Analyzing top-down visual attention in the context of gamma oscillations: a layer- dependent network-of- networks approach.

Top-down visual attention is a fundamental cognitive process that allows individuals to selectively attend to salient visual stimuli in the environment. Recent empirical findings have revealed that gamma oscillations participate in the modulation of visual attention. However, computational studies face challenges when analyzing the attentional process in the context of gamma oscillation due to the unstable nature of gamma oscillations and the complexity induced by the layered fashion in the visual cortex. In this study, we propose a layer-dependent network-of-networks approach to analyze such attention with gamma oscillations. The model is validated by reproducing empirical findings on orientation preference and the enhancement of neuronal response due to top-down attention. We perform parameter plane analysis to classify neuronal responses into several patterns and find that the neuronal response to sensory and attention signals was modulated by the heterogeneity of the neuronal population. Furthermore, we revealed a counter-intuitive scenario that the excitatory populations in layer 2/3 and layer 5 exhibit opposite responses to the attentional input. By modification of the original model, we confirmed layer 6 plays an indispensable role in such cases. Our findings uncover the layer-dependent dynamics in the cortical processing of visual attention and open up new possibilities for further research on layer-dependent properties in the cerebral cortex.

Caballero-Engel meet Lasry-Lions: A uniqueness result.

In a Mean Field Game (MFG) each decision maker cares about the cross sectional distribution of the state and the dynamics of the distribution is generated by the agents' optimal decisions. We prove the uniqueness of the equilibrium in a class of MFG where the decision maker controls the state at optimally chosen times. This setup accommodates several problems featuring non-convex adjustment costs, and complements the well known drift-control case studied by Lasry-Lions. Examples of such problems are described by Caballero and Engel in several papers, which introduce the concept of the generalized hazard function of adjustment. We extend the analysis to a general "impulse control problem" by introducing the concept of the "Impulse Hamiltonian". Under the monotonicity assumption (a form of strategic substitutability), we establish the uniqueness of equilibrium. In this context, the Impulse Hamiltonian and its derivative play a similar role to the classical Hamiltonian that arises in the drift-control case.

Model-agnostic neural mean field with a data-driven transfer function.

As one of the most complex systems known to science, modeling brain behavior and function is both fascinating and extremely difficult. Empirical data is increasingly available from ex vivo human brain organoids and surgical samples, as well as in vivo animal models, so the problem of modeling the behavior of large-scale neuronal systems is more relevant than ever. The statistical physics concept of a mean-field model offers a tractable way to bridge the gap between single-neuron and population-level descriptions of neuronal activity, by modeling the behavior of a single representative neuron and extending this to the population. However, existing neural mean-field methods typically either take the limit of small interaction sizes, or are applicable only to the specific neuron models for which they were derived. This paper derives a mean-field model by fitting a transfer function called Refractory SoftPlus, which is simple yet applicable to a broad variety of neuron types. The transfer function is fitted numerically to simulated spike time data, and is entirely agnostic to the underlying neuronal dynamics. The resulting mean-field model predicts the response of a network of randomly connected neurons to a time-varying external stimulus with a high degree of accuracy. Furthermore, it enables an accurate approximate bifurcation analysis as a function of the level of recurrent input. This model does not assume large presynaptic rates or small postsynaptic potential size, allowing mean-field models to be developed even for populations with large interaction terms.

Multiscale modeling of neuronal dynamics in hippocampus CA1.

