Search results for: bayesian regularization

Authors: Gabrielle Robertson, Matthew Downs, Joseph Dagher

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Iron deposition in the brain has been linked with a host of neurological disorders such as Alzheimer’s, Parkinson’s, and Multiple Sclerosis. While some treatment options exist, there are no objective measurement tools that allow for the monitoring of iron levels in the brain in vivo. An emerging Magnetic Resonance Imaging (MRI) method has been recently proposed to deduce iron concentration through quantitative measurement of magnetic susceptibility. This is a multi-step process that involves repeated modeling of physical processes via approximate numerical solutions. For example, the last two steps of this Quantitative Susceptibility Mapping (QSM) method involve I) mapping magnetic field into magnetic susceptibility and II) mapping magnetic susceptibility into iron concentration. Process I involves solving an ill-posed inverse problem by using regularization via injection of prior belief. The end result from Process II highly depends on the model used to describe the molecular content of each voxel (type of iron, water fraction, etc.) Due to these factors, the accuracy and repeatability of QSM have been an active area of research in the MRI and medical imaging community. This work aims to estimate iron concentration in the brain via a single step. A synthetic numerical model of the human head was created by automatically and manually segmenting the human head on a high-resolution grid (640x640x640, 0.4mm³) yielding detailed structures such as microvasculature and subcortical regions as well as bone, soft tissue, Cerebral Spinal Fluid, sinuses, arteries, and eyes. Each segmented region was then assigned tissue properties such as relaxation rates, proton density, electromagnetic tissue properties and iron concentration. These tissue property values were randomly selected from a Probability Distribution Function derived from a thorough literature review. In addition to having unique tissue property values, different synthetic head realizations also possess unique structural geometry created by morphing the boundary regions of different areas within normal physical constraints. This model of the human brain is then used to create synthetic MRI measurements. This is repeated thousands of times, for different head shapes, volume, tissue properties and noise realizations. Collectively, this constitutes a training-set that is similar to in vivo data, but larger than datasets available from clinical measurements. This 3D convolutional U-Net neural network architecture was used to train data-driven Deep Learning models to solve for iron concentrations from raw MRI measurements. The performance was then tested on both synthetic data not used in training as well as real in vivo data. Results showed that the model trained on synthetic MRI measurements is able to directly learn iron concentrations in areas of interest more effectively than other existing QSM reconstruction methods. For comparison, models trained on random geometric shapes (as proposed in the Deep QSM method) are less effective than models trained on realistic synthetic head models. Such an accurate method for the quantitative measurement of iron deposits in the brain would be of important value in clinical studies aiming to understand the role of iron in neurological disease.

Keywords: magnetic resonance imaging, MRI, iron deposition, machine learning, quantitative susceptibility mapping

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Authors: Ipek Kivanc, Demet Ozgur-Unluakin

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Over the past years, technological innovations and advancements have played an important role in the industrial world. Due to technological improvements, the degree of complexity of the systems has increased. Hence, all systems are getting more uncertain that emerges from increased complexity, resulting in more cost. It is challenging to cope with this situation. So, implementing efficient planning of maintenance activities in such systems are getting more essential. Partially Observable Markov Decision Processes (POMDPs) are powerful tools for stochastic sequential decision problems under uncertainty. Although maintenance optimization in a dynamic environment can be modeled as such a sequential decision problem, POMDPs are not widely used for tackling maintenance problems. However, they can be well-suited frameworks for obtaining optimal maintenance policies. In the classical representation of the POMDP framework, the system is denoted by a single node which has multiple states. The main drawback of this classical approach is that the state space grows exponentially with the number of state variables. On the other side, factored representation of POMDPs enables to simplify the complexity of the states by taking advantage of the factored structure already available in the nature of the problem. The main idea of factored POMDPs is that they can be compactly modeled through dynamic Bayesian networks (DBNs), which are graphical representations for stochastic processes, by exploiting the structure of this representation. This study aims to demonstrate how maintenance planning of dynamic systems can be modeled with factored POMDPs. An empirical maintenance planning problem of a dynamic system consisting of four partially observable components deteriorating in time is designed. To solve the empirical model, we resort to Symbolic Perseus solver which is one of the state-of-the-art factored POMDP solvers enabling approximate solutions. We generate some more predefined policies based on corrective or proactive maintenance strategies. We execute the policies on the empirical problem for many replications and compare their performances under various scenarios. The results show that the computed policies from the POMDP model are superior to the others. Acknowledgment: This work is supported by the Scientific and Technological Research Council of Turkey (TÜBİTAK) under grant no: 117M587.

Keywords: factored representation, maintenance, multi-component system, partially observable Markov decision processes

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Authors: Yegnanew A. Shiferaw

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Background: commodity price volatility originating from excessive commodity price fluctuation has been a global problem especially after the recent financial crises. Volatility is a measure of risk or uncertainty in financial analysis. It plays a vital role in risk management, portfolio management, and pricing equity. Objectives: the core objective of this paper is to examine the relationship between the prices of agricultural commodities with oil price, gas price, coal price and exchange rate (USD/Rand). In addition, the paper tries to fit an appropriate model that best describes the log return price volatility and estimate Value-at-Risk and expected shortfall. Data and methods: the data used in this study are the daily returns of agricultural commodity prices from 02 January 2007 to 31st October 2016. The data sets consists of the daily returns of agricultural commodity prices namely: white maize, yellow maize, wheat, sunflower, soya, corn, and sorghum. The paper applies the three-state Markov-switching (MS) regression, the standard single-regime GARCH and the two regime Markov-switching GARCH (MS-GARCH) models. Results: to choose the best fit model, the log-likelihood function, Akaike information criterion (AIC), Bayesian information criterion (BIC) and deviance information criterion (DIC) are employed under three distributions for innovations. The results indicate that: (i) the price of agricultural commodities was found to be significantly associated with the price of coal, price of natural gas, price of oil and exchange rate, (ii) for all agricultural commodities except sunflower, k=3 had higher log-likelihood values and lower AIC and BIC values. Thus, the three-state MS regression model outperformed the two-state MS regression model (iii) MS-GARCH(1,1) with generalized error distribution (ged) innovation performs best for white maize and yellow maize; MS-GARCH(1,1) with student-t distribution (std) innovation performs better for sorghum; MS-gjrGARCH(1,1) with ged innovation performs better for wheat, sunflower and soya and MS-GARCH(1,1) with std innovation performs better for corn. In conclusion, this paper provided a practical guide for modelling agricultural commodity prices by MS regression and MS-GARCH processes. This paper can be good as a reference when facing modelling agricultural commodity price problems.

