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On Generalizing Kolmogorov

Richard Dietz
2010 Notre Dame Journal of Formal Logic  
Weatherson's generalized notion of probability can hardly be regarded as adequate, as the example of supervaluationist logic shows.  ...  It is suggested that for supervaluationist logic, the third option is the most attractive one, for (unlike the other options) it preserves respect for single-premise entailment.  ...  If one takes respect for logic, and general additivity as 'essential' features of any notion of probability, trivially, one ends up with generalized probability.  ... 
doi:10.1215/00294527-2010-019 fatcat:eactkxetsrbxlfjvs2c4vdw4hy

On generalized symmetric powers and a generalization of Kolmogorov-Gelfand-Buchstaber-Rees theory [article]

H. M. Khudaverdian, Th. Th. Voronov
2007 arXiv   pre-print
We give a further natural generalization of Kolmogorov-Gelfand-Buchstaber-Rees theory.  ...  The classical Kolmogorov-Gelfand theorem gives an embedding of a (compact Hausdorff) topological space X into the linear space of all linear functionals C(X)^* on the algebra of continuous functions C(  ...  Kolmogorov. On rings of continuous functions on topological spaces.Dokl. Akad. NaukSSSR, 22: 11-15, 1939 [Russian]. That means by the definition that the equationb(b − 1)(b − 2) . . .  ... 
arXiv:math/0612072v3 fatcat:snserxdpafedxpbud7iv752lm4

Magnetic-Field Generation in Kolmogorov Turbulence

Stanislav Boldyrev, Fausto Cattaneo
2004 Physical Review Letters  
For the Kolmogorov velocity field, this gives H k ∝ k −7/3 .  ...  To address magnetic energy on larger scales we have to understand how the magnetic field is generated in the inertial interval of fluid turbulence (the interval of scales much smaller than the external  ... 
doi:10.1103/physrevlett.92.144501 pmid:15089544 fatcat:ob456eg57fht5i22ig5fecyikq

Generic image similarity based on Kolmogorov complexity

Nima Nikvand, Zhou Wang
2010 2010 IEEE International Conference on Image Processing  
The theory of Kolmogorov complexity and the related normalized information distance (NID) measure provide an attractive theoretic framework for generic image similarity that is applicable to any scenario  ...  While this is appealing, the difficulty lies in the implementation due to the non-computable nature of Kolmogorov complexity.  ...  Moreover, due to their focuses on specific applications, the generic property of NID was not fully exploited.  ... 
doi:10.1109/icip.2010.5653405 dblp:conf/icip/NikvandW10 fatcat:sxtg4u25cfeerniipqqtyycotu

On the Connections of Generalized Entropies With Shannon and Kolmogorov–Sinai Entropies

Fryderyk Falniowski
2014 Entropy  
Under mild assumptions on this function we show that this isomorphism invariant is linearly dependent on the Kolmogorov-Sinai entropy.  ...  We consider the concept of generalized measure-theoretic entropy, where instead of the Shannon entropy function we consider an arbitrary concave function defined on the unit interval, vanishing in the  ...  on every generator of the σ-algebra Σ.  ... 
doi:10.3390/e16073732 fatcat:iirh4ignhjbqnpvossh677mkp4

Operators on superspaces and generalizations of the Gelfand–Kolmogorov theorem

H. M. Khudaverdian, Th. Th. Voronov, Piotr Kielanowski, Anatol Odzijewicz, Martin Schlichenmeier, Theodore Voronov
2007 AIP Conference Proceedings  
We give a simplification and a further extension of this theory, which is based, rather unexpectedly, on results from super linear lgebra.  ...  Gelfand and Kolmogorov in 1939 proved that a compact Hausdorff topological space X can be canonically embedded into the infinite-dimensional vector space C(X)^* , the dual space of the algebra of continuous  ...  Recently Buchstaber and Rees have suggested a generalization of the Gelfand-Kolmogorov theorem based on their notion of an n-homomorphism or 'Frobenius n-homomorphism'.  ... 
doi:10.1063/1.2820962 fatcat:7m4cnah7zrcg5nsaa6ziec344i

Nucleation and growth in one dimension. I. The generalized Kolmogorov-Johnson-Mehl-Avrami model

Suckjoon Jun, Haiyang Zhang, John Bechhoefer
2005 Physical Review E  
Motivated by a recent application of the Kolmogorov-Johnson-Mehl-Avrami (KJMA) model to the study of DNA replication, we consider the one-dimensional version of this model.  ...  We generalize previous work to the case where the nucleation rate is an arbitrary function I(t) and obtain analytical results for the time-dependent distributions of various quantities (such as the island  ...  ACKNOWLEDGMENTS We thank Tom Chou, Massimo Fanfoni, Govind Menon, Nick Rhind, and Ken Sekimoto, Massimo Tomellini for helpful comments and discussions on 1D nucleation-and-growth models.  ... 
doi:10.1103/physreve.71.011908 pmid:15697631 fatcat:6gzoaicfirhftgwtoowy4iyajq

Thermostatistics based on Kolmogorov–Nagumo averages: unifying framework for extensive and nonextensive generalizations

