Institute of Applied Mathematics

The perturbations of a uniform Friedmannian universe, leading to galaxy formation, are explained by the strings, formed during the symmetry loss of vacuum of a complex Higgs field with mass characteristic of grand unification. Difficulties are pointed out inherent to phase transition, particle decay and black hole evaporation as sources of growing perturbations.

An up-to-date survey of the theory of port-Hamiltonian systems is given, emphasizing novel developments and relationships with other formalisms. Port-Hamiltonian systems theory yields a systematic framework for network modeling of multi-physics systems. Examples from different areas show the range of applicability. While the emphasis is on modeling and analysis, the last part provides a brief introduction to control of port-Hamiltonian systems.

The gravitational instability of a spatially uniform state of a relativistic scalar field on a time-independent background is considered. The instability is demonstrated to be similar to the well-known Jeans instability of dust-like non-relativistic matter. The consideration is generalized to incorporate ‘hydrodynamics’, i.e. self-interaction of the field. It is demonstrated that ‘hydrodynamic’ effects may drastically alter the character of the instability; in particular, the dependence of the instability growth rate on perturbation wavenumber may become non-monotone. The non-linear stage of instability development is analysed half-quantitatively. It is demonstrated that, the ‘hydrodynamics’ being stabilizing, the instability growth may result in establishing stable spatially periodic structures in the one-dimensional situation. The results obtained are applied to estimating the probability of primordial black hole formation from perturbations growing due to gravitational instability in a universe dominated by a scalar axion field.

Article ArtDefo: accurate real time deformable objects Share on Authors: Doug L. James Institute of Applied Mathematics, University of British Columbia Institute of Applied Mathematics, University of British ColumbiaView Profile , Dinesh K. Pai Institute of Applied Mathematics and Dept. of Computer Science, 2366 Main Mall, UBC, Vancouver, Canada and University of British Columbia Institute of Applied Mathematics and Dept. of Computer Science, 2366 Main Mall, UBC, Vancouver, Canada and University of British ColumbiaView Profile Authors Info & Claims SIGGRAPH '99: Proceedings of the 26th annual conference on Computer graphics and interactive techniquesJuly 1999 Pages 65–72https://doi.org/10.1145/311535.311542Online:01 July 1999Publication History 303citation1,655DownloadsMetricsTotal Citations303Total Downloads1,655Last 12 Months56Last 6 weeks8 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteGet Access

The restrictions on elementary particle properties which can be derived from cosmological and astrophysical data are considered. The inverse relations between micro- and macrophysics are also discussed, in particular the origin of the baryon asymmetry of the universe.

In the 1934 paper [L] Leray raised the question of the existence of self-similar solutions of the Navier{Stokes equations ut u +(u r)u+rp=0 div u =0

Abstract The choice of smoothing parameter or bandwidth is crucial when applying nonparametric regression estimators such as kernel estimators. The optimal choice depends on the data at hand. A data-driven bandwidth selection, close to the optimal one, would make these curve estimators objective, more reliable, and easier to use. Minimizing residual mean squared error criteria, such as cross-validation, have been frequently proposed to estimate the optimal smoothing parameter. Empirical and theoretical evidence indicates that cross-validation rules and related methods lead to rather variable estimated optimal bandwidths. The method presented here builds on estimating the asymptotically optimal bandwidth from the data. Since estimators for the residual variance and for an asymptotic expression for the bias are plugged into the asymptotic formula, such selection rules are called “plug-in” estimators. The functional that quantifies bias is approximated by the integrated squared second derivative of the regression function. This functional is determined by an iterative procedure with good convergence properties in theory and practice. A theoretical large-sample analysis shows that the plug-in estimator is attractive in terms of variability, with a relative rate OP (n -1/2) for smooth functions. In contrast, cross-validation leads to a relative rate OP (n -1/10). Despite the estimation of second derivatives involved, asymptotic properties are still adequate for nonsmooth functions. This robustness is desirable for a non-parametric approach. An extensive simulation study confirms the theoretical findings: The plug-in estimator of the bandwidth has much lower variability than cross-validation estimators for a broad variety of situations, including nonsmooth functions. Despite its asymptotic background, it works well for sample sizes as small as n = 15–25. It applies to fixed and to random design, to equally spaced and nonequally spaced design. Additional assets are computational speed and the great flexibility of this approach. It can also be extended to estimating the optimal bandwidth when determining derivatives of a regression function or probability densities and spectrum densities.

