29 research outputs found
Institutional paraconsciousness and its pathologies
This analysis extends a recent mathematical treatment of the Baars consciousness model to analogous, but far more complicated, phenomena of institutional cognition. Individual consciousness is limited to a single, tunable, giant component of interacting cognitive modules, instantiating a Global Workspace. Human institutions, by contrast, support several, sometimes many, such giant components simultaneously, although their behavior remains constrained to a topology generated by cultural context and by the path-dependence inherent to organizational history. Such highly parallel multitasking - institutional paraconsciousness - while clearly limiting inattentional blindness and the consequences of failures within individual workspaces, does not eliminate them, and introduces new characteristic dysfunctions involving the distortion of information sent between global workspaces. Consequently, organizations (or machines designed along these principles), while highly efficient at certain kinds of tasks, remain subject to canonical and idiosyncratic failure patterns similar to, but more complicated than, those afflicting individuals. Remediation is complicated by the manner in which pathogenic externalities can write images of themselves on both institutional function and therapeutic intervention, in the context of relentless market selection pressures. The approach is broadly consonant with recent work on collective efficacy, collective consciousness, and distributed cognition
Evaluation of railway systems: a network approach
Resilience and the efficiency of transportation systems are crucial for the economic development of geographical areas, and network analysis applied to railways can provide insight into the importance of branch lines and their impacts on the entire system. This paper explores the behavior of the ERC measure, a local robustness measure, on the railway network in Lombardy, Italy, and analyzes the impacts of deactivating stations or journeys on the networkâs robustness. Changes in the topological properties of the network were studied by simulating potential external disturbances and analyzing the impact of deleting the most connected stations or railway lines. The numerical results show how the measures provided effectively identify critical stations and journeys within the network structure and outperform classical topological metrics. Since ERC measures take into account all of the alternative paths present in the network, they can provide valuable information for rerouting traffic along alternative paths in case of failures or disruptions. The paperâs original contribution lies in demonstrating the effectiveness of the ERC measure in identifying critical stations and journeys within the network structure
Ferromagnetic Potts Model: Refined #BIS-hardness and Related Results
Recent results establish for 2-spin antiferromagnetic systems that the
computational complexity of approximating the partition function on graphs of
maximum degree D undergoes a phase transition that coincides with the
uniqueness phase transition on the infinite D-regular tree. For the
ferromagnetic Potts model we investigate whether analogous hardness results
hold. Goldberg and Jerrum showed that approximating the partition function of
the ferromagnetic Potts model is at least as hard as approximating the number
of independent sets in bipartite graphs (#BIS-hardness). We improve this
hardness result by establishing it for bipartite graphs of maximum degree D. We
first present a detailed picture for the phase diagram for the infinite
D-regular tree, giving a refined picture of its first-order phase transition
and establishing the critical temperature for the coexistence of the disordered
and ordered phases. We then prove for all temperatures below this critical
temperature that it is #BIS-hard to approximate the partition function on
bipartite graphs of maximum degree D. As a corollary, it is #BIS-hard to
approximate the number of k-colorings on bipartite graphs of maximum degree D
when k <= D/(2 ln D).
The #BIS-hardness result for the ferromagnetic Potts model uses random
bipartite regular graphs as a gadget in the reduction. The analysis of these
random graphs relies on recent connections between the maxima of the
expectation of their partition function, attractive fixpoints of the associated
tree recursions, and induced matrix norms. We extend these connections to
random regular graphs for all ferromagnetic models and establish the Bethe
prediction for every ferromagnetic spin system on random regular graphs. We
also prove for the ferromagnetic Potts model that the Swendsen-Wang algorithm
is torpidly mixing on random D-regular graphs at the critical temperature for
large q.Comment: To appear in SIAM J. Computin
Advances and Novel Approaches in Discrete Optimization
Discrete optimization is an important area of Applied Mathematics with a broad spectrum of applications in many fields. This book results from a Special Issue in the journal Mathematics entitled âAdvances and Novel Approaches in Discrete Optimizationâ. It contains 17 articles covering a broad spectrum of subjects which have been selected from 43 submitted papers after a thorough refereeing process. Among other topics, it includes seven articles dealing with scheduling problems, e.g., online scheduling, batching, dual and inverse scheduling problems, or uncertain scheduling problems. Other subjects are graphs and applications, evacuation planning, the max-cut problem, capacitated lot-sizing, and packing algorithms
Discrete Mathematics and Symmetry
Some of the most beautiful studies in Mathematics are related to Symmetry and Geometry. For this reason, we select here some contributions about such aspects and Discrete Geometry. As we know, Symmetry in a system means invariance of its elements under conditions of transformations. When we consider network structures, symmetry means invariance of adjacency of nodes under the permutations of node set. The graph isomorphism is an equivalence relation on the set of graphs. Therefore, it partitions the class of all graphs into equivalence classes. The underlying idea of isomorphism is that some objects have the same structure if we omit the individual character of their components. A set of graphs isomorphic to each other is denominated as an isomorphism class of graphs. The automorphism of a graph will be an isomorphism from G onto itself. The family of all automorphisms of a graph G is a permutation group
Domination in graphs with application to network reliability
In this thesis we investigate different domination-related graph polynomials, like the connected domination polynomial, the independent domination polynomial, and the total domination polynomial. We prove some basic properties of these polynomials and obtain formulas for the calculation in special graph classes. Furthermore, we also prove results about the calculation of the different graph polynomials in product graphs and different representations of the graph polynomials.
