Blind Source Separation by Nonnegative Matrix Factorization with Minimum-Volume Constraint

Recently, nonnegative matrix factorization (NMF) attracts more and more attentions for the promising of wide applications. A problem that still remains is that, however, the factors resulted from it may not necessarily be realistically interpretable. Some constraints are usually added to the standard NMF to generate such interpretive results. In this paper, a minimum-volume constrained NMF is proposed and an efficient multiplicative update algorithm is developed based on the natural gradient optimization. The proposed method can be applied to the blind source separation (BSS) problem, a hot topic with many potential applications, especially if the sources are mutually dependent. Simulation results of BSS for images show the superiority of the proposed method.

Online blind source separation using incremental nonnegative matrix factorization with volume constraint

Online blind source separation (BSS) is proposed to overcome the high computational cost problem, which limits the practical applications of traditional batch BSS algorithms. However, the existing online BSS methods are mainly used to separate independent or uncorrelated sources. Recently, nonnegative matrix factorization (NMF) shows great potential to separate the correlative sources, where some constraints are often imposed to overcome the non-uniqueness of the factorization. In this paper, an incremental NMF with volume constraint is derived and utilized for solving online BSS. The volume constraint to the mixing matrix enhances the identifiability of the sources, while the incremental learning mode reduces the computational cost. The proposed method takes advantage of the natural gradient based multiplication updating rule, and it performs especially well in the recovery of dependent sources. Simulations in BSS for dual-energy X-ray images, online encrypted speech signals, and high correlative face images show the validity of the proposed method.

Species occurrence and richness of lichen, bryophytes and vascular plants near Abisko, Sweden and Toolik lake, Alaska

Little is known about the impact of changing temperature regimes on composition and diversity of cryptogam communities in the Arctic and Subarctic, despite the well-known importance of lichens and bryophytes to the functioning and climate feedbacks of northern ecosystems. We investigated changes in diversity and abundance of lichens and bryophytes within long-term (9-16 years) warming experiments and along natural climatic gradients, ranging from Swedish subarctic birch forest and subarctic/subalpine tundra to Alaskan arctic tussock tundra. In both Sweden and Alaska, lichen diversity responded negatively to experimental warming (with the exception of a birch forest) and to higher temperatures along climatic gradients. Bryophytes were less sensitive to experimental warming than lichens, but depending on the length of the gradient, bryophyte diversity decreased both with increasing temperatures and at extremely low temperatures. Among bryophytes, Sphagnum mosses were particularly resistant to experimental warming in terms of both abundance and diversity. Temperature, on both continents, was the main driver of species composition within experiments and along gradients, with the exception of the Swedish subarctic birch forest where amount of litter constituted the best explanatory variable. In a warming experiment in moist acidic tussock tundra in Alaska, temperature together with soil ammonium availability were the most important factors influencing species composition. Overall, dwarf shrub abundance (deciduous and evergreen) was positively related to warming but so were the bryophytes Sphagnum girgensohnii, Hylocomium splendens and Pleurozium schreberi; the majority of other cryptogams showed a negative relationship to warming. This unique combination of intercontinental comparison, natural gradient studies and experimental studies shows that cryptogam diversity and abundance, especially within lichens, is likely to decrease under arctic climate warming. Given the many ecosystem processes affected by cryptogams in high latitudes (e.g. carbon sequestration, N2-fixation, trophic interactions), these changes will have important feedback consequences for ecosystem functions and climate.

Incorporating curvature information into on-line learning

We analyse the dynamics of a number of second order on-line learning algorithms training multi-layer neural networks, using the methods of statistical mechanics. We first consider on-line Newton's method, which is known to provide optimal asymptotic performance. We determine the asymptotic generalization error decay for a soft committee machine, which is shown to compare favourably with the result for standard gradient descent. Matrix momentum provides a practical approximation to this method by allowing an efficient inversion of the Hessian. We consider an idealized matrix momentum algorithm which requires access to the Hessian and find close correspondence with the dynamics of on-line Newton's method. In practice, the Hessian will not be known on-line and we therefore consider matrix momentum using a single example approximation to the Hessian. In this case good asymptotic performance may still be achieved, but the algorithm is now sensitive to parameter choice because of noise in the Hessian estimate. On-line Newton's method is not appropriate during the transient learning phase, since a suboptimal unstable fixed point of the gradient descent dynamics becomes stable for this algorithm. A principled alternative is to use Amari's natural gradient learning algorithm and we show how this method provides a significant reduction in learning time when compared to gradient descent, while retaining the asymptotic performance of on-line Newton's method.

