Variability Model Research Articles

A fractal model of granitic intrusion and variability based on cellular automata

Among the various mechanisms for magma ascent and emplacement, rock fracturing is a highly significant factor. In this study, a cellular automaton based on the Olami-Feder-Christensen model was used to generate a self-organized network in which magma can ascend and be arrested to form granitic intrusions under the influence of their buoyancy. The model embodies the ascent of discrete magma batches in a stepwise style by opening the fractures and then closing them after passage of the magma. In the model, magma ascends towards the subsurface via self-organized networks of rock fractures as long as the density of the surrounding rocks is greater than that of the magma. If magma rises to a zone with negative buoyancy, it stops and starts to solidify; thus forming granitic intrusions. Two fractal dimensional measures, perimeter-area (P-A) and number-area (N-A), were used to quantify the irregularity and spatial distribution of the modeled intrusions. The fractal dimension DAP of P-A, as well as the fractal dimension DP of the perimeter, show that the irregularity of the intrusions increases as the thickness of the negative buoyancy region increases. The N-A exponent D reflects the irregular size and spatial scale-invariance of the intrusions, and an abrupt inflection point occurs at an area of 100 cells, owing to the coalescence of small batches of intrusions into a larger intrusion. The scale-invariance exhibited by this system indicates that magma ascent and the formation process of granitic intrusions is a self-organized critical process and we demonstrate that a cellular automaton and fractal model is suitable for capturing, quantifying and modeling the spatial and temporal evolution of complex granitic intrusions.

Spatial analysis of soil aggregate stability in a small catchment of the Loess Plateau, China: II. Spatial prediction

As indicators of soil degradation vulnerability, soil aggregate stability indices play important roles in representing soil resistance to water erosion, and their spatial variability provides both agriculturally and environmentally important information. The spatial variability of aggregate stability indices is synergistically affected by the soil, topography, vegetation, and human factors. To understand the formation processes of aggregates by a spatial analysis, a prediction model combining soil properties with natural and human factors should be developed to improve the accuracy of the spatial interpolation of soil aggregate stability indices. In this study, the mean weight-diameter (MWD, mm), water-stable aggregates greater than 0.25 mm (WSA>0.25, %) and soil erodibility factor (K factor) were satisfactorily predicted by multiple stepwise regression (MSR) and regression kriging (RK) based on soil properties and natural and human factors (0.436≤ R2 ≤0.578). In addition, spatial variability and prediction modeling of aggregate stability indices were highly dependent on the quantification of land use type and landscape structure (the spatial structure of landscape elements and the connections between the different ecosystem types or landscape elements). It has received little attention in previous studies. The exclusion of all soil variables did not affect the predictions of K factor, and for MWD and WSA>0.25, even though the performance of the models may appear relatively low, but also significant (0.183≤ R2 ≤0.312), indicating that the prediction of the spatial distributions of aggregate stability indices with easily available auxiliary data is practicable and effective. Residual maps showed that high residuals are distributed around built-up land (transportation land and residential land) or farmland, indicating that anthropogenic factors increase the uncertainty of the models. The spatial distribution maps of MWD, WSA>0.25 and K factor can be useful in landscape planning and decision making to minimize water erosion risks.

Characterization of karst structures using quasi-3D electrical resistivity tomography

Karst is characteristically complex, hydrogeologically, due to a high degree of heterogeneity, which is often typified by specific features, for example, cavities and sinkholes, embedded in a landscape with significant spatial variability of weathering. Characterization of such heterogeneity is challenging with conventional hydrogeological methods, however, geophysical tools offer the potential to gain insight into key features that control the hydrological function of a karst aquifer. Electrical resistivity tomography (ERT) is recognized as the most effective technique for mapping karstic features. This method is typically carried out along transects to reveal 2D models of resistivity variability. However, karstic systems are rarely 2D in nature. In this study, ERT is employed in valley and hillslope regions of a karst critical zone observatory (Chenqi watershed, Guizhou province, China), using a quasi-3D approach. The results from the extensive geophysical surveys show that there is a strong association between resistivity anomalies and known karstic features. They highlight the significance of a marlstone layer in channeling spring flow in the catchment and confining deeper groundwater flow, evidenced by, for example, localized artesian conditions in observation wells. Our results highlight the need to analyze and interpret geophysical data in a three-dimensional manner in such highly heterogeneous karstic environments, and the value of combining geological and hydrogeological data with geophysical models to help improve our understanding of the hydrological function of a karst system.

