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Hyperspectral unmixing, which decomposes mixed pixels into the endmembers and corresponding abundances, is an important image process for the further application of hyperspectral images (HSIs). Lately, the unmixing problem has been solved using deep learning techniques, particularly autoencoders (AEs). However, the majority of them are based on the simple linear mixing model (LMM), which disregards the spectral variability of endmembers in different pixels. In this article, we present a multi-attention AE network (MAAENet) based on the extended LMM to address the issue of the spectral variability problem in real scenes. Moreover, the majority of AE networks ignore the global spatial information in HSIs and operate pixel- or patch-wise. We employ attention mechanisms to design a spatial–spectral attention (SSA) module that can deal with the band redundancy in HSIs and extract global spatial features through spectral correlation. Moreover, noticing that the mixed pixels are always present in the intersection of different materials, a novel sparse constraint based on spatial homogeneity is designed to constrain the abundance and abstract local spatial features. Ablation experiments are conducted to verify the effectiveness of the proposed AE structure, SSA module, and sparse constraint. The proposed method is compared with several state-of-the-art unmixing methods and exhibits competitiveness on both synthetic and real datasets.

This work is concerned with the doubly degenerate cross-diffusion system (*) { u t = ( u v u x ) x − ( u 2 v v x ) x + u v , v t = v x x − u v , \begin{equation}\tag {*} \left \{ \begin {array}{l} u_t = (uvu_x)_x - (u^2 vv_x)_x + uv, \\[1mm] v_t = v_{xx}-uv, \end{array} \right . \end{equation} that has been proposed as a model for experimentally observable quite complex pattern formation phenomena in bacterial populations. It is shown that for any initial data satisfying adequate regularity and positivity assumptions, a no-flux initial-boundary value problem for the above in a bounded real interval possesses a global weak solution which is continuous in its first and essentially smooth in its second component. This solution is seen to asymptotically stabilize in the sense that (**) u ( ⋅ , t ) → u ∞ and v ( ⋅ , t ) → 0 as t → ∞ \begin{equation}\tag {**} u(\cdot ,t) \to u_\infty \quad \text {and} \quad v(\cdot ,t)\to 0 \qquad \text {as } t\to \infty \end{equation} with some nonnegative u ∞ ∈ C 0 ( Ω ¯ ) u_\infty \in C^0(\overline {\Omega }) which can be obtained as the evaluation of a weak solution z ∈ C 0 ( Ω ¯ × [ 0 , 1 ] ) z\in C^0(\overline {\Omega }\times [0,1]) to a porous medium-type parabolic problem at the finite time 1 1 . It is, moreover, revealed that for each suitably regular nonnegative function u ⋆ u_\star on Ω \Omega , the pair ( u ⋆ , 0 ) (u_\star ,0) , formally constituting an equilibrium of \eqref{01}, is stable in an appropriate sense. This finally implies a sufficient criterion for the limit u ∞ u_\infty in \eqref{02} to be spatially heterogeneous. The latter properties are in sharp contrast to known asymptotic features of corresponding nutrient taxis systems involving linear nondegenerate diffusion, as for which the literature appears to exclusively provide results on solutions which approach spatially constant states in the large time limit.

This study investigates presence/absence of homogeneity in 32-yr (1981–2012) rainfall record of four individual monsoon months (June–September) and monsoon season (JJAS) for 16 stations in Saraswati River basin, Gujarat, India. Temporal homogeneity is examined by Hartley, Link-Wallace, Bartlett, and Tukey tests, and spatial homogeneity is tested by Levene’s and Tukey tests. Coefficient of variation for rainfall in June (72–163%), July (48–100%), August (78–114%) and September (93–127%) indicate a large variability in comparison to that in JJAS period (45–60%). Correlation coefficient (r) finds moderately significant (r ≥ 0.7) to highly significant (0.7 > r ≥ 0.3) relationships in rainfall for 68 (57%), 120 (100%), 120 (100%), 109 (91%), and 120 (100%) pairs of stations in June, July, August, September, and JJAS, respectively. Distribution of rainfall is uniform and stable in July, and hence, kharif crops may be sown in July to mitigate impact of uncertain rainfall on agriculture. Dissimilar results of four homogeneity tests justify approach of adopting multiple statistical tests. Considering the likely findings of Link–Wallace and Tukey tests, both are recommended for testing homogeneity. Non-homogeneity is found at Paswadal (June, September, and JJAS), Navawas (August and JJAS), Palanpur (JJAS), and Pilucha (September) stations. The Levene’s test reveals spatial homogeneity in July, August, September, and JJAS; and non-homogeneity in June. Hierarchical cluster analysis delineates four clusters of rainfall stations in four months and JJAS with their geographically distinct locations and a remarkable difference in inter-annual rainfall dynamics.

