Ab initio theory of Fano resonances in plasmonic nanostructures and metamaterials

An ab initio theory for Fano resonances in plasmonic nanostructures and metamaterials is developed using Feshbach formalism. It reveals the role played by the electromagnetic modes and material losses in the system, and enables the engineering of Fano resonances in arbitrary geometries. A general formula for the asymmetric resonance in a non-conservative system is derived. The influence of the electromagnetic interactions on the resonance line shape is discussed and it is shown that intrinsic losses drive the resonance contrast, while its width is mostly determined by the coupling strength between the non-radiative mode and the continuum. The analytical model is in perfect agreement with numerical simulations.Comment: 13 pages, 5 figure

Exactly solvable models of adaptive networks

A satisfiability (SAT-UNSAT) transition takes place for many optimization problems when the number of constraints, graphically represented by links between variables nodes, is brought above some threshold. If the network of constraints is allowed to adapt by redistributing its links, the SAT-UNSAT transition may be delayed and preceded by an intermediate phase where the structure self-organizes to satisfy the constraints. We present an analytic approach, based on the recently introduced cavity method for large deviations, which exactly describes the two phase transitions delimiting this adaptive intermediate phase. We give explicit results for random bond models subject to the connectivity or rigidity percolation transitions, and compare them with numerical simulations.Comment: 4 pages, 4 figure

Coordination of development approval processes revisited – Lagoon Bay Lifestyle Estate (Pty) Ltd v The Minister of Local Government, Environmental Affairs & Development Planning of the Western Cape and Others [2011] 4 All SA 270 (WCC)

From text: This article deals with the decision-making powers of different spheres of government, in terms of various pieces of legislation, with regard to the development of agricultural land and, more specifically, the subdivision or rezoning of such land

Wary Holdings (Pty) Ltd v Stalwo (Pty) Ltd & Another (Trustees of the Hoogekraal Highlands Trust & SAFAMCO Enterprises (Pty) Ltd (amicus curiae); Minister of Agriculture & Land Affairs (intervening)) [2008] JOL 22099 (CC)

In terms of the Subdivision of Agricultural Land Act 70 of 1970, the (national) Minister of Agriculture, Forestry and Fisheries has to authorise, in writing, every application for the subdivision of agricultural land. The following proviso was added to the definition of ‘agricultural land’ in the Act in 1995: “Provided that land situated in the area of jurisdiction of a transitional council as defined in section 1 of the Local Government Transition Act, 1993 (Act No. 209 of 1993), which immediately prior to the first election of the members of such transitional council was classified as agricultural land, shall remain classified as such.” The question that arose in this case was whether the proviso only existed during the lifetime of transitional councils. An affirmative answer to the above question would result in the de facto and de jure implicit termination (and disappearance) of agricultural land as a category in South African law and, consequently, of the Minister’s power to approve any subdivision of agricultural land. A negative answer would imply that agricultural land remains as a category, that the provisions of SALA need to be complied with, and that the Minister’s written approval needs to be obtained for each and every application for subdivision of agricultural land. This article contends that the Constitutional Court was correct in finding that the proviso (and the Act) is still applicable today

The phenotype of circulating follicular-helper T cells in patients with rheumatoid arthritis defines CD200 as a potential therapeutic target

Rheumatoid arthritis (RA) is a systemic autoimmune disease primarily affecting synovial joints in which the development of autoantibodies represents a failure of normal tolerance mechanisms, suggesting a role for follicular helper T cells (TFH) in the genesis of autoimmunity. To determine whether quantitative or qualitative abnormalities in the circulating TFH cell population exist, we analysed by flow cytometry the number and profile of these cells in 35 patients with RA and 15 matched controls. Results were correlated with patient characteristics, including the presence of autoantibodies, disease activity, and treatment with biologic agents. Circulating TFH cells from patients with RA show significantly increased expression of the immunoglobulin superfamily receptor CD200, with highest levels seen in seropositive patients (P=0.0045) and patients treated with anti-TNFα agents (P=0.0008). This occurs in the absence of any change in TFH numbers or overt bias towards Th1, Th2, or Th17 phenotypes. CD200 levels did not correlate with DAS28 scores (P=0.887). Although the number of circulating TFH cells is not altered in the blood of patients with RA, the TFH cells have a distinct phenotype. These differences associate TFH cells with the pathogenesis of RA and support the relevance of the CD200/CD200R signalling pathway as a potential therapeutic target

Landscape of solutions in constraint satisfaction problems

We present a theoretical framework for characterizing the geometrical properties of the space of solutions in constraint satisfaction problems, together with practical algorithms for studying this structure on particular instances. We apply our method to the coloring problem, for which we obtain the total number of solutions and analyze in detail the distribution of distances between solutions.Comment: 4 pages, 4 figures. Replaced with published versio

Statistics of eigenfunctions in open chaotic systems: a perturbative approach

We investigate the statistical properties of the complexness parameter which characterizes uniquely complexness (biorthogonality) of resonance eigenstates of open chaotic systems. Specifying to the regime of isolated resonances, we apply the random matrix theory to the effective Hamiltonian formalism and derive analytically the probability distribution of the complexness parameter for two statistical ensembles describing the systems invariant under time reversal. For those with rigid spectra, we consider a Hamiltonian characterized by a picket-fence spectrum without spectral fluctuations. Then, in the more realistic case of a Hamiltonian described by the Gaussian Orthogonal Ensemble, we reveal and discuss the r\^ole of spectral fluctuations