人脑默认模式网络的动力学行为

大脑具有自适应、自组织、多稳态等重要特征,是典型的复杂系统.人脑在静息态下的关键功能子网络--默认模式网络(DMN)的激活处于多状态间持续跳转的非平衡过程,揭示该过程背后的动力学机制具有重要的科学意义和临床应用前景.本文基于功能磁共振获得的血氧水平依赖(BOLD)信号,建立了DMN吸引子跳转非平衡过程的能量图景、吸引子非联通图、跳转关系网络等;以高级视觉皮层和听觉等皮层活动为例,通过对应激活DMN状态空间的分布,以及XGBoost、深度神经网络等算法验证了DMN状态变化与外部脑区状态的密切依赖关系;通过偏相关、收敛交叉映射等方法分析了DMN内各个脑区之间的相互作用.本文结果有助于理解静息态下大脑内在非平衡过程的动力学机制,以及从动力学的角度探索具有临床意义的脑功能障碍生物标志物.     

基于可分解马尔科夫网的视频图像检测方法研究

研究了可分解马尔科夫网的概念、方法,分析了可分解马尔科夫网在序列图像数据挖掘中的作用与意义,并直接将马尔科夫网的结构作为决策或推理依据,应用于问题求解,拓广了可分解马尔科夫网应用的可能性;以真实交通违章的视频图像为例,以多种粒度(节点数)广泛研究建立视频图像间的可分解马尔科夫网并分析其对问题的适用性,通过网络结构分析来检测视频图像间的差异,从而发现某种有意义的模式(例如,交通违章);仿真结果表明所提方法具有实用价值和较好效果;研究结果表明可分解马尔科夫网可以很好地揭示数据间的抽象近邻关系,并且这种网络具有很好的知识表达和逻辑推理的作用,是重要的模式识别方法。     

Aberrant default mode network in subjects with amnestic mild cognitive impairment using resting-state functional MRI

Amnestic mild cognitive impairment (aMCI) is a syndrome associated with faster memory decline than normal aging and frequently represents the prodromal phase of Alzheimer's disease. When a person is not actively engaged in a goal-directed task, spontaneous functional magnetic resonance imaging (fMRI) signals can reveal functionally connected brain networks, including the so-called default mode network (DMN). To date, only a few studies have investigated DMN functions in aMCI populations. In this study, group-independent component analysis was conducted for resting-state fMRI data, with slices acquired perpendicular to the long axis of the hippocampus, from eight subjects with aMCI and eight normal control subjects. Subjects with aMCI showed an increased DMN activity in middle cingulate cortex, medial prefrontal cortex and left inferior parietal cortex compared to the normal control group. Decreased DMN activity for the aMCI group compared to the normal control group was noted in lateral prefrontal cortex, left medial temporal lobe (MTL), left medial temporal gyrus, posterior cingulate cortex/retrosplenial cortex/precuneus and right angular gyrus. Although MTL volume difference between the two groups was not statistically significant, a decreased activity in left MTL was observed for the aMCI group. Positive correlations between the DMN activity and memory scores were noted for left lateral prefrontal cortex, left medial temporal gyrus and right angular gyrus. These findings support the premise that alterations of the DMN occur in aMCI and may indicate deficiencies in functional, intrinsic brain architecture that correlate with memory function, even before significant MTL atrophy is detectable by structural MRI.     

Reducing Neuronal Networks to Discrete Dynamics

We consider a general class of purely inhibitory and excitatory-inhibitory neuronal networks, with a general class of network architectures, and characterize the complex firing patterns that emerge. Our strategy for studying these networks is to first reduce them to a discrete model. In the discrete model, each neuron is represented as a finite number of states and there are rules for how a neuron transitions from one state to another. In this paper, we rigorously demonstrate that the continuous neuronal model can be reduced to the discrete model if the intrinsic and synaptic properties of the cells are chosen appropriately. In a companion paper [W. Just, S. Ahn, D. Terman. Minimal attractors in digraph system models of neuronal networks (preprint)], we analyse the discrete model.     

