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Research in high energy physics (HEP) requires huge amounts of computing and storage, putting strong constraints on the code speed and resource usage. To meet these requirements, a compiled high-performance language is typically used; while for physicists, who focus on the application when developing the code, better research productivity pleads for a high-level programming language. A popular approach consists of combining Python, used for the high-level interface, and C++, used for the computing intensive part of the code. A more convenient and efficient approach would be to use a language that provides both high-level programming and high-performance. The Julia programming language, developed at MIT especially to allow the use of a single language in research activities, has followed this path. In this paper the applicability of using the Julia language for HEP research is explored, covering the different aspects that are important for HEP code development: runtime performance, handling of large projects, interface with legacy code, distributed computing, training, and ease of programming. The study shows that the HEP community would benefit from a large scale adoption of this programming language. The HEP-specific foundation libraries that would need to be consolidated are identified

This paper addresses the problem of designing the {\it continuous-discrete} unscented Kalman filter (UKF) implementation methods. More precisely, the aim is to propose the MATLAB-based UKF algorithms for {\it accurate} and {\it robust} state estimation of stochastic dynamic systems. The accuracy of the {\it continuous-discrete} nonlinear filters heavily depends on how the implementation method manages the discretization error arisen at the filter prediction step. We suggest the elegant and accurate implementation framework for tracking the hidden states by utilizing the MATLAB built-in numerical integration schemes developed for solving ordinary differential equations (ODEs). The accuracy is boosted by the discretization error control involved in all MATLAB ODE solvers. This keeps the discretization error below the tolerance value provided by users, automatically. Meanwhile, the robustness of the UKF filtering methods is examined in terms of the stability to roundoff. In contrast to the pseudo-square-root UKF implementations established in engineering literature, which are based on the one-rank Cholesky updates, we derive the stable square-root methods by utilizing the $J$-orthogonal transformations for calculating the Cholesky square-root factors.

This paper proposes a novel signed $\beta$-model for directed signed network, which is frequently encountered in application domains but largely neglected in literature. The proposed signed $\beta$-model decomposes a directed signed network as the difference of two unsigned networks and embeds each node with two latent factors for in-status and out-status. The presence of negative edges leads to a non-concave log-likelihood, and a one-step estimation algorithm is developed to facilitate parameter estimation, which is efficient both theoretically and computationally. We also develop an inferential procedure for pairwise and multiple node comparisons under the signed $\beta$-model, which fills the void of lacking uncertainty quantification for node ranking. Theoretical results are established for the coverage probability of confidence interval, as well as the false discovery rate (FDR) control for multiple node comparison. The finite sample performance of the signed $\beta$-model is also examined through extensive numerical experiments on both synthetic and real-life networks.

Keystroke dynamics is a behavioural biometric utilised for user identification and authentication. We propose a new set of features based on the distance between keys on the keyboard, a concept that has not been considered before in keystroke dynamics. We combine flight times, a popular metric, with the distance between keys on the keyboard and call them as Distance Enhanced Flight Time features (DEFT). This novel approach provides comprehensive insights into a person's typing behaviour, surpassing typing velocity alone. We build a DEFT model by combining DEFT features with other previously used keystroke dynamic features. The DEFT model is designed to be device-agnostic, allowing us to evaluate its effectiveness across three commonly used devices: desktop, mobile, and tablet. The DEFT model outperforms the existing state-of-the-art methods when we evaluate its effectiveness across two datasets. We obtain accuracy rates exceeding 99% and equal error rates below 10% on all three devices.

We present a multigrid algorithm to solve efficiently the large saddle-point systems of equations that typically arise in PDE-constrained optimization under uncertainty. The algorithm is based on a collective smoother that at each iteration sweeps over the nodes of the computational mesh, and solves a reduced saddle-point system whose size depends on the number $N$ of samples used to discretized the probability space. We show that this reduced system can be solved with optimal $O(N)$ complexity. We test the multigrid method on three problems: a linear-quadratic problem, possibly with a local or a boundary control, for which the multigrid method is used to solve directly the linear optimality system; a nonsmooth problem with box constraints and $L^1$-norm penalization on the control, in which the multigrid scheme is used within a semismooth Newton iteration; a risk-adverse problem with the smoothed CVaR risk measure where the multigrid method is called within a preconditioned Newton iteration. In all cases, the multigrid algorithm exhibits excellent performances and robustness with respect to the parameters of interest.

