Nonconcave entropies in multifractals and the thermodynamic formalism

We discuss a subtlety involved in the calculation of multifractal spectra when these are expressed as Legendre-Fenchel transforms of functions analogous to free energy functions. We show that the Legendre-Fenchel transform of a free energy function yields the correct multifractal spectrum only when the latter is wholly concave. If the spectrum has no definite concavity, then the transform yields the concave envelope of the spectrum rather than the spectrum itself. Some mathematical and physical examples are given to illustrate this result, which lies at the root of the nonequivalence of the microcanonical and canonical ensembles. On a more positive note, we also show that the impossibility of expressing nonconcave multifractal spectra through Legendre-Fenchel transforms of free energies can be circumvented with the help of a generalized free energy function, which relates to a recently introduced generalized canonical ensemble. Analogies with the calculation of rate functions in large deviation theory are finally discussed.Comment: 9 pages, revtex4, 3 figures. Changes in v2: sections added on applications plus many new references; contains an addendum not contained in published versio

Does police size matter?:A review of the evidence regarding restructuring police organisations

Restructuring and merging public sector organisations is often seen as a way to enhance efficiency and efficacy. There is ongoing debate about the impact of police force sizes, structures and mergers as police organisations attempt to adapt to reductions in their budgets and changes in patterns of criminality. The article reviews the evidence regarding key aspects of police reform: finding mixed evidence regarding the links between size and performance, while noting risks that mergers may impair local policing. The article discusses the impact of mergers on protective services, governance and accountability, while also discussing potential risks and opportunities associated with the merger process itself. The review finds significant gaps in the available evidence, and significant opportunities to expand the evidence base on this topic. Given current gaps in the evidence regarding size, efficacy and efficiency, it is important to give due consideration to symbolic and rhetorical aspects of mergers

Riding on the Coat-Tails of Traditional Cultural Expressions

Matters related to the protection of traditional cultural expressions (‘TCEs’) or expressions of folklore (‘EoFs’) are sensitive and intricate as a blend of legal, economic, philosophical and anthropological considerations jostle to capture their core features. This results in disparate views surrounding what should qualify as TCEs or EoFs, who should be considered their ‘owner’ (assuming that ownership per se is conceptually compatible with these items), which is the most appropriate legal protection regime and how broad their scope of protection should be. Drawing from these various accounts on TCEs, this article focuses on the interaction between TCEs and EoFs originating on the European continent and the European Union (‘EU’) trade mark legislation. Specifically, this article examines whether the limitations of the effects of trade mark rights and of the absolute grounds of refusal, as developed by the case law of the Court of Justice of the European Union, are effective in preserving the cohesion of TCEs. This article advances the thesis that registration of TCEs and EoFs as trade marks generates an imbalance between the rights of the trade mark owner and the defences available to others under the EU trade mark law framework. Furthermore, such an imbalance is likely to hinder the unfettered circulation of TCEs and undermine their original meaning. Lastly, in some cases, trade mark registration of TCEs contributes to their appropriation and misappropriation. The article concludes that, de lege ferenda, the direct exclusion of TCEs as eligible subject matter for trade mark registration is preferable to seeking a post factum remedy