Uniform Distribution Of Samples Research Articles

Machine Learning Deciphered Molecular Mechanistics with Accurate Kinetic and Thermodynamic Prediction.

Time-lagged independent component analysis (tICA) and the Markov state model (MSM) have been extensively employed for extracting conformational dynamics and kinetic community networks from unbiased trajectory ensembles. However, these techniques may not be the optimal choice for elucidating transition mechanisms within low-dimensional representations, especially for intricate biosystems. Unraveling the association mechanism in such complex systems always necessitates permutations of several essential independent components or collective variables, a process that is inherently obscure and may require empirical knowledge for selection. To address these challenges, we have implemented an integrated unsupervised dimension reduction model: uniform manifold approximation and projection (UMAP) with hierarchy density-based spatial clustering of applications with noise (HDBSCAN). This approach effectively generates low-dimensional configurational embeddings. The hierarchical application of this architecture, in conjunction with MSM, reveals global kinetic connectivity while identifying local conformational states. Consequently, our methodology establishes a multiscale mechanistic elucidation framework. Leveraging the benefits of the uniform sample distribution and a denoising approach, our model demonstrates robustness in preserving global and local data structures compared to traditional dimension reduction methods in the field of MD analysis area. The interpretability of hyperparameter selection and compatibility with downstream tasks are cross-validated across various simulation data sets, utilizing both computational evaluation metrics and experimental kinetic observables. Furthermore, the predicted Mcl1-BH3 association kinetics (0.76 s-1) is in close agreement with surface plasmon resonance experiments (0.12 s-1), affirming the plausibility of the identified pathway composed of representative conformations. We anticipate that the devised workflow will serve as a foundational framework for studying recognition patterns in complex biological systems. Its contributions extend to the exploration of protein functional dynamics and rational drug design, offering a potent avenue for advancing research in these domains.

De-cluttering Scatterplots with Integral Images.

Scatterplots provide a visual representation of bivariate data (or 2D embeddings of multivariate data) that allows for effective analyses of data dependencies, clusters, trends, and outliers. Unfortunately, classical scatterplots suffer from scalability issues, since growing data sizes eventually lead to overplotting and visual clutter on a screen with a fixed resolution, which hinders the data analysis process. We propose an algorithm that compensates for irregular sample distributions by a smooth transformation of the scatterplot's visual domain. Our algorithm evaluates the scatterplot's density distribution to compute a regularization mapping based on integral images of the rasterized density function. The mapping preserves the samples' neighborhood relations. Few regularization iterations suffice to achieve a nearly uniform sample distribution that efficiently uses the available screen space. We further propose approaches to visually convey the transformation that was applied to the scatterplot and compare them in a user study. We present a novel parallel algorithm for fast GPU-based integral-image computation, which allows for integrating our de-cluttering approach into interactive visual data analysis systems.

NR-RRT: Neural Risk-Aware Near-Optimal Path Planning in Uncertain Nonconvex Environments

Balancing the trade-off between safety and efficiency is of significant importance for path planning under uncertainty. Many risk-aware path planners have been developed to explicitly limit the probability of collision to an acceptable bound in uncertain environments. However, convex obstacles or Gaussian uncertainties are usually assumed to make the problem tractable in the existing method. These assumptions limit the generalization and application of path planners in real-world implementations. In this article, we propose to apply deep learning methods to the sampling-based planner, developing a novel risk bounded near-optimal path planning algorithm named neural risk-aware RRT (NR-RRT). Specifically, a deterministic risk contours map is maintained by perceiving the probabilistic nonconvex obstacles, and a neural network sampler is proposed to predict the next most-promising safe state. Furthermore, the recursive divide-and-conquer planning and bidirectional search strategies are used to accelerate the convergence to a near-optimal solution with guaranteed bounded risk. Worst-case theoretical guarantees can also be proven owing to a standby safety guaranteed planner utilizing a uniform sampling distribution. Simulation experiments demonstrate that the proposed algorithm outperforms the state-of-the-art remarkably for finding risk bounded low-cost paths in seen and unseen environments with uncertainty and nonconvex constraints.

