Multifractal analysis of Birkhoff averages for countable Markov maps

In this paper we prove a multifractal formalism of Birkhoff averages for interval maps with countably many branches. Furthermore, we prove that under certain regularity assumptions on the potential the Birkhoff spectrum is real analytic. Applications of these results to number theory are also given. Finally, we compute the Hausdorff dimension of the set of points for which the Birkhoff average is infinite.Comment: 27 pages. Substantial changes have been made to Theorem 1.2 and sections 4,5 and 6. Some minor corrections have been made elsewher

Multifractal structure of Bernoulli convolutions

Let $\nu_\lambda^p$ be the distribution of the random series $\sum_{n=1}^\infty i_n \lambda^n$, where $i_n$ is a sequence of i.i.d. random variables taking the values 0,1 with probabilities $p,1-p$. These measures are the well-known (biased) Bernoulli convolutions. In this paper we study the multifractal spectrum of $\nu_\lambda^p$ for typical $\lambda$. Namely, we investigate the size of the sets $$\Delta_{\lambda,p}(\alpha) = \left\{x\in\R: \lim_{r\searrow 0} \frac{\log \nu_\lambda^p(B(x,r))}{\log r} =\alpha\right\}.$$ Our main results highlight the fact that for almost all, and in some cases all, $\lambda$ in an appropriate range, $\Delta_{\lambda,p}(\alpha)$ is nonempty and, moreover, has positive Hausdorff dimension, for many values of $\alpha$. This happens even in parameter regions for which $\nu_\lambda^p$ is typically absolutely continuous.Comment: 24 pages, 2 figure

Sustainable urban development in practice:the SAVE concept

The need for sustainable development of the urban environment presents the research community with a number of challenges and opportunities. A considerable volume of research has been undertaken into the constituent parts of this complex problem and a number of tool kits and methodologies have been developed to enable and encourage the application of specific aspects of research in practice. However, there is limited evidence of the holistic integration of the body of knowledge arising from the research within real-life decision-making practices. In this paper we present an overview of the existing body of knowledge relating to sustainable development of the urban environment and propose a generic framework for its integration within current practices. This framework recognises the need to: understand social, economic, and environmental issues; understand the decision-making processes; provide a means of measurement, assessment, or valuation of the issues; provide analytical methods for the comparative assessment of complex data to enable an evaluation of strategies and design options and to communicate effectively throughout the process with a wide range of stakeholders. The components of a novel sustainability assessment, visualisation and enhancement (SAVE) framework, developed by the authors to ‘operationalise’ the body of knowledge are presented and justified. These include: decision-mapping methods to identify points of intervention; indicator identification and measurement approaches; appropriate mathematical and analytical tools and an interactive simulation and visualisation platform which integrates and communicates complex multivariate information to diverse stakeholder groups. We report on the application of the SAVE framework to a major urban development project and reflect on its current and potential impact on the development. Conclusions are also drawn about its general applicability

Bayesian Regression Markets

Machine learning tasks are vulnerable to the quality of data used as input. Yet, it is often challenging for firms to obtain adequate datasets, with them being naturally distributed amongst owners, that in practice, may be competitors in a downstream market and reluctant to share information. Focusing on supervised learning for regression tasks, we develop a \textit{regression market} to provide a monetary incentive for data sharing. Our proposed mechanism adopts a Bayesian framework, allowing us to consider a more general class of regression tasks. We present a thorough exploration of the market properties, and show that similar proposals in current literature expose the market agents to sizeable financial risks, which can be mitigated in our probabilistic setting.Comment: 46 pages, 11 figures, 2 table

Incentivizing Data Sharing for Energy Forecasting: Analytics Markets with Correlated Data

Reliably forecasting uncertain power production is beneficial for the social welfare of electricity markets by reducing the need for balancing resources. Describing such forecasting as an analytics task, the current literature proposes analytics markets as an incentive for data sharing to improve accuracy, for instance by leveraging spatio-temporal correlations. The challenge is that, when used as input features for forecasting, correlated data complicates the market design with respect to the revenue allocation, as the value of overlapping information is inherently combinatorial. We develop a correlation-aware analytics market for a wind power forecasting application. To allocate revenue, we adopt a Shapley value-based attribution policy, framing the features of agents as players and their interactions as a characteristic function game. We illustrate that there are multiple options to describe such a game, each having causal nuances that influence market behavior when features are correlated. We argue that no option is correct in a general sense, but that the decision hinges on whether the market should address correlations from a data-centric or model-centric perspective, a choice that can yield counter-intuitive allocations if not considered carefully by the market designer.Comment: 15 pages, 9 figures, 1 tabl

Pregeometric Concepts on Graphs and Cellular Networks as Possible Models of Space-Time at the Planck-Scale