Keywords: commodity prices, MS-GARCH model, MS regression model, South Africa, volatility

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Authors: Xiaoyuan Chen

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Background: This study aimed to characterize the epidemiological and clinical features of five rare subtypes of hepatocellular carcinoma (HCC) and to create a competing risk nomogram for predicting cancer-specific survival. Methods: This study used the Surveillance, Epidemiology, and End Results database to analyze the clinicopathological data of 50,218 patients with classic HCC and five rare subtypes (ICD-O-3 Histology Code=8170/3-8175/3) between 2004 and 2018. The annual percent change (APC) was calculated using Joinpoint regression, and a nomogram was developed based on multivariable competing risk survival analyses. The prognostic performance of the nomogram was evaluated using the Akaike information criterion, Bayesian information criterion, C-index, calibration curve, and area under the receiver operating characteristic curve. Decision curve analysis was used to assess the clinical value of the models. Results: The incidence of scirrhous carcinoma showed a decreasing trend (APC=-6.8%, P=0.025), while the morbidity of other rare subtypes remained stable from 2004 to 2018. The incidence-based mortality plateau in all subtypes during the period. Clear cell carcinoma was the most common subtype (n=551, 1.1%), followed by fibrolamellar (n=241, 0.5%), scirrhous (n=82, 0.2%), spindle cell (n=61, 0.1%), and pleomorphic (n=17, ~0%) carcinomas. Patients with fibrolamellar carcinoma were younger and more likely to have non-cirrhotic liver and better prognoses. Scirrhous carcinoma shared almost the same macro clinical characteristics and outcomes as classic HCC. Clear cell carcinoma tended to occur in the Asia-Pacific elderly male population, and more than half of them were large HCC (Size>5cm). Sarcomatoid (including spindle cell and pleomorphic) carcinoma was associated with larger tumor size, poorer differentiation, and more dismal prognoses. The pathological subtype, T stage, M stage, surgery, alpha-fetoprotein, and cancer history were identified as independent predictors in patients with rare subtypes. The nomogram showed good calibration, discrimination, and net benefits in clinical practice. Conclusion: The rare subtypes of HCC had distinct clinicopathological features and biological behaviors compared with classic HCC. Our findings could provide a valuable reference for clinicians. The constructed nomogram could accurately predict prognoses, which is beneficial for individualized management.

Keywords: hepatocellular carcinoma, pathological subtype, fibrolamellar carcinoma, scirrhous carcinoma, clear cell carcinoma, spindle cell carcinoma, pleomorphic carcinoma

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Authors: Hyohun Kim, Dongwha Shin, Yeonseok Kim, Ji-Su Ahn, Kensuke Nakamura, Dongeun Choi, Byung-Woo Hong

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Artefacts are commonly encountered in the imaging process of clinical computed tomography (CT) where the artefact refers to any systematic discrepancy between the reconstructed observation and the true attenuation coefficient of the object. It is known that CT images are inherently more prone to artefacts due to its image formation process where a large number of independent detectors are involved, and they are assumed to yield consistent measurements. There are a number of different artefact types including noise, beam hardening, scatter, pseudo-enhancement, motion, helical, ring, and metal artefacts, which cause serious difficulties in reading images. Thus, it is desired to remove nuisance factors from the degraded image leaving the fundamental intrinsic information that can provide better interpretation of the anatomical and pathological characteristics. However, it is considered as a difficult task due to the high dimensionality and variability of data to be recovered, which naturally motivates the use of machine learning techniques. We propose an image restoration algorithm based on the deep neural network framework where the denoising auto-encoders are stacked building multiple layers. The denoising auto-encoder is a variant of a classical auto-encoder that takes an input data and maps it to a hidden representation through a deterministic mapping using a non-linear activation function. The latent representation is then mapped back into a reconstruction the size of which is the same as the size of the input data. The reconstruction error can be measured by the traditional squared error assuming the residual follows a normal distribution. In addition to the designed loss function, an effective regularization scheme using residual-driven dropout determined based on the gradient at each layer. The optimal weights are computed by the classical stochastic gradient descent algorithm combined with the back-propagation algorithm. In our algorithm, we initially decompose an input image into its intrinsic representation and the nuisance factors including artefacts based on the classical Total Variation problem that can be efficiently optimized by the convex optimization algorithm such as primal-dual method. The intrinsic forms of the input images are provided to the deep denosing auto-encoders with their original forms in the training phase. In the testing phase, a given image is first decomposed into the intrinsic form and then provided to the trained network to obtain its reconstruction. We apply our algorithm to the restoration of the corrupted CT images by the artefacts. It is shown that our algorithm improves the readability and enhances the anatomical and pathological properties of the object. The quantitative evaluation is performed in terms of the PSNR, and the qualitative evaluation provides significant improvement in reading images despite degrading artefacts. The experimental results indicate the potential of our algorithm as a prior solution to the image interpretation tasks in a variety of medical imaging applications. This work was supported by the MISP(Ministry of Science and ICT), Korea, under the National Program for Excellence in SW (20170001000011001) supervised by the IITP(Institute for Information and Communications Technology Promotion).

Keywords: auto-encoder neural network, CT image artefact, deep learning, intrinsic image representation, noise reduction, total variation

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Authors: Tzu-Ting Hu, Jung-Der Wang, Ming-Yeng Lin, Jin-Luh Chen, Perng-Jy Tsai

