Convexity is a major concept used to design and develop endmember finding algorithms (EFAs). For abundance unconstrained techniques, Pixel Purity Index (PPI) and Automatic Target Generation Process (ATGP) which use Orthogonal Projection (OP) as a criterion, are commonly used method. For abundance partially constrained techniques, Convex Cone Analysis is generally preferred which makes use of convex cones to impose Abundance Non-negativity Constraint (ANC). For abundance fully constrained N-FINDR and Simplex Growing Algorithm (SGA) are most popular methods which use simplex volume as a criterion to impose ANC and Abundance Sum-to-one Constraint (ASC). This paper analyze an issue encountered in volume calculation with a hyperplane introduced to illustrate an idea of bounded convex cone. Geometric Convex Cone Volume Analysis (GCCVA) projects the boundary vectors of a convex cone orthogonally on a hyperplane to reduce the effect of background signatures and a geometric volume approach is applied to address the issue arose from calculating volume and further improve the performance of convex cone-based EFAs.

The effects of a convex rear-view mirror on ocular accommodative responses.

PubMed

Nagata, Tatsuo; Iwasaki, Tsuneto; Kondo, Hiroyuki; Tawara, Akihiko

2013-11-01

Convex mirrors are universally used as rear-view mirrors in automobiles. However, the ocular accommodative responses during the use of these mirrors have not yet been examined. This study investigated the effects of a convex mirror on the ocular accommodative systems. Seven young adults with normal visual functions were ordered to binocularly watch an object in a convex or plane mirror. The accommodative responses were measured with an infrared optometer. The average of the accommodation of all subjects while viewing the object in the convex mirror were significantly nearer than in the plane mirror, although all subjects perceived the position of the object in the convex mirror as being farther away. Moreover, the fluctuations of accommodation were significantly larger for the convex mirror. The convex mirror caused the 'false recognition of distance', which induced the large accommodative fluctuations and blurred vision. Manufactures should consider the ocular accommodative responses as a new indicator for increasing automotive safety. Copyright © 2013 Elsevier Ltd and The Ergonomics Society. All rights reserved.

Smart optical writing head design for laser-based manufacturing

NASA Astrophysics Data System (ADS)

Amin, M. Junaid; Riza, Nabeel A.

2014-03-01

Proposed is a smart optical writing head design suitable for high precision industrial laser based machining and manufacturing applications. The design uses an Electronically Controlled Variable Focus Lens (ECVFL) which enables the highest achievable spatial resolution of writing head spot sizes for axial target distances reaching 8 meters. A proof-of-concept experiment is conducted using a visible wavelength laser with a collimated beam that is coupled to beam conditioning optics which includes an electromagnetically actuated deformable membrane liquid ECVFL cascaded with a bias convex lens of fixed focal length. Electronic tuning and control of the ECVFL keeps the laser writing head far-field spot beam radii under 1 mm that is demonstrated over a target range of 20 cm to 800 cm. Applications for the proposed writing head design, which can accommodate both continuous wave and pulsed wave sources, include laser machining, high precision industrial molding of components, as well as materials processing requiring material sensitive optical power density control.

Fiber-optic projected-fringe digital interferometry

NASA Technical Reports Server (NTRS)

Mercer, Carolyn R.; Beheim, Glenn

1990-01-01

A phase-stepped projected-fringe interferometer was developed which uses a closed-loop fiber-optic phase-control system to make very accurate surface profile measurements. The closed-loop phase-control system greatly reduces phase-stepping error, which is frequently the dominant source of error in digital interferometers. Two beams emitted from a fiber-optic coupler are combined to form an interference fringe pattern on a diffusely reflecting object. Reflections off of the fibers' output faces are used to create a phase-indicating signal for the closed-loop optical phase controller. The controller steps the phase difference between the two beams by pi/2 radians in order to determine the object's surface profile using a solid-state camera and a computer. The system combines the ease of alignment and automated data reduction of phase-stepping projected-fringe interferometry with the greatly improved phase-stepping accuracy of our closed-loop phase-controller. The system is demonstrated by measuring the profile of a plate containing several convex surfaces whose heights range from 15 to 25 micron high.

Optical clearing of the dura mater using glycerol: a reversible process to aid the post-mortem investigation of infant head injury.

PubMed

Cheshire, Emma C; Malcomson, Roger D G; Joseph, Shiju; Biggs, Mike J B; Adlam, David; Rutty, Guy N

2015-09-01

In cases of suspected abusive head trauma, a thorough and systematic study of the cranium and its contents is essential, preferably using the best available methods for observing the brain and its coverings. Building upon recent developments in skull bone removal techniques in infant autopsies, we have assessed the use of two optical clearing agents (OCAs), glycerol and mannitol, on pediatric dura mater in an attempt to increase the transparency of this tissue and thereby enhance the post-mortem assessment of infant head injuries, particularly subdural hematomas. Extracorporeal testing revealed glycerol to be the more effective OCA. Therefore, in situ investigations were commenced using glycerol during 33 pediatric post-mortem examinations. An increase in the transparency of the dura was observed in 32 of the 33 cases, within 1 min of application of the OCA. In a 2 year old with cerebral palsy, only partial optical clearance of the dura was seen, most likely due to a significantly atrophic brain, prominent gelatinous leptomeninges, and abnormally thickened dura. This technique allowed for detection of minimal amounts of subdural bleeding over the convexities, before dissection of the dura, avoiding post-mortem blood spillage from artifactually disrupted bridging veins. Optical clearing of the dura aided in the evaluation of patterns of subdural hemorrhage in three cases of non-accidental head injury, three cases of peri-natal head injury and one case of overlaying, apparently resulting in minor crush injury to the head. We have demonstrated that glycerol is an effective and easy-to-use OCA to effect the readily reversible optical clearing of human infant calvarial dura at autopsy.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Valentino, Eleonora Di; Mersini-Houghton, Laura, E-mail: valentin@iap.fr, E-mail: mersini@physics.unc.edu

The 2015 Planck data release tightened the region of the allowed inflationary models. Inflationary models with convex potentials have now been ruled out since they produce a large tensor to scalar ratio. Meanwhile the same data offers interesting hints on possible deviations from the standard picture of CMB perturbations. Here we revisit the predictions of the theory of the origin of the universe from the landscape multiverse for the case of exponential inflation, for two reasons: firstly to check the status of the anomalies associated with this theory, in the light of the recent Planck data; secondly, to search formore » a counterexample whereby new physics modifications may bring convex inflationary potentials, thought to have been ruled out, back into the region of potentials allowed by data. Using the exponential inflation as an example of convex potentials, we find that the answer to both tests is positive: modifications to the perturbation spectrum and to the Newtonian potential of the universe originating from the quantum entanglement, bring the exponential potential, back within the allowed region of current data; and, the series of anomalies previously predicted in this theory, is still in good agreement with current data. Hence our finding for this convex potential comes at the price of allowing for additional thermal relic particles, equivalently dark radiation, in the early universe.« less

Revisiting separation properties of convex fuzzy sets

USDA-ARS?s Scientific Manuscript database

Separation of convex sets by hyperplanes has been extensively studied on crisp sets. In a seminal paper separability and convexity are investigated, however there is a flaw on the definition of degree of separation. We revisited separation on convex fuzzy sets that have level-wise (crisp) disjointne...

Rapid Process to Generate Beam Envelopes for Optical System Analysis

NASA Technical Reports Server (NTRS)

Howard, Joseph; Seals, Lenward

2012-01-01

The task of evaluating obstructions in the optical throughput of an optical system requires the use of two disciplines, and hence, two models: optical models for the details of optical propagation, and mechanical models for determining the actual structure that exists in the optical system. Previous analysis methods for creating beam envelopes (or cones of light) for use in this obstruction analysis were found to be cumbersome to calculate and take significant time and resources to complete. A new process was developed that takes less time to complete beam envelope analysis, is more accurate and less dependent upon manual node tracking to create the beam envelopes, and eases the burden on the mechanical CAD (computer-aided design) designers to form the beam solids. This algorithm allows rapid generation of beam envelopes for optical system obstruction analysis. Ray trace information is taken from optical design software and used to generate CAD objects that represent the boundary of the beam envelopes for detailed analysis in mechanical CAD software. Matlab is used to call ray trace data from the optical model for all fields and entrance pupil points of interest. These are chosen to be the edge of each space, so that these rays produce the bounding volume for the beam. The x and y global coordinate data is collected on the surface planes of interest, typically an image of the field and entrance pupil internal of the optical system. This x and y coordinate data is then evaluated using a convex hull algorithm, which removes any internal points, which are unnecessary to produce the bounding volume of interest. At this point, tolerances can be applied to expand the size of either the field or aperture, depending on the allocations. Once this minimum set of coordinates on the pupil and field is obtained, a new set of rays is generated between the field plane and aperture plane (or vice-versa). These rays are then evaluated at planes between the aperture and field, at a desired number of steps perceived necessary to build up the bounding volume or cone shape. At each plane, the ray coordinates are again evaluated using the convex hull algorithm to reduce the data to a minimal set. When all of the coordinates of interest are obtained for every plane of the propagation, the data is formatted into an xyz file suitable for FRED optical analysis software to import and create a STEP file of the data. This results in a spiral-like structure that is easily imported by mechanical CAD users who can then use an automated algorithm to wrap a skin around it and create a solid that represents the beam.

A compact spectrum splitting concentrator for high concentration photovoltaics based on the dispersion of a lens

NASA Astrophysics Data System (ADS)

He, J.; Flowers, C. A.; Yao, Y.; Atwater, H. A.; Rockett, A. A.; Nuzzo, R. G.

2018-06-01

Photovoltaic devices used in conjunction with functional optical elements for light concentration and spectrum splitting are known to be a viable approach for highly efficient photovoltaics. Conventional designs employ discrete optical elements, each with the task of either performing optical concentration or separating the solar spectrum. In the present work, we examine the performance of a compact photovoltaic architecture in which a single lens plays a dual role as both a concentrator and a spectrum splitter, the latter made possible by exploiting its intrinsic dispersion. A four-terminal two-junction InGaP/GaAs device is prepared to validate the concept and illustrates pathways for improvements. A spectral separation in the visible range is demonstrated at the focal point of a plano-convex lens with a geometric concentration ratio of 1104X with respect to the InGaP subcell.

Use of Convexity in Ostomy Care: Results of an International Consensus Meeting.

PubMed

Hoeflok, Jo; Salvadalena, Ginger; Pridham, Sue; Droste, Werner; McNichol, Laurie; Gray, Mikel

Ostomy skin barriers that incorporate a convexity feature have been available in the marketplace for decades, but limited resources are available to guide clinicians in selection and use of convex products. Given the widespread use of convexity, and the need to provide practical guidelines for appropriate use of pouching systems with convex features, an international consensus panel was convened to provide consensus-based guidance for this aspect of ostomy practice. Panelists were provided with a summary of relevant literature in advance of the meeting; these articles were used to generate and reach consensus on 26 statements during a 1-day meeting. Consensus was achieved when 80% of panelists agreed on a statement using an anonymous electronic response system. The 26 statements provide guidance for convex product characteristics, patient assessment, convexity use, and outcomes.

Design and analysis of a curved cylindrical Fresnel lens that produces high irradiance uniformity on the solar cell.

PubMed

González, Juan C

2009-04-10

A new type of convex Fresnel lens for linear photovoltaic concentration systems is presented. The lens designed with this method reaches 100% of geometrical optical efficiency, and the ratio (Aperture area)/(Receptor area) is up to 75% of the theoretical limit. The main goal of the design is high uniformity of the radiation on the cell surface for each input angle inside the acceptance. The ratio between the maximum and the minimum irradiance on points of the solar cell is less than 2. The lens has been designed with the simultaneous multiple surfaces (SMS) method of nonimaging optics, and ray tracing techniques have been used to characterize its performance for linear symmetry systems.

Application of phase-diverse phase retrieval to wavefront sensing in non-connected complicated pupil optics

NASA Astrophysics Data System (ADS)

Mao, Heng; Wang, Xiao; Zhao, Dazun

2007-07-01

Baseline algorithm, as a tool in wavefront sensing (WFS), incorporates the phase-diverse phase retrieval (PDPR) method with hybrid-unwrapping approach to ensure a unique pupil phase estimate with high WFS accuracy even in the case of high dynamic range aberration, as long as the pupil shape is of a convex set. However, for a complicated pupil, such as that in obstructed pupil optics, the said unwrapping approach would fail owing to the fake values at points located in obstructed areas of the pupil. Thus a modified unwrapping approach that can minimize the negative effects of the obstructed areas is proposed. Simulations have shown the validity of this unwrapping approach when it is embedded in Baseline algorithm.

Detection of Convexity and Concavity in Context

ERIC Educational Resources Information Center

Bertamini, Marco

2008-01-01

Sensitivity to shape changes was measured, in particular detection of convexity and concavity changes. The available data are contradictory. The author used a change detection task and simple polygons to systematically manipulate convexity/concavity. Performance was high for detecting a change of sign (a new concave vertex along a convex contour…

A continuous-wave, widely tunable, intra-cavity, singly resonant, magnesium-doped, periodically poled lithium niobate optical parametric oscillator

NASA Astrophysics Data System (ADS)

Li, Z. P.; Duan, Y. M.; Wu, K. R.; Zhang, G.; Zhu, H. Y.; Wang, X. L.; Chen, Y. H.; Xue, Z. Q.; Lin, Q.; Song, G. C.; Su, H.

2013-05-01

We report a continuous-wave (CW), intra-cavity singly resonant optical parametric oscillator (OPO), based on periodically poled MgO:LiNbO3 pumped by a diode-end-pumped CW Nd:YVO4 laser, and calculate the gain of optical parametric amplification as a function of pump beam waist (at 1064 nm) in the singly resonant OPO (SRO) cavity, to balance the mode-matching and the intensity for the higher gain of a signal wave in the operation of the SRO. In order to achieve maximum gain, we use a convex lens to limit the 1064 nm beam waist. In the experiment, a tunable signal output from 1492 to 1614 nm and an idler output from 3122 to 3709 nm are obtained. For an 808 nm pump power of 11.5 W, a maximum signal output power of up to 2.48 W at 1586 nm and an idler output power of 1.1 W at 3232 nm are achieved with a total optical-to-optical conversion efficiency of 31%.

Airfoil

DOEpatents

Ristau, Neil; Siden, Gunnar Leif

2015-07-21

An airfoil includes a leading edge, a trailing edge downstream from the leading edge, a pressure surface between the leading and trailing edges, and a suction surface between the leading and trailing edges and opposite the pressure surface. A first convex section on the suction surface decreases in curvature downstream from the leading edge, and a throat on the suction surface is downstream from the first convex section. A second convex section is on the suction surface downstream from the throat, and a first convex segment of the second convex section increases in curvature.

Superiorization with level control

NASA Astrophysics Data System (ADS)

Cegielski, Andrzej; Al-Musallam, Fadhel

2017-04-01

The convex feasibility problem is to find a common point of a finite family of closed convex subsets. In many applications one requires something more, namely finding a common point of closed convex subsets which minimizes a continuous convex function. The latter requirement leads to an application of the superiorization methodology which is actually settled between methods for convex feasibility problem and the convex constrained minimization. Inspired by the superiorization idea we introduce a method which sequentially applies a long-step algorithm for a sequence of convex feasibility problems; the method employs quasi-nonexpansive operators as well as subgradient projections with level control and does not require evaluation of the metric projection. We replace a perturbation of the iterations (applied in the superiorization methodology) by a perturbation of the current level in minimizing the objective function. We consider the method in the Euclidean space in order to guarantee the strong convergence, although the method is well defined in a Hilbert space.

An optimized algorithm for multiscale wideband deconvolution of radio astronomical images

NASA Astrophysics Data System (ADS)

Offringa, A. R.; Smirnov, O.

2017-10-01

We describe a new multiscale deconvolution algorithm that can also be used in a multifrequency mode. The algorithm only affects the minor clean loop. In single-frequency mode, the minor loop of our improved multiscale algorithm is over an order of magnitude faster than the casa multiscale algorithm, and produces results of similar quality. For multifrequency deconvolution, a technique named joined-channel cleaning is used. In this mode, the minor loop of our algorithm is two to three orders of magnitude faster than casa msmfs. We extend the multiscale mode with automated scale-dependent masking, which allows structures to be cleaned below the noise. We describe a new scale-bias function for use in multiscale cleaning. We test a second deconvolution method that is a variant of the moresane deconvolution technique, and uses a convex optimization technique with isotropic undecimated wavelets as dictionary. On simple well-calibrated data, the convex optimization algorithm produces visually more representative models. On complex or imperfect data, the convex optimization algorithm has stability issues.

Optical Testing of Diamond Machined, Aspheric Mirrors for Groundbased, Near-IR Astronomy

NASA Technical Reports Server (NTRS)

Chambers, V. John; Mink, Ronald G.; Ohl, Raymond G.; Connelly, Joseph A.; Mentzell, J. Eric; Arnold, Steven M.; Greenhouse, Matthew A.; Winsor, Robert S.; MacKenty, John W.

2002-01-01

The Infrared Multi-Object Spectrometer (IRMOS) is a facility-class instrument for the Kitt Peak National Observatory 4 and 2.1 meter telescopes. IRMOS is a near-IR (0.8-2.5 micron) spectrometer and operates at approximately 80 K. The 6061-T651 aluminum bench and mirrors constitute an athermal design. The instrument produces simultaneous spectra at low- to mid-resolving power (R=lambda/delta lambda= 300-3000) of approximately 100 objects in its 2.8 x 2.0 arcmin field. We describe ambient and cryogenic optical testing of the IRMOS mirrors across a broad range in spatial frequency (figure error, mid-frequency error, and microroughness). The mirrors include three rotationally symmetric, off-axis conic sections, one off-axis biconic, and several flat fold mirrors. The symmetric mirrors include convex and concave prolate and oblate ellipsoids. They range in aperture from 94x86 mm to 286x269 mm and in f-number from 0.9 to 2.4. The biconic mirror is concave and has a 94x76 mm aperture, R(sub x)=377 mm, k(sub x)=0.0778, R(sub y)=407 mm, and k(sub y)=0.1265 and is decentered by -2 mm in X and 227 mm in Y. All of the mirrors have an aspect ratio of approximately 6:1. The surface error fabrication tolerances are less than 10 nm RMS microroughness, 'best effort' for mid-frequency error, and less than 63.3 nm RMS figure error. Ambient temperature (approximately 293 K) testing is performed for each of the three surface error regimes, and figure testing is also performed at approximately 80 K. Operation of the ADE Phaseshift MicroXAM white light interferometer (micro-roughness) and the Bauer Model 200 profilometer (mid-frequency error) is described. Both the sag and conic values of the aspheric mirrors make these tests challenging. Figure testing is performed using a Zygo GPI interferometer, custom computer generated holograms (CGH), and optomechanical alignment fiducials. Cryogenic CGH null testing is discussed in detail. We discuss complications such as the change in prescription with temperature and thermal gradients. Correction for the effect of the dewar window is also covered. We discuss the error budget for the optical test and alignment procedure. Data reduction is accomplished using commercial optical design and data analysis software packages. Results from CGH testing at cryogenic temperatures are encouraging thus far.

Hermite-Hadamard type inequality for φ{sub h}-convex stochastic processes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sarıkaya, Mehmet Zeki, E-mail: sarikayamz@gmail.com; Kiriş, Mehmet Eyüp, E-mail: kiris@aku.edu.tr; Çelik, Nuri, E-mail: ncelik@bartin.edu.tr

2016-04-18

The main aim of the present paper is to introduce φ{sub h}-convex stochastic processes and we investigate main properties of these mappings. Moreover, we prove the Hadamard-type inequalities for φ{sub h}-convex stochastic processes. We also give some new general inequalities for φ{sub h}-convex stochastic processes.

A Novel Method of Aircraft Detection Based on High-Resolution Panchromatic Optical Remote Sensing Images

PubMed Central

Wang, Wensheng; Nie, Ting; Fu, Tianjiao; Ren, Jianyue; Jin, Longxu

2017-01-01

In target detection of optical remote sensing images, two main obstacles for aircraft target detection are how to extract the candidates in complex gray-scale-multi background and how to confirm the targets in case the target shapes are deformed, irregular or asymmetric, such as that caused by natural conditions (low signal-to-noise ratio, illumination condition or swaying photographing) and occlusion by surrounding objects (boarding bridge, equipment). To solve these issues, an improved active contours algorithm, namely region-scalable fitting energy based threshold (TRSF), and a corner-convex hull based segmentation algorithm (CCHS) are proposed in this paper. Firstly, the maximal variance between-cluster algorithm (Otsu’s algorithm) and region-scalable fitting energy (RSF) algorithm are combined to solve the difficulty of targets extraction in complex and gray-scale-multi backgrounds. Secondly, based on inherent shapes and prominent corners, aircrafts are divided into five fragments by utilizing convex hulls and Harris corner points. Furthermore, a series of new structure features, which describe the proportion of targets part in the fragment to the whole fragment and the proportion of fragment to the whole hull, are identified to judge whether the targets are true or not. Experimental results show that TRSF algorithm could improve extraction accuracy in complex background, and that it is faster than some traditional active contours algorithms. The CCHS is effective to suppress the detection difficulties caused by the irregular shape. PMID:28481260

An angular biasing method using arbitrary convex polyhedra for Monte Carlo radiation transport calculations

DOE PAGES

Kulesza, Joel A.; Solomon, Clell J.; Kiedrowski, Brian C.

2018-01-02

This paper presents a new method for performing angular biasing in Monte Carlo radiation transport codes using arbitrary convex polyhedra to define regions of interest toward which to project particles (DXTRAN regions). The method is derived and is implemented using axis-aligned right parallelepipeds (AARPPs) and arbitrary convex polyhedra. Attention is also paid to possible numerical complications and areas for future refinement. A series of test problems are executed with void, purely absorbing, purely scattering, and 50% absorbing/50% scattering materials. For all test problems tally results using AARPP and polyhedral DXTRAN regions agree with analog and/or spherical DXTRAN results within statisticalmore » uncertainties. In cases with significant scattering the figure of merit (FOM) using AARPP or polyhedral DXTRAN regions is lower than with spherical regions despite the ability to closely fit the tally region. This is because spherical DXTRAN processing is computationally less expensive than AARPP or polyhedral DXTRAN processing. Thus, it is recommended that the speed of spherical regions be considered versus the ability to closely fit the tally region with an AARPP or arbitrary polyhedral region. It is also recommended that short calculations be made prior to final calculations to compare the FOM for the various DXTRAN geometries because of the influence of the scattering behavior.« less

High-precision MoSi multilayer coatings for radial and 2D designs on curved optics

NASA Astrophysics Data System (ADS)

Kriese, Michael D.; Li, Yang; Platonov, Yuriy Y.

2017-10-01

The development of industrial infrastructure for EUV lithography requires a wide array of optics beyond the mask and the scanner optics, which include optics for critical instruments such as exposure testing and actinic inspection. This paper will detail recent results in the production of a variety of high-precision multilayer coatings achieved to support this development. It is critical that the optical designs factor in the capabilities of the achievable multilayer gradients and the associated achievable precision, including impact to surface distortion from the added figure error of the multilayer coating, which adds additional requirements of a specific shape to the period distribution. For example, two different coatings may achieve a ±0.2% variation in multilayer period, but have considerably different added figure error. Part I of the paper will focus on radially-symmetric spherical and aspherical optics. Typical azimuthal uniformity (variation at a fixed radius) achieved is less than ±0.005nm total variation, including measurement precision, on concave optics up to 200mm diameter. For highly curved convex optics (radius of curvature less than 50mm), precision is more challenging and the total variation increases to ±0.01nm total variation for optics 10-30mm in diameter. Total added figure error achieved has been as low as 0.05nm. Part II of the paper will focus on multilayer designs graded in two directions, rather than radially, in order to accommodate the increased complexity of elliptical, toroidal and hyperbolic surfaces. In most cases, the symmetry of the required multilayer gradient does not match the symmetry of the optical surface, and this interaction must be countered via the process design. Achieving such results requires additional flexibility in the design of the deposition equipment, and will be discussed with several examples in the paper, such as the use of variable velocity of an inline substrate carrier in conjunction with a shaped target aperture to produce ±0.03nm total variation on an off-axis elliptical surface.

L2CXCV: A Fortran 77 package for least squares convex/concave data smoothing

NASA Astrophysics Data System (ADS)

Demetriou, I. C.

2006-04-01

Fortran 77 software is given for least squares smoothing to data values contaminated by random errors subject to one sign change in the second divided differences of the smoothed values, where the location of the sign change is also unknown of the optimization problem. A highly useful description of the constraints is that they follow from the assumption of initially increasing and subsequently decreasing rates of change, or vice versa, of the process considered. The underlying algorithm partitions the data into two disjoint sets of adjacent data and calculates the required fit by solving a strictly convex quadratic programming problem for each set. The piecewise linear interpolant to the fit is convex on the first set and concave on the other one. The partition into suitable sets is achieved by a finite iterative algorithm, which is made quite efficient because of the interactions of the quadratic programming problems on consecutive data. The algorithm obtains the solution by employing no more quadratic programming calculations over subranges of data than twice the number of the divided differences constraints. The quadratic programming technique makes use of active sets and takes advantage of a B-spline representation of the smoothed values that allows some efficient updating procedures. The entire code required to implement the method is 2920 Fortran lines. The package has been tested on a variety of data sets and it has performed very efficiently, terminating in an overall number of active set changes over subranges of data that is only proportional to the number of data. The results suggest that the package can be used for very large numbers of data values. Some examples with output are provided to help new users and exhibit certain features of the software. Important applications of the smoothing technique may be found in calculating a sigmoid approximation, which is a common topic in various contexts in applications in disciplines like physics, economics, biology and engineering. Distribution material that includes single and double precision versions of the code, driver programs, technical details of the implementation of the software package and test examples that demonstrate the use of the software is available in an accompanying ASCII file. Program summaryTitle of program:L2CXCV Catalogue identifier:ADXM_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXM_v1_0 Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Computer:PC Intel Pentium, Sun Sparc Ultra 5, Hewlett-Packard HP UX 11.0 Operating system:WINDOWS 98, 2000, Unix/Solaris 7, Unix/HP UX 11.0 Programming language used:FORTRAN 77 Memory required to execute with typical data:O(n), where n is the number of data No. of bits in a byte:8 No. of lines in distributed program, including test data, etc.:29 349 No. of bytes in distributed program, including test data, etc.:1 276 663 No. of processors used:1 Has the code been vectorized or parallelized?:no Distribution format:default tar.gz Separate documentation available:Yes Nature of physical problem:Analysis of processes that show initially increasing and then decreasing rates of change (sigmoid shape), as, for example, in heat curves, reactor stability conditions, evolution curves, photoemission yields, growth models, utility functions, etc. Identifying an unknown convex/concave (sigmoid) function from some measurements of its values that contain random errors. Also, identifying the inflection point of this sigmoid function. Method of solution:Univariate data smoothing by minimizing the sum of the squares of the residuals (least squares approximation) subject to the condition that the second order divided differences of the smoothed values change sign at most once. Ideally, this is the number of sign changes in the second derivative of the underlying function. The remarkable property of the smoothed values is that they consist of one separate section of optimal components that give nonnegative second divided differences (convexity) and one separate section of optimal components that give nonpositive second divided differences (concavity). The solution process finds the joint (that is the inflection point estimate of the underlying function) of the sections automatically. The underlying method is iterative, each iteration solving a structured strictly convex quadratic programming problem in order to obtain a convex or a concave section over a subrange of data. Restrictions on the complexity of the problem:Number of data, n, is not limited in the software package, but is limited to 2000 in the main driver. The total work of the method requires 2n-2 structured quadratic programming calculations over subranges of data, which in practice does not exceed the amount of O(n) computer operations. Typical running times:CPU time on a PC with an Intel 733 MHz processor operating in Windows 98: About 2 s to smooth n=1000 noisy measurements that follow the shape of the sine function over one period. Summary:L2CXCV is a package of Fortran 77 subroutines for least squares smoothing to n univariate data values contaminated by random errors subject to one sign change in the second divided differences of the smoothed values, where the location of the sign change is unknown. The piecewise linear interpolant to the smoothed values gives a convex/concave fit to the data. The underlying algorithm is based on the property that in this best convex/concave fit, the convex and the concave section are both optimal and separate. The algorithm is iterative, each iteration solving a strictly convex quadratic programming problem for the best convex fit to the first k data, starting from the best convex fit to the first k-1 data. By reversing the order and sign of the data, the algorithm obtains the best concave fit to the last n-k data. Then it chooses that k as the optimal position of the required sign change (which defines the inflection point of the fit), if the convex and the concave components to the first k and the last n-k data, respectively, form a convex/concave vector that gives the least sum of squares of residuals. In effect the algorithm requires at most 2n-2 quadratic programming calculations over subranges of data. The package employs a technique for quadratic programming, which takes advantage of a B-spline representation of the smoothed values and makes use of some efficient O(k) updating procedures, where k is the number of data of a subrange. The package has been tested on a variety of data sets and it has performed very efficiently, terminating in an overall number of active set changes that is about n, thus exhibiting quadratic performance in n. The Fortran codes have been designed to minimize the use of computing resources. Attention has been given to computer rounding errors details, which are essential to the robustness of the software package. Numerical examples with output are provided to help the use of the software and exhibit certain features of the method. Distribution material that includes driver programs, technical details of the installation of the package and test examples that demonstrate the use of the software is available in an ASCII file that accompanies this work.

Novel methods for Solving Economic Dispatch of Security-Constrained Unit Commitment Based on Linear Programming

NASA Astrophysics Data System (ADS)

Guo, Sangang

2017-09-01

There are two stages in solving security-constrained unit commitment problems (SCUC) within Lagrangian framework: one is to obtain feasible units’ states (UC), the other is power economic dispatch (ED) for each unit. The accurate solution of ED is more important for enhancing the efficiency of the solution to SCUC for the fixed feasible units’ statues. Two novel methods named after Convex Combinatorial Coefficient Method and Power Increment Method respectively based on linear programming problem for solving ED are proposed by the piecewise linear approximation to the nonlinear convex fuel cost functions. Numerical testing results show that the methods are effective and efficient.

Did Caravaggio employ optical projections? An image analysis of the parity in the artist's paintings

NASA Astrophysics Data System (ADS)

Stork, David G.

2011-03-01

We examine one class of evidence put forth in support of the recent claim that the Italian Baroque master Caravaggio secretly employed optical projectors as a direct drawing aid. Specically, we test the claims that there is an "abnormal number" of left-handed gures in his works and, more specically, that "During the Del Monte period he had too many left-handed models." We also test whether there was a reversal in the handedness of specic models in different paintings. Such evidence would be consistent with the claim that Caravaggio switched between using a convex-lens projector to using a concave-mirror projector and would support, but not prove, the claim that Caravaggio used optical projections. We estimate the parity (+ or -) of each of Caravaggio's 76 appropriate oil paintings based on the handedness of gures, the orientation of asymmetric objects, placement of scabbards, depicted text, and so on, and search for statistically significant changes in handedness in figures. We also track the direction of the illumination over time in the artist's uvre. We discuss some historical evidence as it relates to the question of his possible use of optics. We nd the proportion of left-handed figures lower than that in the general population (not higher), and no significant change in estimated handedness even of individual models. Optical proponents have argued that Bacchus (1597) portrays a left-handed gure, but we give visual and cultural evidence showing that this gure is instead right-handed, thereby rebutting this claim that the painting was executed using optical projections. Moreover, scholars recently re-discovered the image of the artist with easel and canvas reflected in the carafe of wine at the front left in the tableau in Bacchus, showing that this painting was almost surely executed using traditional (non-optical) easel methods. We conclude that there is 1) no statistically signicant abnormally high number of left-handed gures in Caravaggio's uvre, including during any limited working period, 2) no statistically significant change in handedness among all gures or even individual gures that might be consistent with a change in optical projector, and 3) the visual and cultural evidence in Bacchus shows the gure was right-handed and that the artist executed this work by traditional (non-optical) easel methods. We conclude that the general parity and handedness evidence does not support the claim that Caravaggio employed optical projections.

Active Mirror Predictive and Requirements Verification Software (AMP-ReVS)

NASA Technical Reports Server (NTRS)

Basinger, Scott A.

2012-01-01

This software is designed to predict large active mirror performance at various stages in the fabrication lifecycle of the mirror. It was developed for 1-meter class powered mirrors for astronomical purposes, but is extensible to other geometries. The package accepts finite element model (FEM) inputs and laboratory measured data for large optical-quality mirrors with active figure control. It computes phenomenological contributions to the surface figure error using several built-in optimization techniques. These phenomena include stresses induced in the mirror by the manufacturing process and the support structure, the test procedure, high spatial frequency errors introduced by the polishing process, and other process-dependent deleterious effects due to light-weighting of the mirror. Then, depending on the maturity of the mirror, it either predicts the best surface figure error that the mirror will attain, or it verifies that the requirements for the error sources have been met once the best surface figure error has been measured. The unique feature of this software is that it ties together physical phenomenology with wavefront sensing and control techniques and various optimization methods including convex optimization, Kalman filtering, and quadratic programming to both generate predictive models and to do requirements verification. This software combines three distinct disciplines: wavefront control, predictive models based on FEM, and requirements verification using measured data in a robust, reusable code that is applicable to any large optics for ground and space telescopes. The software also includes state-of-the-art wavefront control algorithms that allow closed-loop performance to be computed. It allows for quantitative trade studies to be performed for optical systems engineering, including computing the best surface figure error under various testing and operating conditions. After the mirror manufacturing process and testing have been completed, the software package can be used to verify that the underlying requirements have been met.

Remote Continuous Wave and Pulsed Laser Raman Detection of Chemical Warfare Agents Simulants and Toxic Industrial Compounds

NASA Astrophysics Data System (ADS)

Ortiz-Rivera, William; Pacheco-Londoño, Leonardo C.; Hernández-Rivera, Samuel P.

2010-09-01

This study describes the design, assembly, testing and comparison of two Remote Raman Spectroscopy (RRS) systems intended for standoff detection of hazardous chemical liquids. Raman spectra of Chemical Warfare Agents Simulants (CWAS) and Toxic Industrial Compounds (TIC) were measured in the laboratory at a 6.6 m source-target distance using continuous wave (CW) laser detection. Standoff distances for pulsed measurements were 35 m for dimethyl methylphosphonate (DMMP) detection and 60, 90 and 140 m for cyclohexane detection. The prototype systems consisted of a Raman spectrometer equipped with a CCD detector (for CW measurements) and an I-CCD camera with time-gated electronics (for pulsed laser measurements), a reflecting telescope, a fiber optic assembly, a single-line CW laser source (514.5, 488.0, 351.1 and 363.8 nm) and a frequency-doubled single frequency Nd:YAG 532 nm laser (5 ns pulses at 10 Hz). The telescope was coupled to the spectrograph using an optical fiber, and filters were used to reject laser radiation and Rayleigh scattering. Two quartz convex lenses were used to collimate the light from the telescope from which the telescope-focusing eyepiece was removed, and direct it to the fiber optic assembly. To test the standoff sensing system, the Raman Telescope was used in the detection of liquid TIC: benzene, chlorobenzene, toluene, carbon tetrachloride, cyclohexane and carbon disulfide. Other compounds studied were CWAS: dimethylmethyl phosphonate, 2-chloroethyl ethyl sulfide and 2-(butylamino)-ethanethiol. Relative Raman scattering cross sections of liquid CWAS were measured using single-line sources at 532.0, 488.0, 363.8 and 351.1 nm. Samples were placed in glass and quartz vials at the standoff distances from the telescope for the Remote Raman measurements. The mass of DMMP present in water solutions was also quantified as part of the system performance tests.

Lateral facial profile may reveal the risk for sleep disordered breathing in children--the PANIC-study.

PubMed

Ikävalko, Tiina; Närhi, Matti; Lakka, Timo; Myllykangas, Riitta; Tuomilehto, Henri; Vierola, Anu; Pahkala, Riitta

2015-01-01

To evaluate the lateral view photography of the face as a tool for assessing morphological properties (i.e. facial convexity) as a risk factor for sleep disordered breathing (SDB) in children and to test how reliably oral health and non-oral healthcare professionals can visually discern the lateral profile of the face from the photographs. The present study sample consisted of 382 children 6-8 years of age who were participants in the Physical Activity and Nutrition in Children (PANIC) Study. Sleep was assessed by a sleep questionnaire administered by the parents. SDB was defined as apnoeas, frequent or loud snoring or nocturnal mouth breathing observed by the parents. The facial convexity was assessed with three different methods. First, it was clinically evaluated by the reference orthodontist (T.I.). Second, lateral view photographs were taken to visually sub-divide the facial profile into convex, normal or concave. The photos were examined by a reference orthodontist and seven different healthcare professionals who work with children and also by a dental student. The inter- and intra-examiner consistencies were calculated by Kappa statistics. Three soft tissue landmarks of the facial profile, soft tissue Glabella (G`), Subnasale (Sn) and soft tissue Pogonion (Pg`) were digitally identified to analyze convexity of the face and the intra-examiner reproducibility of the reference orthodontist was determined by calculating intra-class correlation coefficients (ICCs). The third way to express the convexity of the face was to calculate the angle of facial convexity (G`-Sn-Pg`) and to group it into quintiles. For analysis the lowest quintile (≤164.2°) was set to represent the most convex facial profile. The prevalence of the SDB in children with the most convex profiles expressed with the lowest quintile of the angle G`-Sn-Pg` (≤164.2°) was almost 2-fold (14.5%) compared to those with normal profile (8.1%) (p = 0.084). The inter-examiner Kappa values between the reference orthodontist and the other examiners for visually assessing the facial profile with the photographs ranged from poor-to-moderate (0.000-0.579). The best Kappa values were achieved between the two orthodontists (0.579). The intra-examiner Kappa value of the reference orthodontist for assessing the profiles was 0.920, with the agreement of 93.3%. In the ICC and its 95% CI between the two digital measurements, the angles of convexity of the facial profile (G`-Sn-Pg`) of the reference orthodontist were 0.980 and 0.951-0.992. In addition to orthodontists, it would be advantageous if also other healthcare professionals could play a key role in identifying certain risk features for SDB. However, the present results indicate that, in order to recognize the morphological risk for SDB, one would need to be trained for the purpose and, as well, needs sufficient knowledge of the growth and development of the face.

A Convex Hull-Based New Metric for Quantification of Bladder Wall Irregularity in Pediatric Patients With Congenital Anomalies of the Kidney and Urinary Tract.

PubMed

Stember, Joseph N; Newhouse, Jeffrey; Behr, Gerald; Alam, Shumyle

2017-11-01

Early identification and quantification of bladder damage in pediatric patients with congenital anomalies of the kidney and urinary tract (CAKUT) is crucial to guiding effective treatment and may affect the eventual clinical outcome, including progression of renal disease. We have developed a novel approach based on the convex hull to calculate bladder wall trabecularity in pediatric patients with CAKUT. The objective of this study was to test whether our approach can accurately predict bladder wall irregularity. Twenty pediatric patients, half with renal compromise and CAKUT and half with normal renal function, were evaluated. We applied the convex hull approach to calculate T, a metric proposed to reflect the degree of trabeculation/bladder wall irregularity, in this set of patients. The average T value was roughly 3 times higher for diseased than healthy patients (0.14 [95% confidence interval, 0.10-0.17] versus 0.05 [95% confidence interval, 0.03-0.07] for normal bladders). This disparity was statistically significant (P < .01). We have demonstrated that a convex hull-based procedure can measure bladder wall irregularity. Because bladder damage is a reversible precursor to irreversible renal parenchymal damage, applying such a measure to at-risk pediatric patients can help guide prompt interventions to avert disease progression. © 2017 by the American Institute of Ultrasound in Medicine.

Derivative-free generation and interpolation of convex Pareto optimal IMRT plans

NASA Astrophysics Data System (ADS)

Hoffmann, Aswin L.; Siem, Alex Y. D.; den Hertog, Dick; Kaanders, Johannes H. A. M.; Huizenga, Henk

2006-12-01

In inverse treatment planning for intensity-modulated radiation therapy (IMRT), beamlet intensity levels in fluence maps of high-energy photon beams are optimized. Treatment plan evaluation criteria are used as objective functions to steer the optimization process. Fluence map optimization can be considered a multi-objective optimization problem, for which a set of Pareto optimal solutions exists: the Pareto efficient frontier (PEF). In this paper, a constrained optimization method is pursued to iteratively estimate the PEF up to some predefined error. We use the property that the PEF is convex for a convex optimization problem to construct piecewise-linear upper and lower bounds to approximate the PEF from a small initial set of Pareto optimal plans. A derivative-free Sandwich algorithm is presented in which these bounds are used with three strategies to determine the location of the next Pareto optimal solution such that the uncertainty in the estimated PEF is maximally reduced. We show that an intelligent initial solution for a new Pareto optimal plan can be obtained by interpolation of fluence maps from neighbouring Pareto optimal plans. The method has been applied to a simplified clinical test case using two convex objective functions to map the trade-off between tumour dose heterogeneity and critical organ sparing. All three strategies produce representative estimates of the PEF. The new algorithm is particularly suitable for dynamic generation of Pareto optimal plans in interactive treatment planning.

Generalized Bregman distances and convergence rates for non-convex regularization methods

NASA Astrophysics Data System (ADS)

Grasmair, Markus

2010-11-01

We generalize the notion of Bregman distance using concepts from abstract convexity in order to derive convergence rates for Tikhonov regularization with non-convex regularization terms. In particular, we study the non-convex regularization of linear operator equations on Hilbert spaces, showing that the conditions required for the application of the convergence rates results are strongly related to the standard range conditions from the convex case. Moreover, we consider the setting of sparse regularization, where we show that a rate of order δ1/p holds, if the regularization term has a slightly faster growth at zero than |t|p.

Passive OCT probe head for 3D duct inspection

NASA Astrophysics Data System (ADS)

Ford, Helen D.; Tatam, Ralph P.

2013-09-01

A passive, endoscopic optical coherence tomography (OCT) probe has been demonstrated, incorporating an imaging fibre bundle and 45° conical mirror, and with no electromechanical components at the probe tip. Circular scanning, of the beam projected onto the proximal face of the imaging bundle, produces a corresponding circular scan at the distal end of the bundle. The beam is turned through 90° by the conical mirror and converted into a radially-scanned sample beam, permitting circumferential OCT scanning in quasi-cylindrical ducts. OCT images, displayed as polar plots and as 3D reconstructions, are presented, showing the internal profile of a metallic test sample containing a 660 µm step in the internal wall. Results have been acquired using two methods: one that makes use of multiple beam-circle diameters, and a mechanical ‘pull-back’ technique. The effects of the convex surface of the conical mirror on spatial resolution are discussed, with suggested working distances given for different application regimes.

Cholesteric microlenses and micromirrors in the beetle cuticle and in synthetic oligomer films: a comparative study

NASA Astrophysics Data System (ADS)

Agez, Gonzague; Bayon, Chloé; Mitov, Michel

2017-02-01

The polygonal texture in cholesteric liquid crystals consist in an array of contiguous polygonal cells. The optical response and the structure of polygonal texture are investigated in the cuticle of beetle Chrysina gloriosa and in synthetic oligomer films. In the insect carapace, the polygons are concave and behave as spherical micro-mirrors whereas they are convex and behave as diverging microlenses in synthetic films. The characteristics of light focusing (spot, donut or continuum background) are highly tunable with the wavelength and the polarization of the incident light.

First Evaluation of the New Thin Convex Probe Endobronchial Ultrasound Scope: A Human Ex Vivo Lung Study.

PubMed

Patel, Priya; Wada, Hironobu; Hu, Hsin-Pei; Hirohashi, Kentaro; Kato, Tatsuya; Ujiie, Hideki; Ahn, Jin Young; Lee, Daiyoon; Geddie, William; Yasufuku, Kazuhiro

2017-04-01

Endobronchial ultrasonography (EBUS)-guided transbronchial needle aspiration allows for sampling of mediastinal lymph nodes. The external diameter, rigidity, and angulation of the convex probe EBUS renders limited accessibility. This study compares the accessibility and transbronchial needle aspiration capability of the prototype thin convex probe EBUS against the convex probe EBUS in human ex vivo lungs rejected for transplant. The prototype thin convex probe EBUS (BF-Y0055; Olympus, Tokyo, Japan) with a thinner tip (5.9 mm), greater upward angle (170 degrees), and decreased forward oblique direction of view (20 degrees) was compared with the current convex probe EBUS (6.9-mm tip, 120 degrees, and 35 degrees, respectively). Accessibility and transbronchial needle aspiration capability was assessed in ex vivo human lungs declined for lung transplant. The distance of maximum reach and sustainable endoscopic limit were measured. Transbronchial needle aspiration capability was assessed using the prototype 25G aspiration needle in segmental lymph nodes. In all evaluated lungs (n = 5), the thin convex probe EBUS demonstrated greater reach and a higher success rate, averaging 22.1 mm greater maximum reach and 10.3 mm further endoscopic visibility range than convex probe EBUS, and could assess selectively almost all segmental bronchi (98% right, 91% left), demonstrating nearly twice the accessibility as the convex probe EBUS (48% right, 47% left). The prototype successfully enabled cytologic assessment of subsegmental lymph nodes with adequate quality using the dedicated 25G aspiration needle. Thin convex probe EBUS has greater accessibility to peripheral airways in human lungs and is capable of sampling segmental lymph nodes using the aspiration needle. That will allow for more precise assessment of N1 nodes and, possibly, intrapulmonary lesions normally inaccessible to the conventional convex probe EBUS. Copyright © 2017 The Society of Thoracic Surgeons. Published by Elsevier Inc. All rights reserved.

Modified optical fiber daylighting system with sunlight transportation in free space.

PubMed

Vu, Ngoc-Hai; Pham, Thanh-Tuan; Shin, Seoyong

2016-12-26

We present the design, optical simulation, and experiment of a modified optical fiber daylighting system (M-OFDS) for indoor lighting. The M-OFDS is comprised of three sub-systems: concentration, collimation, and distribution. The concentration part is formed by coupling a Fresnel lens with a large-core plastic optical fiber. The sunlight collected by the concentration sub-system is propagated in a plastic optical fiber and then collimated by the collimator, which is a combination of a parabolic mirror and a convex lens. The collimated beam of sunlight travels in free space and is guided to the interior by directing flat mirrors, where it is diffused uniformly by a distributor. All parameters of the system are calculated theoretically. Based on the designed system, our simulation results demonstrated a maximum optical efficiency of 71%. The simulation results also showed that sunlight could be delivered to the illumination destination at distance of 30 m. A prototype of the M-OFDS was fabricated, and preliminary experiments were performed outdoors. The simulation results and experimental results confirmed that the M-OFDS was designed effectively. A large-scale system constructed by several M-OFDSs is also proposed. The results showed that the presented optical fiber daylighting system is a strong candidate for an inexpensive and highly efficient application of solar energy in buildings.

Nonexpansiveness of a linearized augmented Lagrangian operator for hierarchical convex optimization

NASA Astrophysics Data System (ADS)

Yamagishi, Masao; Yamada, Isao

2017-04-01

Hierarchical convex optimization concerns two-stage optimization problems: the first stage problem is a convex optimization; the second stage problem is the minimization of a convex function over the solution set of the first stage problem. For the hierarchical convex optimization, the hybrid steepest descent method (HSDM) can be applied, where the solution set of the first stage problem must be expressed as the fixed point set of a certain nonexpansive operator. In this paper, we propose a nonexpansive operator that yields a computationally efficient update when it is plugged into the HSDM. The proposed operator is inspired by the update of the linearized augmented Lagrangian method. It is applicable to characterize the solution set of recent sophisticated convex optimization problems found in the context of inverse problems, where the sum of multiple proximable convex functions involving linear operators must be minimized to incorporate preferable properties into the minimizers. For such a problem formulation, there has not yet been reported any nonexpansive operator that yields an update free from the inversions of linear operators in cases where it is utilized in the HSDM. Unlike previously known nonexpansive operators, the proposed operator yields an inversion-free update in such cases. As an application of the proposed operator plugged into the HSDM, we also present, in the context of the so-called superiorization, an algorithmic solution to a convex optimization problem over the generalized convex feasible set where the intersection of the hard constraints is not necessarily simple.

