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This document is a preface to a special issue of the journal Mathematics titled "State-of-the-Art Mathematical Applications in Europe." The special issue features twelve original research papers and one review paper from European researchers and their collaborators in various fields of mathematics. The papers cover topics such as mathematical physics, applied mathematics, algebra, navigation algorithms, decision-making models, Lagrange interpolation polynomials, and nonlinear fractional differential equations. The preface provides a brief overview of each paper and expresses gratitude to the authors and reviewers. The special issue has received significant interest and demonstrates the importance of open access research in applied mathematics. [Extracted from the article]

The method for analysing transversal plane images from computer tomography scans is considered in the paper. This method allows not only approximating ribs-bounded contour but also evaluating patient rotation around the vertical axis during a scan. In this method, a mathematical model describing the ribs-bounded contour was created and the problem of approximation has been solved by finding the optimal parameters of the mathematical model using least-squares-type objective function. The local search has been per-formed using local descent by quasi-Newton methods. The benefits of analytical derivatives of the function are disclosed in the paper.

One of the problems in the analysis of the set of images of a moving object is to evaluate the degree of freedom of motion and the angle of rotation. Here the intrinsic dimensionality of multidimensional data, characterizing the set of images, can be used. Usually, the image may be represented by a high-dimensional point whose dimensionality depends on the number of pixels in the image. The knowledge of the intrinsic dimensionality of a data set is very useful information in exploratory data analysis, because it is possible to reduce the dimensionality of the data without losing much information. In this paper, the maximum likelihood estimator (MLE) of the intrinsic dimensionality is explored experimentally. In contrast to the previous works, the radius of a hypersphere, which covers neighbours of the analysed points, is fixed instead of the number of the nearest neighbours in the MLE. A way of choosing the radius in this method is proposed. We explore which metric—Euclidean or geodesic—must be evaluated in the MLE algorithm in order to get the true estimate of the intrinsic dimensionality. The MLE method is examined using a number of artificial and real (images) data sets.

Safe navigation at sea is more important than ever. Cargo is usually transported by vessel because it makes economic sense. However, marine accidents can cause huge losses of people, cargo, and the vessel itself, as well as irreversible ecological disasters. These are the reasons to strive for safe vessel navigation. The navigator shall ensure safe vessel navigation. He must plan every maneuver and act safely. At the same time, he must evaluate and predict the actions of other vessels in dense maritime traffic. This is a complicated process and requires constant human concentration. It is a very tiring and long-lasting duty. Therefore, human error is the main reason of collisions between vessels. In this paper, different reinforcement learning strategies have been explored in order to find the most appropriate one for the real-life problem of ensuring safe maneuvring in maritime traffic. An experiment using different algorithms was conducted to discover a suitable method for autonomous vessel navigation. The experiments indicate that the most effective algorithm (Deep SARSA) allows reaching 92.08% accuracy. The efficiency of the proposed model is demonstrated through a real-life collision between two vessels and how it could have been avoided. [ABSTRACT FROM AUTHOR]

To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.ejor.2005.05.030 Byline: Jolita BernataviAienA, Gintautas Dzemyda, Olga Kurasova, Virginijus MarcinkeviAius Keywords: Neural networks; Visual interactive modelling; Optimization; SOM; Visual data mining Abstract: Visual data mining is an efficient way to involve human in search for a optimal decision. This paper focuses on the optimization of the visual presentation of multidimensional data. A variety of methods for projection of multidimensional data on the plane have been developed. At present, a tendency of their joint use is observed. In this paper, two consequent combinations of the self-organizing map (SOM) with two other well-known nonlinear projection methods are examined theoretically and experimentally. These two methods are: Sammon's mapping and multidimensional scaling (MDS). The investigations showed that the combinations (SOM_Sammon and SOM_MDS) have a similar efficiency. This grounds the possibility of application of the MDS with the SOM, because up to now in most researches SOM is applied together with Sammon's mapping. The problems on the quality and accuracy of such combined visualization are discussed. Three criteria of different nature are selected for evaluation the efficiency of the combined mapping. The joint use of these criteria allows us to choose the best visualization result from some possible ones. Several different initialization ways for nonlinear mapping are examined, and a new one is suggested. A new approach to the SOM visualization is suggested. The obtained results allow us to make better decisions in optimizing the data visualization. Author Affiliation: Institute of Mathematics and Informatics, Akademijos St. 4, 08663 Vilnius, Lithuania Article History: Received 5 November 2004; Accepted 24 May 2005

The efficacy of self-organizing map (SOM) and SammonEs mapping and multidimensional scaling (MDS) neural network based methods, which are useful for optimization of the visual presentation of multidimensional data, is analyzed.

