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Distributive Laws for Monotone Specifications

Jurriaan Rot
2017 Electronic Proceedings in Theoretical Computer Science  
We show that monotone specifications - that disallow negative premises - do induce a canonical distributive law of a monad over a comonad, and therefore a unique, compositional interpretation.  ...  Both formats are well behaved, in the sense that each specification has a unique model on which behavioural equivalence is a congruence.  ...  Distributive laws for biGSOS specifications In the previous section we have seen how to construct a least supported model of a monotone biGSOS specification, as the least fixed point of a monotone function  ... 
doi:10.4204/eptcs.255.6 fatcat:j7e5k6hg2zbutnczybyycisgq4

Distributive laws for monotone specifications

Jurriaan Rot
2019 Acta Informatica  
We show that monotone specifications-that disallow negative premises-do induce a canonical distributive law of a monad over a comonad, and therefore a unique, compositional interpretation.  ...  Both formats are well behaved, in the sense that each specification has a unique model on which behavioural equivalence is a congruence.  ...  Above, we have shown how to construct a distributive law for a monotone biGSOS specification, in terms of a lifting.  ... 
doi:10.1007/s00236-019-00333-x pmid:31631892 pmcid:PMC6790200 fatcat:5bnwmmwilvgyfmhpfoodmioqx4

Imperfect interfaces with graded materials and unilateral conditions: theoretical and numerical study

Serge Dumont, Frédéric Lebon, Raffaella Rizzoni
2017 Mathematics and mechanics of solids  
In particular, different types of stiffness distributions are studied in detail.  ...  Classically, it is possible to derive an interface imperfect law using asymptotic expansions as the thickness ε tends to zero.  ...  Results for a non-monotone stiffness distribution.  ... 
doi:10.1177/1081286517732826 fatcat:ndpxvb6uerbfpj7nfbyotb2keq

Random sampling of skewed distributions does not necessarily imply Taylor's law: Fig. 1

Youhua Chen
2015 Proceedings of the National Academy of Sciences of the United States of America  
Some highly skewed distributions can generate random data rejecting the law. Here, I show examples for this using beta, lognormal, and Poisson distributions (the last one is used for comparison).  ...  These specific parameter intervals can generate positively skewed or symmetric distribution curves (thus the fitted coefficient b ≥ 0).  ...  By contrast, the supporting rate of TL in Poisson distribution changes monotonically with skewness ( Fig. 1E) , which is in turn monotonically controlled by the parameter λ (Fig. 1F) .  ... 
doi:10.1073/pnas.1507266112 pmid:26034297 pmcid:PMC4485107 fatcat:jxcyafe6a5gttkbm6bc2afnreq

In praise of algebra

Tony Hoare, Stephan van Staden
2012 Formal Aspects of Computing  
We give the provable concurrency laws for Milner transitions, for the Back/Morgan refinement calculus, and for Dijkstra's weakest preconditions.  ...  We survey the well-known algebraic laws of sequential programming, and extend them with some less familiar laws for concurrent programming.  ...  Acknowledgments We are grateful to the anonymous referees of this paper, who made many suggestions for its improvement.  ... 
doi:10.1007/s00165-012-0249-0 fatcat:6jsnrjik7fc5nhiqlu3w5edpii

Lax Bialgebras and Up-To Techniques for Weak Bisimulations

Filippo Bonchi, Daniela Petrisan, Damien Pous, Jurriaan Rot, Marc Herbstritt
2015 International Conference on Concurrency Theory  
Up-to techniques are useful tools for optimising proofs of behavioural equivalence of processes. Bisimulations up-to context can be safely used in any language specified by GSOS rules.  ...  In this paper, we prove the soundness of up-to contextual closure for weak bisimulations of systems specified by cool rule formats, as defined by Bloom to ensure congruence of weak bisimilarity.  ...  Lax models for a monotone GSOS specification λ induce lax bialgebras for the distributive law obtained as in Lemma 16. Lemma 19.  ... 
doi:10.4230/lipics.concur.2015.240 dblp:conf/concur/BonchiPPR15 fatcat:scfhrqbogzaqtfobw3ikz3at5a

Entropy, Age and Time Operator

Ilias Gialampoukidis, Ioannis Antoniou
2015 Entropy  
Time operators were originally introduced for quantum systems and highly unstable dynamical systems.  ...  It is remarkable that the entropy functionals evolve, violating the second law of thermodynamics, while the norm functionals evolve thermodynamically.  ...  We are also grateful to Karl Gustafson for useful discussions and remarks. The comments and recommendations of the referees improved the clarity and presentation of this work.  ... 
doi:10.3390/e17010407 fatcat:vzizoogubffcjp23542iaoh3v4

Page 2311 of Mathematical Reviews Vol. , Issue 95d [page]

1995 Mathematical Reviews  
This requires that (x) holds for all laws of Y.} Anthony G. Pakes (5-WA; Nedlands)  ...  Sufficient conditions for monotonicity of E(T|X = x) have been given by Efron (1965) and Lehmann (1966).  ... 

