Spatial Mixing Research Articles

Integrated farming system approaches to achieve food and nutritional security for enhancing profitability, employment, and climate resilience in India

AbstractIntegrated farming systems (IFS) entail a holistic approach to farming aimed at meeting the multiple demands (impart farm resilience, farmer livelihoods, food security, ecosystem services, and making farms adaptive and resilient, etc.). IFS are characterized by temporal and spatial mixing of crops, livestock, fishery, and allied activities in a single farm. It is hypothesized that these complex farms are more productive at a system level, are less vulnerable to volatility, and produce less negative externalities than simplified farms. Thereby, they cater the needs of small and marginal farmers, who are the backbone of agriculture in India. Our review of literature shows that IFS have the potential to improve farm profitability (265%) and employment (143%) compared to single enterprise farms. The literature showed that IFS enhance nutrient recycling through composting, mulching, and residue incorporation and, as a consequence, have the capacity to reduce the external purchase of inputs. The nutrient recycling in turn helps to increase the soil quality indicators such as soil nutrient availability and also improves soil microbial activity. The IFS play a major role in biodiversity conservation through adoption of diversified cropping system and through integration of indigenous livestock breeds. IFS also played important role in improving soil organic carbon from 0.75 to 0.82%. Due to increased carbon sequestration, biomass production by trees, reduced consumption of fertilizers, and pesticides the greenhouse gas emission could be reduced significantly. This results in a linked system making it sustainable and climate‐resilient. The main challenge associated with adoption of IFS is it requires skill, knowledge, resources, labor, and capital which are not always available with small and marginal farmers. There is a need for integrating productivity, profitability, and environmental sustainability variables in a single evaluation framework to effectively generate information toward enhancing adaptability of IFS.

Correlation decay and the absence of zeros property of partition functions

AbstractAbsence of (complex) zeros property is at the heart of the interpolation method developed by Barvinok for designing deterministic approximation algorithms for various graph counting and related problems. An earlier method used for the same problem is one based on the correlation decay property. Remarkably, the classes of graphs for which the two methods apply often coincide or nearly coincide. In this article we show that this is not a coincidence. We establish that if the interpolation method is valid for a family of graphs, then this family exhibits a form of the correlation decay property which is asymptotic strong spatial mixing at superlogarithmic distances. Our proof is based on a certain graph polynomial representation of the associated partition function. This representation is at the heart of the design of the polynomial time algorithms underlying the interpolation method itself. We conjecture that our result holds for all, and not just amenable graphs. Indeed this conjecture was recently confirmed by Regts. See the body of the article for details.

Is sensor space analysis good enough? Spatial patterns as a tool for assessing spatial mixing of EEG/MEG rhythms

Analyzing non-invasive recordings of electroencephalography (EEG) and magnetoencephalography (MEG) directly in sensor space, using the signal from individual sensors, is a convenient and standard way of working with this type of data. However, volume conduction introduces considerable challenges for sensor space analysis. While the general idea of signal mixing due to volume conduction in EEG/MEG is recognized, the implications have not yet been clearly exemplified. Here, we illustrate how different types of activity overlap on the level of individual sensors. We show spatial mixing in the context of alpha rhythms, which are known to have generators in different areas of the brain. Using simulations with a realistic 3D head model and lead field and data analysis of a large resting-state EEG dataset, we show that electrode signals can be differentially affected by spatial mixing by computing a sensor complexity measure. While prominent occipital alpha rhythms result in less heterogeneous spatial mixing on posterior electrodes, central electrodes show a diversity of rhythms present. This makes the individual contributions, such as the sensorimotor mu-rhythm and temporal alpha rhythms, hard to disentangle from the dominant occipital alpha. Additionally, we show how strong occipital rhythms can contribute the majority of activity to frontal channels, potentially compromising analyses that are solely conducted in sensor space. We also outline specific consequences of signal mixing for frequently used assessment of power, power ratios and connectivity profiles in basic research and for neurofeedback application. With this work, we hope to illustrate the effects of volume conduction in a concrete way, such that the provided practical illustrations may be of use to EEG researchers to in order to evaluate whether sensor space is an appropriate choice for their topic of investigation.

