Search results for: Gaussian copula

Authors: Aamir Shahzad, Mao-Gang He

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Currently, dusty plasmas motivated the researchers' widespread interest. Since the last two decades, substantial efforts have been made by the scientific and technological community to investigate the transport properties and their nonlinear behavior of three-dimensional and two-dimensional nonideal complex (dusty plasma) liquids (NICDPLs). Different calculations have been made to sustain and utilize strongly coupled NICDPLs because of their remarkable scientific and industrial applications. Understanding of the thermophysical properties of complex liquids under various conditions is of practical interest in the field of science and technology. The determination of thermal conductivity is also a demanding question for thermophysical researchers, due to some reasons; very few results are offered for this significant property. Lack of information of the thermal conductivity of dense and complex liquids at different parameters related to the industrial developments is a major barrier to quantitative knowledge of the heat flux flow from one medium to another medium or surface. The exact numerical investigation of transport properties of complex liquids is a fundamental research task in the field of thermophysics, as various transport data are closely related with the setup and confirmation of equations of state. A reliable knowledge of transport data is also important for an optimized design of processes and apparatus in various engineering and science fields (thermoelectric devices), and, in particular, the provision of precise data for the parameters of heat, mass, and momentum transport is required. One of the promising computational techniques, the homogenous nonequilibrium molecular dynamics (HNEMD) simulation, is over viewed with a special importance on the application to transport problems of complex liquids. This proposed work is particularly motivated by the FIRST TIME to modify the problem of heat conduction equations leads to polynomial velocity and temperature profiles algorithm for the investigation of transport properties with their nonlinear behaviors in the NICDPLs. The aim of proposed work is to implement a NEMDS algorithm (Poiseuille flow) and to delve the understanding of thermal conductivity behaviors in Yukawa liquids. The Yukawa system is equilibrated through the Gaussian thermostat in order to maintain the constant system temperature (canonical ensemble ≡ NVT)). The output steps will be developed between 3.0×105/ωp and 1.5×105/ωp simulation time steps for the computation of λ data. The HNEMD algorithm shows that the thermal conductivity is dependent on plasma parameters and the minimum value of lmin shifts toward higher G with an increase in k, as expected. New investigations give more reliable simulated data for the plasma conductivity than earlier known simulation data and generally the plasma λ0 by 2%-20%, depending on Γ and κ. It has been shown that the obtained results at normalized force field are in satisfactory agreement with various earlier simulation results. This algorithm shows that the new technique provides more accurate results with fast convergence and small size effects over a wide range of plasma states.

Keywords: molecular dynamics simulation, thermal conductivity, nonideal complex plasma, Poiseuille flow

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Authors: Ramiz M. Shubbar, Dong In Lee, Hatem A. Gzar, Arthur S. Rood

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Air pollution is one of the biggest environmental problems in Baghdad, Iraq. The Daura refinery located nearest the center of Baghdad, represents the largest industrial area, which transmits enormous amounts of pollutants, therefore study the gaseous pollutants and particulate matter are very important to the environment and the health of the workers in refinery and the people whom leaving in areas around the refinery. Actually, some studies investigated the studied area before, but it depended on the basic Gaussian equation in a simple computer programs, however, that kind of work at that time is very useful and important, but during the last two decades new largest production units were added to the Daura refinery such as, PU_3 (Power unit_3 (Boiler 11&12)), CDU_1 (Crude Distillation unit_70000 barrel_1), and CDU_2 (Crude Distillation unit_70000 barrel_2). Therefore, it is necessary to use new advanced model to study air pollution at the region for the new current years, and calculation the monthly emission rate of pollutants through actual amounts of fuel which consumed in production unit, this may be lead to accurate concentration values of pollutants and the behavior of dispersion or transport in study area. In this study to the best of author’s knowledge CALPUFF model was used and examined for first time in Iraq. CALPUFF is an advanced non-steady-state meteorological and air quality modeling system, was applied to investigate the pollutants concentration of SO2, NO2, CO, and PM1-10μm, at areas adjacent to Daura refinery which located in the center of Baghdad in Iraq. The CALPUFF modeling system includes three main components: CALMET is a diagnostic 3-dimensional meteorological model, CALPUFF (an air quality dispersion model), CALPOST is a post processing package, and an extensive set of preprocessing programs produced to interface the model to standard routinely available meteorological and geophysical datasets. The targets of this work are modeling and simulation the four pollutants (SO2, NO2, CO, and PM1-10μm) which emitted from Daura refinery within one year. Emission rates of these pollutants were calculated for twelve units includes thirty plants, and 35 stacks by using monthly average of the fuel amount consumption at this production units. Assess the performance of CALPUFF model in this study and detect if it is appropriate and get out predictions of good accuracy compared with available pollutants observation. CALPUFF model was investigated at three stability classes (stable, neutral, and unstable) to indicate the dispersion of the pollutants within deferent meteorological conditions. The simulation of the CALPUFF model showed the deferent kind of dispersion of these pollutants in this region depends on the stability conditions and the environment of the study area, monthly, and annual averages of pollutants were applied to view the dispersion of pollutants in the contour maps. High values of pollutants were noticed in this area, therefore this study recommends to more investigate and analyze of the pollutants, reducing the emission rate of pollutants by using modern techniques and natural gas, increasing the stack height of units, and increasing the exit gas velocity from stacks.

