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A non-linear problem involving a critical Sobolev exponent
Bae, S.,Hadiji, R.,Vigneron, F.,Yazidi, H. Academic Press 2012 Journal of mathematical analysis and applications Vol.396 No.1
We study a non-linear minimization problem on H<SUB>0</SUB><SUP>1</SUP>(Ω)@?L<SUP>q</SUP> with q=2nn-2: inf@?u@?<SUB>L^q</SUB>=1∫<SUB>Ω</SUB>(1+|x|<SUP>β</SUP>|u|<SUP>k</SUP>)|@?u|<SUP>2</SUP>. We show that minimizers exist only for the range β<kn/q which corresponds to a dominant non-linear term. However, for β≥kn/q the influence of linearity prevents their existence.
Reachability by paths of bounded curvature in a convex polygon
Ahn, H.K.,Cheong, O.,Matousek, J.,Vigneron, A. Elsevier 2012 Computational Geometry Vol.45 No.1
Let B be a point robot moving in the plane, whose path is constrained to forward motions with curvature at most 1, and let P be a convex polygon with n vertices. Given a starting configuration (a location and a direction of travel) for B inside P, we characterize the region of all points of P that can be reached by B, and show that it has complexity O(n). We give an O(n<SUP>2</SUP>) time algorithm to compute this region. We show that a point is reachable only if it can be reached by a path of type CCSCS, where C denotes a unit circle arc and S denotes a line segment.
Autry, Adam W.,Hashizume, Rintaro,James, C. David,Larson, Peder E. Z.,Vigneron, Daniel B.,Park, Ilwoo Hindawi 2018 Contrast media and molecular imaging Vol.2018 No.-
<P><B>Objective</B></P><P> The purpose of this study was to demonstrate the feasibility of using hyperpolarized carbon-13 (<SUP>13</SUP>C) metabolic imaging with [1-<SUP>13</SUP>C]-labeled pyruvate for evaluating real-time <I>in vivo</I> metabolism of orthotopic diffuse intrinsic pontine glioma (DIPG) xenografts. </P><P><B>Materials and Methods</B></P><P> 3D <SUP>13</SUP>C magnetic resonance spectroscopic imaging (MRSI) data were acquired on a 3T scanner from 8 rats that had been implanted with human-derived DIPG cells in the brainstem and 5 healthy controls, following injection of 2.5 mL (100 mM) hyperpolarized [1-<SUP>13</SUP>C]-pyruvate. </P><P><B>Results</B></P><P> Anatomical images from DIPG-bearing rats characteristically exhibited T<SUB>2</SUB>-hyperintensity throughout the cerebellum and pons that was not accompanied by contrast enhancement. Evaluation of real-time <I>in vivo</I><SUP>13</SUP>C spectroscopic data revealed ratios of lactate-to-pyruvate (<I>p</I> < 0.002), lactate-to-total carbon (<I>p</I> < 0.002), and normalized lactate (<I>p</I> < 0.002) that were significantly higher in T<SUB>2</SUB> lesions harboring tumor relative to corresponding values of healthy normal brain. Elevated levels of lactate in lesions demonstrated a distinct metabolic profile that was associated with infiltrative, viable tumor recapitulating the histopathology of pediatric DIPG. </P><P><B>Conclusions</B></P><P> Results from this study characterized pyruvate and lactate metabolism in orthotopic DIPG xenografts and suggest that hyperpolarized <SUP>13</SUP>C MRSI may serve as a noninvasive imaging technique for <I>in vivo</I> monitoring of biochemical processes in patients with DIPG.</P>
Maximizing the overlap of two planar convex sets under rigid motions
Ahn, Hee-Kap,Cheong, Otfried,Park, Chong-Dae,Shin, Chan-Su,Vigneron, Antoine Elsevier 2007 Computational geometry Vol.37 No.1
<P><B>Abstract</B></P><P>Given two compact convex sets <I>P</I> and <I>Q</I> in the plane, we compute an image of <I>P</I> under a rigid motion that approximately maximizes the overlap with <I>Q</I>. More precisely, for any &z.epsiv;>0, we compute a rigid motion such that the area of overlap is at least 1−&z.epsiv; times the maximum possible overlap. Our algorithm uses O(1/&z.epsiv;) extreme point and line intersection queries on <I>P</I> and <I>Q</I>, plus O((1/<SUP>&z.epsiv;2</SUP>)log(1/&z.epsiv;)) running time. If only translations are allowed, the extra running time reduces to O((1/&z.epsiv;)log(1/&z.epsiv;)). If <I>P</I> and <I>Q</I> are convex polygons with <I>n</I> vertices in total that are given in an array or balanced tree, the total running time is O((1/&z.epsiv;)logn+(1/<SUP>&z.epsiv;2</SUP>)log(1/&z.epsiv;)) for rigid motions and O((1/&z.epsiv;)logn+(1/&z.epsiv;)log(1/&z.epsiv;)) for translations.</P>
Fast 3D <sup>1</sup>H MRSI of the corticospinal tract in pediatric brain
