An Improved Distributed Sampling PPO Algorithm Based on Beta Policy for Continuous Global Path Planning Scheme.

Traditional path planning is mainly utilized for path planning in discrete action space, which results in incomplete ship navigation power propulsion strategies during the path search process. Moreover, reinforcement learning experiences low success rates due to its unbalanced sample collection and unreasonable design of reward function. In this paper, an environment framework is designed, which is constructed using the Box2D physics engine and employs a reward function, with the distance between the agent and arrival point as the main, and the potential field superimposed by boundary control, obstacles, and arrival point as the supplement. We also employ the state-of-the-art PPO (Proximal Policy Optimization) algorithm as a baseline for global path planning to address the issue of incomplete ship navigation power propulsion strategy. Additionally, a Beta policy-based distributed sample collection PPO algorithm is proposed to overcome the problem of unbalanced sample collection in path planning by dividing sub-regions to achieve distributed sample collection. The experimental results show the following: (1) The distributed sample collection training policy exhibits stronger robustness in the PPO algorithm; (2) The introduced Beta policy for action sampling results in a higher path planning success rate and reward accumulation than the Gaussian policy at the same training time; (3) When planning a path of the same length, the proposed Beta policy-based distributed sample collection PPO algorithm generates a smoother path than traditional path planning algorithms, such as A*, IDA*, and Dijkstra.

Simultaneous confidence intervals for quantile differences of several heterogeneous normal populations: With application to vitamin D supplement treatment on colorectal cancer patients.

In many applications, comparing the q-quantiles of several normal populations are more advantageous than comparing their means. In this paper, we consider the problem of constructing simultaneous confidence intervals (SCIs) for quantile differences of several heterogeneous normal distributions. To the best of our knowledge, this problem remains unsolved. We propose a novel method for constructing a set of SCI. We propose two new sets of SCI by using the proposed technique and discuss two classic and two simulation-based SCIs. We show that the proposed classic SCIs are conservative for all population parameters configuration. We also show that the simulation-based SCIs have correct coverage probability asymptotically. We then compare these six sets of SCI in terms of average volume and coverage probability via an extensive simulation study. Results show that one of the proposed classic SCI can be recommended. Finally, the proposed methods are illustrated by a real example that is a vitamin D study on colorectal cancer patients.

Airborne estimation of SO2 emissions rates from a coal-fired power plant using two top-down methods: A mass balance model and Gaussian footprint approach.

In this study, two top-down methods-mass balance and Gaussian footprint-were used to determine SO2 emissions rates via three airborne sampling studies over Korea's largest coal power plant in October 2019 and 2020. During the first two flights in October 2019, mass balance approaches significantly underestimated the SO2 emissions rates by 75 % and 28 %, respectively, as obtained from the real-time stack monitoring system. Notably, this large discrepancy accounted for the insufficient number of transects altitudes and high levels of background SO2 along the upwind side. Alternatively, the estimated SO2 emissions rates of the third flight (October 2020) displayed a difference of <10 % from rea-time monitoring data (630 vs. 690 kg·hr-1), owing to the enhanced vertical resolution with increased transects and lower background SO2 levels. In contrast to the mass balance method, Gaussian footprints offered significantly improved accuracy (relative error: 41 %, 32 %, and 2 % for Flights 1, 2, and 3, respectively). This relatively good performance was attributed to prior emissions knowledge via the Clean Air Policy Support System (CAPSS) emissions inventory and its unique ability to accurately estimate stack-level SO2 emissions rates. Theoretically, the Gaussian footprint was less prone to sparse transects and upwind background levels. However, it can be substantially influenced by atmospheric stability and consequently by effective stack heights and dispersion parameters; basically, all factors with minimal-to-no influence on the mass balance approach. Conversely, the mass balance method was the only plausible approach to estimate unidentified source emissions rates when well-defined prior emission information was unknown. Here, the footprint approach supplemented the mass balance method when the emission inventories were known, and employing both strategies approaches greatly enhanced the integrity of top-down emissions inventories from the power plant sources, thus, supporting their potential for ensuring operational compliance with SO2 emissions regulation.

Calibrating cardiac electrophysiology models using latent Gaussian processes on atrial manifolds.

