Related papers: Coarse-graining and compounding as monads
We show from a categorical point of view that probability measures on certain measurable or topological spaces arise canonically as the extension of probability distributions on countable sets. We do this by constructing probability monads…
This paper presents equational-based logics for proving first order properties of programming languages involving effects. We propose two dual inference system patterns that can be instanciated with monads or comonads in order to be used…
Computational effects are commonly modelled by monads, but often a monad can be presented by an algebraic theory of operations and equations. This talk is about monads and algebraic theories for languages for inference, and their…
A model of a quantum measurement process is presented: a system consisting of a qubit in a superposition interacts with a measuring apparatus consisting of a N qubit state. Looking at the emerging, effective description of the apparatus…
Multiscale phenomena which include several processes occuring simultaneously at different length scales and exchanging energy with each other, are widespread in magnetism. These phenomena often govern the magnetization reversal dynamics,…
We introduce a straightforward numerical coarse-graining scheme to estimate quantum states for a set of noisy measurement outcomes, which are difficult to calibrate, that is based solely on the measurement data collected from these…
Recent works have shown that defining a behavioural equivalence that matches the observational properties of a quantum-capable, concurrent, non-deterministic system is a surprisingly difficult task. We explore coalgebras over distributions…
We propose a highly coarse-grained simulation model for crystalline polymer solids with crystalline lamellar structures. The mechanical properties of a crystalline polymer solid are mainly determined by the crystalline lamellar structures.…
Functor coalgebras capture a wide range of transition systems that must however evolve in discrete steps. We introduce graded coalgebras of graded monads and propose them to model continuous-time transition systems. We develop the theory of…
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…
Coarse-graining techniques play a central role in reducing the complexity of stochastic models, and are typically characterised by a mapping which projects the full state of the system onto a smaller set of variables which captures 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…
One can perform equational reasoning about computational effects with a purely functional programming language thanks to monads. Even though equational reasoning for effectful programs is desirable, it is not yet mainstream. This is partly…
The prediction of the equation of state and the phase behavior of simple fluids (noble gases, carbon dioxide, benzene, methane, short alkane chains) and their mixtures by Monte Carlo computer simulation and analytic approximations based on…
We show how the mathematical structure of large-deviation principles matches well with the concept of coarse-graining. For those systems with a large-deviation principle, this may lead to a general approach to coarse-graining through the…
Molecular dynamics simulations provide theoretical insight into the microscopic behavior of materials in condensed phase and, as a predictive tool, enable computational design of new compounds. However, because of the large temporal and…
We systematically derive an exact coarse-grained description for interacting particles with thermodynamically consistent stochastic dynamics, applicable across different observation scales, the mesoscopic and the macroscopic. We implement…
Biological systems exhibit processes on a wide range of time and length scales. This work demonstrates that models, wherein the interaction between system constituents is captured by algebraic operations, inherently allow for successive…
We coarse-grain a model of closely-packed ellipses that can vary their aspect ratio to derive continuum equations for materials comprising confluent deformable particles such as epithelial cell layers. We show that contractile nearest…
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…