Related papers: Coarse graining: lessons from simple examples
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…
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…
Two very basic constructions involving experimental procedures are the formation of coarse-grained versions of experiments, and the formation of branching sequential experiments. The latter allow for the conditioning of states on the…
We propose to employ the hierarchical coarse-grained structure in the artificial neural networks explicitly to improve the interpretability without degrading performance. The idea has been applied in two situations. One is a neural network…
Lumping a Markov process introduces a coarser level of description that is useful in many contexts and applications. The dynamics on the coarse grained states is often approximated by its Markovian component. In this letter we derive…
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…
In this paper we introduce a canonical quantum coarse-graining and use negentropy to connect ignorance as measured by quantum information entropy and ignorance related to quantum coarse-graining. For our procedure, macro-states are the set…
We show that the class of conditional distributions satisfying the coarsening at random (CAR) property for discrete data has a simple and robust algorithmic description based on randomized uniform multicovers: combinatorial objects…
Using an information theoretic point of view, we investigate how a dynamics acting on a network can be coarse grained through the use of graph partitions. Specifically, we are interested in how aggregating the state space of a Markov…
We show how to coarse grain polymers in a good solvent as single particles, interacting with density-independent or density-dependent interactions. These interactions can be between the centres of mass, the mid-points or end-points of the…
We provide a construction of examples of semistable degeneration via toric geometry. The applications include a higher dimensional generalization of classical degeneration of K3 surface into 4 rational components, an algebraic geometric…
Understanding the structure and dynamics of liquids is pivotal for the study of larger spatiotemporal processes, especially in glass-forming materials at low temperatures. Density scaling, observed in many molecular systems through…
In this paper we present a variational technique that handles coarse-graining and passing to a limit in a unified manner. The technique is based on a duality structure, which is present in many gradient flows and other variational…
We review a few representative examples of granular experiments or models where phase separation, accompanied by domain coarsening, is a relevant phenomenon. We first elucidate the intrinsic non-equilibrium, or athermal, nature of granular…
First results on the autocorrelation behaviour of a recently proposed fermion algorithm by M. L\"uscher are presented and discussed. The occurence of unexpected large autocorrelation times is explained. Possible improvements are discussed.
Motivated by the understanding of holography as realized in tensor networks, we develop a bulk procedure that can be interpreted as generating a sequence of coarse-grained holographic states. The coarse-graining procedure involves…
Due to the wide range of timescales that are present in macromolecular systems, hierarchical multiscale strategies are necessary for their computational study. Coarse-graining (CG) allows to establish a link between different system…
We address aspects of coarse-graining in classical Statistical Physics from the viewpoint of the symplectic non-squeezing theorem. We make some comments regarding the implications of the symplectic non-squeezing theorem for the BBGKY…
We compare real and complex dynamics for automorphisms of rational surfaces that are obtained by lifting \chg{some} quadratic birational maps of the plane. In particular, we show how to exploit the existence of an invariant cubic curve to…
Granular segregation is an important mechanism for industrial processes aiming at mixing grains. Additionally, it plays a pivotal role in determining the kinematics of geophysical flows. Because of segregation, the grainsize distribution…