Computational science and re-discovery: open-source implementations of ellipsoidal harmonics for problems in potential theory

We present two open-source (BSD) implementations of ellipsoidal harmonic expansions for solving problems of potential theory using separation of variables. Ellipsoidal harmonics are used surprisingly infrequently, considering their substantial value for problems ranging in scale from molecules to the entire solar system. In this article, we suggest two possible reasons for the paucity relative to spherical harmonics. The first is essentially historical---ellipsoidal harmonics developed during the late 19th century and early 20th, when it was found that only the lowest-order harmonics are expressible in closed form. Each higher-order term requires the solution of an eigenvalue problem, and tedious manual computation seems to have discouraged applications and theoretical studies. The second explanation is practical: even with modern computers and accurate eigenvalue algorithms, expansions in ellipsoidal harmonics are significantly more challenging to compute than those in Cartesian or spherical coordinates. The present implementations reduce the "barrier to entry" by providing an easy and free way for the community to begin using ellipsoidal harmonics in actual research. We demonstrate our implementation using the specific and physiologically crucial problem of how charged proteins interact with their environment, and ask: what other analytical tools await re-discovery in an era of inexpensive computation?Comment: 25 pages, 3 figure

Alternative Fourier Expansions for Inverse Square Law Forces

Few-body problems involving Coulomb or gravitational interactions between pairs of particles, whether in classical or quantum physics, are generally handled through a standard multipole expansion of the two-body potentials. We discuss an alternative based on a compact, cylindrical Green's function expansion that should have wide applicability throughout physics. Two-electron "direct" and "exchange" integrals in many-electron quantum systems are evaluated to illustrate the procedure which is more compact than the standard one using Wigner coefficients and Slater integrals.Comment: 10 pages, latex/Revtex4, 1 figure

Bayes-X: a Bayesian inference tool for the analysis of X-ray observations of galaxy clusters

We present the first public release of our Bayesian inference tool, Bayes-X, for the analysis of X-ray observations of galaxy clusters. We illustrate the use of Bayes-X by analysing a set of four simulated clusters at z=0.2-0.9 as they would be observed by a Chandra-like X-ray observatory. In both the simulations and the analysis pipeline we assume that the dark matter density follows a spherically-symmetric Navarro, Frenk and White (NFW) profile and that the gas pressure is described by a generalised NFW (GNFW) profile. We then perform four sets of analyses. By numerically exploring the joint probability distribution of the cluster parameters given simulated Chandra-like data, we show that the model and analysis technique can robustly return the simulated cluster input quantities, constrain the cluster physical parameters and reveal the degeneracies among the model parameters and cluster physical parameters. We then analyse Chandra data on the nearby cluster, A262, and derive the cluster physical profiles. To illustrate the performance of the Bayesian model selection, we also carried out analyses assuming an Einasto profile for the matter density and calculated the Bayes factor. The results of the model selection analyses for the simulated data favour the NFW model as expected. However, we find that the Einasto profile is preferred in the analysis of A262. The Bayes-X software, which is implemented in Fortran 90, is available at http://www.mrao.cam.ac.uk/facilities/software/bayesx/.Comment: 22 pages, 11 figure

Non-invasive, near-field terahertz imaging of hidden objects using a single pixel detector

Terahertz (THz) imaging has the ability to see through otherwise opaque materials. However, due to the long wavelengths of THz radiation ({\lambda}=300{\mu}m at 1THz), far-field THz imaging techniques are heavily outperformed by optical imaging in regards to the obtained resolution. In this work we demonstrate near-field THz imaging with a single-pixel detector. We project a time-varying optical mask onto a silicon wafer which is used to spatially modulate a pulse of THz radiation. The far-field transmission corresponding to each mask is recorded by a single element detector and this data is used to reconstruct the image of an object placed on the far side of the silicon wafer. We demonstrate a proof of principal application where we image a printed circuit board on the underside of a 115{\mu}m thick silicon wafer with ~100{\mu}m ({\lambda}/4) resolution. With subwavelength resolution and the inherent sensitivity to local conductivity provided by the THz probe frequencies, we show that it is possible to detect fissures in the circuitry wiring of a few microns in size. Imaging systems of this type could have other uses where non-invasive measurement or imaging of concealed structures with high resolution is necessary, such as in semiconductor manufacturing or in bio-imaging

Characterizing Planetary Orbits and the Trajectories of Light

Exact analytic expressions for planetary orbits and light trajectories in the Schwarzschild geometry are presented. A new parameter space is used to characterize all possible planetary orbits. Different regions in this parameter space can be associated with different characteristics of the orbits. The boundaries for these regions are clearly defined. Observational data can be directly associated with points in the regions. A possible extension of these considerations with an additional parameter for the case of Kerr geometry is briefly discussed.Comment: 49 pages total with 11 tables and 10 figure

Novel loss-of-function mutation in HERC2 is associated with severe developmental delay and paediatric lethality

Background: The HERC2 gene encodes a 527 kDa E3 ubiquitin protein ligase that has key roles in cell cycle regulation, spindle formation during mitosis, mitochondrial functions and DNA damage responses. It has essential roles during embryonic development, particularly for neuronal and muscular functions. To date, missense mutations in HERC2 have been associated with an autosomal recessive neurodevelopmental disorder with some phenotypical similarities to Angelman syndrome, and a homozygous deletion spanning HERC2 and OCA2 causing a more severe neurodevelopmental phenotype. Methods and results: We ascertained a consanguineous family with a presumed autosomal recessive severe neurodevelopmental disorder that leads to paediatric lethality. In affected individuals, we identified a homozygous HERC2 frameshift variant that results in a premature stop codon and complete loss of HERC2 protein. Functional characterisation of this variant in fibroblasts, from one living affected individual, revealed impaired mitochondrial network and function as well as disrupted levels of known interacting proteins such as XPA. Conclusion: This study extends the genotype–phenotype correlation for HERC2 variants to include a distinct lethal neurodevelopmental disorder, highlighting the importance of further characterisation for HERC2-related disorders

Interactional positioning and narrative self-construction in the first session of psychodynamic-interpersonal psychotherapy

The purpose of this study is to identify possible session one indicators of end of treatment psychotherapy outcome using the framework of three types of interactional positioning; client’s self-positioning, client’s positioning between narrated self and different partners, and the positioning between client and therapist. Three successful cases of 8-session psychodynamic-interpersonal (PI) therapy were selected on the basis of client Beck Depression Inventory scores. One unsuccessful case was also selected against which identified patterns could be tested. The successful clients were more descriptive about their problems and demonstrated active rapport-building, while the therapist used positionings expressed by the client in order to explore the positionings developed between them during therapy. The unsuccessful case was characterized by lack of positive self-comment, minimization of agentic self-capacity, and empathy-disrupting narrative confusions. We conclude that the theory of interactional positioning has been useful in identifying patterns worth exploring as early indicators of success in PI therapy

Foundation of Statistical Mechanics under experimentally realistic conditions

We demonstrate the equilibration of isolated macroscopic quantum systems, prepared in non-equilibrium mixed states with significant population of many energy levels, and observed by instruments with a reasonably bound working range compared to the resolution limit. Both properties are fulfilled under many, if not all, experimentally realistic conditions. At equilibrium, the predictions and limitations of Statistical Mechanics are recovered.Comment: Accepted in Phys. Rev. Let