Generating Realistic Labelled, Weighted Random Graphs

Generative algorithms for random graphs have yielded insights into the structure and evolution of real-world networks. Most networks exhibit a well-known set of properties, such as heavy-tailed degree distributions, clustering and community formation. Usually, random graph models consider only structural information, but many real-world networks also have labelled vertices and weighted edges. In this paper, we present a generative model for random graphs with discrete vertex labels and numeric edge weights. The weights are represented as a set of Beta Mixture Models (BMMs) with an arbitrary number of mixtures, which are learned from real-world networks. We propose a Bayesian Variational Inference (VI) approach, which yields an accurate estimation while keeping computation times tractable. We compare our approach to state-of-the-art random labelled graph generators and an earlier approach based on Gaussian Mixture Models (GMMs). Our results allow us to draw conclusions about the contribution of vertex labels and edge weights to graph structure.

Fecundity and reproductive strategies in deep-sea incirrate octopuses (Cephalopoda: Octopoda).

Coleoid cephalopods show flexibility in their reproductive strategies or mode of spawning, which can range from simultaneous terminal spawning over a short period at the end of the animal’s life to continuous spawning over a long period of the animal’s life. Although a simultaneous terminal spawning strategy is typical of shallow water temperate octopuses, it is not known whether deep-sea octopods would have the same reproductive strategy. The reproductive strategies and fecundity were investigated in nine species of deep-sea incirrate octopuses: Bathypolypus arcticus, Bathypolypus bairdii, Bathypolypus ergasticus, Bathypolypus sponsalis, Bathypolypus valdiviae, Benthoctopus levis, Benthoctopus normani, Benthoctopus sp., and Graneledone verrucosa (total n = 85). Egg-length frequency graphs and multivariate analysis (principal components analysis) suggest that B. sponsalis has a synchronous ovulation pattern and therefore a simultaneous terminal spawning strategy. Although a simultaneous terminal spawning strategy is most likely for B. levis and B. normani, the egg-length frequency graphs and multivariate analysis also suggest a greater variation in egglengths which could lead to spawning over an extended period.

Compact Toffoli gate using weighted graph states

We introduce three compact graph states that can be used to perform a measurement-based Toffoli gate. Given a weighted graph of six, seven, or eight qubits, we show that success probabilities of 1/4, 1/2, and 1, respectively, can be achieved. Our study puts a measurement-based version of this important quantum logic gate within the reach of current experiments. As the graphs are setup independent, they could be realized in a variety of systems, including linear optics and ion traps.

The chronic fatigue syndrome: A comparative pathway analysis

In this paper, we introduce a method to detect pathological pathways of a disease. We aim to identify biological processes rather than single genes affected by the chronic fatigue syndrome (CFS). So far, CFS has neither diagnostic clinical signals nor abnormalities that could be diagnosed by laboratory examinations. It is also unclear if the CFS represents one disease or can be subdivided in different categories. We use information from clinical trials, the gene ontology (GO) database as well as gene expression data to identify undirected dependency graphs (UDGs) representing biological processes according to the GO database. The structural comparison of UDGs of sick versus non-sick patients allows us to make predictions about the modification of pathways due to pathogenesis.

Rigorous conditions for food-web intervality in high-dimensional trophic niche spaces

Food webs represent trophic (feeding) interactions in ecosystems. Since the late 1970s, it has been recognized that food-webs have a surprisingly close relationship to interval graphs. One interpretation of food-web intervality is that trophic niche space is low-dimensional, meaning that the trophic character of a species can be expressed by a single or at most a few quantitative traits. In a companion paper we demonstrated, by simulating a minimal food-web model, that food webs are also expected to be interval when niche-space is high-dimensional. Here we characterize the fundamental mechanisms underlying this phenomenon by proving a set of rigorous conditions for food-web intervality in high-dimensional niche spaces. Our results apply to a large class of food-web models, including the special case previously studied numerically.

The structural information content of chemical networks

We present an information-theoretic method to measure the structural information content of networks and apply it to chemical graphs. As a result, we find that our entropy measure is more general than classical information indices known in mathematical and computational chemistry. Further, we demonstrate that our measure reflects the essence of molecular branching meaningfully by determining the structural information content of some chemical graphs numerically.

Structural information content of networks: Graph entropy based on local vertex functionals

In this paper we define the structural information content of graphs as their corresponding graph entropy. This definition is based on local vertex functionals obtained by calculating-spheres via the algorithm of Dijkstra. We prove that the graph entropy and, hence, the local vertex functionals can be computed with polynomial time complexity enabling the application of our measure for large graphs. In this paper we present numerical results for the graph entropy of chemical graphs and discuss resulting properties. (C) 2007 Elsevier Ltd. All rights reserved.