Statistical analysis of hypersonic glide vehicle radar cross section

AbstractThe capability to design, manufacture and test Hypersonic Glide Vehicles (HGVs) has been demonstrated by a number of nations, and they are increasingly forming part of military inventories, potentially offering capabilities highly unique to this technology. This article reports the simulated Monostatic Radar Cross Section of a generic HGV in five frequency ranges, HF, VHF, UHF, L, and S‐bands associated with different radar types. Full spherical datasets of complex co‐ and cross‐polar data are synthesised so that backscatter resulting from illumination by r.f./microwave energy of linear or circular polarisation can subsequently be computed from the raw dataset. Circular polarisation is commonly employed by ground‐based Ballistic Missile Early Warning Systems and Space Object Surveillance and Identification radars to avoid polarisation mis‐match losses resulting from ionospheric Faraday rotation effects. The data was generated using Ansys' Finite Element Solver at 10, 150 and 430 MHz, with the Geometric Optics/Physical Optics based SBR+ solver employed for 1.3 and 3 GHz data. All data was produced at below the Nyquist sampling interval relevant to the target's electrical size. These datasets were then imported into a Matlab routine which extracted data over limited angular ranges associated with the likely radar line‐of‐sight in particular scenarios, typically having a standard deviation of ±10° about the direction of flight, applying either a Gaussian or Uniform sampling distribution as part of a Monte Carlo analysis. These extracted data were then used to form histograms giving the probability of sampling particular RCS values. Probability density functions and cumulative distribution functions were then fitted, to aid in the representation of statistical target fluctuations for each band and angular sampling range. The HGV exists in either the ‘Rayleigh’, ‘resonance’ or ‘optical’ scattering regimes, depending on its relative electrical size. The results suggest that for this target shape at HF and VHF cases a simple Swerling 0 (fluctuation invariant) approximation is adequate in most instances, whilst a Gamma distribution may be applied for UHF band cases. At L and S‐band a Beta distribution was found to provide a good fit to the available data.

Direct single-cell antimicrobial susceptibility testing of Escherichia coli in urine using a ready-to-use 3D microwell array chip.

Empirical antibiotic therapies are prescribed for treating uncomplicated urinary tract infections (UTIs) due to the long turnaround time of conventional antimicrobial susceptibility testing (AST), leading to the prevalence of multi-drug resistant pathogens. We present a ready-to-use 3D microwell array chip to directly conduct comprehensive AST of pathogenic agents in urine at the single-cell level. The developed device features a highly integrated 3D microwell array, offering a dynamic range from 102 to 107 CFU mL-1, and a capillary valve-based flow distributor for flow equidistribution in dispensing channels and uniform sample distribution. The chip with pre-loaded reagents and negative pressure inside only requires the user to initiate AST by loading samples (∼3 s) and can work independently. We demonstrate an accessible sample-to-result workflow, including syringe filter-based bacteria separation and rapid single-cell AST on chip, which enables us to bypass the time-consuming bacteria isolation and pre-culture, speeding up the AST in ∼3 h from 2 days of conventional methods. Moreover, the bacterial concentration and AST with minimum inhibitory concentrations can be assessed simultaneously to provide comprehensive information on infections. With further development for multiple antibiotic conditions, the Dsc-AST assay could contribute to timely prescription of targeted drugs for better patient outcomes and mitigation of the threat of drug-resistant bacteria.

