Airy Distribution Function: From the Area Under a Brownian Excursion to the Maximal Height of Fluctuating Interfaces

The Airy distribution function describes the probability distribution of the area under a Brownian excursion over a unit interval. Surprisingly, this function has appeared in a number of seemingly unrelated problems, mostly in computer science and graph theory. In this paper, we show that this distribution also appears in a rather well studied physical system, namely the fluctuating interfaces. We present an exact solution for the distribution P(h_m,L) of the maximal height h_m (measured with respect to the average spatial height) in the steady state of a fluctuating interface in a one dimensional system of size L with both periodic and free boundary conditions. For the periodic case, we show that P(h_m,L)=L^{-1/2}f(h_m L^{-1/2}) for all L where the function f(x) is the Airy distribution function. This result is valid for both the Edwards-Wilkinson and the Kardar-Parisi-Zhang interfaces. For the free boundary case, the same scaling holds P(h_m,L)=L^{-1/2}F(h_m L^{-1/2}), but the scaling function F(x) is different from that of the periodic case. We compute this scaling function explicitly for the Edwards-Wilkinson interface and call it the F-Airy distribution function. Numerical simulations are in excellent agreement with our analytical results. Our results provide a rather rare exactly solvable case for the distribution of extremum of a set of strongly correlated random variables. Some of these results were announced in a recent Letter [ S.N. Majumdar and A. Comtet, Phys. Rev. Lett., 92, 225501 (2004)].Comment: 27 pages, 10 .eps figures included. Two figures improved, new discussion and references adde

Developing Secure Power Systems Professional Competence: Alignment and Gaps in Workforce Development Programs?Summary Report

This document is a summarization of the report, Developing Secure Power Systems Professional Competence: Alignment and Gaps in Workforce Development Programs, the final report for phase 2 of the SPSP (DOE workforce study) project

Noncovalent Functionalization of Graphene and Graphene Oxide for Energy Materials, Biosensing, Catalytic, and Biomedical Applications

This Review focuses on noncovalent functionalization of graphene and graphene oxide with various species involving biomolecules, polymers, drugs, metals and metal oxide-based nanoparticles, quantum dots, magnetic nanostructures, other carbon allotropes (fullerenes, nanodiamonds, and carbon nanotubes), and graphene analogues (MoS2, WS2). A brief description of pi-pi interactions, van der Waals forces, ionic interactions, and hydrogen bonding allowing noncovalent modification of graphene and graphene oxide is first given. The main part of this Review is devoted, to tailored functionalization for applications in drug delivery, energy materials, solar cells, water splitting, biosensing, bioimaging, environmental, catalytic, photocatalytic, and biomedical technologies. A significant part of this Review explores the possibilities of graphene/graphene oxide-based 3D superstructures and their use in lithium-ion batteries. This Review ends with a look at challenges and future prospects of noncovalently modified graphene and graphene oxideope

Technological Change in Resource Extraction and Endogenous Growth

We add an extractive sector to an endogenous growth model of expanding varieties and directed technological change. Extractive firms reduce the stock of non-renewable resources through extraction, but also increase the stock through R&D investment in extraction technology. Our model replicates long-term trends in non-renewable resource markets, namely stable prices and exponentially increasing extraction, for which we present data from 1792 to 2009. The model suggests that the development of new extraction technologies neutralizes the increasing demand for non-renewable resources in industrializing countries like China in the long term

A hemimetric extension of simulation for semi-markov decision processes

Semi-Markov decision processes (SMDPs) are continuous-time Markov decision processes where the residence-time on states is governed by generic distributions on the positive real line. In this paper we consider the problem of comparing two SMDPs with respect to their time-dependent behaviour. We propose a hemimetric between processes, which we call simulation distance, measuring the least acceleration factor by which a process needs to speed up its actions in order to behave at least as fast as another process. We show that this distance can be computed in time O(n2(f(l)+k)+mn7), where n is the number of states, m the number of actions, k the number of atomic propositions, and f(l) the complexity of comparing the residence-time between states. The theoretical relevance and applicability of this distance is further argued by showing that (i) it is suitable for compositional reasoning with respect to CSP-like parallel composition and (ii) has a logical characterisation in terms of a simple Markovian logic

On visual pigment templates and the spectral shape of invertebrate rhodopsins and metarhodopsins

The absorbance spectra of visual pigments can be approximated with mathematical expressions using as single parameter the absorbance peak wavelength. A comparison of the formulae of Stavenga et al. in Vision Res 33:1011–1017 (1993) and Govardovskii et al. in Vis Neurosci 17:509–528 (2000) applied to a number of invertebrate rhodopsins reveals that both templates well describe the normalized α-band of rhodopsins with peak wavelength > 400 nm; the template spectra are virtually indistinguishable in an absorbance range of about three log units. The template formulae of Govardovskii et al. in Vis Neurosci 17:509–528 (2000) describe the rhodopsin spectra better for absorbances below 10−3. The template predicted spectra deviate in the ultraviolet wavelength range from each other as well as from measured spectra, preventing a definite conclusion about the spectral shape in the wavelength range <400 nm. The metarhodopsin spectra of blowfly and fruitfly R1-6 photoreceptors derived from measured data appear to be virtually identical. The established templates describe the spectral shape of fly metarhodopsin reasonably well. However, the best fitting template spectrum slightly deviates from the experimental spectra near the peak and in the long-wavelength tail. Improved formulae for fitting the fly metarhodopsin spectra are proposed