Controlling the radiative properties of monolayer transition metal dichalcogenides is key to the development of atomically thin optoelectronic devices applicable to a wide range of industries. A common problem for exfoliated materials is the inherent disorder causing spatially varying nonradiative losses and therefore inhomogeneity. Here we demonstrate a five-fold reduction in the spatial inhomogeneity in monolayer WS

Spatial regression models have been widely used to describe the relationship between a response variable and some explanatory variables over a region of interest, taking into account the spatial de...

We consider the spatially 2D version of the model $$\begin{equation*} \qquad\quad\left\{ \begin{array}{@{}rcll} n_t + u\cdot\nabla n &=& \Delta n - \nabla \cdot \big(nS(x,n,c) \cdot \nabla c \big), \qquad &\qquad x\in \Omega, \ t>0, \\ c_t + u\cdot \nabla c &=& \Delta c - n f(c), \qquad &\qquad x\in \Omega, \ t>0, \\ u_t &=& \Delta u + \nabla P + n\nabla\phi, \qquad \nabla\cdot u=0, \qquad &\qquad x\in \Omega, \ t>0, \end{array} \right. \qquad \qquad (\star) \end{equation*}$$for nutrient taxis processes, possibly interacting with liquid environments. Here the particular focus is on the situation when the chemotactic sensitivity $S$ is not a scalar function but rather attains general values in ${\mathbb{R}}^{2\times 2}$, thus accounting for rotational flux components in accordance with experimental findings and recent modeling approaches. Reflecting significant new challenges that mainly stem from apparent loss of energy-like structures, especially for initial data with large size, the knowledge on ($\star$) so far seems essentially restricted to results on global existence of certain generalized solutions with possibly quite poor boundedness and regularity properties; widely unaddressed seem aspects related to possible effects of such non-diagonal taxis mechanisms on the qualitative solution behavior, especially with regard to the fundamental question whether spatial structures may thereby be supported. The present work answers the latter in the negative in the following sense: under the assumptions that the initial data $(n_0,c_0,u_0)$ and the parameter functions $S$, $f$, and $\phi$ are sufficiently smooth, and that $S$ is bounded and $f$ is positive on $(0,\infty )$ with $f(0)=0$, it is shown that any nontrivial of these solutions eventually becomes smooth and satisfies $$\begin{equation*} n(\cdot,t)\to - \int_\Omega n_0, \quad c(\cdot,t)\to 0 \quad \text{and} \quad u(\cdot,t)\to 0 \qquad \text{as} \ t\to\infty, \end{equation*}$$uniformly with respect to $x\in \Omega$. By not requiring any smallness condition on the initial data, the latter seems new even in the corresponding fluid-free version obtained on letting $u\equiv 0$ in ($\star$).

The atomic magnetometer in the application of simultaneous multichannel biomagnetic field measurement has gained increasing attention in recent researches. In this paper, a novel asymmetrical heating method for improving the temperature spatial homogeneity of the vapor cell in atomic magnetometer based on the finite element method was investigated. The homogeneity of temperature spatial distribution and the consistency of output signal from multilocation in a large vapor cell were numerically analyzed considering multichannel magnetic field measurement. With this asymmetrical heating method, the multilocation measurement signal regularity in the large vapor cell has been improved and the minimum variation coefficient of nine sensing areas' measurement signals decrease over 70% compared with the common heating method with the same heating temperature for the quadrate cell. This method is of great interest for the applications in miniaturing magnetometers of multichannel biomagnetic field measurement.

