Theoretical Metrics Research Articles

Comment: Network disruption as a common framework for factors contributing to dementia.

There is mounting evidence that large-scale functional brain networks are fundamental to the pathophysiology of dementing illnesses.1 Functional networks require intact white matter, and small vessel disease (SVD) may disrupt this infrastructure. Tuladhar et al.2 conducted an analysis of imaging biomarkers as predictors of all-cause dementia in a prospective hospital-based cohort of patients with presumed evidence of SVD. The imaging biomarkers included white matter network–based graph theoretical metrics (e.g., global network efficiency), white matter volume, gray matter volume, hippocampal volume, manually segmented white matter hyperintensity volume, and presence/absence of lacunes and microbleeds.

Space-Time Topological Graphs

GIScience 2016 Short Paper Proceedings Space-Time Topological Graphs C. Robertson 1 Wilfrid Laurier University, 75 University Ave, Waterloo, ON Email: crobertson@wlu.ca Abstract The integration of space and time in geospatial analyses is an active research area. While methods for characterizing sequences of spatial point objects over time have evolved greatly over recent years, the treatment of space-time change in complex geographic objects such as linear features and polygons has seen much less attention. In this paper we consider the directed graph as a representation for temporal change in spatial objects, where edges are formed by spatial relationships. With this representation, the large foundation of graph- theoretic metrics and algorithms can be used for the analysis of space-time change in geographic objects. We present preliminary findings using several exemplar datasets: range expansion of polygons representing animal home ranges, the spatial path of Hurricane Katrina, and a forest insect outbreak. In particular, we investigate the dynamics of space-time change in these datasets using well-known metrics for characterizing graph structures. 1. Introduction Understanding space-time change continues to be a challenging and increasingly required task for geospatial analysis, as more spatial datasets are evolving into long-term records of spatial and temporal change (e.g, satellite archives, long-term radio collar studies). However, models of space-time change remain to be fulll developed. Stell et al. (2011) introduced a bigraph representation of space-time change, whereby objects were represented as nodes at discrete time points, and linked through relations. As well, Del Mondo et al. 2012 further developed this model with an explicit spatiotemporal graph representation, distinguishing between filial relations (based on explicit identity) and purely topological relations (derived from spatial relationships). We build on these ideas from the perspective of space-time analysis in order to analyze spatial changes in polygon objects over time. We use several space-time polygon datasets in order to explore a how space-time topological graphs can be used as a representation for spatial-temporal analysis generally. 1.1 Polygon models of space-time change Sadahiro and Umemura (2001) introduced a framework for the analysis of spatio-temporal polygon distributions based on events derived from spatial overlap relations in neighbouring time-steps. The scope of events was extended in Robertson et al. (2007) to include proximity- based spatial relations, describing various types of movement occurring over the change interval, known as spatial-temporal analysis of moving polygons (STAMP). The STAMP framework is temporally discrete, such that an appropriate temporal grain is required a priori in order to represent change. Metrics associated with space-time change include counts of event types, area change, directional change, all of which can be accumulated along paths of the graph representing continuous spatial relationships over time. In Sadahiro (2001) the graph representation of polygon change events was introduced. In this paper we build on this framework order to integrate existing graph metrics into the spatial-temporal analysis of polygon distributions.

Sequence information gain based motif analysis.

BackgroundThe detection of regulatory regions in candidate sequences is essential for the understanding of the regulation of a particular gene and the mechanisms involved. This paper proposes a novel methodology based on information theoretic metrics for finding regulatory sequences in promoter regions.ResultsThis methodology (SIGMA) has been tested on genomic sequence data for Homo sapiens and Mus musculus. SIGMA has been compared with different publicly available alternatives for motif detection, such as MEME/MAST, Biostrings (Bioconductor package), MotifRegressor, and previous work such Qresiduals projections or information theoretic based detectors. Comparative results, in the form of Receiver Operating Characteristic curves, show how, in 70 % of the studied Transcription Factor Binding Sites, the SIGMA detector has a better performance and behaves more robustly than the methods compared, while having a similar computational time. The performance of SIGMA can be explained by its parametric simplicity in the modelling of the non-linear co-variability in the binding motif positions.ConclusionsSequence Information Gain based Motif Analysis is a generalisation of a non-linear model of the cis-regulatory sequences detection based on Information Theory. This generalisation allows us to detect transcription factor binding sites with maximum performance disregarding the covariability observed in the positions of the training set of sequences. SIGMA is freely available to the public at http://b2slab.upc.edu.

