A martingale analysis of first passage times of time-dependent Wiener diffusion models

Research in psychology and neuroscience has successfully modeled decision making as a process of noisy evidence accumulation to a decision bound. While there are several variants and implementations of this idea, the majority of these models make use of a noisy accumulation between two absorbing boundaries. A common assumption of these models is that decision parameters, e.g., the rate of accumulation (drift rate), remain fixed over the course of a decision, allowing the derivation of analytic formulas for the probabilities of hitting the upper or lower decision threshold, and the mean decision time. There is reason to believe, however, that many types of behavior would be better described by a model in which the parameters were allowed to vary over the course of the decision process. In this paper, we use martingale theory to derive formulas for the mean decision time, hitting probabilities, and first passage time (FPT) densities of a Wiener process with time-varying drift between two time-varying absorbing boundaries. This model was first studied by Ratcliff (1980) in the two-stage form, and here we consider the same model for an arbitrary number of stages (i.e. intervals of time during which parameters are constant). Our calculations enable direct computation of mean decision times and hitting probabilities for the associated multistage process. We also provide a review of how martingale theory may be used to analyze similar models employing Wiener processes by re-deriving some classical results. In concert with a variety of numerical tools already available, the current derivations should encourage mathematical analysis of more complex models of decision making with time-varying evidence

A ‘healthy baby’: The double imperative of preimplantation genetic diagnosis

This is the author's accepted manuscript. The final published article is available from the link below. Copyright @ 2010 The Authors.This article reports from a study exploring the social processes, meanings and institutions that frame and produce ‘ethical problems’ and clinical dilemmas for practitioners, scientists and others working in the specialty of preimplantation genetic diagnosis (PGD). A major topic in the data was that, in contrast to IVF, the aim of PGD is to transfer to the woman’s womb only those embryos likely to be unaffected by serious genetic disorders; that is, to produce ‘healthy babies’. Staff described the complex processes through which embryos in each treatment cycle must meet a double imperative: they must be judged viable by embryologists and ‘unaffected’ by geneticists. In this article, we focus on some of the ethical, social and occupational issues for staff ensuing from PGD’s double imperative.The Wellcome Trus

On the theory of specification, implementation, and parametrization of abstract data types

ABSTRACT. In the framework of a category spec of equational speoficatlons of abstract data types, tmplementations are defined to be certain pairs of morphlsms with a common target Th~s concept covers, among others, arbitrary recurslon schemes for defining the derived operations It is shown that for given single steps of a multilevel tmplementatlon, there is always a multtlevel tmplementatlon composed of these steps, but there ts no effective construction of th~s overall implementauon Some suggestions are gtven for practtcal composition of tmplementat~ons Utdlzmg pushouts Parametric specifications and parameter assignments are defined to be spectal morphlsms in spec, and parameter substitution ~s made precise by means of pushouts Since actual parameters can agam be parametrtc, parameter subsututton can be tterated. Thts tterauon ts shown to be assoctatwe Whtle the subject is being treated on a syntactical level in terms of speclfieauons, the imtlal algebra approach ts adopted as providing an appropriate semantics for spec~ficauons, and the effects of the present concepts and results on the initial algebras are studie

Can reindeer husbandry management slow down the shrubification of the Arctic?

Rapid climate change is threatening the stability and functioning of Arctic ecosystems. As the Arctic warms, shrubs have been widely observed to expand, which has potentially serious consequences for global climate regulation and for the ecological processes characterising these ecosystems. However, it is currently unclear why this shrubification has been spatially uneven across the Arctic, with herbivory being suggested as a key regulating factor. By taking advantage of freely available satellite imagery spanning three decades, we mapped changes in shrub cover in the Yamal Peninsula and related these to changes in summer temperature and reindeer population size. We found no evidence that shrubs had expanded in the study site, despite increasing summer temperatures. At the same time, herbivore pressure increased significantly, with the local reindeer population size growing by about 75%. Altogether, our results thus point towards increases in large herbivore pressure having compensated for the warming of the Peninsula, halting the shrubification of the area. This suggests that strategic semi-domesticated reindeer husbandry, which is a common practice across the Eurasian Arctic, could represent an efficient environmental management strategy for maintaining open tundra landscapes in the face of rapid climate change

