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An Effective Characterization of Computability in Anonymous Networks [chapter]

Paolo Boldi, Sebastiano Vigna
2001 Lecture Notes in Computer Science  
., recursive) characterizations of the relations that can be computed on networks where all processors use the same algorithm, start from the same state, and know at least a bound on the network size.  ...  With respect to the proof of Theorem 3, we have to show that we can break symmetry in such a way to obtain a fibration ϕ : G → B which is acyclic.  ...  The view construction A classical tool in the study of anonymous networks is the concept of view, introduced for bidirectional networks in [YK96] and extended to the directed case in [BCG + 96] (to  ... 
doi:10.1007/3-540-45414-4_3 fatcat:zn72fprvijcutbd3cex6uu7jmy

Characterizing Well-Behaved vs. Pathological Deep Neural Networks [article]

Antoine Labatie
2019 arXiv   pre-print
We introduce a novel approach, requiring only mild assumptions, for the characterization of deep neural networks at initialization.  ...  Our key insight is to consider the evolution with depth of statistical moments of signal and noise, thereby characterizing the presence or absence of pathologies in the hypothesis space encoded by the  ...  Acknowledgements Many thanks are due to Jean-Baptiste Fiot for his precious feedback on initial drafts and to the anonymous reviewers for their insightful comments.  ... 
arXiv:1811.03087v5 fatcat:7m5oiw2ueffczdzhozbws5kaem

Network Orientation

GERARD TEL
1994 International Journal of Foundations of Computer Science  
This paper analyses how the symmetry of a processor network in uences the existence of a solution for the network orientation problem.  ...  identities, and under the assumption that the network is anonymous.  ...  Breaking symmetry, however, is a non{trivial task even in oriented networks (even though in oriented networks it is easier than in unoriented networks).  ... 
doi:10.1142/s0129054194000037 fatcat:h2syqucx6nfbpl43d64rewt6um

Experimenting with Convolutional Neural Network architectures for the automatic characterization of Solitary Pulmonary Nodules' malignancy rating

Ioannis Dimitris Apostolopoulos
2020 Zenodo  
In this study, we consider the problem of diagnostic classification between benign and malignant lung nodules in CT images, derived from a PET/CT scanner.  ...  Furthermore, we apply simple data augmentation to generate new instances and inspect the performance of the developed networks.  ...  Further research should look towards enhancing the learning capacity of the CNNs in order to improve the robustness of the networks.  ... 
doi:10.5281/zenodo.3711239 fatcat:agwacpyvazepnkzsy6kp5pelrm

Randomness vs. Time in Anonymous Networks [chapter]

Jochen Seidel, Jara Uitto, Roger Wattenhofer
2015 Lecture Notes in Computer Science  
In an anonymous network, symmetry breaking tasks can only be solved if randomization is available. But how many random bits are required to solve any such task?  ...  Since any randomized anonymous network algorithm can be decomposed into a randomized 2-hop coloring stage and a deterministic stage, we tackle the question by focusing on the randomized stage.  ...  In contrast to that, when randomization is available, there are well known algorithms that solve the local symmetry breaking problems coloring [27] and MIS [1, 28] also in anonymous networks.  ... 
doi:10.1007/978-3-662-48653-5_18 fatcat:i2tvb55hhvhb7fs6tu7plh42wy

Strongly stable networks

Matthew O. Jackson, Anne van den Nouweland
2005 Games and Economic Behavior  
We show that the existence of strongly stable networks is equivalent to core existence in a derived cooperative game and use that result to characterize the class of value functions for which there exist  ...  We analyze the formation of networks among individuals. In particular, we examine the existence of networks that are stable against changes in links by any coalition of individuals.  ...  In fact, it seems Y does not have any particular properties besides anonymity, component decomposability, and component balancedness and this suggests that a characterization similar to that in Theorem  ... 
doi:10.1016/j.geb.2004.08.004 fatcat:bjglqfxhebafdglt2v3mqk5mhi

Strongly Stable Networks

Matthew O. Jackson, Anne van den Nouweland
2003 Social Science Research Network  
We show that the existence of strongly stable networks is equivalent to core existence in a derived cooperative game and use that result to characterize the class of value functions for which there exist  ...  We analyze the formation of networks among individuals. In particular, we examine the existence of networks that are stable against changes in links by any coalition of individuals.  ...  In fact, it seems Y does not have any particular properties besides anonymity, component decomposability, and component balancedness and this suggests that a characterization similar to that in Theorem  ... 
doi:10.2139/ssrn.436540 fatcat:dkrfzl6awfhrtc6y4qmnqhu7si

Groupings and Pairings in Anonymous Networks [chapter]