Heritability of the network architecture of intrinsic brain functional connectivity

The brain's functional network exhibits many features facilitating functional specialization, integration, and robustness to attack. Using graph theory to characterize brain networks, studies demonstrate their small-world, modular, and “rich-club” properties, with deviations reported in many common neuropathological conditions. Here we estimate the heritability of five widely used graph theoretical metrics (mean clustering coefficient (γ), modularity (Q), rich-club coefficient (ϕnorm), global efficiency (λ), small-worldness (σ)) over a range of connection densities (k=5–25%) in a large cohort of twins (N=592, 84 MZ and 89 DZ twin pairs, 246 single twins, age 23±2.5). We also considered the effects of global signal regression (GSR). We found that the graph metrics were moderately influenced by genetic factors h2 (γ=47–59%, Q=38–59%, ϕnorm=0–29%, λ=52–64%, σ=51–59%) at lower connection densities (≤15%), and when global signal regression was implemented, heritability estimates decreased substantially h2 (γ=0–26%, Q=0–28%, ϕnorm=0%, λ=23–30%, σ=0–27%). Distinct network features were phenotypically correlated (|r|=0.15–0.81), and γ, Q, and λ were found to be influenced by overlapping genetic factors. Our findings suggest that these metrics may be potential endophenotypes for psychiatric disease and suitable for genetic association studies, but that genetic effects must be interpreted with respect to methodological choices.

A heuristic branch-and-bound based thresholding algorithm for unveiling cognitive activity from EEG data

One of the biggest challenges in the field of computational neuroscience from the perspective of complex network analysis is the measurement of dynamic local and global interactions of the brain regions during cognitive function. Graph theoretic analysis has been extensively applied to study the dynamics of functional brain networks in the recent years. The selection of appropriate thresholding methods to construct weighted/unweighted subnetworks to detect cognitive load induced changes in brain׳s electrical activity remains an open challenge in the functional brain network research. This paper reviews the application of statistical and information theoretic metrics to construct the functional brain networks, proposes a novel Branch-and-Bound based thresholding algorithm that extracts the influential subnetwork, and applies efficient computational techniques and complex network metrics to detect and quantify the cognitive activities. The empirical analyses showcase the efficiency of the proposed thresholding algorithm by highlighting the changing neuronal patterns during cognitive activity when compared to that of baseline activity. Statistical evaluation of the results further validates the efficiency of the proposed method as well. The results demonstrate the ability of the proposed algorithm in detecting subtle cognitive load induced changes in functional brain networks.

Meaning in the avian auditory cortex: neural representation of communication calls.

Understanding how the brain extracts the behavioral meaning carried by specific vocalization types that can be emitted by various vocalizers and in different conditions is a central question in auditory research. This semantic categorization is a fundamental process required for acoustic communication, and presupposes discriminative and invariance properties of the auditory system for conspecific vocalizations. Songbirds have been used extensively to study vocal learning, but the communicative function of all their vocalizations and their neural representation has yet to be examined. In this study, we first generated a library containing almost the entire zebra finch vocal repertoire, and organised communication calls along nine different categories according to their behavioral meaning. We then investigated the neural representations of these semantic categories in the primary and secondary auditory areas of six anesthetised zebra finches. To analyse how single units encode these call categories, we described neural responses in terms of their discrimination, selectivity and invariance properties. Quantitative measures for these neural properties were obtained with an optimal decoder using both spike counts and spike patterns. Information theoretic metrics show that almost half of the single units encode semantic information. Neurons achieve higher discrimination of these semantic categories by being more selective and more invariant. These results demonstrate that computations necessary for semantic categorization of meaningful vocalizations are already present in the auditory cortex, and emphasise the value of a neuro-ethological approach to understand vocal communication.

