Constraint-Based Representations of Statistical Graphs

Abstract

Pictor is an environment for statistical graphics that promotes simple commands for common uses and offers the ability to experiment with whole new paradigms. Pictor describes graphs as graphical objects whose component pieces are related by several sorts of constraints. This article describes in detail the constraint system that Pictor uses.     

Investigation of quadrature imbalance compensation algorithm for coherent 6PolSK-QPSK

6PolSK-QPSK is a promising modulation format in optical fiber communication. Because of the damage suffered during the transmission and reception, a series of algorithms are needed to be adopted to recover the original data. We proposed a novel quadrature imbalance compensation algorithm based on the data statistical properties. Simulation results show that the quadrature imbalance can be well compensated with the proposed algorithm.     

What can statistical process control show us about ionization chamber stability?

PurposeStatistical process control (SPC) has been shown to be a suitable tool for medical physicists to monitor quality and keep variability low and within specifications. We report our findings regarding ionisation chamber stability in our department when using a radioactive stability check device (RSCD) and we compare them with similar previously published records, including calibration results.MethodsWe retrospectively studied the stability of a PPC 40 parallel-plate chamber, and two Farmer chambers (FC65-G and FC65-P) by checking them with dedicated RSCDs. We analysed the data following SPC methodology which includes plotting I-MR control charts, monitoring out-of-control observations, calculating process capability ratios (C_p), and estimating conformance to specifications. We also estimated the C_p and adherence to specifications of previously published data.ResultsThe PPC40 chamber hardly went out of the control limits over the whole six-year period assessed. However, Farmer chamber verifications drifted in opposite directions in phase II, and the deviations observed did not agree with their calibration records, which only increased by a maximum of 0.5%. In phase I the most unstable chamber was the FC65-P with a C_p equal to 0.9 at a specification level of ±1%. The PPC40 chamber was stable to within a maximum C_p of 1.3. Several sets of analysed data, including ours and those from other authors, fitted well within these limits: within ±1.9% and ±1.5% for a C_p of 1.5 and 1.33 respectively.ConclusionsSPC with constant long-term RSCD checking gave us a meaningful plot of the instability of our ionisation chambers. Although a period of two years between calibrations should not be surpassed, in the interim this check can conform to specifications of ±1.5%.     

Geometric derivation of the microscopic stress: A covariant central force decomposition

We revisit the derivation of the microscopic stress, linking the statistical mechanics of particle systems and continuum mechanics. The starting point in our geometric derivation is the Doyle–Ericksen formula, which states that the Cauchy stress tensor is the derivative of the free-energy with respect to the ambient metric tensor and which follows from a covariance argument. Thus, our approach to define the microscopic stress tensor does not rely on the statement of balance of linear momentum as in the classical Irving–Kirkwood–Noll approach. Nevertheless, the resulting stress tensor satisfies balance of linear and angular momentum. Furthermore, our approach removes the ambiguity in the definition of the microscopic stress in the presence of multibody interactions by naturally suggesting a canonical and physically motivated force decomposition into pairwise terms, a key ingredient in this theory. As a result, our approach provides objective expressions to compute a microscopic stress for a system in equilibrium and for force-fields expanded into multibody interactions of arbitrarily high order. We illustrate the proposed methodology with molecular dynamics simulations of a fibrous protein using a force-field involving up to 5-body interactions.     

Extremal A-statistical limit points via ideals

In this paper, following the line of recent work of Savaş et al. [20] we apply the notion of ideals to A-statistical limit superior and inferior for a sequence of real numbers.     

Importance of verifying queue model assumptions before planning with simulation software

This case study uses empirical data gathered at an Australian refinery to verify the assumptions for queue distributions before using special-purpose software to plan the off-road-truck hauling of titanium dioxide to a refinery (n = 773). Easy-to-use spreadsheet software is utilized to verify assumptions for queue models. Managers are able to make decisions based on economic implications of queue models to avoid making costly planning mistakes. Analysts can use nonparametric hypothesis-testing techniques to verify distribution assumptions for optimization without having to write hard-to-maintain and complex algebraic linear equations or nonlinear search routines.     

Statistical discrimination of steroid profiles in doping control with support vector machines

Due to their performance enhancing properties, use of anabolic steroids (e.g. testosterone, nandrolone, etc.) is banned in elite sports. Therefore, doping control laboratories accredited by the World Anti-Doping Agency (WADA) screen among others for these prohibited substances in urine. It is particularly challenging to detect misuse with naturally occurring anabolic steroids such as testosterone (T), which is a popular ergogenic agent in sports and society.     

A mesh simplification strategy for a spatial regression analysis over the cortical surface of the brain

We present a new mesh simplification technique developed for a statistical analysis of a large data set distributed on a generic complex surface, topologically equivalent to a sphere. In particular, we focus on an application to cortical surface thickness data. The aim of this approach is to produce a simplified mesh which does not distort the original data distribution so that the statistical estimates computed over the new mesh exhibit good inferential properties. To do this, we propose an iterative technique that, for each iteration, contracts the edge of the mesh with the lowest value of a cost function. This cost function takes into account both the geometry of the surface and the distribution of the data on it. After the data are associated with the simplified mesh, they are analyzed via a spatial regression model for non-planar domains. In particular, we resort to a penalized regression method that first conformally maps the simplified cortical surface mesh into a planar region. Then, existing planar spatial smoothing techniques are extended to non-planar domains by suitably including the flattening phase. The effectiveness of the entire process is numerically demonstrated via a simulation study and an application to cortical surface thickness data.