Thermo-capillarity in microfluidic binary systems via phase modulated sinusoidal thermal stimuli

In this article, we have explored the theoretical aspects of thermo-capillarity driven hydrodynamics at the interface of an immiscible binary-fluid system within a microfluidic domain. The top and bottom walls of the microfluidic confinement are exposed to sinusoidal thermal stimuli with different mean values, wave numbers, and phase differences. We explore the influence of different governing parameters on the thermal and hydrodynamic transport due to interfacial thermo-capillarity and within the constituent fluids. To this end, we deduce the full solutions for the temperature field, hydrodynamics, and the interfacial deformation characteristics in an analytical framework, by appealing to the assumption of the creeping flow (vanishingly small Reynolds, Marangoni, and Capillary number regime) and nearly un-deformed interface. Complicated spatial distribution of the isotherms is generated across the fluids, leading to spatially varying thermal gradients across and along the interface. This leads to periodic circulation of the fluids within the microchannel due to the sinusoidal thermal stimulus. It is observed that the interfacial flow strength depends on the relative film thickness and the thermal conductivities of the two fluids. Vortex enveloping phenomenon is observed for lower values of film thickness ratio when the thermal conductivity of the lower fluid is higher relative to the upper fluid. The findings may hold significance for the design and development of thermal stimulus-controlled spatial mixing and solute transport mechanisms in reactive micro- and nano-fluidic devices.

Perfect sampling from spatial mixing.

We introduce a new perfect sampling technique that can be applied to general Gibbs distributions and runs in linear time if the correlation decays faster than the neighborhood growth. In particular, in graphs with subexponential neighborhood growth like , our algorithm achieves linear running time as long as Gibbs sampling is rapidly mixing. As concrete applications, we obtain the currently best perfect samplers for colorings and for monomer-dimer models in such graphs.

Large eddy simulation of supersonic mixing layers using a compressible filtered mass density function method

To verify the applicability and superiority of the compressible filtered mass density function method in real supersonic mixing flows, a classical experimental subsonic-supersonic spatial mixing layer is numerically investigated. In the present method, a transport equation for the scalar filtered mass density function is solved using the Lagrangian particle solver, while the filtered mass, momentum, and energy equations are fully coupled and solved by the large eddy simulation finite difference solver. First, a parametric study of the mixing model constant controlling the scalar mixing rate is conducted in the two-dimensional case. It is found that the mixing model constant has a significant effect on the root mean square profile of the mixture fraction. The appropriate mixing model constant for this supersonic mixing layer is given by comparing the root mean square results under three different mixing model constants. These results also show that the suitable mixing model constant used in compressible flows is much larger than that used in incompressible flows. Second, three-dimensional simulations are performed to verify the current method. For comparison, a traditional large eddy simulation with the gradient diffusion model is also conducted. The results show that the scalar mixing is better predicted by the filtered mass density function method than the gradient diffusion model. In particular, the mean and root mean square mixture fraction computed by the present method are in excellent agreement with the experimental data whereas the gradient diffusion model overestimates the peak root mean square mixture fraction by about 45%.

On the interplay between electromigration and electroosmosis during electrokinetic transport in heterogeneous porous media

Electrokinetic techniques represent a valuable approach to enhance solute transport, reactant delivery and contaminant degradation in complex environmental matrices, such as contaminated soil and groundwater, and have a great potential for the remediation of many organic and inorganic pollutants.This study investigates the complex interplay between the key electrokinetic transport mechanisms, electromigration and electroosmosis, in physically heterogeneous porous media and its impact on tracer distribution, reactant mixing and degradation efficiency. We perform experiments in a multidimensional setup, considering different types of heterogeneities, injected tracers and reactants, as well as background electrolyte pore water with different chemical composition and pH. We show that EK transport is significantly affected by the physical heterogeneities, due to the interaction between electrokinetic and hydraulic processes, and by the pore water chemistry that plays a key role on the magnitude and spatial distribution of electroosmotic fluxes. The latter affect the overall transport of charged and non-charged species, including the migration velocity of injected plumes, their spatial patterns, spreading and mixing with the background groundwater, and the extent of degradation and the spatio-temporal evolution of reactive zones in the heterogeneous porous media. Process-based numerical modeling allowed us to interpret the experimental observations and to disentangle the coupled effects of physical, chemical and electrostatic processes in the multidimensional, heterogeneous setups. Besides elucidating the mechanisms controlling electrokinetic transport, the results of this study have also important implications for practical field implementation of EK approaches in intrinsically heterogeneous subsurface systems.

