Unified functional network and nonlinear time series analysis for complex systems science: The pyunicorn package

We introduce the \texttt{pyunicorn} (Pythonic unified complex network and recurrence analysis toolbox) open source software package for applying and combining modern methods of data analysis and modeling from complex network theory and nonlinear time series analysis. \texttt{pyunicorn} is a fully object-oriented and easily parallelizable package written in the language Python. It allows for the construction of functional networks such as climate networks in climatology or functional brain networks in neuroscience representing the structure of statistical interrelationships in large data sets of time series and, subsequently, investigating this structure using advanced methods of complex network theory such as measures and models for spatial networks, networks of interacting networks, node-weighted statistics or network surrogates. Additionally, \texttt{pyunicorn} provides insights into the nonlinear dynamics of complex systems as recorded in uni- and multivariate time series from a non-traditional perspective by means of recurrence quantification analysis (RQA), recurrence networks, visibility graphs and construction of surrogate time series. The range of possible applications of the library is outlined, drawing on several examples mainly from the field of climatology.Comment: 28 pages, 17 figure

Statistical Mechanics and Information-Theoretic Perspectives on Complexity in the Earth System

Peer reviewedPublisher PD

The Embedding Capacity of Information Flows Under Renewal Traffic

Given two independent point processes and a certain rule for matching points between them, what is the fraction of matched points over infinitely long streams? In many application contexts, e.g., secure networking, a meaningful matching rule is that of a maximum causal delay, and the problem is related to embedding a flow of packets in cover traffic such that no traffic analysis can detect it. We study the best undetectable embedding policy and the corresponding maximum flow rate ---that we call the embedding capacity--- under the assumption that the cover traffic can be modeled as arbitrary renewal processes. We find that computing the embedding capacity requires the inversion of very structured linear systems that, for a broad range of renewal models encountered in practice, admits a fully analytical expression in terms of the renewal function of the processes. Our main theoretical contribution is a simple closed form of such relationship. This result enables us to explore properties of the embedding capacity, obtaining closed-form solutions for selected distribution families and a suite of sufficient conditions on the capacity ordering. We evaluate our solution on real network traces, which shows a noticeable match for tight delay constraints. A gap between the predicted and the actual embedding capacities appears for looser constraints, and further investigation reveals that it is caused by inaccuracy of the renewal traffic model rather than of the solution itself.Comment: Sumbitted to IEEE Trans. on Information Theory on March 10, 201

A Review of Atrial Fibrillation Detection Methods as a Service

Atrial Fibrillation (AF) is a common heart arrhythmia that often goes undetected, and even if it is detected, managing the condition may be challenging. In this paper, we review how the RR interval and Electrocardiogram (ECG) signals, incorporated into a monitoring system, can be useful to track AF events. Were such an automated system to be implemented, it could be used to help manage AF and thereby reduce patient morbidity and mortality. The main impetus behind the idea of developing a service is that a greater data volume analyzed can lead to better patient outcomes. Based on the literature review, which we present herein, we introduce the methods that can be used to detect AF efficiently and automatically via the RR interval and ECG signals. A cardiovascular disease monitoring service that incorporates one or multiple of these detection methods could extend event observation to all times, and could therefore become useful to establish any AF occurrence. The development of an automated and efficient method that monitors AF in real time would likely become a key component for meeting public health goals regarding the reduction of fatalities caused by the disease. Yet, at present, significant technological and regulatory obstacles remain, which prevent the development of any proposed system. Establishment of the scientific foundation for monitoring is important to provide effective service to patients and healthcare professionals

Time-Varying Graphs and Dynamic Networks

The past few years have seen intensive research efforts carried out in some apparently unrelated areas of dynamic systems -- delay-tolerant networks, opportunistic-mobility networks, social networks -- obtaining closely related insights. Indeed, the concepts discovered in these investigations can be viewed as parts of the same conceptual universe; and the formal models proposed so far to express some specific concepts are components of a larger formal description of this universe. The main contribution of this paper is to integrate the vast collection of concepts, formalisms, and results found in the literature into a unified framework, which we call TVG (for time-varying graphs). Using this framework, it is possible to express directly in the same formalism not only the concepts common to all those different areas, but also those specific to each. Based on this definitional work, employing both existing results and original observations, we present a hierarchical classification of TVGs; each class corresponds to a significant property examined in the distributed computing literature. We then examine how TVGs can be used to study the evolution of network properties, and propose different techniques, depending on whether the indicators for these properties are a-temporal (as in the majority of existing studies) or temporal. Finally, we briefly discuss the introduction of randomness in TVGs.Comment: A short version appeared in ADHOC-NOW'11. This version is to be published in Internation Journal of Parallel, Emergent and Distributed System

Publications of the Jet Propulsion Laboratory July 1965 through July 1966

Bibliography on Jet Propulsion Laboratory technical reports and memorandums, space programs summary, astronautics information, and literature searche

Geometric deep learning: going beyond Euclidean data

Many scientific fields study data with an underlying structure that is a non-Euclidean space. Some examples include social networks in computational social sciences, sensor networks in communications, functional networks in brain imaging, regulatory networks in genetics, and meshed surfaces in computer graphics. In many applications, such geometric data are large and complex (in the case of social networks, on the scale of billions), and are natural targets for machine learning techniques. In particular, we would like to use deep neural networks, which have recently proven to be powerful tools for a broad range of problems from computer vision, natural language processing, and audio analysis. However, these tools have been most successful on data with an underlying Euclidean or grid-like structure, and in cases where the invariances of these structures are built into networks used to model them. Geometric deep learning is an umbrella term for emerging techniques attempting to generalize (structured) deep neural models to non-Euclidean domains such as graphs and manifolds. The purpose of this paper is to overview different examples of geometric deep learning problems and present available solutions, key difficulties, applications, and future research directions in this nascent field