Maxwell Institute for Mathematical Sciences

Abstract In this article, we consider the evolution of the post‐age‐60 mortality curve in the United Kingdom and its impact on the pricing of the risk associated with aggregate mortality improvements over time: so‐called longevity risk. We introduce a two‐factor stochastic model for the development of this curve through time. The first factor affects mortality‐rate dynamics at all ages in the same way, whereas the second factor affects mortality‐rate dynamics at higher ages much more than at lower ages. The article then examines the pricing of longevity bonds with different terms to maturity referenced to different cohorts. We find that longevity risk over relatively short time horizons is very low, but at horizons in excess of ten years it begins to pick up very rapidly. A key component of the article is the proposal and development of a method for calculating the market risk‐adjusted price of a longevity bond. The proposed adjustment includes not just an allowance for the underlying stochastic mortality, but also makes an allowance for parameter risk. We utilize the pricing information contained in the November 2004 European Investment Bank longevity bond to make inferences about the likely market prices of the risks in the model. Based on these, we investigate how future issues might be priced to ensure an absence of arbitrage between bonds with different characteristics.

Abstract We compare quantitatively eight stochastic models explaining improvements in mortality rates in England and Wales and in the United States. On the basis of the Bayes Information Criterion (BIC), we find that, for higher ages, an extension of the Cairns-Blake-Dowd (CBD) model that incorporates a cohort effect fits the England and Wales males data best, while for U.S. males data, the Renshaw and Haberman (RH) extension to the Lee and Carter model that also allows for a cohort effect provides the best fit. However, we identify problems with the robustness of parameter estimates under the RH model, calling into question its suitability for forecasting. A different extension to the CBD model that allows not only for a cohort effect, but also for a quadratic age effect, while ranking below the other models in terms of the BIC, exhibits parameter stability across different time periods for both datasets. This model also shows, for both datasets, that there have been approximately linear improvements over time in mortality rates at all ages, but that the improvements have been greater at lower ages than at higher ages, and that there are significant cohort effects.

During commissioning observations, the Sloan Digital Sky Survey (SDSS) has produced one of the largest existing galaxy redshift samples selected from CCD images. Using 11,275 galaxies complete to r^* = 17.6 over 140 square degrees, we compute the luminosity function of galaxies in the r^* band over a range -23 < M < -16 (for h=1). The result is well-described by a Schechter function with parameters phi_* = 0.0146 +/- 0.0012 h^3 Mpc^{-3}, M_* = -20.83 +/- 0.03, and alpha = -1.20 +/- 0.03. The implied luminosity density in r^* is j = (2.6 +/- 0.3) x 10^8 h L_sun Mpc^{-3}. The surface brightness selection threshold has a negligible impact for M < -18. We measure the luminosity function in the u^*, g^*, i^*, and z^* bands as well; the slope at low luminosities ranges from alpha=-1.35 to alpha=-1.2. We measure the bivariate distribution of r^* luminosity with half-light surface brightness, intrinsic color, and morphology. High surface brightness, red, highly concentrated galaxies are on average more luminous than low surface brightness, blue, less concentrated galaxies. If we synthesize results for R-band or b_j-band using the Petrosian magnitudes with which the SDSS measures galaxy fluxes, we obtain luminosity densities 2.5 times that found by the Las Campanas Redshift Survey in R and 1.4 times that found by the Two-degree Field Galaxy Redshift Survey in b_j. We are able to reproduce the luminosity functions obtained by these surveys if we also mimic their isophotal limits for defining galaxy magnitudes, which are shallower and more redshift dependent than the Petrosian magnitudes used by the SDSS. (Abridged)