Marek Czachor, Jan Naudts
2002 Physics Letters A  
We use this correspondence to generalize thermostatistics to a large class of Kolmogorov-Nagumo means and suitably adapted definitions of entropy.  ...  We show that extensive thermostatistics based on Renyi entropy and Kolmogorov-Nagumo averages can be expressed in terms of Tsallis non- extensive thermostatistics.  ...  One of the authors (M.C.) wishes to thank the NATO for a research fellowship enabling his stay at the Universiteit Antwerpen.  ... 
doi:10.1016/s0375-9601(02)00540-6 fatcat:ldtgr43ppneetngzjvpkzwg63e

The Kolmogorov-Sinaj Theorem on Generators for Fuzzy Dynamical Systems

B. Riečan, D. Markechová
1997 Demonstratio Mathematica  
The Kolmogorov-Sinaj theorem on generators In this section we shall present a new proof of Kolmogorov-Sinaj's theorem on generators for fuzzy dynamical systems.  ...  Probably one of the most important results of the theory of invariant measures for practical purposes is the Kolmogorov-Sinaj theorem stating that h(T) = h(T,A), whenever A is a partition generating the  ... 
doi:10.1515/dema-1997-0221 fatcat:bar7gjbhxzctrl7iqvjslrzkpy

On classical and quantal Kolmogorov entropies

J W Helton, M Tabor
1985 Journal of Physics A: Mathematical and General  
The construction of a quantal Kolmogorov entropy that tends to the classical Kolmogorov entropy in the limit h -t 0 is discussed.  ...  interesting illustration of a quantal definition of a statistical quantity not having the correct classical limit (a feature that by no means invalidates its usefulness) has been in the context of quantal Kolmogorov  ...  By contrast, generic Hamiltonians are non-integrable. Now the phase space has a most complicated structure of stable and unstable orbits pathologically intertwined.  ... 
doi:10.1088/0305-4470/18/14/025 fatcat:fqfsxl46j5aurfhcerkpvlqrie

Generalizations and extensions of the Fokker- Planck-Kolmogorov equations

R. Pawula
1967 IEEE Transactions on Information Theory  
As illustrations of their applicability, the generalized Fokker-Planck-Kolmogorov equations are presented for certain joint probability density functions associated with the linear filter.  ...  These partial differential equations are interpreted as generalized forms of the classical Fokker-Planck-Kolmogorov equations and a re shown to imply the classical equations for certain classes of Markov  ...  Finally, we consider generalizations of the Kolmogorov equations for discrete random processes. B. The Generalized Fokker-Planck Equation. generalized Fokker-Planck-Kolmogorov equations.  ... 
doi:10.1109/tit.1967.1053955 fatcat:5qex3iyqxvebtmxrwcphjbox4e

Randomized Kolmogorov and Linear Widths on Generalized Besov Classes with Mixed Smoothness

Liqin Duan, Peixin Ye
2012 Procedia Engineering  
In this paper, we study the Kolmogorov and the linear widths on the generalized Besov classes , p B θ Ω with mixed smoothness in the Monte Carlo setting.  ...  Applying the discretization technique and some properties of pseudo-s-scale, we determine the exact asymptotic orders of the Kolmogorov and the linear widths for some values of the parameters , , p q θ  ...  . , the σ -algebras generated by the open sets. Definition 1[3].  ... 
doi:10.1016/j.proeng.2012.01.638 fatcat:4liu2xhwczffjh5z7tg6taixem

Structured audio, Kolmogorov complexity, and generalized audio coding

E.D. Scheirer
2001 IEEE Transactions on Speech and Audio Processing  
A theoretical basis for this coding model is presented, grounded in information theory and Kolmogorov complexity theory.  ...  It points the direction toward a new paradigm of generalized audio coding, in which structured-audio coding subsumes all other audio-coding techniques.  ...  ACKNOWLEDGMENT The paper was initiated based on discussions with P. Smaragdis and B. Butera of the Media Lab. As always, Prof. B.  ... 
doi:10.1109/89.966095 fatcat:rblhu5h3mvfb3nab4qok5fl7wy

Stochastic models of heat and nuclear particle transfer based on generalized equation of Fokker-Planck-Kolmogorov

Igor Soloviev, Diana Dolicanin-Djekic
2016 Nuclear Technology and Radiation Protection  
Sto chas tic dif fer en tial equa tions are pro posed on the ba sis of gen er al ized Fokker-Planck--Kolmogorov equa tion.  ...  Know ing the tran si tion func tion gives in for ma tion on the equi lib rium dis tribu tion (if one ex ists), and con ver gence to the equi librium dis tri bu tion.  ...  ANALYTICAL METHOD AND RESULTS Clas si cal Fokker-Planck-Kolmogorov equa tion [5] [6] [7] , is writ ten with out the term which is re spon si ble for spas modic be hav ior of ran dom phe nom ena which  ... 
doi:10.2298/ntrp1604335s fatcat:txlkfzetz5bdvehlkeq46hvi7i

The Complexity of General-Valued CSPs

Vladimir Kolmogorov, Andrei Krokhin, Michal Rolínek
2017 SIAM journal on computing (Print)  
We study, assuming that P = NP, how the complexity of this very general problem depends on the set of functions allowed in the instances, the so-called constraint language.  ...  problem (which cannot generally be taken for granted).  ...  A graph of generalized operations.  ... 
doi:10.1137/16m1091836 fatcat:zfnnwzkui5fdljkba2kd7e2aou
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