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Towards Computability over Effectively Enumerable Topological Spaces

Margarita Korovina, Oleg Kudinov
2008 Electronical Notes in Theoretical Computer Science  
In this paper we study different approaches to computability over effectively enumerable topological spaces.  ...  Under natural assumptions on effectively enumerable topological spaces the notions of computability and weakly-computability coincide.  ...  Computability on Effectively Enumerable Topological Spaces Now we introduce notions of computable function over effectively enumerable topological spaces based on the well-known definition of enumeration  ... 
doi:10.1016/j.entcs.2008.12.011 fatcat:wvimfg63znai7iro2gxfoq3ciq

Computable Partial Solids and Voxels Sets [chapter]

André Lieutier
1999 Lecture Notes in Computer Science  
The model of computable partial solids has been recently introduced in order to address computational geometry and solid modeling issues within the Turing model of computation.  ...  This approach provides a model that reflects well the observable properties of real solids and the computation on realistic computers [5] .  ...  The set PDVS is effectively enumerable.  ... 
doi:10.1007/3-540-49126-0_27 fatcat:7pyzi56ds5grvmj2mgjgodrypm

Novelty-Driven Binary Particle Swarm Optimisation for Truss Optimisation Problems [article]

Hirad Assimi, Frank Neumann, Markus Wagner, Xiaodong Li
2021 arXiv   pre-print
We introduce exact enumeration to rigorously analyse the topology search space and remove randomness for small problems.  ...  Bilevel optimisation has been successfully applied to truss optimisation to consider topology and sizing in upper and lower levels, respectively.  ...  Exact enumeration enables us to enumerate over all possible combinations of binary strings in the search space in the upper level, where each represents a topology design.  ... 
arXiv:2112.07875v1 fatcat:guzxfauhvjcytnvm4yyoapn4ni

Computability and the morphological complexity of some dynamics on continuous domains

Mathieu Hoyrup, Arda Kolçak, Giuseppe Longo
2008 Theoretical Computer Science  
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  ...  The partially ordered set of compact intervals provides a convenient embedding space for the analysis of some Dynamical Systems.  ...  But approximation means order and topology, or, at least, a weak form of approximation as "limit" over filter (non-topological) spaces, as suggested by [19] and recently developed by [8] (see also  ... 
doi:10.1016/j.tcs.2008.01.048 fatcat:pbesijwghngjzioblranl242ty

Effectivity and effective continuity of multifunctions

Dieter Spreen
2010 Journal of Symbolic Logic (JSL)  
By effectively transforming such descriptions for the generation of the input (respectively, their codes) into (the code of) a description for the generation of the output another type of computable operation  ...  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 into better  ...  In the context of effective topology one is only interested in enumerable unions.  ... 
doi:10.2178/jsl/1268917496 fatcat:pkwzxy3x65ejlcy7uanziyvwxu

An Application of Computable Distributions to the Semantics of Probabilistic Programs [article]

Daniel Huang, Greg Morrisett, Bas Spitters
2019 arXiv   pre-print
Towards this end, we sketch an encoding of computable distributions in a fragment of Haskell and show how topological domains can be used to model the resulting PCF-like language.  ...  We also examine the implications that a (Type-2) computable semantics has for implementing conditioning.  ...  Towards this end, recall that we can associate a theory of effectivity with a space by defining it as a quotient of Baire space B ∼ by a partial equivalence relation (PER) ∼.  ... 
arXiv:1806.07966v2 fatcat:csz7pdbd45fsvoy4oac23eixie

Evolvability Is Inevitable: Increasing Evolvability without the Pressure to Adapt

Joel Lehman, Kenneth O. Stanley, Sebastian D. Fugmann
2013 PLoS ONE  
Why evolvability appears to have increased over evolutionary time is an important unresolved biological question.  ...  diffuse more quickly through the space of possible phenotypes.  ...  Because the space cannot be fully enumerated due to computational limits, it is impossible to fully characterize the genotypic space and precisely calculate evolvability (as was done in the fully passive  ... 
doi:10.1371/journal.pone.0062186 pmid:23637999 pmcid:PMC3634764 fatcat:7rfvsfkkrff2pllg5ht5ubjpnq

Limit spaces with approximations

Iosif Petrakis
2016 Annals of Pure and Applied Logic  
Clearly, rlimp0, 1 2 n q, while The Birkhoff-Baer topology where if A Ď X , we define ev A pxnq :" Dn 0 @něn 0 pxn P Aq.  ...  An L-space which is not a limit space: pR, rlimq, where rlimpx, xnq :Ø ÿ nPN |x´xn| ă 8.  ...  ), but it is not S1-S9 definable over the total Kleene-Kreisel functionals]. 2 It is "useful to see how far we can get towards constructing an effective infrastructure on such spaces without introducing  ... 
doi:10.1016/j.apal.2016.04.013 fatcat:5xvrtahmendlpnppzr3xkqecwe

Computability of probability measures and Martin-Lof randomness over metric spaces [article]

