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The hippocampal-entorhinal circuit is considered to play an important role in the spatial cognition of animals. However, the mechanism of the information flow within the circuit and its contribution to the function of the grid-cell module are still topics of discussion. Prevailing theories suggest that grid cells are primarily influenced by self-motion inputs from the Medial Entorhinal Cortex, with place cells serving a secondary role by contributing to the visual calibration of grid cells. However, recent evidence suggests that both self-motion inputs and visual cues may collaboratively contribute to the formation of grid-like patterns. In this paper, we introduce a novel Continuous Attractor Network model based on a spatial transformation mechanism. This mechanism enables the integration of self-motion inputs and visual cues within grid-cell modules, synergistically driving the formation of grid-like patterns. From the perspective of individual neurons within the network, our model successfully replicates grid firing patterns. From the view of neural population activity within the network, the network can form and drive the activated bump, which describes the characteristic feature of grid-cell modules, namely, path integration. Through further exploration and experimentation, our model can exhibit significant performance in path integration. This study provides a new insight into understanding the mechanism of how the self-motion and visual inputs contribute to the neural activity within grid-cell modules. Furthermore, it provides theoretical support for achieving accurate path integration, which holds substantial implications for various applications requiring spatial navigation and mapping.

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The brain is targeted for processing temporal sequence information. It remains largely unclear how the brain learns to store and retrieve sequence memories. Here, we study how recurrent networks of binary neurons learn sequence attractors to store predefined pattern sequences and retrieve them robustly. We show that to store arbitrary pattern sequences, it is necessary for the network to include hidden neurons even though their role in displaying sequence memories is indirect. We develop a local learning algorithm to learn sequence attractors in the networks with hidden neurons. The algorithm is proven to converge and lead to sequence attractors. We demonstrate that the network model can store and retrieve sequences robustly on synthetic and real-world datasets. We hope that this study provides new insights in understanding sequence memory and temporal information processing in the brain.

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Memristors are of great theoretical and practical significance for chaotic dynamics research of brain-like neural networks due to their excellent physical properties such as brain synapse-like memorability and nonlinearity, especially crucial for the promotion of AI big models, cloud computing, and intelligent systems in the artificial intelligence field. In this paper, we introduce memristors as self-connecting synapses into a four-dimensional Hopfield neural network, constructing a central cyclic memristive neural network (CCMNN), and achieving its effective control. The model adopts a central loop topology and exhibits a variety of complex dynamic behaviors such as chaos, bifurcation, and homogeneous and heterogeneous coexisting attractors. The complex dynamic behaviors of the CCMNN are investigated in depth numerically by equilibrium point stability analysis as well as phase trajectory maps, bifurcation maps, time-domain maps, and LEs. It is found that with the variation of the internal parameters of the memristor, asymmetric heterogeneous attractor coexistence phenomena appear under different initial conditions, including the multi-stable coexistence behaviors of periodic-periodic, periodic-stable point, periodic-chaotic, and stable point-chaotic. In addition, by adjusting the structural parameters, a wide range of amplitude control can be realized without changing the chaotic state of the system. Finally, based on the CCMNN model, an adaptive synchronization controller is designed to achieve finite-time synchronization control, and its application prospect in simple secure communication is discussed. A microcontroller-based hardware circuit and NIST test are conducted to verify the correctness of the numerical results and theoretical analysis.

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Sea surface temperature (SST), with its complex and dynamic behavior, is a major driver of ocean-atmosphere interactions. The purpose of this study is to investigate the behavior of SST and its prediction using a chaotic approach. Average mutual information (AMI) and Cao methods were used to reconstruct the phase space. The Lyapunov exponent and correlation dimension were used to investigate chaos. The Lyapunov exponent index was used to predict SST with a 5-year average prediction horizon using the local prediction method between 2023 and 2027. The results showed a 3-month delay time for the Pacific and Antarctic Oceans, and a 2-month delay time for the Atlantic, Indian, and Arctic Oceans. The optimal embedding dimension for all oceans is between 6 and 7. Our analysis reveals that the dynamics of SST in all oceans exhibit varying degrees of chaos, as indicated by the correlation dimension. The local prediction method achieves relatively accurate short-term SST predictions due to the clustering of SST points around specific attractors in the phase space. However, in the long term, the accuracy of this method decreases as the points in the phase space of SST can spread randomly. The model performance ranking with a Percent Mean Relative Absolute Error shows that the Indian Ocean has the best performance compared to other oceans, while the Atlantic, Pacific, and Antarctic and Arctic Oceans are in the next ranks. This study contributes to understanding the dynamics of SST and has practical value for use in the development of climate models.