Development of a heart rate variability and complexity model in predicting the need for life-saving interventions amongst trauma patients

BackgroundTriage trauma scores are utilised to determine patient disposition, interventions and prognostication in the care of trauma patients. Heart rate variability (HRV) and heart rate complexity (HRC) reflect the autonomic nervous system and are derived from electrocardiogram (ECG) analysis. In this study, we aimed to develop a model incorporating HRV and HRC, to predict the need for life-saving interventions (LSI) in trauma patients, within 24 h of emergency department presentation.MethodsWe included adult trauma patients (≥ 18 years of age) presenting at the emergency department of Singapore General Hospital between October 2014 and October 2015. We excluded patients who had non-sinus rhythms and larger proportions of artefacts and/or ectopics in ECG analysis. We obtained patient demographics, laboratory results, vital signs and outcomes from electronic health records. We conducted univariate and multivariate analyses for predictive model building.ResultsTwo hundred and twenty-five patients met inclusion criteria, in which 49 patients required LSIs. The LSI group had a higher proportion of deaths (10, 20.41% vs 1, 0.57%, p < 0.001). In the LSI group, the mean of detrended fluctuation analysis (DFA)-α1 (1.24 vs 1.12, p = 0.045) and the median of DFA-α2 (1.09 vs 1.00, p = 0.027) were significantly higher. Multivariate stepwise logistic regression analysis determined that a lower Glasgow Coma Scale, a higher DFA-α1 and higher DFA-α2 were independent predictors of requiring LSIs. The area under the curve (AUC) for our model (0.75, 95% confidence interval, 0.66–0.83) was higher than other scoring systems and selected vital signs.ConclusionsAn HRV/HRC model outperforms other triage trauma scores and selected vital signs in predicting the need for LSIs but needs to be validated in larger patient populations.

Towards an empirical model to estimate the spatial variability of grapevine phenology at the within field scale

The aim of this study is to propose an empirical spatial model to estimate the spatial variability of grapevine phenology at the within-field scale. This spatial model allows the characterization of the spatial variability of a given variable of the fields through a single measurement performed in the field (reference site) and a combination of site-specific coefficients calculated through historical information. This approach was compared to classical approaches requiring extensive sampling and phenology models based on climatic data, which do not consider the spatial variability of the field. The study was conducted on two fields of Vitis vinifera, one of cv Cabernet Sauvignon (CS, 1.56 ha) and the other one of cv Chardonnay (CH, 1.66 ha) located in Maule Valley, Chile. Date of occurrence of grapevine phenology (budburst, flowering and veraison) were observed at the within field level following a regular sampling grid during 4 seasons for cv CS and 2 seasons for cv CH. The best results were obtained with the devised spatial model in almost all cases, with a Root Mean Square Errors (RMSE) lower than 3 days. However, if the variability of phenology is low, the traditional method of sampling could lead to better results. This study is the first step towards a modeling of the spatial variability of grapevine phenology at the within-field scale. To be fully operational in commercial vineyards, the calibration process needs simplification, for example, using low cost, inexpensive ancillary information to zone vineyards according to grapevine phenology.

Sickle Cell Disease Subjects Have a Distinct Abnormal Autonomic Phenotype Characterized by Peripheral Vasoconstriction With Blunted Cardiac Response to Head-Up Tilt.

