Related papers: Fixed point forms of the parallel symmetric sandpi…

Sand Pile Models are discrete dynamical systems emphasizing the phenomenon of Self-Organized Criticality. From a configuration composed of a finite number of stacked grains, we apply on every possible positions (in parallel) two grain…

A symmetric version of the well-known SPM model for sandpiles is introduced. We prove that the new model has fixed point dynamics. Although there might be several fixed points, a precise description of the fixed points is given. Moreover,…

Harnessing parallelism in seemingly sequential models is a central challenge for modern machine learning. Several approaches have been proposed for evaluating sequential processes in parallel using iterative fixed-point methods, like…

We define a new version of sandpile model which is very similar to Abelian Sandpile Model (ASM), but the height variables are continuous ones. With the toppling rule we define in our model, we show that the model can be mapped to ASM, so…

We prove fixed points results for sandpiles starting with arbitrary initial conditions. We give an effective algorithm for computing such fixed points, and we refine it in the particular case of SPM.

We introduce a sandpile model where, at each unstable site, all grains are transferred randomly to downstream neighbors. The model is local and conservative, but not Abelian. This does not appear to change the universality class for the…

This paper is about cubic sand grains moving around on nicely packed columns in one dimension (the physical sand pile is two dimensional, but the support of sand columns is one dimensional). The Kadanoff Sand Pile Model is a discrete…

We present a solution for the stationary state of an asymmetric exclusion model with sequential update and open boundary conditions. We solve the model exactly for random hopping in both directions by applying a matrix-product formalism…

This paper introduces the concept of a synchronous model as an extension of the internal model concept used in observer design for dynamical systems. A system is said to contain a synchronous model of another if there is a suitable error…

In this paper, we introduce two novel parallel projection methods for finding a solution of a system of variational inequalities which is also a common fixed point of a family of (asymptotically) $\kappa$ - strict pseudocontractive…

Two characteristics that make convex decomposition algorithms attractive are simplicity of operations and generation of parallelizable structures. In principle, these schemes require that all coordinates update at the same time, i.e., they…

Sand pile models are dynamical systems describing the evolution from $N$ stacked grains to a stable configuration. It uses local rules to depict grain moves and iterate it until reaching a fixed configuration from which no rule can be…

Sand pile models are dynamical systems describing the evolution from $N$ stacked grains to a stable configuration. It uses local rules to depict grain moves and iterate it until reaching a fixed configuration from which no rule can be…

We introduce a new type of mappings in metric space which are three-point analogue of the well-known Chatterjea type mappings, and call them generalized Chatterjea type mappings. It is shown that such mappings can be discontinuous as is the…

We performed the renormalization group analysis of scalar models exhibiting spontaneous symmetry breaking. It is shown that an infrared fixed point appears in the broken symmetric phase of the models, which induces a dynamical scale, that…

Kinetic self-avoiding trails are introduced and used to generate a substrate of randomly quenched flow vectors. Sandpile model is studied on such a substrate with asymmetric toppling matrices where the precise balance between the net…

In this paper, we perform a theoretical analysis of the sequential convergence of elementary cellular automata that have at least one fixed point. Our aim is to establish which elementary rules always reach fixed points under sequential…

Distributed model fitting refers to the process of fitting a mathematical or statistical model to the data using distributed computing resources, such that computing tasks are divided among multiple interconnected computers or nodes, often…

We consider a generic convex-concave saddle point problem with separable structure, a form that covers a wide-ranged machine learning applications. Under this problem structure, we follow the framework of primal-dual updates for saddle…

In this paper, we introduce and study the Parallel Polyhedral Projection Method (3PM) and the Approximate Parallel Polyhedral Projection Method (A3PM) for finding a point in the intersection of finitely many closed convex sets. Each…