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...

Given an arbitrary spacetime (M, g), we prove a simple criterion to check when many of the good properties of the time-separation (Lorentzian distance) d valid in globally hyperbolic spacetimes hold for M . Concretely, when the product P = M × R, g̃ = g + dy is causally simple, then not only M is causally simple, but also d is continuous and AvezSeifert connectedness (each two causally related e...

The ubiquity of online programs in higher education requires continued focus on designing instructional environments that improve students’ learning. We examine students’ perceptions of sense of community and learning, as well as academic achievement, using grades obtained from a final project and participation in asynchronous discussion forums. Findings indicate a significant correlation betwe...

We propose several connectedness measures built from pieces of variance decompositions, and we argue that they provide natural and insightful measures of connectedness among financial asset returns and volatilities. We also show that variance decompositions define weighted, directed networks, so that our connectedness measures are intimately-related to key measures of connectedness used in the ...

Counselors, psychologists, and evaluators of intervention programs for youth increasingly view the promotion of connectedness as an important intervention outcome. When evaluating these programs, researchers frequently test whether the treatment effects differ across gender and ethnic or racial groups. Doing so necessitates the availability of culturally and gender-invariant measures. We used t...

We propose several connectedness measures built from pieces of variance decompositions, and we argue that they provide natural and insightful measures of connectedness among financial asset returns and volatilities. We also show that variance decompositions define weighted, directed networks, so that our connectedness measures are intimately-related to key measures of connectedness used in the ...

IMPLEMENTATION This reprint corresponds to the book-chapter " Algorithms for the detection of connectedness and their neural implementation " , Connectedness is one of the most important grouping criteria that allow the visual system to segregate objects from each other and from the background. We review algorithms for the detection of connectedness from a physiological point of view. Connected...

a r t i c l e i n f o This study compared perceptions of school connectedness to traditional community schools and residential treatment center (RTC) schools for youths between the ages of 12 and 18 receiving treatment within two RTCs. The influence of gender, report card grades, and engagement in treatment were also examined in relation to school connectedness in the RTC schools. Findings indi...