Predicting the Output From a Stochastic Computer Model When a Deterministic Approximation is Available

The analysis of computer models can be aided by the construction of surrogate models, or emulators, that statistically model the numerical computer model. Increasingly, computer models are becoming stochastic, yielding different outputs each time they are run, even if the same input values are used. Stochastic computer models are more difficult to analyse and more difficult to emulate - often requiring substantially more computer model runs to fit. We present a method of using deterministic approximations of the computer model to better construct an emulator. The method is applied to numerous toy examples, as well as an idealistic epidemiology model, and a model from the building performance field

Valuing natural assets

Key points New Zealand producers and consumers get much value from natural assets. Much of this value is intangible. This is a fundamental reason to make special effort to measure the value of natural assets, to make sure we make the right decisions about their use and conservation.But a key barrier to using economic valuation is the cost and uncertainty of values obtained from the variety of techniques being used. This is a real issue, to the extent that doubts are being expressed in resource management cases whether economics has much to add when considering environmental effects.To remove this barrier, valuations need to be cheaper and easier to compare. A standardised technique could provide relative values for different types of natural asset or service. This would make economic value estimates from across a range of natural asset settings more consistent.Developing a practical, reliable standardised technique would involve: building on studies done to date , showing how much economic activity depends on natural assets in a robust and comparable waycarrying out a meta - analysis, to obtain consistent and comparable value estimates for a range of ensure economic activities from economic impact studies done to datelearning how biophysical cause - and - effect relationships translate into economic value, to identify the sensitivity of econo mic activity to changes in natural assets , such as biodiversitycommissioning a stated preference study of the value of broad categories of natural assets, as a starting point for identifying value in specific situations. Decision - makers need to understand how and where economic valuation can support their decisions. Providing them with explanatory materials will help.It is important to make progress. There is currently a gap in the knowledge about the full contribution of natural assets to New Zealand’s economic well-being. This creates a risk that natural assets will be undervalued. Ecosystems and the valuable services they provide may be lost or damaged.Economic valuation of environmental assets can fill the knowledge gap. To date, non-market valuations in New Zealand do not appear to have been used much to make management choices in conservation, whether those relate to responding to pest incursions or to economic development.A less ad hoc approach to weighing up the value of natural assets can make treatment of natural assets more consistent in decisions, and increase the efficiency of use of natural resources. A better approach is needed so studies inform policy and decisions about New Zealand’s natural assets. Our proposed approach could improve understanding of the value of natural assets — giving them more consistent weight in decisions, and improving the way we manage them

Point-Particle Effective Field Theory I: Classical Renormalization and the Inverse-Square Potential

Singular potentials (the inverse-square potential, for example) arise in many situations and their quantum treatment leads to well-known ambiguities in choosing boundary conditions for the wave-function at the position of the potential's singularity. These ambiguities are usually resolved by developing a self-adjoint extension of the original problem; a non-unique procedure that leaves undetermined which extension should apply in specific physical systems. We take the guesswork out of this picture by using techniques of effective field theory to derive the required boundary conditions at the origin in terms of the effective point-particle action describing the physics of the source. In this picture ambiguities in boundary conditions boil down to the allowed choices for the source action, but casting them in terms of an action provides a physical criterion for their determination. The resulting extension is self-adjoint if the source action is real (and involves no new degrees of freedom), and not otherwise (as can also happen for reasonable systems). We show how this effective-field picture provides a simple framework for understanding well-known renormalization effects that arise in these systems, including how renormalization-group techniques can resum non-perturbative interactions that often arise, particularly for non-relativistic applications. In particular we argue why the low-energy effective theory tends to produce a universal RG flow of this type and describe how this can lead to the phenomenon of reaction {\em catalysis}, in which physical quantities (like scattering cross sections) can sometimes be surprisingly large compared to the underlying scales of the source in question. We comment in passing on the possible relevance of these observations to the phenomenon of the catalysis of baryon-number violation by scattering from magnetic monopoles.Comment: LaTeX, 20 pages plus appendi

Every Hilbert space frame has a Naimark complement

Naimark complements for Hilbert space Parseval frames are one of the most fundamental and useful results in the field of frame theory. We will show that actually all Hilbert space frames have Naimark complements which possess all the usual properties for Naimark complements with one notable exception. So these complements can be used for equiangular frames, RIP property, fusion frames etc. Along the way, we will correct a mistake in a recent fusion frame paper where chordal distances for Naimark complements are computed incorrectly.Comment: Changes after Refereein

QuaRel: A Dataset and Models for Answering Questions about Qualitative Relationships

Many natural language questions require recognizing and reasoning with qualitative relationships (e.g., in science, economics, and medicine), but are challenging to answer with corpus-based methods. Qualitative modeling provides tools that support such reasoning, but the semantic parsing task of mapping questions into those models has formidable challenges. We present QuaRel, a dataset of diverse story questions involving qualitative relationships that characterize these challenges, and techniques that begin to address them. The dataset has 2771 questions relating 19 different types of quantities. For example, "Jenny observes that the robot vacuum cleaner moves slower on the living room carpet than on the bedroom carpet. Which carpet has more friction?" We contribute (1) a simple and flexible conceptual framework for representing these kinds of questions; (2) the QuaRel dataset, including logical forms, exemplifying the parsing challenges; and (3) two novel models for this task, built as extensions of type-constrained semantic parsing. The first of these models (called QuaSP+) significantly outperforms off-the-shelf tools on QuaRel. The second (QuaSP+Zero) demonstrates zero-shot capability, i.e., the ability to handle new qualitative relationships without requiring additional training data, something not possible with previous models. This work thus makes inroads into answering complex, qualitative questions that require reasoning, and scaling to new relationships at low cost. The dataset and models are available at http://data.allenai.org/quarel.Comment: 9 pages, AAAI 201

Molecular and fossil evidence place the origin of cichlid fishes long after Gondwanan rifting.

Cichlid fishes are a key model system in the study of adaptive radiation, speciation and evolutionary developmental biology. More than 1600 cichlid species inhabit freshwater and marginal marine environments across several southern landmasses. This distributional pattern, combined with parallels between cichlid phylogeny and sequences of Mesozoic continental rifting, has led to the widely accepted hypothesis that cichlids are an ancient group whose major biogeographic patterns arose from Gondwanan vicariance. Although the Early Cretaceous (ca 135 Ma) divergence of living cichlids demanded by the vicariance model now represents a key calibration for teleost molecular clocks, this putative split pre-dates the oldest cichlid fossils by nearly 90 Myr. Here, we provide independent palaeontological and relaxed-molecular-clock estimates for the time of cichlid origin that collectively reject the antiquity of the group required by the Gondwanan vicariance scenario. The distribution of cichlid fossil horizons, the age of stratigraphically consistent outgroup lineages to cichlids and relaxed-clock analysis of a DNA sequence dataset consisting of 10 nuclear genes all deliver overlapping estimates for crown cichlid origin centred on the Palaeocene (ca 65-57 Ma), substantially post-dating the tectonic fragmentation of Gondwana. Our results provide a revised macroevolutionary time scale for cichlids, imply a role for dispersal in generating the observed geographical distribution of this important model clade and add to a growing debate that questions the dominance of the vicariance paradigm of historical biogeography