Joint state-parameter estimation of a nonlinear stochastic energy balance model from sparse noisy data

While nonlinear stochastic partial differential equations arise naturally in spatiotemporal modeling, inference for such systems often faces two major challenges: sparse noisy data and ill-posedness of the inverse problem of parameter estimation. To overcome the challenges, we introduce a strongly regularized posterior by normalizing the likelihood and by imposing physical constraints through priors of the parameters and states. We investigate joint parameter-state estimation by the regularized posterior in a physically motivated nonlinear stochastic energy balance model (SEBM) for paleoclimate reconstruction. The high-dimensional posterior is sampled by a particle Gibbs sampler that combines MCMC with an optimal particle filter exploiting the structure of the SEBM. In tests using either Gaussian or uniform priors based on the physical range of parameters, the regularized posteriors overcome the ill-posedness and lead to samples within physical ranges, quantifying the uncertainty in estimation. Due to the ill-posedness and the regularization, the posterior of parameters presents a relatively large uncertainty, and consequently, the maximum of the posterior, which is the minimizer in a variational approach, can have a large variation. In contrast, the posterior of states generally concentrates near the truth, substantially filtering out observation noise and reducing uncertainty in the unconstrained SEBM

New methods for B meson decay constants and form factors from lattice NRQCD

We determine the normalisation of scalar and pseudoscalar current operators made from non-relativistic $b$ quarks and Highly Improved Staggered light quarks in lattice Quantum Chromodynamics (QCD) through $\mathcal{O}(\alpha_s)$ and $\Lambda_{\text{QCD}}/m_b$. We use matrix elements of these operators to extract $B$ meson decay constants and form factors, then compare to those obtained using the standard vector and axial-vector operators. This provides a test of systematic errors in the lattice QCD determination of the $B$ meson decay constants and form factors. We provide a new value for the $B$ and $B_s$ meson decay constants from lattice QCD calculations on ensembles that include $u$, $d$, $s$ and $c$ quarks in the sea and those which have the $u/d$ quark mass going down to its physical value. Our results are $f_B=0.196(6)$ GeV, $f_{B_s}=0.236(7)$ GeV and $f_{B_s}/f_B =1.207(7)$, agreeing well with earlier results using the temporal axial current. By combining with these previous results, we provide updated values of $f_B=0.190(4)$ GeV, $f_{B_s}=0.229(5)$ GeV and $f_{B_s}/f_B = 1.206(5)$.Comment: 14 pages, 10 figure

Fostering Mathematical Creativity Among Middle School Mathematics Teachers

The purpose of this research was to understand in-service teachers’ experiences with and ideas about mathematical creativity after participating in a targeted professional development program. The professional development program encouraged participants to think creatively and foster students’ creativity. In this study I present the results from the main unit of analysis, 12 participants in a professional development program, along with a deep analysis of three exemplar teachers from each of the identified groups, adherence to traditional teaching practices (traditional), appreciation for teaching for creativity (creative but hesitant), and teaching for creativity (creative). The findings of this study highlight the combination of participants’ personal characteristics, lesson plans, problem-solving processes, and the environment that allowed teachers to foster creativity among middle school mathematics students. It also describes challenges participants faced when addressing mathematical creativity and how professional development programs can further support teachers as they implement elements of mathematical creativity into their teaching practice

How close are time series to power tail L\'evy diffusions?

This article presents a new and easily implementable method to quantify the so-called coupling distance between the law of a time series and the law of a differential equation driven by Markovian additive jump noise with heavy-tailed jumps, such as $\alpha$-stable L\'evy flights. Coupling distances measure the proximity of the empirical law of the tails of the jump increments and a given power law distribution. In particular they yield an upper bound for the distance of the respective laws on path space. We prove rates of convergence comparable to the rates of the central limit theorem which are confirmed by numerical simulations. Our method applied to a paleoclimate time series of glacial climate variability confirms its heavy tail behavior. In addition this approach gives evidence for heavy tails in data sets of precipitable water vapor of the Western Tropical Pacific.Comment: 30 pages, 10 figure

