Age‐specific fertility trajectories are fundamental to understanding population structure and the evolutionary ecology of diverse life histories. However, characterizing reproductive ageing has been ...difficult with cross‐sectional data, where senescence especially late in life can be confounded by selective disappearance. Addressing such challenge requires longitudinal data tracking the reproductive life span of known individuals, but such data are rare, especially for very long‐lived species such as primates.
We analyse the entire life span trajectory of annual fertility, from reproductive maturity to death, for 673 free‐ranging female rhesus macaques, Macaca mulatta, on Cayo Santiago, Puerto Rico.
Using generalized linear mixed‐effects models (GLMMs), we first tested if time to death explains the ageing pattern independently of and additionally to chronological age, and if so, whether there is interaction between them. While GLMM captures the patterns in the data well, it is not a generative model. For example, given the GLMM and an individual's reproductive trajectory up to a given age, we cannot directly predict the probability of reproduction or death in the next year. For this reason, we further fitted a hidden Markov chain model (HMM) which allows just such a prediction, and additionally helps infer the process underlying the observed trajectory.
We show that, after accounting for individual differences in fertility, reproductive ageing exhibits both age‐dependent decline and also an abrupt terminal decline independently of age at death. We infer from the HMM that the underlying process of reproductive trajectory is where individuals cycle between reproductive bouts until they enter an irreversible frail condition that constrains fertility.
The findings provide valuable insights into the longitudinal progression of reproductive trajectories in primates, by revealing both age‐dependent and age‐independent patterns and processes of ageing, and contribute to a growing body of literature on reproductive ageing and senescence across animal taxa.
Resumen
Las trayectorias de fertilidad específicas de la edad son pieza clave en los estudios que pretenden entender la estructura de la población y la ecología evolutiva de las diversas historias de vida. Sin embargo, la caracterización del envejecimiento reproductivo ha sido difícil con datos transversales, en los que los patrones asociados a la edad avanzada, como la senescencia, pueden verse confundidos por la desaparición selectiva. Los datos longitudinales que rastrean la vida reproductiva de individuos específicos son fundamentales, pero tales datos son escasos, especialmente para especies muy longevas como los primates.
En este estudio analizamos la trayectoria completa de la fertilidad anual, desde la madurez reproductiva hasta la muerte, de 673 macaco rhesus (Macaca mulatta) hembras que habitan libremente la isla de Cayo Santiago, Puerto Rico.
Mostramos que, después de tener en cuenta las diferencias individuales en la fertilidad, el envejecimiento reproductivo exhibe tanto un declive dependiente de la edad, como un declive terminal abrupto independiente de la edad al morir. Aplicando un modelo de cadena de Markov oculta, caracterizamos además el proceso reproductivo subyacente, en el que los individuos pasan por ciclos reproductivos hasta que entran en una condición de fragilidad irreversible que limita la fertilidad.
Los resultados proporcionan una valiosa visión de la progresión longitudinal de las trayectorias reproductivas en los primates, al revelar patrones y procesos de senescencia dependientes e independientes de la edad, y contribuyen a un creciente cuerpo de literatura sobre el envejecimiento reproductivo en todos los taxones animales.
With a diminishing number of individuals with age, studying the pattern of reproductive ageing has been difficult especially in long‐lived species. The authors characterize the entire reproductive trajectory from 673 free‐ranging female rhesus macaques of Cayo Santiago, and provide clear evidence for both reproductive senescence and age‐independent terminal decline in fertility. Image credit: D. Susie Lee.
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SEARCH VIA QUANTUM WALK MAGNIEZ, Frédéric; NAYAK, Ashwin; ROLAND, Jeremie ...