Spatial Distance-based Uniformity Evaluation Method for Power Flow Datasets

Research on the application of artificial intelligence (AI) methods in power grid analysis has been widely conducted. The power flow dataset required for the training of AI models is not uniformly distributed, and to improve the quality of the dataset, related research has generally applied tuning methods that tend to have a more uniform sample distribution, resulting in improved performance of AI models. However, the lack of research on methods to evaluate the uniformity of distribution of the dataset poses an obstacle to the judgment of the validity of uniformity adjustment and the analysis of the impact of uniformly distributed datasets on the performance of AI models. This paper proposes a method to evaluate the uniformity of power flow datasets by using the calculation of distances in the high-dimensional feature space of the flow datasets and plotting the minimum distance statistics as a way to evaluate the uniformity of the flow datasets. It was also tested on the power flow dataset of 36-node grid and evaluated separately for two uniformity levels, which can clearly represent the uniformity of distribution of the dataset in the high-dimensional feature space.

Comparison of two commonly used methods for identifying water quality thresholds in freshwater ecosystems using field and synthetic data

Defining ecological thresholds has become increasingly relevant for water resource management. Despite the fact that there has been a rapid expansion in methods to evaluate ecological threshold responses to environmental stressors, evaluation of the relative benefits of various methods has received less attention. This study compares the performance of Gradient Forest (GF) and Threshold Indicator Taxa Analysis (TITAN) for identifying water quality thresholds in both field and synthetic data. Analysis of 14 years of macroinvertebrates data from the Mediterranean catchments of the Torrens and Onkaparinga Rivers, South-Australia, identified electrical conductivity (EC) and total phosphorus (TP) as the most important water quality variables affecting macroinvertebrates. Water quality thresholds for macroinvertebrates identified by both methods largely corresponded at low EC (GF: 400–900 μS cm−1 vs. TITAN: 407–951 μScm−1), total phosphorus (TP) (GF: 0.02–0.18 mg L−1 vs. TITAN: 0.02–0.04 mg L−1) and total nitrogen (TN) (GF: 0.2 mg L−1 vs. TITAN: 0.28–0.67 mg L−1) concentrations. However, multiple GF-derived thresholds, particularly at high stressor concentrations, were representative of low data distribution, and thus need to be considered with caution. In another case study of South Australian diatom data, there were marked differences in GF and TITAN identified thresholds for EC (GF: 5000 μScm−1 vs. TITAN 1004–2440 μS cm−1) and TP (GF: 250–500 μg L−1 vs. TITAN: 11–329 μg L−1). These differences were due to the fact that while TITAN parsed species responses into negative and positive taxa, GF overestimated thresholds by aggregating the response of taxa that increase and decrease along environmental gradients. Given these findings, we also evaluated the methods' performance using different distributions of synthetic data i.e. with both skewed and uniform distribution of samples and species responses. Both methods identified similar change-points in the case of a uniform environmental gradient, except when species optima were simulated at centre of the gradient. Here GF detected the change-points but TITAN failed to do so. GF also outperformed TITAN when four simulated species change-points were present. Thus, the distribution of species responses and optima and the evenness of the environment gradient can affect the models' performance. This study has shown that both methods are robust in identifying change in species response but threshold identification differs depending both on the analysis used and the nature of ecological data. We recommend the careful application of GF and TITAN, noting these differences in performance, will improve their application for water resource management.

Imbalanced Data Classification for Multi-Source Heterogenous Sensor Networks

Most of the traditional classification algorithms are based on the uniform distribution of samples, and the effect is not ideal when dealing with such data, which mainly shows that the classification results incline to the majority class. Therefore, we propose the imbalanced multi-source heterogeneous data classification algorithms in this paper, which are mainly based on the expansion and extension of Support Vector Machines. Considering that there are complex connections within multi-source data, express them as a unified, concise and efficient mathematical model can completely retain data information and improve data processing efficiency. We perform tensor representation and feature extraction on the heterogeneous data, and two different classification algorithms are proposed in this paper. In the first method, we represent multi-source heterogeneous data into a unified tensor form directly and obtain a high-quality core data through dimensionality reduction algorithm, then realize data classification by Support Tensor Machine. In the other method, we extract data from different data sources and classify them with Ensemble Deep Support Vector Machine (DSVM), which combined three DSVM with different kernel functions. The algorithms are compared on CUAVE data set, which contains two different modalities of sound and picture.

