Complex structures in galaxy cluster fields: implications for gravitational lensing mass models

The distribution of mass on galaxy cluster scales is an important test of structure formation scenarios, providing constraints on the nature of dark matter itself. Several techniques have been used to probe the mass distributions of clusters, sometimes yielding results which are discrepant, or at odds with clusters formed in simulations - for example giving NFW concentration parameters much higher than expected in the standard CDM model. In addition, the velocity fields of some well studied galaxy clusters reveal the presence of several structures close to the line-of-sight, often not dynamically bound to the cluster itself. We investigate what impact such neighbouring but unbound massive structures would have on the determination of cluster profiles using weak gravitational lensing. Depending on its concentration and mass ratio to the primary halo, one secondary halo close to the line-of-sight can cause the estimated NFW concentration parameter to be significantly higher than that of the primary halo, and also cause the estimated mass to be biased high. Although it is difficult to envisage how this mechanism alone could yield concentrations as high as reported for some clusters, multiple haloes close to the line-of-sight, such as in the case of Abell 1689, can substantially increase the concentration parameter estimate. Together with the fact that clusters are triaxial, and that including baryonic physics also leads to an increase in the concentration of a dark matter halo, the tension between observations and the standard CDM model is eased. If the alignment with the secondary structure is imprecise, then the estimated concentration parameter can also be even lower than that of the primary halo, reinforcing the importance of identifying structures in cluster fields.Comment: To appear in MNRAS letters, 5 pages, 3 figure

An MCMC Fitting Method for Triaxial Dark Matter Haloes

Measuring the 3D distribution of mass on galaxy cluster scales is a crucial test of the LCDM model, providing constraints on the behaviour of dark matter. Recent work investigating mass distributions of individual galaxy clusters (e.g. Abell 1689) using weak and strong gravitational lensing has revealed potential inconsistencies between the predictions of structure formation models relating halo mass to concentration and those relationships as measured in massive clusters. However, such analyses employ simple spherical halo models while a growing body of work indicates that triaxial 3D halo structure is both common and important in parameter estimates. The very strong assumptions about the symmetry of the lensing halo implied with circular or perturbative elliptical NFW models are not physically motivated and lead to incorrect parameter estimates with significantly underestimated error bars. We here introduce a Markov Chain Monte Carlo (MCMC) method to fit fully triaxial models to weak lensing data that gives parameter and error estimates that fully incorporate the true uncertainty present in nature. Applying the MCMC triaxial fitting method to a population of NFW triaxial lenses drawn from the shape distribution of structure formation simulations, we find that including triaxiality cannot explain a population of massive, highly concentrated clusters within the framework of LCDM, but easily explains rare cases of apparently massive, highly concentrated, very efficient lensing clusters. Our MCMC triaxial NFW fitting method is easily expandable to include constraints from additional data types, and its application returns model parameters and errors that more accurately capture the true (and limited) extent of our knowledge of the structure of galaxy cluster lenses. (abridged)Comment: 18 pages, 15 figures. Updated to match published versio

A New Look at Massive Clusters: weak lensing constraints on the triaxial dark matter halos of Abell 1689, Abell 1835, & Abell 2204

Measuring the 3D distribution of mass on galaxy cluster scales is a crucial test of the LCDM model, providing constraints on the nature of dark matter. Recent work investigating mass distributions of individual galaxy clusters (e.g. Abell 1689) using weak and strong gravitational lensing has revealed potential inconsistencies between the predictions of structure formation models relating halo mass to concentration and those relationships as measured in massive clusters. However, such analyses employ simple spherical halo models while a growing body of work indicates that triaxial 3D halo structure is both common and important in parameter estimates. We recently introduced a Markov Chain Monte Carlo (MCMC) method to fit fully triaxial models to weak lensing data that gives parameter and error estimates that fully incorporate the true shape uncertainty present in nature. In this paper we apply that method to weak lensing data obtained with the ESO/MPG Wide-Field Imager for galaxy clusters A1689, A1835, and A2204, under a range of Bayesian priors derived from theory and from independent X-ray and strong lensing observations. For Abell 1689, using a simple strong lensing prior we find marginalized mean parameter values M_200 = (0.83 +- 0.16)x10^15 M_solar/h and C=12.2 +- 6.7, which are marginally consistent with the mass-concentration relation predicted in LCDM. The large error contours that accompany our triaxial parameter estimates more accurately represent the true extent of our limited knowledge of the structure of galaxy cluster lenses, and make clear the importance of combining many constraints from other theoretical, lensing (strong, flexion), or other observational (X-ray, SZ, dynamical) data to confidently measure cluster mass profiles. (Abridged)Comment: 21 pages, 10 figures, accepted for publication in MNRA

