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We show that the mean number of attractors in a critical Boolean network under asynchronous stochastic update grows like a power law and that the mean size of the attractors increases as a stretched exponential with the system size. This is in strong contrast to the synchronous case, where the number of attractors grows faster than any power law.
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Large and long-lasting cytosolic calcium surges in astrocytes have been described in cultured cells and acute slice preparations. The mechanisms that give rise to these calcium events have been extensively studied in vitro. However, their existence and functions in the intact brain are unknown. We have topically applied Fluo-4 AM on the cerebral cortex of anesthetized rats, and imaged cytosolic calcium fluctuation in astrocyte populations of superficial cortical layers in vivo, using two-photon laser scanning microscopy. Spontaneous [Ca(2+)](i) events in individual astrocytes were similar to those observed in vitro. Coordination of [Ca(2+)](i) events among astrocytes was indicated by the broad cross-correlograms. Increased neuronal discharge was associated with increased astrocytic [Ca(2+)](i) activity in individual cells and a robust coordination of [Ca(2+)](i) signals in neighboring astrocytes. These findings indicate potential neuron-glia communication in the intact brain.
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Due to certain specificities in the HIV epidemic, its spread has escaped the random transmission pattern of other infectious diseases. Observation of the epidemic has shown that individual behavior - relational patterns among individuals - plays a crucial role in HIV transmission and that strategies to prevent the epidemic's spread should take this factor into account in order to foster efficient allocation of existing resources. Mathematical and statistical models applying the behavioral approach to the epidemic have estimated interactions between groups whose characteristics and behaviors varied. However, such models have been more "post-dictive" than predictive, due to the inadequate representation of social structures in populations through which infectious agents spread. The social network methodology thus came to be applied to the approach to the HIV epidemic. This article discusses alternatives for the application of this methodology to the Brazilian epidemic, considering that sociometric risk networks structure the flow of infectious agents in communities, creating unique opportunities to interrupt their spread.
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A simulation procedure is described for making feasible large-scale simulations of recurrent neural networks of spiking neurons and plastic synapses. The procedure is applicable if the dynamic variables of both neurons and synapses evolve deterministically between any two successive spikes. Spikes introduce jumps in these variables, and since spike trains are typically noisy, spikes introduce stochasticity into both dynamics. Since all events in the simulation are guided by the arrival of spikes, at neurons or synapses, we name this procedure event-driven. The procedure is described in detail, and its logic and performance are compared with conventional (synchronous) simulations. The main impact of the new approach is a drastic reduction of the computational load incurred upon introduction of dynamic synaptic efficacies, which vary organically as a function of the activities of the pre- and postsynaptic neurons. In fact, the computational load per neuron in the presence of the synaptic dynamics grows linearly with the number of neurons and is only about 6% more than the load with fixed synapses. Even the latter is handled quite efficiently by the algorithm. We illustrate the operation of the algorithm in a specific case with integrate-and-fire neurons and specific spike-driven synaptic dynamics. Both dynamical elements have been found to be naturally implementable in VLSI. This network is simulated to show the effects on the synaptic structure of the presentation of stimuli, as well as the stability of the generated matrix to the neural activity it induces.
We investigate the dynamics of a neural network where each neuron evolves according to the combined effects of deterministic integrate-and-fire dynamics and purely inhibitory coupling with K randomly chosen "neighbors." The inhibition reduces the voltage of a given neuron by an amount Delta when one of its neighbors fires. The interplay between the integration and inhibition leads to a steady state that is determined by solving the rate equations for the neuronal voltage distribution. We also study the evolution of a single neuron and find that the mean lifetime between firing events equals 1+K delta and that the probability that a neuron has not yet fired decays exponentially with time.
This letter aims at studying the impact of iterative Hebbian learning algorithms on the recurrent neural network's underlying dynamics. First, an iterative supervised learning algorithm is discussed. An essential improvement of this algorithm consists of indexing the attractor information items by means of external stimuli rather than by using only initial conditions, as Hopfield originally proposed. Modifying the stimuli mainly results in a change of the entire internal dynamics, leading to an enlargement of the set of attractors and potential memory bags. The impact of the learning on the network's dynamics is the following: the more information to be stored as limit cycle attractors of the neural network, the more chaos prevails as the background dynamical regime of the network. In fact, the background chaos spreads widely and adopts a very unstructured shape similar to white noise. Next, we introduce a new form of supervised learning that is more plausible from a biological point of view: the network has to learn to react to an external stimulus by cycling through a sequence that is no longer specified a priori. Based on its spontaneous dynamics, the network decides "on its own" the dynamical patterns to be associated with the stimuli. Compared with classical supervised learning, huge enhancements in storing capacity and computational cost have been observed. Moreover, this new form of supervised learning, by being more "respectful" of the network intrinsic dynamics, maintains much more structure in the obtained chaos. It is still possible to observe the traces of the learned attractors in the chaotic regime. This complex but still very informative regime is referred to as "frustrated chaos."