Keywords: CALPUFF, daura refinery, Iraq, pollutants

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Authors: Yi Li, Rui Lu, Lianjun Wang

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With the rapid development of chemical industry, the consumption of volatile organic compounds (VOCs) has increased extensively. In the process of VOCs production and application, plenty of them have been transferred to environment. As a result, it has led to pollution problems not only in soil and ground water but also to human beings. Thus, it is important to develop a sensitive and cost-effective analytical method for trace VOCs detection in environment. Surface-enhanced Raman Spectroscopy (SERS), as one of the most sensitive optical analytical technique with rapid response, pinpoint accuracy and noninvasive detection, has been widely used for ultratrace analysis. Based on the plasmon resonance on the nanoscale metallic surface, SERS technology can even detect single molecule due to abundant nanogaps (i.e. 'hot spots') on the nanosubstrate. In this work, a self-supported flexible silver nitrate (AgNO3)/ethylene-propylene copolymer (EPM) hybrid nanofibers was fabricated by electrospinning. After an in-situ chemical reduction using ice-cold sodium borohydride as reduction agent, numerous silver nanoparticles were formed on the nanofiber surface. By adjusting the reduction time and AgNO3 content, the morphology and dimension of silver nanoparticles could be controlled. According to the principles of solid-phase extraction, the hydrophobic substance is more likely to partition into the hydrophobic EPM membrane in an aqueous environment while water and other polar components are excluded from the analytes. By the enrichment of EPM fibers, the number of hydrophobic molecules located on the 'hot spots' generated from criss-crossed nanofibers is greatly increased, which further enhances SERS signal intensity. The as-prepared Ag/EPM hybrid nanofibers were first employed to detect common SERS probe molecule (p-aminothiophenol) with the detection limit down to 10-12 M, which demonstrated an excellent SERS performance. To further study the application of the fabricated substrate for monitoring hydrophobic substance in water, several typical VOCs, such as benzene, toluene and p-xylene, were selected as model compounds. The results showed that the characteristic peaks of these target analytes in the mixed aqueous solution could be distinguished even at a concentration of 10-6 M after multi-peaks gaussian fitting process, including C-H bending (850 cm-1), C-C ring stretching (1581 cm-1, 1600 cm-1) of benzene, C-H bending (844 cm-1 ,1151 cm-1), C-C ring stretching (1001 cm-1), CH3 bending vibration (1377 cm-1) of toluene, C-H bending (829 cm-1), C-C stretching (1614 cm-1) of p-xylene. The SERS substrate has remarkable advantages which combine the enrichment capacity from EPM and the Raman enhancement of Ag nanoparticles. Meanwhile, the huge specific surface area resulted from electrospinning is benificial to increase the number of adsoption sites and promotes 'hot spots' formation. In summary, this work provides powerful potential in rapid, on-site and accurate detection of trace VOCs using a portable Raman.