It is shown that a necessary and sufficient condition for an Archimedean copula generator to generate a d-dimensional copula is that the generator is a d-monotone function. The class of d-dimensional Archimedean copulas is shown to coincide with the class of survival copulas of d-dimensional ℓ1-norm symmetric distributions that place no point mass at the origin. The d-monotone Archimedean copula generators may be characterized using a little-known integral transform of Williamson [Duke Math. J. 23 (1956) 189–207] in an analogous manner to the well-known Bernstein–Widder characterization of completely monotone generators in terms of the Laplace transform. These insights allow the construction of new Archimedean copula families and provide a general solution to the problem of sampling multivariate Archimedean copulas. They also yield useful expressions for the d-dimensional Kendall function and Kendall’s rank correlation coefficients and facilitate the derivation of results on the existence of densities and the description of singular components for Archimedean copulas. The existence of a sharp lower bound for Archimedean copulas with respect to the positive lower orthant dependence ordering is shown.

Sensitivity analysis (SA) is en route to becoming an integral part of mathematical modeling. The tremendous potential benefits of SA are, however, yet to be fully realized, both for advancing mechanistic and data-driven modeling of human and natural systems, and in support of decision making. In this perspective paper, a multidisciplinary group of researchers and practitioners revisit the current status of SA, and outline research challenges in regard to both theoretical frameworks and their applications to solve real-world problems. Six areas are discussed that warrant further attention, including (1) structuring and standardizing SA as a discipline, (2) realizing the untapped potential of SA for systems modeling, (3) addressing the computational burden of SA, (4) progressing SA in the context of machine learning, (5) clarifying the relationship and role of SA to uncertainty quantification, and (6) evolving the use of SA in support of decision making. An outlook for the future of SA is provided that underlines how SA must underpin a wide variety of activities to better serve science and society.

Colloidal particles or nanoparticles, with equal affinity for two fluids, are known to adsorb irreversibly to the fluid-fluid interface. We present large-scale computer simulations of the demixing of a binary solvent containing such particles. The newly formed interface sequesters the colloidal particles; as the interface coarsens, the particles are forced into close contact by interfacial tension. Coarsening is markedly curtailed, and the jammed colloidal layer seemingly enters a glassy state, creating a multiply connected, solidlike film in three dimensions. The resulting gel contains percolating domains of both fluids, with possible uses as, for example, a microreaction medium.

It is shown that a necessary and sufficient condition for an Archimedean copula generator to generate a d-dimensional copula is that the generator is a d-monotone function. The class of d-dimensional Archimedean copulas is shown to coincide with the class of survival copulas of d-dimensional ℓ1-norm symmetric distributions that place no point mass at the origin. The d-monotone Archimedean copula generators may be characterized using a little-known integral transform of Williamson [Duke Math. J. 23 (1956) 189–207] in an analogous manner to the well-known Bernstein–Widder characterization of completely monotone generators in terms of the Laplace transform. These insights allow the construction of new Archimedean copula families and provide a general solution to the problem of sampling multivariate Archimedean copulas. They also yield useful expressions for the d-dimensional Kendall function and Kendall’s rank correlation coefficients and facilitate the derivation of results on the existence of densities and the description of singular components for Archimedean copulas. The existence of a sharp lower bound for Archimedean copulas with respect to the positive lower orthant dependence ordering is shown.

BACKGROUND AND OBJECTIVES: Epilepsy affects 0.5% to 1% of children and is the most frequent chronic neurologic condition in childhood. Incidence rates appear to be declining in high-income countries. The validity of epilepsy diagnoses from different data sources varies, and contemporary population-based incidence studies are needed. METHODS: The study was based on the Norwegian Mother and Child Cohort Study. Potential epilepsy cases were identified through registry linkages and parental questionnaires. Cases were validated through medical record reviews and telephone interviews of parents. RESULTS: The study population included 112 744 children aged 3 to 13 years (mean 7.4 years) at end of registry follow-up (December 31, 2012). Of these, 896 had registry recordings and/or questionnaire reports of epilepsy. After validation, 587 (66%) met the criteria for an epilepsy diagnosis. The incidence rate of epilepsy was 144 per 100 000 person-years in the first year of life and 58 per 100 000 for ages 1 to 10 years. The cumulative incidence of epilepsy was 0.66% at age 10 years, with 0.62% having active epilepsy. The 309 children (34%) with erroneous reports of epilepsy from the registry and/or the questionnaires had mostly been evaluated for nonepileptic paroxysmal events, or they had undergone electroencephalography examinations because of other developmental or neurocognitive difficulties. CONCLUSIONS: Approximately 1 out of 150 children is diagnosed with epilepsy during the first 10 years of life, with the highest incidence rate observed during infancy. Validation of epilepsy diagnoses in administrative data and cohort studies is crucial because reported diagnoses may not meet diagnostic criteria for epilepsy.