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The vinyl chloride monomer (VCM) has been classified as group 1 (human) carcinogen by the IARC. Workers exposed to VCM are known associated with the development of the liver cancer and hence might cause economical and health losses. Particularly, for those work for the petrochemical industry have been seriously concerned in the environmental and occupational health field. Considering assessing workers’ health risks and their resultant economical and health losses requires the establishment of long-term VCM exposure data for any similar exposure group (SEG) of interest, the development of suitable technologies has become an urgent and important issue. In the present study, VCM exposures for petrochemical industry workers were determined firstly based on the database of the 'Workplace Environmental Monitoring Information Systems (WEMIS)' provided by Taiwan OSHA. Considering the existence of miss data, the reconstruction of historical exposure techniques were then used for completing the long-term exposure data for SEGs with routine operations. For SEGs with non-routine operations, exposure modeling techniques, together with their time/activity records, were adopted for determining their long-term exposure concentrations. The Bayesian decision analysis (BDA) was adopted for conducting exposure and health risk assessments for any given SEG in the petrochemical industry. The resultant excessive cancer risk was then used to determine the corresponding loss of quality-adjusted life expectancy (QALE). Results show that low average concentrations can be found for SEGs with routine operations (e.g., VCM rectification 0.0973 ppm, polymerization 0.306 ppm, reaction tank 0.33 ppm, VCM recovery 1.4 ppm, control room 0.14 ppm, VCM storage tanks 0.095 ppm and wastewater treatment 0.390 ppm), and the above values were much lower than that of the permissible exposure limit (PEL; 3 ppm) of VCM promulgated in Taiwan. For non-routine workers, though their high exposure concentrations, their low exposure time and frequencies result in low corresponding health risks. Through the consideration of exposure assessment results, health risk assessment results, and QALE results simultaneously, it is concluded that the proposed method was useful for prioritizing SEGs for conducting exposure abatement measurements. Particularly, the obtained QALE results further indicate the importance of reducing workers’ VCM exposures, though their exposures were low as in comparison with the PEL and the acceptable health risk.

Keywords: exposure assessment, health risk assessment, petrochemical industry, quality-adjusted life years, vinyl chloride monomer

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Authors: Hesam Gholami

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Elevated suspended sediment loads in riverine systems resulting from accelerated erosion due to human activities are a serious threat to the sustainable management of watersheds and ecosystem services therein worldwide. Therefore, mitigation of deleterious sediment effects as a distributed or non-point pollution source in the catchments requires reliable provenance information. Sediment tracing or sediment fingerprinting, as a combined process consisting of sampling, laboratory measurements, different statistical tests, and the application of mixing or unmixing models, is a useful technique for discriminating the sources of sediments. From 1996 to the present, different aspects of this technique, such as grouping the sources (spatial and individual sources), discriminating the potential sources by different statistical techniques, and modification of mixing and unmixing models, have been introduced and modified by many researchers worldwide, and have been applied to identify the provenance of fine materials in agricultural, rural, mountainous, and coastal catchments, and in large catchments with numerous lakes and reservoirs. In the last two decades, efforts exploring the uncertainties associated with sediment fingerprinting results have attracted increasing attention. The frameworks used to quantify the uncertainty associated with fingerprinting estimates can be divided into three groups comprising Monte Carlo simulation, Bayesian approaches and generalized likelihood uncertainty estimation (GLUE). Given the above background, the primary goal of this study was to apply geochemical fingerprinting within the GLUE framework in the estimation of sub-basin spatial sediment source contributions in the arid Mehran River catchment in southern Iran, which drains into the Persian Gulf. The accuracy of GLUE predictions generated using four different sets of statistical tests for discriminating three sub-basin spatial sources was evaluated using 10 virtual sediments (VS) samples with known source contributions using the root mean square error (RMSE) and mean absolute error (MAE). Based on the results, the contributions modeled by GLUE for the western, central and eastern sub-basins are 1-42% (overall mean 20%), 0.5-30% (overall mean 12%) and 55-84% (overall mean 68%), respectively. According to the mean absolute fit (MAF; ≥ 95% for all target sediment samples) and goodness-of-fit (GOF; ≥ 99% for all samples), our suggested modeling approach is an accurate technique to quantify the source of sediments in the catchments. Overall, the estimated source proportions can help watershed engineers plan the targeting of conservation programs for soil and water resources.

Keywords: sediment source tracing, generalized likelihood uncertainty estimation, virtual sediment mixtures, Iran

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Authors: Kevin De Castro Cogle, Mirian Kubo, Maria Anastasiadi, Fady Mohareb, Claire Rossi

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Background: The bioaccessibility of bioactive compounds is a critical determinant of the nutritional quality of various food products. Despite its importance, there is a limited number of comprehensive studies aimed at assessing how the composition of a food matrix influences the bioaccessibility of a compound of interest. This knowledge gap has prompted a growing need to investigate the intricate relationship between food matrix formulations and the bioaccessibility of bioactive compounds. One such class of bioactive compounds that has attracted considerable attention is curcuminoids. These naturally occurring phytochemicals, extracted from the roots of Curcuma longa, have gained popularity owing to their purported health benefits and also well known for their poor bioaccessibility Project aim: The primary objective of this research project is to systematically assess the influence of matrix composition on the bioaccessibility of curcuminoids. Additionally, this study aimed to develop a series of predictive models for bioaccessibility, providing valuable insights for optimising the formula for functional foods and provide more descriptive nutritional information to potential consumers. Methods: Food formulations enriched with curcuminoids were subjected to in vitro digestion simulation, and their bioaccessibility was characterized with chromatographic and spectrophotometric techniques. The resulting data served as the foundation for the development of predictive models capable of estimating bioaccessibility based on specific physicochemical properties of the food matrices. Results: One striking finding of this study was the strong correlation observed between the concentration of macronutrients within the food formulations and the bioaccessibility of curcuminoids. In fact, macronutrient content emerged as a very informative explanatory variable of bioaccessibility and was used, alongside other variables, as predictors in a Bayesian hierarchical model that predicted curcuminoid bioaccessibility accurately (optimisation performance of 0.97 R2) for the majority of cross-validated test formulations (LOOCV of 0.92 R2). These preliminary results open the door to further exploration, enabling researchers to investigate a broader spectrum of food matrix types and additional properties that may influence bioaccessibility. Conclusions: This research sheds light on the intricate interplay between food matrix composition and the bioaccessibility of curcuminoids. This study lays a foundation for future investigations, offering a promising avenue for advancing our understanding of bioactive compound bioaccessibility and its implications for the food industry and informed consumer choices.

