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Trivial pursuit: Remarks on the main gap

John T. Baldwin, Leo Harrington
1987 Annals of Pure and Applied Logic  
Although the actual study of trivial types is rather trivial the pursuit of them is an exciting game.  ...  The improvements in the proof of the main gap results came about during long discussions between the authors and later with Buechler.  ...  This stronger result gives one way to formalize the insight that the main gap theorems prove much more than just the calculation of the spectrum functions.  ... 
doi:10.1016/0168-0072(87)90001-7 fatcat:6bezaadvgrb4xfis47g3lmsu2u

Triviality Pursuit

Alan Hájek
2011 Topoi  
I will look at some objections to Lewis's famous triviality results, and thus some reasons for the pursuit of further triviality results.  ...  I will generalize Lewis's results in ways that meet the objections. I will conclude with some reflections on the demise of the thesis-or otherwise.  ...  Acknowledgments I am indebted to Ned Hall, Richard Jeffrey, David Lewis, Bas van Fraassen, and Lyle Zynda for very helpful comments on a short, early precursor to this paper.  ... 
doi:10.1007/s11245-010-9083-2 fatcat:s3qtmdp5ebcpjkovm2ua4nibfi

Triviality pursuit: Can elementary scalar particles exist?

David J.E. Callaway
1988 Physics reports  
I would additionally like to thank the CERN Theory Division; the University of Rome II ("Tor Vergata"); the University of Bern; the Tata Institute for Fundamental Research, Bombay; the University of Delhi  ...  ; the Centro Atomico, Bariloche, Argentina; and the Department of Physics, Tribhuvan University, Kathmandu, Nepal, where much of this review was written.  ...  Callaway, Triviality pursuit unique model with trivial and! or nonrenormalizable interactions.  ... 
doi:10.1016/0370-1573(88)90008-7 fatcat:rqjb727u3zbmhdoxokxwpmkj2u

Matching pursuit shrinkage in Hilbert spaces

Tieyong Zeng, François Malgouyres
2011 Signal Processing  
In this paper, we study a variant of the Matching Pursuit named Matching Pursuit Shrinkage.  ...  The difference with the usual Matching Pursuit is that, once an atom has been selected, we do not erase all the information along the direction of this atom.  ...  The main difference is that it uses a shrinkage 1 function θ : R → R .  ... 
doi:10.1016/j.sigpro.2011.04.010 fatcat:hf5njzeo2natdgfnghn3db54ju

Functional Penalised Basis Pursuit on Spheres [article]

Matthieu Simeoni
2021 arXiv   pre-print
We illustrate the versatility of our framework on real-life examples from the field of environmental sciences.  ...  More specifically, we consider recovering spherical fields directly in the continuous domain using functional penalised basis pursuit problems with gTV regularisation terms.  ...  Acknowledgements The author is indebted to Michael Unser, Julien Fageot, and Sepand Kashani, and thank  ... 
arXiv:2006.05761v3 fatcat:3f6kjfllyzc5fmlmjaj2qdoqvq

Solving Basis Pursuit

Dirk A. Lorenz, Marc E. Pfetsch, Andreas M. Tillmann
2015 ACM Transactions on Mathematical Software  
The problem of finding a minimum 1 -norm solution to an underdetermined linear system is an important problem in compressed sensing, where it is also known as basis pursuit.  ...  Moreover, we provide an extensive numerical comparison of various state-of-the-art 1 -solvers that have been proposed during the last decade, on a large test set with a variety of explicitly given matrices  ...  ACKNOWLEDGMENTS We thank the anonymous referees for their useful comments and suggestions, which helped improve this paper.  ... 
doi:10.1145/2689662 fatcat:vy4r27vzdvdpjejgsbdmz7tezm

Majorana Zero Modes Protected by a Hopf Invariant in Topologically Trivial Superconductors

Zhongbo Yan, Ren Bi, Zhong Wang
2017 Physical Review Letters  
This work will stimulate investigations of Majorana zero modes in superconductors in the topologically trivial regime.  ...  The construction of this minimal single-band model is facilitated by the Hopf map and the Hopf invariant.  ...  y τ y ) + d z τ z , (16) For η ≪ 1, H η describes a superconductor with weak pairing (in the main article, we focused on the η = 1 case).  ... 
doi:10.1103/physrevlett.118.147003 pmid:28430502 fatcat:vjtpj6rtuvglfkfjyrkpgfc4jq

Positive Alexander Duality for Pursuit and Evasion [article]

Robert Ghrist, Sanjeevi Krishnan
2016 arXiv   pre-print
The principal tools are (1) a refinement of the Cech cohomology of a coverage region with a positive cone encoding spatial orientation, (2) a refinement of the Borel-Moore homology of the coverage gaps  ...  Considered is a class of pursuit-evasion games, in which an evader tries to avoid detection.  ...  We make some immediate remarks on the definition.  ... 
arXiv:1507.04741v2 fatcat:vzy6tbjgkngndcsbj4lhpruvi4