Exploring the Role of Domain Partitioning on Efficiency of Parallel Distributed Hydrologic Model Simulations

Exploring the Role of Domain Partitioning on Efficiency of Parallel Distributed Hydrologic Model Simulations Spatially distributed hydrologic models of watersheds and river basins are data and computation intensive because of the combined nature of hydrodynamics, complex forcings and heterogeneous parameter fields. Application of these models at fine temporal and spatial resolutions, and on large problem domains, is facilitated by parallel computation on multi-processor clusters. Notably, the computation efficiency of parallel simulations is crucially determined by the efficiency with which data are divided-and-distributed in a multiprocessor environment and how the information is shared between processors. While numerous data partitioning algorithms exist and have been extensively studied in computer science literature, detailed elucidation of the role of hydrologic model structure on data partitioning has not been presented yet. In addition, the relative role of computational load balance and interprocessor communication on parallel computation efficiency of a hydrologic model is not known. Considering the unstructured domain discretization scheme used in PIHM hydrologic model as an example, the paper first presents a generic methodology for incorporating hydrologic factors in optimal domain partitioning algorithms. The partitions are then used to explore the isolated role of computation load balance and interprocessor communication on parallel efficiency. Results confirm that parallel simulations on partitions that minimize interprocessor communication and divide the computational load equally are the most efficient. More importantly, load balance between processors is observed to be a more sensitive control on parallel efficiency than minimization of interprocessor communication. Further analyses of the efficiency and scalability of the parallel code for different partitioning configurations reveal a direct correspondence between parallel efficiency and theoretical metrics such as load balance ratio and communication to computation ratio. Results indicate that theoretical metrics can be used for the selection of best partitions before computationally intensive parallel simulations are performed. The study serves as a proof-of-concept evaluation of the impact of computation and communication on the efficiency of parallelized distributed hydrologic models at multiple resolutions.

Change of Brain Functional Connectivity in Patients With Spinal Cord Injury: Graph Theory Based Approach.

ObjectiveTo investigate the global functional reorganization of the brain following spinal cord injury with graph theory based approach by creating whole brain functional connectivity networks from resting state-functional magnetic resonance imaging (rs-fMRI), characterizing the reorganization of these networks using graph theoretical metrics and to compare these metrics between patients with spinal cord injury (SCI) and age-matched controls.MethodsTwenty patients with incomplete cervical SCI (14 males, 6 females; age, 55±14.1 years) and 20 healthy subjects (10 males, 10 females; age, 52.9±13.6 years) participated in this study. To analyze the characteristics of the whole brain network constructed with functional connectivity using rs-fMRI, graph theoretical measures were calculated including clustering coefficient, characteristic path length, global efficiency and small-worldness.ResultsClustering coefficient, global efficiency and small-worldness did not show any difference between controls and SCIs in all density ranges. The normalized characteristic path length to random network was higher in SCI patients than in controls and reached statistical significance at 12%-13% of density (p<0.05, uncorrected).ConclusionThe graph theoretical approach in brain functional connectivity might be helpful to reveal the information processing after SCI. These findings imply that patients with SCI can build on preserved competent brain control. Further analyses, such as topological rearrangement and hub region identification, will be needed for better understanding of neuroplasticity in patients with SCI.

Exercise training reinstates cortico-cortical sensorimotor functional connectivity following striatal lesioning: development and application of a subregional-level analytic toolbox for perfusion autoradiographs of the rat brain.

Current rodent connectome projects are revealing brain structural connectivity with unprecedented resolution and completeness. How subregional structural connectivity relates to subregional functional interactions is an emerging research topic. We describe a method for standardized, mesoscopic-level data sampling from autoradiographic coronal sections of the rat brain, and for correlation-based analysis and intuitive display of cortico-cortical functional connectivity (FC) on a flattened cortical map. A graphic user interface “Cx-2D” allows for the display of significant correlations of individual regions-of-interest, as well as graph theoretical metrics across the cortex. Cx-2D was tested on an autoradiographic data set of cerebral blood flow (CBF) of rats that had undergone bilateral striatal lesions, followed by 4 weeks of aerobic exercise training or no exercise. Effects of lesioning and exercise on cortico-cortical FC were examined during a locomotor challenge in this rat model of Parkinsonism. Subregional FC analysis revealed a rich functional reorganization of the brain in response to lesioning and exercise that was not apparent in a standard analysis focused on CBF of isolated brain regions. Lesioned rats showed diminished degree centrality of lateral primary motor cortex, as well as neighboring somatosensory cortex—changes that were substantially reversed in lesioned rats following exercise training. Seed analysis revealed that exercise increased positive correlations in motor and somatosensory cortex, with little effect in non-sensorimotor regions such as visual, auditory, and piriform cortex. The current analysis revealed that exercise partially reinstated sensorimotor FC lost following dopaminergic deafferentation. Cx-2D allows for standardized data sampling from images of brain slices, as well as analysis and display of cortico-cortical FC in the rat cerebral cortex with potential applications in a variety of autoradiographic and histologic studies.