SIAM journal on computing,
2011, 2011-01-00, 20110101, Volume:
40, Issue:
1
Journal Article
Peer reviewed
Open access
We propose a new method for designing quantum search algorithms for finding a "marked" element in the state space of a classical Markov chain. The algorithm is based on a quantum walk a la Szegedy ...Quantum speed-up of Markov chain based algorithms, in Proceedings of the 45th IEEE Symposium on Foundations of Computer Science, IEEE Computer Society Press, 2004, pp. 32--41 that is defined in terms of the Markov chain. The main new idea is to apply quantum phase estimation to the quantum walk in order to implement an approximate reflection operator. This operator is then used in an amplitude amplification scheme. As a result we considerably expand the scope of the previous approaches of Ambainis Quantum walk algorithm for Element Distinctness, in Proceedings of the 45th IEEE Symposium on Foundations of Computer Science, IEEE Computer Society Press, 2004, pp. 22--31 and Szegedy (2004). Our algorithm combines the benefits of these approaches in terms of being able to find marked elements, incurring the smaller cost of the two, and being applicable to a larger class of Markov chains. In addition, it is conceptually simple and avoids some technical difficulties in the previous analyses of several algorithms based on quantum walk. PUBLICATION ABSTRACT
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Urban sprawl is a universal phenomenon and can be seen as a city’s low-density and haphazard development from the centre to suburban areas, and it has different adverse environmental effects at local ...and regional scales, including increasing the cost of infrastructure. Geospatial data and technology can be used to measure urban sprawl and predict urban expansion. This technology can shed light on the characteristics, causes, and consequences of urban expansion. Unlike other studies, the methodology proposed in this paper works on a regional level rather than an individual city. In this article, Land Use Land Cover changes and the magnitude and direction of city-region sprawl in the Isfahan Metropolitan area were modelled using a multi-temporal analysis of remote sensing imagery. Shannon’s Entropy was used to quantify city-region dispersion during the last fifty years. A Multi-Layer Perceptron Neural Network and Markov Chain Analysis were then used to forecast future city-region sprawl based on past patterns and physical constraints. The results revealed that this region has been suffering from sprawl during this period in different directions. Moreover, it will continue in specific directions due to several economic, political, demographic, environmental, and (urban) planning factors. In addition, the size and speed of city-region sprawl were higher than core city sprawl. The proposed approach can be generalized for other city-regions with a similar spatial structure.
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Prediction of lithology/fluid (LF) characteristics is always the bottleneck problem and difficulty of reservoir characterization. Deep-learning-based data-driven methods can review data and find ...specific trends and patterns that would not be apparent to humans, and have been successfully used in many geophysical applications including LF prediction (LFP). However, the above methods mostly predict LF point-by-point, which means that the spatial correlation of LF is not considered. When the predicted LF results are combined to form a 2-D/3-D image, the resulting image will be noisy or even geologically unreliable. To overcome these issues, we proposed a spatially coupled data-driven (convolutional neural network, CNN) approach for LFP from the poststack seismic data and well observations. Here, the vertical couplings of the LF are modeled by a Markov chain (MC) prior and the lateral continuity of the LF is further defined by a Markov random field (MRF) prior. We also proposed to perform spectral decomposition via inversion strategies (ISD) to get a time-frequency (TF) spectrum as the input of CNN. ISD helps make full use of the information hidden in the frequency domain of the poststack seismic data. Well-logs and poststack seismic data are integrated in a consistent manner to obtain predictions of the LF classes with the associated uncertainty statements. The LFP results of the proposed approach are more laterally continuous and geologically reliable than the LFP results of the point-by-point. We determined the effectiveness of this methodology on a 2-D synthetic model and a 3-D field seismic data set.
Galaxies follow a tight radial acceleration relation (RAR): the acceleration observed at every radius correlates with that expected from the distribution of baryons. We use the Markov chain Monte ...Carlo method to fit the mean RAR to 175 individual galaxies in the SPARC database, marginalizing over stellar mass-to-light ratio (ϒ⋆), galaxy distance, and disk inclination. Acceptable fits with astrophysically reasonable parameters are found for the vast majority of galaxies. The residuals around these fits have an rms scatter of only 0.057 dex (~13%). This is in agreement with the predictions of modified Newtonian dynamics (MOND). We further consider a generalized version of the RAR that, unlike MOND, permits galaxy-to-galaxy variation in the critical acceleration scale. The fits are not improved with this additional freedom: there is no credible indication of variation in the critical acceleration scale. The data are consistent with the action of a single effective force law. The apparent universality of the acceleration scale and the small residual scatter are key to understanding galaxies.
