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We provide a framework to prove convergence rates for discretizations of kinetic Langevin dynamics for M -∇Lipschitz m-log-concave densities. Our approach provides convergence rates of O(m/M ), with explicit stepsize restrictions, which are of the same order as the stability threshold for Gaussian targets and are valid for a large interval of the friction parameter. We apply this methodology to various integration methods which are popular in the molecular dynamics and machine learning communities. Finally we introduce the property "γ-limit convergent" (GLC) to characterise underdamped Langevin schemes that converge to overdamped dynamics in the high friction limit and which have stepsize restrictions that are independent of the friction parameter; we show that this property is not generic by exhibiting methods from both the class and its complement.
This research provides a critical approach to the assessment and evaluation of tourism destinations from the perspective of traditional administratively-based boundaries. It suggests that researchers and managers should abandon their focus on destinations as all-inclusive administratively-defined areas, readjusting to a more flexible model tied to tourists' travel patterns.Given the centrality of attractions to the leisure tourism process, the flows that an attraction is able to generate from neighbouring accommodation hubs explains an important share of the way a destination is consumed and offers a means of identifying more 'natural' destination areas. The analysis also explores how several factors affect the influence areas of attractions, and how the elements of conjoining destinations can be interconnected due to tourism flows representing overlapping influence areas and traversing administrative boundaries.Based on three rural case studies, this research investigates the movements of tourists within and between destination areas, focusing on the relationship between accommodation hubs and attractions as represented by visitor flows. The graphical representation of such flows has enabled the identification of influence areas of attractions which traverse administrative boundaries, and overlap with those of other attractions. The application of a distance decay curve approach clarifies the relationship between accommodations and the visiting of attractions in the three selected rural areas. Furthermore, the overlapping of several attractions influence areas allow the detection of unexploited cooperation within the destination.
In the last decade several sampling methods have been proposed which rely on piecewise deterministic Markov processes (PDMPs). PDMPs are based on following deterministic trajectories with stochastic events which correspond to jumps in the state space. We propose implementing constraints in this setting to exploit geometries of high-dimensional problems by introducing a PDMP version of Riemannian manifold Hamiltonian Monte Carlo, which we call randomized time Riemannian manifold Hamiltonian Monte Carlo. Efficient sampling on constrained spaces is also needed in many applications including protein conformation modelling, directional statistics and free energy computations. We will show how randomizing the duration parameter for Hamiltonian flow can improve the robustness of Riemannian manifold Hamiltonian Monte Carlo methods. We will then compare methods on some example distributions which arise in application and provide an application of sampling on manifolds in high-dimensional covariance estimation.
This paper provides an in-depth discussion of a methodological approach to the study of music festival experience, using phenomenological psychology to understand the ideographic experiences of attendees. The research is grounded in the philosophy of existential phenomenology and its' conceptualisation of experience, using the work of Husserl (1936Husserl ( /1970 as its' phenomenological foundation. From this position, the research argues for the adoption of an interpretative phenomenological perspective (Heidegger, 1929(Heidegger, /1962 Merleau-Ponty, 1945/1962 in order to more fully understand the live music festival experience. By engaging with the phenomenological psychology of Smith, Harre and Van Langenhove (1995) and Ashworth (2006;, it becomes possible to better understand the contribution that the music festival experience makes to an individual's Lifeworld. Smith's (1996; Interpretative Phenomenological Analysis (IPA) then provides a robust process for understanding the music festival experience on an idiographic basis.Nine participants used the Descriptive Experience Sampling (Hurlburt & Heavey, 2001) approach to gather data about their experiences before, during and after the Green Man Music festival and then further explored in detail during subsequent individual phenomenological interviews. The use of Descriptive Experience Sampling method and Interpretative Phenomenological Analysis also provides a contrasting conceptualisation of experience to previous research, with findings that contribute to Ashworth's (2003) theories of Lifeworld as well as Krueger's (2014Krueger's ( , 2015 Hypothesis of Individual Extended Emotions and his Hypothesis of Collective Extended Emotions. The main focus of this paper is on the method's application and adaptability to the Music Festival context and gives consideration for future studies.
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