Constitutional Law - Jury Selection - Peremptory Challenges

The United States Supreme Court held that intentional gender discrimination by state actors when exercising peremptory challenges in the jury selection process violates the Equal Protection Clause of the Fourteenth Amendment. J.E.B. v. Alabama ex rel. T.B., 114 S. Ct. 1419 (1994)

Efficient numerical approaches for predicting supersonic flows with viscous-inviscid interaction

Three different approaches for efficiently computing supersonic flow fields with strong viscous/inviscid interaction are critically examined. First, the single-pass philosophy employed for the solution of the parabolized Navier-Stokes (PNS) equations is considered. Through study of a model problem, the divergent space-marching solution that occurs when the streamwise pressure gradient is approximated using a backward difference is shown to be the response of the numerical algorithm to an ill-posed problem. In addition, it is shown that the so-called minimum marching step size is related to the longest wavelength that the finite-difference mesh is capable of resolving, not the thickness of the subsonic layer. Based on comparisons with other computed results, the single-pass philosophy is inadequate purely from the standpoint that it suppresses the streamwise elliptic behavior present in the solution;A second-order global pressure iteration (GPI) algorithm is developed using the Vigneron splitting to determine the portion of the streamwise pressure gradient that is responsible for streamwise elliptic behavior. A second-order finite-difference scheme is developed from a heuristic stability analysis of a model problem. A GPI algorithm is discussed in terms of upwind relaxation schemes that appear in the literature. For flows with streamwise separation, the FLARE approximation is employed to stabilize the iteration. Results predicted using the GPI algorithm show good agreement with results presented in the literature;In addition to the GPI algorithm, a new second-order algorithm is developed using a hybrid approach. The standard conservative PNS algorithm is employed in the outer supersonic flow, while in the subsonic region near the wall a split coefficient matrix (SCM) scheme is used to determine the direction of differencing for the streamwise convective flux vector. The second-order streamwise differencing scheme developed for the GPI algorithm is used in the SCM scheme while central differencing is employed for the transverse derivatives. Results predicted using the hybrid algorithm are very similar to results predicted using the GPI scheme except in the regions of reversed flow. The hybrid algorithm is less efficient than the GPI algorithm but more robust

Measuring dark matter ellipticity of Abell 901/902 using Particle Based Lensing

We present a non-parametric measure of the ellipticity and the alignment of the dark matter halos in Abell 901/902 supercluster. This super-cluster is a system of four separate peaks in a $0.5^{\circ}\times0.5^{\circ}$ field of view. We map the mass distribution of each individual peak using an improved version of Particle Based Lensing (PBL) and measure the ellipticity of the dark matter halos associated with two of the peaks directly from the mass map and by fitting them to a singular isothermal ellipse. The parametric and non-parametric measurements are consistent for A901b while the position angle for the Southwest Group is different for the two techniques. We account for this discrepancy to substructure present in the Southwest Peak. We estimate an axis ratio of $0.37\pm 0.1$ for A901b and $0.54^{+0.08}_{-0.09}$ for the Southwest Group.Comment: submitted to APJ, 25 pages, 13 figure

A Comparison of Simple Mass Estimators for Galaxy Clusters

High-resolution N-body simulations are used to investigate systematic trends in the mass profiles and total masses of clusters as derived from 3 simple estimators: (1) the weak gravitational lensing shear field under the assumption of an isothermal cluster potential, (2) the dynamical mass obtained from the measured velocity dispersion under the assumption of an isothermal cluster potential, and (3) the classical virial estimator. The clusters consist of order 2.5e+05 particles of mass m_p \simeq 10^{10} \Msun, have triaxial mass distributions, and significant substructure exists within their virial radii. Not surprisingly, the level of agreement between the mass profiles obtained from the various estimators and the actual mass profiles is found to be scale-dependent. The virial estimator yields a good measurement of the total cluster mass, though it is systematically underestimated by of order 10%. This result suggests that, at least in the limit of ideal data, the virial estimator is quite robust to deviations from pure spherical symmetry and the presence of substructure. The dynamical mass estimate based upon a measurement of the cluster velocity dispersion and an assumption of an isothermal potential yields a poor measurement of the total mass. The weak lensing estimate yields a very good measurement of the total mass, provided the mean shear used to determine the equivalent cluster velocity dispersion is computed from an average of the lensing signal over the entire cluster (i.e. the mean shear is computed interior to the virial radius). [abridged]Comment: Accepted for publication in The Astrophysical Journal. Complete paper, including 3 large colour figures can also be obtained from http://bu-ast.bu.edu/~brainerd/preprints

MC2^2: Subaru and Hubble Space Telescope Weak-Lensing Analysis of the Double Radio Relic Galaxy Cluster PLCK G287.0+32.9

