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Fibration symmetries uncover the building blocks of biological networks

Flaviano Morone, Ian Leifer, Hernán A. Makse
2020 Proceedings of the National Academy of Sciences of the United States of America  
Nodes in a fiber have isomorphic input trees and thus process equivalent dynamics and synchronize their activity.  ...  In this representation, we find remarkable symmetries in the input trees that deconstruct the network into functional building blocks called fibers.  ...  Nodes in a fiber have isomorphic input trees and thus process equivalent dynamics and synchronize their activity.  ... 
doi:10.1073/pnas.1914628117 pmid:32234788 fatcat:eime7ybw7nemppqf3e46vd255e

Lossless Compression of Structured Convolutional Models via Lifting [article]

Gustav Sourek, Filip Zelezny, Ondrej Kuzelka
2021 arXiv   pre-print
To address the irregular structure of the data, the models typically extrapolate on the idea of convolution, effectively introducing parameter sharing in their, dynamically unfolded, computation graphs  ...  Inspired by lifting, we introduce a simple and efficient technique to detect the symmetries and compress the neural models without loss of any information.  ...  We display progression of the selected metrics w.r.t. increasing number of significant digits (inits=1) used in value comparisons (left), and number of non-isomorphic subgraph value clashes detected by  ... 
arXiv:2007.06567v2 fatcat:3ea3dzdeufd4bjnn5bsjwf5cgi

A Case for Efficient Solution Enumeration [chapter]

Sarfraz Khurshid, Darko Marinov, Ilya Shlyakhter, Daniel Jackson
2004 Lecture Notes in Computer Science  
In unit testing of object-oriented programs, for example, the invariant constrains the representation of an object; the test cases are then objects on which to invoke a method under test.  ...  We outline an approach to automatic test case generation in which an invariant is expressed in a simple relational logic and translated to a propositional formula.  ...  The goal of symmetry breaking in AA was to make the analysis faster and not to generate exactly non-isomorphic instances.  ... 
doi:10.1007/978-3-540-24605-3_21 fatcat:tdgvjku2ifan7ixrstgvmo6j2e

An adaptive prefix-assignment technique for symmetry reduction [article]

Tommi Junttila, Jukka Kohonen
2018 arXiv   pre-print
This paper presents a technique for symmetry reduction that adaptively assigns a prefix of variables in a system of constraints so that the generated prefix-assignments are pairwise nonisomorphic under  ...  can be processed in parallel independently of each other; (iii) versatility---the method is applicable whenever the group of symmetries can be concisely represented as the automorphism group of a vertex-colored  ...  A preliminary conference abstract of this paper appeared in Junttila T., Karppa M., Kaski  ... 
arXiv:1706.08325v2 fatcat:7ymscoewdrgdjbhx6yyjm6rziu

Discovery of Large Disjoint Motif in Biological Network using Dynamic Expansion Tree [article]

Sabyasachi Patra, Anjali Mohapatra
2018 bioRxiv   pre-print
The growth of Dynamic Expansion Tree (DET) depends on availability of patterns in the target network.  ...  Motivated by the challenges involved in this field we have proposed an efficient and scalable Motif discovery algorithm using a Dynamic Expansion Tree (MDET).  ...  Acknowledgements The authors acknowledge the support by the FIST project of Department of Science and Technology, Govt. of India, the Department of Computer Science and Engineering, IIIT Bhubaneswar, for  ... 
doi:10.1101/308254 fatcat:5ihdh3esh5hmpflec5dcpot3sm

From interpreting to compiling binding times [chapter]

Charles Consel, Olivier Danvy
1990 Lecture Notes in Computer Science  
The result is an action trees isomorphic to the abstract syntax tree of the source pro-gran~ This approach suggests to reorganize the specializer so that it is driven first by the action tree and then  ...  or dynamic, given a static/dynamic division of the input.  ...  Let us build an action tree isomorphic to the binding time tree and tagged with the two directives Rd (for reduce) and Rb (for rebuild). The result is displayed in figure 4 .  ... 
doi:10.1007/3-540-52592-0_57 fatcat:nyjatlfak5cn3o4s2rqngyx4by

A Symmetry-Breaking Node Equivalence for Pruning the Search Space in Backtracking Algorithms

Uroš Čibej, Luka Fürst, Jurij Mihelič
2019 Symmetry  
Striving for a practical usability of the approach, we devise a heuristic method for general graphs and optimal algorithms for trees and cycles.  ...  In particular, we show that the verifier lies between P and NP -complete problems.  ...  Conflicts of Interest: The authors declare no conflict of interest. Abbreviations The following abbreviations are used in this manuscript:  ... 
doi:10.3390/sym11101300 fatcat:t6ylgwj7jraydo5uixu27ddfua

The Advantages of Multiple Parallelizations in Combinatorial Search

L.A. Crowl, M.E. Crovella, T.J. Leblanc, M.L. Scott
1994 Journal of Parallel and Distributed Computing  
and the use of their KSR 1, and Sequent Computer Systems for providing the Balance and Symmetry.  ...  ACKNOWLEDGMENTS We thank Argonne National Laboratories for the use of their TC2000, International Business Machines for providing the 8CE, Donna Bergmark and the Cornell Theory Center for their assistance  ...  Since our loop parallelism can display no more than linear speedup, these are the situations in which one would expect tree parallelism to dominate.  ... 
doi:10.1006/jpdc.1994.1045 fatcat:tibn2jnu5zcidkzko7p2fmkrti