One focus of this thesis lays on the generalization of domination-related polynomials. In this context the trivariate domination polynomial is defined and some results about the bipartition polynomial, which is also a generalization of the domination polynomial, is presented. These two polynomials have many useful properties and interesting connections to other graph polynomials. Furthermore, some more general domination-related polynomials are defined in this thesis, which shows some possible directions for further research.In dieser Dissertation werden verschiedene, zum Dominationspolynom verwandte, Graphenpolynome, wie das zusammenhĂ€ngende Dominationspolynom, das unabhĂ€ngige Dominationspolynom und das totale Dominationspolynom, untersucht. Es werden grundlegende Eigenschaften erforscht und SĂ€tze fĂŒr die Berechnung dieser Polynome in speziellen Graphenklassen bewiesen. Weiterhin werden Ergebnisse fĂŒr die Berechnung in Produktgraphen und verschiedene ReprĂ€sentationen fĂŒr diese Graphenpolynome gezeigt.
Ein Fokus der Dissertation liegt auf der Verallgemeinerung der verschiedenen Dominationspolynome. In diesem Zusammenhang wird das trivariate Dominationspolynom definiert. AuĂerdem werden Ergebnisse fĂŒr das Bipartitionspolynom bewiesen. Diese beiden Polynome haben viele interessante Eigenschaften und Beziehungen zu anderen Graphenpolynomen. DarĂŒber hinaus werden weitere multivariate Graphenpolynome definiert, die eine mögliche Richtung fĂŒr weitere Forschung auf diesem Gebiet aufzeigen
Designing Efficient Algorithms for Distributed Systems.
Search for efficient algorithms for distributed systems has become an important area of computer science. This research is driven by the need to efficiently process and communicate information generated by the system. In distributed systems, topological information plays an important role in the design of fast algorithms for problems such as routing, broadcasting, and sorting. The central focus of this dissertation is the design and analysis of distributed algorithms for determining topological information in asynchronous communication networks. Specifically, we present distributed algorithms for two generic problems: distributed graph problems and network traversal problems. Network location and network recognition are two important graph problems in distributed systems. We present unified algorithms for locating centers and medians of asynchronous communication networks. Also, we present both the centralized and decentralized versions of the algorithm. Furthermore, this is the first decentralized algorithm reported in the literature. These results are further extended to weighted networks. In addition, the unified algorithm can also be used to determine other topological parameters such as the diameter, and centroids of distributed networks. Efficient algorithms for problems such as finding shortest paths, centers, and sorting could be designed if the network topology is known a priori. Towards this end, we solve an open problem of recognizing mesh (grid) structures. We formulate both centralized and decentralized algorithms for recognizing mesh networks. The time and message complexities of the algorithm are O(n\sp{1.6}) and O(e+nlogn), respectively, where n is the number of nodes and e is the number of edges of the graph underlying the network. Network traversal is a fundamental activity in a distributed system and it has been widely studied in the literature. We present efficient distributed algorithms for depth first traversal of an asynchronous communication network and show the usefulness of this algorithm in deriving efficient solutions to the problems related to network learning. Finally, we discuss application of some of these algorithms in distributed sensor networks