Bulk, surface and corner free energy series for the chromatic polynomial on the square and triangular lattices

We present an efficient algorithm for computing the partition function of the q-colouring problem (chromatic polynomial) on regular two-dimensional lattice strips. Our construction involves writing the transfer matrix as a product of sparse matrices, each of dimension ~ 3^m, where m is the number of lattice spacings across the strip. As a specific application, we obtain the large-q series of the bulk, surface and corner free energies of the chromatic polynomial. This extends the existing series for the square lattice by 32 terms, to order q^{-79}. On the triangular lattice, we verify Baxter's analytical expression for the bulk free energy (to order q^{-40}), and we are able to conjecture exact product formulae for the surface and corner free energies.Comment: 17 pages. Version 2: added 4 further term to the serie

Impact of the council of europe resolution on quality and safety assurance requirements for medicinal products prepared in pharmacies for the special needs of patients

Introduction and objective: The regulation of pharmacy preparations, especially for standards for quality assurance and safety, is not harmonised across Europe and falls under the national competencies of individual states. There are concerns about quality control and safety for the medicinal products made in pharmacies, which is widespread in European countries. There are, however, good reasons to continue this practice, which is able to tailor preparations to the specific needs of a particular patient or patient group and to provide a supplementary source of supply when an industrially manufactured product, which is authorised for marketing is not available or when there are temporary shortages of licensed medicines. In seeking to provide guidelines for legislation and acting on the advice of an expert group dealing in pharmaceutical practices, the Committee of Ministers of the Council of Europe passed a resolution in 2011. The Council of Europe Resolution provides authorities and pharmacists with the means to reinforce safety measures for medicinal products prepared in pharmacies and to harmonise quality assurance and safety standards. It dealt with aspects of pharmacy preparation such as quality standards for preparation and distribution, marketing authorisation, product dossiers, labelling, reporting, and safety. In 2013 and 2014 the Committee of Experts carried out a survey to evaluate the impact of the resolution within a cross section of member states,Methods: In the resolution of 2011 the member states were recommended to adapt their legislation in line with its provisions. The survey that was carried out in 2013 and 2014 followed the recommendations in the reso-lution. A questionnaire was made and sent to across section of member states.Results: Among the member states involved, the results of this survey show a clear commitment to imple-ment the recommendations of the resolution.Conclusions: This report presents the results of the survey with a discussion of outstanding issues

Resolving the molecular architecture of the photoreceptor active zone with 3D-MINFLUX

Cells assemble macromolecular complexes into scaffoldings that serve as substrates for catalytic processes. Years of molecular neurobiology research indicate that neurotransmission depends on such optimization strategies. However, the molecular topography of the presynaptic active zone (AZ), where transmitter is released upon synaptic vesicle (SV) fusion, remains to be visualized. Therefore, we implemented MINFLUX optical nanoscopy to resolve the AZ of rod photoreceptors. This was facilitated by a novel sample immobilization technique that we name heat-assisted rapid dehydration (HARD), wherein a thin layer of rod synaptic terminals (spherules) was transferred onto glass coverslips from fresh retinal slices. Rod ribbon AZs were readily immunolabeled and imaged in 3D with a precision of a few nanometers. Our 3D-MINFLUX results indicate that the SV release site in rods is a molecular complex of bassoon–RIM2–ubMunc13-2–Cav1.4, which repeats longitudinally on both sides of the ribbon

The synaptic ribbon is critical for sound encoding at high rates and with temporal precision.

We studied the role of the synaptic ribbon for sound encoding at the synapses between inner hair cells (IHCs) and spiral ganglion neurons (SGNs) in mice lacking RIBEYE (RBEKO/KO). Electron and immunofluorescence microscopy revealed a lack of synaptic ribbons and an assembly of several small active zones (AZs) at each synaptic contact. Spontaneous and sound-evoked firing rates of SGNs and their compound action potential were reduced, indicating impaired transmission at ribbonless IHC-SGN synapses. The temporal precision of sound encoding was impaired and the recovery of SGN-firing from adaptation indicated slowed synaptic vesicle (SV) replenishment. Activation of Ca2+-channels was shifted to more depolarized potentials and exocytosis was reduced for weak depolarizations. Presynaptic Ca2+-signals showed a broader spread, compatible with the altered Ca2+-channel clustering observed by super-resolution immunofluorescence microscopy. We postulate that RIBEYE disruption is partially compensated by multi-AZ organization. The remaining synaptic deficit indicates ribbon function in SV-replenishment and Ca2+-channel regulation

Series studies of the Potts model. I: The simple cubic Ising model

The finite lattice method of series expansion is generalised to the $q$-state Potts model on the simple cubic lattice. It is found that the computational effort grows exponentially with the square of the number of series terms obtained, unlike two-dimensional lattices where the computational requirements grow exponentially with the number of terms. For the Ising ($q=2$) case we have extended low-temperature series for the partition functions, magnetisation and zero-field susceptibility to $u^{26}$ from $u^{20}$. The high-temperature series for the zero-field partition function is extended from $v^{18}$ to $v^{22}$. Subsequent analysis gives critical exponents in agreement with those from field theory.Comment: submitted to J. Phys. A: Math. Gen. Uses preprint.sty: included. 24 page

Foundation and empire : a critique of Hardt and Negri

In this article, Thompson complements recent critiques of Hardt and Negri's Empire (see Finn Bowring in Capital and Class, no. 83) using the tools of labour process theory to critique the political economy of Empire, and to note its unfortunate similarities to conventional theories of the knowledge economy

Series expansions from the corner transfer matrix renormalization group method: the hard squares model

The corner transfer matrix renormalization group method is an efficient method for evaluating physical quantities in statistical mechanical models. It originates from Baxter's corner transfer matrix equations and method, and was developed by Nishino and Okunishi in 1996. In this paper, we review and adapt this method, previously used for numerical calculations, to derive series expansions. We use this to calculate 92 terms of the partition function of the hard squares model. We also examine the claim that the method is subexponential in the number of generated terms and briefly analyse the resulting series.Comment: 10 figure