Many real world applications are modelled by coupled systems on undirected networks. Two striking classes of such systems are the gradient and the Hamiltonian systems. In fact, within these two classes, coupled systems are admissible only by the undirected networks. For the coupled systems associated with a network, there can be flow-invariant spaces (synchrony subspaces where some subsystems evolve synchronously), whose existence is independent of the systems equations and depends only on the network topology. Moreover, any coupled system on the network, when restricted to such a synchrony subspace, determines a new coupled system associated with a smaller network (quotient). The original network is said to be a lift of the quotient network. In this paper, we characterize the conditions for the coupled systems property of being gradient or Hamiltonian to be preserved by the lift and quotient coupled systems. This characterization is based on determining necessary and sufficient conditions for a quotient (lift) network of an undirected network to be also undirected. We show that the extra gradient or Hamiltonian structure of a coupled system admissible by an undirected network can be lost by the systems admissible by a (directed) quotient network. Conversely, gradient (Hamiltonian) dynamics can appear for an undirected quotient network of a directed network or of an undirected network whose associated dynamics is not gradient (Hamiltonian). We illustrate with a neural network given by two groups of neurons that are mutually coupled through either excitatory or inhibitory synapses, which is modelled by a coupled system exhibiting both gradient and Hamiltonian structures.
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Bull Math Biol
January 2025
Section of Epidemiology, University of Copenhagen, Copenhagen, Denmark.
Using genetic data to infer evolutionary distances between molecular sequence pairs based on a Markov substitution model is a common procedure in phylogenetics, in particular for selecting a good starting tree to improve upon. Many evolutionary patterns can be accurately modelled using substitution models that are available in closed form, including the popular general time reversible model (GTR) for DNA data. For more complex biological phenomena, such as variations in lineage-specific evolutionary rates over time (heterotachy), other approaches such as the GTR with rate variation (GTR ) are required, but do not admit analytical solutions and do not automatically allow for likelihood calculations crucial for Bayesian analysis.
View Article and Find Full Text PDFNat Commun
January 2025
Department of Physics and Astronomy, and Institute of Applied Physics, Seoul National University, Seoul, Korea.
Addressing and mitigating decoherence sources plays an essential role in the development of a scalable quantum computing system, which requires low gate errors to be consistently maintained throughout the circuit execution. While nuclear spin-free materials, such as isotopically purified silicon, exhibit intrinsically promising coherence properties for electron spin qubits, the omnipresent charge noise, when converted to magnetic noise under a strong magnetic field gradient, often hinders stable qubit operation within a time frame comparable to the data acquisition time. Here, we demonstrate both open- and closed-loop suppression techniques for the transduced noise in silicon spin qubits, resulting in a more than two-fold (ten-fold) improvement of the inhomogeneous coherence time (Rabi oscillation quality) that leads to a single-qubit gate fidelity of over 99.
View Article and Find Full Text PDFJ Fixed Point Theory Appl
December 2024
Weizmann Institute of Science, Rehovot, Israel.
We study a local-to-global inequality for spectral invariants of Hamiltonians whose supports have a "large enough" disjoint tubular neighborhood on semipositive symplectic manifolds. As a corollary, we deduce this inequality for disjointly supported Hamiltonians that are -small (when fixing the supports). In particular, we present the first examples of such an inequality when the Hamiltonians are not necessarily supported in domains with contact-type boundaries, or when the ambient manifold is irrational.
View Article and Find Full Text PDFJ Mol Model
November 2024
Department of Physics, College of Science, University of Anbar, Ramadi, Anbar, Iraq.
Context: Theoretical investigation for thermoelectric characteristics of organic Thienoisoindigo single-molecule is carried out using the first-principles calculations based on the density functional theory. It reveals that modifying the position or removing oxygen atoms significantly alters the thermoelectric properties. Transmission coefficient calculations show that the lowest unoccupied molecular orbital (LUMO) dominates across all molecular configurations.
View Article and Find Full Text PDFJ Phys Chem Lett
November 2024
Institute for Theoretical Physics, Heidelberg University, 69120 Heidelberg, Germany.
Thermodynamic integration (TI) offers a rigorous method for estimating free-energy differences by integrating over a sequence of interpolating conformational ensembles. However, TI calculations are computationally expensive and typically limited to coupling a small number of degrees of freedom due to the need to sample numerous intermediate ensembles with sufficient conformational-space overlap. In this work, we propose to perform TI along an alchemical pathway represented by a trainable neural network, which we term Neural TI.
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