Noisy Profiles Research Articles

P-519 Relationship between the quality control parameters in PGT-A results by NGS with the chromosomal mosaicism diagnosis in trophoectoderm biopsies

Abstract Study question Are quality control (QC) parameters in NGS results related to mosaicism rate in trophoectoderm samples? Summary answer A high number of filtered reads in PGT-A results correlates with a higher mosaicism rate. But the overall noise does not influence the mosaicism rate. What is known already The implementation of NGS have led to increased reporting of mosaicism. There is intense research on the biological mechanisms behind mosaicism, but also on the technical factors that might be influencing in its diagnosis. Low quality samples and DNA amplification artefacts lead to an increase in overall noise after sample analysis. The Derivative Log Ratio (DLR) quality control parameter in sequencing results measures the overall noise present in a sample. High DLR values indicate noisy profiles. Additionally, insufficient numbers of sequencing reads will result in noisy profiles and false copy number assignments. Study design, size, duration A retrospective analysis of PGT-A results, corresponding to trophoectoderm biopsies from embryos on day 5, 6 or 7 of development, was performed (February 2017- November 2021). After the quality analysis, 5245 samples that reached the optimum QC measures were included (samples with DLR < 0.4 and number of filtered reads > 250.000). Participants/materials, setting, methods PGT-A was carried out with the VeriSeq kit (Illumina), after genome amplification with the Picoplex technique. Sequencing data was analyzed with BlueFuse Multi software (Illumina). Data analysis was performed using SPSSv20.0. An embryo was designated as mosaic when the percentage of aneuploidy for at least one chromosome was between 25 and 50%. For this study, we considered euploid-aneuploid and aneuploid-aneuploid mosaic embryos. Main results and the role of chance Considering the 5245 samples included in the analysis, the number of embryos carrying chromosomal mosaicism was 960, which corresponds to 18.3%. To analyze whether the percentage of mosaic embryos varied according to the DRL, we used a logistic regression analysis, introducing maternal and paternal age, embryo quality, and biopsy day as confounding variables, and categorized the DLR using as a point cut the median (0.19). There were no significant differences in the percentage of embryos carrying mosaicism between the group of higher DLR (≥0.19) compared to the group of lower DLR (<0.19) (18.7% vs 18.0%; p = 0.278). On the other hand, to study the relationship between mosaicism and the number of filtered reads obtained in the sequencing analysis, we performed the same analysis using the median of filtered reads (556.688) as cut point. The samples with a number of filtered reads higher than the median had a higher rate of mosaicism (19.3% vs 17.4%, p = 0.041). Moreover, we analyse the data according to the type of mosaicism (segmental or whole chromosome) and we did not observe any difference neither for the DLR nor for the reads. Limitations, reasons for caution The main limitation of this study compared with other studies is the different criteria in the mosaicism diagnosis between the different laboratories. Moreover, we are not able to identify if worse QC are due to issues with the biopsy procedure, sample quality, DNA amplification or library preparation. Wider implications of the findings The overall noise in PGT-A results doesn't seem to influence the mosaicism rate. However, increased mosaicism rate is observed in samples with high number of filtered reads. This finding suggests that too many cells may lead to amplification saturation and underestimation of the relative quantity of DNA. Trial registration number Not applicable

AutoGeneS: Automatic gene selection using multi-objective optimization for RNA-seq deconvolution.

Knowing cell-type proportions in a tissue is very important to identify which cells or cell types are targeted by a disease or perturbation. Hence, several deconvolution methods have been proposed to infer cell-type proportions from bulk RNA samples. Their performance with noisy reference profiles and closely correlated cell types highly depends on the set of genes undergoing deconvolution. In this work, we introduce AutoGeneS, a platform that automatically extracts discriminative genes and reveals the cellular heterogeneity of bulk RNA samples. AutoGeneS requires no prior knowledge about marker genes and selects genes by simultaneously optimizing multiple criteria: minimizing the correlation and maximizing the distance between cell types. AutoGeneS can be applied to reference profiles from various sources like single-cell experiments or sorted cell populations. Ground truth cell proportions analyzed by flow cytometry confirmed the accuracy of AutoGeneS in identifying cell-type proportions. AutoGeneS is available for use via a standalone Python package (https://github.com/theislab/AutoGeneS).