Quantification of Visual Texture and Presentation of Intermediate Visual Texture by Spatial Mixing.

We proposed a method to display an intermediate visual texture by spatial mixing. In addition to color information, the visual texture is an important element that characterizes the nature of an object’s surface. While the system to display various color information has well matured in engineering, there is no method to reproduce visual textures in ambient light. In our method, the matte and glossy surfaces are used as “primary visual textures”, and an intermediate visual texture is displayed by spatially mixing the primary visual textures. In this paper, we first quantified the visual texture of an object’s surface based on measured intensities of scattered and reflected lights. Next, based on the quantification, we evaluated spatially mixed surfaces consisting of two primary visual textures, an acrylic plate and a holed sheet of drawing paper, by changing the area proportion of the two primary visual textures. Finally, a sensory evaluation showed significant differences between each intermediate visual texture, and the results corresponded to a trend in the optical evaluation. This study illustrates that visual textures could be quantified based on the intensity of scattered and reflected light and reveals the applicability of our method to the display for intermediate visual texture.

The Spectral Mixture Residual: A Source of Low‐Variance Information to Enhance the Explainability and Accuracy of Surface Biology and Geology Retrievals

AbstractSpectrally mixed pixels are the rule, not the exception, in decameter terrestrial imaging. By definition, the reflectance spectrum of a mixed pixel is a function of more than one generative process. Physically based surface biology and geology retrievals must therefore isolate the component of interest from a myriad of unrelated processes, each occurring with unknown presence and abundance across the hundreds of square meters sampled by each pixel. Foliar traits, for example, must be isolated from canopy structure and substrate composition. In many cases, these unrelated processes can dominate overall variance of spatially integrated reflectance. We propose a new approach to isolate low‐variance spectral signatures in mixed pixels. The aggregate effects of (high‐variance) spatial mixing processes within each pixel are modeled by treating the observed reflectance as a linear mixture of a small set of generic endmember spectra. Spatial mixing effects are removed by computing the (low‐variance) difference between the modeled and observed spectra, named the Mixture Residual (MR). The MR, a residual reflectance spectrum that is presumed to carry the subtler and variable signals of interest, is then leveraged as a source of signal. We illustrate the approach using three independent collections of reflectance spectra: synthetic composites computed from field measurements, NEON AOP airborne image compilations, and DESIS satellite data. The MR is found to discriminate between land cover versus plant trait signals, and to accentuate subtle absorption features. Mean band‐to‐band correlations within the visible, NIR, and SWIR wavebands decrease from 0.97, 0.94, and 0.97 to 0.95, 0.04, and 0.31 (respectively). The number of dimensions required to explain 99% of image variance increases from 4 to 13. We focus on vegetation as an illustrative example, but note that the concept can be extended to other classes of spectra and used as an input to other algorithms.

Four-dimensional equations for the study of electromagnetic plasma turbulence in a drift kinetic limit

For a magnetised plasma in a straight magnetic guide field, we derive a set of four-dimensional kinetic equations, which can capture electromagnetic turbulence in the drift kinetic limit. To do so, we start from the gyrokinetic equations, employ a Laguerre decomposition in the perpendicular velocity direction, retaining only the dominant gyroaverage contributions and only the first two Laguerre moments that source the electromagnetic fluctuations. The model conserves free energy, and can describe electromagnetic turbulence for a plasma at the transition between fluid and gyrokinetic regimes ( $k_\perp \rho _i\approx 1$ range of scales), as dominant finite-Larmor-radius (FLR) effects are considered. In addition to the three dimensions in positions space, we retain the parallel velocity dependence, which we describe via a Hermite representation. Employing this system, but without any other physics-based assumptions for the plasma species that can bias results, will allow us to investigate how fluid effects transition into the kinetic range, and analyse the interplay between spatial and velocity space mixing for electromagnetic plasma turbulence.

A Time-Modulated Transparent Nonlinear Active Metasurface for Spatial Frequency Mixing.

