arXiv subjects

Alexander V. Goltsev

Publications and source records attributed to Alexander V. Goltsev.

3 recordsLinked to original sources

arXiv2025

Observer in quantum cosmology

Within the framework of the new formalism of quantum theory - the quantum principle of least action - the initial state of the universe is determined, which is an analogue of the Hartle-Hawking no-boundary wave function. The quantum evolution of the universe is modified by additional conditions in a certain compact region of space-time, which is called the observation region. Additional conditions are Noether identities related to the general covariance of the theory and internal symmetries of matter fields. The consequences of the local law of conservation of the energy-momentum tensor of matter are considered in detail. Its consequence is the deterministic nature of the motion of the energy and momentum densities of matter in the observation area. The geometric parameters of the region boundary are also determined by the deterministic motion of the matter fields inside. The choice of boundary conditions for the energy-momentum flow at the boundary serves as a mechanism for decoherence of the quantum evolution of the universe. The result of decoherence is a certain correspondence between the final state of the universe and the state of the observer in the specified region. This correspondence allows us to formulate the extremum principle in quantum cosmology, in which the action functional constructed using the final state determines the world history of the universe as the observer sees it.

gr-qc↗

arXiv2019

Distinct dynamical behavior in Erdős-Rényi networks, regular random networks, ring lattices, and all-to-all neuronal networks

Neuronal network dynamics depends on network structure. In this paper we study how network topology underpins the emergence of different dynamical behaviors in neuronal networks. In particular, we consider neuronal network dynamics on Erdős-Rényi (ER) networks, regular random (RR) networks, ring lattices, and all-to-all networks. We solve analytically a neuronal network model with stochastic binary-state neurons in all the network topologies, except ring lattices. Given that apart from network structure, all four models are equivalent, this allows us to understand the role of network structure in neuronal network dynamics. Whilst ER and RR networks are characterized by similar phase diagrams, we find strikingly different phase diagrams in the all-to-all network. Neuronal network dynamics is not only different within certain parameter ranges, but it also undergoes different bifurcations (with a richer repertoire of bifurcations in ER and RR compared to all-to-all networks). This suggests that local heterogeneity in the ratio between excitation and inhibition plays a crucial role on emergent dynamics. Furthermore, we also observe one subtle discrepancy between ER and RR networks, namely ER networks undergo a neuronal activity jump at lower noise levels compared to RR networks, presumably due to the degree heterogeneity in ER networks that is absent in RR networks. Finally, a comparison between network oscillations in RR networks and ring lattices shows the importance of small-world properties in sustaining stable network oscillations.

q-bio.NC↗

arXiv2017

A neuronal network model of interictal and recurrent ictal activity

We propose a neuronal network model which undergoes a saddle-node bifurcation on an invariant circle as the mechanism of the transition from the interictal to the ictal (seizure) state. In the vicinity of this transition, the model captures important dynamical features of both interictal and ictal states. We study the nature of interictal spikes and early warnings of the transition predicted by this model. We further demonstrate that recurrent seizures emerge due to the interaction between two networks.

q-bio.NC↗