To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.ejor.2004.09.011 Byline: Gintautas Dzemyda, Olga Kurasova Keywords: Heuristics; Neural networks; Parallel computing; Optimization; Data visualization Abstract: In this paper, we have developed and examined a heuristic approach for minimizing the projection error in Sammon's mapping applied in combination with the self-organizing map (SOM). As a final result, we need to visualize the neurons-winners of the SOM. The criterion of visualization quality is the projection error of Sammon's mapping. Two combinations were considered: (1) a consecutive application of the SOM and Sammon's mapping and (2) Sammon's mapping taking into account the learning flow of the self-organizing neural network (integrated combination of the mapping methods). The goal is to obtain a lower projection error and its lower dependence on the so-called 'magic factor' in Sammon's mapping. Different modifications of Sammon's mapping are examined experimentally and applied in the combination with the SOM. A parallel algorithm of the integrated combination has been proposed. Author Affiliation: Institute of Mathematics and Informatics, Akademijos St. 4, 08663 Vilnius, Lithuania

Multidimensional scaling (MDS) is a widely used technique for mapping data from a high-dimensional to a lower-dimensional space and for visualizing data. Recently, a new method, known as Geometric MDS, has been developed to minimize the MDS stress function by an iterative procedure, where coordinates of a particular point of the projected space are moved to the new position defined analytically. Such a change in position is easily interpreted geometrically. Moreover, the coordinates of points of the projected space may be recalculated simultaneously, i.e. in parallel, independently of each other. This paper has several objectives. Two implementations of Geometric MDS are suggested and analysed experimentally. The parallel implementation of Geometric MDS is developed for multithreaded multi-core processors. The sequential implementation is optimized for computational speed, enabling it to solve large data problems. It is compared with the SMACOF version of MDS. Python codes for both Geometric MDS and SMACOF are presented to highlight the differences between the two implementations. The comparison was carried out on several aspects: the comparative performance of Geometric MDS and SMACOF depending on the projection dimension, data size and computation time. Geometric MDS usually finds lower stress when the dimensionality of the projected space is smaller. [ABSTRACT FROM AUTHOR]

Machine learning is compelling in solving various applied problems. Nevertheless, machine learning methods lack the contextual reasoning capabilities and cannot be fitted to utilize additional information about circumstances, environments, backgrounds, etc. Such information provides essential knowledge about possible reasons for particular actions. This knowledge could not be processed directly by either machine learning methods. This paper presents the context-aware machine learning approach for actor behavior contextual reasoning analysis and context-based prediction for threat assessment. Moreover, the proposed approach uses context-aware prediction to tackle the interaction between actors. An idea of the technique lies in the cooperative use of two classification methods when one way predicts an actor's behavior. The second method discloses such predicted action (behavior) that is non-typical or unusual. Such integration of two-method allows the actor to make the self-awareness threat assessment based on relations between different actors where some multidimensional numerical data define the connections. This approach predicts the possible further situation and makes its threat assessment without any waiting for future actions. The suggested approach is based on the Decision Tree and Support Vector Method algorithm. Due to the complexity of context, marine traffic data was chosen to demonstrate the proposed approach capability. This technique could deal with the end-to-end approach for safe vessel navigation in maritime traffic with considerable ship congestion. [ABSTRACT FROM AUTHOR]

(1) Background: Identifying early pancreas parenchymal changes remains a challenging radiologic diagnostic task. In this study, we hypothesized that applying artificial intelligence (AI) to contrast-enhanced ultrasound (CEUS) along with measurement of Heat Shock Protein (HSP)-70 levels could improve detection of early pancreatic necrosis in acute pancreatitis. (2) Methods: Acute pancreatitis (n = 146) and age- and sex matched healthy controls (n = 50) were enrolled in the study. The severity of acute pancreatitis was determined according to the revised Atlanta classification. The selected severe acute pancreatitis (AP) patient and an age/sex-matched healthy control were analysed for the algorithm initiation. Peripheral blood samples from the pancreatitis patient were collected on admission and HSP-70 levels were measured using ELISA. A CEUS device acquired multiple mechanical index contrast-specific mode images. Manual contour selection of the two-dimensional (2D) spatial region of interest (ROI) followed by calculations of the set of quantitative parameters. Image processing calculations and extraction of quantitative parameters from the CEUS diagnostic images were performed using algorithms implemented in the MATLAB software. (3) Results: Serum HSP-70 levels were 100.246 ng/ml (mean 76.4 ng/ml) at the time of the acute pancreatitis diagnosis. The CEUS Peek value was higher (155.5) and the mean transit time was longer (40.1 s) for healthy pancreas than in parenchyma affected by necrosis (46.5 and 34.6 s, respectively). (4) Conclusions: The extracted quantitative parameters and HSP-70 biochemical changes are suitable to be used further for AI-based classification of pancreas pathology cases and automatic estimation of pancreatic necrosis in AP. [ABSTRACT FROM AUTHOR]