In this article, a time-modulated transparent nonlinear active metasurface loaded with varactor diodes was proposed to realize spatial electromagnetic (EM) wave frequency mixing. The nonlinear transmission characteristic of the active metasurface was designed and measured under time-modulated biasing signals. The transmission phase can be continuously controlled across a full 360° range at 5 GHz when the bias voltage of the varactor diodes changes from 0 V to 25.5 V, while the transmission amplitude is between −2.1 dB to −2.7 dB. By applying the bias voltage in time-modulated sequences, frequency mixing can be achieved. Due to the nonlinearity of the transmission amplitude and transmission phase of the metasurface versus a time-modulated bias voltage, harmonics of the fundamental mode were observed using an upper triangle bias voltage. Furthermore, with a carefully designed bias voltage sequence, unwanted higher order harmonics were suppressed. The proposed theoretical results are validated with the measured results.

Modulation instability of two TE modes in a thin left-handed film on a nonlinear right-handed substrate

The intramode wave beams in a thin left-handed film on a Kerr substrate are considered at a frequency near zero mode group velocity. Four coupled (1 + 1)-dimensional nonlinear Schrödinger equations, describing the interaction of forward and backward propagating beams with positive and negative group velocities, are derived. It is shown that self- and cross-phase modulation for four simultaneously propagating modes is possible only at strictly matched perturbations of their propagation constants, which is due to the contribution of spatial parametric mixing. The modulation instability of only two waveguide modes is analysed for different versions of their propagation. The specific features of modulation instability, related to the propagation of modes with negative group velocities, are investigated.

Contraction: A Unified Perspective of Correlation Decay and Zero-Freeness of 2-Spin Systems

We study the connection between the correlation decay property (more precisely, strong spatial mixing) and the zero-freeness of the partition function of 2-spin systems on graphs of bounded degree. We show that for 2-spin systems on an entire family of graphs of a given bounded degree, the contraction property that ensures correlation decay exists for certain real parameters implies the zero-freeness of the partition function and the existence of correlation decay for some corresponding complex neighborhoods. Based on this connection, we are able to extend any real parameter of which the 2-spin system on graphs of bounded degree exhibits correlation decay to its complex neighborhood where the partition function is zero-free and correlation decay still exists. We give new zero-free regions in which the edge interaction parameters and the uniform external field are all complex-valued, and we show the existence of correlation decay for such complex regions. As a consequence, we obtain approximation algorithms for computing the partition function of 2-spin systems on graphs of bounded degree for these complex parameter settings.

Block Factorization of the Relative Entropy via Spatial Mixing

We consider spin systems in the d-dimensional lattice {mathbb Z} ^d satisfying the so-called strong spatial mixing condition. We show that the relative entropy functional of the corresponding Gibbs measure satisfies a family of inequalities which control the entropy on a given region Vsubset {mathbb Z} ^d in terms of a weighted sum of the entropies on blocks Asubset V when each A is given an arbitrary nonnegative weight alpha _A. These inequalities generalize the well known logarithmic Sobolev inequality for the Glauber dynamics. Moreover, they provide a natural extension of the classical Shearer inequality satisfied by the Shannon entropy. Finally, they imply a family of modified logarithmic Sobolev inequalities which give quantitative control on the convergence to equilibrium of arbitrary weighted block dynamics of heat bath type.

Far-field acoustic subwavelength imaging with blind structured illumination

The blind structured illumination microscopy (blind-SIM) is an optical method to surpass the diffraction limit, a fundamental limitation to all wave-based imaging techniques. By illuminating the object with multiple structured illumination patterns, the spatial frequency mixing between the object and the illuminations converts evanescent waves to propagating waves that can be detected by sensors in the far field. In this work, we develop blind-SIM in the acoustic domain. The blind acoustic structured illuminations (ASI) are generated by randomly located scatterers with subwavelength spatial distributions. The image of the object can be reconstructed with a subwavelength resolution from multiple far-field measurements (each produced by an ASI pattern) utilizing a compressed sensing algorithm. We demonstrate subwavelength acoustic imaging resolution in both kilohertz airborne and megahertz underwater acoustic imaging systems. The developed blind-SIM method has great potential in medical imaging, non-destructive testing, and underwater acoustic imaging for improving the imaging resolution of objects far away from the sensors.