The development of biologically realistic models of brain microcircuits and regions constitutes currently a very relevant topic in computational neuroscience. One of the main challenges of such models is the passage between different scales, going from the microscale (cellular) to the meso (microcircuit) and macroscale (region or whole-brain level), while keeping at the same time a constraint on the demand of computational resources. In this paper we introduce a multiscale modeling framework for the hippocampal CA1, a region of the brain that plays a key role in functions such as learning, memory consolidation and navigation. Our modeling framework goes from the single cell level to the macroscale and makes use of a novel mean-field model of CA1, introduced in this paper, to bridge the gap between the micro and macro scales. We test and validate the model by analyzing the response of the system to the main brain rhythms observed in the hippocampus and comparing our results with the ones of the corresponding spiking network model of CA1. Then, we analyze the implementation of synaptic plasticity within our framework, a key aspect to study the role of hippocampus in learning and memory consolidation, and we demonstrate the capability of our framework to incorporate the variations at synaptic level. Finally, we present an example of the implementation of our model to study a stimulus propagation at the macro-scale level, and we show that the results of our framework can capture the dynamics obtained in the corresponding spiking network model of the whole CA1 area.

Variational Bayesian Approximation (VBA): Implementation and Comparison of Different Optimization Algorithms.

In any Bayesian computations, the first step is to derive the joint distribution of all the unknown variables given the observed data. Then, we have to do the computations. There are four general methods for performing computations: Joint MAP optimization; Posterior expectation computations that require integration methods; Sampling-based methods, such as MCMC, slice sampling, nested sampling, etc., for generating samples and numerically computing expectations; and finally, Variational Bayesian Approximation (VBA). In this last method, which is the focus of this paper, the objective is to search for an approximation for the joint posterior with a simpler one that allows for analytical computations. The main tool in VBA is to use the Kullback-Leibler Divergence (KLD) as a criterion to obtain that approximation. Even if, theoretically, this can be conducted formally, for practical reasons, we consider the case where the joint distribution is in the exponential family, and so is its approximation. In this case, the KLD becomes a function of the usual parameters or the natural parameters of the exponential family, where the problem becomes parametric optimization. Thus, we compare four optimization algorithms: general alternate functional optimization; parametric gradient-based with the normal and natural parameters; and the natural gradient algorithm. We then study their relative performances on three examples to demonstrate the implementation of each algorithm and their efficiency performance.

Mean-field interacting multi-type birth-death processes with a view to applications in phylodynamics.

Multi-type birth-death processes underlie approaches for inferring evolutionary dynamics from phylogenetic trees across biological scales, ranging from deep-time species macroevolution to rapid viral evolution and somatic cellular proliferation. A limitation of current phylogenetic birth-death models is that they require restrictive linearity assumptions that yield tractable message-passing likelihoods, but that also preclude interactions between individuals. Many fundamental evolutionary processes - such as environmental carrying capacity or frequency-dependent selection - entail interactions, and may strongly influence the dynamics in some systems. Here, we introduce a multi-type birth-death process in mean-field interaction with an ensemble of replicas of the focal process. We prove that, under quite general conditions, the ensemble's stochastically evolving interaction field converges to a deterministic trajectory in the limit of an infinite ensemble. In this limit, the replicas effectively decouple, and self-consistent interactions appear as nonlinearities in the infinitesimal generator of the focal process. We investigate a special case that is rich enough to model both carrying capacity and frequency-dependent selection while yielding tractable message-passing likelihoods in the context of a phylogenetic birth-death model.

Lattice-based mesoscale simulations and mean-field theory of cell membrane adhesion.

Adhesion of cell membranes involves multi-scale phenomena, ranging from specific molecular binding at Angstrom scale all the way up to membrane deformations and phase separation at micrometer scale. Consequently, theory and simulations of cell membrane adhesion require multi-scale modeling and suitable approximations that capture the essential physics of these phenomena. Here, we present a mesoscale model for membrane adhesion which we have employed in a series of our recent studies. This model quantifies, in particular, how nanoscale lipid clusters physically affect and respond to the intercellular receptor-ligand binding that mediates membrane adhesion. The goal of this Chapter is to present all details and subtleties of the mean-field theory and Monte Carlo simulations of this mesoscale model, which can be used to further explore physical phenomena related to cell membrane adhesion.

EEG-fMRI in awake rat and whole-brain simulations show decreased brain responsiveness to sensory stimulations during absence seizures.