PRF Selection in Formation-Flying SAR: Experimental Verification on Sentinel-1 Monostatic Repeat-Pass Data

Formation-flying synthetic aperture radar (FF-SAR) enables new working modes and can achieve very high performance through a series of very compact, low-weight, satellite platforms thanks to passive operations of conveniently distributed formation-flying receivers. System timing is a crucial aspect of FF-SAR. The manuscript presents a novel approach to pulse repetition frequency (PRF) selection in order to obtain a uniform distribution of samples at given platform positions. A digital beamforming algorithm is applied on a stack of monostatic repeat-pass images collected by the Sentinel-1 system to test the validity of the PRF selection method. Processed images were thus properly selected to achieve the best merit index measuring the quality of samples distribution. The results show that: (a) the image resulting from beamforming features better azimuth ambiguity-to-signal ratio and (b) the proposed approach for PRF selection allows one to individuate a subset of the available images leading to uniform distribution of samples which can be used to support FF-SAR processing.

A comparison of colour appearance for surface colours between outdoor and indoor environments

AbstractPsychophysical experiments of colour appearance, in terms of lightness, colourfulness, and hue, were conducted outdoors and indoors to investigate whether there was any difference in colour appearance between outdoor and indoor environments. A panel of 10 observers participated in the outdoor experiment, while 13 observers took part in the indoor experiment. The reference white had an average luminance of 12784 cd/m2 in the outdoor experiment and 129 cd/m2 in the indoor experiment. Test colours included 42 colour patches selected from the Practical Coordinate Color System to achieve a reasonable uniform distribution of samples in CIECAM02. Experimental results show that for both outdoor and indoor environments, there was good agreement between visual data and predicted values by CIECAM02 for the three colour appearance scales, with the coefficient of variation values all lower than 25 and the R2 values all higher than 0.73, indicating little difference in the three dimensions of colour appearance between indoor and outdoor viewing conditions. Experimental data also suggest that the observers were more sensitive to variation in lightness for grayish colours than for highly saturated colours, a phenomenon that seems to relate with the Helmholtz‐Kohlrausch effect. This phenomenon was modeled for predicting perceived lightness (J′) using the present experimental data. The new J′ model was tested using three extra sets of visual data obtained both outdoors and indoors, showing good predictive performance of the new model, with an average coefficient of variation of 14, an average R2 of 0.88, and an average STRESS index of 14.18.

Sampling Big Trajectory Data for Traversal Trajectory Aggregate Query

This paper defines and investigates a novel trajectory query, namely, Traversal Trajectory Aggregate (TTA) Query: Given a trajectory database and a pair of upstream and downstream spatio-temporal (ST) regions (i.e., spatial area coupled with a time interval), a TTA query aims to retrieve the total number of unique trajectories that traverse through these two ST regions. Such TTA queries play an important role in various urban applications, such as route planning, taxi dispatching, and location-based advertising. Two baselines can answer such TTA queries: (a) exact search (over the entire ST query regions) can obtain the exact answer, but it leads to extremely long running time when the ST query regions are huge; (b) uniform-sampling-based approaches estimate the query answer with sampled trajectories. However, the uniform sampling distribution may lead to significant estimation variance for TTA query, because traversal trajectories are relatively few and unevenly distributed in the query regions. To tackle these challenges, this paper proposes a novel Targeted Index Sampling (TIS) framework to answer TTA queries with high estimation accuracy. TIS employs a two-stage framework, with a Pilot Sampling Estimation (PSE) stage to estimate the distribution of trajectories in ST query region, and an Integrated Importance Sampling (IIS) stage, which collects trajectories with the importance sampling distribution obtained in PSE, and estimates the query result with an asymptotically unbiased estimator. Extensive experiments and case studies using a large-scale real taxi trajectory dataset from Shenzhen, China demonstrate that our TIS framework achieves $\leq$ ≤ 10 percent estimation error with $\geq$ ≥ 90 percent computational time reduction over exact search, and 50 percent reduction on estimation error (with similar running time) over uniform-distribution-based sampling approaches.