Two different types of directed networks are investigated, transcriptional regulation networks and neural networks. The directed network structure is studied and is also shown to reflect the different processes taking place on the networks. The distribution of influence, identified as the the number of downstream vertices, are used as a tool for investigating random vertex removal. In the transcriptional regulation networks we observe that only a small number of vertices have a large influence. The small influences of most vertices limit the effect of a random removal to, in most cases, only a small fraction of vertices in the network. The neural network has a rather different topology with respect to the influence, which are large for most vertices. To further investigate the effect of vertex removal we simulate the biological processes taking place on the networks. Opposed to the presumed large effect of random vertex removal in the neural network, the high density of edges in conjunction with the dynamics used makes the change in the state of the system to be highly localized around the removed vertex.
It is well established that various cortical regions can implement a wide array of neural processes, yet the mechanisms which integrate these processes into behavior-producing, brain-scale activity remain elusive. We propose that an important role in this respect might be played by executive structures controlling the traffic of information between the cortical regions involved. To illustrate this hypothesis, we present a neural network model comprising a set of interconnected structures harboring stimulus-related activity (visual representation, working memory, and planning), and a group of executive units with task-related activity patterns that manage the information flowing between them. The resulting dynamics allows the network to perform the dual task of either retaining an image during a delay (delayed-matching to sample task), or recalling from this image another one that has been associated with it during training (delayed-pair association task). The model reproduces behavioral and electrophysiological data gathered on the inferior temporal and prefrontal cortices of primates performing these same tasks. It also makes predictions on how neural activity coding for the recall of the image associated with the sample emerges and becomes prospective during the training phase. The network dynamics proves to be very stable against perturbations, and it exhibits signs of scale-invariant organization and cooperativity. The present network represents a possible neural implementation for active, top-down, prospective memory retrieval in primates. The model suggests that brain activity leading to performance of cognitive tasks might be organized in modular fashion, simple neural functions becoming integrated into more complex behavior by executive structures harbored in prefrontal cortex and/or basal ganglia.
OBJECTIVE: The authors present a Measurement and Analysis System for Capillary Oxygen Transport (MASCOT) to study red blood cell (RBC) dynamics and oxygenation in capillary networks. The system enables analysis of capillaries to study geometry and morphology and provides values for capillary parameters such as diameter and segment length. It also serves as an analysis tool for capillary RBC flow characteristics, including RBC velocity, lineal density, and supply rate. Furthermore, the system provides a means of determining the oxygen saturation of hemoglobin contained within RBCs, by analysis of synchronized videotapes containing images at two wavelengths, enabling the quantification of the oxygen content of individual RBCs. METHODS: Video recordings of RBC flow at two wavelengths, 420 nm (isosbestic) and 436 nm (oxygen sensitive), are made using a dual camera video microscopy system. The 420-nm recording is used to generate images based on the variance of light intensity fluctuations that help to identify capillaries in a given field of view that are in sharp focus and exhibit flow of individual RBCs separated by plasma gaps. A region of interest enclosing the desired capillary is defined and a fixed number of successive video frames at the two wavelengths are captured. Next a difference image is created, which delineates the RBC column, whose width is used to estimate the internal diameter of the capillary. The 420-nm images are also used to identify the location and centroid of each RBC within the capillary. A space-time image is generated to compute the average RBC velocity. Lineal density is calculated as the number of RBCs per unit length of a capillary segment. The mean optical density (OD) of each RBC is calculated at both wavelengths, and the average SO(2) for each cell is determined from OD(436)/OD(420). RESULTS AND CONCLUSIONS: MASCOT is a robust and flexible system that requires simple hardware, including a SGI workstation fitted with an audio-visual module, a VCR, and an oscilloscope. Since the new system provides information on an individual cell basis from entire capillary segments, the authors believe that results obtained using MASCOT will be more accurate than those obtained from previous systems. Due to its flexibility and ease of extension to other applications, MASCOT has the potential to be applied widely as an analysis tool for capillary oxygen transport measurements.