In sickle cell disease (SCD), prolonged capillary transit times, resulting from reduced peripheral blood flow, increase the likelihood of rigid red cells entrapment in the microvasculature, predisposing to vaso-occlusive crisis. Since changes in peripheral flow are mediated by the autonomic nervous system (ANS), we tested the hypothesis that the cardiac and peripheral vascular responses to head-up tilt (HUT) are abnormal in SCD. Heart rate, respiration, non-invasive continuous blood pressure and finger photoplethysmogram (PPG) were monitored before, during, and after HUT in SCD, anemic controls and healthy subjects. Percent increase in heart rate from baseline was used to quantify cardiac ANS response, while percent decrease in PPG amplitude represented degree of peripheral vasoconstriction. After employing cluster analysis to determine threshold levels, the HUT responses were classified into four phenotypes: (CP) increased heart rate and peripheral vasoconstriction; (C) increased heart rate only; (P) peripheral vasoconstriction only; and (ST) subthreshold cardiac and peripheral vascular responses. Multinomial logistic regression (MLR) was used to relate these phenotypic responses to various parameters representing blood properties and baseline cardiovascular activity. The most common phenotypic response, CP, was found in 82% of non-SCD subjects, including those with chronic anemia. In contrast, 70% of SCD subjects responded abnormally to HUT: C-phenotype = 22%, P-phenotype = 37%, or ST-phenotype = 11%. MLR revealed that the HUT phenotypes were significantly associated with baseline cardiac parasympathetic activity, baseline peripheral vascular variability, hemoglobin level and SCD diagnosis. Low parasympathetic activity at baseline dramatically increased the probability of belonging to the P-phenotype in SCD subjects, even after adjusting for hemoglobin level, suggesting a characteristic autonomic dysfunction that is independent of anemia. Further analysis using a mathematical model of heart rate variability revealed that the low parasympathetic activity in P-phenotype SCD subjects was due to impaired respiratory-cardiac coupling rather than reduced cardiac baroreflex sensitivity. By having strong peripheral vasoconstriction without compensatory cardiac responses, P-phenotype subjects may be at increased risk for vaso-occlusive crisis. The classification of autonomic phenotypes based on HUT response may have potential use for guiding therapeutic interventions to alleviate the risk of adverse outcomes in SCD.

Winter Mid-Tropospheric Weather Regimes in the Eastern North Pacific

Background: The eastern North Pacific (ENPac) is a region of climatologically significant cyclone activity, often associated with extreme weather in North America. Regions of high (ridges) and low (troughs) 500- hPa height typically drive this activity. We identify 500-hPa height time variability extremes as “regimes.” Our objectives are to determine the regimes’ characteristics, predictability, and relationships to North American extreme weather. Methods: We define weather regimes, separating them into two types based on whether the 500-hPa height variance is extremely low or high. We analyze their general characteristics during the winter (December, January, and February) and relationships to extreme North American weather. To analyze the regimes’ predictability, we define forecast discontinuities as significantly improved extreme 500-hPa height variability model forecasts compared with model forecasts verifying at the same time, but initialized 24 hours earlier. We analyze their effects on anticipated weather. Results: ENPac low variance regimes are usually dominated by one or two large, slow-moving features, usually a trough with an associated surface cyclone 200-700 km to the west and a ridge with an associated surface anticyclone 200-700 km to the east. This pattern leads to anomalous southerly winds and moisture transport. Low variance regimes are generally associated with anomalous wetness in northwestern Canada, warmth in western North America, and dryness in the southwest U.S. High variance regimes are usually dominated by smaller, faster-moving features that alter the 500-hPa heights substantially. These regimes are more varied, but there is a tendency to have a ridge 200-700 km to the west and a trough 200-700 km to the east, leading to anomalous northerly winds and transport of drier polar air into the ENPac region. High variance regimes are generally associated with anomalously cold air in western North America and wetness in the western U.S. Some forecast discontinuities are associated with changes in anticipated weather locally in the ENPac region, while other discontinuities are associated with changes in anticipated weather on a much larger scale, extending to North America. Limitations: Limitations include the small sample of regimes found during the period of record (18 low variance and 10 high variance), the metric being limited to the 500-hPa level, and the study of only the ENPac winter. Conclusion: Low and high variance regimes generally lead to different ENPac weather patterns and North American extreme weather. Forecast discontinuities differ significantly from each other in their spatial extents. Further work is necessary to identify their causes and characteristics.

False confidence: are we ignoring significant sources of uncertainty?