Evaluation of KDP Estimation Algorithm Performance in Rain Using a Known-Truth Framework

AbstractAccurate estimation of specific differential phase (KDP) is necessary for rain rate estimation, attenuation correction, and hydrometeor classification algorithms. There are numerous published methods to process polarimetric radar observations of propagation differential phase shift (ΦDP) and estimate KDP, but the corresponding KDP estimate uncertainty is unquantified. This study provides guidance on how commonly used KDP estimation algorithms perform in various environments. We create numerous synthetic (“true”) KDP profiles, integrate over them to obtain “smoothed” ΦDP, and then add noise typical of S-band operational weather radar measurements. Each algorithm is applied to our noisy ΦDP profiles and compared to the true KDP profile such that the errors and uncertainty are quantified. The synthetic KDP profiles are Gaussian in shape, which allows systematic variations in their magnitude and width to determine how each algorithm performs in smooth, slowly changing KDP profiles, as well as steep profiles. Results demonstrate that algorithm performance is dependent on the ΦDP field received. These results are further supported by an error analysis of each algorithm for two more complicated synthetic KDP profiles. Some KDP algorithms allow users to change various tuning parameters; a subset of these tuning parameters is tested to provide guidance on how changing these parameters impacts algorithm performance. We then provide evidence that our known-truth framework provides insight into algorithm performance in observed data through two case studies.

BnpC: Bayesian non-parametric clustering of single-cell mutation profiles.

MotivationThe high resolution of single-cell DNA sequencing (scDNA-seq) offers great potential to resolve intratumor heterogeneity (ITH) by distinguishing clonal populations based on their mutation profiles. However, the increasing size of scDNA-seq datasets and technical limitations, such as high error rates and a large proportion of missing values, complicate this task and limit the applicability of existing methods.ResultsHere, we introduce BnpC, a novel non-parametric method to cluster individual cells into clones and infer their genotypes based on their noisy mutation profiles. We benchmarked our method comprehensively against state-of-the-art methods on simulated data using various data sizes, and applied it to three cancer scDNA-seq datasets. On simulated data, BnpC compared favorably against current methods in terms of accuracy, runtime and scalability. Its inferred genotypes were the most accurate, especially on highly heterogeneous data, and it was the only method able to run and produce results on datasets with 5000 cells. On tumor scDNA-seq data, BnpC was able to identify clonal populations missed by the original cluster analysis but supported by Supplementary Experimental Data. With ever growing scDNA-seq datasets, scalable and accurate methods such as BnpC will become increasingly relevant, not only to resolve ITH but also as a preprocessing step to reduce data size.Availability and implementationBnpC is freely available under MIT license at https://github.com/cbg-ethz/BnpC.Supplementary information Supplementary data are available at Bioinformatics online.

Tracer kinetic models as temporal constraints during brain tumor DCE-MRI reconstruction.