Models of electrical excitation and recovery in the heart have become increasingly detailed, but have yet to be used routinely in the clinical setting to guide personalized intervention in patients. One of the main challenges is calibrating models from the limited measurements that can be made in a patient during a standard clinical procedure. In this work, we propose a novel framework for the probabilistic calibration of electrophysiology parameters on the left atrium of the heart using local measurements of cardiac excitability. Parameter fields are represented as Gaussian processes on manifolds and are linked to measurements via surrogate functions that map from local parameter values to measurements. The posterior distribution of parameter fields is then obtained. We show that our method can recover parameter fields used to generate localised synthetic measurements of effective refractory period. Our methodology is applicable to other measurement types collected with clinical protocols, and more generally for calibration where model parameters vary over a manifold.

Bayesian EMAX model with a mixture of normal distributions for dose-response in clinical trials.

When a dose-response relationship is monotonic, the EMAX model has been shown to provide a good empirical fit for designing and analyzing dose-response data across a wide range of pharmaceutical studies. However, the EMAX model has never been applied to a finite mixture distribution. Motivated by a proposal investigating DHA dose effect on preterm birth (PTB, <37 weeks gestation) rate, we developed a Bayesian EMAX mixture model incorporating the three normal components finite mixture model into the EMAX framework. The proposed Bayesian EMAX mixture model analyzes gestational age as a continuous variable, which allows for statistically efficient estimates of PTB rate using various cut point with the same parsimonious model. For example, we can estimate the rate of early PTB (ePTB, <34 weeks gestation), PTB (<37 weeks gestation), and late-term birth (>41 weeks gestation) using the same model. We compared our proposed EMAX mixture model with an EMAX logistic model and an independent doses logistic model for a dichotomized endpoint using extensive simulations. Across the scenarios under consideration, the EMAX mixture model achieved higher power than the EMAX logistic model and the independent doses logistic model in detecting the effect of DHA supplementation on the PTB rate. The EMAX mixture model also resulted in smaller mean squared errors (MSE) in PTB rate estimates.

Comprehensive Modeling in Predicting Biodiesel Density Using Gaussian Process Regression Approach.

In this study, four Gaussian process regression (GPR) approaches by various kernel functions have been proposed for the estimation of biodiesel density as the functions of pressure, temperature, molecular weight, and the normal melting point of fatty acid esters. Comparing the actual values with GPR outputs shows that these approaches have good accuracy, but the performance of the rational quadratic GPR model is better than others. In this GPR model, RMSE = 0.47, MSE = 0.22, MRE = 0.04, R 2 = 1, and STD is equal to 0.3. In addition, for the first time, this study shows that the effective parameters affect the biodiesel density. According to this analysis, it was shown that among the input parameters, pressure has the greatest effect on the target values with a relevancy factor of 0.59. This study can be used as a suitable and valuable work/tool for chemical and petroleum engineers who attempt environment protection and recovery improvement.

Random Effects in Magnetobiology and a Way to Summarize Them.

In magnetobiology, it is difficult to reproduce the nonspecific (not associated with specialized receptors) biological effects of weak magnetic fields. This means that some important characteristic of the data may be missed in standard statistical processing, where the set of measurements to be averaged belongs to the same population so that the contribution of fluctuations decreases according to the Central Limit Theorem. It has been shown that a series of measurements of a nonspecific magnetic effect contains not only the usual scatter of data around the mean but also a significant random component in the mean itself. This random component indicates that measurements belong to different statistical populations, which requires special processing. This component, otherwise called heterogeneity, is an additional characteristic that is typically overlooked, and which reduces reproducibility. The current method for studying and summarizing highly heterogeneous data is the random-effect meta-analysis of absolute values, i.e., of magnitudes, rather than the values themselves. However, this estimator-the average of absolute values-has a significant positive bias when it comes to the small effects that are characteristic of magnetobiology. To solve this problem, an improved estimator based on the folded normal distribution that gives several times less bias is proposed. We used this improved estimator to analyze the nonspecific effect of the hypomagnetic field in the Stroop test in 40 subjects and found a statistically significant meta-effect with a standardized average of magnitudes of about 0.1. It has been shown that the proposed approach can also be applied to a single study. © 2021 Bioelectromagnetics Society.

Self-consistent field modeling of mesomorphic phase changes of monoolein and phospholipids in response to additives.