With the increasing use of stochastic simulation, also known as Monte Carlo simulation, to perform uncertainty analysis in life cycle assessment, it is important to consider whether the predominant methods and practices in the field accurately represent uncertainty in the results. Two quantitative aspects of uncertainty characterization in ecoinvent, namely the derivation of additional uncertainty from the pedigree matrix and the use of static market activities to model consumption mixes, are reviewed with respect to their effects on stochastic simulation results. A discrete choice simulation is applied to model uncertainty in a consumption mix, and the results are compared to the conventional approach. Both practices studied are found to systematically underestimate uncertainty as measured by the size of the confidence interval. In markets with multiple suppliers, the uncertainty in the market average is dramatically narrower than the variability in the suppliers themselves. The current state of practice leads to false inferences and may be misleading to the public. Life cycle assessment researchers should distinguish between synthetic variability models, such as those used in ecoinvent, and authentic estimates of uncertainty in foreground models. The community must continue to develop and critically evaluate methods for uncertainty characterization.

FM-CF: A framework for classifying feature model building approaches

Software product line engineering has emerged as a prominent software engineering paradigm, as it comprises a set of core assets sharing functionality and quality attributes. Feature modelling is one of the most frequently used techniques for modelling the variability within a software product line. There are several proposals for building Feature Models which rely on semi-automated or fully automated means. Unfortunately, automatic feature model construction has been addressed from different viewpoints, so it is not easy to know which is the best approach for automating the building of variability models. In fact, there is no clarity regarding common elements, and the main differences that characterise such approaches. Additionally, the wide variety of terms used to refer to the process of building a Feature Model (e.g. synthesis, location, re-engineering, and weaving) means that approaches are varied and very heterogeneous, making them complex to understand and classify. This paper introduces FM-CF, which is a Conceptual experience-based Framework for classifying approaches for the automatic building of Feature Models. The framework considers a set of categories mainly focused on characterising some aspects, such as input sources, methods and techniques, results, and types of evaluation. A literature review of (semi-) automated Feature Model construction was performed to identify approaches for building Feature Models by (semi-)automatic means, and the main terms used by those approaches. Then the completeness of the framework was evaluated by mapping the set of dimensions and their items, and the terms extracted from the literature.The conceptual framework provides guidance to researchers for choosing the appropriate aspects with which to build Feature Models, and helps in the understanding and clarification of the proposed approaches.

Method for Estimating Vehicle-to-Vehicle Travel Time Variability Models at the Link and Network Levels of Freeways/Expressways through Censoring Mechanism

A method was proposed to estimate vehicle-to-vehicle travel time variability (TTV) at the link and network levels of the entire freeway network. Standard deviation (SD) of travel time rate (TTR) was selected for the TTV. Models estimating the TTV were developed through a Tobit model using a left-censored limit. For the analysis of impact factors on TTV including day-to-day, the model included various types of variables: density, occupancy, traffic flow, link lengths, lane count, speed limits, rainfall amount, crash indicator, weekend indicator, and holiday indicator. According to the exploration and modeling results, TTR and its SD (vehicle-to-vehicle and day-to-day) have a statistical positive significant relationship at the link and network levels. Furthermore, it was confirmed that there is network fundamental diagram (NFD) at the network level. According to the modeling results, an increase in the number of lanes and speed limits, and crash occurrence, raises vehicle-to-vehicle and day-to-day TTV. However, TTV decreases if the link length is long. A high rainfall amount would reduce vehicle-to-vehicle TTV, but raise day-to-day TTV. Weekends and holidays increase vehicle-to-vehicle TTV but diminish day-to-day TTV. Finally, a linear regression model between TTV and TTR at the network level was developed. Through the relationship between the linear regression model and NFD, it is possible to develop new traffic management strategies and algorithms optimizing the vehicle-to-vehicle TTV at the network level. The developed vehicle-to-vehicle TTV models can be applied to validate the mobility improvement potential of vehicle-to-everything (V2X) communication applications on a segment, corridor, and regional scale.

A Novel Tool for Configurable Process Evolution and Service Derivation

In recent years, variability management in business processes is considered a key of reuse. Research works in this field focused mainly on variability modeling and resolution; whereas, evolution has been somehow neglected. In fact, new business requirements may occur, and business processes must evolve in order to meet the new needs. Furthermore, the evolution at business layer represented by configurable processes impact the IT layer represented by services. In this case, it is necessary to synchronize the changes between these two layers. In other words, the alignment of configurable processes and configurable services must occur to maintain an integrated view of an organization. This can be reached by the concept of service-based configurable processes. The study of existing tools in this domain shows the lack of solutions integrating both the evolution management, and the change propagation with respect to the variability. This article aims to represent the CPMEv, a novel tool for evolution management of service-based configurable processes.