In patients suffering absence epilepsy, recurring seizures can significantly decrease their quality of life and lead to yet untreatable comorbidities. Absence seizures are characterized by spike-and-wave discharges on the electroencephalogram associated with a transient alteration of consciousness. However, it is still unknown how the brain responds to external stimuli during and outside of seizures. This study aimed to investigate responsiveness to visual and somatosensory stimulation in Genetic Absence Epilepsy Rats from Strasbourg (GAERS), a well-established rat model for absence epilepsy. Animals were imaged under non-curarized awake state using a quiet, zero echo time, functional magnetic resonance imaging (fMRI) sequence. Sensory stimulations were applied during interictal and ictal periods. Whole-brain hemodynamic responses were compared between these two states. Additionally, a mean-field simulation model was used to explain the changes of neural responsiveness to visual stimulation between states. During a seizure, whole-brain responses to both sensory stimulations were suppressed and spatially hindered. In the cortex, hemodynamic responses were negatively polarized during seizures, despite the application of a stimulus. The mean-field simulation revealed restricted propagation of activity due to stimulation and agreed well with fMRI findings. Results suggest that sensory processing is hindered or even suppressed by the occurrence of an absence seizure, potentially contributing to decreased responsiveness during this absence epileptic process.

Electronic structure of the strongly correlated electron system plutonium hexaboride: A study from single-particle approximations and many-body calculations.

The electronic structure of the strongly correlated electron system plutonium hexaboride is studied by using single-particle approximations and a many-body approach. Imaginary components of impurity Green's functions show that 5fj=5/2 and 5fj=7/2 manifolds are in conducting and insulating regimes, respectively. Quasi-particle weights and their ratio suggest that the intermediate coupling mechanism is applicable for Pu 5f electrons, and PuB6 might be in the orbital-selective localized state. The weighted summation of occupation probabilities yields the interconfiguration fluctuation and average occupation number of 5f electrons n5f ~ 5.101. The interplay of 5f-5f correlation, spin-orbit coupling, Hund's exchange interaction, many-body transition of 5f configurations, and final state effects might be responsible for the quasiparticle multiplets in electronic spectrum functions. Prominent characters in the density of state, such as the coexistence of atomic multiplet peaks in the vicinity of the Fermi level and broad Hubbard bands in the high-lying regime, suggest that PuB6 could be identified as a Racah material. Finally, the quasiparticle band structure is also presented.

Light-induced insulator-metal transition in Sr2IrO4 reveals the nature of the insulating ground state.

Sr2IrO4 has attracted considerable attention due to its structural and electronic similarities to La2CuO4, the parent compound of high-Tc superconducting cuprates. It was proposed as a strong spin-orbit-coupled Jeff = 1/2 Mott insulator, but the Mott nature of its insulating ground state has not been conclusively established. Here, we use ultrafast laser pulses to realize an insulator-metal transition in Sr2IrO4 and probe the resulting dynamics using time- and angle-resolved photoemission spectroscopy. We observe a gap closure and the formation of weakly renormalized electronic bands in the gap region. Comparing these observations to the expected temperature and doping evolution of Mott gaps and Hubbard bands provides clear evidence that the insulating state does not originate from Mott correlations. We instead propose a correlated band insulator picture, where antiferromagnetic correlations play a key role in the gap opening. More broadly, our results demonstrate that energy-momentum-resolved nonequilibrium dynamics can be used to clarify the nature of equilibrium states in correlated materials.

Incorporating slow NMDA-type receptors with nonlinear voltage-dependent magnesium block in a next generation neural mass model: derivation and dynamics.

