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The weaponization of digital communications and social media to conduct disinformation campaigns at immense scale, speed, and reach presents new challenges to identify and counter hostile influence operations (IOs). This paper presents an end-to-end framework to automate detection of disinformation narratives, networks, and influential actors. The framework integrates natural language processing, machine learning, graph analytics, and a network causal inference approach to quantify the impact of individual actors in spreading IO narratives. We demonstrate its capability on real-world hostile IO campaigns with Twitter datasets collected during the 2017 French presidential elections and known IO accounts disclosed by Twitter over a broad range of IO campaigns (May 2007 to February 2020), over 50,000 accounts, 17 countries, and different account types including both trolls and bots. Our system detects IO accounts with 96% precision, 79% recall, and 96% area-under-the precision-recall (P-R) curve; maps out salient network communities; and discovers high-impact accounts that escape the lens of traditional impact statistics based on activity counts and network centrality. Results are corroborated with independent sources of known IO accounts from US Congressional reports, investigative journalism, and IO datasets provided by Twitter.

Gaussian beams describe the amplitude and phase of rays and are widely used to model acoustic propagation. This paper describes four new results in the theory of Gaussian beams. (1) A new version of the Červený equations for the amplitude and phase of Gaussian beams is developed by applying the equivalence of Hamilton–Jacobi theory with Jacobi's equation that connects Riemannian curvature to geodesic flow. Thus the paper makes a fundamental connection between Gaussian beams and an acoustic channel's so-called intrinsic Gaussian curvature from differential geometry. (2) A new formula π(c/c″)1/2 for the distance between convergence zones is derived and applied to the Munk and other well-known profiles. (3) A class of \"model spaces\" are introduced that connect the acoustics of ducting/divergence zones with the channel's Gaussian curvature K = cc″ – (c′)2. The model sound speed profiles (SSPs) yield constant Gaussian curvature in which the geometry of ducts corresponds to great circles on a sphere and convergence zones correspond to antipodes. The distance between caustics π(c/c″)1/2 is equated with an ideal hyperbolic cosine SSP duct. (4) An intrinsic version of Červený's formulae for the amplitude and phase of Gaussian beams is derived that does not depend on an extrinsic, arbitrary choice of coordinates such as range and depth. Direct comparisons are made between the computational frameworks used by the three different approaches to Gaussian beams: Snell's law, the extrinsic Frenet–Serret formulae, and the intrinsic Jacobi methods presented here. The relationship of Gaussian beams to Riemannian curvature is explained with an overview of the modern covariant geometric methods that provide a general framework for application to other special cases.

In this paper we develop new Newton and conjugate gradient algorithms on the Grassmann and Stiefel manifolds. These manifolds represent the constraints that arise in such areas as the symmetric eigenvalue problem, nonlinear eigenvalue problems, electronic structures computations, and signal processing. In addition to the new algorithms, we show how the geometrical framework gives penetrating new insights allowing us to create, understand, and compare algorithms. The theory proposed here provides a taxonomy for numerical linear algebra algorithms that provide a top level mathematical view of previously unrelated algorithms. It is our hope that developers of new algorithms and perturbation theories will benefit from the theory, methods, and examples in this paper.

Year-long classroom teaching experiments in two predominantly Latino low-socioeconomic-status (SES) urban classrooms (one English-speaking and one Spanish-speaking) sought to support first graders' thinking of 2-digit quantities as tens and ones. A model of a developmental sequence of conceptual structures for 2-digit numbers (the UDSSI triad model) is presented to describe children's thinking. By the end of the year, most of the children could accurately add and subtract 2-digit numbers that require trading (regrouping) by using drawings or objects and gave answers by using tens and ones on various tasks. Their performance was substantially above that reported in other studies for U. S. first graders of higher SES and for older U. S. children. Their responses looked more like those of East Asian children than of U. S. children in other studies.

The 1st Armored Division (1AD) completed National Training Center (NTC) rotation 24-03, the Army's first \"division in the dirt\" NTC rotation, which highlighted the crucible and challenges divisions will face in large-scale combat operations (LSCO). [...]during the first battle period, the 142nd DSSB occupied TV Hill, which is in open terrain located south of Life Support Area (LSA) Santa Fe. [...]a Russian command post was destroyed by Ukrainian fires, and the Russians' advance stalled due to their extended lines of communication. The 142nd DSSB staff focused heavily on developing analog products using operational graphics and measures, maps, and overlays by warfighting function in the event enemy fires successfully targeted our power generation or our command post decoys.

The weaponization of digital communications and social media to conduct disinformation campaigns at immense scale, speed, and reach presents new challenges to identify and counter hostile influence operations (IOs). This paper presents an end-to-end framework to automate detection of disinformation narratives, networks, and influential actors. The framework integrates natural language processing, machine learning, graph analytics, and a novel network causal inference approach to quantify the impact of individual actors in spreading IO narratives. We demonstrate its capability on real-world hostile IO campaigns with Twitter datasets collected during the 2017 French presidential elections, and known IO accounts disclosed by Twitter over a broad range of IO campaigns (May 2007 to February 2020), over 50,000 accounts, 17 countries, and different account types including both trolls and bots. Our system detects IO accounts with 96% precision, 79% recall, and 96% area-under-the-PR-curve, maps out salient network communities, and discovers high-impact accounts that escape the lens of traditional impact statistics based on activity counts and network centrality. Results are corroborated with independent sources of known IO accounts from U.S. Congressional reports, investigative journalism, and IO datasets provided by Twitter.

Statistical modeling of spatiotemporal phenomena often requires selecting a covariance matrix from a covariance class. Yet standard parametric covariance families can be insufficiently flexible for practical applications, while non-parametric approaches may not easily allow certain kinds of prior knowledge to be incorporated. We propose instead to build covariance families out of geodesic curves. These covariances offer more flexibility for problem-specific tailoring than classical parametric families, and are preferable to simple convex combinations. Once the covariance family has been chosen, one typically needs to select a representative member by solving an optimization problem, e.g., by maximizing the likelihood of a data set. We consider instead a differential geometric interpretation of this problem: minimizing the geodesic distance to a sample covariance matrix (``natural projection'). Our approach is consistent with the notion of distance employed to build the covariance family and does not require assuming a particular probability distribution for the data. We show that natural projection and maximum likelihood are locally equivalent up to second order. We also demonstrate that natural projection may yield more accurate estimates with noise-corrupted data.