Red Bird was a Cherokee murdered at the Red Bird River Petroglyph site (15Cy51) and buried at the Red Bird River Rockshelter (15Cy52) during the late eighteenth century, where he left an important record of traditional petroglyphs. His legacy is key to understanding the origins of Sequoyah's Cherokee Syllabary and its relationship to rock art. Personal testimonies of Red Bird's descendants are supported by primary documents and archaeological evidence, including the letters of Sequoyah's maternal uncle, John Watts, and prototypes of Cherokee Syllabary characters engraved at 15Cy52 in 1808, when members of Sequoyah's matrilineal family resided nearby.

Let $\unicode[STIX]{x1D707}(m,n)$ (respectively, $\unicode[STIX]{x1D702}(m,n)$ ) denote the number of odd-balanced unimodal sequences of size $2n$ and rank $m$ with even parts congruent to $2\!\!\hspace{0.6em}{\rm mod}\hspace{0.2em}4$ (respectively, $0\!\!\hspace{0.6em}{\rm mod}\hspace{0.2em}4$ ) and odd parts at most half the peak. We prove that two-variable generating functions for $\unicode[STIX]{x1D707}(m,n)$ and $\unicode[STIX]{x1D702}(m,n)$ are simultaneously quantum Jacobi forms and mock Jacobi forms. These odd-balanced unimodal rank generating functions are also duals to partial theta functions originally studied by Ramanujan. Our results also show that there is a single $C^{\infty }$ function in $\mathbb{R}\times \mathbb{R}$ to which the errors to modularity of these two different functions extend. We also exploit the quantum Jacobi properties of these generating functions to show, when viewed as functions of the two variables $w$ and $q$ , how they can be expressed as the same simple Laurent polynomial when evaluated at pairs of roots of unity. Finally, we make a conjecture which fully characterizes the parity of the number of odd-balanced unimodal sequences of size $2n$ with even parts congruent to $0\!\!\hspace{0.6em}{\rm mod}\hspace{0.2em}4$ and odd parts at most half the peak.

The study of white dwarfs, the end stage of stellar evolution for more than 95% of stars, is critical to bettering our understanding of the late stages of the lives of low mass stars. In particular, the post main sequence evolution of binary star systems is complex, and the identification and analysis of double degenerate systems is a crucial step in constraining models of binary star systems. Binary white dwarfs in open star clusters are particularly useful because cluster parameters such as distance, metal content, and total system age are more tightly constrained than for field double degenerates. Here we use the precision astrometry from the Gaia Data Release 2 catalog to study two other white dwarfs which were identified as candidate double degenerates in the field of the open star cluster NGC 6633. One of the two objects, LAWDS 4, is found to have astrometric properties fully consistent with that of the cluster. In such a case, the object is significantly overluminous for a single white dwarf, strongly indicating binarity. The second candidate binary, LAWDS 7, appears to be inconsistent with cluster membership, though a more thorough analysis is necessary to properly quantify the probability. At present we are proceeding to model the photometric and spectroscopic data for both objects as if they were cluster member double degenerates. Results of this latter analysis are forthcoming. Our results will add crucial data to the study of binary star evolution in open star clusters.

A monetary production model of financial firms is employed to investigate supply-side inside-money aggregation, augmented to include credit card transaction services. Inside money is a supply-side concept. Financial firms are conceived to produce monetary and credit card transaction services as outputs through financial intermediation. While credit cards provide transactions services, credit cards have never been included into measures of the money supply. The reason is accounting conventions, which do not permit adding liabilities to assets. However, index number theory measures service flows and is based on microeconomic aggregation theory, not accounting. We derive theory needed to measure the supply of the joint services of credit cards and inside money, needed to estimate the output supply function and to compute value added. The data needed for empirical implementation of our theory are available online from the Center for Financial Stability in New York City.

A robust biomedical informatics infrastructure is essential for academic health centers engaged in translational research. There are no templates for what such an infrastructure encompasses or how it is funded. An informatics workgroup within the Clinical and Translational Science Awards network conducted an analysis to identify the scope, governance, and funding of this infrastructure. After we identified the essential components of an informatics infrastructure, we surveyed informatics leaders at network institutions about the governance and sustainability of the different components. Results from 42 survey respondents showed significant variations in governance and sustainability; however, some trends also emerged. Core informatics components such as electronic data capture systems, electronic health records data repositories, and related tools had mixed models of funding including, fee-for-service, extramural grants, and institutional support. Several key components such as regulatory systems (e.g., electronic Institutional Review Board [IRB] systems, grants, and contracts), security systems, data warehouses, and clinical trials management systems were overwhelmingly supported as institutional infrastructure. The findings highlighted in this report are worth noting for academic health centers and funding agencies involved in planning current and future informatics infrastructure, which provides the foundation for a robust, data-driven clinical and translational research program.

While credit cards provide transactions services, as do currency and demand deposits, credit cards have never been included in measures of the money supply. The reason is accounting conventions, which do not permit adding liabilities, such as credit card balances, to assets, such as money. However, economic aggregation theory and index number theory measure service flows and are based on microeconomic theory, not accounting. Barnett et al. derived the aggregation and index number theory needed to measure the joint services of credit cards and money. They derived and applied the theory under the assumption of risk neutrality. But since credit card interest rates are high and volatile, risk aversion may not be negligible. We extend the theory by removing the assumption of risk neutrality to permit risk aversion in the decision of the representative consumer.

