Orthogonal extended infomax algorithm.

Objective.The extended infomax algorithm for independent component analysis (ICA) can separate sub- and super-Gaussian signals but converges slowly as it uses stochastic gradient optimization. In this paper, an improved extended infomax algorithm is presented that converges much faster.Approach.Accelerated convergence is achieved by replacing the natural gradient learning rule of extended infomax by a fully-multiplicative orthogonal-group based update scheme of the ICA unmixing matrix, leading to an orthogonal extended infomax algorithm (OgExtInf). The computational performance of OgExtInf was compared with original extended infomax and with two fast ICA algorithms: the popular FastICA and Picard, a preconditioned limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm belonging to the family of quasi-Newton methods.Main results.OgExtInf converges much faster than original extended infomax. For small-size electroencephalogram (EEG) data segments, as used for example in online EEG processing, OgExtInf is also faster than FastICA and Picard.Significance.OgExtInf may be useful for fast and reliable ICA, e.g. in online systems for epileptic spike and seizure detection or brain-computer interfaces.

VSSI-GGD: A Variation Sparse EEG Source Imaging Approach Based on Generalized Gaussian Distribution.

Electroencephalographic (EEG) source imaging (ESI) is a powerful method for studying brain functions and surgical resection of epileptic foci. However, accurately estimating the location and extent of brain sources remains challenging due to noise and background interference in EEG signals. To reconstruct extended brain sources, we propose a new ESI method called Variation Sparse Source Imaging based on Generalized Gaussian Distribution (VSSI-GGD). VSSI-GGD uses the generalized Gaussian prior as a sparse constraint on the spatial variation domain and embeds it into the Bayesian framework for source estimation. Using a variational technique, we approximate the intractable true posterior with a Gaussian density. Through convex analysis, the Bayesian inference problem is transformed entirely into a series of regularized L2p -norm ( ) optimization problems, which are efficiently solved with the ADMM algorithm. Imaging results of numerical simulations and human experimental dataset analysis reveal the superior performance of VSSI-GGD, which provides higher spatial resolution with clear boundaries compared to benchmark algorithms. VSSI-GGD can potentially serve as an effective and robust spatiotemporal EEG source imaging method. The source code of VSSI-GGD is available at https://github.com/Mashirops/VSSI-GGD.git.

Gaussian accelerated molecular dynamics simulations facilitate prediction of the permeability of cyclic peptides.

Despite their widespread use as therapeutics, clinical development of small molecule drugs remains challenging. Among the many parameters that undergo optimization during the drug development process, increasing passive cell permeability (i.e., log(P)) can have some of the largest impact on potency. Cyclic peptides (CPs) have emerged as a viable alternative to small molecules, as they retain many of the advantages of small molecules (oral availability, target specificity) while being highly effective at traversing the plasma membrane. However, the relationship between the dominant conformations that typify CPs in an aqueous versus a membrane environment and cell permeability remain poorly characterized. In this study, we have used Gaussian accelerated molecular dynamics (GaMD) simulations to characterize the effect of solvent on the free energy landscape of lariat peptides, a subset of CPs that have recently shown potential for drug development (Kelly et al., JACS 2021). Differences in the free energy of lariat peptides as a function of solvent can be used to predict permeability of these molecules, and our results show that permeability is most greatly influenced by N-methylation and exposure to solvent. Our approach lays the groundwork for using GaMD as a way to virtually screen large libraries of CPs and drive forward development of CP-based therapeutics.

Giant honeybees (Apis dorsata) trade off defensiveness against periodic mass flight activity.