Examining the Relationship Between Road Structure and Burglary Risk Via Quantitative Network Analysis

To test the hypothesis that the spatial distribution of residential burglary is shaped by the configuration of the street network, as predicted by, for example, crime pattern theory. In particular, the study examines whether burglary risk is higher on street segments with higher usage potential. Residential burglary data for Birmingham (UK) are examined at the street segment level using a hierarchical linear model. Estimates of the usage of street segments are derived from the graph theoretical metric of betweenness, which measures how frequently segments feature in the shortest paths (those most likely to be used) through the network. Several variants of betweenness are considered. The geometry of street segments is also incorporated—via a measure of their linearity—as are several socio-demographic factors. As anticipated by theory, the measure of betweenness was found to be a highly-significant predictor of the burglary victimization count at the street segment level for all but one of the variants considered. The non-significant result was found for the most localized measure of betweenness considered. More linear streets were generally found to be at lower risk of victimization. Betweenness offers a more granular and objective means of measuring the street network than categorical classifications previously used, and its meaning links more directly to theory. The results provide support for crime pattern theory, suggesting a higher risk of burglary for streets with more potential usage. The apparent negative effect of linearity suggests the need for further research into the visual component of target choice, and the role of guardianship.

Representing connectivity: quantifying effective habitat availability based on area and connectivity for conservation status assessment and recovery.

We apply a comprehensive suite of graph theoretic metrics to illustrate how landscape connectivity can be effectively incorporated into conservation status assessments and in setting conservation objectives. These metrics allow conservation practitioners to evaluate and quantify connectivity in terms of representation, resiliency, and redundancy and the approach can be applied in spite of incomplete knowledge of species-specific biology and dispersal processes. We demonstrate utility of the graph metrics by evaluating changes in distribution and connectivity that would result from implementing two conservation plans for three endangered plant species (Erigeron parishii, Acanthoscyphus parishii var. goodmaniana, and Eriogonum ovalifolium var. vineum) relative to connectivity under current conditions. Although distributions of the species differ from one another in terms of extent and specific location of occupied patches within the study landscape, the spatial scale of potential connectivity in existing networks were strikingly similar for Erigeron and Eriogonum, but differed for Acanthoscyphus. Specifically, patches of the first two species were more regularly distributed whereas subsets of patches of Acanthoscyphus were clustered into more isolated components. Reserves based on US Fish and Wildlife Service critical habitat designation would not greatly contribute to maintain connectivity; they include 83–91% of the extant occurrences and >92% of the aerial extent of each species. Effective connectivity remains within 10% of that in the whole network for all species. A Forest Service habitat management strategy excluded up to 40% of the occupied habitat of each species resulting in both range reductions and loss of occurrences from the central portions of each species’ distribution. Overall effective network connectivity was reduced to 62–74% of the full networks. The distance at which each CHMS network first became fully connected was reduced relative to the full network in Erigeron and Acanthoscyphus due to exclusion of peripheral patches, but was slightly increased for Eriogonum. Distances at which networks were sensitive to loss of connectivity due to presence non-redundant connections were affected mostly for Acanthoscyphos. Of most concern was that the range of distances at which lack of redundancy yielded high risk was much greater than in the full network. Through this in-depth example evaluating connectivity using a comprehensive suite of developed graph theoretic metrics, we establish an approach as well as provide sample interpretations of subtle variations in connectivity that conservation managers can incorporate into planning.

Bayesian Inference of Information Theoretic Metrics of Anonymity

Information theoretic metrics is popular theory to measure anonymity. However the difficulty in getting the probability distribution of subjects hampers its practical usage. In this paper we propose a Bayesian inference method to tackle this problem. Our method makes it possible to compare the anonymity of different anonymous systems. We use this method to analyze Threshold Mix and point out different system parameters which do and do not have influence on anonymity.