Keywords: bioactive bioaccessibility, food formulation, food matrix, machine learning, probabilistic modelling

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Authors: Masoud Sheidai, Fahimeh Koohdar, Hashem Sharifi

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Juglans regia (L.) commonly known as Persian walnut of the genus Juglans L. (Juglandaceae) is one of the most important cultivated plant species due to its high-quality wood and edible nuts. The genetic diversity analysis is essential for conservation and management of tree species. Persian walnut is native from South-Eastern Europe to North-Western China through Tibet, Nepal, Northern India, Pakistan, and Iran. The species like Persian walnut, which has a wide range of geographical distribution, should harbor extensive genetic variability to adapt to environmental fluctuations they face. We aimed to study the population genetic structure of seven Persian walnut populations including three wild and four cultivated populations by using ISSR (Inter simple sequence repeats) and SRAP (Sequence related amplified polymorphism) molecular markers. We also aimed to compare the genetic variability revealed by ISSR neutral multilocus marker and rDNA ITS sequences. The studied populations differed in morphological features as the samples in each population were clustered together and were separate from the other populations. Three wild populations studied were placed close to each other. The mantel test after 5000 times permutation performed between geographical distance and morphological distance in Persian walnut populations produced significant correlation (r = 0.48, P = 0.002). Therefore, as the populations become farther apart, they become more divergent in morphological features. ISSR analysis produced 47 bands/ loci, while we obtained 15 SRAP bands. Gst and other differentiation statistics determined for these loci revealed that most of the ISSR and SRAP loci have very good discrimination power and can differentiate the studied populations. AMOVA performed for these loci produced a significant difference (< 0.05) supporting the above-said result. AMOVA produced significant genetic difference based on ISSR data among the studied populations (PhiPT = 0.52, P = 0.001). AMOVA revealed that 53% of the total variability is due to among population genetic difference, while 47% is due to within population genetic variability. The results showed that both multilocus molecular markers and ITS sequences can differentiate Persian walnut populations. The studied populations differed genetically and showed isolation by distance (IBD). ITS sequence based MP and Bayesian phylogenetic trees revealed that Iranian walnut cultivars form a distinct clade separated from the cultivars studied from elsewhere. Almost all clades obtained have high bootstrap value. The results indicated that a combination of multilpcus and sequencing molecular markers can be used in genetic differentiation of Persian walnut.

Keywords: genetic diversity, population, molecular markers, genetic difference

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Authors: Yonas Shuke Kitawa

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Background: Although malaria incidence has substantially fallen sharply over the past few years, the rate of decline varies by district, time, and malaria type. Despite this turn-down, malaria remains a major public health threat in various districts of Ethiopia. Consequently, the present study is aimed at developing a predictive model that helps to identify the spatio-temporal variation in malaria risk by multiple plasmodium species. Methods: We propose a multivariate spatio-temporal Bayesian model to obtain a more coherent picture of the temporally varying spatial variation in disease risk. The spatial autocorrelation in such a data set is typically modeled by a set of random effects that assign a conditional autoregressive prior distribution. However, the autocorrelation considered in such cases depends on a binary neighborhood matrix specified through the border-sharing rule. Over here, we propose a graph-based optimization algorithm for estimating the neighborhood matrix that merely represents the spatial correlation by exploring the areal units as the vertices of a graph and the neighbor relations as the series of edges. Furthermore, we used aggregated malaria count in southern Ethiopia from August 2013 to May 2019. Results: We recognized that precipitation, temperature, and humidity are positively associated with the malaria threat in the area. On the other hand, enhanced vegetation index, nighttime light (NTL), and distance from coastal areas are negatively associated. Moreover, nonlinear relationships were observed between malaria incidence and precipitation, temperature, and NTL. Additionally, lagged effects of temperature and humidity have a significant effect on malaria risk by either species. More elevated risk of P. falciparum was observed following the rainy season, and unstable transmission of P. vivax was observed in the area. Finally, P. vivax risks are less sensitive to environmental factors than those of P. falciparum. Conclusion: The improved inference was gained by employing the proposed approach in comparison to the commonly used border-sharing rule. Additionally, different covariates are identified, including delayed effects, and elevated risks of either of the cases were observed in districts found in the central and western regions. As malaria transmission operates in a spatially continuous manner, a spatially continuous model should be employed when it is computationally feasible.

Keywords: disease mapping, MSTCAR, graph-based optimization algorithm, P. falciparum, P. vivax, waiting matrix

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Authors: Jianan Sun, Ziwen Ye

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Multidimensional computerized adaptive testing (MCAT) is a popular research topic in psychometrics. It is important for practitioners to clearly know the item-trait patterns of administered items when a test like MCAT is operated. Item-trait pattern recognition refers to detecting which latent traits in a psychological test are measured by each of the specified items. If the item-trait patterns of the replenished items in MCAT item pool are well detected, the interpretability of the items can be improved, which can further promote the abilities of the examinees who attending the MCAT to be accurately estimated. This research explores to solve the item-trait pattern recognition problem of the replenished items in MCAT item pool from the perspective of statistical variable selection. The popular multidimensional item response theory model, multidimensional two-parameter logistic model, is assumed to fit the response data of MCAT. The proposed method uses the least absolute shrinkage and selection operator (LASSO) to detect item-trait patterns of replenished items based on the essential information of item responses and ability estimates of examinees collected from a designed MCAT procedure. Several advantages of the proposed method are outlined. First, the proposed method does not strictly depend on the relative order between the replenished items and the selected operational items, so it allows the replenished items to be mixed into the operational items in reasonable order such as considering content constraints or other test requirements. Second, the LASSO used in this research improves the interpretability of the multidimensional replenished items in MCAT. Third, the proposed method can exert the advantage of shrinkage method idea for variable selection, so it can help to check item quality and key dimension features of replenished items and saves more costs of time and labors in response data collection than traditional factor analysis method. Moreover, the proposed method makes sure the dimensions of replenished items are recognized to be consistent with the dimensions of operational items in MCAT item pool. Simulation studies are conducted to investigate the performance of the proposed method under different conditions for varying dimensionality of item pool, latent trait correlation, item discrimination, test lengths and item selection criteria in MCAT. Results show that the proposed method can accurately detect the item-trait patterns of the replenished items in the two-dimensional and the three-dimensional item pool. Selecting enough operational items from the item pool consisting of high discriminating items by Bayesian A-optimality in MCAT can improve the recognition accuracy of item-trait patterns of replenished items for the proposed method. The pattern recognition accuracy for the conditions with correlated traits is better than those with independent traits especially for the item pool consisting of comparatively low discriminating items. To sum up, the proposed data-driven method based on the LASSO can accurately and efficiently detect the item-trait patterns of replenished items in MCAT.