This paper analyzes the dynamical properties of monetary models with regime switching. We start with the analysis of the evolution of inflation when policy is guided by a simple monetary rule where coefficients switch with the policy regime. We rule out the possibility of a Hopf bifurcation and demonstrate the possibility of a period-doubling bifurcation. As a result, a small change in the parameters (e.g., a more active policy response) can lead to a drastic change in the path of inflation. We show that the New Keynesian model with a current-looking Taylor rule is not prone to bifurcations. A New Keynesian model with a hybrid rule, however, exhibits the same pattern of period-doubling bifurcations as the analysis with a simple monetary rule.

This paper is an up-to-date survey of the state of the art in dynamical systems theory relevant to high levels of dynamical complexity, characterizing chaos and near-chaos, as commonly found in the physical sciences. The paper also surveys applications in economics and finance. This survey does not include bifurcation analyses at lower levels of dynamical complexity, such as Hopf and transcritical bifurcations, which arise closer to the stable region of the parameter space. We discuss the geometric approach (based on the theory of differential/difference equations) to dynamical systems and make the basic notions of complexity, chaos, and other related concepts precise, having in mind their (actual or potential) applications to economically motivated questions. We also introduce specific applications in microeconomics, macroeconomics, and finance and discuss the policy relevance of chaos.

We explore bifurcation phenomena in the open-economy New Keynesian model developed by Galí and Monacelli in 2005. We find that the open economy framework brings about more complex dynamics, along with a wider variety of qualitative behaviors and policy responses. Introducing parameters related to the open economy structure affects the values of bifurcation parameters and changes the location of bifurcation boundaries. As a result, the stratification of the confidence region, as previously seen in closed-economy New Keynesian models, remains an important research and policy risk to be considered in the context of the open-economy New Keynesian functional structures. In fact, econometrics and optimal policy design become more complex within an open economy. Dynamical inferences need to be qualified by the risk of bifurcation boundaries crossing the confidence regions. Policy design needs to take into consideration that a change in monetary policy can produce an unanticipated bifurcation, without adequate prior econometrics research.

Hans Urs von Balthasar claimed that Barth's Church Dogmatics demonstrates a weakening of his distinctive actualism in order to make space for ‘the concept of authentic objective form’, a point illustrated by the discourse on divine beauty in CD II/1. There Barth treats the divine being as an objective form to be contemplated, a seeming departure from Barth's privileged conceptualisation of God as personal subject whose free action humbles our theoretical gaze and graciously provides the material content for proper speech about God. Bruce McCormack has challenged von Balthasar's general thesis, arguing that no weakening has in fact taken place in the Church Dogmatics. If this is the case, what then of Barth's discourse on divine beauty? Is it consistent with his actualistic doctrine of God? Is it possible to speak of God both as a free, dynamic event and an object of beauty? Can theological aesthetics find a home within Barth's actualism? This article answers in the affirmative by demonstrating the systematic integrity between Barth's claims about divine beauty and the actualism permeating CD II/1. First, the article examines the ambiguity of Barth's specific claims about divine beauty. Barth is both enthusiastic and hesitant in speaking about divine beauty, affirming the concept yet placing careful qualifications on its use. Next, the article illustrates how the nature of these claims is anticipated by the actualism of CD II/1, specifically by (1) Barth's clear rejection of divine formlessness, (2) his argument that God's act of self-revelation in Jesus Christ implies an objective triune form for God's being and, lastly, (3) how he grounds discourse on divine beauty in the event of God's dynamic, free love. The article finally contends that the key to Barth's puzzling position on divine beauty is in understanding the precise reason why he registers beauty as a necessary but insufficient theological concept. This qualification is rooted in an important content–form, spirit–nature distinction which frames all discussion about God's being-in-act. Throughout CD II/1, objective form is a necessary condition for divine self-expression, but objectivity is always grounded in the freedom of the Spirit. Thus, the freedom-to-love at the heart of God's triune existence is the ground of our experience of God as beautiful, not any continuity with our contemplation of created forms. As such, the creative freedom animating God's triune life provides the space for, but also the limit to, theological aesthetics by imbuing divine beauty in mystery.

Few studies have formally examined the relationship between meteorological factors and the incidence of child pneumonia in the tropics, despite the fact that most child pneumonia deaths occur there. We examined the association between four meteorological exposures (rainy days, sunshine, relative humidity, temperature) and the incidence of clinical pneumonia in young children in the Philippines using three time-series methods: correlation of seasonal patterns, distributed lag regression, and case-crossover. Lack of sunshine was most strongly associated with pneumonia in both lagged regression [overall relative risk over the following 60 days for a 1-h increase in sunshine per day was 0·67 (95% confidence interval (CI) 0·51–0·87)] and case-crossover analysis [odds ratio for a 1-h increase in mean daily sunshine 8–14 days earlier was 0·95 (95% CI 0·91–1·00)]. This association is well known in temperate settings but has not been noted previously in the tropics. Further research to assess causality is needed.