Graph Metrics for Temporal Networks

Temporal networks, i.e., networks in which the interactions among a set of elementary units change over time, can be modelled in terms of time-varying graphs, which are time-ordered sequences of graphs over a set of nodes. In such graphs, the concepts of node adjacency and reachability crucially depend on the exact temporal ordering of the links. Consequently, all the concepts and metrics proposed and used for the characterisation of static complex networks have to be redefined or appropriately extended to time-varying graphs, in order to take into account the effects of time ordering on causality. In this chapter we discuss how to represent temporal networks and we review the definitions of walks, paths, connectedness and connected components valid for graphs in which the links fluctuate over time. We then focus on temporal node-node distance, and we discuss how to characterise link persistence and the temporal small-world behaviour in this class of networks. Finally, we discuss the extension of classic centrality measures, including closeness, betweenness and spectral centrality, to the case of time-varying graphs, and we review the work on temporal motifs analysis and the definition of modularity for temporal graphs.Comment: 26 pages, 5 figures, Chapter in Temporal Networks (Petter Holme and Jari Saram\"aki editors). Springer. Berlin, Heidelberg 201

Simplified form of tinnitus retraining therapy in adults: a retrospective study

BACKGROUND: Since the first description of tinnitus retraining therapy (TRT), clinicians have modified and customised the method of TRT in order to suit their practice and their patients. A simplified form of TRT is used at Ealing Primary Care Trust Audiology Department. Simplified TRT is different from TRT in the type and (shorter) duration of the counseling but is similar to TRT in the application of sound therapy except for patients exhibiting tinnitus with no hearing loss and no decreased sound tolerance (wearable sound generators were not mandatory or recommended here, whereas they are for TRT). The main goal of this retrospective study was to assess the efficacy of simplified TRT. METHODS: Data were collected from a series of 42 consecutive patients who underwent simplified TRT for a period of 3 to 23 months. Perceived tinnitus handicap was measured by the Tinnitus Handicap Inventory (THI) and perceived tinnitus loudness, annoyance and the effect of tinnitus on life were assessed through the Visual Analog Scale (VAS). RESULTS: The mean THI and VAS scores were significantly decreased after 3 to 23 months of treatment. The mean decline of the THI score was 45 (SD = 22) and the difference between pre- and post-treatment scores was statistically significant. The mean decline of the VAS scores was 1.6 (SD = 2.1) for tinnitus loudness, 3.6 (SD = 2.6) for annoyance, and 3.9 (SD = 2.3) for effect on life. The differences between pre- and post-treatment VAS scores were statistically significant for tinnitus loudness, annoyance, and effect on life. The decline of THI scores was not significantly correlated with age and duration of tinnitus. CONCLUSION: The results suggest that benefit may be obtained from a substantially simplified form of TRT

Simplified form of tinnitus retraining therapy in adults: a retrospective study.

BACKGROUND: Since the first description of tinnitus retraining therapy (TRT), clinicians have modified and customised the method of TRT in order to suit their practice and their patients. A simplified form of TRT is used at Ealing Primary Care Trust Audiology Department. Simplified TRT is different from TRT in the type and (shorter) duration of the counseling but is similar to TRT in the application of sound therapy except for patients exhibiting tinnitus with no hearing loss and no decreased sound tolerance (wearable sound generators were not mandatory or recommended here, whereas they are for TRT). The main goal of this retrospective study was to assess the efficacy of simplified TRT. METHODS: Data were collected from a series of 42 consecutive patients who underwent simplified TRT for a period of 3 to 23 months. Perceived tinnitus handicap was measured by the Tinnitus Handicap Inventory (THI) and perceived tinnitus loudness, annoyance and the effect of tinnitus on life were assessed through the Visual Analog Scale (VAS). RESULTS: The mean THI and VAS scores were significantly decreased after 3 to 23 months of treatment. The mean decline of the THI score was 45 (SD = 22) and the difference between pre- and post-treatment scores was statistically significant. The mean decline of the VAS scores was 1.6 (SD = 2.1) for tinnitus loudness, 3.6 (SD = 2.6) for annoyance, and 3.9 (SD = 2.3) for effect on life. The differences between pre- and post-treatment VAS scores were statistically significant for tinnitus loudness, annoyance, and effect on life. The decline of THI scores was not significantly correlated with age and duration of tinnitus. CONCLUSION: The results suggest that benefit may be obtained from a substantially simplified form of TRT