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Accurate development of satellite maneuvers necessitates a broad orbital dynamical system and efficient nonlinear control techniques. For achieving the intended formation, a framework of a discrete fractional difference satellite model is constructed by the use of commensurate and non-commensurate orders for the control and synchronization of fractional-order chaotic satellite system. The efficacy of the suggested framework is evaluated employing a numerical simulation of the concerning dynamic systems of motion while taking into account multiple considerations such as Lyapunov exponent research, phase images and bifurcation schematics. With the aid of discrete nabla operators, we monitor the qualitative behavioural patterns of satellite systems in order to provide justification for the structure's chaos. We acquire the fixed points of the proposed trajectory. At each fixed point, we calculate the eigenvalue of the satellite system's Jacobian matrix and check for zones of instability. The outcomes exhibit a wide range of multifaceted behaviours resulting from the interaction with various fractional-orders in the offered system. Additionally, the sample entropy evaluation is employed in the research to determine complexities and endorse the existence of chaos. To maintain stability and synchronize the system, nonlinear controllers are additionally provided. The study highlights the technique's vulnerability to fractional-order factors, resulting in exclusive, changing trends and equilibrium frameworks. Because of its diverse and convoluted behaviour, the satellite chaotic model is an intriguing and crucial subject for research.

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Glioblastoma Multiforme is a brain tumor distinguished by its aggressiveness. We suggested that this aggressiveness leads single-cell RNA-sequence data (scRNA-seq) to span a representative portion of the cancer attractors domain. This conjecture allowed us to interpret the scRNA-seq heterogeneity as reflecting a representative trajectory within the attractor's domain. We considered factors such as genomic instability to characterize the cancer dynamics through stochastic fixed points. The fixed points were derived from centroids obtained through various clustering methods to verify our method sensitivity. This methodological foundation is based upon sample and time average equivalence, assigning an interpretative value to the data cluster centroids and supporting parameters estimation. We used stochastic simulations to reproduce the dynamics, and our results showed an alignment between experimental and simulated dataset centroids. We also computed the Waddington landscape, which provided a visual framework for validating the centroids and standard deviations as characterizations of cancer attractors. Additionally, we examined the stability and transitions between attractors and revealed a potential interplay between subtypes. These transitions might be related to cancer recurrence and progression, connecting the molecular mechanisms of cancer heterogeneity with statistical properties of gene expression dynamics. Our work advances the modeling of gene expression dynamics and paves the way for personalized therapeutic interventions.