Loading Mode and Environment Effects on Surface Profile Characteristics of Martensite Plates in Cu-Based SMAs

NASA Astrophysics Data System (ADS)

Suru, Marius-Gabriel; Paraschiv, Adrian-Liviu; Lohan, Nicoleta Monica; Pricop, Bogdan; Ozkal, Burak; Bujoreanu, Leandru-Gheorghe

2014-07-01

The present work reports the influence of the loading mode provided during training under constant stress, in bending, applied to lamellar specimens of Cu-Zn-Al shape memory alloys (SMAs). During training, the specimens were bent by a load fastened at their free end, while being martensitic at room temperature and they lifted the load by one-way effect (1WE), during heating up to austenitic field. On cooling to martensite field, the lower concave surface of bent specimens was compressed, and during heating it was elongated, being subjected to a series of tension-compression cycles, during heating-cooling, respectively. Conversely, the upper convex surface of bent specimens was elongated during cooling and compressed during heating, being subjected to compression-tension cycles. Furthermore, 2WE-trained actuators were tested by means of a hydraulic installation where, this time heating-cooling cycles were performed in oil conditions. Considering that the lower concave surface of the specimens was kept in compressed state, while the upper convex surface was kept in elongated state, the study reveals the influence of the two loading modes and environments on the width of martensite plates of the specimens trained under various numbers of cycles. In this purpose, Cu-Zn-Al specimens, trained under 100-300-500 cycles, were prepared and analyzed by atomic force microscopy (AFM) as well as optical and scanning electron microscopy (OM and SEM, respectively). The analysis also included AFM micrographs corroborated with statistical evaluations in order to reveal the effects of loading mode (tension or compression) in different environmental conditions of the specimens, on the surface profile characteristics of martensite plates, revealed by electropolishing.

Radius of convexity of a certain class of close-to-convex functions

NASA Astrophysics Data System (ADS)

Yahya, Abdullah; Soh, Shaharuddin Cik

2017-11-01

In the present paper, we consider and investigate a certain class of close-to-convex functions that defined in the unit disk, U = {z : |z| < 1}, which denotes as Re { ei αz/f '(z ) f (z )-f (-z ) } >δ where |α| < π, cos (α) > δ and 0 δ <1. Furthermore, we obtain preliminary result for bound f'(z) and determine result for radius of convexity.

Convex Graph Invariants

DTIC Science & Technology

2010-12-02

Motzkin, T. and Straus, E. (1965). Maxima for graphs and a new proof of a theorem of Turan . Canad. J. Math. 17 533–540. [33] Rendl, F. and Sotirov, R...Convex Graph Invariants Venkat Chandrasekaran, Pablo A . Parrilo, and Alan S. Willsky ∗ Laboratory for Information and Decision Systems Department of...this paper we study convex graph invariants, which are graph invariants that are convex functions of the adjacency matrix of a graph. Some examples

Allometric relationships between traveltime channel networks, convex hulls, and convexity measures

NASA Astrophysics Data System (ADS)

Tay, Lea Tien; Sagar, B. S. Daya; Chuah, Hean Teik

2006-06-01

The channel network (S) is a nonconvex set, while its basin [C(S)] is convex. We remove open-end points of the channel connectivity network iteratively to generate a traveltime sequence of networks (Sn). The convex hulls of these traveltime networks provide an interesting topological quantity, which has not been noted thus far. We compute lengths of shrinking traveltime networks L(Sn) and areas of corresponding convex hulls C(Sn), the ratios of which provide convexity measures CM(Sn) of traveltime networks. A statistically significant scaling relationship is found for a model network in the form L(Sn) ˜ A[C(Sn)]0.57. From the plots of the lengths of these traveltime networks and the areas of their corresponding convex hulls as functions of convexity measures, new power law relations are derived. Such relations for a model network are CM(Sn) ˜ ? and CM(Sn) ˜ ?. In addition to the model study, these relations for networks derived from seven subbasins of Cameron Highlands region of Peninsular Malaysia are provided. Further studies are needed on a large number of channel networks of distinct sizes and topologies to understand the relationships of these new exponents with other scaling exponents that define the scaling structure of river networks.

Time-frequency filtering and synthesis from convex projections

NASA Astrophysics Data System (ADS)

White, Langford B.

1990-11-01

This paper describes the application of the theory of projections onto convex sets to time-frequency filtering and synthesis problems. We show that the class of Wigner-Ville Distributions (WVD) of L2 signals form the boundary of a closed convex subset of L2(R2). This result is obtained by considering the convex set of states on the Heisenberg group of which the ambiguity functions form the extreme points. The form of the projection onto the set of WVDs is deduced. Various linear and non-linear filtering operations are incorporated by formulation as convex projections. An example algorithm for simultaneous time-frequency filtering and synthesis is suggested.

Effects of orientation and downward-facing convex curvature on pool-boiling critical heat flux

NASA Astrophysics Data System (ADS)

Howard, Alicia Ann Harris

Photographic studies of near-saturated pool boiling on both inclined flat surfaces and a downward-facing convex surface were conducted in order to determine the physical mechanisms that trigger critical heat flux (CHF). Based on the vapor behavior observed just prior to CHF, it is shown for the flat surfaces that the surface orientations can be divided into three regions: upward-facing (0-60°), near-vertical (60-165°), and downward-facing (165-180°) each region is associated with a unique CHIP trigger mechanism. In the upward-facing region, the buoyancy forces remove the vapor vertically off the heater surface. The near- vertical region is characterized by a wavy liquid-vapor interface which sweeps along the heater surface. In the downward-facing region, the vapor repeatedly stratifies on the heater surface, greatly decreasing CHF. The vapor behavior along the convex surface is cyclic in nature and similar to the nucleation/coalescence/stratification/release procedure observed for flat surfaces in the downward-facing region. The vapor stratification occurred at the bottom (downward-facing) heaters on the convex surface. CHF is always triggered on these downward-facing heaters and then propagates up the convex surface, and the orientations of these heaters are comparable with the orientation range of the flat surface downward-facing region. The vast differences between the observed vapor behavior within the three regions and on the convex surface indicate that a single overall pool boiling CHF model cannot possibly account for all the observed effects. Upward-facing surfaces have been examined and modeled extensively by many investigators and a few investigators have addressed downward-facing surfaces, so this investigation focuses on modeling the near-vertical region. The near-vertical CHF model incorporates classical two-dimensional interfacial instability theory, a separated flow model, an energy balance, and a criterion for separation of the wavy interface from the surface at CHF. The model was tested for different fluids and shows good agreement with CHF data. Additionally, the instability theory incorporated into this model accurately predicts the angle of transition between the near-vertical and downward-facing regions.

Condenser for illuminating a ringfield camera with synchrotron emission light

DOEpatents

Sweatt, W.C.

1996-04-30

The present invention relates generally to the field of condensers for collecting light from a synchrotron radiation source and directing the light into a ringfield of a lithography camera. The present invention discloses a condenser comprising collecting, processing, and imaging optics. The collecting optics are comprised of concave and convex spherical mirrors that collect the light beams. The processing optics, which receive the light beams, are comprised of flat mirrors that converge and direct the light beams into a real entrance pupil of the camera in a symmetrical pattern. In the real entrance pupil are located flat mirrors, common to the beams emitted from the preceding mirrors, for generating substantially parallel light beams and for directing the beams toward the ringfield of a camera. Finally, the imaging optics are comprised of a spherical mirror, also common to the beams emitted from the preceding mirrors, images the real entrance pupil through the resistive mask and into the virtual entrance pupil of the camera. Thus, the condenser is comprised of a plurality of beams with four mirrors corresponding to a single beam plus two common mirrors. 9 figs.

Condenser for illuminating a ringfield camera with synchrotron emission light

DOEpatents

Sweatt, William C.

1996-01-01

The present invention relates generally to the field of condensers for collecting light from a synchrotron radiation source and directing the light into a ringfield of a lithography camera. The present invention discloses a condenser comprising collecting, processing, and imaging optics. The collecting optics are comprised of concave and convex spherical mirrors that collect the light beams. The processing optics, which receive the light beams, are comprised of flat mirrors that converge and direct the light beams into a real entrance pupil of the camera in a symmetrical pattern. In the real entrance pupil are located flat mirrors, common to the beams emitted from the preceding mirrors, for generating substantially parallel light beams and for directing the beams toward the ringfield of a camera. Finally, the imaging optics are comprised of a spherical mirror, also common to the beams emitted from the preceding mirrors, images the real entrance pupil through the resistive mask and into the virtual entrance pupil of the camera. Thus, the condenser is comprised of a plurality of beams with four mirrors corresponding to a single beam plus two common mirrors.

Ion beam figuring of small optical components

NASA Astrophysics Data System (ADS)

Drueding, Thomas W.; Fawcett, Steven C.; Wilson, Scott R.; Bifano, Thomas G.

1995-12-01

Ion beam figuring provides a highly deterministic method for the final precision figuring of optical components with advantages over conventional methods. The process involves bombarding a component with a stable beam of accelerated particles that selectively removes material from the surface. Figure corrections are achieved by rastering the fixed-current beam across the workplace at appropriate, time-varying velocities. Unlike conventional methods, ion figuring is a noncontact technique and thus avoids such problems as edge rolloff effects, tool wear, and force loading of the workpiece. This work is directed toward the development of the precision ion machining system at NASA's Marshall Space Flight Center. This system is designed for processing small (approximately equals 10-cm diam) optical components. Initial experiments were successful in figuring 8-cm-diam fused silica and chemical-vapor-deposited SiC samples. The experiments, procedures, and results of figuring the sample workpieces to shallow spherical, parabolic (concave and convex), and non-axially-symmetric shapes are discussed. Several difficulties and limitations encountered with the current system are discussed. The use of a 1-cm aperture for making finer corrections on optical components is also reported.

Photovoltaic modules with cylindrical waveguides in a system for the secondary concentration of solar radiation

NASA Astrophysics Data System (ADS)

Andreev, V. M.; Davidyuk, N. Yu.; Ionova, E. A.; Rumyantsev, V. D.

2013-09-01

The parameters of the concentrating photoelectric modules with triple-junction (InGaP/GaAs/Ge) solar cells whose focusing system contains an original secondary optical element are studied. The element consists of a plane-convex lens in optical contact with the front surface of an intermediate glass plate and a cylindrical waveguide that is located on the rear side of the glass plate above the surface of the solar element. It is demonstrated that the structure of the secondary optical element provides a wide misorientation characteristic of the concentrator and the cylindrical waveguide allows a more uniform radiation density over the surface of the solar cell. The effect of chromatic aberration in the primary and secondary optical systems on the parameters of photoelectric modules is analyzed. It is demonstrated that the presence of waveguides with a length of 3-5 mm leads to effective redistribution of radiation over the surface of the solar cell whereas shorter and longer waveguides provide the local concentration of radiation at the center of the photodetecting area.

Three-dimensional motion-picture imaging of dynamic object by parallel-phase-shifting digital holographic microscopy using an inverted magnification optical system

NASA Astrophysics Data System (ADS)

Fukuda, Takahito; Shinomura, Masato; Xia, Peng; Awatsuji, Yasuhiro; Nishio, Kenzo; Matoba, Osamu

2017-04-01

We constructed a parallel-phase-shifting digital holographic microscopy (PPSDHM) system using an inverted magnification optical system, and succeeded in three-dimensional (3D) motion-picture imaging for 3D displacement of a microscopic object. In the PPSDHM system, the inverted and afocal magnification optical system consisted of a microscope objective (16.56 mm focal length and 0.25 numerical aperture) and a convex lens (300 mm focal length and 82 mm aperture diameter). A polarization-imaging camera was used to record multiple phase-shifted holograms with a single-shot exposure. We recorded an alum crystal, sinking down in aqueous solution of alum, by the constructed PPSDHM system at 60 frames/s for about 20 s and reconstructed high-quality 3D motion-picture image of the crystal. Then, we calculated amounts of displacement of the crystal from the amounts in the focus plane and the magnifications of the magnification optical system, and obtained the 3D trajectory of the crystal by that amounts.

Compensation of modal dispersion in multimode fiber systems using adaptive optics via convex optimization

NASA Astrophysics Data System (ADS)

Panicker, Rahul Alex

Multimode fibers (MMF) are widely deployed in local-, campus-, and storage-area-networks. Achievable data rates and transmission distances are, however, limited by the phenomenon of modal dispersion. We propose a system to compensate for modal dispersion using adaptive optics. This leads to a 10- to 100-fold improvement in performance over current standards. We propose a provably optimal technique for minimizing inter-symbol interference (ISI) in MMF systems using adaptive optics via convex optimization. We use a spatial light modulator (SLM) to shape the spatial profile of light launched into an MMF. We derive an expression for the system impulse response in terms of the SLM reflectance and the field patterns of the MMF principal modes. Finding optimal SLM settings to minimize ISI, subject to physical constraints, is posed as an optimization problem. We observe that our problem can be cast as a second-order cone program, which is a convex optimization problem. Its global solution can, therefore, be found with minimal computational complexity. Simulations show that this technique opens up an eye pattern originally closed due to ISI. We then propose fast, low-complexity adaptive algorithms for optimizing the SLM settings. We show that some of these converge to the global optimum in the absence of noise. We also propose modified versions of these algorithms to improve resilience to noise and speed of convergence. Next, we experimentally compare the proposed adaptive algorithms in 50-mum graded-index (GRIN) MMFs using a liquid-crystal SLM. We show that continuous-phase sequential coordinate ascent (CPSCA) gives better bit-error-ratio performance than 2- or 4-phase sequential coordinate ascent, in concordance with simulations. We evaluate the bandwidth characteristics of CPSCA, and show that a single SLM is able to simultaneously compensate over up to 9 wavelength-division-multiplexed (WDM) 10-Gb/s channels, spaced by 50 GHz, over a total bandwidth of 450 GHz. We also show that CPSCA is able to compensate for modal dispersion over up to 2.2 km, even in the presence of mid-span connector offsets up to 4 mum (simulated in experiment by offset splices). A known non-adaptive launching technique using a fusion-spliced single-mode-to-multimode patchcord is shown to fail under these conditions. Finally, we demonstrate 10 x 10 Gb/s dense WDM transmission over 2.2 km of 50-mum GRIN MMF. We combine transmitter-based adaptive optics and receiver-based single-mode filtering, and control the launched field pattern for ten 10-Gb/s non-return-to-zero channels, wavelength-division multiplexed on a 200-GHz grid in the C band. We achieve error-free transmission through 2.2 km of 50-mum GRIN MMF for launch offsets up to 10 mum and for worst-case launched polarization. We employ a ten-channel transceiver based on parallel integration of electronics and photonics.

CPU timing routines for a CONVEX C220 computer system

NASA Technical Reports Server (NTRS)

Bynum, Mary Ann

1989-01-01

The timing routines available on the CONVEX C220 computer system in the Structural Mechanics Division (SMD) at NASA Langley Research Center are examined. The function of the timing routines, the use of the timing routines in sequential, parallel, and vector code, and the interpretation of the results from the timing routines with respect to the CONVEX model of computing are described. The timing routines available on the SMD CONVEX fall into two groups. The first group includes standard timing routines generally available with UNIX 4.3 BSD operating systems, while the second group includes routines unique to the SMD CONVEX. The standard timing routines described in this report are /bin/csh time,/bin/time, etime, and ctime. The routines unique to the SMD CONVEX are getinfo, second, cputime, toc, and a parallel profiling package made up of palprof, palinit, and palsum.

Image deblurring based on nonlocal regularization with a non-convex sparsity constraint

NASA Astrophysics Data System (ADS)

Zhu, Simiao; Su, Zhenming; Li, Lian; Yang, Yi

2018-04-01

In recent years, nonlocal regularization methods for image restoration (IR) have drawn more and more attention due to the promising results obtained when compared to the traditional local regularization methods. Despite the success of this technique, in order to obtain computational efficiency, a convex regularizing functional is exploited in most existing methods, which is equivalent to imposing a convex prior on the nonlocal difference operator output. However, our conducted experiment illustrates that the empirical distribution of the output of the nonlocal difference operator especially in the seminal work of Kheradmand et al. should be characterized with an extremely heavy-tailed distribution rather than a convex distribution. Therefore, in this paper, we propose a nonlocal regularization-based method with a non-convex sparsity constraint for image deblurring. Finally, an effective algorithm is developed to solve the corresponding non-convex optimization problem. The experimental results demonstrate the effectiveness of the proposed method.

SiO2 nanofluid planar jet impingement cooling on a convex heated plate

NASA Astrophysics Data System (ADS)

Asghari Lafmajani, Neda; Ebrahimi Bidhendi, Mahsa; Ashjaee, Mehdi

2016-12-01

The main objective of this paper is to investigate the heat transfer coefficient of a planar jet of SiO2 nanofluid that impinges vertically on the middle of a convex heated plate for cooling purposes. The planar jet issues from a rectangular slot nozzle. The convex aluminum plate has a thickness, width and length of 0.2, 40 and 130 mm, respectively, and is bent with a radius of 200 mm. A constant heat-flux condition is employed. 7 nm SiO2 particles are added to water to prepare the nanofluid with 0.1, 1 and 2 % (ml SiO2/ml H2O) concentrations. The tests are also performed at different Reynolds numbers from 1803 to 2782. Results indicate that adding the SiO2 nanoparticles can effectively increase both local and average heat transfer coefficients up to 39.37 and 32.78 %, respectively. These positive effects often are more pronounced with increasing Reynolds numbers. This enhancement increases with ascending the concentration of nanofluid, especially from 0.1 to 1 %.

Development of a three-dimensional correction method for optical distortion of flow field inside a liquid droplet.

PubMed

Gim, Yeonghyeon; Ko, Han Seo

2016-04-15

In this Letter, a three-dimensional (3D) optical correction method, which was verified by simulation, was developed to reconstruct droplet-based flow fields. In the simulation, a synthetic phantom was reconstructed using a simultaneous multiplicative algebraic reconstruction technique with three detectors positioned at the synthetic object (represented by the phantom), with offset angles of 30° relative to each other. Additionally, a projection matrix was developed using the ray tracing method. If the phantom is in liquid, the image of the phantom can be distorted since the light passes through a convex liquid-vapor interface. Because of the optical distortion effect, the projection matrix used to reconstruct a 3D field should be supplemented by the revision ray, instead of the original projection ray. The revision ray can be obtained from the refraction ray occurring on the surface of the liquid. As a result, the error on the reconstruction field of the phantom could be reduced using the developed optical correction method. In addition, the developed optical method was applied to a Taylor cone which was caused by the high voltage between the droplet and the substrate.

Convex Optimization over Classes of Multiparticle Entanglement

NASA Astrophysics Data System (ADS)

Shang, Jiangwei; Gühne, Otfried

2018-02-01

A well-known strategy to characterize multiparticle entanglement utilizes the notion of stochastic local operations and classical communication (SLOCC), but characterizing the resulting entanglement classes is difficult. Given a multiparticle quantum state, we first show that Gilbert's algorithm can be adapted to prove separability or membership in a certain entanglement class. We then present two algorithms for convex optimization over SLOCC classes. The first algorithm uses a simple gradient approach, while the other one employs the accelerated projected-gradient method. For demonstration, the algorithms are applied to the likelihood-ratio test using experimental data on bound entanglement of a noisy four-photon Smolin state [Phys. Rev. Lett. 105, 130501 (2010), 10.1103/PhysRevLett.105.130501].

Methods and apparatus for laser beam scanners with different actuating mechanisms

NASA Astrophysics Data System (ADS)

Chen, Si-hai; Xiang, Si-hua; Wu, Xin; Dong, Shan; Xiao, Ding; Zheng, Xia-wei

2009-07-01

In this paper, 3 types of laser beam scanner are introduced. One is transmissive beam scanner, which is composed of convex and concave microlens arrays (MLAs). By moving the concave lens in the plane vertical to the optical axis, the incident beam can be deflected in two dimensions. Those two kinds of MLAs are fabricated by thermal reflow and replication process. A set of mechanical scanner frame is fabricated with the two MLAs assembling in it. The testing result shown that the beam deflection angles are 9.5° and 9.6°, in the 2 dimension(2D) with the scanning frequency of 2 HZ and 8 HZ, respectively. The second type of laser beam scanner is actuated by voice coil actuators (VCAs). Based on ANSOFT MAXWELL software, we have designed VCAs with small size and large force which have optimized properties. The model of VCAs is built using AutoCAD and is analyzed by Ansoft maxwell. According to the simulation results, high performance VCAs are fabricated and tested. The result is that the force of the VCAs is 6.39N/A, and the displacement is +/-2.5mm. A set up of beam scanner is fabricated and actuated by the designed VCAs. The testing result shown that the two dimensional scanning angle is 15° and 10° respectively at the frequency of 60HZ. The two dimensional scanning angle is 8.3° and 6° respectively at the frequency of 100HZ. The third type of scanner is actuated by amplified piezoelectric actuators (APAs). The scanning mirror is actuated by the piezoelectric (PZ) actuators with the scanning frequency of 700HZ, 250HZ and 87HZ respectively. The optical scanning angle is +/-0.5° at the three frequencies.

Optical touch sensing: practical bounds for design and performance

NASA Astrophysics Data System (ADS)

Bläßle, Alexander; Janbek, Bebart; Liu, Lifeng; Nakamura, Kanna; Nolan, Kimberly; Paraschiv, Victor

2013-02-01

Touch sensitive screens are used in many applications ranging in size from smartphones and tablets to display walls and collaborative surfaces. In this study, we consider optical touch sensing, a technology best suited for large-scale touch surfaces. Optical touch sensing utilizes cameras and light sources placed along the edge of the display. Within this framework, we first find a sufficient number of cameras necessary for identifying a convex polygon touching the screen, using a continuous light source on the boundary of a circular domain. We then find the number of cameras necessary to distinguish between two circular objects in a circular or rectangular domain. Finally, we use Matlab to simulate the polygonal mesh formed from distributing cameras and light sources on a circular domain. Using this, we compute the number of polygons in the mesh and the maximum polygon area to give us information about the accuracy of the configuration. We close with summary and conclusions, and pointers to possible future research directions.

CVXPY: A Python-Embedded Modeling Language for Convex Optimization.

PubMed

Diamond, Steven; Boyd, Stephen

2016-04-01

CVXPY is a domain-specific language for convex optimization embedded in Python. It allows the user to express convex optimization problems in a natural syntax that follows the math, rather than in the restrictive standard form required by solvers. CVXPY makes it easy to combine convex optimization with high-level features of Python such as parallelism and object-oriented design. CVXPY is available at http://www.cvxpy.org/ under the GPL license, along with documentation and examples.

WE-AB-209-07: Explicit and Convex Optimization of Plan Quality Metrics in Intensity-Modulated Radiation Therapy Treatment Planning

DOE Office of Scientific and Technical Information (OSTI.GOV)

Engberg, L; KTH Royal Institute of Technology, Stockholm; Eriksson, K

Purpose: To formulate objective functions of a multicriteria fluence map optimization model that correlate well with plan quality metrics, and to solve this multicriteria model by convex approximation. Methods: In this study, objectives of a multicriteria model are formulated to explicitly either minimize or maximize a dose-at-volume measure. Given the widespread agreement that dose-at-volume levels play important roles in plan quality assessment, these objectives correlate well with plan quality metrics. This is in contrast to the conventional objectives, which are to maximize clinical goal achievement by relating to deviations from given dose-at-volume thresholds: while balancing the new objectives means explicitlymore » balancing dose-at-volume levels, balancing the conventional objectives effectively means balancing deviations. Constituted by the inherently non-convex dose-at-volume measure, the new objectives are approximated by the convex mean-tail-dose measure (CVaR measure), yielding a convex approximation of the multicriteria model. Results: Advantages of using the convex approximation are investigated through juxtaposition with the conventional objectives in a computational study of two patient cases. Clinical goals of each case respectively point out three ROI dose-at-volume measures to be considered for plan quality assessment. This is translated in the convex approximation into minimizing three mean-tail-dose measures. Evaluations of the three ROI dose-at-volume measures on Pareto optimal plans are used to represent plan quality of the Pareto sets. Besides providing increased accuracy in terms of feasibility of solutions, the convex approximation generates Pareto sets with overall improved plan quality. In one case, the Pareto set generated by the convex approximation entirely dominates that generated with the conventional objectives. Conclusion: The initial computational study indicates that the convex approximation outperforms the conventional objectives in aspects of accuracy and plan quality.« less

SU-F-T-340: Direct Editing of Dose Volume Histograms: Algorithms and a Unified Convex Formulation for Treatment Planning with Dose Constraints

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ungun, B; Stanford University School of Medicine, Stanford, CA; Fu, A

2016-06-15

Purpose: To develop a procedure for including dose constraints in convex programming-based approaches to treatment planning, and to support dynamic modification of such constraints during planning. Methods: We present a mathematical approach that allows mean dose, maximum dose, minimum dose and dose volume (i.e., percentile) constraints to be appended to any convex formulation of an inverse planning problem. The first three constraint types are convex and readily incorporated. Dose volume constraints are not convex, however, so we introduce a convex restriction that is related to CVaR-based approaches previously proposed in the literature. To compensate for the conservatism of this restriction,more » we propose a new two-pass algorithm that solves the restricted problem on a first pass and uses this solution to form exact constraints on a second pass. In another variant, we introduce slack variables for each dose constraint to prevent the problem from becoming infeasible when the user specifies an incompatible set of constraints. We implement the proposed methods in Python using the convex programming package cvxpy in conjunction with the open source convex solvers SCS and ECOS. Results: We show, for several cases taken from the clinic, that our proposed method meets specified constraints (often with margin) when they are feasible. Constraints are met exactly when we use the two-pass method, and infeasible constraints are replaced with the nearest feasible constraint when slacks are used. Finally, we introduce ConRad, a Python-embedded free software package for convex radiation therapy planning. ConRad implements the methods described above and offers a simple interface for specifying prescriptions and dose constraints. Conclusion: This work demonstrates the feasibility of using modifiable dose constraints in a convex formulation, making it practical to guide the treatment planning process with interactively specified dose constraints. This work was supported by the Stanford BioX Graduate Fellowship and NIH Grant 5R01CA176553.« less

Design of a projection display screen with vanishing color shift for rear-projection HDTV

NASA Astrophysics Data System (ADS)

Liu, Xiu; Zhu, Jin-lin

1996-09-01

Using bi-convex cylinder lens with matrix structure, the transmissive projection display screen with high contrast and wider viewing angle has been widely used in large rear projection TV and video projectors, it obtained a inhere color shift and puzzled the designer of display screen for RGB projection tube in-line adjustment. Based on the method of light beam racing, the general software of designing projection display screen has been developed and the computer model of vanishing color shift for rear projection HDTV has bee completed. This paper discussed the practical designing method to vanish the defect of color shift and mentioned the relations between the primary optical parameters of display screen and relative geometry sizes of lens' surface. The distributions of optical gain to viewing angle and the influences on engineering design are briefly analyzed.

The secondary mirror concept for the European Extremely Large Telescope

NASA Astrophysics Data System (ADS)

Mueller, Michael; Cayrel, Marc; Bonnet, Henri; Ciattaglia, Emanuela; Esselborn, Michael; Koch, Franz; Kurlandczyk, Herve; Pettazzi, Lorenzo; Rakich, Andrew; Sedghi, Babak

2014-07-01

The E-ELT is an active and adaptive 39-m telescope, with an anastigmat optical solution (5 mirrors including two flats), currently being developed by the European Southern Observatory (ESO). The convex 4-metre-class secondary mirror (M2) is a thin Zerodur meniscus passively supported by an 18 point axial whiffletree. A warping harness system allows to correct low order deformations of the M2 Mirror. Laterally the mirror is supported on 12 points along the periphery by pneumatic jacks. Due to its high optical sensitivity and the telescope gravity deflections, the M2 unit needs to allow repositioning the mirror during observation. Considering its exposed position 30m above the primary, the M2 unit has to provide good wind rejection. The M2 concept is described and major performance characteristics are presented.

CVXPY: A Python-Embedded Modeling Language for Convex Optimization

PubMed Central

Diamond, Steven; Boyd, Stephen

2016-01-01

CVXPY is a domain-specific language for convex optimization embedded in Python. It allows the user to express convex optimization problems in a natural syntax that follows the math, rather than in the restrictive standard form required by solvers. CVXPY makes it easy to combine convex optimization with high-level features of Python such as parallelism and object-oriented design. CVXPY is available at http://www.cvxpy.org/ under the GPL license, along with documentation and examples. PMID:27375369

Duality of caustics in Minkowski billiards

NASA Astrophysics Data System (ADS)

Artstein-Avidan, S.; Florentin, D. I.; Ostrover, Y.; Rosen, D.

2018-04-01

In this paper we study convex caustics in Minkowski billiards. We show that for the Euclidean billiard dynamics in a planar smooth, centrally symmetric, strictly convex body K, for every convex caustic which K possesses, the ‘dual’ billiard dynamics in which the table is the Euclidean unit ball and the geometry that governs the motion is induced by the body K, possesses a dual convex caustic. Such a pair of caustics are dual in a strong sense, and in particular they have the same perimeter, Lazutkin parameter (both measured with respect to the corresponding geometries), and rotation number. We show moreover that for general Minkowski billiards this phenomenon fails, and one can construct a smooth caustic in a Minkowski billiard table which possesses no dual convex caustic.

Multi-Stage Convex Relaxation Methods for Machine Learning

DTIC Science & Technology

2013-03-01

Many problems in machine learning can be naturally formulated as non-convex optimization problems. However, such direct nonconvex formulations have...original nonconvex formulation. We will develop theoretical properties of this method and algorithmic consequences. Related convex and nonconvex machine learning methods will also be investigated.

On approximation and energy estimates for delta 6-convex functions.

PubMed

Saleem, Muhammad Shoaib; Pečarić, Josip; Rehman, Nasir; Khan, Muhammad Wahab; Zahoor, Muhammad Sajid

2018-01-01

The smooth approximation and weighted energy estimates for delta 6-convex functions are derived in this research. Moreover, we conclude that if 6-convex functions are closed in uniform norm, then their third derivatives are closed in weighted [Formula: see text]-norm.

Nonconvex Sparse Logistic Regression With Weakly Convex Regularization

NASA Astrophysics Data System (ADS)

Shen, Xinyue; Gu, Yuantao

2018-06-01

In this work we propose to fit a sparse logistic regression model by a weakly convex regularized nonconvex optimization problem. The idea is based on the finding that a weakly convex function as an approximation of the $\\ell_0$ pseudo norm is able to better induce sparsity than the commonly used $\\ell_1$ norm. For a class of weakly convex sparsity inducing functions, we prove the nonconvexity of the corresponding sparse logistic regression problem, and study its local optimality conditions and the choice of the regularization parameter to exclude trivial solutions. Despite the nonconvexity, a method based on proximal gradient descent is used to solve the general weakly convex sparse logistic regression, and its convergence behavior is studied theoretically. Then the general framework is applied to a specific weakly convex function, and a necessary and sufficient local optimality condition is provided. The solution method is instantiated in this case as an iterative firm-shrinkage algorithm, and its effectiveness is demonstrated in numerical experiments by both randomly generated and real datasets.

Assessing the influence of lower facial profile convexity on perceived attractiveness in the orthognathic patient, clinician, and layperson.

PubMed

Naini, Farhad B; Donaldson, Ana Nora A; McDonald, Fraser; Cobourne, Martyn T

2012-09-01

The aim was a quantitative evaluation of how the severity of lower facial profile convexity influences perceived attractiveness. The lower facial profile of an idealized image was altered incrementally between 14° to -16°. Images were rated on a Likert scale by orthognathic patients, laypeople, and clinicians. Attractiveness ratings were greater for straight profiles in relation to convex/concave, with no significant difference between convex and concave profiles. Ratings decreased by 0.23 of a level for every degree increase in the convexity angle. Class II/III patients gave significantly reduced ratings of attractiveness and had greater desire for surgery than class I. A straight profile is perceived as most attractive and greater degrees of convexity or concavity deemed progressively less attractive, but a range of 10° to -12° may be deemed acceptable; beyond these values surgical correction is desired. Patients are most critical, and clinicians are more critical than laypeople. Copyright © 2012 Elsevier Inc. All rights reserved.

The spectral positioning algorithm of new spectrum vehicle based on convex programming in wireless sensor network

NASA Astrophysics Data System (ADS)

Zhang, Yongjun; Lu, Zhixin

2017-10-01

Spectrum resources are very precious, so it is increasingly important to locate interference signals rapidly. Convex programming algorithms in wireless sensor networks are often used as localization algorithms. But in view of the traditional convex programming algorithm is too much overlap of wireless sensor nodes that bring low positioning accuracy, the paper proposed a new algorithm. Which is mainly based on the traditional convex programming algorithm, the spectrum car sends unmanned aerial vehicles (uses) that can be used to record data periodically along different trajectories. According to the probability density distribution, the positioning area is segmented to further reduce the location area. Because the algorithm only increases the communication process of the power value of the unknown node and the sensor node, the advantages of the convex programming algorithm are basically preserved to realize the simple and real-time performance. The experimental results show that the improved algorithm has a better positioning accuracy than the original convex programming algorithm.

Steven J. Ostro: Pioneer in Asteroid Lightcurve Inversion

NASA Astrophysics Data System (ADS)

Harris, Alan W.

2009-09-01

In 1906, Henry Norris Russell wrote a landmark paper (Astrophys. J. 24, 1-18, 1906) that set the field of lightcurve inversion back by more than three quarters of a century, until Steve Ostro and Robert Connolly published a paper on "convex profile inversion” (Icarus 57, 443-463, 1984). Russell's stifling contribution was innocent enough, and entirely correct: he showed that with "two cans of paint", one can decorate any arbitrarily shaped body in an infinite number of ways to yield any particular lightcurve, even, for example, a cigar shape that is brightest viewed end-on. This sufficed to discourage serious mathematical attack on the problem until Ostro & Connolly's landmark paper of 1984. They showed that if you have only "one can of paint", that is, in the absence of albedo variegation, the problem is tractable and one can make remarkable progress in lightcurve inversion to obtain shapes, or at least the "convex profile” of the real shape. As we now know, nature appears to have only one can of paint (per asteroid), that is, asteroids seem to paint themselves grey so that the uniform reflectivity assumption is quite excellent. Both radar and optical lightcurve inversion techniques are now quite mature, thanks to Steve's pioneering insights.

Fabrication of micro-lens array on convex surface by meaning of micro-milling

NASA Astrophysics Data System (ADS)

Zhang, Peng; Du, Yunlong; Wang, Bo; Shan, Debin

2014-08-01

In order to develop the application of the micro-milling technology, and to fabricate ultra-precision optical surface with complex microstructure, in this paper, the primary experimental research on micro-milling complex microstructure array is carried out. A complex microstructure array surface with vary parameters is designed, and the mathematic model of the surface is set up and simulated. For the fabrication of the designed microstructure array surface, a micro three-axis ultra-precision milling machine tool is developed, aerostatic guideway drove directly by linear motor is adopted in order to guarantee the enough stiffness of the machine, and novel numerical control strategy with linear encoders of 5nm resolution used as the feedback of the control system is employed to ensure the extremely high motion control accuracy. With the help of CAD/CAM technology, convex micro lens array on convex spherical surface with different scales on material of polyvinyl chloride (PVC) and pure copper is fabricated using micro tungsten carbide ball end milling tool based on the ultra-precision micro-milling machine. Excellent nanometer-level micro-movement performance of the axis is proved by motion control experiment. The fabrication is nearly as the same as the design, the characteristic scale of the microstructure is less than 200μm and the accuracy is better than 1μm. It prove that ultra-precision micro-milling technology based on micro ultra-precision machine tool is a suitable and optional method for micro manufacture of microstructure array surface on different kinds of materials, and with the development of micro milling cutter, ultraprecision micro-milling complex microstructure surface will be achieved in future.

Optical differentiation between malignant and benign lymphadenopathy by grey scale texture analysis of endobronchial ultrasound convex probe images.

PubMed

Nguyen, Phan; Bashirzadeh, Farzad; Hundloe, Justin; Salvado, Olivier; Dowson, Nicholas; Ware, Robert; Masters, Ian Brent; Bhatt, Manoj; Kumar, Aravind Ravi; Fielding, David

2012-03-01

Morphologic and sonographic features of endobronchial ultrasound (EBUS) convex probe images are helpful in predicting metastatic lymph nodes. Grey scale texture analysis is a well-established methodology that has been applied to ultrasound images in other fields of medicine. The aim of this study was to determine if this methodology could differentiate between benign and malignant lymphadenopathy of EBUS images. Lymph nodes from digital images of EBUS procedures were manually mapped to obtain a region of interest and were analyzed in a prediction set. The regions of interest were analyzed for the following grey scale texture features in MATLAB (version 7.8.0.347 [R2009a]): mean pixel value, difference between maximal and minimal pixel value, SEM pixel value, entropy, correlation, energy, and homogeneity. Significant grey scale texture features were used to assess a validation set compared with fluoro-D-glucose (FDG)-PET-CT scan findings where available. Fifty-two malignant nodes and 48 benign nodes were in the prediction set. Malignant nodes had a greater difference in the maximal and minimal pixel values, SEM pixel value, entropy, and correlation, and a lower energy (P < .0001 for all values). Fifty-one lymph nodes were in the validation set; 44 of 51 (86.3%) were classified correctly. Eighteen of these lymph nodes also had FDG-PET-CT scan assessment, which correctly classified 14 of 18 nodes (77.8%), compared with grey scale texture analysis, which correctly classified 16 of 18 nodes (88.9%). Grey scale texture analysis of EBUS convex probe images can be used to differentiate malignant and benign lymphadenopathy. Preliminary results are comparable to FDG-PET-CT scan.

Electrowetting based infrared lens using ionic liquids

NASA Astrophysics Data System (ADS)

Hu, Xiaodong; Zhang, Shiguo; Liu, Yu; Qu, Chao; Lu, Liujin; Ma, Xiangyuan; Zhang, Xiaoping; Deng, Youquan

2011-11-01

We demonstrated an infrared variable focus ionic liquids lens using electrowetting, which could overcome the problems caused by use of water, e.g., evaporation and poor thermostability, while keeping good optical transparency in visible light and near-infrared region. Besides, the type of lens (convex or concave) could be tuned by applied voltage or refractive index of ILs used, and the transmittance was measured to exceed 90% over the spectrum of visible light and near-infrared. We believe this infrared variable focus ionic liquids lens has a great application prospect in both visible light and infrared image systems.

Multi-modality nanoparticles having optically responsive shape

DOEpatents

Chen, Fanqing; Bouchard, Louis-Serge

2015-05-19

In certain embodiments novel nanoparticles (nanowontons) are provided that are suitable for multimodal imaging and/or therapy. In one embodiment, the nanoparticles include a first biocompatible (e.g., gold) layer, an inner core layer (e.g., a non-biocompatible material), and a biocompatible (e.g., gold) layer. The first gold layer includes a concave surface that forms a first outer surface of the layered nanoparticle. The second gold layer includes a convex surface that forms a second outer surface of the layered nanoparticle. The first and second gold layers encapsulate the inner core material layer. Methods of fabricating such nanoparticles are also provided.

Strengthening the SDP Relaxation of AC Power Flows with Convex Envelopes, Bound Tightening, and Valid Inequalities

DOE PAGES

Coffrin, Carleton James; Hijazi, Hassan L; Van Hentenryck, Pascal R

2016-12-01

Here this work revisits the Semidefine Programming (SDP) relaxation of the AC power flow equations in light of recent results illustrating the benefits of bounds propagation, valid inequalities, and the Convex Quadratic (QC) relaxation. By integrating all of these results into the SDP model a new hybrid relaxation is proposed, which combines the benefits from all of these recent works. This strengthened SDP formulation is evaluated on 71 AC Optimal Power Flow test cases from the NESTA archive and is shown to have an optimality gap of less than 1% on 63 cases. This new hybrid relaxation closes 50% ofmore » the open cases considered, leaving only 8 for future investigation.« less

Probabilistic Guidance of Swarms using Sequential Convex Programming

DTIC Science & Technology

2014-01-01

quadcopter fleet [24]. In this paper, sequential convex programming (SCP) [25] is implemented using model predictive control (MPC) to provide real-time...in order to make Problem 1 convex. The details for convexifying this problem can be found in [26]. The main steps are discretizing the problem using

Rapid figure-ground responses to stereograms reveal an advantage for a convex foreground.

PubMed

Bertamini, Marco; Lawson, Rebecca

2008-01-01

Convexity has long been recognised as a factor that affects figure - ground segmentation, even when pitted against other factors such as symmetry [Kanizsa and Gerbino, 1976 Art and Artefacts Ed.M Henle (New York: Springer) pp 25-32]. It is accepted in the literature that the difference between concave and convex contours is important for the visual system, and that there is a prior expectation favouring convexities as figure. We used bipartite stimuli and a simple task in which observers had to report whether the foreground was on the left or the right. We report objective evidence that supports the idea that convexity affects figure-ground assignment, even though our stimuli were not pictorial in that depth order was specified unambiguously by binocular disparity.

A Fast Algorithm of Convex Hull Vertices Selection for Online Classification.

PubMed

Ding, Shuguang; Nie, Xiangli; Qiao, Hong; Zhang, Bo

2018-04-01

Reducing samples through convex hull vertices selection (CHVS) within each class is an important and effective method for online classification problems, since the classifier can be trained rapidly with the selected samples. However, the process of CHVS is NP-hard. In this paper, we propose a fast algorithm to select the convex hull vertices, based on the convex hull decomposition and the property of projection. In the proposed algorithm, the quadratic minimization problem of computing the distance between a point and a convex hull is converted into a linear equation problem with a low computational complexity. When the data dimension is high, an approximate, instead of exact, convex hull is allowed to be selected by setting an appropriate termination condition in order to delete more nonimportant samples. In addition, the impact of outliers is also considered, and the proposed algorithm is improved by deleting the outliers in the initial procedure. Furthermore, a dimension convention technique via the kernel trick is used to deal with nonlinearly separable problems. An upper bound is theoretically proved for the difference between the support vector machines based on the approximate convex hull vertices selected and all the training samples. Experimental results on both synthetic and real data sets show the effectiveness and validity of the proposed algorithm.

The Knaster-Kuratowski-Mazurkiewicz theorem and abstract convexities

NASA Astrophysics Data System (ADS)

Cain, George L., Jr.; González, Luis

2008-02-01

The Knaster-Kuratowski-Mazurkiewicz covering theorem (KKM), is the basic ingredient in the proofs of many so-called "intersection" theorems and related fixed point theorems (including the famous Brouwer fixed point theorem). The KKM theorem was extended from Rn to Hausdorff linear spaces by Ky Fan. There has subsequently been a plethora of attempts at extending the KKM type results to arbitrary topological spaces. Virtually all these involve the introduction of some sort of abstract convexity structure for a topological space, among others we could mention H-spaces and G-spaces. We have introduced a new abstract convexity structure that generalizes the concept of a metric space with a convex structure, introduced by E. Michael in [E. Michael, Convex structures and continuous selections, Canad. J. MathE 11 (1959) 556-575] and called a topological space endowed with this structure an M-space. In an article by Shie Park and Hoonjoo Kim [S. Park, H. Kim, Coincidence theorems for admissible multifunctions on generalized convex spaces, J. Math. Anal. Appl. 197 (1996) 173-187], the concepts of G-spaces and metric spaces with Michael's convex structure, were mentioned together but no kind of relationship was shown. In this article, we prove that G-spaces and M-spaces are close related. We also introduce here the concept of an L-space, which is inspired in the MC-spaces of J.V. Llinares [J.V. Llinares, Unified treatment of the problem of existence of maximal elements in binary relations: A characterization, J. Math. Econom. 29 (1998) 285-302], and establish relationships between the convexities of these spaces with the spaces previously mentioned.

Experimental data and model for the turbulent boundary layer on a convex, curved surface

NASA Technical Reports Server (NTRS)

Gillis, J. C.; Johnson, J. P.; Moffat, R. J.; Kays, W. M.

1981-01-01

Experiments were performed to determine how boundary layer turbulence is affected by strong convex curvature. The data gathered on the behavior of the Reynolds stress suggested the formulation of a simple turbulence model. Data were taken on two separate facilities. Both rigs had flow from a flat surface, over a convex surface with 90 deg of turning and then onto a flat recovery surface. The geometry was adjusted so that, for both rigs, the pressure gradient along the test surface was zero. Two experiments were performed at delta/R approximately 0.10, and one at weaker curvature with delta/R approximately 0.05. Results show that after a sudden introduction of curvature the shear stress in the outer part of the boundary layer is sharply diminished and is even slightly negative near the edge. The wall shear also drops off quickly downstream. When the surface suddenly becomes flat again, the wall shear and shear stress profiles recover very slowly towards flat wall conditions. A simple turbulence model, which was based on the theory that the Prandtl mixing length in the outer layer should scale on the velocity gradient layer, was shown to account for the slow recovery.

Laplace Inversion of Low-Resolution NMR Relaxometry Data Using Sparse Representation Methods

PubMed Central

Berman, Paula; Levi, Ofer; Parmet, Yisrael; Saunders, Michael; Wiesman, Zeev

2013-01-01

Low-resolution nuclear magnetic resonance (LR-NMR) relaxometry is a powerful tool that can be harnessed for characterizing constituents in complex materials. Conversion of the relaxation signal into a continuous distribution of relaxation components is an ill-posed inverse Laplace transform problem. The most common numerical method implemented today for dealing with this kind of problem is based on L2-norm regularization. However, sparse representation methods via L1 regularization and convex optimization are a relatively new approach for effective analysis and processing of digital images and signals. In this article, a numerical optimization method for analyzing LR-NMR data by including non-negativity constraints and L1 regularization and by applying a convex optimization solver PDCO, a primal-dual interior method for convex objectives, that allows general linear constraints to be treated as linear operators is presented. The integrated approach includes validation of analyses by simulations, testing repeatability of experiments, and validation of the model and its statistical assumptions. The proposed method provides better resolved and more accurate solutions when compared with those suggested by existing tools. © 2013 Wiley Periodicals, Inc. Concepts Magn Reson Part A 42A: 72–88, 2013. PMID:23847452

An interface reconstruction method based on an analytical formula for 3D arbitrary convex cells

DOE PAGES

Diot, Steven; François, Marianne M.

