Single Modeling Framework Research Articles

Cellular diffusion processes in singularly perturbed domains

There are many processes in cell biology that can be modeled in terms of particles diffusing in a two-dimensional (2D) or three-dimensional (3D) bounded domain Ω⊂Rd\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varOmega \\subset {\\mathbb {R}}^d$$\\end{document} containing a set of small subdomains or interior compartments Uj\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {U}}_j$$\\end{document}, j=1,…,N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$j=1,\\ldots ,N$$\\end{document} (singularly-perturbed diffusion problems). The domain Ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varOmega $$\\end{document} could represent the cell membrane, the cell cytoplasm, the cell nucleus or the extracellular volume, while an individual compartment could represent a synapse, a membrane protein cluster, a biological condensate, or a quorum sensing bacterial cell. In this review we use a combination of matched asymptotic analysis and Green’s function methods to solve a general type of singular boundary value problems (BVP) in 2D and 3D, in which an inhomogeneous Robin condition is imposed on each interior boundary ∂Uj\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\partial {\\mathcal {U}}_j$$\\end{document}. This allows us to incorporate a variety of previous studies of singularly perturbed diffusion problems into a single mathematical modeling framework. We mainly focus on steady-state solutions and the approach to steady-state, but also highlight some of the current challenges in dealing with time-dependent solutions and randomly switching processes.

Hydrodynamic reconstruction of the paleoflood from the Early Holocene ice-dammed lake Nedre Glomsjø, Norway

Study regionNorway Study focusNumerous geological traces provide evidence for the existence, size and catastrophic drainage of the Early Holocene glacial lake Nedre Glomsjø in southern Norway. We present, for the first time, a hydraulic reconstruction that links the three domains of the glacial lake outburst flood process chain: lake hypsometry, tunneling under the remnant ice sheet and subsequent deluge downstream. This is done by first reconstructing the hypsometry of the lake using paleo shorelines observed from modern high-resolution elevation data. The development of an ice tunnel under the remnant ice sheet is then simulated using an ensemble approach to determine a suite of hydrographs for the range of possible parameter combinations. These hydrographs are applied as upstream input to a 2D hydrodynamic model of the flood propagation. The flood marker dataset includes abundant landforms and flood traces at multiple scales, such as erosive paleostage indicators, sediment records and large-scale flood bars. The results from each domain are constrained by the flood marker dataset, which adds to the robustness of our interpretation. New hydrological insights for the regionThe reconstruction shows that glacial lake Nedre Glomsjø covered roughly 1250 km2, and that ∼100 km3 of water was available for drainage. The peak discharge of the glacier lake outburst flood was at least 1.5 ×106 m3/s and probably closer to 2.0 ×106 m3/s. Our results demonstrate the benefit of assembling the entire process chain from glacial lake, tunnel expansion and flood propagation in a single modeling framework to give robust results that satisfy multiple geological constraints for each component of the glacial lake outburst flood (GLOF) system. The methodology described in this paper can be applied to contemporary and future glacial lakes to better predict GLOFs in a changing climate.

Ecological and anthropogenic drivers of waterfowl productivity are synchronous across species, space, and time.

Knowledge of interspecific and spatiotemporal variation in demography-environment relationships is key for understanding the population dynamics of sympatric species and developing multispecies conservation strategies. We used hierarchical random-effects models to examine interspecific and spatial variation in annual productivity in six migratory ducks (i.e., American wigeon [Mareca americana], blue-winged teal [Spatula discors], gadwall [Mareca strepera], green-winged teal [Anas crecca], mallard [Anas platyrhynchos] and northern pintail [Anas acuta]) across six distinct ecostrata in the Prairie Pothole Region of North America. We tested whether breeding habitat conditions (seasonal pond counts, agricultural intensification, and grassland acreage) or cross-seasonal effects (indexed by flooded rice acreage in primary wintering areas) better explained variation in the proportion of juveniles captured during late summer banding. The proportion of juveniles (i.e., productivity) was highly variable within species and ecostrata throughout 1961-2019 and generally declined through time in blue-winged teal, gadwall, mallard, pintail, and wigeon, but there was no support for a trend in green-winged teal. Productivity in Canadian ecostrata declined with increasing agricultural intensification and increased with increasing pond counts. We also found a strong cross-seasonal effect, whereby more flooded rice hectares during winter resulted in higher subsequent productivity. Our results suggest highly consistent environmental and anthropogenic effects on waterfowl productivity across species and space. Our study advances our understanding of current year and cross-seasonal effects on duck productivity across a suite of species and at finer spatial scales, which could help managers better target working-lands conservation programs on both breeding and wintering areas. We encourage other researchers to evaluate environmental drivers of population dynamics among species in a single modeling framework for a deeper understanding of whether conservation plans should be generalized or customized given limited financial resources.