International audience; Soil heterogeneity influences microbial access to substrates and creates habitats varying in substrate concentrations, thus leading to local variations in carbon (C) dynamics. Based on theoretical considerations, we expected that higher heterogeneity would decrease microbial activity. To test this hypothesis, we modified substrate spatial heterogeneity using 3D-printed cylinders with four compartments (either preventing or allowing diffusion between compartments). The same total amount of glucose (1.5 mg glucose C per cylinder) was added either to one compartment (highest local concentration, 2.0 mg glucose C g − 1 soil, and highest heterogeneity), to two (medium concentration, 1.0 mg glucose C g − 1 soil, and intermediate heterogeneity), or to four compartments (lowest local concentration, 0.5 mg glucose C g − 1 soil, and equivalent to homogeneous conditions). Thus, we experimentally created a gradient of substrate spatial heterogeneity. The 3D cylinders containing soil were transferred into standard calorimetry ampoules and were incubated in isothermal calorimeters to monitor soil heat dissipation rates as a proxy of soil microbial activity over 51 h at 18 • C. When diffusion among compartments was prevented, the most heterogeneous treatment showed the lowest heat dissipation rates, despite having the highest local substrate concentration. Compared to homogeneous conditions, the heat dissipation rate from the most heterogeneous treatment was 110% lower at the beginning of the experiment (12.7 μJ g − 1 soil s − 1) and 50% lower when heat dissipation rates reached a peak (72.6 μJ g − 1 soil s − 1). Moreover, the peak was delayed by approximately 2 h compared to the most homogeneous treatment. When diffusion among compartments was allowed, the effect of substrate spatial heterogeneity on microbial activity was strongly diminished. Our findings emphasize the influence of substrate spatial heterogeneity on soil microbial dynamics, highlighting the importance of including it in C cycling models for a better understanding of soil C dynamics.

In this work, we performed a Mueller matrix imaging analysis of two commercial optical components usually employed to generate and manipulate vector beams&mdash, a radial polarizer and a liquid-crystal q-plate. These two elements generate vector beams by different polarization mechanisms&mdash, polarizance and retardance, respectively. The quality of the vector beams relies on the quality of the device that generates them. Therefore, it is of interest to apply the well-established polarimetric imaging techniques to evaluate these optical components by identifying their spatial homogeneity in diattenuation, polarizance, depolarization, and retardance, as well as the spatial variation of the angles of polarizance and retardance vectors. For this purpose, we applied a customized imaging Mueller matrix polarimeter based on liquid-crystal retarders and a polarization camera. Experimental results were compared to the numerical simulations, considering the theoretical Mueller matrix. This kind of polarimetric characterization could be very helpful to the manufacturers and users of these devices.

As the performance of supervised classification using convolutional neural networks (CNNs) are affected significantly by training patches, it is necessary to analyze the effects of the information content of training patches in patch-based classification. The objective of this study is to quantitatively investigate the effects of class purity of a training patch on performance of crop classification. Here, class purity that refers to a degree of compositional homogeneity of classes within a training patch is considered as a primary factor for the quantification of information conveyed by training patches. New quantitative indices for class homogeneity and variations of local class homogeneity over the study area are presented to characterize the spatial homogeneity of the study area. Crop classification using 2D-CNN was conducted in two regions (Anbandegi in Korea and Illinois in United States) with distinctive spatial distributions of crops and class homogeneity over the area to highlight the effect of class purity of a training patch. In the Anbandegi region with high class homogeneity, superior classification accuracy was obtained when using large size training patches with high class purity (7.1%p improvement in overall accuracy over classification with the smallest patch size and the lowest class purity). Training patches with high class purity could yield a better identification of homogenous crop parcels. In contrast, using small size training patches with low class purity yielded the highest classification accuracy in the Illinois region with low class homogeneity (19.8%p improvement in overall accuracy over classification with the largest patch size and the highest class purity). Training patches with low class purity could provide useful information for the identification of diverse crop parcels. The results indicate that training samples in patch-based classification should be selected based on the class purity that reflects the local class homogeneity of the study area.

Background Drug mass spectrometry imaging (MSI) data contain knowledge about drug and several other molecular ions present in a biological sample. However, a proper approach to fully explore the potential of such type of data is still missing. Therefore, a computational pipeline that combines different spatial and non-spatial methods is proposed to link the observed drug distribution profile with tumor heterogeneity in solid tumor. Our data analysis steps include pre-processing of MSI data, cluster analysis, drug local indicators of spatial association (LISA) map, and ions selection. Results The number of clusters identified from different tumor tissues. The spatial homogeneity of the individual cluster was measured using a modified version of our drug homogeneity method. The clustered image and drug LISA map were simultaneously analyzed to link identified clusters with observed drug distribution profile. Finally, ions selection was performed using the spatially aware method. Conclusions In this paper, we have shown an approach to correlate the drug distribution with spatial heterogeneity in untargeted MSI data. Our approach is freely available in an R package 'CorrDrugTumorMSI'.