Jérémie Chalopin, Shantanu Das, Nicola Santoro
2006 Lecture Notes in Computer Science  
The grouping problem for k ≥ 2 requires to break the symmetry between the processors partially, as opposed to problems like leader election or enumeration where the symmetry must be broken completely (  ...  In each case, we characterize the classes of networks where Pairing is solvable and determine the necessary and sufficient conditions for solving the problem.  ...  In fact, the k-grouping problem for k ≥ 2 requires to break the symmetry between the nodes only partially, as opposed to problems like leader election or enumeration where the symmetry must be broken completely  ... 
doi:10.1007/11864219_8 fatcat:icfknz7savb7jn4c3clblshfpm

Characterizing the neural correlates of reasoning [article]

David Papo
2015 arXiv   pre-print
While for perceptuo-motor functions neural activity is shaped by the input's statistical properties, and processing is carried out at high speed in hardwired spatially segregated modules, in reasoning,  ...  It is argued that the neural correlates of reasoning should in fact be defined in terms of non-trivial generic properties of spontaneous brain activity, and that this implies resorting to concepts, analytical  ...  same symmetries.  ... 
arXiv:1501.05174v2 fatcat:74du3kpjvbh2zjoaezxqwdy7bi

Counting in Anonymous Dynamic Networks: An Experimental Perspective [chapter]

Giuseppe Antonio Di Luna, Silvia Bonomi, Ioannis Chatzigiannakis, Roberto Baldoni
2013 Lecture Notes in Computer Science  
In addition, we also extended ALCO by defining a new algorithm, namely A * LCO , that is the basic ALCO augmented with a symmetry breaking condition that helps to speed up the convergence time.  ...  In a companion paper [14] , two leader-based algorithms, namely ANoK and ALCO, to count the number of processes in an anonymous dynamic network have been proposed.  ...  The Local Counting Oracle-based Algorithm with Symmetry Breaking A * LCO A LCO in Based on this intuition, we defined a new algorithm, namely A * LCO , by breaking some symmetry in A LCO .  ... 
doi:10.1007/978-3-642-45346-5_11 fatcat:2m7tadj4e5culjytpk526m3m4u

Symmetry in Complex Networks

Angel Garrido
2011 Symmetry  
So, we will dedicate this Special Issue paper to show measures of symmetry in Complex Networks, and highlight their close relation with measures of information and entropy.  ...  Modeling and characterizing these networks, looking for their governing laws, are the current lines of research.  ...  Also I want to be grateful for their wise advices to the anonymous referees of my paper.  ... 
doi:10.3390/sym3010001 fatcat:qb3po3ekrrfcpfewzuu6yluore

Guessing games and distributed computations in synchronous networks [chapter]

Jan Leeuwen, Nicola Santoro, Jorge Urrutia, Shmuel Zaks
1987 Lecture Notes in Computer Science  
A fundamental computation in this environment is the election process; that is, the process of changing from an initial system configuration, where every processor in the network is in the same state,  ...  available to the network processors.  ...  Symmetry Breaking As mentioned in the introduction, the election problem cannot be deterministically solved in an anonymous synchronous network [2] ; probabilistic solutions to this problem (also known  ... 
doi:10.1007/3-540-18088-5_29 fatcat:tztub4otzzhmto2jkfvimjibii

Naming and Counting in Anonymous Unknown Dynamic Networks [chapter]

Othon Michail, Ioannis Chatzigiannakis, Paul G. Spirakis
2013 Lecture Notes in Computer Science  
In this work, we study the fundamental naming and counting problems (and some variations) in networks that are anonymous, unknown, and possibly dynamic.  ...  In counting, nodes must determine the size of the network n and in naming they must end up with unique identities.  ...  In several cases, and in order to break symmetry, we may assume a unique leader node (or source) l.  ... 
doi:10.1007/978-3-319-03089-0_20 fatcat:mvraktfpd5f7jkykgytivsughm

Naming and Counting in Anonymous Unknown Dynamic Networks [article]

Othon Michail and Ioannis Chatzigiannakis and Paul G. Spirakis
2012 arXiv   pre-print
In this work, we study the fundamental naming and counting problems (and some variations) in networks that are anonymous, unknown, and possibly dynamic.  ...  In counting, nodes must determine the size of the network n and in naming they must end up with unique identities.  ...  In several cases, and in order to break symmetry, we may assume a unique leader node (or source) l.  ... 
arXiv:1208.0180v1 fatcat:fd5gwthmvjartmx6qqozqnjw64

Symmetries and cluster synchronization in multilayer networks

Fabio Della Rossa, Louis Pecora, Karen Blaha, Afroza Shirin, Isaac Klickstein, Francesco Sorrentino
2020 Nature Communications  
Here we first define and compute the symmetries of multilayer networks, and then study the emergence of cluster synchronization in these networks.  ...  We distinguish between independent layer symmetries, which occur in one layer and are independent of the other layers, and dependent layer symmetries, which involve nodes in different layers.  ...  In particular, a symmetry-breaking bifurcation, associated with the ILS subgroup, breaks up a clustered pattern in one layer of the multilayer network without altering the possible clusters in the other  ... 
doi:10.1038/s41467-020-16343-0 pmid:32576813 fatcat:toj5udy2zna23f7oio66i246r4
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