Keywords: item-trait pattern recognition, least absolute shrinkage and selection operator, multidimensional computerized adaptive testing, variable selection

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Authors: Dahia Chibouti, Benoit Trouette, Eric Chenier

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With the development of micro-electro-mechanical systems (MEMS), understanding fluid flow and heat transfer at the micrometer scale is crucial. In the case where the flow characteristic length scale is narrowed to around ten times the mean free path of gas molecules, the classical fluid mechanics and energy equations are still valid in the bulk flow, but particular attention must be paid to the gas/solid interface boundary conditions. Indeed, in the vicinity of the wall, on a thickness of about the mean free path of the molecules, called the Knudsen layer, the gas molecules are no longer in local thermodynamic equilibrium. Therefore, macroscopic models based on the continuity of velocity, temperature and heat flux jump conditions must be applied at the fluid/solid interface to take this non-equilibrium into account. Although these macroscopic models are widely used, the assumptions on which they depend are not necessarily verified in realistic cases. In order to get rid of these assumptions, simulations at the molecular scale are carried out to study how molecule interaction with walls can change the fluid flow and heat transfers at the vicinity of the walls. The developed approach is based on a kind of heterogeneous multi-scale method: micro-domains overlap the continuous domain, and coupling is carried out through exchanges of information between both the molecular and the continuum approaches. In practice, molecular dynamics describes the fluid flow and heat transfers in micro-domains while the Navier-Stokes and energy equations are used at larger scales. In this framework, two kinds of micro-simulation are performed: i) in bulk, to obtain the thermo-physical properties (viscosity, conductivity, ...) as well as the equation of state of the fluid, ii) close to the walls to identify the relationships between the slip velocity and the shear stress or between the temperature jump and the normal temperature gradient. The coupling strategy relies on an implicit formulation of the quantities extracted from micro-domains. Indeed, using the results of the molecular simulations, a Bayesian regression is performed in order to build continuous laws giving both the behavior of the physical properties, the equation of state and the slip relationships, as well as their uncertainties. These latter allow to set up a learning strategy to optimize the number of micro simulations. In the present contribution, the first results regarding this coupling associated with the learning strategy are illustrated through parametric studies of convergence criteria, choice of basis functions and noise of input data. Anisothermic flows of a Lennard Jones fluid in micro-channels are finally presented.

Keywords: multi-scale, microfluidics, micro-channel, hybrid approach, coupling

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Authors: Alexandru-Ion Marinescu

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There exist a plethora of methods in the scientific literature which tackle the well-established task of credit score evaluation. In its most abstract form, a credit scoring algorithm takes as input several credit applicant properties, such as age, marital status, employment status, loan duration, etc. and must output a binary response variable (i.e. “GOOD” or “BAD”) stating whether the client is susceptible to payment return delays. Data imbalance is a common occurrence among financial institution databases, with the majority being classified as “GOOD” clients (clients that respect the loan return calendar) alongside a small percentage of “BAD” clients. But it is the “BAD” clients we are interested in since accurately predicting their behavior is crucial in preventing unwanted loss for loan providers. We add to this whole context the constraint that the algorithm must yield an actual, tractable mathematical formula, which is friendlier towards financial analysts. To this end, we have turned to genetic algorithms and genetic programming, aiming to evolve actual mathematical expressions using specially tailored mutation and crossover operators. As far as data representation is concerned, we employ a very flexible mechanism – LINQ expression trees, readily available in the C# programming language, enabling us to construct executable pieces of code at runtime. As the title implies, they model trees, with intermediate nodes being operators (addition, subtraction, multiplication, division) or mathematical functions (sin, cos, abs, round, etc.) and leaf nodes storing either constants or variables. There is a one-to-one correspondence between the client properties and the formula variables. The mutation and crossover operators work on a flattened version of the tree, obtained via a pre-order traversal. A consequence of our chosen technique is that we can identify and discard client properties which do not take part in the final score evaluation, effectively acting as a dimensionality reduction scheme. We compare ourselves with state of the art approaches, such as support vector machines, Bayesian networks, and extreme learning machines, to name a few. The data sets we benchmark against amount to a total of 8, of which we mention the well-known Australian credit and German credit data sets, and the performance indicators are the following: percentage correctly classified, area under curve, partial Gini index, H-measure, Brier score and Kolmogorov-Smirnov statistic, respectively. Finally, we obtain encouraging results, which, although placing us in the lower half of the hierarchy, drive us to further refine the algorithm.

Keywords: expression trees, financial credit scoring, genetic algorithm, genetic programming, symbolic evolution

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Authors: Lydia Tan, Philippe Lemey, Lieselot Houspie, Marco Viveen, Darren Martin, Frank Coenjaerts

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Introduction: Human respiratory syncytial virus (hRSV) is the leading cause of severe respiratory tract infections in infants under the age of two. Genomic substitutions and related evolutionary dynamics of hRSV are of great influence on virus transmission behavior. The evolutionary patterns formed are due to a precarious interplay between the host immune response and RSV, thereby selecting the most viable and less immunogenic strains. Studying genomic profiles can teach us which genes and consequent proteins play an important role in RSV survival and transmission dynamics. Study design: In this study, genetic diversity and evolutionary rate analysis were conducted on 36 RSV subgroup B whole genome sequences and 37 subgroup A genome sequences. Clinical RSV isolates were obtained from nasopharyngeal aspirates and swabs of children between 2 weeks and 5 years old of age. These strains, collected during epidemic seasons from 2001 to 2011 in the Netherlands and Belgium by either conventional or 454-sequencing. Sequences were analyzed for genetic diversity, recombination events, synonymous/non-synonymous substitution ratios, epistasis, and translational consequences of mutations were mapped to known 3D protein structures. We used Bayesian statistical inference to estimate the rate of RSV genome evolution and the rate of variability across the genome. Results: The A and B profiles were described in detail and compared to each other. Overall, the majority of the whole RSV genome is highly conserved among all strains. The attachment protein G was the most variable protein and its gene had, similar to the non-coding regions in RSV, more elevated (two-fold) substitution rates than other genes. In addition, the G gene has been identified as the major target for diversifying selection. Overall, less gene and protein variability was found within RSV-B compared to RSV-A and most protein variation between the subgroups was found in the F, G, SH and M2-2 proteins. For the F protein mutations and correlated amino acid changes are largely located in the F2 ligand-binding domain. The small hydrophobic phosphoprotein and nucleoprotein are the most conserved proteins. The evolutionary rates were similar in both subgroups (A: 6.47E-04, B: 7.76E-04 substitution/site/yr), but estimates of the time to the most recent common ancestor were much lower for RSV-B (B: 19, A: 46.8 yrs), indicating that there is more turnover in this subgroup. Conclusion: This study provides a detailed description of whole RSV genome mutations, the effect on translation products and the first estimate of the RSV genome evolution tempo. The immunogenic G protein seems to require high substitution rates in order to select less immunogenic strains and other conserved proteins are most likely essential to preserve RSV viability. The resulting G gene variability makes its protein a less interesting target for RSV intervention methods. The more conserved RSV F protein with less antigenic epitope shedding is, therefore, more suitable for developing therapeutic strategies or vaccines.

