Formalized linear algebra over Elementary Divisor Rings in Coq

This paper presents a Coq formalization of linear algebra over elementary divisor rings, that is, rings where every matrix is equivalent to a matrix in Smith normal form. The main results are the formalization that these rings support essential operations of linear algebra, the classification theorem of finitely presented modules over such rings and the uniqueness of the Smith normal form up to multiplication by units. We present formally verified algorithms computing this normal form on a variety of coefficient structures including Euclidean domains and constructive principal ideal domains. We also study different ways to extend B\'ezout domains in order to be able to compute the Smith normal form of matrices. The extensions we consider are: adequacy (i.e. the existence of a gdco operation), Krull dimension $\leq 1$ and well-founded strict divisibility

Project for the 1992 Chicago World\u27s Fair

In 1992 Chicago will be the site of a centennial celebration of America\u27s discovery. As in 1892, Chicago will host a World\u27s Columbian Exposition dedicated to the theme of discovery

Triangulum II: Not Especially Dense After All

Among the Milky Way satellites discovered in the past three years, Triangulum II has presented the most difficulty in revealing its dynamical status. Kirby et al. (2015a) identified it as the most dark matter-dominated galaxy known, with a mass-to-light ratio within the half-light radius of 3600 +3500 -2100 M_sun/L_sun. On the other hand, Martin et al. (2016) measured an outer velocity dispersion that is 3.5 +/- 2.1 times larger than the central velocity dispersion, suggesting that the system might not be in equilibrium. From new multi-epoch Keck/DEIMOS measurements of 13 member stars in Triangulum II, we constrain the velocity dispersion to be sigma_v < 3.4 km/s (90% C.L.). Our previous measurement of sigma_v, based on six stars, was inflated by the presence of a binary star with variable radial velocity. We find no evidence that the velocity dispersion increases with radius. The stars display a wide range of metallicities, indicating that Triangulum II retained supernova ejecta and therefore possesses or once possessed a massive dark matter halo. However, the detection of a metallicity dispersion hinges on the membership of the two most metal-rich stars. The stellar mass is lower than galaxies of similar mean stellar metallicity, which might indicate that Triangulum II is either a star cluster or a tidally stripped dwarf galaxy. Detailed abundances of one star show heavily depressed neutron-capture abundances, similar to stars in most other ultra-faint dwarf galaxies but unlike stars in globular clusters.Comment: accepted to ApJ, Table 5 available as a machine-readable table by clicking on "Other formats" on the right. Proof corrections reflected in version

Longitudinal Effects of the Family Support Program Chancenreich on Parental Involvement and the Language Skills of Preschool Children

When they enter primary school children already vary significantly in their language skills, depending at least in part on their family’s social background. In particular, the home learning environment plays a significant role in children’s development. For that reason, early intervention programs have been developed to obviate learning difficulties and to promote health, children’s development, and educational equality. The family support program Chancenreich aims to encourage the interaction and relationship between parents and children through two different course formats. The present study examines the longitudinal effects of attending the Chancenreich program and different course formats on (a) parents attending further educational services for children after completing the program, (b) children’s vocabulary and level of grammar development at the age of 5 and (c) the children’s vocabulary development between the ages of 3 and 5. Furthermore, we examine the relationship between family characteristics and the attendance rates of different course formats of the Chancenreich program at the first and second point of measurement. The study follows a longitudinal design with two points of measurements (T1: Mage = 41 months, T2: Mage = 68 months), and a sample size of 121 parents and their children at T2 in the intervention group and 41 parents and their children in the comparison group. Findings indicate that attendance of the Chancenreich program’s courses is related to child and family characteristics and to later patterns of course participation after completing the program. Further, both children’s level of vocabulary skills (PPVT) at the age of 5 and their development between the ages of 3 and 5 benefit from the parental participation in parenting skills training at the age of 3. Implications and future research on the effectiveness of family support programs are discussed

Systematic analysis of a novel human renal glomerulus-enriched gene expression dataset.

Glomerular diseases account for the majority of cases with chronic renal failure. Several genes have been identified with key relevance for glomerular function. Quite a few of these genes show a specific or preferential mRNA expression in the renal glomerulus. To identify additional candidate genes involved in glomerular function in humans we generated a human renal glomerulus-enriched gene expression dataset (REGGED) by comparing gene expression profiles from human glomeruli and tubulointerstitium obtained from six transplant living donors using Affymetrix HG-U133A arrays. This analysis resulted in 677 genes with prominent overrepresentation in the glomerulus. Genes with 'a priori' known prominent glomerular expression served for validation and were all found in the novel dataset (e.g. CDKN1, DAG1, DDN, EHD3, MYH9, NES, NPHS1, NPHS2, PDPN, PLA2R1, PLCE1, PODXL, PTPRO, SYNPO, TCF21, TJP1, WT1). The mRNA expression of several novel glomerulus-enriched genes in REGGED was validated by qRT-PCR. Gene ontology and pathway analysis identified biological processes previously not reported to be of relevance in glomeruli of healthy human adult kidneys including among others axon guidance. This finding was further validated by assessing the expression of the axon guidance molecules neuritin (NRN1) and roundabout receptor ROBO1 and -2. In diabetic nephropathy, a prevalent glomerulopathy, differential regulation of glomerular ROBO2 mRNA was found.In summary, novel transcripts with predominant expression in the human glomerulus could be identified using a comparative strategy on microdissected nephrons. A systematic analysis of this glomerulus-specific gene expression dataset allows the detection of target molecules and biological processes involved in glomerular biology and renal disease