Consensus clustering in complex networks

The community structure of complex networks reveals both their organization and hidden relationships among their constituents. Most community detection methods currently available are not deterministic, and their results typically depend on the specific random seeds, initial conditions and tie-break rules adopted for their execution. Consensus clustering is used in data analysis to generate stable results out of a set of partitions delivered by stochastic methods. Here we show that consensus clustering can be combined with any existing method in a self-consistent way, enhancing considerably both the stability and the accuracy of the resulting partitions. This framework is also particularly suitable to monitor the evolution of community structure in temporal networks. An application of consensus clustering to a large citation network of physics papers demonstrates its capability to keep track of the birth, death and diversification of topics.Comment: 11 pages, 12 figures. Published in Scientific Report

Moment-based parameter estimation in binomial random intersection graph models

Binomial random intersection graphs can be used as parsimonious statistical models of large and sparse networks, with one parameter for the average degree and another for transitivity, the tendency of neighbours of a node to be connected. This paper discusses the estimation of these parameters from a single observed instance of the graph, using moment estimators based on observed degrees and frequencies of 2-stars and triangles. The observed data set is assumed to be a subgraph induced by a set of $n_0$ nodes sampled from the full set of $n$ nodes. We prove the consistency of the proposed estimators by showing that the relative estimation error is small with high probability for $n_0 \gg n^{2/3} \gg 1$. As a byproduct, our analysis confirms that the empirical transitivity coefficient of the graph is with high probability close to the theoretical clustering coefficient of the model.Comment: 15 pages, 6 figure

Superhyperfine interactions in inhomogeneously broadened paramagnetic centers observed via a hole-burned free induction decay

Superhyperfine interactions in inhomogeneously broadened paramagnetic centers are observed using a single high-turn-angle microwave pulse. The free induction signal that follows the hole-burning pulse exhibits oscillations that are distinct from the oscillatory free induction decay observable in some inhomogeneously broadened systems. It contains frequencies characteristic of the superhyperfine splittings, together with a zero frequency component. Experimental examples of the effect in both orientationally disordered (powdered) and structurally disordered (glassy) systems are presented and compared with the conceptually similar Fourier transform electron paramagnetic resonance detected nuclear magnetic resonance experiment, together with numerical simulations. (C) 2003 American Institute of Physics

Mining and analysis of audiology data to find significant factors associated with tinnitus masker

Objectives: The objective of this research is to find the factors associated with tinnitus masker from the literature, and by using the large amount of audiology data available from a large NHS (National Health Services, UK) hearing aid clinic. The factors evaluated were hearing impairment, age, gender, hearing aid type, mould and clinical comments. Design: The research includes literature survey for factors associated with tinnitus masker, and performs the analysis of audiology data using statistical and data mining techniques. Setting: This research uses a large audiology data but it also faced the problem of limited data for tinnitus. Participants: It uses 1,316 records for tinnitus and other diagnoses, and 10,437 records of clinical comments from a hearing aid clinic. Primary and secondary outcome measures: The research is looking for variables associated with tinnitus masker, and in future, these variables can be combined into a single model to develop a decision support system to predict about tinnitus masker for a patient. Results: The results demonstrated that tinnitus maskers are more likely to be fit to individuals with milder forms of hearing loss, and the factors age, gender, type of hearing aid and mould were all found significantly associated with tinnitus masker. In particular, those patients having Age<=55 years were more likely to wear a tinnitus masker, as well as those with milder forms of hearing loss. ITE (in the ear) hearing aids were also found associated with tinnitus masker. A feedback on the results of association of mould with tinnitus masker from a professional audiologist of a large NHS (National Health Services, UK) was also taken to better understand them. The results were obtained with different accuracy for different techniques. For example, the chi-squared test results were obtained with 95% accuracy, for Support and Confidence only those results were retained which had more than 1% Support and 80% Confidence. Conclusions: The variables audiograms, age, gender, hearing aid type and mould were found associated with the choice of tinnitus masker in the literature and by using statistical and data mining techniques. The further work in this research would lead to the development of a decision support system for tinnitus masker with an explanation that how that decision was obtained

Inference of hidden structures in complex physical systems by multi-scale clustering

We survey the application of a relatively new branch of statistical physics--"community detection"-- to data mining. In particular, we focus on the diagnosis of materials and automated image segmentation. Community detection describes the quest of partitioning a complex system involving many elements into optimally decoupled subsets or communities of such elements. We review a multiresolution variant which is used to ascertain structures at different spatial and temporal scales. Significant patterns are obtained by examining the correlations between different independent solvers. Similar to other combinatorial optimization problems in the NP complexity class, community detection exhibits several phases. Typically, illuminating orders are revealed by choosing parameters that lead to extremal information theory correlations.Comment: 25 pages, 16 Figures; a review of earlier work