There is a general belief that the distribution of tourist activity in space does not respond to a random pattern, so having a thorough knowledge of said activity will require analyzing and understanding its distribution pattern. At the same time, the adequate planning of this sector requires exhaustive knowledge, on the one hand to be able to enhance the positive effects of concentrations in the space, and on the other hand to avoid those possible adverse effects. Therefore, various studies focus on providing information on the random pattern of these activities, especially in developing destinations with a great interest in generating a model of sustainable tourism development. This paper aims to contrast the results achieved by previous studies at the destination while describing the pattern identified through the use of alternative statistical techniques rather than those commonly used. In particular, an intensity function is estimated using three different methods: quadrant counting, K-function, and kernel smoothing. The results achieved allow the identification of the areas with the greatest tourist intensity while describing the practical implications of the results achieved.

The principle of transparency not only is changing but its importance is increasing. International organizations, including the OECD, are seeking to develop harmonized standards of transparency in public administration. This fact is of particular importance in the search for common solutions for the OECD countries in the implementation of transparency standards, but also this organisation has sought adequate methods for measuring implementation of these standards. The main purpose of the study is to analyze the level of spatial homogeneity in the area of application of the standards of “integrity” of the OECD, which are an expression of the principle of transparency in the member states of this organization, on the European continent. In the study vector calculus was used.

This study fully addressed the modifiable areal unit problem (MAUP) that was well-known in geography but generally ignored by safety analysis. The basic issue of MAUP was introduced firstly with a case study to explicitly demonstrate the existence of the problem in macro level crash modeling, and then four potential strategies, i.e., using disaggregate data as possible, capturing spatial non-stationarity, designing optimal zoning systems, conducting sensitivity analysis to report the scope and magnitude of MAUP, were proposed and illustrated in an integrated way, followed by the future research directions. Results revealed that more efforts are desired to calibrate the state-of-art modeling technique at various levels of aggregation based on spatial homogeneity in traffic safety, transport characteristics, and demographical factors. The awareness of this problem in traffic safety domain is expected to the delineation of basic spatial units (e.g. the traffic safety analysis zones), as well as to provide new insights into the nature of MAUP in statistics and geography.

Marine spatial planning (MSP) is to manage incompatible functional use for achieving spatial homogeneity in sea. However most MSP strategies focus on single-target sea use demand ignoring multiple-conflicts of different demands. Thus, this study develops a spatial management model and quantitatively recognizes two types of spatial conflicts among eight sea use functions in the Zhejiang coasts, China. Under the simulation of three different management scenarios including independent, joint and overall-value managements respectively, we further propose a conflict optimization scheme in the scenarios of sea uses with different intensities, different types of sea use combinations, and different site selection. Most importantly, this study demonstrates the spatial management model is a powerful and efficient tool for spatial multiple-conflicts trade-off and matching sea use demands under the practical approach of marine functional zoning (MFC) in China.

In connection with the ongoing climatic changes, the tasks of monitoring the climate of the high-mountainous zone of the Caucasus are of particular importance. Climatological studies in this work are based on the material of long-term meteorological observations from 1961 to 2020. according to the Terskol weather station. Correlation analysis showed the spatial homogeneity of temperature changes in Terskol and weather stations of all climatic zones of southern Russia, in contrast to the regional precipitation regime with a small scale of coherence (up to 200 km). In the modern period (1991-2020), the change in average temperatures in comparison with climatic norms (1961-1990) is not confirmed by statistical estimates, with the exception of the summer season. Over the 60-year period, from 1961 to 2020, there was a statistically significant increase in average summer temperatures by 0.31 °C/10 years (D = 26.8%). At the turn of the 20th and 21st centuries a steady increase in winter, spring and annual temperatures is formed, while summer temperatures maintain a positive trend, but statistically insignificant at this time interval. Period from 2006 characterized by the addition of a statistically significant increase in the absolute maximums of all seasonal temperatures, in contrast to the sums and daily maximum precipitation, the decrease in which in the winter season is statistically insignificant, and there are no trends in other seasons. Such a prevailing thermal and precipitation regime in recent decades has become the main component of many factors leading to dangerous slope phenomena, glacier degradation and significant changes in the hydrological regime.