The giant honeybee Apis dorsata (Fabricius, 1793) is an evolutionarily ancient species that builds its nests in the open. The nest consists of a single honeycomb covered with the bee curtain which are several layers of worker bees that remain almost motionless with their heads up and abdomens down on the nest surface, except for the mouth area, the hub between inner- and outer-nest activities. A colony may change this semi-quiescence several times a day, depending on its reproductive state and ambient temperature, to enter the state of mass flight activity (MFA), in which nest organisation is restructured and defense ability is likely to be suppressed (predicted by the mass-flight-suspend-defensiveness hypothesis). For this study, three episode of MFA (mfa1-3) of a selected experimental nest were analysed in a case study with sequences of >60 000 images at 50 Hz, each comprise a short pre-MFA session, the MFA and the post-MFA phase of further 10 min. To test colony defensiveness under normative conditions, a dummy wasp was cyclically presented with a standardised motion programme (Pd) with intervening sessions without such a presentation (nPd). Motion activity at five selected surveillance zones (sz1-5) on the nest were analysed. In contrast to mfa1,2, in mfa3 the experimental regime started with the cyclic presentation of the dummy wasp only after the MFA had subsided. As a result, the MFA intensity in mfa3 was significantly lower than in mfa1-2, suggesting that a colony is able to perceive external threats during the MFA. Characteristic ripples appear in the motion profiles, which can be interpreted as a start signal for the transition to MFA. Because they are strongest in the mouth zone and shift to higher frequencies on their way to the nest periphery, it can be concluded that MFA starts earlier in the mouth zone than in the peripheral zones, also suggesting that the mouth zone is a control centre for the scheduling of MFA. In Pd phases of pre- and postMFA, the histogram-based motion spectra are biphasic, suggesting two cohorts in the process, one remaining at quiescence and the other involved in shimmering. Under MFA, nPd and Pd spectra were typically Gaussian, suggesting that the nest mates with a uniform workload shifted to higher motion activity. At the end of the MFA, the spectra shift back to the lower motion activities and the Pd spectra form a biphasic again. This happens a few minutes earlier in the peripheral zones than in the mouth zone. Using time profiles of the skewness of the Pd motion spectra, the mass-flight-suspend-defensiveness hypothesis is confirmed, whereby the inhibition of defense ability was found to increase progressively during the MFA. These sawtooth-like time profiles of skewness during MFA show that defense capability is recovered again quite quickly at the end of MFA. Finally, with the help of the Pd motion spectra, clear indications can be obtained that the giant honeybees engage in a decision in the sense of a tradeoff between MFA and collective defensiveness, especially in the regions in the periphery to the mouth zone.

Asymptotic uncertainty of false discovery proportion.

Multiple testing has been a prominent topic in statistical research. Despite extensive work in this area, controlling false discoveries remains a challenging task, especially when the test statistics exhibit dependence. Various methods have been proposed to estimate the false discovery proportion (FDP) under arbitrary dependencies among the test statistics. One key approach is to transform arbitrary dependence into weak dependence and subsequently establish the strong consistency of FDP and false discovery rate under weak dependence. As a result, FDPs converge to the same asymptotic limit within the framework of weak dependence. However, we have observed that the asymptotic variance of FDP can be significantly influenced by the dependence structure of the test statistics, even when they exhibit only weak dependence. Quantifying this variability is of great practical importance, as it serves as an indicator of the quality of FDP estimation from the data. To the best of our knowledge, there is limited research on this aspect in the literature. In this paper, we aim to fill in this gap by quantifying the variation of FDP, assuming that the test statistics exhibit weak dependence and follow normal distributions. We begin by deriving the asymptotic expansion of the FDP and subsequently investigate how the asymptotic variance of the FDP is influenced by different dependence structures. Based on the insights gained from this study, we recommend that in multiple testing procedures utilizing FDP, reporting both the mean and variance estimates of FDP can provide a more comprehensive assessment of the study's outcomes.

A latent class linear mixed model for monotonic continuous processes measured with error.

Motivated by measurement errors in radiographic diagnosis of osteoarthritis, we propose a Bayesian approach to identify latent classes in a model with continuous response subject to a monotonic, that is, non-decreasing or non-increasing, process with measurement error. A latent class linear mixed model has been introduced to consider measurement error while the monotonic process is accounted for via truncated normal distributions. The main purpose is to classify the response trajectories through the latent classes to better describe the disease progression within homogeneous subpopulations.

An Unsupervised Machine Learning Approach for the Automatic Construction of Local Chemical Descriptors.