Therapist and clinic effects in psychotherapy: A three-level model of outcome variability.

The study aimed to (a) investigate the effect of treatment location on clinical outcomes for patients receiving psychological therapy (a clinic effect, akin to the concept of a therapist effect) and (b) assess the impact of explanatory individual and aggregate demographic and process variables on the clinic and therapist effects. The sample comprised 26,888 patients, seen by 462 therapists, across 30 clinics. Mean patient age was 38 years (69% female, 90% White, 92% planned ending). The dependent variable was patients' posttherapy score on the Clinical Outcomes in Routine Evaluation-Outcome Measure. An incremental 3-level multilevel model was constructed. Markov Chain Monte Carlo estimation created 95% probability intervals for the clinic and therapist effects. A 3-level model with no explanatory variables detected a clinic effect of 8.2%, significantly larger than the therapist effect of 3.2%. Adding explanatory variables significantly reduced the clinic effect to 1.9% but did not significantly alter the therapist effect (3.4%). Patient-level symptom severity and employment status, and clinic-level percentage of White patients and health care sector, explained the most clinic outcome variance and overall outcome variance. Substantial variability in clinical outcomes was found between clinics providing psychological therapy. Socioeconomic mix of patients explained significant proportions of variability at the clinic level but not the therapist level. Clinical implications include the need to go beyond the therapist-patient interaction to deliver effective psychological therapy. Future research is also needed to identify the mechanisms by which clinic and/or area-level factors impact on clinical outcomes. (PsycINFO Database Record (c) 2019 APA, all rights reserved).

Evaluation of spatio‐temporal rainfall variability and performance of a stochastic rainfall model in Bangladesh

Rainfall in Bangladesh exhibits persistent wet and dry anomalies associated with occurrence of floods and droughts. Assessing inter‐annual variability of rainfall is vital to account these hydrological extremes in the design and operations of water systems. However, the inter‐annual variability obtained from short record rainfall data might be misleading as it does not contain whole climate variability which signifies the utmost importance of stochastic rainfall models. Since the inter‐annual variability and stochastic models have not been explored adequately for rainfall in Bangladesh, this study evaluated (a) the spatio‐temporal variability of rainfall focusing on inter‐annual variability, and (b) applicability of a stochastic daily rainfall model, referred as the Decadal and Hierarchical Markov Chain (DHMC) model. Daily rainfall data of 1973–2012 for 18 stations across Bangladesh were used to investigate the probability distributions and autocorrelations of rainfall, and the model performances. Results show a higher magnitude of inter‐annual variabilities of rainfall depth (standard deviation 80–250 mm) and wet spells (standard deviation 4–6 days) in wetter months (June to September) across rainfall stations in the east region of the country. In contrast, higher rates of inter‐annual variabilities (i.e., coefficients of variations) were observed in drier months across the west region. Spatially, the dry spells were observed consistent across the country. Monthly rainfall showed decreasing trend over the region from west to the middle part of the country, whereas monthly number of wet days showed increasing trend over the eastern part. The DHMC was found to preserve the observed variabilities of rainfall at daily to multiyear resolutions at all stations, except a tendency to underestimate the autocorrelation of monthly rainfall depth. Despite this limitation, DHMC can be considered as a suitable stochastic rainfall simulator for a tropical monsoon climate like Bangladesh.