A hybrid atomistic-continuum framework for multiscale simulations of boiling

Boiling is a multiscale physics process where the nucleation of vapour bubbles occurs due to molecular-scale interactions between the fluid and a heated wall, but it also depends on the larger-scale hydrodynamics and thermal boundary layers determined by the outer system boundary conditions. Modelling boiling from the nanometre up to the millimetre scales at which bubble departure occurs is not possible via state-of-the-art simulation methods: Molecular Dynamics (MD) simulations can capture nucleation from first principles but are limited to nanometre scales due to their computational cost, whereas computational fluid dynamics (CFD) simulations based on the continuum Navier-Stokes equations cannot capture nucleation. Here, we present a novel multiscale simulation method which merges MD and CFD descriptions into a single modelling framework, where MD resolves the near-wall region where molecular interactions are important, and a CFD solver resolves the bulk flow. We model the progressive heating of a Lennard-Jones fluid via contact with a solid wall until a vapour bubble nucleates in the MD region of the domain and grows by entering in the CFD domain. Our results show that an incompressible CFD flow model based on the Volume Of Fluid method with interphase mass transfer calculated via the Hertz-Knudsen-Schrage equation is sufficient to obtain seamless coupling of phase fraction, velocity and temperature fields, with the hybrid MD-CFD framework yielding bubble dynamics closely matching those of MD alone.

Quantifying climate risks to infrastructure systems: A comparative review of developments across infrastructure sectors

Infrastructure systems are particularly vulnerable to climate hazards, such as flooding, wildfires, cyclones and temperature fluctuations. Responding to these threats in a proportionate and targeted way requires quantitative analysis of climate risks, which underpins infrastructure resilience and adaptation strategies. The aim of this paper is to review the recent developments in quantitative climate risk analysis for key infrastructure sectors, including water and wastewater, telecommunications, health and education, transport (seaports, airports, road, rail and inland waterways), and energy (generation, transmission and distribution). We identify several overarching research gaps, which include the (i) limited consideration of multi-hazard and multi-infrastructure interactions within a single modelling framework, (ii) scarcity of studies focusing on certain combinations of climate hazards and infrastructure types, (iii) difficulties in scaling-up climate risk analysis across geographies, (iv) increasing challenge of validating models, (v) untapped potential of further knowledge spillovers across sectors, (vi) need to embed equity considerations into modelling frameworks, and (vii) quantifying a wider set of impact metrics. We argue that a cross-sectoral systems approach enables knowledge sharing and a better integration of infrastructure interdependencies between multiple sectors.

A unified pseudo-elastic model of continuous and discontinuous softening in the finite deformation of isotropic soft solids

Building on a recently devised approach of hyperelasticity with intrinsic softening, a new framework for capturing both continuous and discontinuous softening in the finite deformation of isotropic incompressible elastomers is considered here. The continuous and discontinuous softening effects of interest pertain to the loading and unloading paths, respectively, and the model is developed within the theory of pseudo-elasticity. The performance of the model in capturing these effects is then compared with the deformation behaviour of a variety of elastomers, including a range of hydrogels from truly independent double-network (t-DN) to tough and nanocomposite hydrogels, dielectric elastomers and carbon-black filled rubber specimens, under uniaxial and multiaxial deformations. The model is demonstrated to show a favourable simulation and prediction of the extant experimental data. The application of the model is then extended to capturing the softening behaviour under rate-dependent loading, based on a prior work by the authors incorporating the rate effects directly into the pseudo-hyperelastic model, by assuming that the model parameters evolve with the deformation rate. The capability of the model to capture the rate-dependent effects accurately will be shown by considering the rate-dependent behaviour of two hydrogel specimens. Given the simplicity of the functional form of the model, akin to a standard pseudo-elastic model, the low(er) number of model parameters, the ability to capturing the softening behaviour in the deformation of a wide range of elastomeric materials, and the easy extension for incorporating additional features such as the rate-effects, the proposed model provides another step towards the unification of various complex deformation features into a single modelling framework, for a more universal application to the finite deformation of soft solids.