Keywords: drug target selection, epidemiology, respiratory syncytial virus, RSV

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Authors: Jean-Philippe Amat, Timothée Vergne, Aymeric Hans, Bénédicte Ferry, Pascal Hendrikx, Jackie Tapprest, Barbara Dufour, Agnès Leblond

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The surveillance of infectious diseases is necessary to describe their occurrence and help the planning, implementation and evaluation of risk mitigation activities. However, the exact number of detected cases may remain unknown whether surveillance is based on serological tests because identifying seroconversion may be difficult. Moreover, incomplete detection of cases or outbreaks is a recurrent issue in the field of disease surveillance. This study addresses these two issues. Using a viral animal disease as an example (equine viral arteritis), the goals were to establish suitable rules for identifying seroconversion in order to estimate the number of cases and outbreaks detected by a surveillance system in France between 2006 and 2013, and to assess the sensitivity of this system by estimating the total number of outbreaks that occurred during this period (including unreported outbreaks) using a capture-recapture model. Data from horses which exhibited at least one positive result in serology using viral neutralization test between 2006 and 2013 were used for analysis (n=1,645). Data consisted of the annual antibody titers and the location of the subjects (towns). A consensus among multidisciplinary experts (specialists in the disease and its laboratory diagnosis, epidemiologists) was reached to consider seroconversion as a change in antibody titer from negative to at least 32 or as a three-fold or greater increase. The number of seroconversions was counted for each town and modeled using a unilist zero-truncated binomial (ZTB) capture-recapture model with R software. The binomial denominator was the number of horses tested in each infected town. Using the defined rules, 239 cases located in 177 towns (outbreaks) were identified from 2006 to 2013. Subsequently, the sensitivity of the surveillance system was estimated as the ratio of the number of detected outbreaks to the total number of outbreaks that occurred (including unreported outbreaks) estimated using the ZTB model. The total number of outbreaks was estimated at 215 (95% credible interval CrI95%: 195-249) and the surveillance sensitivity at 82% (CrI95%: 71-91). The rules proposed for identifying seroconversion may serve future research. Such rules, adjusted to the local environment, could conceivably be applied in other countries with surveillance programs dedicated to this disease. More generally, defining ad hoc algorithms for interpreting the antibody titer could be useful regarding other human and animal diseases and zoonosis when there is a lack of accurate information in the literature about the serological response in naturally infected subjects. This study shows how capture-recapture methods may help to estimate the sensitivity of an imperfect surveillance system and to valorize surveillance data. The sensitivity of the surveillance system of equine viral arteritis is relatively high and supports its relevance to prevent the disease spreading.

Keywords: Bayesian inference, capture-recapture, epidemiology, equine viral arteritis, infectious disease, seroconversion, surveillance

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Authors: Samia Elfekih, Wee Tek Tay, Karl Gordon, Paul De Barro

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Invasive species represent an increasing threat to food biosecurity, causing significant economic losses in agricultural systems. An example is the sweet potato whitefly, Bemisia tabaci, which is a complex of morphologically indistinguishable species causing average annual global damage estimated at US$2.4 billion. The Bemisia complex represents an interesting model for evolutionary studies because of their extensive distribution and potential for invasiveness and population expansion. Within this complex, two species, Middle East-Asia Minor 1 (MEAM1) and Mediterranean (MED) have invaded well beyond their home ranges whereas others, such as Indian Ocean (IO) and Australia (AUS), have not. In order to understand why some Bemisia species have become invasive, genome-wide sequence scans were used to estimate population dynamics over time and relate these to climate. The Bayesian Skyline Plot (BSP) method as implemented in BEAST was used to infer the historical effective population size. In order to overcome sampling bias, the populations were combined based on geographical origin. The datasets used for this particular analysis are genome-wide SNPs (single nucleotide polymorphisms) called separately in each of the following groups: Sub-Saharan Africa (Burkina Faso), Europe (Spain, France, Greece and Croatia), USA (Arizona), Mediterranean-Middle East (Israel, Italy), Middle East-Central Asia (Turkmenistan, Iran) and Reunion Island. The non-invasive ‘AUS’ species endemic to Australia was used as an outgroup. The main findings of this study show that the BSP for the Sub-Saharan African MED population is different from that observed in MED populations from the Mediterranean Basin, suggesting evolution under a different set of environmental conditions. For MED, the effective size of the African (Burkina Faso) population showed a rapid expansion ≈250,000-310,000 years ago (YA), preceded by a period of slower growth. The European MED populations (i.e., Spain, France, Croatia, and Greece) showed a single burst of expansion at ≈160,000-200,000 YA. The MEAM1 populations from Israel and Italy and the ones from Iran and Turkmenistan are similar as they both show the earlier expansion at ≈250,000-300,000 YA. The single IO population lacked the latter expansion but had the earlier one. This pattern is shared with the Sub-Saharan African (Burkina Faso) MED, suggesting IO also faced a similar history of environmental change, which seems plausible given their relatively close geographical distributions. In conclusion, populations within the invasive species MED and MEAM1 exhibited signatures of population expansion lacking in non-invasive species (IO and AUS) during the Pleistocene, a geological epoch marked by repeated climatic oscillations with cycles of glacial and interglacial periods. These expansions strongly suggested the potential of some Bemisia species’ genomes to affect their adaptability and invasiveness.

