The distribution theory for discrete-time renewal–reward processes with dependent rewards is developed through the derivation of double transforms. By dependent, we mean the more realistic setting in which the reward for an interarrival period is dependent on the duration of the associated interarrival time. The double transforms are the generating functions in time of the time-dependent reward probability-generating functions. Residue and saddlepoint approximations are used to invert such double transforms so that the reward distribution at arbitrary time n can be accurately approximated. In addition, double transforms are developed for the first-passage time distribution that the cumulative reward exceeds a fixed threshold amount. These distributions are accurately approximated by inverting the double transforms using residue and saddlepoint approximation methods. The residue methods also provide asymptotic expansions for moments and allow for the proof of central limit theorems related to these first passage times and reward amounts.

The average maturity of newly issued corporate bonds has declined substantially over the past 40 years, and the traditional determinants of debt maturity fail to explain this decline fully. We show that the changing composition of investors in the corporate bond market influences bond maturities. The results of a Granger causality test, an instrumental variable approach, and a natural experiment suggest that a decline in the insurance companies’ – which prefer long-term bonds – ownership share in the corporate bond market explains a significant part of the unexplained maturity decline. These findings illustrate how investor preferences can have real effects on corporations.

We consider residue expansions for survival and density/mass functions of first-passage distributions in finite-state semi-Markov processes (SMPs) in continuous and integer time. Conditions are given which guarantee that the residue expansions for these functions have a dominant exponential/geometric term. The key condition assumes that the relevant states for first passage contain an irreducible class, thus ensuring the same sort of dominant exponential/geometric terms as one gets for phase-type distributions in Markov processes. Essentially, the presence of an irreducible class along with some other conditions ensures that the boundary singularity b for the moment generating function (MGF) of the first-passage-time distribution is a simple pole. In the continuous-time setting we prove that b is a dominant pole, in that the MGF has no other pole on the vertical line $\{\text{Re}(s)=b\}.$ In integer time we prove that b is dominant if all holding-time mass functions for the SMP are aperiodic and non-degenerate. The expansions and pole characterisations address first passage to a single new state or a subset of new states, and first return to the starting state. Numerical examples demonstrate that the residue expansions are considerably more accurate than saddlepoint approximations and can provide a substitute for exact computation above the 75th percentile.

Democratic cooperation is a particularly complex type of arrangement that requires attendant institutions to ensure that the problems inherent in collective action do not subvert the public good. It is perhaps due to this complexity that historians, political scientists, and others generally associate the birth of democracy with the emergence of so-called states and center it geographically in the “West,” where it then diffused to the rest of the world. We argue that the archaeological record of the American Southeast provides a case to examine the emergence of democratic institutions and to highlight the distinctive ways in which such long-lived institutions were—and continue to be—expressed by Native Americans. Our research at the Cold Springs site in northern Georgia, USA, provides important insight into the earliest documented council houses in the American Southeast. We present new radiocarbon dating of these structures along with dates for the associated early platform mounds that place their use as early as cal AD 500. This new dating makes the institution of the Muskogean council, whose active participants have always included both men and women, at least 1,500 years old, and therefore one of the most enduring and inclusive democratic institutions in world history.

The COllaborative project of Development of Anthropometrical measures in Twins (CODATwins) project is a large international collaborative effort to analyze individual-level phenotype data from twins in multiple cohorts from different environments. The main objective is to study factors that modify genetic and environmental variation of height, body mass index (BMI, kg/m2) and size at birth, and additionally to address other research questions such as long-term consequences of birth size. The project started in 2013 and is open to all twin projects in the world having height and weight measures on twins with information on zygosity. Thus far, 54 twin projects from 24 countries have provided individual-level data. The CODATwins database includes 489,981 twin individuals (228,635 complete twin pairs). Since many twin cohorts have collected longitudinal data, there is a total of 1,049,785 height and weight observations. For many cohorts, we also have information on birth weight and length, own smoking behavior and own or parental education. We found that the heritability estimates of height and BMI systematically changed from infancy to old age. Remarkably, only minor differences in the heritability estimates were found across cultural–geographic regions, measurement time and birth cohort for height and BMI. In addition to genetic epidemiological studies, we looked at associations of height and BMI with education, birth weight and smoking status. Within-family analyses examined differences within same-sex and opposite-sex dizygotic twins in birth size and later development. The CODATwins project demonstrates the feasibility and value of international collaboration to address gene-by-exposure interactions that require large sample sizes and address the effects of different exposures across time, geographical regions and socioeconomic status.

Filamentary structures can form within the beam of protons accelerated during the interaction of an intense laser pulse with an ultrathin foil target. Such behaviour is shown to be dependent upon the formation time of quasi-static magnetic field structures throughout the target volume and the extent of the rear surface proton expansion over the same period. This is observed via both numerical and experimental investigations. By controlling the intensity profile of the laser drive, via the use of two temporally separated pulses, both the initial rear surface proton expansion and magnetic field formation time can be varied, resulting in modification to the degree of filamentary structure present within the laser-driven proton beam.