Reasoning algebraically about recursion

P.H.B. Gardiner, P.K. Pandaya
1992 Science of Computer Programming  
When such inverses do exist, the method can be used in presence of noncontinuous but monotonic operators occurring in languages containing unbounded nondeterminism, fairness constraints and specification  ...  An algebraic technique for reasoning about recursive programs is proposed.  ...  Hoare for his advise and encouragement during this work. We also thank Carroll Morgan and Jifeng He for their helpful comments.  ... 
doi:10.1016/0167-6423(92)90019-8 fatcat:wlnalupid5fjznbdpebem6aisa

Generalised rely-guarantee concurrency: An algebraic foundation [article]

Ian J. Hayes
2016 arXiv   pre-print
The Jones-style rely-guarantee theory can be interpreted as a model of the general algebraic theory and hence the general laws presented here hold for that theory.  ...  In order to investigate rely-guarantee reasoning more generally, in this paper we allow interference to be represented by a process rather than a relation and hence derive more general rely-guarantee laws  ...  Special thanks go to Julian Fell and Andrius Velykis for mechanising the proofs of the laws in Isabelle/HOL.  ... 
arXiv:1603.01776v1 fatcat:hye5bl74nzcdherwurpgrcqbzm

A strong law of large numbers for capacities

Fabio Maccheroni, Massimo Marinacci
2005 Annals of Probability  
We consider a totally monotone capacity on a Polish space and a sequence of bounded p.i.i.d. random variables.  ...  Introduction In this paper we prove a strong law of large numbers for totally monotone capacities.  ...  Specifically, given a totally monotone capacity ν dened on the Borel σ-algebra B of a Polish space , and a sequence {X n } n≥1 of bounded, pairwise independent and identically distributed random variables  ... 
doi:10.1214/009117904000001062 fatcat:7t4ofe36vndinahjo3fa3zeeiy

First digit law from Laplace transform

Mingshu Cong, Congqiao Li, Bo-Qiang Ma
2019 Physics Letters A  
We prove that the whole family of completely monotonic distributions can satisfy Benford's law within a small bound.  ...  The slight variation from the Benford term leads to deviations from Benford's law for distributions which oscillate violently in the inverse Laplace space.  ...  It is also supported by National Innovation Training Program for Undergraduates.  ... 
doi:10.1016/j.physleta.2019.03.017 fatcat:sowaxvskfzddnhbyvsxii63ogi

Force oscillations distort avalanche shapes

Louis W. McFaul, Wendelin J. Wright, Jordan Sickle, Karin A. Dahmen
2019 Materials Research Letters  
The results provide critical guidance for experimental tests for universality and a quantitative understanding of avalanche dynamics under a wide range of driving conditions.  ...  Acknowledgments We thank Robert Maaß and Gregory Sparks for helpful conversations and experimental data [27] .  ...  Figure 3 (c) shows the complementary cumulative distribution function (CCDF) for the avalanche sizes S. Without oscillations, it follows the expected -0.5 power law.  ... 
doi:10.1080/21663831.2019.1659437 fatcat:3nxdqecxtfe2xbn5emhcye45vy

Classification of budget-invariant monotonic preferences

Walter Trockel
1989 Economics Letters  
Dierker's result does not provide an answer for non-convex preferences, for convex ones whose induced demand fails to satisfy Walras' Law and for those for which there does not even exist a demand correspondence  ...  , on assumptions of preference distributions rather than on income distributions.  ... 
doi:10.1016/0165-1765(89)90148-1 fatcat:fmdgm5yat5hallaf66b6cqvara

Laws of Programming [chapter]

C. A. R. Hoare, I. J. Hayes, He Jifeng, C. C. Morgan, A. W. Roscoe, J. W. Sanders, I. H. Sorenson, J. M. Spivey, B. A. Sufrin
1992 Programming and Mathematical Method  
In fact, every operation that distributes through U is also monotonic. THEOREM.  ...  This distributive law extends to limits of arbitrary sets: P\(nS) = n[P\R 1 R E S). The following laws are very similar to the corresponding laws for weakest preconditions.  ... 
doi:10.1007/978-3-642-77572-7_7 fatcat:n2fijmuxybgxpjdkvyjztgw3ue
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