Unitary equivalence to a truncated Toeplitz operator: analytic symbols

Unlike Toeplitz operators on $H^2$, truncated Toeplitz operators do not have a natural matricial characterization. Consequently, these operators are difficult to study numerically. In this note we provide criteria for a matrix with distinct eigenvalues to be unitarily equivalent to a truncated Toeplitz operator having an analytic symbol. This test is constructive and we illustrate it with several examples. As a byproduct, we also prove that every complex symmetric operator on a Hilbert space of dimension $\leq 3$ is unitarily equivalent to a direct sum of truncated Toeplitz operators.Comment: 15 page

RascalC: A Jackknife Approach to Estimating Single and Multi-Tracer Galaxy Covariance Matrices

To make use of clustering statistics from large cosmological surveys, accurate and precise covariance matrices are needed. We present a new code to estimate large scale galaxy two-point correlation function (2PCF) covariances in arbitrary survey geometries that, due to new sampling techniques, runs $\sim 10^4$ times faster than previous codes, computing finely-binned covariance matrices with negligible noise in less than 100 CPU-hours. As in previous works, non-Gaussianity is approximated via a small rescaling of shot-noise in the theoretical model, calibrated by comparing jackknife survey covariances to an associated jackknife model. The flexible code, RascalC, has been publicly released, and automatically takes care of all necessary pre- and post-processing, requiring only a single input dataset (without a prior 2PCF model). Deviations between large scale model covariances from a mock survey and those from a large suite of mocks are found to be be indistinguishable from noise. In addition, the choice of input mock are shown to be irrelevant for desired noise levels below $\sim 10^5$ mocks. Coupled with its generalization to multi-tracer data-sets, this shows the algorithm to be an excellent tool for analysis, reducing the need for large numbers of mock simulations to be computed.Comment: 29 pages, 8 figures. Accepted by MNRAS. Code is available at http://github.com/oliverphilcox/RascalC with documentation at http://rascalc.readthedocs.io

Assessing Changeability in Aerospace Systems Architecting and Design Using Dynamic Multi-Attribute Tradespace Exploration

A framework for assessing changeability in the context of dynamic Multi-Attribute Tradespace Exploration (MATE) is proposed and applied to three aerospace systems. The framework consists of two parts. First, changeability concepts such as flexibility, scalability, and robustness are defined in a value-centric context. These system properties are shown to relate “real-space to value-space” dynamic mappings to stakeholder-defined subjective “acceptable cost” thresholds. Second, network analysis is applied to a series of temporally linked tradespaces, allowing for the quantification of changeability as a decision metric for comparison across system architecture and design options. The quantifiable is defined as the filtered outdegree of each design node in a tradespace network formed by linking design options through explicitly defined prospective transition paths. Each of the system application studies are assessed in the two part framework and within each study, observations are made regarding the changeability of various design options. The three system applications include a hypothetical low Earth orbit satellite mission, a currently deployed weapon system, and a proposed large astronomical on-orbit observatory. Preliminary cross-application observations are made regarding the embedding of changeability into the system architecture or design. Results suggest that the low Earth orbit satellite mission can increase its changeability by having the ability to readily change its orbit. The weapon system can increase its changeability by continuing to embrace modularity, use of commercial off-the-shelf parts (COTS), and simple, excess capacity interfaces. The large astronomical observatory can increase its potential changeability by having the ability to reconfigure its physical payloads and reschedule its observing tasks. The analysis approach introduced in this paper is shown to be a powerful concept for focusing discussion, design, and assessment of the changeability of aerospace systems

Pervasive Foreshock Activity Across Southern California

Foreshocks have been documented as preceding less than half of all mainshock earthquakes. These observations are difficult to reconcile with laboratory earthquake experiments and theoretical models of earthquake nucleation, which both suggest that foreshock activity should be nearly ubiquitous. Here we use a state‐of‐the‐art, high‐resolution earthquake catalog to study foreshock sequences of magnitude M4 and greater mainshocks in southern California from 2008–2017. This highly complete catalog provides a new opportunity to examine smaller magnitude precursory seismicity. Seventy‐two percent of mainshocks within this catalog are preceded by foreshock activity that is significantly elevated compared to the local background seismicity rate. Foreshock sequences vary in duration from several days to weeks, with a median of 16.6 days. The results suggest that foreshock occurrence in nature is more prevalent than previously thought and that our understanding of earthquake nucleation may improve in tandem with advances in our ability to detect small earthquakes

