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Performing statistical inference on collections of graphs is of import to many disciplines. Graph embedding, in which the vertices of a graph are mapped to vectors in a low-dimensional Euclidean space, has gained traction as a basic tool for graph analysis. Here we describe an omnibus embedding in which multiple graphs on the same vertex set are jointly embedded into a single space with a distinct representation for each graph. We prove a central limit theorem for this omnibus embedding and show that simultaneous embedding into a common space allows comparison of graphs without the need to perform pairwise alignments of graph embeddings. Experimental results demonstrate that the omnibus embedding improves upon existing methods. (Please note: per the D3M workshop organizers' request, this is an extended abstract of a paper that has already been posted to arXiv at https://arxiv.org/abs/1705.09355)

The ability to detect change-points in a dynamic network or a time series of graphs is an increasingly important task in many applications of the emerging discipline of graph signal processing. This paper formulates change-point detection as a hypothesis testing problem in terms of Stochastic Block Model time series. We analyze two classes of scan statistics, based on distinct underlying locality statistics presented in the literature. Our main contribution is the derivation of the limiting distributions and power characteristics of the competing scan statistics. Performance is compared theoretically, on synthetic data, and on the Enron email corpus. We demonstrate that both statistics are admissible in one simple setting, while one of the statistics is inadmissible in a second setting.

Given an attributed graph representation of data, vertex nomination works to find the group of vertices which are of interest, e.g., those vertices whose attributes are different from others', or the connection among those vertices are more frequent. In this paper we present an algorithm to estimate the power of nominating these interesting vertices. This algorithm is based on Wilcoxon rank sum test. It requires to embed graph vertices into a low dimensional space. Two graph embedding methods, adjacency spectral embedding and multidimensional scaling composed with canonical correlation analysis are employed. We investigate a case where two graphs are available for modeling the same objects in different spaces, and show the effects of data fusion on vertex nomination power.

This paper presents a novel antenna system that employs a "non- focused reflector" (NFR) to reconfigure the beams of communications payloads of HIEO (highly inclined elliptical orbit) and GEO (geo-stationary) satellites. The key advantages of the NFR are that it minimizes the number of feed array elements for a given coverage, has better scan performance, and has reduced complexity. Design examples for both HlEO and GEO satellites are shown indicating that the beams are fully reconfigurable on-orbit using the NFR with a small active array feed.

This paper addresses some of the recent developments at LMCSS in the area of multiple beam and reconfigurable beam antennas for communication satellite payloads. These advancements include (a) multiple aperture dual-band reflector antennas, (b) high efficiency horns covering 50% bandwidth, (c) a novel ?stepped-reflector antenna? (SRA) technology, and (d) reconfigurable beam antennas for HIEO and GEO satellites. It is shown that by combining the reflector improvements through the use of SRA with the feed improvements through the use of dual-band high efficiency horns (DBHEH), significant improvements in EIRP, G/T, and co-polar isolation (C/I) can be achieved. The SRA system produces ?flat-top? radiation patterns for receive beams and highly efficient Gaussian patterns for transmit beams over a geographic coverage as seen by the satellite. The DBHEH designs employ ?slope-discontinuities? to generate desired higher order modes over both transmit and receive bands. By employing a ?frequency-dependant? horn design for the DBHEH, it is shown that the step size can be significantly reduced and can be easily blended into the reflector surface for ease of fabrication. Detailed design of a K/Ka band MBA with about 68 spot beams is presented. The RF performance of this novel MBA has been evaluated and shows significant improvements in EIRP, G/T, and C/I in comparison with a conventional MBA. Comparison results of the advanced MBA with conventional MBA are presented in the paper. Design examples for both FSS and DBS satellites are discussed. A novel reconfigurable antenna suitable for HIEO and GEO satellites has been developed at LMCSS. It employs a non-focused reflector (NFR) antenna using a shaped mesh-reflector, and a small active feed array located in the focal-plane of the NFR in order to continuously reconfigure the beam(s), as the satellite goes through the HIEO orbit. The NFR approach has the advantages of reducing the number of feed array elements significantly while achieving the desired beam flexibility. Feed technology advancement for FSS and BSS satellites that includes high efficiency horns, trifurcated horns, feed networks, and trends in high power TVAC testing are briefly discussed.

This paper presents a novel "Stepped-Reflector Antenna" (SRA) suitable for multiple beam dual-band satellite communications. The SRA generates "flat-top" receive beams and highly efficient transmit beams over a geographic coverage region as seen by the satellite. It combines the reflector improvements through the use of stepped-regions with the feed horn advancements through the use of dual-band high efficiency horns (DBHEH) [1,2] in order to realize an efficient multiple beam antenna (MBA) system supporting both uplink and downlink frequencies simultaneously. It is shown that the SRA provides a congruent set of spot beams at both frequency bands with the benefits of significantly improved edge-of-coverage (EOC) gain, improved copolar isolation (C/I) among re-use beams, receive beam patterns that are less sensitive to pointing errors, and reduced number of reflector antennas when compared to conventional MBAs.

This paper presents a dual-band antenna system that is suitable for satellite communications at K/Ka-band frequencies. It employs a minimum number of reflectors, each being fed with multiple feed horns. It is shown that the MBA performance in terms of coverage gain and co-polar isolation can be significantly improved by using optimal designs for the feed horn and the reflector. The performance results of this MBA are compared with conventional designs and the trade-offs are discussed.