Affine quantum super Schur-Weyl duality

The Schur-Weyl duality, which started as the study of the commuting actions of the symmetric group $S_d$ and $\mathrm{GL}(n,\mathbb{C})$ on $V^{\otimes d}$ where $V=\mathbb{C}^n$, was extended by Drinfeld and Jimbo to the context of the finite Iwahori-Hecke algebra $H_d(q^2)$ and quantum algebras $U_q(\mathrm{gl}(n))$, on using universal $R$-matrices, which solve the Yang-Baxter equation. There were two extensions of this duality in the Hecke-quantum case: to the affine case, by Chari and Pressley, and to the super case, by Moon and by Mitsuhashi. We complete this chain of works by completing the cube, dealing with the general affine super case, relating the commuting actions of the affine Iwahori-Hecke algebra $H^a_d(q^2)$ and of the affine quantum Lie superalgebra $U_{q,a}^\sigma(\mathrm{sl}(m,n))$ using the presentation by Yamane in terms of generators and relations, acting on the $d$th tensor power of the superspace $V=\mathbb{C}^{m+n}$. Thus we construct a functor and show it is an equivalence of categories of $H_d^a(q^2)$ and $U_{q,a}^\sigma(\mathrm{sl}(m,n))$-modules when $d<n'=m+n$

Superconvergence of Topological Entropy in the Symbolic Dynamics of Substitution Sequences

We consider infinite sequences of superstable orbits (cascades) generated by systematic substitutions of letters in the symbolic dynamics of one-dimensional nonlinear systems in the logistic map universality class. We identify the conditions under which the topological entropy of successive words converges as a double exponential onto the accumulation point, and find the convergence rates analytically for selected cascades. Numerical tests of the convergence of the control parameter reveal a tendency to quantitatively universal double-exponential convergence. Taking a specific physical example, we consider cascades of stable orbits described by symbolic sequences with the symmetries of quasilattices. We show that all quasilattices can be realised as stable trajectories in nonlinear dynamical systems, extending previous results in which two were identified.Comment: This version: updated figures and added discussion of generalised time quasilattices. 17 pages, 4 figure

Charge Ordering Geometries in Uniaxially-Strained NbSe2_2

Recent STM experiments reveal niobium diselenide to support domains of striped (1Q) charge order side-by-side with its better-known triangular (3Q) phase, suggesting that small variations in local strain may induce a quantum phase transition between the two. We use a theoretical model of the charge order in NbSe$_2$, based on a strong momentum- and orbital-dependent electron-phonon coupling, to study the effect of uniaxial strain. We find that as little as $0.1\%$ anisotropic shift in phonon energies breaks the threefold symmetry in favor of a 1Q state, in agreement with the experimental results. The altered symmetries change the transition into the ordered state from weakly-first-order in the 3Q case, to second order in the 1Q regime. Modeling the pseudogap phase of NbSe$_2$ as the range of temperatures above the onset of long-range order in which phase coherence is destroyed by local phonon fluctuations, we find a shortening of the local ordering wavevector with increasing temperature, complementing recent X-ray diffraction observations within the low-temperature phase.Comment: 5 pages, 3 figure

Aboriginal and Torres Strait Islander People and dementia: a review of the research

This report outlines the prevalence of dementia and modifiable risk factors in Aboriginal and Torres Strait Islander communities. Executive summary The high rate of dementia in Aboriginal and Torres Strait Islander communities requires urgent attention. Aboriginal and Torres Strait Islander people experience dementia at an earlier age then the general population and this, combined with the steadily growing number of older Aboriginal and Torres Strait Islander people, will result in the number of people effected by&nbsp; dementia growing significantly in the coming years. Although higher rates of dementia have been reported in Aboriginal and Torres Strait Islander people, the disease is often overlooked by Aboriginal and Torres Strait Islander&nbsp; communities, health workers and service providers. Geographical constraints in the provision of services, a lack of education and awareness in communities and by health workers and the prevalence of other chronic diseases have all posed considerable barriers to the recognition of dementia as an emerging health issue. This paper includes the following recommendations to ensure that Aboriginal and Torres Strait Islander people, family members and communities have access to awareness, information, and appropriate support services for people with dementia

Admiralty Litigation In Perpetuum: The Continuing Saga of Package Litigation and Third World Delivery Problems

Certain admiralty cargo issues are litigated frequently, often in search of a magical test which will preclude all further litigation. Three such issues are package limitations, the burden of proving the condition and quantity of cargo stowed within containers, and the point at which the ocean carrier delivers cargo at discharge and thus completes its duties under the contract of carriage. Despite the frequency with which these issues have been litigated, significant disagreement remains among the circuit courts as to their proper resolution. This article will examine the current state of judicial uncertainty in these areas and the indications given by the courts as the positions most likely to be adopted in the future