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Effective content of the calculus of variations I: Semi-continuity and the chattering lemma

Xiaolin Ge, Anil Nerode
1996 Annals of Pure and Applied Logic  
An algorithm has been developed which captures the natural algorithmic content of the notion of a semi-continuous function and this is used to obtain an effective version of the "chattering lemma" of control  ...  The content of existence theorems in the calculus of variations has been explored and an effective treatment of semi-continuity has been achieved.  ...  In contrast to the standard definition of a recursive real function given above, neither sequential computability nor effective continuity are required in the definition of a recursive lower semi-continuous  ... 
doi:10.1016/0168-0072(95)00034-8 fatcat:q4hs4gk72vdmjck7azylzrb55i

Improving the Improved Training of Wasserstein GANs: A Consistency Term and Its Dual Effect [article]

Xiang Wei, Boqing Gong, Zixia Liu, Wei Lu, Liqiang Wang
2018 arXiv   pre-print
In this paper, we propose a novel approach to enforcing the Lipschitz continuity in the training procedure of WGANs.  ...  Our approach seamlessly connects WGAN with one of the recent semi-supervised learning methods.  ...  B.G. and L.W. would also like to thank Adobe Research and NVIDIA, and Amazon, respectively, for their gift donations.  ... 
arXiv:1803.01541v1 fatcat:ijilhnz6vvadfefpsyqbawwk3u

On the Weak Computability of Continuous Real Functions

Matthew S. Bauer, Xizhong Zheng
2010 Electronic Proceedings in Theoretical Computer Science  
In this paper, we are interested in the weak computability of continuous real functions and try to introduce an analogous classification of weakly computable real functions.  ...  In computable analysis, sequences of rational numbers which effectively converge to a real number x are used as the (rho-) names of x.  ...  it approaches a real number x.  ... 
doi:10.4204/eptcs.24.8 fatcat:wwcgwwxxmvcsreqcsxgoahtnye

Computability over Topological Structures [chapter]

Vasco Brattka
2003 Computability and Models  
considered as a generalization of the classical concept of µ-recursive functions.  ...  Important examples of perfect structures are provided by metric spaces and additional attention is paid to their effective subsets.  ...  Acknowledgement The author would like to thank Klaus Weihrauch, Matthias Schröder and the anonymous referee for several helpful comments, suggestions and corrections.  ... 
doi:10.1007/978-1-4615-0755-0_5 fatcat:7v4cgwf5xnafxdbaksc7axfmma

On the Continuity of Effective Multifunctions

Dieter Spreen
2008 Electronical Notes in Theoretical Computer Science  
multifunction which are effectively continuous with respect to the continuity notion under consideration.  ...  If one wants to compute with infinite objects like real numbers or data streams, continuity is a necessary requirement: better and better (finite) approximations of the input are transformed in better  ...  functions, and that compact-valued multifunctions are effectively upper semi-continuous exactly if they are effective with respect to covering indices and also possess certain witness functions.  ... 
doi:10.1016/j.entcs.2008.12.023 fatcat:s2nq2k6g5fhqbd3dbwl7q3o6gu

Modeling Involuntary Dynamic Behaviors to Support Intelligent Tutoring (Student Abstract)

Mononito Goswami, Lujie Chen, Chufan Gao, Artur Dubrawski
However, effectively coaching young students in problem solving is challenging because teachers must continuously monitor their cognitive and affective states and make real-time pedagogical interventions  ...  In this paper, we explore a semi-supervised learning framework that can learn low-dimensional representations of involuntary dynamic behavioral signals (mainly gross-body movements) from a modest number  ...  Thus, effectively coaching young students for problem solving requires teachers to continuously monitor their cognitive and affective states and make real time pedagogical decisions such as when and how  ... 
doi:10.1609/aaai.v34i10.7171 fatcat:nzqnlbi3zrcchke5iw4ai4r23e

Generalizing Skills with Semi-Supervised Reinforcement Learning [article]

Chelsea Finn, Tianhe Yu, Justin Fu, Pieter Abbeel, Sergey Levine
2017 arXiv   pre-print
However, real-world applications of such methods require generalizing to the vast variability of the real world.  ...  However, this learning requires access to a reward function, which is often hard to measure in real-world domains, where the reward could depend on, for example, unknown positions of objects or the emotional  ...  ACKNOWLEDGMENTS The authors would like to thank Anca Dragan for insightful discussions, and Aviv Tamar and Roberto Calandra for helpful feedback on the paper.  ... 
arXiv:1612.00429v2 fatcat:54cwjyislfedzeeak7qppiuaby

Computable Partial Solids and Voxels Sets [chapter]