Keywords: electrospinning, ethylene-propylene copolymer, silver nanoparticles, SERS, VOCs

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Authors: B. R. Campomanes-Alvarez, P. Quiros, B. Fernandez

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Automatic Speech Recognition (ASR) is a machine-based process of decoding and transcribing oral speech. A typical ASR system receives acoustic input from a speaker or an audio file, analyzes it using algorithms, and produces an output in the form of a text. Some speech recognition systems use Hidden Markov Models (HMMs) to deal with the temporal variability of speech and Gaussian Mixture Models (GMMs) to determine how well each state of each HMM fits a short window of frames of coefficients that represents the acoustic input. Another way to evaluate the fit is to use a feed-forward neural network that takes several frames of coefficients as input and produces posterior probabilities over HMM states as output. Deep neural networks (DNNs) that have many hidden layers and are trained using new methods have been shown to outperform GMMs on a variety of speech recognition systems. Acoustic models for state-of-the-art ASR systems are usually training on massive amounts of data. However, audio files with their corresponding transcriptions can be difficult to obtain, especially in the Spanish language. Hence, in the case of these low-resource scenarios, building an ASR model is considered as a complex task due to the lack of labeled data, resulting in an under-trained system. Semi-supervised learning approaches arise as necessary tasks given the high cost of transcribing audio data. The main goal of this proposal is to develop a procedure based on acoustic semi-supervised learning for Spanish ASR systems by using DNNs. This semi-supervised learning approach consists of: (a) Training a seed ASR model with a DNN using a set of audios and their respective transcriptions. A DNN with a one-hidden-layer network was initialized; increasing the number of hidden layers in training, to a five. A refinement, which consisted of the weight matrix plus bias term and a Stochastic Gradient Descent (SGD) training were also performed. The objective function was the cross-entropy criterion. (b) Decoding/testing a set of unlabeled data with the obtained seed model. (c) Selecting a suitable subset of the validated data to retrain the seed model, thereby improving its performance on the target test set. To choose the most precise transcriptions, three confidence scores or metrics, regarding the lattice concept (based on the graph cost, the acoustic cost and a combination of both), was performed as selection technique. The performance of the ASR system will be calculated by means of the Word Error Rate (WER). The test dataset was renewed in order to extract the new transcriptions added to the training dataset. Some experiments were carried out in order to select the best ASR results. A comparison between a GMM-based model without retraining and the DNN proposed system was also made under the same conditions. Results showed that the semi-supervised ASR-model based on DNNs outperformed the GMM-model, in terms of WER, in all tested cases. The best result obtained an improvement of 6% relative WER. Hence, these promising results suggest that the proposed technique could be suitable for building ASR models in low-resource environments.

Keywords: automatic speech recognition, deep neural networks, machine learning, semi-supervised learning

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Authors: Sree Bash Chandra Debnath, Didier Tonneau, Carole Fauquet, Agnes Tallet, Julien Darreon

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Purpose: Inorganic scintillating dosimetry is the most recent promising technique to solve several dosimetric issues and provide quality assurance in radiation therapy. Despite several advantages, the major issue of using scintillating detectors is the Cerenkov effect, typically induced in the visible emission range. In this context, the purpose of this research work is to evaluate the performance of a novel infrared inorganic scintillator detector (IR-ISD) in the radiation therapy treatment to ensure Cerenkov free signal and the best matches between the delivered and prescribed doses during treatment. Methods: A simple and small-scale infrared inorganic scintillating detector of 100 µm diameter with a sensitive scintillating volume of 2x10-6 mm3 was developed. A prototype of the dose verification system has been introduced based on PTIR1470/F (provided by Phosphor Technology®) material used in the proposed novel IR-ISD. The detector was tested on an Elekta LINAC system tuned at 6 MV/15MV and a brachytherapy source (Ir-192) used in the patient treatment protocol. The associated dose rate was measured in count rate (photons/s) using a highly sensitive photon counter (sensitivity ~20ph/s). Overall measurements were performed in IBATM water tank phantoms by following international Technical Reports series recommendations (TRS 381) for radiotherapy and TG43U1 recommendations for brachytherapy. The performance of the detector was tested through several dosimetric parameters such as PDD, beam profiling, Cerenkov measurement, dose linearity, dose rate linearity repeatability, and scintillator stability. Finally, a comparative study is also shown using a reference microdiamond dosimeter, Monte-Carlo (MC) simulation, and data from recent literature. Results: This study is highlighting the complete removal of the Cerenkov effect especially for small field radiation beam characterization. The detector provides an entire linear response with the dose in the 4cGy to 800 cGy range, independently of the field size selected from 5 x 5 cm² down to 0.5 x 0.5 cm². A perfect repeatability (0.2 % variation from average) with day-to-day reproducibility (0.3% variation) was observed. Measurements demonstrated that ISD has superlinear behavior with dose rate (R2=1) varying from 50 cGy/s to 1000 cGy/s. PDD profiles obtained in water present identical behavior with a build-up maximum depth dose at 15 mm for different small fields irradiation. A low dimension of 0.5 x 0.5 cm² field profiles have been characterized, and the field cross profile presents a Gaussian-like shape. The standard deviation (1σ) of the scintillating signal remains within 0.02% while having a very low convolution effect, thanks to lower sensitive volume. Finally, during brachytherapy, a comparison with MC simulations shows that considering energy dependency, measurement agrees within 0.8% till 0.2 cm source to detector distance. Conclusion: The proposed scintillating detector in this study shows no- Cerenkov radiation and efficient performance for several radiation therapy measurement parameters. Therefore, it is anticipated that the IR-ISD system can be promoted to validate with direct clinical investigations, such as appropriate dose verification and quality control in the Treatment Planning System (TPS).

