Mean-field Model Research Articles

Mean-Field Stackelberg Game-Based Security Defense and Resource Optimization in Edge Computing

Edge computing brings computation and storage resources to the edge of the mobile network to solve the problems of low latency and high real-time demand. However, edge computing is more vulnerable to malicious attacks due to its open and dynamic environments. In this article, we investigate security defense strategies in edge computing systems, focusing on scenarios with one attacker and multiple defenders to determine optimal defense strategies with minimal resource allocation. Firstly, we formulate the interactions between the defenders and the attackers as the mean-field Stackelberg game model, where the state and the objective functions of the defenders are coupled through the mean-field term, and are strongly influenced by the strategy of the attacker. Then, we analyze the local optimal strategies of the defenders given an arbitrary strategy of the attackers. We demonstrate the Nash equilibrium and the mean-field equilibrium for both the defenders and the attackers. Finally, simulation analysis will illustrate the dynamic evolution of the defense strategy of the defenders and the trajectory of the attackers based on the proposed Stackelberg game model.

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.

Coverage- and Facet-Dependent Multiscale Modeling of O* and H* Adsorption on Pt Catalytic Nanoparticles.

Within computational heterogeneous catalysis, two critical factors exist-coverage and multifaceted effects-which are challenging to incorporate and contribute to differences between the results obtained from computational and experimental studies. Such disparities exist when significant adsorbate-adsorbate interactions are present, particularly when coupled with computationally limited facet sampling. Here, we designed a study to demonstrate the significance of coverage and facet effects on the predicted coverages for O* and H* on Pt nanoparticles. This is accomplished by employing multiscale modeling techniques using a three-pronged approach consisting of density functional theory (DFT), ab initio phase diagrams, and mean-field microkinetic models. Overall, adsorbate-adsorbate interactions are repulsive and far stronger for O*/Pt than for H*/Pt. For O* on Pt(111), repulsive interactions are both two- and three-body, but on Pt(100) and Pt(110), they are predominantly three-body. Through benchmarks to existing experimental literature, we demonstrate that experimentally observed coverages and desorption temperatures can be accurately estimated by computational models when the adsorbate-adsorbate interactions are included. Finally, by combining microkinetic models at the equilibrium limit with kubic harmonic interpolation, we model the impacts of the treatment of adsorbate-adsorbate interactions on the predicted O* and H* coverages over multifaceted Pt nanoparticles. Omitting adsorbate-adsorbate interactions over Pt nanoparticles leads to an overestimation of equilibrium coverages of the adsorbates (maximum of 0.29 and 0.11 ML for O* and H*, respectively) across a wide range of temperatures and pressures relevant to heterogeneous catalysis. Altogether, our work demonstrates that the inclusion of coverage and facet effects increases the accuracy of computational models for heterogeneous catalysts.

Minimal Mechanisms of Microtubule Length Regulation in Living Cells.

The microtubule cytoskeleton is responsible for sustained, long-range intracellular transport of mRNAs, proteins, and organelles in neurons. Neuronal microtubules must be stable enough to ensure reliable transport, but they also undergo dynamic instability, as their plus and minus ends continuously switch between growth and shrinking. This process allows for continuous rebuilding of the cytoskeleton and for flexibility in injury settings. Motivated by in vivo experimental data on microtubule behavior in Drosophila neurons, we propose a mathematical model of dendritic microtubule dynamics, with a focus on understanding microtubule length, velocity, and state-duration distributions. We find that limitations on microtubule growth phases are needed for realistic dynamics, but the type of limiting mechanism leads to qualitatively different responses to plausible experimental perturbations. We therefore propose and investigate two minimally-complex length-limiting factors: limitation due to resource (tubulin) constraints and limitation due to catastrophe of large-length microtubules. We combine simulations of a detailed stochastic model with steady-state analysis of a mean-field ordinary differential equations model to map out qualitatively distinct parameter regimes. This provides a basis for predicting changes in microtubule dynamics, tubulin allocation, and the turnover rate of tubulin within microtubules in different experimental environments.

