Probability and Statistics for Computer Scientists

In recent years, text mining has become a branch of Natural Language Processing. This chapter focuses on the analysis of textual data, illustrated by examples treated with the software R, which will be used to manipulate texts and strings, to transform them by word embedding methods and to analyse them by supervised and unsupervised statistical and machine learning methods. It discusses methods of topic modeling and sentiment analysis. There are two types of methods in textual data analysis: descriptive methods and predictive methods. The chapter describes the various lexical analyses that are often performed to categorize documents or to detect the topics contained in a set of documents. The analysis of textual data is most often done on vector representations of the data, which are stored in matrices containing the documents in rows and the terms in columns. A recent application of natural language processing is sentiment analysis.

Stochastic simulation is an essential method for modeling complex geological structures in geosciences. Evaluating the uncertainty of the realizations of stochastic simulations can better describe real phenomena. However, uncertainty evaluation of stochastic simulation methods remains a challenge due to the limited data from geological surveys and the uncertainty in reliability estimation with stochastic simulation models. In addition, understanding the sensitivity of the parameters in stochastic simulation models is invaluable when exploring the parameters with a higher influence on the uncertainty associated with predictions generated from stochastic simulation. To facilitate uncertainty evaluation in stochastic simulation methods, we use the circular treemap as an interactive workflow to explore prediction uncertainty in and the parameter sensitivity of multiple-point geostatistical (MPS) stochastic simulation methods. In this work, we present a novel visualization framework for assessing the uncertainty in MPS stochastic simulation methods and exploring the parameter sensitivity of the MPS methods. We present a new indicator to integrate multiple metrics that characterize geospatial features and visualize these metrics to assist domain experts in making decisions. Parallel coordinates-scatter matrix plots and multi-dimensional scaling (MDS) plots are used to analyze the parametric sensitivity of MPS stochastic simulation methods. The realizations and parameters of two MPS stochastic simulation methods are used to test the applicability of the proposed visualization workflow and the visualization methods. The results demonstrate that our workflow and the visualization methods can assist experts in finding the model with less uncertainty and improve the efficiency of parameter adjustment using different MPS stochastic simulation methods.

The SMILE (Solar wind Magnetosphere Ionosphere Link Explorer) mission (http://www.nssc.cas.cn/smile/) is a scientific space mission, jointly supported by the European Space Agency (ESA) and the Chinese Academy of Sciences (CAS). SMILE aims to study the solar wind-magnetosphere coupling in a novel approach: global imaging of the Earth’s magnetosheath and cusps in the soft X-ray band. At the same time, it also provides UV imaging of the northern auroral regions, completing the detection of solar wind–magnetosphere–ionosphere coupling in a global way. The time frame for launch is in 2025. This talk summarizes the recent progress of SMILE Modeling Working Group (MWG), specifically a special issue on Earth and Planetary Physics (EPP) with 23 articles to provide the international space science community with works regarding the modeling and data analysis methods developed during the pre-studies of the SMILE mission. We categorize the articles into the following topics and give some brief comments: (1) instrument descriptions of the Soft X-ray Imager (SXI), (2) modeling of the X-ray signals, (3) data processing of the images, (4) tracing the boundary locations from the simulated images, (5) physical phenomenon related to the scientific goals of SMILE-SXI, (6) modeling of the aurora, and (7) ground-based support for SMILE.

Measurements of CO2 flux emitted at the surface of volcanic lakes have been performed using the so-called floating accumulation chamber method. Two statistical methods are used to process data: the graphical statistical and stochastic simulation methods. The results of graphical statistical approach allow the quantification of two degassing processes acting at the lake surface: one corresponding to CO2 fluxes resulting from rising bubbles and the second corresponding to equilibrium diffusion of dissolved CO2 at the water-air surface. The sequential Gaussian simulation method has been used for mapping the CO2 flux and estimating the total CO2 emission rate at the surface of volcanic lakes. The study of two volcanic lakes is presented in this chapter: Kelud, Indonesia and El Chichon, Mexico. Before a lava dome appeared in the middle of Kelud Lake on the 4th November 2007, the lake contained near neutral waters with a pH of 6. The total CO2 emission rate estimated by stochastic simulation ranged from 105 t day−1 for 2001 to 35 t day−1 for 2006. In early July 2007, the total flux for the lake area was estimated at 307 t day−1, showing that CO2 flux monitoring at the surface of volcanic lakes is a powerful tool in the improvement of early warning systems of volcanic eruptions. A significant change in CO2 flux was not detected for El Chichon lake during the period of survey (2007–2008) but the mapping of the CO2 flux on the lake area highlighted lineaments reflecting structures controlled by the main local and regional tectonic patterns.