New directions in the pursuit of Majorana fermions in solid state systems

Jason Alicea
2012 Reports on progress in physics (Print)  
Finally, we discuss the most remarkable properties of condensed matter Majorana fermions--the non-Abelian exchange statistics that they generate and their associated potential for quantum computation.  ...  The all-important question of how one experimentally detects Majorana fermions in these setups is then addressed.  ...  pursuit of topological quantum computation.  ... 
doi:10.1088/0034-4885/75/7/076501 pmid:22790778 fatcat:kepxpt7o5zgsvji36y33ftl7i4

Classification using margin pursuit [article]

Matthew J. Holland
2018 arXiv   pre-print
Empirical tests on real-world benchmark data reinforce the basic principles highlighted by the theory, and are suggestive of a promising new technique for classification.  ...  This procedure is easily implemented using gradient descent, and admits finite-sample bounds on the excess risk under unbounded inputs.  ...  On the computational side, proper settings of α and β in practice is non-trivial.  ... 
arXiv:1810.04863v1 fatcat:ogxqnmycgjd6tedrugryrs4j3e

Pursuit Evasion on Polyhedral Surfaces

Kyle Klein, Subhash Suri
2015 Algorithmica  
We consider the following variant of a classical pursuit-evasion problem: how many pursuers are needed to capture a single (adversarial) evader on a closed polyhedral surface in three dimensions?  ...  Our main result is that four pursuers always suffice (upper bound), and that three are sometimes necessary (lower bound), for catching an adversarial evader on any polyhedral surface with genus zero.  ...  Closing Remarks In this paper, we considered a natural extension of the well-known pursuit-evasion game lion-and-the-man.  ... 
doi:10.1007/s00453-015-9988-7 fatcat:r43ejmo3frchhgcrrl64ux2r3y

Pursuit Evasion on Polyhedral Surfaces [chapter]

Kyle Klein, Subhash Suri
2013 Lecture Notes in Computer Science  
We consider the following variant of a classical pursuit-evasion problem: how many pursuers are needed to capture a single (adversarial) evader on a closed polyhedral surface in three dimensions?  ...  Our main result is that four pursuers always suffice (upper bound), and that three are sometimes necessary (lower bound), for catching an adversarial evader on any polyhedral surface with genus zero.  ...  Closing Remarks In this paper, we considered a natural extension of the well-known pursuit-evasion game lion-and-the-man.  ... 
doi:10.1007/978-3-642-45030-3_27 fatcat:mp4qrzy3hjc2bf4kudtiwkxcki

Positive Alexander Duality for Pursuit and Evasion

Robert Ghrist, Sanjeevi Krishnan
2017 SIAM Journal on applied algebra and geometry  
Such games can be formulated as the search for sections to the complement of a coverage region in a (trivial) vector bundle over a timeline.  ...  The principal tools are (1) a refinement of the cohomology of a coverage region with a positive cone encoding spatial orientation, (2) a refinement of the homology of the coverage gaps with a positive  ...  Concluding remarks (1) The assumptions for the necessary-and-sufficient condition are stricter than need be.  ... 
doi:10.1137/16m1089083 fatcat:ksuqb4d5nff5plscnglk4y34u4

Exact Recovery of Sparse Signals via Orthogonal Matching Pursuit: How Many Iterations Do We Need? [article]

Jian Wang, Byonghyo Shim
2016 arXiv   pre-print
Orthogonal matching pursuit (OMP) is a greedy algorithm widely used for the recovery of sparse signals from compressed measurements.  ...  Our result improves upon the recent result of Zhang and also bridges the gap between Zhang's result and the fundamental limit of OMP at which exact recovery of K-sparse signals cannot be uniformly guaranteed  ...  Our result bridges the gap between the result of Zhang [21] and this fundamental limit.  ... 
arXiv:1211.4293v5 fatcat:hmmu3mzyr5c6ncgmyuvtoouxvu

Functional penalised basis pursuit on spheres

Matthieu Simeoni
2021 Applied and Computational Harmonic Analysis  
We illustrate the versatility of our framework on real-life examples from the field of environmental sciences.  ...  In this paper, we propose a unified theoretical and practical spherical approximation framework for functional inverse problems on the hypersphere S d−1 .  ...  Acknowledgments The author is indebted to Michael Unser, Julien Fageot, and thank them for the insightful discussions, as well as their invaluable feedback on earlier versions of this manuscript.  ... 
doi:10.1016/j.acha.2020.12.004 fatcat:3u4yovx5qnhelivab7buhcfliu
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