2015-10-22

In this study, we are interested in an interface reconstruction method for 3D arbitrary convex cells that could be used in multi-material flow simulations for instance. We assume that the interface is represented by a plane whose normal vector is known and we focus on the volume-matching step that consists in finding the plane constant so that it splits the cell according to a given volume fraction. We follow the same approach as in the recent authors' publication for 2D arbitrary convex cells in planar and axisymmetrical geometries, namely we derive an analytical formula for the volume of the specificmore » prismatoids obtained when decomposing the cell using the planes that are parallel to the interface and passing through all the cell nodes. This formula is used to bracket the interface plane constant such that the volume-matching problem is rewritten in a single prismatoid in which the same formula is used to find the final solution. Finally, the proposed method is tested against an important number of reproducible configurations and shown to be at least five times faster.« less

Evaluation of cooling performance of impinging jet array over various dimpled surfaces

NASA Astrophysics Data System (ADS)

Kim, Sun-Min; Kim, Kwang-Yong

2016-04-01

Various configurations of an impinging jet-dimple array cooling system were evaluated in terms of their heat transfer and pressure drop performances. The steady incompressible laminar flow and heat transfer in the cooling system were analyzed using three-dimensional Navier-Stokes equations. The obtained numerical results were validated by a comparison with experimental data for the local Nusselt number distribution. The area-averaged Nusselt number on the projected area and the pressure drop through the system were selected as the performance parameters. Among the four tested configurations—inline concave, staggered concave, inline convex, and staggered convex—the staggered convex impinging jet-dimple array showed the best heat transfer performance whereas the staggered-concave configuration showed the lowest pressure drop. A parametric study with two geometric variables, i.e., the height of dimple and the diameter of dimple, was also conducted for the staggered-convex impinging jet-dimple array. As a result, the best heat transfer and pressure drop performances were achieved when the ratio of the height of dimple to the diameter of jet was 0.8. And, the increase in the ratio of the diameter of dimple to the diameter of jet yielded monotonous increase in the heat transfer performance.

Laplace Inversion of Low-Resolution NMR Relaxometry Data Using Sparse Representation Methods.

PubMed

Berman, Paula; Levi, Ofer; Parmet, Yisrael; Saunders, Michael; Wiesman, Zeev

2013-05-01

Low-resolution nuclear magnetic resonance (LR-NMR) relaxometry is a powerful tool that can be harnessed for characterizing constituents in complex materials. Conversion of the relaxation signal into a continuous distribution of relaxation components is an ill-posed inverse Laplace transform problem. The most common numerical method implemented today for dealing with this kind of problem is based on L 2 -norm regularization. However, sparse representation methods via L 1 regularization and convex optimization are a relatively new approach for effective analysis and processing of digital images and signals. In this article, a numerical optimization method for analyzing LR-NMR data by including non-negativity constraints and L 1 regularization and by applying a convex optimization solver PDCO, a primal-dual interior method for convex objectives, that allows general linear constraints to be treated as linear operators is presented. The integrated approach includes validation of analyses by simulations, testing repeatability of experiments, and validation of the model and its statistical assumptions. The proposed method provides better resolved and more accurate solutions when compared with those suggested by existing tools. © 2013 Wiley Periodicals, Inc. Concepts Magn Reson Part A 42A: 72-88, 2013.

The Band around a Convex Body

ERIC Educational Resources Information Center

Swanson, David

2011-01-01

We give elementary proofs of formulas for the area and perimeter of a planar convex body surrounded by a band of uniform thickness. The primary tool is a integral formula for the perimeter of a convex body which describes the perimeter in terms of the projections of the body onto lines in the plane.

A path following algorithm for the graph matching problem.

PubMed

Zaslavskiy, Mikhail; Bach, Francis; Vert, Jean-Philippe

2009-12-01

We propose a convex-concave programming approach for the labeled weighted graph matching problem. The convex-concave programming formulation is obtained by rewriting the weighted graph matching problem as a least-square problem on the set of permutation matrices and relaxing it to two different optimization problems: a quadratic convex and a quadratic concave optimization problem on the set of doubly stochastic matrices. The concave relaxation has the same global minimum as the initial graph matching problem, but the search for its global minimum is also a hard combinatorial problem. We, therefore, construct an approximation of the concave problem solution by following a solution path of a convex-concave problem obtained by linear interpolation of the convex and concave formulations, starting from the convex relaxation. This method allows to easily integrate the information on graph label similarities into the optimization problem, and therefore, perform labeled weighted graph matching. The algorithm is compared with some of the best performing graph matching methods on four data sets: simulated graphs, QAPLib, retina vessel images, and handwritten Chinese characters. In all cases, the results are competitive with the state of the art.

Validation of Association between Breastfeeding Duration, Facial Profile, Occlusion, and Spacing: A Cross-sectional Study

PubMed Central

Sharma, Mohit; Nehra, Karan; Jayan, Balakrishna; Poonia, Anish; Bhattal, Hiteshwar

2016-01-01

ABSTRACT Introduction: This cross-sectional retrospective study was designed to assess the relationships among breastfeeding duration, nonnutritive sucking habits, convex facial profile, nonspaced dentition, and distoclusion in the deciduous dentition. Materials and methods: A sample of 415 children (228 males, 187 females) aged 4 to 6 years from a mixed Indian population was clinically examined by two orthodontists. Information about breastfeeding duration and nonnutritive sucking habits was obtained by written questionnaire which was answered by the parents. Results: Chi-square test did not indicate any significant association among breastfeeding duration, convex facial profile, and distoclusion. Statistically significant association was observed between breastfeeding duration and nonspaced dentition and also between breastfeeding duration and nonnutritive sucking habits. Nonnutritive sucking habits had a statistically significant association with distoclusion and convex facial profile (odds ratio 7.04 and 4.03 respectively). Nonnutritive sucking habits did not have a statistically significant association with nonspaced dentition. Conclusion: The children breastfed < 6 months had almost twofold increased probability for developing sucking habits and nonspaced dentition, respectively, than the children who had breastfeeding > 6 months duration. It can also be hypothesized that nonnutritive sucking habits may act as a dominant variable in the relationship between breastfeeding duration and occurrence of convex facial profile and distoclusion in deciduous dentition. How to cite this article: Agarwal SS, Sharma M, Nehra K, Jayan B, Poonia A, Bhattal H. Validation of Association between Breastfeeding Duration, Facial Profile, Occlusion, and Spacing: A Cross-sectional Study. Int J Clin Pediatr Dent 2016;9(2):162-166. PMID:27365941

Nested Conjugate Gradient Algorithm with Nested Preconditioning for Non-linear Image Restoration.

PubMed

Skariah, Deepak G; Arigovindan, Muthuvel

2017-06-19

We develop a novel optimization algorithm, which we call Nested Non-Linear Conjugate Gradient algorithm (NNCG), for image restoration based on quadratic data fitting and smooth non-quadratic regularization. The algorithm is constructed as a nesting of two conjugate gradient (CG) iterations. The outer iteration is constructed as a preconditioned non-linear CG algorithm; the preconditioning is performed by the inner CG iteration that is linear. The inner CG iteration, which performs preconditioning for outer CG iteration, itself is accelerated by an another FFT based non-iterative preconditioner. We prove that the method converges to a stationary point for both convex and non-convex regularization functionals. We demonstrate experimentally that proposed method outperforms the well-known majorization-minimization method used for convex regularization, and a non-convex inertial-proximal method for non-convex regularization functional.

Characterizing Time Series Data Diversity for Wind Forecasting: Preprint

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hodge, Brian S; Chartan, Erol Kevin; Feng, Cong

Wind forecasting plays an important role in integrating variable and uncertain wind power into the power grid. Various forecasting models have been developed to improve the forecasting accuracy. However, it is challenging to accurately compare the true forecasting performances from different methods and forecasters due to the lack of diversity in forecasting test datasets. This paper proposes a time series characteristic analysis approach to visualize and quantify wind time series diversity. The developed method first calculates six time series characteristic indices from various perspectives. Then the principal component analysis is performed to reduce the data dimension while preserving the importantmore » information. The diversity of the time series dataset is visualized by the geometric distribution of the newly constructed principal component space. The volume of the 3-dimensional (3D) convex polytope (or the length of 1D number axis, or the area of the 2D convex polygon) is used to quantify the time series data diversity. The method is tested with five datasets with various degrees of diversity.« less

Curvature of iris profile in spectral domain optical coherence tomography and dependency to refraction, age and pupil size - the MIPH Eye&Health Study.

PubMed

Schuster, Alexander K; Fischer, Joachim E; Vossmerbaeumer, Urs

2017-03-01

Optical coherence tomography (OCT) of the anterior segment allows quantitative analysis of the geometry of the iris. We performed spectral domain OCT examinations in healthy emmetropic, hyperopic and myopic subjects to investigate iris curvature and its associations. In a cross-sectional study, out of 4617 eyes (2309 subjects) those with refractive errors of <-4 or >+3 dioptres were identified by objective refraction. The iris was examined using the anterior segment mode of a spectral domain 3D OCT-2000 (Topcon Inc., Japan) in the temporal meridian, and OCT scans were investigated with respect to presence and amount of convex and concave iris configuration. Ninety-three eyes of 50 subjects served as emmetropic group (-0.5 ≤ x ≤+0.5 dioptres). Previous ocular surgery was exclusion criterion. Six hundred and sixty-eight eyes of 398 persons [292 male (76%); age range; 18-66 years] were included in the study. In the myopic group, 105 eyes had a concave iris configuration (26%), while in the hyperopic group, no eye had this configuration (0%) and in the emmetropic group five eyes (5%). Convex iris configuration was found in 96% of hyperopic, in 85% of the emmetropic and in 67% of the myopic eyes. There was an association between concave iris configuration and myopia, younger age and male gender, and with anterior chamber angle width. Spectral domain OCT images can be used for analysis of the iris structure and geometry. Our results are limited to the properties of the study population having an age range from 18 to 66 years and consisting mainly of men. © 2016 Acta Ophthalmologica Scandinavica Foundation. Published by John Wiley & Sons Ltd.

Association of iris surface features with iris parameters assessed by swept-source optical coherence tomography in Asian eyes.

PubMed

Tun, Tin A; Chua, Jacqueline; Shi, Yuan; Sidhartha, Elizabeth; Thakku, Sri Gowtham; Shei, William; Tan, Marcus Chiang Lee; Quah, Joanne Hui Min; Aung, Tin; Cheng, Ching-Yu

2016-12-01

To characterise the association of iris surface features (crypts, furrows and colour) with iris volume and curvature assessed by swept-source optical coherence tomography (SSOCT) in Asian eyes. Iris crypts (by number and size) and furrows (by number and circumferential extent) were graded from iris photographs. Iris colour was measured by a customised algorithm written on MATLAB (MathWorks, Natick, Massachusetts, USA). The iris was imaged by SSOCT (SS-1000, CASIA, Tomey, Nagoya, Japan). The associations of surface features with iris parameters were analysed using a generalised estimating equation. A total of 1704 subjects (3297 eyes) were included in the analysis. The majority was Chinese (86.4%), and 63.2% were females, and their mean age (±SD) was 61.4±6.6 years. After adjusting for age, sex, ethnicity, pupil size and corneal arcus, higher iris crypt grade was independently associated with smaller iris volume (β=-0.54, p<0.001), whereas darker irides and higher iris furrow grade were associated with larger iris volume (β=-0.041, p<0.001) and (β=0.233, p<0.001), respectively. Lighter coloured irides with more crypts and/or more furrows were also associated with less convexity (crypts: β=-0.003, p=0.03; furrows: β=-0.004, p=0.007; and colour: β=-0.001, p=0.005). Iris surface features were highly correlated with iris volume and curvature. Irides with more crypts have a smaller volume; and darker irides with more furrows have a larger volume. Lighter irides with more crypts and/or furrows have less convexity. Published by the BMJ Publishing Group Limited. For permission to use (where not already granted under a licence) please go to http://www.bmj.com/company/products-services/rights-and-licensing/.

Method of making an integral window hermetic fiber optic component

DOEpatents

Dalton, R.D.; Kramer, D.P.; Massey, R.T.; Waker, D.A.

1996-11-12

In the fabrication of igniters, actuators, detonators, and other pyrotechnic devices to be activated by a laser beam, an integral optical glass window is formed by placing a preform in the structural member of the device and then melting the glass and sealing it in place by heating at a temperature between the ceramming temperature of the glass and the melting point of the metal, followed by rapid furnace cooling to avoid devitrification. No other sealing material is needed to achieve hermeticity. A preferred embodiment of this type of device is fabricated by allowing the molten glass to flow further and form a plano-convex lens integral with and at the bottom of the window. The lens functions to decrease the beam divergence caused by refraction of the laser light passing through the window when the device is fired by means of a laser beam. 9 figs.

Method of making an integral window hermetic fiber optic component

DOEpatents

Dalton, Rick D.; Kramer, Daniel P.; Massey, Richard T.; Waker, Damon A.

1996-11-12

In the fabrication of igniters, actuators, detonators, and other pyrotechnic devices to be activated by a laser beam, an integral optical glass window is formed by placing a preform in the structural member of the device and then melting the glass and sealing it in place by heating at a temperature between the ceramming temperature of the glass and the melting point of the metal, followed by rapid furnace cooling to avoid devitrification. No other sealing material is needed to achieve hermeticity. A preferred embodiment of this type of device is fabricated by allowing the molten glass to flow further and form a plano-convex lens integral with and at the bottom of the window. The lens functions to decrease the beam divergence caused by refraction of the laser light passing through the window when the device is fired by means of a laser beam.

Mirrors for High Resolution X-Ray Optics---Figure Preserving IR/PT Coating

NASA Technical Reports Server (NTRS)

Chan, Kai-Wing; Olsen, Lawrence; Sharpe, Marton; Numata, Ai; McClelland, Ryan; Saha, Timo; Zhang, Will

2016-01-01

Coating stress of 10 - 20 nm of Ir is sufficiently high to distort the figure of arc-second thin lightweight mirrors. For iridium: --Stress sigma 4 GPa for 15 nm film implies 60 Nm integrated stress-- Need less than 3 N/m (or stress less than 200 MPa) for sub-arcsecond optics. Basic Approaches for Mitigation. A. Annealing the film-- Glass can be heat up to 400 C without distortion. Silicon is even more resistant.-- It was found that recovery is limited by residual thermal stress from taking the mirror down from high T. B. Coating bi-layer films with compressive stress with tensile stress. C. Front-and-back coating with magnetron sputtering or atomic layer deposition-- Sputtering involve spanning of substrates. Geometric difference in setup (convexness/concaveness of curved mirrors) does not permit precise front-and-back matching-- Atomic layer deposition can provide a uniform deposition front and back simultaneously.

Cellular dye lasers: lasing thresholds and sensing in a planar resonator

PubMed Central

Humar, Matjaž; Gather, Malte C.; Yun, Seok-Hyun

2015-01-01

Biological cell lasers are promising novel building blocks of future biocompatible optical systems and offer new approaches to cellular sensing and cytometry in a microfluidic setting. Here, we demonstrate a simple method for providing optical gain by using a variety of standard fluorescent dyes. The dye gain medium can be located inside or outside a cell, or in both, which gives flexibility in experimental design and makes the method applicable to all cell types. Due to the higher refractive index of the cytoplasm compared to the surrounding medium, a cell acts as a convex lens in a planar Fabry-Perot cavity. Its effect on the stability of the laser cavity is analyzed and utilized to suppress lasing outside cells. The resonance modes depend on the shape and internal structure of the cell. As proof of concept, we show how the laser output modes are affected by the osmotic pressure. PMID:26480446

Tapered chalcogenide-tellurite hybrid microstructured fiber for mid-infrared supercontinuum generation

NASA Astrophysics Data System (ADS)

Yang, Peilong; Zhang, Peiqing; Dai, Shixun; Wu, Yuehao; Wang, Xunsi; Tao, Guangming; Nie, Qiuhua

2015-05-01

Fibers exhibiting flattened and decreasing dispersion are important in nonlinear applications. Such fibers are difficult to design, particularly in soft glass. In this work, we develop a preliminary design of a highly nonlinear tapered hybrid microstructured optical fiber (TH-MOF) with chalcogenide glass core and tellurite glass microstructure cladding. We then numerically studied its dispersion, loss, and nonlinearity-related optical properties under fundamental mode systematically using the infinitesimal method. The designed TH-MOF exhibits low chromatic dispersion that is similar to a convex function with two zero-dispersion wavelengths and decreases with fiber length from 2 to 5 μm band. The potential use of the TH-MOF in nonlinear applications is demonstrated numerically by a supercontinuum spectrum of 20 dB bandwidth covering 1.96-4.76 μm generated in 2-cm-long TH-MOF using near 3.25-μm fs-laser pump.

Patterns of functional vision loss in glaucoma determined with archetypal analysis

PubMed Central

Elze, Tobias; Pasquale, Louis R.; Shen, Lucy Q.; Chen, Teresa C.; Wiggs, Janey L.; Bex, Peter J.

2015-01-01

Glaucoma is an optic neuropathy accompanied by vision loss which can be mapped by visual field (VF) testing revealing characteristic patterns related to the retinal nerve fibre layer anatomy. While detailed knowledge about these patterns is important to understand the anatomic and genetic aspects of glaucoma, current classification schemes are typically predominantly derived qualitatively. Here, we classify glaucomatous vision loss quantitatively by statistically learning prototypical patterns on the convex hull of the data space. In contrast to component-based approaches, this method emphasizes distinct aspects of the data and provides patterns that are easier to interpret for clinicians. Based on 13 231 reliable Humphrey VFs from a large clinical glaucoma practice, we identify an optimal solution with 17 glaucomatous vision loss prototypes which fit well with previously described qualitative patterns from a large clinical study. We illustrate relations of our patterns to retinal structure by a previously developed mathematical model. In contrast to the qualitative clinical approaches, our results can serve as a framework to quantify the various subtypes of glaucomatous visual field loss. PMID:25505132

Development of a continuous roll-to-roll processing system for mass production of plastic optical film

NASA Astrophysics Data System (ADS)

Chang, Chih-Yuan; Tsai, Meng-Hsun

2015-12-01

This paper reports a highly effective method for the mass production of large-area plastic optical films with a microlens array pattern based on a continuous roll-to-roll film extrusion and roller embossing process. In this study, a thin steel mold with a micro-circular hole array pattern is fabricated by photolithography and a wet chemical etching process. The thin steel mold was then wrapped onto a metal cylinder to form an embossing roller mold. During the roll-to-roll process operation, a thermoplastic raw material (polycarbonate grains) was put into the barrel of the plastic extruder with a flat T-die. Then, the molten polymer film was extruded and immediately pressed against the surface of the embossing roller mold. Under the proper processing conditions, the molten polymer will just partially fill the micro-circular holes of the mold and due to surface tension form a convex lens surface. A continuous plastic optical film with a microlens array pattern was obtained. Experiments are carried out to investigate the effect of plastic microlens formation on the roll-to-roll process. Finally, the geometrical and optical properties of the fabricated plastic optical film were measured and proved satisfactory. This technique shows great potential for the mass production of large-area plastic optical films with a microlens array pattern.

Anatomical study of the pelvis in patients with adolescent idiopathic scoliosis

PubMed Central

Qiu, Xu-Sheng; Zhang, Jun-Jie; Yang, Shang-Wen; Lv, Feng; Wang, Zhi-Wei; Chiew, Jonathan; Ma, Wei-Wei; Qiu, Yong

2012-01-01

Standing posterior–anterior (PA) radiographs from our clinical practice show that the concave and convex ilia are not always symmetrical in patients with adolescent idiopathic scoliosis (AIS). Transverse pelvic rotation may explain this observation, or pelvic asymmetry may be responsible. The present study investigated pelvic symmetry by examining the volume and linear measurements of the two hipbones in patients with AIS. Forty-two female patients with AIS were recruited for the study. Standing PA radiographs (covering the thoracic and lumbar spinal regions and the entire pelvis), CT scans and 3D reconstructions of the pelvis were obtained for all subjects. The concave/convex ratio of the inferior ilium at the sacroiliac joint medially (SI) and the anterior superior iliac spine laterally (ASIS) were measured on PA radiographs. Hipbone volumes and several distortion and abduction parameters were measured by post-processing software. The concave/convex ratio of SI–ASIS on PA radiographs was 0.97, which was significantly < 1 (P < 0.001). The concave and convex hipbone volumes were comparable in patients with AIS. The hipbone volumes were 257.3 ± 43.5 cm3 and 256.9 ± 42.6 cm3 at the concave and convex sides, respectively (P > 0.05). Furthermore, all distortion and abduction parameters were comparable between the convex and concave sides. Therefore, the present study showed that there was no pelvic asymmetry in patients with AIS, although the concave/convex ratio of SI–ASIS on PA radiographs was significantly < 1. The clinical phenomenon of asymmetrical concave and convex ilia in patients with AIS in preoperative standing PA radiographs may be caused by transverse pelvic rotation, but it is not due to developmental asymmetry or distortion of the pelvis. PMID:22133294

Anatomical study of the pelvis in patients with adolescent idiopathic scoliosis.

PubMed

Qiu, Xu-Sheng; Zhang, Jun-Jie; Yang, Shang-Wen; Lv, Feng; Wang, Zhi-Wei; Chiew, Jonathan; Ma, Wei-Wei; Qiu, Yong

2012-02-01

Standing posterior-anterior (PA) radiographs from our clinical practice show that the concave and convex ilia are not always symmetrical in patients with adolescent idiopathic scoliosis (AIS). Transverse pelvic rotation may explain this observation, or pelvic asymmetry may be responsible. The present study investigated pelvic symmetry by examining the volume and linear measurements of the two hipbones in patients with AIS. Forty-two female patients with AIS were recruited for the study. Standing PA radiographs (covering the thoracic and lumbar spinal regions and the entire pelvis), CT scans and 3D reconstructions of the pelvis were obtained for all subjects. The concave/convex ratio of the inferior ilium at the sacroiliac joint medially (SI) and the anterior superior iliac spine laterally (ASIS) were measured on PA radiographs. Hipbone volumes and several distortion and abduction parameters were measured by post-processing software. The concave/convex ratio of SI-ASIS on PA radiographs was 0.97, which was significantly < 1 (P < 0.001). The concave and convex hipbone volumes were comparable in patients with AIS. The hipbone volumes were 257.3 ± 43.5 cm(3) and 256.9 ± 42.6 cm(3) at the concave and convex sides, respectively (P > 0.05). Furthermore, all distortion and abduction parameters were comparable between the convex and concave sides. Therefore, the present study showed that there was no pelvic asymmetry in patients with AIS, although the concave/convex ratio of SI-ASIS on PA radiographs was significantly < 1. The clinical phenomenon of asymmetrical concave and convex ilia in patients with AIS in preoperative standing PA radiographs may be caused by transverse pelvic rotation, but it is not due to developmental asymmetry or distortion of the pelvis. © 2011 The Authors. Journal of Anatomy © 2011 Anatomical Society.

Investigations into the shape-preserving interpolants using symbolic computation

NASA Technical Reports Server (NTRS)

Lam, Maria

1988-01-01

Shape representation is a central issue in computer graphics and computer-aided geometric design. Many physical phenomena involve curves and surfaces that are monotone (in some directions) or are convex. The corresponding representation problem is given some monotone or convex data, and a monotone or convex interpolant is found. Standard interpolants need not be monotone or convex even though they may match monotone or convex data. Most of the methods of investigation of this problem involve the utilization of quadratic splines or Hermite polynomials. In this investigation, a similar approach is adopted. These methods require derivative information at the given data points. The key to the problem is the selection of the derivative values to be assigned to the given data points. Schemes for choosing derivatives were examined. Along the way, fitting given data points by a conic section has also been investigated as part of the effort to study shape-preserving quadratic splines.

Congruency effects in dot comparison tasks: convex hull is more important than dot area.

PubMed

Gilmore, Camilla; Cragg, Lucy; Hogan, Grace; Inglis, Matthew

2016-11-16

The dot comparison task, in which participants select the more numerous of two dot arrays, has become the predominant method of assessing Approximate Number System (ANS) acuity. Creation of the dot arrays requires the manipulation of visual characteristics, such as dot size and convex hull. For the task to provide a valid measure of ANS acuity, participants must ignore these characteristics and respond on the basis of number. Here, we report two experiments that explore the influence of dot area and convex hull on participants' accuracy on dot comparison tasks. We found that individuals' ability to ignore dot area information increases with age and display time. However, the influence of convex hull information remains stable across development and with additional time. This suggests that convex hull information is more difficult to inhibit when making judgements about numerosity and therefore it is crucial to control this when creating dot comparison tasks.

Space ultra-vacuum facility and method of operation

NASA Technical Reports Server (NTRS)

Naumann, Robert J. (Inventor)

1988-01-01

A wake shield space processing facility (10) for maintaining ultra-high levels of vacuum is described. The wake shield (12) is a truncated hemispherical section having a convex side (14) and a concave side (24). Material samples (68) to be processed are located on the convex side of the shield, which faces in the wake direction in operation in orbit. Necessary processing fixtures (20) and (22) are also located on the convex side. Support equipment including power supplies (40, 42), CMG package (46) and electronic control package (44) are located on the convex side (24) of the shield facing the ram direction. Prior to operation in orbit the wake shield is oriented in reverse with the convex side facing the ram direction to provide cleaning by exposure to ambient atomic oxygen. The shield is then baked-out by being pointed directed at the sun to obtain heating for a suitable period.

Simple alignment procedure for a VNIR imaging spectrometer with a Shack-Hartmann wavefront sensor and a field identifier

NASA Astrophysics Data System (ADS)

Lee, Jun Ho; Hwang, Sunglyoung; Jeong, Dohwan; Hong, Jinsuk; Kim, Youngsoo; Kim, Yeonsoo; Kim, Hyunsook

2017-09-01

We report an innovative simple alignment method for a VNIR spectrometer in the wavelength region of 400-900 nm; this device is later combined with fore-optics (a telescope) to form a f/2.5 hyperspectral imaging spectrometer with a field of view of +/-7.68°. The detector at the final image plane is a 640×480 charge-coupled device with a 24 μm pixel size. We first assembled the fore-optics and the spectrometer separately and then combined them via a slit co-located on the image plane of the fore-optics and the object plane of the spectrometer. The spectrometer was assembled in three steps. In the initial step, the optics was simply assembled with an optical axis guiding He-Ne laser. In the second step, we located a pin-hole on the slit plane and a Shack-Hartmann sensor on the detector plane. The wavefront errors over the full field were scanned simply by moving the point source along the slit direction while the Shack-Hartmann sensor was constantly conjugated to the pin-hole position by a motorized stage. Optimal alignment was then performed based on the reverse sensitivity method. In the final stage, the pin-hole and the Shack-Hartmann sensor were exchanged with an equispaced 10 pin-hole slit called a field identifier and a detector. The light source was also changed from the laser (single wavelength source) to a krypton lamp (discrete multi-wavelength source). We were then easily able to calculate the distortion and keystone on the detector plane without any scanning or moving optical components; rather, we merely calculated the spectral centroids of the 10 pin-holes on the detector. We then tuned the clocking angles of the convex grating and the detector to minimize the distortion and keystone. The final assembly was tested and found to have an RMS WFE < 90 nm over the entire field of view, a keystone of 0.08 pixels, a smile of 1.13 pixels and a spectral resolution of 4.32 nm.

Calculating and controlling the error of discrete representations of Pareto surfaces in convex multi-criteria optimization.

PubMed

Craft, David

2010-10-01

A discrete set of points and their convex combinations can serve as a sparse representation of the Pareto surface in multiple objective convex optimization. We develop a method to evaluate the quality of such a representation, and show by example that in multiple objective radiotherapy planning, the number of Pareto optimal solutions needed to represent Pareto surfaces of up to five dimensions grows at most linearly with the number of objectives. The method described is also applicable to the representation of convex sets. Copyright © 2009 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.

Inhibitory competition in figure-ground perception: context and convexity.

PubMed

Peterson, Mary A; Salvagio, Elizabeth

2008-12-15

Convexity has long been considered a potent cue as to which of two regions on opposite sides of an edge is the shaped figure. Experiment 1 shows that for a single edge, there is only a weak bias toward seeing the figure on the convex side. Experiments 1-3 show that the bias toward seeing the convex side as figure increases as the number of edges delimiting alternating convex and concave regions increases, provided that the concave regions are homogeneous in color. The results of Experiments 2 and 3 rule out a probability summation explanation for these context effects. Taken together, the results of Experiments 1-3 show that the homogeneity versus heterogeneity of the convex regions is irrelevant. Experiment 4 shows that homogeneity of alternating regions is not sufficient for context effects; a cue that favors the perception of the intervening regions as figures is necessary. Thus homogeneity alone does not alone operate as a background cue. We interpret our results within a model of figure-ground perception in which shape properties on opposite sides of an edge compete for representation and the competitive strength of weak competitors is further reduced when they are homogeneous.

Natural-Scene Statistics Predict How the Figure–Ground Cue of Convexity Affects Human Depth Perception

PubMed Central

Fowlkes, Charless C.; Banks, Martin S.

2010-01-01

The shape of the contour separating two regions strongly influences judgments of which region is “figure” and which is “ground.” Convexity and other figure–ground cues are generally assumed to indicate only which region is nearer, but nothing about how much the regions are separated in depth. To determine the depth information conveyed by convexity, we examined natural scenes and found that depth steps across surfaces with convex silhouettes are likely to be larger than steps across surfaces with concave silhouettes. In a psychophysical experiment, we found that humans exploit this correlation. For a given binocular disparity, observers perceived more depth when the near surface's silhouette was convex rather than concave. We estimated the depth distributions observers used in making those judgments: they were similar to the natural-scene distributions. Our findings show that convexity should be reclassified as a metric depth cue. They also suggest that the dichotomy between metric and nonmetric depth cues is false and that the depth information provided many cues should be evaluated with respect to natural-scene statistics. Finally, the findings provide an explanation for why figure–ground cues modulate the responses of disparity-sensitive cells in visual cortex. PMID:20505093

Convex Banding of the Covariance Matrix

PubMed Central

Bien, Jacob; Bunea, Florentina; Xiao, Luo

2016-01-01

We introduce a new sparse estimator of the covariance matrix for high-dimensional models in which the variables have a known ordering. Our estimator, which is the solution to a convex optimization problem, is equivalently expressed as an estimator which tapers the sample covariance matrix by a Toeplitz, sparsely-banded, data-adaptive matrix. As a result of this adaptivity, the convex banding estimator enjoys theoretical optimality properties not attained by previous banding or tapered estimators. In particular, our convex banding estimator is minimax rate adaptive in Frobenius and operator norms, up to log factors, over commonly-studied classes of covariance matrices, and over more general classes. Furthermore, it correctly recovers the bandwidth when the true covariance is exactly banded. Our convex formulation admits a simple and efficient algorithm. Empirical studies demonstrate its practical effectiveness and illustrate that our exactly-banded estimator works well even when the true covariance matrix is only close to a banded matrix, confirming our theoretical results. Our method compares favorably with all existing methods, in terms of accuracy and speed. We illustrate the practical merits of the convex banding estimator by showing that it can be used to improve the performance of discriminant analysis for classifying sound recordings. PMID:28042189

Convex Banding of the Covariance Matrix.

PubMed

Bien, Jacob; Bunea, Florentina; Xiao, Luo

2016-01-01

We introduce a new sparse estimator of the covariance matrix for high-dimensional models in which the variables have a known ordering. Our estimator, which is the solution to a convex optimization problem, is equivalently expressed as an estimator which tapers the sample covariance matrix by a Toeplitz, sparsely-banded, data-adaptive matrix. As a result of this adaptivity, the convex banding estimator enjoys theoretical optimality properties not attained by previous banding or tapered estimators. In particular, our convex banding estimator is minimax rate adaptive in Frobenius and operator norms, up to log factors, over commonly-studied classes of covariance matrices, and over more general classes. Furthermore, it correctly recovers the bandwidth when the true covariance is exactly banded. Our convex formulation admits a simple and efficient algorithm. Empirical studies demonstrate its practical effectiveness and illustrate that our exactly-banded estimator works well even when the true covariance matrix is only close to a banded matrix, confirming our theoretical results. Our method compares favorably with all existing methods, in terms of accuracy and speed. We illustrate the practical merits of the convex banding estimator by showing that it can be used to improve the performance of discriminant analysis for classifying sound recordings.

Statistical estimation via convex optimization for trending and performance monitoring

NASA Astrophysics Data System (ADS)

Samar, Sikandar

This thesis presents an optimization-based statistical estimation approach to find unknown trends in noisy data. A Bayesian framework is used to explicitly take into account prior information about the trends via trend models and constraints. The main focus is on convex formulation of the Bayesian estimation problem, which allows efficient computation of (globally) optimal estimates. There are two main parts of this thesis. The first part formulates trend estimation in systems described by known detailed models as a convex optimization problem. Statistically optimal estimates are then obtained by maximizing a concave log-likelihood function subject to convex constraints. We consider the problem of increasing problem dimension as more measurements become available, and introduce a moving horizon framework to enable recursive estimation of the unknown trend by solving a fixed size convex optimization problem at each horizon. We also present a distributed estimation framework, based on the dual decomposition method, for a system formed by a network of complex sensors with local (convex) estimation. Two specific applications of the convex optimization-based Bayesian estimation approach are described in the second part of the thesis. Batch estimation for parametric diagnostics in a flight control simulation of a space launch vehicle is shown to detect incipient fault trends despite the natural masking properties of feedback in the guidance and control loops. Moving horizon approach is used to estimate time varying fault parameters in a detailed nonlinear simulation model of an unmanned aerial vehicle. An excellent performance is demonstrated in the presence of winds and turbulence.

Piecewise convexity of artificial neural networks.

PubMed

Rister, Blaine; Rubin, Daniel L

2017-10-01

Although artificial neural networks have shown great promise in applications including computer vision and speech recognition, there remains considerable practical and theoretical difficulty in optimizing their parameters. The seemingly unreasonable success of gradient descent methods in minimizing these non-convex functions remains poorly understood. In this work we offer some theoretical guarantees for networks with piecewise affine activation functions, which have in recent years become the norm. We prove three main results. First, that the network is piecewise convex as a function of the input data. Second, that the network, considered as a function of the parameters in a single layer, all others held constant, is again piecewise convex. Third, that the network as a function of all its parameters is piecewise multi-convex, a generalization of biconvexity. From here we characterize the local minima and stationary points of the training objective, showing that they minimize the objective on certain subsets of the parameter space. We then analyze the performance of two optimization algorithms on multi-convex problems: gradient descent, and a method which repeatedly solves a number of convex sub-problems. We prove necessary convergence conditions for the first algorithm and both necessary and sufficient conditions for the second, after introducing regularization to the objective. Finally, we remark on the remaining difficulty of the global optimization problem. Under the squared error objective, we show that by varying the training data, a single rectifier neuron admits local minima arbitrarily far apart, both in objective value and parameter space. Copyright © 2017 Elsevier Ltd. All rights reserved.

FMCSA’s advanced system testing utilizing a data acquisition system on the highways (FAST DASH) safety technology evaluation project #3 : novel convex mirrors : technology brief.

DOT National Transportation Integrated Search

2016-11-01

The Federal Motor Carrier Safety Administration (FMCSA) established the FAST DASH program to perform efficient independent evaluations of promising safety technologies aimed at commercial vehicle operations. In this third FAST DASH safety technology ...

LANZ: Software solving the large sparse symmetric generalized eigenproblem

NASA Technical Reports Server (NTRS)

Jones, Mark T.; Patrick, Merrell L.

1990-01-01

A package, LANZ, for solving the large symmetric generalized eigenproblem is described. The package was tested on four different architectures: Convex 200, CRAY Y-MP, Sun-3, and Sun-4. The package uses a Lanczos' method and is based on recent research into solving the generalized eigenproblem.

Relationship between spontaneous expiratory flow-volume curve pattern and air-flow obstruction in elderly COPD patients.

PubMed

Nozoe, Masafumi; Mase, Kyoshi; Murakami, Shigefumi; Okada, Makoto; Ogino, Tomoyuki; Matsushita, Kazuhiro; Takashima, Sachie; Yamamoto, Noriyasu; Fukuda, Yoshihiro; Domen, Kazuhisa

2013-10-01

Assessment of the degree of air-flow obstruction is important for determining the treatment strategy in COPD patients. However, in some elderly COPD patients, measuring FVC is impossible because of cognitive dysfunction or severe dyspnea. In such patients a simple test of airways obstruction requiring only a short run of tidal breathing would be useful. We studied whether the spontaneous expiratory flow-volume (SEFV) curve pattern reflects the degree of air-flow obstruction in elderly COPD patients. In 34 elderly subjects (mean ± SD age 80 ± 7 y) with stable COPD (percent-of-predicted FEV(1) 39.0 ± 18.5%), and 12 age-matched healthy subjects, we measured FVC and recorded flow-volume curves during quiet breathing. We studied the SEFV curve patterns (concavity/convexity), spirometry results, breathing patterns, and demographics. The SEFV curve concavity/convexity prediction accuracy was examined by calculating the receiver operating characteristic curves, cutoff values, area under the curve, sensitivity, and specificity. Fourteen subjects with COPD had a concave SEFV curve. All the healthy subjects had convex SEFV curves. The COPD subjects who had concave SEFV curves often had very severe airway obstruction. The percent-of-predicted FEV(1)% (32.4%) was the most powerful SEFV curve concavity predictor (area under the curve 0.92, 95% CI 0.83-1.00), and had the highest sensitivity (0.93) and specificity (0.88). Concavity of the SEFV curve obtained during tidal breathing may be a useful test for determining the presence of very severe obstruction in elderly patients unable to perform a satisfactory FVC maneuver.

Object Recognition in Flight: How Do Bees Distinguish between 3D Shapes?

PubMed Central

Werner, Annette; Stürzl, Wolfgang; Zanker, Johannes

2016-01-01

Honeybees (Apis mellifera) discriminate multiple object features such as colour, pattern and 2D shape, but it remains unknown whether and how bees recover three-dimensional shape. Here we show that bees can recognize objects by their three-dimensional form, whereby they employ an active strategy to uncover the depth profiles. We trained individual, free flying honeybees to collect sugar water from small three-dimensional objects made of styrofoam (sphere, cylinder, cuboids) or folded paper (convex, concave, planar) and found that bees can easily discriminate between these stimuli. We also tested possible strategies employed by the bees to uncover the depth profiles. For the card stimuli, we excluded overall shape and pictorial features (shading, texture gradients) as cues for discrimination. Lacking sufficient stereo vision, bees are known to use speed gradients in optic flow to detect edges; could the bees apply this strategy also to recover the fine details of a surface depth profile? Analysing the bees’ flight tracks in front of the stimuli revealed specific combinations of flight maneuvers (lateral translations in combination with yaw rotations), which are particularly suitable to extract depth cues from motion parallax. We modelled the generated optic flow and found characteristic patterns of angular displacement corresponding to the depth profiles of our stimuli: optic flow patterns from pure translations successfully recovered depth relations from the magnitude of angular displacements, additional rotation provided robust depth information based on the direction of the displacements; thus, the bees flight maneuvers may reflect an optimized visuo-motor strategy to extract depth structure from motion signals. The robustness and simplicity of this strategy offers an efficient solution for 3D-object-recognition without stereo vision, and could be employed by other flying insects, or mobile robots. PMID:26886006

Object Recognition in Flight: How Do Bees Distinguish between 3D Shapes?

PubMed

Werner, Annette; Stürzl, Wolfgang; Zanker, Johannes

2016-01-01

Honeybees (Apis mellifera) discriminate multiple object features such as colour, pattern and 2D shape, but it remains unknown whether and how bees recover three-dimensional shape. Here we show that bees can recognize objects by their three-dimensional form, whereby they employ an active strategy to uncover the depth profiles. We trained individual, free flying honeybees to collect sugar water from small three-dimensional objects made of styrofoam (sphere, cylinder, cuboids) or folded paper (convex, concave, planar) and found that bees can easily discriminate between these stimuli. We also tested possible strategies employed by the bees to uncover the depth profiles. For the card stimuli, we excluded overall shape and pictorial features (shading, texture gradients) as cues for discrimination. Lacking sufficient stereo vision, bees are known to use speed gradients in optic flow to detect edges; could the bees apply this strategy also to recover the fine details of a surface depth profile? Analysing the bees' flight tracks in front of the stimuli revealed specific combinations of flight maneuvers (lateral translations in combination with yaw rotations), which are particularly suitable to extract depth cues from motion parallax. We modelled the generated optic flow and found characteristic patterns of angular displacement corresponding to the depth profiles of our stimuli: optic flow patterns from pure translations successfully recovered depth relations from the magnitude of angular displacements, additional rotation provided robust depth information based on the direction of the displacements; thus, the bees flight maneuvers may reflect an optimized visuo-motor strategy to extract depth structure from motion signals. The robustness and simplicity of this strategy offers an efficient solution for 3D-object-recognition without stereo vision, and could be employed by other flying insects, or mobile robots.

On equivalent characterizations of convexity of functions

NASA Astrophysics Data System (ADS)

Gkioulekas, Eleftherios

2013-04-01

A detailed development of the theory of convex functions, not often found in complete form in most textbooks, is given. We adopt the strict secant line definition as the definitive definition of convexity. We then show that for differentiable functions, this definition becomes logically equivalent with the first derivative monotonicity definition and the tangent line definition. Consequently, for differentiable functions, all three characterizations are logically equivalent.

Asymmetric Bulkheads for Cylindrical Pressure Vessels

NASA Technical Reports Server (NTRS)

Ford, Donald B.

2007-01-01

Asymmetric bulkheads are proposed for the ends of vertically oriented cylindrical pressure vessels. These bulkheads, which would feature both convex and concave contours, would offer advantages over purely convex, purely concave, and flat bulkheads (see figure). Intended originally to be applied to large tanks that hold propellant liquids for launching spacecraft, the asymmetric-bulkhead concept may also be attractive for terrestrial pressure vessels for which there are requirements to maximize volumetric and mass efficiencies. A description of the relative advantages and disadvantages of prior symmetric bulkhead configurations is prerequisite to understanding the advantages of the proposed asymmetric configuration: In order to obtain adequate strength, flat bulkheads must be made thicker, relative to concave and convex bulkheads; the difference in thickness is such that, other things being equal, pressure vessels with flat bulkheads must be made heavier than ones with concave or convex bulkheads. Convex bulkhead designs increase overall tank lengths, thereby necessitating additional supporting structure for keeping tanks vertical. Concave bulkhead configurations increase tank lengths and detract from volumetric efficiency, even though they do not necessitate additional supporting structure. The shape of a bulkhead affects the proportion of residual fluid in a tank that is, the portion of fluid that unavoidably remains in the tank during outflow and hence cannot be used. In this regard, a flat bulkhead is disadvantageous in two respects: (1) It lacks a single low point for optimum placement of an outlet and (2) a vortex that forms at the outlet during outflow prevents a relatively large amount of fluid from leaving the tank. A concave bulkhead also lacks a single low point for optimum placement of an outlet. Like purely concave and purely convex bulkhead configurations, the proposed asymmetric bulkhead configurations would be more mass-efficient than is the flat bulkhead configuration. In comparison with both purely convex and purely concave configurations, the proposed asymmetric configurations would offer greater volumetric efficiency. Relative to a purely convex bulkhead configuration, the corresponding asymmetric configuration would result in a shorter tank, thus demanding less supporting structure. An asymmetric configuration provides a low point for optimum location of a drain, and the convex shape at the drain location minimizes the amount of residual fluid.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, L; Han, Y; Jin, M

Purpose: To develop an iterative reconstruction method for X-ray CT, in which the reconstruction can quickly converge to the desired solution with much reduced projection views. Methods: The reconstruction is formulated as a convex feasibility problem, i.e. the solution is an intersection of three convex sets: 1) data fidelity (DF) set – the L2 norm of the difference of observed projections and those from the reconstructed image is no greater than an error bound; 2) non-negativity of image voxels (NN) set; and 3) piecewise constant (PC) set - the total variation (TV) of the reconstructed image is no greater thanmore » an upper bound. The solution can be found by applying projection onto convex sets (POCS) sequentially for these three convex sets. Specifically, the algebraic reconstruction technique and setting negative voxels as zero are used for projection onto the DF and NN sets, respectively, while the projection onto the PC set is achieved by solving a standard Rudin, Osher, and Fatemi (ROF) model. The proposed method is named as full sequential POCS (FS-POCS), which is tested using the Shepp-Logan phantom and the Catphan600 phantom and compared with two similar algorithms, TV-POCS and CP-TV. Results: Using the Shepp-Logan phantom, the root mean square error (RMSE) of reconstructed images changing along with the number of iterations is used as the convergence measurement. In general, FS- POCS converges faster than TV-POCS and CP-TV, especially with fewer projection views. FS-POCS can also achieve accurate reconstruction of cone-beam CT of the Catphan600 phantom using only 54 views, comparable to that of FDK using 364 views. Conclusion: We developed an efficient iterative reconstruction for sparse-view CT using full sequential POCS. The simulation and physical phantom data demonstrated the computational efficiency and effectiveness of FS-POCS.« less

SU-E-QI-16: Reproducibility of Computed Tomography Quantitative Structural Features Using the FDA Thoracic Phantom Image Database

DOE Office of Scientific and Technical Information (OSTI.GOV)

Budzevich, M; Grove, O; Balagurunathan, Y

Purpose: To assess the reproducibility of quantitative structural features using images from the computed tomography thoracic FDA phantom database under different scanning conditions. Methods: Development of quantitative image features to describe lesion shape and size, beyond conventional RECIST measures, is an evolving area of research in need of benchmarking standards. Gavrielides et al. (2010) scanned a FDA-developed thoracic phantom with nodules of various Hounsfield units (HU) values, shapes and sizes close to vascular structures using several scanners and varying scanning conditions/parameters; these images are in the public domain. We tested six structural features, namely, Convexity, Perimeter, Major Axis, Minor Axis,more » Extent Mean and Eccentricity, to characterize lung nodules. Convexity measures lesion irregularity referenced to a convex surface. Previously, we showed it to have prognostic value in lung adenocarcinoma. The above metrics and RECIST measures were evaluated on three spiculated (8mm/-300HU, 12mm/+30HU and 15mm/+30HU) and two non-spiculated (8mm/+100HU and 10mm/+100HU) nodules (from layout 2) imaged at three different mAs values: 25, 100 and 200 mAs; on a Phillips scanner (16-slice Mx8000-IDT; 3mm slice thickness). The nodules were segmented semi-automatically using a commercial software tool; the same HU range was used for all nodules. Results: Analysis showed convexity having the lowest maximum coefficient of variation (MCV): 1.1% and 0.6% for spiculated and non-spiculated nodules, respectively, much lower compared to RECIST Major and Minor axes whose MCV were 10.1% and 13.4% for spiculated, and 1.9% and 2.3% for non-spiculated nodules, respectively, across the various mAs. MCVs were consistently larger for speculated nodules. In general, the dependence of structural features on mAs (noise) was low. Conclusion: The FDA phantom CT database may be used for benchmarking of structural features for various scanners and scanning conditions; we used only a small fraction of available data. Our feature convexity outperformed other structural features including RECIST measures.« less

Convexity and concavity constants in Lorentz and Marcinkiewicz spaces

NASA Astrophysics Data System (ADS)

Kaminska, Anna; Parrish, Anca M.

2008-07-01

We provide here the formulas for the q-convexity and q-concavity constants for function and sequence Lorentz spaces associated to either decreasing or increasing weights. It yields also the formula for the q-convexity constants in function and sequence Marcinkiewicz spaces. In this paper we extent and enhance the results from [G.J.O. Jameson, The q-concavity constants of Lorentz sequence spaces and related inequalities, Math. Z. 227 (1998) 129-142] and [A. Kaminska, A.M. Parrish, The q-concavity and q-convexity constants in Lorentz spaces, in: Banach Spaces and Their Applications in Analysis, Conference in Honor of Nigel Kalton, May 2006, Walter de Gruyter, Berlin, 2007, pp. 357-373].

Convexity of quantum χ2-divergence.

PubMed

Hansen, Frank

2011-06-21

The general quantum χ(2)-divergence has recently been introduced by Temme et al. [Temme K, Kastoryano M, Ruskai M, Wolf M, Verstrate F (2010) J Math Phys 51:122201] and applied to quantum channels (quantum Markov processes). The quantum χ(2)-divergence is not unique, as opposed to the classical χ(2)-divergence, but depends on the choice of quantum statistics. It was noticed that the elements in a particular one-parameter family of quantum χ(2)-divergences are convex functions in the density matrices (ρ,σ), thus mirroring the convexity of the classical χ(2)(p,q)-divergence in probability distributions (p,q). We prove that any quantum χ(2)-divergence is a convex function in its two arguments.

