Hierarchies of invariant spin models

In this paper we present classes of state sum models based on the recoupling theory of angular momenta of SU(2) (and of its q-counterpart $U_q(sl(2))$, q a root of unity). Such classes are arranged in hierarchies depending on the dimension d, and include all known closed models, i.e. the Ponzano-Regge state sum and the Turaev-Viro invariant in dimension d=3, the Crane-Yetter invariant in d=4. In general, the recoupling coefficient associated with a d-simplex turns out to be a $\{3(d-2)(d+1)/2\}j$ symbol, or its q-analog. Each of the state sums can be further extended to compact triangulations $(T^d,\partial T^d)$ of a PL-pair $(M^d,\partial M^d)$, where the triangulation of the boundary manifold is not keeped fixed. In both cases we find out the algebraic identities which translate complete sets of topological moves, thus showing that all state sums are actually independent of the particular triangulation chosen. Then, owing to Pachner's theorems, it turns out that classes of PL-invariant models can be defined in any dimension d.Comment: 42 pages, 25 figure

Extended matter coupled to BF theory

Recently, a topological field theory of membrane-matter coupled to BF theory in arbitrary spacetime dimensions was proposed [1]. In this paper, we discuss various aspects of the four-dimensional theory. Firstly, we study classical solutions leading to an interpretation of the theory in terms of strings propagating on a flat spacetime. We also show that the general classical solutions of the theory are in one-to-one correspondence with solutions of Einstein's equations in the presence of distributional matter (cosmic strings). Secondly, we quantize the theory and present, in particular, a prescription to regularize the physical inner product of the canonical theory. We show how the resulting transition amplitudes are dual to evaluations of Feynman diagrams coupled to three-dimensional quantum gravity. Finally, we remove the regulator by proving the topological invariance of the transition amplitudes.Comment: 27 pages, 7 figure

A calculus for ideal triangulations of three-manifolds with embedded arcs

Refining the notion of an ideal triangulation of a compact three-manifold, we provide in this paper a combinatorial presentation of the set of pairs (M,a), where M is a three-manifold and a is a collection of properly embedded arcs. We also show that certain well-understood combinatorial moves are sufficient to relate to each other any two refined triangulations representing the same (M,a). Our proof does not assume the Matveev-Pergallini calculus for ideal triangulations, and actually easily implies this calculus.Comment: 32 pages, 30 figure

Grounded (Re-)Construction of the Self-Reflection Core Competence from Statements of Adult Education Professionals

This article discusses the significance that is assigned to the core competence of self-reflection by adult education professionals. Therefore, a conceptual classification in connection with the research design and initial results of an empirical study will be introduced with the intention of providing a grounded (re-)construction of the self-reflection competence

Canonical formalism for simplicial gravity

We summarise a recently introduced general canonical formulation of discrete systems which is fully equivalent to the covariant formalism. This framework can handle varying phase space dimensions and is applied to simplicial gravity in particular.Comment: 4 pages, 5 figures, based on a talk given at Loops '11 in Madrid, to appear in Journal of Physics: Conference Series (JPCS

A Reservation Aggregation Framework Design for Demand Estimation

Effective management practices in the tourism and hotel area have seldom been more important than at the present time. Pricing decisions cannot be taken without serious thought. IT has provided the opportunity for a customer to make a quick market search and it offers decision support systems that can be used in the hotel management. The heart of yield management system consists of the predicting machine, which estimates the number of incoming reservations. Incoming reservations arrive randomly in time. The time series calculi as well as the estimators known from control engineering require properly defined time rows (with a constant period). This requirement is usually not fulfilled, so the input data are not exploited properly. This paper outlines a procedure that aggregates the reservations into a time series that is useful for demand prediction. The algorithm prepares the data systematically for further processing. Any method that process time rows can be used for subsequent prediction: time series, linear models or time extrapolation.

A Reservation Aggregation Framework Design for Demand Estimation

Effective management practices in the tourism and hotel area have seldom been more important than at the present time. Pricing decisions cannot be taken without serious thought. IT has provided the opportunity for a customer to make a quick market search and it offers decision support systems that can be used in the hotel management. The heart of yield management system consists of the predicting machine, which estimates the number of incoming reservations. Incoming reservations arrive randomly in time. The time series calculi as well as the estimators known from control engineering require properly defined time rows (with a constant period). This requirement is usually not fulfilled, so the input data are not exploited properly. This paper outlines a procedure that aggregates the reservations into a time series that is useful for demand prediction. The algorithm prepares the data systematically for further processing. Any method that process time rows can be used for subsequent prediction: time series, linear models or time extrapolation.

Challenges for Children and Adolescents with Autism and Their Families during the Covid-19 Pandemic

The restrictions and lockdown measures implemented in response to the Covid-19 pandemic have posed a pronounced risk to the mental health of people with autism and their families. We discuss specific difficulties affecting children and adolescents with autism and their families during the pandemic, drawing on a broad range of recently published research in many countries and regions. A global perspective is adopted to provide an overview of the state of affairs and identify good practices. We consider challenges in four areas: research and practice related to autism, challenges facing children and adolescents with autism, specific difficulties in their education and care, and challenges facing their parents and families. Based on the reviewed work and our experience in group support sessions with parents of children with autism, we conclude that supporting families affected by autism should emphasize promoting the parents\u27 well-being and coping potential to improve their resilience