Loss of the PTCH1 tumor suppressor defines a new subset of plexiform fibromyxoma.

BackgroundPlexiform fibromyxoma (PF) is a rare gastric tumor often confused with gastrointestinal stromal tumor. These so-called "benign" tumors often present with upper GI bleeding and gastric outlet obstruction. It was recently demonstrated that approximately one-third of PF have activation of the GLI1 oncogene, a transcription factor in the hedgehog (Hh) pathway, via a MALAT1-GLI1 fusion protein or GLI1 up-regulation. Despite this discovery, the biology of most PFs remains unknown.MethodsNext generation sequencing (NGS) was performed on formalin-fixed paraffin-embedded (FFPE) samples of PF specimens collected from three institutions (UCSD, NCI and OHSU). Fresh frozen tissue from one tumor was utilized for in vitro assays, including quantitative RT-PCR and cell viability assays following drug treatment.ResultsEight patients with PF were identified and 5 patients' tumors were analyzed by NGS. An index case had a mono-allelic PTCH1 deletion of exons 15-24 and a second case, identified in a validation cohort, also had a PTCH1 gene loss associated with a suspected long-range chromosome 9 deletion. Building on the role of Hh signaling in PF, PTCH1, a tumor suppressor protein, functions upstream of GLI1. Loss of PTCH1 induces GLI1 activation and downstream gene transcription. Utilizing fresh tissue from the index PF case, RT-qPCR analysis demonstrated expression of Hh pathway components, SMO and GLI1, as well as GLI1 transcriptional targets, CCND1 and HHIP. In turn, short-term in vitro treatment with a Hh pathway inhibitor, sonidegib, resulted in dose-dependent cell killing.ConclusionsFor the first time, we report a novel association between PTCH1 inactivation and the development of plexiform fibromyxoma. Hh pathway inhibition with SMO antagonists may represent a target to study for treating a subset of plexiform fibromyxomas

A Simple Theory of Condensation

A simple assumption of an emergence in gas of small atomic clusters consisting of $c$ particles each, leads to a phase separation (first order transition). It reveals itself by an emergence of ``forbidden'' density range starting at a certain temperature. Defining this latter value as the critical temperature predicts existence of an interval with anomalous heat capacity behaviour $c_p\propto\Delta T^{-1/c}$. The value $c=13$ suggested in literature yields the heat capacity exponent $\alpha=0.077$.Comment: 9 pages, 1 figur

Resultant-based methods for plane curves intersection problems

http://www.springeronline.com/3-540-28966-6We present an algorithm for solving polynomial equations, which uses generalized eigenvalues and eigenvectors of resultant matrices. We give special attention to the case of two bivariate polynomials and the Sylvester or Bezout resultant constructions. We propose a new method to treat multiple roots, detail its numerical aspects and describe experiments on tangential problems, which show the efficiency of the approach. An industrial application of the method is presented at the end of the paper. It consists in recovering cylinders from a large cloud of points and requires intensive resolution of polynomial equations

Approximate parametrization of plane algebraic curves by linear systems of curves

t is well known that an irreducible algebraic curve is rational (i.e. parametric) if and only if its genus is zero. In this paper, given a tolerance ϵ>0 and an ϵ-irreducible algebraic affine plane curve C of proper degree d, we introduce the notion of ϵ-rationality, and we provide an algorithm to parametrize approximately affine ϵ-rational plane curves by means of linear systems of (d−2)-degree curves. The algorithm outputs a rational parametrization of a rational curve of degree d which has the same points at infinity as C. Moreover, although we do not provide a theoretical analysis, our empirical analysis shows that and C are close in practice

A case of recurrent epilepsy-associated rosette-forming glioneuronal tumor with anaplastic transformation in the absence of therapy.