André Lieutier
1999 Lecture Notes in Computer Science  
This approach provides a model that reflects well the observable properties of real solids and the computation on realistic computers [5] .  ...  Since a central notion of discrete geometry, voxel sets, can be used to define computable partial solids, this approach throws a bridge between discrete geometry and solid modeling in R n .  ...  Acknowledgements Original contents in this paper are the result of our common work with Abbas Edalat [6] .  ... 
doi:10.1007/3-540-49126-0_27 fatcat:7pyzi56ds5grvmj2mgjgodrypm

Many-body method for infinite nonperiodic systems

G. Fratesi, G. P. Brivio, L. G. Molinari
2004 Physical Review B  
For example, it can be applied to surfaces or localized impurities. We illustrate the method with a study of the surface of semi-infinite jellium.  ...  It is suitable to treat systems of known "asymptotic" properties which enter as boundary conditions, while the effects of the lower symmetry are restricted to regions of finite volume.  ...  Analytical continuation improves the resolution: first, the values of G are fitted with a rational function, then the expression is continued to the real frequency axis. IV.  ... 
doi:10.1103/physrevb.69.245113 fatcat:uoh3ajqi6zardb4dgn5encvyhm

Live Query - Visualized Process Analysis

Dennis M. Riehle, Steffen Höhenberger, Rainer Cording, Patrick Delfmann
2017 Wissensbasierte Systeme  
For enabling an effective and efficient control of business processes, (semi-)automatic approaches are necessary as a supporting means.  ...  This work aims to close this gap by providing an approach that supports a widely applicable, (semi-)automatic analysis of business process models and makes the analysis comprehensible using a graphical  ...  To focus on real-world problems and continuous improvement, we followed the Design Science methodology of PEFFERS ET AL. [9] .  ... 
dblp:conf/wi/RiehleHCD17 fatcat:rbkqcz3gm5en7icodxtpr4oksi

Computability and the morphological complexity of some dynamics on continuous domains

Mathieu Hoyrup, Arda Kolçak, Giuseppe Longo
2008 Theoretical Computer Science  
Crucial dynamical properties are transferred to it, while allowing an investigation of stability and chaoticity, in terms of computability, in particular in the presence of singularities.  ...  We will survey some results which display the connections between the geometric complexity of the dynamics and computability issues, as well as new relations between dynamic predictability and effective  ...  (Preliminary or revised versions of Longo's papers are downloadable from: or Search: Google: Giuseppe Longo).  ... 
doi:10.1016/j.tcs.2008.01.048 fatcat:pbesijwghngjzioblranl242ty

Page 752 of Mathematical Reviews Vol. , Issue 2001B [page]

2001 Mathematical Reviews  
Klaus Weihrauch (D-HGN-TI1; Hagen) 2001b:03070 03F60 Zheng, Xizhong (D-HGN-TI1; Hagen); Brattka, Vasco (D-HGN-TI1; Hagen); Weihrauch, Klaus (D-HGN-TI1; Hagen) Approaches to effective semi-continuity of  ...  Various types of semi-continuous functions are studied via the computability of epigraphs and hypographs.  ... 

Tornadoes and related damage costs: statistical modeling with a semi-Markov approach [article]

Chiara Corini, Guglielmo D'Amico, Filippo Petroni, Flavio Prattico, Raimondo Manca
2015 arXiv   pre-print
We demonstrate that the semi-Markov approach is able to reproduce the duration effect that is detected in tornadoes occurrence.  ...  that semi-Markov models represent an effective tool for physical analysis of tornadoes as well as for the estimation of the economic damages to human things.  ...  In both Figures the continuous lines are referred to real data while the dashed lines to the synthetic one.  ... 
arXiv:1503.05127v1 fatcat:23wygs7jwna5pfdc4ity4mbyca

Construction of Lyapunov Functions for the Stability of Fifth Order Nonlinear Ordinary Differential Equations

Patrick O. Aye, D. Jayeola, David O. Oyewola
2022 Earthline Journal of Mathematical Sciences  
This study employed Lyapunov function method to examine the stability of nonlinear ordinary differential equations.  ...  Using direct Lyapunov method, we constructed Lyapunov function to investigate the stability of fifth order nonlinear ordinary differential equations.  ...  The concept of stability in problems arising from theory and application of differential equations is very important and an effective approach is the second approach of Lyapunov [7] .  ... 
doi:10.34198/ejms.8222.313324 fatcat:gsziucmo4bbyhm4jaabh2ehe7q

Denotational Semantics of Hybrid Automata [chapter]

Abbas Edalat, Dirk Pattinson
2006 Lecture Notes in Computer Science  
The semantics is defined as least fixpoint of an operator on the continuous domain of functions of time that take values in the lattice of compact subsets of n-dimensional Euclidean space.  ...  The semantic function assigns to every point in time the set of states the automaton can visit at that time, starting from one of its initial states.  ...  It is a straightforward exercise to see that Scott continuous functions of type A → U ⊤ B are precisely the semi continuous functions of set-valued analysis [4] .  ... 
doi:10.1007/11690634_16 fatcat:q74gvt4gwzfzfftimpaltdzoea
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