Dense, irregular, yet always-graphic 3-uniform hypergraph degree sequences

A 3-uniform hypergraph is a generalization of a simple graph where each hyperedge is a subset of exactly three vertices. The degree of a vertex in a hypergraph is the number of hyperedges incident with it. The degree sequence of a hypergraph is the sequence of the degrees of its vertices. The degree sequence problem for 3-uniform hypergraphs asks whether a 3-uniform hypergraph with a given degree sequence exists. Such a hypergraph is called a realization. Recently, Deza et al. proved that this problem is NP-complete. Although some special cases are simple, polynomial-time algorithms are only known for highly restricted degree sequences. The main result of our research is the following: if all degrees in a sequence D of length n are between [Formula presented]+O(n) and [Formula presented]−O(n), the number of vertices is at least 45, and the degree sum is divisible by 3, then D has a 3-uniform hypergraph realization. Our proof is constructive, providing a polynomial-time algorithm for constructing such a hypergraph. To our knowledge, this is the first polynomial-time algorithm to construct a 3-uniform hypergraph realization of a highly irregular and dense degree sequence. © 2025 The Author

Low-impact, near real-time risk assessment for legacy IT infrastructures

In an era where cybersecurity threats are evolving at an unprecedented pace, this paper introduces a methodology for near real-time risk assessment of high-profile, high security infrastructures, where data security and operational continuity inherently limits observability. Our approach addresses the challenges of this limited observability and minimized disruption, offering a new perspective on processing and evaluating cybersecurity knowledge. We present an innovative method that leverages attack graphs and attacker behavior analysis to assess risks and vulnerabilities. Our research includes the development of an automated risk assessment mechanism, graphical security modeling, and a Markov chain-based model for attacker behavior. Our methodology utilizes a blend of direct and indirect event sources, incorporating an attacker behavioral model based on a random walk method akin to Google’s PageRank. The proof-of-concept solution calculates potential risk according to the actual threat landscape, providing a more accurate and timely assessment

Machine learning prediction of breast cancer local recurrence localization, and distant metastasis after local recurrences

Local recurrences (LR) can occur within residual breast tissue, chest wall, skin, or newly formed scar tissue. Artificial intelligence (AI) technologies can extract a wide range of tumor features from large datasets helping in oncological decision-making. Recently, machine learning (ML) models have been developed to predict breast cancer recurrence or distant metastasis (DM). However, there is still a lack of models that consider the localization of LR as a tumor feature. To address this gap, here, we analysed data from 154 patients including pathological, clinical, and follow-up data (with an average follow-up of 133.16 months) on both primary tumors (PT) and recurrences. By using ML methods we predicted the localization of LR and the occurrence of DM after LR. The performance (ROC AUC) of the best ML models was 0.75, and 0.69 for predicting LR in breast parenchyma, and surgical scar tissue, respectively, and 0.74 for predicting DM after LR. We identified recurrence localization, and the time elapsed between the detection of primary breast carcinoma and the recurrence, and adjuvant chemotherapy as the most important features associated with further DM. We conclude that combining traditional prognostic factors with ML may provide important tools in the risk assessment of patients with breast LR

Morphology in the Age of Pre-trained Language Models

The field of natural language processing (NLP) has adopted deep learning methods in the past 15 years. Nowadays the state-of-the-art in most NLP tasks is some kind of neural model, often the fine-tuned version of a pre-trained language model. The efficacy of these models is demonstrated on various English benchmarks and increasingly, other monolingual and multimultilingual benchmarks. In this dissertation I explore the application of deep learning models on low level tasks, particularly morphosyntactic tasks in multiple languages. The first part of this dissertation (Chapters 3 and 4) explores the application of deep learning models for classical morphosyntactic tasks such as morphological analysis and generation in dozens of languages with special focus on Hungarian. The second part of this dissertation (Chapters 5 to 8) deals with pre-trained language models, mostly models from the BERT family. I include some experiments on GPT-4o and GPT-4o-mini. These models show excellent performance on various tasks in English and some high density languages. However, their evaluation in medium and low density languages is lacking. I present a methodology for generating morphosyntactic benchmarks in arbitrary languages and I analyze multiple BERT-like models in detail. My main tool for analysis is the probing methodology which I extend the with perturbations, the systematic removal of certain information from the sentence. I use Shapley values to further refine my analysis

The Use of Voice Control in 3D Medical Data Visualization Implementation, Legal, and Ethical Issues

Voice-controlled devices are becoming increasingly common in our everyday lives as well as in medicine. Whether it is our smartphones, with voice assistants that make it easier to access functions, or IoT (Internet of Things) devices that let us control certain areas of our home with voice commands using sensors and different communication networks, or even medical robots that can be controlled by a doctor with voice instructions. Over the last decade, systems using voice control have made great progress, both in terms of accuracy of voice processing and usability. The topic of voice control is intertwined with the application of artificial intelligence (AI), as the mapping of spoken commands into written text and their understanding is mostly conducted by some kind of trained AI model. Our research had two objectives. The first was to design and develop a system that enables doctors to evaluate medical data in 3D using voice control. The second was to describe the legal and ethical issues involved in using AI-based solutions for voice control. During our research, we created a voice control module for an existing software called PathoVR, using a model taught by Google to interpret the voice commands given by the user. Our research, presented in this paper, can be divided into two parts. In the first, we have designed and developed a system that allows the user to evaluate 3D pathological medical serial sections using voice commands. In contrast, in the second part of our research, we investigated the legal and ethical issues that may arise when using voice control in the medical field. In our research, we have identified legal and ethical barriers to the use of artificial intelligence in voice control, which need to be answered in order to make this technology part of everyday medicine