Weighted mining of massive collections of [Formula: see text]-values by convex optimization.

PubMed

Dobriban, Edgar

2018-06-01

Researchers in data-rich disciplines-think of computational genomics and observational cosmology-often wish to mine large bodies of [Formula: see text]-values looking for significant effects, while controlling the false discovery rate or family-wise error rate. Increasingly, researchers also wish to prioritize certain hypotheses, for example, those thought to have larger effect sizes, by upweighting, and to impose constraints on the underlying mining, such as monotonicity along a certain sequence. We introduce Princessp , a principled method for performing weighted multiple testing by constrained convex optimization. Our method elegantly allows one to prioritize certain hypotheses through upweighting and to discount others through downweighting, while constraining the underlying weights involved in the mining process. When the [Formula: see text]-values derive from monotone likelihood ratio families such as the Gaussian means model, the new method allows exact solution of an important optimal weighting problem previously thought to be non-convex and computationally infeasible. Our method scales to massive data set sizes. We illustrate the applications of Princessp on a series of standard genomics data sets and offer comparisons with several previous 'standard' methods. Princessp offers both ease of operation and the ability to scale to extremely large problem sizes. The method is available as open-source software from github.com/dobriban/pvalue_weighting_matlab (accessed 11 October 2017).

Effective application of optical sensing technology for sustainable liquid level sensing and rainfall measurement

NASA Astrophysics Data System (ADS)

Afzal, Muhammad Hassan Bin

2015-05-01

Rainfall measurement is performed on regular basis to facilitate effectively the weather stations and local inhabitants. Different types of rain gauges are available with different measuring principle for rainfall measurement. In this research work, a novel optical rain sensor is designed, which precisely calculate the rainfall level according to rainfall intensity. This proposed optical rain sensor model introduced in this paper, which is basically designed for remote sensing of rainfall and it designated as R-ORMS (Remote Optical Rainfall Measurement sensor). This sensor is combination of some improved method of tipping bucket rain gauge and most of the optical hydreon rain sensor's principle. This optical sensor can detect the starting time and ending time of rain, rain intensity and rainfall level. An infrared beam from Light Emitting Diode (LED) through powerful convex lens can accurately determines the diameter of each rain drops by total internal reflection principle. Calculations of these accumulative results determine the rain intensity and rainfall level. Accurate rainfall level is determined by internal optical LED based sensor which is embedded in bucket wall. This internal sensor is also following the total internal reflection (TIR) principle and the Fresnel's law. This is an entirely novel design of optical sensing principle based rain sensor and also suitable for remote sensing rainfall level. The performance of this proposed sensor has been comprehensively compared with other sensors with similar attributes and it showed better and sustainable result. Future related works have been proposed at the end of this paper, to provide improved and enhanced performance of proposed novel rain sensor.

A Sparse Representation-Based Deployment Method for Optimizing the Observation Quality of Camera Networks

PubMed Central

Wang, Chang; Qi, Fei; Shi, Guangming; Wang, Xiaotian

2013-01-01

Deployment is a critical issue affecting the quality of service of camera networks. The deployment aims at adopting the least number of cameras to cover the whole scene, which may have obstacles to occlude the line of sight, with expected observation quality. This is generally formulated as a non-convex optimization problem, which is hard to solve in polynomial time. In this paper, we propose an efficient convex solution for deployment optimizing the observation quality based on a novel anisotropic sensing model of cameras, which provides a reliable measurement of the observation quality. The deployment is formulated as the selection of a subset of nodes from a redundant initial deployment with numerous cameras, which is an ℓ0 minimization problem. Then, we relax this non-convex optimization to a convex ℓ1 minimization employing the sparse representation. Therefore, the high quality deployment is efficiently obtained via convex optimization. Simulation results confirm the effectiveness of the proposed camera deployment algorithms. PMID:23989826

Entropy and convexity for nonlinear partial differential equations

PubMed Central

Ball, John M.; Chen, Gui-Qiang G.

2013-01-01

Partial differential equations are ubiquitous in almost all applications of mathematics, where they provide a natural mathematical description of many phenomena involving change in physical, chemical, biological and social processes. The concept of entropy originated in thermodynamics and statistical physics during the nineteenth century to describe the heat exchanges that occur in the thermal processes in a thermodynamic system, while the original notion of convexity is for sets and functions in mathematics. Since then, entropy and convexity have become two of the most important concepts in mathematics. In particular, nonlinear methods via entropy and convexity have been playing an increasingly important role in the analysis of nonlinear partial differential equations in recent decades. This opening article of the Theme Issue is intended to provide an introduction to entropy, convexity and related nonlinear methods for the analysis of nonlinear partial differential equations. We also provide a brief discussion about the content and contributions of the papers that make up this Theme Issue. PMID:24249768

Stochastic Dual Algorithm for Voltage Regulation in Distribution Networks with Discrete Loads: Preprint

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dall-Anese, Emiliano; Zhou, Xinyang; Liu, Zhiyuan

This paper considers distribution networks with distributed energy resources and discrete-rate loads, and designs an incentive-based algorithm that allows the network operator and the customers to pursue given operational and economic objectives, while concurrently ensuring that voltages are within prescribed limits. Four major challenges include: (1) the non-convexity from discrete decision variables, (2) the non-convexity due to a Stackelberg game structure, (3) unavailable private information from customers, and (4) different update frequency from two types of devices. In this paper, we first make convex relaxation for discrete variables, then reformulate the non-convex structure into a convex optimization problem together withmore » pricing/reward signal design, and propose a distributed stochastic dual algorithm for solving the reformulated problem while restoring feasible power rates for discrete devices. By doing so, we are able to statistically achieve the solution of the reformulated problem without exposure of any private information from customers. Stability of the proposed schemes is analytically established and numerically corroborated.« less

H∞ memory feedback control with input limitation minimization for offshore jacket platform stabilization

NASA Astrophysics Data System (ADS)

Yang, Jia Sheng

2018-06-01

In this paper, we investigate a H∞ memory controller with input limitation minimization (HMCIM) for offshore jacket platforms stabilization. The main objective of this study is to reduce the control consumption as well as protect the actuator when satisfying the requirement of the system performance. First, we introduce a dynamic model of offshore platform with low order main modes based on mode reduction method in numerical analysis. Then, based on H∞ control theory and matrix inequality techniques, we develop a novel H∞ memory controller with input limitation. Furthermore, a non-convex optimization model to minimize input energy consumption is proposed. Since it is difficult to solve this non-convex optimization model by optimization algorithm, we use a relaxation method with matrix operations to transform this non-convex optimization model to be a convex optimization model. Thus, it could be solved by a standard convex optimization solver in MATLAB or CPLEX. Finally, several numerical examples are given to validate the proposed models and methods.

Entropy and convexity for nonlinear partial differential equations.

PubMed

Ball, John M; Chen, Gui-Qiang G

2013-12-28

Partial differential equations are ubiquitous in almost all applications of mathematics, where they provide a natural mathematical description of many phenomena involving change in physical, chemical, biological and social processes. The concept of entropy originated in thermodynamics and statistical physics during the nineteenth century to describe the heat exchanges that occur in the thermal processes in a thermodynamic system, while the original notion of convexity is for sets and functions in mathematics. Since then, entropy and convexity have become two of the most important concepts in mathematics. In particular, nonlinear methods via entropy and convexity have been playing an increasingly important role in the analysis of nonlinear partial differential equations in recent decades. This opening article of the Theme Issue is intended to provide an introduction to entropy, convexity and related nonlinear methods for the analysis of nonlinear partial differential equations. We also provide a brief discussion about the content and contributions of the papers that make up this Theme Issue.

The roles of the convex hull and the number of potential intersections in performance on visually presented traveling salesperson problems.

PubMed

Vickers, Douglas; Lee, Michael D; Dry, Matthew; Hughes, Peter

2003-10-01

The planar Euclidean version of the traveling salesperson problem requires finding the shortest tour through a two-dimensional array of points. MacGregor and Ormerod (1996) have suggested that people solve such problems by using a global-to-local perceptual organizing process based on the convex hull of the array. We review evidence for and against this idea, before considering an alternative, local-to-global perceptual process, based on the rapid automatic identification of nearest neighbors. We compare these approaches in an experiment in which the effects of number of convex hull points and number of potential intersections on solution performance are measured. Performance worsened with more points on the convex hull and with fewer potential intersections. A measure of response uncertainty was unaffected by the number of convex hull points but increased with fewer potential intersections. We discuss a possible interpretation of these results in terms of a hierarchical solution process based on linking nearest neighbor clusters.

Convexity Conditions and the Legendre-Fenchel Transform for the Product of Finitely Many Positive Definite Quadratic Forms

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhao Yunbin, E-mail: zhaoyy@maths.bham.ac.u

2010-12-15

While the product of finitely many convex functions has been investigated in the field of global optimization, some fundamental issues such as the convexity condition and the Legendre-Fenchel transform for the product function remain unresolved. Focusing on quadratic forms, this paper is aimed at addressing the question: When is the product of finitely many positive definite quadratic forms convex, and what is the Legendre-Fenchel transform for it? First, we show that the convexity of the product is determined intrinsically by the condition number of so-called 'scaled matrices' associated with quadratic forms involved. The main result claims that if the conditionmore » number of these scaled matrices are bounded above by an explicit constant (which depends only on the number of quadratic forms involved), then the product function is convex. Second, we prove that the Legendre-Fenchel transform for the product of positive definite quadratic forms can be expressed, and the computation of the transform amounts to finding the solution to a system of equations (or equally, finding a Brouwer's fixed point of a mapping) with a special structure. Thus, a broader question than the open 'Question 11' in Hiriart-Urruty (SIAM Rev. 49, 225-273, 2007) is addressed in this paper.« less

CudaChain: an alternative algorithm for finding 2D convex hulls on the GPU.

PubMed

Mei, Gang

2016-01-01

This paper presents an alternative GPU-accelerated convex hull algorithm and a novel S orting-based P reprocessing A pproach (SPA) for planar point sets. The proposed convex hull algorithm termed as CudaChain consists of two stages: (1) two rounds of preprocessing performed on the GPU and (2) the finalization of calculating the expected convex hull on the CPU. Those interior points locating inside a quadrilateral formed by four extreme points are first discarded, and then the remaining points are distributed into several (typically four) sub regions. For each subset of points, they are first sorted in parallel; then the second round of discarding is performed using SPA; and finally a simple chain is formed for the current remaining points. A simple polygon can be easily generated by directly connecting all the chains in sub regions. The expected convex hull of the input points can be finally obtained by calculating the convex hull of the simple polygon. The library Thrust is utilized to realize the parallel sorting, reduction, and partitioning for better efficiency and simplicity. Experimental results show that: (1) SPA can very effectively detect and discard the interior points; and (2) CudaChain achieves 5×-6× speedups over the famous Qhull implementation for 20M points.

A parallel Discrete Element Method to model collisions between non-convex particles

NASA Astrophysics Data System (ADS)

Rakotonirina, Andriarimina Daniel; Delenne, Jean-Yves; Wachs, Anthony

2017-06-01

In many dry granular and suspension flow configurations, particles can be highly non-spherical. It is now well established in the literature that particle shape affects the flow dynamics or the microstructure of the particles assembly in assorted ways as e.g. compacity of packed bed or heap, dilation under shear, resistance to shear, momentum transfer between translational and angular motions, ability to form arches and block the flow. In this talk, we suggest an accurate and efficient way to model collisions between particles of (almost) arbitrary shape. For that purpose, we develop a Discrete Element Method (DEM) combined with a soft particle contact model. The collision detection algorithm handles contacts between bodies of various shape and size. For nonconvex bodies, our strategy is based on decomposing a non-convex body into a set of convex ones. Therefore, our novel method can be called "glued-convex method" (in the sense clumping convex bodies together), as an extension of the popular "glued-spheres" method, and is implemented in our own granular dynamics code Grains3D. Since the whole problem is solved explicitly, our fully-MPI parallelized code Grains3D exhibits a very high scalability when dynamic load balancing is not required. In particular, simulations on up to a few thousands cores in configurations involving up to a few tens of millions of particles can readily be performed. We apply our enhanced numerical model to (i) the collapse of a granular column made of convex particles and (i) the microstructure of a heap of non-convex particles in a cylindrical reactor.

Real-time data processing for in-line monitoring of a pharmaceutical coating process by optical coherence tomography

NASA Astrophysics Data System (ADS)

Markl, Daniel; Ziegler, Jakob; Hannesschläger, Günther; Sacher, Stephan; Buchsbaum, Andreas; Leitner, Michael; Khinast, Johannes G.

2014-05-01

Coating of tablets is a widely applied unit operation in the pharmaceutical industry. Thickness and uniformity of the coating layer are crucial for efficacy as well as for compliance. Not only due to different initiatives it is thus essential to monitor and control the coating process in-line. Optical coherence tomography (OCT) was already shown in previous works to be a suitable candidate for in-line monitoring of coating processes. However, to utilize the full potential of the OCT technology an automatic evaluation of the OCT measurements is essential. The automatic evaluation is currently implemented in MATLAB and includes several steps: (1) extraction of features of each A-scan, (2) classification of Ascan measurements based on their features, (3) detection of interfaces (air/coating and coating/tablet core), (4) correction of distortions due to the curvature of the bi-convex tablets and the oblique orientation of the tablets, and (5) determining the coating thickness. The algorithm is tested on OCT data acquired by moving the sensor head of the OCT system across a static tablet bed. The coating thickness variations of single tablets (i.e., intra-tablet coating variability) can additionally be analyzed as OCT allows the measurement of the coating thickness on multiple displaced positions on one single tablet. Specifically, the information about those parameters emphasizes the high capability of the OCT technology to improve process understanding and to assure a high product quality.

Semidefinite Relaxation-Based Optimization of Multiple-Input Wireless Power Transfer Systems

NASA Astrophysics Data System (ADS)

Lang, Hans-Dieter; Sarris, Costas D.

2017-11-01

An optimization procedure for multi-transmitter (MISO) wireless power transfer (WPT) systems based on tight semidefinite relaxation (SDR) is presented. This method ensures physical realizability of MISO WPT systems designed via convex optimization -- a robust, semi-analytical and intuitive route to optimizing such systems. To that end, the nonconvex constraints requiring that power is fed into rather than drawn from the system via all transmitter ports are incorporated in a convex semidefinite relaxation, which is efficiently and reliably solvable by dedicated algorithms. A test of the solution then confirms that this modified problem is equivalent (tight relaxation) to the original (nonconvex) one and that the true global optimum has been found. This is a clear advantage over global optimization methods (e.g. genetic algorithms), where convergence to the true global optimum cannot be ensured or tested. Discussions of numerical results yielded by both the closed-form expressions and the refined technique illustrate the importance and practicability of the new method. It, is shown that this technique offers a rigorous optimization framework for a broad range of current and emerging WPT applications.

Computational Efficiency of the Simplex Embedding Method in Convex Nondifferentiable Optimization

NASA Astrophysics Data System (ADS)

Kolosnitsyn, A. V.

2018-02-01

The simplex embedding method for solving convex nondifferentiable optimization problems is considered. A description of modifications of this method based on a shift of the cutting plane intended for cutting off the maximum number of simplex vertices is given. These modification speed up the problem solution. A numerical comparison of the efficiency of the proposed modifications based on the numerical solution of benchmark convex nondifferentiable optimization problems is presented.

Another convex combination of product states for the separable Werner state

DOE Office of Scientific and Technical Information (OSTI.GOV)

Azuma, Hiroo; Ban, Masashi; CREST, Japan Science and Technology Agency, 1-1-9 Yaesu, Chuo-ku, Tokyo 103-0028

2006-03-15

In this paper, we write down the separable Werner state in a two-qubit system explicitly as a convex combination of product states, which is different from the convex combination obtained by Wootters' method. The Werner state in a two-qubit system has a single real parameter and varies from inseparable to separable according to the value of its parameter. We derive a hidden variable model that is induced by our decomposed form for the separable Werner state. From our explicit form of the convex combination of product states, we understand the following: The critical point of the parameter for separability ofmore » the Werner state comes from positivity of local density operators of the qubits.« less

Thermal Protection System with Staggered Joints

NASA Technical Reports Server (NTRS)

Simon, Xavier D. (Inventor); Robinson, Michael J. (Inventor); Andrews, Thomas L. (Inventor)

2014-01-01

The thermal protection system disclosed herein is suitable for use with a spacecraft such as a reentry module or vehicle, where the spacecraft has a convex surface to be protected. An embodiment of the thermal protection system includes a plurality of heat resistant panels, each having an outer surface configured for exposure to atmosphere, an inner surface opposite the outer surface and configured for attachment to the convex surface of the spacecraft, and a joint edge defined between the outer surface and the inner surface. The joint edges of adjacent ones of the heat resistant panels are configured to mate with each other to form staggered joints that run between the peak of the convex surface and the base section of the convex surface.

A fast adaptive convex hull algorithm on two-dimensional processor arrays with a reconfigurable BUS system

NASA Technical Reports Server (NTRS)

Olariu, S.; Schwing, J.; Zhang, J.

1991-01-01

A bus system that can change dynamically to suit computational needs is referred to as reconfigurable. We present a fast adaptive convex hull algorithm on a two-dimensional processor array with a reconfigurable bus system (2-D PARBS, for short). Specifically, we show that computing the convex hull of a planar set of n points taken O(log n/log m) time on a 2-D PARBS of size mn x n with 3 less than or equal to m less than or equal to n. Our result implies that the convex hull of n points in the plane can be computed in O(1) time in a 2-D PARBS of size n(exp 1.5) x n.

The concave cusp as a determiner of figure-ground.

PubMed

Stevens, K A; Brookes, A

1988-01-01

The tendency to interpret as figure, relative to background, those regions that are lighter, smaller, and, especially, more convex is well known. Wherever convex opaque objects abut or partially occlude one another in an image, the points of contact between the silhouettes form concave cusps, each indicating the local assignment of figure versus ground across the contour segments. It is proposed that this local geometric feature is a preattentive determiner of figure-ground perception and that it contributes to the previously observed tendency for convexity preference. Evidence is presented that figure-ground assignment can be determined solely on the basis of the concave cusp feature, and that the salience of the cusp derives from local geometry and not from adjacent contour convexity.

Remodelling of the bovine placenta: Comprehensive morphological and histomorphological characterization at the late embryonic and early accelerated fetal growth stages.

PubMed

Estrella, Consuelo Amor S; Kind, Karen L; Derks, Anna; Xiang, Ruidong; Faulkner, Nicole; Mohrdick, Melina; Fitzsimmons, Carolyn; Kruk, Zbigniew; Grutzner, Frank; Roberts, Claire T; Hiendleder, Stefan

2017-07-01

Placental function impacts growth and development with lifelong consequences for performance and health. We provide novel insights into placental development in bovine, an important agricultural species and biomedical model. Concepti with defined genetics and sex were recovered from nulliparous dams managed under standardized conditions to study placental gross morphological and histomorphological parameters at the late embryo (Day48) and early accelerated fetal growth (Day153) stages. Placentome number increased 3-fold between Day48 and Day153. Placental barrier thickness was thinner, and volume of placental components, and surface areas and densities were higher at Day153 than Day48. We confirmed two placentome types, flat and convex. At Day48, there were more convex than flat placentomes, and convex placentomes had a lower proportion of maternal connective tissue (P < 0.01). However, this was reversed at Day153, where convex placentomes were lower in number and had greater volume of placental components (P < 0.01- P < 0.001) and greater surface area (P < 0.001) than flat placentomes. Importantly, embryo (r = 0.50) and fetal (r = 0.30) weight correlated with total number of convex but not flat placentomes. Extensive remodelling of the placenta increases capacity for nutrient exchange to support rapidly increasing embryo-fetal weight from Day48 to Day153. The cellular composition of convex placentomes, and exclusive relationships between convex placentome number and embryo-fetal weight, provide strong evidence for these placentomes as drivers of prenatal growth. The difference in proportion of maternal connective tissue between placentome types at Day48 suggests that this tissue plays a role in determining placentome shape, further highlighting the importance of early placental development. Copyright © 2017 Elsevier Ltd. All rights reserved.

Sclerochronology of Holocene oyster shells (Crassostrea gigas) from the West Coast of Bohai Sea, China

NASA Astrophysics Data System (ADS)

Fan, C.; Koeniger, P.; Wang, H.; Frechen, M.

2009-04-01

Sclerochronology, the study of periodic increments in skeletal organisms, can decipher the life history and environmental records preserved in fossil shells. Although there have been a number of studies that apply isotopic analyses to shells in open ocean and fresh water, investigations for brackish environments are rare. One of the common inhabitants in estuaries is the Crassostrea oyster. Kirby et al. (1998) demonstrated a close correspondence between the ligamental increments of convex and concave bands and yearly ^18O cycles; Andrus and Crowe (2000) found a close correspondence between translucent growth bands on the cross-section of the hinge and yearly ^18O cycles. They conclude that the morphological features on hinge and growth bands on the cross-section are formed annually and can be used to determine accurately age and growth rate in this species. However, Surge et al. (2001) could not find that these morphologic features have seasonal significance in the C. virginica shells. Therefore, these concave ridges are not reliable independent proxies of seasonality. These studies were carried out with C. virginica shells; none was studied with nature C. gigas, which was widely distributed along the Pacific coastal area. C. gigas has been introduced from its native home to all over the world, ranging from North America to Australia and Europe; it has become an important commercial harvest in many of these places. Buried Holocene oyster shells of C. gigas were sampled from a huge buried oyster reef on the West of Bohai Sea, China. One of these shells was selected for high resolution micro-sampling and stable isotope analyses testing the assumption that C. gigas ligamental increments are annual in nature. We analyzed 236 consecutive samples from the shell to show that morphologic features both on hinge and cross-section are annual by comparing them to the ^18O profiles. We tested the assumption that the morphologic features of C.gigas are delineated by convex tops and concave bottoms on hinge and corresponding translucent growth bands on cross-section. The shell has 13.5 ligamental increments, based on 13.5 convex bands and 13 concave bottoms on hinge. Convex tops correspond to ^18O minima (summers), whereas concave bottoms correspond to ^18O maxima, which were formed during the low temperature of winter in the study area. We demonstrate that the ligamental increments of convex tops, concave bottoms and translucent growth bands in the studied C. gigas shell are suitable indicators of annual growth increments. The life spans, growth rates, and the timing of death can be determined from the ligament increments and isotope profiles of buried oyster shells.

Polar DuaLs of Convex Bodies

DTIC Science & Technology

1990-01-01

Verlag 1976. 17. C. G. Lekkerkerker, Geometry of Numbers, Wolters-Noordhoff, Groningen, 1969. 18. E . Lutwak , "Dual Mixed Volumes," Pacific Journal of...Mathematics, Vol. 58, No. 2, 1975. 19. E . Lutwak , "On Cross-Sectional Measures of Polar Reciprocal Convex Bodies," Geometriae Dedicata 5, (1976) 79-80...20. E . Lutwak , "Blaschke-Santal6 Inequality, Discrete Geometry and Convexity," Annals of the New York Academy of Sciences 440 (1985) pp 106-112. 21. V

Single lens laser beam shaper

DOEpatents

Liu, Chuyu [Newport News, VA; Zhang, Shukui [Yorktown, VA

2011-10-04

A single lens bullet-shaped laser beam shaper capable of redistributing an arbitrary beam profile into any desired output profile comprising a unitary lens comprising: a convex front input surface defining a focal point and a flat output portion at the focal point; and b) a cylindrical core portion having a flat input surface coincident with the flat output portion of the first input portion at the focal point and a convex rear output surface remote from the convex front input surface.

Film cooling on a convex wall: Heat transfer and hydrodynamic measurements for full and partial coverage

NASA Technical Reports Server (NTRS)

Furuhama, K.; Moffat, R. J.; Johnston, J. P.; Kays, W. M.

1985-01-01

Turbine-blade cooling is an important issue for high-efficiency turbine engines, and discrete-hole injection is widely used as a cooling method. In the present study, detailed measurements were made of the heat transfer and hydrodynamics of a film-cooled flow on a convex wall, both for full and partial coverage. Two important parameters were altered: the blowing ratio, m, and the number of rows of injection holes. Three values of m were tested: m = 0.2, 0.4, and 0.6. In the blown region, m = 0.4 results in the lowest Stanton numbers of the three blowing ratios tested. This indicates that the value of m = 0.4 is near optimum on the convex wall from the point of view of cooling effect by injection. In the recovery region, Stanton numbers gradually approach the no injection values. Although the heat-transfer behavior during recovery from injection looks relatively complicated, the behavior of Stanton number can be explained in terms of two mechanisms: recovery from the thermal effect of injection and recovery from the turbulence augmentation. This interpretation of the data is supported by the hydrodynamic and temperture-profile measurements. For partial blowing cases, the data follow the full-coverage values inside the blown region. In the unblown region, both in the curved and in the flat plate, the effect of the number of blown rows is clearly seen. Hydrodynamic boundary-layer profiles were measured with the aid of a triple hot-water probe. Three mean-velocity components and six turbulence quantities were simultaneously measured, and inside the blown region strong three-dimensionality was observed.

ON THE STRUCTURE OF \\mathcal{H}_{n - 1}-ALMOST EVERYWHERE CONVEX HYPERSURFACES IN \\mathbf{R}^{n + 1}

NASA Astrophysics Data System (ADS)

Dmitriev, V. G.

1982-04-01

It is proved that a hypersurface f imbedded in \\mathbf{R}^{n + 1}, n \\geq 2, which is locally convex at all points except for a closed set E with (n - 1)-dimensional Hausdorff measure \\mathcal{K}_{n - 1}(E) = 0, and strictly convex near E is in fact locally convex everywhere. The author also gives various corollaries. In particular, let M be a complete two-dimensional Riemannian manifold of nonnegative curvature K and E \\subset M a closed subset for which \\mathcal{K}_1(E) = 0. Assume further that there exists a neighborhood U \\supset E such that K(x) > 0 for x \\in U \\setminus E, f \\colon M \\to \\mathbf{R}^3 is such that f\\big\\vert _{U \\setminus E} is an imbedding, and f\\big\\vert _{M \\setminus E} \\in C^{1, \\alpha}, \\alpha > 2/3. Then f(M) is a complete convex surface in \\mathbf{R}^3. This result is an generalization of results in the paper reviewed in MR 51 # 11374.Bibliography: 19 titles.

Adaptable Diffraction Gratings With Wavefront Transformation

NASA Technical Reports Server (NTRS)

Iazikov, Dmitri; Mossberg, Thomas W.; Greiner, Christoph M.

2010-01-01

Diffraction gratings are optical components with regular patterns of grooves, which angularly disperse incoming light by wavelength. Traditional diffraction gratings have static planar, concave, or convex surfaces. However, if they could be made so that they can change the surface curvature at will, then they would be able to focus on particular segments, self-calibrate, or perform fine adjustments. This innovation creates a diffraction grating on a deformable surface. This surface could be bent at will, resulting in a dynamic wavefront transformation. This allows for self-calibration, compensation for aberrations, enhancing image resolution in a particular area, or performing multiple scans using different wavelengths. A dynamic grating gives scientists a new ability to explore wavefronts from a variety of viewpoints.

History of mirrors dating back 8000 years.

PubMed

Enoch, Jay M

2006-10-01

The purpose of this study is to consider the ancient history and early development of mirrors, because mirrors played a key role in refraction and magnification for an extended period of time before the invention of spectacles, including broad use in Roman times. The earliest known manufactured mirrors (approximately 8000 years old) have been found in Anatolia (south central modern-day Turkey). These were made from obsidian (volcanic glass), had a convex surface and remarkably good optical quality. Mirrors from more recent periods have been found both in Egypt and Mesopotamia and still later in China and in the New World. In each of these areas, mirrors were in use by approximately 2000 BC or 4000 years ago.

Small size yet big action: a simple sulfate anion templated a discrete 78-nuclearity silver sulfur nanocluster with a multishell structure.

PubMed

Cheng, Li-Ping; Wang, Zhi; Wu, Qiao-Yu; Su, Hai-Feng; Peng, Tao; Luo, Geng-Geng; Li, Yan-An; Sun, Di; Zheng, Lan-Sun

2018-03-07

A discrete 78-nucleus silver-sulfur nanocluster with a sulfate-centered multishell structure was isolated and characterized. Its crystal structure revealed 18 and 60 Ag atoms in the inner and outer shell, respectively. The inner shell of 18-nuclearity Ag atoms is a very rare convex polyhedron featuring an elongated triangular orthobicupola. The incorporation of a sulfate anion and multishell arrangement in the nanocluster led to a dramatic decrease in the band gap (E g = 1.40 eV). Our study showed that simple anions can also induce the formation of high-nuclearity silver clusters with excellent optical properties.

Growth of benzil crystals by vertical dynamic gradient freeze technique in a transparent furnace

NASA Astrophysics Data System (ADS)

Lan, C. W.; Song, C. R.

1997-09-01

The vertical dynamic gradient freeze technique using a transparent furnace was applied to the growth of benzil single crystals. A flat-bottom ampoule with a <0001> seed was used for growth. During crystal growth, dynamic heating profiles were controlled through a computer, and the growth interface was recorded by a CCD camera. Computer simulation was also conducted, and the calculated convex interface and dynamic growth rate were consistent with the observed ones for various growth conditions. Conditions for growing single crystals were also determined, and they were mainly limited by constitutional supercooling. As the grown crystals were clear in appearance, their optical absorption spectra were insensitive to growth conditions and post-annealing.

Non-convex dissipation potentials in multiscale non-equilibrium thermodynamics

NASA Astrophysics Data System (ADS)

Janečka, Adam; Pavelka, Michal

2018-04-01

Reformulating constitutive relation in terms of gradient dynamics (being derivative of a dissipation potential) brings additional information on stability, metastability and instability of the dynamics with respect to perturbations of the constitutive relation, called CR-stability. CR-instability is connected to the loss of convexity of the dissipation potential, which makes the Legendre-conjugate dissipation potential multivalued and causes dissipative phase transitions that are not induced by non-convexity of free energy, but by non-convexity of the dissipation potential. CR-stability of the constitutive relation with respect to perturbations is then manifested by constructing evolution equations for the perturbations in a thermodynamically sound way (CR-extension). As a result, interesting experimental observations of behavior of complex fluids under shear flow and supercritical boiling curve can be explained.

Wide-angle flat field telescope

NASA Technical Reports Server (NTRS)

Hallam, K. L.; Howell, B. J.; Wilson, M. E.

1986-01-01

Described is an unobscured three mirror wide angle telescopic imaging system comprised of an input baffle which provides a 20 deg (Y axis) x 30 deg (X axis) field of view, a primary mirror having a convex spherical surface, a secondary mirror having a concave ellipsoidal reflecting surface, a tertiary mirror having a concave spherical reflecting surface. The mirrors comprise mirror elements which are offset segments of parent mirrors whose axes and vertices commonly lie on the system's optical axis. An iris diaphragm forming an aperture stop is located between the secondary and tertiary mirror with its center also being coincident with the optical axis and being further located at the beam waist of input light beams reflected from the primary and secondary mirror surfaces. At the system focus following the tertiary mirror is located a flat detector which may be, for example, a TV imaging tube or a photographic film. When desirable, a spectral transmission filter is placed in front of the detector in close proximity thereto.

Fast calculation of the light differential scattering cross section of optically soft and convex bodies

NASA Astrophysics Data System (ADS)

Gruy, Frédéric

2014-02-01

Depending on the range of size and the refractive index value, an optically soft particle follows Rayleigh-Debye-Gans or RDG approximation or Van de Hulst approximation. Practically the first one is valid for small particles whereas the second one works for large particles. Klett and Sutherland (Klett JD, Sutherland RA. App. Opt. 1992;31:373) proved that the Wentzel-Kramers-Brillouin or WKB approximation leads to accurate values of the differential scattering cross section of sphere and cylinder over a wide range of size. In this paper we extend the work of Klett and Sutherland by proposing a method allowing a fast calculation of the differential scattering cross section for any shape of particle with a given orientation and illuminated by unpolarized light. Our method is based on a geometrical approximation of the particle by replacing each geometrical cross section by an ellipse and then by exactly evaluating the differential scattering cross section of the newly generated body. The latter one contains only two single integrals.

Super-resolution for scanning light stimulation systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bitzer, L. A.; Neumann, K.; Benson, N., E-mail: niels.benson@uni-due.de

Super-resolution (SR) is a technique used in digital image processing to overcome the resolution limitation of imaging systems. In this process, a single high resolution image is reconstructed from multiple low resolution images. SR is commonly used for CCD and CMOS (Complementary Metal-Oxide-Semiconductor) sensor images, as well as for medical applications, e.g., magnetic resonance imaging. Here, we demonstrate that super-resolution can be applied with scanning light stimulation (LS) systems, which are common to obtain space-resolved electro-optical parameters of a sample. For our purposes, the Projection Onto Convex Sets (POCS) was chosen and modified to suit the needs of LS systems.more » To demonstrate the SR adaption, an Optical Beam Induced Current (OBIC) LS system was used. The POCS algorithm was optimized by means of OBIC short circuit current measurements on a multicrystalline solar cell, resulting in a mean square error reduction of up to 61% and improved image quality.« less

On The Behavior of Subgradient Projections Methods for Convex Feasibility Problems in Euclidean Spaces

PubMed Central

Butnariu, Dan; Censor, Yair; Gurfil, Pini; Hadar, Ethan

2010-01-01

We study some methods of subgradient projections for solving a convex feasibility problem with general (not necessarily hyperplanes or half-spaces) convex sets in the inconsistent case and propose a strategy that controls the relaxation parameters in a specific self-adapting manner. This strategy leaves enough user-flexibility but gives a mathematical guarantee for the algorithm’s behavior in the inconsistent case. We present numerical results of computational experiments that illustrate the computational advantage of the new method. PMID:20182556

On The Behavior of Subgradient Projections Methods for Convex Feasibility Problems in Euclidean Spaces.

PubMed

Butnariu, Dan; Censor, Yair; Gurfil, Pini; Hadar, Ethan

2008-07-03

We study some methods of subgradient projections for solving a convex feasibility problem with general (not necessarily hyperplanes or half-spaces) convex sets in the inconsistent case and propose a strategy that controls the relaxation parameters in a specific self-adapting manner. This strategy leaves enough user-flexibility but gives a mathematical guarantee for the algorithm's behavior in the inconsistent case. We present numerical results of computational experiments that illustrate the computational advantage of the new method.

Additive manufacturing of transparent fused quartz

NASA Astrophysics Data System (ADS)

Luo, Junjie; Hostetler, John M.; Gilbert, Luke; Goldstein, Jonathan T.; Urbas, Augustine M.; Bristow, Douglas A.; Landers, Robert G.; Kinzel, Edward C.

2018-04-01

This paper investigates a filament-fed process for additive manufacturing (AM) of fused quartz. Glasses such as fused quartz have significant scientific and engineering applications, which include optics, communications, electronics, and hermetic seals. AM has several attractive benefits such as increased design freedom, faster prototyping, and lower processing costs for small production volumes. However, current research into glass AM has focused primarily on nonoptical applications. Fused quartz is studied here because of its desirability for use in high-quality optics due to its high transmissivity and thermal stability. Fused quartz filaments are fed into a CO2 laser-generated molten region, smoothly depositing material onto the workpiece. Spectroscopy and pyrometry are used to measure the thermal radiation incandescently emitted from the molten region. The effects of the laser power and scan speed are determined by measuring the morphology of single tracks. Thin walls are printed to study the effects of layer-to-layer height. This information is used to deposit solid pieces including a cylindrical-convex shape capable of focusing visible light. The transmittance and index homogeneity of the printed fused quartz are measured. These results show that the filament-fed process has the potential to print transmissive optics.

Water window imaging x ray microscope

NASA Technical Reports Server (NTRS)

Hoover, Richard B. (Inventor)

1992-01-01

A high resolution x ray microscope for imaging microscopic structures within biological specimens has an optical system including a highly polished primary and secondary mirror coated with identical multilayer coatings, the mirrors acting at normal incidence. The coatings have a high reflectivity in the narrow wave bandpass between 23.3 and 43.7 angstroms and have low reflectivity outside of this range. The primary mirror has a spherical concave surface and the secondary mirror has a spherical convex surface. The radii of the mirrors are concentric about a common center of curvature on the optical axis of the microscope extending from the object focal plane to the image focal plane. The primary mirror has an annular configuration with a central aperture and the secondary mirror is positioned between the primary mirror and the center of curvature for reflecting radiation through the aperture to a detector. An x ray filter is mounted at the stage end of the microscope, and film sensitive to x rays in the desired band width is mounted in a camera at the image plane of the optical system. The microscope is mounted within a vacuum chamber for minimizing the absorption of x rays in air from a source through the microscope.

Federal Motor Carrier Safety Administration’s advanced system testing utilizing a data acquisition system on the highways (FAST DASH) safety technology evaluation project #3 : novel convex mirrors.

DOT National Transportation Integrated Search

2016-11-01

An independent evaluation of a set of novel prototype mirrors was conducted to determine whether the mirrors perform as well as traditional production mirrors across the basic functions of field of view (FOV), image distortion, and distance estimatio...

SOFIA secondary mirror Hindle test analysis

NASA Astrophysics Data System (ADS)

Davis, Paul K.

2003-02-01

The Stratospheric Observatory for Infrared Astronomy (SOFIA) is a NASA facility, nearing completion, consisting of an infrared telescope of 2.5 meter system aperture flying in a modified Boeing 747. Its Cassegrain secondary mirror has recently completed polishing. The SOFIA Project Office at Ames Research Center considered it important to perform an independent analysis of secondary mirror figure. The polishing was controlled by the standard test for a convex hyperboloid, the Hindle test, in a modified form with a meniscus lens partially reflecting on the concave face, rather than a fully reflecting mirror with a central hole. The spacing between this meniscus lens and the secondary mirror was controlled by three peripherally located spacing spheres. This necessitated special analysis to determine what the resulting curvature and conic constant of the mirror would be, if manufacturing imprecisions of the test set-up components were to be taken into account. This set-up was specially programmed, and the resulting hyperboloid calculated for the nominal case, and all extreme cases from the reported error limits on the manufacturing of the components. The results were then verified using the standard program CODE-V of Optical Research Associates. The conclusion is that the secondary mirror has a vertex radius of curvature of 954.05 mm +/- .1 mm (design value: 954.13), and a conic constant of -1.2965 +/- .001 (dimensionless, design value: -1.298). Such small divergences from design are to be expected, and these are within the refocusing ability of SOFIA, and would result in an acceptably small amount of spherical aberration in the image.

Improved flight-simulator viewing lens

NASA Technical Reports Server (NTRS)

Kahlbaum, W. M.

1979-01-01

Triplet lens system uses two acrylic plastic double convex lenses and one polystyrene plastic single convex lens to reduce chromatic distortion and lateral aberation, especially at large field angles within in-line systems of flight simulators.

Stereotype locally convex spaces

NASA Astrophysics Data System (ADS)

Akbarov, S. S.

2000-08-01

We give complete proofs of some previously announced results in the theory of stereotype (that is, reflexive in the sense of Pontryagin duality) locally convex spaces. These spaces have important applications in topological algebra and functional analysis.

Interface Shape Control Using Localized Heating during Bridgman Growth

NASA Technical Reports Server (NTRS)

Volz, M. P.; Mazuruk, K.; Aggarwal, M. D.; Croll, A.

2008-01-01

Numerical calculations were performed to assess the effect of localized radial heating on the melt-crystal interface shape during vertical Bridgman growth. System parameters examined include the ampoule, melt and crystal thermal conductivities, the magnitude and width of localized heating, and the latent heat of crystallization. Concave interface shapes, typical of semiconductor systems, could be flattened or made convex with localized heating. Although localized heating caused shallower thermal gradients ahead of the interface, the magnitude of the localized heating required for convexity was less than that which resulted in a thermal inversion ahead of the interface. A convex interface shape was most readily achieved with ampoules of lower thermal conductivity. Increasing melt convection tended to flatten the interface, but the amount of radial heating required to achieve a convex interface was essentially independent of the convection intensity.

Pin stack array for thermoacoustic energy conversion

DOEpatents

Keolian, Robert M.; Swift, Gregory W.

1995-01-01

A thermoacoustic stack for connecting two heat exchangers in a thermoacoustic energy converter provides a convex fluid-solid interface in a plane perpendicular to an axis for acoustic oscillation of fluid between the two heat exchangers. The convex surfaces increase the ratio of the fluid volume in the effective thermoacoustic volume that is displaced from the convex surface to the fluid volume that is adjacent the surface within which viscous energy losses occur. Increasing the volume ratio results in an increase in the ratio of transferred thermal energy to viscous energy losses, with a concomitant increase in operating efficiency of the thermoacoustic converter. The convex surfaces may be easily provided by a pin array having elements arranged parallel to the direction of acoustic oscillations and with effective radial dimensions much smaller than the thicknesses of the viscous energy loss and thermoacoustic energy transfer volumes.

On the complexity of a combined homotopy interior method for convex programming

NASA Astrophysics Data System (ADS)

Yu, Bo; Xu, Qing; Feng, Guochen

2007-03-01

In [G.C. Feng, Z.H. Lin, B. Yu, Existence of an interior pathway to a Karush-Kuhn-Tucker point of a nonconvex programming problem, Nonlinear Anal. 32 (1998) 761-768; G.C. Feng, B. Yu, Combined homotopy interior point method for nonlinear programming problems, in: H. Fujita, M. Yamaguti (Eds.), Advances in Numerical Mathematics, Proceedings of the Second Japan-China Seminar on Numerical Mathematics, Lecture Notes in Numerical and Applied Analysis, vol. 14, Kinokuniya, Tokyo, 1995, pp. 9-16; Z.H. Lin, B. Yu, G.C. Feng, A combined homotopy interior point method for convex programming problem, Appl. Math. Comput. 84 (1997) 193-211.], a combined homotopy was constructed for solving non-convex programming and convex programming with weaker conditions, without assuming the logarithmic barrier function to be strictly convex and the solution set to be bounded. It was proven that a smooth interior path from an interior point of the feasible set to a K-K-T point of the problem exists. This shows that combined homotopy interior point methods can solve the problem that commonly used interior point methods cannot solveE However, so far, there is no result on its complexity, even for linear programming. The main difficulty is that the objective function is not monotonically decreasing on the combined homotopy path. In this paper, by taking a piecewise technique, under commonly used conditions, polynomiality of a combined homotopy interior point method is given for convex nonlinear programming.

Relationship of college student characteristics and inquiry-based geometrical optics instruction to knowledge of image formation with light-ray tracing

NASA Astrophysics Data System (ADS)

Isik, Hakan

This study is premised on the fact that student conceptions of optics appear to be unrelated to student characteristics of gender, age, years since high school graduation, or previous academic experiences. This study investigated the relationships between student characteristics and student performance on image formation test items and the changes in student conceptions of optics after an introductory inquiry-based physics course. Data was collected from 39 college students who were involved in an inquiry-based physics course teaching topics of geometrical optics. Student data concerning characteristics and previous experiences with optics and mathematics were collected. Assessment of student understanding of optics knowledge for pinholes, plane mirrors, refraction, and convex lenses was collected with, the Test of Image Formation with Light-Ray Tracing instrument. Total scale and subscale scores representing the optics instrument content were derived from student pretest and posttest responses. The types of knowledge, needed to answer each optics item correctly, were categorized as situational, conceptual, procedural, and strategic knowledge. These types of knowledge were associated with student correct and incorrect responses to each item to explain the existences and changes in student scientific and naive conceptions. Correlation and stepwise multiple regression analyses were conducted to identify the student characteristics and academic experiences that significantly predicted scores on the subscales of the test. The results showed that student experience with calculus was a significant predictor of student performance on the total scale as well as on the refraction subscale of the Test of Image Formation with Light-Ray Tracing. A combination of student age and previous academic experience with precalculus was a significant predictor of student performance on the pretest pinhole subscale. Student characteristic of years since high school graduation significantly predicted the gain in student scores on pinhole and plane-mirror items from the pretest to the posttest with those students who were most recent graduates from high school doing better. Multivariate and univariate analyses of variance of the Test of Image Formation with Light-Ray Tracing pinhole scale and individual item changes from the pretest to the posttest resulted in statistically significant mean differences between total scores as well as between various individual pinhole items. There were no significant changes for individual plane-mirror items from pretest to posttest. Results revealed that there is a perceivable relationship between student optics-content knowledge and the types of knowledge required by items. At the pretest, the greatest selection of wrong responses related to the items requiring situational type of knowledge and the fewest selection of wrong responses was relate to the items requiring procedural type of knowledge. Student selection of wrong options for each item revealed the following naive optics conceptions: pinholes do not create reversed images (pretest), size and sharpness of pinhole images are related to the focus of a pinhole camera (pretest and posttest); propagation of light rays are interpreted as being radial rather than directional (pretest and posttest); no conception of image formation and observation for parallel mirrors (pretest and posttest), the place of an image depends on the position of the observer (pretest and posttest), a plane mirror reflects the images of the objects placed at one side of the mirror and the observers who were positioned at the other side of the mirror can see them (pretest and posttest); applying the law of reflection to plane mirrors without considering the variations in angles of incidence and reflection (pretest and posttest), and image observation is confused with the image formation in mirrors placed perpendicular to one another (pretest and posttest). Future research should focus on the acquisition, development, and identification of reliable measures of optics concepts, processes, types of knowledge, and specific optics understanding (i.e., pinhole, plane-mirror). Future research should focus on the identification of the more critical concepts such as changes in size and sharpness of pinhole images, image observation, image formation in general, and image formation and observation in parallel mirrors. Future research can be conducted with a larger set of participants so as to compare different instructional methods and address instructional deficiencies using more efficient statistical methods. Comparative studies can be conducted to investigate the relations of various instructional strategies on student conceptions of optics.

Preconditioning 2D Integer Data for Fast Convex Hull Computations.

PubMed

Cadenas, José Oswaldo; Megson, Graham M; Luengo Hendriks, Cris L

2016-01-01

In order to accelerate computing the convex hull on a set of n points, a heuristic procedure is often applied to reduce the number of points to a set of s points, s ≤ n, which also contains the same hull. We present an algorithm to precondition 2D data with integer coordinates bounded by a box of size p × q before building a 2D convex hull, with three distinct advantages. First, we prove that under the condition min(p, q) ≤ n the algorithm executes in time within O(n); second, no explicit sorting of data is required; and third, the reduced set of s points forms a simple polygonal chain and thus can be directly pipelined into an O(n) time convex hull algorithm. This paper empirically evaluates and quantifies the speed up gained by preconditioning a set of points by a method based on the proposed algorithm before using common convex hull algorithms to build the final hull. A speedup factor of at least four is consistently found from experiments on various datasets when the condition min(p, q) ≤ n holds; the smaller the ratio min(p, q)/n is in the dataset, the greater the speedup factor achieved.