We derive a next generation neural mass model of a population of quadratic-integrate-and-fire neurons, with slow adaptation, and conductance-based AMPAR, GABAR and nonlinear NMDAR synapses. We show that the Lorentzian ansatz assumption can be satisfied by introducing a piece-wise polynomial approximation of the nonlinear voltage-dependent magnesium block of NMDAR current. We study the dynamics of the resulting system for two example cases of excitatory cortical neurons and inhibitory striatal neurons. Bifurcation diagrams are presented comparing the different dynamical regimes as compared to the case of linear NMDAR currents, along with sample comparison simulation time series demonstrating different possible oscillatory solutions. The omission of the nonlinearity of NMDAR currents results in a shift in the range (and possible disappearance) of the constant high firing rate regime, along with a modulation in the amplitude and frequency power spectrum of oscillations. Moreover, nonlinear NMDAR action is seen to be state-dependent and can have opposite effects depending on the type of neurons involved and the level of input firing rate received. The presented model can serve as a computationally efficient building block in whole brain network models for investigating the differential modulation of different types of synapses under neuromodulatory influence or receptor specific malfunction.

Ising-Like Model Hasn't Yet Said Its Last Word: Exact and Mean-Field Investigations of 2, 3 and 4-Body Interactions in 1D Ising Chain of Binuclear Spin-Crossover Solids.

We investigate the static properties of a new class of 1D Ising-like Hamiltonian for binuclear spin-crossover materials accounting for two-, three-, and four-body short-range interactions between binuclear units of spins ( s 1 A , s 1 B ) ${(s_1^A, s_1^B )}$ and ( s 2 A , s 2 B ) ${(s_2^A, s_2^B )}$ . The following 2-, 3-, and 4-body J 1 ( s 1 A + s 1 B ) ( s 2 A + s 2 B ) ${J_1 (s_1^A + s_1^B )(s_2^A + s_2^B )}$ , K 1 s 1 A s 1 B ( s 2 A + s 2 B ) ${K_1 s_1^A s_1^B (s_2^A + s_2^B )}$ , and K 2 ( s 1 A s 1 B ) ( s 2 A s 2 B ) ${K_2 (s_1^A s_1^B )(s_2^A s_2^B )}$ terms are considered, in addition to intra-binuclear interactions, such as effective ligand-field energy and exchange-like coupling. An exact treatment is carried out within the frame of the transfer matrix method, leading to a 4×4 matrix from which, we obtained the thermal evolution of the thermodynamic quantities. Several situations of model parameter values were tested, among which that of competing intra- and inter-molecular interactions, leading to the occurrence of (i) one-step spin transition, (ii) two-, three-, and four-step transitions, obtained with a reasonable number of parameters. To reproduce first-order phase transitions, we accounted for inter-chains interactions, treated in the mean-field approach. Hysteretic multi-step transitions, recalling experimental observations, are then achieved. Overall, the present model not only suggests new landscapes of interaction configurations between SCO molecules but also opens new avenues to tackle the complex behaviors often observed in the properties of SCO materials.

Exploring the role of mean-field potentials and short-range wave function behavior in the adiabatic connection.

In this article, we explore the construction of Hamiltonians with long-range interactions and their corrections using the short-range behavior of the wave function. A key aspect of our investigation is the examination of the one-particle potential, kept constant in our previous work, and the effects of its optimization on the adiabatic connection. Our methodology involves the use of a parameter-dependent potential dependent on a single parameter to facilitate practical computations. We analyze the energy errors and densities in a two-electron system (harmonium) under various conditions, employing different confinement potentials and interaction parameters. The study reveals that while the mean-field potential improves the expectation value of the physical Hamiltonian, it does not necessarily improve the energy of the system within the bounds of chemical accuracy. We also delve into the impact of density variations in adiabatic connections, challenging the common assumption that a mean field improves results. Our findings indicate that as long as energy errors remain within chemical accuracy, the mean field does not significantly outperform a bare potential. This observation is attributed to the effectiveness of corrections based on the short-range behavior of the wave function, a universal characteristic that diminishes the distinction between using a mean field or not.

Effective model and electron correlations in trilayer nickelate superconductor La4Ni3O10.