PurposeTo apply tracer kinetic models as temporal constraints during reconstruction of under‐sampled brain tumor dynamic contrast enhanced (DCE) magnetic resonance imaging (MRI).MethodsA library of concentration vs time profiles is simulated for a range of physiological kinetic parameters. The library is reduced to a dictionary of temporal bases, where each profile is approximated by a sparse linear combination of the bases. Image reconstruction is formulated as estimation of concentration profiles and sparse model coefficients with a fixed sparsity level. Simulations are performed to evaluate modeling error, and error statistics in kinetic parameter estimation in presence of noise. Retrospective under‐sampling experiments are performed on a brain tumor DCE digital reference object (DRO), and 12 brain tumor in‐vivo 3T datasets. The performances of the proposed under‐sampled reconstruction scheme and an existing compressed sensing‐based temporal finite‐difference (tFD) under‐sampled reconstruction were compared against the fully sampled inverse Fourier Transform‐based reconstruction.ResultsSimulations demonstrate that sparsity levels of 2 and 3 model the library profiles from the Patlak and extended Tofts‐Kety (ETK) models, respectively. Noise sensitivity analysis showed equivalent kinetic parameter estimation error statistics from noisy concentration profiles, and model approximated profiles. DRO‐based experiments showed good fidelity in recovery of kinetic maps from 20‐fold under‐sampled data. In‐vivo experiments demonstrated reduced bias and uncertainty in kinetic mapping with the proposed approach compared to tFD at under‐sampled reduction factors >= 20.ConclusionsTracer kinetic models can be applied as temporal constraints during brain tumor DCE‐MRI reconstruction. The proposed under‐sampled scheme resulted in model parameter estimates less biased with respect to conventional fully sampled DCE MRI reconstructions and parameter estimation. The approach is flexible, can use nonlinear kinetic models, and does not require tuning of regularization parameters.

LA-ICP-MS trace element analysis of arsenopyrite from the Samgwang gold deposit, South Korea, and its genetic implications

The Samgwang deposit, previously classified as an orogenic gold deposit, consists of several structurally controlled auriferous quartz veins hosted by metasedimentary rocks of the Precambrian Gyeonggi massif, South Korea. The gold at Samgwang occurs as electrum commonly associated with arsenopyrite. Laser ablation-inductively coupled plasma-mass spectrometry (LA-ICP-MS), coupled with ore microscopy, was conducted on Au and trace elements distributed in arsenopyrite grains contained in quartz vein and wall rock samples. Resulting profiles for Au, Co, Ni, and Sb were relatively flat and showed little variability, indicating that the elements were relatively homogeneously distributed and exchanged via substitution in arsenopyrite, while variability and noisy depth profiles inferred that Pb was present as tiny inclusions or discrete particles. Furthermore, measured gold concentrations were typically higher in arsenopyrite grains from laminated quartz veins (avg. 2.07 ppm) than in grains from massive quartz veins (avg. 0.26 ppm) and wall rock samples (avg. 0.33 ppm). In the case of wall rock and massive quartz vein samples, arsenopyrite grains of euhedral shape illustrate an element distribution pattern whereby Au concentrations tend to decrease towards the rims of the analyzed grains. In contrast, the rims of arsenopyrite grains in laminated quartz vein samples recorded much higher Au concentrations of up to 20.1 ppm, with increasing Pb, Bi, and Ag, particularly within domains of fractured or recrystallized arsenopyrite grains. The newly acquired LA-ICP-MS data, along with textural evidence, may be interpreted in terms of the release and remobilization of invisible gold that was originally locked up in the arsenopyrite. This release is linked to late deformation and hydrothermal event during which the remobilized invisible gold was redeposited as electrum. In addition, there is evidence for the introduction of additional gold and other precious and base metals by the late-stage hydrothermal fluids. Based on the above and in contrast to previous genetic models, we propose a more complex metallogenic concept for Samgwang in which the economically important gold enrichment process was genetically related to intrusive activity during the waning stages of Jurassic to Early Cretaceous Daebo orogenesis.

Processes Associated with Convection Initiation in the North American Mesoscale Forecast System, Version 3 (NAMv3)