Mapping the topological phase behaviour of lipids in aqueous solution is time consuming and finding the ideal lipid system for a desired application is often a matter of trial and error. Modelling techniques that can accurately predict the mesomorphic phase behaviour of lipid systems are therefore of paramount importance. Here, the self-consistent field theory of Scheutjens and Fleer (SF-SCF) in which a lattice refinement has been implemented, is used to scrutinize how various additives modify the self-assembled phase behaviour of monoolein (MO) and 1,2-dioleoyl-phosphatidylcholine (DOPC) lipids in water. The mesomorphic behaviour is inferred from trends in the mechanical properties of equilibrium lipid bilayers with increasing additive content. More specifically, we focus on the Helfrich parameters, that is, the mean and Gaussian bending rigidities (κ and [small kappa, Greek, macron], respectively) supplemented with the spontaneous curvature of the monolayer (Jm0). We use previously established interaction parameters that position the unperturbed DOPC system in the lamellar Lα phase ([small kappa, Greek, macron] < 0, κ > 0 and Jm0 ≈ 0). Similar interaction parameters position the MO system firmly in a bicontinuous cubic phase ([small kappa, Greek, macron] > 0). In line with experimental data, a mixture of MO and DOPC tends to be in one of these two phases, depending on the mixing ratio. Moreover we find good correlations between predicted trends and experimental data concerning the phase changes of MO in response to a wide range of additives. These correlations give credibility to the use of SF-SCF modelling as a valuable tool to quickly explore the mesomorphic phase space of (phospho)lipid bilayer systems including additives.

Challenging handheld NIR spectrometers with moisture analysis in plant matrices: Performance of PLSR vs. GPR vs. ANN modelling.

The global demand for natural products grows rapidly, intensifying the request for the development of high-throughput, fast, non-invasive tools for quality control applicable on-site. Moisture content is one of the most important quality parameters of natural products. It determines their market suitability, stability and shelf life and should preferably be constantly monitored. Miniaturized near-infrared (NIR) spectroscopy is a powerful method for on-site analysis, potentially fulfilling this requirement. Here, a feasibility study for applicability and analytical performance of three miniaturized NIR spectrometers and two benchtop instruments was evaluated in that scenario. The case study involved 192 dried plant extracts composed of five different plants harvested in different countries at various times within two years. The reference analysis by Karl Fischer titration determined the water content in this sample set between 1.36% and 6.47%. For the spectroscopic analysis half of the samples were laced with a drying agent to comply with the industry standard. The performance of various calibration models for NIR analysis was evaluated on the basis of root-mean square error of prediction (RMSEP) determined for an independent test set. Partial least squares regression (PLSR), Gaussian process regression (GPR) and artificial neural network (ANN) models were constructed for the spectral sets from each instrument. GPR and ANN models performed superior for all samples measured by handheld spectrometers and for native ones analyzed by benchtop instruments. Moreover, the accuracy penalty when analyzing native samples was lower for GPR and ANN prediction as well. With GPR or ANN calibration, miniaturized spectrometers offered the prediction performance at the level of the benchtop instruments. Therefore, in this analytical application miniaturized spectrometers can be used on-site with no penalty to the performance vs. laboratory-based NIR analysis.

Dynamic interactions between oil price and exchange rate.

This paper contributes to better understand the dynamic interactions between effective exchange rate (EER) and oil price for an oil-importing country like the U.S. by considering a Time-Varying Parameter VAR model with the use of monthly data from 1974:01 to 2019:07. Our findings show a depreciation after an oil price shock in the short-run for any period of time, although the pattern of long-run responses of U.S. EER is diverse across time periods, with an appreciation being observed before the mid-2000s and after the mid-2010s, and a depreciation between both periods. This diversity of response should lead policy makers to react differently in order to counteract such shocks. Furthermore, the reaction of oil price to an appreciation of U.S. EER is negative and different over time, which may generate different adverse effects on investment. The knowledge of such effects may help financial investors to diversify their investments in order to optimize the risk-return profile of their portfolios.

Numerical analysis of local non-equilibrium heat transfer in layered spherical tissue during magnetic hyperthermia.