Changing Arctic snow cover: A review of recent developments and assessment of future needs for observations, modelling, and impacts

Open Access Journal (SHERPA RoMEO Green) DOI: 10.1007/s13280-016-0770-0Snow is a critically important and rapidly changing feature of the Arctic. However, snow-cover and snowpack conditions change through time pose challenges for measuring and prediction of snow. Plausible scenarios of how Arctic snow cover will respond to changing Arctic climate are important for impact assessments and adaptation strategies. Although much progress has been made in understanding and predicting snow-cover changes and their multiple consequences, many uncertainties remain. In this paper, we review advances in snow monitoring and modelling, and the impact of snow changes on ecosystems and society in Arctic regions. Interdisciplinary activities are required to resolve the current limitations on measuring and modelling snow characteristics through the cold season and at different spatial scales to assure human well-being, economic stability, and improve the ability to predict manage and adapt to natural hazards in the Arctic region

On the origin of the Norwegian lemming.

The Pleistocene glacial cycles resulted in significant changes in species distributions, and it has been discussed whether this caused increased rates of population divergence and speciation. One species that is likely to have evolved during the Pleistocene is the Norwegian lemming (Lemmus lemmus). However, the origin of this species, both in terms of when and from what ancestral taxon it evolved, has been difficult to ascertain. Here, we use ancient DNA recovered from lemming remains from a series of Late Pleistocene and Holocene sites to explore the species' evolutionary history. The results revealed considerable genetic differentiation between glacial and contemporary samples. Moreover, the analyses provided strong support for a divergence time prior to the Last Glacial Maximum (LGM), therefore likely ruling out a postglacial colonization of Scandinavia. Consequently, it appears that the Norwegian lemming evolved from a small population that survived the LGM in an ice-free Scandinavian refugium

Unsteady Flow and Whirl-Inducing Forces in Axial-Flow Compressors: Part I—Experiment

An experimental and theoretical investigation has been conducted to evaluate the effects seen in axial-flow compressors when the centerline of the rotor is displaced from the centerline of the static structure of the engine. This creates circumferentially nonuniform rotor-tip clearances, unsteady flow, and potentially increased clearances if the rotating and stationary parts come in contact. The result not only adversely affects compressor stall margin, pressure rise capability, and efficiency, but also generates an unsteady, destabilizing, aerodynamic force, called the Thomas/Alford force, which contributes significantly to rotor whirl instabilities in turbomachinery. Determining both the direction and magnitude of this force in compressors, relative to those in turbines, is especially important for the design of mechanically stable turbomachinery components. Part I of this two-part paper addresses these issues experimentally and Part II presents analyses from relevant computational models. Our results clearly show that the Thomas/Alford force can promote significant backward rotor whirl over much of the operating range of modern compressors, although some regions of zero and forward whirl were found near the design point. This is the first time that definitive measurements, coupled with compelling analyses, have been reported in the literature to resolve the long-standing disparity in findings concerning the direction and magnitude of whirl-inducing forces important in the design of modern axial-flow compressors

SPATIAL REASONING IN REMOTELY SENSED DATA

Photointerpreters employ a variety of implicit spatial models to provide interpretations from remotely sensed aerial or satellite imagery. The process of making the implicit models explicit and the subsequent use of explicit models in computer processing is difficult. In this paper one application is illustrated: how ridges and valleys can be automatically interpreted from LANDSAT imagery of a mountainous area and how a relative elevation terrain model can be constructed from this interpretation. It is shown how an illumination model is being used to explain many of the features of a LANDSAT image. Finally, it is shown how to examine valleys for the possible presence of streams or rivers and it is shown how a spatial relational model can be set up to make a final interpretation of the river drainage network