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Growth curve analysis (GCA) has a wide range of applications in various fields where growth trajectories need to be modeled. Heteroscedasticity is often present in the error term, which can not be handled with sufficient flexibility by…

Neural Cellular Automata (NCA) have shown a remarkable ability to learn the required rules to "grow" images, classify morphologies, segment images, as well as to do general computation such as path-finding. We believe the inductive prior…

Stochastic computing (SC) allows reducing hardware complexity and improving energy efficiency of error resilient applications. However, a main limitation of the computing paradigm is the low throughput induced by the intrinsic serial…

Lattice spin models are useful for studying critical phenomena and allow the extraction of equilibrium and dynamical properties. Simulations of such systems are usually based on Monte Carlo (MC) techniques, and the main difficulty is often…

The topic we address in this paper concerns the minimization of a Hamiltonian function for an Ising model through the application of simulated annealing algorithms based on (single-site) Glauber dynamics and stochastic cellular automata…

The study of biological systems witnessed a pervasive cross-fertilization between experimental investigation and computational methods. This gave rise to the development of new methodologies, able to tackle the complexity of biological…

The past two decades showed a rapid growing of physically-based modeling of fluids for computer graphics applications. In this area, a common top down approach is to model the fluid dynamics by Navier-Stokes equations and apply a numerical…

We introduce a new method based on cellular automata dynamics to study stochastic growth equations. The method defines an interface growth process which depends on height differences between neighbors. The growth rule assigns a probability…

We employ the Partially Saturated Cells Method (PSM) to model the interaction between the fluid flow and solid moving objects as an extension to the conventional lattice Boltzmann method. We introduce an efficient and accurate method for…

High-dimensional multimodal sampling problems from lattice field theory (LFT) have become important benchmarks for machine learning assisted sampling methods. We show that GPU-accelerated particle methods, Sequential Monte Carlo (SMC) and…

The ability to train large-scale neural networks has resulted in state-of-the-art performance in many areas of computer vision. These results have largely come from computational break throughs of two forms: model parallelism, e.g. GPU…

In the fields of computation and neuroscience, much is still unknown about the underlying computations that enable key cognitive functions including learning, memory, abstraction and behavior. This paper proposes a mathematical and…

Neural Cellular Automata (NCA) have proven to be effective in a variety of fields, with numerous biologically inspired applications. One of the fields, in which NCAs perform well is the generation of textures, modelling global patterns from…

Cellular Automata (CA) have long been foundational in simulating dynamical systems computationally. With recent innovations, this model class has been brought into the realm of deep learning by parameterizing the CA's update rule using an…

We present a method to derive an analytical expression for the roughness of an eroded surface whose dynamics are ruled by cellular automaton. Starting from the automaton, we obtain the time evolution of the height average and height…

In this paper we present two interesting properties of stochastic cellular automata that can be helpful in analyzing the dynamical behavior of such automata. The first property allows for calculating cell-wise probability distributions over…

In this work, we study a family of wireless channel simulation models called geometry-based stochastic channel models (GBSCMs). Compared to more complex ray-tracing simulation models, GBSCMs do not require an extensive characterization of…

For lattice Monte Carlo simulations parallelization is crucial to make studies of large systems and long simulation time feasible, while sequential simulations remain the gold-standard for correlation-free dynamics. Here, various domain…

We study a neural network model of interacting stochastic discrete two--state cellular automata on a regular lattice. The system is externally tuned to a critical point which varies with the degree of stochasticity (or the effective…

We derive a set of algorithms for simulating the diffusion-limited growth of faceted crystals using local cellular automata. This technique has been shown to work well in reproducing realistic crystal morphologies, and the present work…