Abstract Myelin is required for the function of neuronal axons in the central nervous system, but the mechanisms that support myelin health are unclear. Although macrophages in the central nervous system have been implicated in myelin health 1 , it is unknown which macrophage populations are involved and which aspects they influence. Here we show that resident microglia are crucial for the maintenance of myelin health in adulthood in both mice and humans. We demonstrate that microglia are dispensable for developmental myelin ensheathment. However, they are required for subsequent regulation of myelin growth and associated cognitive function, and for preservation of myelin integrity by preventing its degeneration. We show that loss of myelin health due to the absence of microglia is associated with the appearance of a myelinating oligodendrocyte state with altered lipid metabolism. Moreover, this mechanism is regulated through disruption of the TGFβ1–TGFβR1 axis. Our findings highlight microglia as promising therapeutic targets for conditions in which myelin growth and integrity are dysregulated, such as in ageing and neurodegenerative disease 2,3 .

A self-healing mechanism may render nanomaterials highly useful for nuclear applications.

Although urban greening is universally recognized as an essential part of sustainable and climate-responsive cities, a growing literature on green gentrification argues that new green infrastructure, and greenspace in particular, can contribute to gentrification, thus creating social and racial inequalities in access to the benefits of greenspace and further environmental and climate injustice. In response to limited quantitative evidence documenting the temporal relationship between new greenspaces and gentrification across entire cities, let alone across various international contexts, we employ a spatially weighted Bayesian model to test the green gentrification hypothesis across 28 cities in 9 countries in North America and Europe. Here we show a strong positive and relevant relationship for at least one decade between greening in the 1990s-2000s and gentrification that occurred between 2000-2016 in 17 of the 28 cities. Our results also determine whether greening plays a "lead", "integrated", or "subsidiary" role in explaining gentrification.

Abstract Initially, Grid technologies were principally associated with supercomputer centres and large‐scale scientific applications in physics and astronomy. They are now increasingly seen as being relevant to many areas of e‐Science and e‐Business. The emergence of the Open Grid Services Architecture (OGSA), to complement the ongoing activity on Web Services standards, promises to provide a service‐based platform that can meet the needs of both business and scientific applications. Early Grid applications focused principally on the storage, replication and movement of file‐based data. Now the need for the full integration of database technologies with Grid middleware is widely recognized. Not only do many Grid applications already use databases for managing metadata, but increasingly many are associated with large databases of domain‐specific information (e.g. biological or astronomical data). This paper describes the design and implementation of OGSA‐DAI, a service‐based architecture for database access over the Grid. The approach involves the design of Grid Data Services that allow consumers to discover the properties of structured data stores and to access their contents. The initial focus has been on support for access to Relational and XML data, but the overall architecture has been designed to be extensible to accommodate different storage paradigms. The paper describes and motivates the design decisions that have been taken, and illustrates how the approach supports a range of application scenarios. The OGSA‐DAI software is freely available from http://www.ogsadai.org.uk . Copyright © 2005 John Wiley & Sons, Ltd.