Keywords: IR-Scintillating detector, dose measurement, micro-scintillators, Cerenkov effect

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Authors: Mohammad Shajid Rahman, Tarik Kaya, Edgar Matida

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Electronic cigarettes, also known as e-cigarettes, may have become a tool to improve smoking cessation due to their ability to provide nicotine at a selected rate. Unlike traditional cigarettes, which produce toxic elements from tobacco combustion, e-cigarettes generate aerosols by heating a liquid solution (commonly a mixture of propylene glycol, vegetable glycerin, nicotine and some flavoring agents). However, caution still needs to be taken when using e-cigarettes due to the presence of addictive nicotine and some harmful substances produced from the heating process. Particle size distribution (PSD) and associated velocities generated by e-cigarettes have significant influence on aerosol deposition in different regions of human respiratory tracts. On another note, low actuation power is beneficial in aerosol generating devices since it exhibits a reduced emission of toxic chemicals. In case of e-cigarettes, lower heating powers can be considered as powers lower than 10 W compared to a wide range of powers (0.6 to 70.0 W) studied in literature. Due to the importance regarding inhalation risk reduction, deeper understanding of particle size characteristics of e-cigarettes demands thorough investigation. However, comprehensive study on PSD and velocities of e-cigarettes with a standard testing condition at relatively low heating powers is still lacking. The present study aims to measure particle number count and size distribution of undiluted aerosols of a latest fourth-generation e-cigarette at low powers, within 6.5 W using real-time particle counter (time-of-flight method). Also, temporal and spatial evolution of particle size and velocity distribution of aerosol jets are examined using phase Doppler anemometry (PDA) technique. To the authors’ best knowledge, application of PDA in e-cigarette aerosol measurement is rarely reported. In the present study, preliminary results about particle number count of undiluted aerosols measured by time-of-flight method depicted that an increase of heating power from 3.5 W to 6.5 W resulted in an enhanced asymmetricity in PSD, deviating from log-normal distribution. This can be considered as an artifact of rapid vaporization, condensation and coagulation processes on aerosols caused by higher heating power. A novel mathematical expression, combining exponential, Gaussian and polynomial (EGP) distributions, was proposed to describe asymmetric PSD successfully. The value of count median aerodynamic diameter and geometric standard deviation laid within a range of about 0.67 μm to 0.73 μm, and 1.32 to 1.43, respectively while the power varied from 3.5 W to 6.5 W. Laser Doppler velocimetry (LDV) and PDA measurement suggested a typical centerline streamwise mean velocity decay of aerosol jet along with a reduction of particle sizes. In the final submission, a thorough literature review, detailed description of experimental procedure and discussion of the results will be provided. Particle size and turbulent characteristics of aerosol jets will be further examined, analyzing arithmetic mean diameter, volumetric mean diameter, volume-based mean diameter, streamwise mean velocity and turbulence intensity. The present study has potential implications in PSD simulation and validation of aerosol dosimetry model, leading to improving related aerosol generating devices.

