Endoscopic orbital decompression for Graves' ophthalmopathy

Graves’ disease may occasionally result in significant proptosis that is either cosmetically unacceptable or causes visual loss. This has traditionally been managed surgically by external decompression of the orbital bony skeleton. Trans-nasal endoscopic orbital decompression is emerging as a new minimally-invasive technique, that avoids the need for cutaneous or gingival incisions. Decompression of the medial orbital wall can be performed up to the anterior wall of the sphenoid sinus. This can be combined with resection of the medial and posterior portion of the orbital floor (preserving the infra-orbital nerve). This technique produces decompression which is comparable to external techniques. We present a series of 10 endoscopic orbital decompressions with an average improvement of 4.4 mm in orbital proptosis. There was an improvement in visual acuity in all patients with visual impairment. Endoscopic orbital decompression is recommended as an alternative to traditional decompression techniques.Desmond T. H. Wee, A. Simon Carney, Mark Thorpe and Peter J. Wormal

Colourings of cubic graphs inducing isomorphic monochromatic subgraphs

A $k$-bisection of a bridgeless cubic graph $G$ is a $2$-colouring of its vertex set such that the colour classes have the same cardinality and all connected components in the two subgraphs induced by the colour classes (monochromatic components in what follows) have order at most $k$. Ban and Linial conjectured that every bridgeless cubic graph admits a $2$-bisection except for the Petersen graph. A similar problem for the edge set of cubic graphs has been studied: Wormald conjectured that every cubic graph $G$ with $|E(G)| \equiv 0 \pmod 2$ has a $2$-edge colouring such that the two monochromatic subgraphs are isomorphic linear forests (i.e. a forest whose components are paths). Finally, Ando conjectured that every cubic graph admits a bisection such that the two induced monochromatic subgraphs are isomorphic. In this paper, we give a detailed insight into the conjectures of Ban-Linial and Wormald and provide evidence of a strong relation of both of them with Ando's conjecture. Furthermore, we also give computational and theoretical evidence in their support. As a result, we pose some open problems stronger than the above mentioned conjectures. Moreover, we prove Ban-Linial's conjecture for cubic cycle permutation graphs. As a by-product of studying $2$-edge colourings of cubic graphs having linear forests as monochromatic components, we also give a negative answer to a problem posed by Jackson and Wormald about certain decompositions of cubic graphs into linear forests.Comment: 33 pages; submitted for publicatio

Multi-spatial-mode effects in squeezed-light-enhanced interferometric gravitational wave detectors

Proposed near-future upgrades of the current advanced interferometric gravitational wave detectors include the usage of frequency dependent squeezed light to reduce the current sensitivity-limiting quantum noise. We quantify and describe the degradation effects that spatial mode-mismatches between optical resonators have on the squeezed field. These mode-mismatches can to first order be described by scattering of light into second-order Gaussian modes. As a demonstration of principle, we also show that squeezing the second-order Hermite-Gaussian modes $\mathrm{HG}_{02}$ and $\mathrm{HG}_{20}$, in addition to the fundamental mode, has the potential to increase the robustness to spatial mode-mismatches. This scheme, however, requires independently optimized squeeze angles for each squeezed spatial mode, which would be challenging to realise in practise.Comment: 10 pages, 12 figure

Efficacy of endoscopic sinus surgery for paranasal sinus mucocele including modified endoscopic Lothrop procedure for frontal sinus mucocele

This study evaluated the efficacy of the modified endoscopic Lothrop procedure (MELP) for complicated frontal mucoceles and endoscopic marsupialization for other paranasal sinus mucoceles. It was a retrospective, consecutive case review of sinus mucoceles treated endoscopically by a single surgeon over a four-year period (1998-2002). There were 41 mucoceles in 28 patients, including 24 frontal, eight frontoethmoidal, three ethmoidal, five maxillary and one frontal mucocele. Twenty-one patients underwent the modified Lothrop procedure for frontal mucoceles, and seven underwent simple drainage and marsupialization for frontoethmoidal, ethmoidal and maxillary mucoceles. At median follow-up of 16 months, all patients had a patent mucocele opening. Patients treated by drainage and marsupialization did not have any complications or mucocele recurrence. All patients treated by the modified endoscopic Lothrop procedure had improvement in symptoms and signs. Four patients had minor complications including epistaxis and adhesions and five required further surgery. The average hospital in-patient stay was 2 ± 1.4 days. Endoscopic techniques, including MELP are effective in the short term for the management of complex and simple paranasal sinus mucoceles. MELP has a useful place in the management of mucoceles with a significant bony partition from an adjacent sinus or nasal cavity. It is also indicated when the mucocele is associated with loss of lateral support in the sinus with risk of medial-wall collapse of the orbital contents obstructing drainage.Jwu Jin Khong, Raman Malhotra, Dinesh Selva and Peter John Wormal