The arbuscular mycorrhizal (AM) fungi are a globally distributed group of soil organisms that play critical roles in ecosystem function. However, the ecological niches of individual AM fungal taxa are poorly understood. We collected > 300 soil samples from natural ecosystems worldwide and modelled the realised niches of AM fungal virtual taxa (VT; approximately species-level phylogroups). We found that environmental and spatial variables jointly explained VT distribution worldwide, with temperature and pH being the most important abiotic drivers, and spatial effects generally occurring at local to regional scales. While dispersal limitation could explain some variation in VT distribution, VT relative abundance was almost exclusively driven by environmental variables. Several environmental and spatial effects on VT distribution and relative abundance were correlated with phylogeny, indicating that closely related VT exhibit similar niche optima and widths. Major clades within the Glomeraceae exhibited distinct niche optima, Acaulosporaceae generally had niche optima in low pH and low temperature conditions, and Gigasporaceae generally had niche optima in high precipitation conditions. Identification of the realised niche space occupied by individual and phylogenetic groups of soil microbial taxa provides a basis for building detailed hypotheses about how soil communities respond to gradients and manipulation in ecosystems worldwide.

Recently, important contributions on convergence studies of conjugate gradient methods were made by Gilbert and Nocedal [SIAM J. Optim., 2 (1992), pp. 21--42]. They introduce a "sufficient descent condition" to establish global convergence results. Although this condition is not needed in the convergence analyses of Newton and quasi-Newton methods, Gilbert and Nocedal hint that the sufficient descent condition, which was enforced by their two-stage line search algorithm, may be crucial for ensuring the global convergence of conjugate gradient methods. This paper shows that the sufficient descent condition is actually not needed in the convergence analyses of conjugate gradient methods. Consequently, convergence results on the Fletcher--Reeves- and Polak--Ribière-type methods are established in the absence of the sufficient descent condition. To show the differences between the convergence properties of Fletcher--Reeves- and Polak--Ribière-type methods, two examples are constructed, showing that neither the boundedness of the level set nor the restriction $\beta_k \geq 0$ can be relaxed for the Polak--Ribière-type methods.

BACKGROUND AND AIMS: The province of British Columbia (BC) Canada has experienced a rapid increase in illicit drug overdoses and deaths during the last 4 years, with a provincial emergency declared in April 2016. These deaths have been driven primarily by the introduction of synthetic opioids into the illicit opioid supply. This study aimed to measure the combined impact of large-scale opioid overdose interventions implemented in BC between April 2016 and December 2017 on the number of deaths averted. DESIGN: We expanded on the mathematical modelling methodology of our previous study to construct a Bayesian hierarchical latent Markov process model to estimate monthly overdose and overdose-death risk, along with the impact of interventions. SETTING AND CASES: Overdose events and overdose-related deaths in BC from January 2012 to December 2017. INTERVENTIONS: The interventions considered were take-home naloxone kits, overdose prevention/supervised consumption sites and opioid agonist therapy MEASUREMENTS: Counterfactual simulations were performed with the fitted model to estimate the number of death events averted for each intervention and in combination. FINDINGS: Between April 2016 and December 2017, BC observed 2177 overdose deaths (77% fentanyl-detected). During the same period, an estimated 3030 (2900-3240) death events were averted by all interventions combined. In isolation, 1580 (1480-1740) were averted by take-home naloxone, 230 (160-350) by overdose prevention services and 590 (510-720) were averted by opioid agonist therapy. CONCLUSIONS: A combined intervention approach has been effective in averting overdose deaths during British Columbia's opioid overdose crisis in the period since declaration of a public health emergency (April 2016-December 2017). However, the absolute numbers of overdose deaths have not changed.

