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Trivial pursuit: Remarks on the main gap
1987
Annals of Pure and Applied Logic
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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
2011
Topoi
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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?
1988
Physics reports
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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
2011
Signal Processing
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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]
2021
arXiv
pre-print
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2020 pre-print arXiv:2006.05761v2 fatcat:qiqornbcmnatjioxx4ttcl7ioaOther Versions
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
2015
ACM Transactions on Mathematical Software
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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
2017
Physical Review Letters
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2017 pre-print arXiv:1701.02558v2 fatcat:6rp5umtrmrcy5pofusmra2gw3iOther Versions
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]
2016
arXiv
pre-print
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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
2012
Reports on progress in physics (Print)
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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]
2018
arXiv
pre-print
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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
2015
Algorithmica
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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]
2013
Lecture Notes in Computer Science
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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
2017
SIAM Journal on applied algebra and geometry
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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]
2016
arXiv
pre-print
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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
2021
Applied and Computational Harmonic Analysis
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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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