On the Critical-Subcritical Moments of Moments of Random Characteristic Polynomials: A GMC Perspective.

We study the 'critical moments' of subcritical Gaussian multiplicative chaos (GMCs) in dimensions . In particular, we establish a fully explicit formula for the leading order asymptotics, which is closely related to large deviation results for GMCs and demonstrates a similar universality feature. We conjecture that our result correctly describes the behaviour of analogous moments of moments of random matrices, or more generally structures which are asymptotically Gaussian and log-correlated in the entire mesoscopic scale.

A Spin Glass Model for the Loss Surfaces of Generative Adversarial Networks.

We present a novel mathematical model that seeks to capture the key design feature of generative adversarial networks (GANs). Our model consists of two interacting spin glasses, and we conduct an extensive theoretical analysis of the complexity of the model's critical points using techniques from Random Matrix Theory. The result is insights into the loss surfaces of large GANs that build upon prior insights for simpler networks, but also reveal new structure unique to this setting which explains the greater difficulty of training GANs.

Quantification of Spatial and Temporal Trends in Atmospheric Mercury Deposition across Canada over the Past 30 Years.

Mercury (Hg) is a pollutant of concern across Canada and transboundary anthropogenic Hg sources presently account for over 95% of national anthropogenic Hg deposition. This study applies novel statistical analyses of 82 high-resolution dated lake sediment cores collected from 19 regions across Canada, including nearby point sources and in remote regions and spanning a full west-east geographical range of ∼4900 km (south of 60°N and between 132 and 64°W) to quantify the recent (1990-2018) spatial and temporal trends in anthropogenic atmospheric Hg deposition. Temporal trend analysis shows significant synchronous decreasing trends in post-1990 anthropogenic Hg fluxes in western Canada in contrast to increasing trends in the east, with spatial patterns largely driven by longitude and proximity to known point source(s).

Sources of atmospheric metal(loid) pollution recorded in Thompson Manitoba lake sediment cores within the Canadian boreal biome.

Global atmospheric emissions and subsequent deposition of numerous metal(loid)s has increased markedly since the industrial revolution. Due to a paucity of long-term metal(loid) flux measurements, the magnitude and timing of change are largely unknown, resulting in limited ability to predict time-scales of ecosystem recovery in response to emission decreases. In the absence of long-term data, palaeo-reconstructions provide continuous records of atmospheric metal(loid) deposition on an ecosystem, and landscape, scale.

Widespread Atmospheric Tellurium Contamination in Industrial and Remote Regions of Canada.

High tech applications, primarily photovoltaics, have greatly increased demand for the rare and versatile but toxic element tellurium (Te). Here we examine dated lake sediment Te concentration profiles collected near potential point sources (metal smelters, coal mining/combustion facilities, oil sands operations) and from rural regions and remote natural areas of Canada. Te contamination was most prevalent near a Cu/Zn smelter where observed deposition infers 21 g Te released per metric ton (t) of Cu processed.

Anthropogenic mercury deposition in Flin Flon Manitoba and the Experimental Lakes Area Ontario (Canada): A multi-lake sediment core reconstruction.

High-resolution records of anthropogenic mercury (Hg) deposition were constructed from 9 lakes located 5-75km from the Flin Flon, Manitoba smelter (formerly one of North America's largest atmospheric Hg point sources) and 5 lakes in Experimental Lakes Area (ELA), Ontario; a region remote from major Hg point sources. Anthropogenic Hg deposition, as both a flux and inventory, was determined after accounting for lake-specific natural Hg background concentrations, changes in sedimentation and sediment focusing. Results show that records of anthropogenic flux and inventory of Hg were remarkably consistent among the ELA lakes, but varied by 2 orders of magnitude among Flin Flon lakes.

Pair correlation and twin primes revisited.

We establish a connection between the conjectural two-over-two ratios formula for the Riemann zeta-function and a conjecture concerning correlations of a certain arithmetic function. Specifically, we prove that the ratios conjecture and the arithmetic correlations conjecture imply the same result. This casts a new light on the underpinnings of the ratios conjecture, which previously had been motivated by analogy with formulae in random matrix theory and by a heuristic recipe.

Moments of zeta and correlations of divisor-sums: I.

We examine the calculation of the second and fourth moments and shifted moments of the Riemann zeta-function on the critical line using long Dirichlet polynomials and divisor correlations. Previously, this approach has proved unsuccessful in computing moments beyond the eighth, even heuristically. A careful analysis of the second and fourth moments illustrates the nature of the problem and enables us to identify the terms that are missed in the standard application of these methods.