Algorithm for Finding kk-Vertex Out-trees and its Application to kk-Internal Out-branching Problem

An out-tree $T$ is an oriented tree with only one vertex of in-degree zero. A vertex $x$ of $T$ is internal if its out-degree is positive. We design randomized and deterministic algorithms for deciding whether an input digraph contains a given out-tree with $k$ vertices. The algorithms are of runtime $O^*(5.704^k)$ and $O^*(5.704^{k(1+o(1))})$, respectively. We apply the deterministic algorithm to obtain a deterministic algorithm of runtime $O^*(c^k)$, where $c$ is a constant, for deciding whether an input digraph contains a spanning out-tree with at least $k$ internal vertices. This answers in affirmative a question of Gutin, Razgon and Kim (Proc. AAIM'08)

Influence of XUV radiation on Pv ionization fraction in hot star winds

Different diagnostics of hot star wind mass-loss rates provide results that are difficult to reconcile with each other. The widely accepted presence of clumping in hot star winds implies a significant reduction of observational mass-loss rate estimates from diagnostics that depend on the square of the density. Moreover, the ultraviolet Pv resonance lines indicate a possible need for even stronger reduction of hot star mass-loss rates, provided that Pv is a dominant ionization stage of phosphorus at least in some hot stars. The latter assumption is challenged by a possible presence of the XUV radiation. Here we study the influence of the XUV radiation on the Pv ionization fraction in the hot star winds. By a detailed solution of the hydrodynamical, radiative transfer, and statistical equilibrium equations we confirm that sufficiently strong XUV radiation source may decrease the Pv ionization fraction, possibly depreciating the Pv lines as a reliable mass-loss rate indicator. On the other hand, the XUV radiation influences also the ionization fraction of heavier ions that drive the wind, leading to a decrease of the wind terminal velocity. Consequently, we conclude that the XUV radiation alone can not bring theory and observations in accord. We fit our predicted wind mass-loss rates by a suitable formula and compare the results with the observational mass-loss rate diagnostics. We show that for supergiants and giants the theoretical predictions do not contradict the mass-loss rate estimates based on X-ray line profiles or density squared diagnostics. On the other hand, for main-sequence stars the predicted mass-loss rates are still significantly higher than that inferred from Pv or X-ray lines. This indicates that the "weak wind problem" recently detected in low-luminosity main-sequence stars may occur to some extent also for the stars with higher luminosity.Comment: Accepted for publication in MNRAS. The definitive version is available at www.blackwell-synergy.com. 8 pages, 5 figure

Pedagogical content knowledge of specialist counselling in parental cooperation

Im Zuge gesellschaftlicher Veränderungen gewinnt auch die Zusammenarbeit zwischen Kindertageseinrichtung und Familien an Bedeutung. Frühpädagogische Fachkräfte stehen vor der Herausforderung, ihre Kompetenzen aktuellen Entwicklungen anzupassen. Vor diesem Hintergrund dient Fachberatung als Qualifizierungsressource für Einrichtungen und ihre pädagogischen Fachkräfte. Die vorliegende Studie untersucht daher an 166 Fachberatungen die professionelle Kompetenzfacette des fachdidaktischen Wissens im Handlungsfeld Zusammenarbeit mit Familien. Die Ergebnisse zeigen, dass die Fachberatungen in vier verschiedene Wissenstypen eingeteilt werden können, die sich teilweise auf deren professionelle Voraussetzungen (z.B. Fort- und Weiterbildungsaktivität) zurückführen lassen. Die Befunde werden im Hinblick auf Implikationen für die Praxis und weiteren Forschungsbedarf diskutiert. (DIPF/Orig.)In the course of societal changes, the cooperation between daycare centers and families has also gained importance. Early childhood professionals face the challenge of adapting their competencies to current developments. Against this background, pedagogical quality consultants serve as a qualification resource for daycare institutions and their staff. Drawing on a sample of 166 pedagogical quality consultants, the present study investigates pedagogical content knowledge in the competence area \u27cooperation with families\u27. Results from cluster analysis show that the pedagogical quality consultants can be divided into four different types with regard to their knowledge. Further regression analysis reveal that these types are predicted by the professional qualifications of the pedagogical quality consultants (e.g., professional development activities). The findings are discussed with regard to the implications for practice and further research needs. (DIPF/Orig.

Refinements for Free!

International audienceFormal verification of algorithms often requires a choice be-tween definitions that are easy to reason about and definitions that are computationally efficient. One way to reconcile both consists in adopt-ing a high-level view when proving correctness and then refining stepwise down to an efficient low-level implementation. Some refinement steps are interesting, in the sense that they improve the algorithms involved, while others only express a switch from data representations geared towards proofs to more efficient ones geared towards computations. We relieve the user of these tedious refinements by introducing a framework where correctness is established in a proof-oriented context and automatically transported to computation-oriented data structures. Our design is gen-eral enough to encompass a variety of mathematical objects, such as rational numbers, polynomials and matrices over refinable structures. Moreover, the rich formalism of the Coq proof assistant enables us to develop this within Coq, without having to maintain an external tool