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The standard consolidation theory states that short-term memories located in the hippocampus enable the consolidation of long-term memories in the neocortex. In other words, the neocortex slowly learns long-term memories with a transient support of the hippocampus that quickly learns unstable memories. However, it is not clear yet what could be the neurobiological mechanisms underlying these differences in learning rates and memory time-scales. Here, we propose a novel modeling approach of the standard consolidation theory, that focuses on its potential neurobiological mechanisms. In addition to synaptic plasticity and spike frequency adaptation, our model incorporates adult neurogenesis in the dentate gyrus as well as the difference in size between the neocortex and the hippocampus, that we associate with distance-dependent synaptic plasticity. We also take into account the interconnected spatial structure of the involved brain areas, by incorporating the above neurobiological mechanisms in a coupled neural field framework, where each area is represented by a separate neural field with intra- and inter-area connections. To our knowledge, this is the first attempt to apply neural fields to this process. Using numerical simulations and mathematical analysis, we explore the short-term and long-term dynamics of the model upon alternance of phases of hippocampal replay and retrieval cue of an external input. This external input is encodable as a memory pattern in the form of a multiple bump attractor pattern in the individual neural fields. In the model, hippocampal memory patterns become encoded first, before neocortical ones, because of the smaller distances between the bumps of the hippocampal memory patterns. As a result, retrieval of the input pattern in the neocortex at short time-scales necessitates the additional input delivered by the memory pattern of the hippocampus. Neocortical memory patterns progressively consolidate at longer times, up to a point where their retrieval does not need the support of the hippocampus anymore. At longer times, perturbation of the hippocampal neural fields by neurogenesis erases the hippocampus pattern, leading to a final state where the memory pattern is exclusively evoked in the neocortex. Therefore, the dynamics of our model successfully reproduces the main features of the standard consolidation theory. This suggests that neurogenesis in the hippocampus and distance-dependent synaptic plasticity coupled to synaptic depression and spike frequency adaptation, are indeed critical neurobiological processes in memory consolidation.

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Neuronal networks possess the ability to regulate their activity states in response to disruptions. How and when neuronal networks turn from physiological into pathological states, leading to the manifestation of neuropsychiatric disorders, remains largely unknown. Here, we propose that neuronal networks intrinsically maintain network stability even at the cost of neuronal loss. Despite the new stable state being potentially maladaptive, neural networks may not reverse back to states associated with better long-term outcomes. These maladaptive states are often associated with hyperactive neurons, marking the starting point for activity-dependent neurodegeneration. Transitions between network states may occur rapidly, and in discrete steps rather than continuously, particularly in neurodegenerative disorders. The self-stabilizing, metastable, and noncontinuous characteristics of these network states can be mathematically described as attractors. Maladaptive attractors may represent a distinct pathophysiological entity that could serve as a target for new therapies and for fostering resilience.

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Studying gene regulatory networks associated with cancer provides valuable insights for therapeutic purposes, given that cancer is fundamentally a genetic disease. However, as the number of genes in the system increases, the complexity arising from the interconnections between network components grows exponentially. In this study, using Boolean logic to adjust the existing relationships between network components has facilitated simplifying the modeling process, enabling the generation of attractors that represent cell phenotypes based on breast cancer RNA-seq data. A key therapeutic objective is to guide cells, through targeted interventions, to transition from the current cancer attractor to a physiologically distinct attractor unrelated to cancer. To achieve this, we developed a computational method that identifies network nodes whose inhibition can facilitate the desired transition from one tumor attractor to another associated with apoptosis, leveraging transcriptomic data from cell lines. To validate the model, we utilized previously published in vitro experiments where the downregulation of specific proteins resulted in cell growth arrest and death of a breast cancer cell line. The method proposed in this manuscript combines diverse data sources, conducts structural network analysis, and incorporates relevant biological knowledge on apoptosis in cancer cells. This comprehensive approach aims to identify potential targets of significance for personalized medicine.

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Abstract Floating structures, both natural and artificial, attract fish by providing shelter, feeding areas, and nesting sites. Occupancy can be either more permanent, leading to a gradual gathering of the assembly, or transient, occurring randomly. The ability of an attractor to hold a fish assemblage may depend on the availability of habitat resources in the environment. New artificial attractors are more valuable when natural ones are scarce. Additionally, fish characteristics play a role; young and small fishes may need new habitat for shelter more than adult fish. As aquatic herbaceous areas are abundant during high water, coinciding with the period of fish reproduction, they are particularly relevant for juveniles. We constructed fish attractors composed of natural materials to investigate the structure of fish assemblages during the flood of an Amazonian floodplain lake. Our aim was to test the hypothesis that assembly processes during the flood period would be random, with a predominance of juveniles in the attractors. We collected fish at intervals of 5, 15, and 30 days, resulting in 39 observations, and classified them as either adult or juvenile. Species composition was compared among treatments using Principal Coordinates Analysis (PCoA). The assembly process was tested through species co-occurrence patterns employing null models and the C-score index. The proportion of juveniles and adults was compared using a Chi-square test. Species composition remained consistent throughout the experiment. The assembly was random, with a prevalence of juveniles, possibly serving only as temporary shelter and feeding areas. Our study contributes to understanding the role of habitat availability for floodplain fishes during high waters. The results suggest that floating attractors and new habitats may be more valuable for the juveniles than adult fish and can be used as a management strategy for population recovery, especially when floating herbaceous habitats are scarce.

