Angular reduction in multiparticle matrix elements

A general method for the reduction of coupled spherical harmonic products is presented. When the total angular coupling is zero, the reduction leads to an explicitly real expression in the scalar products within the unit vector arguments of the spherical harmonics. For non-scalar couplings, the reduction gives Cartesian tensor forms for the spherical harmonic products, with tensors built from the physical vectors in the original expression. The reduction for arbitrary couplings is given in closed form, making it amenable to symbolic manipulation on a computer. The final expressions do not depend on a special choice of coordinate axes, nor do they contain azimuthal quantum number summations, nor do they have complex tensor terms for couplings to a scalar. Consequently, they are easily interpretable from the properties of the physical vectors they contain.Comment: This version contains added comments and typographical corrections to the original article. Now 27 pages, 0 figure

An Algorithm for FIML and 3SLS Estimation of Large Nonlinear Models

This paper presents a numerical algorithm for computing full information maximum likelihood (FIML) and nonlinear three-stage least squares (3SLS) coefficient estimates for large nonlinear macroeconomic models. The new algorithm, which is demonstrated by actually computing FIML and 3SLS coefficient estimates for two versions of the 97 equation Fair Model, is substantially more effective than other algorithms on FIML and 3SLS estimation problems

Montana Fish, Wildlife and Parks Statewide Forest Management Plan

Montana Fish, Wildlife & Parks (FWP) is responsible for managing approximately 150,000 acres of forested land across 36 Wildlife Management Areas (WMAs).  Since 2009, Montana’s legislature has passed several bills prescribing forest management on these lands and requiring FWP to adopt forest management plans. Work is progressing towards developing a statewide forest management plan. FWP is proposing a forest management plan that employs a “filter” approach with emphasis on conserving biodiversity.  Our premise is that implementing this approach will provide sustainable habitat conditions for the variety of species endemic to these forests

Supersymmetry Relations and MHV Amplitudes in Superstring Theory

We discuss supersymmetric Ward identities relating various scattering amplitudes in type I open superstring theory. We show that at the disk level, the form of such relations remains exactly the same, to all orders in alpha', as in the low-energy effective field theory describing the alpha'-> 0 limit. This result holds in D=4 for all compactifications, even for those that break supersymmetry. We apply SUSY relations to the computations of N-gluon MHV superstring amplitudes, simplifying the existing results for N<7 and deriving a compact expression for N=7.Comment: 34 pages, harvmac; v2: 2 figs added; final version to appear in NP

Peer-to-peer phone calls as a method of providing proactive and personalised support to enhance student engagement

Disruptive changes to the lives of students and running of universities, due to the COVID-19 pandemic, has forced institutions to adapt their approaches to supporting students (Crawford et al., 2020; Frampton & Smithies, 2021). Student engagement has long been regarded by universities as an important indicator for other aspects of student success (Kahu, 2013), but with many varying approaches and definitions (Ashwin & Mcvitty, 2015). Furthermore, the potential involvement of current students to provide peer-to-peer support has received much attention in previous research (Stigmar, 2016; Raisanen et al., 2020; Ala et al., 2021). What has not been thoroughly investigated is how different communications channels, such as phone calls, can be utilised as methods to provide supportive interventions to students. This article provides insights into how supportive peer-to-peer phone interventions within a context of blended learning can have an impact on both students’ levels of engagement and their confidence levels. This was achieved through a mixed-methods approach utilising results of a student questionnaire, targeted at those who had received such supportive interventions, and a detailed analysis of student engagement and progression data. The results show that phone call interventions by peers can lead to increased short-term levels of student engagement, especially when targeted nearer the start of an academic year. Meanwhile, multiple phone call interventions throughout the year leads to a cumulative effect where students continue to see an increase in engagement beyond the months of individual interventions. It is only when students received multiple phone call interventions that they had a significantly higher likelihood to progress in their studies. The process of attempting to call, but not reaching, students also helps to identify students who are then likely to exhibit lower levels of engagement throughout the rest of the academic year. Students who received a phone call intervention reported increases in confidence levels and awareness of support. Almost nine in ten students reported taking at least one proactive action following their supportive call with a peer

Complete Six-Gluon Disk Amplitude in Superstring Theory

We evaluate all next-to-maximal helicity violating (NMHV) six-gluon amplitudes in type I open superstring theory in four dimensions, at the disk level, to all orders in alpha'. Although the computation utilizes supersymmetric Ward identities, the result holds for all compactifications, even for those that break supersymmetry and is completely model-independent. Together with the maximally helicity violating (MHV) amplitudes presented in the previous work, our results provide the complete six-gluon disk amplitude.Comment: 29 pages, harvmac, v2: Appendix B3 added, v3: Final version to appear in NP

Ultraviolet C II and Si III Transit Spectroscopy and Modeling of the Evaporating Atmosphere of GJ436b

Hydrogen gas evaporating from the atmosphere of the hot-Neptune GJ436b absorbs over 50% of the stellar Ly$\alpha$ emission during transit. Given the planet's atmospheric composition and energy-limited escape rate, this hydrogen outflow is expected to entrain heavier atoms such as C and O. We searched for C and Si in the escaping atmosphere of GJ436b using far-ultraviolet HST COS G130M observations made during the planet's extended H I transit. These observations show no transit absorption in the C II 1334,1335 \AA\ and Si III 1206 \AA\ lines integrated over [-100, 100] km s$^{-1}$, imposing 95% (2$\sigma$) upper limits of 14% (C II) and 60% (Si III) depth on the transit of an opaque disk and 22% (C II) and 49% (Si III) depth on an extended, highly asymmetric transit similar to that of H I Ly$\alpha$. C$^+$ is likely present in the outflow according to a simulation we carried out using a spherically-symmetric, photochemical-hydrodynamical model. This simulation predicts a $\sim$2% transit over the integrated bandpass, consistent with the data. At line center, we predict the C II transit depth to be as high as 19%. Our model predicts a neutral hydrogen escape rate of $1.6\times10^{9}$ g s$^{-1}$ ($3.1\times10^{9}$ g s$^{-1}$ for all species) for an upper atmosphere composed of hydrogen and helium.Comment: 7 pages, 4 figures, 1 table; accepted to ApJ Letter

Identification of Transnational Threats

In the past, the starting point for threat identification was the nation state. Today, national boundaries have lost much of their significance and global forces lacking identifiable national frontiers represent a real threat to US security. New technologies have facilitated the development of advanced terrorist methodologies and tactics. A new and increasingly significant threat is hostile forces which operate within the borders of states which are friendly to the United States. American universities are increasingly vulnerable to new transnational threats by virtue of the opportunities they present for acquisition of dual use technological skills. With its new cellular structure, terrorism has been privatized, is more difficult to counter, and enjoys great access to funds, weapons, and training. The broad anti-war coalition has created threats to the US critical infrastructure in connection with “direct action” against the Iraqi war. In one year alone, computer criminals funneled over 2.6 billion dollars out of Russia through Cyprus. Traffic in false documents constitutes an especially significant threat to our critical infrastructure and has become more serious with technological advances that have eased the production of such documents. The rise of identity theft, an important variation of traffic in false documents, threatens to undermine an important infrastructure base