Zobrazeno 1 - 10
of 51
pro vyhledávání: '"Rustum Choksi"'
Publikováno v:
Royal Society Open Science, Vol 11, Iss 6 (2024)
This article addresses how diverse collective behaviours arise from simple and realistic decisions made entirely at the level of each agent’s personal space in the sense of the Voronoi diagram. We present a discrete-time model in two dimensions in
Externí odkaz:
https://doaj.org/article/255586842e944fa7b3d66ec8e4399581
Publikováno v:
IEEE Transactions on Pattern Analysis and Machine Intelligence. 43:77-88
Barcode encoding schemes impose symbolic constraints which fix certain segments of the image. We present, implement, and assess a method for blind deblurring and denoising based entirely on Kullback-Leibler divergence. The method is designed to incor
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::dd9fa2f4964c33929dd85d9a2dcdffde
https://doi.org/10.1109/tpami.2019.2927311
https://doi.org/10.1109/tpami.2019.2927311
Autor:
Rustum Choksi, Xin Yang Lu
Publikováno v:
Communications in Mathematical Physics. 377:2429-2450
Gersho’s conjecture in 3D asserts the asymptotic periodicity and structure of the optimal centroidal Voronoi tessellation. This relatively simple crystallization problem remains to date open. We prove bounds on the geometric complexity of optimal c
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::0ab05e588d9a2f16e1b14922e42355cf
https://doi.org/10.1007/s00220-020-03789-y
https://doi.org/10.1007/s00220-020-03789-y
Using the recently developed theory of rigorously validated numerics, we address the Phase-Field-Crystal (PFC) model at the microscopic (atomistic) level. We show the existence of critical points and local minimizers associated with "classical" candi
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4448c81ec9bbd3964e0062f09e51d6d0
http://arxiv.org/abs/2102.02338
http://arxiv.org/abs/2102.02338
Publikováno v:
Inverse Problems.
Image deblurring is a notoriously challenging ill-posed inverse problem. In recent years, a wide variety of approaches have been proposed based upon regularization at the level of the image or on techniques from machine learning. We propose an altern
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::667dc812df5d7c4c37d58370dd3cd17a
https://doi.org/10.1088/1361-6420/abc32e
https://doi.org/10.1088/1361-6420/abc32e
Finding optimal (or low energy) centroidal Voronoi tessellations (CVTs) on a 2D domain is a challenging problem. One must navigate an energy landscape whose desirable critical points have sufficiently small basins of attractions that they are inacces
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::81da7a42399184d7d4f29e24168ed8b4
Publikováno v:
Indiana University Mathematics Journal. 67:375-395
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 potential in power-law form. We find that the existence of minimizers of this shape optimiz
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c7ec10dc2f3bbf557ee988f8024c4e70
https://doi.org/10.1512/iumj.2018.67.6234
https://doi.org/10.1512/iumj.2018.67.6234
Autor:
Rustum Choksi
While partial differential equations (PDEs) are fundamental in mathematics and throughout the sciences, most undergraduate students are only exposed to PDEs through the method of separation of variations. This text is written for undergraduate studen
This note concerns the problem of minimizing a certain family of non-local energy functionals over measures on $\mathbb{R}^n$, subject to a mass constraint, in a strong attraction limit. In these problems, the total energy is an integral over pair in
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::617ecd5a41781128f68f5e168de52cab
http://arxiv.org/abs/1911.02539
http://arxiv.org/abs/1911.02539
Publikováno v:
SIAM Journal on Applied Mathematics. 76:1101-1125
Self-assembly of shapes from spheres to nonsmooth and possibly nonconvex shapes is pervasive throughout the sciences. These arrangements arise in biology for animal flocking and herding, in condensed matter physics with molecular and nano self-assemb
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::c1689eba2c631286c4b03e317bf030a7
https://doi.org/10.1137/15m1034167
https://doi.org/10.1137/15m1034167