Keywords: whitefly, RADseq, invasive species, SNP, climate change

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Authors: Vitor M. Vilas Boas, Cleison D. Silva, Gustavo S. Mafra, Alexandre Trofino Neto

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Motor imagery (MI) based brain-computer interfaces (BCI) uses event-related (de)synchronization (ERS/ ERD), typically recorded using electroencephalography (EEG), to translate brain electrical activity into control commands. To mitigate undesirable artifacts and noise measurements on EEG signals, methods based on band-pass filters defined by a specific frequency band (i.e., 8 – 30Hz), such as the Infinity Impulse Response (IIR) filters, are typically used. Spatial techniques, such as Common Spatial Patterns (CSP), are also used to estimate the variations of the filtered signal and extract features that define the imagined motion. The CSP effectiveness depends on the subject's discriminative frequency, and approaches based on the decomposition of the band of interest into sub-bands with smaller frequency ranges (SBCSP) have been suggested to EEG signals classification. However, despite providing good results, the SBCSP approach generally increases the computational cost of the filtering step in IM-based BCI systems. This paper proposes the use of the Fast Fourier Transform (FFT) algorithm in the IM-based BCI filtering stage that implements SBCSP. The goal is to apply the FFT algorithm to reduce the computational cost of the processing step of these systems and to make them more efficient without compromising classification accuracy. The proposal is based on the representation of EEG signals in a matrix of coefficients resulting from the frequency decomposition performed by the FFT, which is then submitted to the SBCSP process. The structure of the SBCSP contemplates dividing the band of interest, initially defined between 0 and 40Hz, into a set of 33 sub-bands spanning specific frequency bands which are processed in parallel each by a CSP filter and an LDA classifier. A Bayesian meta-classifier is then used to represent the LDA outputs of each sub-band as scores and organize them into a single vector, and then used as a training vector of an SVM global classifier. Initially, the public EEG data set IIa of the BCI Competition IV is used to validate the approach. The first contribution of the proposed method is that, in addition to being more compact, because it has a 68% smaller dimension than the original signal, the resulting FFT matrix maintains the signal information relevant to class discrimination. In addition, the results showed an average reduction of 31.6% in the computational cost in relation to the application of filtering methods based on IIR filters, suggesting FFT efficiency when applied in the filtering step. Finally, the frequency decomposition approach improves the overall system classification rate significantly compared to the commonly used filtering, going from 73.7% using IIR to 84.2% using FFT. The accuracy improvement above 10% and the computational cost reduction denote the potential of FFT in EEG signal filtering applied to the context of IM-based BCI implementing SBCSP. Tests with other data sets are currently being performed to reinforce such conclusions.

Keywords: brain-computer interfaces, fast Fourier transform algorithm, motor imagery, sub-band common spatial patterns

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Authors: Vikas Kumar, Kailash Chandra, Kaomud Tyagi

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The insect order Thysanoptera includes small insects commonly called thrips. As insect vectors, only thrips are capable of Tospoviruses transmission (genus Tospovirus, family Bunyaviridae) affecting various crops. Currently, fifteen species of subfamily Thripinae (Thripidae) have been reported as vectors for tospoviruses. Frankliniella schultzei, which is reported as act as a vector for at least five tospovirses, have been suspected to be a species complex with more than one species. It is one of the historical unresolved issues where, two species namely, F. schultzei Trybom and F. sulphurea Schmutz were erected from South Africa and Srilanaka respectively. These two species were considered to be valid until 1968 when sulphurea was treated as colour morph (pale form) and synonymised under schultzei (dark form) However, these two have been considered as valid species by some of the thrips workers. Parallel studies have indicated that brown form of schultzei is a vector for tospoviruses while yellow form is a non-vector. However, recent studies have shown that yellow populations have also been documented as vectors. In view of all these facts, it is highly important to have a clear understanding whether these colour forms represent true species or merely different populations with different vector carrying capacities and whether there is some hidden diversity in 'Frankliniella schultzei species complex'. In this study, we aim to study the 'Frankliniella schultzei species complex' with molecular spectacles with DNA data from India and Australia and Africa. A total of fifty-five specimens was collected from diverse locations in India and Australia. We generated molecular data using partial fragments of mitochondrial cytochrome c oxidase I gene (mtCOI) and 28S rRNA gene. For COI dataset, there were seventy-four sequences, out of which data on fifty-five was generated in the current study and others were retrieved from NCBI. All the four different tree construction methods: neighbor-joining, maximum parsimony, maximum likelihood and Bayesian analysis, yielded the same tree topology and produced five cryptic species with high genetic divergence. For, rDNA, there were forty-five sequences, out of which data on thirty-nine was generated in the current study and others were retrieved from NCBI. The four tree building methods yielded four cryptic species with high bootstrap support value/posterior probability. Here we could not retrieve one cryptic species from South Africa as we could not generate data on rDNA from South Africa and sequence for rDNA from African region were not available in the database. The results of multiple species delimitation methods (barcode index numbers, automatic barcode gap discovery, general mixed Yule-coalescent, and Poisson-tree-processes) also supported the phylogenetic data and produced 5 and 4 Molecular Operational Taxonomic Units (MOTUs) for mtCOI and 28S dataset respectively. These results of our study indicate the likelihood that F. sulphurea may be a valid species, however, more morphological and molecular data is required on specimens from type localities of these two species and comparison with type specimens.

Keywords: DNA barcoding, species complex, thrips, species delimitation

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Authors: Hsiang-Yu Yuan, Marc Baguelin, Kin O. Kwok, Nimalan Arinaminpathy, Edwin Leeuwen, Steven Riley

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Traditional syndromic surveillance for influenza has substantial public health value in characterizing epidemics. Because the relationship between syndromic incidence and the true infection events can vary from one population to another and from one year to another, recent studies rely on combining serological test results with syndromic data from traditional surveillance into epidemic models to make inference on epidemiological processes of influenza. However, despite the widespread availability of serological data, epidemic models have thus far not explicitly represented antibody titre levels and their correspondence with immunity. Most studies use dichotomized data with a threshold (Typically, a titre of 1:40 was used) to define individuals as likely recently infected and likely immune and further estimate the cumulative incidence. Underestimation of Influenza attack rate could be resulted from the dichotomized data. In order to improve the use of serosurveillance data, here, a refinement of the concept of the stratified immunity within an epidemic model for influenza transmission was proposed, such that all individual antibody titre levels were enumerated explicitly and mapped onto a variable scale of susceptibility in different age groups. Haemagglutination inhibition titres from 523 individuals and 465 individuals during pre- and post-pandemic phase of the 2009 pandemic in Hong Kong were collected. The model was fitted to serological data in age-structured population using Bayesian framework and was able to reproduce key features of the epidemics. The effects of age-specific antibody boosting and protection were explored in greater detail. RB was defined to be the effective reproductive number in the presence of stratified immunity and its temporal dynamics was compared to the traditional epidemic model using use dichotomized seropositivity data. Deviance Information Criterion (DIC) was used to measure the fitness of the model to serological data with different mechanisms of the serological response. The results demonstrated that the differential antibody response with age was present (ΔDIC = -7.0). The age-specific mixing patterns with children specific transmissibility, rather than pre-existing immunity, was most likely to explain the high serological attack rates in children and low serological attack rates in elderly (ΔDIC = -38.5). Our results suggested that the disease dynamics and herd immunity of a population could be described more accurately for influenza when the distribution of immunity was explicitly represented, rather than relying only on the dichotomous states 'susceptible' and 'immune' defined by the threshold titre (1:40) (ΔDIC = -11.5). During the outbreak, RB declined slowly from 1.22[1.16-1.28] in the first four months after 1st May. RB dropped rapidly below to 1 during September and October, which was consistent to the observed epidemic peak time in the late September. One of the most important challenges for infectious disease control is to monitor disease transmissibility in real time with statistics such as the effective reproduction number. Once early estimates of antibody boosting and protection are obtained, disease dynamics can be reconstructed, which are valuable for infectious disease prevention and control.