Condensing the many physical variables defining a chemical system into a fixed-size array poses a significant challenge in the development of chemical Machine Learning (ML). Atom Centered Symmetry Functions (ACSFs) offer an intuitive featurization approach by means of a tedious and labor-intensive selection of tunable parameters. In this work, we implement an unsupervised ML strategy relying on a Gaussian Mixture Model (GMM) to automatically optimize the ACSF parameters. GMMs effortlessly decompose the vastness of the chemical and conformational spaces into well-defined radial and angular clusters, which are then used to build tailor-made ACSFs. The unsupervised exploration of the space has demonstrated general applicability across a diverse range of systems, spanning from various unimolecular landscapes to heterogeneous databases. The impact of the sampling technique and temperature on space exploration is also addressed, highlighting the particularly advantageous role of high-temperature Molecular Dynamics (MD) simulations. The reliability of the resulting features is assessed through the estimation of the atomic charges of a prototypical capped amino acid and a heterogeneous collection of CHON molecules. The automatically constructed ACSFs serve as high-quality descriptors, consistently yielding typical prediction errors below 0.010 electrons bound for the reported atomic charges. Altering the spatial distribution of the functions with respect to the cluster highlights the critical role of symmetry rupture in achieving significantly improved features. More specifically, using two separate functions to describe the lower and upper tails of the cluster results in the best performing models with errors as low as 0.006 electrons. Finally, the effectiveness of finely tuned features was checked across different architectures, unveiling the superior performance of Gaussian Process (GP) models over Feed Forward Neural Networks (FFNNs), particularly in low-data regimes, with nearly a 2-fold increase in prediction quality. Altogether, this approach paves the way toward an easier construction of local chemical descriptors, while providing valuable insights into how radial and angular spaces should be mapped. Finally, this work opens the possibility of encoding many-body information beyond angular terms into upcoming ML features.

An efficient detection model based on improved YOLOv5s for abnormal surface features of fish.

Detecting abnormal surface features is an important method for identifying abnormal fish. However, existing methods face challenges in excessive subjectivity, limited accuracy, and poor real-time performance. To solve these challenges, a real-time and accurate detection model of abnormal surface features of in-water fish is proposed, based on improved YOLOv5s. The specific enhancements include: 1) We optimize the complete intersection over union and non-maximum suppression through the normalized Gaussian Wasserstein distance metric to improve the model's ability to detect tiny targets. 2) We design the DenseOne module to enhance the reusability of abnormal surface features, and introduce MobileViTv2 to improve detection speed, which are integrated into the feature extraction network. 3) According to the ACmix principle, we fuse the omni-dimensional dynamic convolution and convolutional block attention module to solve the challenge of extracting deep features within complex backgrounds. We carried out comparative experiments on 160 validation sets of in-water abnormal fish, achieving precision, recall, mAP50, mAP50:95 and frames per second (FPS) of 99.5, 99.1, 99.1, 73.9% and 88 FPS, respectively. The results of our model surpass the baseline by 1.4, 1.2, 3.2, 8.2% and 1 FPS. Moreover, the improved model outperforms other state-of-the-art models regarding comprehensive evaluation indexes.

An integrated model of the human cornea as a linear biaxial birefringent medium.

A novel model of human corneal birefringence is presented. The cornea is treated as a homogeneous biaxial linear birefringent medium in which the values of the binormal axes angle and organization of the main refractive indices vary continuously from the apex to the limbus. In its central part, the angle between binormal axes is 35°, and para centrally, it smoothly increases to 83.7°. The values of the main refractive indices (nx, ny, nz) change, as well as their order, from nx < nz < ny to nz < nx < ny. The transition between these two states was described with a normal distribution (µ = 0.45, σ = 0.1). The presented model corresponds with the experimental results presented in the literature. To our knowledge, it is the first model that presents the anisotropic properties' distributions of the entire cornea. The presented model facilitates a better understanding of the corneal birefringence phenomenon directly related to its lamellar structure.

Self-correction of cycle threshold values by a normal distribution-based process to improve accuracy of quantification in real-time digital PCR.

