Related papers: Coarse graining dynamical triangulations: a new sc…
Spin foams are models of quantum gravity and therefore quantum space time. A key open issue is to determine the possible continuum phases of these models. Progress on this issue has been prohibited by the complexity of the full…
A novel scheme to simulate the evolution of a restricted set of observables of a quantum system is proposed. The set comprises the spectrum-generating algebra of the Hamiltonian. The idea is to consider a certain open-system evolution,…
A first step towards implementing a notion of coarse graining in an intrinsically Lorentzian, discrete quantum- gravity approach, namely causal set quantum gravity is taken. It makes use of an abstract notion of scale, based on counting the…
Quantum state tomography often operates in the highly idealised scenario of assuming perfect measurements. The errors implied by such an approach are entwined with other imperfections relating to the information processing protocol or…
Stochastic dynamics, such as molecular dynamics, are important in many scientific applications. However, summarizing and analyzing the results of such simulations is often challenging, due to the high dimension in which simulations are…
Coarse-grained descriptions of dislocation motion in crystalline metals inherently represent a loss of information regarding dislocation-dislocation interactions. In the present work, we consider a coarse-graining framework capable of…
We review some recent coarse-graining and multi-scale methods, but also put forward some new ideas for addressing such issues. We find that, if one is guided by nonequilibrium statistical mechanics and thermodynamics, it is possible to…
Atomistic or ab-initio molecular dynamics simulations are widely used to predict thermodynamics and kinetics and relate them to molecular structure. A common approach to go beyond the time- and length-scales accessible with such…
Several recently proposed semi--automatic and fully--automatic coarse--graining schemes for polymer simulations are discussed. All these techniques derive effective potentials for multi--atom units or super--atoms from atomistic…
The emergence of macroscopic variables can be effected through {\it coarse graining}. Despite practical and fundamental benefits conveyed by this partitioning of state space, the apparently subjective nature of the selection of coarse…
We propose a novel and systematic method for coarse-graining oscillator networks described by phase equations. Our coarse-graining method enables us to obtain the closed coarse-grained equations for a few effective eigenmodes, which is…
One of the most pressing issues for loop quantum gravity and spin foams is the construction of the continuum limit. In this paper, we propose a systematic coarse-graining scheme for three-dimensional lattice gauge models including spin…
We investigate how various coarse-graining methods affect the scaling properties of long-range power-law correlated and anti-correlated signals, quantified by the detrended fluctuation analysis. Specifically, for coarse-graining in the…
A method of ``blocking'' triangulations that rests on the self-similarity feature of dynamically triangulated random manifolds is proposed. The method is used to define the renormalization group for random geometries. As an illustration,…
Coarse-graining is a molecular modeling technique in which an atomistic system is represented in a simplified fashion that retains the most significant system features that contribute to a target output, while removing the degrees of…
Brownian dynamics of colloidal particles on complex surfaces has found important applications in diverse physical, chemical and biological processes. However, current Brownian dynamics simulation algorithms mostly work for relatively simple…
An expression for the stress tensor near an external boundary of a discrete mechanical system is derived explicitly in terms of the constituents' degrees of freedom and interaction forces. Starting point is the exact and general coarse…
Weighted Gaussian Curvature is an important measurement for images. However, its conventional computation scheme has low performance, low accuracy and requires that the input image must be second order differentiable. To tackle these three…
Many real-world networks display a natural bipartite structure, while analyzing or visualizing large bipartite networks is one of the most challenges. As a result, it is necessary to reduce the complexity of large bipartite systems and…
How does one generalize differential geometric constructs such as curvature of a manifold to the discrete world of graphs and other combinatorial structures? This problem carries significant importance for analyzing models of discrete…