This paper has two objectives. First, it reformulates the theory of optimal use of an exhaustible resource with more attention to the costs of extraction than has been customary in the literature. The output and shadow-price implications of optimal extraction are studied under these broader assumptions. Second, the paper provides some numerical solutions of a simple two-grade case, to give some feeling for the quantitative importance of changes in the supply of exhausti-ble resources. Our most striking result is, in fact, the suggestion that relatively large changes in resource availability generate very small changes in the sustainable level of finalconsumption. l The newer aggregative literature on the socially optimal manage-ment of a given pool of exhaustible resources has ignored one impor-tant characteristic of natural resources: the differential quality of mineral deposits. This note is intended to fill the gap by offering a treatment of differential extraction costs in the context of an aggrega-tive model. We embed the analysis of differential quality in one particular formulation of the macroeconomic problem of the optimal exploitation of exhaustible resources; but we think it would carry over straightforwardly to other ways of setting up the problem. l The basic economic model is that of Solow (1974), so it need only be sketched here. There is a single produced commodity, whose output (Q) can be either consumed directly (C) or accumulated as a stock of reproducible capital (K). Output is produced under constant returns to scale according to a well-behaved production function Q = F(K,R,L), whose inputs are the services of capital and labor and the using-up of resources. Population and employment (L) are con-stant, so-given constant returns to scale-we might as well nor-malize to L = 1, after which Q, K, C, and R can be thought of as output, capital, consumption, and resource use per head. R, as men-tioned, is the flow of the single natural resource into production. For reasons given in Solow (1974), we take F(K,R,L) to be the Cobb-

Abstract We present the online MultiDark Database – a Virtual Observatory‐oriented, relational database for hosting various cos‐mological simulations. The data is accessible via an SQL (Structured Query Language) query interface, which also allows users to directly pose scientific questions, as shown in a number of examples in this paper. Further examples for the usage of the database are given in its extensive online documentation. The database is based on the same technology as the Millennium Database, a fact that will greatly facilitate the usage of both suites of cosmological simulations. The first release of the MultiDark Database hosts two 8.6 billion particle cosmological N‐body simulations: the Bolshoi (250 h –1 Mpc simulation box, 1 h –1 kpc resolution) and MultiDark Run1 simulation (MDR1, or BigBolshoi, 1000 h –1 Mpc simulation box, 7 h –1 kpc resolution). The extraction methods for halos/subhalos from the raw simulation data, and how this data is structured in the database are explained in this paper. With the first data release, users get full access to halo/subhalo catalogs, various profiles of the halos at redshifts z = 0–15, and raw dark matter data for one time‐step of the Bolshoi and four time‐steps of the MultiDark simulation. Later releases will also include galaxy mock catalogs and additional merger trees for both simulations as well as new large volume simulations with high resolution. This project is further proof of the viability to store and present complex data using relational database technology. We encourage other simulators to publish their results in a similar manner. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

The influence of viscoelastic effects on blood flow in large arteries is studied numerically. The description of the blood flow uses the conservation of mass and momentum and a constitutive relation of Jeffreys' type (Oldroyd-B) and appropriate relations to describe the shear thinning behaviour. The steady flow studies are carried out in an axisymmetric tube with a local constriction modelling a stenosed blood vessel and in a three-dimensional 90 degrees curved tube. The numerical approach applies a decoupled technique where the computation of kinematics and stresses is separated. The governing equations are solved by means of an upwind stabilised Galerkin finite element method. The numerical results indicate significant influence of viscoelastic effects in the stenosed model. The flow through the curved tube shows minor quantitative viscoelastic influence. The influence of the shear thinning effect can be observed in both geometries. The results demonstrate that the viscoelastic behaviour of the local flow patterns in large arteries is dependent on the shape of the flow domain.

Abstract Kernel estimators with a global bandwidth are commonly used to estimate regression functions. On the other hand, it is obvious that the choice of a local bandwidth can lead to better results, because a larger class of kernel estimators is available. Evidently, this may in turn affect variability. The optimal bandwidths depend essentially on the regression function itself and on the residual variance, and it is desirable to estimate them from the data. In this article, a local bandwidth estimator is studied. A comparison with its global bandwidth equivalent is performed both in theory and in simulations. As the main result it is shown that the possible gain in mean integrated squared error of the resulting regression estimator must be paid for by a larger variability of the estimator. This may lead to worse results if the sample size is small. An algorithm has been devised that puts special weight on stability aspects. Our simulation study shows that improvements over a global bandwidth estimator often can be realized even at small or moderate sample sizes.

