Numerably Contractible Spaces

Numerably contractible spaces play an important role in the theory of homotopy pushouts and pullbacks. The corresponding results imply that a number of well known weak homotopy equivalences are genuine ones if numerably contractible spaces are involved. In this paper we give a first systematic investigation of numerably contractible spaces. We list the elementary properties of the category of these spaces. We then study simplicial objects in this category. In particular, we show that the topological realization functor preserves fibration sequences if the base is path-connected and numerably contractible in each dimension. Consequently, the loop space functor commutes with realization up to homotopy. We give simple conditions which assure that free algebras over a topological operad are numerably contractible.Comment: 24 page

Hacia un modelo de análisis de políticas públicas operativ : Un enfoque basado en los actores, sus recursos y las instituciones

Towards an operative analysis of public policies: An approach focused on actors, resources and institutions. This article develops an analytical model which is centred on the individual and collective behaviour of actors involved during different stages of public policy. We postulate that the content and institutional characteristics of public action (dependent variable) are the result of interactions between political-administrative authorities, on the one hand, and, on the other, social groups which cause or suffer the negative effects of a collective problem which public action attempts to resolve (independent variables). The 'game' of the actors depends not only on their particular interests, but also on their resources (money, time, consensus, organization, rights, infrastructure, information, personnel, strength, political support) which they are able to exploit to defend their positions, as well as on the institutional rules which frame these policy games

Dynamical modeling of collective behavior from pigeon flight data: flock cohesion and dispersion

Several models of flocking have been promoted based on simulations with qualitatively naturalistic behavior. In this paper we provide the first direct application of computational modeling methods to infer flocking behavior from experimental field data. We show that this approach is able to infer general rules for interaction, or lack of interaction, among members of a flock or, more generally, any community. Using experimental field measurements of homing pigeons in flight we demonstrate the existence of a basic distance dependent attraction/repulsion relationship and show that this rule is sufficient to explain collective behavior observed in nature. Positional data of individuals over time are used as input data to a computational algorithm capable of building complex nonlinear functions that can represent the system behavior. Topological nearest neighbor interactions are considered to characterize the components within this model. The efficacy of this method is demonstrated with simulated noisy data generated from the classical (two dimensional) Vicsek model. When applied to experimental data from homing pigeon flights we show that the more complex three dimensional models are capable of predicting and simulating trajectories, as well as exhibiting realistic collective dynamics. The simulations of the reconstructed models are used to extract properties of the collective behavior in pigeons, and how it is affected by changing the initial conditions of the system. Our results demonstrate that this approach may be applied to construct models capable of simulating trajectories and collective dynamics using experimental field measurements of herd movement. From these models, the behavior of the individual agents (animals) may be inferred

Quantum symmetric pairs and representations of double affine Hecke algebras of type C∨CnC^\vee C_n

We build representations of the affine and double affine braid groups and Hecke algebras of type $C^\vee C_n$, based upon the theory of quantum symmetric pairs $(U,B)$. In the case $U=U_q(gl_N)$, our constructions provide a quantization of the representations constructed by Etingof, Freund and Ma in arXiv:0801.1530, and also a type $BC$ generalization of the results in arXiv:0805.2766.Comment: Final version, to appear in Selecta Mathematic

Equivariant cohomology and analytic descriptions of ring isomorphisms

In this paper we consider a class of connected closed $G$-manifolds with a non-empty finite fixed point set, each $M$ of which is totally non-homologous to zero in $M_G$ (or $G$-equivariantly formal), where $G={\Bbb Z}_2$. With the help of the equivariant index, we give an explicit description of the equivariant cohomology of such a $G$-manifold in terms of algebra, so that we can obtain analytic descriptions of ring isomorphisms among equivariant cohomology rings of such $G$-manifolds, and a necessary and sufficient condition that the equivariant cohomology rings of such two $G$-manifolds are isomorphic. This also leads us to analyze how many there are equivariant cohomology rings up to isomorphism for such $G$-manifolds in 2- and 3-dimensional cases.Comment: 20 pages, updated version with two references adde

Combinatorial Stokes formulas via minimal resolutions

We describe an explicit chain map from the standard resolution to the minimal resolution for the finite cyclic group Z_k of order k. We then demonstrate how such a chain map induces a "Z_k-combinatorial Stokes theorem", which in turn implies "Dold's theorem" that there is no equivariant map from an n-connected to an n-dimensional free Z_k-complex. Thus we build a combinatorial access road to problems in combinatorics and discrete geometry that have previously been treated with methods from equivariant topology. The special case k=2 for this is classical; it involves Tucker's (1949) combinatorial lemma which implies the Borsuk-Ulam theorem, its proof via chain complexes by Lefschetz (1949), the combinatorial Stokes formula of Fan (1967), and Meunier's work (2006).Comment: 18 page

Optimal bounds for a colorful Tverberg--Vrecica type problem

We prove the following optimal colorful Tverberg-Vrecica type transversal theorem: For prime r and for any k+1 colored collections of points C^l of size |C^l|=(r-1)(d-k+1)+1 in R^d, where each C^l is a union of subsets (color classes) C_i^l of size smaller than r, l=0,...,k, there are partition of the collections C^l into colorful sets F_1^l,...,F_r^l such that there is a k-plane that meets all the convex hulls conv(F_j^l), under the assumption that r(d-k) is even or k=0. Along the proof we obtain three results of independent interest: We present two alternative proofs for the special case k=0 (our optimal colored Tverberg theorem (2009)), calculate the cohomological index for joins of chessboard complexes, and establish a new Borsuk-Ulam type theorem for (Z_p)^m-equivariant bundles that generalizes results of Volovikov (1996) and Zivaljevic (1999).Comment: Substantially revised version: new notation, improved results, additional references; 12 pages, 2 figure

A Theoretical Model of Augmented Reality Acceptance

Recent tourism research increasingly explored the opportunities of using Augmented Reality (AR) in order to boost tourism and increase the value for tourists while travelling within a destination. The Technology Acceptance Model (TAM) has been applied to a number of research disciplines, lately also AR however, studies focusing on the tourism context are still scarce. As this field is expected to increase in importance rapidly due to technological advancements and research into functionality, acceptance and usefulness, it is important to identify what the basic requirements are for AR to be accepted by users. Furthermore, the provision of a conceptual model provides researchers with a starting point on which they can base their future research. Therefore, this paper proposes an AR acceptance model including five external variables that might be included in future AR acceptance research

Mapping Requirements for the Wearable Smart Glasses Augmented Reality Museum Application

Purpose: Recent advancements in wearable computing offer opportunities for art galleries to provide a unique experience. However, in order to ensure successful implementation of this new technology in the visitor industry, it is essential to understand user requirements from a visitor's point of view. Therefore, the aim of this paper is to investigate visitors' requirements for the development of a wearable smart glasses Augmented Reality (AR) application in the museum and art gallery context. Design/Methodology/Approach: Interviews with 28 art gallery visitors were conducted and an affinity diagram technique was used to analyze the interviews. Findings: The findings reveal that wearable AR is in its infancy and that technical and design issues have to be overcome for a full adoption. It reveals that content requirement, functional requirement, comfort, experience and resistance are important when developing and implementing the wearable AR application in the museum and art gallery context. Originality/Value: Mapping user requirements in the wearable smart glasses AR context using an affinity diagram is a new approach and therefore contributes to the creation of knowledge in the tourism domain. Practically, the area of wearable technologies and AR within the tourism and visitor industry context is still relatively unexplored and the present paper provides a first foundation for the implementation of wearable smart glasses AR applications in the museum and art gallery context