Pancreas adenocarcinoma is a lethal disease with poor outcomes. With increasing incidence worldwide, it is predicted to become the second leading cause of cancer death in many countries. The main factor influencing disease outcome is the tumor stage at the time of diagnosis. The first step to successfully diagnose and treat pancreatic cancer is the efficient recognition and segmentation of the target organ. Several methods based on deep learning and data fusion for pancreas segmentation have been developed and applied over the years. This paper presents a state of the art in the application of the existing methods that have been presented for the pancreas and pancreatic cyst detection and segmentation. The most successful method so far has accuracy equal to 90.18% and AUC equal to 94.55%. Also, this paper looks into software designed for 3D segmentation that is simple and potentially might be used by users from non-medical fields. [ABSTRACT FROM AUTHOR]

Emotion recognition from facial expressions has gained much interest over the last few decades. In the literature, the common approach, used for facial emotion recognition (FER), consists of these steps: image pre-processing, face detection, facial feature extraction, and facial expression classification (recognition). We have developed a method for FER that is absolutely different from this common approach. Our method is based on the dimensional model of emotions as well as on using the kriging predictor of Fractional Brownian Vector Field. The classification problem, related to the recognition of facial emotions, is formulated and solved. The relationship of different emotions is estimated by expert psychologists by putting different emotions as the points on the plane. The goal is to get an estimate of a new picture emotion on the plane by kriging and determine which emotion, identified by psychologists, is the closest one. Seven basic emotions (Joy, Sadness, Surprise, Disgust, Anger, Fear, and Neutral) have been chosen. The accuracy of classification into seven classes has been obtained approximately 50%, if we make a decision on the basis of the closest basic emotion. It has been ascertained that the kriging predictor is suitable for facial emotion recognition in the case of small sets of pictures. More sophisticated classification strategies may increase the accuracy, when grouping of the basic emotions is applied. [ABSTRACT FROM AUTHOR]

Eye fundus imaging is a useful, non-invasive tool in disease progress tracking, in early detection of disease and other cases. Often, the disease diagnosis ismade by an ophthalmologist and automatic analysis systems are used only for support. There are several commonly used features for disease detection, one of them is the artery and vein ratio measured according to the width of the main vessels. Arteries must be separated from veins automatically in order to calculate the ratio, therefore, vessel classification is a vital step. For most analysis methods high quality images are required for correct classification. This paper presents an adaptive algorithm for vessel measurements without the necessity to tune the algorithm for concrete imaging equipment or a specific situation. The main novelty of the proposed method is the extraction of blood vessel features based on vessel width measurement algorithm and vessel spatial dependency. Vessel classification accuracy rates of 0.855 and 0.859 are obtained on publicly available eye fundus image databases used for comparison with another state of the art algorithms for vessel classification in order to evaluate artery-vein ratio (AV R). The method is also evaluated with images that represent artery and vein size changes before and after physical load. Optomed OY digital mobile eye fundus camera SmartscopeM5 PRO is used for image gathering. [ABSTRACT FROM AUTHOR]

In this paper, a method for analyzing transversal plane images obtained by computer tomography (CT) scans is presented. A mathematical model that describes the ribs-bounded contour was created and the problem of approximation is solved by finding out the optimal parameters of the model in the least-squares sense. The paper discloses the problems that appear in building the proper model. Such a model would be useful in the registration of images independently on the patient position on the bed and of the radiocontrast agent injection. We consider the slices where ribs are visible because many important internal organs are located here: liver, heart, stomach, pancreas, lungs, etc. The model is flexible and describes the ribs-bounded contour independently on the patient age, sex and disease. The only exception is patients with the bone fracture. This makes the basis for the proper registration of slices. [ABSTRACT FROM AUTHOR]

