Network-adaptive robust penalized estimation of time-varying coefficient models with longitudinal data

On the use of correlation as a measure of network connectivity

In cognitive network neuroscience, the connectivity and community structure of the brain network is related to measures of cognitive performance, like attention and memory. Research in this emerging discipline has largely focused on two measures of connectivity—modularity and flexibility—which, for the most part, have been examined in isolation. The current project investigates the relationship between these two measures of connectivity and how they make separable contribution to predicting individual differences in performance on cognitive tasks. Using resting state fMRI data from 52 young adults, we show that flexibility and modularity are highly negatively correlated. We use a Brodmann parcellation of the fMRI data and a sliding window approach for calculation of the flexibility. We also demonstrate that flexibility and modularity make unique contributions to explain task performance, with a clear result showing that modularity, not flexibility, predicts performance for simple tasks and that flexibility plays a greater role in predicting performance on complex tasks that require cognitive control and executive functioning. The theory and results presented here allow for stronger links between measures of brain network connectivity and cognitive processes.

This paper explores measures of pedestrian accessibility and network connectivity with a network that includes pedestrian facilities in addition to the street network. Studies that focus on walkability usually use available street networks that do not include pedestrian-only facilities. The effect of missing pedestrian connections where the street network is richer than the pedestrian network has been examined in some studies, but the case of suburban environments with robust pedestrian networks has mostly been ignored. In the current study, various measures of connectivity and accessibility were compared between the pedestrian network and the street network in different suburban settings and for accessibility to different land use activities, such as schools and retail centers. Documenting the degree to which the pedestrian network enhanced pedestrian accessibility over the street network alone was motivated by the desire to inform research and to inform policy. Nine neighborhoods in the city of Davis, California, with typical suburban densities, a variety of street network types, and an extensive system of off-street bicycle and pedestrian facilities were used in the study. A network that included all minor and primary roads in the city plus pedestrian ways was also used. This network included 60 mi of off-street facilities and excluded freeways not open to pedestrians. Households were used as origins and schools and retail centers as destinations to demonstrate the effect of the pedestrian network on connectivity and accessibility in different parts of the city. The results of this study can be used to improve the measurement of built environment in studies of active travel and to increase understanding of the effect of the pedestrian network in the suburban environment.

An improved linear systems model of hydrothermal isometric tension testing to aid in assessing bone collagen quality: Effects of ribation and type-2 diabetes.

This chapter gives our measures of unconditional (or traditional) and conditional connectivity and fault-tolerance of two-dimensional k-covered wireless sensor networks. The latter measures are more realistic than the former as they impose a restriction on the subsets of sensors that can fail at the same time. Precisely, conditional measures take into consideration the inherent properties of k-covered wireless sensor networks, such as high sensor density and sensor heterogeneity. In particular, the neighbour set of a sensor is defined as a forbidden faulty set, and hence cannot fail at the same time. This concept defines the new measure of connectivity, called conditional connectivity, which seems to be more realistic.

This chapter gives our measures of unconditional (or traditional) and conditional connectivity and fault-tolerance of planar k-covered wireless sensor networks. The latter measures are more realistic than the former ones as they impose a restriction on the subsets of sensors that can fail at the same time. Precisely, conditional measures take into consideration the inherent properties of k-covered wireless sensor networks, such as high planar sensor density and sensor heterogeneity. In particular, the neighbor set of a sensor is defined as a forbidden faulty set, and hence cannot fail at the same time. This concept defines the new measure of connectivity, called conditional connectivity, which seems to be more realistic.

Brain function is often characterized by the connections and interactions between highly interconnected brain regions. Pathological disruptions in these networks often result in brain dysfunction, which manifests as brain disease. Typical analysis investigates disruptions in network connectivity based correlations between large brain regions. To obtain a more detailed description of disruptions in network connectivity, we propose a new method where functional nodes are identified in each region based on their maximum connectivity to another brain region in a given network. Since this method provides a unique approach to identifying functionally relevant nodes in a given network, we can provide a more detailed map of brain connectivity and determine new measures of network connectivity. We applied this method to resting state fMRI of Alzheimer's disease patients to validate our method and found decreased connectivity within the default mode network. In addition, new measure of network connectivity revealed a more detailed description of how the network connections deteriorate with disease progression. This suggests that analysis using key relative network hub regions based on regional correlation can be used to detect detailed changes in resting state network connectivity.

Networks are ubiquitous in many high impact domains. Among the various aspects of network studies, connectivity is the one that plays important role in many applications (e.g., information dissemination, robustness analysis, community detection, etc.). The diversified applications have spurred numerous connectivity measures. Accordingly, ad-hoc connectivity optimization methods are designed for each measure, making it hard to model and control the connectivity of the network in a uniformed framework. On the other hand, it is often impossible to maintain an accurate structure of the network due to network dynamics and noise in real applications, which would affect the accuracy of connectivity measures and the effectiveness of corresponding connectivity optimization methods. In this work, we aim to address the challenges on network connectivity by (1)unifying a wide range of classic network connectivity measures into one uniform model; (2)proposing effective approaches to infer connectivity measures and network structures from dynamic and incomplete input data, and (3) providing a general framework to optimize the connectivity measures in the network.