Machine learning for fluid flow reconstruction from limited measurements

This paper investigates the use of data-driven methods for the reconstruction of unsteady fluid flow fields. The proposed framework is based on the combination of machine learning tools: dimensionality reduction to extract dominant spatial directions from data, reconstruction algorithm to recover encoded data by limited measurements and cross-validation for hyperparameter optimization. For the encoding part, linear and nonlinear extraction of patterns are considered: proper orthogonal decomposition (POD), linear autoencoder (LAE) and variational autoencoder (VAE). For the reconstruction part, regressive reconstruction (neural network, linear, support vector, gradient boosting) and library-based reconstruction are compared, each method being cross-validated to ensure good generalization on testing data. The position of sensors is optimized using an enhanced clustering algorithm. The robustness of regressive reconstructions to noise measurements is also addressed, showing the benefits of variational approaches in the reduction phase. The strategy is tested for three increasing complexity flows: 2D vortex shedding (Re=200), 2D spatial mixing layer and 3D vortex shedding (Re=20000). The results suggest that proper machine learning approaches to fluid flow data can lead to effective reconstruction models that can be used for the rapid estimation of complex flows.

Agent-based modelling reveals a disproportionate exposure of females and calves to a local increase in shipping and associated noise in an endangered beluga population

Vessel underwater noise (VUN) is one of the main threats to the recovery of the endangered St. Lawrence Estuary Beluga population (SLEB). The 1% yearly population decline indicates that the cumulative threats are already beyond sustainable limits for the SLEB. However, a potential threefold increase in shipping traffic is expected within its critical habitat in the coming years resulting from proposed port-industrial projects in the Saguenay River. Current data indicate that SLEB typically use multiple sectors within their summer range, likely leading to differential VUN exposure among individuals. The degree of displacement and spatial mixing among habitats are not yet well understood but can be simulated under different assumptions about movement patterns at the individual and population levels. Here, we propose using an agent-based model (ABM) to explore the biases introduced when estimating exposure to stressors such as VUN, where individual-centric movement patterns and habitat use are derived from different spatial behaviour assumptions.Simulations of the ABM revealed that alternative behavioural assumptions for individual belugas can significantly alter the estimation of instantaneous and cumulative exposure of SLEB to VUN. Our simulations also predicted that with the projected traffic increase in the Saguenay River, the characteristics making it a quiet zone for SLEB within its critical habitat would be nullified. Whereas spending more time in the Saguenay than in the Estuary allows belugas to be exposed to less noise under the current traffic regime, this relationship is reversed under the increased traffic scenario. Considering the importance of the Saguenay for SLEB females and calves, our results support the need to understand its role as a possible acoustic refuge for this endangered population. This underlines the need to understand and describe individual and collective beluga behaviours using the best available data to conduct a thorough acoustic impact assessment concerning future increased traffic.

Modifications of the Multi-Layer Perceptron for Hyperspectral Image Classification

Recently, many convolutional neural network (CNN)-based methods have been proposed to tackle the classification task of hyperspectral images (HSI). In fact, CNN has become the de-facto standard for HSI classification. It seems that the traditional neural networks such as multi-layer perceptron (MLP) are not competitive for HSI classification. However, in this study, we try to prove that the MLP can achieve good classification performance of HSI if it is properly designed and improved. The proposed Modified-MLP for HSI classification contains two special parts: spectral–spatial feature mapping and spectral–spatial information mixing. Specifically, for spectral–spatial feature mapping, each input sample of HSI is divided into a sequence of 3D patches with fixed length and then a linear layer is used to map the 3D patches to spectral–spatial features. For spectral–spatial information mixing, all the spectral–spatial features within a single sample are feed into the solely MLP architecture to model the spectral–spatial information across patches for following HSI classification. Furthermore, to obtain the abundant spectral–spatial information with different scales, Multiscale-MLP is proposed to aggregate neighboring patches with multiscale shapes for acquiring abundant spectral–spatial information. In addition, the Soft-MLP is proposed to further enhance the classification performance by applying soft split operation, which flexibly capture the global relations of patches at different positions in the input HSI sample. Finally, label smoothing is introduced to mitigate the overfitting problem in the Soft-MLP (Soft-MLP-L), which greatly improves the classification performance of MLP-based method. The proposed Modified-MLP, Multiscale-MLP, Soft-MLP, and Soft-MLP-L are tested on the three widely used hyperspectral datasets. The proposed Soft-MLP-L leads to the highest OA, which outperforms CNN by 5.76%, 2.55%, and 2.5% on the Salinas, Pavia, and Indian Pines datasets, respectively. The obtained results reveal that the proposed models provide competitive results compared to the state-of-the-art methods, which shows that the MLP-based methods are still competitive for HSI classification.