Abstract In support of the Next Generation Global Prediction System (NGGPS) project, processes leading to convection initiation in the North American Mesoscale Forecast System, version 3 (NAMv3) are explored. Two severe weather outbreaks—occurring over the southeastern United States on 28 April 2014 and the central Great Plains on 6 May 2015—are forecast retrospectively using the NAMv3 CONUS (4 km) and Fire Weather (1.33 km) nests, each with 5-min output. Points of convection initiation are identified, and patterns leading to convection initiation in the model forecasts are determined. Results indicate that in the 30 min preceding convection initiation at a grid point, upward motion at low levels of the atmosphere enables a parcel to rise to its level of free convection, above which it is accelerated by the buoyancy force. A moist absolutely unstable layer (MAUL) typically is produced at the top of the updraft. However, when strong updrafts are collocated with large vertical gradients of potential temperature and moisture, noisy vertical profiles of temperature, moisture, and hydrometeor concentration develop beneath the rising MAUL. The noisy profiles found in this study are qualitatively similar to those that resulted in NAMv3 failures during simulations of Hurricane Joaquin in 2015. The CM1 cloud model is used to reproduce these noisy profiles, and results indicate that the noise can be mitigated by including explicit vertical diffusion in the model. Left unchecked, the noisy profiles are shown to impact convective storm features such as cold pools, precipitation, updraft helicity intensity and tracks, and the initiation of spurious convection.

The potential of many-line inversions of photospheric spectropolarimetric data in the visible and near UV

Our knowledge of the lower solar atmosphere is mainly obtained from spectropolarimetric observations, which are often carried out in the red or infrared spectral range and almost always cover only a single or a few spectral lines. Here we compare the quality of Stokes inversions of only a few spectral lines with many-line inversions. In connection with this, we have also investigated the feasibility of spectropolarimetry in the short-wavelength range, 3000 Å−4300 Å, where the line density but also the photon noise are considerably higher than in the red, so that many-line inversions could be particularly attractive in that wavelength range. This is also timely because this wavelength range will be the focus of a new spectropolarimeter in the third science flight of the balloon-borne solar observatory SUNRISE. For an ensemble of state-of-the-art magneto-hydrodynamical atmospheres we synthesize exemplarily spectral regions around 3140 Å (containing 371 identified spectral lines), around 4080 Å (328 lines), and around 6302 Å (110 lines). The spectral coverage is chosen such that at a spectral resolving power of 150 000 the spectra can be recorded by a 2K × 2K detector. The synthetic Stokes profiles are degraded with a typical photon noise and afterward inverted. The atmospheric parameters of the inversion of noisy profiles are compared with the inversion of noise-free spectra. We find that significantly more information can be obtained from many-line inversions than from a traditionally used inversion of only a few spectral lines. We further find that information on the upper photosphere can be significantly more reliably obtained at short wavelengths. In the mid and lower photosphere, the many-line approach at 4080 Å provides equally good results as the many-line approach at 6302 Å for the magnetic field strength and the line-of-sight (LOS) velocity, while the temperature determination is even more precise by a factor of three. We conclude from our results that many-line spectropolarimetry should be the preferred option in the future, and in particular at short wavelengths it offers a high potential in solar physics.

Adaptive event-triggered anomaly detection in compressed vibration data

Abstract Anomaly detection is a crucial task in Prognostics and Condition Monitoring (PCM) of machinery. In modern remote PCM systems, data compression techniques are regularly used to reduce the need for bandwidth and storage. In these systems the challenge arises of how the compressed (distorted) vibration data affects the condition monitoring algorithms. This paper introduces a novel algorithm that can adaptively establish normal bounds of operation from continuous noisy vibration profiles working with compressed vibration data. The proposed technique is based on four modules, including feature extraction, feature fusion, extreme value vibration modeling and adaptive thresholding for anomaly detection. The proposed method has been validated with experiments using three time-series datasets. The experimental results indicate that the proposed algorithm is able to perform detection of malfunctions in rotating machines effectively without faulty reference data. Moreover, the proposed method is able to produce accurate early warning and alarm indications from both the raw and compressed (distorted) datasets with equal veracity.

Single-pixel correlated imaging with high-quality reconstruction using iterative phase retrieval algorithm

A single-pixel correlated imaging scheme based on iterative phase retrieval algorithm, which can encode an original object into a series of measured intensities, is proposed in this paper. Initially, a plenty of intensity patterns are derived from the Hadamard matrix with the certain order, and a pair of noisy phase profiles can be obtained by decomposing an intensity pattern via an iterative phase retrieval algorithm. When a pair of phase profiles is cascaded and sequentially embedded into two spatial light modulators in the proposed optical configuration, a measured intensity can be recorded by the bucket detector without spatial resolution. By only making the use of second-order correlation algorithm, the object with high quality can be reconstructed with measured intensities. Meanwhile, the number of recording the measured intensities can be reduced greatly in the process of imaging, which results in high efficiency. The reported approach provides an effective alternative for enriching the related research on single-pixel correlated imaging systems.

