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Processes and unfoldings: concurrent computations in adhesive categories

PAOLO BALDAN, ANDREA CORRADINI, TOBIAS HEINDEL, BARBARA KÖNIG, PAWEŁ SOBOCIŃSKI
2014 Mathematical Structures in Computer Science  
As a categorical framework, as mentioned above, we consider adhesive categories, which turn out to be appropriate for spo rewriting as the needed pushouts in the partial map category Par(C) can be shown  ...  As the unfolding represents potentially infinite computations, we need to work in adhesive categories with "well-behaved" colimits of ω-chains of monos.  ...  of partial maps.  ... 
doi:10.1017/s096012951200031x fatcat:umx7pscecfep7aozlehi72dsny

Unfolding Grammars in Adhesive Categories [chapter]

Paolo Baldan, Andrea Corradini, Tobias Heindel, Barbara König, Paweł Sobociński
2009 Lecture Notes in Computer Science  
As the unfolding represents potentially infinite computations, we need to work in adhesive categories with "well-behaved" colimits of ω-chains of monomorphisms.  ...  We generalize the unfolding semantics, previously developed for concrete formalisms such as Petri nets and graph grammars, to the abstract setting of (single pushout) rewriting over adhesive categories  ...  Given a category C with pullbacks along monomorphisms, its category of partial maps is defined as follows (see [19] ). Definition 5 (Partial maps).  ... 
doi:10.1007/978-3-642-03741-2_24 fatcat:ly7g2r4jrncdddmmbq2owwqgsm

Reconfigurable Decorated PT Nets with Inhibitor Arcs and Transition Priorities [article]

Julia Padberg
2014 arXiv   pre-print
This concept is shown to be compatible with reconfigurable Petri nets.  ...  The first ensure that a marking can inhibit the firing of a transition.  ...  Similar to the proof of Lemma 1 in [9] using PTp instead of PT as the basis.  ... 
arXiv:1409.6856v1 fatcat:xywrxxdo5rc3hl5vv7nqedoilu

Attribution of Graphs by Composition of M, N-adhesive Categories

Christoph Peuser, Annegret Habel
2015 International Conference on Graph Transformation  
We use these constructions for an alternative, short proof for the M, N -adhesiveness of partially labelled graphs.  ...  This paper continues the work on M, N -adhesive categories and shows some important constructions on these categories.  ...  We would like to thank the anonymous referees and Wolfram Kahl for helpful feedback on an early version of this paper.  ... 
dblp:conf/gg/PeuserH15 fatcat:2xeiivuqbnc6bll5skzasmw63u

Co-tabulations, Bicolimits and Van-Kampen Squares in Collagories

Wolfram Kahl
2010 Electronic Communications of the EASST  
Heindel and Sobocinski have recently characterised the Van-Kampen colimits used in adhesive categories as bicolimits in span categories.  ...  From this, we also obtain an interesting characterisation of Van-Kampen squares in collagories.  ...  Instead of src(f ) = A ∧ trg(f ) = B we write f : A → B.  ... 
doi:10.14279/tuj.eceasst.29.421 dblp:journals/eceasst/Kahl10 fatcat:wsvz27337vc2bp7ssiq7j26paa

Single Pushout Rewriting in Comprehensive Systems [chapter]

Harald König, Patrick Stünkel
2020 Lecture Notes in Computer Science  
There is a wide range of work on the question when pushouts exist in categories with partial morphisms starting with the pioneering work of Löwe and Kennaway and ending with an essential characterisation  ...  Although this inherent partiality produces amplified complexity, Heindel's characterisation still yields cocompleteness of the category of comprehensive systems equipped with closed partial morphisms and  ...  Likewise, "∀x ∈ A" means "for all x of any sort s in the carrier set of A". Partial Map Categories Consider an arbitrary category C with pullbacks.  ... 
doi:10.1007/978-3-030-51372-6_6 fatcat:db6tdyjbovdqlnssfhwzydlqsm

Tracelet Hopf algebras and decomposition spaces [article]

Nicolas Behr
2021 arXiv   pre-print
Tracelets are the intrinsic carriers of causal information in categorical rewriting systems.  ...  This Hopf algebra captures important combinatorial and algebraic aspects of rewriting theory, and is motivated by applications of its representation theory to stochastic rewriting systems such as chemical  ...  Instead of having simply chains of n composable spans in degree n, he defined it to be diagrams of shape , that is composable spans, together with all the relevant pullbacks.  ... 
arXiv:2105.06186v2 fatcat:x5ljdpjq6bcojexh3slbq6ht7m

On Term Graphs as an Adhesive Category

Andrea Corradini, Fabio Gadducci
2005 Electronical Notes in Theoretical Computer Science  
The main technical achievement concerns the proof that the category of term graphs is actually quasi-adhesive, obtained by proving the existence of suitable Van Kampen squares.  ...  In this paper we consider the category of term graphs, and we prove that it (partly) fits in the general framework for adhesive categories, developed in [19, 26] , extended in [12] and applied to reduction  ...  At the same time, it put forward an investigation of the relationship between reduction formalisms, usually given by a set of states simply equipped with This work has been partially supported by the EU  ... 
doi:10.1016/j.entcs.2005.02.014 fatcat:rykwyd5jwzdprpzf3dx6wz4tvi