This paper proposes a strategy to solve the problems of the conventional s-version of finite element method (SFEM) fundamentally. Because SFEM can reasonably model an analytical domain by superimposing meshes with different spatial resolutions, it has intrinsic advantages of local high accuracy, low computation time, and simple meshing procedure. However, it has disadvantages such as accuracy of numerical integration and matrix singularity. Although several additional techniques have been proposed to mitigate these limitations, they are computationally expensive or ad-hoc, and detract from its strengths. To solve these issues, we propose a novel strategy called B-spline based SFEM. To improve the accuracy of numerical integration, we employed cubic B-spline basis functions with $C^2$-continuity across element boundaries as the global basis functions. To avoid matrix singularity, we applied different basis functions to different meshes. Specifically, we employed the Lagrange basis functions as local basis functions. The numerical results indicate that using the proposed method, numerical integration can be calculated with sufficient accuracy without any additional techniques used in conventional SFEM. Furthermore, the proposed method avoids matrix singularity and is superior to conventional methods in terms of convergence for solving linear equations. Therefore, the proposed method has the potential to reduce computation time while maintaining a comparable accuracy to conventional SFEM.

Subspace clustering methods which embrace a self-expressive model that represents each data point as a linear combination of other data points in the dataset provide powerful unsupervised learning techniques. However, when dealing with large datasets, representation of each data point by referring to all data points via a dictionary suffers from high computational complexity. To alleviate this issue, we introduce a parallelizable multi-subset based self-expressive model (PMS) which represents each data point by combining multiple subsets, with each consisting of only a small proportion of the samples. The adoption of PMS in subspace clustering (PMSSC) leads to computational advantages because the optimization problems decomposed over each subset are small, and can be solved efficiently in parallel. Furthermore, PMSSC is able to combine multiple self-expressive coefficient vectors obtained from subsets, which contributes to an improvement in self-expressiveness. Extensive experiments on synthetic and real-world datasets show the efficiency and effectiveness of our approach in comparison to other methods.

Data-driven modeling can suffer from a constant demand for data, leading to reduced accuracy and impractical for engineering applications due to the high cost and scarcity of information. To address this challenge, we propose a progressive reduced order modeling framework that minimizes data cravings and enhances data-driven modeling's practicality. Our approach selectively transfers knowledge from previously trained models through gates, similar to how humans selectively use valuable knowledge while ignoring unuseful information. By filtering relevant information from previous models, we can create a surrogate model with minimal turnaround time and a smaller training set that can still achieve high accuracy. We have tested our framework in several cases, including transport in porous media, gravity-driven flow, and finite deformation in hyperelastic materials. Our results illustrate that retaining information from previous models and utilizing a valuable portion of that knowledge can significantly improve the accuracy of the current model. We have demonstrated the importance of progressive knowledge transfer and its impact on model accuracy with reduced training samples. For instance, our framework with four parent models outperforms the no-parent counterpart trained on data nine times larger. Our research unlocks data-driven modeling's potential for practical engineering applications by mitigating the data scarcity issue. Our proposed framework is a significant step toward more efficient and cost-effective data-driven modeling, fostering advancements across various fields.

One central theme in machine learning is function estimation from sparse and noisy data. An example is supervised learning where the elements of the training set are couples, each containing an input location and an output response. In the last decades, a substantial amount of work has been devoted to design estimators for the unknown function and to study their convergence to the optimal predictor, also characterizing the learning rate. These results typically rely on stationary assumptions where input locations are drawn from a probability distribution that does not change in time. In this work, we consider kernel-based ridge regression and derive convergence conditions under non stationary distributions, addressing also cases where stochastic adaption may happen infinitely often. This includes the important exploration-exploitation problems where e.g. a set of agents/robots has to monitor an environment to reconstruct a sensorial field and their movements rules are continuously updated on the basis of the acquired knowledge on the field and/or the surrounding environment.

Decision trees offer the benefit of easy interpretation because they allow the classification of input data based on if--then rules. However, as decision trees are constructed by an algorithm that achieves clear classification with minimum necessary rules, the trees possess the drawback of extracting only minimum rules, even when various latent rules exist in data. Approaches that construct multiple trees using randomly selected feature subsets do exist. However, the number of trees that can be constructed remains at the same scale because the number of feature subsets is a combinatorial explosion. Additionally, when multiple trees are constructed, numerous rules are generated, of which several are untrustworthy and/or highly similar. Therefore, we propose "MAABO-MT" and "GS-MRM" algorithms that strategically construct trees with high estimation performance among all possible trees with small computational complexity and extract only reliable and non-similar rules, respectively. Experiments are conducted using several open datasets to analyze the effectiveness of the proposed method. The results confirm that MAABO-MT can discover reliable rules at a lower computational cost than other methods that rely on randomness. Furthermore, the proposed method is confirmed to provide deeper insights than single decision trees commonly used in previous studies. Therefore, MAABO-MT and GS-MRM can efficiently extract rules from combinatorially exploded decision trees.