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A Sharp Phase Transition Threshold for Elementary Descent Recursive Functions

A. den Boer, A. Weiermann
2007 Journal of Logic and Computation  
Using bounds on the asymptotic of the resulting global count functions we classify precisely the phase transition for the parameterized hierarchy of elementary descent recursive functions and hence for  ...  We consider in this article parameterized versions of a specific Friedman-style scheme and classify exactly the threshold for the transition from provability to unprovability in PA.  ...  Acknowledgements We would like to thank the referee for some helpful remarks which in particular led to a stylistic improvement of the article.  ... 
doi:10.1093/logcom/exm035 fatcat:ngswh2sr65hgjlz743ob7nvtpm

Phase transitions for Gödel incompleteness

Andreas Weiermann
2009 Annals of Pure and Applied Logic  
recursive functions.  ...  For these independence principles we classify (as a part of a general research program) their phase transitions, i.e. we classify exactly the bounding conditions which lead from provability to unprovability  ...  The author also thanks the John Templeton foundation for supporting generously his phase transition project via the ''Exploring the infinite initiative''.  ... 
doi:10.1016/j.apal.2008.09.012 fatcat:qdcffliq2zanll6nbfsfn3j67y

Phase Transition Thresholds for Some Natural Subclasses of the Computable Functions [chapter]

Andreas Weiermann
2006 Lecture Notes in Computer Science  
Special emphasis is put on descent recursive functions, witness bounding functions for well-partial orders and Ramsey functions.  ...  In this paper we first survey recent advances on phase transition phenomena which are related to natural subclasses of the recursive functions.  ...  marked by a sharp 'threshold point'.  ... 
doi:10.1007/11780342_57 fatcat:epkdvlcmija7tdynj37u4zutxa

Analytic combinatorics, proof-theoretic ordinals, and phase transitions for independence results

Andreas Weiermann
2005 Annals of Pure and Applied Logic  
Using a versatile and flexible (logarithmic) compression technique we give applications to phase transitions for independence results, Hilbert's basis theorem, local number theory, Ramsey theory, Hydra  ...  This paper is intended to give for a general mathematical audience (including non logicians) a survey about intriguing connections between analytic combinatorics and logic.  ...  Since IΣ 1 (∀d)[PH d+1 ↔ KM d+1 (id)] it is now an obvious question whether the sharp thresholds for the phase transition of PH d+1 (f ) in IΣ d also provides the sharp thresholds for KM d+1 (f ).  ... 
doi:10.1016/j.apal.2005.05.012 fatcat:dxkq6aj46ffmhkupj6mmhrqazq

Inhomogeneous mean-field approach to collective excitations in disordered interacting bosons [article]

Martin Puschmann, João C. Getelina, José A. Hoyos, Thomas Vojta
2021 arXiv   pre-print
We develop an inhomogeneous quantum mean-field theory for disordered particle-hole symmetric Bose-Hubbard models in two dimensions.  ...  Each is described by a disordered Bogoliubov Hamiltonian which can be solved by an inhomogeneous multi-mode Bogoliubov transformation.  ...  in a quasi-one-dimensional geometry by means of the recursive Green function approach [43] [44] [45] .  ... 
arXiv:2101.11065v1 fatcat:ik4tmcsa3zb3rfplta65mjrije

Robust Feature Classification and Editing

Yu-kun Lai, Qian-yi Zhou, Shi-min Hu, Johannes Wallner, Helmut Pottmann
2007 IEEE Transactions on Visualization and Computer Graphics  
Sharp edges, ridges, valleys, and prongs are critical for the appearance and an accurate representation of a 3D model.  ...  In this paper, we propose a novel approach that deals with the global shape of features in a robust way.  ...  The authors would like to thank the reviewers for their helpful comments.  ... 
doi:10.1109/tvcg.2007.19 pmid:17093334 fatcat:lsqj3hmmebeb5gxm7movoyb5qe

Abstracts of Current Computer Literature

1969 IEEE transactions on computers  
The procedure uses a descent method to minimize the Chebyshev norm of the error function.  ...  The error in this approximation was studied empirically. 6948 A Method of Descent for Chebyshev Approximation, L.  ... 
doi:10.1109/t-c.1969.222770 fatcat:3u7q7ac3b5hx5fdffcemcrpsay

A Generalization of the Allreduce Operation [article]

Dmitry Kolmakov, Xuecang Zhang
2020 arXiv   pre-print
This new approach allows constructing a generalization of the widely used Allreduce algorithms such as Ring, Recursive Doubling and Recursive Halving.  ...  The proposed algorithm provides a general solution for any number of processes with the dynamically changing amount of communication steps between logP for the latency-optimal version and 2 ·logP for the  ...  It is a transitive permutation Table 1 .  ... 
arXiv:2004.09362v2 fatcat:3f2dsitm7jccbbv776oskg2iji

Backscatter analysis based algorithms for increasing transmission through highly scattering random media using phase-only-modulated wavefronts