A solid multi-layered concentric sphere with Gaussian space source is considered as the tissue model for magnetic hyperthermia treatment. The generalized dual-phase-lag model of bioheat transfer is used to describe the behavior of heat transport in tissue in the hyperthermia treatment process for accounting the local non-equilibrium effect. The effects of blood perfusion with the transient temperature are included in the tissue model. The hybrid numerical scheme based on Laplace transform, change of variables, and the modified discretization technique is extended to solve the present problem. The analytical solution for constant heat generation in the inner sphere is presented and evidences the accuracy and rationality of the present numerical results. In an ideal hyperthermia treatment, all the diseased tissues should be selectively heated without affecting any healthy tissue. Attempting to achieve the ideal temperature distribution, the thermal dose is estimated at the specified condition. The corresponding thermal efficacy of tumor damage has also been assessed based on the Arrenius equation.

Extraction of bioimpedance phase information from its magnitude using a non-uniform Kramers-Kronig transform.

A novel non-uniform Kramers-Kronig Transform algorithm for bioimpedance phase extraction is proposed and tested in this work. The algorithm error is studied and compared with a previously proposed phase extraction technique, also based on the Kramers-Kronig transform. Results using simulated datasets and experimental datasets confirm the excellent performance of the algorithm.

Magnetic fluid hyperthermia simulations in evaluation of SAR calculation methods.

PURPOSE: The purpose of this study is to employ magnetic fluid hyperthermia simulations in the precise computation of Specific Absorption Rate functions -SAR(T)-, and in the evaluation of the predictive capacity of different SAR calculation methods. METHODS: Magnetic fluid hyperthermia experiments were carried out using magnetite-based nanofluids. The respective SAR values were estimated through four different calculation methods including the initial slope method, the Box-Lucas method, the corrected slope method and the incremental analysis method (INCAM). A novel numerical model combining the heat transfer equations and the Navier-Stokes equations was developed to reproduce the experimental heating process. To address variations in heating efficiency with temperature, the expression of the power dissipation as a Gaussian function of temperature was introduced and the Levenberg-Marquardt optimization algorithm was employed to compute the function parameters and determine the function's effective branch within each measurement's temperature range. The power dissipation function was then reduced to the respective SAR function. RESULTS: The INCAM exhibited the lowest relative errors ranging between 0.62 and 15.03% with respect to the simulations. SAR(T) functions exhibited significant variations, up to 45%, within the MFH-relevant temperature range. CONCLUSIONS: The examined calculation methods are not suitable to accurately quantify the heating efficiency of a magnetic fluid. Numerical models can be exploited to effectively compute SAR(T) and contribute to the development of robust hyperthermia treatment planning applications.

A model of auditory brainstem response wave I morphology.

Use of the auditory brainstem response (ABR) in research has increased in the search for physiological correlates of noise-induced damage to the cochlea. The extraction of data from the ABR has traditionally relied on visual determination of peaks and troughs to calculate metrics such as wave amplitude. Visual determination can be reliable when evaluated by trained, experienced personnel, but noisy waveforms and overlapping waves produce uncertain data. The present study proposes and validates a method of fitting summed Gaussian functions to the summating potential and wave I of the ABR. This method could be useful to the research community studying these potentials by providing more accurate measures of wave amplitude than by visual determination.

A novel normalization for amide proton transfer CEST MRI to correct for fat signal-induced artifacts: application to human breast cancer imaging.

PURPOSE: The application of amide proton transfer (APT) CEST MRI for diagnosis of breast cancer is of emerging interest. However, APT imaging in the human breast is affected by the ubiquitous fat signal preventing a straightforward application of existing acquisition protocols. Although the spectral region of the APT signal does not coincide with fat resonances, the fat signal leads to an incorrect normalization of the Z-spectrum, and therefore to distorted APT effects. In this study, we propose a novel normalization for APT-CEST MRI that corrects for fat signal-induced artifacts in the postprocessing without the need for application of fat saturation schemes or water-fat separation approaches. METHODS: The novel normalization uses the residual signal at the spectral position of the direct water saturation to estimate the fat contribution. A comprehensive theoretical description of the normalization for an arbitrary phase relation of the water and fat signal is provided. Functionality and applicability of the proposed normalization was demonstrated by in vitro and in vivo experiments. RESULTS: In vitro, an underestimation of the conventional APT contrast of approximately -1.2% per 1% fat fraction was observed. The novel normalization yielded an APT contrast independent of the fat contribution, which was also independent of the water-fat phase relation. This allowed APT imaging in patients with mamma carcinoma corrected for fat signal contribution, field inhomogeneities, spillover dilution, and water relaxation effects. CONCLUSION: The proposed normalization increases the specificity of APT imaging in tissues with varying fat content and represents a time-efficient and specific absorption rate-efficient alternative to fat saturation and water-fat separation approaches.

