A Method Based on Total Variation for Network Modularity Optimization using the MBO Scheme

The study of network structure is pervasive in sociology, biology, computer science, and many other disciplines. One of the most important areas of network science is the algorithmic detection of cohesive groups of nodes called "communities". One popular approach to find communities is to maximize a quality function known as {\em modularity} to achieve some sort of optimal clustering of nodes. In this paper, we interpret the modularity function from a novel perspective: we reformulate modularity optimization as a minimization problem of an energy functional that consists of a total variation term and an $\ell_2$ balance term. By employing numerical techniques from image processing and $\ell_1$ compressive sensing -- such as convex splitting and the Merriman-Bence-Osher (MBO) scheme -- we develop a variational algorithm for the minimization problem. We present our computational results using both synthetic benchmark networks and real data.Comment: 23 page

Transonic Navier-Stokes solutions of three-dimensional afterbody flows

The performance of a three-dimensional Navier-Stokes solution technique in predicting the transonic flow past a nonaxisymmetric nozzle was investigated. The investigation was conducted at free-stream Mach numbers ranging from 0.60 to 0.94 and an angle of attack of 0 degrees. The numerical solution procedure employs the three-dimensional, unsteady, Reynolds-averaged Navier-Stokes equations written in strong conservation form, a thin layer assumption, and the Baldwin-Lomax turbulence model. The equations are solved by using the finite-volume principle in conjunction with an approximately factored upwind-biased numerical algorithm. In the numerical procedure, the jet exhaust is represented by a solid sting. Wind-tunnel data with the jet exhaust simulated by high pressure air were also obtained to compare with the numerical calculations

On Estimating the High-Energy Cutoff in the X-ray Spectra of Black Holes via Reflection Spectroscopy

The fundamental parameters describing the coronal spectrum of an accreting black hole are the slope $\Gamma$ of the power-law continuum and the energy $E_{cut}$ at which it rolls over. Remarkably, this parameter can be accurately measured for values as high as 1 MeV by modeling the spectrum of X-rays reflected from a black hole accretion disk at energies below 100 keV. This is possible because the details in the reflection spectrum, rich in fluorescent lines and other atomic features, are very sensitive to the spectral shape of the hardest coronal radiation illuminating the disk. We show that fitting simultaneous NuSTAR (3-79 keV) and low-energy (e.g., Suzaku) data with the most recent version of our reflection model RELXILL, one can obtain reasonable constraints on $E_{cut}$ at energies from tens of keV up to 1 MeV, for a source as faint as 1 mCrab in a 100 ks observation.Comment: Accepted for publication in ApJL, 6 pages, 5 figure

Sub-systems in nearby solar-type wide binaries

We conducted a deep survey of resolved sub-systems among wide binaries with solar-type components within 67 pc from the Sun. Images of 61 stars in the K and H bands were obtained with the NICI adaptive-optics instrument on the 8-m Gemini-South telescope. Our maximum detectable magnitude difference is about 5mag and 7.8mag at 0.15" and 0.9" separations, respectively. This enables a complete census of sub-systems with stellar companions in the projected separation range from 5 to 100 AU. Out of 7 such companions found in our sample, only one was known previously. We determine that the fraction of sub-systems with projected separations above 5 AU is 0.12 +- 0.04 and that the distribution of their mass ratio is flat, with a power-law index 0.2 +- 0.5. Comparing this with the properties of closer spectroscopic sub-systems (separations below 1 AU), it appears that the mass-ratio distribution does not depend on the separation. The frequency of sub-systems in the separation ranges below 1 AU and between 5 and 100 AU is similar, about 0.15. Unbiased statistics of multiplicity higher than two, advanced by this work, provide constraints on star-formation theory.Comment: Accepted by Astronomical Journal. 13 pages, 5 figure

Introduction: Celebrating the Mound City Bar Association Centennial: Looking Back, Leading Forward

In 2022, the Mound City Bar Association in St. Louis, one of the first Black bar associations in the country, celebrates its 100th anniversary. In this volume of the Washington University Journal of Law & Policy, distinguished authors look back at a century of contributions of Mound City Bar Association lawyers, judges, and allies, documenting their efforts to eliminate racial discrimination and break down barriers to equal justice. The volume is a testament to the work of countless individuals in the fight for civil rights since the beginning of the association in 1922. The authors also anticipate and examine the challenges ahead and the work yet to be done to achieve equal justice for all in our city, the region, and the country in the years to come

Toward Monodisperse Poly(γ-benzyl α,L-glutamate): Uniform, Polar, Molecular Rods

Poly(γ-benzyl α,L-glutamate) (PBLG) has been widely used in studies of the physics of rod-like polymer chains. The helical structure of PBLG gives rise to considerable chain stiffness, such that the persistence length of the chain is on the order of 70 nm in helicogenic solvents. This feature, coupled with the ease of synthesis and good solubility of the polymer has made PBLG the system of choice for the study of both isotropic and liquid crystalline solutions of rod-like macromolecules

Engineered Proteins in Materials Research

Peptides and proteins have attracted scientific and technological interest largely because of their intriguing properties as catalysts, receptors, signalling molecules, and therapeutic agents. In attempts to understand and exploit these properties, protein engineering has been used primarily to obtain precious proteins in increased quantities, or to explore systematic alterations in protein sequence through site-directed mutagenesis. Design of protein structures de novo ("from scratch") has attracted less attention, and has been directed in the main toward studies of protein folding (Kamtekar et al., 1993). Such studies represent a key element in the current vigorous investigation of the connections between amino acid sequence and the three-dimensional structures of isolated protein chains in aqueous solution. This chapter describes protein engineering of quite another sort, in which the proteinacious nature of the product is less important than its macromolecular character