Shear thickening and jamming in suspensions of different particle shapes

NASA Astrophysics Data System (ADS)

Brown, Eric; Zhang, Hanjun; Forman, Nicole; Betts, Douglas; Desimone, Joseph; Maynor, Benjamin; Jaeger, Heinrich

2012-02-01

We investigated the role of particle shape on shear thickening and jamming in densely packed suspensions. Various particle shapes were fabricated including rods of different aspect ratios and non-convex hooked rods. A rheometer was used to measure shear stress vs. shear rate for a wide range of packing fractions for each shape. Each suspensions exhibits qualitatively similar Discontinuous Shear Thickening, in which the logarithmic slope of the stress vs. shear rate has the same scaling for each convex shape and diverges at a critical packing fraction φc. The value of φc varies with particle shape, and coincides with the onset of a yield stress, a.k.a. the jamming transition. This suggests the jamming transition controls shear thickening, and the only effect of particle shape on steady state bulk rheology of convex particles is a shift of φc. Intriguingly, viscosity curves for non-convex particles do not collapse on the same set as convex particles, showing strong shear thickening over a wider range of packing fraction. Qualitative shape dependence was only found in steady state rheology when the system was confined to small gaps where large aspect ratio particle are forced to order.

Convex Curved Crystal Spectograph for Pulsed Plasma Sources.

DTIC Science & Technology

The geometry of a convex curved crystal spectrograph as applied to pulsed plasma sources is presented. Also presented are data from the dense plasma focus with particular emphasis on the absolute intensity of line radiations.

A simple optical system delivering a tunable micrometer pink beam that can compensate for heat-induced deformations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Reininger, Ruben; Liu, Zunping; Doumy, Gilles

2015-06-09

The radiation from an undulator reflected from one or more optical elements (usually termed `pink-beam') is used in photon-hungry experiments. The optical elements serve as a high-energy cutoff and for focusing purposes. One of the issues with this configuration is maintaining the focal spot dimension as the energy of the undulator is varied, since this changes the heat load absorbed by the first optical element. Finite-element analyses of the power absorbed by a side water-cooled mirror exposed to the radiation emitted by an undulator at the Advanced Photon Source (APS) and at the APS after the proposed upgrade (APSU) revealsmore » that the mirror deformation is very close to a convex cylinder creating a virtual source closer to the mirror than the undulator source. Here a simple optical system is described based on a Kirkpatrick–Baez pair which keeps the focus size to less than 2 µm (in the APSU case) with a working distance of 350 mm despite the heat-load-induced change in source distance. Detailed ray tracings at several photon energies for both the APS and APSU show that slightly decreasing the angle of incidence on the mirrors corrects the change in the `virtual' position of the source. The system delivers more than 70% of the first undulator harmonic with very low higher-orders contamination for energies between 5 and 10 keV.« less

Optimal boundary regularity for a singular Monge-Ampère equation

NASA Astrophysics Data System (ADS)

Jian, Huaiyu; Li, You

2018-06-01

In this paper we study the optimal global regularity for a singular Monge-Ampère type equation which arises from a few geometric problems. We find that the global regularity does not depend on the smoothness of domain, but it does depend on the convexity of the domain. We introduce (a , η) type to describe the convexity. As a result, we show that the more convex is the domain, the better is the regularity of the solution. In particular, the regularity is the best near angular points.

Compliant tactile sensor that delivers a force vector

NASA Technical Reports Server (NTRS)

Torres-Jara, Eduardo (Inventor)

2010-01-01

Tactile Sensor. The sensor includes a compliant convex surface disposed above a sensor array, the sensor array adapted to respond to deformation of the convex surface to generate a signal related to an applied force vector. The applied force vector has three components to establish the direction and magnitude of an applied force. The compliant convex surface defines a dome with a hollow interior and has a linear relation between displacement and load including a magnet disposed substantially at the center of the dome above a sensor array that responds to magnetic field intensity.

Convexity of level lines of Martin functions and applications

NASA Astrophysics Data System (ADS)

Gallagher, A.-K.; Lebl, J.; Ramachandran, K.

2018-01-01

Let Ω be an unbounded domain in R× Rd. A positive harmonic function u on Ω that vanishes on the boundary of Ω is called a Martin function. In this note, we show that, when Ω is convex, the superlevel sets of a Martin function are also convex. As a consequence we obtain that if in addition Ω has certain symmetry with respect to the t-axis, and partial Ω is sufficiently flat, then the maximum of any Martin function along a slice Ω \\cap ({t}× R^d) is attained at (t, 0).

The Compressible Stokes Flows with No-Slip Boundary Condition on Non-Convex Polygons

NASA Astrophysics Data System (ADS)

Kweon, Jae Ryong

2017-03-01

In this paper we study the compressible Stokes equations with no-slip boundary condition on non-convex polygons and show a best regularity result that the solution can have without subtracting corner singularities. This is obtained by a suitable Helmholtz decomposition: {{{u}}={{w}}+nablaφ_R} with div w = 0 and a potential φ_R. Here w is the solution for the incompressible Stokes problem and φ_R is defined by subtracting from the solution of the Neumann problem the leading two corner singularities at non-convex vertices.

Phenotypic characteristics of adolescents with concave and convex facial profiles - The National Health Examination Survey.

PubMed

Hujoel, P P; Bollen, A-M; Yuen, K C J; Hujoel, I A

2016-10-01

It has been suggested that facial traits are informative on the inherited susceptibility to tuberculosis and obesity, two current global health issues. Our aim was to compare the phenotypic characteristics of adolescents with dental markers for a concave (n=420), a convex (n=978), and a straight (n=3542) facial profile in a nationally representative sample of United States adolescents. The results show that adolescents with a concave facial profile, when compared to a straight facial profile, had an increased waist-to-height ratio (Δ, 1.1 [95% CI 0.5-1.7], p<0.003) and an increased acne prevalence (OR, 1.5 [95% CI 1.2-1.9], p<0.001). Adolescents with a convex facial profile, when compared to a straight facial profile, had an increased prevalence of tuberculosis (OR, 4.3 [95% CI 1.4-13.1], p<0.02), increased ectomorphy (Δ, 0.3 [95% CI 0.2-0.4], p<0.0001), increased left-handedness (OR, 1.4 [95% CI 1.1-1.7], p<0.007), increased color-blindness (OR, 1.7 [95% CI 1.3-2.3], p<0.004), and rhesus ee phenotype (OR, 1.3 [95% CI 1.1-1.5], p<0.008). Adolescents with a concave facial profile, when compared to a convex profile, had increased mesomorphy (Δ, 1.3 [95% CI 1.1-1.5], p<0.0001), increased endomorphy (Δ, 0.5 [95% CI 0.4-0.6], p<0.0001), lower ectomorphy (Δ, 0.5 [95% CI 0.4-0.6], p<0.0001), and lower vocabulary test scores (Δ, 2.3 [95% CI 0.8-3.8], p<0.008). It is concluded that population-based survey data confirm that distinct facial features are associated with distinct somatotypes and distinct disease susceptibilities. Copyright © 2016 Elsevier GmbH. All rights reserved.

A Target-Less Vision-Based Displacement Sensor Based on Image Convex Hull Optimization for Measuring the Dynamic Response of Building Structures.

PubMed

Choi, Insub; Kim, JunHee; Kim, Donghyun

2016-12-08

Existing vision-based displacement sensors (VDSs) extract displacement data through changes in the movement of a target that is identified within the image using natural or artificial structure markers. A target-less vision-based displacement sensor (hereafter called "TVDS") is proposed. It can extract displacement data without targets, which then serve as feature points in the image of the structure. The TVDS can extract and track the feature points without the target in the image through image convex hull optimization, which is done to adjust the threshold values and to optimize them so that they can have the same convex hull in every image frame and so that the center of the convex hull is the feature point. In addition, the pixel coordinates of the feature point can be converted to physical coordinates through a scaling factor map calculated based on the distance, angle, and focal length between the camera and target. The accuracy of the proposed scaling factor map was verified through an experiment in which the diameter of a circular marker was estimated. A white-noise excitation test was conducted, and the reliability of the displacement data obtained from the TVDS was analyzed by comparing the displacement data of the structure measured with a laser displacement sensor (LDS). The dynamic characteristics of the structure, such as the mode shape and natural frequency, were extracted using the obtained displacement data, and were compared with the numerical analysis results. TVDS yielded highly reliable displacement data and highly accurate dynamic characteristics, such as the natural frequency and mode shape of the structure. As the proposed TVDS can easily extract the displacement data even without artificial or natural markers, it has the advantage of extracting displacement data from any portion of the structure in the image.

SU-E-J-272: Auto-Segmentation of Regions with Differentiating CT Numbers for Treatment Response Assessment

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yang, C; Noid, G; Dalah, E

2015-06-15

Purpose: It has been reported recently that the change of CT number (CTN) during and after radiation therapy (RT) may be used to assess RT response. The purpose of this work is to develop a tool to automatically segment the regions with differentiating CTN and/or with change of CTN in a series of CTs. Methods: A software tool was developed to identify regions with differentiating CTN using K-mean Cluster of CT numbers and to automatically delineate these regions using convex hull enclosing method. Pre- and Post-RT CT, PET, or MRI images acquired for sample lung and pancreatic cancer cases weremore » used to test the software tool. K-mean cluster of CT numbers within the gross tumor volumes (GTVs) delineated based on PET SUV (standard uptake value of fludeoxyglucose) and/or MRI ADC (apparent diffusion coefficient) map was analyzed. The cluster centers with higher value were considered as active tumor volumes (ATV). The convex hull contours enclosing preset clusters were used to delineate these ATVs with color washed displays. The CTN defined ATVs were compared with the SUV- or ADC-defined ATVs. Results: CTN stability of the CT scanner used to acquire the CTs in this work is less than 1.5 Hounsfield Unit (HU) variation annually. K-mean cluster centers in the GTV have difference of ∼20 HU, much larger than variation due to CTN stability, for the lung cancer cases studied. The dice coefficient between the ATVs delineated based on convex hull enclosure of high CTN centers and the PET defined GTVs based on SUV cutoff value of 2.5 was 90(±5)%. Conclusion: A software tool was developed using K-mean cluster and convex hull contour to automatically segment high CTN regions which may not be identifiable using a simple threshold method. These CTN regions were reasonably overlapped with the PET or MRI defined GTVs.« less

Worst case estimation of homology design by convex analysis

NASA Technical Reports Server (NTRS)

Yoshikawa, N.; Elishakoff, Isaac; Nakagiri, S.

1998-01-01

The methodology of homology design is investigated for optimum design of advanced structures. for which the achievement of delicate tasks by the aid of active control system is demanded. The proposed formulation of homology design, based on the finite element sensitivity analysis, necessarily requires the specification of external loadings. The formulation to evaluate the worst case for homology design caused by uncertain fluctuation of loadings is presented by means of the convex model of uncertainty, in which uncertainty variables are assigned to discretized nodal forces and are confined within a conceivable convex hull given as a hyperellipse. The worst case of the distortion from objective homologous deformation is estimated by the Lagrange multiplier method searching the point to maximize the error index on the boundary of the convex hull. The validity of the proposed method is demonstrated in a numerical example using the eleven-bar truss structure.

A search asymmetry reversed by figure-ground assignment.

PubMed

Humphreys, G W; Müller, H

2000-05-01

We report evidence demonstrating that a search asymmetry favoring concave over convex targets can be reversed by altering the figure-ground assignment of edges in shapes. Visual search for a concave target among convex distractors is faster than search for a convex target among concave distractors (a search asymmetry). By using shapes with ambiguous local figure-ground relations, we demonstrated that search can be efficient (with search slopes around 10 ms/item) or inefficient (with search slopes around 30-40 ms/item) with the same stimuli, depending on whether edges are assigned to concave or convex "figures." This assignment process can operate in a top-down manner, according to the task set. The results suggest that attention is allocated to spatial regions following the computation of figure-ground relations in parallel across the elements present. This computation can also be modulated by top-down processes.

QUADRATIC SERENDIPITY FINITE ELEMENTS ON POLYGONS USING GENERALIZED BARYCENTRIC COORDINATES.

PubMed

Rand, Alexander; Gillette, Andrew; Bajaj, Chandrajit

2014-01-01

We introduce a finite element construction for use on the class of convex, planar polygons and show it obtains a quadratic error convergence estimate. On a convex n -gon, our construction produces 2 n basis functions, associated in a Lagrange-like fashion to each vertex and each edge midpoint, by transforming and combining a set of n ( n + 1)/2 basis functions known to obtain quadratic convergence. The technique broadens the scope of the so-called 'serendipity' elements, previously studied only for quadrilateral and regular hexahedral meshes, by employing the theory of generalized barycentric coordinates. Uniform a priori error estimates are established over the class of convex quadrilaterals with bounded aspect ratio as well as over the class of convex planar polygons satisfying additional shape regularity conditions to exclude large interior angles and short edges. Numerical evidence is provided on a trapezoidal quadrilateral mesh, previously not amenable to serendipity constructions, and applications to adaptive meshing are discussed.

Transient disturbance growth in flows over convex surfaces

NASA Astrophysics Data System (ADS)

Karp, Michael; Hack, M. J. Philipp

2017-11-01

Flows over curved surfaces occur in a wide range of applications including airfoils, compressor and turbine vanes as well as aerial, naval and ground vehicles. In most of these applications the surface has convex curvature, while concave surfaces are less common. Since monotonic boundary-layer flows over convex surfaces are exponentially stable, they have received considerably less attention than flows over concave walls which are destabilized by centrifugal forces. Non-modal mechanisms may nonetheless enable significant disturbance growth which can make the flow susceptible to secondary instabilities. A parametric investigation of the transient growth and secondary instability of flows over convex surfaces is performed. The specific conditions yielding the maximal transient growth and strongest instability are identified. The effect of wall-normal and spanwise inflection points on the instability process is discussed. Finally, the role and significance of additional parameters, such as the geometry and pressure gradient, is analyzed.

Clearance detector and method for motion and distance

DOEpatents

Xavier, Patrick G [Albuquerque, NM

2011-08-09

A method for correct and efficient detection of clearances between three-dimensional bodies in computer-based simulations, where one or both of the volumes is subject to translation and/or rotations. The method conservatively determines of the size of such clearances and whether there is a collision between the bodies. Given two bodies, each of which is undergoing separate motions, the method utilizes bounding-volume hierarchy representations for the two bodies and, mappings and inverse mappings for the motions of the two bodies. The method uses the representations, mappings and direction vectors to determine the directionally furthest locations of points on the convex hulls of the volumes virtually swept by the bodies and hence the clearance between the bodies, without having to calculate the convex hulls of the bodies. The method includes clearance detection for bodies comprising convex geometrical primitives and more specific techniques for bodies comprising convex polyhedra.

Anomalous dynamics triggered by a non-convex equation of state in relativistic flows

NASA Astrophysics Data System (ADS)

Ibáñez, J. M.; Marquina, A.; Serna, S.; Aloy, M. A.

2018-05-01

The non-monotonicity of the local speed of sound in dense matter at baryon number densities much higher than the nuclear saturation density (n0 ≈ 0.16 fm-3) suggests the possible existence of a non-convex thermodynamics which will lead to a non-convex dynamics. Here, we explore the rich and complex dynamics that an equation of state (EoS) with non-convex regions in the pressure-density plane may develop as a result of genuinely relativistic effects, without a classical counterpart. To this end, we have introduced a phenomenological EoS, the parameters of which can be restricted owing to causality and thermodynamic stability constraints. This EoS can be regarded as a toy model with which we may mimic realistic (and far more complex) EoSs of practical use in the realm of relativistic hydrodynamics.

Short-term and long-term treatment outcomes with Class III activator

PubMed Central

Ryu, Hyo-kyung; Chong, Hyun-Jeong; An, Ki-Yong

2015-01-01

Objective The purpose of this retrospective study was to investigate short-term and long-term skeletodental outcomes of Class III activator treatment. Methods A Class III activator treatment group (AG) comprised of 22 patients (9 boys, 13 girls) was compared with a Class III control group (CG) comprised of 17 patients (6 boys, 11 girls). The total treatment period was divided into three stages; the initial stage (T1), the post-activator treatment or post-mandibular growth peak stage (T2), and the long-term follow-up stage (T3). Cephalometric changes were evaluated statistically via the Mann-Whitney U-test and the Friedman test. Results The AG exhibited significant increases in the SNA angle, ANB angle, Wits appraisal, A point-N perpendicular, Convexity of A point, and proclination of the maxillary incisors, from T1 to T2. In the long-term follow-up (T1-T3), the AG exhibited significantly greater increases in the ANB angle, Wits appraisal, and Convexity of A point than the CG. Conclusions Favorable skeletal outcomes induced during the Class III activator treatment period were generally maintained until the long-term follow-up period of the post-mandibular growth peak stage. PMID:26445717

Novel high-NA MRF toolpath supports production of concave hemispheres

NASA Astrophysics Data System (ADS)

Maloney, Chris; Supranowitz, Chris; Dumas, Paul

2017-10-01

Many optical system designs rely on high numerical aperture (NA) optics, including lithography and defense systems. Lithography systems require high-NA optics to image the fine patterns from a photomask, and many defense systems require the use of domes. The methods for manufacturing such optics with large half angles have often been treated as proprietary by most manufacturers due to the challenges involved. In the past, many high-NA concave surfaces could not be polished by magnetorheological finishing (MRF) due to collisions with the hardware underneath the polishing head. By leveraging concepts that were developed to enable freeform raster MRF capabilities, QED Technologies has implemented a novel toolpath to facilitate a new high-NA rotational MRF mode. This concept involves the use of the B-axis (rotational axis) in combination with a "virtual-axis" that utilizes the geometry of the polishing head. Hardware collisions that previously restricted the concave half angle limit can now be avoided and the new functionality has been seamlessly integrated into the software. This new MRF mode overcomes past limitations for polishing concave surfaces to now accommodate full concave hemispheres as well as extend the capabilities for full convex hemispheres. We discuss some of the previous limitations, and demonstrate the extended capabilities using this novel toolpath. Polishing results are used to qualify the new toolpath to ensure similar results to the "standard" rotational MRF mode.

Evaluation of the OSC-TV iterative reconstruction algorithm for cone-beam optical CT

DOE Office of Scientific and Technical Information (OSTI.GOV)

Matenine, Dmitri, E-mail: dmitri.matenine.1@ulaval.ca; Mascolo-Fortin, Julia, E-mail: julia.mascolo-fortin.1@ulaval.ca; Goussard, Yves, E-mail: yves.goussard@polymtl.ca

Purpose: The present work evaluates an iterative reconstruction approach, namely, the ordered subsets convex (OSC) algorithm with regularization via total variation (TV) minimization in the field of cone-beam optical computed tomography (optical CT). One of the uses of optical CT is gel-based 3D dosimetry for radiation therapy, where it is employed to map dose distributions in radiosensitive gels. Model-based iterative reconstruction may improve optical CT image quality and contribute to a wider use of optical CT in clinical gel dosimetry. Methods: This algorithm was evaluated using experimental data acquired by a cone-beam optical CT system, as well as complementary numericalmore » simulations. A fast GPU implementation of OSC-TV was used to achieve reconstruction times comparable to those of conventional filtered backprojection. Images obtained via OSC-TV were compared with the corresponding filtered backprojections. Spatial resolution and uniformity phantoms were scanned and respective reconstructions were subject to evaluation of the modulation transfer function, image uniformity, and accuracy. The artifacts due to refraction and total signal loss from opaque objects were also studied. Results: The cone-beam optical CT data reconstructions showed that OSC-TV outperforms filtered backprojection in terms of image quality, thanks to a model-based simulation of the photon attenuation process. It was shown to significantly improve the image spatial resolution and reduce image noise. The accuracy of the estimation of linear attenuation coefficients remained similar to that obtained via filtered backprojection. Certain image artifacts due to opaque objects were reduced. Nevertheless, the common artifact due to the gel container walls could not be eliminated. Conclusions: The use of iterative reconstruction improves cone-beam optical CT image quality in many ways. The comparisons between OSC-TV and filtered backprojection presented in this paper demonstrate that OSC-TV can potentially improve the rendering of spatial features and reduce cone-beam optical CT artifacts.« less

Evaluation of the OSC-TV iterative reconstruction algorithm for cone-beam optical CT.

PubMed

Matenine, Dmitri; Mascolo-Fortin, Julia; Goussard, Yves; Després, Philippe

2015-11-01

The present work evaluates an iterative reconstruction approach, namely, the ordered subsets convex (OSC) algorithm with regularization via total variation (TV) minimization in the field of cone-beam optical computed tomography (optical CT). One of the uses of optical CT is gel-based 3D dosimetry for radiation therapy, where it is employed to map dose distributions in radiosensitive gels. Model-based iterative reconstruction may improve optical CT image quality and contribute to a wider use of optical CT in clinical gel dosimetry. This algorithm was evaluated using experimental data acquired by a cone-beam optical CT system, as well as complementary numerical simulations. A fast GPU implementation of OSC-TV was used to achieve reconstruction times comparable to those of conventional filtered backprojection. Images obtained via OSC-TV were compared with the corresponding filtered backprojections. Spatial resolution and uniformity phantoms were scanned and respective reconstructions were subject to evaluation of the modulation transfer function, image uniformity, and accuracy. The artifacts due to refraction and total signal loss from opaque objects were also studied. The cone-beam optical CT data reconstructions showed that OSC-TV outperforms filtered backprojection in terms of image quality, thanks to a model-based simulation of the photon attenuation process. It was shown to significantly improve the image spatial resolution and reduce image noise. The accuracy of the estimation of linear attenuation coefficients remained similar to that obtained via filtered backprojection. Certain image artifacts due to opaque objects were reduced. Nevertheless, the common artifact due to the gel container walls could not be eliminated. The use of iterative reconstruction improves cone-beam optical CT image quality in many ways. The comparisons between OSC-TV and filtered backprojection presented in this paper demonstrate that OSC-TV can potentially improve the rendering of spatial features and reduce cone-beam optical CT artifacts.

Computing convex quadrangulations☆

PubMed Central

Schiffer, T.; Aurenhammer, F.; Demuth, M.

2012-01-01

We use projected Delaunay tetrahedra and a maximum independent set approach to compute large subsets of convex quadrangulations on a given set of points in the plane. The new method improves over the popular pairing method based on triangulating the point set. PMID:22389540

Investigation of internal friction in fused quartz, steel, Plexiglass, and Westerly granite from 0.01 to 1.00 Hertz at 10- 8 to 10-7 strain amplitude.

USGS Publications Warehouse

Hsi-Ping, Liu; Peselnick, L.

1983-01-01

A detailed evaluation on the method of internal friction measurement by the stress-strain hysteresis loop method from 0.01 to 1 Hz at 10-8-10-7 strain amplitude and 23.9oC is presented. Significant systematic errors in relative phase measurement can result from convex end surfaces of the sample and stress sensor and from end surface irregularities such as nicks and asperities. Preparation of concave end surfaces polished to optical smoothness having a radius of curvature >3.6X104 cm reduces the systematic error in relative phase measurements to <(5.5+ or -2.2)X10-4 radians. -from Authors

Compliant tactile sensor for generating a signal related to an applied force

NASA Technical Reports Server (NTRS)

Torres-Jara, Eduardo (Inventor)

2012-01-01

Tactile sensor. The sensor includes a compliant convex surface disposed above a sensor array, the sensor array adapted to respond to deformation of the convex surface to generate a signal related to an applied force vector.

Distributed Nash Equilibrium Seeking for Generalized Convex Games with Shared Constraints

NASA Astrophysics Data System (ADS)

Sun, Chao; Hu, Guoqiang

2018-05-01

In this paper, we deal with the problem of finding a Nash equilibrium for a generalized convex game. Each player is associated with a convex cost function and multiple shared constraints. Supposing that each player can exchange information with its neighbors via a connected undirected graph, the objective of this paper is to design a Nash equilibrium seeking law such that each agent minimizes its objective function in a distributed way. Consensus and singular perturbation theories are used to prove the stability of the system. A numerical example is given to show the effectiveness of the proposed algorithms.

Convex Regression with Interpretable Sharp Partitions

PubMed Central

Petersen, Ashley; Simon, Noah; Witten, Daniela

2016-01-01

We consider the problem of predicting an outcome variable on the basis of a small number of covariates, using an interpretable yet non-additive model. We propose convex regression with interpretable sharp partitions (CRISP) for this task. CRISP partitions the covariate space into blocks in a data-adaptive way, and fits a mean model within each block. Unlike other partitioning methods, CRISP is fit using a non-greedy approach by solving a convex optimization problem, resulting in low-variance fits. We explore the properties of CRISP, and evaluate its performance in a simulation study and on a housing price data set. PMID:27635120

Optshrink LR + S: accelerated fMRI reconstruction using non-convex optimal singular value shrinkage.

PubMed

Aggarwal, Priya; Shrivastava, Parth; Kabra, Tanay; Gupta, Anubha

2017-03-01

This paper presents a new accelerated fMRI reconstruction method, namely, OptShrink LR + S method that reconstructs undersampled fMRI data using a linear combination of low-rank and sparse components. The low-rank component has been estimated using non-convex optimal singular value shrinkage algorithm, while the sparse component has been estimated using convex l 1 minimization. The performance of the proposed method is compared with the existing state-of-the-art algorithms on real fMRI dataset. The proposed OptShrink LR + S method yields good qualitative and quantitative results.

The role of spinal concave–convex biases in the progression of idiopathic scoliosis

PubMed Central

Driscoll, Mark; Moreau, Alain; Villemure, Isabelle; Parent, Stefan

2009-01-01

Inadequate understanding of risk factors involved in the progression of idiopathic scoliosis restrains initial treatment to observation until the deformity shows signs of significant aggravation. The purpose of this analysis is to explore whether the concave–convex biases associated with scoliosis (local degeneration of the intervertebral discs, nucleus migration, and local increase in trabecular bone-mineral density of vertebral bodies) may be identified as progressive risk factors. Finite element models of a 26° right thoracic scoliotic spine were constructed based on experimental and clinical observations that included growth dynamics governed by mechanical stimulus. Stress distribution over the vertebral growth plates, progression of Cobb angles, and vertebral wedging were explored in models with and without the biases of concave–convex properties. The inclusion of the bias of concave–convex properties within the model both augmented the asymmetrical loading of the vertebral growth plates by up to 37% and further amplified the progression of Cobb angles and vertebral wedging by as much as 5.9° and 0.8°, respectively. Concave–convex biases are factors that influence the progression of scoliotic curves. Quantifying these parameters in a patient with scoliosis may further provide a better clinical assessment of the risk of progression. PMID:19130096

Preconditioning 2D Integer Data for Fast Convex Hull Computations

PubMed Central

2016-01-01

In order to accelerate computing the convex hull on a set of n points, a heuristic procedure is often applied to reduce the number of points to a set of s points, s ≤ n, which also contains the same hull. We present an algorithm to precondition 2D data with integer coordinates bounded by a box of size p × q before building a 2D convex hull, with three distinct advantages. First, we prove that under the condition min(p, q) ≤ n the algorithm executes in time within O(n); second, no explicit sorting of data is required; and third, the reduced set of s points forms a simple polygonal chain and thus can be directly pipelined into an O(n) time convex hull algorithm. This paper empirically evaluates and quantifies the speed up gained by preconditioning a set of points by a method based on the proposed algorithm before using common convex hull algorithms to build the final hull. A speedup factor of at least four is consistently found from experiments on various datasets when the condition min(p, q) ≤ n holds; the smaller the ratio min(p, q)/n is in the dataset, the greater the speedup factor achieved. PMID:26938221

Convex Formulations of Learning from Crowds

NASA Astrophysics Data System (ADS)

Kajino, Hiroshi; Kashima, Hisashi

It has attracted considerable attention to use crowdsourcing services to collect a large amount of labeled data for machine learning, since crowdsourcing services allow one to ask the general public to label data at very low cost through the Internet. The use of crowdsourcing has introduced a new challenge in machine learning, that is, coping with low quality of crowd-generated data. There have been many recent attempts to address the quality problem of multiple labelers, however, there are two serious drawbacks in the existing approaches, that are, (i) non-convexity and (ii) task homogeneity. Most of the existing methods consider true labels as latent variables, which results in non-convex optimization problems. Also, the existing models assume only single homogeneous tasks, while in realistic situations, clients can offer multiple tasks to crowds and crowd workers can work on different tasks in parallel. In this paper, we propose a convex optimization formulation of learning from crowds by introducing personal models of individual crowds without estimating true labels. We further extend the proposed model to multi-task learning based on the resemblance between the proposed formulation and that for an existing multi-task learning model. We also devise efficient iterative methods for solving the convex optimization problems by exploiting conditional independence structures in multiple classifiers.

Effect of Deviated Nasal Septum Type on Nasal Mucociliary Clearance, Olfactory Function, Quality of Life, and Efficiency of Nasal Surgery.

PubMed

Berkiten, Güler; Kumral, Tolgar Lütfi; Saltürk, Ziya; Atar, Yavuz; Yildirim, Güven; Uyar, Yavuz; Aydoğdu, Imran; Arslanoğlu, Ahmet

2016-07-01

The aim of this study was to analyze the influence of deviated nasal septum (DNS) type on nasal mucociliary clearance, quality of life (QoL), olfactory function, and efficiency of nasal surgery (septoplasty with or without inferior turbinate reduction and partial middle turbinectomy). Fifty patients (20 females and 30 males) with septal deviation were included in the study and were divided into 6 groups according to deviation type after examination by nasal endoscopy and paranasal computed tomography. The saccharin clearance test to evaluate the nasal mucociliary clearance time, Connecticut Chemosensory Clinical Research Center smell test for olfactory function, and sinonasal outcome test-22 (SNOT-22) for patient satisfaction were applied preoperatively and postoperatively at the sixth week after surgery. Nasal mucociliary clearance, smell, and SNOT-22 scores were measured before surgery and at the sixth week following surgery. No significant difference was found in olfactory and SNOT-22 scores for any of the DNS types (both convex and concave sides) (P > 0.05). In addition, there was no difference in the saccharin clearance time (SCT) of the concave and convex sides (P > 0.05). According to the DNS type, the mean SCT of the convex sides showed no difference, but that of the concave sides showed a difference in types 3, 4, 5, and 6. These types had a prolonged SCT (P < 0.05). Olfactory scores revealed no difference postoperatively in types 5 and 6 but were decreased significantly in types 1 to 4 (P < 0.05). There was no significant difference in the healing of both the mucociliary clearance (MCC) and olfactory functions. SNOT-22 results showed a significant decrease in type 3. All DNS types disturb the QoL regarding nasal MCC and olfaction functions. MCC values, olfactory function, and QoL scores are similar among the DNS types. Both sides of the DNS types affect the MCC scores symmetrically. Septal surgery improves olfaction function and QoL at the sixth week following surgery but disturbs nasal MCC; thus, the sixth week is too early to assess nasal MCC.

The GCT camera for the Cherenkov Telescope Array

NASA Astrophysics Data System (ADS)

Lapington, J. S.; Abchiche, A.; Allan, D.; Amans, J.-P.; Armstrong, T. P.; Balzer, A.; Berge, D.; Boisson, C.; Bousquet, J.-J.; Bose, R.; Brown, A. M.; Bryan, M.; Buchholtz, G.; Buckley, J.; Chadwick, P. M.; Costantini, H.; Cotter, G.; Daniel, M. K.; De Franco, A.; De Frondat, F.; Dournaux, J.-L.; Dumas, D.; Ernenwein, J.-P.; Fasola, G.; Funk, S.; Gironnet, J.; Graham, J. A.; Greenshaw, T.; Hervet, O.; Hidaka, N.; Hinton, J. A.; Huet, J.-M.; Jankowsky, D.; Jegouzo, I.; Jogler, T.; Kawashima, T.; Kraus, M.; Laporte, P.; Leach, S.; Lefaucheur, J.; Markoff, S.; Melse, T.; Minaya, I. A.; Mohrmann, L.; Molyneux, P.; Moore, P.; Nolan, S. J.; Okumura, A.; Osborne, J. P.; Parsons, R. D.; Rosen, S.; Ross, D.; Rowell, G.; Rulten, C. B.; Sato, Y.; Sayede, F.; Schmoll, J.; Schoorlemmer, H.; Servillat, M.; Sol, H.; Stamatescu, V.; Stephan, M.; Stuik, R.; Sykes, J.; Tajima, H.; Thornhill, J.; Tibaldo, L.; Trichard, C.; Varner, G.; Vink, J.; Watson, J. J.; White, R.; Yamane, N.; Zech, A.; Zink, A.; Zorn, J.; CTA Consortium

2017-12-01

The Gamma Cherenkov Telescope (GCT) is one of the designs proposed for the Small Sized Telescope (SST) section of the Cherenkov Telescope Array (CTA). The GCT uses dual-mirror optics, resulting in a compact telescope with good image quality and a large field of view with a smaller, more economical, camera than is achievable with conventional single mirror solutions. The photon counting GCT camera is designed to record the flashes of atmospheric Cherenkov light from gamma and cosmic ray initiated cascades, which last only a few tens of nanoseconds. The GCT optics require that the camera detectors follow a convex surface with a radius of curvature of 1 m and a diameter of 35 cm, which is approximated by tiling the focal plane with 32 modules. The first camera prototype is equipped with multi-anode photomultipliers, each comprising an 8×8 array of 6×6 mm2 pixels to provide the required angular scale, adding up to 2048 pixels in total. Detector signals are shaped, amplified and digitised by electronics based on custom ASICs that provide digitisation at 1 GSample/s. The camera is self-triggering, retaining images where the focal plane light distribution matches predefined spatial and temporal criteria. The electronics are housed in the liquid-cooled, sealed camera enclosure. LED flashers at the corners of the focal plane provide a calibration source via reflection from the secondary mirror. The first GCT camera prototype underwent preliminary laboratory tests last year. In November 2015, the camera was installed on a prototype GCT telescope (SST-GATE) in Paris and was used to successfully record the first Cherenkov light of any CTA prototype, and the first Cherenkov light seen with such a dual-mirror optical system. A second full-camera prototype based on Silicon Photomultipliers is under construction. Up to 35 GCTs are envisaged for CTA.

Optical fundamentals of an adaptive substance-on-surface chemical recognizer

NASA Astrophysics Data System (ADS)

Fauconier, Richard; Ndoye, Mandoye; Montlouis, Webert

2017-10-01

The objective is to identify the chemical composition of (isotropic and homogeneous) thin liquid and gel films on various surfaces by their infrared reflectance spectra. A bistatic optical sensing concept is proposed here in which a multi-wavelength laser source and a detector are physically displaced from each other. With the aid of the concept apparatus proposed, key optical variables can be measured in real time. The variables in question (substance thickness, refractive index, etc.) are those whose un-observability causes many types of monostatic sensor (in use today) to give ambiguous identifications. Knowledge of the aforementioned key optical variables would allow an adaptive signal-processing algorithm to make unambiguous identifications of the unknown chemicals by their infrared spectra, despite their variable presentations. The proposed bistatic sensor system consists of an optical transmitter and an optical receiver. The whole system can be mounted on a stable platform. Both the optical transmitter subsystem and the optical receiver subsystem contain auxiliary sensors to determine their relative spatial positions and orientations. For each subsystem, these auxiliary sensors include an orientation sensor, and rotational sensors for absolute angular position. A profilometer-and-machine-vision subsystem is also included. An important aspect of determining the necessary optical variables is an aperture that limits the interrogatory beams to a coherent pair, rejecting those resulting from successive multiple reflections. A set of equations is developed to characterize the propagation of a coherent pair of frequency-modulated thin beams through the system. It is also shown that frequency modulation can produce easily measurable beat frequencies for determination of sample thicknesses on the order of microns to millimeters. Also shown is how the apparatus's polarization features allow it to measure the refractive index of any isotropic, homogeneous dielectric surface on which the unknown substance can sit. Concave, convex and flat supporting surfaces and menisci are discussed.

First-order convex feasibility algorithms for x-ray CT

PubMed Central

Sidky, Emil Y.; Jørgensen, Jakob S.; Pan, Xiaochuan

2013-01-01

Purpose: Iterative image reconstruction (IIR) algorithms in computed tomography (CT) are based on algorithms for solving a particular optimization problem. Design of the IIR algorithm, therefore, is aided by knowledge of the solution to the optimization problem on which it is based. Often times, however, it is impractical to achieve accurate solution to the optimization of interest, which complicates design of IIR algorithms. This issue is particularly acute for CT with a limited angular-range scan, which leads to poorly conditioned system matrices and difficult to solve optimization problems. In this paper, we develop IIR algorithms which solve a certain type of optimization called convex feasibility. The convex feasibility approach can provide alternatives to unconstrained optimization approaches and at the same time allow for rapidly convergent algorithms for their solution—thereby facilitating the IIR algorithm design process. Methods: An accelerated version of the Chambolle−Pock (CP) algorithm is adapted to various convex feasibility problems of potential interest to IIR in CT. One of the proposed problems is seen to be equivalent to least-squares minimization, and two other problems provide alternatives to penalized, least-squares minimization. Results: The accelerated CP algorithms are demonstrated on a simulation of circular fan-beam CT with a limited scanning arc of 144°. The CP algorithms are seen in the empirical results to converge to the solution of their respective convex feasibility problems. Conclusions: Formulation of convex feasibility problems can provide a useful alternative to unconstrained optimization when designing IIR algorithms for CT. The approach is amenable to recent methods for accelerating first-order algorithms which may be particularly useful for CT with limited angular-range scanning. The present paper demonstrates the methodology, and future work will illustrate its utility in actual CT application. PMID:23464295

Particle Streak Anemometry: A New Method for Proximal Flow Sensing from Aircraft

NASA Astrophysics Data System (ADS)

Nichols, T. W.

Accurate sensing of relative air flow direction from fixed-wing small unmanned aircraft (sUAS) is challenging with existing multi-hole pitot-static and vane systems. Sub-degree direction accuracy is generally not available on such systems and disturbances to the local flow field, induced by the airframe, introduce an additional error source. An optical imaging approach to make a relative air velocity measurement with high-directional accuracy is presented. Optical methods offer the capability to make a proximal measurement in undisturbed air outside of the local flow field without the need to place sensors on vulnerable probes extended ahead of the aircraft. Current imaging flow analysis techniques for laboratory use rely on relatively thin imaged volumes and sophisticated hardware and intensity thresholding in low-background conditions. A new method is derived and assessed using a particle streak imaging technique that can be implemented with low-cost commercial cameras and illumination systems, and can function in imaged volumes of arbitrary depth with complex background signal. The new technique, referred to as particle streak anemometry (PSA) (to differentiate from particle streak velocimetry which makes a field measurement rather than a single bulk flow measurement) utilizes a modified Canny Edge detection algorithm with a connected component analysis and principle component analysis to detect streak ends in complex imaging conditions. A linear solution for the air velocity direction is then implemented with a random sample consensus (RANSAC) solution approach. A single DOF non-linear, non-convex optimization problem is then solved for the air speed through an iterative approach. The technique was tested through simulation and wind tunnel tests yielding angular accuracies under 0.2 degrees, superior to the performance of existing commercial systems. Air speed error standard deviations varied from 1.6 to 2.2 m/s depending on the techniques of implementation. While air speed sensing is secondary to accurate flow direction measurement, the air speed results were in line with commercial pitot static systems at low speeds.

Dynamical trade-offs arise from antagonistic coevolution and decrease intraspecific diversity.

PubMed

Huang, Weini; Traulsen, Arne; Werner, Benjamin; Hiltunen, Teppo; Becks, Lutz

2017-12-12

Trade-offs play an important role in evolution. Without trade-offs, evolution would maximize fitness of all traits leading to a "master of all traits". The shape of trade-offs has been shown to determine evolutionary trajectories and is often assumed to be static and independent of the actual evolutionary process. Here we propose that coevolution leads to a dynamical trade-off. We test this hypothesis in a microbial predator-prey system and show that the bacterial growth-defense trade-off changes from concave to convex, i.e., defense is effective and cheap initially, but gets costly when predators coevolve. We further explore the impact of such dynamical trade-offs by a novel mathematical model incorporating de novo mutations for both species. Predator and prey populations diversify rapidly leading to higher prey diversity when the trade-off is concave (cheap). Coevolution results in more convex (costly) trade-offs and lower prey diversity compared to the scenario where only the prey evolves.

Effective Lagrangian in nonlinear electrodynamics and its properties of causality and unitarity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shabad, Anatoly E.; Usov, Vladimir V.

2011-05-15

In nonlinear electrodynamics, by implementing the causality principle as the requirement that the group velocity of elementary excitations over a background field should not exceed the speed of light in the vacuum c=1, and the unitarity principle as the requirement that the residue of the propagator should be nonnegative, we establish the positive convexity of the effective Lagrangian on the class of constant fields, also the positivity of all characteristic dielectric and magnetic permittivity constants that are derivatives of the effective Lagrangian with respect to the field invariants. Violation of the general principles by the one-loop approximation in QED atmore » exponentially large magnetic field is analyzed, resulting in complex energy ghosts that signal the instability of the magnetized vacuum. Superluminal excitations (tachyons) appear, too, but for the magnetic field exceeding its instability threshold. Also other popular Lagrangians are tested to establish that the ones leading to spontaneous vacuum magnetization possess wrong convexity.« less

Turbulent boundary layer heat transfer experiments: Convex curvature effects including introduction and recovery

NASA Technical Reports Server (NTRS)

Simon, T. W.; Moffat, R. J.; Johnston, J. P.; Kays, W. M.

1982-01-01

Measurements were made of the heat transfer rate through turbulent and transitional boundary layers on an isothermal, convexly curved wall and downstream flat plate. The effect of convex curvature on the fully turbulent boundary layer was a reduction of the local Stanton numbers 20% to 50% below those predicted for a flat wall under the same circumstances. The recovery of the heat transfer rates on the downstream flat wall was extremely slow. After 60 cm of recovery length, the Stanton number was still typically 15% to 20% below the flat wall predicted value. Various effects important in the modeling of curved flows were studied separately. These are: the effect of initial boundary layer thickness, the effect of freestream velocity, the effect of freestream acceleration, the effect of unheated starting length, and the effect of the maturity of the boundary layer. An existing curvature prediction model was tested against this broad heat transfer data base to determine where it could appropriately be used for heat transfer predictions.

Adaptive control of interface by temperature and interface profile feedback in transparent multi-zone crystal growth furnace

NASA Technical Reports Server (NTRS)

Batur, Celal

1991-01-01

The objective of this research is to control the dynamics of multizone programmable crystal growth furnaces. Due to the inevitable heat exchange among different heating zones and the transient nature of the process, the dynamics of multizone furnaces is time varying, distributed, and therefore complex in nature. Electrical power to heating zones and the translational speed of the ampoule are employed as inputs to control the dynamics. Structural properties of the crystal is the ultimate aim of this adaptive control system. These properties can be monitored in different ways. Following an order of complexity, these may include: (1) on line measurement of the material optical properties such as the refractive index of crystal; (2) on line x-ray imaging of the interface topology; (3) on line optical quantification of the interface profile such as the determination of concavity or convexity of the interface shape; and (4) on line temperature measurement at points closest to the material such as measurements of the ampoule's outside and inside surface temperatures. The research performed makes use of the temperature and optical measurements, specified in (3) and (4) as the outputs of furnace dynamics. However, if the instrumentation is available, the proposed control methodology can be extended to the measurements listed in (1) and (2).

Broad Band Intra-Cavity Total Reflection Chemical Sensor

DOEpatents

Pipino, Andrew C. R.

1998-11-10

A broadband, ultrahigh-sensitivity chemical sensor is provided that allows etection through utilization of a small, extremely low-loss, monolithic optical cavity. The cavity is fabricated from highly transparent optical material in the shape of a regular polygon with one or more convex facets to form a stable resonator for ray trajectories sustained by total internal reflection. Optical radiation enters and exits the monolithic cavity by photon tunneling in which two totally reflecting surfaces are brought into close proximity. In the presence of absorbing material, the loss per pass is increased since the evanescent waves that exist exterior to the cavity at points where the circulating pulse is totally reflected, are absorbed. The decay rate of an injected pulse is determined by coupling out an infinitesimal fraction of the pulse to produce an intensity-versus-time decay curve. Since the change in the decay rate resulting from absorption is inversely proportional to the magnitude of absorption, a quantitative sensor of concentration or absorption cross-section with 1 part-per-million/pass or better sensitivity is obtained. The broadband nature of total internal reflection permits a single device to be used over a broad wavelength range. The absorption spectrum of the surrounding medium can thereby be obtained as a measurement of inverse decay time as a function of wavelength.

Non-Gaussian operations on bosonic modes of light: Photon-added Gaussian channels

NASA Astrophysics Data System (ADS)

Sabapathy, Krishna Kumar; Winter, Andreas

2017-06-01

We present a framework for studying bosonic non-Gaussian channels of continuous-variable systems. Our emphasis is on a class of channels that we call photon-added Gaussian channels, which are experimentally viable with current quantum-optical technologies. A strong motivation for considering these channels is the fact that it is compulsory to go beyond the Gaussian domain for numerous tasks in continuous-variable quantum information processing such as entanglement distillation from Gaussian states and universal quantum computation. The single-mode photon-added channels we consider are obtained by using two-mode beam splitters and squeezing operators with photon addition applied to the ancilla ports giving rise to families of non-Gaussian channels. For each such channel, we derive its operator-sum representation, indispensable in the present context. We observe that these channels are Fock preserving (coherence nongenerating). We then report two examples of activation using our scheme of photon addition, that of quantum-optical nonclassicality at outputs of channels that would otherwise output only classical states and of both the quantum and private communication capacities, hinting at far-reaching applications for quantum-optical communication. Further, we see that noisy Gaussian channels can be expressed as a convex mixture of these non-Gaussian channels. We also present other physical and information-theoretic properties of these channels.

Partially deuterated potassium dihydrogen phosphate optimized for ultra-broadband optical parametric amplification

NASA Astrophysics Data System (ADS)

Fujioka, K.; Fujimoto, Y.; Tsubakimoto, K.; Kawanaka, J.; Shoji, I.; Miyanaga, N.

2015-03-01

The refractive index of a potassium dihydrogen phosphate (KDP) crystal strongly depends on the deuteration fraction of the crystal. The wavelength dependence of the phase-matching angle in the near-infrared optical parametric process shows convex and concave characteristics for pure KDP and pure deuterated KDP (DKDP), respectively, when pumped by the second harmonic of Nd- or Yb-doped solid state lasers. Using these characteristics, ultra-broadband phase matching can be realized by optimization of the deuteration fraction. The refractive index of DKDP that was grown with a different deuteration fraction (known as partially deuterated KDP or pDKDP) was measured over a wide wavelength range of 0.4-1.5 μm by the minimum deviation method. The wavelength dispersions of the measured refractive indices were fitted using a modified Sellmeier equation, and the deuteration fraction dependence was analyzed using the Lorentz-Lorenz equation. The wavelength-dependent phase-matching angle for an arbitrary deuteration fraction was then calculated for optical parametric amplification with pumping at a wavelength of 526.5 nm. The results revealed that a refractive index database with precision of more than 2 × 10-5 was necessary for exact evaluation of the phase-matching condition. An ultra-broad gain bandwidth of up to 490 nm will be feasible when using the 68% pDKDP crystal.

Automated pharmaceutical tablet coating layer evaluation of optical coherence tomography images

NASA Astrophysics Data System (ADS)

Markl, Daniel; Hannesschläger, Günther; Sacher, Stephan; Leitner, Michael; Khinast, Johannes G.; Buchsbaum, Andreas

2015-03-01

Film coating of pharmaceutical tablets is often applied to influence the drug release behaviour. The coating characteristics such as thickness and uniformity are critical quality parameters, which need to be precisely controlled. Optical coherence tomography (OCT) shows not only high potential for off-line quality control of film-coated tablets but also for in-line monitoring of coating processes. However, an in-line quality control tool must be able to determine coating thickness measurements automatically and in real-time. This study proposes an automatic thickness evaluation algorithm for bi-convex tables, which provides about 1000 thickness measurements within 1 s. Beside the segmentation of the coating layer, optical distortions due to refraction of the beam by the air/coating interface are corrected. Moreover, during in-line monitoring the tablets might be in oblique orientation, which needs to be considered in the algorithm design. Experiments were conducted where the tablet was rotated to specified angles. Manual and automatic thickness measurements were compared for varying coating thicknesses, angles of rotations, and beam displacements (i.e. lateral displacement between successive depth scans). The automatic thickness determination algorithm provides highly accurate results up to an angle of rotation of 30°. The computation time was reduced to 0.53 s for 700 thickness measurements by introducing feasibility constraints in the algorithm.