Sparse Estimation Strategies in Linear Mixed Effect Models for High-Dimensional Data Application

In a host of business applications, biomedical and epidemiological studies, the problem of multicollinearity among predictor variables is a frequent issue in longitudinal data analysis for linear mixed models (LMM). We consider an efficient estimation strategy for high-dimensional data application, where the dimensions of the parameters are larger than the number of observations. In this paper, we are interested in estimating the fixed effects parameters of the LMM when it is assumed that some prior information is available in the form of linear restrictions on the parameters. We propose the pretest and shrinkage estimation strategies using the ridge full model as the base estimator. We establish the asymptotic distributional bias and risks of the suggested estimators and investigate their relative performance with respect to the ridge full model estimator. Furthermore, we compare the numerical performance of the LASSO-type estimators with the pretest and shrinkage ridge estimators. The methodology is investigated using simulation studies and then demonstrated on an application exploring how effective brain connectivity in the default mode network (DMN) may be related to genetics within the context of Alzheimer’s disease.     

Model architecture for associative memory in a neural network of spiking neurons

A synaptic connectivity model is assembled on a spiking neuron network aiming to build up a dynamic pattern recognition system. The connection architecture includes gap junctions and both inhibitory and excitatory chemical synapses based on Hebb’s hypothesis. The network evolution resulting from external stimulus is sampled in a properly defined frequency space. Neurons’ responses to different current injections are mapped onto a subspace using Principal Component Analysis. Departing from the base attractor, related to a quiescent state, different external stimuli drive the network to different fixed points through specific trajectories in this subspace.     

Coexistence of regular and irregular dynamics in complex networks of pulse-coupled oscillators

For general networks of pulse-coupled oscillators, including regular, random, and more complex networks, we develop an exact stability analysis of synchronous states. As opposed to conventional stability analysis, here stability is determined by a multitude of linear operators. We treat this multioperator problem exactly and show that for inhibitory interactions the synchronous state is stable, independent of the parameters and the network connectivity. In randomly connected networks with strong interactions this synchronous state, displaying regular dynamics, coexists with a balanced state exhibiting irregular dynamics. External signals may switch the network between qualitatively distinct states.     

Exploring the role of inhibitory coupling in duplex networks

The electrical coupling of myocytes and fibroblasts can play a role in inhibiting electrical impluse propagation in cardiac muscle. To understand the function of fibroblast–myocyte coupling in the aging heart, the spiral-wave dynamics in the duplex networks with inhibitory coupling is numerically investigated by the Br–Eiswirth model. The numerical results show that the inhibitory coupling can change the wave amplitude, excited phase duration and excitability of the system. When the related parameters are properly chosen, the inhibitory coupling can induce local abnormal oscillation in the system and the Eckhaus instability of the spiral wave. For the dense inhibitory network, the maximal decrement(maximal increment) in the excited phase duration can reach 24.3%(13.4%), whereas the maximal decrement in wave amplitude approaches 28.1%. Upon increasing the inhibitory coupling strength, the system excitability is reduced and even completely suppressed when the interval between grid points in the inhibitory network is small enough. Moreover, the inhibitory coupling can lead to richer phase transition scenarios of the system, such as the transition from a stable spiral wave to turbulence and the transition from a meandering spiral wave to a planar wave. In addition, the self-sustaining planar wave, the unique meandering of spiral wave and inward spiral wave are observed. The physical mechanisms behind the phenomena are analyzed.     

在兴奋-抑制混沌神经元网络中有序波的自发形成

大脑皮层在一定条件下可以自发出现螺旋波和平面波,为了了解这些有序波的产生机制,构造了一个双层的二维神经元网络.该网络由最近邻兴奋性耦合和长程抑制性耦合层组成,采用修改后的Hindmarsh-Rose神经元模型研究了该混沌神经元网络从具有随机相位分布的初态演化是否能自发出现各种有序波.数值模拟结果表明:当抑制性耦合强度比较小时,系统一般不会自发出现有序波;在兴奋性耦合强度足够大的情况下,抑制性耦合强度越大,系统越容易产生有序波.系统出现不同的有序波与系统初态和耦合强度有密切关系,适当选择兴奋性和抑制性耦合的耦合强度,系统会自发出现迷宫斑图、平面波、单螺旋波、多螺旋波、旋转方向相反的螺旋波对、双臂螺旋波、靶波、向内方形波等有序波斑图.螺旋波、迷宫斑图和内向方形波出现概率分别达到27.5%, 21.5%和10.0%,这里的迷宫斑图是由不同传播方向的许多平面波组成,其他有序波出现概率比较小.研究结果有助于理解发生在大脑皮层中的自组织现象.     