Rosette-forming glioneuronal tumor (RGNT) most commonly occurs adjacent to the fourth ventricle and therefore rarely presents with epilepsy. Recent reports describe RGNT occurrence in other anatomical locations with considerable morphologic and genetic overlap with the epilepsy-associated dysembryoplastic neuroepithelial tumor (DNET). Examples of RGNT or DNET with anaplastic change are rare, and typically occur in the setting of radiation treatment. We present the case of a 5-year-old girl with seizures, who underwent near total resection of a cystic temporal lobe lesion. Pathology showed morphologic and immunohistochemical features of RGNT, albeit with focally overlapping DNET-like patterns. Resections of residual or recurrent tumor were performed 1 year and 5 years after the initial resection, but no adjuvant radiation or chemotherapy was given. Ten years after the initial resection, surveillance imaging identified new and enhancing nodules, leading to another gross total resection. This specimen showed areas similar to the original tumor, but also high-grade foci with oligodendroglial morphology, increased cellularity, palisading necrosis, microvascular proliferation, and up to 13 mitotic figures per 10 high power fields. Ancillary studies the status by sequencing showed wild-type of the isocitrate dehydrogenase 1 (IDH1), IDH2, and human histone 3.3 (H3F3A) genes, and BRAF studies were negative for mutation or rearrangement. Fluorescence in situ hybridization (FISH) showed codeletion of 1p and 19q limited to the high-grade regions. By immunohistochemistry there was loss of nuclear alpha-thalassemia mental retardation syndrome, X-linked (ATRX) expression only in the high-grade region. Next-generation sequencing showed an fibroblast growth factor receptor receptor 1 (FGFR1) kinase domain internal tandem duplication in three resection specimens. ATRX mutation in the high-grade tumor was confirmed by sequencing which showed a frameshift mutation (p.R1427fs), while the apparent 1p/19q-codeletion by FISH was due to loss of chromosome arm 1p and only partial loss of 19q. Exceptional features of this case include the temporal lobe location, 1p/19q loss by FISH without true whole-arm codeletion, and anaplastic transformation associated with ATRX mutation without radiation or chemotherapy

Specific "scientific" data structures, and their processing

Programming physicists use, as all programmers, arrays, lists, tuples, records, etc., and this requires some change in their thought patterns while converting their formulae into some code, since the "data structures" operated upon, while elaborating some theory and its consequences, are rather: power series and Pad\'e approximants, differential forms and other instances of differential algebras, functionals (for the variational calculus), trajectories (solutions of differential equations), Young diagrams and Feynman graphs, etc. Such data is often used in a [semi-]numerical setting, not necessarily "symbolic", appropriate for the computer algebra packages. Modules adapted to such data may be "just libraries", but often they become specific, embedded sub-languages, typically mapped into object-oriented frameworks, with overloaded mathematical operations. Here we present a functional approach to this philosophy. We show how the usage of Haskell datatypes and - fundamental for our tutorial - the application of lazy evaluation makes it possible to operate upon such data (in particular: the "infinite" sequences) in a natural and comfortable manner.Comment: In Proceedings DSL 2011, arXiv:1109.032

The T=0 random-field Ising model on a Bethe lattice with large coordination number: hysteresis and metastable states

In order to elucidate the relationship between rate-independent hysteresis and metastability in disordered systems driven by an external field, we study the Gaussian RFIM at T=0 on regular random graphs (Bethe lattice) of finite connectivity z and compute to O(1/z) (i.e. beyond mean-field) the quenched complexity associated with the one-spin-flip stable states with magnetization m as a function of the magnetic field H. When the saturation hysteresis loop is smooth in the thermodynamic limit, we find that it coincides with the envelope of the typical metastable states (the quenched complexity vanishes exactly along the loop and is positive everywhere inside). On the other hand, the occurence of a jump discontinuity in the loop (associated with an infinite avalanche) can be traced back to the existence of a gap in the magnetization of the metastable states for a range of applied field, and the envelope of the typical metastable states is then reentrant. These findings confirm and complete earlier analytical and numerical studies.Comment: 29 pages, 9 figure