MOREMATA: Stata module (Mata) to provide various functions

This package includes various Mata functions. kern(): various kernel functions; kint(): kernel integral functions; kdel0(): canonical bandwidth of kernel; quantile(): quantile function; median(): median; iqrange(): inter-quartile range; ecdf(): cumulative distribution function; relrank(): grade transformation; ranks(): ranks/cumulative frequencies; freq(): compute frequency counts; histogram(): produce histogram data; mgof(): multinomial goodness-of-fit tests; collapse(): summary statistics by subgroups; _collapse(): summary statistics by subgroups; gini(): Gini coefficient; sample(): draw random sample; srswr(): SRS with replacement; srswor(): SRS without replacement; upswr(): UPS with replacement; upswor(): UPS without replacement; bs(): bootstrap estimation; bs2(): bootstrap estimation; bs_report(): report bootstrap results; jk(): jackknife estimation; jk_report(): report jackknife results; subset(): obtain subsets, one at a time; composition(): obtain compositions, one by one; ncompositions(): determine number of compositions; partition(): obtain partitions, one at a time; npartitionss(): determine number of partitions; rsubset(): draw random subset; rcomposition(): draw random composition; colvar(): variance, by column; meancolvar(): mean and variance, by column; variance0(): population variance; meanvariance0(): mean and population variance; mse(): mean squared error; colmse(): mean squared error, by column; sse(): sum of squared errors; colsse(): sum of squared errors, by column; benford(): Benford distribution; cauchy(): cumulative Cauchy-Lorentz dist.; cauchyden(): Cauchy-Lorentz density; cauchytail(): reverse cumulative Cauchy-Lorentz; invcauchy(): inverse cumulative Cauchy-Lorentz; rbinomial(): generate binomial random numbers; cebinomial(): cond. expect. of binomial r.v.; root(): Brent's univariate zero finder; nrroot(): Newton-Raphson zero finder; finvert(): univariate function inverter; integrate_sr(): univariate function integration (Simpson's rule); integrate_38(): univariate function integration (Simpson's 3/8 rule); ipolate(): linear interpolation; polint(): polynomial inter-/extrapolation; plot(): Draw twoway plot; _plot(): Draw twoway plot; panels(): identify nested panel structure; _panels(): identify panel sizes; npanels(): identify number of panels; nunique(): count number of distinct values; nuniqrows(): count number of unique rows; isconstant(): whether matrix is constant; nobs(): number of observations; colrunsum(): running sum of each column; linbin(): linear binning; fastlinbin(): fast linear binning; exactbin(): exact binning; makegrid(): equally spaced grid points; cut(): categorize data vector; posof(): find element in vector; which(): positions of nonzero elements; locate(): search an ordered vector; hunt(): consecutive search; cond(): matrix conditional operator; expand(): duplicate single rows/columns; _expand(): duplicate rows/columns in place; repeat(): duplicate contents as a whole; _repeat(): duplicate contents in place; unorder2(): stable version of unorder(); jumble2(): stable version of jumble(); _jumble2(): stable version of _jumble(); pieces(): break string into pieces; npieces(): count number of pieces; _npieces(): count number of pieces; invtokens(): reverse of tokens(); realofstr(): convert string into real; strexpand(): expand string argument; matlist(): display a (real) matrix; insheet(): read spreadsheet file; infile(): read free-format file; outsheet(): write spreadsheet file; callf(): pass optional args to function; callf_setup(): setup for mm_callf().

A Bootstrap Test for the Probability of Ruin in the Compound Poisson Risk Process

In this article we propose a bootstrap test for the probability of ruin in the compound Poisson risk process. We adopt the P-value approach, which leads to a more complete assessment of the underlying risk than the probability of ruin alone. We provide second-order accurate P-values for this testing problem and consider both parametric and nonparametric estimators of the individual claim amount distribution. Simulation studies show that the suggested bootstrap P-values are very accurate and outperform their analogues based on the asymptotic normal approximation.