Keywords: E-cigarette aerosol, laser doppler velocimetry, particle size distribution, particle velocity, phase Doppler anemometry

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Authors: V. Saccà, A. Sarica, F. Novellino, S. Barone, T. Tallarico, E. Filippelli, A. Granata, P. Valentino, A. Quattrone

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The work aim was to evaluate how well Random Forest (RF) and Support Vector Machine (SVM) algorithms could support the early diagnosis of Multiple Sclerosis (MS) from resting-state functional connectivity data. In particular, we wanted to explore the ability in distinguishing between controls and patients of mean signals extracted from ICA components corresponding to 15 well-known networks. Eighteen patients with early-MS (mean-age 37.42±8.11, 9 females) were recruited according to McDonald and Polman, and matched for demographic variables with 19 healthy controls (mean-age 37.55±14.76, 10 females). MRI was acquired by a 3T scanner with 8-channel head coil: (a)whole-brain T1-weighted; (b)conventional T2-weighted; (c)resting-state functional MRI (rsFMRI), 200 volumes. Estimated total lesion load (ml) and number of lesions were calculated using LST-toolbox from the corrected T1 and FLAIR. All rsFMRIs were pre-processed using tools from the FMRIB's Software Library as follows: (1) discarding of the first 5 volumes to remove T1 equilibrium effects, (2) skull-stripping of images, (3) motion and slice-time correction, (4) denoising with high-pass temporal filter (128s), (5) spatial smoothing with a Gaussian kernel of FWHM 8mm. No statistical significant differences (t-test, p < 0.05) were found between the two groups in the mean Euclidian distance and the mean Euler angle. WM and CSF signal together with 6 motion parameters were regressed out from the time series. We applied an independent component analysis (ICA) with the GIFT-toolbox using the Infomax approach with number of components=21. Fifteen mean components were visually identified by two experts. The resulting z-score maps were thresholded and binarized to extract the mean signal of the 15 networks for each subject. Statistical and machine learning analysis were then conducted on this dataset composed of 37 rows (subjects) and 15 features (mean signal in the network) with R language. The dataset was randomly splitted into training (75%) and test sets and two different classifiers were trained: RF and RBF-SVM. We used the intrinsic feature selection of RF, based on the Gini index, and recursive feature elimination (rfe) for the SVM, to obtain a rank of the most predictive variables. Thus, we built two new classifiers only on the most important features and we evaluated the accuracies (with and without feature selection) on test-set. The classifiers, trained on all the features, showed very poor accuracies on training (RF:58.62%, SVM:65.52%) and test sets (RF:62.5%, SVM:50%). Interestingly, when feature selection by RF and rfe-SVM were performed, the most important variable was the sensori-motor network I in both cases. Indeed, with only this network, RF and SVM classifiers reached an accuracy of 87.5% on test-set. More interestingly, the only misclassified patient resulted to have the lowest value of lesion volume. We showed that, with two different classification algorithms and feature selection approaches, the best discriminant network between controls and early MS, was the sensori-motor I. Similar importance values were obtained for the sensori-motor II, cerebellum and working memory networks. These findings, in according to the early manifestation of motor/sensorial deficits in MS, could represent an encouraging step toward the translation to the clinical diagnosis and prognosis.

Keywords: feature selection, machine learning, multiple sclerosis, random forest, support vector machine

