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We give a new proof of a sumset conjecture of Furstenberg that was first proved by Hochman and Shmerkin in 2012: if logr/logs is irrational and X and Y are ×r- and ×s-invariant subsets of [0,1], respectively, then $\dim_\text{ ...
We develop random graph models where graphs are generated by connecting not only pairs of vertices by edges, but also larger subsets of vertices by copies of small atomic subgraphs of arbitrary topology. This allows for the generation of graphs with extens ...
The dependence of the Shannon entropy (SE) of a speckle pattern on the degree of polarization (DoP) of the pattern is investigated both experimentally and numerically. The superposition of two uncorrelated speckle patterns with polarization diversity is ut ...
Motivated by the recent success of tensor networks to calculate the residual entropy of spin ice and kagome Ising models, we develop a general framework to study frustrated Ising models in terms of infinite tensor networks that can be contracted using stan ...
The entropy production is one of the most essential features for systems operating out of equilibrium. The formulation for discrete-state systems goes back to the celebrated Schnakenberg's work and hitherto can be carried out when for each transition betwe ...
The Alkali-Silica Reaction (ASR) in concrete is a chemical reaction, which produces an expansive product, generally called “ASR gel”, and causes cracking and damage in concrete over time. Affecting numerous infrastructures all around the world, ASR has bee ...
This study presents a methodology developed for estimating effective connectivity in brain networks (BNs) using multichannel scalp EEG recordings. The methodology uses transfer entropy as an information transfer measure to detect pair-wise directed informa ...
The entropy change during spin relaxation for a realistic model system is studied, whose spin dynamics can be handled with the Boltzmann equation. The time evolution of the von Neumann entropy is monitored during the process and is compared with the recent ...
A general framework to describe a vast majority of biology-inspired systems is to model them as stochastic processes in which multiple couplings are in play at the same time. Molecular motors, chemical reaction networks, catalytic enzymes, and particles ex ...
Atomistic simulations provide insights into structure-property relations on an atomic size and length scale, that are complementary to the macroscopic observables that can be obtained from experiments. Quantitative predictions, however, are usually hindere ...