Graphical Modeling for Multivariate Hawkes Processes with Nonparametric Link Functions

Hawkes (1971) introduced a powerful multivariate point process model of mutually exciting processes to explain causal structure in data. In this paper it is shown that the Granger causality structure of such processes is fully encoded in the corresponding link functions of the model. A new nonparametric estimator of the link functions based on a time-discretized version of the point process is introduced by using an infinite order autoregression. Consistency of the new estimator is derived. The estimator is applied to simulated data and to neural spike train data from the spinal dorsal horn of a rat.Comment: 20 pages, 4 figure

The affinely invariant distance correlation

Sz\'{e}kely, Rizzo and Bakirov (Ann. Statist. 35 (2007) 2769-2794) and Sz\'{e}kely and Rizzo (Ann. Appl. Statist. 3 (2009) 1236-1265), in two seminal papers, introduced the powerful concept of distance correlation as a measure of dependence between sets of random variables. We study in this paper an affinely invariant version of the distance correlation and an empirical version of that distance correlation, and we establish the consistency of the empirical quantity. In the case of subvectors of a multivariate normally distributed random vector, we provide exact expressions for the affinely invariant distance correlation in both finite-dimensional and asymptotic settings, and in the finite-dimensional case we find that the affinely invariant distance correlation is a function of the canonical correlation coefficients. To illustrate our results, we consider time series of wind vectors at the Stateline wind energy center in Oregon and Washington, and we derive the empirical auto and cross distance correlation functions between wind vectors at distinct meteorological stations.Comment: Published in at http://dx.doi.org/10.3150/13-BEJ558 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Dependencies in Complex Systems

A task in statistics is to find meaningful associations or dependencies between multivariate random variables or in multivariate, time-dependent stochastic processes. Hawkes (1971) introduced the powerful multivariate point process model of mutually exciting processes (Hawkes model) to explain causal structure in data. Therefore, we discuss several causality concepts and show that causal structure is fully encoded in the corresponding Hawkes kernels. Hence, for causal inference and for establishing graphical models induced by causality it is necessary to estimate the Hawkes kernels. We provide a nonparametric, consistent and asymptotically normal estimator of the Hawkes kernels depending on the increments on a time scale with mesh $\Delta$ using methods from infinite order regression and time series analysis. To illustrate our results we apply our method to EEG data from the spinal dorsal horn of a rat. To tackle the problem for random samples of random vectors we examine a new dependence measure, namely distance correlation (Sz\'ekely, Rizzo and Bakirov; 2007). Distance correlation provides a strikingly simple sample version in order to test for independence between two random vectors of arbitrary dimensions and finite first moments. However, distance correlation is not well understood on the population side and it fails to be invariant under the group of all invertible affine transformations. Hence, we introduce the affinely invariant distance correlation and compute the analytic usual distance correlation and affinely invariant distance correlation in various settings: for multivariate normal distributions and for Lancaster probabilities (e.g. the bivariate gamma distribution) explicitly. Furthermore, we generalize an integral which is at the core of distance correlation

Introducing EDEN ISS - A European project on advancing plant cultivation technologies and operations

Plant cultivation in large-scale closed environments is challenging and several key technologies necessary for space-based plant production are not yet space-qualified or remain in early stages of development. The EDEN ISS project foresees development and demonstration of higher plant cultivation technologies, suitable for future deployment on the International Space Station and from a long-term perspective, within Moon and Mars habitats. The EDEN ISS consortium will design and test essential plant cultivation technologies using an International Standard Payload Rack form factor cultivation system for potential testing on-board the International Space Station. Furthermore, a Future Exploration Greenhouse will be designed with respect to future planetary bio-regenerative life support system deployments. The technologies will be tested in a laboratory environment as well as at the highly-isolated German Antarctic Neumayer Station III. A small and mobile container-sized test facility will be built in order to provide realistic mass flow relationships. In addition to technology development and validation, food safety and plant handling procedures will be developed. This paper describes the goals and objectives of EDEN ISS and the different project phases and milestones. Furthermore, the project consortium will be introduced and the role of each partner within the project is explained

Immobility-associated thromboprotection is conserved across mammalian species from bear to human

Venous thromboembolism (VTE) comprising deep venous thrombosis and pulmonary embolism is a major cause of morbidity and mortality. Short-term immobility-related conditions are a major risk factor for the development of VTE. Paradoxically, long-term immobilized free-ranging hibernating brown bears and paralyzed spinal cord injury (SCI) patients are protected from VTE. Here we aimed to identify mechanisms of immobility-associated VTE protection in a cross-species approach. Mass spectrometry-based proteomics revealed an antithrombotic signature in platelets of hibernating brown bears with heat shock protein 47 (HSP47) as most substantially reduced protein. HSP47 downregulation or ablation attenuated immune cell activation and NET formation, contributing to thromboprotection in bears, SCI patients and mice. This cross-species conserved platelet signature may give rise to antithrombotic therapeutics and prognostic markers beyond immobility-associated VTE

Searching for backbones — an efficient parallel algorithm for the traveling salesman problem

The Traveling Salesman Problem (TSP) plays an important role in Operations Research, Applied Mathematics and Computational Physics. We investigated it using a stochastic approach. Studying several solutions of a special TSP we found that many parts of a good solution are the same in all other good solutions for this problem. In this paper we discuss an efficient parallel method to reduce the TSP to a smaller one by finding these backbones and eliminating them to get even better solutions in a very short time and a few observables of interest corresponding to this parallel approach