SUMMARY: This study presents dAMN, a genome-scale neural-mechanistic hybrid model that combines neural networks with dynamic flux balance analysis to predict bacterial growth dynamics across diverse nutrient environments. Using a residual network architecture, dAMN predicts reaction fluxes and lag-phase parameters from initial medium composition, then integrates these predictions under stoichiometric constraints derived from genome-scale metabolic models. Trained on Escherichia coli and Pseudomonas putida growth datasets across combinatorial media, dAMN accurately forecasts temporal growth dynamics and generalizes to unseen media conditions, with mean R² ≥ 0.9. The model also reproduces biologically relevant behaviors including substrate depletion, acetate overflow, and diauxic shifts, while explicitly modeling lag phases usually absent from standard dFBA. AVAILABILITY AND IMPLEMENTATION: The dAMN software, associated models, and datasets are available at https://github.com/brsynth/dAMN-main-release and via Zenodo DOI: 10.5281/zenodo.17908125.
Systematic studies of the organization of biochemical networks that make up the living cell can be defined by studying the organization and dynamics of protein interaction networks (PINs). Here, we describe recent conceptual and experimental advances that can achieve this aim and how chemical perturbations of interactions can be used to define the organization of biochemical networks. Resulting perturbation profiles and subcellular locations of interactions allow us to 'place' each gene product at its relevant point in a network. We discuss how experimental strategies can be used in conjunction with other genome-wide analyses of physical and genetic protein interactions and gene transcription profiles to determine network dynamic linkage (NDL) in the living cell. It is through such dynamic studies that the intricate networks that make up the chemical machinery of the cell will be revealed.
In this paper, an algorithm that forms a dynamic and self-organizing network is demonstrated. The hypothesis of this work is that in order to achieve a resilient and adaptive peer-to-peer (P2P) network, each network node must proactively maintain a minimum number of edges. Specifically, low-level communication protocols are not sufficient by themselves to achieve high-service availability, especially in the case of ad hoc or dynamic networks with a high degree of node addition and deletion. The concept has been evaluated within a P2P agent application in which each agent has a goal to maintain a preferred number of connections to a number of service providing agents. Using this algorithm, the agents update a weight value associated with each connection, based on the perceived utility of the connection to the corresponding agent. This utility function can be a combination of several node or edge parameters, such as degree k of the target node, or frequency of the message response from the node. This weight is updated using a set of Hebbian-style learning rules, such that the network as a whole exhibits adaptive self-organizing behavior. The principal result is the finding that by limiting the connection neighborhood within the overlay topology, the resulting P2P network can be made highly resilient to targeted attacks on high-degree nodes, while maintaining search efficiency.
The reaction dynamics of vibrationally excited vinyl bromide have been investigated using classical trajectory methods on a neural network potential surface that is fitted to an ab initio database of 12 122 configuration energies obtained from electronic structure calculations conducted at the MP4(SDQ) level of theory using a 6-31G(d,p) basis set for the carbon and hydrogen atoms and Huzinaga's (43334334) basis set augmented with split outer s and p orbitals (4332143214) and a polarization f orbital with an exponent of 0.5 for the bromine atom. The sampling of the 12-dimensional configuration hyperspace of vinyl bromide prior to execution of the electronic structure calculations is accomplished by combining novelty-sampling methods, chemical intuition, and trajectory sampling on empirical and neural network surfaces. The final potential is obtained using a two-layer feed-forward neural network comprising 38 and 1 neurons, respectively, with hyperbolic tangent sigmoid and linear transfer functions in the hidden and output layers, respectively. The fitting is accomplished using the Levenberg-Marquardt algorithm with early stopping and Bayesian regularization methods to avoid overfitting. The interpolated potentials have a standard deviation from the ab initio results of 0.0578 eV, which is within the range generally regarded as "chemical accuracy" for the purposes of electronic structure calculations. It is shown that the potential surface may be easily and conveniently transferred from one research group to another. The files required for transfer of the vinyl bromide surface can be obtained from the Electronic Physics Auxiliary Publication Service. Total dissociation rate coefficients for vinyl bromide are obtained at five different excitation energies between 4.50 and 6.44 eV. Branching ratios into each of the six open reaction channels are computed at 24 vibrational energies in the range between 4.00 and 6.44 eV. The distribution of vibrational energies in HBr formed via three-center dissociation from vinyl bromide is determined and compared with previous theoretical and experimental results. It is concluded that the combination of ab initio electronic structure calculations, novelty sampling with chemical intuition and trajectories on empirical analytic surfaces, and feed-forward neural networks provides a viable framework in which to execute purely ab initio molecular-dynamics studies on complex systems with multiple open reaction channels.