A portable rainfall simulator was built for assessing runoff and soil erosion processes at interrill scale. Within this study, requirements and constraints of the rainfall simulator are identified and discussed. The focus lies on the calibration of the simulator with regard to spatial rainfall homogeneity, rainfall intensity, drop size, drop fall velocity and rainfall kinetic energy. These parameters were obtained using different methods including a Laser Precipitation Monitor. A detailed presentation of the operational characteristics is given. The presented rainfall simulator setup featured a rainfall intensity of 45.4 mm·h-1 with a spatial homogeneity of 80.4% based on a plot area of 0.64 m². Because of the comparatively low drop height (2 m), the diameter-dependent terminal fall velocity (1.87 m·s-1) was lower than benchmark values for natural rainfall. This conditioned also a reduced rainfall kinetic energy (4.6 J·m-2·mm-1) compared to natural rainfall with same intensity. These shortfalls, a common phenomenon concerning portable rainfall simulators, represented the best possible trade-off between all relevant rainfall parameters obtained with the given simulator setup. Field experiments proved that the rainfall erosivity was constant and replicable.

Intra-tumour genetic heterogeneity (ITH) fosters drug resistance and is a critical hurdle to clinical treatment. ITH can be well-measured using multi-region sampling but this is costly and challenging to implement. There is therefore a need for tools to estimate ITH in individual samples, using standard genomic data such as SNP-arrays, that could be implemented routinely. We designed two novel scores S and R, respectively based on the Shannon diversity index and Ripley’s L statistic of spatial homogeneity, to quantify ITH in single SNP-array samples. We created in-silico and in-vitro mixtures of tumour clones, in which diversity was known for benchmarking purposes. We found significant but highly-variable associations of our scores with diversity in-silico (p in–vitro (p = 0.015 and p = 0.085). Our scores were also correlated to previous ITH estimates from sequencing data but heterogeneity in the fraction of tumour cells present across samples hampered accurate quantification. The prognostic potential of both scores was moderate but significantly predictive of survival in several tumour types (corrected p = 0.03). Our work thus shows how individual SNP-arrays reveal intra-sample clonal diversity with moderate accuracy.

We report on the sharpness of the magnetostructural transition in a Ni-Co-Mn-Ga-In Heusler alloy, which has a key role in defining the magnetocaloric effect exploitable in efficient and environmentally friendly magnetic refrigerators. Magnetic and calorimetric analysis together with optical microscopy in phase-imaging mode are compared to correlate the transition broadening with microscopic features of the sample. The three techniques give the same temperature behavior of the martensitic transition. Microscopy analysis of different sample areas and during cycles in temperature reveals the spatial homogeneity of the transition width and its reproducibility in subsequent transformations.

System Vicarious Calibration (SVC) is the fundamental process commonly implemented to meet uncertainty requirements in satellite ocean color data. It is performed by applying gain factors, g-factors, to the pre-launch calibration coefficients of the space sensor already corrected for sensitivity decay with time. Mission specific g-factors are determined from top-of-the-atmosphere data computed by propagating highly accurate in situ values of the water-leaving radiance, Lw, to the satellite sensor. Values of Lw from marine regions characterized by oligotrophic/mesotrophic waters and maritime aerosols, high environmental stability and spatial homogeneity, low cloudiness and absence of any source of land contamination, are essential to determine g-factors applicable to the creation of Climate Data Records (CDRs) from multiple ocean color missions. Accounting for the location of existing and potential new SVC fixed sites, marine regions satisfying SVC requirements for the generation of CDRs have been identified through the analysis of satellite data from recent ocean color missions., Highlights • System Vicarious Calibration (SVC) for ocean color missions • Climatology of marine and atmospheric optical properties of regions relevant for SVC • Recommendations for new SVC regions

The output characteristics of potentiometric biosensor arrays having 128 × 128 elements with an area of 37.30 μm × 37.30 μm were investigated. For the sensing of adenosine-5′-triphosphate (ATP) as a target molecule, apyrase was immobilized in poly-ion complex (PIC) membranes deposited on sensor surfaces. Two different methods for the deposition of PIC membranes, a conventional layer-by-layer (LBL) method and a novel mixed layer (ML) method, were compared to characterize the spatial homogeneity of the sensor output. It was revealed that the standard deviation of the output distribution was smaller for the ML membrane than that for the LBL membrane. Furthermore, the ML membrane exhibited a superior detection limit of 100 μM ATP, compared with 300 μM for the LBL membrane, indicating the promising properties of the ML membrane for imaging applications. The factors causing the distribution of the output were also discussed.

