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Towards a Complexity-through-Realisability Theory [article]

Thomas Seiller
2015 arXiv   pre-print
We explain how recent developments in the fields of realisability models for linear logic -- or geometry of interaction -- and implicit computational complexity can lead to a new approach of implicit computational  ...  This paper provides the background, motivations and perspectives of this complexity-through-realisability theory to be developed, and illustrates it with recent results.  ...  However, the proposed proof method does not naturally appear as a natural proof in the sense of Razborov and Rudich [11] .  ... 
arXiv:1502.01257v2 fatcat:p5b36gxqizbohi3wfwk4unmj2e

Quantifying the Link between Anatomical Connectivity, Gray Matter Volume and Regional Cerebral Blood Flow: An Integrative MRI Study

Bálint Várkuti, Mustafa Cavusoglu, Alexander Kullik, Björn Schiffler, Ralf Veit, Özge Yilmaz, Wolfgang Rosenstiel, Christoph Braun, Kamil Uludag, Niels Birbaumer, Ranganatha Sitaram, Olaf Sporns
2011 PLoS ONE  
But regions of the brain can be characterised further with respect to their gray matter volume or resting state perfusion.  ...  In the graph theoretical analysis of anatomical brain connectivity, the white matter connections between regions of the brain are identified and serve as basis for the assessment of regional connectivity  ...  We would also especially like to thank the developers of the DTI and Fibertools Software Package from the Department of Radiology, Medical Physics, University Hospital Freiburg Dr. Björn Kreher, Dr.  ... 
doi:10.1371/journal.pone.0014801 pmid:21525993 pmcid:PMC3078126 fatcat:n2voftly7zdhffy5ernbisivbm

A dynamic graph characterisation of the fixed part of the controllable subspace of a linear structured system

Jacob van der Woude, Christian Commault, Taha Boukhobza
2019 Systems & control letters (Print)  
The latter dimension equals the size of the minimal set of nodes in the dynamic graph that separates between the set of input nodes and the set of final state nodes.  ...  A dynamic graph characterisation of the fixed part of the controllable subspace of a linear structured system van der Woude, Jacob; Commault, Christian; Boukhobza, Taha Abstract In this paper we study  ...  subspace by means of graph theoretic methods.  ... 
doi:10.1016/j.sysconle.2019.05.002 fatcat:mk24jsmq55e2pg7ipnfrvtokby

Combinatorial laplacians and positivity under partial transpose

ROLAND HILDEBRAND, STEFANO MANCINI, SIMONE SEVERINI
2008 Mathematical Structures in Computer Science  
If the vertices of a graph are arranged as an array, its density matrix carries a block structure with respect to which properties such as separability can be considered.  ...  Finally, we derive a rational upper bound on the concurrence of density matrices of graphs and show that this bound is exact for graphs on four vertices.  ...  graph theoretic properties; from the perspective of quantum mechanics, density matrices of graphs can be seen as 'simple' and 'highly symmetric' states.  ... 
doi:10.1017/s0960129508006634 fatcat:p7cwvsvl3bhlnfy42c7oadj6oq

Page 1504 of Mathematical Reviews Vol. , Issue 99c [page]

1991 Mathematical Reviews  
The authors characterise bounded bitol- erance digraphs which have complete underlying graphs and this characterisation implies a polynomial time algorithm for recog- nising such digraphs.  ...  The paper goes on to give some separating examples, one of which is a counterexample to the conjecture that there are only two subgraphs that separate the class of 50% toler- ance digraphs from interval  ... 

Characterisation of Cooper pair boxes for quantum computing

J.J. Toppari, K. Hansen, N. Kim, M.T. Savolainen, L. Taskinen, J.P. Pekola
2001 Physica. C, Superconductivity  
The SCB and SET were characterised separately and the box storage performance for Cooper pairs was analysed by observing the changes in the SCB island potential while sweeping the gate voltage. Ó  ...  The electrometer is sensitive to the potential changes of the SCB island and thus measures the number of excess Cooper pairs on the island. The boxes were of the Al/AlOx/Al Josephson junction type.  ...  In the lowest graph one can see the combination of two dierent modulations.  ... 
doi:10.1016/s0921-4534(00)01719-6 fatcat:skzm244nzvhj7kege7yxcj75ii

Robustness of Dynamical Systems Attraction Basins Against State Perturbations: Theoretical Protocol and Application in Systems Biology