Composition of M,N-adhesive Categories with Application to Attribution of Graphs

Christoph Peuser, Annegret Habel
2016 Electronic Communications of the EASST  
We present a new concept of attributed graphs and show that the corresponding category is M,N-adhesive.  ...  As a consequence, we inherit all nice properties for M,N-adhesive systems such as the Local Church-Rosser Theorem, the Parallelism Theorem, and the Concurrency Theorem for this type of attributed graphs  ...  We would like to thank the anonymous referees as well as Wolfram Kahl and Berthold Hoffmann for helpful feedback on earlier versions of this paper. Bibliography  ... 
doi:10.14279/tuj.eceasst.73.1035 dblp:journals/eceasst/PeuserH15 fatcat:bqd34vsb2bbpzgoqo6ts4xf4wm

Collagories for Relational Adhesive Rewriting [chapter]

Wolfram Kahl
2009 Lecture Notes in Computer Science  
Collagories closely correspond to the adhesive categories important for the categorical DPO approach to graph transformation. but thanks to their relation-algebraic flavour provide a more accessible and  ...  C are injective in C, the mapping category Map C is adhesive.  ...  With that, we can show that, essentially, a pushout over an injective mapping is also a pullback: Lemma 4.12 If a span B P ' A Q E C of mappings is given with Q injective, and B R E D S ' C is a co-tabulation  ... 
doi:10.1007/978-3-642-04639-1_15 fatcat:bm25nypvrzg45d2bujmxtazhse

Crystal plasticity of Cu nanocrystals during collision

Bingqing Cheng, Alfonso H.W. Ngan
2013 Materials Science & Engineering: A  
For small nanocubes with large {100} flat surfaces, however, a dislocation-free direct geometrical conversion process that leads to five-fold twinning dominates except at highly retarded approaching rates  ...  In this work, we simulate the response of two Cu nanoparticles colliding at different approaching rates at room temperature by MD.  ...  Acknowledgement The work described in this paper was supported by funding from the Research Grants Council (Project No. 7159/10E) of the Hong Kong Special Administration Region, as well as the Kingboard  ... 
doi:10.1016/j.msea.2013.07.065 fatcat:nwj6gwsysbb7zdlw4w24d6duqu

Topological Data Analysis of Collective and Individual Epithelial Cells using Persistent Homology of Loops [article]

Dhananjay Bhaskar, William Y. Zhang, Ian Y. Wong
2021 arXiv   pre-print
We use TDA to map out phase diagrams for simulated particles with varying adhesion and propulsion, at constant population size as well as when proliferation is permitted.  ...  Finally, we characterize the robustness of this approach at varying length scales, with sparse sampling, and over time.  ...  Instead, in the limit of weak polarity force P < 0.015 and strong adhesion strength 0.14 < α, particles were typically organized into large clusters (Fig. 5b ,iv), with n ≈ 5 nearest neighbors.  ... 
arXiv:2003.10008v2 fatcat:4h6pe672rzcivojhf45bujmgp4

Subtyping for Hierarchical, Reconfigurable Petri Nets [article]

Julia Padberg
2018 arXiv   pre-print
These subnets are themselves reconfigurable, so they are supplied with their own set of rules. Moreover, global rules that can be applied in all of the net, are provided.  ...  In this contribution we present the combination of reconfigurable Petri nets and hierarchical Petri nets yielding hierarchical structure for reconfigurable Petri nets.  ...  Definition 2.9 Category of partial ordered sets with a greatest element poSetsg The objects (A, ≤ A , g) are partially orders sets with a greatest element g and the morphisms are order-preserving maps  ... 
arXiv:1802.04698v1 fatcat:d77bd3rkq5fefflwwdsgt2fi5q

Van Kampen Colimits as Bicolimits in Span [chapter]

Tobias Heindel, Paweł Sobociński
2009 Lecture Notes in Computer Science  
We show that these properties can be understood as a single universal property in the associated bicategory of spans.  ...  The exactness properties of coproducts in extensive categories and pushouts along monos in adhesive categories have found various applications in theoretical computer science, e.g. in program semantics  ...  Hence -in a similar way as one can restrict the span bicategory to all partial map spans, i.e. those with the left leg monic -we let Span ⇐ The above lets us pass between diagrams in Span C and C: for  ... 
doi:10.1007/978-3-642-03741-2_23 fatcat:if2wkhyq7bdmbavcnfrzwzbs5y

Multiple loop structures critical for ligand binding of the integrin 4 subunit in the upper face of the -propeller mode 1

A. Irie, T. Kamata, Y. Takada
1997 Proceedings of the National Academy of Sciences of the United States of America  
with the corresponding regions of ␣5.  ...  To localize regions of ␣4 critical for ligand binding, we swapped several predicted loops within or near the putative ligand-binding site of ␣4 (which spans repeats 2-5 of the seven N-terminal repeats)  ...  This work was supported by National Institutes of Health Grants GM47157 and GM49899. This is publication 10075-VB from The Scripps Research Institute.  ... 
doi:10.1073/pnas.94.14.7198 pmid:9207068 pmcid:PMC23791 fatcat:6pa4mzol4fczdfjpjwc4udiake
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