Despite intensive research in the area of network connectivity, there is an important category of problems that remain unsolved: how to characterize and measure the quality of connectivity of a wireless network which has a realistic number of nodes, not necessarily large enough to warrant the use of asymptotic analysis, and which has unreliable connections, reflecting the inherent unreliability of wireless communications? The quality of connectivity measures how easily and reliably a packet sent by a node can reach another node. It complements the use of capacity to measure the quality of a network in saturated traffic scenarios and provides an intuitive measure of the quality of (end-to-end) network connections. In this paper, we introduce a probabilistic connectivity matrix as a tool to measure the quality of network connectivity. Some interesting properties of the probabilistic connectivity matrix and their connections to the quality of connectivity are demonstrated. We demonstrate that the largest magnitude eigenvalue of the probabilistic connectivity matrix, which is positive, can serve as a good measure of the quality of network connectivity. We provide a flooding algorithm whereby the nodes repeatedly flood the network with packets, and by measuring just the number of packets a given node receives, the node is able to asymptotically estimate this largest eigenvalue.

Time varying coefficient models are widely employed in the realm of longitudinal and functional data analysis. The present paper primarily concentrates on quantile regression in time varying coefficient models, without making any assumptions about the error distribution or intra-subject dependence structure. Although the estimation process traditionally involves discontinuous indicator functions, we choose to employ smoothed estimating equations instead. We demonstrate that when the local linear method is utilised to estimate the undisclosed functions in time-varying coefficient models, for both sparse and dense longitudinal/functional data, the asymptotic results differ significantly between sparse and dense longitudinal/functional data scenarios. Leveraging the smoothed estimating equations, we retrieve a ‘sandwich’ formula for variance estimation and formulate methodologies that can acclimatise to both sparse and dense situations within a unified paradigm. To demonstrate the effectiveness of the proposed unified inference method, we conduct simulation studies and two real data analyses.

Asymmetric global network connectivities in the world city network, 2013

We addressed the principles of micro-level organization of neuronal circuits and explored how the neuronal morphology constrains this organization. Several studies have demonstrated the non-trivial properties of the network connectivity using in vitro recordings from multiple neurons [1-3], yet it is unclear to what extent this structure reflects reorganization caused by synaptic plasticity, and what is imposed by the morphological constraints. Two recent articles explored this issue using the simulated neural circuits and demonstrated the specific structural properties in those circuits [4,5]. We analyzed a model that emphasizes the role of single-cell morphology, a homogeneous population of neurons in a planar space without boundaries. Each neuron is composed of two displaced neurite fields defined on the limited support. A neurite field describes the likelihood of finding a neurite segment at a certain point in the plane. Using a proximity criterion (Peters' rule) the expected number of potential synapses is estimated between each pair of neurons. Alternatively, this number can be estimated from the realistic morphology of a simulated neuron, or from the morphologies reconstructed from in vitro/in vivo recordings. The number of potential synapses depends on the axon-dendrite distance, which leads to a definition of the expected radius. An axon-dendrite pair that is expected to form at least one synapse must be on a distance not larger than the effective radius. All considered statistical measures of network connectivity are expressed as the functions of the effective radius normalized with the neuron size. In this study, we considered the standard graph theoretic measures of network connectivity, the motif counts, clustering coefficient, path length, and small-world coefficient. It has been demonstrated that they have a significant impact on the population activity in simulated networks [6]. Changing the normalized effective radius from small ( 10) we vary the network properties between the two extremes. For the small values of the effective radius, the networks favor unidirectional connections and sparse local connectivity. The clustering coefficient and the path length are similar to those obtained in uniform random networks, i.e. in the networks independent of topology. For the large values of the effective radius, the local connectivity is dense with the majority of bidirectional connections. As the normalized effective radius increases, the clustering coefficient increases towards the values obtained for the networks with dominant local connectivity, while the path length remains close to the one of the uniform random networks. The normalized effective radius on the interval 1-2, provides the biggest variability of connectivity patterns and the optimized properties relevant for the information transfer.

The growing popularity of online social networks gave researchers access to large amount of network data and renewed interest in methods for automatic community detection. Existing algorithms, including the popular modularity-optimization methods, look for regions of the network that are better connected internally, e.g., have higher than expected number of edges within them. We believe, however, that edges do not give the true measure of network connectivity. Instead, we argue that influence, which we define as the number of paths, of any length, that exist between two nodes, gives a better measure of network connectivity. We use the influence metric to partition a network into groups or communities by looking for regions of the network where nodes have more influence over each other than over nodes outside the community. We evaluate our approach on several networks and show that it often outperforms the edge-based modularity algorithm.

Cells self-organize into functional, ordered structures during tissue morphogenesis, a process that is evocative of colloidal self-assembly into engineered soft materials. Understanding how intercellular mechanical interactions may drive the formation of ordered and functional multicellular structures is important in developmental biology and tissue engineering. Here, by combining an agent-based model for contractile cells on elastic substrates with endothelial cell culture experiments, we show that substrate deformation-mediated mechanical interactions between cells can cluster and align them into branched networks. Motivated by the structure and function of vasculogenic networks, we predict how measures of network connectivity like percolation probability and fractal dimension as well as local morphological features including junctions, branches, and rings depend on cell contractility and density and on substrate elastic properties including stiffness and compressibility. We predict and confirm with experiments that cell network formation is substrate stiffness dependent, being optimal at intermediate stiffness. We also show the agreement between experimental data and predicted cell cluster types by mapping a combined phase diagram in cell density substrate stiffness. Overall, we show that long-range, mechanical interactions provide an optimal and general strategy for multicellular self-organization, leading to more robust and efficient realizations of space-spanning networks than through just local intercellular interactions.

Shrinkage estimation of network spillovers with factor structured errors