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.

We consider the set Ω2 of double zeros in (0, 1) for power series with coefficients in {−1, 0, 1}. We prove that Ω2 is disconnected, and estimate minΩ2 with high accuracy. We also show that [2 − η, 1) ⊂ Ω2 for some small, but explicit η > 0 (this was only known for η = 0). These results have applications in the study of infinite Bernoulli convolutions and connectedness properties of self-affine...

Genetic connectedness refers to a measure of genetic relatedness across management units (e.g., herds and flocks). With the presence of high genetic connectedness in management units, best linear unbiased prediction (BLUP) is known to provide reliable comparisons between estimated genetic values. Genetic connectedness has been studied for pedigree-based BLUP; however, relatively little attentio...

Which is the most reliable graph with n nodes and m edges? This celebrated problem has several aspects, according to notion of optimality (in a local or uniform sense), failure type (either edges), reliability model (all-terminal connectedness, two-terminal multiterminal setting). article presents chronological survey multiple proposals address problem, together recent trends enigmatic conjectu...

We consider the following definition of connectedness in k-uniform hypergraphs: two j-sets (sets of j vertices) are j-connected if there is a walk of edges between them such that two consecutive edges intersect in at least j vertices. The hypergraph is jconnected if all j-sets are pairwise j-connected. We determine the threshold at which the random k-uniform hypergraph with edge probability p b...

The impact of types of social connectedness-family, other adult, and school-on suicide ideation and attempts among all youth, the relative impact of each type, and effect modification by sexual orientation was assessed. Data were from the 2007-2009 Milwaukee Youth Risk Behavior Surveys. Multivariable logistic regression analyses calculated the risk of suicide ideation and attempts by sexual ori...

The P4–structure of a graph G is a hypergraph H on the same vertex set such that four vertices form a hyperedge in H whenever they induce a P4 in G. We present a constructive algorithm which tests in polynomial time whether a given 4–uniform hypergraph is the P4–structure of a claw–free graph and of (banner,chair,dart)–free graphs. The algorithm relies on new structural results for (banner,chai...

In this paper, we study the relation between uniform Roe algebra and quasi-local associated to a metric space of bounded geometry. process, introduce weakening notion expanders, called asymptotic expanders. We show that being sequence expanders is coarse property under certain connectedness condition, it implies non-uniformly local amenability. Moreover, also analyse some $C^*$-algebraic proper...

We prove that any unicritical polynomial fc : z 7→ z+c which is at most finitely renormalizable and has only repelling periodic points is combinatorially rigid. It implies that the connectedness locus (the “Multibrot set”) is locally connected at the corresponding parameter values. It generalizes Yoccoz’s Theorem for quadratics to the higher degree case. Stony Brook IMS Preprint #2005/05 July 2005

Yeshun Sun & Yongcheng Yin [3] and H. Ishida & T. Itoh [2] presented a precise description of the real cross section of the connectedness locus of the family of bi-quadratic polynomials {(z2+a)2+b}. In this note, we shall give a precise description of the real cross section of the connectedness locus of the family of polynomials {(P2n+1,b ◦P2n+1,a)(z)} = {(z2n+1 + a)2n+1 + b}, where a, b are co...