This paper investigates the growth of the most massive cosmological objects. We utilize the Simsilun simulation, which is based on the approximation of the silent universe. In the limit of spatial homogeneity and isotropy the silent universes reduce to the standard FLRW models. We show that within the approximation of the silent universe the formation of the most massive cosmological objects differs from the standard background-dependent approaches. For objects with masses above $10^{15} M_\odot$ the effect of spatial curvature (overdense regions are characterized by positive spatial curvature) leads to measurable effects. The effect is analogous to the effect that the background cosmological model has on the formation of these objects (i.e. the higher matter density and spatial curvature the faster the growth of cosmic structures). We measure this by the means of the mass function and show that the mass function obtained from the Simsilun simulation has a higher amplitude at the high-mass end compared to standard mass function such as the Press-Schechter or the Tinker mass function. For comparison, we find that the expected mass of most massive objects using the Tinker mass function is $4.4^{+0.8}_{-0.6} \, \times 10^{15} M_\odot$, whereas for the Simsilun simulation is $6.3^{+1.0}_{-0.8} \, \times 10^{15} M_\odot$. We conclude that the nonlinear relativistic effects could affect the formation of the most massive cosmological objects, leading to a relativistic environment-dependence of the growth rate of the most massive clusters., 9 pages, 6 figures

Normal nuclear magnetic resonance (NMR) probes cannot be used to make high frequency resolution measurements in a cryogenic environment because they lose their frequency resolution when the liquid sample in the probe freezes. A gaseous $^3$He NMR probe, designed and constructed to work naturally in such cryogenic environments, is demonstrated at 4.2 K and 5.3 Tesla to have a frequency resolution better than 0.4 part per billion. As a demonstration of its usefulness, the cryogenic probe is used to shim a superconducting solenoid with a cryogenic interior to produce a magnetic field with a high spatial homogeneity, and to measure the magnetic field stability., 9 pages, 11 figures

Six global, gridded, gap-free, daily sea surface temperature (SST) analyses covering a period of at least 20 years have been intercompared: ESA SST CCI analysis long-term product v1.0, MyOcean OSTIA reanalysis v1.0, CMC 0.2 degree, AVHRR_ONLY Daily 1/4 degree OISST v2.0, HadISST2.1.0.0 and MGDSST. A seventh SST product of the ensemble median of all six has also been produced using the GMPE (Group for High Resolution SST Multi-Product Ensemble) system. Validation against independent near-surface Argo data, a long timeseries of moored buoy data from the tropics and anomalies to the GMPE median have been used to examine the temporal and spatial homogeneity of the analyses. A comparison of the feature resolution of the analyses has also been undertaken. A summary of relative strengths and weaknesses of the SST datasets is presented, intended to help users to make an informed choice of which analysis is most suitable for their proposed application.

We consider the Gierer-Meinhardt system with small inhibitor diffusivity and very small activator diffusivity on a compact two-dimensional Riemannian manifold without boundary. We study steady state solutions which are far from spatial homogeneity. We construct two different spike clusters, each consisting of two spikes, which both approach the same nondegenerate local maximum point of the Gaussian curvature. We show that one of these spike clusters is stable, the other one is unstable.

Video projectors allow interesting applications in vision sciences since they provide a large projection area. We have colorimetrically characterized a LCoS projector using a mathematical model requiring additivity and constancy of the primaries -a sigmoid function in our case. Significant differences in chromaticity in the CIELAB space, but not in lightness, were found between the center and the corners of the screen. The lack of spatial homogeneity led us to estimate the parameters of the model as a function of spatial position, using different strategies. The best result was obtained by interpolating the values of the parameters of the model determined from experimental measurements in a regular spatial grid on the screen.

Since sparse unmixing has emerged as a promising approach to hyperspectral unmixing, some spatial-contextual information in the hyperspectral images has been exploited to improve the performance of the unmixing recently. The total variation (TV) has been widely used to promote the spatial homogeneity as well as the smoothness between adjacent pixels. However, the computation task for hyperspectral sparse unmixing with a TV regularization term is heavy. Besides, the convergence of the primal alternating direction method of multipliers (ADMM) for the hyperspectral sparse unmixing with a TV regularization term has not been explained in details. In this paper, we design an efficient and convergent dual symmetric Gauss-Seidel ADMM (sGS-ADMM) for hyperspectral sparse unmixing with a TV regularization term. We also present the global convergence and local linear convergence rate analysis for this algorithm. As demonstrated in numerical experiments, our algorithm can obviously improve the efficiency of the unmixing compared with the state-of-the-art algorithm. More importantly, we can obtain images with higher quality., Comment: 30 pages, 6 figures

Random media emerge in several applications in reactor physics and safety analysis. Most often, models of stochastic media assume spatial homogeneity, whereas real-world complex materials, such as fuel chunks resulting from core degradation, typically display apparent heterogeneities. In a series of previous works, we have shown that stochastic tessellations can be successfully used in order to describe the material properties of several classes of random media. In this paper we extend these results to the case of heterogeneous random media by using Voronoi tessellations with space-dependent seed distributions, allowing for spatial gradients.

