Multi-Sensor Multi-Scan Radar Sensing of Multiple Extended Targets

We propose an efficient solution to the state estimation problem in multi-scan multi-sensor multiple extended target sensing scenarios. We first model the measurement process by a doubly inhomogeneous-generalized shot noise Cox process and then estimate the parameters using a jump Markov chain Monte Carlo sampling technique. The proposed approach scales linearly in the number of measurements and can take spatial properties of the sensors into account, herein, sensor noise covariance, detection probability, and resolution. Numerical experiments using radar measurement data suggest that the algorithm offers improvements in high clutter scenarios with closely spaced targets over state-of-the-art clustering techniques used in existing multiple extended target tracking algorithms

Testing goodness of fit for point processes via topological data analysis

We introduce tests for the goodness of fit of point patterns via methods from topological data analysis. More precisely, the persistent Betti numbers give rise to a bivariate functional summary statistic for observed point patterns that is asymptotically Gaussian in large observation windows. We analyze the power of tests derived from this statistic on simulated point patterns and compare its performance with global envelope tests. Finally, we apply the tests to a point pattern from an application context in neuroscience. As the main methodological contribution, we derive sufficient conditions for a functional central limit theorem on bounded persistent Betti numbers of point processes with exponential decay of correlations.Comment: 34 pages, 8 figure

A Unified Approach for Multi-Scale Synchronous Correlation Search in Big Time Series -- Full Version

The wide deployment of IoT sensors has enabled the collection of very big time series across different domains, from which advanced analytics can be performed to find unknown relationships, most importantly the correlations between them. However, current approaches for correlation search on time series are limited to only a single temporal scale and simple types of relations, and cannot handle noise effectively. This paper presents the integrated SYnchronous COrrelation Search (iSYCOS) framework to find multi-scale correlations in big time series. Specifically, iSYCOS integrates top-down and bottom-up approaches into a single auto-configured framework capable of efficiently extracting complex window-based correlations from big time series using mutual information (MI). Moreover, iSYCOS includes a novel MI-based theory to identify noise in the data, and is used to perform pruning to improve iSYCOS performance. Besides, we design a distributed version of iSYCOS that can scale out in a Spark cluster to handle big time series. Our extensive experimental evaluation on synthetic and real-world datasets shows that iSYCOS can auto-configure on a given dataset to find complex multi-scale correlations. The pruning and optimisations can improve iSYCOS performance up to an order of magnitude, and the distributed iSYCOS can scale out linearly on a computing cluster.Comment: 18 page

Using the R Package Spatstat to Assess Inhibitory Effects of Microregional Hypoxia on the Infiltration of Cancers of the Head and Neck Region by Cytotoxic T Lymphocytes

(1) Background: The immune system has physiological antitumor activity, which is partially mediated by cytotoxic T lymphocytes (CTL). Tumor hypoxia, which is highly prevalent in cancers of the head and neck region, has been hypothesized to inhibit the infiltration of tumors by CTL. In situ data validating this concept have so far been based solely upon the visual assessment of the distribution of CTL. Here, we have established a set of spatial statistical tools to address this problem mathematically and tested their performance. (2) Patients and Methods: We have analyzed regions of interest (ROI) of 22 specimens of cancers of the head and neck region after 4-plex immunofluorescence staining and whole-slide scanning. Single cell-based segmentation was carried out in QuPath. Specimens were analyzed with the endpoints clustering and interactions between CTL, normoxic, and hypoxic tumor areas, both visually and using spatial statistical tools implemented in the R package Spatstat. (3) Results: Visual assessment suggested clustering of CTL in all instances. The visual analysis also suggested an inhibitory effect between hypoxic tumor areas and CTL in a minority of the whole-slide scans (9 of 22, 41%). Conversely, the objective mathematical analysis in Spatstat demonstrated statistically significant inhibitory interactions between hypoxia and CTL accumulation in a substantially higher number of specimens (16 of 22, 73%). It showed a similar trend in all but one of the remaining samples. (4) Conclusion: Our findings provide non-obvious but statistically rigorous evidence of inhibition of CTL infiltration into hypoxic tumor subregions of cancers of the head and neck. Importantly, these shielded sites may be the origin of tumor recurrences. We provide the methodology for the transfer of our statistical approach to similar questions. We discuss why versions of the Kcross and pcf.cross functions may be the methods of choice among the repertoire of statistical tests in Spatstat for this type of analysis

The Accumulated Persistence Function, a New Useful Functional Summary Statistic for Topological Data Analysis, With a View to Brain Artery Trees and Spatial Point Process Applications

We start with a simple introduction to topological data analysis where the most popular tool is called a persistence diagram. Briefly, a persistence diagram is a multiset of points in the plane describing the persistence of topological features of a compact set when a scale parameter varies. Since statistical methods are difficult to apply directly on persistence diagrams, various alternative functional summary statistics have been suggested, but either they do not contain the full information of the persistence diagram or they are two-dimensional functions. We suggest a new functional summary statistic that is one-dimensional and hence easier to handle, and which under mild conditions contains the full information of the persistence diagram. Its usefulness is illustrated in statistical settings concerned with point clouds and brain artery trees. The supplementary materials include additional methods and examples, technical details, and the R code used for all examples

The Accumulated Persistence Function, a New Useful Functional Summary Statistic for Topological Data Analysis, With a View to Brain Artery Trees and Spatial Point Process Applications

We start with a simple introduction to topological data analysis where the most popular tool is called a persistence diagram. Briefly, a persistence diagram is a multiset of points in the plane describing the persistence of topological features of a compact set when a scale parameter varies. Since statistical methods are difficult to apply directly on persistence diagrams, various alternative functional summary statistics have been suggested, but either they do not contain the full information of the persistence diagram or they are two-dimensional functions. We suggest a new functional summary statistic that is one-dimensional and hence easier to handle, and which under mild conditions contains the full information of the persistence diagram. Its usefulness is illustrated in statistical settings concerned with point clouds and brain artery trees. The supplementary materials include additional methods and examples, technical details, and the R code used for all examples

The accumulated persistence function, a new useful functional summary statistic for topological data analysis, with a view to brain artery trees and spatial point process applications

We start with a simple introduction to topological data analysis where the most popular tool is called a persistence diagram. Briefly, a persistence diagram is a multiset of points in the plane describing the persistence of topological features of a compact set when a scale parameter varies. Since statistical methods are difficult to apply directly on persistence diagrams, various alternative functional summary statistics have been suggested, but either they do not contain the full information of the persistence diagram or they are two-dimensional functions. We suggest a new functional summary statistic that is one-dimensional and hence easier to handle, and which under mild conditions contains the full information of the persistence diagram. Its usefulness is illustrated in statistical settings concerned with point clouds and brain artery trees. The supplementary materials include additional methods and examples, technical details, and the R-code used for all examples