Altered Development and Multifaceted Band-Specific Abnormalities of Resting State Networks in Autism

BackgroundExtensive evidence indicates that cortical connectivity patterns are abnormal in autism spectrum disorders (ASD), showing both overconnectivity and underconnectivity. Since, however, studies to date have focused on either spatial or spectral dimensions, but not both simultaneously, much remains unknown about the nature of these abnormalities. In particular, it remains unknown whether abnormal connectivity patterns in ASD are driven by specific frequency bands, by spatial network properties, or by some combination of these factors. MethodsMagnetoencephalography recordings (15 ASD, 15 control subjects) mapped back onto cortical space were used to study resting state networks in ASD with both spatial and spectral specificity. The data were quantified using graph theoretic metrics. ResultsThe two major factors that drove the nature of connectivity abnormalities in ASD were the mediating frequency band and whether the network included frontal nodes. These factors determined whether clustering and integration were increased or decreased in cortical resting state networks in ASD. These measures also correlated with abnormalities in the developmental trajectory of resting state networks in ASD. Lastly, these measures correlated with ASD severity in some frequency bands and spatially specific subnetworks. ConclusionsOur findings suggest that network abnormalities in ASD are widespread, are more likely in subnetworks that include the frontal lobe, and can be opposite in nature depending on the frequency band. These findings thus elucidate seemingly contradictory prior findings of both overconnectivity and underconnectivity in ASD.

The Alzheimer structural connectome: changes in cortical network topology with increased amyloid plaque burden.

To evaluate differences in the structural connectome among patients with normal cognition (NC), mild cognitive impairment (MCI), and Alzheimer disease (AD) and to determine associations between the structural connectome and cortical amyloid deposition. Patients enrolled in a multicenter biomarker study (Alzheimer's Disease Neuroimaging Initiative [ADNI] 2) who had both baseline diffusion-tensor (DT) and florbetapir positron emission tomography (PET) data at the time of data analyses in November 2012 were studied. All institutions received institutional review board approval. There were 102 patients in ADNI 2 who met criteria for analysis. Patients' T1-weighted images were automatically parcellated into cortical regions of interest. Standardized uptake value ratio (SUVr) was calculated from florbetapir PET images for composite cortical regions (frontal, cingulate, parietal, and temporal). Structural connectome graphs were created from DT images, and connectome topology was analyzed in each region by using graph theoretical metrics. Analysis of variance of structural connectome metrics and florbetapir SUVr across diagnostic group was performed. Linear mixed-effects models were fit to analyze the effect of florbetapir SUVr on structural connectome metrics. Diagnostic group (NC, MCI, or AD) was associated with changes in weighted structural connectome metrics, with decreases from the NC group to the MCI group to the AD group shown for (a) strength in the bilateral frontal, right parietal, and bilateral temporal regions (P < .05); (b) weighted local efficiency in the left temporal region (P < .05); and (c) weighted clustering coefficient in the bilateral frontal and left temporal regions (P < .05). Increased cortical florbetapir SUVr was associated with decreases in weighted structural connectome metrics; namely, strength (P = .00001), weighted local efficiency (P = .00001), and weighted clustering coefficient (P = .0006), independent of brain region. For every 0.1-unit increase in florbetapir SUVr, there was a 14% decrease in strength, an 11% decrease in weighted local efficiency, and a 9% decrease in weighted clustering coefficient, regardless of the analyzed cortical region or, in the case of weighted local efficiency and clustering coefficient, diagnostic group. Increased amyloid burden, as measured with florbetapir PET imaging, is related to changes in the topology of the large-scale cortical network architecture of the brain, as measured with graph theoretical metrics of DTI tractography, even in the preclinical stages of AD. Online supplemental material is available for this article.

Functional and Structural Network Impairment in Childhood Frontal Lobe Epilepsy

In childhood frontal lobe epilepsy (FLE), cognitive impairment and educational underachievement are serious, well-known co-morbidities. The broad scale of affected cognitive domains suggests wide-spread network disturbances that not only involves, but also extends beyond the frontal lobe. In this study we have investigated whole brain connectional properties of children with FLE in relation to their cognitive impairment and compared them with healthy controls. Functional connectivity (FC) of the networks was derived from dynamic fluctuations of resting state fMRI and structural connectivity (SC) was obtained from fiber tractograms of diffusion weighted MRI. The whole brain network was characterized with graph theoretical metrics and decomposed into modules. Subsequently, the graph metrics and the connectivity within and between modules were related to cognitive performance. Functional network disturbances in FLE were related to increased clustering, increased path length, and stronger modularity compared to healthy controls, which was accompanied by stronger within- and weaker between-module functional connectivity. Although structural path length and clustering appeared normal in children with FLE, structural modularity increased with stronger cognitive impairment. It is concluded that decreased coupling between large-scale functional network modules is a hallmark for impaired cognition in childhood FLE.

