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

The Role of Fluids in Ore Remobilization at the Balmat Zinc Deposit, NY

Shear zone-hosted orebodies at the Balmat, NY, zinc deposit were remobilized at the kilometer scale during amphibolite facies regional metamorphism ca. 1180 Ma. Despite there being little evidence for interaction of hydrous fluids and ores during deformation, such translocation distances are considered unlikely without the assistance of fluids. Two independent research methods, SEM-EDS micro-petrography and zinc isotope geochemical analysis, demonstrate that anatectic sulfide and silicate melts were generated during metamorphism. Micro-petrography of the Fowler ore body reveals low melting-temperature micro-inclusions of sulfosalt and sulfide assemblages which occur predominantly in Qtz-Py and Kfs-Py domains that cross-cut peak metamorphic assemblages. These results indicate that localized anatexis occurred on the prograde path, producing low volumes of melts of varying composition. Polymetallic sulfide melts were initiated by the prograde breakdown of minor phases containing low melting temperature chalcophile elements including As, Sb, Pb, and Cu. Alkaline silicate±carbonate±sulfide melts were fluxed by halogens, sulfur and other volatile components released during metamorphism of evaporitic and organic-rich horizons in the marble-dominated host sequence. Measurements of Zn isotopic composition of sphalerite from six Balmat orebodies that originated from the same stratigraphic level (Upper Marble Unit 6) reveal variation between ore bodies, as well as intra-orebody trends of down-plunge decrease in ẟ66Zn. In general, increasing distance of remobilization correlates with decreasing ẟ66Zn. The syn-tectonic isotopic fractionation recorded in Balmat sphalerite is interpreted to have resulted from the interaction between the ore and low-volume sulfide magmas that were fluxed by H2S localized in Upper Marble Unit 7 (fetid dolomite). Lighter isotopes of Zn were enriched in the melt, leaving the residual ore enriched in heavier Zn isotopes. Down-plunge and along-fault migration of fluids resulted in lower ẟ66Zn at the down-plunge end of orebodies that occur in cross-stratigraphic fault zones. These observations support petrographic evidence for the presence of anatectic melts at Balmat and help to explain the unusual scale of translocation at Balmat by means of fluid-assisted remobilization during which rock competency was decreased due to the presence of intergrain fluid films

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

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