The Social Cost of Carbon on an Optimal Balanced Growth Path

This paper derives analytically the growth rate of the social cost of carbon (SSC) on an optimal balanced growth path. More specifically, the paper examines a deterministic Ramsey model of optimal economic growth with carbon emissions. In this model, restrictions on technology and preferences are imposed that guarantee optimal balanced growth, i.e., that guarantee an optimal path with constant and positive economic growth and a constant stock of carbon in the atmosphere. The paper exploits these restrictions to show that the growth rate of the SCC on the optimal balanced growth path is negative, provided the elasticity of marginal utility of consumption with respect to consumption is larger than or equal to one. There seems to be consensus in the literature that this latter requirement is fulfilled in reality

Effects of microperfusion in hepatic diffusion weighted imaging

Clinical hepatic diffusion weighted imaging (DWI) generally relies on mono-exponential diffusion. The aim was to demonstrate that mono-exponential diffusion in the liver is contaminated by microperfusion and that the bi-exponential model is required. Nineteen fasting healthy volunteers were examined with DWI (seven b-values) using fat suppression and respiratory triggering (1.5 T). Five different regions in the liver were analysed regarding the mono-exponentially fitted apparent diffusion coefficient (ADC), and the bi-exponential model: molecular diffusion (D (slow) ) microperfusion (D (fast) ) and the respective fractions (f (slow/fast)). Data were compared using ANOVA and Kruskal-Wallis tests. Simulations were performed by repeating our data analyses, using just the DWI series acquired with b-values approximating those of previous studies. Median mono-exponentially fitted ADCs varied significantly (P <0.001) between 1.107 and 1.423 x 10(-3) mm(2)/s for the five regions. Bi-exponential fitted D-slow varied between 0.923 and 1.062 x 10(-3) mm(2)/s without significant differences (P = 0.140). D (fast) varied significantly, between 17.8 and 46.8 x 10(-3) mm(2)/s (P <0.001). F-tests showed that the diffusion data fitted the bi-exponential model significantly better than the mono-exponential model (F > 21.4, P <0.010). These results were confirmed by the simulations. ADCs of normal liver tissue are significantly dependent on the measurement location because of substantial microperfusion contamination; therefore the bi-exponential model should be used. Diffusion weighted MR imaging helps clinicians to differentiate tumours by diffusion properties Fast moving water molecules experience microperfusion, slow molecules diffusion Hepatic diffusion should be measured by bi-exponential models to avoid microperfusion contamination Mono-exponential models are contaminated with microperfusion, resulting in apparent regional diffusion differences Bi-exponential models are necessary to measure diffusion and microperfusion in the liver

The role of valuation and bargaining in optimising transboundary watercourse treaty regimes

In the face of water scarcity, growing water demands, population increase, ecosystem degradation, climate change, and so on transboundary watercourse states inevitably have to make difficult decisions on how finite quantities of water are distributed. Such waters, and their associated ecosystem services, offer multiple benefits. Valuation and bargaining can play a key role in the sharing of these ecosystems services and their associated benefits across sovereign borders. Ecosystem services in transboundary watercourses essentially constitute a portfolio of assets. Whilst challenging, their commodification, which creates property rights, supports trading. Such trading offers a means by which to resolve conflicts over competing uses and allows states to optimise their ‘portfolios’. However, despite this potential, adoption of appropriate treaty frameworks that might facilitate a market-based approach to the discovery and allocation of water-related ecosystem services at the transboundary level remains both a challenge, and a topic worthy of further study. Drawing upon concepts in law and economics, this paper therefore seeks to advance the study of how treaty frameworks might be developed in a way that supports such a market-based approach to ecosystem services and transboundary waters

The SPECTRUM Consortium: a new UK Prevention Research Partnership consortium focussed on the commercial determinants of health, the prevention of non-communicable diseases, and the reduction of health inequalities

The main causes of non-communicable diseases (NCDs), health inequalities and health inequity include consumption of unhealthy commodities such as tobacco, alcohol and/or foods high in fat, salt and/or sugar. These exposures are preventable, but the commodities involved are highly profitable. The economic interests of ‘Unhealthy Commodity Producers’ (UCPs) often conflict with health goals but their role in determining health has received insufficient attention. In order to address this gap, a new research consortium has been established. This open letter introduces the SPECTRUM (Shaping Public hEalth poliCies To Reduce ineqUalities and harM) Consortium: a multi-disciplinary group comprising researchers from 10 United Kingdom (UK) universities and overseas, and partner organisations including three national public health agencies in Great Britain (GB), five multi-agency alliances and two companies providing data and analytic support. Through eight integrated work packages, the Consortium seeks to provide an understanding of the nature of the complex systems underlying the consumption of unhealthy commodities, the role of UCPs in shaping these systems and influencing health and policy, the role of systems-level interventions, and the effectiveness of existing and emerging policies. Co-production is central to the Consortium’s approach to advance research and achieve meaningful impact and we will involve the public in the design and delivery of our research. We will also establish and sustain mutually beneficial relationships with policy makers, alongside our partners, to increase the visibility, credibility and impact of our evidence. The Consortium’s ultimate aim is to achieve meaningful health benefits for the UK population by reducing harm and inequalities from the consumption of unhealthy commodities over the next five years and beyond