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Authors: Abderrazak Bannari

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Acid Mine Drainage (AMD) from mine wastes and contaminations of soils and water with metals are considered as a major environmental problem in mining areas. It is produced by interactions of water, air, and sulphidic mine wastes. This environment problem results from a series of chemical and biochemical oxidation reactions of sulfide minerals e.g. pyrite and pyrrhotite. These reactions lead to acidity as well as the dissolution of toxic and heavy metals (Fe, Mn, Cu, etc.) from tailings waste rock piles, and open pits. Soil and aquatic ecosystems could be contaminated and, consequently, human health and wildlife will be affected. Furthermore, secondary minerals, typically formed during weathering of mine waste storage areas when the concentration of soluble constituents exceeds the corresponding solubility product, are also important. The most common secondary mineral compositions are hydrous iron oxide (goethite, etc.) and hydrated iron sulfate (jarosite, etc.). The objectives of this study focus on the detection and mapping of MIOP in the soil using Hyperion EO-1 (Earth Observing - 1) hyperspectral data and constrained linear spectral mixture analysis (CLSMA) algorithm. The abandoned Kettara mine, located approximately 35 km northwest of Marrakech city (Morocco) was chosen as study area. During 44 years (from 1938 to 1981) this mine was exploited for iron oxide and iron sulphide minerals. Previous studies have shown that Kettara surrounding soils are contaminated by heavy metals (Fe, Cu, etc.) as well as by secondary minerals. To achieve our objectives, several soil samples representing different MIOP classes have been resampled and located using accurate GPS ( ≤ ± 30 cm). Then, endmembers spectra were acquired over each sample using an Analytical Spectral Device (ASD) covering the spectral domain from 350 to 2500 nm. Considering each soil sample separately, the average of forty spectra was resampled and convolved using Gaussian response profiles to match the bandwidths and the band centers of the Hyperion sensor. Moreover, the MIOP content in each sample was estimated by geochemical analyses in the laboratory, and a ground truth map was generated using simple Kriging in GIS environment for validation purposes. The acquired and used Hyperion data were corrected for a spatial shift between the VNIR and SWIR detectors, striping, dead column, noise, and gain and offset errors. Then, atmospherically corrected using the MODTRAN 4.2 radiative transfer code, and transformed to surface reflectance, corrected for sensor smile (1-3 nm shift in VNIR and SWIR), and post-processed to remove residual errors. Finally, geometric distortions and relief displacement effects were corrected using a digital elevation model. The MIOP fraction map was extracted using CLSMA considering the entire spectral range (427-2355 nm), and validated by reference to the ground truth map generated by Kriging. The obtained results show the promising potential of the proposed methodology for the detection and mapping of mine iron oxide pollution in the soil.

Keywords: hyperion eo-1, hyperspectral, mine iron oxide pollution, environmental impact, unmixing

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Authors: Mario Tauzene Afonso Matangue, Ivan Andres Sanchez Ortiz

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The Metropolitan area of Maputo (Mozambique Capital City) is located in semi-arid zone (800 mm annual rainfall) with 1101170 million inhabitants. On the west side, there are the flatlands of Infulene where the Mulauze River flows towards to the Indian Ocean, receiving at this site, the storm water contaminated with sanitary sewage from Maputo, transported through a concrete open channel. In Infulene, local communities grow salads crops such as tomato, onion, garlic, lettuce, and cabbage, which are then commercialized and consumed in several markets in Maputo City. Lettuce is the most daily consumed salad crop in different meals, generally in fast-foods, breakfasts, lunches, and dinners. However, the risk of infection by several pathogens due to the consumption of lettuce, using the Quantitative Microbial Risk Assessment (QMRA) tools, is still unknown since there are few studies or publications concerning to this matter in Mozambique. This work is aimed at determining the annual risk arising from the consumption of lettuce grown in Infulene valley, in Maputo, using QMRA tools. The exposure model was constructed upon the volume of contaminated water remaining in the lettuce leaves, the empirical relations between the number of pathogens and the indicator of microorganisms (E. coli), the consumption of lettuce (g) and reduction of pathogens (days). The reference pathogens were Vibrio cholerae, Cryptosporidium, norovirus, and Ascaris. The water quality samples (E. coli) were collected in the storm water channel from January 2016 to December 2018, comprising 65 samples, and the urban lettuce consumption data were collected through inquiry in Maputo Metropolis covering 350 persons. A non-parametric bootstrap was performed involving 10,000 iterations over the collected dataset, namely, water quality (E. coli) and lettuce consumption. The dose-response models were: Exponential for Cryptosporidium, Kummer Confluent hypergeomtric function (1F1) for Vibrio and Ascaris Gaussian hypergeometric function (2F1-(a,b;c;z) for norovirus. The annual infection risk estimates were performed using R 3.6.0 (CoreTeam) software by Monte Carlo (Latin hypercubes), a sampling technique involving 10,000 iterations. The annual infection risks values expressed by Median and the 95th percentile, per person per year (pppy) arising from the consumption of lettuce are as follows: Vibrio cholerae (1.00, 1.00), Cryptosporidium (3.91x10⁻³, 9.72x 10⁻³), nororvirus (5.22x10⁻¹, 9.99x10⁻¹) and Ascaris (2.59x10⁻¹, 9.65x10⁻¹). Thus, the consumption of the lettuce would result in greater risks than the tolerable levels ( < 10⁻³ pppy or 10⁻⁶ DALY) for all pathogens, and the Vibrio cholerae is the most virulent pathogens, according to the hit-single models followed by the Ascaris lumbricoides and norovirus. The sensitivity analysis carried out in this work pointed out that in the whole QMRA, the most important input variable was the reduction of pathogens (Spearman rank value was 0.69) between harvest and consumption followed by water quality (Spearman rank value was 0.69). The decision-makers (Mozambique Government) must strengthen the prevention measures related to pathogens reduction in lettuce (i.e., washing) and engage in wastewater treatment engineering.