Boson peak in the vibrational spectra of glasses

A hallmark of glasses is an excess of low-frequency, nonphononic vibrations. It is manifested as a terahertz peak—the boson peak—in the ratio of the vibrational density of state (VDoS) and Debye's VDoS of phonons. Here, using experimental data, extensive computer simulations, and a mean-field model, we show that the nonphononic part of the VDoS itself features both a universal power-law tail and a peak at higher frequencies, entirely accounted for by quasilocalized nonphononic vibrations, whose existence and spectra power-law tail were recently established in computer glasses. We rationalize the variation of the peak's frequency and magnitude with glasses' thermal history, which is much weaker than the variation of the tail and may follow an opposite trend, and show that the peak's modes are composed of many spatially coupled quasilocalized nonphononic vibrations. Our results shed light on the origin, nature, and properties of the boson peak in glasses. Published by the American Physical Society 2024

Impact of carbon segregation on transition carbides and cementite precipitation during tempering of low carbon steels: Experiments and modeling

Tempering of low-carbon steels (less than about 0.3 wt.% C) may differ from the traditional precipitation sequence, which includes transition carbide precipitation, retained austenite decomposition and cementite precipitation. The main difference is the partial or total absence of transition carbides. In the present work, the effect of the carbon segregation on the mitigation of the precipitation of the latter is analyzed by combining multi-scale experimental investigations with a new precipitation model accounting for the carbon heterogeneities induced by the segregation. The full precipitation sequence is considered in order to study the impact of the segregation not only on the transition carbides, but also on the cementite which forms afterwards. The experimental work includes APT characterization of carbon segregation, in-situ HEXRD experiments to reveal precipitation kinetics, and TEM observations for carbide size measurements.The here-in developed precipitation mean-field and physics-based model combines two previous ones dedicated to the nucleation and growth of transition carbides and cementite and to the segregation of carbon at dislocations. It is shown that, even after water-quench, carbon atoms are already segregated on dislocations. The mitigation of transition carbide precipitation is caused by the presence of such segregations, which decrease the driving force for the transition carbide nucleation and enhance cementite precipitation. In agreement with previous experiments, the model also demonstrates that inside a martensitic microstructure, the precipitation sequence is different between the first (formed close to Ms temperature) and the last martensite (formed at room temperature) formed upon cooling, because of the difference in dislocation density, which influences the intensity of the segregation phenomenon.

Meta predictive learning model of languages in neural circuits.

Large language models based on self-attention mechanisms have achieved astonishing performances, not only in natural language itself, but also in a variety of tasks of different nature. However, regarding processing language, our human brain may not operate using the same principle. Then, a debate is established on the connection between brain computation and artificial self-supervision adopted in large language models. One of most influential hypotheses in brain computation is the predictive coding framework, which proposes to minimize the prediction error by local learning. However, the role of predictive coding and the associated credit assignment in language processing remains unknown. Here, we propose a mean-field learning model within the predictive coding framework, assuming that the synaptic weight of each connection follows a spike and slab distribution, and only the distribution, rather than specific weights, is trained. This meta predictive learning is successfully validated on classifying handwritten digits where pixels are input to the network in sequence, and moreover, on the toy and real language corpus. Our model reveals that most of the connections become deterministic after learning, while the output connections have a higher level of variability. The performance of the resulting network ensemble changes continuously with data load, further improving with more training data, in analogy with the emergent behavior of large language models. Therefore, our model provides a starting point to investigate the connection among brain computation, next-token prediction, and general intelligence.