Fuel poverty, older people and cold weather: An all-island analysis

Executive Summary This report covers a number of different aspects of fuel poverty and older people. 1. An exploration of existing government survey data from Northern Ireland and the Republic of Ireland with a particular focus on older people and conducting additional targeted analyses where required. 2. An original survey in the Republic of Ireland exploring the lived experience of older people in cold weather. 3. A feasibility study of data logging thermometers placed in the homes of older tenants in local authority accommodation. 4. Analysis of excess winter mortality among older people including a consideration of differences between the two jurisdictions. Older people on the island of Ireland, as in many other countries, experience a ‘dual burden’ in terms of fuel poverty. They are more likely to experience fuel poverty and are also particularly vulnerable to health and social harm as a result of this experience. The numbers of older people vulnerable to ill-effects from cold homes will rise as numbers of people aged 80 and over, and those living with chronic illness or disability, increase. There were significant differences observed between expenditure-based, and subjective (EU-SILC) based fuel poverty indicators, for older people, and between Northern Ireland and Republic of Ireland data. This data required careful interpretation. The higher levels of fuel poverty recorded for older people on the island of Ireland appeared to be driven by all aspects of the fuel poverty model - poor housing condition, energy inefficient housing, rising fuel prices and low income. The majority of older people live in their own home and these homes tend to be older properties which are detached or semi-detached. Older people on the island are over-represented among houses which are in poor condition and which lack central heating in both jurisdictions. Lacking central heating was a more common experience for older people in the Republic of Ireland than in Northern Ireland. Data on energy efficiency measures were not comparable North/South but similar patterns were observed. Older people were less likely than the general population to have attic/loft or wall insulation or double glazing. Older people were also vulnerable from an income point of view. This would seem to be a particular issue in Northern Ireland where rates of income poverty are significantly increasing. In both jurisdictions older people were heavily reliant on social transfers to keep them out of poverty. Coupled with this, there is evidence that many older people are not claiming their full entitlements. Oil dependency was a particular issue in Northern Ireland. Very significant increases were observed in the price of heating oil, as well as electricity and gas in recent years. There was little available research evidence on the relationship between the older consumer and heating oil suppliers

Perturbation dynamics of a planktonic ecosystem

Planktonic ecosystems provide a key mechanism for the transfer of carbon from the atmosphere to the deep ocean via the so-called biological pump. Mathematical models of these ecosystems have been used to predict CO2 uptake in surface waters at particular locations, and more recently have been embedded in global climate models. While the equilibrium properties of these models are well studied, less attention has been paid to their response to external perturbations, despite the fact that as a result of the variability of environmental forcing such ecosystems are rarely, if ever, in equilibrium. In this study, linear theory is used to determine the structure of perturbations to state variables of an ecosystem model describing summertime conditions at Ocean Station P (50°N 145°W) that maximize either instantaneous or integrated export flux. As a result of the presence of both direct and indirect pathways to export in this model, these perturbations involve the dynamics of the entire ecosystem. For all optimal perturbations considered, it is found that the flux to higher trophic levels is the primary contributor to export flux, followed by sinking detritus. In contrast, the contribution of aggregation is negligible. In addition, small phytoplankton contribute significantly (comparable to large phytoplankton) to the export flux through indirect pathways, primarily through the microzooplankton, even following a bloom in only large phytoplankton. While the details of these results may be specific to the particular model under consideration, the optimal perturbation framework is general and can be used to probe the dynamics of any mechanistic ecosystem model

Trust economics feasibility study

We believe that enterprises and other organisations currently lack sophisticated methods and tools to determine if and how IT changes should be introduced in an organisation, such that objective, measurable goals are met. This is especially true when dealing with security-related IT decisions. We report on a feasibility study, Trust Economics, conducted to demonstrate that such methodology can be developed. Assuming a deep understanding of the IT involved, the main components of our trust economics approach are: (i) assess the economic or financial impact of IT security solutions; (ii) determine how humans interact with or respond to IT security solutions; (iii) based on above, use probabilistic and stochastic modelling tools to analyse the consequences of IT security decisions. In the feasibility study we apply the trust economics methodology to address how enterprises should protect themselves against accidental or malicious misuse of USB memory sticks, an acute problem in many industries