Recently, signatures of superconductivity with critical temperature from 20 to 30 K have been reported in pressured trilayer nickelate La4Ni3O10through a pressure-induced structure transition. Here we explore the evolution of electronic structures and electronic correlations in different phases of La4Ni3O10under corresponding pressure regions, by using density functional theory (DFT) combined with dynamical mean-field theory (DMFT). Similar to bilayer superconductor La3Ni2O7, the electronic bands in superconducting La4Ni3O10are dominated by Ni-3dx2-y2and 3dz2orbits near the Fermi level, in contrast, the inner Ni-O plane in La4Ni3O10generates a doublet hole-pocket Fermi surfaces around the Brillouin-zone corner, meanwhile one branch of the Ni-3dz2bands is pushed very close above the Fermi level, which can induce an electron pocket through small electron doping. The DFT+DMFT simulations suggest that the electronic correlations only give minor modification to the Fermi surfaces, meanwhile the Ni-3dz2and 3dx2-y2states on outer Ni-O layers have considerable greater mass enhancements than on the inner layer. The sensitiveness of electronic structure under doping and unique layer dependence of correlation suggest a distinct superconducting mechanism with respect to bilayer La3Ni2O7. Based on the DFT and DFT+DMFT simulations, we eventually derive a trilayer effective tight-binding model, which can produce rather precise electronic bands and Fermi surfaces, hence can serve as an appropriate model to further study the superconducting mechanism and paring symmetry in trilayer La4Ni3O10.

Computationally Efficient Algorithm for Modeling Grain Growth Using Hillert's Mean-Field Approach.

To investigate the interconnected effects of manufacturing processes on microstructure evolution during hot-rolling, a through process model is required. A novel numerical implementation of the mean-field approach was introduced to efficiently describe the grain growth of larger systems and extended durations. In this approach, each grain is embedded within an average medium and interacts with the average medium, thus avoiding the complexities of individual grain interactions. The proposed upsampling approach dynamically adjusts the simulation grain ensemble, ensuring efficiency and accuracy regardless of the initial number of grains present. This adaptation prevents undersampling artifacts during grain growth. The accuracy of the model is verified against analytical solutions and experimental data, demonstrating high agreement. Moreover, the effects of different initial conditions are successfully investigated, demonstrating the model's versatility. Due to its simplicity and efficiency, the model can be seamlessly integrated into other microstructure evolution models.

A dynamic computational model of the parallel circuit on the basal ganglia-cortex associated with Parkinson's disease dementia.

The cognitive impairment will gradually appear over time in Parkinson's patients, which is closely related to the basal ganglia-cortex network. This network contains two parallel circuits mediated by putamen and caudate nucleus, respectively. Based on the biophysical mean-field model, we construct a dynamic computational model of the parallel circuit in the basal ganglia-cortex network associated with Parkinson's disease dementia. The simulated results show that the decrease of power ratio in the prefrontal cortex is mainly caused by dopamine depletion in the caudate nucleus and is less related to that in the putamen, which indicates Parkinson's disease dementia may be caused by a lesion of the caudate nucleus rather than putamen. Furthermore, the underlying dynamic mechanism behind the decrease of power ratio is investigated by bifurcation analysis, which demonstrates that the decrease of power ratio is due to the change of brain discharge pattern from the limit cycle mode to the point attractor mode. More importantly, the spatiotemporal course of dopamine depletion in Parkinson's disease patients is well simulated, which states that with the loss of dopaminergic neurons projecting to the striatum, motor dysfunction of Parkinson's disease is first observed, whereas cognitive impairment occurs after a period of onset of motor dysfunction. These results are helpful to understand the pathogenesis of cognitive impairment and provide insights into the treatment of Parkinson's disease dementia.

A mean-field model of gamma-frequency oscillations in networks of excitatory and inhibitory neurons.

Gamma oscillations are widely seen in the cerebral cortex in different states of the wake-sleep cycle and are thought to play a role in sensory processing and cognition. Here, we study the emergence of gamma oscillations at two levels, in networks of spiking neurons, and a mean-field model. At the network level, we consider two different mechanisms to generate gamma oscillations and show that they are best seen if one takes into account the synaptic delay between neurons. At the mean-field level, we show that, by introducing delays, the mean-field can also produce gamma oscillations. The mean-field matches the mean activity of excitatory and inhibitory populations of the spiking network, as well as their oscillation frequencies, for both mechanisms. This mean-field model of gamma oscillations should be a useful tool to investigate large-scale interactions through gamma oscillations in the brain.