Virtual reality modeling application based on multi perspective and deep learning in the new media presentation and brand building of Dongguan City memory

AbstractTo help the new media presentation and brand building of Dongguan City memory, a virtual reality modeling model based on multi‐perspective and deep learning is proposed. First, in order to address the issue of imbalanced input and output information in depth map prediction tasks, as well as poor accuracy of predicted depth map boundaries, a depth map prediction model based on multiple perspectives and deep learning is built. Then, a single perspective modeling framework is proposed to address the scarcity of perspectives in practical situations, and a dynamic fusion model is built for single‐view virtual reality scenes based on multi‐view generation networks. The results indicated that the mean square error, average relative error, and average logarithmic error were minimized at 0.52, 0.138, and 0.068, respectively. The multi‐threshold accuracy index demonstrated peak values at 0.772, 0.8821, and 0.947, respectively. The grid simplification algorithm exhibited the shortest running times at 1.57, 2.52, 3.91, and 6.53 s, respectively. Moreover, the single‐view modeling frame displayed the smallest angle distance at 0.1449, while the overlap degree of the point cloud scene reached the highest levels at 77.47, 79.49, 83.5, and 84.47, respectively. To sum up, the model has a good application effect in virtual reality modeling and positively affects virtual reality technology development.

Contributed Session II: Binocular combination of the pupil response depends on photoreceptor pathway.

The pupillary light response is driven by three classes of retinal photoreceptor. Cones and rods are involved in the initial constriction of the pupil, whereas melanopsin-containing intrinsically photosensitive Retinal Ganglion Cells (ipRGCs) maintain constriction over longer timescales. Previous work has characterized the contributions of photoreceptor signals to pupil control, but relatively little is known about binocular combination of these signals when simultaneously stimulating the retina in both eyes. We measured changes in pupil size in 48 participants using a binocular eye-tracker, targeting specific photoreceptor classes with a binocular 10-primary light engine and the silent substitution method. We stimulated the periphery of the retina using light flickering at 0.4 and 0.5 Hz. Participants viewed a disc of either achromatic flickering light, or contrast modulations that targeted the ipRGCs, or the opponent colour pathways L-M or S-(L+M). Using a modified virtual reality headset, we presented the stimuli at a range of modulation amplitudes in three different ocular configurations: monocular, binocular, and dichoptic. We obtained clear pupil responses at both the first and the second harmonic frequencies. Suppression levels differed across conditions with the strongest suppression measured for the L-M condition. We account for the results in a single modelling framework where the weight of interocular suppression determines the binocular combination properties.

Asymptotic Matching between Weather and Climate Models

Abstract The Deep Numerical Analysis for Climate (DNA-Climate) is a pilot project to develop an Earth system model on a kilometer-scale horizontal mesh. The acronym “DNA” is based on the analogies between the hierarchical structures of atmospheric phenomena and living organisms. The multiscale structure of clouds and circulations may be analogous to the multiscale structure of cells and organs organized according to the blueprint, deoxyribonucleic acid (DNA). Whereas global cloud-resolving models (CRMs) can produce better solutions on shorter time scales that are decisively governed by the initial conditions, global climate models (GCMs) may generate reliable solutions on longer time scales that are largely determined to balance energy inputs and outputs. Our challenge is to build a physically valid model that consistently bridges the shorter- and longer-time-scale solutions in the intermediate time scales. Research topics of DNA-Climate are configured in consideration of the structural similarity between the climate modeling and the technique of matched asymptotic expansions in mathematics. The central question is whether a single modeling framework using only either global CRM or GCM will work adequately at all time scales of climate, or whether a multiscale modeling framework combining several models, of which each is only valid for limited time scales, will be needed. A multiscale modeling is an attractive framework for advancing climate modeling and would be an intriguing topic to be studied in parallel with global CRMs and GCMs.