The results of a numerical experiment are given that describe the non-linear stages of the development of perturbations in gravitating matter density in the expanding Universe. This process simulates the formation of the large-scale structure of the Universe from an initially almost homogeneous medium. In the one- and two-dimensional cases of this numerical experiment the evolution of the system from 4096 point masses that interact gravitationally only was studied with periodic boundary conditions (simulation of the infinite space). The initial conditions were chosen that resulted from the theory of the evolution of small perturbations in the expanding Universe. The results of numerical experiments are systematically compared with the approximate analytic theory. The results of the calculations show that in the case of collisionless particles, as well as in the gas-dynamic case, the cellular structure appeared at the non-linear stage (when δρ/ρ ≳ 1) in the case of the adiabatic perturbations. The greater part of the matter is in thin layers that separate vast regions of low density. In a Robertson–Walker universe (Ω = 1) the cellular structure exists for a finite time and then fragments into a few compact objects. In the open Universe (Ω > 1) the cellular structure also exists if the amplitude of initial perturbations is large enough. But the following disruption of the cellular structure is more difficult because of too rapid an expansion of the Universe. The large-scale structure is frozen. Formation of the cellular structure depends mainly on the choice of the spectrum of initial perturbations (short waves must be suppressed).

A method for the sequential mapping of points in a high-dimensional space onto a plane is presented. Whenever a new point is mapped, its distgnces to two points previously mapped are exactly preserved. On the resulting map, 2M -3 of the original distances can be exactly preserved. The mapping is based on the distances of a minimal spanning tree constructed from the points. All of the distances on the minimal spanning tree are exactly preserved.

The influence of wind on extreme wave events in deep water is investigated experimentally and numerically. A series of experiments conducted in the Large Air–Sea Interactions Facility (LASIF-Marseille, France) shows that wind blowing over a short wave group due to the dispersive focusing of a longer frequency-modulated wavetrain (chirped wave packet) may increase the time duration of the extreme wave event by delaying the defocusing stage. A detailed analysis of the experimental results suggests that extreme wave events may be sustained longer by the air flow separation occurring on the leeward side of the steep crests. Furthermore it is found that the frequency downshifting observed during the formation of the extreme wave event is more important when the wind velocity is larger. These experiments have pointed out that the transfer of momentum and energy is strongly increased during extreme wave events. Two series of numerical simulations have been performed using a pressure distribution over the steep crests given by the Jeffreys sheltering theory. The first series corresponding to the dispersive focusing confirms the experimental results. The second series which corresponds to extreme wave events due to modulational instability, shows that wind sustains steep waves which then evolve into breaking waves. Furthermore, it was shown numerically that during extreme wave events the wind-driven current could play a significant role in their persistence.

Abstract This paper establishes some maximum and comparison principles relative to lower and upper solutions of nonlinear parabolic partial differential equations with impulsive effects. These principles are applied to obtain some sufficient conditions for the global asymptotic stability of a unique positive equilibrium in a reaction-diffusion equation modeling the growth of a single-species population subject to abrupt changes of certain important system parameters.

In weather forecasting, non-homogeneous regression (NR) is used to statistically post-process forecast ensembles in order to obtain calibrated predictive distributions. For wind speed forecasts, the regression model is given by a truncated normal (TN) distribution, where location and spread derive from the ensemble. This article proposes two alternative approaches which utilise the generalised extreme value (GEV) distribution. A direct alternative to the TN regression is to apply a predictive distribution from the GEV family, while a regime-switching approach based on the median of the forecast ensemble incorporates both distributions. In a case study on daily maximum wind speed over Germany with the forecast ensemble from the European Centre for Medium-Range Weather Forecasts (ECMWF), all three approaches significantly improve the calibration as well as the overall skill of the raw ensemble with the regime-switching approach showing the highest skill in the upper tail.

Microtubules confined to the two-dimensional cortex of elongating plant cells must form a parallel yet dispersed array transverse to the elongation axis for proper cell wall expansion. Some of these microtubules exhibit free minus-ends, leading to migration at the cortex by hybrid treadmilling. Collisions between microtubules can result in plus-end entrainment ("zippering") or rapid depolymerization. Here, we present a computational model of cortical microtubule organization. We find that plus-end entrainment leads to self-organization of microtubules into parallel arrays, whereas catastrophe-inducing collisions do not. Catastrophe-inducing boundaries (e.g., upper and lower cross-walls) can tune the orientation of an ordered array to a direction transverse to elongation. We also find that changes in dynamic instability parameters, such as in mor1-1 mutants, can impede self-organization, in agreement with experimental data. Increased entrainment, as seen in clasp-1 mutants, conserves self-organization, but delays its onset and fails to demonstrate increased ordering. We find that branched nucleation at acute angles off existing microtubules results in distinctive sparse arrays and infer either that microtubule-independent or coparallel nucleation must dominate. Our simulations lead to several testable predictions, including the effects of reduced microtubule severing in katanin mutants.