Observing continental boundary-layer structure and evolution over the South African savannah using a ceilometer

The atmospheric boundary layer (BL) is the atmospheric layer coupled to the Earth’s surface at relatively short timescales. A key quantity is the BL depth, which is important in many applied areas of weather and climate such as air-quality forecasting. Studying BLs in climates and biomes across the globe is important, particularly in the under-sampled southern hemisphere. The present study is based on a grazed grassland-savannah area in northwestern South Africa during October 2012–August 2014. Ceilometers are probably the cheapest method for measuring continuous aerosol profiles up to several kilometers above ground and are thus an ideal tool for long-term studies of BLs. A ceilometer-estimated BL depth is based on profiles of attenuated backscattering coefficients from atmospheric aerosols; the sharpest drop often occurs at BL top. Based on this, we developed a new method for layer detection that we call the signal-limited layer method. The new algorithm was applied to ceilometer profiles which thus classified BL into classic regime types: daytime convective mixing, and a double layer at night of surface-based stable with a residual layer above it. We employed wavelet fitting to increase successful BL estimation for noisy profiles. The layer-detection algorithm was supported by an eddy-flux station, rain gauges, and manual inspection. Diurnal cycles were often clear, with BL depth detected for 50% of the daytime typically being 1–3 km, and for 80% of the night-time typically being a few hundred meters. Variability was also analyzed with respect to seasons and years. Finally, BL depths were compared with ERA-Interim estimates of BL depth to show reassuring agreement.

Ionic shot noise in an electrochemical capacitor system made of poly(3,4-ethylenedioxythiophene)-poly(styrenesulfonate) film and silver-coated polybenzoxazole-stainless steel electrodes on textile fabrics

Unusual noisy discharge profiles were observed from some of our textile-based energy storage devices having asymmetrical electrodes consisting of pure stainless steel and silver-coated polybenzoxazole yarns. Our hypothesis was that it was due to the ionic shot noise behavior that occurred in electrochemical devices and is a well-known phenomenon in electronic devices. The poly(3,4-ethylenedioxythiophene)-poly(styrenesulfonate) (PEDOT:PSS) polymer coverage on the cell surface, which functioned as a solid electrolyte in this system, was believed to play an important role. To confirm this assumption, devices made with different drop-coating strategies to obtain thin and thick layers of PEDOT:PSS polymer on the cell surface were prepared. The noisy discharge profiles were observed from devices with thin polymer layers, while those with thick layers exhibited normal discharge profiles. The morphology of cell surfaces was characterized by a stereo microscope. Cross-section analysis of a device with a thick layer was employed to further characterize its film formation and elemental properties using Scanning Electron Microscopy-Electron Dispersive Spectroscopy. Formation of multilayers of PEDOT:PSS polymer on the cell surface allowed a continuous interaction between electrode metals and PEDOT:PSS ions at the interface area. The noisy component was caused by the movement of silver ions hopping from one trap to the next. A qualitative model of the autocorrelation function executed to the data with noisy behavior further confirmed the ionic shot noise phenomenon.

Optimum efficiency lidar sensing of multilayer hydrometeors through a turbid atmosphere

The detected lidar return power is a basic factor determining the brightness of the detected lidar images and the signal-to-noise ratio (SNR) of a given measurement. At equal other characteristics, the laser radiation wavelength should influence the lidar return signal and assume an optimum value depending on the specificity of the objects investigated. As such a problem had not been considered systematically, we recently began developing a modeling approach to solving it, based on evaluating the mean and the noisy lidar profiles and the SNR profile of the measurement along the lidar line of sight by using the lidar equation and well known realistic models of the atmospheric objects and background. The main purpose of the present work is to estimate by numerical modeling the detectability of the lidar return from different distances and multilayer cirrus clouds, depending on the laser radiation wavelengths. The results obtained confirm the expectations that at a higher atmospheric turbidity, a relatively higher sensing efficiency (return power) is achievable by longer-wavelength laser radiation, within the NIR range.

