We determine the optimal horoball packing densities for Koszul-type Coxeter simplex tilings in hyperbolic 3-space. Using a parametrization of horoballs by the Busemann function and the symmetry of the tilings, we obtain families of packings that attain the universal simplicial density upper bound d_3(∞) = ( 2 √(3)Λ(π3) )^-1≈ 0.853276, where Λ denotes the Lobachevsky function. These results show that extremal packing densities in ℍ^3 are realized by multiple explicit Coxeter tilings and are closely tied to special values of L-functions and hyperbolic manifold volumes.

The hypothesis that foci that are visualized with fMRI are signs of hubs rather than modules can be tested by combining hemodynamic imaging (Buxton, Introduction to functional magnetic resonance imaging: principles and techniques, Cambridge University Press, Cambridge, 2001, [1]) with EEG imaging (Barlow, The electroencephalogram: its patterns and origins, MIT Press, Cambridge, 1993, [2], Pfurtscheller, Functional brain imaging. Hans Huber Publishers, Lewiston, 1988, [3]) and MEG (Hamalainen, JAMA, Rev Mod Phys 65:413–497, 1993, [4]). Experimental data indicate that the necessary macroscopic frames with beta-gamma carrier frequencies are readily found in human volunteers engaged in cognitive tasks by several research groups.

For many years, topological data analysis (TDA) and deep learning (DL) have been considered separate data analysis and representation learning approaches, which have nothing in common. The root cause of this challenge comes from the difficulties in building, extracting, and integrating TDA constructs, such as barcodes or persistent diagrams, within deep neural network architectures. Therefore, the powers of these two approaches are still on their islands and have not yet combined to form more powerful tools for dealing with multiple complex data analysis tasks. Fortunately, we have witnessed several remarkable attempts to integrate DL-based architectures with topological learning paradigms in recent years. These topology-driven DL techniques have notably improved data-driven analysis and mining problems, especially within graph datasets. Recently, graph neural networks (GNNs) have emerged as a popular deep neural architecture, demonstrating significant performance in various graph-based analysis and learning problems. Explicitly, within the manifold paradigm, the graph is naturally considered as a topological object (e.g., the topological properties of the given graph can be represented by the edge weights). Therefore, integrating TDA and GNN is considered an excellent combination. Many well-known studies have recently presented the effectiveness of TDA-assisted GNN-based architectures in dealing with complex graph-based data representation analysis and learning problems. Motivated by the successes of recent research, we present systematic literature about this nascent and promising research direction in this article, which includes general taxonomy, preliminaries, and recently proposed state-of-the-art topology-driven GNN models and perspectives.

Here, Freeman Neurodynamics is explored to introduce the reader to the challenges of analyzing electrocorticogram or electroencephalogram signals to make sense of two things: (a) how the brain participates in the creation of knowledge and meaning and (b) how to differentiate between cognitive states or modalities in brain dynamics. The first (a) is addressed via a Hilbert transform-based methodology and the second (b) via a Fourier transform methodology. These methodologies, it seems to us, conform with the systems' neuroscience views, models, and signal analysis methods that Walter J. Freeman III used and left for us as his legacy.

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Cutting-edge AI, AGI, ChatGPT and other advanced computational technologies demonstrate outstanding performance in many important tasks requiring intelligent data processing under well-known conditions. Generative AI requires huge amount of data and computational resources, and real-time robotics applications cannot rely only on such brute power of AI. They need to develop their own intelligent control system within the constraints represented by their physical body, leading to the need for situated cognition and embodied robotics. Results of cognitive science and brain-monitoring provide valuable support to develop embodied robotics approaches. This talk overviews the achievements and challenges to intelligent systems today, outlines crucial insights from brain studies. It introduces brain-inspired system designs combing the benefits of advanced AI/AGI and neuromorphic technologies. Applications include intelligent control and decision making, robot autonomy, human-robot and robot-robot interaction.

There are well-documented examples of sudden switches in human cognitive states, including visual illusions. Cognitive switches, however, are much more common than often assumed. In fact, recent research shows that abrupt switches happen several times per second in the human mind. It is of interest to explore the neural mechanisms which may lead to the observed cognitive switches and their significance in intelligent behaviors. In this work, first we briefly summarize the state-of-art of detecting cognitive switches and describe the corresponding neural processes. We argue that rapid switches between relatively stable states are inevitable attributes of brain dynamics and they are the very source of intelligent behaviors.The key question is whether the switching patterns of brain dynamics and human cognition are obscure evolutionary/historical artifacts which should be ignored in engineering designs, or they are crucial manifestations of intelligence to be incorporated in AI systems as well. Our approach is based on the observation that intelligence is neither local nor global, rather it is a delicate balance between integration and fragmentation tendencies, and sequential switches are the expressions of such competing tendencies. This motivates the development of practically useful modeling tools for intelligence using switching oscillatory dynamics. A practical model is based on percolation theory and phase transitions over random graphs, which provide a powerful tool for rigorously describe neural processes as intermittent phase transitions over the cerebral cortex. The introduced results lead to recommendations to use sequential switching patterns as the underlying modus operandi of sustainable AI systems, which can become true partners of human beings in future endeavors.

Robot autonomy becomes increasingly prolific with the development of advanced artificially intelligent technologies. Embodied robotics is related to real-time interaction of the robot platforms with the environment. An important aspect of embod-ied robotics is the use of multi-sensory information fusion for robust autonomous decisions and actions. Biologically-inspired approaches to multi-sensory integration (Gestalt formation) gained popularity in embodied robotics due to their flexibility and robustness in noisy and unpredictable practical scenarios. In this work, we discuss dynamic behaviors in multi-robot interaction which emerge as a result of implementing cognitively-motivated multi-sensory integration and action selection. A testbed using mobile quadruped Spot robots is proposed, to evaluate hypotheses on the formation of sequential communication patterns in robot-robot collaboration.

Embodiment is a key aspect of human intelligence, related to our ability of to identify the context of the individual experiences at a given time, corresponding to the natural constraints represented by our body. Learning from higher cognitive functions and social coordination between humans can support building intelligent robot systems and facilitates harmonious human-machine interactions. This position paper provides an overview of neural structures and neural dynamics contributing to human cognitive functions, including multisensory integration, Gestalt formation, perception, and building sensory associations. Embodied cognitive principles are illustrated through the intentional action-perception cycle. The results are applied to the design novel algorithms for brain-inspired cognitive robotics. Example scenarios include imitation learning, and the emergence of dialogue patterns in social robotics settings.

EEG-based identification of brain states has advanced significantly, enabling cognitive monitoring during daily tasks. Brain dynamics can be studied as a Markovian, Semi-Markovian, or Non-Markovian stochastic process, prescribed by Transition Probability Matrices derived from EEG measurements. This study models brain dynamics as discrete Markov chains using second-by-second dominant frequencies derived from the power spectrum of high-density array EEG signals. By analyzing transition and limiting probabilities across modalities, we reveal distinct neural signatures that differentiate engaged from meditative states. Though preliminary, these findings highlight the method’s potential to enhance BCI systems and deepen our understanding of brain dynamics, brain health and the benefits of meditation in future studies.