Defining System Changeability: Reconciling Flexibility, Adaptability, Scalability, and Robustness for Maintaining System Lifecycle Value

Designing and maintaining systems in a dynamic contemporary environment requires a rethinking of how systems provide value to stakeholders over time. Classically, two different approaches to promoting value sustainment may include developing either alterable or robust systems. The first accomplishes value delivery through altering the system to meet new needs, while the second accomplishes value delivery through maintaining a system to meet needs in spite of changes. The definitions of flexibility, adaptability, scalability, and robustness are shown to be different parts of the core concept of “changeability,” which can be described by three aspects: change agents, change effects, and change mechanisms. Cast in terms of system parameter changes, flexibility and adaptability are shown to relate to the origin of the change agent (external or internal to a system boundary respectively). Scalability and robustness, along with the additional property of modifiability, are shown to relate to change effects. The extent of changeability is determined by the number of possible change mechanisms available to the system as accepted by decision makers. Creating changeable systems, which can incorporate both classical notions of alterability and robustness, empowers systems to maintain value delivery over their lifecycle, in spite of changes in their contexts, thereby achieving value robustness to stakeholders over time

Innovating the Study of Context: Using a Qualitative Study on Subjugation and Resistance to Explore the Utility of Foucauldian Governmentality as a Framework for Enriching Situational Analyses

Situational analysis has, as an emerging poststructuralist approach to grounded theory, recently grown in use across a diverse range of disciplines and substantive areas. In this paper, we consider the complementarity of Foucauldian governmentality as a theoretical framework for supporting and enriching situational analyses. Our work is based on the findings of a recent study, informed by situational analysis, in which we interviewed 27 HIV-positive (n=16) and HIV-negative (n=11) gay men ages 50 and over about their health care experiences, and used these data to examine processes of subjugation and resistance reflected in their accounts. Drawing on our analytical process, we consider the utility of governmentality in identifying salient discursive forces within a situation of interest, in theorizing how contextual factors operate on and influence the experiences of key actors in a field of inquiry, and in generating insight on fluid uses of power within an area under examination

Functional correlates of optic flow motion processing in Parkinson’s disease

The visual input created by the relative motion between an individual and the environment, also called optic flow, influences the sense of self-motion, postural orientation, veering of gait, and visuospatial cognition. An optic flow network comprising visual motion areas V6, V3A, and MT+, as well as visuo-vestibular areas including posterior insula vestibular cortex (PIVC) and cingulate sulcus visual area (CSv), has been described as uniquely selective for parsing egomotion depth cues in humans. Individuals with Parkinson’s disease (PD) have known behavioral deficits in optic flow perception and visuospatial cognition compared to age- and education-matched control adults (MC). The present study used functional magnetic resonance imaging (fMRI) to investigate neural correlates related to impaired optic flow perception in PD. We conducted fMRI on 40 non-demented participants (23 PD and 17 MC) during passive viewing of simulated optic flow motion and random motion. We hypothesized that compared to the MC group, PD participants would show abnormal neural activity in regions comprising this optic flow network. MC participants showed robust activation across all regions in the optic flow network, consistent with studies in young adults, suggesting intact optic flow perception at the neural level in healthy aging. PD participants showed diminished activity compared to MC particularly within visual motion area MT+ and the visuo-vestibular region CSv. Further, activation in visuo-vestibular region CSv was associated with disease severity. These findings suggest that behavioral reports of impaired optic flow perception and visuospatial performance may be a result of impaired neural processing within visual motion and visuo-vestibular regions in PD.Published versio

Directivity Modes of Earthquake Populations with Unsupervised Learning

We present a novel approach for resolving modes of rupture directivity in large populations of earthquakes. A seismic spectral decomposition technique is used to first produce relative measurements of radiated energy for earthquakes in a spatially compact cluster. The azimuthal distribution of energy for each earthquake is then assumed to result from one of several distinct modes of rupture propagation. Rather than fitting a kinematic rupture model to determine the most likely mode of rupture propagation, we instead treat the modes as latent variables and learn them with a Gaussian mixture model. The mixture model simultaneously determines the number of events that best identify with each mode. The technique is demonstrated on four datasets in California, each with compact clusters of several thousand earthquakes with comparable slip mechanisms. We show that the datasets naturally decompose into distinct rupture propagation modes that correspond to different rupture directions, and the fault plane is unambiguously identified for all cases. We find that these small earthquakes exhibit unilateral ruptures 63–73% of the time on average. The results provide important observational constraints on the physics of earthquakes and faults