Jacques Demongeot, Michel Morvan, Sylvain Sené
2008 2008 International Conference on Complex, Intelligent and Software Intensive Systems  
Then, we give an application of this protocol by giving the results obtained on a specific system which is a model of the Arabidopsis thaliana flower's morphogenesis, depending on a specific boundary condition  ...  In this paper, we give an exhaustive stochastic study protocol to understand what happens on attraction basins of dynamical systems when the latter are subjected to state perturbations.  ...  Moreover, in a context of theoretical biology, we present an application of this protocol in order to characterise the influence of a fixed boundary on the dynamics of a genetic regulatory network modelling  ... 
doi:10.1109/cisis.2008.23 dblp:conf/cisis/DemongeotMS08 fatcat:64nfee3xdfhxjpfvuyhbvx4d54

Page 5389 of Mathematical Reviews Vol. , Issue 94i [page]

1994 Mathematical Reviews  
Summary: “We present an overview of the series of results con- cerned with the exploration of the theoretical graph model used for parallel calculations which underlies the class of the proposed nondeterministic  ...  Trace nets are con- nected by an adjunction to a particular class of trace automata in the sense of Stark, namely the separated trace automata.  ... 

Page 1497 of Mathematical Reviews Vol. 57, Issue 4 [page]

1979 Mathematical Reviews  
A. Turski (Warsaw) . Zubarev, A. L. 57 #11547 The method of separation of variables in problems of nuclear physics. (Russian. English summary) Fiz. Elementar. Castic i Atom.  ...  Author’s summary: “A number of papers on the application of the method of separation of variables to the two-body problem and multichannel scattering theory are analyzed.  ... 

Page 1191 of Mathematical Reviews Vol. 46, Issue 4 [page]

1973 Mathematical Reviews  
Author’s summary: “All possible linearly separable Boolean functions may be geometrically characterised by certain patterns on Karnaugh-map layouts, or mathemati- cally characterised by the magnitude of  ...  Authors’ summary: “A method of analyzing directed graphs by establishing a particular ordering for the nodes is presented, and properties of the ordered graph are de- rived.  ... 

The Hydrostructure: a Universal Framework for Safe and Complete Algorithms for Genome Assembly [article]

Massimo Cairo and Shahbaz Khan and Romeo Rizzi and Sebastian Schmidt and Alexandru I. Tomescu and Elia C. Zirondelli
2021 arXiv   pre-print
A notion of genome assembly solution is that of an arc-covering walk of the graph.  ...  This is based on a novel graph structure, called the hydrostructure of a walk, which highlights the reachability properties of the graph from the perspective of the walk.  ...  Acknowledgments We thank Manuel A. Cáceres for helpful comments on the manuscript's introduction.  ... 
arXiv:2011.12635v3 fatcat:q4gqkfagx5gqzou7doyn7nwut4

Page 2816 of Mathematical Reviews Vol. , Issue 93e [page]

1993 Mathematical Reviews  
Stable functions between dI-domains may then be characterised as the “continuous” functions, and there is also a characterisation of the stable order on functions in terms of a certain order U C, V on  ...  In the framework of graph rewriting which, in contrast to the Berlin school’s approach, does not make use of gluing conditions, the author defines graph reduction rules, a matching procedure and a reduction  ... 

Of wlp and CSP

Steve Dunne
2009 Electronical Notes in Theoretical Computer Science  
We extend Morgan's well-known derivation of the Failures-Divergences semantics of an action system endowed with a wp sequential semantics, by showing how various other CSP semantics can be extracted from  ...  The first explicit state-based characterisations of a behavioural process to attract widespread attention were that of Josephs [11] describing how a non-divergent CSP process could be represented as  ...  Such a purely behavioural characterisation abstracts away from any operational notion of a process as an evolving entity with an evolving internal state which at any given point determines how the process  ... 
doi:10.1016/j.entcs.2009.12.016 fatcat:6qnxnscl3rh33o6g6rgpsdhzxi

Spin statistics, partition functions and network entropy

Jianjia Wang, Richard C Wilson, Edwin R Hancock
2017 Journal of Complex Networks  
Here the energy states of a network are captured using the eigenvalues of a matrix representation of network structure.  ...  As a result of this thermalization, the energy states are occupied according to the Boltzmann distribution [21, 43] .  ...  We characterise the similarities of a set of graphs using a kernel matrix and then embed the graphs into a vector space using kernel-embedding for the purposes of visualisation.  ... 
doi:10.1093/comnet/cnx017 fatcat:ksa7vxybcbhwldf7beq2yaqk74

A Bestiary of Sets and Relations

Stefano Gogioso
2015 Electronic Proceedings in Theoretical Computer Science  
Building on established literature and recent developments in the graph-theoretic characterisation of its CPM category, we provide a treatment of pure state and mixed state quantum mechanics in the category  ...  fRel of finite sets and relations.  ...  We show that the degree of purity of a state, characterised in graph theoretic terms as the number of edges present, cannot be measured in our setup, and conclude that fRel is a local theory.  ... 
doi:10.4204/eptcs.195.16 fatcat:k343c5x5fbgrhnchtypvpyvywa
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