An algorithm for counting circuits: application to real-world and random graphs

We introduce an algorithm which estimates the number of circuits in a graph as a function of their length. This approach provides analytical results for the typical entropy of circuits in sparse random graphs. When applied to real-world networks, it allows to estimate exponentially large numbers of circuits in polynomial time. We illustrate the method by studying a graph of the Internet structure.Comment: 7 pages, 3 figures, minor corrections, accepted versio

The exponent set of symmetric primitive (0, 1) matrices with zero trace

AbstractWe prove that the exponent set of symmetric primitive (0, 1) matrices with zero trace (the adjacency matrices of the simple graphs) is {2,3,…,2n−4}⧹S, where S is the set of all odd numbers in {n−2,n−1,…,2n−5}. We also obtain a characterization of the symmetric primitive matrices with zero trace whose exponents attain the upper bound 2n−4

The role of electronic triplets and high-lying singlet states in the deactivation mechanism of the parent BODIPY: An ADC(2) and CASPT2 study

The potential tunability of the spectroscopic properties of the BODIPY parent dye by suitable functionalization makes it attractive for a number of applications. Unfortunately, its strong fluorescence against minor intersystem crossing to the triplet states prevents its application in photodynamic therapy. With the perspective of designing BODIPY derivatives with enhanced intersystem crossing, the goal of this work is two-fold: (i) investigate the main deactivation channels of the parent BODIPY following irradiation, paying particular attention to the accessibility of the triplet state potential energy surfaces, as well as the non-radiative pathways involving the second brightest more stable singlet electronic state, S2, and (ii) evaluate the performance of the computationally efficient second order algebraic-diagrammatic construction scheme for the polarization propagator, (ADC(2)) against the complete active space second-order perturbation theory (CASPT2) method. Three singlet/triplet crossings were found, all of them with small spin-orbit couplings, being the S1/T2 crossing the most plausible for the observed intersystem crossing yield. Methodologically, it is found that the ADC(2) method qualitatively reproduces the landscape of the potential energy profiles for the photophysical processes investigated; however, it systematically underestimates the energies of the stationary points and crossings of the same and different multiplicity, with the largest discrepancies found at S1/S0 crossing points. Our CASPT2 results provide a comprehensive picture of the landscape of the excited state potential energy surfaces of the parent BODIPY that might serve as a basis for the rational design of photosensitizers with a particular photophysical profileThis work has been supported by the Project CTQ2015-63997- C2 of the Ministerio de Economía y Competitividad of Spain. I.C. gratefully acknowledges the “Ramón y Cajal” program of the Ministerio de Economía y Competitividad of Spain. M.D.V. thanks the Marie Curie Actions, within the Innovative Training Network-European Join Doctorate in Theoretical Chemistry and Computational Modelling TCCM-ITN-EJD-642294, for financial suppor

A variable amplitude fretting fatigue life estimation technique: formulation and experimental validation

The aims of the research work summarised in this paper are twofold. The first goal is to make available a large number of new experimental results generated by testing specimens of grey cast iron under both constant and variable amplitude fretting fatigue loading. The second goal is to formulate an advanced fretting fatigue design approach based on the combined use of the Modified Wӧhler Curve Method, the Theory of Critical Distances and the Shear Stress-Maximum Variance Method. The validation exercise based on the experimental results being produced demonstrates that the proposed methodology is a powerful tool suitable for designing mechanical assemblies against fretting fatigue

Ising Model on Networks with an Arbitrary Distribution of Connections

We find the exact critical temperature $T_c$ of the nearest-neighbor ferromagnetic Ising model on an `equilibrium' random graph with an arbitrary degree distribution $P(k)$. We observe an anomalous behavior of the magnetization, magnetic susceptibility and specific heat, when $P(k)$ is fat-tailed, or, loosely speaking, when the fourth moment of the distribution diverges in infinite networks. When the second moment becomes divergent, $T_c$ approaches infinity, the phase transition is of infinite order, and size effect is anomalously strong.Comment: 5 page