Project description:Complex networks abound in physical, biological and social sciences. Quantifying a network's topological structure facilitates network exploration and analysis, and network comparison, clustering and classification. A number of Wiener type indices have recently been incorporated as distance-based descriptors of complex networks, such as the R package QuACN. Wiener type indices are known to depend both on the network's number of nodes and topology. To apply these indices to measure similarity of networks of different numbers of nodes, normalization of these indices is needed to correct the effect of the number of nodes in a network. This paper aims to fill this gap. Moreover, we introduce an f-Wiener index of network G, denoted by Wf(G). This notion generalizes the Wiener index to a very wide class of Wiener type indices including all known Wiener type indices. We identify the maximum and minimum of Wf(G) over a set of networks with n nodes. We then introduce our normalized-version of f-Wiener index. The normalized f-Wiener indices were demonstrated, in a number of experiments, to improve significantly the hierarchical clustering over the non-normalized counterparts.
Project description:It is often of interest to decompose the total effect of an exposure into a component that acts on the outcome through some mediator and a component that acts independently through other pathways. Said another way, we are interested in the direct and indirect effects of the exposure on the outcome. Even if the exposure is randomly assigned, it is often infeasible to randomize the mediator, leaving the mediator-outcome confounding not fully controlled. We develop a sensitivity analysis technique that can bound the direct and indirect effects without parametric assumptions about the unmeasured mediator-outcome confounding.
Project description:BackgroundSufficient-cause interaction is a type of interaction that has received much attention recently. The sufficient component cause model on which the sufficient-cause interaction is based is however a non-identifiable model. Estimating the interaction parameters from the model is mathematically impossible.MethodsIn this paper, I derive bounding formulae for sufficient-cause interactions under the assumption of no redundancy.ResultsTwo real data sets are used to demonstrate the method (R codes provided). The proposed bounds are sharp and sharper than previous bounds.ConclusionsSufficient-cause interactions can be quantified by setting bounds on them.
Project description:Many monostable reaction-diffusion equations admit one-dimensional travelling waves if and only if the wave speed is sufficiently high. The values of these minimum wave speeds are not known exactly, except in a few simple cases. We present methods for finding upper and lower bounds on minimum wave speed. They rely on constructing trapping boundaries for dynamical systems whose heteroclinic connections correspond to the travelling waves. Simple versions of this approach can be carried out analytically but often give overly conservative bounds on minimum wave speed. When the reaction-diffusion equations being studied have polynomial nonlinearities, our approach can be implemented computationally using polynomial optimization. For scalar reaction-diffusion equations, we present a general method and then apply it to examples from the literature where minimum wave speeds were unknown. The extension of our approach to multi-component reaction-diffusion systems is then illustrated using a cubic autocatalysis model from the literature. In all three examples and with many different parameter values, polynomial optimization computations give upper and lower bounds that are within 0.1% of each other and thus nearly sharp. Upper bounds are derived analytically as well for the scalar reaction-diffusion equations.
Project description:Complex networks are ubiquitous in biological, physical and social sciences. Network robustness research aims at finding a measure to quantify network robustness. A number of Wiener type indices have recently been incorporated as distance-based descriptors of complex networks. Wiener type indices are known to depend both on the network's number of nodes and topology. The Wiener polarity index is also related to the cluster coefficient of networks. In this paper, based on some graph transformations, we determine the sharp upper bound of the Wiener polarity index among all bicyclic networks. These bounds help to understand the underlying quantitative graph measures in depth.
Project description:The discovery of new tumor subtypes has been aided by transcriptomics profiling. However, some new subtypes can be irreproducible due to data artifacts that arise from disparate experimental handling. To deal with these artifacts, methods for data normalization and batch-effect correction have been utilized before performing sample clustering for disease subtyping, despite that these methods were primarily developed for group comparison. It remains to be elucidated whether they are effective for sample clustering. We examined this issue with a re-sampling-based simulation study that leverages a pair of microRNA microarray data sets. Our study showed that (i) normalization generally benefited the discovery of sample clusters and quantile normalization tended to be the best performer, (ii) batch-effect correction was harmful when data artifacts confounded with biological signals, and (iii) their performance can be influenced by the choice of clustering method with the Prediction Around Medoid method based on Pearson correlation being consistently a best performer. Our study provides important insights on the use of data normalization and batch-effect correction in connection with the design of array-to-sample assignment and the choice of clustering method for facilitating accurate and reproducible discovery of tumor subtypes with microRNAs.
Project description:The geometry of polynomials explores geometrical relationships between the zeros and the coefficients of a polynomial. A classical problem in this theory is to locate the zeros of a given polynomial by determining disks in the complex plane in which all its zeros are situated. In this paper, we infer bounds for general polynomials and apply classical and new results to graph polynomials namely Wiener and distance polynomials whose zeros have not been yet investigated. Also, we examine the quality of such bounds by considering four graph classes and interpret the results.
Project description:Uncertain data are observations that cannot be uniquely mapped to a referent. In the case of uncertainty due to incompleteness, possibility theory can be used as an appropriate model for processing such data. In particular, granular counting is a way to count data in presence of uncertainty represented by possibility distributions. Two algorithms were proposed in literature to compute granular counting: exact granular counting, with quadratic time complexity, and approximate granular counting, with linear time complexity. This paper extends approximate granular counting by computing bounds for exact granular count. In this way, the efficiency of approximate granular count is combined with certified bounds whose width can be adjusted in accordance to user needs.
Project description:Originally developed as a theory of consciousness, integrated information theory provides a mathematical framework to quantify the causal irreducibility of systems and subsets of units in the system. Specifically, mechanism integrated information quantifies how much of the causal powers of a subset of units in a state, also referred to as a mechanism, cannot be accounted for by its parts. If the causal powers of the mechanism can be fully explained by its parts, it is reducible and its integrated information is zero. Here, we study the upper bound of this measure and how it is achieved. We study mechanisms in isolation, groups of mechanisms, and groups of causal relations among mechanisms. We put forward new theoretical results that show mechanisms that share parts with each other cannot all achieve their maximum. We also introduce techniques to design systems that can maximize the integrated information of a subset of their mechanisms or relations. Our results can potentially be used to exploit the symmetries and constraints to reduce the computations significantly and to compare different connectivity profiles in terms of their maximal achievable integrated information.
Project description:In order to understand the identity of the Central American species of the genus Phaenonotum Sharp, 1882, the type specimens of the species described by Sharp (1882) deposited in the David Sharp collection in the Natural History Museum in London have been re-examined. The following species are redescribed: Phaenonotum apicale Sharp, 1882, Phaenonotum collare Sharp, 1882, Phaenonotum dubium Sharp, 1882 (confirmed as junior synonym of Phaenonotum exstriatum (Say, 1835)), Phaenonotum laevicolle Sharp, 1882, Phaenonotum rotundulum Sharp, 1882 and Phaenonotum tarsale Sharp, 1882. Lectotypes are designated for Phaenonotum apicale, Phaenonotum collare, Phaenonotum rotundulum and Phaenonotum tarsale. External diagnostic characters and morphology of male genitalia are illustrated. A table summarizing diagnostic characters allowing the identification of the species is provided.