Kriging based on Gaussian random fields is widely used in reconstructing unknown functions. The kriging method has pointwise predictive distributions which are computationally simple. However, in many applications one would like to predict for a range of untried points simultaneously. In this work, we obtain some error bounds for the simple and universal kriging predictor under the uniform metric. It works for a scattered set of input points in an arbitrary dimension, and also covers the case where the covariance function of the Gaussian process is misspecified. These results lead to a better understanding of the rate of convergence of kriging under the Gaussian or the Matérn correlation functions, the relationship between space-filling designs and kriging models, and the robustness of the Matérn correlation functions. Supplementary materials for this article are available online.

Introduction: The molecular mechanisms underlying cartilage destruction in osteoarthritis are poorly understood. Proteolysis is a key feature in the turnover and degradation of cartilage extracellular matrix where the focus of research has been on the metzincin family of metalloproteinases. However, there is strong evidence to indicate important roles for other catalytic classes of proteases, with both extracellular and intracellular activities. The aim of this study was to profile the expression of the majority of protease genes in all catalytic classes in normal human cartilage and that from patients with osteoarthritis (OA) using a quantitative method. Methods: Human cartilage was obtained from femoral heads at joint replacement for either osteoarthritis or following fracture to the neck of femur (NOF). Total RNA was purified, and expression of genes assayed using Taqman^® low-density array quantitative RT-PCR. Results: A total of 538 protease genes were profiled, of which 431 were expressed in cartilage. A total of 179 genes were differentially expressed in OA versus NOF cartilage: eight aspartic proteases, 44 cysteine proteases, 76 metalloproteases, 46 serine proteases and five threonine proteases. Wilcoxon ranking as well as the LogitBoost-NR machine learning approach were used to assign significance to each gene, with the most highly ranked genes broadly similar using each method. Conclusions: This study is the most complete quantitative analysis of protease gene expression in cartilage to date. The data help give direction to future research on the specific function(s) of individual proteases or protease families in cartilage and may help to refine anti-proteolytic strategies in OA.

Scientists and engineers commonly use simulation models to study real systems for which actual experimentation is costly, difficult, or impossible. Many simulations are stochastic in the sense that repeated runs with the same input configuration will result in different outputs. For expensive or time-consuming simulations, stochastic kriging is commonly used to generate predictions for simulation model outputs subject to uncertainty due to both function approximation and stochastic variation. Here, we develop and justify a few guidelines for experimental design, which ensure accuracy of stochastic kriging emulators. We decompose error in stochastic kriging predictions into nominal, numeric, parameter estimation, and parameter estimation numeric components and provide means to control each in terms of properties of the underlying experimental design. The design properties implied for each source of error are weakly conflicting and broad principles are proposed. In brief, space-filling properties, “small fill distance” and “large separation distance,” should be balanced with replication at distinct input configurations, with number of replications depending on the relative magnitudes of stochastic and process variability. Nonstationarity implies higher input density in more active regions, while regression functions imply a balance with traditional design properties. A few examples are presented to illustrate the results. Supplementary materials providing proofs of the theoretical results and code for comparisons are available online.

Hydrological data are collected automatically from remote water level monitoring stations and then transmitted to the national water management centre via telemetry system. However, the data received at the centre can be incomplete or anomalous due to some issues with the instruments such as power and sensor failures. Usually, the detected anomalies or missing data are just simply eliminated from the data, which could lead to inaccurate analysis or even false alarms. Therefore, it is very helpful to identify missing values and correct them as accurate as possible. In this paper, we introduced a new approach - Full Subsequence Matching (FSM), for imputing missing values in telemetry water level data. The FSM firstly identifies a sequence of missing values and replaces them with some constant values to create a dummy complete sequence. Then, searching for the most similar subsequence from the historical data. Finally, the identified subsequence will be adapted to fit the missing part based on their similarity. The imputation accuracy of the FSM was evaluated with telemetry water level data and compared to some well-established methods - Interpolation, k-NN, MissForest, and also a leading deep learning method - the Long Short-Term Memory (LSTM) technique. Experimental results show that the FSM technique can produce more precise imputations, particularly for those with strong periodic patterns.

Effective drug delivery systems are paramount in enhancing pharmaceutical outcomes, particularly through the use of cell-penetrating peptides (CPPs). These peptides are gaining prominence due to their ability to penetrate eukaryotic cells efficiently without inflicting significant damage to the cellular membrane, thereby ensuring optimal drug delivery. However, the identification and characterization of CPPs remain a challenge due to the laborious and time-consuming nature of conventional methods, despite advances in proteomics. Current computational models, however, are predominantly tailored for balanced datasets, an approach that falls short in real-world applications characterized by a scarcity of known positive CPP instances. To navigate this shortfall, we introduce PractiCPP, a novel deep-learning framework tailored for CPP prediction in highly imbalanced data scenarios. Uniquely designed with the integration of hard negative sampling and a sophisticated feature extraction and prediction module, PractiCPP facilitates an intricate understanding and learning from imbalanced data. Our extensive computational validations highlight PractiCPP’s exceptional ability to outperform existing state-of-the-art methods, demonstrating remarkable accuracy, even in datasets with an extreme positive-to-negative ratio of 1:1000. Furthermore, through methodical embedding visualizations, we have established that models trained on balanced datasets are not conducive to practical, large-scale CPP identification, as they do not accurately reflect real-world complexities. In summary, PractiCPP potentially offers new perspectives in CPP prediction methodologies. Its design and validation, informed by real-world dataset constraints, suggest its utility as a valuable tool in supporting the acceleration of drug delivery advancements. The source code of PractiCPP is available on Figshare at https://doi.org/10.6084/m9.figshare.25053878.v1. Supplementary data is available at Bioinformatics online.

Feature selection is increasingly important in data analysis and machine learning in big data era. However, how to use the data in feature selection, i.e. using either ALL or PART of a dataset, has become a serious and tricky issue. Whilst the conventional practice of using all the data in feature selection may lead to selection bias, using part of the data may, on the other hand, lead to underestimating the relevant features under some conditions. This paper investigates these two strategies systematically in terms of reliability and effectiveness, and then determines their suitability for datasets with different characteristics. The reliability is measured by the Average Tanimoto Index and the Inter-method Average Tanimoto Index, and the effectiveness is measured by the mean generalisation accuracy of classification. The computational experiments are carried out on ten real-world benchmark datasets and fourteen synthetic datasets. The synthetic datasets are generated with a pre-set number of relevant features and varied numbers of irrelevant features and instances, and added with different levels of noise. The results indicate that the PART approach is more effective in reducing the bias when the size of a dataset is small but starts to lose its advantage as the dataset size increases.