A Theorem of Sanderson on Link Bordisms in Dimension 4

The groups of link bordism can be identified with homotopy groups via the Pontryagin-Thom construction. B.J. Sanderson computed the bordism group of 3 component surface-links using the Hilton-Milnor Theorem, and later gave a geometric interpretation of the groups in terms of intersections of Seifert hypersurfaces and their framings. In this paper, we geometrically represent every element of the bordism group uniquely by a certain standard form of a surface-link, a generalization of a Hopf link. The standard forms give rise to an inverse of Sanderson's geometrically defined invariant.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol1/agt-1-14.abs.htm

Manifolds with non-stable fundamental groups at infinity, II

In this paper we continue an earlier study of ends non-compact manifolds. The over-arching goal is to investigate and obtain generalizations of Siebenmann's famous collaring theorem that may be applied to manifolds having non-stable fundamental group systems at infinity. In this paper we show that, for manifolds with compact boundary, the condition of inward tameness has substatial implications for the algebraic topology at infinity. In particular, every inward tame manifold with compact boundary has stable homology (in all dimensions) and semistable fundamental group at each of its ends. In contrast, we also construct examples of this sort which fail to have perfectly semistable fundamental group at infinity. In doing so, we exhibit the first known examples of open manifolds that are inward tame and have vanishing Wall finiteness obstruction at infinity, but are not pseudo-collarable.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol7/paper7.abs.htm

Database challenges for exploratory computing

Helping users to make sense of very big datasets is nowadays considered an important research topic. However, the tools that are available for data analysis purposes typically address professional data scientists, who, besides a deep knowledge of the domain of interest, master one or more of the following disciplines: mathematics, statistics, computer science, computer engineering, and programming. On the contrary, in our vision it is vital to support also different kinds of users who, for various reasons, may want to analyze the data and obtain new insight from them. Examples of these data enthusiasts [4, 9] are journalists, investors, or politicians: non-technical users who can draw great advantage from exploring the data, achieving new and essential knowledge, instead of reading query results with tons of records. The term data exploration generally refers to a data user being able to find her way through large amounts of data in order to gather the necessary information. A more technical definition comes from the field of statistics, introduced by Tukey [12]: with exploratory data analysis the researcher explores the data in many possible ways, including the use of graphical tools like boxplots or histograms, gaining knowledge from the way data are displayed. Despite the emphasis on visualization, exploratory data analysis still assumes that the user understands at least the basics of statistics, while in this paper we propose a paradigm for database exploration which is in turn inspired by the exploratory computing vision [2]. We may describe exploratory computing as the step-by-step “conversation” of a user and a system that “help each other” to refine the data exploration process, ultimately gathering new knowledge that concretely fullfils the user needs. The process is seen as a conversation since the system provides active support: it not only answers user’s requests, but also suggests one or more possible actions that may help the user to focus the exploratory session. This activity may entail the use of a wide range of different techniques, including the use of statistics and data analysis, query suggestion, advanced visualization tools, etc. The closest analogy [2] is that of a human-tohuman dialogue, in which two people talk, and continuously make reference to their lives, priorities, knowledge and beliefs, leveraging them in order to provide the best possible contribution to the dialogue. In essence, through the conversation they are exploring themselves as well as the information that is conveyed through their words. This exploration process therefore means investigation, exploration-seeking, comparison-making, and learning altogether. It is most appropriate for big collections of semantically rich data, which typically hide precious knowledge behind their complexity. In this broad and innovative context, this paper intends to make a significant step further: it proposes a model to concretely perform this kind of exploration over a database. The model is general enough to encompass most data models and query languages that have been proposed for data management in the last few years. At the same time, it is precise enough to provide a first formalization of the problem and reason about the research challenges posed to database researchers by this new paradigm of interaction

Snowflake groups, Perron-Frobenius eigenvalues, and isoperimetric spectra

The k-dimensional Dehn (or isoperimetric) function of a group bounds the volume of efficient ball-fillings of k-spheres mapped into k-connected spaces on which the group acts properly and cocompactly; the bound is given as a function of the volume of the sphere. We advance significantly the observed range of behavior for such functions. First, to each non-negative integer matrix P and positive rational number r, we associate a finite, aspherical 2-complex X_{r,P} and calculate the Dehn function of its fundamental group G_{r,P} in terms of r and the Perron-Frobenius eigenvalue of P. The range of functions obtained includes x^s, where s is an arbitrary rational number greater than or equal to 2. By repeatedly forming multiple HNN extensions of the groups G_{r,P} we exhibit a similar range of behavior among higher-dimensional Dehn functions, proving in particular that for each positive integer k and rational s greater than or equal to (k+1)/k there exists a group with k-dimensional Dehn function x^s. Similar isoperimetric inequalities are obtained for arbitrary manifold pairs (M,\partial M) in addition to (B^{k+1},S^k).Comment: 42 pages, 8 figures. Version 2: 47 pages, 8 figures; minor revisions and reformatting; to appear in Geom. Topo

Regionalne i sociodemografske odrednice učestalosti prekomjerne tjelesne mase i debljine u djece u dobi od 7-9 godina u Hrvatskoj