Putative functions of extracellular matrix glycoproteins in secondary palate morphogenesis

Cleft palate is a common birth defect in humans. Elevation and fusion of paired palatal shelves are coordinated by growth and transcription factors, and mutations in these can cause malformations. Among the effector genes for growth factor signaling are extracellular matrix (ECM) glycoproteins. These provide substrates for cell adhesion (e.g., fibronectin, tenascins), but also regulate growth factor availability (e.g., fibrillins). Cleft palate in Bmp7 null mouse embryos is caused by a delay in palatal shelf elevation. In contrast, palatal shelves of Tgf-β3 knockout mice elevate normally, but a cleft develops due to their failure to fuse. However, nothing is known about a possible functional interaction between specific ECM proteins and Tgf-β/Bmp family members in palatogenesis. To start addressing this question, we studied the mRNA and protein distribution of relevant ECM components during secondary palate development, and compared it to growth factor expression in wildtypewild type and mutant mice. We found that fibrillin-2 (but not fibrillin-1) mRNA appeared in the mesenchyme of elevated palatal shelves adjacent to the midline epithelial cells, which were positive for Tgf-β3 mRNA. Moreover, midline epithelial cells started expressing fibronectin upon contact of the two palatal shelves. These findings support the hypothesis that fibrillin-2 and fibronectin are involved in regulating the activity of Tgf-β3 at the fusing midline. In addition, we observed that tenascin-W (but not tenascin-C) was misexpressed in palatal shelves of Bmp7-deficient mouse embryos. In contrast to tenascin-C, tenascin-W secretion was strongly induced by Bmp7 in embryonic cranial fibroblasts in vitro. These results are consistent with a putative function for tenascin-W as a target of Bmp7 signaling during palate elevation. Our results indicate that distinct ECM proteins are important for morphogenesis of the secondary palate, both as downstream effectors and as regulators of Tgf-β/Bmp activity.

Distribution of the glutamate transporters GLT-1 (SLC1A2) and GLAST (SLC1A3) in peripheral organs

The glutamate transporters GLT-1 and GLAST are widely expressed in astrocytes in the brain where they fulfill important functions during glutamatergic neurotransmission. The present study examines their distribution in peripheral organs using in situ hybridization (ISH) and immunocytochemistry. GLAST was found to be more widely distributed than GLT-1. GLAST was expressed primarily in epithelial cells, cells of the macrophage-lineage, lymphocytes, fat cells, interstitial cells, and salivary gland acini. GLT-1 was primarily expressed in glandular tissue, including mammary gland, lacrimal gland, and ducts and acini in salivary glands, but also by perivenous hepatocytes and follicular dendritic cells in spleen and lymph nodes. The findings demonstrate that, although expressed by the same cells in the brain, these two glutamate transporters have different distribution patterns in peripheral tissues and that they fulfill glutamate transport functions apart from glutamatergic neurotransmission in these areas.

Subcellular distribution of the insulin-like growth factor (IGF) binding proteins (IGFBPs) 2 and 3 in articular chondrocytes

The insulin-like growth factor (IGF) is a major anabolic regulator in articular cartilage. The IGF-binding proteins (IGFBPs) are increased during osteoarthritis (OA), but the function of the later proteins remains unknown. In general, the IGFBPs are pluripotential effectors capable of IGF regulation and of acting on their own to control key cell functions, including survival and proliferation. The independent functions are often associated with their cell location, and therefore this study explores the distribution of IGFBP-2 and IGFBP-3 in articular chondrocytes. Immunohistochemistry was used to localize IGFBP-2 in normal human articular cartilage. Bovine chondrocytes were used for subcellular fractionation (hypotonic cell lysis) under nonreducing conditions and nuclear purification (centrifugation on sucrose cushions). Cell fraction markers and IGFBPs were assayed in the subcellular fractions by Western immunoblot. The IHC results showed association of IGFBP-2 with chondrocytes, but not with the nuclei. Subcellular fractionation of isolated chondrocytes yielded intact nuclei as assessed at the light microscopic level; the nuclear marker histone H1 was exclusively associated with this fraction. More than 90% of the cytoplasmic marker GAPDH and all the detectable IGFBP-2 were in the cytoplasmic fraction. Immunoreactive IGFBP-3 was found in the cytoplasmic and peri-nuclear/nuclear fractions. Chondrocytes contain intracellular IGFBP-2 and IGFBP-3 but only IGFBP-3 is associated with nuclei. This suggests the hypothesis that the actions of these IGFBPs in articular cartilage extend beyond the classic modulation of IGF receptor action.

