arXiv subjects

Jie Zang

Publications and source records attributed to Jie Zang.

4 recordsLinked to original sources

arXiv2026

Sequential chaotic oscillations in excitatory-inhibitory threshold-linear networks

Metastable states, a phenomenon observed in brain dynamics and many other systems, have been proposed as a key feature of healthy brain function, reflecting a balance between integration and segregation. However, it remains unclear how to capture this behavior within a dynamical-systems framework. In this paper, we propose sequential chaotic oscillations (SCOs), arising in excitatory-inhibitory threshold-linear networks (E-I TLNs), as a candidate dynamical mechanism for sequential metastability. As a simple form of chaotic itinerancy, SCOs occur under constant input and consist of a sequence of metastable states whose transition order can be predicted by the underlying graph. To identify the parameter regime for SCOs, we develop new graph rules for E-I TLNs and use them to characterize the fixed point structure of E-I TLNs on paths and cycles. Our results show that the emergence of SCOs requires unstable singleton fixed points and sufficiently strong inhibition. In addition to SCOs, we find that E-I oscillations need not be synchronized. Motivated by this, we introduce a decomposition into the z-mode and the mean mode, which capture excitatory differences and overall network activity, respectively. These modes are then used to distinguish attractors associated with the full-support fixed point of E-I TLNs on cycles.

q-bio.NC↗

arXiv2025

Renormalization group analysis of noisy neural field

Neurons in the brain show great diversity in their individual properties and their connections to other neurons. To develop an understanding of how neuronal diversity contributes to brain dynamics and function at large scales we start with a linearized version of the Wilson-Kowan model and introduce a random anisotropy to inter-neuron connection. The resultant model is Edwards-Wilkinson model with a random anisotropic term. Averaging over the quenched randomness with the replica method we obtain a bi-quadratic nonlinearity. We use Wilsonian dynamic renormalization group to analyze this model. We find that, up to one loop order, for dimensions higher than two, the effect of the noise is to change dynamic exponent from two to one.

cond-mat.dis-nn↗

arXiv2023

Structural constraints on the emergence of oscillations in multi-population neural networks

Oscillations arise in many real-world systems and are associated with both functional and dysfunctional states. Whether a network can oscillate can be estimated if we know the strength of interaction between nodes. But in real-world networks (in particular in biological networks) it is usually not possible to know the exact connection weights. Therefore, it is important to determine the structural properties of a network necessary to generate oscillations. Here, we provide a proof that uses dynamical system theory to prove that an odd number of inhibitory nodes and strong enough connections are necessary to generate oscillations in a single cycle threshold-linear network. We illustrate these analytical results in a biologically plausible network with either firing-rate based or spiking neurons. Our work provides structural properties necessary to generate oscillations in a network. We use this knowledge to reconcile recent experimental findings about oscillations in basal ganglia with classical findings.

q-bio.NC↗

arXiv2016

Extended Eckart Theorem and New Variation Method for Excited States of Atoms

We extend the Eckart theorem, from the ground state to excited statew, which introduces an energy augmentation to the variation criterion for excited states. It is shown that the energy of a very good excited state trial function can be slightly lower than the exact eigenvalue. Further, the energy calculated by the trial excited state wave function, which is the closest to the exact eigenstate through Gram-Schmidt orthonormalization to a ground state approximant, is lower than the exact eigenvalue as well. In order to avoid the variation restrictions inherent in the upper bound variation theory based on Hylleraas, Undheim, and McDonald [HUM] and Eckart Theorem, we have proposed a new variation functional Omega-n and proved that it has a local minimum at the eigenstates, which allows approaching the eigenstate unlimitedly by variation of the trial wave function. As an example, we calculated the energy and the radial expectation values of Triplet-S(even) Helium atom by the new variation functional, and by HUM and Eckart theorem, respectively, for comparison. Our preliminary numerical results reveal that the energy of the calculated excited states 3rd Triplet-S(even) and 4th Triplet-S(even) may be slightly lower than the exact eigenvalue (inaccessible by HUM theory) according to the General Eckart Theorem proved here, while the approximate wave function is better than HUM.

physics.comp-ph↗