This article presents a novel computational approach to visualizing memristor dynamics within a simulated neural network. Memristors, known for their ability to emulate synaptic plasticity due to their variable resistance characteristics, are key components in neuromorphic computing and hold potential for advancing our understanding of neural processes. Our study introduces a sophisticated memristor model that incorporates non-linear resistance changes, simulating the complex behavior of synaptic connections in a neural network.The neural network, consisting of multiple interconnected neurons with memristor-based synapses, is subjected to a series of electrical stimuli. Each memristor's resistance is modulated in response to the applied voltage, mimicking the synaptic weight adjustments that occur during learning and memory formation in biological neural networks. To effectively illustrate these changes, we employ a high-contrast color mapping scheme, where the varying resistance of each memristor is represented by distinct colors, providing a clear and intuitive visualization of synaptic modifications over time.Our simulation runs through multiple iterations, demonstrating how synaptic weights evolve in response to different input patterns. The use of an extended voltage range and increased scaling factors ensures pronounced changes in memristance, enhancing the visibility of synaptic adaptations. The resulting visualizations offer a compelling representation of how memristors can mimic the dynamic nature of biological synapses, contributing to the field of neuromorphic engineering and deepening our comprehension of neural mechanisms underlying learning and memory.This work not only showcases the potential of memristors in simulating neural behavior but also provides a valuable educational tool for illustrating complex concepts in neuroscience and neuromorphic computing. The insights gained from this study pave the way for further exploration into the development of advanced neural network models and the design of memristor-based computing systems.

This study presents a computational simulation to explore the distinctive patterns of neural connectivity in Autism Spectrum Disorder (ASD), focusing on the concepts of spatial and topological proximities. ASD is characterized by unique cognitive and behavioral profiles, often attributed to atypical neural development and connectivity. Our simulation employs a two-pronged approach: first, by modeling spatial proximity through the generation of clustered 3D node positions, we mimic the observed over-connectivity in localized brain regions in ASD. Second, we construct a topological network to represent the complex interplay of under-connectivity and over-connectivity in functional brain networks, a hallmark of ASD's neural landscape. The spatial model demonstrates pronounced clustering, reflecting the structural brain differences and atypical growth patterns reported in neuroimaging studies of individuals with ASD. In contrast, the topological model reveals a network with a mix of sparse and dense connections, simulating the diverse and often contradictory findings of functional connectivity in ASD, such as reduced long-range connections and increased local connections. Our simulation provides a visual and conceptual framework for understanding the altered neural connectivity in ASD. It underscores the importance of considering both physical (spatial) and functional (topological) aspects of brain connectivity to grasp the full extent of neurodevelopmental deviations in ASD. This approach not only aids in elucidating the neural underpinnings of ASD's core symptoms but also offers a foundation for developing targeted interventions. Future research, integrating more complex and individual-specific data, could further refine this model, enhancing our understanding of ASD's neural dynamics and contributing to personalized therapeutic strategies.

This article explores the intricate dynamics of complexity and emergence through the lens of a graphical model representing hippocampal functions. Utilizing a series of overlapping curves that intersect at varying degrees and frequencies, we create a visual metaphor for the sophisticated processes to store information observed in the hippocampus. This model not only depicts the spatial and frequency-related interactions of these curves but also illustrates the emergent patterns that arise from these interactions. These patterns exemplify the principles of complexity and emergence, where the collective behavior of simple elements results in intricate and unexpected outcomes. This graphical representation serves as a bridge between the abstract mathematical concepts of complexity theory and the tangible biological processes observed in neuroscience. By drawing parallels to the hippocampus, known for its role in memory formation and spatial navigation, the article sheds light on how complex systems, such as neural networks, exhibit properties that are more than just the sum of their parts. The model thus offers a unique perspective on understanding complex systems, not only in neuroscience but in broader scientific inquiries where complexity and emergent phenomena are pivotal.

This article explores the intricate journey of neural progenitor cells from the ventricular zones of the embryonic brain, focusing on their pivotal role in the formation of rich club networks, which are integral to the brain's functional architecture. Initially, the ventricular zones, particularly the cerebral ventricular zone, serve as the primary sites for the proliferation and differentiation of neural progenitors, giving rise to various types of neurons and glial cells. We delve into the sequential migration patterns of these cells, emphasizing how early-migrating neurons, destined to form deeper cortical layers, establish extensive and robust connections, potentially evolving into rich club nodes. These nodes are characterized by their high-degree connectivity and serve as crucial hubs for integrating and disseminating information across disparate brain regions.The article further discusses the implications of this developmental pathway in the context of brain network efficiency, resilience, and cognitive function. We highlight how disruptions in early cell migration can lead to anomalies in rich club formation, drawing connections to various neurodevelopmental disorders such as autism, ADHD and schizophrenia. Additionally, the significance of rich club nodes in maintaining efficient information transfer and network resilience is elucidated, underscoring their role in supporting complex cognitive processes and overall brain dynamics.In summary, this article offers a comprehensive overview of the developmental trajectory from the ventricular zones to the establishment of rich club networks, providing insights into the fundamental processes that shape the brain's intricate connectivity and functional capabilities. Ric