Enhancing oscillations in intracranial electrophysiological recordings with data-driven spatial filters.

In invasive electrophysiological recordings, a variety of neural oscillations can be detected across the cortex, with overlap in space and time. This overlap complicates measurement of neural oscillations using standard referencing schemes, like common average or bipolar referencing. Here, we illustrate the effects of spatial mixing on measuring neural oscillations in invasive electrophysiological recordings and demonstrate the benefits of using data-driven referencing schemes in order to improve measurement of neural oscillations. We discuss referencing as the application of a spatial filter. Spatio-spectral decomposition is used to estimate data-driven spatial filters, a computationally fast method which specifically enhances signal-to-noise ratio for oscillations in a frequency band of interest. We show that application of these data-driven spatial filters has benefits for data exploration, investigation of temporal dynamics and assessment of peak frequencies of neural oscillations. We demonstrate multiple use cases, exploring between-participant variability in presence of oscillations, spatial spread and waveform shape of different rhythms as well as narrowband noise removal with the aid of spatial filters. We find high between-participant variability in the presence of neural oscillations, a large variation in spatial spread of individual rhythms and many non-sinusoidal rhythms across the cortex. Improved measurement of cortical rhythms will yield better conditions for establishing links between cortical activity and behavior, as well as bridging scales between the invasive intracranial measurements and noninvasive macroscale scalp measurements.

Genetic diversity reduces competition and increases tree growth on a Norway spruce (Picea abies [L.] Karst.) provenance mixing experiment

Many recent studies address that diversification of tree species and stand structure can increase the level and stability of growth and other forest functions and services to mitigate natural and human disturbances. Most studies so far focussed on the diversification of tree species mixing and stand structure. The potential of intra-specific genetic diversification in terms of provenance mixture was hardly explored so far.Here we analyse how a mixing of species provenances of Norway spruce (Picea abies [L.] Karst.) affects the competition between neighboring trees and their growth. We based our study on the 40-years-old provenance-mixing experiment Vohenstrauß 622 in the Upper Palatinate Forest in South Germany. Here 21 different provenances from clonal propagation of Norway spruce across Germany were combined in individual tree mixture, replicated in different spacing, and thinning. Our main objective was to analyze how the individual tree competition, tree growth, and stand productivity were affected by neighboring trees of different provenances.First we show that at an tree age of 43 years the different provenances strongly vary between 10 and 27% in their crown diameter, cd, stem diameter, d, crown length, cl, and tree height, h, with a ranking cvcd > cvd > cvcl > cvh in the coefficient of variation, cv. We found significant differences of the stem and crown allometry between the provenances; e.g. the range of the allometric exponents of h∝dα was α = 0.12–0.58 and of cd∝dα α = 0.47–0.84.Second we found that different provenances in the neighborhood reduced the inter-individual competition and increased the stem diameter growth. Having 10 different provenances in the neighborhood increases the diameter growth of a tree on average by 28 % compared with having only 5 provenances in the neighborhood. Stem diameter followed a saturation curve with increasing number of provenances.Third we showed that an increasing number of provenances also increased the productivity at the stand level. The effects on stand growth are not only determined by the number of different provenances per area but also by their spatial mixing pattern.The inter-provenance complementarity of tree allometry is discussed as main cause of the revealed reduction of competition and increase of growth. We further discuss how spatially explicit individual tree models may incorporate tree structure as proxy of provenance characteristics. We conclude that genetic diversification in terms of provenance mixture can increase and stabilize tree and stand growth analogously to tree species mixing and may be further explored and considered as seminal silvicultural option.