Keywords: annual infections risk, lettuce, non-parametric bootstrapping, quantitative microbial risk assessment tools

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Authors: Jeremie Coullon, Robert J. Webber

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We introduce a Markov chain Monte Carlo (MCMC) sam-pler for infinite-dimensional inverse problems. Our sam-pler is based on the affine invariant ensemble sampler, which uses interacting walkers to adapt to the covariance structure of the target distribution. We extend this ensem-ble sampler for the first time to infinite-dimensional func-tion spaces, yielding a highly efficient gradient-free MCMC algorithm. Because our ensemble sampler does not require gradients or posterior covariance estimates, it is simple to implement and broadly applicable. In many Bayes-ian inverse problems, Markov chain Monte Carlo (MCMC) meth-ods are needed to approximate distributions on infinite-dimensional function spaces, for example, in groundwater flow, medical imaging, and traffic flow. Yet designing efficient MCMC methods for function spaces has proved challenging. Recent gradi-ent-based MCMC methods preconditioned MCMC methods, and SMC methods have improved the computational efficiency of functional random walk. However, these samplers require gradi-ents or posterior covariance estimates that may be challenging to obtain. Calculating gradients is difficult or impossible in many high-dimensional inverse problems involving a numerical integra-tor with a black-box code base. Additionally, accurately estimating posterior covariances can require a lengthy pilot run or adaptation period. These concerns raise the question: is there a functional sampler that outperforms functional random walk without requir-ing gradients or posterior covariance estimates? To address this question, we consider a gradient-free sampler that avoids explicit covariance estimation yet adapts naturally to the covariance struc-ture of the sampled distribution. This sampler works by consider-ing an ensemble of walkers and interpolating and extrapolating between walkers to make a proposal. This is called the affine in-variant ensemble sampler (AIES), which is easy to tune, easy to parallelize, and efficient at sampling spaces of moderate dimen-sionality (less than 20). The main contribution of this work is to propose a functional ensemble sampler (FES) that combines func-tional random walk and AIES. To apply this sampler, we first cal-culate the Karhunen–Loeve (KL) expansion for the Bayesian prior distribution, assumed to be Gaussian and trace-class. Then, we use AIES to sample the posterior distribution on the low-wavenumber KL components and use the functional random walk to sample the posterior distribution on the high-wavenumber KL components. Alternating between AIES and functional random walk updates, we obtain our functional ensemble sampler that is efficient and easy to use without requiring detailed knowledge of the target dis-tribution. In past work, several authors have proposed splitting the Bayesian posterior into low-wavenumber and high-wavenumber components and then applying enhanced sampling to the low-wavenumber components. Yet compared to these other samplers, FES is unique in its simplicity and broad applicability. FES does not require any derivatives, and the need for derivative-free sam-plers has previously been emphasized. FES also eliminates the requirement for posterior covariance estimates. Lastly, FES is more efficient than other gradient-free samplers in our tests. In two nu-merical examples, we apply FES to challenging inverse problems that involve estimating a functional parameter and one or more scalar parameters. We compare the performance of functional random walk, FES, and an alternative derivative-free sampler that explicitly estimates the posterior covariance matrix. We conclude that FES is the fastest available gradient-free sampler for these challenging and multimodal test problems.

Keywords: Bayesian inverse problems, Markov chain Monte Carlo, infinite-dimensional inverse problems, dimensionality reduction

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