The theory of on-line learning: a statistical physics approach

In this paper we review recent theoretical approaches for analysing the dynamics of on-line learning in multilayer neural networks using methods adopted from statistical physics. The analysis is based on monitoring a set of macroscopic variables from which the generalisation error can be calculated. A closed set of dynamical equations for the macroscopic variables is derived analytically and solved numerically. The theoretical framework is then employed for defining optimal learning parameters and for analysing the incorporation of second order information into the learning process using natural gradient descent and matrix-momentum based methods. We will also briefly explain an extension of the original framework for analysing the case where training examples are sampled with repetition.

Vegetation:environment relationships and water management in Shark Slough, Everglades National Park

The hydrologic regime of Shark Slough, the most extensive long hydroperiod marsh in Everglades National Park, is largely controlled by the location, volume, and timing of water delivered to it through several control structures from Water Conservation Areas north of the Park. Where natural or anthropogenic barriers to water flow are present, water management practices in this highly regulated system may result in an uneven distribution of water in the marsh, which may impact regional vegetation patterns. In this paper, we use data from 569 sampling locations along five cross-Slough transects to examine regional vegetation distribution, and to test and describe the association of marsh vegetation with several hydrologic and edaphic parameters. Analysis of vegetation:environment relationships yielded estimates of both mean and variance in soil depth, as well as annual hydroperiod, mean water depth, and 30-day maximum water depth within each cover type during the 1990’s. We found that rank abundances of the three major marsh cover types (Tall Sawgrass, Sparse Sawgrass, and Spikerush Marsh) were identical in all portions of Shark Slough, but regional trends in the relative abundance of individual communities were present. Analysis also indicated clear and consistent differences in the hydrologic regime of three marsh cover types, with hydroperiod and water depths increasing in the order Tall Sawgrass , Sparse Sawgrass , Spikerush Marsh. In contrast, soil depth decreased in the same order. Locally, these differences were quite subtle; within a management unit of Shark Slough, mean annual values for the two water depth parameters varied less than 15 cm among types, and hydroperiods varied by 65 days or less. More significantly, regional variation in hydrology equaled or exceeded the variation attributable to cover type within a small area. For instance, estimated hydroperiods for Tall Sawgrass in Northern Shark Slough were longer than for Spikerush Marsh in any of the other regions. Although some of this regional variation may reflect a natural gradient within the Slough, a large proportion is the result of compartmentalization due to current water management practices within the marsh.We conclude that hydroperiod or water depth are the most important influences on vegetation within management units, and attribute larger scale differences in vegetation pattern to the interactions among soil development, hydrology and fire regime in this pivotal portion of Everglades.

Interhemispheric gradient of atmospheric radiocarbon reveals natural variability of Southern Ocean winds

Tree ring Delta C-14 data (Reimer et al., 2004; McCormac et al., 2004) indicate that atmospheric Delta C-14 varied on multi-decadal to centennial timescales, in both hemispheres, over the period between AD 950 and 1830. The Northern and Southern Hemispheric Delta C-14 records display similar variability, but from the data alone is it not clear whether these variations are driven by the production of C-14 in the stratosphere (Stuiver and Quay, 1980) or by perturbations to exchanges between carbon reservoirs (Siegenthaler et al., 1980). As the sea-air flux of (CO2)-C-14 has a clear maximum in the open ocean regions of the Southern Ocean, relatively modest perturbations to the winds over this region drive significant perturbations to the interhemispheric gradient. In this study, model simulations are used to show that Southern Ocean winds are likely a main driver of the observed variability in the interhemispheric gradient over AD 950-1830, and further, that this variability may be larger than the Southern Ocean wind trends that have been reported for recent decades (notably 1980-2004). This interpretation also implies that there may have been a significant weakening of the winds over the Southern Ocean within a few decades of AD 1375, associated with the transition between the Medieval Climate Anomaly and the Little Ice Age. The driving forces that could have produced such a shift in the winds at the Medieval Climate Anomaly to Little Ice Age transition remain unknown. Our process-focused suite of perturbation experiments with models raises the possibility that the current generation of coupled climate and earth system models may underestimate the natural background multi-decadal- to centennial-timescale variations in the winds over the Southern Ocean.