Gillespie's stochastic simulation algorithm (SSA) has been a conventional method for stochastic modeling and simulation of biochemical systems. However, as a population-based algorithm it faces the challenge of combinatorial complexity in many biochemical models where species may present with multiple states. To solve this problem, the rules-based modeling was proposed by Hlavacek's group and the particle-based Network-Free Algorithm (NFA) was used for its simulation. In this paper, we first improve the NFA to efficiently integrate the population-based and particle-based features. Then we propose a population-based SSA scheme for the stochastic simulation of rule-based models. Complexity analysis is presented for the proposed methods. Numerical experiments on two rule-based models demonstrate the power of the proposed methods.

Introduction. The development and enhancement of the management efficiency of the forestry sector in the Macroregion of the Northwest and the Arctic zone of the Russian Federation are strategically significant for the country's development, oriented towards global competitiveness. The aim of this study is to analyze the prospects for personnel training within the system of secondary vocational education for the forestry sector in the Northwest and Arctic zones of the Russian Federation. Materials and Methods. The materials for the study were statistical data from two forms of state federal reporting for 2022: No. 1-T (prof) "Information on the number and demand for workers in organizations by professional groups" and form No. SPO-1 "Information about the educational organization that carries out educational activities in educational programs of secondary vocational education." The study employed methods of descriptive statistics, economic-mathematical modeling, and comparative data analysis. Results of the Study. An extended list of 23 directions and specialties of secondary vocational education organizations training qualified personnel for the forestry complex in the Arctic Macroregion and Northwest Russia has been identified. An assessment of the provision of the economy of enterprises and organizations in the forestry sector with qualified personnel has been presented. The analysis revealed 12 entities in the macroregion whose personnel needs for mid-level specialists can be met by graduates from their own region, as well as 13 entities in the macroregion that need to train their personnel beyond the macroregion in other regions of Russia to meet the demand for qualified workers and employees. A mapping tool has been developed, comprising 85 subjects of the Russian Federation, divided into three groups based on the total admission to specialties and directions related to the forestry sector. Discussion and Conclusion. The mapping tool obtained demonstrates that the regions with the highest preparation of forestry specialists are located far from the Arctic zone and Northwest Russia. Meanwhile, the main forest resources of the macroregion's entities are unevenly distributed across their territories, concentrated mainly in the central and southern parts. The proposed mapping tool contributes to addressing the issues of personnel training for the forestry sector through the involvement of all interested actors: applicants, employers, secondary vocational education organizations, and regional executive authorities.

The increasing penetration of distributed energy resources (DERs) into power systems has transformed the landscape of energy distribution, bringing both opportunities and significant challenges. This study examines the impact of DER integration on power system stability, focusing on voltage stability, frequency stability, and transient stability. A comprehensive review of 50 high-quality studies from peer-reviewed journals and reputable conference proceedings was conducted, utilizing advanced modeling, simulation, and empirical analysis methods. The findings reveal that the intermittent nature of renewable DERs, such as solar and wind, leads to voltage fluctuations, necessitating advanced control strategies to maintain stability. Additionally, the displacement of traditional synchronous generators by inverter-based DERs reduces system inertia, posing severe frequency stability challenges that require innovative solutions like synthetic inertia and fast frequency response mechanisms. Transient stability issues are also exacerbated by DER integration, highlighting the need for advanced inverter controls and enhanced fault ride-through capabilities. Energy storage systems (ESS) are identified as crucial for buffering the variability of renewable DERs, providing essential services such as frequency regulation and voltage support. However, high costs and scalability issues remain barriers to widespread ESS adoption. The study underscores the importance of supportive regulatory and policy frameworks in facilitating the seamless integration of DERs while maintaining grid stability. Effective policies that promote smart grid technologies and DER-friendly regulations are essential for ensuring a stable, resilient, and sustainable power grid. This research contributes to a deeper understanding of the complex dynamics introduced by DERs and offers insights into developing robust strategies to address stability challenges in modern power systems.