Integrating resource memory and cue-based territoriality to simulate movement dynamics: a process-explicit and pattern-oriented approach

Animal movement is central to ecology and of paramount importance to understand processes underlying the emergence of empirical space-use patterns. In this study, we investigated how integrating two well-established movement processes in the field of theoretical movement ecology, (i) memory-based resource use; and (ii) cue- or scent-based territoriality, affects emergent space-use patterns. We integrated the two mechanisms of space-use into a single individual-based modelling framework, and then quantified how varying degrees of each process affects emergent space-use patterns. Both mechanisms together led to the formation of exclusive, resource- and population density-dependent utilisation distributions, which were responsive to perturbations in the conspecific environment (i.e., removing individuals). Utilisation distribution patterns (area and overlap) were primarily influenced by memory and scent decay rate parameters, controlling an animal's inherent exploratory tendency and its desire to avoid conspecifics respectively. Model application to a population of feral cats demonstrated that general space-use measures (e.g., median UD area, resident and transient dynamics) could be approximated through simulation, though replication of finer-scale space use patterns (e.g., cumulative UD area) was poorly matched. Though application of mechanistic movement models remains both challenging and limited, the potential of such endeavours to ultimately predict population response cannot be overstated.

On spare parts demand and the installed base concept: A theoretical approach

Original Equipment Manufacturers (OEMs) aim to design their service supply chain before the introduction of their products to maximize their aftersales business revenues, reduce waste and achieve sustainability. In this study, we develop a stochastic model that unifies the installed base, i.e., the number of products in use, spare parts demand, and the number of discarded products within a single modeling framework based on three product characteristics: sales rate, usage time, and failure rate. Our model describes the installed base and spare part demand evolution over the entire life cycle of a parent product using stochastic point processes. At the same time we propose under very general assumptions on the cdf of the usage time and the mean arrival functions of the sales and failure processes an easy bisection procedure to compute the time at which the expected installed base and rate of the expected demand for spare parts is maximal. Our numerical experiments show that the volume of aftersales services increases in the expected usage time if the products face an increasing failure rate. The same experiments also reveal a 20 percent shift of the time at which the expected installed base is maximal in case the expected usage time is increased threefold. At the same time, we observe a boosting effect of the intensity of the sales process on this point in time.

Combining varying training data-based artificial intelligence models for energy price forecasting

ABSTRACT In this work, the price-forecasting accuracy of an ensemble of seasonal auto-regressive integrated moving average (SARIMA), multiple linear regression (MLR), feed-forward neural network (FFNN), and radial basis function (RBF) network models has been assessed in a single series modeling framework. The methodology involved training the individual models using past data windows of varying sizes and making the forecast for the next five days on a daily rolling basis. The hourly spot price data of the Iberian Electricity Market (MIBEL) is selected as the test case system. All the models have been tested on high and low-volatile data sets to assess their forecasting abilities. The forecast performance has also been assessed by participating in a real-time forecasting competition and comparing it with the earlier models proposed in the literature. The results show that the ensemble model is effective in producing better forecasts. But its forecast accuracy is greatly affected by the size of the training window and the combination of various models. The ensemble of the FFNN and RBF network models performs best when conditions are volatile. Moreover, during volatile periods it is better to use a small window size for training as compared to a large window size.

A density functional theory for ecology across scales

Ecology lacks a holistic approach that can model phenomena across temporal and spatial scales, largely because of the challenges in modelling systems with a large number of interacting constituents. This hampers our understanding of complex ecosystems and the impact that human interventions (e.g., deforestation, wildlife harvesting and climate change) have on them. Here we use density functional theory, a computational method for many-body problems in physics, to develop a computational framework for ecosystem modelling. Our methods accurately fit experimental and synthetic data of interacting multi-species communities across spatial scales and can project to unseen data. As the key concept we establish and validate a cost function that encodes the trade-offs between the various ecosystem components. We show how this single general modelling framework delivers predictions on par with established, but specialised, approaches for systems from predatory microbes to territorial flies to tropical tree communities. Our density functional framework thus provides a promising avenue for advancing our understanding of ecological systems.

Combined composites layup architecture and mechanical evaluation of type IV pressure vessels: A novel analytical approach

Strict requirements for cost and reliability of compressed gaseous pressure vessels as on-board hydrogen storage necessitates in-depth understanding on the mechanical responses of the composite structure. General numerical methodology to assess this involves a two-step setup: composite layup generation and mechanical property calculation, which becomes highly time and resource-consuming, particularly if multiple designs are scanned for optimization. This study presents a multi-functional analytical tool, combining both aforementioned steps in a single modeling framework. The model enables quick prediction of the strain/stress distribution in correlation with uncomplicated inputs describing the layup design, i.e. stacking sequence with desired winding angles. Additionally, the mechanical evaluation specially focuses on the dome region whose calculation has hardly been inspected analytically in the literature. The results are validated against a three-dimensional finite element calculation implemented in Ansys Workbench, showing qualitative and quantitative agreement. Overall, the study paves the way for composite tank design using analytical approaches, with easy implementation, minimum computational cost and great transparency.