Algorithmic computation of knot polynomials of secondary structure elements of proteins

The classification of protein structures is an important and still outstanding problem. The purpose of this paper is threefold. First, we utilize a relation between the Tutte and homfly polynomial to show that the Alexander-Conway polynomial can be algorithmically computed for a given planar graph. Second, as special cases of planar graphs, we use polymer graphs of protein structures. More precisely, we use three building blocks of the three-dimensional protein structure-alpha-helix, antiparallel beta-sheet, and parallel beta-sheet-and calculate, for their corresponding polymer graphs, the Tutte polynomials analytically by providing recurrence equations for all three secondary structure elements. Third, we present numerical results comparing the results from our analytical calculations with the numerical results of our algorithm-not only to test consistency, but also to demonstrate that all assigned polynomials are unique labels of the secondary structure elements. This paves the way for an automatic classification of protein structures.

Signal and variability within a Holocene peat bog - Chronological uncertainties of pollen, macrofossil and fungal proxies

A single raised bog from the eastern Netherlands has been repeatedly analysed and ¹⁴C dated over the past few decades. Here we assess the within-site variability of fossil proxy data through comparing the regional
pollen, macrofossils and non-pollen palynomorphs of four of these profiles. High-resolution chronologies were obtained using ¹⁴C dating and Bayesian age-depth modelling. Where chronologies of profiles overlap, proxy curves are compared between the profiles using greyscale graphs that visualise chronological uncertainties. Even at this small spatial scale, there is considerable variability of the fossil proxy curves. Implications regarding signal (climate) and noise (internal dynamics) of the different types of fossil proxies are discussed. Single cores are of limited value for reconstructing centennial-scale climate change, and only by combining multiple cores and proxies can we obtain a reliable understanding of past environmental change and possible forcing factors (e.g., solar variability).

The Computational Complexity of Dominance and Consistency in CP-Nets

We investigate the computational complexity of testing dominance and consistency in CP-nets. Previously, the complexity of dominance has been determined for restricted classes in which the dependency graph of the CP-net is acyclic. However, there are preferences of interest that define cyclic dependency graphs; these are modeled with general CP-nets. In our main results, we show here that both dominance and consistency for general CP-nets are PSPACE-complete. We then consider the concept of strong dominance, dominance equivalence and dominance incomparability, and several notions of optimality, and identify the complexity of the corresponding decision problems. The reductions used in the proofs are from STRIPS planning, and thus reinforce the earlier established connections between both areas.

Developing Approaches for Solving a Telecommunications Feature Subscription Problem

Call control features (e.g., call-divert, voice-mail) are primitive options to which users can subscribe off-line to personalise their service. The configuration of a feature subscription involves choosing and sequencing features from a catalogue and is subject to constraints that prevent undesirable feature interactions at run-time. When the subscription requested by a user is inconsistent, one problem is to find an optimal relaxation, which is a generalisation of the feedback vertex set problem on directed graphs, and thus it is an NP-hard task. We present several constraint programming formulations of the problem. We also present formulations using partial weighted maximum Boolean satisfiability and mixed integer linear programming. We study all these formulations by experimentally comparing them on a variety of randomly generated instances of the feature subscription problem.

Veiled Aspects of Bach Reception in the Long Nineteenth Century Exposed through a Macro-examination of Printed Music: with Particular Focus on The Well-Tempered Clavier

It presents questions that have arisen as a result of more than 20 years of collecting the data for the Bach Bibliography. Taking editions of The Well-Tempered Clavier as an example and using figures and graphs extracted from the Bach Bibliography, Tomita explores the various facets of the work's reception including its market appeal, the ambitions that steered its editors and publishers, and trends in its interpretation.

Rapid design of application specific FFT cores

Methods are presented for developing synthesizable FFT cores. These are based on a modular approach in which parameterized commutator and processor blocks are cascaded to implement the computations required in many important FFT signal flow graphs. In addition, it is shown how the use of a digital serial data organization can be used to produce systems that offer 100% processor utilization along with reductions in storage requirements. The approach has been used to create generators for the automated synthesis of FFT cores that are portable across a broad range of silicon technologies. Resulting chip designs are competitive with ones created using manual methods but with significant reductions in design times.

Synthesizable FFT cores

Methods are presented for developing synthesizable FFT cores. These are based on a modular approach in which parameterizable blocks are cascaded to implement the computations required across a range of typical FFT signal flow graphs. The underlying architectural approach combines the use of a digital serial data organization with generic commutator blocks to produce systems that offer 100% processor utilization with storage requirements less than previous designs. The approach has been used to create generators for the automated synthesis of FFT cores that are portable across a broad range of silicon technologies. Resulting chip designs are competitive with manual methods but with significant reductions in design times.

A correction to the analytical solution of the mixed-mode bending (MMB) problem

This paper addresses the analytical solution of the mixed-mode bending (MMB) problem. The first published solutions used a load separation in pure mode I and mode II and were applied for a crack length less than the beam half-span, a <= L. In later publications, the same mode separation was used in deriving the analytical solution for crack lengths bigger than the beam half-span, a > L. In this paper it is shown that this mode separation is not valid when a > L and in some cases may lead to very erroneous results. The correct mode separation and the corresponding analytical solutions, when a > L, are presented. Results, of force vs. displacement and force vs. crack length graphs, obtained using the existing formulation and the corrected formulation are compared. A finite element solution, which does not use mode separation, is also presented