Anadromous char as an alternate food choice to marine animals: a synthesis of Hg concentrations, population features and other influencing factors.

This study was conducted to confirm sporadic measurements made over the late 1970s to the early 1990 s which determined that mercury (Hg) concentrations were low in anadromous char across Arctic and subarctic Canada including northern Québec and Labrador. Over 2004-2013, anadromous char populations across northern Canada were investigated at 20 sites for Hg concentrations and life history characteristics. Hg concentrations were extremely low in anadromous char muscle, typically <0.

Local structure and speciation of platinum in fresh and road-aged North American sourced vehicle emissions catalysts: an X-ray absorption spectroscopic study.

Given emerging concerns about the bioavailability and toxicity of anthropogenic platinum compounds emitted into the environment from sources including vehicle emission catalysts (VEC), the platinum species present in selected North American sourced fresh and road-aged VEC were determined by Pt and Cl X-ray absorption spectroscopy. Detailed analysis of the Extended X-ray Absorption Fine Structure at the Pt L3 and L2 edges of the solid phase catalysts revealed mainly oxidic species in the fresh catalysts and metallic components dominant in the road-aged catalysts. In addition, some bimetallic components (Pt-Ni, Pt-Pd, Pt-Rh) were observed in the road-aged catalysts from supporting Ni-, Pd-, and Rh-K edge XAS studies.

Freezing transitions and extreme values: random matrix theory, ζ (1/2 + it) and disordered landscapes.

We argue that the freezing transition scenario, previously conjectured to occur in the statistical mechanics of 1/f-noise random energy models, governs, after reinterpretation, the value distribution of the maximum of the modulus of the characteristic polynomials pN(θ) of large N×N random unitary (circular unitary ensemble) matrices UN; i.e. the extreme value statistics of pN(θ) when N → ∞.

Mercury trends in predatory fish in Great Slave Lake: the influence of temperature and other climate drivers.

Here we report on trends in mercury (Hg) concentrations in lake trout (Salvelinus namaycush), burbot (Lota lota), and northern pike (Esox lucius) from Great Slave Lake, located in the Mackenzie River Basin (MRB) and investigate how climate factors may be influencing these trends. Hg concentrations in lake trout and burbot increased significantly over the early 1990s to 2012 in the two major regions of the lake; no trend was evident for northern pike over 1999-2012. Temporal variations in Hg concentrations in lake trout and burbot were similar with respect to timing of peaks and troughs.

Elucidation of structure and nature of the PdO-Pd transformation using in situ PDF and XAS techniques.

The PdO-Pd phase transformation in a 4 wt% Pd/Al2O3 catalyst has been investigated using in situ X-ray absorption spectroscopy (XAS) and in situ X-ray total scattering (also known as high-energy X-ray diffraction) techniques. Both the partial and total pair distribution functions (PDF) from these respective techniques have been analysed in depth. New information from PDF analysis of total scattering data has been garnered using the differential PDF (d-PDF) approach where only correlations orginating from PdO and metallic Pd are extracted.

Freezing transition, characteristic polynomials of random matrices, and the Riemann zeta function.

We argue that the freezing transition scenario, previously explored in the statistical mechanics of 1/f-noise random energy models, also determines the value distribution of the maximum of the modulus of the characteristic polynomials of large N×N random unitary matrices. We postulate that our results extend to the extreme values taken by the Riemann zeta function ζ(s) over sections of the critical line s=1/2+it of constant length and present the results of numerical computations in support. Our main purpose is to draw attention to possible connections between the statistical mechanics of random energy landscapes, random-matrix theory, and the theory of the Riemann zeta function.

Biomarker responses in nesting, common eiders in the Canadian arctic in relation to tissue cadmium, mercury and selenium concentrations.

Populations of many North American sea ducks are declining. Biomarkers may offer valuable insights regarding the health and fitness of sea ducks in relation to contaminant burdens. In this study we examined body condition, immune function, corticosterone stress response, liver glycogen levels and vitamin A status in relation to tissue concentrations of mercury, selenium and cadmium in female common eiders during the nesting period.

The semiclassical functional equation.

A semiclassical analog of the functional equation for the Riemann zeta function is considered. In the case of the zeta function itself, this equation forms the basis for a finite approximation to the Dirichlet series, known as the approximate functional equation. In the same way, the semiclassical functional equation can be shown to give rise to a finite approximation to the semiclassical representation of the quantum spectral determinant as a sum over classical pseudo-orbits.