The aim of this study was to determine the prevalence and analyze the determinants of overweight and obesity among Croatian schoolchildren aged 7-9 years in relation to sociodemographic factors. This study used data that were gathered as part of the WHO Europe Childhood Obesity Surveillance Initiative in 2015/2016. The sample for the study was nationally representative. Anthropometric measurements of 5591 children, 2811 boys and 2780 girls, were collected during 8 weeks using standardized equipment. Studied variables included child’s anthropometric measurements and demographics, maternal education and employment status. The results showed a 35.9% prevalence of overweight and obesity in Croatian 7-9-year-old children. Overweight and obesity were more frequent in boys in comparison to girls, especially among boys from the Adriatic region (42.1%). The risk of overweight and obesity was increased in boys living in the Adriatic region (ORadj=1.33; 95% CI 1.03-1.71) and in girls with high-school educated mothers (ORadj=1.36; 95% CI 1.11-1.66). Girls with unemployed mothers had a lower risk of overweight and obesity (ORadj=0.73; 95% CI 0.58-0.92). The observed prevalence of childhood overweight and obesity warrants national and local time-bound targets for reduction of childhood obesity, accompanied by detailed action plans and monitoring mechanisms.Cilj ovoga istraživanja bio je utvrditi učestalost i analizirati odrednice prekomjerne tjelesne mase i debljine kod školske djece u dobi od 7-9 godina u Hrvatskoj u odnosu na sociodemografske čimbenike. U istraživanju su korišteni podaci prikupljeni u sklopu istraživanja SZO Europa ”Europska inicijativa praćenja debljine u djece, Hrvatska 2015./2016.”. Uzorak u ovom istraživanju bio je nacionalno reprezentativan. Antropometrijska mjerenja 5591 djeteta, 2811 dječaka i 2780 djevojčica, provedena su standardiziranom opremom kroz 8 tjedana. Proučavane varijable bili su antropometrijski i demografski podaci djece, obrazovanje i zaposlenost majki. Prema rezultatima, učestalost prekomjerne tjelesne mase i debljine u hrvatske djece u dobi od 7-9 godina iznosi 35,9%. Učestalost prekomjerne tjelesne mase i debljine veća je kod dječaka nego kod djevojčica, a izrazito je velika kod dječaka iz jadranske regije (42,1%). Rizik za prekomjernu tjelesnu masu i debljinu veći je za dječake koji žive u jadranskoj regiji (ORadj=1,33; 95% CI 1,03-1,71) i djevojčice čije majke imaju srednjoškolsko obrazovanje (ORadj=1,36; 95% CI 1,11-1,66). Djevojčice čije su majke nezaposlene imaju manji rizik od prekomjerne tjelesne mase i debljine (ORadj=0,73; 95% CI 0,58-0,92). Uočena učestalost prekomjerne tjelesne mase i debljine zahtijeva vremenski ograničene, nacionalne i lokalne, ciljeve za smanjenje debljine kod djece, praćene detaljnim akcijskim planovima i mehanizmima praćenja

Classification of smooth embeddings of 4-manifolds in 7-space, I

We work in the smooth category. Let N be a closed connected n-manifold and assume that m>n+2. Denote by E^m(N) the set of embeddings N -> R^m up to isotopy. The group E^m(S^n) acts on E^m(N) by embedded connected sum of a manifold and a sphere. If E^m(S^n) is non-zero (which often happens for 2m<3n+4) then no results on this action and no complete description of E^m(N) were known. Our main results are examples of the triviality and the effectiveness of this action, and a complete isotopy classification of embeddings into R^7 for certain 4-manifolds N. The proofs are based on the Kreck modification of surgery theory and on construction of a new embedding invariant. Corollary. (a) There is a unique embedding CP^2 -> R^7 up to isoposition. (b) For each embedding f : CP^2 -> R^7 and each non-trivial knot g : S^4 -> R^7 the embedding f#g is isotopic to f.Comment: 22 pages, no figures, statement and proof of the Effectiveness Theorem correcte

Do Italian pregnant women use periconceptional folate supplementation?

Deficiency of Folic Acid (FA) has been identified as a risk factor for neural tube defects (NTDs) as well as other congenital abnormalities. Thus, periconceptional folate supplementation is recommended for all women planning to get pregnant.We conducted a KAP (knowledge, attitude, practice) survey to investigate the use of FA and its appropriateness. The survey included a sample of 562 women who delivered in Lazio region between 2013 and 2014. Two logistic regression analyses were performed to evaluate the association between the characteristics of participating women and both the information received on FA intake and its use. The prevalence of periconceptional FA assumption was  19.4% although 82.2% of the interviewed women had planned their pregnancies. It shows that more periconceptional counseling is needed to increase women's awareness on the opportunity of FA supplementation

Topologically invariant Chern numbers of projective varieties

We prove that a rational linear combination of Chern numbers is an oriented diffeomorphism invariant of smooth complex projective varieties if and only if it is a linear combination of the Euler and Pontryagin numbers. In dimension at least three we prove that only multiples of the top Chern number, which is the Euler characteristic, are invariant under diffeomorphisms that are not necessarily orientation-preserving. These results solve a long-standing problem of Hirzebruch's. We also determine the linear combinations of Chern numbers that can be bounded in terms of Betti numbers.Comment: 11 pages; minor edits in final version, to appear in Adv. Mat

Dietary habits among children aged 8-9 years in Italy

Objective To describe dietary habits and related geographic and socio-demographic characteristics among children aged 8-9 years in Italy. Materials and methods Data from the 2012 national nutritional surveillance system collected from children, parents and teachers, have been linked to determine the children's eating habits. Logistic regression analyses were used to investigate the association between incorrect dietary habits and their potential predictors. Results Of the 46307 children, 8.6% skipped breakfast, 48.8% did not eat vegetables and 28.7% did not eat fruit daily, 64.8% ate an abundant mid-morning snack, 41.4% drank sugary beverages and 12.5% drank carbonated beverages at least once a day. Three or more incorrect habits were found in 43.9% of the children. Incorrect dietary habits were more common among children with lower socio-economic conditions, who were resident in the South of the country and who spent more time watching TV. Conclusion In Italy, unhealthy dietary habits are common among children. The deficiencies identified may well be a harbinger of future public health problems