Keywords: effective reproductive number, epidemic model, influenza epidemic dynamics, stratified immunity

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Authors: T. C. C. Soo, S. Bhassu

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Unlike the common presence of both innate and adaptive immunity in vertebrates, crustaceans, in particular, shrimps, have been discovered to possess only innate immunity. This further emphasizes the importance of innate immunity within shrimps in pathogenic resistance. Under the study of pathogenic immune challenge, different shrimp species actually exhibit varying degrees of immune resistance towards the same pathogen. Furthermore, even within the same shrimp species, different batches of challenged shrimps can have different strengths of immune defence. Several important pathways are activated within shrimps during pathogenic infection. One of them is JAK-STAT pathway that is activated during bacterial, viral and fungal infections by which STAT(Signal Transducer and Activator of Transcription) gene is the core element of the pathway. Based on theory of Central Dogma, the genomic information is transmitted in the order of DNA, RNA and protein. This study is focused in uncovering the important evolutionary patterns present within the DNA (non-coding region) and RNA (coding region). The three shrimp species involved are Macrobrachium rosenbergii, Penaeus monodon and Litopenaeus vannamei which all possess commercial significance. The shrimp species were challenged with a famous penaeid shrimp virus called white spot syndrome virus (WSSV) which can cause serious lethality. Tissue samples were collected during time intervals of 0h, 3h, 6h, 12h, 24h, 36h and 48h. The DNA and RNA samples were then extracted using conventional kits from the hepatopancreas tissue samples. PCR technique together with designed STAT gene conserved primers were utilized for identification of the STAT coding sequences using RNA-converted cDNA samples and subsequent characterization using various bioinformatics approaches including Ramachandran plot, ProtParam and SWISS-MODEL. The varying levels of immune STAT gene activation for the three shrimp species during WSSV infection were confirmed using qRT-PCR technique. For one sample, three biological replicates with three technical replicates each were used for qRT-PCR. On the other hand, DNA samples were important for uncovering the structural variations within the genomic region of STAT gene which would greatly assist in understanding the STAT protein functional variations. The partially-overlapping primers technique was used for the genomic region sequencing. The evolutionary inferences and event predictions were then conducted through the Bayesian Inference method using all the acquired coding and non-coding sequences. This was supplemented by the construction of conventional phylogenetic trees using Maximum likelihood method. The results showed that adaptive evolution caused STAT gene sequence mutations between different shrimp species which led to evolutionary divergence event. Subsequently, the divergent sites were correlated to the differing expressions of STAT gene. Ultimately, this study assists in knowing the shrimp species innate immune variability and selection of disease resistant shrimps for breeding purpose. The deeper understanding of STAT gene evolution from the perspective of both purifying and adaptive approaches not only can provide better immunological insight among shrimp species, but also can be used as a good reference for immunological studies in humans or other model organisms.

Keywords: gene evolution, JAK-STAT pathway, immunology, STAT gene

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Authors: André Python

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To this day, terrorism persists as a worldwide threat, exemplified by the recent deadly attacks in January 2015 in Paris and the ongoing massacres perpetrated by ISIS in Iraq and Syria. In response to this threat, states deploy various counterterrorism measures, the cost of which could be reduced through effective preventive measures. In order to increase the efficiency of preventive measures, policy-makers may benefit from accurate predictive models that are able to capture the complex spatial dynamics of terrorism occurring at a local scale. Despite empirical research carried out at country-level that has confirmed theories explaining the diffusion processes of terrorism across space and time, scholars have failed to assess diffusion’s theories on a local scale. Moreover, since scholars have not made the most of recent statistical modelling approaches, they have been unable to build up predictive models accurate in both space and time. In an effort to address these shortcomings, this research suggests a novel approach to systematically assess the theories of terrorism’s diffusion on a local scale and provide a predictive model of the local spatial dynamics of terrorism worldwide. With a focus on the lethal terrorist events that occurred after 9/11, this paper addresses the following question: why and how does lethal terrorism diffuse in space and time? Based on geolocalised data on worldwide terrorist attacks and covariates gathered from 2002 to 2013, a binomial spatio-temporal point process is used to model the probability of terrorist attacks on a sphere (the world), the surface of which is discretised in the form of Delaunay triangles and refined in areas of specific interest. Within a Bayesian framework, the model is fitted through an integrated nested Laplace approximation - a recent fitting approach that computes fast and accurate estimates of posterior marginals. Hence, for each location in the world, the model provides a probability of encountering a lethal terrorist attack and measures of volatility, which inform on the model’s predictability. Diffusion processes are visualised through interactive maps that highlight space-time variations in the probability and volatility of encountering a lethal attack from 2002 to 2013. Based on the previous twelve years of observation, the location and lethality of terrorist events in 2014 are statistically accurately predicted. Throughout the global scope of this research, local diffusion processes such as escalation and relocation are systematically examined: the former process describes an expansion from high concentration areas of lethal terrorist events (hotspots) to neighbouring areas, while the latter is characterised by changes in the location of hotspots. By controlling for the effect of geographical, economical and demographic variables, the results of the model suggest that the diffusion processes of lethal terrorism are jointly driven by contagious and non-contagious factors that operate on a local scale – as predicted by theories of diffusion. Moreover, by providing a quantitative measure of predictability, the model prevents policy-makers from making decisions based on highly uncertain predictions. Ultimately, this research may provide important complementary tools to enhance the efficiency of policies that aim to prevent and combat terrorism.

Keywords: diffusion process, terrorism, spatial dynamics, spatio-temporal modeling

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