Persistence diagrams are common descriptors of the topological structure of data appearing in various classification and regression tasks. They can be generalized to Radon measures supported on the birth-death plane and endowed with an optimal transport distance. Examples of such measures are expectations of probability distributions on the space of persistence diagrams. In this paper, we develop methods for approximating continuous functions on the space of Radon measures supported on the birth-death plane, as well as their utilization in supervised learning tasks. Indeed, we show that any continuous function defined on a compact subset of the space of such measures (e.g., a classifier or regressor) can be approximated arbitrarily well by polynomial combinations of features computed using a continuous compactly supported function on the birth-death plane (a template). We provide insights into the structure of relatively compact subsets of the space of Radon measures, and test our approximation methodology on various data sets and supervised learning tasks.

The circular coordinates algorithm of de Silva, Morozov, and Vejdemo-Johansson takes as input a dataset together with a cohomology class representing a $1$-dimensional hole in the data; the output is a map from the data into the circle that captures this hole, and that is of minimum energy in a suitable sense. However, when applied to several cohomology classes, the output circle-valued maps can be "geometrically correlated" even if the chosen cohomology classes are linearly independent. It is shown in the original work that less correlated maps can be obtained with suitable integer linear combinations of the cohomology classes, with the linear combinations being chosen by inspection. In this paper, we identify a formal notion of geometric correlation between circle-valued maps which, in the Riemannian manifold case, corresponds to the Dirichlet form, a bilinear form derived from the Dirichlet energy. We describe a systematic procedure for constructing low energy torus-valued maps on data, starting from a set of linearly independent cohomology classes. We showcase our procedure with computational examples. Our main algorithm is based on the Lenstra--Lenstra--Lov\'asz algorithm from computational number theory.

具有非平凡大规模拓扑的数据集可能很难嵌入具有现有维度降低算法的低维欧几里得空间中。我们建议使用向量束对拓扑复杂的数据集建模，以使基本空间解释大型拓扑，而纤维则解释了局部几何形状。这使人们可以在保留大规模拓扑的同时降低纤维的尺寸。我们将此观点形式化，并且作为一个应用程序，我们描述了一种算法，该算法将数据集和在欧几里得空间中的初始表示形式一起作为输入，假定其大规模拓扑的一部分，并输出了一种新的表示，并输出一种新的表示形式，该表示是集成了沿着初始全局表示，通过局部线性维度降低获得的局部表示。我们在来自动态系统和化学的示例上证明了这种算法。在这些示例中，与各种基于众所周知的基于度量的降低算法相比，我们的算法能够在较低的目标维度中学习拓扑忠实的数据嵌入。

Ithaca is a Fuzzy Logic (FL) plugin for developing artificial intelligence systems within the Unity game engine. Its goal is to provide an intuitive and natural way to build advanced artificial intelligence systems, making the implementation of such a system faster and more affordable. The software is made up by a C\# framework and an Application Programming Interface (API) for writing inference systems, as well as a set of tools for graphic development and debugging. Additionally, a Fuzzy Control Language (FCL) parser is provided in order to import systems previously defined using this standard.

Grasping is an incredible ability of animals using their arms and limbs in their daily life. The human hand is an especially astonishing multi-fingered tool for precise grasping, which helped humans to develop the modern world. The implementation of the human grasp to virtual reality and telerobotics is always interesting and challenging at the same time. In this work, authors surveyed, studied, and analyzed the human hand-grasping behavior for the possibilities of haptic grasping in the virtual and remote environment. This work is focused on the motion and force analysis of fingers in human hand grasping scenarios and the paper describes the transition of the human hand grasping towards a tripod haptic grasp model for effective interaction in virtual reality.

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.

Efficient localization plays a vital role in many modern applications of Unmanned Ground Vehicles (UGV) and Unmanned aerial vehicles (UAVs), which would contribute to improved control, safety, power economy, etc. The ubiquitous 5G NR (New Radio) cellular network will provide new opportunities for enhancing localization of UAVs and UGVs. In this paper, we review the radio frequency (RF) based approaches for localization. We review the RF features that can be utilized for localization and investigate the current methods suitable for Unmanned vehicles under two general categories: range-based and fingerprinting. The existing state-of-the-art literature on RF-based localization for both UAVs and UGVs is examined, and the envisioned 5G NR for localization enhancement, and the future research direction are explored.

This paper proposes a novel multivariate definition of statistical dependence using a functional methodology inspired by Alfred R\'enyi. We define a new symmetric and self-adjoint cross density kernel through a recursive bidirectional statistical mapping between conditional densities of continuous random processes, which estimates their statistical dependence. Therefore, the kernel eigenspectrum is proposed as a new multivariate statistical dependence measure, and the formulation requires fewer assumptions about the data generation model than current methods. The measure can also be estimated from realizations. The proposed functional maximum correlation algorithm (FMCA) is applied to a learning architecture with two multivariate neural networks. The FMCA optimal solution is an equilibrium point that estimates the eigenspectrum of the cross density kernel. Preliminary results with synthetic data and medium size image datasets corroborate the theory. Four different strategies of applying the cross density kernel are thoroughly discussed and implemented to show the versatility and stability of the methodology, and it transcends supervised learning. When two random processes are high-dimensional real-world images and white uniform noise, respectively, the algorithm learns a factorial code i.e., the occurrence of a code guarantees that a certain input in the training set was present, which is quite important for feature learning.

Nowadays, the applications of hydraulic systems are present in a wide variety of devices in both industrial and everyday environments. The implementation and usage of hydraulic systems have been well documented; however, today, this still faces a challenge, the integration of tools that allow more accurate information about the functioning and operation of these systems for proactive decision-making. In industrial applications, many sensors and methods exist to measure and determine the status of process variables (e.g., flow, pressure, force). Nevertheless, little has been done to have systems that can provide users with device-health information related to hydraulic devices integrated into the machinery. Implementing artificial intelligence (AI) technologies and machine learning (ML) models in hydraulic system components has been identified as a solution to the challenge many industries currently face: optimizing processes and carrying them out more safely and efficiently. This paper presents a solution for the characterization and estimation of anomalies in one of the most versatile and used devices in hydraulic systems, cylinders. AI and ML models were implemented to determine the current operating status of these hydraulic components and whether they are working correctly or if a failure mode or abnormal condition is present.

Auxiliary Learning is a machine learning approach in which the model acknowledges the existence of objects that do not come under any of its learned categories.The name Auxiliary learning was chosen due to the introduction of an auxiliary class. The paper focuses on increasing the generality of existing narrow purpose neural networks and also highlights the need to handle unknown objects. The Cat & Dog binary classifier is taken as an example throughout the paper.