One-Sided Position-Dependent Smoothness-Increasing Accuracy-Conserving (SIAC) Filtering Over Uniform and Non-Uniform Meshes

In this paper, we introduce a new position-dependent Smoothness-Increasing Accuracy-Conserving (SIAC) filter that retains the benefits of position dependence while ameliorating some of its shortcomings. As in the previous position-dependent filter, our new filter can be applied near domain boundaries, near a discontinuity in the solution, or at the interface of different mesh sizes; and as before, in general, it numerically enhances the accuracy and increases the smoothness of approximations obtained using the discontinuous Galerkin (dG) method. However, the previously proposed position-dependent one-sided filter had two significant disadvantages: (1) increased computational cost (in terms of function evaluations), brought about by the use of $4k+1$ central B-splines near a boundary (leading to increased kernel support) and (2) increased numerical conditioning issues that necessitated the use of quadruple precision for polynomial degrees of $k\ge 3$ for the reported accuracy benefits to be realizable numerically. Our new filter addresses both of these issues --- maintaining the same support size and with similar function evaluation characteristicsas the symmetric filter in a way that has better numerical conditioning --- making it, unlike its predecessor, amenable for GPU computing. Our new filter was conceived by revisiting the original error analysis for superconvergence of SIAC filters and by examining the role of the B-splines and their weights in the SIAC filtering kernel. We demonstrate, in the uniform mesh case, that our new filter is globally superconvergent for $k=1$ and superconvergent in the interior (e.g., region excluding the boundary) for $k\ge2$. Furthermore, we present the first theoretical proof of superconvergence for postprocessing over smoothly varying meshes, and explain the accuracy-order conserving nature of this new filter when applied to certain non-uniform meshes cases. We provide numerical examples supporting our theoretical results and demonstrating that our new filter, in general, enhances the smoothness and accuracy of the solution. Numerical results are presented for solutions of both linear and nonlinear equation solved on both uniform and non-uniform one- and two-dimensional meshes

Paired and clustered quantum Hall states

We briefly summarize properties of quantum Hall states with a pairing or clustering property. Their study employs a fundamental connection with parafermionic Conformal Field Theories. We report on closed form expressions for the many-body wave functions and on multiplicities of the fundamental quasi-hole excitations.Comment: 13 pages, Contribution to the proceedings of the NATO Advanced Research Workshop "Statistical Field Theories" Como (Italy), June 18-23 200

Smoothness-Increasing Accuracy-Conserving (SIAC) filtering and quasi interpolation: A unified view

Filtering plays a crucial role in postprocessing and analyzing data in scientific and engineering applications. Various application-specific filtering schemes have been proposed based on particular design criteria. In this paper, we focus on establishing the theoretical connection between quasi-interpolation and a class of kernels (based on B-splines) that are specifically designed for the postprocessing of the discontinuous Galerkin (DG) method called Smoothness-Increasing Accuracy-Conserving (SIAC) filtering. SIAC filtering, as the name suggests, aims to increase the smoothness of the DG approximation while conserving the inherent accuracy of the DG solution (superconvergence). Superconvergence properties of SIAC filtering has been studied in the literature. In this paper, we present the theoretical results that establish the connection between SIAC filtering to long-standing concepts in approximation theory such as quasi-interpolation and polynomial reproduction. This connection bridges the gap between the two related disciplines and provides a decisive advancement in designing new filters and mathematical analysis of their properties. In particular, we derive a closed formulation for convolution of SIAC kernels with polynomials. We also compare and contrast cardinal spline functions as an example of filters designed for image processing applications with SIAC filters of the same order, and study their properties

Model selection in historical research using approximate Bayesian computation

Formal Models and History Computational models are increasingly being used to study historical dynamics. This new trend, which could be named Model-Based History, makes use of recently published datasets and innovative quantitative methods to improve our understanding of past societies based on their written sources. The extensive use of formal models allows historians to reevaluate hypotheses formulated decades ago and still subject to debate due to the lack of an adequate quantitative framework. The initiative has the potential to transform the discipline if it solves the challenges posed by the study of historical dynamics. These difficulties are based on the complexities of modelling social interaction, and the methodological issues raised by the evaluation of formal models against data with low sample size, high variance and strong fragmentation. This work examines an alternate approach to this evaluation based on a Bayesian-inspired model selection method. The validity of the classical Lanchester's laws of combat is examined against a dataset comprising over a thousand battles spanning 300 years. Four variations of the basic equations are discussed, including the three most common formulations (linear, squared, and logarithmic) and a new variant introducing fatigue. Approximate Bayesian Computation is then used to infer both parameter values and model selection via Bayes Factors. Results indicate decisive evidence favouring the new fatigue model. The interpretation of both parameter estimations and model selection provides new insights into the factors guiding the evolution of warfare. At a methodological level, the case study shows how model selection methods can be used to guide historical research through the comparison between existing hypotheses and empirical evidence.Funding for this work was provided by the SimulPast Consolider Ingenio project (CSD2010-00034) of the former Ministry for Science and Innovation of the Spanish Government and the European Research Council Advanced Grant EPNet (340828).Peer ReviewedPostprint (published version