The papers in this special section examine modeling and simulation methods for the analysis and design of advanced energy conversion systems. Energy conversion lies aEnergyveral fronts including materials, conversion methods, power electronics, and controls have created new opportunities for efficient energy conversion from both the conventional and new sources of energy. Our urgent need to solve many critical problems with regards to the sustainability and security of our energy system as well as the ever-increasing environmental challenges facing humanity have further spurred unprecedented opportunities for creation of innovative solutions to address these challenges.

SUMMARYThis paper considers novel Bayesian non-parametric methods for stochastic epidemic models. Many standard modeling and data analysis methods use underlying assumptions (e.g. concerning the rate at which new cases of disease will occur) which are rarely challenged or tested in practice. To relax these assumptions, we develop a Bayesian non-parametric approach using Gaussian Processes, specifically to estimate the infection process. The methods are illustrated with both simulated and real data sets, the former illustrating that the methods can recover the true infection process quite well in practice, and the latter illustrating that the methods can be successfully applied in different settings.

Uncertainty in geological structural modeling, especially geological corrosion(a kind of karst cave), is a bottleneck that restricts the development and application of geological computer modeling and effect estimation. To solve this issue, a stochastic modeling method based on the random field theory is proposed in comparison with the deterministic geometric modeling method. Then the constraint random field modeling method and the random field modeling method without constrained parameters are compared and analyzed. A case study shows that the novel stochastic simulation method is an effective tool to describe the distribution characteristics of corrosion parameters and reflect the updated geological prospecting information. The influence of geological corrosion on the dam behavior can also be better analyzed by using the stochastic simulation method. At the same time, the unconfined random field ignores the sample location information and may lead to higher variability. Therefore, the constraint random field modeling method can provide a useful reference for the numerical analysis under complex geological conditions.

Data mining with a multitude of methodologies is a good basis for the integration of intelligent systems. Small, specialised systems have a large number of feasible solutions, but developing truly adaptive, and still understandable, systems for highly complex systems require domain expertise and more compact approaches at the basic level. This paper focuses on the integration of methodologies in the smart adaptive applications. Statistical methods and arti cial neural networks form a good basis for the data-driven analysis of interactions and fuzzy logic introduces solutions for knowledge-based understanding the system behaviour and the meaning of variable levels. Efficient normalisation, scaling and decomposition approaches are the key methodologies in developing large-scale applications. Linguistic equation (LE) approach originating from fuzzy logic is an efficient technique for these problems. The nonlinear scaling methodology based on advanced statistical analysis is the corner stone in representing the variable meanings in a compact way to introduce intelligent indices for control and diagnostics. The new constraint handling together with generalised norms and moments facilitates recursive parameter estimation approaches for the adaptive scaling. Well-known linear methodologies are used for the steady state, dynamic and case-based modelling in connection with the cascade and interactive structures in building complex large scale applications. To achieve insight and robustness the parameters are de ned separately for the scaling and the interactions. Introduction EK Juuso Intelligent Methods in Modelling and Simulation of Complex Systems 2 SNE 24(1) – 4/2014 ON 1 Steady-State Modelling multiple input, multiple output MIMO response surface methodology RSM multiple input, single output MISO Fuzzy set theory Extension principle Type-2 fuzzy Figure 1: Methodologies for modelling of complex system. EK Juuso Intelligent Method of Modelling and Simulation in Complex Systems SNE 24(1) – 4/2014 3 O N Linguistic fuzzy models Takagi-Sugeno (TS) fuzzy models Singleton models Fuzzy relational models Figure 2: Combined fuzzy modelling. Artificial neural networks ANN Linear networks multilayer perceptron MLP backpropagation learning Neurofuzzy systems Figure 3: A fuzzy neuron. function expansion Approximate reasoning 2 Decomposition Methodologies EK Juuso Intelligent Methods in Modelling and Simulation of Complex Systems 4 SNE 24(1) – 4/2014 ON Decomposition Figure 4: Decomposition for modelling. Hierarchical clustering Partitioning-based clustering algorithms fuzzy clustering Fuzzy c-means (FCM) Subtractive clustering Neural clustering Robust clustering number of clusters Composite local model Linear parameter varying (LPV) models Piecewise affine (PWA) systems Fuzzy models Multiple neural network systems mixed approach EK Juuso Intelligent Method of Modelling and Simulation in Complex Systems SNE 24(1) – 4/2014 5 O N 3 Adaptive Nonlinear Scaling Membership 3.1 Working point and feasible ranges Figure 5: Nonlinear scaling [28] EK Juuso Intelligent Methods in Modelling and Simulation of Complex Systems 6 SNE 24(1) – 4/2014 ON 3.2 Membership definitions linguistic range linguistic values • the corner points (Figure 5) are good for visualisation; • the parameters suit for tuning; • the coefficients are used in the calculations. 3.3 Adaptation of nonlinear scaling EK Juuso Intelligent Method of Modelling and Simulation in Complex Systems SNE 24(1) – 4/2014 7 O N 4 Intelligent Systems 4.1 LE models 4.2 Hybrid LE systems EK Juuso Intelligent Methods in Modelling and Simulation of Complex Systems 8 SNE 24(1) – 4/2014 ON extension principle linguistification

