Implementing in vivo cellular automata using toggle switch and inter-bacteria communication mechanism

An investigation of the efficient implementation of cellular automata on multi-core CPU and GPU hardware

Dobby weaves are decorative structures, which are characterised by small design or geometric figures woven in the fabric structure. Classical methods to diversify dobby weaves can be completed with a series of unconventional methods that derive from mathematics. Theories like fractals, chaos, and cellular automata, applied by CAD, can make easier and more efficient the creation process. The paper presents a CAD application for dobby weaves design (named TexCel) based on Cellular Automata theory, created by researchers from Faculty of Textile-Leather and Industrial Management of Iasi, Romania. Cellular automaton consists in a regular lattice of elements named "cells", which pass simultaneously through a finite number of states, in discrete time steps. Each cell evolves according to the same rule, which depends only on the state of the cell and on a finite number of neighbouring cells. The successive states of certain cellular automata that evolve in a square lattice and that have only two possible states of cells - coloured in black or white), are similar to the graphical representation of weave structures for woven fabrics. TexCel software contains two distinct parts: a drawing modulus and a drawing analysis modulus. The drawing modulus can be activated after the initialisation of the cellular automaton parameters (neighbourhood size, boundary conditions, initial condition and transition rule). The analysis modulus is necessary to eliminate those drawings that don't correspond to the fabric weaves conditions concerning the yarns' binding and the maximum float size. TexCel can select automatically and display only the balanced weaves or those that contain a settled maximum size of yarn floats. The theory of Cellular Automata is immensely rich, with simple rules and structures being capable to produce a great variety of dobby weave patterns. Even after the drawing selection, still remain an impressive number of interesting graphical configurations that can be used to diversify the fabric structure. TEXCEL represent a real "drawing engine" for dobby weave design, with very large resources for pattern creation process.

Non-uniform or inhomogeneous cellular automata (NunCA) [28] are spatio-temporal models for dynamical systems in which space and time are discrete, and there is a distinct transition rule for each cell, with a finite number of states. The cells are in a regular lattice and the transition from one state to another is performed synchronously. The next state of a given cell will then be provided by a local and fixed transition rule that associates its current state and the current state of the neighbouring cells with the next state. The neighbourhood could also be specific for each cell, but will be considered the same, except for the cells at the frontiers of the regular lattice. So, the only distinct feature between NunCA and the traditional uniform cellular automata (CA) [29,34] is the adoption of a specific transition rule for each cell instead of a single transition rule for all the cells in the lattice.KeywordsCellular AutomatonCellular AutomatonTransition RuleCellular Neural NetworkRegular LatticeThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Image segmentation with Cellular Automata

Cellular Automata (CA) have a long history being employed as pseudo-random number generators (PRNG), especially for cryptographic applications such as keystream generation in stream ciphers. Initially starting from the study of rule 30 of elementary CA, multiple rules where the objects of investigation and were shown to be able to pass most of the rigorous statistical tests used to assess the quality of PRNG. In all cases, the CA employed where of the classical, synchronous kind. This assumes a global clock regulating all CA updates which can be a weakness if an attacker is able to tamper it. Here we study how much asynchrony is necessary to make a CA-based PRNG ineffective. We have found that elementary CA are subdivided into three class: (1) there is a “state transition” where, after a certain level of asynchrony, the CA loses the ability to generate strong random sequences, (2) the randomness of the sequences increases with a limited level of asynchrony, or (3) CA normally unable to be used as PRNG exhibit a much stronger ability to generate random sequences when asynchrony is introduced.