Resumo As estruturas flutuantes, naturais ou artificiais, atraem os peixes, fornecendo abrigo, áreas de alimentação e locais de nidificação. A ocupação pode ser mais permanente, resultando em um recolhimento gradativo da assembleia, ou transitória, ocorrendo aleatoriamente. A capacidade de um atrator de manter uma assembleia de peixes pode depender da disponibilidade de recursos de habitat no ambiente. Novos atratores artificiais são mais valiosos quando os naturais são escassos. Além disso, as características dos peixes desempenham um papel, já que peixes jovens e pequenos podem necessitar de novos habitats como abrigo mais do que peixes adultos. Como as áreas com herbáceas aquáticas são abundantes durante as cheias, coincidindo com o período de reprodução dos peixes, elas são especialmente relevantes para peixes juvenis. Construímos atratores de peixes compostos de material natural para investigar a estrutura das assembleias de peixes durante a cheia de um lago de várzea amazônico, a fim de testar a hipótese de que durante o período de cheia, os processos de montagem seriam aleatórios e com predominância de juvenis nos atratores. Os peixes foram coletados em intervalos de 5, 15 e 30 dias, resultando em 39 observações, e classificados como adultos ou juvenis. A composição de espécies foi comparada entre os tratamentos usando uma Análise de Coordenadas Principais (PCoA). O processo de montagem foi testado por meio de padrões de coocorrência de espécies usando modelos nulos e o índice C-score. A proporção de jovens e adultos foi comparada usando um teste Qui-quadrado. A composição de espécies permaneceu a mesma ao longo do experimento. A montagem da assembleia foi aleatória com prevalência de juvenis nos atratores, que possivelmente serviam apenas como abrigo temporário e áreas de alimentação. Nosso estudo contribui para entender o papel da disponibilidade de novos habitats para peixes de várzea durante a cheia. Os resultados sugerem que atratores flutuantes e novos habitats podem ser mais valiosos para os peixes jovens do que para adultos e podem ser usados como estratégia de manejo para a recuperação populacional, especialmente quando habitats de herbáceas flutuantes são escassos.

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Adolescent-onset schizophrenia (AOS) is a relatively rare and under-studied form of schizophrenia with more severe cognitive impairments and poorer outcome compared to adult-onset schizophrenia. Several neuroimaging studies have reported alterations in regional activations that account for activity in individual regions (first-order model) and functional connectivity that reveals pairwise co-activations (second-order model) in AOS compared to controls. The pairwise maximum entropy model, also called the Ising model, can integrate both first-order and second-order terms to elucidate a comprehensive picture of neural dynamics and captures both individual and pairwise activity measures into a single quantity known as energy, which is inversely related to the probability of state occurrence. We applied the MEM framework to task functional MRI data collected on 23 AOS individuals in comparison with 53 healthy control subjects while performing the Penn Conditional Exclusion Test (PCET), which measures executive function that has been repeatedly shown to be more impaired in AOS compared to adult-onset schizophrenia. Accuracy of PCET performance was significantly reduced among AOS compared to controls as expected. Average cumulative energy achieved for a participant over the course of the fMRI negatively correlated with task performance, and the association was stronger than any first-order associations. The AOS subjects spent more time in higher energy states that represent lower probability of occurrence and were associated with impaired executive function suggesting that the neural dynamics may be less efficient compared to controls who spent more time in lower energy states occurring with higher probability and hence are more stable and efficient. The energy landscapes in both conditions featured attractors that corresponded to two distinct subnetworks, namely fronto-temporal and parieto-motor. Attractor basins were larger in the controls than in AOS; moreover, fronto-temporal basin size was significantly correlated with cognitive performance in controls but not among the AOS. The single trial trajectories for the AOS group also showed higher variability in concordance with shallow attractor basins among AOS. These findings suggest that the neural dynamics of AOS features more frequent occurrence of less probable states with narrower attractors, which lack the relation to executive function associated with attractors in control subjects suggesting a diminished capacity of AOS to generate task-effective brain states.