Proton ENDOR of dimethylnitramine free radicals

Electron nuclear double resonance (ENDOR) spectra of free radicals produced by ultraviolet (UV) photolysis of polycrystalline and single crystal dimethylnitramine (or N-methyl-N-nitromethanamine) [DMN; (CH₃)₂NNO₂ were studied atca. ?30°C. Results suggest that multiple radical species are formed during UV photolysis of DMN, perdeutero-DMN-d₆, and¹⁵N-labeled DMN. Proton ENDOR spectra are consistent with assignment of a cation radical (CH₃)₂NNO ₂ ⁺ as the major DMN radical species. Proton hyperfine coupling anisotropy, which is observed from the ENDOR spectra, is attributed to inequivalence of the two DMN methyl groups.     

互联网流量控制的朗之万模型及相变分析

为互联网中的流量控制协议构建恰当模型,从而阐明具体协议算法与网络宏观性能间的关系,一直是互联网研究者面临的重大挑战.本文通过逻辑演绎,建立了互联网传输控制协议下流量的朗之万方程.在此基础上,细致分析了主动队列管理算法的有效性,在理论上证明了此类算法存在从畅通态到拥塞态到瘫痪态的相变过程,并给出了相变临界点与系统参数的显式关系.本建模与分析方法虽以具体的主动队列管理算法为例,但其方法可以应用于一般的网络流量控制问题. 关键词： 互联网 流量控制 朗之万方程 相变     

Intermittent synchronization in a network of bursting neurons

Synchronized oscillations in networks of inhibitory and excitatory coupled bursting neurons are common in a variety of neural systems from central pattern generators to human brain circuits. One example of the latter is the subcortical network of the basal ganglia, formed by excitatory and inhibitory bursters of the subthalamic nucleus and globus pallidus, involved in motor control and affected in Parkinson's disease. Recent experiments have demonstrated the intermittent nature of the phase-locking of neural activity in this network. Here, we explore one potential mechanism to explain the intermittent phase-locking in a network. We simplify the network to obtain a model of two inhibitory coupled elements and explore its dynamics. We used geometric analysis and singular perturbation methods for dynamical systems to reduce the full model to a simpler set of equations. Mathematical analysis was completed using three slow variables with two different time scales. Intermittently, synchronous oscillations are generated by overlapped spiking which crucially depends on the geometry of the slow phase plane and the interplay between slow variables as well as the strength of synapses. Two slow variables are responsible for the generation of activity patterns with overlapped spiking, and the other slower variable enhances the robustness of an irregular and intermittent activity pattern. While the analyzed network and the explored mechanism of intermittent synchrony appear to be quite generic, the results of this analysis can be used to trace particular values of biophysical parameters (synaptic strength and parameters of calcium dynamics), which are known to be impacted in Parkinson's disease.     

Duality Between Spin Networks and the 2D Ising Model

The goal of this paper is to exhibit a deep relation between the partition function of the Ising model on a planar trivalent graph and the generating series of the spin network evaluations on the same graph. We provide respectively a fermionic and a bosonic Gaussian integral formulation for each of these functions and we show that they are the inverse of each other (up to some explicit constants) by exhibiting a supersymmetry relating the two formulations. We investigate three aspects and applications of this duality. First, we propose higher order supersymmetric theories that couple the geometry of the spin networks to the Ising model and for which supersymmetric localization still holds. Secondly, after interpreting the generating function of spin network evaluations as the projection of a coherent state of loop quantum gravity onto the flat connection state, we find the probability distribution induced by that coherent state on the edge spins and study its stationary phase approximation. It is found that the stationary points correspond to the critical values of the couplings of the 2D Ising model, at least for isoradial graphs. Third, we analyze the mapping of the correlations of the Ising model to spin network observables, and describe the phase transition on those observables on the hexagonal lattice. This opens the door to many new possibilities, especially for the study of the coarse-graining and continuum limit of spin networks in the context of quantum gravity.     

STDP-driven networks and the C. elegans neuronal network

We study the dynamics of the structure of a formal neural network wherein the strengths of the synapses are governed by spike-timing-dependent plasticity (STDP). For properly chosen input signals, there exists a steady state with a residual network. We compare the motif profile of such a network with that of a real neural network of C. elegans and identify robust qualitative similarities. In particular, our extensive numerical simulations show that this STDP-driven resulting network is robust under variations of the model parameters.     