Classification Method of Teaching Resources Based on Improved KNN Algorithm

In order to effectively utilize the network teaching resources, a teaching resource classification method based on the improved KNN (K-Nearest Neighbor) algorithm was proposed. Taking the text class primary and secondary school teaching resources as the research object, combined with the domain characteristics, the KNN algorithm was improved. By measuring the sample space density, the text of the high-density area was found. Different clipping methods were proposed for both intra-class and inter-class regions. The problem of cropping in the space of multiple class boundaries was considered. Results showed that the method ensured uniform distribution of samples and reduced the time of classification. Therefore, under the Weka platform, the improved KNN algorithm is effective.

RETRACTED ARTICLE: Unsupervised video multi-target tracking based on fast resampling particle filter

In order to improve non-supervision and monitoring effect for moving target of video, target tracking algorithm without supervision video based on resampling particle filter is proposed. A fast resampling particle filter algorithm designed in the paper is adopted, and it is based on quasi-Monte Carlo method which owns the property of low difference for determining sequences for acquiring more uniform sample distribution in space and is able to avoid degeneracy of sampling particle for improving calculation efficiency and accuracy of particle filter algorithm; subsequently, background difference algorithm is used for reducing algorithm for frame of video supervision image. Dynamic particle filter is established according to quantity of moving target in image with color distribution character to trace it, and the establishment of filter and reducing algorithm is used for reducing algorithm redundancy; eventually, according to simulation test in instance of supervision image, it shows that target tracking accuracy and calculation efficiency of the proposed method are better.

A high sensitive and contaminant tolerant matrix for facile detection of membrane proteins by matrix-assisted laser desorption/ionization mass spectrometry

Despite the significance of membrane proteins (MPs) in biological system is indisputable, their specific natures make them notoriously difficult to be analyzed. Particularly, the widely used Matrix-assisted laser desorption/ionization mass spectrometry (MALDI-MS) prefers analyses of hydrophilic cytosolic proteins and has a limited ionization efficiency towards hydrophobic MPs. Herein, a hydrophobic compound (E)-propyl α-Cyano-4-Hydroxyl Cinnamylate (CHCA-C3), a propyl-esterified derivative of α-cyano-4-hydroxycinnamic acid (CHCA), was applied as a contaminant tolerant matrix for high sensitivity MALDI-MS analyses of MPs. With CHCA-C3, the detection limits of hydrophobic peptides were 10- to 100-fold better than those using CHCA. Furthermore, high quality of spectra could be achieved in the presence of high concentration of chaotropes, salts and detergents, as well as human urinary and serum environment. Also, CHCA-C3 could generate uniform sample distribution even in the presence of contaminants. This high contaminant-resistance was revealed to be ascribed to the enhanced hydrophobicity of CHCA-C3 with a lower affinity towards hydrophilic contaminants. The application of CHCA-C3 is further demonstrated by the analysis of trypsin/CNBr digests of bacteriorhodopsin containing seven transmembrane domains (TMDs), which dramatically increased numbers of identified hydrophobic peptides in TMDs and sequence coverage (∼100%). Besides, a combined method by using CHCA-C3 with fluoride solvent and a patterned paraffin plate was established for analysis of integral MPs. We achieved a low detection limit of 10 fmol for integral bacteriorhodopsin, which could not be detected using traditional matrices such as 3,5-dimethoxy-4-hydroxycinamic acid, 2,5-dihydroxyacetophenone even at sample concentration of 10 pmol.

