Early tumor detection save lives. Each year, more than 300 million computed tomography (CT) scans are performed worldwide, offering a vast opportunity for effective cancer screening. However, detecting small or early-stage tumors on these CT scans remains challenging, even for experts. Artificial intelligence (AI) models can assist by highlighting suspicious regions, but training such models typically requires extensive tumor masks--detailed, voxel-wise outlines of tumors manually drawn by radiologists. Drawing these masks is costly, requiring years of effort and millions of dollars. In contrast, nearly every CT scan in clinical practice is already accompanied by medical reports describing the tumor's size, number, appearance, and sometimes, pathology results--information that is rich, abundant, and often underutilized for AI training. We introduce R-Super, which trains AI to segment tumors that match their descriptions in medical reports. This approach scales AI training with large collections of readily available medical reports, substantially reducing the need for manually drawn tumor masks. When trained on 101,654 reports, AI models achieved performance comparable to those trained on 723 masks. Combining reports and masks further improved sensitivity by +13% and specificity by +8%, surpassing radiologists in detecting five of the seven tumor types. Notably, R-Super enabled segmentation of tumors in the spleen, gallbladder, prostate, bladder, uterus, and esophagus, for which no public masks or AI models previously existed. This study challenges the long-held belief that large-scale, labor-intensive tumor mask creation is indispensable, establishing a scalable and accessible path toward early detection across diverse tumor types. We plan to release our trained models, code, and dataset at https://github.com/MrGiovanni/R-Super

Creating responsible artificial intelligence (AI) systems is an important issue in contemporary research and development of works on AI. One of the characteristics of responsible AI systems is their explain-ability. In the paper, we are interested in explainable deep learning (XDL) systems. On the basis of the creation of digital twins of physical objects, we introduce the idea of creating readable twins (in the form of imprecise information flow models) for unreadable deep learning models. The complete procedure for switching from the deep learning model (DLM) to the imprecise information flow model (IIFM) is presented. The proposed approach is illustrated with an example of a deep learning classification model for image recognition of handwritten digits from the MNIST data set.

Rough sets (RS)proved a thriving realm with successes inn many fields of ML and AI. In this note, we expand RS to RM - rough mereology which provides a measurable degree of uncertainty to those areas.

The fast progress in applications of Artificial Neural Networks (NN) promotes new directions of research and generalizations. This involves advanced mathematical concepts such as group theory [19], differential geometry [5, 6], or topological methods in data analysis [7]. The core of NN implementations lies in linear algebra usage.

Neural networks used in computations with more advanced algebras than real numbers perform better in some applications. However, there is no general framework for constructing hypercomplex neural networks. We propose a library integrated with Keras that can do computations within TensorFlow and PyTorch. It provides Dense and Convolutional 1D, 2D, and 3D layers architectures.

Despite the number of successful applications of the Extreme Learning Machine (ELM), we show that its underlying foundational principles do not have a rigorous mathematical justification. Specifically, we refute the proofs of two main statements, and we also create a dataset that provides a counterexample to the ELM learning algorithm and explain its design, which leads to many such counterexamples. Finally, we provide alternative statements of the foundations, which justify the efficiency of ELM in some theoretical cases.

Given a raw knowledge in the form of a data table/a decision system, one is facing two possible venues. One, to treat the system as closed, i.e., its universe does not admit new objects, or, to the contrary, its universe is open on admittance of new objects. In particular, one may obtain new objects whose sets of values of features are new to the system. In this case the problem is to assign a decision value to any such new object. This problem is somehow resolved in the rough set theory, e.g., on the basis of similarity of the value set of a new object to value sets of objects already assigned a decision value. It is crucial for online learning when each new object must have a predicted decision value.\ There is a vast literature on various methods for decision prediction for new yet unseen object. The approach we propose is founded in the theory of rough mereology and it requires a theory of sets/concepts, and, we root our theory in classical set theory of Syllogistic within which we recall the theory of parts known as Mereology. Then, we recall our theory of Rough Mereology along with the theory of weight assignment to the Tarski algebra of Mereology.\ This allows us to introduce the notion of a part to a degree. Once we have defined basics of Mereology and rough Mereology, we recall our theory of weight assignment to elements of the Boolean algebra within Mereology and this allows us to define the relation of parts to the degree and we apply this notion in a procedure to select a decision for new yet unseen objects.\ In selecting a plausible candidate which would pass its decision value to the new object, we employ the notion of Vapnik - Chervonenkis dimension in order to select at the first stage the candidate with the largest VC-dimension of the family of its $\varepsilon$-components for some choice of $\varepsilon$.

In this paper, we present an innovative technique for the path planning of flying robots in a 3D environment in Rough Mereology terms. The main goal was to construct the algorithm that would generate the mereological potential fields in 3-dimensional space. To avoid falling into the local minimum, we assist with a weighted Euclidean distance. Moreover, a searching path from the start point to the target, with respect to avoiding the obstacles was applied. The environment was created by connecting two cameras working in real-time. To determine the gate and elements of the world inside the map was responsible the Python Library OpenCV [1] which recognized shapes and colors. The main purpose of this paper is to apply the given results to drones.

The three classes of architectures for time series prediction were tested. They differ by input layers which contain either convolutional, LSTM, or dense hypercomplex layers for 4D algebras. The input was four related Stock Market time series, and the prediction of one of them is expected. The optimization of hyperparameters related to the classes of architectures was performed in order to compare the best neural networks within the class. The results show that in most cases, the architecture with a hypercomplex dense layer provides similar MAE accuracy to other architectures, however, with considerably less trainable parameters. Thanks to it, hypercomplex neural networks can be learned and process data faster than the other tested architectures. Moreover, the order of the input time series has an impact on effectively.

This short report reviews the current state of the research and methodology on theoretical and practical aspects of Artificial Neural Networks (ANN). It was prepared to gather state-of-the-art knowledge needed to construct complex, hypercomplex and fuzzy neural networks. The report reflects the individual interests of the authors and, by now means, cannot be treated as a comprehensive review of the ANN discipline. Considering the fast development of this field, it is currently impossible to do a detailed review of a considerable number of pages. The report is an outcome of the Project 'The Strategic Research Partnership for the mathematical aspects of complex, hypercomplex and fuzzy neural networks' meeting at the University of Warmia and Mazury in Olsztyn, Poland, organized in September 2022.