Climatic drivers of hourly to yearly tree radius variations along a 6°C natural warming gradient

Climate affects the timing, rate and dynamics of tree growth, over time scales ranging from seconds to centuries. Monitoring how a tree's stem radius varies over these time scales can provide insight into intra-annual stem dynamics and improve our understanding of climate impacts on tree physiology and growth processes. Here, we quantify the response of radial conifer stem size to environmental fluctuations via a novel assessment of tree circadian cycles. We analyze four years of sub-hourly data collected from 56 larch and spruce trees growing along a natural temperature gradient of ∼6 °C in the central Swiss Alps. During the growing season, tree stem diameters were greatest at mid-morning and smallest in the late evening, reflecting the daily cycle of water uptake and loss. Along the gradient, amplitudes calculated from the stem radius cycle were ∼50% smaller at the upper site (∼2200 m a.s.l.) relative to the lower site (∼800 m a.s.l.). We show changes in precipitation, temperature and cloud cover have a substantial effect on typical growing season diurnal cycles; amplitudes were nine times smaller on rainy days (>10 mm), and daily amplitudes are approximately 40% larger when the mean daily temperature is 15–20 °C than when it is 5–10 °C. We find that over the growing season in the sub-alpine forests, spruce show greater daily stem water movement than larch. However, under projected future warming, larch could experience up to 50% greater stem water use, which may severely affect future growth on already dry sites. Our data further indicate that because of the confounding influences of radial growth and short-term water dynamics on stem size, conventional methodology probably overstates the effect of water-linked meteorological variables (i.e. precipitation and relative humidity) on intra-annual tree growth. We suggest future studies use intra-seasonal measurements of cell development and consider whether climatic factors produce reversible changes in stem diameter. These study design elements may help researchers more accurately quantify and attribute changes in forest productivity in response to future warming.

Reefs shift from net accretion to net erosion along a natural environmental gradient

Coral reefs persist in an accretion-erosion balance and ocean acidification resulting from anthropogenic CO2 emissions threatens to shift this balance in favor of net reef erosion. Corals and calcifying algae, largely responsible for reef accretion, are vulnerable to environmental changes associated with ocean acidification, but the direct effects of lower pH on reef erosion has received less attention, particularly in the context of known drivers of bioerosion and natural variability. This study examines the balance between reef accretion and erosion along a well-characterized natural environmental gradient in Kane'ohe Bay, Hawai'i using experimental blocks of coral skeleton. Comparing before and after micro-computed tomography (µCT) scans to quantify net accretion and erosion, we show that, at the small spatial scale of this study (tens of meters), pH was a better predictor of the accretion-erosion balance than environmental drivers suggested by prior studies, including resource availability, temperature, distance from shore, or depth. In addition, this study highlights the fine-scale variation of pH in coastal systems and the importance of microhabitat variation for reef accretion and erosion processes. We demonstrate significant changes in both the mean and variance of pH on the order of meters, providing a local perspective on global increases in pCO2. Our findings suggest that increases in reef erosion, combined with expected decreases in calcification, will accelerate the shift of coral reefs to an erosion-dominated system in a high-CO2 world. This shift will make reefs increasingly susceptible to storm damage and sea-level rise, threatening the maintenance of the ecosystem services that coral reefs provide.

Decline in Coccolithophore Diversity and Impact on Coccolith Morphogenesis Along a Natural CO2 Gradient

A natural pH gradient caused by marine CO2 seeps off Vulcano Island (Italy) was used to assess the effects of ocean acidification on coccolithophores, which are abundant planktonic unicellular calcifiers. Such seeps are used as natural laboratories to study the effects of ocean acidification on marine ecosystems, since they cause long-term changes in seawater carbonate chemistry and pH, exposing the organisms to elevated CO2 concentrations and therefore mimicking future scenarios. Previous work at CO2 seeps has focused exclusively on benthic organisms. Here we show progressive depletion of 27 coccolithophore species, in terms of cell concentrations and diversity, along a calcite saturation gradient from Omega calcite 6.4 to <1. Water collected close to the main CO2 seeps had the highest concentrations of malformed Emiliania huxleyi. These observations add to a growing body of evidence that ocean acidification may benefit some algae but will likely cause marine biodiversity loss, especially by impacting calcifying species, which are affected as carbonate saturation falls.

Shallow water marine sediment bacterial community shifts along a natural CO2 gradient in the Mediterranean Sea Off vulcano, Italy