Predicting ambient aerosol thermal–optical reflectance measurements from infrared spectra: elemental carbon

Abstract. Elemental carbon (EC) is an important constituent of atmospheric particulate matter because it absorbs solar radiation influencing climate and visibility and it adversely affects human health. The EC measured by thermal methods such as thermal–optical reflectance (TOR) is operationally defined as the carbon that volatilizes from quartz filter samples at elevated temperatures in the presence of oxygen. Here, methods are presented to accurately predict TOR EC using Fourier transform infrared (FT-IR) absorbance spectra from atmospheric particulate matter collected on polytetrafluoroethylene (PTFE or Teflon) filters. This method is similar to the procedure developed for OC in prior work (Dillner and Takahama, 2015). Transmittance FT-IR analysis is rapid, inexpensive and nondestructive to the PTFE filter samples which are routinely collected for mass and elemental analysis in monitoring networks. FT-IR absorbance spectra are obtained from 794 filter samples from seven Interagency Monitoring of PROtected Visual Environment (IMPROVE) sites collected during 2011. Partial least squares regression is used to calibrate sample FT-IR absorbance spectra to collocated TOR EC measurements. The FT-IR spectra are divided into calibration and test sets. Two calibrations are developed: one developed from uniform distribution of samples across the EC mass range (Uniform EC) and one developed from a uniform distribution of Low EC mass samples (EC < 2.4 μg, Low Uniform EC). A hybrid approach which applies the Low EC calibration to Low EC samples and the Uniform EC calibration to all other samples is used to produce predictions for Low EC samples that have mean error on par with parallel TOR EC samples in the same mass range and an estimate of the minimum detection limit (MDL) that is on par with TOR EC MDL. For all samples, this hybrid approach leads to precise and accurate TOR EC predictions by FT-IR as indicated by high coefficient of determination (R2; 0.96), no bias (0.00 μg m−3, a concentration value based on the nominal IMPROVE sample volume of 32.8 m3), low error (0.03 μg m−3) and reasonable normalized error (21 %). These performance metrics can be achieved with various degrees of spectral pretreatment (e.g., including or excluding substrate contributions to the absorbances) and are comparable in precision and accuracy to collocated TOR measurements. Only the normalized error is higher for the FT-IR EC measurements than for collocated TOR. FT-IR spectra are also divided into calibration and test sets by the ratios OC/EC and ammonium/EC to determine the impact of OC and ammonium on EC prediction. We conclude that FT-IR analysis with partial least squares regression is a robust method for accurately predicting TOR EC in IMPROVE network samples, providing complementary information to TOR OC predictions (Dillner and Takahama, 2015) and the organic functional group composition and organic matter estimated previously from the same set of sample spectra (Ruthenburg et al., 2014).

Uniform spinning sampling gradient electron paramagnetic resonance imaging

To improve the quality and speed of electron paramagnetic resonance imaging (EPRI) acquisition by combining a uniform sampling distribution with spinning gradient acquisition. A uniform sampling distribution was derived for spinning gradient EPRI acquisition (uniform spinning sampling, USS) and compared to the existing (equilinear spinning sampling, ESS) acquisition strategy. Novel corrections were introduced to reduce artifacts in experimental data. Simulations demonstrated that USS puts an equal number of projections near each axis whereas ESS puts excessive projections at one axis, wasting acquisition time. Artifact corrections added to the magnetic gradient waveforms reduced noise and correlation between projections. USS images had higher SNR (85.9 ± 0.8 vs. 56.2 ± 0.8) and lower mean-squared error than ESS images. The quality of the USS images did not vary with the magnetic gradient orientation, in contrast to ESS images. The quality of rat heart images was improved using USS compared to that with ESS or traditional fast-scan acquisitions. A novel EPRI acquisition which combines spinning gradient acquisition with a uniform sampling distribution was developed. This USS spinning gradient acquisition offers superior SNR and reduced artifacts compared to prior methods enabling potential improvements in speed and quality of EPR imaging in biological applications.

