Tensor regression based on linked multiway parameter analysis

Classical regression methods take vectors as covariates and estimate the corresponding vectors of regression parameters. When addressing regression problems on covariates of more complex form such as multi-dimensional arrays (i.e. tensors), traditional computational models can be severely compromised by ultrahigh dimensionality as well as complex structure. By exploiting the special structure of tensor covariates, the tensor regression model provides a promising solution to reduce the model’s dimensionality to a manageable level, thus leading to efficient estimation. Most of the existing tensor-based methods independently estimate each individual regression problem based on tensor decomposition which allows the simultaneous projections of an input tensor to more than one direction along each mode. As a matter of fact, multi-dimensional data are collected under the same or very similar conditions, so that data share some common latent components but can also have their own independent parameters for each regression task. Therefore, it is beneficial to analyse regression parameters among all the regressions in a linked way. In this paper, we propose a tensor regression model based on Tucker Decomposition, which identifies not only the common components of parameters across all the regression tasks, but also independent factors contributing to each particular regression task simultaneously. Under this paradigm, the number of independent parameters along each mode is constrained by a sparsity-preserving regulariser. Linked multiway parameter analysis and sparsity modeling further reduce the total number of parameters, with lower memory cost than their tensor-based counterparts. The effectiveness of the new method is demonstrated on real data sets.

The inconstancy of the transient climate response parameter under increasing CO₂

In the Coupled Model Intercomparison Project Phase 5 (CMIP5), the model-mean increase in global mean surface air temperature T under the 1pctCO2 scenario (atmospheric CO2 increasing at 1% yr−1) during the second doubling of CO2 is 40% larger than the transient climate response (TCR), i.e. the increase in T during the first doubling. We identify four possible contributory effects. First, the surface climate system loses heat less readily into the ocean beneath as the latter warms. The model spread in the thermal coupling between the upper and deep ocean largely explains the model spread in ocean heat uptake efficiency. Second, CO2 radiative forcing may rise more rapidly than logarithmically with CO2 concentration. Third, the climate feedback parameter may decline as the CO2 concentration rises. With CMIP5 data, we cannot distinguish the second and third possibilities. Fourth, the climate feedback parameter declines as time passes or T rises; in 1pctCO2, this effect is less important than the others. We find that T projected for the end of the twenty-first century correlates more highly with T at the time of quadrupled CO2 in 1pctCO2 than with the TCR, and we suggest that the TCR may be underestimated from observed climate change.

Moisture can be the dominant environmental parameter governing cadaver decomposition in soil

Forensic taphonomy involves the use of decomposition to estimate postmortem interval (PMI) or locate clandestine graves. Yet, cadaver decomposition remains poorly understood, particularly following burial in soil. Presently, we do not know how most edaphic and environmental parameters, including soil moisture, influence the breakdown of cadavers following burial and alter the processes that are used to estimate PMI and locate clandestine graves. To address this, we buried juvenile rat (Rattus rattus) cadavers (∼18 g wet weight) in three contrasting soils from tropical savanna ecosystems located in Pallarenda (sand), Wambiana (medium clay), or Yabulu (loamy sand), Queensland, Australia. These soils were sieved (2 mm), weighed (500 g dry weight), calibrated to a matric potential of -0.01 megapascals (MPa), -0.05 MPa, or -0.3 MPa (wettest to driest) and incubated at 22 °C. Measurements of cadaver decomposition included cadaver mass loss, carbon dioxide-carbon (CO2-C) evolution, microbial biomass carbon (MBC), protease activity, phosphodiesterase activity, ninhydrin-reactive nitrogen (NRN) and soil pH. Cadaver burial resulted in a significant increase in CO2-C evolution, MBC, enzyme activities, NRN and soil pH. Cadaver decomposition in loamy sand and sandy soil was greater at lower matric potentials (wetter soil). However, optimal matric potential for cadaver decomposition in medium clay was exceeded, which resulted in a slower rate of cadaver decomposition in the wettest soil. Slower cadaver decomposition was also observed at high matric potential (-0.3 MPa). Furthermore, wet sandy soil was associated with greater cadaver decomposition than wet fine-textured soil. We conclude that gravesoil moisture content can modify the relationship between temperature and cadaver decomposition and that soil microorganisms can play a significant role in cadaver breakdown. We also conclude that soil NRN is a more reliable indicator of gravesoil than soil pH.

On L2 Clustering and Resetting the Null Subject Parameter in L2 Spanish: Implications and Observations.

In this article, along with others, we take the position that the Null-Subject Parameter (NSP) (Chomsky 1981; Rizzi 1982) cluster of properties is narrower in scope than some originally contended. We test for the resetting of the NSP by English L2 learners of Spanish at the intermediate level, including poverty-of-the stimulus knowledge of the Overt Pronoun Constraint (Montalbetti 1984). Our participants are tested before and after five months' residency in Spain in an effort to see if increased amounts of native exposure are particularly beneficial for parameter resetting. Although we demonstrate NSP resetting for some of the L2 learners, our data essentially demonstrate that even with the advent of time/exposure to native input, there is no immediate gainful effect for NSP resetting.