Modeling Subgrid Variability of Snow Depth Using the Fokker‐Planck Equation Approach

AbstractA physically based subgrid variability model for snow process using the Fokker‐Planck equation (FPE) approach was proposed. This FPE can express the evolution of the probability density function (PDF) of snow depth within a finite area, possibly a grid cell of distributed models or a small basin, whose shape can be irregular. The main advantage of this approach is that it does not rely on a given PDF but dynamically computes the PDF through an advection‐diffusion‐type equation, the FPE, which was derived from point‐scale process‐based governing equations. Snow depth was treated as a random variable, while the snow redistribution and snowmelt rate were treated as the sources of stochasticity. The main challenge in solving this FPE is evaluating the time‐space covariances appearing in the diffusion coefficient. In this study, approximations to evaluate the covariance terms, accounting for snowmelt and snow redistribution, were proposed. The simulated results of the FPE model were validated by the measured time series of snow depth at one site and the spatial distributions of snow depth measured by ground penetrating radar and airborne light detection and ranging (Lidar). It was shown that the point‐observed snow depth fell within the simulated range during most of the 2‐year study period. The simulated PDFs of snow depth within the study area were similar to the observed PDFs of snow depth by ground penetrating radar and Lidar. In summary, these results demonstrate the efficacy of the proposed FPE model representing the subgrid variability of snow depth.

Bio-Inspired Requirements Variability Modeling with use Case

Background. Feature Model (FM) is the most important technique used to manage the variability through products in Software Product Lines (SPLs). Often, the SPLs requirements variability is by using variable use case model which is a real challenge in actual approaches: large gap between their concepts and those of real world leading to bad quality, poor supporting FM, and the variability does not cover all requirements modeling levels. Aims. This paper proposes a bio-inspired use case variability modeling methodology dealing with the above shortages. Method. The methodology is carried out through variable business domain use case meta modeling, variable applications family use case meta modeling, and variable specific application use case generating. Results. This methodology has leaded to integrated solutions to the above challenges: it decreases the gap between computing concepts and real world ones. It supports use case variability modeling by introducing versions and revisions features and related relations. The variability is supported at three meta levels covering business domain, applications family, and specific application requirements. Conclusion. A comparative evaluation with the closest recent works, upon some meaningful criteria in the domain, shows the conceptual and practical great value of the proposed methodology and leads to promising research perspectives

Variability of the UHF Signals Generated by Partial Discharges in Mineral Oil.

The paper presents the results of the analysis on the variability of the ultra-high frequency (UHF) signals generated by partial discharges (PD) under the long-term AC voltage. Surface PD (SD) are generated by model PD source (PDS) immersed in brand new mineral oil. Three scenarios are compared and investigated, where different solid dielectrics are applied: pressboard paper (PBP), polytetrafluoroethylene (PTFE) and glass-ceramic (GLS). The PDS is powered continuously by the AC voltage with its relative level of 1.3 of the inception voltage (Ui) within 168 h. UHF signals generated by the continuously occurred SD within 168 h are registered. Various indicators describing the variability of the UHF signals emitted by SD are assigned and analyzed in order to discover if there are any relevant trends presented. Furthermore, some long-term characteristics of the UHF signals emitted by the applied PDS are also announced. As a result, some relevant trends are discovered and related to the properties of the applied dielectric materials, thus the variability of the UHF signals emitted by SD is confirmed. The highest variability of the UHF signals is associated with PBP and the first 48 h after PD inception. Moreover achieved results may be potentially applied for modeling of the PD variability in time, which may be useful for works that concern the development of the UHF method.

A source of systematic bias in self-reported physical activity: The cutpoint bias hypothesis

ObjectivesEstimates of adults’ moderate-to-vigorous physical activity (MVPA) based on self-report are generally higher than estimates derived from criterion measures. This study examines a possible explanation for part of this discrepancy: the cutpoint bias hypothesis. This hypothesis proposes that inter- and intra-individual variability in energy expenditure, combined with the fact that adults perform a high proportion of daily activities at or just above the traditional 3 MET cutpoint, result in systematic over-estimates of MVPA. DesignCross-sectional. MethodsTime-use recalls (n = 6862) were collected using the Multimedia Activity Recall for Children and Adults from 2210 adults (1215 female, age 16–93 years) from 16 studies conducted in Australia and New Zealand between 2008-2017. Minutes spent in MVPA were estimated using models with varying levels of intra- and inter-individual (total variability) Unadjusted (0% total variability), Low (11.9%), Best Guess (20.7%), and High (30.0%). ResultsIn the Unadjusted model, participants accumulated an average of 129 (standard deviation 127) min/day of MVPA. Estimated MVPA was 98 (110), 99 (107) and 108 (107) min/day in the Low, Best Guess and High variability models, respectively, with intra-class correlation coefficients with the Unadjusted model ranging from 0.78 to 0.83. ConclusionsThese findings support the hypothesis of a cutpoint bias, which probably contributes to the large disparities seen between self-reported and criterion measures of MVPA. Future studies are needed to confirm these findings using other self-report instruments and in other populations.