A comprehensive strategy for modeling watershed restoration priority areas under epistemic uncertainty: A case study in the Atlantic Forest, Brazil

Hydrological models are useful to support ecosystem services restoration. However, when planning the expansion of Nature-based Solutions and Payments for Ecosystem Services, there are requirements including the principle of additionality, representation of multiple runoff mechanisms and calculation of farm-scale spatial outputs and epistemic uncertainty. While addressing these aspects is important to make future planning more effective (investment costs and water benefits) it is also challenging. This paper integrates, in a single modeling framework, the main requirements highlighted. This allows an improved selection of top priority areas with farm-scale spatial resolution and a deeper understanding of how epistemic modeling uncertainty affects the results, which is relevant to evaluate the risks of overestimating ecosystem services benefits. The modeling approach is demonstrated in a case study watershed in the Atlantic Forest biome (Brazil). The PLANS model is introduced, which uses the design of TOPMODEL to simulate both simulates both saturation-excess and infiltration-excess runoff at the farm-scale resolution. Also, it uses a novel saturation index based in a composition of Height Above the Nearest Drainage and Topographical Wetness Index terrain descriptors. We applied the Generalized Likelihood Uncertainty Estimation method, aided by an evolutionary algorithm, to estimate output epistemic uncertainty. Results show that uncertainty substantially affects priority definition (97% ranking change), and that simulated topographic effects can overcome local effects of land cover and soil type. With better data, uncertainty evaluation indicates that the restoration program in the study case could have the cost of its allocation policy reduced by up to 27%, showing that it can be made more cost- effective with the methods proposed.

DynamAedes: a unified modelling framework for invasive Aedes mosquitoes

Mosquito species belonging to the genus Aedes have attracted the interest of scientists and public health officers because of their capacity to transmit viruses that affect humans. Some of these species were brought outside their native range by means of trade and tourism and then colonised new regions thanks to a unique combination of eco-physiological traits. Considering mosquito physiological and behavioural traits to understand and predict their population dynamics is thus a crucial step in developing strategies to mitigate the local densities of invasive Aedes populations. Here, we synthesised the life cycle of four invasive Aedes species (Ae. aegypti, Ae. albopictus, Ae. japonicus and Ae. koreicus) in a single multi-scale stochastic modelling framework which we coded in the R package dynamAedes. We designed a stage-based and time-discrete stochastic model driven by temperature, photo-period and inter-specific larval competition that can be applied to three different spatial scales: punctual, local and regional. These spatial scales consider different degrees of spatial complexity and data availability by accounting for both active and passive dispersal of mosquito species as well as for the heterogeneity of the input temperature data. Our overarching aim was to provide a flexible, open-source and user-friendly tool rooted in the most updated knowledge on the species’ biology which could be applied to the management of invasive Aedes populations as well as to more theoretical ecological inquiries.Graphical

Development and Evaluation of Spatio-Temporal Air Pollution Exposure Models and Their Combinations in the Greater London Area, UK.

Land use regression (LUR) and dispersion/chemical transport models (D/CTMs) are frequently applied to predict exposure to air pollution concentrations at a fine scale for use in epidemiological studies. Moreover, the use of satellite aerosol optical depth data has been a key predictor especially for particulate matter pollution and when studying large populations. Within the STEAM project we present a hybrid spatio-temporal modeling framework by (a) incorporating predictions from dispersion modeling of nitrogen dioxide (NO2), ozone (O3) and particulate matter with an aerodynamic diameter equal or less than 10 μm (PM10) and less than 2.5 μm (PM2.5) into a spatio-temporal LUR model; and (b) combining the predictions LUR and dispersion modeling and additionally, only for PM2.5, from an ensemble machine learning approach using a generalized additive model (GAM). We used air pollution measurements from 2009 to 2013 from 62 fixed monitoring sites for O3, 115 for particles and up to 130 for NO2, obtained from the dense network in the Greater London Area, UK. We assessed all models following a 10-fold cross validation (10-fold CV) procedure. The hybrid models performed better compared to separate LUR models. Incorporation of the dispersion estimates in the LUR models as a predictor, improved the LUR model fit: CV-R2 increased to 0.76 from 0.71 for NO2, to 0.79 from 0.57 for PM10, to 0.81 to 0.66 for PM2.5 and to 0.75 from 0.62 for O3. The CV-R2 obtained from the hybrid GAM framework was also increased compared to separate LUR models (CV-R2 = 0.80 for NO2, 0.76 for PM10, 0.79 for PM2.5 and 0.75 for O3). Our study supports the combined use of different air pollution exposure assessment methods in a single modeling framework to improve the accuracy of spatio-temporal predictions for subsequent use in epidemiological studies.