Biophysical models applied to dementia patients reveal links between geographical origin, gender, disease duration, and loss of neural inhibition

BackgroundThe hypothesis of decreased neural inhibition in dementia has been sparsely studied in functional magnetic resonance imaging (fMRI) data across patients with different dementia subtypes, and the role of social and demographic heterogeneities on this hypothesis remains to be addressed.MethodsWe inferred regional inhibition by fitting a biophysical whole-brain model (dynamic mean field model with realistic inter-areal connectivity) to fMRI data from 414 participants, including patients with Alzheimer’s disease, behavioral variant frontotemporal dementia, and controls. We then investigated the effect of disease condition, and demographic and clinical variables on the local inhibitory feedback, a variable related to the maintenance of balanced neural excitation/inhibition.ResultsDecreased local inhibitory feedback was inferred from the biophysical modeling results in dementia patients, specific to brain areas presenting neurodegeneration. This loss of local inhibition correlated positively with years with disease, and showed differences regarding the gender and geographical origin of the patients. The model correctly reproduced known disease-related changes in functional connectivity.ConclusionsResults suggest a critical link between abnormal neural and circuit-level excitability levels, the loss of grey matter observed in dementia, and the reorganization of functional connectivity, while highlighting the sensitivity of the underlying biophysical mechanism to demographic and clinical heterogeneities in the patient population.

Phase transition and universality of the majority-rule model on complex networks

In this paper, we investigate the phenomena of order-disorder phase transition and the universality of the majority-rule model defined on three complex networks, namely the Barabási–Albert, Watts–Strogatz and Erdős–Rényi networks. Assume each agent holds two possible opinions randomly distributed across the networks’ nodes. Agents adopt anticonformity and independence behaviors, represented by the probability p, where with a probability p, agents adopt anticonformity or independence behavior. Based on our numerical simulation results and finite-size scaling analysis, it is found that the model undergoes a continuous phase transition for all networks, with critical points for the independence model greater than those for the anticonformity model in all three networks. We obtain critical exponents identical to the opinion dynamics model defined on a complete graph, indicating that the model exhibits the same universality class as the mean-field Ising model.

Propagation of chaos and Poisson hypothesis for replica mean-field models of intensity-based neural networks

Propagation of chaos and Poisson hypothesis for replica mean-field models of intensity-based neural networks

Relativistic energy density functional from momentum space to coordinate space within a coherent density fluctuation model

In this theoretical study, we have derived a simplified analytical expression for the binding energy per nucleon as a function of density and isospin asymmetry within the relativistic mean-field model. We have generated a new parameterization for the density-dependent DD-ME2 parameter set using the Relativistic-Hartree-Bogoliubov approach. Moreover, this work attempts to revisit the prior polynomial fitting in Kumar A. et al. Phys. Rev. C, 103 (2021) 024305 for the non-linear NL3 force parameter to provide a simplified set of equations for the energy density functional which is used for calculating the surface properties of finite nuclei. The current study improves the existing fitting procedure by effectively proposing a simpler model that provides comparably precise results while lowering the computational expense. To study the surface properties of finite nuclei with these parameterizations, we have adopted the coherent density fluctuation model, which effectively translates the quantities of nuclear matter from momentum space to coordinate space at local density. The isospin properties, such as symmetry energy and its surface and volume components, slope parameter, finite nuclear incompressibility, and surface incompressibility for even-even nuclei, are calculated for different mass regions. Moreover, we have studied the effect of density, weight function, and choice of relativistic force parameters on the surface properties. The significance of this work will help to determine the properties of nuclei along the nuclear landscape and can facilitate an improved understanding of the island of stability, heavy-ion collision, and nucleosynthesis, among others.

Constraining the Onset Density for the QCD Phase Transition with the Neutrino Signal from Core-collapse Supernovae

