The role of the loss function in the probabilistic function approximation

Generalising results on the time series estimation it is natural to consider function approximation with finite data observations in a probabilistic setting. The function is treated as a stochastic process where for each point in the functions domain the function is a random variable. Equivalently the function can be considered as a single random variable whose range is a space of functions. In this paper two results well known within the context of time series estimation and stochastic control are generalised to probabilistic function approximation problems. Under mild conditions on the space of functions it is shown that the optimal function estimate corresponds for all reasonable symmetrical loss functions to the pointwise conditioned expectation given the observed data. Further in the case where the space of functions belongs to the class of Gaussian process the optimal estimate is the conditional expectation even for asymmetric loss functions

Synchronisation and MSW sharpening of neutrinos propagating in a flavour blind medium

We consider neutrino oscillations in a medium in which scattering processes are blind to the neutrino flavour. We present an analytical derivation of the synchronised behaviour obtained in the limit where the average scattering rate is much larger than the oscillation frequency. We also examine MSW transitions in these circumstances, and show that a sharpening of the transition can result.Comment: 8 pages, 3 figures, accepted for publication in Phys. Lett.

The Extended Coupled Cluster Treatment of Correlations in Quantum Magnets

The spin-half XXZ model on the linear chain and the square lattice are examined with the extended coupled cluster method (ECCM) of quantum many-body theory. We are able to describe both the Ising-Heisenberg phase and the XY-Heisenberg phase, starting from known wave functions in the Ising limit and at the phase transition point between the XY-Heisenberg and ferromagnetic phases, respectively, and by systematically incorporating correlations on top of them. The ECCM yields good numerical results via a diagrammatic approach, which makes the numerical implementation of higher-order truncation schemes feasible. In particular, the best non-extrapolated coupled cluster result for the sublattice magnetization is obtained, which indicates the employment of an improved wave function. Furthermore, the ECCM finds the expected qualitatively different behaviours of the linear chain and the square lattice cases.Comment: 22 pages, 3 tables, and 15 figure

The Role of the Loss Function in Probabilistic Function Approximation

Generalising results on time series estimation, it is natural to consider function approximation with finite data observations in a probabilistic setting. The function is treated as a stochastic process where for each point in the functions domain, the function is a random variable. Equivalently the function can be considered as a single random variable whose range is a space of functions. In this paper, two results, well known within the the context of time series estimation and stochastic control, are generalised to probabilistic function approximation problems. Under mild conditions, on the space of functions, it is shown that the optimal function estimate corresponds, for all reasonable symmetrical loss functions, to the pointwise conditional expectation given the observed data. Further, in the case where the space of functions belongs to the class of Gaussian processes the optimal estimate is the conditional expectation even for asymmetric loss functions

Coupled-Cluster Approach to Electron Correlations in the Two-Dimensional Hubbard Model

We have studied electron correlations in the doped two-dimensional (2D) Hubbard model by using the coupled-cluster method (CCM) to investigate whether or not the method can be applied to correct the independent particle approximations actually used in ab-initio band calculations. The double excitation version of the CCM, implemented using the approximate coupled pair (ACP) method, account for most of the correlation energies of the 2D Hubbard model in the weak ($U/t \simeq 1$) and the intermediate $U/t$ regions ($U/t \simeq 4$). The error is always less than 1% there. The ACP approximation gets less accurate for large $U/t$ ($U/t \simeq 8$) and/or near half-filling. Further incorporation of electron correlation effects is necessary in this region. The accuracy does not depend on the system size and the gap between the lowest unoccupied level and the highest occupied level due to the finite size effect. Hence, the CCM may be favorably applied to ab-initio band calculations on metals as well as semiconductors and insulators.Comment: RevTeX3.0, 4 pages, 4 figure

Assessment of soil water, carbon and nitrogen cycling in reseeded grassland on the North Wyke Farm Platform using a process-based model

The North Wyke Farm Platform (NWFP) generates large volumes of temporally-indexed data that provides a valuable test-bed for agricultural mathematical models in temperate grasslands. In our study, we used the primary datasets generated from the NWFP (https://nwfp.rothamsted.ac.uk/) to validate the SPACSYS model in terms of the dynamics of water loss and forage dry matter yield estimated through cutting. The SPACSYS model is capable of simulating soil water, carbon (C) and nitrogen (N) balance in the soil-plant-atmosphere system. The validated model was then used to simulate the responses of soil water, C and N to reseeding grass cultivars with either high sugar (Lolium perenne L cv. AberMagic) or deep rooting (Festulotium cv. Prior) traits. Simulation results demonstrated that the SPACSYS model could predict reliably soil water, C and N cycling in reseeded grassland. Compared to AberMagic, the Nor grass could fix more C in the second year following reseeding, whereas less C was lost through soil respiration in the first transition year. In comparison to the grass cifitivar of the permanent pasture that existed before reseeding, both grasses reduced N losses through runoff and conhibuted to reducing water loss, especially Prior in relation to the latter. The SPACSYS model could predict these differences as supported by the rich dataset from the NWFP, providing a tool for future predictions on less characterized pasture. (C) 2017 The Authors. Published by Elsevier B.V. This is an open access articleRN the CC BY licens