Predicting synchronized gene coexpression patterns from fibration symmetries in gene regulatory networks in bacteria

Ian Leifer, Mishael Sánchez-Pérez, Cecilia Ishida, Hernán A. Makse
2021 BMC Bioinformatics  
We showed that symmetry fibrations partition the genes into groups called fibers based on the symmetries of their 'input trees', the set of paths in the network through which signals can reach a gene.  ...  Results To study the functional role of gene fibers and to test whether some of the fiber-induced coexpression remains in reality, we analyze gene fibrations for the gene regulatory networks of E. coli  ...  Since C is minimal, nodes of the different colors will have input trees that are not isomorphic. Therefore, there is a node n ∈ c j and a node m ∈ c k input trees of which are not isomorphic.  ... 
doi:10.1186/s12859-021-04213-5 pmid:34238210 pmcid:PMC8265036 fatcat:cbgx6id64reg7j7j7oh3gwqhuq

Symmetry in Integer Linear Programming [chapter]

François Margot
2009 50 Years of Integer Programming 1958-2008  
It also surveys related topics, such as symmetry detection, polyhedral studies of symmetric ILPs, and enumeration of all non isomorphic optimal solutions. * Supported by ONR grant N00014-97-1-0196. 2 The  ...  This paper reviews techniques developed to take advantage of the symmetry in an ILP during its solution.  ...  However, while solving the ILP by branch-and-bound, it is sometimes the case that, at node a of the enumeration tree, additional symmetries exist in ILP a , as seen in Example 2 in Section 5.  ... 
doi:10.1007/978-3-540-68279-0_17 fatcat:vzpul5elmfdo3dt4dbflnbxx5u

An algorithm for drawing general undirected graphs

Tomihisa Kamada, Satoru Kawai
1989 Information Processing Letters  
Katuhiro Ota (University of Tokyo), who studies graph theory, for many helpful discussions about the problems in drawing graphs and our drawing algorithm.  ...  Isomorphic graphs When the viewer wants to compare some graphs, it is highly required of the system to display isomorphic graphs as the same picture.  ...  Figure 5 illustrates pictures of isomorphic graphs. Figure 5 (a) and 5(b) show the picture of two initial states in our algorithm.  ... 
doi:10.1016/0020-0190(89)90102-6 fatcat:eeldyr2f5bfwre5jxby6bzmr3q

Algorithms for drawing graphs: an annotated bibliography

Giuseppe Di Battista, Peter Eades, Roberto Tamassia, Ioannis G Tollis
1994 Computational geometry  
In this paper we present a bibliographic survey on algorithms whose goal is to produce aesthetically pleasing drawings of graphs.  ...  Research on this topic is spread over the broad spectrum of Computer Science.  ...  Acknowledgements The authors wish to thank the many graph drawers who have pointed out errors and omissions in the first three versions, and those who have helped with updates to create this fourth version  ... 
doi:10.1016/0925-7721(94)00014-x fatcat:rwudrni2evgkle42lecplbjhle

A computational comparison of symmetry handling methods for mixed integer programs

Marc E. Pfetsch, Thomas Rehn
2018 Mathematical Programming Computation  
The handling of symmetries in the tree received more attention in mathematical programming beginning with "isomorphism pruning" by Margot [29, 30, 31, 32] .  ...  The handling of symmetries in mixed integer programs in order to speed up the solution process of branch-and-cut solvers has recently received signi cant attention, both in theory and practice.  ...  The results of these two variants are displayed in Table 10 and 11.  ... 
doi:10.1007/s12532-018-0140-y fatcat:wlqlkurbd5bf3kbbe77r6byqly

Isomorph-free model enumeration: a new method for checking relational specifications

Daniel Jackson, Somesh Jha, Craig A. Damon
1998 ACM Transactions on Programming Languages and Systems  
The notion of symmetry depends on the type structure of the formula; by picking the weakest typing, larger equivalence classes (and thus fewer representatives) are obtained.  ...  A more refined notion of symmetry that exploits the meaning of the relational operators is also described.  ...  Isomorph-Free Model Enumeration • In our method, the interpretations are constructed incrementally in a tree.  ... 
doi:10.1145/276393.276396 fatcat:c4lwdv2tjjfi7hskefflwshcoe

Hypothesis of Cyclic Structures of Pre- and Consciousness as a Transition in Neuron-like Graphs to a Special Type of Symmetry

Vladimir Aristov, Ivan Stepanyan
2022 Symmetry  
This is due to the tree-like architecture of the neural graph, which mimics the columnar structures of the neocortex.  ...  The presented results are promising in neurocomputer interfaces, man-machine systems and artificial intelligence systems.  ...  Social connections can be displayed in the form of graph structures, and the actual identification and modeling (design) of closed cycles of different scales, fractal structures, and symmetries in social  ... 
doi:10.3390/sym14030505 fatcat:aaugpawcgzghvgrvctrvzd5m4u
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