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The most general one dimensional reaction-diffusion model with nearest-neighbor interactions, which is exactly-solvable through the empty interval method, has been introduced. Assuming translationally-invariant initial conditions, the…
The most general exclusion single species reaction-diffusion models with nearest-neighbor interactions one a one dimensional lattice are investigated, for which the evolution of full intervals are closed. Using a generating function method,…
The most general one dimensional reaction-diffusion model with nearest-neighbor interactions solvable through the empty interval method, and without any restriction on the particle-generation from two adjacent empty sites is studied. It is…
Multi-species reaction-diffusion systems, with nearest-neighbor interaction on a one-dimensional lattice are considered. Necessary and sufficient constraints on the interaction rates are obtained, that guarantee the closedness of the time…
Multi-species reaction-diffusion systems, with more-than-two-site interaction on a one-dimensional lattice are considered. Necessary and sufficient constraints on the interaction rates are obtained, that guarantee the closedness of the time…
Single-species reaction-diffusion systems on a one-dimensional lattice are considered, in them more than two neighboring sites interact. Constraints on the interaction rates are obtained, that guarantee the closedness of the time evolution…
The most general nonuniform reaction-diffusion models on a one-dimensional lattice with boundaries, for which the time evolution equations of corre- lation functions are closed, are considered. A transfer matrix method is used to find the…
The one-dimensional coagulation-diffusion process describes the strongly fluctuating dynamics of particles, freely hopping between the nearest-neighbour sites of a chain such that one of them disappears with probability 1 if two particles…
The long-time dynamics of reaction-diffusion processes in low dimensions is dominated by fluctuation effects. The one-dimensional coagulation-diffusion process describes the kinetics of particles which freely hop between the sites of a…
Reaction-diffusion equations are treated on infinite networks using semigroup methods. To blend high fidelity local analysis with coarse remote modeling, initial data and solutions come from a uniformly closed algebra generated by functions…
In a recent article the most general non-uniform reaction-diffusion models on a one-dimensional lattice with boundaries were considered, for which the time evolution equations of correlation functions are closed and the stationary profile…
The most general single species autonomous reaction-diffusion model on a Cayley tree with nearest-neighbor interactions is introduced. The stationary solutions of such models, as well as their dynamics, are discussed. To study dynamics of…
The most general reaction-diffusion model on a Cayley tree with nearest-neighbor interactions is introduced, which can be solved exactly through the empty-interval method. The stationary solutions of such models, as well as their dynamics,…
Autonomous multispecies systems with more-than-two-neighbor interactions are studied. Conditions necessary and sufficient for closedness of the evolution equations of the $n$-point functions are obtained. The average number of the particles…
A self-consistent projection operator method for single-particle excitations is developed. It describes the nonlocal correlations on the basis of a projection technique to the retarded Green function and the off-diagonal effective medium.…
Hidden variable graphical models can sometimes imply constraints on the observable distribution that are more complex than simple conditional independence relations. These observable constraints can falsify assumptions of the model that…
In this work we study, on a finite and periodic lattice, a class of one-dimensional (bimolecular and single-species) reaction-diffusion models which cannot be mapped onto free-fermion models. We extend the conventional empty-interval…
We propose several prediction intervals procedures for the individual treatment effect with either finite-sample or asymptotic coverage guarantee in a non-parametric regression setting, where non-linear regression functions,…
The one-dimensional reaction diffusion process AA->A and A0A->AAA is exactly solvable through the empty interval method if the diffusion rate equals the coagulation rate. Independently of the particle production rate, the model is always in…
With nonignorable missing data, likelihood-based inference should be based on the joint distribution of the study variables and their missingness indicators. These joint models cannot be estimated from the data alone, thus requiring the…