The digital polymerase chain reaction (dPCR) is a new and developing nucleic acid detection technology with high sensitivity that can realize the absolute quantitative analysis of samples. In order to improve the accuracy of quantitative results, real-time digital PCR emphasizes the kinetic information during amplification to identify prominent abnormal data. However, it is challenging to use a unified standard to accurately classify the amplification curve of each well as negative and positive, due to the interference caused by various factors in the experiment. In this work, a normal distribution-based cycle threshold value self-correcting model (NCSM) was established, which focused on the feature of the cycle threshold values in amplification curves and conducted continuous detection and correction on the whole. The cycle threshold value distribution was closer to the ideal normal distribution to avoid the influence of interference. Thus, the model achieves a more accurate classification between positive and negative results. The corrective process was applied to plasmid samples and resulted in an accuracy improvement from 92 to 99%. The coefficient of variation was below 5% when considering the quantitation of a range between 100 and 10,000 copies. At the same time, by utilizing this model, the distribution of cycle threshold values at the endpoint can be predicted with fewer thermal cycles, which can reduce the cycling time by around 25% while maintaining a consistency of more than 98%. Therefore, using the NCSM can effectively enhance the quantitative accuracy and increase the detection efficiency based on the real-time dPCR platform.

A Comparison of Statistical Methods to Construct Confidence Intervals and Fiducial Intervals for Measures of Health Disparities.

Health disparities are differences in health status across different socioeconomic groups. Classical methods, e.g., the Delta method, have been used to estimate the standard errors of estimated measures of health disparities and to construct confidence intervals for these measures. However, the confidence intervals constructed using the classical methods do not have good coverage properties for situations involving sparse data. In this article, we introduce three new methods to construct fiducial intervals for measures of health disparities based on approximate fiducial quantities. Through a comprehensive simulation study, We compare the empirical coverage properties of the proposed fiducial intervals against two Monte Carlo simulation-based methods-utilizing either a truncated Normal distribution or the Gamma distribution-as well as the classical method. The findings of the simulation study advocate for the adoption of the Monte Carlo simulation-based method with the Gamma distribution when a unified approach is sought for all health disparity measures.

Underwater image enhancement using multi-task fusion.

Underwater images are often scattered due to suspended particles in the water, resulting in light scattering and blocking and reduced visibility and contrast. Color shifts and distortions are also caused by the absorption of different wavelengths of light in the water. This series of problems will make the underwater image quality greatly impaired, resulting in some advanced visual work can not be carried out underwater. In order to solve these problems, this paper proposes an underwater image enhancement method based on multi-task fusion, called MTF. Specifically, we first use linear constraints on the input image to achieve color correction based on the gray world assumption. The corrected image is then used to achieve visibility enhancement using an improved type-II fuzzy set-based algorithm, while the image is contrast enhanced using standard normal distribution probability density function and softplus function. However, in order to obtain more qualitative results, we propose multi-task fusion, in which we solve for similarity, then we obtain fusion weights that guarantee the best features of the image as much as possible from the obtained similarity, and finally we fuse the image with the weights to obtain the output image, and we find that multi-task fusion has excellent image enhancement and restoration capabilities, and also produces visually pleasing results. Extensive qualitative and quantitative evaluations show that MTF method achieves optimal results compared to ten state-of-the-art underwater enhancement algorithms on 2 datasets. Moreover, the method can achieve better results in application tests such as target detection and edge detection.

Large effects and the infinitesimal model.

The infinitesimal model of quantitative genetics relies on the Central Limit Theorem to stipulate that under additive models of quantitative traits determined by many loci having similar effect size, the difference between an offspring's genetic trait component and the average of their two parents' genetic trait components is Normally distributed and independent of the parents' values. Here, we investigate how the assumption of similar effect sizes affects the model: if, alternatively, the tail of the effect size distribution is polynomial with exponent α<2, then a different Central Limit Theorem implies that sums of effects should be well-approximated by a "stable distribution", for which single large effects are often still important. Empirically, we first find tail exponents between 1 and 2 in effect sizes estimated by genome-wide association studies of many human disease-related traits. We then show that the independence of offspring trait deviations from parental averages in many cases implies the Gaussian aspect of the infinitesimal model, suggesting that non-Gaussian models of trait evolution must explicitly track the underlying genetics, at least for loci of large effect. We also characterize possible limiting trait distributions of the infinitesimal model with infinitely divisible noise distributions, and compare our results to simulations.