Mathieu Hoyrup, Cristobal Rojas
2008 arXiv   pre-print
We show that any computable metric space with a computable probability measure is isomorphic to the Cantor space in a computable and measure-theoretic sense.  ...  In this paper we investigate algorithmic randomness on more general spaces than the Cantor space, namely computable metric spaces.  ...  Extensions of the algorithmic theory of randomness to general spaces have previously been proposed: on effective topological spaces by Hertling and Weihrauch (see [6] , [7] ) and on computable metric  ... 
arXiv:0709.0907v2 fatcat:ftwryuijj5gsjnoabdbzwxlhxu

Page 7294 of Mathematical Reviews Vol. , Issue 2003j [page]

2003 Mathematical Reviews  
The authors generalize Martin-L6f’s definition of infinite random sequences over a finite alphabet to effective topological spaces with a measure.  ...  Kuéera (CZ-KARLMP-TC; Prague) 2003j:03055 03D80 03D45 28C15 54H99 60A05 Hertling, Peter (D-HGN-TI1; Hagen) ; Weihrauch, Klaus (D-HGN-TI1; Hagen) Random elements in effective topological spaces with measure  ... 

In silico prediction and screening of modular crystal structures via a high-throughput genomic approach

Yi Li, Xu Li, Jiancong Liu, Fangzheng Duan, Jihong Yu
2015 Nature Communications  
High-throughput computational methods capable of predicting, evaluating and identifying promising synthetic candidates with desired properties are highly appealing to today's scientists.  ...  By enumerating these gene-like stacking sequences, we have identified 1,127 most realizable new ABC-6 structures out of 78 groups of 84,292 theoretical ones, and experimentally realized 2 of them.  ...  Considering the computational cost, we have enumerated 84,292 stacking sequences corresponding to all topologically unique and chemically feasible ABC-6 topologies comprised of N stacking layers (Nr16)  ... 
doi:10.1038/ncomms9328 pmid:26395233 pmcid:PMC4667440 fatcat:2wrptlyuerbk5kl4zo66xgtcua

Computability of topological entropy: From general systems to transformations on Cantor sets and the interval

Silvére Gangloff, ,Center for sleep and consciousness, University of Wisconsin-Madison, WI, United States, Alonso Herrera, Cristobal Rojas, Mathieu Sablik, ,Departamento de Matemáticas, Universidad Andres Bello, República 498, Santiago, Chile, ,Institut de Mathématiques de Toulouse, Université Paul Sabatier, 118 route de Narbonne, F-3106214 Toulouse Cedex 9, France
2020 Discrete and Continuous Dynamical Systems. Series A  
In analogy to effective subshifts, we consider computable maps over effective compact sets in general metric spaces, and study the computability properties of their topological entropies.  ...  Part of the great importance of these symbolic systems relies on the role they have played in understanding more general systems over non-symbolic spaces.  ...  We then analyse the effect of changing the geometry of the ambient space and study Problem 1 for computable systems over [0, 1] .  ... 
doi:10.3934/dcds.2020180 fatcat:ykp3zovuqjaubdbqmv42fe5xrm

Exploring zipping and assembly as a protein folding principle

Vincent A. Voelz, Ken A. Dill
2006 Proteins: Structure, Function, and Bioinformatics  
Using the HP model, we can address this question by enumerating full conformation and sequence spaces.  ...  Using the HP model, we can address this question by enumerating full conformation and sequence spaces.  ...  Toward that end, we use the HP lattice model, which is the only model currently available, as far as we know, for which the full conformational spaces can be enumerated exhaustively (in order to prove  ... 
doi:10.1002/prot.21234 pmid:17154424 fatcat:quzci4nuhrgbxekcoguee7kida

Exploring quadrangulations

Chi-Han Peng, Michael Barton, Caigui Jiang, Peter Wonka
2014 ACM Transactions on Graphics  
Second, different topologies are enumerated and explored in each patch.  ...  Finally, we apply the framework to shape-space exploration, remeshing, and design to underline the importance of topology exploration.  ...  Most existing algorithms for quad mesh generation are geared towards computing a single optimized quad mesh.  ... 
doi:10.1145/2541533 fatcat:pkxosjea2vg7jcyoumhhcngf7i

Towards Effective Elicitation of NIN-AND Tree Causal Models [chapter]

Yang Xiang, Yu Li, Zoe Jingyu Zhu
2009 Lecture Notes in Computer Science  
It has linear complexity, but requires elicitation of a tree topology for types of causal interactions. We study their topology space and develop two novel techniques for more effective elicitation.  ...  To specify a Bayes net (BN), a conditional probability table (CPT), often of an effect conditioned on its n causes, needs assessed for each node. It generally has the complexity exponential on n.  ...  We study the topology space of NIN-AND tree models and develop novel techniques for more effective elicitation. One allows expert to select a topology from an enumeration.  ... 
doi:10.1007/978-3-642-04388-8_22 fatcat:s7wibynbbfffdl7p3d34mnyx4e
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