Collective dynamics in multicellular systems such as biological organs and tissues plays a key role in biological development, regeneration, and pathological conditions. Collective tissue dynamics—understood as population behaviour arising from the interplay of the constituting discrete cells—can be studied with on- and off-lattice agent-based models. However, classical on-lattice agent-based models, also known as cellular automata, fail to replicate key aspects of collective migration, which is a central instance of collective behaviour in multicellular systems. To overcome drawbacks of classical on-lattice models, we introduce an on-lattice, agent-based modelling class for collective cell migration, which we call biological lattice-gas cellular automaton (BIO-LGCA). The BIO-LGCA is characterised by synchronous time updates, and the explicit consideration of individual cell velocities. While rules in classical cellular automata are typically chosen ad hoc, rules for cell-cell and cell-environment interactions in the BIO-LGCA can also be derived from experimental cell migration data or biophysical laws for individual cell migration. We introduce elementary BIO-LGCA models of fundamental cell interactions, which may be combined in a modular fashion to model complex multicellular phenomena. We exemplify the mathematical mean-field analysis of specific BIO-LGCA models, which allows to explain collective behaviour. The first example predicts the formation of clusters in adhesively interacting cells. The second example is based on a novel BIO-LGCA combining adhesive interactions and alignment. For this model, our analysis clarifies the nature of the recently discovered invasion plasticity of breast cancer cells in heterogeneous environments.

Aiming at Bernoulli serial lines with batching machines and finite buffers, this study develops analytical methods for performance analysis and system-theoretic properties. Batching machines can process several jobs simultaneously as a batch, as long as the number of jobs in a batch does not exceed the machine’s batch capacity. The batch capacities of all machines are not necessarily equal. Batching machines bring about a new characteristic of state transitions depending on batch capacities and machine states. For two-machine lines, the joint impacts of batching machines on state transitions are analyzed. Theoretically, the state transition rules are revealed. Based on the state transition rules, this study proposes a hierarchical state transition diagram, proves the ergodicity condition, and derives analytical formulas to evaluate the performance measures. Then, for multi-machine lines, this study develops a computationally efficient aggregation method with high accuracy. Furthermore, the impacts of system parameters, including machine efficiency pattern, batch capacity pattern, batch capacity mismatch, and system size, on the accuracy are qualitatively analyzed. Finally, this study investigates the reversibility and monotonicity properties. These analytical methods and results help production managers to scientifically evaluate, accurately predict, and continuously improve Bernoulli serial lines with batching machines.

A class of fine-grained (FG) parallel models and algorithms is defined as a generalization of Cellular Automata (CA). It comprises all CA-modifications, in which two main CA-properties (locality and parallelism of intercell interaction) are preserved, no constraint being imposed on state alphabets and transition functions. A set of methods for composing a complex FG-algorithm out of a number of simple ones is proposed. To make compatible FG-algorithms with different alphabets, a number of algebraic operations on cellular arrays are introduced. The set of proposed composition methods has a two-level structure: the lower level comprises composition of cell transition functions, while the higher level deals with global operators on cellular arrays. For each type of proposed methods an example is given and the domain of application is determined.

Authors propose a hardware based approach for reliable encryption in wireless network using Cellular Automata (CA). Distinct layers of encryption have been utilized in proposed model for enhancing data security. Transmitter and receiver modules are designed for performing state transition based encrypted activities. Transmitter module is required for capturing environmental turbulences (noise) from a specific geographical location and send encrypted signal to receiver module through wireless network. Receiver module analyses received signal after decryption for desired activities based on real time situations. Different hardware components are selected and compared based on market study targeting efficient construction of proposed modules. Time complexity and code break complexity are measured using different key lengths, keysets, and data sizes for proposed CA based encryption scheme achieving unique results in hardware based cryptography system. Encryption key length, index, and keyset are required for computing code break complexity in design model. Large data size is effectively managed to calculate protection ratio and reliability factor for realizing efficient protectiveness and accuracy. Comparative study between existing encryption technique and proposed CA based encryption technique is established based on time complexity and code break complexity.