The occurrence of a first-order hadron–quark matter phase transition at high baryon densities is investigated in astrophysical simulations of core-collapse supernovae, to decipher yet incompletely understood properties of the dense matter equation of state (EOS) using neutrinos from such cosmic events. It is found that the emission of a nonstandard second neutrino burst, dominated by electron antineutrinos, is not only a measurable signal for the appearance of deconfined quark matter but also reveals information about the state of matter at extreme conditions encountered at the supernova (SN) interior. To this end, a large set of spherically symmetric SN models is investigated, studying the dependence on the EOS and the stellar progenitor. General relativistic neutrino-radiation hydrodynamics is employed featuring three-flavor Boltzmann neutrino transport and a microscopic hadron-quark hybrid matter EOS class. Therefore, the DD2 relativistic mean-field hadronic model is employed, and several variations of it, and the string-flip model for the description of deconfined quark matter. The resulting hybrid model covers a representative range of onset densities for the phase transition and latent heats. This facilitates the direct connection between intrinsic signatures of the neutrino signal and properties of the EOS. In particular, a set of linear relations has been found empirically. These potentially provide a constraint for the onset density of a possible QCD phase transition from the future neutrino observation of the next galactic core-collapse SN, if a millisecond electron anti-neutrino burst is present around or less than 1 s.

Discontinuous phase transition from ferromagnetic to oscillating states in a nonequilibrium mean-field spin model.

We study a nonequilibrium ferromagnetic mean-field spin model exhibiting a phase with spontaneous temporal oscillations of the magnetization, on top of the usual paramagnetic and ferromagnetic phases. This behavior is obtained by introducing dynamic field variables coupled to the spins through nonreciprocal couplings. We determine a nonequilibrium generalization of the Landau free energy in terms of the large deviation function of the magnetization and of an appropriately defined smoothed stochastic time derivative of the magnetization. While the transition between paramagnetic and oscillating phase is continuous, the transition between ferromagnetic and oscillating phases is found to be discontinuous, with a coexistence of both phases, one being stable and the other one metastable. Depending on parameter values, the ferromagnetic points may either be inside or outside the limit cycle, leading to different transition scenarios. The stability of these steady states is determined from the large deviation function. We also show that in the coexistence region, the entropy production has a pronounced maximum as a function of system size.

Magnetic field transport in geometrically thick discs: multidimensional effects on the field strength and inclination angle

ABSTRACT We theoretically investigate the magnetic flux transport in geometrically thick accretion discs which may form around black holes. We utilize a two-dimensional (2D) kinematic mean-field model for poloidal field transport which is governed by both inward advection and outward diffusion of the field. Assuming a steady state, we analytically show that the multidimensional effects prevent the field accumulation towards the centre and reduce the field inclination angle. We also numerically investigate the radial profile of the field strength and the inclination angle for two geometrically thick discs for which (quasi-)analytical solutions exist: radiatively inefficient accretion flows (RIAFs) and super-Eddington accretion flows. We develop a 2D kinematic mean-field code and perform simulations of flux transport to study the multidimensional effects. The numerical simulations are consistent with our analytical prediction. We also discuss a condition for the external field strength that RIAF can be a magnetically arrested disc. This study could be important for understanding the origin of a large-scale magnetic field that drives jets and disc winds around black holes.

Constraining a relativistic mean field model using neutron star mass–radius measurements I: nucleonic models

ABSTRACT Measurements of neutron star mass and radius or tidal deformability deliver unique insight into the equation of state (EOS) of cold dense matter. EOS inference is very often done using generalized parametric or non-parametric models, which deliver no information on composition. In this paper, we consider a microscopic nuclear EOS model based on a field theoretical approach. We show that current measurements from NICER and gravitational wave observations constrain primarily the symmetric nuclear matter EOS. We then explore what could be delivered by measurements of mass and radius at the level anticipated for future large-area X-ray timing telescopes. These should be able to place very strong limits on the symmetric nuclear matter EOS, in addition to constraining the nuclear symmetry energy that determines the proton fraction inside the neutron star.

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.

Hyper-Ballistic Superdiffusion of Competing Microswimmers.

Hyper-ballistic diffusion is shown to arise from a simple model of microswimmers moving through a porous media while competing for resources. By using a mean-field model where swimmers interact through the local concentration, we show that a non-linear Fokker-Planck equation arises. The solution exhibits hyper-ballistic superdiffusive motion, with a diffusion exponent of four. A microscopic simulation strategy is proposed, which shows excellent agreement with theoretical analysis.

