Graphs with an ideally restricted spectrum are known as Ramanujan graphs. In computer science and combinatorics, these graphs have several uses. This paper explores the metric dimension of Ramanujan graphs. Metric dimension is the minimum “Locator points” needed to uniquely locate every spot in a network. Ramanujan graphs are highly efficient and well-connected networks. Our research investigates how their unique mathematical properties influence this “Locator points” requirement, a problem typically very complex. By using their inherent design, this work aims to understand these networks better and show their potential for precise location-finding in large systems. General codes for these graphs have also been discussed.

Abstract Prototype-based models are a good candidate for explainable artificial intelligence, and in these models the prototypes store a primary – rough – information about the classes and the classification problem. If backgrounds are defined as anything but the other classes , then we argue that “prototypizing” this background class is redundant: even if there are examples of background data, due to its nature, a thresholding mechanism with a bias value will suffice. To validate the non-prototype background, we use prototype-based learning on medical image classification. Our model has a good performance, whilst maintaining interpretability and – due to the simple wavelet-based prototypes – the reduced computational complexity. In the conclusions, we argue that, by eliminating the prototypes from the background, we have a simpler and more intuitive model.

Artificial Intelligence and infectious diseases prediction have recently experienced a common development and advancement. Machine learning apparition, along with deep learning emergence, extended many approaches against diseases apparition and their spread. And despite their outstanding results in predicting infectious diseases, conflicts appeared regarding the types of data used and how they can be studied, analyzed, and exploited using various emerging methods. This has led to some ongoing discussions in the field. This research aims not only to provide an overview of what has been accomplished, but also to highlight the difficulties related to the types of data used, and the learning methods applied for each research objective. It categorizes these contributions into three areas: predictions using Public Health Data to prevent the spread of a transmissible disease within a region; predictions using Patients’ Medical Data to detect whether a person is infected by a transmissible disease; and predictions using both Public and patient medical data to estimate the extent of disease spread in a population. The paper also critically assesses the potential of Artificial Intelligence and outlines its limitations in infectious disease management.

Sapientia Hungarian University of Transylvania Scientia Publishing House. The Sapientia Hungarian University of Transylvania is a higher education institution in România, providing tertiary education in Hungarian language.

Let 퐺 be a simple connected graph of size 푚. Let 퐴 be the adjacency matrix of 퐺 and let 휌(퐺) be the spectral radius of 퐺. A graph is said to be 퐻free if it does not contain a subgraph isomorphic to 퐻. Let 퐻(ℓ, 3) be the graph formed by taking a cycle of length ℓ and a triangle on a common vertex. Recently, Li, Lu and Peng [Y. Li, L. Lu, Y. Peng, Spectral extremal graphs for the bowtie, Discrete Math. 346(12) (2023) 113680.] showed that the unique 푚-edge 퐻(3, 3)-free spectral extremal graph is the join of 퐾2 with an independent set of 푚−1 2 vertices if 푚 ≥ 8 and the condition 푚 ≥ 8 is tight. In particular, if 퐺 does not contain 퐻(3, 3) as induced subgraph, they proved that 휌(퐺) ≤ 1+ √ 4푚−3 2 and equality holds when 퐺 is isomorphic to 푆 푚+3 2 ,2 . Note that Li et al. denoted 퐻(3, 3) by 퐹2. In this paper, we find the maximum spectral radius and identify the graph with the largest spectral radius among all {퐻(3, 3), 퐻(4, 3)}- free graphs of size odd 푚, where 푚 ≥ 259. Coincidently, we show that 휌(퐺) ≤ 1+ √ 4푚−3 2 when 퐺 forbids both 퐻(3, 3) and 퐻(4, 3). In our case, the equality holds when 퐺 is isomorphic to the same graph.

Programmers can benefit from static source code analysis techniques in various ways: they can understand their code better, test it more effectively, debug it more efficiently, and so on. However, they often face the challenge of discovering how to reproduce faulty executions that cause runtime errors. The term symbolic execution refers to a static source code analysis method that can help with this challenge. In this paper, we are showing a symbolic execution-based analysis method to find the source of a runtime error. The method uses a control-flow graph to select the execution paths reaching the targeted runtime error. The algorithm is implemented as part of the RefactorErl static program analysis and transformation framework.

One crucial task in 3D computer vision is the correction of geometric distortions, since most algorithms rely on the assumption that the image formation process can be described by a specific camera model, e.g. the pinhole camera model. In an autonomous driving scenario, however, the front-facing camera is most commonly placed behind the windshield, causing complex, nonlinear distortions. Previous attempts have been made to undistort such images using deep learning based methods. The input of these deep networks usually consists of one or more images, and they optionally include additional tasks such as semantic segmentation to improve the results. We hypothesize that the well-constrained nature of optical flow in rigid, static scenes provides useful cues for the process of image undistortion. By using optical flow as an additional input, we present a multi-view distortion correction method achieving superior results on both synthetic and real-world images compared to previous works, demonstrating the usability of optical flow for correcting highly complex distortions.

Abstract The analysis of networks involves several crucial parameters. In this paper, we consider the closeness parameter, which is based on the total distance between every pair of vertices. Initially, we delve into a discussion about the applicability of the closeness parameter to Mycielski graphs. Our findings are categorized based on the underlying graph’s diameter. The formula for calculating the closeness of a Mycielski graph is derived for graphs with a diameter of less than or equal to 4. Furthermore, we establish a sharp lower bound for the closeness of a Mycielski graph when the diameter of the underlying graph is greater than 4. To achieve this, the closeness of the Mycielski transformation of a path graph plays an important role. Additionally, leveraging the obtained results, we examine the closeness of a special planar construction composed of path and cycle graphs, as well as its Mycielski transformation.

Abstract Colposcopy imaging is pivotal in cervical cancer diagnosis, a major health concern for women. The computational challenge lies in accurate lesion recognition. A significant hindrance for many existing machine learning solutions is the scarcity of comprehensive training datasets. To reduce this gap, we present AnnoCerv: a comprehensive dataset tailored for feature-driven and image-based colposcopy analysis. Distinctively, AnnoCerv include detailed segmentations, expert-backed colposcopic annotations and Swede scores, and a wide image variety including acetic acid, iodine, and green-filtered captures. This rich dataset supports the training of models for classifying and segmenting low-grade squamous intraepithelial lesions, detecting high-grade lesions, aiding colposcopy-guided biopsies, and predicting Swede scores – a crucial metric for medical assessments and treatment strategies. To further assist researchers, our release includes code that demonstrates data handling and processing and exemplifies a simple feature extraction and classification technique.

Abstract For a graph G with n vertices, average distance µ(G) is the ratio of sum of the lengths of the shortest paths between all pairs of vertices to the number of edges in a complete graph on n vertices. In this paper, we introduce average distance colouring and find the average distance colouring number of certain classes of graphs.