Directional Convexity and Finite Optimality Conditions.

DTIC Science & Technology

1984-03-01

system, Necessary Conditions for optimality. Work Unit Number 5 (Optimization and Large Scale Systems) *Istituto di Matematica Applicata, Universita...that R(T) is convex would then imply x(u,T) e int R(T). Cletituto di Matematica Applicata, Universita di Padova, 35100 ITALY. Sponsored by the United

Localized Multiple Kernel Learning A Convex Approach

DTIC Science & Technology

2016-11-22

data. All the aforementioned approaches to localized MKL are formulated in terms of non-convex optimization problems, and deep the- oretical...learning. IEEE Transactions on Neural Networks, 22(3):433–446, 2011. Jingjing Yang, Yuanning Li, Yonghong Tian, Lingyu Duan, and Wen Gao. Group-sensitive

Framework to model neutral particle flux in convex high aspect ratio structures using one-dimensional radiosity

NASA Astrophysics Data System (ADS)

Manstetten, Paul; Filipovic, Lado; Hössinger, Andreas; Weinbub, Josef; Selberherr, Siegfried

2017-02-01

We present a computationally efficient framework to compute the neutral flux in high aspect ratio structures during three-dimensional plasma etching simulations. The framework is based on a one-dimensional radiosity approach and is applicable to simulations of convex rotationally symmetric holes and convex symmetric trenches with a constant cross-section. The framework is intended to replace the full three-dimensional simulation step required to calculate the neutral flux during plasma etching simulations. Especially for high aspect ratio structures, the computational effort, required to perform the full three-dimensional simulation of the neutral flux at the desired spatial resolution, conflicts with practical simulation time constraints. Our results are in agreement with those obtained by three-dimensional Monte Carlo based ray tracing simulations for various aspect ratios and convex geometries. With this framework we present a comprehensive analysis of the influence of the geometrical properties of high aspect ratio structures as well as of the particle sticking probability on the neutral particle flux.

Solution of monotone complementarity and general convex programming problems using a modified potential reduction interior point method

DOE PAGES

Huang, Kuo -Ling; Mehrotra, Sanjay

2016-11-08

We present a homogeneous algorithm equipped with a modified potential function for the monotone complementarity problem. We show that this potential function is reduced by at least a constant amount if a scaled Lipschitz condition (SLC) is satisfied. A practical algorithm based on this potential function is implemented in a software package named iOptimize. The implementation in iOptimize maintains global linear and polynomial time convergence properties, while achieving practical performance. It either successfully solves the problem, or concludes that the SLC is not satisfied. When compared with the mature software package MOSEK (barrier solver version 6.0.0.106), iOptimize solves convex quadraticmore » programming problems, convex quadratically constrained quadratic programming problems, and general convex programming problems in fewer iterations. Moreover, several problems for which MOSEK fails are solved to optimality. In addition, we also find that iOptimize detects infeasibility more reliably than the general nonlinear solvers Ipopt (version 3.9.2) and Knitro (version 8.0).« less

Strain relaxation in convex-graded InxAl1-xAs (x = 0.05-0.79) metamorphic buffer layers grown by molecular beam epitaxy on GaAs(001)

NASA Astrophysics Data System (ADS)

Solov'ev, V. A.; Chernov, M. Yu; Baidakova, M. V.; Kirilenko, D. A.; Yagovkina, M. A.; Sitnikova, A. A.; Komissarova, T. A.; Kop'ev, P. S.; Ivanov, S. V.

2018-01-01

This paper presents a study of structural properties of InGaAs/InAlAs quantum well (QW) heterostructures with convex-graded InxAl1-xAs (x = 0.05-0.79) metamorphic buffer layers (MBLs) grown by molecular beam epitaxy on GaAs substrates. Mechanisms of elastic strain relaxation in the convex-graded MBLs were studied by the X-ray reciprocal space mapping combined with the data of spatially-resolved selected area electron diffraction implemented in a transmission electron microscope. The strain relaxation degree was approximated for the structures with different values of an In step-back. Strong contribution of the strain relaxation via lattice tilt in addition to the formation of the misfit dislocations has been observed for the convex-graded InAlAs MBL, which results in a reduced threading dislocation density in the QW region as compared to a linear-graded MBL.

Efficient Compressed Sensing Based MRI Reconstruction using Nonconvex Total Variation Penalties

NASA Astrophysics Data System (ADS)

Lazzaro, D.; Loli Piccolomini, E.; Zama, F.

2016-10-01

This work addresses the problem of Magnetic Resonance Image Reconstruction from highly sub-sampled measurements in the Fourier domain. It is modeled as a constrained minimization problem, where the objective function is a non-convex function of the gradient of the unknown image and the constraints are given by the data fidelity term. We propose an algorithm, Fast Non Convex Reweighted (FNCR), where the constrained problem is solved by a reweighting scheme, as a strategy to overcome the non-convexity of the objective function, with an adaptive adjustment of the penalization parameter. We propose a fast iterative algorithm and we can prove that it converges to a local minimum because the constrained problem satisfies the Kurdyka-Lojasiewicz property. Moreover the adaptation of non convex l0 approximation and penalization parameters, by means of a continuation technique, allows us to obtain good quality solutions, avoiding to get stuck in unwanted local minima. Some numerical experiments performed on MRI sub-sampled data show the efficiency of the algorithm and the accuracy of the solution.

Liquid phase heteroepitaxial growth on convex substrate using binary phase field crystal model

NASA Astrophysics Data System (ADS)

Lu, Yanli; Zhang, Tinghui; Chen, Zheng

2018-06-01

The liquid phase heteroepitaxial growth on convex substrate is investigated with the binary phase field crystal (PFC) model. The paper aims to focus on the transformation of the morphology of epitaxial films on convex substrate with two different radiuses of curvature (Ω) as well as influences of substrate vicinal angles on films growth. It is found that films growth experience different stages on convex substrate with different radiuses of curvature (Ω). For Ω = 512 Δx , the process of epitaxial film growth includes four stages: island coupled with layer-by-layer growth, layer-by-layer growth, island coupled with layer-by-layer growth, layer-by-layer growth. For Ω = 1024 Δx , film growth only experience islands growth and layer-by-layer growth. Also, substrate vicinal angle (π) is an important parameter for epitaxial film growth. We find the film can grow well when π = 2° for Ω = 512 Δx , while the optimized film can be obtained when π = 4° for Ω = 512 Δx .

QUADRATIC SERENDIPITY FINITE ELEMENTS ON POLYGONS USING GENERALIZED BARYCENTRIC COORDINATES

PubMed Central

RAND, ALEXANDER; GILLETTE, ANDREW; BAJAJ, CHANDRAJIT

2013-01-01

We introduce a finite element construction for use on the class of convex, planar polygons and show it obtains a quadratic error convergence estimate. On a convex n-gon, our construction produces 2n basis functions, associated in a Lagrange-like fashion to each vertex and each edge midpoint, by transforming and combining a set of n(n + 1)/2 basis functions known to obtain quadratic convergence. The technique broadens the scope of the so-called ‘serendipity’ elements, previously studied only for quadrilateral and regular hexahedral meshes, by employing the theory of generalized barycentric coordinates. Uniform a priori error estimates are established over the class of convex quadrilaterals with bounded aspect ratio as well as over the class of convex planar polygons satisfying additional shape regularity conditions to exclude large interior angles and short edges. Numerical evidence is provided on a trapezoidal quadrilateral mesh, previously not amenable to serendipity constructions, and applications to adaptive meshing are discussed. PMID:25301974

Torsional deformity of apical vertebra in adolescent idiopathic scoliosis.

PubMed

Kotwicki, Tomasz; Napiontek, Marek

2002-01-01

CT scans of structural thoracic idiopathic scoliosis were reviewed in nine patients admitted to our department for scoliosis surgery. The apical vertebra scans were chosen and the following parameters were evaluated: 1) alpha angle formed by the axis of vertebra and the axis of spinous process 2) beta concave and beta convex angle between the spinous process and the left and right transverse process, respectively, 3) gamma concave and gamma convex angle between the axis of vertebra and the left and right transverse process, respectively, 4) the rotation angle to the sagittal plane. The constant deviation of the spinous process towards the convex side of the curve was observed. The vertebral body itself was distorted towards the concavity of the curve. The angle between the spinous process and the transverse process was smaller on the convex side of the curve. The torsional, intravertebral deformity of the apical vertebra was a factor acting in the direction opposite to the rotation, in the sense to reduce the deformity of the spine in idiopathic scoliosis.

An axial temperature profile curvature criterion for the engineering of convex crystal growth interfaces in Bridgman systems

NASA Astrophysics Data System (ADS)

Peterson, Jeffrey H.; Derby, Jeffrey J.

2017-06-01

A unifying idea is presented for the engineering of convex melt-solid interface shapes in Bridgman crystal growth systems. Previous approaches to interface control are discussed with particular attention paid to the idea of a "booster" heater. Proceeding from the idea that a booster heater promotes a converging heat flux geometry and from the energy conservation equation, we show that a convex interface shape will naturally result when the interface is located in regions of the furnace where the axial thermal profile exhibits negative curvature, i.e., where d2 T / dz2 < 0 . This criterion is effective in explaining prior literature results on interface control and promising for the evaluation of new furnace designs. We posit that the negative curvature criterion may be applicable to the characterization of growth systems via temperature measurements in an empty furnace, providing insight about the potential for achieving a convex interface shape, without growing a crystal or conducting simulations.

New Convex and Spherical Structures of Bare Boron Clusters

NASA Astrophysics Data System (ADS)

Boustani, Ihsan

1997-10-01

New stable structures of bare boron clusters can easily be obtained and constructed with the help of an "Aufbau Principle" suggested by a systematicab initioHF-SCF and direct CI study. It is concluded that boron cluster formation can be established by elemental units of pentagonal and hexagonal pyramids. New convex and small spherical clusters different from the classical known forms of boron crystal structures are obtained by a combination of both basic units. Convex structures simulate boron surfaces which can be considered as segments of open or closed spheres. Both convex clusters B16and B46have energies close to those of their conjugate quasi-planar clusters, which are relatively stable and can be considered to act as a calibration mark. The closed spherical clusters B12, B22, B32, and B42are less stable than the corresponding conjugated quasi-planar structures. As a consequence, highly stable spherical boron clusters can systematically be predicted when their conjugate quasi-planar clusters are determined and energies are compared.

Scaling of Convex Hull Volume to Body Mass in Modern Primates, Non-Primate Mammals and Birds

PubMed Central

Brassey, Charlotte A.; Sellers, William I.

2014-01-01

The volumetric method of ‘convex hulling’ has recently been put forward as a mass prediction technique for fossil vertebrates. Convex hulling involves the calculation of minimum convex hull volumes (vol CH) from the complete mounted skeletons of modern museum specimens, which are subsequently regressed against body mass (M b) to derive predictive equations for extinct species. The convex hulling technique has recently been applied to estimate body mass in giant sauropods and fossil ratites, however the biomechanical signal contained within vol CH has remained unclear. Specifically, when vol CH scaling departs from isometry in a group of vertebrates, how might this be interpreted? Here we derive predictive equations for primates, non-primate mammals and birds and compare the scaling behaviour of M b to vol CH between groups. We find predictive equations to be characterised by extremely high correlation coefficients (r 2 = 0.97–0.99) and low mean percentage prediction error (11–20%). Results suggest non-primate mammals scale body mass to vol CH isometrically (b = 0.92, 95%CI = 0.85–1.00, p = 0.08). Birds scale body mass to vol CH with negative allometry (b = 0.81, 95%CI = 0.70–0.91, p = 0.011) and apparent density (vol CH/M b) therefore decreases with mass (r 2 = 0.36, p<0.05). In contrast, primates scale body mass to vol CH with positive allometry (b = 1.07, 95%CI = 1.01–1.12, p = 0.05) and apparent density therefore increases with size (r 2 = 0.46, p = 0.025). We interpret such departures from isometry in the context of the ‘missing mass’ of soft tissues that are excluded from the convex hulling process. We conclude that the convex hulling technique can be justifiably applied to the fossil record when a large proportion of the skeleton is preserved. However we emphasise the need for future studies to quantify interspecific variation in the distribution of soft tissues such as muscle, integument and body fat. PMID:24618736

Integrating NOE and RDC using sum-of-squares relaxation for protein structure determination.

PubMed

Khoo, Y; Singer, A; Cowburn, D

2017-07-01

We revisit the problem of protein structure determination from geometrical restraints from NMR, using convex optimization. It is well-known that the NP-hard distance geometry problem of determining atomic positions from pairwise distance restraints can be relaxed into a convex semidefinite program (SDP). However, often the NOE distance restraints are too imprecise and sparse for accurate structure determination. Residual dipolar coupling (RDC) measurements provide additional geometric information on the angles between atom-pair directions and axes of the principal-axis-frame. The optimization problem involving RDC is highly non-convex and requires a good initialization even within the simulated annealing framework. In this paper, we model the protein backbone as an articulated structure composed of rigid units. Determining the rotation of each rigid unit gives the full protein structure. We propose solving the non-convex optimization problems using the sum-of-squares (SOS) hierarchy, a hierarchy of convex relaxations with increasing complexity and approximation power. Unlike classical global optimization approaches, SOS optimization returns a certificate of optimality if the global optimum is found. Based on the SOS method, we proposed two algorithms-RDC-SOS and RDC-NOE-SOS, that have polynomial time complexity in the number of amino-acid residues and run efficiently on a standard desktop. In many instances, the proposed methods exactly recover the solution to the original non-convex optimization problem. To the best of our knowledge this is the first time SOS relaxation is introduced to solve non-convex optimization problems in structural biology. We further introduce a statistical tool, the Cramér-Rao bound (CRB), to provide an information theoretic bound on the highest resolution one can hope to achieve when determining protein structure from noisy measurements using any unbiased estimator. Our simulation results show that when the RDC measurements are corrupted by Gaussian noise of realistic variance, both SOS based algorithms attain the CRB. We successfully apply our method in a divide-and-conquer fashion to determine the structure of ubiquitin from experimental NOE and RDC measurements obtained in two alignment media, achieving more accurate and faster reconstructions compared to the current state of the art.

A Novel Method Using Abstract Convex Underestimation in Ab-Initio Protein Structure Prediction for Guiding Search in Conformational Feature Space.

PubMed

Hao, Xiao-Hu; Zhang, Gui-Jun; Zhou, Xiao-Gen; Yu, Xu-Feng

2016-01-01

To address the searching problem of protein conformational space in ab-initio protein structure prediction, a novel method using abstract convex underestimation (ACUE) based on the framework of evolutionary algorithm was proposed. Computing such conformations, essential to associate structural and functional information with gene sequences, is challenging due to the high-dimensionality and rugged energy surface of the protein conformational space. As a consequence, the dimension of protein conformational space should be reduced to a proper level. In this paper, the high-dimensionality original conformational space was converted into feature space whose dimension is considerably reduced by feature extraction technique. And, the underestimate space could be constructed according to abstract convex theory. Thus, the entropy effect caused by searching in the high-dimensionality conformational space could be avoided through such conversion. The tight lower bound estimate information was obtained to guide the searching direction, and the invalid searching area in which the global optimal solution is not located could be eliminated in advance. Moreover, instead of expensively calculating the energy of conformations in the original conformational space, the estimate value is employed to judge if the conformation is worth exploring to reduce the evaluation time, thereby making computational cost lower and the searching process more efficient. Additionally, fragment assembly and the Monte Carlo method are combined to generate a series of metastable conformations by sampling in the conformational space. The proposed method provides a novel technique to solve the searching problem of protein conformational space. Twenty small-to-medium structurally diverse proteins were tested, and the proposed ACUE method was compared with It Fix, HEA, Rosetta and the developed method LEDE without underestimate information. Test results show that the ACUE method can more rapidly and more efficiently obtain the near-native protein structure.

A theoretical stochastic control framework for adapting radiotherapy to hypoxia

NASA Astrophysics Data System (ADS)

Saberian, Fatemeh; Ghate, Archis; Kim, Minsun

2016-10-01

Hypoxia, that is, insufficient oxygen partial pressure, is a known cause of reduced radiosensitivity in solid tumors, and especially in head-and-neck tumors. It is thus believed to adversely affect the outcome of fractionated radiotherapy. Oxygen partial pressure varies spatially and temporally over the treatment course and exhibits inter-patient and intra-tumor variation. Emerging advances in non-invasive functional imaging offer the future possibility of adapting radiotherapy plans to this uncertain spatiotemporal evolution of hypoxia over the treatment course. We study the potential benefits of such adaptive planning via a theoretical stochastic control framework using computer-simulated evolution of hypoxia on computer-generated test cases in head-and-neck cancer. The exact solution of the resulting control problem is computationally intractable. We develop an approximation algorithm, called certainty equivalent control, that calls for the solution of a sequence of convex programs over the treatment course; dose-volume constraints are handled using a simple constraint generation method. These convex programs are solved using an interior point algorithm with a logarithmic barrier via Newton’s method and backtracking line search. Convexity of various formulations in this paper is guaranteed by a sufficient condition on radiobiological tumor-response parameters. This condition is expected to hold for head-and-neck tumors and for other similarly responding tumors where the linear dose-response parameter is larger than the quadratic dose-response parameter. We perform numerical experiments on four test cases by using a first-order vector autoregressive process with exponential and rational-quadratic covariance functions from the spatiotemporal statistics literature to simulate the evolution of hypoxia. Our results suggest that dynamic planning could lead to a considerable improvement in the number of tumor cells remaining at the end of the treatment course. Through these simulations, we also gain insights into when and why dynamic planning is likely to yield the largest benefits.

Design and experimental evidence of a flat graded-index photonic crystal lens

NASA Astrophysics Data System (ADS)

Gaufillet, F.; Akmansoy, É.

2013-08-01

We report on the design and the experimental evidence of a flat graded index photonic crystal lens. The gradient has been designed so that the flat slab focuses a plane wave and so that it converts the wave issued from a point source into a plane wave. This graded-index photonic crystal lens operates as a convex lens. The gradient of index results from varying the filling factor of the photonic crystal in the direction perpendicular to that of the propagation of the electromagnetic field. The shape of the gradient of index has been designed by engineering the iso-frequency curves of the photonic crystal. As only a few layers were necessary and as graded photonic crystals may be fabricated by a variety of processes, this shows the ability of graded photonic crystals to efficiently apply for various photonic devices, from microwave range to the optical domain. 42.70.Qs Photonic bandgap materials, 78.67.Pt Optical properties of photonic structures, 41.20.Jb Electromagnetic wave propagation; radiowave propagation 84.40.Ba Antennas.

In- and Ga-based inorganic double perovskites with direct bandgaps for photovoltaic applications.

PubMed

Dai, Jun; Ma, Liang; Ju, Minggang; Huang, Jinsong; Zeng, Xiao Cheng

2017-08-16

Double perovskites in the form of A 2 B'B''X 6 (A = Cs, B' = Ag, B'' = Bi) have been reported as potential alternatives to lead-containing organometal trihalide perovskites. However, all double perovskites synthesized to date exhibit indirect bandgaps >1.95 eV, which are undesirable for photovoltaic and optoelectronic applications. Herein, we report a comprehensive computer-aided screening of In- and Ga-based double perovskites for potential photovoltaic applications. To this end, several preconditions are implemented for the screening of optimal candidates, which include structural stability, electronic bandgaps, and optical absorption. Importantly, four In- and Ga-based double perovskites are identified to possess direct bandgaps within the desirable range of 0.9-1.6 eV for photovoltaic applications. Dominant optical absorption of the four double perovskites is found to be in the UV range. The structural and thermal stability of the four double perovskites are examined using both the empirical Goldschmidt ratio and convex-hull calculations. Only Cs 2 AgInBr 6 is predicted to be thermodynamically stable.

Electrowetting liquid lens array on curved substrates for wide field of view image sensor

NASA Astrophysics Data System (ADS)

Bang, Yousung; Lee, Muyoung; Won, Yong Hyub

2016-03-01

In this research, electrowetting liquid lens array on curved substrates is developed for wide field of view image sensor. In the conventional image sensing system, this lens array is usually in the form of solid state. However, in this state, the lens array which is similar to insect-like compound eyes in nature has several limitations such as degradation of image quality and narrow field of view because it cannot adjust focal length of lens. For implementation of the more enhanced system, the curved array of lenses based on electrowetting effect is developed in this paper, which can adjust focal length of lens. The fabrication of curved lens array is conducted upon the several steps, including chamber fabrication, electrode & dielectric layer deposition, liquid injection, and encapsulation. As constituent materials, IZO coated convex glass, UV epoxy (NOA 68), DI water, and dodecane are used. The number of lenses on the fabricated panel is 23 by 23 and each lens has 1mm aperture with 1.6mm pitch between adjacent lenses. When the voltage is applied on the device, it is observed that each lens is changed from concave state to convex state. From the unique optical characteristics of curved array of liquid lenses such as controllable focal length and wide field of view, we can expect that it has potential applications in various fields such as medical diagnostics, surveillance systems, and light field photography.

Evaluating convex roof entanglement measures.

PubMed

Tóth, Géza; Moroder, Tobias; Gühne, Otfried

2015-04-24

We show a powerful method to compute entanglement measures based on convex roof constructions. In particular, our method is applicable to measures that, for pure states, can be written as low order polynomials of operator expectation values. We show how to compute the linear entropy of entanglement, the linear entanglement of assistance, and a bound on the dimension of the entanglement for bipartite systems. We discuss how to obtain the convex roof of the three-tangle for three-qubit states. We also show how to calculate the linear entropy of entanglement and the quantum Fisher information based on partial information or device independent information. We demonstrate the usefulness of our method by concrete examples.

Interpolation Error Estimates for Mean Value Coordinates over Convex Polygons

PubMed Central

Rand, Alexander; Gillette, Andrew; Bajaj, Chandrajit

2012-01-01

In a similar fashion to estimates shown for Harmonic, Wachspress, and Sibson coordinates in [Gillette et al., AiCM, to appear], we prove interpolation error estimates for the mean value coordinates on convex polygons suitable for standard finite element analysis. Our analysis is based on providing a uniform bound on the gradient of the mean value functions for all convex polygons of diameter one satisfying certain simple geometric restrictions. This work makes rigorous an observed practical advantage of the mean value coordinates: unlike Wachspress coordinates, the gradient of the mean value coordinates does not become large as interior angles of the polygon approach π. PMID:24027379

Interpolation Error Estimates for Mean Value Coordinates over Convex Polygons.

PubMed

Rand, Alexander; Gillette, Andrew; Bajaj, Chandrajit

2013-08-01

In a similar fashion to estimates shown for Harmonic, Wachspress, and Sibson coordinates in [Gillette et al., AiCM, to appear], we prove interpolation error estimates for the mean value coordinates on convex polygons suitable for standard finite element analysis. Our analysis is based on providing a uniform bound on the gradient of the mean value functions for all convex polygons of diameter one satisfying certain simple geometric restrictions. This work makes rigorous an observed practical advantage of the mean value coordinates: unlike Wachspress coordinates, the gradient of the mean value coordinates does not become large as interior angles of the polygon approach π.

Impact of trailing edge shape on the wake and propulsive performance of pitching panels

NASA Astrophysics Data System (ADS)

Van Buren, T.; Floryan, D.; Brunner, D.; Senturk, U.; Smits, A. J.

2017-01-01

The effects of changing the trailing edge shape on the wake and propulsive performance of a pitching rigid panel are examined experimentally. The panel aspect ratio is AR=1 , and the trailing edges are symmetric chevron shapes with convex and concave orientations of varying degree. Concave trailing edges delay the natural vortex bending and compression of the wake, and the mean streamwise velocity field contains a single jet. Conversely, convex trailing edges promote wake compression and produce a quadfurcated wake with four jets. As the trailing edge shape changes from the most concave to the most convex, the thrust and efficiency increase significantly.

A Convex Approach to Fault Tolerant Control

NASA Technical Reports Server (NTRS)

Maghami, Peiman G.; Cox, David E.; Bauer, Frank (Technical Monitor)

2002-01-01

The design of control laws for dynamic systems with the potential for actuator failures is considered in this work. The use of Linear Matrix Inequalities allows more freedom in controller design criteria than typically available with robust control. This work proposes an extension of fault-scheduled control design techniques that can find a fixed controller with provable performance over a set of plants. Through convexity of the objective function, performance bounds on this set of plants implies performance bounds on a range of systems defined by a convex hull. This is used to incorporate performance bounds for a variety of soft and hard failures into the control design problem.

Rapid Generation of Optimal Asteroid Powered Descent Trajectories Via Convex Optimization

NASA Technical Reports Server (NTRS)

Pinson, Robin; Lu, Ping

2015-01-01

This paper investigates a convex optimization based method that can rapidly generate the fuel optimal asteroid powered descent trajectory. The ultimate goal is to autonomously design the optimal powered descent trajectory on-board the spacecraft immediately prior to the descent burn. Compared to a planetary powered landing problem, the major difficulty is the complex gravity field near the surface of an asteroid that cannot be approximated by a constant gravity field. This paper uses relaxation techniques and a successive solution process that seeks the solution to the original nonlinear, nonconvex problem through the solutions to a sequence of convex optimal control problems.

Relaxation in control systems of subdifferential type

NASA Astrophysics Data System (ADS)

Tolstonogov, A. A.

2006-02-01

In a separable Hilbert space we consider a control system with evolution operators that are subdifferentials of a proper convex lower semicontinuous function depending on time. The constraint on the control is given by a multivalued function with non-convex values that is lower semicontinuous with respect to the variable states. Along with the original system we consider the system in which the constraint on the control is the upper semicontinuous convex-valued regularization of the original constraint. We study relations between the solution sets of these systems. As an application we consider a control variational inequality. We give an example of a control system of parabolic type with an obstacle.

Density of convex intersections and applications

PubMed Central

Rautenberg, C. N.; Rösel, S.

2017-01-01

In this paper, we address density properties of intersections of convex sets in several function spaces. Using the concept of Γ-convergence, it is shown in a general framework, how these density issues naturally arise from the regularization, discretization or dualization of constrained optimization problems and from perturbed variational inequalities. A variety of density results (and counterexamples) for pointwise constraints in Sobolev spaces are presented and the corresponding regularity requirements on the upper bound are identified. The results are further discussed in the context of finite-element discretizations of sets associated with convex constraints. Finally, two applications are provided, which include elasto-plasticity and image restoration problems. PMID:28989301

Reducing the duality gap in partially convex programming

DOE Office of Scientific and Technical Information (OSTI.GOV)

Correa, R.

1994-12-31

We consider the non-linear minimization program {alpha} = min{sub z{element_of}D, x{element_of}C}{l_brace}f{sub 0}(z, x) : f{sub i}(z, x) {<=} 0, i {element_of} {l_brace}1, ..., m{r_brace}{r_brace} where f{sub i}(z, {center_dot}) are convex functions, C is convex and D is compact. Following Ben-Tal, Eiger and Gershowitz we prove the existence of a partial dual program whose optimum is arbitrarily close to {alpha}. The idea, corresponds to the branching principle in Branch and Bound methods. We describe such a kind of algorithm for obtaining the desired partial dual.

On the polarizability dyadics of electrically small, convex objects

NASA Astrophysics Data System (ADS)

Lakhtakia, Akhlesh

1993-11-01

This communication on the polarizability dyadics of electrically small objects of convex shapes has been prompted by a recent paper published by Sihvola and Lindell on the polarizability dyadic of an electrically gyrotropic sphere. A mini-review of recent work on polarizability dyadics is appended.

On new fractional Hermite-Hadamard type inequalities for n-time differentiable quasi-convex functions and P-functions

NASA Astrophysics Data System (ADS)

Set, Erhan; Özdemir, M. Emin; Alan, E. Aykan

2017-04-01

In this article, by using the Hölder's inequality and power mean inequality the authors establish several inequalities of Hermite-Hadamard type for n- time differentiable quasi-convex functions and P- functions involving Riemann-Liouville fractional integrals.

Convexity of Energy-Like Functions: Theoretical Results and Applications to Power System Operations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dvijotham, Krishnamurthy; Low, Steven; Chertkov, Michael

2015-01-12

Power systems are undergoing unprecedented transformations with increased adoption of renewables and distributed generation, as well as the adoption of demand response programs. All of these changes, while making the grid more responsive and potentially more efficient, pose significant challenges for power systems operators. Conventional operational paradigms are no longer sufficient as the power system may no longer have big dispatchable generators with sufficient positive and negative reserves. This increases the need for tools and algorithms that can efficiently predict safe regions of operation of the power system. In this paper, we study energy functions as a tool to designmore » algorithms for various operational problems in power systems. These have a long history in power systems and have been primarily applied to transient stability problems. In this paper, we take a new look at power systems, focusing on an aspect that has previously received little attention: Convexity. We characterize the domain of voltage magnitudes and phases within which the energy function is convex in these variables. We show that this corresponds naturally with standard operational constraints imposed in power systems. We show that power of equations can be solved using this approach, as long as the solution lies within the convexity domain. We outline various desirable properties of solutions in the convexity domain and present simple numerical illustrations supporting our results.« less

L 1-2 minimization for exact and stable seismic attenuation compensation

NASA Astrophysics Data System (ADS)

Wang, Yufeng; Ma, Xiong; Zhou, Hui; Chen, Yangkang

2018-06-01

Frequency-dependent amplitude absorption and phase velocity dispersion are typically linked by the causality-imposed Kramers-Kronig relations, which inevitably degrade the quality of seismic data. Seismic attenuation compensation is an important processing approach for enhancing signal resolution and fidelity, which can be performed on either pre-stack or post-stack data so as to mitigate amplitude absorption and phase dispersion effects resulting from intrinsic anelasticity of subsurface media. Inversion-based compensation with L1 norm constraint, enlightened by the sparsity of the reflectivity series, enjoys better stability over traditional inverse Q filtering. However, constrained L1 minimization serving as the convex relaxation of the literal L0 sparsity count may not give the sparsest solution when the kernel matrix is severely ill conditioned. Recently, non-convex metric for compressed sensing has attracted considerable research interest. In this paper, we propose a nearly unbiased approximation of the vector sparsity, denoted as L1-2 minimization, for exact and stable seismic attenuation compensation. Non-convex penalty function of L1-2 norm can be decomposed into two convex subproblems via difference of convex algorithm, each subproblem can be solved efficiently by alternating direction method of multipliers. The superior performance of the proposed compensation scheme based on L1-2 metric over conventional L1 penalty is further demonstrated by both synthetic and field examples.

Linear Controller Design: Limits of Performance

DTIC Science & Technology

1991-01-01

where a sensor should be placed eg where an accelerometer is to be positioned on an aircraft or where a strain gauge is placed along a beam The...309 VIII CONTENTS 14 Special Algorithms for Convex Optimization 311 Notation and Problem Denitions...311 On Algorithms for Convex Optimization 312 CuttingPlane Algorithms

Algorithms for Mathematical Programming with Emphasis on Bi-level Models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Goldfarb, Donald; Iyengar, Garud

2014-05-22

The research supported by this grant was focused primarily on first-order methods for solving large scale and structured convex optimization problems and convex relaxations of nonconvex problems. These include optimal gradient methods, operator and variable splitting methods, alternating direction augmented Lagrangian methods, and block coordinate descent methods.

The Modified HZ Conjugate Gradient Algorithm for Large-Scale Nonsmooth Optimization.

PubMed

Yuan, Gonglin; Sheng, Zhou; Liu, Wenjie

2016-01-01

In this paper, the Hager and Zhang (HZ) conjugate gradient (CG) method and the modified HZ (MHZ) CG method are presented for large-scale nonsmooth convex minimization. Under some mild conditions, convergent results of the proposed methods are established. Numerical results show that the presented methods can be better efficiency for large-scale nonsmooth problems, and several problems are tested (with the maximum dimensions to 100,000 variables).

Angular photogrammetric comparison of the soft-tissue facial profile of Kenyans and Chinese.

PubMed

Wamalwa, Peter; Amisi, Stella Kabarika; Wang, Yunji; Chen, Song

2011-05-01

The purpose of this study was to determine the average angular dimensions that define the normal soft-tissue facial profiles of black Kenyans and Chinese and compare them with each other and with values proposed for whites. Standardized facial profile photographs, taken in natural head position, of 177 black Kenyans and 156 Chinese with normal occlusion and well-balanced faces were analyzed for 12 angular parameters. Two-sample t-tests were used to determine sex and racial differences. Kenyan and Chinese averages were compared with proposed white values using 1-sample t-tests. Eight parameters in Kenyans and 7 in Chinese showed sex differences. All angles, except for facial convexity, nasal dorsum, and inferior facial height, were different between Kenyans and Chinese. Kenyan and Chinese averages for all parameters were different from proposed white average, except for facial convexity. Nasolabial and mentolabial angles showed large individual variability and racial differences. The study demonstrated many differences in average angular measurements of the facial profiles of black Kenyans, Chinese, and white standards. Orthodontists, maxillofacial and plastic surgeons, and other clinicians working in the craniofacial region should bear these in mind when setting aesthetic treatment goals for patients of different races. Mean values from this study can be used for comparison with similar records of subjects with same ethnicity.

Active optics: off axis aspherics generation for high contrast imaging

NASA Astrophysics Data System (ADS)

Hugot, E.; Laslandes, M.; Ferrari, M.; Vives, S.; Moindrot, S.; El Hadi, K.; Dohlen, K.

2017-11-01

Active Optics methods, based on elasticity theory, allow the aspherisation of optical surfaces by stress polishing but also active aspherisation in situ. Researches in this field will impact the final performance and the final cost of any telescope or instrument. The stress polishing method is well suited for the superpolishing of aspheric components for astronomy. Its principle relies on spherical polishing with a full-sized tool of a warped substrate, which becomes aspherical once unwarped. The main advantage of this technique is the very high optical quality obtained either on form or on high spatial frequency errors. Furthermore, the roughness can be decreased down to a few angstroms, thanks the classical polishing with a large pitch tool, providing a substantial gain on the final scientific performance, for instance on the contrast on coronagraphic images, but also on the polishing time and cost. Stress polishing is based on elasticity theory, and requires an optimised deformation system able to provide the right aspherical form on the optical surface during polishing. The optical quality of the deformation is validated using extensive Finite Element Analysis, allowing an estimation of residuals and an optimisation of the warping harness. We describe here the work realised on stress polishing of toric mirrors for VLT-SPHERE and then our actual work on off axis aspherics (OAA) for the ASPIICS-Proba3 mission for solar coronagraphy. The ASPIICS optical design made by Vives et al is a three mirrors anastigmat including a concave off axis hyperboloid and a convex off axis parabola (OAP). We are developing a prototype in order to demonstrate the feasibility of this type of surface, using a multi-mode warping harness (Lemaitre et al). Furthermore, we present our work on variable OAP, meaning the possibility to adjust the shape of a simple OAP in situ with a minimal number of actuators, typically one actuator per optical mode (Focus, Coma and Astigmatism). Applications for future space telescopes and instrumentation are discussed.

Wafer-level fabrication of arrays of glass lens doublets

NASA Astrophysics Data System (ADS)

Passilly, Nicolas; Perrin, Stéphane; Albero, Jorge; Krauter, Johann; Gaiffe, Olivier; Gauthier-Manuel, Ludovic; Froehly, Luc; Lullin, Justine; Bargiel, Sylwester; Osten, Wolfgang; Gorecki, Christophe

2016-04-01

Systems for imaging require to employ high quality optical components in order to dispose of optical aberrations and thus reach sufficient resolution. However, well-known methods to get rid of optical aberrations, such as aspherical profiles or diffractive corrections are not easy to apply to micro-optics. In particular, some of these methods rely on polymers which cannot be associated when such lenses are to be used in integrated devices requiring high temperature process for their further assembly and separation. Among the different approaches, the most common is the lens splitting that consists in dividing the focusing power between two or more optical components. In here, we propose to take advantage of a wafer-level technique, devoted to the generation of glass lenses, which involves thermal reflow in silicon cavities to generate lens doublets. After the convex lens sides are generated, grinding and polishing of both stack sides allow, on the first hand, to form the planar lens backside and, on the other hand, to open the silicon cavity. Nevertheless, silicon frames are then kept and thinned down to form well-controlled and auto-aligned spacers between the lenses. Subsequent accurate vertical assembly of the glass lens arrays is performed by anodic bonding. The latter ensures a high level of alignment both laterally and axially since no additional material is required. Thanks to polishing, the generated lens doublets are then as thin as several hundreds of microns and compatible with micro-opto-electro-systems (MOEMS) technologies since they are only made of glass and silicon. The generated optical module is then robust and provide improved optical performances. Indeed, theoretically, two stacked lenses with similar features and spherical profiles can be almost diffraction limited whereas a single lens characterized by the same numerical aperture than the doublet presents five times higher wavefront error. To demonstrate such assumption, we fabricated glass lens doublets and compared them to single lenses of equivalent focusing power. For similar illumination, the optical aberrations are significantly reduced.

UV spectroscopy with the CETUS multi-object spectrometer

NASA Astrophysics Data System (ADS)

Kendrick, Stephen E.; Woodruff, Robert; Hull, Anthony; Heap, Sara; Kutyrev, Alexander; Purves, Lloyd; Danchi, William

2018-01-01

The ultraviolet multi-object spectrograph (MOS) for the Cosmic Evolution Through UV Spectroscopy (CETUS) concept is a slit-based instrument allowing multiple simultaneous observations over a wide field of view. The UV MOS will be able to target up to 100 objects at a time without the issues of confusion with nearby sources or unwanted background like zodiacal stray light. The multiplexing will allow over 100,000 galaxies to be observed over a typical mission lifetime which greatly enhances the scientific yield. The MOS utilizes a next-generation micro-shutter array, an efficient aspheric Offner-like spectrometer design with a convex grating, and nanotube light traps for suppressing unwanted wavelengths. The optical coatings are also designed for optimizing the UV throughput while minimizing out-of-band signal at the detector.

Multiplexing in astrophysics with a UV multi-object spectrometer on CETUS, a probe-class mission study

NASA Astrophysics Data System (ADS)

Kendrick, Stephen E.; Woodruff, Robert A.; Hull, Tony; Heap, Sara R.; Kutyrev, Alexander; Danchi, William; Purves, Lloyd

2017-09-01

The ultraviolet multi-object spectrograph (MOS) for the Cosmic Evolution Through UV Spectroscopy (CETUS) concept1,2 is a slit-based instrument allowing multiple simultaneous observations over a wide field of view. It utilizes a next-generation micro-shutter array, an efficient aspheric Offner spectrometer design with a convex grating, and carbon nanotube light traps for suppressing unwanted wavelengths. The optical coatings are also designed to optimize the UV throughput while minimizing out-of-band signal at the detector. The UV MOS will be able to target up to 100 objects at a time without the issues of confusion with nearby sources or unwanted background like zodiacal stray light. With this multiplexing, the scientific yield of both Probe and Great Observatories will be greatly enhanced.

Photon-efficient super-resolution laser radar

NASA Astrophysics Data System (ADS)

Shin, Dongeek; Shapiro, Jeffrey H.; Goyal, Vivek K.

2017-08-01

The resolution achieved in photon-efficient active optical range imaging systems can be low due to non-idealities such as propagation through a diffuse scattering medium. We propose a constrained optimization-based frame- work to address extremes in scarcity of photons and blurring by a forward imaging kernel. We provide two algorithms for the resulting inverse problem: a greedy algorithm, inspired by sparse pursuit algorithms; and a convex optimization heuristic that incorporates image total variation regularization. We demonstrate that our framework outperforms existing deconvolution imaging techniques in terms of peak signal-to-noise ratio. Since our proposed method is able to super-resolve depth features using small numbers of photon counts, it can be useful for observing fine-scale phenomena in remote sensing through a scattering medium and through-the-skin biomedical imaging applications.

Method and system for producing sputtered thin films with sub-angstrom thickness uniformity or custom thickness gradients

DOEpatents

Folta, James A.; Montcalm, Claude; Walton, Christopher

2003-01-01

A method and system for producing a thin film with highly uniform (or highly accurate custom graded) thickness on a flat or graded substrate (such as concave or convex optics), by sweeping the substrate across a vapor deposition source with controlled (and generally, time-varying) velocity. In preferred embodiments, the method includes the steps of measuring the source flux distribution (using a test piece that is held stationary while exposed to the source), calculating a set of predicted film thickness profiles, each film thickness profile assuming the measured flux distribution and a different one of a set of sweep velocity modulation recipes, and determining from the predicted film thickness profiles a sweep velocity modulation recipe which is adequate to achieve a predetermined thickness profile. Aspects of the invention include a practical method of accurately measuring source flux distribution, and a computer-implemented method employing a graphical user interface to facilitate convenient selection of an optimal or nearly optimal sweep velocity modulation recipe to achieve a desired thickness profile on a substrate. Preferably, the computer implements an algorithm in which many sweep velocity function parameters (for example, the speed at which each substrate spins about its center as it sweeps across the source) can be varied or set to zero.

Convex central configurations for the n-body problem

NASA Astrophysics Data System (ADS)

Xia, Zhihong

We give a simple proof of a classical result of MacMillan and Bartky (Trans. Amer. Math. Soc. 34 (1932) 838) which states that, for any four positive masses and any assigned order, there is a convex planar central configuration. Moreover, we show that the central configurations we find correspond to local minima of the potential function with fixed moment of inertia. This allows us to show that there are at least six local minimum central configurations for the planar four-body problem. We also show that for any assigned order of five masses, there is at least one convex spatial central configuration of local minimum type. Our method also applies to some other cases.

High power laser welding of thick steel plates in a horizontal butt joint configuration

NASA Astrophysics Data System (ADS)

Atabaki, M. Mazar; Yazdian, N.; Ma, J.; Kovacevic, R.

2016-09-01

In this investigation, two laser-based welding techniques, autogenous laser welding (ALW) and laser welding assisted with a cold wire (LWACW), were applied to join thick plates of a structural steel (A36) in a horizontal narrow gap butt joint configuration. The main practical parameters including welding method and laser power were varied to get the sound weld with a requirement to achieve a full penetration with the reinforcement at the back side of weld in just one pass. The weld-bead shape, cross-section and mechanical properties were evaluated by profilometer, micro-hardness test and optical microscope. In order to investigate the stability of laser-induced plasma plume, the emitted optical spectra was detected and analyzed by the spectroscopy analysis. It was found that at the laser power of 7 kW a fully penetrated weld with a convex back side of weld could be obtained by the LWACW. The microstructural examinations showed that for the ALW the acicular ferrite and for the LWACW the pearlite were formed in the heat affected zone (HAZ). The prediction of microstructure based on continuous cooling transformation (CCT) diagram and cooling curves obtained by thermocouple measurement were in good agreement with each other. According to the plasma ionization values obtained from the spectroscopy analysis the plume for both processes was recognized as dominated weakly ionized plasma including the main vaporized elemental composition. At the optimum welding condition (LWACW at the laser power of 7 kW) the fluctuation of the electron temperature was reduced. The spectroscopy analysis demonstrated that at the higher laser power more of the elemental compositions such as Mn and Fe were evaporated.

What causes the facing-the-viewer bias in biological motion?

PubMed

Weech, Séamas; McAdam, Matthew; Kenny, Sophie; Troje, Nikolaus F

2014-10-13

Orthographically projected biological motion point-light displays are generally ambiguous with respect to their orientation in depth, yet observers consistently prefer the facing-the-viewer interpretation. There has been discussion as to whether this bias can be attributed to the social relevance of biological motion stimuli or relates to local, low-level stimulus properties. In the present study we address this question. In Experiment 1, we compared the facing-the-viewer bias produced by a series of four stick figures and three human silhouettes that differed in posture, gender, and the presence versus absence of walking motion. Using a paradigm in which we asked observers to indicate the spinning direction of these figures, we found no bias when participants observed silhouettes, whereas a pronounced degree of bias was elicited by most stick figures. We hypothesized that the ambiguous surface normals on the lines and dots that comprise stick figures are prone to a visual bias that assumes surfaces to be convex. The local surface orientations of the occluding contours of silhouettes are unambiguous, and as such the convexity bias does not apply. In Experiment 2, we tested the role of local features in ambiguous surface perception by adding dots to the elbows and knees of silhouettes. We found biases consistent with the facing directions implied by a convex body surface. The results unify a number of findings regarding the facing-the-viewer bias. We conclude that the facing-the-viewer bias is established at the level of surface reconstruction from local image features rather than on a semantic level. © 2014 ARVO.

CAD-based Automatic Modeling Method for Geant4 geometry model Through MCAM

NASA Astrophysics Data System (ADS)

Wang, Dong; Nie, Fanzhi; Wang, Guozhong; Long, Pengcheng; LV, Zhongliang; LV, Zhongliang

2014-06-01

Geant4 is a widely used Monte Carlo transport simulation package. Before calculating using Geant4, the calculation model need be established which could be described by using Geometry Description Markup Language (GDML) or C++ language. However, it is time-consuming and error-prone to manually describe the models by GDML. Automatic modeling methods have been developed recently, but there are some problem existed in most of present modeling programs, specially some of them were not accurate or adapted to specifically CAD format. To convert the GDML format models to CAD format accurately, a Geant4 Computer Aided Design (CAD) based modeling method was developed for automatically converting complex CAD geometry model into GDML geometry model. The essence of this method was dealing with CAD model represented with boundary representation (B-REP) and GDML model represented with constructive solid geometry (CSG). At first, CAD model was decomposed to several simple solids which had only one close shell. And then the simple solid was decomposed to convex shell set. Then corresponding GDML convex basic solids were generated by the boundary surfaces getting from the topological characteristic of a convex shell. After the generation of these solids, GDML model was accomplished with series boolean operations. This method was adopted in CAD/Image-based Automatic Modeling Program for Neutronics & Radiation Transport (MCAM), and tested with several models including the examples in Geant4 install package. The results showed that this method could convert standard CAD model accurately, and can be used for Geant4 automatic modeling.

78 FR 68833 - Combined Notice of Filings #1

Federal Register 2010, 2011, 2012, 2013, 2014

2013-11-15

... DEPARTMENT OF ENERGY Federal Energy Regulatory Commission Combined Notice of Filings 1 Take notice... Wallingford--CONVEX Services CL&P Electric Rate Schedule FERC No. 583 to be effective 1/1/2014. Filed Date: 11... Company submits CMEEC--CONVEX Services First Revised Rate Schedule FERC No. 576 to be effective 1/1/2014...

Convexities move because they contain matter.

PubMed

Barenholtz, Elan

2010-09-22

Figure-ground assignment to a contour is a fundamental stage in visual processing. The current paper introduces a novel, highly general dynamic cue to figure-ground assignment: "Convex Motion." Across six experiments, subjects showed a strong preference to assign figure and ground to a dynamically deforming contour such that the moving contour segment was convex rather than concave. Experiments 1 and 2 established the preference across two different kinds of deformational motion. Additional experiments determined that this preference was not due to fixation (Experiment 3) or attentional mechanisms (Experiment 4). Experiment 5 found a similar, but reduced bias for rigid-as opposed to deformational-motion, and Experiment 6 demonstrated that the phenomenon depends on the global motion of the effected contour. An explanation of this phenomenon is presented on the basis of typical natural deformational motion, which tends to involve convex contour projections that contain regions consisting of physical "matter," as opposed to concave contour indentations that contain empty space. These results highlight the fundamental relationship between figure and ground, perceived shape, and the inferred physical properties of an object.