The second most significant detection of the Planck Sunyaev Zel'dovich survey, PLCK~G287.0+32.9 ($z=0.385$) boasts two similarly bright radio relics and a radio halo. One radio relic is located $\sim 400$ kpc northwest of the X-ray peak and the other $\sim 2.8$ Mpc to the southeast. This large difference suggests that a complex merging scenario is required. A key missing puzzle for the merging scenario reconstruction is the underlying dark matter distribution in high resolution. We present a joint Subaru Telescope and {\it Hubble Space Telescope} weak-lensing analysis of the cluster. Our analysis shows that the mass distribution features four significant substructures. Of the substructures, a primary cluster of mass $M_{200\text{c}}=1.59^{+0.25}_{-0.22}\times 10^{15} \ h^{-1}_{70} \ \text{M}_{\odot}$dominates the weak-lensing signal. This cluster is likely to be undergoing a merger with one (or more) subcluster whose mass is approximately a factor of 10 lower. One candidate is the subcluster of mass$M_{200\text{c}}=1.16^{+0.15}_{-0.13}\times 10^{14} \ h^{-1}_{70} \ \text{M}_{\odot}$located$\sim 400$kpc to the southeast. The location of this subcluster suggests that its interaction with the primary cluster could be the source of the NW radio relic. Another subcluster is detected$\sim 2$Mpc to the SE of the X-ray peak with mass$M_{200\text{c}}=1.68^{+0.22}_{-0.20}\times 10^{14} \ h^{-1}_{70} \ \text{M}_{\odot}$. This SE subcluster is in the vicinity of the SE radio relic and may have created the SE radio relic during a past merger with the primary cluster. The fourth subcluster,$M_{200\text{c}}=1.87^{+0.24}_{-0.22}\times 10^{14} \ h^{-1}_{70} \ \text{M}_{\odot}$, is northwest of the X-ray peak and beyond the NW radio relic.Comment: 19 pages, 14 figures; Accepted to Ap

Grave Negotiations: The Rhetorical Foundations of American World War I Cemeteries in Europe

This dissertation uncovers the processes of negotiation between private citizens, President Woodrow Wilson's administration, the War Department, and the Commission of Fine Arts that led to the establishment and final visual presentation of the United States permanent World War I cemeteries in Europe (sites that are still frequented by tens of thousands of international visitors each year). It employs archival research and the analysis of newspapers and photographs to recover the voices of the many stakeholders involved in the cemeteries' foundation. Whereas previous studies have attempted to understand American World War I commemoration practices by focusing on postwar rituals of remembrance alone, my study contextualizes and explains postwar commemoration by analyzing the political ideologies, public rhetoric, and material realities of the war years (1914-1918)—ideologies, rhetoric, and material realities that shaped official and vernacular projects of memory after the Armistice. Providing what I believe is the first complete history of American World War I cemeteries in Europe, my dissertation situates these rhetorically charged sites within contemporary political debates about what it meant for U.S. soldiers to die on foreign soil; what would constitute the "proper" treatment and commemoration of the nation's war dead; how much control the U.S. government should have over the lives and bodies of American citizens; and, how best to communicate the nation's image to international populations

C3NN: Cosmological Correlator Convolutional Neural Network -- an interpretable machine learning tool for cosmological analyses

Modern cosmological research in large scale structure has witnessed an increasing number of applications of machine learning methods. Among them, Convolutional Neural Networks (CNNs) have received substantial attention due to their outstanding performance in image classification, cosmological parameter inference and various other tasks. However, many models which make use of CNNs are criticized as "black boxes" due to the difficulties in relating their outputs intuitively and quantitatively to the cosmological fields under investigation. To overcome this challenge, we present the Cosmological Correlator Convolutional Neural Network (C3NN) -- a fusion of CNN architecture with the framework of cosmological N-point correlation functions (NPCFs). We demonstrate that the output of this model can be expressed explicitly in terms of the analytically tractable NPCFs. Together with other auxiliary algorithms, we are able to open the "black box" by quantitatively ranking different orders of the interpretable convolution outputs based on their contribution to classification tasks. As a proof of concept, we demonstrate this by applying our framework to a series of binary classification tasks using Gaussian and Log-normal random fields and relating its outputs to the analytical NPCFs describing the two fields. Furthermore, we exhibit the model's ability to distinguish different dark energy scenarios ($w_0=-0.95$ and $-1.05$) using N-body simulated weak lensing convergence maps and discuss the physical implications coming from their interpretability. With these tests, we show that C3NN combines advanced aspects of machine learning architectures with the framework of cosmological NPCFs, thereby making it an exciting tool with the potential to extract physical insights in a robust and explainable way from observational data.Comment: 19 pages, 8 figures, 5 tables; Comments are welcome