Calculation of the total corneal astigmatism using the virtual cross cylinder method on the secondary principal plane of the cornea.

This study aimed to establish a virtual cross cylinder method to calculate the total corneal astigmatism by combining the anterior and posterior corneal astigmatism on the secondary principal plane of the cornea based on Gaussian optics. The meridian with the least refractive power, namely, the flattest meridian of the virtual cross cylinder of a ± 0.5 × C diopter, is set as the reference meridian, and the power (F) at an angle of φ between an arbitrary meridian and the reference meridian is defined as F(φ) = - 0.5 × C × cos2φ. The magnitude and axis of the total corneal astigmatism were calculated by applying trigonometric functions and the atan2 function based on the combination of the virtual cross cylinders of the anterior corneal astigmatism and the posterior corneal astigmatism. To verify the performance of the virtual cross cylinder method, a verification experiment with two Jackson cross cylinders and a lensmeter was performed, and the measured and calculated values were compared. The limit of the natural domain of the arctangent function is circumvented by using the atan2 function. The magnitude and axis of the total corneal astigmatism are determined through generalized mathematical expressions. The verification experiment results showed good agreement between the measured and calculated values. Compared to the vector analysis method, the virtual cross cylinder method is mathematically sound and straightforward. A novel technique for calculating total corneal astigmatism, the virtual cross cylinder method, was developed and verified.

EAGS: efficient and adaptive Gaussian smoothing applied to high-resolved spatial transcriptomics.

BACKGROUND: The emergence of high-resolved spatial transcriptomics (ST) has facilitated the research of novel methods to investigate biological development, organism growth, and other complex biological processes. However, high-resolved and whole transcriptomics ST datasets require customized imputation methods to improve the signal-to-noise ratio and the data quality. FINDINGS: We propose an efficient and adaptive Gaussian smoothing (EAGS) imputation method for high-resolved ST. The adaptive 2-factor smoothing of EAGS creates patterns based on the spatial and expression information of the cells, creates adaptive weights for the smoothing of cells in the same pattern, and then utilizes the weights to restore the gene expression profiles. We assessed the performance and efficiency of EAGS using simulated and high-resolved ST datasets of mouse brain and olfactory bulb. CONCLUSIONS: Compared with other competitive methods, EAGS shows higher clustering accuracy, better biological interpretations, and significantly reduced computational consumption.

Gaussian Process Regression-Based Near-Infrared d-Luciferin Analogue Design Using Mutation-Controlled Graph-Based Genetic Algorithm.

Molecular discovery is central to the field of chemical informatics. Although optimization approaches have been developed that target-specific molecular properties in combination with machine learning techniques, optimization using databases of limited size is challenging for efficient molecular design. We present a molecular design method with a Gaussian process regression model and a graph-based genetic algorithm (GB-GA) from a data set comprising a small number of compounds by introducing mutation probability control in the genetic algorithm to enhance the optimization capability and speed up the convergence to the optimal solution. In addition, we propose reducing the number of parameters in the conventional GB-GA focusing on efficient molecular design from a small database. We generated a target-specific database by combining active learning and iterative design in the evolutionary methodologies and chose Gaussian process regression as the prediction model for molecular properties. We show that the proposed scheme is more efficient for optimization toward the target properties from goal-directed benchmarks with several drug-like molecules compared to the conventional GB-GA method. Finally, we provide a demonstration whereby we designed D-luciferin analogues with near-infrared fluorescence for bioimaging, which is desirable for effective in vivo light sources, from a small-size data set.

Rapid, high-contrast, and steady volumetric imaging with Bessel-beam-based two-photon fluorescence microscopy.