A distributed approach to the OPF problem

NASA Astrophysics Data System (ADS)

Erseghe, Tomaso

2015-12-01

This paper presents a distributed approach to optimal power flow (OPF) in an electrical network, suitable for application in a future smart grid scenario where access to resource and control is decentralized. The non-convex OPF problem is solved by an augmented Lagrangian method, similar to the widely known ADMM algorithm, with the key distinction that penalty parameters are constantly increased. A (weak) assumption on local solver reliability is required to always ensure convergence. A certificate of convergence to a local optimum is available in the case of bounded penalty parameters. For moderate sized networks (up to 300 nodes, and even in the presence of a severe partition of the network), the approach guarantees a performance very close to the optimum, with an appreciably fast convergence speed. The generality of the approach makes it applicable to any (convex or non-convex) distributed optimization problem in networked form. In the comparison with the literature, mostly focused on convex SDP approximations, the chosen approach guarantees adherence to the reference problem, and it also requires a smaller local computational complexity effort.

Efficient convex-elastic net algorithm to solve the Euclidean traveling salesman problem.

PubMed

Al-Mulhem, M; Al-Maghrabi, T

1998-01-01

This paper describes a hybrid algorithm that combines an adaptive-type neural network algorithm and a nondeterministic iterative algorithm to solve the Euclidean traveling salesman problem (E-TSP). It begins with a brief introduction to the TSP and the E-TSP. Then, it presents the proposed algorithm with its two major components: the convex-elastic net (CEN) algorithm and the nondeterministic iterative improvement (NII) algorithm. These two algorithms are combined into the efficient convex-elastic net (ECEN) algorithm. The CEN algorithm integrates the convex-hull property and elastic net algorithm to generate an initial tour for the E-TSP. The NII algorithm uses two rearrangement operators to improve the initial tour given by the CEN algorithm. The paper presents simulation results for two instances of E-TSP: randomly generated tours and tours for well-known problems in the literature. Experimental results are given to show that the proposed algorithm ran find the nearly optimal solution for the E-TSP that outperform many similar algorithms reported in the literature. The paper concludes with the advantages of the new algorithm and possible extensions.

Determining Representative Elementary Volume For Multiple Petrophysical Parameters using a Convex Hull Analysis of Digital Rock Data

NASA Astrophysics Data System (ADS)

Shah, S.; Gray, F.; Yang, J.; Crawshaw, J.; Boek, E.

2016-12-01

Advances in 3D pore-scale imaging and computational methods have allowed an exceptionally detailed quantitative and qualitative analysis of the fluid flow in complex porous media. A fundamental problem in pore-scale imaging and modelling is how to represent and model the range of scales encountered in porous media, starting from the smallest pore spaces. In this study, a novel method is presented for determining the representative elementary volume (REV) of a rock for several parameters simultaneously. We calculate the two main macroscopic petrophysical parameters, porosity and single-phase permeability, using micro CT imaging and Lattice Boltzmann (LB) simulations for 14 different porous media, including sandpacks, sandstones and carbonates. The concept of the `Convex Hull' is then applied to calculate the REV for both parameters simultaneously using a plot of the area of the convex hull as a function of the sub-volume, capturing the different scales of heterogeneity from the pore-scale imaging. The results also show that the area of the convex hull (for well-chosen parameters such as the log of the permeability and the porosity) decays exponentially with sub-sample size suggesting a computationally efficient way to determine the system size needed to calculate the parameters to high accuracy (small convex hull area). Finally we propose using a characteristic length such as the pore size to choose an efficient absolute voxel size for the numerical rock.

“Soft that molds the hard:” Geometric morphometry of lateral atlantoaxial joints focusing on the role of cartilage in changing the contour of bony articular surfaces

PubMed Central

Prasad, Prashant Kumar; Salunke, Pravin; Sahni, Daisy; Kalra, Parveen

2017-01-01

Purpose: The existing literature on lateral atlantoaxial joints is predominantly on bony facets and is unable to explain various C1-2 motions observed. Geometric morphometry of facets would help us in understanding the role of cartilages in C1-2 biomechanics/kinematics. Objective: Anthropometric measurements (bone and cartilage) of the atlantoaxial joint and to assess the role of cartilages in joint biomechanics. Materials and Methods: The authors studied 10 cadaveric atlantoaxial lateral joints with the articular cartilage in situ and after removing it, using three-dimensional laser scanner. The data were compared using geometric morphometry with emphasis on surface contours of articulating surfaces. Results: The bony inferior articular facet of atlas is concave in both sagittal and coronal plane. The bony superior articular facet of axis is convex in sagittal plane and is concave (laterally) and convex medially in the coronal plane. The bony articulating surfaces were nonconcordant. The articular cartilages of both C1 and C2 are biconvex in both planes and are thicker than the concavities of bony articulating surfaces. Conclusion: The biconvex structure of cartilage converts the surface morphology of C1-C2 bony facets from concave on concavo-convex to convex on convex. This reduces the contact point making the six degrees of freedom of motion possible and also makes the joint gyroscopic. PMID:29403249

Modeling IrisCode and its variants as convex polyhedral cones and its security implications.

PubMed

Kong, Adams Wai-Kin

2013-03-01

IrisCode, developed by Daugman, in 1993, is the most influential iris recognition algorithm. A thorough understanding of IrisCode is essential, because over 100 million persons have been enrolled by this algorithm and many biometric personal identification and template protection methods have been developed based on IrisCode. This paper indicates that a template produced by IrisCode or its variants is a convex polyhedral cone in a hyperspace. Its central ray, being a rough representation of the original biometric signal, can be computed by a simple algorithm, which can often be implemented in one Matlab command line. The central ray is an expected ray and also an optimal ray of an objective function on a group of distributions. This algorithm is derived from geometric properties of a convex polyhedral cone but does not rely on any prior knowledge (e.g., iris images). The experimental results show that biometric templates, including iris and palmprint templates, produced by different recognition methods can be matched through the central rays in their convex polyhedral cones and that templates protected by a method extended from IrisCode can be broken into. These experimental results indicate that, without a thorough security analysis, convex polyhedral cone templates cannot be assumed secure. Additionally, the simplicity of the algorithm implies that even junior hackers without knowledge of advanced image processing and biometric databases can still break into protected templates and reveal relationships among templates produced by different recognition methods.

Design and measurement of a TE{sub 13} input converter for high order mode gyrotron travelling wave amplifiers

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Yan; Liu, Guo, E-mail: liuguo@uestc.edu.cn; Shu, Guoxiang

2016-03-15

A technique to launch a circular TE{sub 13} mode to interact with the helical electron beam of a gyrotron travelling wave amplifier is proposed and verified by simulation and cold test in this paper. The high order (HOM) TE{sub 13} mode is excited by a broadband Y-type power divider with the aid of a cylindrical waveguide system. Using grooves and convex strips loaded at the lateral planes of the output cylindrical waveguide, the electric fields of the potential competing TE{sub 32} and TE{sub 71} modes are suppressed to allow the transmission of the dominant TE{sub 13} mode. The converter performancemore » for different structural dimensions of grooves and convex strips is studied in detail and excellent results have been achieved. Simulation predicts that the average transmission is ∼−1.8 dB with a 3 dB bandwidth of 7.2 GHz (91.5–98.7 GHz) and port reflection is less than −15 dB. The conversion efficiency to the TE{sub 32} and TE{sub 71} modes are, respectively, under −15 dB and −24 dB in the operating frequency band. Such an HOM converter operating at W-band has been fabricated and cold tested with the radiation boundary. Measurement from the vector network analyzer cold test and microwave simulations show a good reflection performance for the converter.« less

Blind Compressed Image Watermarking for Noisy Communication Channels

DTIC Science & Technology

2015-10-26

Lenna test image [11] for our simulations, and gradient projection for sparse recon- struction (GPSR) [12] to solve the convex optimization prob- lem...E. Candes, J. Romberg , and T. Tao, “Robust uncertainty prin- ciples: exact signal reconstruction from highly incomplete fre- quency information,” IEEE...Images - Requirements and Guidelines,” ITU-T Recommen- dation T.81, 1992. [6] M. Gkizeli, D. Pados, and M. Medley, “Optimal signature de - sign for

Reflections From a Fresnel Lens

ERIC Educational Resources Information Center

Keeports, David

2005-01-01

Reflection of light by a convex Fresnel lens gives rise to two distinct images. A highly convex inverted real reflective image forms on the object side of the lens, while an upright virtual reflective image forms on the opposite side of the lens. I describe here a set of laser experiments performed upon a Fresnel lens. These experiments provide…

Influence of crucible support and radial heating on the interface shape during vertical Bridgman GaAs growth

NASA Astrophysics Data System (ADS)

Koai, K.; Sonnenberg, K.; Wenzl, H.

1994-03-01

Crucible assembly in a vertical Bridgman furnace is investigated by a numerical finite element model with the aim to obtain convex interfaces during the growth of GaAs crystals. During the growth stage of the conic section, a new funnel shaped crucible support has been found more effective than the concentric cylinders design similar to that patented by AT & T in promoting interface convexity. For the growth stages of the constant diameter section, the furnace profile can be effectively modulated by localized radial heating at the gradient zone. With these two features being introduced into a new furnace design, it is shown numerically that enhancement of interface convexity can be achieved using the presently available crucible materials.

[Objective accommodation parameters depending on accommodation task].

PubMed

Tarutta, E P; Tarasova, N A; Dolzhenko, O O

2011-01-01

62 myopic patients were examined to study objective accommodation parameters in different conditions of accommodation stimulus presenting (use of convex lenses). Objective accommodation response (OAR) was studied using binocular open-field autorefractometer in different conditions of stimulus presenting: complete myopia correction and adding of convex lenses with increasing power from +1.0 till +3.0 D. In 88,5% of children and adolescents showed significant decrease of OAR for 1,5-2,75D in 3.0D stimulus. Additional correction with convex lenses with increasing power leads to further reduce of accommodation response. As a result induced dynamic refraction in eye-lens system is lower than accommodation task. Only addition of +2,5D lense approximates it to required index of -3.0D.

ɛ-subgradient algorithms for bilevel convex optimization

NASA Astrophysics Data System (ADS)

Helou, Elias S.; Simões, Lucas E. A.

2017-05-01

This paper introduces and studies the convergence properties of a new class of explicit ɛ-subgradient methods for the task of minimizing a convex function over a set of minimizers of another convex minimization problem. The general algorithm specializes to some important cases, such as first-order methods applied to a varying objective function, which have computationally cheap iterations. We present numerical experimentation concerning certain applications where the theoretical framework encompasses efficient algorithmic techniques, enabling the use of the resulting methods to solve very large practical problems arising in tomographic image reconstruction. ES Helou was supported by FAPESP grants 2013/07375-0 and 2013/16508-3 and CNPq grant 311476/2014-7. LEA Simões was supported by FAPESP grants 2011/02219-4 and 2013/14615-7.

Laser backscattering analytical model of Doppler power spectra about rotating convex quadric bodies of revolution

NASA Astrophysics Data System (ADS)

Gong, YanJun; Wu, ZhenSen; Wang, MingJun; Cao, YunHua

2010-01-01

We propose an analytical model of Doppler power spectra in backscatter from arbitrary rough convex quadric bodies of revolution (whose lateral surface is a quadric) rotating around axes. In the global Cartesian coordinate system, the analytical model deduced is suitable for general convex quadric body of revolution. Based on this analytical model, the Doppler power spectra of cones, cylinders, paraboloids of revolution, and sphere-cones combination are proposed. We analyze numerically the influence of geometric parameters, aspect angle, wavelength and reflectance of rough surface of the objects on the broadened spectra because of the Doppler effect. This analytical solution may contribute to laser Doppler velocimetry, and remote sensing of ballistic missile that spin.

Safe Onboard Guidance and Control Under Probabilistic Uncertainty

NASA Technical Reports Server (NTRS)

Blackmore, Lars James

2011-01-01

An algorithm was developed that determines the fuel-optimal spacecraft guidance trajectory that takes into account uncertainty, in order to guarantee that mission safety constraints are satisfied with the required probability. The algorithm uses convex optimization to solve for the optimal trajectory. Convex optimization is amenable to onboard solution due to its excellent convergence properties. The algorithm is novel because, unlike prior approaches, it does not require time-consuming evaluation of multivariate probability densities. Instead, it uses a new mathematical bounding approach to ensure that probability constraints are satisfied, and it is shown that the resulting optimization is convex. Empirical results show that the approach is many orders of magnitude less conservative than existing set conversion techniques, for a small penalty in computation time.

Convex Accelerated Maximum Entropy Reconstruction

PubMed Central

Worley, Bradley

2016-01-01

Maximum entropy (MaxEnt) spectral reconstruction methods provide a powerful framework for spectral estimation of nonuniformly sampled datasets. Many methods exist within this framework, usually defined based on the magnitude of a Lagrange multiplier in the MaxEnt objective function. An algorithm is presented here that utilizes accelerated first-order convex optimization techniques to rapidly and reliably reconstruct nonuniformly sampled NMR datasets using the principle of maximum entropy. This algorithm – called CAMERA for Convex Accelerated Maximum Entropy Reconstruction Algorithm – is a new approach to spectral reconstruction that exhibits fast, tunable convergence in both constant-aim and constant-lambda modes. A high-performance, open source NMR data processing tool is described that implements CAMERA, and brief comparisons to existing reconstruction methods are made on several example spectra. PMID:26894476

Device-Independent Tests of Entropy

NASA Astrophysics Data System (ADS)

Chaves, Rafael; Brask, Jonatan Bohr; Brunner, Nicolas

2015-09-01

We show that the entropy of a message can be tested in a device-independent way. Specifically, we consider a prepare-and-measure scenario with classical or quantum communication, and develop two different methods for placing lower bounds on the communication entropy, given observable data. The first method is based on the framework of causal inference networks. The second technique, based on convex optimization, shows that quantum communication provides an advantage over classical communication, in the sense of requiring a lower entropy to reproduce given data. These ideas may serve as a basis for novel applications in device-independent quantum information processing.

Integrated vision-based GNC for autonomous rendezvous and capture around Mars

NASA Astrophysics Data System (ADS)

Strippoli, L.; Novelli, G.; Gil Fernandez, J.; Colmenarejo, P.; Le Peuvedic, C.; Lanza, P.; Ankersen, F.

2015-06-01

Integrated GNC (iGNC) is an activity aimed at designing, developing and validating the GNC for autonomously performing the rendezvous and capture phase of the Mars sample return mission as defined during the Mars sample return Orbiter (MSRO) ESA study. The validation cycle includes testing in an end-to-end simulator, in a real-time avionics-representative test bench and, finally, in a dynamic HW in the loop test bench for assessing the feasibility, performances and figure of merits of the baseline approach defined during the MSRO study, for both nominal and contingency scenarios. The on-board software (OBSW) is tailored to work with the sensors, actuators and orbits baseline proposed in MSRO. The whole rendezvous is based on optical navigation, aided by RF-Doppler during the search and first orbit determination of the orbiting sample. The simulated rendezvous phase includes also the non-linear orbit synchronization, based on a dedicated non-linear guidance algorithm robust to Mars ascent vehicle (MAV) injection accuracy or MAV failures resulting in elliptic target orbits. The search phase is very demanding for the image processing (IP) due to the very high visual magnitude of the target wrt. the stellar background, and the attitude GNC requires very high pointing stability accuracies to fulfil IP constraints. A trade-off of innovative, autonomous navigation filters indicates the unscented Kalman filter (UKF) as the approach that provides the best results in terms of robustness, response to non-linearities and performances compatibly with computational load. At short range, an optimized IP based on a convex hull algorithm has been developed in order to guarantee LoS and range measurements from hundreds of metres to capture.

Realization of integral 3-dimensional image using fabricated tunable liquid lens array

NASA Astrophysics Data System (ADS)

Lee, Muyoung; Kim, Junoh; Kim, Cheol Joong; Lee, Jin Su; Won, Yong Hyub

2015-03-01

Electrowetting has been widely studied for various optical applications such as optical switch, sensor, prism, and display. In this study, vari-focal liquid lens array is developed using electrowetting principle to construct integral 3-dimensional imaging. The electrowetting principle that changes the surface tension by applying voltage has several advantages to realize active optical device such as fast response time, low electrical consumption, and no mechanical moving parts. Two immiscible liquids that are water and oil are used for forming lens. By applying a voltage to the water, the focal length of the lens could be tuned as changing contact angle of water. The fabricated electrowetting vari-focal liquid lens array has 1mm diameter spherical lens shape that has 1.6mm distance between each lens. The number of lenses on the panel is 23x23 and the focal length of the lens array is simultaneously tuned from -125 to 110 diopters depending on the applied voltage. The fabricated lens array is implemented to integral 3-dimensional imaging. A 3D object is reconstructed by fabricated liquid lens array with 23x23 elemental images that are generated by 3D max tools. When liquid lens array is tuned as convex state. From vari-focal liquid lens array implemented integral imaging system, we expect that depth enhanced integral imaging can be realized in the near future.

Design of smartphone-based spectrometer to assess fresh meat color

NASA Astrophysics Data System (ADS)

Jung, Youngkee; Kim, Hyun-Wook; Kim, Yuan H. Brad; Bae, Euiwon

2017-02-01

Based on its integrated camera, new optical attachment, and inherent computing power, we propose an instrument design and validation that can potentially provide an objective and accurate method to determine surface meat color change and myoglobin redox forms using a smartphone-based spectrometer. System is designed to be used as a reflection spectrometer which mimics the conventional spectrometry commonly used for meat color assessment. We utilize a 3D printing technique to make an optical cradle which holds all of the optical components for light collection, collimation, dispersion, and a suitable chamber. A light, which reflects a sample, enters a pinhole and is subsequently collimated by a convex lens. A diffraction grating spreads the wavelength over the camera's pixels to display a high resolution of spectrum. Pixel values in the smartphone image are translated to calibrate the wavelength values through three laser pointers which have different wavelength; 405, 532, 650 nm. Using an in-house app, the camera images are converted into a spectrum in the visible wavelength range based on the exterior light source. A controlled experiment simulating the refrigeration and shelving of the meat has been conducted and the results showed the capability to accurately measure the color change in quantitative and spectroscopic manner. We expect that this technology can be adapted to any smartphone and used to conduct a field-deployable color spectrum assay as a more practical application tool for various food sectors.

Fabrication and investigation of the bionic curved visual microlens array films

NASA Astrophysics Data System (ADS)

Kuo, Wen-Kai; Lin, Syuan-You; Hsu, Sheng-Wei; Yu, Hsin Her

2017-04-01

The compound eyes of insects are smaller, lighter, and have a wider field of view and high sensitivity to moving targets. In recent years, these advantages have attracted many researchers to develop minimized optical devices. In this study, a high performance microlens was fabricated, mimicking the biological visual feature. Polystyrene (PS) microspheres were synthesized by dispersion polymerization first, and then a close-packed monolayer of PS microspheres was assembled by the Langmuir-Blodgett (LB) deposition method. Following this, a 2D polydimethylsiloxane (PDMS) concave mold was fabricated by a soft lithography technique. Different aperture sizes of poly(methyl methacrylate) (PMMA) curved microlens array replicated films were prepared using traditional Chinese medicine cupping tool with a temperature-controllable hot plate, which eliminated the need for inconvenient metal modeling. The optical performance of the curved microlens films were evaluated by a system of optical microscopy (OM) and a home-made image capture charge-coupled device (CCD). The field of view (FOV) and the light intensity distribution of the curved microlens array were also investigated. We found that a broader field of view corresponded to a smaller aperture size of the curved microlens films, as the convex heights of the films are identical. The resolution of the curved microlens films was not affected by their aperture sizes, but was determined by their interommatidial angle and the diameter of the microlens.

Wide acceptance angle, high concentration ratio, optical collector

NASA Technical Reports Server (NTRS)

Kruer, Mark Arthur (Inventor)

1990-01-01

The invention is directed to an optical collector requiring a wide acceptance angle, and a high concentration ratio. The invention is particularly adapted for use in solar collectors of cassegrain design. The optical collector system includes a parabolic circular concave primary mirror and a hyperbolic circular convex secondary mirror. The primary mirror includes a circular hole located at its center wherein a solar collector is located. The mirrored surface of the secondary mirror has three distinct zones: a center circle, an on-axis annulus, and an off-axis section. The parabolic shape of the primary mirror is chosen so that the primary mirror reflects light entering the system on-axis onto the on-axis annulus. A substantial amount of light entering the system off-axis is reflected by the primary mirror onto either the off-axis section or onto the center circle. Subsequently, the off-axis sections reflect the off-axis light toward the solar collector. Thus, off-axis light is captured which would otherwise be lost to the system. The novelty of the system appears to lie in the configuration of the primary mirror which focuses off-axis light onto an annular portion of the secondary mirror to enable capture thereof. This feature results in wide acceptance angle and a high concentration ratio, and also compensates for the effects of non-specular reflection, and enables a cassegrain configuration to be used where such characteristics are required.

Design of interferometer system on Versatile Experiment Spherical Torus (VEST) at Seoul National University

NASA Astrophysics Data System (ADS)

Choi, D. H.; An, Y. H.; Chung, K. J.; Hwang, Y. S.

2012-01-01

A 94 GHz heterodyne interferometer system was designed to measure the plasma density of VEST (Versatile Experiment Spherical Torus), which was recently built at Seoul National University. Two 94 GHz Gunn oscillators with a frequency difference of 40 MHz were used in the microwave electronics part of a heterodyne interferometer system. A compact beam focusing system utilizing a pair of plano-convex lenses and a concave mirror was designed to maximize the effective beam reception and spatial resolution. Beam path analysis based on Gaussian optics was used in the design of the beam focusing system. The design of the beam focusing system and the beam path analysis were verified with a couple of experiments that were done within an experimental framework that considered the real dimensions of a vacuum vessel. Optimum distances between the optical components and the beam radii along the beam path obtained from the experiments were in good agreement with the beam path analysis using the Gaussian optics. Both experimentation and numerical calculations confirmed that the designed beam focusing system maximized the spatial resolution of the measurement; moreover, the beam waist was located at the center of the plasma to generate a phase shift more effectively in plasmas. The interferometer system presented in this paper is expected to be used in the measurements of line integrated plasma densities during the start-up phase of VEST.

Transition mixing study

NASA Technical Reports Server (NTRS)

Reynolds, R.; White, C.

1986-01-01

A computer model capable of analyzing the flow field in the transition liner of small gas turbine engines is developed. A FORTRAN code has been assembled from existing codes and physical submodels and used to predict the flow in several test geometries which contain characteristics similar to transition liners, and for which experimental data was available. Comparisons between the predictions and measurements indicate that the code produces qualitative results but that the turbulence models, both K-E and algebraic Reynolds Stress, underestimate the cross-stream diffusion. The code has also been used to perform a numerical experiment to examine the effect of a variety of parameters on the mixing process in transition liners. Comparisons illustrate that geometries with significant curvature show a drift of the jet trajectory toward the convex wall and weaker wake region vortices and decreased penetration for jets located on the convex wall of the liner, when compared to jets located on concave walls. Also shown were the approximate equivalency of angled slots and round holes and a technique by which jet mixing correlations developed for rectangular channels can be used for can geometries.

How tight are beetle hugs? Attachment in mating leaf beetles

NASA Astrophysics Data System (ADS)

Voigt, Dagmar; Tsipenyuk, Alexey; Varenberg, Michael

2017-09-01

Similar to other leaf beetles, rosemary beetles Chrysolina americana exhibit a distinct sexual dimorphism in tarsal attachment setae. Setal discoid terminals occur only in males, and they have been previously associated with a long-term attachment to the female's back (elytra) during copulation and mate guarding. For the first time, we studied living males and females holding to female's elytra. Pull-off force measurements with a custom-made tribometer featuring a self-aligning sample holder confirmed stronger attachment to female elytra compared with glass in both males and females; corresponding to 45 and 30 times the body weight, respectively. In line with previous studies, males generated significantly higher forces than females on convex elytra and flat glass, 1.2 times and 6.8 times, respectively. Convex substrates like elytra seem to improve the attachment ability of rosemary beetles, because they can hold more strongly due to favourable shear angles of legs, tarsi and adhesive setae. A self-aligning sample holder is found to be suitable for running force measurement tests with living biological samples.

How tight are beetle hugs? Attachment in mating leaf beetles.

PubMed

Voigt, Dagmar; Tsipenyuk, Alexey; Varenberg, Michael

2017-09-01

Similar to other leaf beetles, rosemary beetles Chrysolina americana exhibit a distinct sexual dimorphism in tarsal attachment setae. Setal discoid terminals occur only in males, and they have been previously associated with a long-term attachment to the female's back (elytra) during copulation and mate guarding. For the first time, we studied living males and females holding to female's elytra. Pull-off force measurements with a custom-made tribometer featuring a self-aligning sample holder confirmed stronger attachment to female elytra compared with glass in both males and females; corresponding to 45 and 30 times the body weight, respectively. In line with previous studies, males generated significantly higher forces than females on convex elytra and flat glass, 1.2 times and 6.8 times, respectively. Convex substrates like elytra seem to improve the attachment ability of rosemary beetles, because they can hold more strongly due to favourable shear angles of legs, tarsi and adhesive setae. A self-aligning sample holder is found to be suitable for running force measurement tests with living biological samples.

Estimation of positive semidefinite correlation matrices by using convex quadratic semidefinite programming.

PubMed

Fushiki, Tadayoshi

2009-07-01

The correlation matrix is a fundamental statistic that is used in many fields. For example, GroupLens, a collaborative filtering system, uses the correlation between users for predictive purposes. Since the correlation is a natural similarity measure between users, the correlation matrix may be used in the Gram matrix in kernel methods. However, the estimated correlation matrix sometimes has a serious defect: although the correlation matrix is originally positive semidefinite, the estimated one may not be positive semidefinite when not all ratings are observed. To obtain a positive semidefinite correlation matrix, the nearest correlation matrix problem has recently been studied in the fields of numerical analysis and optimization. However, statistical properties are not explicitly used in such studies. To obtain a positive semidefinite correlation matrix, we assume the approximate model. By using the model, an estimate is obtained as the optimal point of an optimization problem formulated with information on the variances of the estimated correlation coefficients. The problem is solved by a convex quadratic semidefinite program. A penalized likelihood approach is also examined. The MovieLens data set is used to test our approach.

Thermal Intertias of Main-Belt Asteroids from Wise Thermal Infrared Data

NASA Astrophysics Data System (ADS)

Hanus, Josef; Delbo', Marco; Durech, Josef; Alí-Lagoa, Victor

2014-11-01

By means of a modified thermophysical model (TPM) that takes into account asteroid shape and pole uncertainties, we analyze the thermal infrared data acquired by the NASA's Wide-field Infrared Survey Explorer (WISE) of about 300 asteroids with derived convex shape models. We adopt convex shape models from the DAMIT database (Durech et al., 2010, A&A 513, A46) and present new determinations based on optical disk-integrated photometry and the lightcurve inversion method (Kaasalainen & Torppa, 2001, Icarus 153, 37). This work more than double the number of asteroids with determined thermophysical properties. We also discuss cases in which shape uncertainties prevent the determination of reliable thermophysical properties. This is per-se a novel result, as the effect of shape has been often neglected in thermophysical modeling of asteroids.We also present the main results of the statistical study of derived thermophysical parameters within the whole population of MBAs and within few asteroid families. The thermal inertia increases with decreasing size, but a large range of thermal inertia values is observed within the similar size ranges between 10-100 km. Surprisingly, we derive low (<20J m^{-2} s^{-1/2} K^{-1}) thermal inertia values for several asteroids with sizes D>10 km, indicating a very fine and mature regolith on these small bodies. The work of JH and MD was carried under the contract 11-BS56-008 (SHOCKS) of the French Agence National de la Recherche (ANR), and JD has been supported by the grant GACR P209/10/0537 of the Czech Science Foundation.

Slope gradient and shape effects on soil profiles in the northern mountainous forests of Iran

NASA Astrophysics Data System (ADS)

Fazlollahi Mohammadi, M.; Jalali, S. G. H.; Kooch, Y.; Said-Pullicino, D.

2016-12-01

In order to evaluate the variability of the soil profiles at two shapes (concave and convex) and five positions (summit, shoulder, back slope, footslope and toeslope) of a slope, a study of a virgin area was made in a Beech stand of mountain forests, northern Iran. Across the slope positions, the soil profiles demonstrated significant changes due to topography for two shape slopes. The solum depth of the convex slope was higher than the concave one in all five positions, and it decreased from the summit to shoulder and increased from the mid to lower slope positions for both convex and concave slopes. The thin solum at the upper positions and concave slope demonstrated that pedogenetic development is least at upper slope positions and concave slope where leaching and biomass productivity are less than at lower slopes and concave slope. A large decrease in the thickness of O and A horizons from the summit to back slope was noted for both concave and convex slopes, but it increased from back slope toward down slope for both of them. The average thickness of B horizons increased from summit to down slopes in the case of the concave slope, but in the case of convex slope it decreased from summit to shoulder and afterwards it increased to the down slope. The thicknesses of the different horizons varied in part in the different positions and shape slopes because they had different plant species cover and soil features, which were related to topography.

Powered Descent Guidance with General Thrust-Pointing Constraints

NASA Technical Reports Server (NTRS)

Carson, John M., III; Acikmese, Behcet; Blackmore, Lars

2013-01-01

The Powered Descent Guidance (PDG) algorithm and software for generating Mars pinpoint or precision landing guidance profiles has been enhanced to incorporate thrust-pointing constraints. Pointing constraints would typically be needed for onboard sensor and navigation systems that have specific field-of-view requirements to generate valid ground proximity and terrain-relative state measurements. The original PDG algorithm was designed to enforce both control and state constraints, including maximum and minimum thrust bounds, avoidance of the ground or descent within a glide slope cone, and maximum speed limits. The thrust-bound and thrust-pointing constraints within PDG are non-convex, which in general requires nonlinear optimization methods to generate solutions. The short duration of Mars powered descent requires guaranteed PDG convergence to a solution within a finite time; however, nonlinear optimization methods have no guarantees of convergence to the global optimal or convergence within finite computation time. A lossless convexification developed for the original PDG algorithm relaxed the non-convex thrust bound constraints. This relaxation was theoretically proven to provide valid and optimal solutions for the original, non-convex problem within a convex framework. As with the thrust bound constraint, a relaxation of the thrust-pointing constraint also provides a lossless convexification that ensures the enhanced relaxed PDG algorithm remains convex and retains validity for the original nonconvex problem. The enhanced PDG algorithm provides guidance profiles for pinpoint and precision landing that minimize fuel usage, minimize landing error to the target, and ensure satisfaction of all position and control constraints, including thrust bounds and now thrust-pointing constraints.

Adaptive lenticular microlens array based on voltage-induced waves at the surface of polyvinyl chloride/dibutyl phthalate gels.

PubMed

Xu, Miao; Jin, Boya; He, Rui; Ren, Hongwen

2016-04-18

We report a new approach to preparing a lenticular microlens array (LMA) using polyvinyl chloride (PVC)/dibutyl phthalate (DBP) gels. The PVD/DBP gels coated on a glass substrate form a membrane. With the aid of electrostatic repulsive force, the surface of the membrane can be reconfigured with sinusoidal waves by a DC voltage. The membrane with wavy surface functions as a LMA. By switching over the anode and cathode, the convex shape of each lenticular microlens in the array can be converted to the concave shape. Therefore, the LMA can present a large dynamic range. The response time is relatively fast and the driving voltage is low. With the advantages of compact structure, optical isotropy, and good mechanical stability, our LMA has potential applications in imaging, information processing, biometrics, and displays.

Fabrication of polymer micro-lens array with pneumatically diaphragm-driven drop-on-demand inkjet technology.

PubMed

Xie, Dan; Zhang, Honghai; Shu, Xiayun; Xiao, Junfeng

2012-07-02

The paper reports an effective method to fabricate micro-lens arrays with the ultraviolet-curable polymer, using an original pneumatically diaphragm-driven drop-on-demand inkjet system. An array of plano convex micro-lenses can be formed on the glass substrate due to surface tension and hydrophobic effect. The micro-lens arrays have uniform focusing function, smooth and real planar surface. The fabrication process showed good repeatability as well, fifty micro-lenses randomly selected form 9 × 9 miro-lens array with an average diameter of 333.28μm showed 1.1% variations. Also, the focal length, the surface roughness and optical property of the fabricated micro-lenses are measured, analyzed and proved satisfactory. The technique shows great potential for fabricating polymer micro-lens arrays with high flexibility, simple technological process and low production cost.

Method and system using power modulation for maskless vapor deposition of spatially graded thin film and multilayer coatings with atomic-level precision and accuracy

DOEpatents

Montcalm, Claude [Livermore, CA; Folta, James Allen [Livermore, CA; Tan, Swie-In [San Jose, CA; Reiss, Ira [New City, NY

2002-07-30

A method and system for producing a film (preferably a thin film with highly uniform or highly accurate custom graded thickness) on a flat or graded substrate (such as concave or convex optics), by sweeping the substrate across a vapor deposition source operated with time-varying flux distribution. In preferred embodiments, the source is operated with time-varying power applied thereto during each sweep of the substrate to achieve the time-varying flux distribution as a function of time. A user selects a source flux modulation recipe for achieving a predetermined desired thickness profile of the deposited film. The method relies on precise modulation of the deposition flux to which a substrate is exposed to provide a desired coating thickness distribution.

Integer Partitions and Convexity

NASA Astrophysics Data System (ADS)

Bouroubi, Sadek

2007-06-01

Let n be an integer >=1, and let p(n,k) and P(n,k) count the number of partitions of n into k parts, and the number of partitions of n into parts less than or equal to k, respectively. In this paper, we show that these functions are convex. The result includes the actual value of the constant of Bateman and Erdos.

Higher order sensitivity of solutions to convex programming problems without strict complementarity

NASA Technical Reports Server (NTRS)

Malanowski, Kazimierz

1988-01-01

Consideration is given to a family of convex programming problems which depend on a vector parameter. It is shown that the solutions of the problems and the associated Lagrange multipliers are arbitrarily many times directionally differentiable functions of the parameter, provided that the data of the problems are sufficiently regular. The characterizations of the respective derivatives are given.

Beam aperture modifier design with acoustic metasurfaces

NASA Astrophysics Data System (ADS)

Tang, Weipeng; Ren, Chunyu

2017-10-01

In this paper, we present a design concept of acoustic beam aperture modifier using two metasurface-based planar lenses. By appropriately designing the phase gradient profile along the metasurface, we obtain a class of acoustic convex lenses and concave lenses, which can focus the incoming plane waves and collimate the converging waves, respectively. On the basis of the high converging and diverging capability of these lenses, two kinds of lens combination scheme, including the convex-concave type and convex-convex type, are proposed to tune up the incoming beam aperture as needed. To be specific, the aperture of the acoustic beam can be shrunk or expanded through adjusting the phase gradient of the pair of lenses and the spacing between them. These lenses and the corresponding aperture modifiers are constructed by the stacking ultrathin labyrinthine structures, which are obtained by the geometry optimization procedure and exhibit high transmission coefficient and a full range of phase shift. The simulation results demonstrate the effectiveness of our proposed beam aperture modifiers. Due to the flexibility in aperture controlling and the simplicity in fabrication, the proposed modifiers have promising potential in applications, such as acoustic imaging, nondestructive evaluation, and communication.

Improving the growth of CZT crystals for radiation detectors: a modeling perspective

NASA Astrophysics Data System (ADS)

Derby, Jeffrey J.; Zhang, Nan; Yeckel, Andrew

2012-10-01

The availability of large, single crystals of cadmium zinc telluride (CZT) with uniform properties is key to improving the performance of gamma radiation detectors fabricated from them. Towards this goal, we discuss results obtained by computational models that provide a deeper understanding of crystal growth processes and how the growth of CZT can be improved. In particular, we discuss methods that may be implemented to lessen the deleterious interactions between the ampoule wall and the growing crystal via engineering a convex solidification interface. For vertical Bridgman growth, a novel, bell-curve furnace temperature profile is predicted to achieve macroscopically convex solid-liquid interface shapes during melt growth of CZT in a multiple-zone furnace. This approach represents a significant advance over traditional gradient-freeze profiles, which always yield concave interface shapes, and static heat transfer designs, such as pedestal design, that achieve convex interfaces over only a small portion of the growth run. Importantly, this strategy may be applied to any Bridgman configuration that utilizes multiple, controllable heating zones. Realizing a convex solidification interface via this adaptive bell-curve furnace profile is postulated to result in better crystallinity and higher yields than conventional CZT growth techniques.

Scalable splitting algorithms for big-data interferometric imaging in the SKA era

NASA Astrophysics Data System (ADS)

Onose, Alexandru; Carrillo, Rafael E.; Repetti, Audrey; McEwen, Jason D.; Thiran, Jean-Philippe; Pesquet, Jean-Christophe; Wiaux, Yves

2016-11-01

In the context of next-generation radio telescopes, like the Square Kilometre Array (SKA), the efficient processing of large-scale data sets is extremely important. Convex optimization tasks under the compressive sensing framework have recently emerged and provide both enhanced image reconstruction quality and scalability to increasingly larger data sets. We focus herein mainly on scalability and propose two new convex optimization algorithmic structures able to solve the convex optimization tasks arising in radio-interferometric imaging. They rely on proximal splitting and forward-backward iterations and can be seen, by analogy, with the CLEAN major-minor cycle, as running sophisticated CLEAN-like iterations in parallel in multiple data, prior, and image spaces. Both methods support any convex regularization function, in particular, the well-studied ℓ1 priors promoting image sparsity in an adequate domain. Tailored for big-data, they employ parallel and distributed computations to achieve scalability, in terms of memory and computational requirements. One of them also exploits randomization, over data blocks at each iteration, offering further flexibility. We present simulation results showing the feasibility of the proposed methods as well as their advantages compared to state-of-the-art algorithmic solvers. Our MATLAB code is available online on GitHub.

Multiple cues add up in defining a figure on a ground.

PubMed

Devinck, Frédéric; Spillmann, Lothar

2013-01-25

We studied the contribution of multiple cues to figure-ground segregation. Convexity, symmetry, and top-down polarity (henceforth called wide base) were used as cues. Single-cue displays as well as ambiguous stimulus patterns containing two or three cues were presented. Error rate (defined by responses to uncued stimuli) and reaction time were used to quantify the figural strength of a given cue. In the first experiment, observers were asked to report which of two regions, left or right, appeared as foreground figure. Error rate did not benefit from adding additional cues if convexity was present, suggesting that responses were based on convexity as the predominant figural determinant. However, reaction time became shorter with additional cues even if convexity was present. For example, when symmetry and wide base were added, figure-ground segregation was facilitated. In a second experiment, stimulus patterns were exposed for 150ms to rule out eye movements. Results were similar to those found in the first experiment. Both experiments suggest that under the conditions of our experiment figure-ground segregation is perceived more readily, when several cues cooperate in defining the figure. Copyright © 2012 Elsevier Ltd. All rights reserved.

Experimental Study of Reciprocating Friction between Rape Stalk and Bionic Nonsmooth Surface Units

PubMed Central

Ma, Zheng; Li, Yaoming; Xu, Lizhang

2015-01-01

Background. China is the largest producer of rape oilseed in the world; however, the mechanization level of rape harvest is relatively low, because rape materials easily adhere to the cleaning screens of combine harvesters, resulting in significant cleaning losses. Previous studies have shown that bionic nonsmooth surface cleaning screens restrain the adhesion of rape materials, but the underlying mechanisms remain unclear. Objective. The reciprocating friction between rape stalk and bionic nonsmooth metal surface was examined. Methods. The short-time Fourier transform method was used to discriminate the stable phase of friction signals and the stick-lag distance was defined to analyze the stable reciprocating friction in a phase diagram. Results. The reciprocating friction between rape stalk and metal surface is a typical stick-slip friction, and the bionic nonsmooth metal surfaces with concave or convex units reduced friction force with increasing reciprocating frequency. The results also showed that the stick-lag distance of convex surface increased with reciprocating frequency, which indicated that convex surface reduces friction force more efficiently. Conclusions. We suggest that bionic nonsmooth surface cleaning screens, especially with convex units, restrain the adhesion of rape materials more efficiently compared to the smooth surface cleaning screens. PMID:27034611

Ultrasound-guided Subclavian Vein Cannulation Using a Micro-Convex Ultrasound Probe

PubMed Central

Fair, James; Hirshberg, Eliotte L.; Grissom, Colin K.; Brown, Samuel M.

2014-01-01

Background: The subclavian vein is the preferred site for central venous catheter placement due to infection risk and patient comfort. Ultrasound guidance is useful in cannulation of other veins, but for the subclavian vein, current ultrasound-guided techniques using high-frequency linear array probes are generally limited to axillary vein cannulation. Methods: We report a series of patients who underwent clinically indicated subclavian venous catheter placement using a micro-convex pediatric probe for real-time guidance in the vein’s longitudinal axis. We identified rates of successful placement and complications by chart review. Results: Twenty-four catheters were placed using the micro-convex pediatric probe with confirmation of placement of the needle medial to the lateral border of the first rib. Sixteen of the catheters were placed by trainee physicians. In 23 patients, the catheter was placed without complication (hematoma, pneumothorax, infection). In one patient, the vein could not be safely cannulated without risk of arterial puncture, so an alternative site was selected. Conclusions: Infraclavicular subclavian vein cannulation using real-time ultrasound with a micro-convex pediatric probe appears to be a safe and effective method of placing subclavian vascular catheters. This technique merits further study to confirm safety and efficacy. PMID:24611628

Systematization, distribution and territory of the middle cerebral artery on the brain surface in chinchilla (Chinchilla lanigera).

PubMed

De Araujo, A C P; Campos, R

2009-02-01

The aim of the present study was to analyse thirty chinchilla (Chinchilla lanigera) brains, injected with latex, and to systematize and describe the distribution and the vascularization territories of the middle cerebral artery. This long vessel, after it has originated from the terminal branch of the basilar artery, formed the following collateral branches: rostral, caudal and striated (perforating) central branches. After crossing the lateral rhinal sulcus, the middle cerebral artery emitted a sequence of rostral and caudal convex hemispheric cortical collateral branches on the convex surface of the cerebral hemisphere to the frontal, parietal, temporal and occipital lobes. Among the rostral convex hemispheric branches, a trunk was observed, which reached the frontal and parietal lobes and, in a few cases, the occipital lobe. The vascular territory of the chinchilla's middle cerebral artery included, in the cerebral hemisphere basis, the lateral cerebral fossa, the caudal third of the olfactory trigone, the rostral two-thirds of the piriform lobe, the lateral olfactory tract, and most of the convex surface of the cerebral hemisphere, except for a strip between the cerebral longitudinal fissure and the vallecula, which extended from the rostral to the caudal poles bordering the cerebral transverse fissure.

Minimal norm constrained interpolation. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Irvine, L. D.

1985-01-01

In computational fluid dynamics and in CAD/CAM, a physical boundary is usually known only discreetly and most often must be approximated. An acceptable approximation preserves the salient features of the data such as convexity and concavity. In this dissertation, a smooth interpolant which is locally concave where the data are concave and is locally convex where the data are convex is described. The interpolant is found by posing and solving a minimization problem whose solution is a piecewise cubic polynomial. The problem is solved indirectly by using the Peano Kernal theorem to recast it into an equivalent minimization problem having the second derivative of the interpolant as the solution. This approach leads to the solution of a nonlinear system of equations. It is shown that Newton's method is an exceptionally attractive and efficient method for solving the nonlinear system of equations. Examples of shape-preserving interpolants, as well as convergence results obtained by using Newton's method are also shown. A FORTRAN program to compute these interpolants is listed. The problem of computing the interpolant of minimal norm from a convex cone in a normal dual space is also discussed. An extension of de Boor's work on minimal norm unconstrained interpolation is presented.

Dynamical tunneling versus fast diffusion for a non-convex Hamiltonian

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pittman, S. M.; Tannenbaum, E.; Heller, E. J.

This paper attempts to resolve the issue of the nature of the 0.01-0.1 cm{sup −1} peak splittings observed in high-resolution IR spectra of polyatomic molecules. One hypothesis is that these splittings are caused by dynamical tunneling, a quantum-mechanical phenomenon whereby energy flows between two disconnected regions of phase-space across dynamical barriers. However, a competing classical mechanism for energy flow is Arnol’d diffusion, which connects different regions of phase-space by a resonance network known as the Arnol’d web. The speed of diffusion is bounded by the Nekhoroshev theorem, which guarantees stability on exponentially long time scales if the Hamiltonian is steep.more » Here we consider a non-convex Hamiltonian that contains the characteristics of a molecular Hamiltonian, but does not satisfy the Nekhoroshev theorem. The diffusion along the Arnol’d web is expected to be fast for a non-convex Hamiltonian. While fast diffusion is an unlikely competitor for longtime energy flow in molecules, we show how dynamical tunneling dominates compared to fast diffusion in the nearly integrable regime for a non-convex Hamiltonian, as well as present a new kind of dynamical tunneling.« less

Temperature actuated shutdown assembly for a nuclear reactor

DOEpatents

Sowa, Edmund S.

1976-01-01

Three identical bimetallic disks, each shaped as a spherical cap with its convex side composed of a layer of metal such as molybdenum and its concave side composed of a metal of a relatively higher coefficient of thermal expansion such as stainless steel, are retained within flanges attached to three sides of an inner hexagonal tube containing a neutron absorber to be inserted into a nuclear reactor core. Each disk holds a metal ball against its normally convex side so that the ball projects partially through a hole in the tube located concentrically with the center of each disk; at a predetermined temperature an imbalance of thermally induced stresses in at least one of the disks will cause its convex side to become concave and its concave side to become convex, thus pulling the ball from the hole in which it is located. The absorber has a conical bottom supported by the three balls and is small enough in relation to the internal dimensions of the tube to allow it to slip toward the removed ball or balls, thus clearing the unremoved balls or ball so that it will fall into the reactor core.

Novel method of finding extreme edges in a convex set of N-dimension vectors

NASA Astrophysics Data System (ADS)

Hu, Chia-Lun J.

2001-11-01

As we published in the last few years, for a binary neural network pattern recognition system to learn a given mapping {Um mapped to Vm, m=1 to M} where um is an N- dimension analog (pattern) vector, Vm is a P-bit binary (classification) vector, the if-and-only-if (IFF) condition that this network can learn this mapping is that each i-set in {Ymi, m=1 to M} (where Ymithere existsVmiUm and Vmi=+1 or -1, is the i-th bit of VR-m).)(i=1 to P and there are P sets included here.) Is POSITIVELY, LINEARLY, INDEPENDENT or PLI. We have shown that this PLI condition is MORE GENERAL than the convexity condition applied to a set of N-vectors. In the design of old learning machines, we know that if a set of N-dimension analog vectors form a convex set, and if the machine can learn the boundary vectors (or extreme edges) of this set, then it can definitely learn the inside vectors contained in this POLYHEDRON CONE. This paper reports a new method and new algorithm to find the boundary vectors of a convex set of ND analog vectors.

Convex relaxations for gas expansion planning

DOE PAGES

Borraz-Sanchez, Conrado; Bent, Russell Whitford; Backhaus, Scott N.; ...

