The Various Views and Controversies on Church Polity in the Lutheran Church of America, to 1827

In order to present an accurate picture of that portion of Lutheran Church History to which this study is devoted, we must have some foundation from which to work common to all of the Lutheran bodies which come into consideration. The only fundamental of that kind we have been able to discover is the statement of the Lutheran position on church polity which is contained in the Lutheran Symbols. However, even this is hardly satisfactory. That is the case partly because the Lutheran Symbols were not held in high regard by some of the Lutheran groups in America; partly because other factors, such as the customs of their European antecedents, political and ecclesiastical conditions in America, experiences and developments during their early organizational life, etc., etc., play an important part in shaping the policies of most bodies concerned

Universal Central Extensions of Gauge Algebras and Groups

We show that the canonical central extension of the group of sections of a Lie group bundle over a compact manifold, constructed in [NW09], is universal. In doing so, we prove universality of the corresponding central extension of Lie algebras in a slightly more general setting.Comment: 9 pages, LaTeX. Changes w.r.t. version 2: minor changes (final version). To appear in J. Reine Angew. Mat

Tradeoff between short-term and long-term adaptation in a changing environment

We investigate the competition dynamics of two microbial or viral strains that live in an environment that switches periodically between two states. One of the strains is adapted to the long-term environment, but pays a short-term cost, while the other is adapted to the short-term environment and pays a cost in the long term. We explore the tradeoff between these alternative strategies in extensive numerical simulations, and present a simple analytic model that can predict the outcome of these competitions as a function of the mutation rate and the time scale of the environmental changes. Our model is relevant for arboviruses, which alternate between different host species on a regular basis.Comment: 9 pages, 3 figures, PRE in pres

Numeracy-Meets: An Innovative Professional Development Model for Adult Numeracy Practitioners in Ireland

Despite the clear and obvious need for adults to be proficient in numeracy, international studies suggest that many continue to struggle in this area. In Ireland, one of the main challenges continues to be the availability of effective adult numeracy education. This is a diverse sector, and little is known about the varied provision of adult numeracy courses and of those who teach on them. Recent research has highlighted an unmet demand for the professional development of adult numeracy practitioners with many looking for opportunities to network and further develop their practice. This study aimed to design, implement and evaluate a professional development model that supported adult numeracy practitioners in developing the necessary skills to support their students. After an initial needs analysis, a series of six ‘Numeracy-Meets’ were designed and implemented between February and May 2022. There was an average of twenty adult numeracy practitioners in attendance at each Numeracy-Meet. After all the Numeracy-Meets had taken place, five practitioners took part in individual semi-structured interviews to evaluate their experiences. This paper details the design, implementation and evaluation of these Numeracy-Meets and discusses whether they are a sustainable model of professional development for adult numeracy practitioners

Dynamics, dynamic soft elasticity and rheology of smectic-C elastomers

We present a theory for the low-frequency, long-wavelength dynamics of soft smectic-C elastomers with locked-in smectic layers. Our theory, which goes beyond pure hydrodynamics, predicts a dynamic soft elasticity of these elastomers and allows us to calculate the storage and loss moduli relevant for rheology experiments as well as the mode structure.Comment: 4 pages, 2 figure

Quantum critical transport, duality, and M-theory

We consider charge transport properties of 2+1 dimensional conformal field theories at non-zero temperature. For theories with only Abelian U(1) charges, we describe the action of particle-vortex duality on the hydrodynamic-to-collisionless crossover function: this leads to powerful functional constraints for self-dual theories. For the n=8 supersymmetric, SU(N) Yang-Mills theory at the conformal fixed point, exact hydrodynamic-to-collisionless crossover functions of the SO(8) R-currents can be obtained in the large N limit by applying the AdS/CFT correspondence to M-theory. In the gravity theory, fluctuating currents are mapped to fluctuating gauge fields in the background of a black hole in 3+1 dimensional anti-de Sitter space. The electromagnetic self-duality of the 3+1 dimensional theory implies that the correlators of the R-currents obey a functional constraint similar to that found from particle-vortex duality in 2+1 dimensional Abelian theories. Thus the 2+1 dimensional, superconformal Yang Mills theory obeys a "holographic self duality" in the large N limit, and perhaps more generally.Comment: 35 pages, 4 figures; (v2) New appendix on CFT2, corrected normalization of gauge field action, added ref

Microscopic Theory for the Markovian Decay of Magnetization Fluctuations in Nanomagnets

We present a microscopic theory for the phonon-driven decay of the magnetization fluctuations in a wide class of nanomagnets where the dominant energy is set by isotropic exchange and/or uniaxial anisotropy. Based on the Zwanzig-Mori projection formalism, the theory reveals that the magnetization fluctuations are governed by a single decay rate $\omega_c$, which we further identify with the zero-frequency portion of the associated self-energy. This dynamical decoupling from the remaining slow degrees of freedom is attributed to a conservation law and the discreteness of the energy spectrum, and explains the omnipresent mono-exponential decay of the magnetization over several decades in time, as observed experimentally. A physically transparent analytical expression for $\omega_c$ is derived which highlights the three specific mechanisms of the slowing down effect which are known so far in nanomagnets.Comment: 7 page