Information Thermodynamics and Reducibility of Large Gene Networks

Gene regulatory networks (GRNs) control biological processes like pluripotency, differentiation, and apoptosis. Omics methods can identify a large number of putative network components (on the order of hundreds or thousands) but it is possible that in many cases a small subset of genes control the state of GRNs. Here, we explore how the topology of the interactions between network components may indicate whether the effective state of a GRN can be represented by a small subset of genes. We use methods from information theory to model the regulatory interactions in GRNs as cascading and superposing information channels. We propose an information loss function that enables identification of the conditions by which a small set of genes can represent the state of all the other genes in the network. This information-theoretic analysis extends to a measure of free energy change due to communication within the network, which provides a new perspective on the reducibility of GRNs. Both the information loss and relative free energy depend on the density of interactions and edge communication error in a network. Therefore, this work indicates that a loss in mutual information between genes in a GRN is directly coupled to a thermodynamic cost, i.e., a reduction of relative free energy, of the system.     

On co-evolution and the importance of initial conditions

We present a generic threshold model for the co-evolution of the structure of a network and the binary state of its nodes. We focus on regular directed networks and derive equations for the evolution of the system toward its absorbing state. It is shown that the system displays a transition from a connected phase to a fragmented phase, and that this transition is driven by the initial configuration of the system, as different initial conditions may lead to drastically different final configurations. Computer simulations are performed and confirm the theoretical predictions.     

Neural-Network Quantum State of Transverse-Field Ising Model

Along the way initiated by Carleo and Troyer [G. Carleo and M. Troyer, Science 355 (2017) 602], we construct the neural-network quantum state of transverse-field Ising model (TFIM) by an unsupervised machine learning method. Such a wave function is a map from the spin-configuration space to the complex number field determined by an array of network parameters. To get the ground state of the system, values of the network parameters are calculated by a Stochastic Reconfiguration (SR) method. We provide for this SR method an understanding from action principle and information geometry aspects. With this quantum state, we calculate key observables of the system, the energy, correlation function, correlation length, magnetic moment, and susceptibility. As innovations, we provide a high efficiency method and use it to calculate entanglement entropy (EE) of the system and get results consistent with previous work very well.     

The effect of adaptive behavior on risk propagation in industrial symbiosis networks

The complex symbiotic relationship in the industrial symbiosis network (ISN) may cause new risks for firms. In view of this problem, previous studies mainly regard the ISN as a static system, without considering the adaptive behavior of firms. This paper establishes a risk propagation model of the ISN based on the change of firm state, proposes four kinds of reconnection strategies to model the adaptive behavior, and uses numerical simulation to investigate the effect of adaptive behavior on risk propagation. The results demonstrate that all the reconnection strategies play an inhibitory role in the risk propagation. Therein, the effectiveness of PP strategy is the best, followed by RR strategy, and DP (SP) strategy. In any case, the effect of reconnection strategies on risk propagation will improve with the increase of the disconnection probability and network resilience. Additionally, the more decentralized weight distribution will weaken the inhibition of adaptive behavior on risk propagation.     

Dynamics of the Langevin model subjected to colored noise: Functional-integral method

We have discussed the dynamics of Langevin model subjected to colored noise, by using the functional-integral method (FIM) combined with equations of motion for mean and variance of the state variable. Two sets of colored noise have been investigated: (a) one additive and one multiplicative colored noise, and (b) one additive and two multiplicative colored noise. The case (b) is examined with relevance to a recent controversy on the stationary subthreshold voltage distribution of an integrate-and-fire model including stochastic excitatory and inhibitory synapses and a noisy input. We have studied the stationary probability distribution and dynamical responses to time-dependent (pulse and sinusoidal) inputs of the linear Langevin model. Model calculations have shown that results of the FIM are in good agreement with those of direct simulations (DSs). A comparison is made among various approximate analytic solutions such as the universal colored noise approximation (UCNA). It has been pointed out that dynamical responses to pulse and sinusoidal inputs calculated by the UCNA are rather different from those of DS and the FIM, although they yield the same stationary distribution.     

Random field Ising model and community structure in complex networks

We propose a method to determine the community structure of a complex network. In this method the ground state problem of a ferromagnetic random field Ising model is considered on the network with the magnetic field B_s = +∞, B_t = -∞, and B_i≠s,t=0 for a node pair s and t. The ground state problem is equivalent to the so-called maximum flow problem, which can be solved exactly numerically with the help of a combinatorial optimization algorithm. The community structure is then identified from the ground state Ising spin domains for all pairs of s and t. Our method provides a criterion for the existence of the community structure, and is applicable equally well to unweighted and weighted networks. We demonstrate the performance of the method by applying it to the Barabási-Albert network, Zachary karate club network, the scientific collaboration network, and the stock price correlation network. (Ising, Potts, etc.)