Algebraic entropy for algebraic maps

We propose an extension of the concept of algebraic entropy, as introduced by Bellon and Viallet for rational maps, to algebraic maps (or correspondences) of a certain kind. The corresponding entropy is an index of the complexity of the map. The definition inherits the basic properties from the definition of entropy for rational maps. We give an example with positive entropy, as well as two examples taken from the theory of Backlund transformations

What is a population-level approach to prevention, and how could we apply it to dementia risk reduction?

The World Health Organisation's 2022 ‘blueprint for dementia research’ highlights the need for more research into population-level risk reduction. However, definitions of population-level prevention vary, and application to dementia is challenging because of its multi-factorial aetiology and a maturing prevention evidence base. This paper compares and contrasts key concepts of ‘population-level prevention’ from the literature, explores related theoretical models and policy frameworks, and applies this to dementia risk reduction. We reach a proposed definition of population-level risk reduction of dementia, which focusses on the need to change societal conditions such that the population is less likely to develop modifiable risk factors known to be associated with dementia, without the need for high-agency behaviour change by individuals. This definition, alongside identified policy frameworks, can inform synthesis of existing evidence and help to co-ordinate the generation of new evidence

Are Population-Level Approaches to Dementia Risk Reduction Under-Researched? A Rapid Review of the Dementia Prevention Literature

Dementia is forecast to become increasingly prevalent, particularly in low- and middle-income countries, and is associated with high human and economic costs. Primary prevention of dementia -preventing risk factors leading to disease development - is an emerging global public health priority. Primary prevention can be achieved in two ways: individual-level or population-level. In this rapid review, we quantify the proportion of contributing interventional evidence to the dementia primary prevention literature that is concerned with either approach. We searched Medline, the National Institute for Health and Care Excellence, Cochrane, the World Health Organization, and Google to identify systematic reviews that described primary prevention interventions for dementia. We used search terms related to dementia risk reduction, intervention/policy, and review. We analysed reference lists of included dementia prevention reviews to identify contributing primary prevention evidence, and categorised these as either individual-level or population-level. Additionally, we examined search strategies to investigate the likelihood of reviews identifying available population-level interventions. We included twelve of the 527 articles retrieved. Population-level evidence was summarised by only two reviews. In these two reviews, <2.5% of the interventions described where population-level interventions. Most search strategies were weighted towards identifying individual-level evidence. Existing systematic reviews of dementia primary prevention interventions include almost no population-level evidence. Correction of this imbalance is needed to ensure that dementia prevention policies can achieve meaningful reductions in the prevalence of, and inequalities in, dementia

Electrophilic boron carboxylate and phosphinate complexes

The reactions of a series of carboxylic acids with H2B(C6F5)·SMe2 are shown to afford species of the form [RC(O)OB(C6F5)]2O, (R = Tol 1, Ph 2, C6F53, Me2BrC 4, Me 5) in 87–95% yields with the concurrent reduction of the carboxylic acid to the corresponding aldehyde. A mechanism for the formation of 1–5 is proposed to proceed via a cyclic eight-membered ring species. Analogues of these species were prepared via reactions of carboxylic and phosphinic acids with HB(C6F5)2 and H2B(C6F5)·SMe2, respectively, to give [TolC(O)OB(C6F5)2]26, [(C6F5)C(O)OB(C6F5)2]27, and [Ph2P(O)OBH(C6F5)]28. These products react subsequently to give TolC(O)OBH(C6F5)(NC5H4NMe2) 9 and Ph2P(O)OBH(C6F5)(NC5H4NMe2) 10. The acyloxyborate derivatives 1–4 were shown to be inactive in mediating the direct amidation of carboxylic acids, consistent with previous observations that infer the need for a sterically congested environment about the boron centres

Solutions to the Optical Cascading Equations

Group theoretical methods are used to study the equations describing \chi^{(2)}:\chi^{(2)} cascading. The equations are shown not to be integrable by inverse scattering techniques. On the other hand, these equations do share some of the nice properties of soliton equations. Large families of explicit analytical solutions are obtained in terms of elliptic functions. In special cases, these periodic solutions reduce to localized ones, i.e., solitary waves. All previously known explicit solutions are recovered, and many additional ones are obtainedComment: 21 page

Lie point symmetries of difference equations and lattices

A method is presented for finding the Lie point symmetry transformations acting simultaneously on difference equations and lattices, while leaving the solution set of the corresponding difference scheme invariant. The method is applied to several examples. The found symmetry groups are used to obtain particular solutions of differential-difference equations

Bose-Hubbard model with occupation dependent parameters

We study the ground-state properties of ultracold bosons in an optical lattice in the regime of strong interactions. The system is described by a non-standard Bose-Hubbard model with both occupation-dependent tunneling and on-site interaction. We find that for sufficiently strong coupling the system features a phase-transition from a Mott insulator with one particle per site to a superfluid of spatially extended particle pairs living on top of the Mott background -- instead of the usual transition to a superfluid of single particles/holes. Increasing the interaction further, a superfluid of particle pairs localized on a single site (rather than being extended) on top of the Mott background appears. This happens at the same interaction strength where the Mott-insulator phase with 2 particles per site is destroyed completely by particle-hole fluctuations for arbitrarily small tunneling. In another regime, characterized by weak interaction, but high occupation numbers, we observe a dynamical instability in the superfluid excitation spectrum. The new ground state is a superfluid, forming a 2D slab, localized along one spatial direction that is spontaneously chosen.Comment: 16 pages, 4 figure

Optimised Traffic Flow at a Single Intersection: Traffic Responsive signalisation

We propose a stochastic model for the intersection of two urban streets. The vehicular traffic at the intersection is controlled by a set of traffic lights which can be operated subject to fix-time as well as traffic adaptive schemes. Vehicular dynamics is simulated within the framework of the probabilistic cellular automata and the delay experienced by the traffic at each individual street is evaluated for specified time intervals. Minimising the total delay of both streets gives rise to the optimum signalisation of traffic lights. We propose some traffic responsive signalisation algorithms which are based on the concept of cut-off queue length and cut-off density.Comment: 10 pages, 11 eps figs, to appear in J. Phys.