Ensemble Modeling Approach Targeting Heterogeneous RNA-Seq data: Application to Melanoma Pseudogenes

We studied the transcriptome landscape of skin cutaneous melanoma (SKCM) using 103 primary tumor samples from TCGA, and measured the expression levels of both protein coding genes and non-coding RNAs (ncRNAs). In particular, we emphasized pseudogenes potentially relevant to this cancer. While cataloguing the profiles based on the known biotypes, all the employed RNA-Seq methods generated just a small consensus of significant biotypes. We thus designed an approach to reconcile the profiles from all methods following a simple strategy: we selected genes that were confirmed as differentially expressed by the ensemble predictions obtained in a regression model. The main advantages of this approach are: 1) Selection of a high-confidence gene set identifying relevant pathways; 2) Use of a regression model whose covariates embed all method-driven outcomes to predict an averaged profile; 3) Method-specific assessment of prediction power and significance. Furthermore, the approach can be generalized to any biological system for which noisy RNA-Seq profiles are computed. As our analyses concerned bio-annotations of both high-quality protein coding genes and ncRNAs, we considered the associations between pseudogenes and parental genes (targets). Among the candidate targets that were validated, we identified PINK1, which is studied in patients with Parkinson and cancer (especially melanoma).

Tree inference for single-cell data.

Understanding the mutational heterogeneity within tumors is a keystone for the development of efficient cancer therapies. Here, we present SCITE, a stochastic search algorithm to identify the evolutionary history of a tumor from noisy and incomplete mutation profiles of single cells. SCITE comprises a flexible Markov chain Monte Carlo sampling scheme that allows the user to compute the maximum-likelihood mutation history, to sample from the posterior probability distribution, and to estimate the error rates of the underlying sequencing experiments. Evaluation on real cancer data and on simulation studies shows the scalability of SCITE to present-day single-cell sequencing data and improved reconstruction accuracy compared to existing approaches.Electronic supplementary materialThe online version of this article (doi:10.1186/s13059-016-0936-x) contains supplementary material, which is available to authorized users.

Investigating the effect of flexible constraints on the accuracy of self‐modeling curve resolution methods in the presence of perturbations

Self‐modeling curve resolution methods have continuously been improved during recent years. Many efforts have been made on curve resolution methods to reduce the rotational ambiguity by means of different types of constraints. Choosing proper constraints and cost functions is critically important for the reduction of the rotational ambiguity because the constraints have a direct influence on the accuracy of the area of feasible solution (AFS).In this work, we introduce a new improved cost function, which serves to apply nonnegativity, unimodality, equality, and closure constraints. We also investigate the reduction of the AFS under hard and soft constraints. Another point of this work is to evaluate the accuracy and precision of the reduced AFS in the presence of noise and perturbations, under hard and soft implementation of nonnegativity, unimodality, equality, and closure constraints. A comparison is given between the reduced AFS with soft constraints (small deviations from constraints are accepted) and the reduced AFS under hard constraints (restrictedly forced constraints). A graphical visualization of this comparison is presented for various model problems. The results show that an AFS computation with soft constraints provides more reliable results, especially in the presence of noise. The test problems substantiate significant advantages of soft constraints over hard constraints because the obtained profiles are closer to the potentially true noisy profiles, which contain small deviations from ideal responses. Using tunable parameters ϵ,γ,ω,δ is one of the advantages of soft constrained cost function that allows the small deviations from ideal responses. Ultimately, soft constraints can help to reduce the lack‐of‐fit, and they are a proper instrument to handle the effect of noise on the AFS. Copyright © 2016 John Wiley & Sons, Ltd.