Modal transition system encoding of featured transition systems

Featured transition systems (FTSs) and modal transition systems (MTSs) are two of the most prominent and well-studied formalisms for modeling and analyzing behavioral variability as apparent in software product line engineering. On one hand, it is well-known that for finite behavior FTSs are strictly more expressive than MTSs, essentially due to the inability of MTSs to express logically constrained behavioral variability such as persistently exclusive behaviors. On the other hand, MTSs enjoy many desirable formal properties such as compositionality of semantic refinement and parallel composition. In order to finally consolidate the two formalisms for variability modeling, we establish a rigorous connection between FTSs and MTSs by means of an encoding of one FTS into an equivalent set of multiple MTSs. To this end, we split the structure of an FTS into several MTSs whenever it is necessary to denote exclusive choices that are not expressible in a single MTS. Moreover, extra care is taken when dealing with infinite behavior: loops may have to be unrolled to accumulate FTS path constraints when encoding them into MTSs. We prove our encoding to be semantic-preserving (i.e., the resulting set of MTSs induces, up to bisimulation, the same set of derivable variants as their FTS counterpart) and to commute with modal refinement. We further give an algorithm to calculate a concise representation of a given FTS as a minimal set of MTSs. Finally, we present experimental results gained from applying a tool implementation of our approach to a collection of case studies.

Stochastic neural field model of stimulus-dependent variability in cortical neurons.

We use stochastic neural field theory to analyze the stimulus-dependent tuning of neural variability in ring attractor networks. We apply perturbation methods to show how the neural field equations can be reduced to a pair of stochastic nonlinear phase equations describing the stochastic wandering of spontaneously formed tuning curves or bump solutions. These equations are analyzed using a modified version of the bivariate von Mises distribution, which is well-known in the theory of circular statistics. We first consider a single ring network and derive a simple mathematical expression that accounts for the experimentally observed bimodal (or M-shaped) tuning of neural variability. We then explore the effects of inter-network coupling on stimulus-dependent variability in a pair of ring networks. These could represent populations of cells in two different layers of a cortical hypercolumn linked via vertical synaptic connections, or two different cortical hypercolumns linked by horizontal patchy connections within the same layer. We find that neural variability can be suppressed or facilitated, depending on whether the inter-network coupling is excitatory or inhibitory, and on the relative strengths and biases of the external stimuli to the two networks. These results are consistent with the general observation that increasing the mean firing rate via external stimuli or modulating drives tends to reduce neural variability.

Categorization of Mineral Resources Based on Different Geostatistical Simulation Algorithms: A Case Study from an Iron Ore Deposit

Mineral resource classification plays an important role in the downstream activities of a mining project. Spatial modeling of the grade variability in a deposit directly impacts the evaluation of recovery functions, such as the tonnage, metal quantity and mean grade above cutoffs. The use of geostatistical simulations for this purpose is becoming popular among practitioners because they produce statistical parameters of the sample dataset in cases of global distribution (e.g., histograms) and local distribution (e.g., variograms). Conditional simulations can also be assessed to quantify the uncertainty within the blocks. In this sense, mineral resource classification based on obtained realizations leads to the likely computation of reliable recovery functions, showing the worst and best scenarios. However, applying the proper geostatistical (co)-simulation algorithms is critical in the case of modeling variables with strong cross-correlation structures. In this context, enhanced approaches such as projection pursuit multivariate transforms (PPMTs) are highly desirable. In this paper, the mineral resources in an iron ore deposit are computed and categorized employing the PPMT method, and then, the outputs are compared with conventional (co)-simulation methods for the reproduction of statistical parameters and for the calculation of tonnage at different levels of cutoff grades. The results show that the PPMT outperforms conventional (co)-simulation approaches not only in terms of local and global cross-correlation reproductions between two underlying grades (Fe and Al2O3) in this iron deposit but also in terms of mineral resource categories according to the Joint Ore Reserves Committee standard.