Kim, Dong-Hyun,Gu, Meng,Cunningham, Charles,Chen, Albert,Baumer, Fiona,Glenn, Orit A.,Vigneron, Daniel B.,Spielman, Daniel Mark,Barkovich, Anthony James Wiley Subscription Services, Inc., A Wiley Company 2009 Journal of Magnetic Resonance Imaging Vol.29 No.1
<B>Purpose</B><P>To develop a <SUP>1</SUP>H magnetic resonance spectroscopic imaging (MRSI) sequence that can be used to image infants/children at 3T and by combining it with diffusion tensor imaging (DTI) tractography, extract relevant metabolic information corresponding to the corticospinal tract (CST).</P><B>Materials and Methods</B><P>A fast 3D MRSI sequence was developed for pediatric neuroimaging at 3T using spiral k-space readout and dual band RF pulses (32 × 32 × 8 cm field of view [FOV], 1 cc iso-resolution, TR/TE = 1500/130, 6:24 minute scan). Using DTI tractography to identify the motor tracts, spectra were extracted from the CSTs and quantified. Initial data from infants/children with suspected motor delay (n = 5) and age-matched controls (n = 3) were collected and N-acetylaspartate (NAA) ratios were quantified.</P><B>Results</B><P>The average signal-to-noise ratio of the NAA peak from the studies was ≈22. Metabolite profiles were successfully acquired from the CST by using DTI tractography. Decreased NAA ratios in those with motor delay compared to controls of ≈10% at the CST were observed.</P><B>Conclusion</B><P>A fast and robust 3D MRSI technique targeted for pediatric neuroimaging has been developed. By combining with DTI tractography, metabolic information from the CSTs can be retrieved and estimated. By combining DTI and 3D MRSI, spectral information from various tracts can be obtained and processed. J. Magn. Reson. Imaging 2009;29:1–6. © 2008 Wiley-Liss, Inc.</P>
Covering and piercing disks with two centers
Ahn, H.K.,Kim, S.S.,Knauer, C.,Schlipf, L.,Shin, C.S.,Vigneron, A. Elsevier 2013 Computational geometry Vol.46 No.3
We give exact and approximation algorithms for two-center problems when the input is a set D of disks in the plane. We first study the problem of finding two smallest congruent disks such that each disk in D intersects one of these two disks. Then we study the problem of covering the set D by two smallest congruent disks.
Photonic crystal type structures of biological origin: Structural and spectral characterization
K. Kertesz,Zs. Balint,Z. Vertesy,G.I. Mark,V. Lousse,J.-P. Vigneron,L.P. Biro 한국물리학회 2006 Current Applied Physics Vol.6 No.2
Photonic crystal type structures of biological origin were investigated by scanning electron microscopy (SEM) and UVVISreectance measurements. It was demonstrated that despite the moderate refractive index contrast between chitin and air, biologicalevolution developed in the wing scale nanostructures of butteries representing various families, numerous structures with dierentuse photonic structures, the UV protection mechanism of the high altitude ower Edelweiss has been investigated. We present fullysupportive data that the protection mechanism is based on coupling by nanostructured, highly selective couplers the harmful UVradiation in propagating modes along bers containing UV absorbing pigment.
Realistic roofs over a rectilinear polygon
Ahn, H.K.,Bae, S.W.,Knauer, C.,Lee, M.,Shin, C.S.,Vigneron, A. Elsevier 2013 Computational geometry Vol.46 No.9
Given a simple rectilinear polygon P in the xy-plane, a roof over P is a terrain over P whose faces are supported by planes through edges of P that make a dihedral angle π/4 with the xy-plane. According to this definition, some roofs may have faces isolated from the boundary of P or even local minima, which are undesirable for several practical reasons. In this paper, we introduce realistic roofs by imposing a few additional constraints. We investigate the geometric and combinatorial properties of realistic roofs and show that the straight skeleton induces a realistic roof with maximum height and volume. We also show that the maximum possible number of distinct realistic roofs over P is ((n-4)/2@?(n-4)/4@?) when P has n vertices. We present an algorithm that enumerates a combinatorial representation of each such roof in O(1) time per roof without repetition, after O(n<SUP>4</SUP>) preprocessing time. We also present an O(n<SUP>5</SUP>)-time algorithm for computing a realistic roof with minimum height or volume.