In this paper we present a deterministic transmission dynamic compartmental model for the spread of the novel coronavirus on a college campus for the purpose of analyzing strategies to mitigate an outbreak. The goal of this project is to determine and compare the utility of certain containment strategies including gateway testing, surveillance testing, and contact tracing as well as individual level control measures such as mask wearing and social distancing. We modify a standard SEIR-type model to reflect what is currently known about COVID-19. We also modify the model to reflect the population present on a college campus, separating it into students and faculty. This is done in order to capture the expected different contact rates between groups as well as the expected difference in outcomes based on age known for COVID-19. We aim to provide insight into which strategies are most effective, rather than predict exact numbers of infections. We analyze effectiveness by looking at relative changes in the total number of cases as well as the effect a measure has on the estimated basic reproductive number. We find that the total number of infections is most sensitive to parameters relating to student behaviors. We also find that contact tracing can be an effective control strategy when surveillance testing is unavailable. Lastly, we validate the model using data from Villanova University's online COVID-19 Dashboard from Fall 2020 and find good agreement between model and data when superspreader events are incorporated in the model as shocks to the number of infected individuals approximately two weeks after each superspreader event.

The fluid, urgent nature of crises requires flexible, responsive information sharing. Recent studies show, however, that in business catastrophes and other kinds of crises conventional access control mechanisms favor security over flexibility. Our work addresses these seemingly contradictory needs for security and flexibility and designs a trust inference model based on fuzzy logic, a model that can be used with pervasive computing technologies using sensors and mobile devices. Drawing upon research on trust, we design a trust inference model using attributes of affiliation, task performance, and urgency; apply the model to a known crisis; discuss implementation issues; and explore issues for further research.This article is dedicated to Alan Jarman, a founding influence in the Journal of Contingencies and Crisis Management who died in Canberra 15 July 2010. Alan's quantitative, engineering background and his long standing commitment to improving crisis decision making prompted him to encourage our applying fuzzy logic to crisis information sharing. We are grateful for Alan's encouragement and advice.

In this paper we investigate the relationship between two different techniques typically used in imaging and estimation problems. We focus on synthetic-aperture radar imaging and compare the methods of backprojection (standard for imaging) and best linear unbiased estimation (BLUE). We aim to reconstruct or estimate the reflectivity function of an object present in a scene of interest. We find that the estimate of the reflectivity (calculated using BLUE) and the reconstructed image (calculated using filtered backprojection) are the same when we utilize a criterion from microlocal analysis to define the optimal backprojection filter and assume the measured data is corrupted by zero-mean independently identically distributed (white) noise. In particular we show that the microlocal criterion for the optimal backprojection filter is equivalent to the unbiased constraint present in the BLUE technique.

In this paper we study waveform design for synthetic-aperture radar (SAR) imaging through dispersive media. Under the assumptions of scalar wave propagation through a causal dielectric medium and single-scattering from an isotropic point scatterer, we use asymptotic analysis to derive the asymptotic approximation to the scattered electric field. From this asymptotic approximation, we define a sensing precursor that we propose for the transmit waveform for SAR imaging through dispersive material. We compare our sensing precursor with previously defined optimal waveforms (Varslot, Morales, and Cheney, Waveform design for synthetic-aperture radar imaging through dispersive media, SIAM J. Appl. Math., 71 (2011), pp. 1780 - 1800) in terms of both propagation and scattering capabilities, as well as imaging performance. With the filtered back-projection imaging algorithm that we use, we find that for high levels of signal-to-noise ratio (SNR), the optimal waveforms contain higher frequencies and thus produce better images. For low levels of SNR, the transmitted optimal waveforms and the sensing precursors are similar, thus giving comparable images.

In this paper we investigate the ability of correlation syntheticaperture radar (SAR) imaging to reconstruct isotropic and anisotropic scatterers. SAR correlation imaging was suggested by the author previously in [34]. Correlation imaging algorithms produce an image of a second-order quantity describing an object an interest, for example, the reflectivity function squared. In the previous work [34] it was argued that the effects of volume scattering clutter on the image can be minimized by choosing which pairs of collected data to correlate prior to applying a backprojection-type reconstruction algorithm. This choice of pairs for the correlation process is determined by what is known as the memory effect of scattering of waves by random scatterers [42, 43, 40, 41, 7, 14]. It is the goal of this current work to determine the different imaging outcomes for an isotropic or point scatterer versus an anisotropic or dipole scatterer. In addition we aim to determine if removing contributions to the image due to the memory effect is necessary for diminishing the contributions of anisotropic or clutter scatterers to the scene of interest. Finally we extend the analysis of [34] to the polarimetric SAR case to determine whether the additional data provided by this modality contributes to decreasing the effects of clutter on the SAR image.

In this work we develop a new reproducing kernel Hilbert space (RKHS) framework for inverse scattering problems using the Born approximation. We assume we have backscattered data of a field that is dependent on an unknown scattering potential. Our goal is to reconstruct or image this scattering potential. Assuming the scattering potential lies in a RKHS, we find that the imaging equation can be rewritten as the inner product of the desired unknown function with the adjoint of the forward operator applied to the kernel of the imaging operator. We therefore may choose the kernel of the imaging operator such that the adjoint applied to this kernel is precisely the reproducing kernel of the Hilbert space the reflectivity function lies in. In this way we are able to obtain an alternative definition of an ideal image. We will demonstrate this theory using synthetic aperture radar imaging as an example, though there are other applicable imaging modalities i.e. inverse diffraction and diffraction tomography [1,6]. We choose SAR as it was the motivating application for this work. We will compare the RKHS ideal imaging technique to the standard microlocal analytic ideal image from backprojection theory. Note this method requires a variation of the standard SAR data model with the assumption of a full two dimensional data collection surface as opposed to a one dimensional flight path, however we are able to perform imaging with a single frequency and avoid the approximations made in the backprojection imaging operator derivation.1. Introduction. In this paper we develop a new reproducing kernel Hilbert space framework for inverse scattering problems using the Born approximation. We assume we have backscattered data of some field that is dependent on an unknown scattering potential. Our goal is to reconstruct or image this scattering potential. We will use synthetic-aperture radar imaging as an example to demonstrate the theory developed in this work in terms of a real application.There are two main mathematical tasks to consider for imaging, first developing a forward model and then creating a method to invert that model to obtain information about the unknown function of interest. We will assume our collected data is in the form of a scattered field which is related to an unknown function to be reconstructed. We will therefore assume our field of interest satisfies the inhomogeneous scalar wave equation in the time domain and the inhomogeneous Helmholtz equation in the frequency domain. Thus we may use a Green's function

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