This note is inspired by a lecture given during the school “Liason theory and related topics” and contains a summary of the results in [15] about the connectedness of the Hilbert scheme of curves of degree d and genus (d−3 2 ) − 1. The only novelty is the list of degrees for which smooth and irreducible curves appear. This short note was inspired by a talk I gave at the Politecnico of Torino du...

This paper expands the role of the new field of computational topology by surveying methods for incorporating connectedness in shape modeling. Two geometric representations in particular, recurrent models and implicit surfaces, can (often unpredictably) become connected or disconnected based on typical changes in modeling parameters. Two methodologies for controlling connectedness are identifie...

OBJECTIVE To determine whether school connectedness demonstrated an independent protective association with risk of depression in students in grades 10 to 12 attending a high school in a rural community in southwestern Nova Scotia. METHODS Students at a high school in rural Nova Scotia participated in a self-completion survey in May 2009. Students were asked about a wide range of health-relat...

Background: The exponential growth of smartphones has afforded many users with ubiquitous access to socialization as seen in the various mobile apps used to communicate and connect with others. The present study employed mixed-method approaches to analyse the impact of phubbing on social connectedness among adolescents in Malaysia. Methods:</stron...

We study continua on which each nonconstant open mapping is light. W. Makuchowski asked if this property is preserved under atomic mappings. It is known that this is true under an additional assumption of arcwise connectedness of the domain continuum. We show that in general this is not true.

This paper concerns the local connectedness of components self-similar sets. Let n≥2 be an integer and let D⊂{0,1,…,n−1}2. The set F satisfying F=⋃d∈D(F+d)/n is called a fractal square. We prove that every component locally connected. same result for three-dimensional analogues does not hold.

In [BMR05] the authors proved a theorem of cell decomposition for the theory CODF of closed ordered differential fields which generalize the usual Cell Decomposition Theorem for o-minimal structures. As a consequence of this result, a particularly well-behaving dimension function on definable sets in CODF was introduced. Here we carry on the study of this cell decomposition in CODF by proving t...

This longitudinal study examined associations between changes in School Connectedness and changes in Affiliation With Deviant Peers among students from high-poverty backgrounds during the year immediately following the transition to middle school. Sixth-graders (N = 328) attending two middle schools in a large school district completed measures of School Connectedness and Affiliation With Devia...

Suppose that a graph process begins with n isolated vertices, to which edges are added randomly one by one so that the maximum degree of the induced graph is always at most d . In a previous article, the authors showed that as n → ∞, with probability tending to 1, the result of this process is a d-regular graph. This graph is shown to be connected with probability asymptotic to 1. 2000 Mathemat...