This paper discusses educational tools, resources and experience in teaching physics-of-failure (PoF) modeling and data analysis methods used in accelerated life testing (ALT) and accelerated degradation testing (ADT). The concepts introduced in this paper include several probabilistic and highly technical approaches such as the PoF and mechanistic approaches to reliability prediction and assessments as well as advanced Bayesian analysis methods used in ALT and ADT to analyze life data obtained through various methods of constant and variable stress testing efforts. Other resources include codes and algorithms from the readily available computational tools R, MATLAB, and WinBUGS for solving advanced model and life estimation methods related to PoF, ALT and ADT analyses. This paper provides an overview of these resources and several example problems.

Small unoccupied aerial systems (sUAS) are increasingly used for field data collection and remote sensing purposes. Their ease of use, ability to carry sensors, low cost, precise manoeuvrability, and navigation makes them versatile tools. The goal of this study is to investigate if sUAS multispectral imagery can be utilized to measure turbidity and total suspended solids (TSS) of small streams. sUAS multispectral imagery and water samples at varying depths were collected before and after rain events on three sampling dates in 2019 from Moores Creek in Lanett, Alabama (AL), United States of America (USA), which was restored in 2017. The water samples were processed for TSS and turbidity and related to pixel values from the multispectral imagery. Linear regression was used to develop models for TSS and turbidity. The models were then tested on Moores Mill Creek in Chewacla State Park, AL, USA. For Lanett, TSS and turbidity regression models for low flows had coefficients of determination (R 2) values of 0.77 and 0.78, respectively. During high flows, different single bands and band ratios were required for comparable R 2 values, suggesting separate models may be needed for high and low flow events. When the Lanett models were applied to Chewacla State Park, predicted TSS and turbidity were not comparable to measured values indicating that location-specific models may be required. Future research should incorporate depth as a variable since streambed visibility likely impacts results, along with other modelling and data analysis methods, such as machine learning.

Recently, there has been an explosive growth in the development of the concept of Industry. One of the most important elements of this concept is the application of methods of mathematical modeling and intelligent data analysis to create models of production processes and final products based on the processing of signals coming from intelligent sensors. A set of such models, which represent a virtual representation of industrial processes, systems and equipment, is called twin. Digital twins use data from sensors installed on production lines or on the basis of final products to predict equipment failures, optimize product quality and reduce the environmental impact of production processes. The model sets, underlying digital twins, can be described as workflows consisting of a set of computational services, each of which is a model of a process step. To provide flexible support for cloud computing to perform digital twins, we offer the concept of Micro-Workflows, which combines the power of the Scientific Workflows concept, the flexibility of container technology and the sustainability of the Stream Processing approach in distributed computing systems.

We derive a new method of conditional Karhunen-Loève (KL) expansions for stochastic coefficients in models of flow and transport in the subsurface, and in particular for the heterogeneous random permeability field. Exact values of this field are never known, and thus one must evaluate uncertainty of solutions to the flow and transport models. This is typically done by constructing independent realizations of the permeability field followed by numerical simulations of flow and transport for each realization and assembling statistical estimates of moments of desired quantities of interest. We follow the well-known framework of KL expansions and derive a new method that incorporates known values of the permeability at given locations so that the realizations of the permeability field honor this data exactly. Our method relies on projections to an appropriate subspace of random weights applied to the eigenfunctions of the covariance operator. We use the permeability realizations constructed with our stochastic simulation method in simulations of flow and transport and compare the results to those obtained when realizations are constructed with sequential Gaussian simulation (SGS). We also compare efficiency and stochastic convergence with that of stochastic collocation.