We show that initial public offerings (IPOs) have nontrivial positive spillover effects on local labor markets, business environments, consumer spending, real estate, and migration. We mitigate endogeneity concerns about unobserved heterogeneity with restrictive geographic fixed effects coupled with a matching procedure. We show that it is the listing decision, which encompasses both a wealth and liquidity shock, that induces economic spillovers. Conditional on an IPO occurring, we estimate that an additional $10 million in IPO proceeds is associated with an extra 41 jobs and 0.7 new establishments locally.

Transform inversions, in which density and survival functions are computed from their associated moment generating function $\mathcal{M}$, have largely been based on methods which use values of $\mathcal{M}$ in its convergence region. Prominent among such methods are saddlepoint approximations and Fourier-series inversion methods, including the fast Fourier transform. In this paper we propose inversion methods which make use of values for $\mathcal{M}$ which lie outside of its convergence region and in its analytic continuation. We focus on the simplest and perhaps richest setting for applications in which $\mathcal{M}$ is either a meromorphic function in its analytic continuation, so that all of its singularities are poles, or else the singularities are isolated essential. Asymptotic expansions of finite- and infinite-orders are developed for density and survival functions using the poles of $\mathcal{M}$ in its analytic continuation. For finite-order expansions, the expansion error is a contour integral in the analytic continuation, which we approximate using the saddlepoint method based on following the path of steepest descent. Such saddlepoint error approximations accurately determine expansion errors and, thus, provide the means for determining the order of the expansion needed to achieve some preset accuracy. They also provide an additive correction term which increases accuracy of the expansion. Further accuracy is achieved by computing the expansion errors numerically using a contour path which ultimately tracks the steepest descent direction. Important applications include Wilks’ likelihood ratio test in MANOVA, compound distributions, and the Sparre Andersen and Cramér–Lundberg ruin models.

The Nanga Parbat massif is a rapidly eroding, thrust-related antiform that is distinct from other regions of the Himalayan orogen in being both intruded by Late Miocene-Pliocene anatectic granites and permeated by a vigorous hydrothermal system. Exhumation is achieved by erosion during thrusting along the Liachar thrust in the apparent absence of extensional tectonics. At depths in excess of 20 km, small batches of leucogranitic melt have been generated by fluid-absent breakdown of muscovite from metapelitic lithologies. These melts ascend several kilometres prior to emplacement, aided by low geothermal gradients at depth and by interaction with meteoric water as they reach shallow levels. At intermediate depths (∼15 km) limited fluid infiltration is restricted to shear zones resulting in localised anatexis. Within the upper 8 km of crust, magmatic and meteoric fluid fluxes are channelised by active structures providing a feedback mechanism for focusing deformation. Leucogranite sheets show a range of pre-full crystallization and high-temperature crystal-plastic textures indicative of strain localisation onto these sheets and away from the country rocks. At subsolidus temperatures meteoric fluids promote strain localisation and may trigger cataclastic deformation. Since near-surface geothermal gradients are unusually steep, the macroscopic transition between distributed shearing and substantial, but localised, cataclastic deformation occurred at amphibolite-facies conditions (∼600°C). Even with the greatest topographic relief in the world, the meteoric system of Nanga Parbat is effectively restricted to the upper 8 km of the crust, strongly controlled by active structures.

Whether monozygotic (MZ) and dizygotic (DZ) twins differ from each other in a variety of phenotypes is important for genetic twin modeling and for inferences made from twin studies in general. We analyzed whether there were differences in individual, maternal and paternal education between MZ and DZ twins in a large pooled dataset. Information was gathered on individual education for 218,362 adult twins from 27 twin cohorts (53% females; 39% MZ twins), and on maternal and paternal education for 147,315 and 143,056 twins respectively, from 28 twin cohorts (52% females; 38% MZ twins). Together, we had information on individual or parental education from 42 twin cohorts representing 19 countries. The original education classifications were transformed to education years and analyzed using linear regression models. Overall, MZ males had 0.26 (95% CI [0.21, 0.31]) years and MZ females 0.17 (95% CI [0.12, 0.21]) years longer education than DZ twins. The zygosity difference became smaller in more recent birth cohorts for both males and females. Parental education was somewhat longer for fathers of DZ twins in cohorts born in 1990–1999 (0.16 years, 95% CI [0.08, 0.25]) and 2000 or later (0.11 years, 95% CI [0.00, 0.22]), compared with fathers of MZ twins. The results show that the years of both individual and parental education are largely similar in MZ and DZ twins. We suggest that the socio-economic differences between MZ and DZ twins are so small that inferences based upon genetic modeling of twin data are not affected.

Phased VLA observations of the Galactic center magnetar J1745-2900 over 8-12 GHz reveal rich single pulse behavior. The average profile is comprised of several distinct components and is fairly stable over day timescales and GHz frequencies. The average profile is dominated by the jitter of relatively narrow pulses. The pulses in each of the four profile components are uncorrelated in phase and amplitude, although the occurrence of pulse components 1 and 2 appear to be correlated. Using a collection of the brightest individual pulses, we verify that the index of the dispersion law is consistent with the expected cold plasma value of 2. The scattering time is weakly constrained, but consistent with previous measurements, while the dispersion measure DM = 1763+3−10 pc cm−3 is lower than previous measurements, which could be a result of time variability in the line-of-sight column density or changing pulse profile shape over time or frequency.