Topological Phase Diagram of an Interacting Kitaev Chain: Mean Field versus DMRG Study

In this work, we study the topological phase transitions of a Kitaev chain generalized by the addition of nearest-neighbor Coulomb interaction. We show the presence of a robust topological phase as a function of the interaction strength and of the on-site energy with associated non-zero energy Majorana states localized at the chain edges. We provide an effective mean-field model that allows for the self-consistent computation of the mean value of the local particle number operator, and we also perform Density Matrix Renormalization Group numerical simulations based on a tensor network approach. We find that the two methods show a good agreement in reporting the phase transition between trivial and topological superconductivity. Temperature robustness within a physically relevant threshold has also been demonstrated. These findings shed light on an entire class of topological interacting one-dimensional systems in which the effects of residual Coulomb interactions play a relevant role.

The study of structural, electronic, magnetic and magnetocaloric properties of antiperovskite carbides M3AlC (M=Mn and Fe): DFT combined with Monte Carlo simulation

This work aims to investigate the structural stability, magnetic and electronic properties of M3AlC antiperovskites using density functional theory (DFT) and Monte Carlo simulation. The obtained ground state results reveal that the antiperovskites M3AlC are stable in the ferromagnetic (FM) state with a metallic character. The calculated total magnetic moments are 5.21[Formula: see text] and 3.34[Formula: see text] for Mn3AlC and Fe3AlC, respectively, with the total moments mainly from the M atom. The ferromagnetic behavior is confirmed by computing the density of state at Fermi level and verified the Stoner criterion. The magnetic and magnetocaloric behavior of M3AlC is investigated using Monte Carlo simulation and the obtained results demonstrate that the transition from ferromagnetic to paramagnetic state occurs at [Formula: see text][Formula: see text]K and [Formula: see text][Formula: see text]K for Mn3AlC and Fe3AlC, respectively. These values of [Formula: see text] are in good agreement with the experimental results. The magnetocaloric effect and critical behavior are studied and the obtained values of magnetic entropy change [Formula: see text] at 4.5[Formula: see text]T is about 4.242[Formula: see text]J/kg.K and 3.666[Formula: see text]J/kg.K and the relative cooling power (RCP) are 342.434[Formula: see text]J/kg.K and 325.26[Formula: see text]J/kg.K for Mn3AlC and Fe3AlC at 4.5T, indicating that these compounds are more appropriate for magnetic refrigeration. Finally, the critical exponents ([Formula: see text],[Formula: see text],[Formula: see text]) are calculated and the obtained values are close to the values of mean-field model.

Extracting the hyperon-nucleon interaction via collective flows in heavy-ion collisions

The 2-body hyperon-nucleon interaction softens the equation of state of neutron star matter and leads to the maximum mass of neutron star to be 1.3-1.6M⊙, which deviates from the recent observation with the masses of PSR J0348+0432 (2.01±0.04M⊙) and J0740+6620 (2.14−0.09+0.10M⊙). One attempt is to introduce the more repulsive hyperon-nucleon interaction above the saturation density. A phenomenological Λ potential by fitting the 3-body ΛNN results of chiral effective field theory is implemented into the quantum molecular dynamics transport model to solve the ‘hyperon puzzle’ in neutron stars. It is found that the directed and elliptic flows are sensitive to the high-density hyperon-nucleon potentials in collisions of 197Au + 197Au and 124Sn + 124Sn. The influence of the phenomenological potential on the Λ yields, rapidity distributions and transverse momentum spectra is negligible in comparison with the ones calculated by the well-known relativistic mean-field model. The inclusion of the ΛN, ΣN and ΞN potentials leads to the reduction of hyperon production in the midrapidity region. The Λ directed flows and the slope in the midrapidity region are enhanced with the phenomenological potential and more consistent with the STAR data in collisions of 197Au + 197Au at sNN=3 GeV.