Anomalously old 40Ar/39Ar ages are commonly obtained from Shergottites and are generally attributed to uncertainties regarding the isotopic composition of the trapped component and/or the presence of excess 40Ar. Old ages can also be obtained if inaccurate corrections for cosmogenic 36Ar are applied. Current methods for making the cosmogenic correction require simplifying assumptions regarding the spatial homogeneity of target elements for cosmogenic production and the distribution of cosmogenic nuclides relative to trapped and reactor-derived Ar isotopes. To mitigate uncertainties arising from these assumptions, a new cosmogenic correction approach utilizing the exposure age determined on an un-irradiated aliquot and step-wise production rate estimates that account for spatial variations in Ca and K is described. Data obtained from NWA 4468 and an unofficial pairing of NWA 2975, which yield anomalously old ages when corrected for cosmogenic 36Ar using conventional techniques, are used to illustrate the efficacy of this new approach. For these samples, anomalous age determinations are rectified solely by the improved cosmogenic correction technique described herein. Ages of 188 ± 17 and 184 ± 17 Ma are obtained for NWA 4468 and NWA 2975, respectively, both of which are indistinguishable from ages obtained by other radioisotopic systems. For other Shergottites that have multiple trapped components, have experienced diffusive loss of Ar, or contain excess Ar, more accurate cosmogenic corrections may aid in the interpretation of anomalous ages. The trapped 40Ar/36Ar ratios inferred from inverse isochron diagrams obtained from NWA 4468 and NWA 2975 are significantly lower than the Martian atmospheric value, and may represent upper mantle or crustal components.

Patterns of nitrogen (N) concentrations in streams sampled by the National Rivers and Streams Assessment (NRSA) were examined semiquantitatively to identify regional differences in stream N levels. The data were categorized and analyzed by watershed size classes to reveal patterns of the concentrations that are consistent with the spatial homogeneity in natural and anthropogenic characteristics associated with regional differences in N levels. Ecoregions and mapped information on human activities including agricultural practices were used to determine the resultant regions. Marked differences in N levels were found among the nine aggregations of ecoregions used to report the results of the NRSA. We identified distinct regional patterns of stream N concentrations within the reporting regions that are associated with the characteristics of specific Level III ecoregions, groups of Level III ecoregions, groups of Level IV ecoregions, certain geographic characteristics within ecoregions, and/or particular watershed size classes. We described each of these regions and illustrated their areal extent and median and range in N concentrations. Understanding the spatial variability of nutrient concentrations in flowing waters and the apparent contributions that human and nonhuman factors have on different sizes of streams and rivers is critical to the development of effective water quality assessment and management plans. This semi-quantitative analysis is also intended to identify areas within which more detailed quantitative work can be conducted to determine specific regional factors associated with variations in stream N concentrations.

Measurements of the number concentration and size distribution of atmospheric nanoparticles were conducted at four sites on the west coast of the Korean Peninsula by using identical scanning mobility particle sizers (SMPSs) in October 2012. The new particle formation and subsequent growth (NPF) of atmospheric nanoparticles, which were identified by the cyclostationary empirical orthogonal function (CSEOF) analysis technique, was observed on 11 out of 21 days at the Baengnyeong-do Comprehensive Monitoring Observatory (BCMO); and on 10 out of 21 days at the Korea Global Atmosphere Watch Center (KGAWC) from October 9 to 29, 2012. We also observed NPF events for 9 out of 21 days at both the Gosan Climate Observatory (GCO) and the Jeju Comprehensive Monitoring Observatory (JCMO). During the study period, NPF was simultaneously observed for five days at all four sites, which indicates that the NPF event had a spatial extent of at least 540 km. A cold, dry and cloud-free continental air mass originated from northern China, formed favorable environmental conditions (e.g., increasing solar insolation at the surface) on simultaneous NPF at the four sites. These synoptic weather patterns were closely associated with an extraordinary typhoon passing over the south of Japan. The mean values of particle formation rates at BCMO (1.26 cm− 3 s− 1) and KGAWC (1.49 cm− 3 s− 1) were relatively higher than those at GCO (0.39 cm− 3 s− 1) and JCMO (0.74 cm− 3 s− 1), however, the growth rate showed a similar level among four sites. An increase in the spatial homogeneity and inter-site correlation of atmospheric particles among the four sites was apparent for small particles (diameter < 30 nm) on simultaneous NPF event days.