Significance: Two-photon fluorescence microscopy (TPFM) excited by Gaussian beams requires axial tomographic scanning for three-dimensional (3D) volumetric imaging, which is a time-consuming process, and the slow imaging speed hinders its application for in vivo brain imaging. The Bessel focus, characterized by an extended depth of focus and constant resolution, facilitates the projection of a 3D volume onto a two-dimensional image, which significantly enhances the speed of volumetric imaging. Aim: We aimed to demonstrate the ability of a TPFM with a sidelobe-free Bessel beam to provide a promising tool for research in live biological specimens. Approach: Comparative in vivo imaging was conducted in live mouse brains and transgenic zebrafish to evaluate the performance of TPFM and Bessel-beam-based TPFM. Additionally, an image-difference method utilizing zeroth-order and third-order Bessel beams was introduced to effectively suppress background interference introduced by sidelobes. Results: In comparison with traditional TPFM, the Bessel-beams-based TPFM demonstrated a 30-fold increase in imaging throughput and speed. Furthermore, the effectiveness of the image-difference method was validated in live biological specimens, resulting in a substantial enhancement of image contrast. Importantly, our TPFM with a sidelobe-free Bessel beam exhibited robustness against axial displacements, a feature of considerable value for in vivo experiments. Conclusions: We achieved rapid, high-contrast, and robust volumetric imaging of the vasculature in live mouse brains and transgenic zebrafish using our TPFM with a sidelobe-free Bessel beam.

Natural gradient ascent in evolutionary games.

We consider evolutionary games with a continuous trait space where the replicator dynamics are restricted to the manifold of multivariate Gaussian distributions. We demonstrate that replicator dynamics are gradient flows with respect to the Fisher information metric. The potential function for these gradient flows is closely related to the mean fitness. Our findings extend previous results on natural gradient ascent in evolutionary games with a finite strategy set. Throughout the paper we pursue an information-geometric point of view on evolutionary games. This sheds a new light on the replicator dynamics as a learning process, realizing the compromise between maximization of the mean fitness and preservation of the diversity.

Are you sure it's an artifact? Artifact detection and uncertainty quantification in histological images.

Modern cancer diagnostics involves extracting tissue specimens from suspicious areas and conducting histotechnical procedures to prepare a digitized glass slide, called Whole Slide Image (WSI), for further examination. These procedures frequently introduce different types of artifacts in the obtained WSI, and histological artifacts might influence Computational Pathology (CPATH) systems further down to a diagnostic pipeline if not excluded or handled. Deep Convolutional Neural Networks (DCNNs) have achieved promising results for the detection of some WSI artifacts, however, they do not incorporate uncertainty in their predictions. This paper proposes an uncertainty-aware Deep Kernel Learning (DKL) model to detect blurry areas and folded tissues, two types of artifacts that can appear in WSIs. The proposed probabilistic model combines a CNN feature extractor and a sparse Gaussian Processes (GPs) classifier, which improves the performance of current state-of-the-art artifact detection DCNNs and provides uncertainty estimates. We achieved 0.996 and 0.938 F1 scores for blur and folded tissue detection on unseen data, respectively. In extensive experiments, we validated the DKL model on unseen data from external independent cohorts with different staining and tissue types, where it outperformed DCNNs. Interestingly, the DKL model is more confident in the correct predictions and less in the wrong ones. The proposed DKL model can be integrated into the preprocessing pipeline of CPATH systems to provide reliable predictions and possibly serve as a quality control tool.

Cryo-EM structure and B-factor refinement with ensemble representation.

Cryo-EM experiments produce images of macromolecular assemblies that are combined to produce three-dimensional density maps. Typically, atomic models of the constituent molecules are fitted into these maps, followed by a density-guided refinement. We introduce TEMPy-ReFF, a method for atomic structure refinement in cryo-EM density maps. Our method represents atomic positions as components of a Gaussian mixture model, utilising their variances as B-factors, which are used to derive an ensemble description. Extensively tested on a substantial dataset of 229 cryo-EM maps from EMDB ranging in resolution from 2.1-4.9 Å with corresponding PDB and CERES atomic models, our results demonstrate that TEMPy-ReFF ensembles provide a superior representation of cryo-EM maps. On a single-model basis, it performs similarly to the CERES re-refinement protocol, although there are cases where it provides a better fit to the map. Furthermore, our method enables the creation of composite maps free of boundary artefacts. TEMPy-ReFF is useful for better interpretation of flexible structures, such as those involving RNA, DNA or ligands.