Predicting high-intensity focused ultrasound thalamotomy lesions using 2D magnetic resonance thermometry and 3D Gaussian modeling.

PURPOSE: To develop a method of using two-dimensional (2D) magnetic resonance thermometry, and three-dimensional (3D) Gaussian modeling to predict the volume, shape, and location of 1 day postoperative T1w high-intensity focused ultrasound lesions in medication refractory tremor patients; thereby facilitating a better comprehension of thermal damage thresholds, which can be utilized to reduce adverse events, and improve patient outcome. METHODS: Fifteen patients underwent magnetic resonance-guided focused ultrasound (MRgFUS) thalamotomy, which was performed at our center using an InSightec ExAblate 4000 system (Haifa, Israel), and guided by magnetic resonance imaging using a 3 T Discovery 750 (General Electric Healthcare, Waukesha, WI, USA). For treatment monitoring, 2D MR thermometry (temperature sensitivity: -0.00909 ppm/°C, bandwidth: 279 Hz/pixel) was performed in multiple orthogonal planes (sagittal, coronal, and axial) intraoperatively. These images were temporally filtered using a general linear model approach to reduce noise. Temporal volumes of filtered temperature maps with a peak temperature ≥ 47°C were aligned and fitted with a 3D Gaussian to create a canonical heating model. We then fitted the filtered 2D temperature maps with a 3D Gaussian, and used the relationships derived from the 3D heating model to estimate the 3D temperature distribution. These temperature distributions were converted into thermal dose distributions and accumulated across time to create an accumulated thermal dose (ATD) profile. Thresholded ATD profiles were then correlated with manually traced T1-weighted 1 day postoperative lesion volumes across patients, and linear regression slopes were plotted against varying ATD thresholds. Additionally, the Dice-Sørensen coefficient (DSC) was calculated to quantify the volumetric overlap between predicted, and actual lesions. RESULTS: On average, 18.1 (standard deviation (SD): ±4.6, range: 10-29) sonications were performed with an average peak temperature achieved of 62.4°C (SD: ±2.4, range: 58.2-67.7). An ATD threshold of 35.8 CEM43 was found to give a unity linear regression slope; this corresponded to an average DSC of 0.689 (SD: ±0.090, range: 0.476-0.815). CONCLUSIONS: Using multiplanar 2D MR thermometry and 3D Gaussian modeling, we were able to achieve very good (DSC = 0.689) predictions of T1w 1 day postoperative lesion volume, shape and location at an ATD threshold of approximately 36 CEM43. Furthermore, this method has the potential to be used in clinical evaluations to further elucidate the relationship between thermal damage and clinical outcome. Accurate 3D lesion prediction will facilitate improved clinical decision making in future MRgFUS thalamotomies.

Rapid analysis of the Tanreqing injection by near-infrared spectroscopy combined with least squares support vector machine and Gaussian process modeling techniques.

Near-infrared spectroscopy (NIRS) combined with chemometrics was used to analyze the main active ingredients including chlorogenic acid, caffeic acid, luteoloside, baicalin, ursodesoxycholic acid, and chenodeoxycholic acid in the Tanreqing injection. In this paper, first, two hundred samples collected in the product line were divided into the calibration set and prediction set, and the reference values were determined by the High Performance Liquid Chromatography- Diode Array Detector/Evaporative Light Scattering Detector (HPLC-DAD/ELSD) method. Partial least squares (PLS) analysis was implemented as a linear method for models calibrated with different preprocessing means. Wavelet transformation (WT) was introduced as a variable selection technique by means of multiscale decomposition, and wavelet coefficients were employed as the input for modeling. Furthermore, two nonlinear approaches, least squares support vector machine (LS-SVM) and Gaussian process (GP), were applied to exploit the complicated relationship between the spectra and active ingredients. The optimal models for each ingredient were obtained by LS-SVM and GP methods. The performance of the final models was evaluated by the root mean square error of calibration (RMSEC), root mean square error of cross-validation (RMSECV), root mean square error of prediction (RMSEP) and correlation coefficient (R). All of the models in the paper give a good calibration ability with an R value above 0.92, and the prediction ability is also satisfactory, with an R value higher than 0.85. The overall results demonstrate that nonlinear models are more stable and predictable than linear ones, and they will be more suitable for the CHM system when high accuracy analysis is required. It can be concluded that NIRS with the LS-SVM and GP modeling methods is promising for the implementation of process analytical technology (PAT) in the pharmaceutical industry of Chinese herbal injections (CHIs).