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Data augmentation (DA) algorithms are slow in massive data settings due to multiple passes through the entire data. We address this problem by developing a DA extension that exploits asynchronous and ...distributed computing. The extended DA algorithm is called Asynchronous and Distributed (AD) DA with the original DA as its parent. Any ADDA is indexed by a parameter
r
∈
(
0
,
1
)
and starts by dividing the entire data into k disjoint subsets and storing them on k processes. Every iteration of ADDA augments only an r-fraction of the k data subsets with some positive probability and leaves the remaining
(
1
−
r
)
-fraction of the augmented data unchanged. The parameter draws are obtained using the r-fraction of new and
(
1
−
r
)
-fraction of old augmented data. We show that the ADDA Markov chain is Harris ergodic with the desired stationary distribution under mild conditions on the parent DA algorithm. We demonstrate that ADDA is significantly faster than its parent for many (k, r) choices in three representative models. We also establish the geometric ergodicity of the ADDA Markov chain for all the three models, which yields asymptotically valid standard errors for estimates of desired posterior quantities.
Supplementary materials
for this article are available online.
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We prove the convergence of the law of grid-valued random walks, which can be seen as time-space Markov chains, to the law of a general diffusion process. This includes processes with sticky ...features, reflecting or absorbing boundaries and skew behavior. We prove that the convergence occurs at any rate strictly inferior to (1/4) ∧ (1/p) in terms of the maximum cell size of the grid, for any p-Wasserstein distance. We also show that it is possible to achieve any rate strictly inferior to (1/2) ∧ (2/p) if the grid is adapted to the speed measure of the diffusion, which is optimal for p ≤ 4 . This result allows us to set up asymptotically optimal approximation schemes for general diffusion processes. Last, we experiment numerically on diffusions that exhibit various features.
We describe NIMBLE, a system for programming statistical algorithms for general model structures within R. NIMBLE is designed to meet three challenges: flexible model specification, a language for ...programming algorithms that can use different models, and a balance between high-level programmability and execution efficiency. For model specification, NIMBLE extends the BUGS language and creates model objects, which can manipulate variables, calculate log probability values, generate simulations, and query the relationships among variables. For algorithm programming, NIMBLE provides functions that operate with model objects using two stages of evaluation. The first stage allows specialization of a function to a particular model and/or nodes, such as creating a Metropolis-Hastings sampler for a particular block of nodes. The second stage allows repeated execution of computations using the results of the first stage. To achieve efficient second-stage computation, NIMBLE compiles models and functions via C++, using the Eigen library for linear algebra, and provides the user with an interface to compiled objects. The NIMBLE language represents a compilable domain-specific language (DSL) embedded within R. This article provides an overview of the design and rationale for NIMBLE along with illustrative examples including importance sampling, Markov chain Monte Carlo (MCMC) and Monte Carlo expectation maximization (MCEM). Supplementary materials for this article are available online.
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Summary
A wide range of spatially explicit simulation models have been developed to forecast landscape dynamics, including models for projecting changes in both vegetation and land use. While these ...models have generally been developed as separate applications, each with a separate purpose and audience, they share many common features.
We present a general framework, called a state‐and‐transition simulation model (STSM), which captures a number of these common features, accompanied by a software product, called ST‐Sim, to build and run such models. The STSM method divides a landscape into a set of discrete spatial units and simulates the discrete state of each cell forward as a discrete‐time‐inhomogeneous stochastic process. The method differs from a spatially interacting Markov chain in several important ways, including the ability to add discrete counters such as age and time‐since‐transition as state variables, to specify one‐step transition rates as either probabilities or target areas, and to represent multiple types of transitions between pairs of states.
We demonstrate the STSM method using a model of land‐use/land‐cover (LULC) change for the state of Hawai'i, USA. Processes represented in this example include expansion/contraction of agricultural lands, urbanization, wildfire, shrub encroachment into grassland and harvest of tree plantations; the model also projects shifts in moisture zones due to climate change. Key model output includes projections of the future spatial and temporal distribution of LULC classes and moisture zones across the landscape over the next 50 years.
State‐and‐transition simulation models can be applied to a wide range of landscapes, including questions of both land‐use change and vegetation dynamics. Because the method is inherently stochastic, it is well suited for characterizing uncertainty in model projections. When combined with the ST‐Sim software, STSMs offer a simple yet powerful means for developing a wide range of models of landscape dynamics.
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