The properties of background aerosols and their dependence on meteorological, geographical and human influence are examined using measured spectral aerosol optical depth (AOD), total mass concentration (MT) and derived number size distribution (NSD) over two distinct coastal locations of Antarctica; Maitri (70° S, 12° E, 123 m m.s.l.) and Larsemann Hills (LH; 69° S, 77° E, 48 m m.s.l.) during southern hemispheric summer of 2007–2008 as a part of the 27th Indian Scientific Expedition to Antarctica (ISEA) during International Polar Year (IPY). Our investigations showed comparable values for the mean columnar AOD at 500 nm over Maitri (0.034±0.005) and LH (0.032±0.006) indicating good spatial homogeneity in the columnar aerosol properties over the coastal Antarctica. Estimation of Angstrom exponent α showed accumulation mode dominance at Maitri (α~1.2±0.3) and coarse mode dominance at LH (0.7±0.2). On the other hand, mass concentration (MT) of ambient aerosols showed relatively high values (≈8.25±2.87 μg m−3) at Maitri in comparison to LH (6.03±1.33 μg m−3).

The major sources of uncertainty in short-term assessment of global horizontal radiation (G) are the pyranometer type and their operation conditions for measurements, whereas the modeling approach and the geographic location are critical for estimations. The influence of all these factors in the uncertainty of the data has rarely been compared. Conversely, solar radiation data users are increasingly demanding more accurate uncertainty estimations. Here we compare the annual bias and uncertainty of all the mentioned factors using 732 weather stations located in Spain, two satellite-based products and three reanalyses. The largest uncertainties were associated to operational errors such as shading (bias = −8.0%) or soiling (bias = −9.4%), which occurred frequently in low-quality monitoring networks but are rarely detected because they pass conventional QC tests. Uncertainty in estimations greatly changed from reanalysis to satellite-based products, ranging from the gross accuracy of ERA-Interim ( + 6.1 - 6.7 + 18.8 %) to the high quality and spatial homogeneity of SARAH-1 ( + 1.4 - 5.3 + 5.6 %). Finally, photodiodes from the Spanish agricultural network SIAR showed an uncertainty of - 5 . 4 + 6 . 9 %, which is far greater than that of secondary standards ( ± 1.5%) and similar to SARAH-1. This is probably caused by the presence of undetectable operational errors and the use of uncorrected photodiodes. Photodiode measurements from low-quality monitoring networks such as SIAR should be used with caution, because the chances of adding extra uncertainties due to poor maintenance or inadequate calibration considerably increase.

Background Deformable image registration (DIR)-based lung ventilation mapping is attractive due to its simplicity, and also challenging due to its susceptibility to errors and uncertainties. In this study, we explored the use of 3D Hyperpolarized (HP) gas tagging MRI to evaluate DIR-based lung ventilation. Method and material Three healthy volunteers included in this study underwent both 3D HP gas tagging MRI (t-MRI) and 3D proton MRI (p-MRI) using balanced steady-state free precession pulse sequence at end of inhalation and end of exhalation. We first obtained the reference displacement vector fields (DVFs) from the t-MRIs by tracking the motion of each tagging grid between the exhalation and the inhalation phases. Then, we determined DIR-based DVFs from the p-MRIs by registering the images at the two phases with two commercial DIR algorithms. Lung ventilations were calculated from both the reference DVFs and the DIR-based DVFs using the Jacobian method and then compared using cross correlation and mutual information. Results The DIR-based lung ventilations calculated using p-MRI varied considerably from the reference lung ventilations based on t-MRI among all three subjects. The lung ventilations generated using Velocity AI were preferable for the better spatial homogeneity and accuracy compared to the ones using MIM, with higher average cross correlation (0.328 vs 0.262) and larger average mutual information (0.528 vs 0.323). Conclusion We demonstrated that different DIR algorithms resulted in different lung ventilation maps due to underlining differences in the DVFs. HP gas tagging MRI provides a unique platform for evaluating DIR-based lung ventilation.