This paper introduces the design and implementation of two parallel dual simplex solvers for general large scale sparse linear programming problems. One approach, called PAMI, extends a relatively unknown pivoting strategy called suboptimization and exploits parallelism across multiple iterations. The other, called SIP, exploits purely single iteration parallelism by overlapping computational components when possible. Computational results show that the performance of PAMI is superior to that of the leading open-source simplex solver, and that SIP complements PAMI in achieving speedup when PAMI results in slowdown. One of the authors has implemented the techniques underlying PAMI within the FICO Xpress simplex solver and this paper presents computational results demonstrating their value. In developing the first parallel revised simplex solver of general utility, this work represents a significant achievement in computational optimization.

We provide a first derivation of the Bekenstein-Hawking entropy of 3D flat cosmological horizons in terms of the counting of states in a dual field theory. These horizons appear in the flat limit of nonextremal rotating Banados-Teitleboim-Zanelli black holes and are remnants of the inner horizons. They also satisfy the first law of thermodynamics. We study flat holography as a limit of AdS(3)/CFT(2) to semiclassically compute the density of states in the dual theory, which is given by a contraction of a 2D conformal field theory, exactly reproducing the bulk entropy in the limit of large charges. We comment on how the dual theory reproduces the bulk first law and how cosmological bulk excitations are matched with boundary quantum numbers.

Exosomes have been implicated in numerous biological processes, and they may serve as important disease markers. Surface proteins on exosomes carry information about their tissues of origin. Because of the heterogeneity of exosomes it is desirable to investigate them individually, but this has so far remained impractical. Here, we demonstrate a proximity-dependent barcoding assay to profile surface proteins of individual exosomes using antibody-DNA conjugates and next-generation sequencing. We first validate the method using artificial streptavidin-oligonucleotide complexes, followed by analysis of the variable composition of surface proteins on individual exosomes, derived from human body fluids or cell culture media. Exosomes from different sources are characterized by the presence of specific combinations of surface proteins and their abundance, allowing exosomes to be separately quantified in mixed samples to serve as markers for tissue-specific engagement in disease.

In the first part of the paper, we consider the wide range of extrapolative stochastic mortality models that have been proposed over the last 15–20 years. A number of models that we consider are framed in discrete time and place emphasis on the statistical aspects of modelling and forecasting. We discuss how these models can be evaluated, compared and contrasted. We also discuss a discrete-time market model that facilitates valuation of mortality-linked contracts with embedded options. We then review several approaches to modelling mortality in continuous time. These models tend to be simpler in nature, but make it possible to examine the potential for dynamic hedging of mortality risk. Finally, we review a range of financial instruments (traded and over-the-counter) that could be used to hedge mortality risk. Some of these, such as mortality swaps, already exist, while others anticipate future developments in the market.

We give algorithms for sampling from non-exchangeable Archimedean copulas created by the nesting of Archimedean copula generators, where in the most general algorithm the generators may be nested to an arbitrary depth. These algorithms are based on mixture representations of these copulas using Laplace transforms. While in principle the approach applies to all nested Archimedean copulas, in practice the approach is restricted to certain cases where we are able to sample distributions with given Laplace transforms. Precise instructions are given for the case when all generators are taken from the Gumbel parametric family or the Clayton family; the Gumbel case in particular proves very easy to simulate.

Several problems in computer algebra can be efficiently solved by reducing them to calculations over finite fields. In this paper, we describe an algorithm for the reconstruction of multivariate polynomials and rational functions from their evaluation over finite fields. Calculations over finite fields can in turn be efficiently performed using machine-size integers in statically-typed languages. We then discuss the application of the algorithm to several techniques related to the computation of scattering amplitudes, such as the four- and six-dimensional spinor-helicity formalism, tree-level recursion relations, and multi-loop integrand reduction via generalized unitarity. The method has good efficiency and scales well with the number of variables and the complexity of the problem. As an example combining these techniques, we present the calculation of full analytic expressions for the two-loop five-point on-shell integrands of the maximal cuts of the planar penta-box and the non-planar double-pentagon topologies in Yang-Mills theory, for a complete set of independent helicity configurations.

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