Starting from the working hypothesis that both physics and the corresponding mathematics have to be described by means of discrete concepts on the Planck-scale, one of the many problems one has to face is to find the discrete protoforms of the building blocks of continuum physics and mathematics. In the following we embark on developing such concepts for irregular structures like (large) graphs or networks which are intended to emulate (some of) the generic properties of the presumed combinatorial substratum from which continuum physics is assumed to emerge as a coarse grained and secondary model theory. We briefly indicate how various concepts of discrete (functional) analysis and geometry can be naturally constructed within this framework, leaving a larger portion of the paper to the systematic developement of dimensional concepts and their properties, which may have a possible bearing on various branches of modern physics beyond quantum gravity.Comment: 16 pages, Invited paper to appear in the special issue of the Journal of Chaos, Solitons and Fractals on: "Superstrings, M, F, S ... Theory" (M.S. El Naschie, C. Castro, Editors

HIV vulnerability of men and women who inject drugs in Kumasi, Ghana

This study was implemented by Boston University in collaboration with the Kwame Nkrumah University of Science and Technology with support from the President’s Emergency Plan for AIDS Relief (PEPFAR) through the U.S. Agency for International Development under Project SEARCH Task Order No. GHH‐I‐00‐07‐00023‐00, beginning August 27, 2010. The content and views expressed here are the authors’ and do not necessarily reflect the opinion or policy of USAID or the U.S. Government.Reducing vulnerability to HIV infection among key populations in Ghana is a major goal for the National AIDS Control Program (NACP) and the GAC. While a number of studies have explored HIV risk behaviours among several key vulnerable populations in Ghana including female sex workers, men who have sex with men, and prisoners, little is known about the drug use and sexual vulnerability of people who inject drugs (PWID). In addition, no programs have been implemented to reduce the vulnerability among this population. This report provides the findings from a qualitative study that aimed to understand the social, economic and behavioral vulnerability to HIV of PWID in Kumasi and to inform the development and implementation of HIV prevention programs for this population. The research was conducted by a collaborative team comprised of researchers from Boston University’s Center for Global and Health and Development (CGHD) and the Kwame Nkrumah University of Science and Technology (KNUST) School of Medical Sciences. It is one of nine studies under the Operations Research on Key Populations project funded by the United States Agency for International Development (USAID). The study was designed and carried out in collaboration with the Ghana AIDS Commission (GAC).Support from the President’s Emergency Plan for AIDS Relief (PEPFAR) through the U.S. Agency for International Development under Project SEARCH Task Order No. GHH‐I‐00‐07‐00023‐00, beginning August 27, 201

"I can decide to use the property I have to make money": HIV vulnerability of bar workers and bar patrons in Kumasi, Ghana

This study was implemented by Boston University in collaboration with the Kwame Nkrumah University of Science and Technology with support from the President’s Emergency Plan for AIDS Relief (PEPFAR) through the U.S. Agency for International Development under Project SEARCH Task Order No. GHH‐I‐00‐07‐00023‐00, beginning August 27, 2010. The content and views expressed here are the authors’ and do not necessarily reflect the opinion or policy of USAID or the U.S. Government.This report provides the findings from a qualitative study exploring the social, economic and behavioral vulnerability to HIV of women working in bars and restaurants in Kumasi, Ghana’s second largest city. This research was conducted by a collaborative team comprised of researchers from Boston University’s Center for Global and Health and Development (CGHD) and the Kwame Nkrumah University of Science and Technology (KNUST) School of Medical Sciences. It is one of nine studies under the Operations Research on Key Populations project funded by the United States Agency for International Development (USAID). The study was designed and carried out in collaboration with the Ghana AIDS Commission (GAC). Reducing vulnerability to HIV infection among key populations in Ghana is a major goal for the National AIDS Control Program (NACP) and the GAC. While a number of studies have explored HIV risk behaviours among self-identified female sex workers and their partners in Ghana, little is known about the vulnerability of women working in small bars and restaurants who may be involved in transactional sex. Further, we have little information about how best to reach this population with services that will enable them and their clientele to protect themselves from HIV and reduce other vulnerabilities related to their health and well-being. To address this gap, this study aimed to explore behavioural, social, and economic factors that contribute to HIV vulnerability; types and extent of transactional sex; the relationship between alcohol/drug use, unsafe sex and transactional sex; and the health and social service needs of this population. The study findings are meant to inform the development and implementation of HIV prevention programs for bar workers and bar patrons.Support from the President’s Emergency Plan for AIDS Relief (PEPFAR) through the U.S. Agency for International Development under Project SEARCH Task Order No. GHH‐I‐00‐07‐00023‐00, beginning August 27, 201