Effects of solar activity on noise in CALIOP profiles above the South Atlantic Anomaly

Abstract. We show that nighttime dark noise measurements from the spaceborne lidar CALIOP contain valuable information about the evolution of upwelling high-energy radiation levels. Above the South Atlantic Anomaly (SAA), CALIOP dark noise levels fluctuate by ±6% between 2006 and 2013, and follow the known anticorrelation of local particle flux with the 11-year cycle of solar activity (with a 1-year lag). By analyzing the geographic distribution of noisy profiles, we are able to reproduce known findings about the SAA region. Over the considered period, it shifts westward by 0.3° year−1, and changes in size by 6° meridionally and 2° zonally, becoming larger with weaker solar activity. All results are in strong agreement with previous works. We predict SAA noise levels will increase anew after 2014, and will affect future spaceborne lidar missions most near 2020.

Calculating the Electrostatic Potential Profiles of Double Layers from Simulation Ion Density Profiles

Computer simulations of the planar double layer geometry provide the charge profile with statistical noise. To compute the mean electrostatic potential profile from the charge profile, one must solve Poisson’s equation with appropriate boundary conditions (BC). In this work, we show that it is advantageous to use the Neumann or Dirichlet BCs at the boundaries of the simulation domain with an integrated version of Poisson’s equation. This minimises errors from the simulation’s noisy density profiles, in contrast to traditional convolution integrals that amplify the noise. The Neumann BC, where the electric field is prescribed, can be used in both the constant surface charge and constant electrode voltage ensembles. In the constant voltage ensemble, where the potential difference between the confining electrodes is prescribed, one can also use the Dirichlet BC, where the potentials at the boundaries are set. We show that the new methods provide converged results for the potential profile faster than the convolution integral does.

Evaluation of weakly compressible SPH variants using derived analytical solutions of Taylor–Couette flows

Smoothed particle hydrodynamics (SPH) is a relatively young meshless particle method used in fluid simulation. The method has not yet reached a mature state and still is in the need of rigorous evaluation tests that contribute to its consolidation as a reliable numerical method. With this need in mind, the first portion of this article is dedicated to presenting a new set of validation tests. The tests consist of different types of planar Taylor–Couette flows which will be equipped with their corresponding Navier–Stokes equations’ analytical solutions. Analytical solutions have been found for compressible and weakly-compressible (WC) regimes. The second part of this article is dedicated to using the obtained solutions as evaluation tests of a WC-SPH variant based on the divergence form of the Navier–Stokes equations and on the simultaneous use of different kernels. The proposed variant is compared to other previous WC-SPH variants commonly used in the literature. Velocities as well as pressure profiles can be compared with the provided analytical solutions. The performed numerical experiments show that, although all the tested WC-SPH variants match quite correctly the theoretical velocity profile, the previous variants present highly noisy pressure profiles or even give erroneous pressure solutions. Among the evaluated WC-SPH formulations, the proposed variant does a better job in matching, both, velocity profiles and pressure profiles with much lower levels of noise.

Parameter Estimation of Biological Phenomena: An Unscented Kalman Filter Approach

Recent advances in high-throughput technologies for biological data acquisition have spurred a broad interest in the construction of mathematical models for biological phenomena. The development of such mathematical models relies on the estimation of unknown parameters of the system using the time-course profiles of different metabolites in the system. One of the main challenges in the parameter estimation of biological phenomena is the fact that the number of unknown parameters is much more than the number of metabolites in the system. Moreover, the available metabolite measurements are corrupted by noise. In this paper, a new parameter estimation algorithm is developed based on the stochastic estimation framework for nonlinear systems, namely the unscented Kalman filter (UKF). A new iterative UKF algorithm with covariance resetting is developed in which the UKF algorithm is applied iteratively to the available noisy time profiles of the metabolites. The proposed estimation algorithm is applied to noisy time-course data synthetically produced from a generic branched pathway as well as real time-course profile for the Cad system of E. coli. The simulation results demonstrate the effectiveness of the proposed scheme.