Matchability of heterogeneous networks pairs

We consider the problem of graph matchability in non-identically distributed networks. In a general class of edge-independent networks, we demonstrate that graph matchability is almost surely lost when matching the networks directly, and is almost perfectly recovered when first centering the networks using Universal Singular Value Thresholding before matching. These theoretical results are then demonstrated in both real and synthetic simulation settings. We also recover analogous core-matchability results in a very general core-junk network model, wherein some vertices do not correspond between the graph pair.First author draf

Universally Consistent Latent Position Estimation and Vertex Classification for Random Dot Product Graphs

In this work we show that, using the eigen-decomposition of the adjacency matrix, we can consistently estimate latent positions for random dot product graphs provided the latent positions are i.i.d. from some distribution. If class labels are observed for a number of vertices tending to infinity, then we show that the remaining vertices can be classified with error converging to Bayes optimal using the $k$-nearest-neighbors classification rule. We evaluate the proposed methods on simulated data and a graph derived from Wikipedia

Matched Filters for Noisy Induced Subgraph Detection

The problem of finding the vertex correspondence between two noisy graphs with different number of vertices where the smaller graph is still large has many applications in social networks, neuroscience, and computer vision. We propose a solution to this problem via a graph matching matched filter: centering and padding the smaller adjacency matrix and applying graph matching methods to align it to the larger network. The centering and padding schemes can be incorporated into any algorithm that matches using adjacency matrices. Under a statistical model for correlated pairs of graphs, which yields a noisy copy of the small graph within the larger graph, the resulting optimization problem can be guaranteed to recover the true vertex correspondence between the networks. However, there are currently no efficient algorithms for solving this problem. To illustrate the possibilities and challenges of such problems, we use an algorithm that can exploit a partially known correspondence and show via varied simulations and applications to {\it Drosophila} and human connectomes that this approach can achieve good performance.Comment: 41 pages, 7 figure

Reinventing Cybersecurity Internships During the COVID-19 Pandemic

The Cybersecurity Ambassador Program provides professional skills training for emerging cybersecurity professionals remotely. The goal is to reach out to underrepresented populations who may use Federal Work-Study (FWS) or grant sponsored internships to participate. Cybersecurity Ambassadors (CAs) develop skills that will serve them well as cybersecurity workers prepared to do research, lead multidisciplinary, technical teams, and educate stakeholders and community members. CAP also reinforces leadership skills so that the next generation of cybersecurity professionals becomes a sustainable source of management talent for the program and profession. The remote curriculum innovatively builds non-technical professional skills (communications, teamwork, leadership) for cybersecurity research through student-led applied research and creating community-focused workshops. These student-produced workshops are in phishing, identity and privacy cyber safety, social media safety, and everyday home cyber safety. The CAs tailor the program to a particularly vulnerable population such as older adults, students, veterans, or similar people that make up most workshop participants. At this time, the data shows that this pedagogical approach to curriculum development, grounded in the Ground Truth Expertise Development Model (GTEDM), is a unique methodology. This curriculum teaches cybersecurity interns with key non-technical but critical KSAs for cybersecurity professional development has proved to be a factor in accelerated hiring for program participants

Exploring the Value of Non-Technical Knowledge, Skills, and Abilities (KSAs) to Cybersecurity Hiring Managers

Industry's demand for cybersecurity workers with non-technical knowledge, skills, and abilities (KSAs) that complement technical prowess is not new. The purpose of this study was to connect with cybersecurity practitioners to determine which non-technical KSAs should be emphasized by educators to help meet workforce demands. This research applies a novel application of the Ground Truth Expertise Development Model (GTEDM) for exploring suitable non-technical and particularly soft KSAs necessary for cybersecurity professional development programs. This study focused on the definition and competency determination step and provided foundational KSA prioritization for further research. The field overwhelmingly agreed that non-technical skills were essential to a cybersecurity worker's success. The qualitative process produced three themes as non-technical KSA areas of the most significant import to the cybersecurity field. These KSA themes required included critically using information, communications skills, and collaboration to pursue customer/client success. The findings produce a more comprehensive list of hard, soft, and mixed non-technical skills that will benefit the public, private, and academic sector organizations as they develop cybersecurity curricula

Maximum Likelihood Estimation and Graph Matching in Errorfully Observed Networks

Given a pair of graphs with the same number of vertices, the inexact graph matching problem consists in finding a correspondence between the vertices of these graphs that minimizes the total number of induced edge disagreements. We study this problem from a statistical framework in which one of the graphs is an errorfully observed copy of the other. We introduce a corrupting channel model, and show that in this model framework, the solution to the graph matching problem is a maximum likelihood estimator. Necessary and sufficient conditions for consistency of this MLE are presented, as well as a relaxed notion of consistency in which a negligible fraction of the vertices need not be matched correctly. The results are used to study matchability in several families of random graphs, including edge independent models, random regular graphs and small-world networks. We also use these results to introduce measures of matching feasibility, and experimentally validate the results on simulated and real-world networks