The effects of increasing atmospheric CO(2) on ocean ecosystems are a major environmental concern, as rapid shoaling of the carbonate saturation horizon is exposing vast areas of marine sediments to corrosive waters worldwide. Natural CO(2) gradients off Vulcano, Italy, have revealed profound ecosystem changes along rocky shore habitats as carbonate saturation levels decrease, but no investigations have yet been made of the sedimentary habitat. Here, we sampled the upper 2 cm of volcanic sand in three zones, ambient (median pCO(2) 419 µatm, minimum Omega (arag) 3.77), moderately CO(2)-enriched (median pCO(2) 592 µatm, minimum Omega (arag) 2.96), and highly CO(2)-enriched (median pCO(2) 1611 µatm, minimum Omega (arag) 0.35). We tested the hypothesis that increasing levels of seawater pCO(2) would cause significant shifts in sediment bacterial community composition, as shown recently in epilithic biofilms at the study site. In this study, 454 pyrosequencing of the V1 to V3 region of the 16S rRNA gene revealed a shift in community composition with increasing pCO(2). The relative abundances of most of the dominant genera were unaffected by the pCO(2) gradient, although there were significant differences for some 5 % of the genera present (viz. Georgenia, Lutibacter, Photobacterium, Acinetobacter, and Paenibacillus), and Shannon Diversity was greatest in sediments subject to long-term acidification (>100 years). Overall, this supports the view that globally increased ocean pCO(2) will be associated with changes in sediment bacterial community composition but that most of these organisms are resilient. However, further work is required to assess whether these results apply to other types of coastal sediments and whether the changes in relative abundance of bacterial taxa that we observed can significantly alter the biogeochemical functions of marine sediments.

Changing Bacterial Growth Efficiencies across a Natural Nutrient Gradient in an Oligotrophic Estuary

Recent studies have characterized coastal estuarine systems as important components of the global carbon cycle. This study investigated carbon cycling through the microbial loop of Florida Bay by use of bacterial growth efficiency calculations. Bacterial production, bacterial respiration, and other environmental parameters were measured at three sites located along a historic phosphorus-limitation gradient in Florida Bay and compared to a relatively nutrient enriched site in Biscayne Bay. A new method for measuring bacterial respiration in oligotrophic waters involving tracing respiration of 13C-glucose was developed. The results of the study indicate that 13C tracer assays may provide a better means of measuring bacterial respiration in low nutrient environments than traditional dissolved oxygen consumption-based methods due to strong correlations between incubation length and δ13C values. Results also suggest that overall bacterial growth efficiency may be lower at the most nutrient limited sites.

Effects of ocean acidification on embryonic respiration and development of a temperate wrasse living along a natural CO2 gradient

Volcanic CO2 seeps provide opportunities to investigate the effects of ocean acidification on organisms in the wild. To understand the influence of increasing CO2 concentrations on the metabolic rate (oxygen consumption) and the development of ocellated wrasse early life stages, we ran two field experiments, collecting embryos from nesting sites with different partial pressures of CO2 [pCO2; ambient (400 µatm) and high (800-1000 µatm)] and reciprocally transplanting embryos from ambient- to high-CO2 sites for 30 h. Ocellated wrasse offspring brooded in different CO2 conditions had similar responses, but after transplanting portions of nests to the high-CO2 site, embryos from parents that spawned in ambient conditions had higher metabolic rates. Although metabolic phenotypic plasticity may show a positive response to high CO2, it often comes at a cost, in this case as a smaller size at hatching. This can have adverse effects because smaller larvae often exhibit a lower survival in the wild. However, the adverse effects of increased CO2 on metabolism and development did not occur when embryos from the high-CO2 nesting site were exposed to ambient conditions, suggesting that offspring from the high-CO2 nesting site could be resilient to a wider range of pCO2 values than those belonging to the site with present-day pCO2 levels. Our study identifies a crucial need to increase the number of studies dealing with these processes under global change trajectories and to expand these to naturally high-CO2 environments, in order to assess further the adaptive plasticity mechanism that encompasses non-genetic inheritance (epigenetics) through parental exposure and other downstream consequences, such as survival of larvae.

Reducing MRI gradient coil vibration with rib stiffeners

This work investigates the effect of rib stiffeners on the free and forced vibration of a gradient coil in a Magnetic Resonance Imaging (MRI) scanner. Several reinforcement schemes are studied in this paper. One scheme utilizes the existing holes in the gradient coil structure (typically reserved for magnetic shims) to produce the reinforcement. Non-ferrous, non-magnetic carbon fibre rib stiffeners are employed to fill these holes in several ways to strengthen a gradient coil. Another scheme replaces the inner half of the gradient coil material with a grid of interconnected axial and circumferential rib stiffeners. It is found that the structural stiffness of the gradient coil increases substantially when the coil is reinforced by carbon fibre rib stiffeners. The reinforcement affects the noise and vibration response of the gradient coil structure in the following ways. It increases the frequency range of forced response of the gradient coil at low frequencies due to the increased resonant frequency of the fundamental mode of the coil. Secondly, it reduces the forced response amplitude of the coil structure (which is governed by the structural stiffness of the coil). Thirdly, it reduces the number of natural modes in the low and medium frequency range and therefore lessens the chance of the coil structure being excited resonantly by magnetic resonance signal acquisition sequences. It is shown that gradient coils modelled by solid finite element models have higher stiffness along the coil’s circumference and lower stiffness in the axial direction than those using shell finite element models.