2016-01-01

Expansion of natural gas networks is a critical process involving substantial capital expenditures with complex decision-support requirements. Here, given the non-convex nature of gas transmission constraints, global optimality and infeasibility guarantees can only be offered by global optimisation approaches. Unfortunately, state-of-the-art global optimisation solvers are unable to scale up to real-world size instances. In this study, we present a convex mixed-integer second-order cone relaxation for the gas expansion planning problem under steady-state conditions. The underlying model offers tight lower bounds with high computational efficiency. In addition, the optimal solution of the relaxation can often be used to derive high-quality solutionsmore » to the original problem, leading to provably tight optimality gaps and, in some cases, global optimal solutions. The convex relaxation is based on a few key ideas, including the introduction of flux direction variables, exact McCormick relaxations, on/off constraints, and integer cuts. Numerical experiments are conducted on the traditional Belgian gas network, as well as other real larger networks. The results demonstrate both the accuracy and computational speed of the relaxation and its ability to produce high-quality solution« less

Low-rank structure learning via nonconvex heuristic recovery.

PubMed

Deng, Yue; Dai, Qionghai; Liu, Risheng; Zhang, Zengke; Hu, Sanqing

2013-03-01

In this paper, we propose a nonconvex framework to learn the essential low-rank structure from corrupted data. Different from traditional approaches, which directly utilizes convex norms to measure the sparseness, our method introduces more reasonable nonconvex measurements to enhance the sparsity in both the intrinsic low-rank structure and the sparse corruptions. We will, respectively, introduce how to combine the widely used ℓp norm (0 < p < 1) and log-sum term into the framework of low-rank structure learning. Although the proposed optimization is no longer convex, it still can be effectively solved by a majorization-minimization (MM)-type algorithm, with which the nonconvex objective function is iteratively replaced by its convex surrogate and the nonconvex problem finally falls into the general framework of reweighed approaches. We prove that the MM-type algorithm can converge to a stationary point after successive iterations. The proposed model is applied to solve two typical problems: robust principal component analysis and low-rank representation. Experimental results on low-rank structure learning demonstrate that our nonconvex heuristic methods, especially the log-sum heuristic recovery algorithm, generally perform much better than the convex-norm-based method (0 < p < 1) for both data with higher rank and with denser corruptions.

Robust, Adaptive Radar Detection and Estimation

DTIC Science & Technology

2015-07-21

cost function is not a convex function in R, we apply a transformation variables i.e., let X = σ2R−1 and S′ = 1 σ2 S. Then, the revised cost function in...1 viv H i . We apply this inverse covariance matrix in computing the SINR as well as estimator variance. • Rank Constrained Maximum Likelihood: Our...even as almost all available training samples are corrupted. Probability of Detection vs. SNR We apply three test statistics, the normalized matched

Investigating the effect of tablet thickness and punch curvature on density distribution using finite elements method.

PubMed

Diarra, Harona; Mazel, Vincent; Busignies, Virginie; Tchoreloff, Pierre

2015-09-30

Finite elements method was used to study the influence of tablet thickness and punch curvature on the density distribution inside convex faced (CF) tablets. The modeling of the process was conducted on 2 pharmaceutical excipients (anhydrous calcium phosphate and microcrystalline cellulose) by using Drucker-Prager Cap model in Abaqus(®) software. The parameters of the model were obtained from experimental tests. Several punch shapes based on industrial standards were used. A flat-faced (FF) punch and 3 convex faced (CF) punches (8R11, 8R8 and 8R6) with a diameter of 8mm were chosen. Different tablet thicknesses were studied at a constant compression force. The simulation of the compaction of CF tablets with increasing thicknesses showed an important change on the density distribution inside the tablet. For smaller thicknesses, low density zones are located toward the center. The density is not uniform inside CF tablets and the center of the 2 faces appears with low density whereas the distribution inside FF tablets is almost independent of the tablet thickness. These results showed that FF and CF tablets, even obtained at the same compression force, do not have the same density at the center of the compact. As a consequence differences in tensile strength, as measured by diametral compression, are expected. This was confirmed by experimental tests. Copyright © 2015 Elsevier B.V. All rights reserved.

The Hyperspectral Thermal Emission Spectrometer (HyTES): Preliminary Results

NASA Technical Reports Server (NTRS)

Hook, Simon; Johnson, William R.; Eng, Bjorn T.; Gunapala, Sarah D.; Lamborn, Andrew U.; Mouroulis, Pantazis, Z.; Mouroulis, Pantazis, Z.; Paine, Christopher G.; Soibel, Alexander; Wilson, Daniel W.

2011-01-01

The Hyperspectral Thermal Emission Spectrometer (HyTES) is being developed as part of the risk reduction activities associated with the Hyperspectral Infrared Imager (HyspIRI). HyspIRI is one of the Tier 2 Decadal Survey Missions. HyTES will provide information on how to place the filters on the HyspIRI Thermal Infrared Instrument (TIR) as well as provide antecedent science data. The pushbroom design has 512 spatial pixels over a 50-degree field of view and 256 spectral channels between 7.5 micrometers to 12 micrometers. HyTES includes many key enabling state-of-the-art technologies including a high performance convex diffraction grating, a quantum well infrared photodetector (QWIP) focal plane array, and a compact Dyson-inspired optical design. The Dyson optical design allows for a very compact and optically fast system (F/1.6). It also minimizes cooling requirements due to the fact it has a single monolithic prism-like grating design which allows baffling for stray light suppression. The monolithic configuration eases mechanical tolerancing requirements which are a concern since the complete optical assembly is operated at cryogenic temperatures ((is) approximately 100K). The QWIP allows for optimum spatial and spectral uniformity and provides adequate responsivity or D-star to allow 200mK noise equivalent temperature difference (NEDT) operation across the LWIR passband. Assembly of the system is nearly complete. After completion, alignment results will be presented which show low keystone and smile distortion. This is required to minimize spatial-spectral mixing between adjacent spectral channels and spatial positions. Predictions show the system will have adequate signal to noise for laboratory calibration targets.

Extremal edges: a powerful cue to depth perception and figure-ground organization.

PubMed

Palmer, Stephen E; Ghose, Tandra

2008-01-01

Extremal edges (EEs) are projections of viewpoint-specific horizons of self-occlusion on smooth convex surfaces. An ecological analysis of viewpoint constraints suggests that an EE surface is likely to be closer to the observer than the non-EE surface on the other side of the edge. In two experiments, one using shading gradients and the other using texture gradients, we demonstrated that EEs operate as strong cues to relative depth perception and figure-ground organization. Image regions with an EE along the shared border were overwhelmingly perceived as closer than either flat or equally convex surfaces without an EE along that border. A further demonstration suggests that EEs are more powerful than classical figure-ground cues, including even the joint effects of small size, convexity, and surroundedness.

Convex lattice polygons of fixed area with perimeter-dependent weights.

PubMed

Rajesh, R; Dhar, Deepak

2005-01-01

We study fully convex polygons with a given area, and variable perimeter length on square and hexagonal lattices. We attach a weight tm to a convex polygon of perimeter m and show that the sum of weights of all polygons with a fixed area s varies as s(-theta(conv))eK(t)square root(s) for large s and t less than a critical threshold tc, where K(t) is a t-dependent constant, and theta(conv) is a critical exponent which does not change with t. Using heuristic arguments, we find that theta(conv) is 1/4 for the square lattice, but -1/4 for the hexagonal lattice. The reason for this unexpected nonuniversality of theta(conv) is traced to existence of sharp corners in the asymptotic shape of these polygons.

A free boundary approach to the Rosensweig instability of ferrofluids

NASA Astrophysics Data System (ADS)

Parini, Enea; Stylianou, Athanasios

2018-04-01

We establish the existence of saddle points for a free boundary problem describing the two-dimensional free surface of a ferrofluid undergoing normal field instability. The starting point is the ferrohydrostatic equations for the magnetic potentials in the ferrofluid and air, and the function describing their interface. These constitute the strong form for the Euler-Lagrange equations of a convex-concave functional, which we extend to include interfaces that are not necessarily graphs of functions. Saddle points are then found by iterating the direct method of the calculus of variations and applying classical results of convex analysis. For the existence part, we assume a general nonlinear magnetization law; for a linear law, we also show, via convex duality, that the saddle point is a constrained minimizer of the relevant energy functional.

Perceptual representation and effectiveness of local figure–ground cues in natural contours

PubMed Central

Sakai, Ko; Matsuoka, Shouhei; Kurematsu, Ken; Hatori, Yasuhiro

2015-01-01

A contour shape strongly influences the perceptual segregation of a figure from the ground. We investigated the contribution of local contour shape to figure–ground segregation. Although previous studies have reported local contour features that evoke figure–ground perception, they were often image features and not necessarily perceptual features. First, we examined whether contour features, specifically, convexity, closure, and symmetry, underlie the perceptual representation of natural contour shapes. We performed similarity tests between local contours, and examined the contribution of the contour features to the perceptual similarities between the contours. The local contours were sampled from natural contours so that their distribution was uniform in the space composed of the three contour features. This sampling ensured the equal appearance frequency of the factors and a wide variety of contour shapes including those comprised of contradictory factors that induce figure in the opposite directions. This sampling from natural contours is advantageous in order to randomly pickup a variety of contours that satisfy a wide range of cue combinations. Multidimensional scaling analyses showed that the combinations of convexity, closure, and symmetry contribute to perceptual similarity, thus they are perceptual quantities. Second, we examined whether the three features contribute to local figure–ground perception. We performed psychophysical experiments to judge the direction of the figure along the local contours, and examined the contribution of the features to the figure–ground judgment. Multiple linear regression analyses showed that closure was a significant factor, but that convexity and symmetry were not. These results indicate that closure is dominant in the local figure–ground perception with natural contours when the other cues coexist with equal probability including contradictory cases. PMID:26579057

Perceptual representation and effectiveness of local figure-ground cues in natural contours.

PubMed

Sakai, Ko; Matsuoka, Shouhei; Kurematsu, Ken; Hatori, Yasuhiro

2015-01-01

A contour shape strongly influences the perceptual segregation of a figure from the ground. We investigated the contribution of local contour shape to figure-ground segregation. Although previous studies have reported local contour features that evoke figure-ground perception, they were often image features and not necessarily perceptual features. First, we examined whether contour features, specifically, convexity, closure, and symmetry, underlie the perceptual representation of natural contour shapes. We performed similarity tests between local contours, and examined the contribution of the contour features to the perceptual similarities between the contours. The local contours were sampled from natural contours so that their distribution was uniform in the space composed of the three contour features. This sampling ensured the equal appearance frequency of the factors and a wide variety of contour shapes including those comprised of contradictory factors that induce figure in the opposite directions. This sampling from natural contours is advantageous in order to randomly pickup a variety of contours that satisfy a wide range of cue combinations. Multidimensional scaling analyses showed that the combinations of convexity, closure, and symmetry contribute to perceptual similarity, thus they are perceptual quantities. Second, we examined whether the three features contribute to local figure-ground perception. We performed psychophysical experiments to judge the direction of the figure along the local contours, and examined the contribution of the features to the figure-ground judgment. Multiple linear regression analyses showed that closure was a significant factor, but that convexity and symmetry were not. These results indicate that closure is dominant in the local figure-ground perception with natural contours when the other cues coexist with equal probability including contradictory cases.

Comparison of BMI, AHI, and apolipoprotein E ε4 (APOE-ε4) alleles among sleep apnea patients with different skeletal classifications.

PubMed

Roedig, Jason J; Phillips, Barbara A; Morford, Lorri A; Van Sickels, Joseph E; Falcao-Alencar, Gabriel; Fardo, David W; Hartsfield, James K; Ding, Xiuhua; Kluemper, G Thomas

2014-04-15

This case-control study investigated whether variations within the APOE-ε gene were associated with having a convex facial profile (skeletal Class II) compared to exhibiting a straight or concave facial profile (Class I or Class III) among patients with obstructive sleep apnea (OSA). Associations between the apnea-hypopnea index (AHI) and body mass index (BMI) scores for these OSA patients were also examined in the context of facial profile. OSA patients with an AHI ≥ 15 were recruited from a sleep clinic and classified by facial and dental occlusal relationships based on a profile facial analysis, lateral photographs, and dental examination. Saliva was collected as a source of DNA. The APOE-ε1-4 allele-defining single nucleotide polymorphisms (SNPs) rs429358 and rs7412 were genotyped. A χ(2) analysis was used to assess Hardy-Weinberg equilibrium and for association analysis (significance at p < 0.05). ANOVA and Fisher exact test were also used. Seventy-six Caucasian OSA patients participated in the study-25 Class II cases and 51 non-Class II cases. There was no association of the APOE-ε4 allele with facial profile among these OSA patients. Class II OSA patients had significantly lower BMIs (30.7 ± 5.78) than Class I (37.3 ± 6.14) or Class III (37.8 ± 6.17) patients (p < 0.001), although there was no statistical difference in AHI for Class II patients compared with other groups. OSA patients with Class II convex profile were more likely to have a lower BMI than those in other skeletal groups. In fact 20% of them were not obese, suggesting that a Class II convex profile may influence or be associated with OSA development independent of BMI.

Acute effects of spinal bracing on scapular kinematics in adolescent idiopathic scoliosis.

PubMed

Gur, Gozde; Turgut, Elif; Ayhan, Cigdem; Baltaci, Gul; Yakut, Yavuz

2017-08-01

Bracing is the most common nonsurgical treatment for adolescent idiopathic scoliosis. Spinal braces affect glenohumeral and scapulothoracic motion because they restrict trunk movements. However, the potential spinal-bracing effects on scapular kinematics are unknown. The present study aimed to investigate the acute effects of spinal bracing on scapular kinematics in adolescent idiopathic scoliosis. Scapular kinematics, including scapular internal/external rotation, posterior/anterior tilting, and downward/upward rotation during scapular plane elevation, were evaluated in 27 in-brace and out-of-brace adolescent idiopathic scoliosis patients with a three-dimensional electromagnetic tracking system. Data on the position and orientation of the scapula at 30°, 60°, 90°, and 120° humerothoracic elevation were used for statistical comparisons. The paired t-test was used to assess the differences between the mean values of in-brace and out-of-brace conditions. The in-brace condition showed significantly increased (P<0.05) scapular anterior tilting and decreased internal rotation in the resting position on the convex and concave sides; increased scapular downward rotation at 120° humerothoracic elevation on the convex side and at 30°, 60°, 90°, and 120° humerothoracic elevation on the concave side; increased scapular anterior tilt at 30°, 60°, 90°, and 120° humerothoracic elevation on the convex and concave sides; and decreased (P<0.05) maximal humerothoracic elevation of the arm. Spinal bracing affects scapular kinematics. Observed changes in scapular kinematics with brace may also affect upper extremity function for adolescents with idiopathic scoliosis. Therefore, clinicians should include assessments of the glenohumeral and scapulothoracic joints when designing rehabilitation protocols for patients with adolescent idiopathic scoliosis. Copyright © 2017 Elsevier Ltd. All rights reserved.

A Fourier dimensionality reduction model for big data interferometric imaging

NASA Astrophysics Data System (ADS)

Vijay Kartik, S.; Carrillo, Rafael E.; Thiran, Jean-Philippe; Wiaux, Yves

2017-06-01

Data dimensionality reduction in radio interferometry can provide savings of computational resources for image reconstruction through reduced memory footprints and lighter computations per iteration, which is important for the scalability of imaging methods to the big data setting of the next-generation telescopes. This article sheds new light on dimensionality reduction from the perspective of the compressed sensing theory and studies its interplay with imaging algorithms designed in the context of convex optimization. We propose a post-gridding linear data embedding to the space spanned by the left singular vectors of the measurement operator, providing a dimensionality reduction below image size. This embedding preserves the null space of the measurement operator and hence its sampling properties are also preserved in light of the compressed sensing theory. We show that this can be approximated by first computing the dirty image and then applying a weighted subsampled discrete Fourier transform to obtain the final reduced data vector. This Fourier dimensionality reduction model ensures a fast implementation of the full measurement operator, essential for any iterative image reconstruction method. The proposed reduction also preserves the independent and identically distributed Gaussian properties of the original measurement noise. For convex optimization-based imaging algorithms, this is key to justify the use of the standard ℓ2-norm as the data fidelity term. Our simulations confirm that this dimensionality reduction approach can be leveraged by convex optimization algorithms with no loss in imaging quality relative to reconstructing the image from the complete visibility data set. Reconstruction results in simulation settings with no direction dependent effects or calibration errors show promising performance of the proposed dimensionality reduction. Further tests on real data are planned as an extension of the current work. matlab code implementing the proposed reduction method is available on GitHub.

Pinned, optically aligned diagnostic dock for use on the Z facility.

PubMed

Gomez, M R; Rochau, G A; Bailey, J E; Dunham, G S; Kernaghan, M D; Gard, P; Robertson, G K; Owen, A C; Argo, J W; Nielsen, D S; Lake, P W

2012-10-01

The pinned optically aligned diagnostic dock (PODD) is a multi-configuration diagnostic platform designed to measure x-ray emission on the Z facility. The PODD houses two plasma emission acquisition (PEA) systems, which are aligned with a set of precision machined pins. The PEA systems are modular, allowing a single diagnostic housing to support several different diagnostics. The PEA configurations fielded to date include both time-resolved and time-integrated, 1D spatially resolving, elliptical crystal spectrometers, and time-integrated, 1D spatially resolving, convex crystal spectrometers. Additional proposed configurations include time-resolved, monochromatic mirrored pinhole imagers and arrays of filtered x-ray diodes, diamond photo-conducting diode detectors, and bolometers. The versatility of the PODD system will allow the diagnostic configuration of the Z facility to be changed without significantly adding to the turn-around time of the machine. Additionally, the PODD has been designed to allow instrument setup to be completed entirely off-line, leaving only a refined alignment process to be performed just prior to a shot, which is a significant improvement over the instrument the PODD replaces. Example data collected with the PODD are presented.

Iterating the Number of Intersection Points of the Diagonals of Irregular Convex Polygons, or C (n, 4) the Hard Way!

ERIC Educational Resources Information Center

Hathout, Leith

2007-01-01

Counting the number of internal intersection points made by the diagonals of irregular convex polygons where no three diagonals are concurrent is an interesting problem in discrete mathematics. This paper uses an iterative approach to develop a summation relation which tallies the total number of intersections, and shows that this total can be…

Scalable Rapidly Deployable Convex Optimization for Data Analytics

DTIC Science & Technology

SOCPs , SDPs, exponential cone programs, and power cone programs. CVXPY supports basic methods for distributed optimization, on...multiple heterogenous platforms. We have also done basic research in various application areas , using CVXPY , to demonstrate its usefulness. See attached report for publication information....Over the period of the contract we have developed the full stack for wide use of convex optimization, in machine learning and many other areas .

Study on feed forward neural network convex optimization for LiFePO4 battery parameters

NASA Astrophysics Data System (ADS)

Liu, Xuepeng; Zhao, Dongmei

2017-08-01

Based on the modern facility agriculture automatic walking equipment LiFePO4 Battery, the parameter identification of LiFePO4 Battery is analyzed. An improved method for the process model of li battery is proposed, and the on-line estimation algorithm is presented. The parameters of the battery are identified using feed forward network neural convex optimization algorithm.

The 1980 Archeological Investigations at the Big Hill Lake, Kansas.

DTIC Science & Technology

1980-01-01

implements as plano -convex scrapers. The modified flake categories are comprised of those specimens which exhibit edge alterations resulting from...stone projectile points, chipped stone blades, polished celts and gorgets, cut deer mandibles, an incised canine tooth and grinding and milling...are characteristic at this Middle Ceramic group of sites, along with plano -convex end scrapers and medium to small-sized projectile points. 31 Many

Ground-based testing of the dynamics of flexible space structures using band mechanisms

NASA Technical Reports Server (NTRS)

Yang, L. F.; Chew, Meng-Sang

1991-01-01

A suspension system based on a band mechanism is studied to provide the free-free conditions for ground based validation testing of flexible space structures. The band mechanism consists of a noncircular disk with a convex profile, preloaded by torsional springs at its center of rotation so that static equilibrium of the test structure is maintained at any vertical location; the gravitational force will be directly counteracted during dynamic testing of the space structure. This noncircular disk within the suspension system can be configured to remain unchanged for test articles with the different weights as long as the torsional spring is replaced to maintain the originally designed frequency ratio of W/k sub s. Simulations of test articles which are modeled as lumped parameter as well as continuous parameter systems, are also presented.

Autonomous optimal trajectory design employing convex optimization for powered descent on an asteroid

NASA Astrophysics Data System (ADS)

Pinson, Robin Marie

Mission proposals that land spacecraft on asteroids are becoming increasingly popular. However, in order to have a successful mission the spacecraft must reliably and softly land at the intended landing site with pinpoint precision. The problem under investigation is how to design a propellant (fuel) optimal powered descent trajectory that can be quickly computed onboard the spacecraft, without interaction from ground control. The goal is to autonomously design the optimal powered descent trajectory onboard the spacecraft immediately prior to the descent burn for use during the burn. Compared to a planetary powered landing problem, the challenges that arise from designing an asteroid powered descent trajectory include complicated nonlinear gravity fields, small rotating bodies, and low thrust vehicles. The nonlinear gravity fields cannot be represented by a constant gravity model nor a Newtonian model. The trajectory design algorithm needs to be robust and efficient to guarantee a designed trajectory and complete the calculations in a reasonable time frame. This research investigates the following questions: Can convex optimization be used to design the minimum propellant powered descent trajectory for a soft landing on an asteroid? Is this method robust and reliable to allow autonomy onboard the spacecraft without interaction from ground control? This research designed a convex optimization based method that rapidly generates the propellant optimal asteroid powered descent trajectory. The solution to the convex optimization problem is the thrust magnitude and direction, which designs and determines the trajectory. The propellant optimal problem was formulated as a second order cone program, a subset of convex optimization, through relaxation techniques by including a slack variable, change of variables, and incorporation of the successive solution method. Convex optimization solvers, especially second order cone programs, are robust, reliable, and are guaranteed to find the global minimum provided one exists. In addition, an outer optimization loop using Brent's method determines the optimal flight time corresponding to the minimum propellant usage over all flight times. Inclusion of additional trajectory constraints, solely vertical motion near the landing site and glide slope, were evaluated. Through a theoretical proof involving the Minimum Principle from Optimal Control Theory and the Karush-Kuhn-Tucker conditions it was shown that the relaxed problem is identical to the original problem at the minimum point. Therefore, the optimal solution of the relaxed problem is an optimal solution of the original problem, referred to as lossless convexification. A key finding is that this holds for all levels of gravity model fidelity. The designed thrust magnitude profiles were the bang-bang predicted by Optimal Control Theory. The first high fidelity gravity model employed was the 2x2 spherical harmonics model assuming a perfect triaxial ellipsoid and placement of the coordinate frame at the asteroid's center of mass and aligned with the semi-major axes. The spherical harmonics model is not valid inside the Brillouin sphere and this becomes relevant for irregularly shaped asteroids. Then, a higher fidelity model was implemented combining the 4x4 spherical harmonics gravity model with the interior spherical Bessel gravity model. All gravitational terms in the equations of motion are evaluated with the position vector from the previous iteration, creating the successive solution method. Methodology success was shown by applying the algorithm to three triaxial ellipsoidal asteroids with four different rotation speeds using the 2x2 gravity model. Finally, the algorithm was tested using the irregularly shaped asteroid, Castalia.

Image analysis of open-door laminoplasty for cervical spondylotic myelopathy: comparing the influence of cord morphology and spine alignment.

PubMed

Lin, Bon-Jour; Lin, Meng-Chi; Lin, Chin; Lee, Meei-Shyuan; Feng, Shao-Wei; Ju, Da-Tong; Ma, Hsin-I; Liu, Ming-Ying; Hueng, Dueng-Yuan

2015-10-01

Previous studies have identified the factors affecting the surgical outcome of cervical spondylotic myelopathy (CSM) following laminoplasty. Nonetheless, the effect of these factors remains controversial. It is unknown about the association between pre-operative cervical spinal cord morphology and post-operative imaging result following laminoplasty. The goal of this study is to analyze the impact of pre-operative cervical spinal cord morphology on post-operative imaging in patients with CSM. Twenty-six patients with CSM undergoing open-door laminoplasty were classified according to pre-operative cervical spine bony alignment and cervical spinal cord morphology, and the results were evaluated in terms of post-operative spinal cord posterior drift, and post-operative expansion of the antero-posterior dura diameter. By the result of study, pre-operative spinal cord morphology was an effective classification in predicting surgical outcome - patients with anterior convexity type, description of cervical spinal cord morphology, had more spinal cord posterior migration than those with neutral or posterior convexity type after open-door laminoplasty. Otherwise, the interesting finding was that cervical spine Cobb's angle had an impact on post-operative spinal cord posterior drift in patients with neutral or posterior convexity type spinal cord morphology - the degree of kyphosis was inversely proportional to the distance of post-operative spinal cord posterior drift, but not in the anterior convexity type. These findings supported that pre-operative cervical spinal cord morphology may be used as screening for patients undergoing laminoplasty. Patients having neutral or posterior convexity type spinal cord morphology accompanied with kyphotic deformity were not suitable candidates for laminoplasty. Copyright © 2015 Elsevier B.V. All rights reserved.

Maximally dense packings of two-dimensional convex and concave noncircular particles.

PubMed

Atkinson, Steven; Jiao, Yang; Torquato, Salvatore

2012-09-01

Dense packings of hard particles have important applications in many fields, including condensed matter physics, discrete geometry, and cell biology. In this paper, we employ a stochastic search implementation of the Torquato-Jiao adaptive-shrinking-cell (ASC) optimization scheme [Nature (London) 460, 876 (2009)] to find maximally dense particle packings in d-dimensional Euclidean space R(d). While the original implementation was designed to study spheres and convex polyhedra in d≥3, our implementation focuses on d=2 and extends the algorithm to include both concave polygons and certain complex convex or concave nonpolygonal particle shapes. We verify the robustness of this packing protocol by successfully reproducing the known putative optimal packings of congruent copies of regular pentagons and octagons, then employ it to suggest dense packing arrangements of congruent copies of certain families of concave crosses, convex and concave curved triangles (incorporating shapes resembling the Mercedes-Benz logo), and "moonlike" shapes. Analytical constructions are determined subsequently to obtain the densest known packings of these particle shapes. For the examples considered, we find that the densest packings of both convex and concave particles with central symmetry are achieved by their corresponding optimal Bravais lattice packings; for particles lacking central symmetry, the densest packings obtained are nonlattice periodic packings, which are consistent with recently-proposed general organizing principles for hard particles. Moreover, we find that the densest known packings of certain curved triangles are periodic with a four-particle basis, and we find that the densest known periodic packings of certain moonlike shapes possess no inherent symmetries. Our work adds to the growing evidence that particle shape can be used as a tuning parameter to achieve a diversity of packing structures.

Maximally dense packings of two-dimensional convex and concave noncircular particles

NASA Astrophysics Data System (ADS)

Atkinson, Steven; Jiao, Yang; Torquato, Salvatore

2012-09-01

Dense packings of hard particles have important applications in many fields, including condensed matter physics, discrete geometry, and cell biology. In this paper, we employ a stochastic search implementation of the Torquato-Jiao adaptive-shrinking-cell (ASC) optimization scheme [Nature (London)NATUAS0028-083610.1038/nature08239 460, 876 (2009)] to find maximally dense particle packings in d-dimensional Euclidean space Rd. While the original implementation was designed to study spheres and convex polyhedra in d≥3, our implementation focuses on d=2 and extends the algorithm to include both concave polygons and certain complex convex or concave nonpolygonal particle shapes. We verify the robustness of this packing protocol by successfully reproducing the known putative optimal packings of congruent copies of regular pentagons and octagons, then employ it to suggest dense packing arrangements of congruent copies of certain families of concave crosses, convex and concave curved triangles (incorporating shapes resembling the Mercedes-Benz logo), and “moonlike” shapes. Analytical constructions are determined subsequently to obtain the densest known packings of these particle shapes. For the examples considered, we find that the densest packings of both convex and concave particles with central symmetry are achieved by their corresponding optimal Bravais lattice packings; for particles lacking central symmetry, the densest packings obtained are nonlattice periodic packings, which are consistent with recently-proposed general organizing principles for hard particles. Moreover, we find that the densest known packings of certain curved triangles are periodic with a four-particle basis, and we find that the densest known periodic packings of certain moonlike shapes possess no inherent symmetries. Our work adds to the growing evidence that particle shape can be used as a tuning parameter to achieve a diversity of packing structures.

Convex geometry of quantum resource quantification

NASA Astrophysics Data System (ADS)

Regula, Bartosz

2018-01-01

We introduce a framework unifying the mathematical characterisation of different measures of general quantum resources and allowing for a systematic way to define a variety of faithful quantifiers for any given convex quantum resource theory. The approach allows us to describe many commonly used measures such as matrix norm-based quantifiers, robustness measures, convex roof-based measures, and witness-based quantifiers together in a common formalism based on the convex geometry of the underlying sets of resource-free states. We establish easily verifiable criteria for a measure to possess desirable properties such as faithfulness and strong monotonicity under relevant free operations, and show that many quantifiers obtained in this framework indeed satisfy them for any considered quantum resource. We derive various bounds and relations between the measures, generalising and providing significantly simplified proofs of results found in the resource theories of quantum entanglement and coherence. We also prove that the quantification of resources in this framework simplifies for pure states, allowing us to obtain more easily computable forms of the considered measures, and show that many of them are in fact equal on pure states. Further, we investigate the dual formulation of resource quantifiers, which provide a characterisation of the sets of resource witnesses. We present an explicit application of the results to the resource theories of multi-level coherence, entanglement of Schmidt number k, multipartite entanglement, as well as magic states, providing insight into the quantification of the four resources by establishing novel quantitative relations and introducing new quantifiers, such as a measure of entanglement of Schmidt number k which generalises the convex roof-extended negativity, a measure of k-coherence which generalises the \

High-Frequency Testing of Composite Fan Vanes With Erosion-Resistant Coating Conducted

NASA Technical Reports Server (NTRS)

Bowman, Cheryl L.; Sutter, James K.; Naik, Subhash; Otten, Kim D.; Perusek, Gail P.

2003-01-01

The mechanical integrity of hard, erosion-resistant coatings were tested using the Structural Dynamics Laboratory at the NASA Glenn Research Center. Under the guidance of Structural Mechanics and Dynamics Branch personnel, fixturing and test procedures were developed at Glenn to simulate engine vibratory conditions on coated polymer-matrix- composite bypass vanes using a slip table in the Structural Dynamics Laboratory. Results from the high-frequency mechanical bench testing, along with concurrent erosion testing of coupons and vanes, provided sufficient confidence to engine-endurance test similarly coated vane segments. The knowledge gained from this program will be applied to the development of oxidation- and erosion-resistant coatings for polymer matrix composite blades and vanes in future advanced turbine engines. Fan bypass vanes from the AE3007 (Rolls Royce America, Indianapolis, IN) gas turbine engine were coated by Engelhard (Windsor, CT) with compliant bond coatings and hard ceramic coatings. The coatings were developed collaboratively by Glenn and Allison Advanced Development Corporation (AADC)/Rolls Royce America through research sponsored by the High-Temperature Engine Materials Technology Project (HITEMP) and the Higher Operating Temperature Propulsion Components (HOTPC) project. High-cycle fatigue was performed through high-frequency vibratory testing on a shaker table. Vane resonant frequency modes were surveyed from 50 to 3000 Hz at input loads from 1g to 55g on both uncoated production vanes and vanes with the erosion-resistant coating. Vanes were instrumented with both lightweight accelerometers and strain gauges to establish resonance, mode shape, and strain amplitudes. Two high-frequency dwell conditions were chosen to excite two strain levels: one approaching the vane's maximum allowable design strain and another near the expected maximum strain during engine operation. Six specimens were tested per dwell condition. Pretest and posttest inspections were performed optically at up to 60 magnification and using a fluorescent-dye penetrant. Accumulation of 10 million cycles at a strain amplitude of two to three times that expected in the engine (approximately 670 Hz and 20g) led to the development of multiple cracks in the coating that were only detectable using fluorescent-dye penetrant inspection. Cracks were prevalent on the trailing edge and on the convex side of the midsection. No cracking or spalling was evident using standard optical inspection at up to 60 magnification. Further inspection may reveal whether these fine cracks penetrated the coating or were strictly on the surface. The dwell condition that simulated actual engine conditions produced no obvious surface flaws even after up to 80 million cycles had been accumulated at strain amplitudes produced at approximately 1500 Hz and 45g.

A novel optical detector concept for dedicated and multi-modality in vivo small animal imaging

NASA Astrophysics Data System (ADS)

Peter, Jörg; Schulz, Ralf B.; Unholtz, Daniel; Semmler, Wolfhard

2007-07-01

An optical detector suitable for inclusion in tomographic arrangements for non-contact in vivo bioluminescence and fluorescence imaging applications is proposed. It consists of a microlens array (MLA) intended for field-of-view definition, a large-field complementary metal-oxide-semiconductor (CMOS) chip for light detection, a septum mask for cross-talk suppression, and an exchangeable filter to block excitation light. Prototype detector units with sensitive areas of 2.5 cm x 5 cm each were assembled. The CMOS sensor constitutes a 512 x 1024 photodiode matrix at 48 μm pixel pitch. Refractive MLAs with plano-convex lenses of 480 μm in diameter and pitch were selected resulting in a 55 x 105 lens matrix. The CMOS sensor is aligned on the focal plane of the MLA at 2.15mm distance. To separate individual microlens images an opaque multi-bore septum mask of 2.1mm in thickness and bore diameters of 400 μm at 480 μm pitch, aligned with the lens pattern, is placed between MLA and CMOS. Intrinsic spatial detector resolution and sensitivity was evaluated experimentally as a function of detector-object distance. Due to its small overall dimensions such detectors can be favorably packed for tomographic imaging (optical diffusion tomography, ODT) yielding complete 2 π field-of-view coverage. We also present a design study of a device intended to simultaneously image positron labeled substrates (positron emission tomography, PET) and optical molecular probes in small animals such as mice and rats. It consists of a cylindrical allocation of optical detector units which form an inner detector ring while PET detector blocks are mounted in radial extension, those gaining complementary information in a single, intrinsically coregistered experimental data acquisition study. Finally, in a second design study we propose a method for integrated optical and magnetic resonance imaging (MRI) which yields in vivo functional/molecular information that is intrinsically registered with the anatomy of the image object.

Riemannian and Lorentzian flow-cut theorems

NASA Astrophysics Data System (ADS)

Headrick, Matthew; Hubeny, Veronika E.

2018-05-01

We prove several geometric theorems using tools from the theory of convex optimization. In the Riemannian setting, we prove the max flow-min cut (MFMC) theorem for boundary regions, applied recently to develop a ‘bit-thread’ interpretation of holographic entanglement entropies. We also prove various properties of the max flow and min cut, including respective nesting properties. In the Lorentzian setting, we prove the analogous MFMC theorem, which states that the volume of a maximal slice equals the flux of a minimal flow, where a flow is defined as a divergenceless timelike vector field with norm at least 1. This theorem includes as a special case a continuum version of Dilworth’s theorem from the theory of partially ordered sets. We include a brief review of the necessary tools from the theory of convex optimization, in particular Lagrangian duality and convex relaxation.

Non-convex Statistical Optimization for Sparse Tensor Graphical Model

PubMed Central

Sun, Wei; Wang, Zhaoran; Liu, Han; Cheng, Guang

2016-01-01

We consider the estimation of sparse graphical models that characterize the dependency structure of high-dimensional tensor-valued data. To facilitate the estimation of the precision matrix corresponding to each way of the tensor, we assume the data follow a tensor normal distribution whose covariance has a Kronecker product structure. The penalized maximum likelihood estimation of this model involves minimizing a non-convex objective function. In spite of the non-convexity of this estimation problem, we prove that an alternating minimization algorithm, which iteratively estimates each sparse precision matrix while fixing the others, attains an estimator with the optimal statistical rate of convergence as well as consistent graph recovery. Notably, such an estimator achieves estimation consistency with only one tensor sample, which is unobserved in previous work. Our theoretical results are backed by thorough numerical studies. PMID:28316459

Distance majorization and its applications.

PubMed

Chi, Eric C; Zhou, Hua; Lange, Kenneth

2014-08-01

The problem of minimizing a continuously differentiable convex function over an intersection of closed convex sets is ubiquitous in applied mathematics. It is particularly interesting when it is easy to project onto each separate set, but nontrivial to project onto their intersection. Algorithms based on Newton's method such as the interior point method are viable for small to medium-scale problems. However, modern applications in statistics, engineering, and machine learning are posing problems with potentially tens of thousands of parameters or more. We revisit this convex programming problem and propose an algorithm that scales well with dimensionality. Our proposal is an instance of a sequential unconstrained minimization technique and revolves around three ideas: the majorization-minimization principle, the classical penalty method for constrained optimization, and quasi-Newton acceleration of fixed-point algorithms. The performance of our distance majorization algorithms is illustrated in several applications.

Optimal Micropatterns in 2D Transport Networks and Their Relation to Image Inpainting

NASA Astrophysics Data System (ADS)

Brancolini, Alessio; Rossmanith, Carolin; Wirth, Benedikt

2018-04-01

We consider two different variational models of transport networks: the so-called branched transport problem and the urban planning problem. Based on a novel relation to Mumford-Shah image inpainting and techniques developed in that field, we show for a two-dimensional situation that both highly non-convex network optimization tasks can be transformed into a convex variational problem, which may be very useful from analytical and numerical perspectives. As applications of the convex formulation, we use it to perform numerical simulations (to our knowledge this is the first numerical treatment of urban planning), and we prove a lower bound for the network cost that matches a known upper bound (in terms of how the cost scales in the model parameters) which helps better understand optimal networks and their minimal costs.

A Walking Method for Non-Decomposition Intersection and Union of Arbitrary Polygons and Polyhedrons

DOE Office of Scientific and Technical Information (OSTI.GOV)

Graham, M.; Yao, J.

We present a method for computing the intersection and union of non- convex polyhedrons without decomposition in O(n log n) time, where n is the total number of faces of both polyhedrons. We include an accompanying Python package which addresses many of the practical issues associated with implementation and serves as a proof of concept. The key to the method is that by considering the edges of the original ob- jects and the intersections between faces as walking routes, we can e ciently nd the boundary of the intersection of arbitrary objects using directional walks, thus handling the concave casemore » in a natural manner. The method also easily extends to plane slicing and non-convex polyhedron unions, and both the polyhedron and its constituent faces may be non-convex.« less

A symmetric version of the generalized alternating direction method of multipliers for two-block separable convex programming.

PubMed

Liu, Jing; Duan, Yongrui; Sun, Min

2017-01-01

This paper introduces a symmetric version of the generalized alternating direction method of multipliers for two-block separable convex programming with linear equality constraints, which inherits the superiorities of the classical alternating direction method of multipliers (ADMM), and which extends the feasible set of the relaxation factor α of the generalized ADMM to the infinite interval [Formula: see text]. Under the conditions that the objective function is convex and the solution set is nonempty, we establish the convergence results of the proposed method, including the global convergence, the worst-case [Formula: see text] convergence rate in both the ergodic and the non-ergodic senses, where k denotes the iteration counter. Numerical experiments to decode a sparse signal arising in compressed sensing are included to illustrate the efficiency of the new method.

Load Tests on a Stiffened Circular Cylindrical Shell

NASA Technical Reports Server (NTRS)

Schapitz, E; Krumling, G

1938-01-01

The present report describes tests in which the stress distribution may be determined in a stiffened circular cylindrical shell loaded longitudinally at four symmetrically situated points. As being of particular importance are the cases investigated of groups of bending and arching or convexing forces, respectively. From the stress measurements on the longitudinal stiffeners, the shear stresses and the bulkhead ring stresses in the skin could be evaluated. These measurements showed that the "simple shear field" used in theoretical computations in which all normal stresses in the skin are neglected, must be extended by the addition of the transverse or circumferential stresses if the bulkhead rings are not riveted to the skin.

An Improved Search Approach for Solving Non-Convex Mixed-Integer Non Linear Programming Problems

NASA Astrophysics Data System (ADS)

Sitopu, Joni Wilson; Mawengkang, Herman; Syafitri Lubis, Riri

2018-01-01

The nonlinear mathematical programming problem addressed in this paper has a structure characterized by a subset of variables restricted to assume discrete values, which are linear and separable from the continuous variables. The strategy of releasing nonbasic variables from their bounds, combined with the “active constraint” method, has been developed. This strategy is used to force the appropriate non-integer basic variables to move to their neighbourhood integer points. Successful implementation of these algorithms was achieved on various test problems.

Square Deal: Lower Bounds and Improved Relaxations for Tensor Recovery

DTIC Science & Technology

2013-08-16

problem size n from 10 to 30 with increment 1, and the observation ratio ρ from 0.01 to 0.2 with increment 0.01. For each (ρ, n)-pair, we simulate 5 test ...Foundations of Computational Mathematics, 12(6):805–849, 2012. [CRT] Emmanuel J. Candès, Justin K. Romberg , and Terence Tao. Stable signal recov- ery...2012. [SDS10] Marco Signoretto, Lieven De Lathauwer, and Johan AK Suykens. Nuclear norms for tensors and their use for convex multilinear estimation

Generalized monogamy inequalities and upper bounds of negativity for multiqubit systems

NASA Astrophysics Data System (ADS)

Yang, Yanmin; Chen, Wei; Li, Gang; Zheng, Zhu-Jun

2018-01-01

In this paper, we present some generalized monogamy inequalities and upper bounds of negativity based on convex-roof extended negativity (CREN) and CREN of assistance (CRENOA). These monogamy relations are satisfied by the negativity of N -qubit quantum systems A B C1⋯CN -2 , under the partitions A B | C1⋯CN -2 and A B C1| C2⋯CN -2 . Furthermore, the W -class states are used to test these generalized monogamy inequalities.

Algorithm for Overcoming the Curse of Dimensionality for Certain Non-convex Hamilton-Jacobi Equations, Projections and Differential Games

DTIC Science & Technology

2016-05-01

Algorithm for Overcoming the Curse of Dimensionality for Certain Non-convex Hamilton-Jacobi Equations, Projections and Differential Games Yat Tin...subproblems. Our approach is expected to have wide applications in continuous dynamic games , control theory problems, and elsewhere. Mathematics...differential dynamic games , control theory problems, and dynamical systems coming from the physical world, e.g. [11]. An important application is to

Determination of refractive index of a simple negative, positive, or zero power lens using wedged plated interferometer

NASA Technical Reports Server (NTRS)

Shukla, R. P.; Perera, G. M.; George, M. C.; Venkateswarlu, P.

1990-01-01

A nondestructive technique for measuring the refractive index of a negative lens using a wedged plate interferometer is described. The method can be also used for measuring the refractive index of convex or zero power lenses. Schematic diagrams are presented for the use of a wedged plate interferometer for measuring the refractive index of a concave lens and of a convex lens.

Core-softened potentials, multiple liquid-liquid critical points, and density anomaly regions: An exact solution

NASA Astrophysics Data System (ADS)

Rizzatti, Eduardo O.; Barbosa, Marco Aurélio A.; Barbosa, Marcia C.

2018-02-01

The pressure versus temperature phase diagram of a system of particles interacting through a multiscale shoulder-like potential is exactly computed in one dimension. The N-shoulder potential exhibits N density anomaly regions in the phase diagram if the length scales can be connected by a convex curve. The result is analyzed in terms of the convexity of the Gibbs free energy.

Performance Analysis of the Unitree Central File

NASA Technical Reports Server (NTRS)

Pentakalos, Odysseas I.; Flater, David

1994-01-01

This report consists of two parts. The first part briefly comments on the documentation status of two major systems at NASA#s Center for Computational Sciences, specifically the Cray C98 and the Convex C3830. The second part describes the work done on improving the performance of file transfers between the Unitree Mass Storage System running on the Convex file server and the users workstations distributed over a large georgraphic area.

Survey and Assessment of the Cultural Resources, Toronto Lake Project.

DTIC Science & Technology

1981-01-01

impressions, cross hatching, rocker stamping, cord- wrapped stick impressions, and roulette impressions generally con- fined within incised zoning...Its surface collection included one fragment of a plano -convex end scraper, one biface midsection probably from a large point (Fig. 3b), one possible...recovered during the entire survey. Eight point or knife tips were found and seven midsections. Scrapers included five plano - convex end scrapers, three

Morphological decomposition of 2-D binary shapes into convex polygons: a heuristic algorithm.

PubMed

Xu, J

2001-01-01

In many morphological shape decomposition algorithms, either a shape can only be decomposed into shape components of extremely simple forms or a time consuming search process is employed to determine a decomposition. In this paper, we present a morphological shape decomposition algorithm that decomposes a two-dimensional (2-D) binary shape into a collection of convex polygonal components. A single convex polygonal approximation for a given image is first identified. This first component is determined incrementally by selecting a sequence of basic shape primitives. These shape primitives are chosen based on shape information extracted from the given shape at different scale levels. Additional shape components are identified recursively from the difference image between the given image and the first component. Simple operations are used to repair certain concavities caused by the set difference operation. The resulting hierarchical structure provides descriptions for the given shape at different detail levels. The experiments show that the decomposition results produced by the algorithm seem to be in good agreement with the natural structures of the given shapes. The computational cost of the algorithm is significantly lower than that of an earlier search-based convex decomposition algorithm. Compared to nonconvex decomposition algorithms, our algorithm allows accurate approximations for the given shapes at low coding costs.

Towards reproducible experimental studies for non-convex polyhedral shaped particles

NASA Astrophysics Data System (ADS)

Wilke, Daniel N.; Pizette, Patrick; Govender, Nicolin; Abriak, Nor-Edine

2017-06-01

The packing density and flat bottomed hopper discharge of non-convex polyhedral particles are investigated in a systematic experimental study. The motivation for this study is two-fold. Firstly, to establish an approach to deliver quality experimental particle packing data for non-convex polyhedral particles that can be used for characterization and validation purposes of discrete element codes. Secondly, to make the reproducibility of experimental setups as convenient and readily available as possible using affordable and accessible technology. The primary technology for this study is fused deposition modeling used to 3D print polylactic acid (PLA) particles using readily available 3D printer technology. A total of 8000 biodegradable particles were printed, 1000 white particles and 1000 black particles for each of the four particle types considered in this study. Reproducibility is one benefit of using fused deposition modeling to print particles, but an extremely important additional benefit is that specific particle properties can be explicitly controlled. As an example in this study the volume fraction of each particle can be controlled i.e. the effective particle density can be adjusted. In this study the particle volumes reduces drastically as the non-convexity is increased, however all printed white particles in this study have the same mass within 2% of each other.

Direct single-layered fabrication of 3D concavo convex patterns in nano-stereolithography

NASA Astrophysics Data System (ADS)

Lim, T. W.; Park, S. H.; Yang, D. Y.; Kong, H. J.; Lee, K. S.

2006-09-01

A nano-surfacing process (NSP) is proposed to directly fabricate three-dimensional (3D) concavo convex-shaped microstructures such as micro-lens arrays using two-photon polymerization (TPP), a promising technique for fabricating arbitrary 3D highly functional micro-devices. In TPP, commonly utilized methods for fabricating complex 3D microstructures to date are based on a layer-by-layer accumulating technique employing two-dimensional sliced data derived from 3D computer-aided design data. As such, this approach requires much time and effort for precise fabrication. In this work, a novel single-layer exposure method is proposed in order to improve the fabricating efficiency for 3D concavo convex-shaped microstructures. In the NSP, 3D microstructures are divided into 13 sub-regions horizontally with consideration of the heights. Those sub-regions are then expressed as 13 characteristic colors, after which a multi-voxel matrix (MVM) is composed with the characteristic colors. Voxels with various heights and diameters are generated to construct 3D structures using a MVM scanning method. Some 3D concavo convex-shaped microstructures were fabricated to estimate the usefulness of the NSP, and the results show that it readily enables the fabrication of single-layered 3D microstructures.