Neural Ordinary Differential Equations for Grey-Box Modelling of Lithium-Ion Batteries on the Basis of an Equivalent Circuit Model

Lithium-ion batteries exhibit a dynamic voltage behaviour depending nonlinearly on current and state of charge. The modelling of lithium-ion batteries is therefore complicated and model parametrisation is often time demanding. Grey-box models combine physical and data-driven modelling to benefit from their respective advantages. Neural ordinary differential equations (NODEs) offer new possibilities for grey-box modelling. Differential equations given by physical laws and NODEs can be combined in a single modelling framework. Here we demonstrate the use of NODEs for grey-box modelling of lithium-ion batteries. A simple equivalent circuit model serves as a basis and represents the physical part of the model. The voltage drop over the resistor–capacitor circuit, including its dependency on current and state of charge, is implemented as a NODE. After training, the grey-box model shows good agreement with experimental full-cycle data and pulse tests on a lithium iron phosphate cell. We test the model against two dynamic load profiles: one consisting of half cycles and one dynamic load profile representing a home-storage system. The dynamic response of the battery is well captured by the model.

A modelling framework for nature-based solutions expansion planning considering the benefits to downstream urban water users

How and when to upscale and finance nature-based solutions in watersheds in order to improve downstream urban water security is a global concern. In this paper we address such challenge by providing a novel method for planning the expansion of a chosen set of nature-based solutions that couples optimization of sequential decision-making, hydrology modelling and hydroeconomics in a single modeling framework. The benefits were considered the avoided costs of water scarcity and water treatment perceived downstream. The optimal expansion schedule of decisions was then defined under the objective function of minimizing total cost. We demonstrated the framework by applying it to a set of benchmark alternative scenarios for the Sinos River watershed (Brazil). We found that the optimal schedule of nature-based solutions expansion is sensitive to the initial land use and future drivers. Treatment cost reduction was the greatest feature in some scenarios, confirming it as a strategy for addressing water quality issues of degraded watersheds. But the accounting of water scarcity cost introduced a tradeoff: expansion of nature-based solutions in well-preserved watersheds may not worth the investment. Future research may improve current limitations in scope and models without structural changes in the framework. Practical implications of this work arise from the funding of watershed payments for environmental services projects by institutions and governments, which demand evidence-based policies to support investment of public resources.

Non-negative Independent Factor Analysis disentangles discrete and continuous sources of variation in scRNA-seq data.

Single-cell RNA-seq analysis has emerged as a powerful tool for understanding inter-cellular heterogeneity. Due to the inherent noise of the data, computational techniques often rely on dimensionality reduction (DR) as both a pre-processing step and an analysis tool. Ideally, DR should preserve the biological information while discarding the noise. However, if the DR is to be used directly to gain biological insight it must also be interpretable-that is the individual dimensions of the reduction should correspond to specific biological variables such as cell-type identity or pathway activity. Maximizing biological interpretability necessitates making assumption about the data structures and the choice of the model is critical. We present a new probabilistic single-cell factor analysis model, Non-negative Independent Factor Analysis (NIFA), that incorporates different interpretability inducing assumptions into a single modeling framework. The key advantage of our NIFA model is that it simultaneously models uni- and multi-modal latent factors, and thus isolates discrete cell-type identity and continuous pathway activity into separate components. We apply our approach to a range of datasets where cell-type identity is known, and we show that NIFA-derived factors outperform results from ICA, PCA, NMF and scCoGAPS (an NMF method designed for single-cell data) in terms of disentangling biological sources of variation. Studying an immunotherapy dataset in detail, we show that NIFA is able to reproduce and refine previous findings in a single analysis framework and enables the discovery of new clinically relevant cell states. NFIA is a R package which is freely available at GitHub (https://github.com/wgmao/NIFA). The test dataset is archived at https://zenodo.org/record/6286646. Supplementary data are available at Bioinformatics online.