Uniformly sampling multi-resolution analysis for image-based relighting

Image-based relighting allows us to efficiently light a scene under complicated illumination conditions. However, the traditional cubemap based multi-resolution analysis unevenly samples the spherical surface, with a higher sampling rate near the face corners and a lower one near the face centers. The non-uniformity penalizes the efficiency of data representation. This paper presents a uniformly sampling multi-resolution analysis approach, namely the icosahedron spherical wavelets (ISW), for image-based relighting under time-varying distant environment. Since the proposed ISW approach provides a highly uniform sampling distribution over the spherical domain, we thus can efficiently handle high frequency variations locally in the illumination changes as well as reduce the number of wavelet coefficients needed in the renderings. Furthermore, visual artifacts are demonstrated to be better suppressed in the proposed ISW approach. Compared with the traditional cubemap based multi-resolution analysis approach, we show that our approach can effectively produce higher quality image sequences that are closer to the ground truth in terms of percentage square errors.

Quality control of archaeomagnetic determination using a modern kiln with a complex NRM

A modern (1959) brick kiln from western Spain has been studied in order to conduct a quality control test of the archaeomagnetic method in a partially heated structure. The kiln exhibits two stable natural remanent magnetisation components: a low-temperature component (150–620 °C) acquired during kiln use and a randomly oriented, high temperature component (500–680 °C) acquired during the original firing of the bricks. A detailed rock magnetic study revealed a magnetic mineralogy dominated by non-stoichiometric magnetite and hematite, both of which contribute to the characteristic remanent magnetisation. Both the direction and intensity of the characteristic magnetisation have been compared with the known values for the geomagnetic field at the site location. Irrespective of the method used to determine the mean archaeomagnetic direction (principal component analysis, great circle analysis, with or without hierarchy) the results are statistically indistinguishable from each other and from the known field direction. In all cases the direction is within 5° of the expected value. Thellier-style archaeointensity determinations have been carried out on a smaller specimen set, with the mean result consistent with the known field value. The results demonstrate the reliability of the archaeomagnetic method in determining the features of the geomagnetic field in the past, even in cases with a complicated magnetic history. Furthermore, they highlight the importance of a uniform sample distribution in order to obtain truly representative values for the direction and intensity of the ancient geomagnetic field.

Does theKubelka-Munktheory describe TLC evaluations correctly?

In thin-layer chromatography the development step distributes the sample throughout the layer, a process which strongly affects the reflection signals. The essential requirement for quantitative thinlayer chromatography is not a constant sample concentration but constant sample distribution in each sample spot. This makes evaporation of the mobile phase extremely important, because all tracks of a TLC plate must be dried uniformly. This paper shows that quantitative TLC is possible even if the concentration of the sample is not constant throughout the layer or if the distribution of the sample is not known. With uniform sample distribution, classical Kubelka-Munk theory is valid for isotropic scattering only. In the absence of this constraint classical Kubelka-Munk theory must be extended to situations where scattering is asymmetric. This can be achieved by modification of the original Kubelka-Munk equation. Extended theory is presented which is not only capable of describing asymmetrical scattering in TL...

Sequential reservoir sampling with a nonuniform distribution

We present a simple algorithm that allows sampling from a stream of data items without knowing the number of items in advance and without having to store all items in main memory. The sampling distribution may be general, that is, the probability of selecting a data item i may depend on the individual item. The main advantage of the algorithms is that they have to pass through the data items only once to produce a sample of arbitrary size n .We give different variants of the algorithm for sampling with and without replacement and analyze their complexity. We generalize earlier results of Knuth on reservoir sampling with a uniform sampling distribution. The general distribution considered here allows us to sample an item with a probability equal to the relative weight (or fitness) of the data item within the whole set of items. Applications include heuristic optimization procedures such as genetic algorithms where solutions are sampled from a population with probability proportional to their fitness.