Evolutionary demography of long-lived monocarpic perennials: a time-lagged integral projection model

1. The evolution of flowering strategies (when and at what size to flower) in monocarpic perennials is determined by balancing current reproduction with expected future reproduction, and these are largely determined by size-specific patterns of growth and survival. However, because of the difficulty in following long-lived individuals throughout their lives, this theory has largely been tested using short-lived species (< 5 years). 2. Here, we tested this theory using the long-lived monocarpic perennial Campanula thyrsoides which can live up to 16 years. We used a novel approach that combined permanent plot and herb chronology data from a 3-year field study to parameterize and validate integral projection models (IPMs). 3. Similar to other monocarpic species, the rosette leaves of C. thyrsoides wither over winter and so size cannot be measured in the year of flowering. We therefore extended the existing IPM framework to incorporate an additional time delay that arises because flowering demography must be predicted from rosette size in the year before flowering. 4. We found that all main demographic functions (growth, survival probability, flowering probability and fecundity) were strongly size-dependent and there was a pronounced threshold size of flowering. There was good agreement between the predicted distribution of flowering ages obtained from the IPMs and that estimated in the field. Mostly, there was good agreement between the IPM predictions and the direct quantitative field measurements regarding the demographic parameters lambda, R-0 and T. We therefore conclude that the model captures the main demographic features of the field populations. 5. Elasticity analysis indicated that changes in the survival and growth function had the largest effect (c. 80%) on lambda and this was considerably larger than in short-lived monocarps. We found only weak selection pressure operating on the observed flowering strategy which was close to the predicted evolutionary stable strategy. 6. Synthesis. The extended IPM accurately described the demography of a long-lived monocarpic perennial using data collected over a relatively short period. We could show that the evolution of flowering strategies in short- and long-lived monocarps seem to follow the same general rules but with a longevity-related emphasis on survival over fecundity.

The von Mises-Fisher distribution of the first exit point from the hypersphere of the drifted Brownian motion and the density of the first exit time

A characterization is provided for the von Mises–Fisher random variable, in terms of first exit point from the unit hypersphere of the drifted Wiener process. Laplace transform formulae for the first exit time from the unit hypersphere of the drifted Wiener process are provided. Post representations in terms of Bell polynomials are provided for the densities of the first exit times from the circle and from the sphere.

Calculating track thrust with track functions

In e+e− event shapes studies at LEP, two different measurements were sometimes performed: a “calorimetric” measurement using both charged and neutral particles and a “track-based” measurement using just charged particles. Whereas calorimetric measurements are infrared and collinear safe, and therefore calculable in perturbative QCD, track-based measurements necessarily depend on nonperturbative hadronization effects. On the other hand, track-based measurements typically have smaller experimental uncertainties. In this paper, we present the first calculation of the event shape “track thrust” and compare to measurements performed at ALEPH and DELPHI. This calculation is made possible through the recently developed formalism of track functions, which are nonperturbative objects describing how energetic partons fragment into charged hadrons. By incorporating track functions into soft-collinear effective theory, we calculate the distribution for track thrust with next-to-leading logarithmic resummation. Due to a partial cancellation between nonperturbative parameters, the distributions for calorimeter thrust and track thrust are remarkably similar, a feature also seen in LEP data.

Bounds for the probability generating functional of a Gibbs point process

We derive explicit lower and upper bounds for the probability generating functional of a stationary locally stable Gibbs point process, which can be applied to summary statistics such as the F function. For pairwise interaction processes we obtain further estimates for the G and K functions, the intensity, and higher-order correlation functions. The proof of the main result is based on Stein's method for Poisson point process approximation.

Uniqueness of the Embedding Continuous Convolution Semigroup of a Gaussian Probability Measure on the Affine Group and an Application in Mathematical Finance

Let {μ(i)t}t≥0 ( i=1,2 ) be continuous convolution semigroups (c.c.s.) of probability measures on Aff(1) (the affine group on the real line). Suppose that μ(1)1=μ(2)1 . Assume furthermore that {μ(1)t}t≥0 is a Gaussian c.c.s. (in the sense that its generating distribution is a sum of a primitive distribution and a second-order differential operator). Then μ(1)t=μ(2)t for all t≥0 . We end up with a possible application in mathematical finance.