Dynamics of parkinsonian oscillations mediated by transmission delays in a mean-field model of the basal ganglia.

Introduction: Neural interactions in the brain are affected by transmission delays which may critically alter signal propagation across different brain regions in both normal and pathological conditions. The effect of interaction delays on the dynamics of the generic neural networks has been extensively studied by theoretical and computational models. However, the role of transmission delays in the development of pathological oscillatory dynamics in the basal ganglia (BG) in Parkinson's disease (PD) is overlooked. Methods: Here, we investigate the effect of transmission delays on the discharge rate and oscillatory power of the BG networks in control (normal) and PD states by using a Wilson-Cowan (WC) mean-field firing rate model. We also explore how transmission delays affect the response of the BG to cortical stimuli in control and PD conditions. Results: Our results show that the BG oscillatory response to cortical stimulation in control condition is robust against the changes in the inter-population delays and merely depends on the phase of stimulation with respect to cortical activity. In PD condition, however, transmission delays crucially contribute to the emergence of abnormal alpha (8-13 Hz) and beta band (13-30 Hz) oscillations, suggesting that delays play an important role in abnormal rhythmogenesis in the parkinsonian BG. Discussion: Our findings indicate that in addition to the strength of connections within and between the BG nuclei, oscillatory dynamics of the parkinsonian BG may also be influenced by inter-population transmission delays. Moreover, phase-specificity of the BG response to cortical stimulation may provide further insight into the potential role of delays in the computational optimization of phase-specific brain stimulation therapies.

Entropic Dynamics of Mutations in SARS-CoV-2 Genomic Sequences.

In this paper, we investigate a certain class of mutations in genomic sequences by studying the evolution of the entropy and relative entropy associated with the base frequencies of a given genomic sequence. Even if the method is, in principle, applicable to every sequence which varies randomly, the case of SARS-CoV-2 RNA genome is particularly interesting to analyze, due to the richness of the available sequence database containing more than a million sequences. Our model is able to track known features of the mutation dynamics like the Cytosine-Thymine bias, but also to reveal new features of the virus mutation dynamics. We show that these new findings can be studied using an approach that combines the mean field approximation of a Markov dynamics within a stochastic thermodynamics framework.

Mean-field analysis of synaptic alterations underlying deficient cortical gamma oscillations in schizophrenia.

Deficient gamma oscillations in the prefrontal cortex (PFC) of individuals with schizophrenia (SZ) are proposed to arise from alterations in the excitatory drive to fast-spiking interneurons (E→I) and in the inhibitory drive from these interneurons to excitatory neurons (I→E). Consistent with this idea, prior postmortem studies showed lower levels of molecular and structural markers for the strength of E→I and I→E synapses and also greater variability in E→I synaptic strength in PFC of SZ. Moreover, simulating these alterations in a network of quadratic integrate-and-fire (QIF) neurons revealed a synergistic effect of their interactions on reducing gamma power. In this study, we aimed to investigate the dynamical nature of this synergistic interaction at macroscopic level by deriving a mean-field description of the QIF model network that consists of all-to-all connected excitatory neurons and fast-spiking interneurons. Through a series of numerical simulations and bifurcation analyses, findings from our mean-field model showed that the macroscopic dynamics of gamma oscillations are synergistically disrupted by the interactions among lower strength of E→I and I→E synapses and greater variability in E→I synaptic strength. Furthermore, the two-dimensional bifurcation analyses showed that this synergistic interaction is primarily driven by the shift in Hopf bifurcation due to lower E→I synaptic strength. Together, these simulations predict the nature of dynamical mechanisms by which multiple synaptic alterations interact to robustly reduce PFC gamma power in SZ, and highlight the utility of mean-field model to study macroscopic neural dynamics and their alterations in the illness.