Persian cats under first opinion veterinary care in the UK:demography, mortality and disorders

Persian cats are a popular cat breed worldwide, and especially in the US, Europe and Asia. This study aimed to describe the demography, common disorders and mortality in Persians under general practice veterinary care in 2013 in the UK. The study population of 285,547 cats overall included 3235 (1.1%) Persians. Mean adult Persian bodyweight was 3.9 kg (SD 0.9) and median age was 7.0 years (IQR 3.3–11.6). At least one disorder was recorded in 2099 (64.9%) Persians. The most common specific disorders were haircoat disorders (411, 12.7%), periodontal disease (365, 11.3%), overgrown nails (234, 7.2%), and ocular discharge (188, 5.8%). The most common disorder groups were dermatological (578, 17.9%), ophthalmological (496, 15.3%) and dental (397, 12.3%). Median longevity was 13.5 years (IQR 9.9–16.0). The most common grouped causes of death were renal disease (102, 23.4%), neoplasia (37, 8.5%) and mass-associated disorder (35, 8.0%). This is the first study to use general practice data to examine the overall health of Persian cats. With haircoat, ocular and dental disorders being the predominant disorders identified, this study highlights the need for increased owner awareness to manage and prevent the typical health problems associated with this breed’s phenotype

Entanglement spectrum of composite fermion states in real space

We study the entanglement spectra of many particle systems in states which are closely related to products of Slater determinants or products of permanents, or combinations of the two. Such states notably include the Laughlin and Jain composite fermion states which describe most of the observed conductance plateaus of the fractional quantum Hall e�ect. We identify a set of 'EntanglementWave Functions' (EWF), for subsets of the particles, which completely describe the entanglement spectra of such product wave functions, both in real space and in particle space. A subset of the EWF for the Laughlin and Jain states can be recognized as Composite Fermion states. These states provide an exact description of the low angular momentum sectors of the real space entanglement spectrum (RSES) of these trial wave functions and a physical explanation of the branches of excitations observed in the RSES of the Jain states

Autosomal dominant hypercalciuria in a mouse model due to a mutation of the epithelial calcium channel, TRPV5

Contains fulltext : 118040.pdf (publisher's version ) (Open Access)Hypercalciuria is a major cause of nephrolithiasis, and is a common and complex disorder involving genetic and environmental factors. Identification of genetic factors for monogenic forms of hypercalciuria is hampered by the limited availability of large families, and to facilitate such studies, we screened for hypercalciuria in mice from an N-ethyl-N-nitrosourea mutagenesis programme. We identified a mouse with autosomal dominant hypercalciuria (HCALC1). Linkage studies mapped the Hcalc1 locus to a 11.94 Mb region on chromosome 6 containing the transient receptor potential cation channel, subfamily V, members 5 (Trpv5) and 6 (Trpv6) genes. DNA sequence analysis of coding regions, intron-exon boundaries and promoters of Trpv5 and Trpv6 identified a novel T to C transition in codon 682 of TRPV5, mutating a conserved serine to a proline (S682P). Compared to wild-type littermates, heterozygous (Trpv5(682P/+)) and homozygous (Trpv5(682P/682P)) mutant mice had hypercalciuria, polyuria, hyperphosphaturia and a more acidic urine, and approximately 10% of males developed tubulointerstitial nephritis. Trpv5(682P/682P) mice also had normal plasma parathyroid hormone but increased 1,25-dihydroxyvitamin D(3) concentrations without increased bone resorption, consistent with a renal defect for the hypercalciuria. Expression of the S682P mutation in human embryonic kidney cells revealed that TRPV5-S682P-expressing cells had a lower baseline intracellular calcium concentration than wild-type TRPV5-expressing cells, suggesting an altered calcium permeability. Immunohistological studies revealed a selective decrease in TRPV5-expression from the renal distal convoluted tubules of Trpv5(682P/+) and Trpv5(682P/682P) mice consistent with a trafficking defect. In addition, Trpv5(682P/682P) mice had a reduction in renal expression of the intracellular calcium-binding protein, calbindin-D(28K), consistent with a specific defect in TRPV5-mediated renal calcium reabsorption. Thus, our findings indicate that the TRPV5 S682P mutant is functionally significant and study of HCALC1, a novel model for autosomal dominant hypercalciuria, may help further our understanding of renal calcium reabsorption and hypercalciuria