Robust reconstruction of sparse network dynamics

Reconstruction of the network interaction structure from multivariate time series is an important problem in multiple fields of science. This problem is ill-posed for large networks leading to the reconstruction of false interactions. We put forward the Ergodic Basis Pursuit (EBP) method that uses the network dynamics' statistical properties to ensure the exact reconstruction of sparse networks when a minimum length of time series is attained. We show that this minimum time series length scales quadratically with the node degree being probed and logarithmic with the network size. Our approach is robust against noise and allows us to treat the noise level as a parameter. We show the reconstruction power of the EBP in experimental multivariate time series from optoelectronic networks.Comment: 48 pages, 6 figure

A Unified Approach to Attractor Reconstruction

In the analysis of complex, nonlinear time series, scientists in a variety of disciplines have relied on a time delayed embedding of their data, i.e. attractor reconstruction. The process has focused primarily on heuristic and empirical arguments for selection of the key embedding parameters, delay and embedding dimension. This approach has left several long-standing, but common problems unresolved in which the standard approaches produce inferior results or give no guidance at all. We view the current reconstruction process as unnecessarily broken into separate problems. We propose an alternative approach that views the problem of choosing all embedding parameters as being one and the same problem addressable using a single statistical test formulated directly from the reconstruction theorems. This allows for varying time delays appropriate to the data and simultaneously helps decide on embedding dimension. A second new statistic, undersampling, acts as a check against overly long time delays and overly large embedding dimension. Our approach is more flexible than those currently used, but is more directly connected with the mathematical requirements of embedding. In addition, the statistics developed guide the user by allowing optimization and warning when embedding parameters are chosen beyond what the data can support. We demonstrate our approach on uni- and multivariate data, data possessing multiple time scales, and chaotic data. This unified approach resolves all the main issues in attractor reconstruction.Comment: 22 pages, revised version as submitted to CHAOS. Manuscript is currently under review. 4 Figures, 31 reference

Dynamic Bayesian networks in molecular plant science: inferring gene regulatory networks from multiple gene expression time series

To understand the processes of growth and biomass production in plants, we ultimately need to elucidate the structure of the underlying regulatory networks at the molecular level. The advent of high-throughput postgenomic technologies has spurred substantial interest in reverse engineering these networks from data, and several techniques from machine learning and multivariate statistics have recently been proposed. The present article discusses the problem of inferring gene regulatory networks from gene expression time series, and we focus our exposition on the methodology of Bayesian networks. We describe dynamic Bayesian networks and explain their advantages over other statistical methods. We introduce a novel information sharing scheme, which allows us to infer gene regulatory networks from multiple sources of gene expression data more accurately. We illustrate and test this method on a set of synthetic data, using three different measures to quantify the network reconstruction accuracy. The main application of our method is related to the problem of circadian regulation in plants, where we aim to reconstruct the regulatory networks of nine circadian genes in Arabidopsis thaliana from four gene expression time series obtained under different experimental conditions

Recurrence flow measure of nonlinear dependence

Couplings in complex real-world systems are often nonlinear and scale dependent. In many cases, it is crucial to consider a multitude of interlinked variables and the strengths of their correlations to adequately fathom the dynamics of a high-dimensional nonlinear system. We propose a recurrence-based dependence measure that quantifies the relationship between multiple time series based on the predictability of their joint evolution. The statistical analysis of recurrence plots (RPs) is a powerful framework in nonlinear time series analysis that has proven to be effective in addressing many fundamental problems, e.g., regime shift detection and identification of couplings. The recurrence flow through an RP exploits artifacts in the formation of diagonal lines, a structure in RPs that reflects periods of predictable dynamics. Using time-delayed variables of a deterministic uni-/multivariate system, lagged dependencies with potentially many time scales can be captured by the recurrence flow measure. Given an RP, no parameters are required for its computation. We showcase the scope of the method for quantifying lagged nonlinear correlations and put a focus on the delay selection problem in time-delay embedding which is often used for attractor reconstruction. The recurrence flow measure of dependence helps to identify non-uniform delays and appears as a promising foundation for a recurrence-based state space reconstruction algorithm

Predictive and Protective Factors for Partial Necrosis in DIEP Flap Breast Reconstruction. Does Nulliparity Bias Flap Viability?

Although success rate of deep inferior epigastric perforator (DIEP) flap breast reconstruction has greatly improved, complications still occasionally occur. Perfusion-related complications (PRCs) (ie, fat necrosis and partial flap necrosis) are the most frequent concern, affecting aesthetic final result of the reconstructed breast.The aim of our study was to retrospectively investigate 287 consecutive DIEP flap breast reconstructions to investigate predictive and protective factors for PRCs.From May 2004 to February 2012, 287 DIEP flap breast reconstructions were performed on 270 patients; 247 unilateral flaps, including Holm vascular zones I to III, were retrospectively selected and analyzed. Tobacco use, mean blood pressure over the first postoperative 48 hours, superficial epigastric vein drainage, medial/lateral row perforator, nulliparity, crystalloid versus combined crystalloid/colloid intravenous fluid infusion therapy, and learning curve were evaluated by univariate and multivariate logistic regression analyses.Perfusion-related complications occurred 32 (12.9%) times, 79 (31.9%) patients were smokers, 48 (19.4%) showed postoperative mean blood pressure less than 75 mm Hg, 29 (11.7%) were nulliparous, and 173 (70%) had superficial epigastric vein drainage. Selected perforators were 110 (44.5%) from lateral row, 137 (55.5%) from medial row; 91 (36.8%) received crystalloid fluid infusion, whereas 156 (63.2%) combined crystalloid/colloid fluid infusion. From univariate analysis emerged significance of nulliparity, perforator row and intravenous fluid infusion for PRC. Nevertheless, multivariate model confirmed only nulliparity as a significant risk factor (P = 0.029), although variable correlations to other predictors were found: both medial row perforator and combined crystalloid/colloid fluid infusion potentially decrease the PRC risk of 11.6% and 27.6%, respectively. Learning curve did not show significant decrease of PRC risk over time.Our study first proved nulliparity as a statistically significant predictor for PRCs in DIEP flap breast reconstruction, possibly due to different superficial abdominal perfusion between pluriparous and nulliparous women, with potential weaker pattern of perforators and smaller angiosomes in the latter. The choice of medial row perforators and combined crystalloid/colloid fluid infusion might reduce PRC risk

Multivariate Spatiotemporal Hawkes Processes and Network Reconstruction

There is often latent network structure in spatial and temporal data and the tools of network analysis can yield fascinating insights into such data. In this paper, we develop a nonparametric method for network reconstruction from spatiotemporal data sets using multivariate Hawkes processes. In contrast to prior work on network reconstruction with point-process models, which has often focused on exclusively temporal information, our approach uses both temporal and spatial information and does not assume a specific parametric form of network dynamics. This leads to an effective way of recovering an underlying network. We illustrate our approach using both synthetic networks and networks constructed from real-world data sets (a location-based social media network, a narrative of crime events, and violent gang crimes). Our results demonstrate that, in comparison to using only temporal data, our spatiotemporal approach yields improved network reconstruction, providing a basis for meaningful subsequent analysis --- such as community structure and motif analysis --- of the reconstructed networks