Nutritional value of suckler beef from temperate pasture systems

The role of beef in human diets has been questioned over the last few decades, due largely to its typically high mass-based carbon footprint. However, recent advancements in sustainability literature challenge this paradigm based on the new theory that climate impacts of food commodities should be measured relative to their overall nutritional value rather than their nominal mass. This shift has opened a new opportunity for the global beef industry, and especially for pasture-based systems that can avoid food-feed competition for land and other resources, as beef is a nutritionally dense food. Nonetheless, the sector’s true capability to supply a wide range of nutrients for humans, consistently across multiple systems under multiple weather patterns, has not been well-documented. Using whole-system datasets from the North Wyke Farm Platform in the South West of England, we investigated the nutritional value of beef produced from the three most common pasture systems in temperate regions: permanent pasture (PP), grass and white clover (GWC) and a short-term monoculture grass ley (MG). Beef produced from these three pasture systems was analysed for key nutrients (fatty acids, minerals and vitamin E) over three production cycles (2015–2017) to determine potential differences between systems. Fatty acid, mineral and vitamin E profiles of the pasture and silage fed to each group were also assessed, with subtle differences between pastures reported. For beef, subtle differences were also observed between systems, with GWC having higher omega-6 polyunsaturated fatty acid (PUFA) concentrations than PP and MG. However, the overall nutritional quality of beef was found to be largely comparable across all systems, suggesting that temperate pasture-based beef can be classified as a single commodity in future sustainability assessments, regardless of specific sward types. A 100 g serving of temperate pasture-based beef was found to be a high source (>20% recommended daily intake: RDI) of protein, monounsaturated fatty acids, saturated fatty acids, vitamins – B2, B3, B12 and minerals – Fe, P, Zn; a good source (10–19% RDI) of vitamin – B6 and mineral – K; and a complementary source (5–9% RDI) of omega-3 PUFA, vitamin – B9 and minerals – Cu, Mg, Se. The nutritional value of a food item should be used in defining its environmental cost (e.g. carbon footprint) to make fair comparisons across different food groups (e.g. protein sources). Here, we showed that pasture-based beef had a nutrient indexed carbon footprint of between 0.19 and 0.23 Kg CO2-eq/1% RDI of key nutrients

Historical environmental change in Africa drives divergence and admixture of Aedes aegypti mosquitoes: a precursor to successful worldwide colonization?

Article PurchasedIncreasing globalization has promoted the spread of exotic species, including disease vectors. Understanding the evolutionary processes involved in such colonizations is both of intrinsic biological interest and important to predict and mitigate future disease risks. The Aedes aegypti mosquito is a major vector of dengue, chikungunya and Zika, the worldwide spread of which has been facilitated by Ae. aegypti's adaption to human-modified environments. Understanding the evolutionary processes involved in this invasion requires characterization of the genetic make-up of the source population(s). The application of approximate Bayesian computation (ABC) to sequence data from four nuclear and one mitochondrial marker revealed that African populations of Ae. aegypti best fit a demographic model of lineage diversification, historical admixture and recent population structuring. As ancestral Ae. aegypti were dependent on forests, this population history is consistent with the effects of forest fragmentation and expansion driven by Pleistocene climatic change. Alternatively, or additionally, historical human movement across the continent may have facilitated their recent spread and mixing. ABC analysis and haplotype networks support earlier inferences of a single out-of-Africa colonization event, while a cline of decreasing genetic diversity indicates that Ae. aegypti moved first from Africa to the Americas and then to Asia. ABC analysis was unable to verify this colonization route, possibly because the genetic signal of admixture obscures the true colonization pathway. By increasing genetic diversity and forming novel allelic combinations, divergence and historical admixture within Africa could have provided the adaptive potential needed for the successful worldwide spread of Ae. aegypti

A device for feasible fidelity, purity, Hilbert-Schmidt distance and entanglement witness measurements

A generic model of measurement device which is able to directly measure commonly used quantum-state characteristics such as fidelity, overlap, purity and Hilbert-Schmidt distance for two general uncorrelated mixed states is proposed. In addition, for two correlated mixed states, the measurement realizes an entanglement witness for Werner's separability criterion. To determine these observables, the estimation only one parameter - the visibility of interference, is needed. The implementations in cavity QED, trapped ion and electromagnetically induced transparency experiments are discussed.Comment: 6 pages, 3 figure