3D space-dependent models for stochastic dosimetry applied to exposure to low frequency magnetic fields.

In this study, an innovative approach that combines Principal Component Analysis (PCA) and Gaussian process regression (Kriging method), never used before in the assessment of human exposure to electromagnetic fields (EMF), was applied to build space-dependent surrogate models of the 3D spatial distribution of the electric field induced in central nervous system (CNS) of children of different ages exposed to uniform magnetic field at 50 Hz of 200 µT of amplitude with uncertain orientation. The 3D surrogate models showed very low normalized percentage mean square error (MSE) values, always lower than 0.16%, confirming the feasibility and accuracy of the approach in estimating the 3D spatial distribution of E with a low number of components. Results showed that the electric field values induced in CNS tissues of children were within the ICNIRP basic restrictions for general public, with 99th percentiles of the E values obtained for each orientation showing median values in the range 1.9-2.1 mV/m. Similar 3D spatial distributions of the electric fields were found to be induced in CNS tissues of children of different ages. Bioelectromagnetics. 9999:1-10, 2018. © 2019 Bioelectromagnetics Society.

Detecting In-Situ oligomerization of engineered STIM1 proteins by diffraction-limited optical imaging.

Several signaling proteins require self-association of individual monomer units to be activated for triggering downstream signaling cascades in cells. Methods that allow visualizing their underlying molecular mechanisms will immensely benefit cell biology. Using enhanced Green Fluorescent Protein (eGFP) complementation, here I present a functional imaging approach for visualizing the protein-protein interaction in cells. Activation mechanism of an ER (endoplasmic reticulum) resident Ca2+ sensor, STIM1 (Stromal Interaction Molecule 1) that regulates store-operated Ca2+ entry in cells is considered as a model system. Co-expression of engineered full-length human STIM1 (ehSTIM1) with N-terminal complementary split eGFP pairs in mammalian cells fluoresces to form 'puncta' upon a drop in ER lumen Ca2+ concentration. Quantization of discrete fluorescent intensities of ehSTIM1 molecules at a diffraction-limited resolution revealed a diverse set of intensity levels not exceeding six-fold. Detailed screening of the ehSTIM1 molecular entities characterized by one to six fluorescent emitters across various in-plane sections shows a greater probability of occurrence for entities with six emitters in the vicinity of the plasma membrane (PM) than at the interior sections. However, the number density of entities with six emitters was lesser than that of others localized close to the PM. This finding led to hypothesize that activated ehSTIM1 dimers perhaps oligomerize in bundles ranging from 1-6 with an increased propensity for the occurrence of hexamers of ehSTIM1 dimer units close to PM even when its partner protein, ORAI1 (PM resident Ca2+ channel) is not sufficiently over-expressed in cells. The experimental data presented here provide direct evidence for luminal domain association of ehSTIM1 monomer units to trigger activation and allow enumerating various oligomers of ehSTIM1 in cells.

The Distribution of Standard Deviations Applied to High Throughput Screening.

High throughput screening (HTS) assesses compound libraries for "activity" using target assays. A subset of HTS data contains a large number of sample measurements replicated a small number of times providing an opportunity to introduce the distribution of standard deviations (DSD). Applying the DSD to some HTS data sets revealed signs of bias in some of the data and discovered a sub-population of compounds exhibiting high variability which may be difficult to screen. In the data examined, 21% of 1189 such compounds were pan-assay interference compounds. This proportion reached 57% for the most closely related compounds within the sub-population. Using the DSD, large HTS data sets can be modelled in many cases as two distributions: a large group of nearly normally distributed "inactive" compounds and a residual distribution of "active" compounds. The latter were not normally distributed, overlapped inactive distributions - on both sides -, and were larger than typically assumed. As such, a large number of compounds are being misclassified as "inactive" or are invisible to current methods which could become the next generation of drugs. Although applied here to HTS, it is applicable to data sets with a large number of samples measured a small number of times.