AI Article Synopsis
- A Hamiltonian path is a route in a graph that visits every vertex exactly once.
- The paper explores the well-known Hamiltonian path problem in more depth.
- It introduces new criteria that can help determine whether such a path exists in a given graph.
Article Abstract
A Hamiltonian path in a graph is a path involving all the vertices of the graph. In this paper, we revisit the famous Hamiltonian path problem and present new sufficient conditions for the existence of a Hamiltonian path in a graph.
Download full-text PDF |
Source |
|---|---|
| http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4090529 | PMC |
| http://dx.doi.org/10.1155/2014/743431 | DOI Listing |
Publication Analysis
Top Keywords
Similar Publications
Artificial molecular communication network based on DNA nanostructures recognition.
Nat Commun
January 2025
Key Laboratory for Organic Electronics and Information Displays (KLOEID), Nanjing University of Posts and Telecommunications, Nanjing, China.
Artificial simulated communication networks inspired by molecular communication in organisms use biological and chemical molecules as information carriers to realize information transmission. However, the design of programmable, multiplexed and general simulation models remains challenging. Here, we develop a DNA nanostructure recognition-based artificial molecular communication network (DR-AMCN), in which rectangular DNA origami nanostructures serve as nodes and their recognition as edges.
View Article and Find Full Text PDFSpectroscopic properties under vibrational strong coupling in disordered matter from path-integral Monte Carlo simulations.
J Chem Phys
November 2024
PASTEUR, Département de chimie, École normale supérieure, PSL University, Sorbonne Université, CNRS, 75005 Paris, France.
Vibrational strong coupling (VSC), the strong coupling between a Fabry-Perrot cavity and molecular vibrations at mid-infrared frequencies, has received important attention in the last years due to its capacity of modifying both vibrational spectra and chemical reactivity. VSC is a collective effect, and in this work, we introduce Path Integral Monte Carlo (PIMC) simulations that not only take into account the quantum character of the molecular vibrations and of the optical resonance of the cavity but also reproduce this collective behavior by considering multiple replicas of the molecular system. Moreover, we show that it is possible to extract from the PIMC simulations the decomposition of the hybrid optical and molecular states in terms of the bare molecular modes.
View Article and Find Full Text PDFFrom Geometry of Hamiltonian Dynamics to Topology of Phase Transitions: A Review.
Entropy (Basel)
October 2024
Aix-Marseille Univ, CNRS, Université de Toulon, 13288 Marseille, France.
In this review work, we outline a conceptual path that, starting from the numerical investigation of the transition between weak chaos and strong chaos in Hamiltonian systems with many degrees of freedom, comes to highlight how, at the basis of equilibrium phase transitions, there must be major changes in the topology of submanifolds of the phase space of Hamiltonian systems that describe systems that exhibit phase transitions. In fact, the numerical investigation of Hamiltonian flows of a large number of degrees of freedom that undergo a thermodynamic phase transition has revealed peculiar dynamical signatures detected through the energy dependence of the largest Lyapunov exponent, that is, of the degree of chaoticity of the dynamics at the phase transition point. The geometrization of Hamiltonian flows in terms of geodesic flows on suitably defined Riemannian manifolds, used to explain the origin of deterministic chaos, combined with the investigation of the dynamical counterpart of phase transitions unveils peculiar geometrical changes of the mechanical manifolds in correspondence to the peculiar dynamical changes at the phase transition point.
View Article and Find Full Text PDFUnified framework for open quantum dynamics with memory.
Nat Commun
September 2024
Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA, USA.
The dynamics of quantum systems coupled to baths are typically studied using the Nakajima-Zwanzig memory kernel ( ) or the influence functions (I), particularly when memory effects are present. Despite their significance, formal connections between the two have not been explicitly known. We establish their connections by examining the system propagator for a N-level system linearly coupled to Gaussian baths with various types of system-bath coupling.
View Article and Find Full Text PDFInterferometry of Non-Abelian Band Singularities and Euler Class Topology.
Phys Rev Lett
August 2024
TCM Group, Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom.
In systems with a real Bloch Hamiltonian band nodes can be characterized by a non-Abelian frame-rotation charge. The ability of these band nodes to annihilate pairwise is path dependent, since by braiding nodes in adjacent gaps the sign of their charges can be changed. Here, we theoretically construct and numerically confirm two concrete methods to experimentally probe these non-Abelian braiding processes and charges in ultracold atomic systems.
View Article and Find Full Text PDFWant AI Summaries of new PubMed Abstracts delivered to your In-box?
Enter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!