http://hdl.handle.net/11089/7 Sat, 31 Oct 2026 12:31:39 GMT 2026-10-31T12:31:39Z https://dspace.uni.lodz.pl:443/bitstream/id/61e5ee3a-a6d8-44c1-b718-28258a5fdf98/ http://hdl.handle.net/11089/7 http://hdl.handle.net/11089/59565 Convex extensions on combinatorial configurations: Theory and optimization methods Yakovlev, Sergiy; Koliechkina, Liudmyla; Matsyi, Olha; Pichugina, Oksana The present monograph develops a systematic mathematical theory at the interface of combinatorial optimization, convex analysis, and Euclidean geometry. Its central subject is the behaviour of functions defined on finite point configurations embedded in Euclidean space, and the exploitation of this behaviour for the solution of combinatorial optimization problems. By choosing the Euclidean immersion so that the image of the combinatorial feasible set coincides with the vertex set of its convex hull, a discrete optimization problem is transformed into a continuous one without any loss of information. This structural property is both the condition for the existence of convex extensions and the ultimate source of efficiency of all optimization methods developed in the monograph. The theoretical core of the work is a complete theory of convex extensions of functions defined on vertex-located configurations: existence theorems for convex, strongly convex, and differentiable extensions; constructive schemes yielding explicit analytic formulas; and a hierarchy of computable extremal estimates and optimality conditions. This theory is applied to the principal classes of finite point configurations arising as Euclidean images of combinatorial sets, including permutation, multipermutation, partial permutation, and Boolean configurations, whose associated polytopes are characterized in full. Building on this foundation, the monograph develops optimization methods including polyhedral and spherical relaxations, branch-and-bound schemes, and penalty function methods, each grounded in the specific geometry of the combinatorial feasible set rather than in general-purpose algorithmic principles. The book is addressed to researchers and graduate students in combinatorial optimization, convex analysis, and discrete mathematics, as well as to practitioners working on optimization problems in scheduling, assignment, logistics, and engineering design. Tue, 27 Oct 2026 00:00:00 GMT http://hdl.handle.net/11089/59565 2026-10-27T00:00:00Z http://hdl.handle.net/11089/59335 Advancing Explainability and Predictive Accuracy in AI-Driven Cardiovascular Risk Assessment: A Hybrid Statistical and Neural Network Approach Hikkaduwa Liyanage, Nishadha Himanshi Cardiovascular disease (CVD) remains a major global health challenge, making accurate and timely risk prediction essential for improving patient outcomes. Traditional statistical approaches, such as the Cox Proportional Hazards Model, provide interpretable results but are limited in their ability to capture complex and nonlinear relationships in clinical data. In contrast, machine learning models, particularly Feedforward Neural Networks (FFNNs), offer strong predictive performance but lack interpretability, which restricts their clinical applicability. This thesis investigates two complementary approaches for cardiovascular risk prediction. First, FFNN models are developed and evaluated to assess their ability to model nonlinear relationships in structured clinical data. Second, a novel hybrid computational framework is proposed, integrating Winner-Takes-All (WTA) competitive learning for patient clustering with cluster-specific Cox proportional hazards models. This approach enables subgroup-level risk estimation and captures heterogeneity within the patient population. To further enhance interpretability, a new cumulative risk measure, termed the Cumulative Prevalence Ratio (CPR), is introduced. CPR summarises time-dependent hazard information into a single interpretable value, facilitating direct comparison of long-term cardiovascular risk across patient clusters. The proposed methods are evaluated using a large-scale cardiovascular dataset, with performance assessed using the Concordance Index and ROC-based measures. Comparative analysis highlights the trade-off between the predictive strength of neural networks and the interpretability of the hybrid framework. The results indicate that the proposed hybrid approach achieves a balance between predictive performance and clinical interpretability. Overall, this work contributes to the development of transparent, subgroup-aware, and clinically meaningful models for cardiovascular risk prediction. Doctoral dissertation submitted for the degree of PhD in Computer Science at the Faculty of Mathematics and Computer Science, University of Łódź. Supervisor: Prof. Andrzej Nowakowski. Co-supervisor: Dr Marta Lipnicka. Thu, 01 Jan 2026 00:00:00 GMT http://hdl.handle.net/11089/59335 2026-01-01T00:00:00Z http://hdl.handle.net/11089/57010 Various Representations of Geometric Objects in Spatial Relational and Spatial Object-Relational Databases Management Systems Stasiak, Aleksandra In this paper we look at various kinds of representations of geometric objects in spatial relational (or object-relational) database management systems. We confront it with Simple Feature Access and SQL/MM (Part: 3) standards. We also try to fnd out some other representations of geometric objects that are used not only in traditional spatial database management systems but also in some NoSQL databases. We indicate functions and methods related to geometry representations such as WKT, WKB, GML, GeoJSON, GeoHash, KML, EWKT, EWKB, TWKB, HEXEWKB used in MySQL, Oracle XE and PostGIS/PostgreSQL. We illustrate this with examples, also showing some ideas for importing/exporting geometries between these database management systems. Wed, 17 Dec 2025 00:00:00 GMT http://hdl.handle.net/11089/57010 2025-12-17T00:00:00Z http://hdl.handle.net/11089/57009 The Dialogical Nature of Iwona Chmielewska’s Picturebooks – Aesthetic and Pedagogical Context Ludwiczak, Joanna Stanisława The issue of art for children as a subject of research has a tradition dating back to the beginnings of the aesthetic-pedagogical movement in Europe. One of the contemporary examples of art for children is the picturebook. As an artefact of visual culture, it fts in particularly well with the current issues of aesthetic education for children. The aim of the presented interpretation is to identify the attributes of Iwona Chmielewska’s work that are important in the context of a child’s encounter with art. The unique form of the phenomenon described, inherent to works of art, responds to the child’s natural characteristics and ofers them full participation in co-creating the work. Wed, 17 Dec 2025 00:00:00 GMT http://hdl.handle.net/11089/57009 2025-12-17T00:00:00Z