Curtis Jin, Raj Rao Nadakuditi, Eric Michielssen, Stephen C. Rand
2014 Optical Society of America. Journal A: Optics, Image Science, and Vision  
of the transmission matrix obey a maximum entropy principle so that they are isotropically random.  ...  We develop physically realizable iterative and non-iterative algorithms for increasing the transmission through such random media using backscatter analysis.  ...  We thank Jeff Fessler for suggesting the gradient descent method so that the advantage of the steepest descent based method could be properly showcased.  ... 
doi:10.1364/josaa.31.001788 pmid:25121536 fatcat:3tnfhtn22fhydey6cazwx77ota

An approach to the approximation problem for nonrecursive digital filters

L. Rabiner, B. Gold, C. McGonegal
1970 IEEE Transactions on Audio and Electroacoustics  
A direct design procedure for nonrecursive digital filters, based primarily on the frequency-response characteristic of the desired filters, is presented.  ...  A brief discussion of the technique of nonuniform sampling is also included.  ...  We would also like to thank Miss June Ley for valuable clerical assistance in the preparation of this manuscript.  ... 
doi:10.1109/tau.1970.1162092 fatcat:ye3kszgtqjbexb6ootevufffwu

REAS: Combining Numerical Optimization with SAT Solving [article]

Jeevana Priya Inala, Sicun Gao, Soonho Kong, Armando Solar-Lezama
2018 arXiv   pre-print
In this paper, we present ReaS, a technique that combines numerical optimization with SAT solving to synthesize unknowns in a program that involves discrete and floating point computation.  ...  On top of this, ReaS uses a SAT solver to help the numerical search overcome local solutions by incrementally fixing values to the Boolean expressions.  ...  The smoothing algorithm we use is a simplified version to what is used in [6] , replacing sharp transitions in conditionals with smooth transition functions such as sigmoid.  ... 
arXiv:1802.04408v1 fatcat:fqqttjdrmbdr5b5y4v5sire5ve

Easy-hard phase transition in parameter estimation for optical waveguides

Gunnar Claussen, Alexander K. Hartmann
2020 Scientific Reports  
Our results indicate that the two phases are separated by sharp phase-transition lines and that the shape of these lines can be described by one "critical" exponent b, which depends slightly on r.  ...  The mismatch $$R(\vec {d})$$ R ( d → ) can be seen as an energy landscape as a function of the diameters.  ...  Acknowledgements We thank Christoph Norrenbrock for critically reading the manuscript.  ... 
doi:10.1038/s41598-020-74366-5 pmid:33060751 fatcat:asvijuftnzhnvnvuuiathgbc2y

Phase diagram of ferroelastic systems in the presence of disorder: Analytical model and experimental verification

R. Vasseur, D. Xue, Y. Zhou, W. Ettoumi, X. Ding, X. Ren, T. Lookman
2012 Physical Review B  
We further predict a spontaneous transition from the glass state to the ordered martensite phase.  ...  We verify this prediction by mapping out the experimental phase diagram for the ternary ferroelastic alloy Ti_50(Pd_50-xCr_x) and demonstrate the emergence of the spontaneous transition.  ...  D.X. and X.R. are grateful to Spring-8 for the use of beamline BL15XU where the synchrotron XRD measurements were made. We thank A. Lazarescu and  ... 
doi:10.1103/physrevb.86.184103 fatcat:krysodqjhjeoriyttxnxiccpui

Thermodynamic properties of the Shastry-Sutherland model throughout the dimer-product phase

Alexander Wietek, Philippe Corboz, Stefan Wessel, B. Normand, Frédéric Mila, Andreas Honecker
2019 Physical Review Research  
Over a wide range on both sides of the quantum phase transition (QPT) from the dimer-product to the plaquette-based ground state, neither analytical nor any available numerical methods have come close  ...  Our methods reveal a remarkably sharp and low-lying feature in the magnetic specific heat around the QPT, whose origin appears to lie in a proliferation of excitations composed of two-triplon bound states  ...  . , 0.66 and for J D values dictated by experiment. Specific-heat data in (a) were taken from Ref. [13] and a phonon contribution of 0.5T 3 mJ/(mol K 4 ) was subtracted.  ... 
doi:10.1103/physrevresearch.1.033038 fatcat:bhsyfyckt5afnoslrlmmhau7ai

Figure-ground discrimination: a combinatorial optimization approach

L. Herault, R. Horaud
1993 IEEE Transactions on Pattern Analysis and Machine Intelligence  
ACKNOWLEDGMENT The authors would like to thank the anonymous reviewers for their insightful comments and suggestions, their colleagues for many enlightful dicussions and suggestions, and especially J.  ...  Bach such elementary transition has associated with it a change AE in the global energy of the system.  ...  As the temperature is lowered, a phase transition occurs at 2' = T, and as T + 0, the pi values represent a specific decision made as to the solution to the problem.  ... 
doi:10.1109/34.232076 fatcat:teulrh2br5e5lgryofhg64tdqm
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