Compositional control of the electrical transport properties in the new series of thiospinels Ga1-xGexV4S8-delta (0 <=x<=1)

A new series of non-stoichiometric sulfides Ga1−xGexV4S8−δ (0≤x≤1; δ≤0.23) has been synthesized at high temperatures by heating stoichiometric mixtures of the elements in sealed quartz tubes. The samples have been characterized by powder X-ray diffraction, SQUID magnetometry and electrical transport-property measurements. Structural analysis reveals that a solid solution is formed throughout this composition range, whilst thermogravimetric data reveal sulfur deficiency of up to 2.9% in the quaternary phases. Magnetic measurements suggest that the ferromagnetic behavior of the end-member phase GaV4S8 is retained at x≤0.7; samples in this composition range showing a marked increase in magnetization at low temperatures. By contrast Ga0.25Ge0.75V4S8−δ appears to undergo antiferromagnetic ordering at ca. 15 K. All materials with x≠1 are n-type semiconductors whose resistivity falls by almost six orders of magnitude with decreasing Ga content, whilst the end-member phase GeV4S8−δ is a p-type semiconductor. The results demonstrate that the physical properties are determined principally by the degree of electron filling of narrow-band states arising from intracluster V–V interactions.

Structure and electrical transport properties of the ordered skutterudites MGe1.5S1.5 (M = Co, Rh, Ir)

High-resolution powder neutron diffraction data collected for the skutterudites MGe1.5S1.5 (M=Co, Rh, Ir) reveal that these materials adopt an ordered skutterudite structure (space group R3¯), in which the anions are ordered in layers perpendicular to the [111] direction. In this ordered structure, the anions form two-crystallographically distinct four-membered rings, with stoichiometry Ge2S2, in which the Ge and S atoms are trans to each other. The transport properties of these materials, which are p-type semiconductors, are discussed in the light of the structural results. The effect of iron substitution in CoGe1.5S1.5 has been investigated. While doping of CoGe1.5S1.5 has a marked effect on both the electrical resistivity and the Seebeck coefficient, these ternary skutterudites exhibit significantly higher electrical resistivities than their binary counterparts.

Time-lapse geophysical investigations over known archaeological features using electrical resistivity imaging and earth resistance

Electrical methods of geophysical survey are known to produce results that are hard to predict at different times of the year, and under differing weather conditions. This is a problem which can lead to misinterpretation of archaeological features under investigation. The dynamic relationship between a ‘natural’ soil matrix and an archaeological feature is a complex one, which greatly affects the success of the feature’s detection when using active electrical methods of geophysical survey. This study has monitored the gradual variation of measured resistivity over a selection of study areas. By targeting difficult to find, and often ‘missing’ electrical anomalies of known archaeological features, this study has increased the understanding of both the detection and interpretation capabilities of such geophysical surveys. A 16 month time-lapse study over 4 archaeological features has taken place to investigate the aforementioned detection problem across different soils and environments. In addition to the commonly used Twin-Probe earth resistance survey, electrical resistivity imaging (ERI) and quadrature electro-magnetic induction (EMI) were also utilised to explore the problem. Statistical analyses have provided a novel interpretation, which has yielded new insights into how the detection of archaeological features is influenced by the relationship between the target feature and the surrounding ‘natural’ soils. The study has highlighted both the complexity and previous misconceptions around the predictability of the electrical methods. The analysis has confirmed that each site provides an individual and nuanced situation, the variation clearly relating to the composition of the soils (particularly pore size) and the local weather history. The wide range of reasons behind survey success at each specific study site has been revealed. The outcomes have shown that a simplistic model of seasonality is not universally applicable to the electrical detection of archaeological features. This has led to the development of a method for quantifying survey success, enabling a deeper understanding of the unique way in which each site is affected by the interaction of local environmental and geological conditions.

A joint state and parameter estimation scheme for nonlinear dynamical systems

We present a novel algorithm for concurrent model state and parameter estimation in nonlinear dynamical systems. The new scheme uses ideas from three dimensional variational data assimilation (3D-Var) and the extended Kalman filter (EKF) together with the technique of state augmentation to estimate uncertain model parameters alongside the model state variables in a sequential filtering system. The method is relatively simple to implement and computationally inexpensive to run for large systems with relatively few parameters. We demonstrate the efficacy of the method via a series of identical twin experiments with three simple dynamical system models. The scheme is able to recover the parameter values to a good level of accuracy, even when observational data are noisy. We expect this new technique to be easily transferable to much larger models.

High-precision measurements of the co-polar correlation coefficient: non-Gaussian errors and retrieval of the dispersion parameter µ in rainfall

The co-polar correlation coefficient (ρhv) has many applications, including hydrometeor classification, ground clutter and melting layer identification, interpretation of ice microphysics and the retrieval of rain drop size distributions (DSDs). However, we currently lack the quantitative error estimates that are necessary if these applications are to be fully exploited. Previous error estimates of ρhv rely on knowledge of the unknown "true" ρhv and implicitly assume a Gaussian probability distribution function of ρhv samples. We show that frequency distributions of ρhv estimates are in fact highly negatively skewed. A new variable: L = -log10(1 - ρhv) is defined, which does have Gaussian error statistics, and a standard deviation depending only on the number of independent radar pulses. This is verified using observations of spherical drizzle drops, allowing, for the first time, the construction of rigorous confidence intervals in estimates of ρhv. In addition, we demonstrate how the imperfect co-location of the horizontal and vertical polarisation sample volumes may be accounted for. The possibility of using L to estimate the dispersion parameter (µ) in the gamma drop size distribution is investigated. We find that including drop oscillations is essential for this application, otherwise there could be biases in retrieved µ of up to ~8. Preliminary results in rainfall are presented. In a convective rain case study, our estimates show µ to be substantially larger than 0 (an exponential DSD). In this particular rain event, rain rate would be overestimated by up to 50% if a simple exponential DSD is assumed.