What is in a name? On the misuse of information theoretic dispersion measures as design complexity metrics

Many metrics of design complexity have been proposed in the literature. Of these, the most popular are information theoretic metrics, such as information content based on Suh's axiomatic theory and differential entropy based on Shannon's information theory. In this paper, we show that these metrics do not provide common sense measures of complexity, and they also do not possess proper mathematical properties. At best, they are geared towards measuring a designs goodness-of-fit rather than its complexity. At least in part, the inappropriate use of these metrics can be attributed to misuse of terms such as ‘entropy’ and ‘minimise information content’.

IDENTIFYING NEURAL NETWORK TOPOLOGIES THAT FOSTER DYNAMICAL COMPLEXITY

We use an ecosystem simulator capable of evolving arbitrary neural network topologies to explore the relationship between an information theoretic measure of the complexity of neural dynamics and several graph theoretical metrics calculated for the underlying network topologies. Evolutionary trends confirm and extend previous results demonstrating an evolutionary selection for complexity and small-world network properties during periods of behavioral adaptation. The resultant mapping of the space of network topologies occupied by the most complex networks yields new insights into the relationship between network structure and function. The highest complexity networks are found within limited numerical ranges of clustering coefficient, characteristic path length, small-world index, and global efficiency. The widths of these ranges vary from quite narrow to modest, and provide a guide to the most productive regions of the space of neural topologies in which to search for complexity. Our demonstration that evolution selects for complex dynamics and small-world networks helps explain biological evidence for these trends and provides evidence for selection of these characteristics based purely on network function—with no physical constraints on network structure—thus suggesting that functional and structural evolutionary pressures cooperate to produce brains optimized for adaptation to a complex, variable world.

Health Internet of Things: Metrics and methods for efficient data transfer

The rapid development of modern Information and Communication Technologies (ICTs) in recent years and their introduction into people’s daily lives worldwide, has led to new circumstances at all levels of the social environment. In health care in particular, sensors and data links offer potential for constant monitoring of patient’s symptoms and needs, in real time, enabling physicians to diagnose and monitor health problems wherever the patient is, either at home or outdoors. However, the use of Internet of Things concepts in the health domain does not come without extra data and therefore a data transfer cost overheads. To deal with these overheads, novel metrics, and methods are introduced in an attempt to maximize the capabilities and widen acceptance/usage provided by the Internet of Things. Without losing its generality, the method discussed is experimentally evaluated in the paradigm of the Health domain. The focus is on the need for an overview of available data formats and transmission methods and selection of the optimal combination, which can result to reduction/minimization of costs. An analytic methodology is presented backed with theoretical metrics and evaluated experimentally.

Probability Distribution of the Quality Factor of a Mode-Stirred Reverberation Chamber

We derive a probability distribution, confidence intervals and statistics of the quality ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> ) factor of an arbitrarily shaped mode-stirred reverberation chamber, based on ensemble distributions of an idealized random cavity field with assumed perfect stir efficiency. It is shown that <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> exhibits a Fisher-Snedecor F-distribution whose degrees of freedom are governed by the number of simultaneously excited cavity modes per stir state. The most probable value of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> is shown to be between a fraction 2/9 and 1 of its mean value, and between a fraction 4/9 and 1 of its asymptotic mean (composite <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> ) value. The arithmetic mean value is found to exceed the values of most other theoretical metrics for centrality of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> . For a rectangular cavity, we retrieve the known asymptotic expression for <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> in the limit of a highly overmoded regime.

Trading privacy with incentives in mobile commerce: A game theoretic approach

In mobile commerce, companies provide location based services to mobile users, who report their locations with a certain level of granularity to maintain a degree of anonymity. This level of granularity depends on their perceived risk as well as the incentives they receive in the form of monetary benefits or improved mobile services. This paper formulates a quantitative model in which information theoretic metrics such as entropy, quantify the anonymity level of mobile users. The individual perceived risks of users and the benefits they obtain are defined as functions of their chosen location information granularity. The interaction between the mobile commerce company and its users is investigated using mechanism design techniques as a privacy game. The user best responses and optimal strategies for the company are derived under budgetary constraints on incentives, which are provided to users in order to convince them to share their private information at the desired level of granularity. Information limitations in the system are analyzed to capture more realistic scenarios where the companies do not have access to user utility functions. Iterative distributed algorithm and regression learning methods are investigated to design mechanisms that overcome these limitations. The results obtained are demonstrated with a numerical example and simulations based on real GPS data.