Bethe Ansatz solution of a decagonal rectangle triangle random tiling

A random tiling of rectangles and triangles displaying a decagonal phase is solved by Bethe Ansatz. Analogously to the solutions of the dodecagonal square triangle and the octagonal rectangle triangle tiling an exact expression for the maximum of the entropy is found.Comment: 17 pages, 4 figures, some remarks added and typos correcte

Exact Solution of an Octagonal Random Tiling Model

We consider the two-dimensional random tiling model introduced by Cockayne, i.e. the ensemble of all possible coverings of the plane without gaps or overlaps with squares and various hexagons. At the appropriate relative densities the correlations have eight-fold rotational symmetry. We reformulate the model in terms of a random tiling ensemble with identical rectangles and isosceles triangles. The partition function of this model can be calculated by diagonalizing a transfer matrix using the Bethe Ansatz (BA). The BA equations can be solved providing {\em exact} values of the entropy and elastic constants.Comment: 4 pages,3 Postscript figures, uses revte

Spectral structure and decompositions of optical states, and their applications

We discuss the spectral structure and decomposition of multi-photon states. Ordinarily `multi-photon states' and `Fock states' are regarded as synonymous. However, when the spectral degrees of freedom are included this is not the case, and the class of `multi-photon' states is much broader than the class of `Fock' states. We discuss the criteria for a state to be considered a Fock state. We then address the decomposition of general multi-photon states into bases of orthogonal eigenmodes, building on existing multi-mode theory, and introduce an occupation number representation that provides an elegant description of such states that in many situations simplifies calculations. Finally we apply this technique to several example situations, which are highly relevant for state of the art experiments. These include Hong-Ou-Mandel interference, spectral filtering, finite bandwidth photo-detection, homodyne detection and the conditional preparation of Schr\"odinger Kitten and Fock states. Our techniques allow for very simple descriptions of each of these examples.Comment: 12 page

MPS VII – Extending the classical phenotype

DATA AVAILABILITY: No data was used for the research described in the article.Mucopolysaccharidosis VII (or Sly syndrome) is an autosomal recessive disorder characterised by a deficiency in the enzyme Beta-glucuronidase (GUSB). Partial degradation of glycosaminoglycans (GAGs); chondroitin sulfate (CS), dermatan sulfate (DS) and heparan sulfate (HS) results in the accumulation of these fragments in the lysosomes of many tissues, eventually leading to multisystem damage. In some cases, early diagnosis on clinical grounds alone can be difficult due to the extreme variability of the clinical presentation and disease progression. We present a case report of a 31-year-old male patient diagnosed with MPS VII at the age of 28, who multiple specialists saw without suspecting the diagnosis due to the unusual presentation. The patient presented with a history of developmental delay, scoliosis, kyphosis, corneal clouding, abnormal gait, short stature, hearing impairment, slightly coarse facial features and progressive deterioration of fine motor skills since childhood. The patient had inguinal hernia repair at around 12 months, bilateral hearing impairment with a left bone-anchored hearing aid, and spinal surgery. During spinal surveillance MPS VII was suspected by a spinal surgeon with interest in MPS, and the diagnosis confirmed with a deficiency in beta-glucuronidase in leucocytes and marginally elevated urinary GAGs. Next-generation sequencing identified two mutations in the GUSB gene (OMIM 611499), c.526C > T p.(Leu176Phe) and c.1820G > C p.(Gly607Ala). Although the patient exhibited features of the severe form of non-classical manifestations, his metabolic condition has remained reasonably stable, surviving into adulthood with only symptomatic treatment. We present the ever-expanding phenotypic spectrum of this ultra-rare disease.https://www.elsevier.com/locate/ymgmrhj2023Paediatrics and Child Healt

Planck intermediate results. XXIX. All-sky dust modelling with Planck, IRAS, and WISE observations

We present all-sky modelling of the high resolution Planck, IRAS, and WISE infrared (IR) observations using the physical dust model presented by Draine and Li in 2007 (DL). We study the performance and results of this model, and discuss implications for future dust modelling. The present work extends the DL dust modelling carried out on nearby galaxies using Herschel and Spitzer data to Galactic dust emission. We employ the DL dust model to generate maps of the dust mass surface density, the optical extinction Av, and the starlight intensity parametrized by Umin. The DL model reproduces the observed spectral energy distribution (SED) satisfactorily over most of the sky, with small deviations in the inner Galactic disk and in low ecliptic latitude areas. We compare the DL optical extinction Av for the diffuse interstellar medium with optical estimates for 2 10^5 quasi-stellar objects (QSOs) observed in the Sloan digital sky survey. The DL Av estimates are larger than those determined towards QSOs by a factor of about 2, which depends on Umin. The DL fitting parameter Umin, effectively determined by the wavelength where the SED peaks, appears to trace variations in the far-IR opacity of the dust grains per unit Av, and not only in the starlight intensity. To circumvent the model deficiency, we propose an empirical renormalization of the DL Av estimate, dependent of Umin, which compensates for the systematic differences found with QSO observations. This renormalization also brings into agreement the DL Av estimates with those derived for molecular clouds from the near-IR colours of stars in the 2 micron all sky survey. The DL model and the QSOs data are used to compress the spectral information in the Planck and IRAS observations for the diffuse ISM to a family of 20 SEDs normalized per Av, parameterized by Umin, which may be used to test and empirically calibrate dust models.Comment: Final version that has appeared in A&