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We describe a strategy for the development of a rational approach of neoplastic disease therapy based on the demonstration that scale-free networks are susceptible to specific attacks directed against its connective hubs. This strategy involves the (i) selection of up-regulated hubs of connectivity in the tumors interactome, (ii) drug repurposing of these hubs, (iii) RNA silencing of non-druggable hubs, (iv) in vitro hub validation, (v) tumor-on-a-chip, (vi) in vivo validation, and (vii) clinical trial. Hubs are protein targets that are assessed as targets for rational therapy of cancer in the context of personalized oncology. We confirmed the existence of a negative correlation between malignant cell aggressivity and the target number needed for specific drugs or RNA interference (RNAi) to maximize the benefit to the patient's overall survival. Interestingly, we found that some additional proteins not generally targeted by drug treatments might justify the addition of inhibitors designed against them in order to improve therapeutic outcomes. However, many proteins are not druggable, or the available pharmacopeia for these targets is limited, which justifies a therapy based on encapsulated RNAi.

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At present, memristive neural networks with various topological structures have been widely studied. However, the memristive neural network with a star structure has not been investigated yet. In order to investigate the dynamic characteristics of neural networks with a star structure, a star memristive neural network (SMNN) model is proposed in this paper. Firstly, an SMNN model is proposed based on a Hopfield neural network and a flux-controlled memristor. Then, its chaotic dynamics are analyzed by using numerical analysis methods including bifurcation diagrams, Lyapunov exponents, phase plots, Poincaré maps, and basins of attraction. The results show that the SMNN can generate complex dynamical behaviors such as chaos, multi-scroll attractors, and initial boosting behavior. The number of multi-scroll attractors can be changed by adjusting the memristor's control parameters. And the position of the coexisting chaotic attractors can be changed by switching the memristor's initial values. Meanwhile, the analog circuit of the SMNN is designed and implemented. The theoretical and numerical results are verified through MULTISIM simulation results. Finally, a color image encryption scheme is designed based on the SMNN. Security performance analysis shows that the designed cryptosystem has good security.

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The ability to navigate effectively in a rich and complex world is crucial for the survival of all animals. Specialist neural structures have evolved that are implicated in facilitating this ability, one such structure being the ring attractor network. In this study, we model a trio of Spiking Neural Network (SNN) ring attractors as part of a bio-inspired navigation system to maintain an internal estimate of planar translation of an artificial agent. This estimate is dynamically calibrated using a memory recall system of landmark-free allotheic multisensory experiences. We demonstrate that the SNN-based ring attractor system can accurately model motion through 2D space by integrating ideothetic velocity information and use recalled allothetic experiences as a positive corrective mechanism. This SNN based navigation system has potential for use in mobile robotics applications where power supply is limited and external sensory information is intermittent or unreliable.

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The neurobiological mechanisms of arousal and anesthesia remain poorly understood. Recent evidence highlights the key role of interactions between the cerebral cortex and the diffusely projecting matrix thalamic nuclei. Here, we interrogate these processes in a whole-brain corticothalamic neural mass model endowed with targeted and diffusely projecting thalamocortical nuclei inferred from empirical data. This model captures key features seen in propofol anesthesia, including diminished network integration, lowered state diversity, impaired susceptibility to perturbation, and decreased corticocortical coherence. Collectively, these signatures reflect a suppression of information transfer across the cerebral cortex. We recover these signatures of conscious arousal by selectively stimulating the matrix thalamus, recapitulating empirical results in macaque, as well as wake-like information processing states that reflect the thalamic modulation of large-scale cortical attractor dynamics. Our results highlight the role of matrix thalamocortical projections in shaping many features of complex cortical dynamics to facilitate the unique communication states supporting conscious awareness.

