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IEEE Transactions on Pattern Analysis and Machine Intelligence, ISSN 0162-8828, 7/2019, pp. 1 - 1
Barcode encoding schemes impose symbolic constraints which fix certain segments of the image. We present, implement, and assess a method for blind deblurring... 
maximum entropy on the mean | Noise reduction | Estimation | UPC barcode | Entropy | Probability distribution | QR barcode | Kullback-Leibler divergence | blind deblurring | denoising | symbology | L-BFGS | Cameras | Fenchel-Rockafellar duality | Kernel
Journal Article
Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire, ISSN 0294-1449, 11/2015, Volume 32, Issue 6, pp. 1283 - 1305
Journal Article
Quarterly of Applied Mathematics, ISSN 0033-569X, 09/2012, Volume 70, Issue 3, pp. 517 - 537
Journal Article
Notices of the American Mathematical Society, ISSN 0002-9920, 12/2017, Volume 64, Issue 11, pp. 1275 - 1283
Journal Article
SIAM Journal on Mathematical Analysis, ISSN 0036-1410, 2010, Volume 42, Issue 3, pp. 1334 - 1370
Journal Article
SIAM Journal on Mathematical Analysis, ISSN 0036-1410, 2011, Volume 43, Issue 2, pp. 739 - 763
We present the second of two articles on the small volume-fraction limit of a nonlocal Cahn-Hilliard functional introduced to model microphase separation of... 
Nonlocal Cahn-Hilliard problem | Γ-convergence | Small volume-fraction limit | Diblock copolymers | small volume-fraction limit | MATHEMATICS, APPLIED | BLOCK-COPOLYMERS | diblock copolymers | GINZBURG-LANDAU | CONVERGENCE | Gamma-convergence | MICROPHASE SEPARATION | MELTS | nonlocal Cahn-Hilliard problem | 2 DIMENSIONS | Studies | Volume | Fractions
Journal Article
Journal of Mathematical Physics, ISSN 0022-2488, 10/2017, Volume 58, Issue 10
We prove that both the liquid drop model in R3 with an attractive background nucleus and theThomas-Fermi-Dirac-von Weizsäcker (TFDW) model attain their... 
Attraction | Decay rate
Journal Article
Journal of Mathematical Physics, ISSN 0022-2488, 10/2017, Volume 58, Issue 10, p. 1
We prove that both the liquid drop model in R3 with an attractive background nucleus and the Thomas-Fermi-Dirac-von Weizsacker (TFDW) model attain their... 
Molecules | Attraction | Decay rate | Atoms & subatomic particles | Mathematical models
Journal Article
Notices of the American Mathematical Society, ISSN 0002-9920, 12/2017, Volume 64, Issue 11, p. 1
Journal Article
Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 11/2013, Volume 48, Issue 3, pp. 337 - 366
Since the pioneering work of Canham and Helfrich, variational formulations involving curvature-dependent functionals, like the classical Willmore functional,... 
49J45 | Systems Theory, Control | Calculus of Variations and Optimal Control; Optimization | Analysis | Theoretical, Mathematical and Computational Physics | 58E99 | Mathematics | 49Q10 | 53C80 | MATHEMATICS | MATHEMATICS, APPLIED | WILLMORE SURFACES | SHAPE | VESICLES | CURVATURE | MEMBRANES | REPRESENTATION | VARIFOLDS | DOMAINS | FUNCTIONALS
Journal Article
Journal of Mathematical Physics, ISSN 0022-2488, 10/2017, Volume 58, Issue 10, p. 103503
We prove that both the liquid drop model in R 3 with an attractive background nucleus and the Thomas-Fermi-Dirac-von Weizsäcker (TFDW) model attain their... 
ATOMS | THOMAS-FERMI | MOND | PHYSICS, MATHEMATICAL
Journal Article
Indiana University Mathematics Journal, ISSN 0022-2518, 2018, Volume 67, Issue 1, pp. 375 - 395
We consider a class of nonlocal shape optimization problems for sets of fixed mass where the energy functional is given by an attractive/repulsive interaction... 
Global minimizers | Self-assembly | Pair-wise interactions (potentials) | Nonlocal shape optimization | OBSTACLE PROBLEM | EXISTENCE | VOLUME-FRACTION LIMIT | pair-wise interactions (potentials) | INTERACTION ENERGY | global | MODEL | LOCAL MINIMIZERS | MATHEMATICS | self-assembly | R-N | EQUILIBRIA | REGULARITY | minimizers | ISOPERIMETRIC PROBLEM
Journal Article
Annales de l'Institut Henri Poincaré / Analyse non linéaire, ISSN 0294-1449, 11/2015, Volume 32, Issue 6, pp. 1283 - 1305
We consider a family of interaction functionals consisting of power-law potentials with attractive and repulsive parts and use the concentration compactness... 
Aggregation | Global minimizers | Interaction of attractive and repulsive potentials | Self-assembly | AGGREGATION EQUATIONS | EXISTENCE | MATHEMATICS, APPLIED | VOLUME-FRACTION LIMIT | STATIONARY STATES | BEHAVIOR | UNIQUENESS | MODELS | DYNAMICS | BLOW-UP
Journal Article
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, ISSN 1534-0392, 01/2020, Volume 19, Issue 1, pp. 175 - 202
We address small volume-fraction asymptotic properties of a non-local isoperimetric functional with a confinement term, derived as the sharp interface limit of... 
MATHEMATICS, APPLIED | NONEXISTENCE | PARTICLES | LIMIT | COPOLYMERS | uniformly charged liquid | MATHEMATICS | phase separation | confinement | MINIMALITY | self-assembly of diblock copolymers | Gamma-convergence | Nonlocal isoperimetric problem
Journal Article
ESAIM - Control, Optimisation and Calculus of Variations, ISSN 1292-8119, 01/2015, Volume 21, Issue 1, pp. 247 - 270
Journal Article
Communications in Contemporary Mathematics, ISSN 0219-1997, 05/2019, Volume 21, Issue 3, p. 1850022
We consider a variant of Gamow’s liquid drop model, with a general repulsive Riesz kernel and a long-range attractive background potential with weight Z . The... 
background potential | droplet breakup | Liquid drop model | generalized minimizer | concentration-compactness method | nonlocal isoperimetric problem | MATHEMATICS, APPLIED | VOLUME-FRACTION LIMIT | NONEXISTENCE | MATHEMATICS | MINIMALITY | MOND | ISOPERIMETRIC PROBLEM
Journal Article
ESAIM - Control, Optimisation and Calculus of Variations, ISSN 1292-8119, 2013, Volume 19, Issue 4, pp. 1014 - 1029
We consider a Canham-Helfrich-type variational problem defined over closed surfaces enclosing a fixed volume and having fixed surface area. The problem models... 
Multicomponent vesicle | Global minimizers | Biomembranes | Helfrich functional | Axisymmetric surfaces | MATHEMATICS, APPLIED | ENERGY | SHAPE | VESICLES | CURVATURE | multicomponent vesicle | VARIFOLDS | global minimizers | AUTOMATION & CONTROL SYSTEMS | biomembranes | axisymmetric surfaces | Studies | Mathematical models | Mathematics | Calculus of variations
Journal Article
IEEE Transactions on Image Processing, ISSN 1057-7149, 09/2015, Volume 24, Issue 9, pp. 2864 - 2873
QR bar codes are prototypical images for which part of the image is a priori known (required patterns). Open source bar code readers, such as ZBar, are readily... 
QR bar code | TV flow | Noise | Noise reduction | Bar codes | Cameras | Kernel | blind deblurring | Standards | finder pattern | TV regularization
Journal Article
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