Radiologists need to find a position of a slice of one computed tomography (CT) scan in another scan. The image registration is a technique used to transform several images into one coordinate system and to compare them. Such transversal plane images obtained by CT scans are considered, where ribs are visible, but it does not lessen the significance of our work because many important internal organs are located here: liver, heart, stomach, pancreas, lungs, etc. The new method is developed for registration based on the mathematical model describing the rib-bounded contour. Parameters of the mathematical model and of distribution of the bone tissue on the CT scan slice form a set of features describing a particular slice. The registration method applies translation, rotation, and scaling invariances. Several strategies of translation invariance and options of the unification of scales are proposed. The method is examined on real CT scans seeking for its best performance. [ABSTRACT FROM AUTHOR]

The estimation of intrinsic dimensionality of high-dimensional data still remains a challenging issue. Various approaches to interpret and estimate the intrinsic dimensionality are developed. Referring to the following two classifications of estimators of the intrinsic dimensionality - local/global estimators and projection techniques/geometric approaches - we focus on the fractalbased methods that are assigned to the global estimators and geometric approaches. The computational aspects of estimating the intrinsic dimensionality of high-dimensional data are the core issue in this paper. The advantages and disadvantages of the fractal-based methods are disclosed and applications of these methods are presented briefly. [ABSTRACT FROM AUTHOR]

A secure and high-quality operation of power grids requires frequency to be managed to keep it stable around a reference value. The deviation of the frequency from this reference value is caused by the imbalance between the active power produced and consumed. In the Smart Grid paradigm, the balance can be achieved by adjusting the demand to the production constraints, instead of the other way round. In this paper, an swarm intelligence-based approach for frequency management is proposed. It is grounded on the idea that a swarm is composed of decentralised individual agents (particles) and that each of them interacts with other ones via a shared environment. Three swarm intelligence-based policies ensure a decentralised frequency management in the smart power grid, where agents of swarm are making decisions and acting on the demand side. Policies differ in behaviour function of agents. Finally, these policies are evaluated and compared using indicators that point out their advantages. [ABSTRACT FROM AUTHOR]

The analysis of medical streaming data is quite difficult when the problem is to estimate health-state situations in real time streaming data in accordance with the previously detected and estimated streaming data of various patients. This paper deals with the multivariate time series analysis seeking to compare the current situation (sample) with that in chronologically collected historical data and to find the subsequences of the multivariate time series most similar to the sample. A visual method for finding the best subsequences matching to the sample is proposed. Using this method, an investigator can consider the results of comparison of the sample and some subsequence of the series from the standpoint of several measures that may be supplementary to one another or may be contradictory among themselves. The advantage of the visual analysis of the data, presented on the plane, is that we can see not only the subsequence best matching to the sample (such a subsequence can be found in an automatic way), but also we can see the distribution of subsequences that are similar to the sample in accordance with different similarity measures. It allows us to evaluate differences among the subsequences and among the measures. [ABSTRACT FROM AUTHOR]

In the paper there are described some rescheduling algorithms which are implemented in the Advanced Planning and Scheduling system, namely PEN System, which is an add-on for the Enterprise Resource Planning system and intended to be used to mitigate the impacts of potential exceptions disrupting shop floor level schedules. The rather simple and quick heuristic algorithms, namely Affected Operations Rescheduling and Active Wilkerson-Irwin algorithm are chosen to cope with the machine disruption. The algorithms are modified for more complicated and realistic enterprise environment model than the Job Shop or the Flexible Job Shop, namely for complex operations' precedence constraints described by any simple directed acyclic graph. [ABSTRACT FROM AUTHOR]

The paper summarizes the results of research on the modeling and implementation of advanced planning and scheduling (APS) systems done in recent twenty years. It discusses the concept of APS system - how it is thought of today - and highlights the modeling and implementation challenges with which the developers of such systems should cope. Some from these challenges were identified as a result of the study of scientific literature, others - through an in-depth analysis of the experience gained during the development of real-world APS system - a Production Efficiency Navigator (PEN system). The paper contributes to APS systems theory by proposing the concept of an ensemble of collaborating algorithms. Straipsnis apibendrina pastarųjų 20 metų tyrimus moderniųjų planavimo ir tvarkaraščių sudarymo (PTS) sistemų modeliavimo ir realizavimo srityje. Jame aptariama šiuolaikinė tokių sistemų koncepcija ir išryškinamos modeliavimo ir realizavimo problemos, kurias tenka spręsti jų kūrėjams. Dalis šių problemų suformuluota analizuojant literatūrinius šaltinius, kitos - apibendrinant autorių patirtį, įgytą kuriant pramoninio pobūdžio sistemą „Gamybos efektyvumo navigatorius". Darbo mokslinis naujumas yra bendradarbiaujančių algoritmų ansamblio samprata. Tai svarbus indėlis į besiformuojančią PTS sistemų teoriją. [ABSTRACT FROM AUTHOR]