Related papers: Can coarse-graining introduce long-range correlati…
We formulate a mean-field-like theory of long-range correlated $L$-alphabets sequences, which are actually systems with $(L-1)$ independent parameters. Depending on the values of these parameters, the variance on the average number of any…
A driven system of three species of particle diffusing on a ring is studied in detail. The dynamics is local and conserves the three densities. A simple argument suggesting that the model should phase separate and break the translational…
A general mean field theory is presented for the construction of equilibrium coarse grained models. Inverse methods that reconstruct microscopic models from low resolution experimental data can be derived as particular implementations of…
This work explores the manner in which classical phase space distribution functions converge to the microcanonical distribution. We first prove a theorem about the lack of convergence, then define a generalization of the coarse-graining…
In real-world data, information is stored in extremely large feature vectors. These variables are typically correlated due to complex interactions involving many features simultaneously. Such correlations qualitatively correspond to…
The Cahn-Hilliard equation with an externally-prescribed chaotic shear flow is studied in two and three dimensions. The main goal is to compare and contrast the phase separation in two and three dimensions, using high-resolution numerical…
We present a study of a phase-separation process induced by the presence of spatially-correlated multiplicative noise. We develop a mean-field approach suitable for conserved-order-parameter systems and use it to obtain the phase diagram of…
Given a causal graph representing the data-generating process shared across different domains/distributions, enforcing sufficient graph-implied conditional independencies can identify domain-general (non-spurious) feature representations.…
Generative methods for graphs need to be sufficiently flexible to model complex dependencies between sets of nodes. At the same time, the generated graphs need to satisfy domain-dependent feasibility conditions, that is, they should not…
Modeling collective motion in non-conservative systems, such as granular materials, is difficult since a general microscopic-to-macroscopic approach is not available: there is no Hamiltonian, no known stationary densities in phase space,…
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…
Self-organized pattern formation is vital for many biological processes. Reaction-diffusion models have advanced our understanding of how biological systems develop spatial structures, starting from homogeneity. However, biological…
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…
When a periodic 1D system described by a tight-binding model is uniformly initialized with equal amplitudes at all sites, yet with completely random phases, it evolves into a thermal distribution with no spatial correlations. However, when…
Understanding phase diagrams is essential for material selection and design, as they provide a comprehensive representation of the thermodynamics of mixtures. This work delivers a broad and systematic overview of possible ternary phase…
We investigate the emergence of long-range correlations in granular shear flow. By increasing the density of a simulated granular flow we observe a spontaneous transition from a dilute regime, where interactions are dominated by binary…
Sign problems in path integrals arise when different field configurations contribute with different signs or phases. Phase unwrapping describes a family of signal processing techniques in which phase differences between elements of a time…
Instabilities and pattern formation is the rule in nonequilibrium systems. Selection of a persistent lengthscale, or coarsening (increase of the lengthscale with time) are the two major alternatives. When and under which conditions one…
Multi-component membranes such as ternary mixtures of lipids and cholesterol can exhibit coexistence regions between two liquid phases. When such membranes adhere to a corrugated substrate, the phase separation process strongly depends on…
A theory of systems with long-range correlations based on the consideration of binary N-step Markov chains is developed. In the model, the conditional probability that the i-th symbol in the chain equals zero (or unity) is a linear function…