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Change in music therapy is often modeled linearly. In linear analysis, change is represented as the difference between the scores recorded before and after treatment, where changes in the input are proportional to the output. However, changes in complex systems are often not linear and depend on time. We propose Dynamic Systems Theory (DST) as a means to overcome the shortcomings of linear analysis and enrich the study of change in music therapy. This article aims to introduce and critically discuss the applications of DST in music therapy, focusing on its theoretical and methodological aspects. DST offers a meta-framework to model nonlinear change in music therapy, considering time as continuous. The application of DST can further enhance the understanding of how music therapy works, the shape of the change, and how the relevant therapeutic processes within music therapy support therapeutic change. An introduction to DST theory is provided along with its history, implications, assessment methods, statistical analyses, mathematical modeling, and implementation examples in music therapy research.

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The present work studies a novel efficient compressed based cryptosystem which combines a dynamical parameter coming from high dimensional system, a dynamics S-box and a 2D compress sensing (2D-CS). Firstly, a secret key depending on input image is gotten via the SHA-256 function. That input image, decomposed into four sub-images uses chaotic sequences of the novel 7D multistable system to perform 2D compress sensing. Afterward, the previous compressed image is substituted by the key-dependent Mordell elliptic curve based dynamic S-box. At the end, the diffusion of the substituted image is proceed by chaotic sequences coming from the novel 7D multistable system. The compressed based cryptosystem presented here is considerably dependent on the original image. Moreover, the 7D chaotic system exhibits phenomenon of transient chaos. Equally, we have found plan equilibria hidden attractors which is a good chaos based property in cryptography. Let's recall that up to date, phenomenon of transient chaos and plan equilibria hidden attractors are rarely reported in Josephson junction systems. This denothing the novelty of this article. Through well-known metrics, the results found are evaluated and validated as well as their robustness over brute force attacks. The obtained results are termed as good in accordances with the existing ones over the literature.

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Characterizing large-scale dynamic organization of the brain relies on both data-driven and mechanistic modeling, which demands a low versus high level of prior knowledge and assumptions about how constituents of the brain interact. However, the conceptual translation between the two is not straightforward. The present work aims to provide a bridge between data-driven and mechanistic modeling. We conceptualize brain dynamics as a complex landscape that is continuously modulated by internal and external changes. The modulation can induce transitions between one stable brain state (attractor) to another. Here, we provide a novel method-Temporal Mapper-built upon established tools from the field of topological data analysis to retrieve the network of attractor transitions from time series data alone. For theoretical validation, we use a biophysical network model to induce transitions in a controlled manner, which provides simulated time series equipped with a ground-truth attractor transition network. Our approach reconstructs the ground-truth transition network from simulated time series data better than existing time-varying approaches. For empirical relevance, we apply our approach to fMRI data gathered during a continuous multitask experiment. We found that occupancy of the high-degree nodes and cycles of the transition network was significantly associated with subjects' behavioral performance. Taken together, we provide an important first step toward integrating data-driven and mechanistic modeling of brain dynamics.

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In this article, we describe a study conducted online with 953 participants of varying levels of education and, when applicable, science/physics teaching experience. These participants were asked to solve a cognitive task in which many different pairs of objects were presented and to identify which, if any, would touch the ground first when dropped (in atmospheric or non-atmospheric environments). Recorded accuracies and response times allowed us to conduct an analysis based on the conceptual prevalence framework, which posits that the coexistence of conceptual and/or misconceptual resources can produce interference in response production. The results show that the influence of some of them decreases or, more surprisingly, increases with training. In fact, secondary and college physics teachers seem to cultivate some of them, and most likely have contributed to their spread. The implications for teaching and research are discussed.