Palette-colouring: a belief-propagation approach

We consider a variation of the prototype combinatorial-optimisation problem known as graph-colouring. Our optimisation goal is to colour the vertices of a graph with a fixed number of colours, in a way to maximise the number of different colours present in the set of nearest neighbours of each given vertex. This problem, which we pictorially call "palette-colouring", has been recently addressed as a basic example of problem arising in the context of distributed data storage. Even though it has not been proved to be NP complete, random search algorithms find the problem hard to solve. Heuristics based on a naive belief propagation algorithm are observed to work quite well in certain conditions. In this paper, we build upon the mentioned result, working out the correct belief propagation algorithm, which needs to take into account the many-body nature of the constraints present in this problem. This method improves the naive belief propagation approach, at the cost of increased computational effort. We also investigate the emergence of a satisfiable to unsatisfiable "phase transition" as a function of the vertex mean degree, for different ensembles of sparse random graphs in the large size ("thermodynamic") limit.Comment: 22 pages, 7 figure

On Cavity Approximations for Graphical Models

We reformulate the Cavity Approximation (CA), a class of algorithms recently introduced for improving the Bethe approximation estimates of marginals in graphical models. In our new formulation, which allows for the treatment of multivalued variables, a further generalization to factor graphs with arbitrary order of interaction factors is explicitly carried out, and a message passing algorithm that implements the first order correction to the Bethe approximation is described. Furthermore we investigate an implementation of the CA for pairwise interactions. In all cases considered we could confirm that CA[k] with increasing $k$ provides a sequence of approximations of markedly increasing precision. Furthermore in some cases we could also confirm the general expectation that the approximation of order $k$, whose computational complexity is $O(N^{k+1})$ has an error that scales as $1/N^{k+1}$ with the size of the system. We discuss the relation between this approach and some recent developments in the field.Comment: Extension to factor graphs and comments on related work adde

Dynamic rewiring in small world networks

We investigate equilibrium properties of small world networks, in which both connectivity and spin variables are dynamic, using replicated transfer matrices within the replica symmetric approximation. Population dynamics techniques allow us to examine order parameters of our system at total equilibrium, probing both spin- and graph-statistics. Of these, interestingly, the degree distribution is found to acquire a Poisson-like form (both within and outside the ordered phase). Comparison with Glauber simulations confirms our results satisfactorily.Comment: 21 pages, 5 figure

Belief propagation algorithm for computing correlation functions in finite-temperature quantum many-body systems on loopy graphs

Belief propagation -- a powerful heuristic method to solve inference problems involving a large number of random variables -- was recently generalized to quantum theory. Like its classical counterpart, this algorithm is exact on trees when the appropriate independence conditions are met and is expected to provide reliable approximations when operated on loopy graphs. In this paper, we benchmark the performances of loopy quantum belief propagation (QBP) in the context of finite-tempereture quantum many-body physics. Our results indicate that QBP provides reliable estimates of the high-temperature correlation function when the typical loop size in the graph is large. As such, it is suitable e.g. for the study of quantum spin glasses on Bethe lattices and the decoding of sparse quantum error correction codes.Comment: 5 pages, 4 figure

Dark open innovation in a criminal organizational context: the case of Madoff’s Ponzi fraud

Purpose The purpose of this paper is to investigate the processes of open innovation in the context of a fraudulent organization and, using the infamous Bernie L. Madoff Investment Securities fraud case, introduces and elaborates upon the concept of dark open innovation. The paper’s conceptual framework is drawn from social capital theory, which is grounded on the socio-economics of Bourdieu, Coleman and Putnam and is employed in order to make sense of the processes that occur within dark open innovation. Design/methodology/approach Given the self-evident access issues, this paper is necessarily based on archival and secondary sources taken from the court records of Madoff v. New York – including victim impact statements, the defendant’s Plea Allocution, and academic and journalistic commentaries – which enable the identification of the processes involved in dark open innovation. Significantly, this paper also represents an important inter-disciplinary collaboration between academic scholars variously informed by business and history subject domains. Findings Although almost invariably cast as a positive process, innovation can also be evidenced as a negative or dark force. This is particularly relevant in open innovation contexts, which often call for the creation of extended trust and close relationships. This paper outlines a case of dark open innovation. Research limitations/implications A key implication of this study is that organizational innovation is not automatically synonymous with human flourishing or progress. This paper challenges the automatic assumption of innovation being positive and introduces the notion of dark open innovation. Although this is accomplished by means of an in-depth single case, the findings have the potential to resonate in a wide spectrum of situations. Practical implications Innovation is a concept that applies across a range of organization and management domains. Criminals also innovate; thus, the paper provides valuable insights into the organizational innovation processes especially involved in relation to dark open innovation contexts. Social implications It is important to develop and fully understand the possible wider meanings of innovation and also to recognize that innovation – particularly dark open innovation – does not always create progress. The Caveat Emptor warning is still relevant. Originality/value The paper introduces the novel notion of dark open innovation

Stagnation point reverse flow combustor

A method for combusting a combustible fuel includes providing a vessel having an opening near a proximate end and a closed distal end defining a combustion chamber. A combustible reactants mixture is presented into the combustion chamber. The combustible reactants mixture is ignited creating a flame and combustion products. The closed end of the combustion chamber is utilized for directing combustion products toward the opening of the combustion chamber creating a reverse flow of combustion products within the combustion chamber. The reverse flow of combustion products is intermixed with combustible reactants mixture to maintain the flame

Intrinsic limitations of inverse inference in the pairwise Ising spin glass

We analyze the limits inherent to the inverse reconstruction of a pairwise Ising spin glass based on susceptibility propagation. We establish the conditions under which the susceptibility propagation algorithm is able to reconstruct the characteristics of the network given first- and second-order local observables, evaluate eventual errors due to various types of noise in the originally observed data, and discuss the scaling of the problem with the number of degrees of freedom

A Homological Approach to Belief Propagation and Bethe Approximations

We introduce a differential complex of local observables given a decomposition of a global set of random variables into subsets. Its boundary operator allows us to define a transport equation equivalent to Belief Propagation. This definition reveals a set of conserved quantities under Belief Propagation and gives new insight on the relationship of its equilibria with the critical points of Bethe free energy.Comment: 14 pages, submitted for the 2019 Geometric Science of Information colloquiu

Stagnation point reverse flow combustor for a combustion system

A combustor assembly includes a combustor vessel having a wall, a proximate end defining an opening and a closed distal end opposite said proximate end. A manifold is carried by the proximate end. The manifold defines a combustion products exit. The combustion products exit being axially aligned with a portion of the closed distal end. A plurality of combustible reactant ports is carried by the manifold for directing combustible reactants into the combustion vessel from the region of the proximate end towards the closed distal end