We generalize our recent discrete cellular automata (CA) model of excitable media [Y. B. Chernyak, A. B. Feldman, and R. J. Cohen, Phys. Rev. E 55, 3215 (1997)] to incorporate the effects of inhibitory processes on the propagation of the excitation wave front. In the common two variable reaction-diffusion (RD) models of excitable media, the inhibitory process is described by the $v$ ``controller'' variable responsible for the restoration of the equilibrium state following excitation. In myocardial tissue, the inhibitory effects are mainly due to the inactivation of the fast sodium current. We represent inhibition using a physical model in which the ``source'' contribution of excited elements to the excitation of their neighbors decreases with time as a simple function with a single adjustable parameter (a rate constant). We sought specific solutions of the CA state transition equations and obtained (both analytically and numerically) the dependence of the wave-front speed $c$ on the four model parameters and the wave-front curvature $\ensuremath{\kappa}$. By requiring that the major characteristics of $c(\ensuremath{\kappa})$ in our CA model coincide with those obtained from solutions of a specific RD model, we find a unique set of CA parameter values for a given excitable medium. The basic structure of our CA solutions is remarkably similar to that found in typical RD systems (similar behavior is observed when the analogous model parameters are varied). Most notably, the ``turn-on'' of the inhibitory process is accompanied by the appearance of a solution branch of slow speed, unstable waves. Additionally, when $\ensuremath{\kappa}$ is small, we obtain a family of ``eikonal'' relations $c(\ensuremath{\kappa})$ that are suitable for the kinematic analysis of traveling waves in the CA medium. We compared the solutions of the CA equations to CA simulations for the case of plane waves and circular (target) waves and found excellent agreement. We then studied a spiral wave using the CA model adjusted to a specific RD system and found good correspondence between the shapes of the RD and CA spiral arms in the region away from the tip where kinematic theory applies. Our analysis suggests that only four physical parameters control the behavior of wave fronts in excitable media.

Increasing experimental evidence suggests that the behaviour of multi-cellular systems, such as tissues and organs, might be largely driven by the complex interplay occurring among metabolic networks. Computational approaches are required to unravel this complexity. However, they currently deal with either the simulation of the spatial dynamics of cell populations or with the simulation of metabolism of individual cells. In order to integrate the modeling of these two key biological processes, we here introduce FBCA (Flux Balance Cellular Automata) a new multi-scale modeling framework that combines a cellular automaton representation of the (higher-level) spatial/morphological dynamics of multi-cellular systems, i.e., the Cellular Potts Model, with a model of the (lower-level) metabolic activity of individual cells, as modeled via Flux Balance Analysis. The representation via cellular automata allows to identify and analyze complex emergent properties and patterns of real-world multi-cellular systems, in a variety of distinct experimental settings. We here present preliminary tests on a simplified model of intestinal crypt, in which cell populations with distinct metabolic properties compete for space and nutrients. The results may allow to cast a new light on the mechanisms linking metabolic properties to clonal dynamics in tissues.

Understanding the dynamics of a system is crucial in various scientific and engineering domains. Machine learning techniques have been employed to learn state transition rules from observed time-series data. However, these data often contain sequences of noisy and ambiguous continuous variables, while we typically seek simplified dynamics rules that capture essential variables. In this work, we propose a method to extract a small number of essential hidden variables from high-dimensional time-series data and learn state transition rules between hidden variables. Our approach is based on the Restricted Boltzmann Machine (RBM), which models observable data in the visible layer and latent features in the hidden layer. However, real-world data, such as video and audio, consist of both discrete and continuous variables with temporal relationships. To address this, we introduce the Recurrent Temporal Gaussian-Bernoulli Restricted Boltzmann Machine (RTGB-RBM), which combines the Gaussian-Bernoulli Restricted Boltzmann Machine (GB-RBM) to handle continuous visible variables and the Recurrent Temporal Restricted Boltzmann Machine (RT-RBM) to capture time dependencies among discrete hidden variables. Additionally, we propose a rule-based method to extract essential information as hidden variables and represent state transition rules in an interpretable form. We evaluate our proposed method on the Bouncing Ball, Moving MNIST, and dSprite datasets. Experimental results demonstrate that our approach effectively learns the dynamics of these physical systems by extracting state transition rules between hidden variables. Moreover, our method can predict unobserved future states based on observed state transitions.

This paper focuses on discrete dynamic optimization on train rescheduling on single-track railway with the consideration of train punctuality and station satisfaction degree. A discrete dynamic system is firstly described to mimic train rescheduling, and a state transition function is specially designed according to the train departure event. The purpose of this function is to improve simulation efficiency by directly confirming the next discrete time. After the construction and analysis of optimization models to discrete dynamic system, a two-stage heuristic search strategy is developed, by using clustering hierarchy theory and stochastic search strategy, to obtain train departure time and arrival time before each state transition of the system. Finally, a numerical experiment is conducted to verify the proposed system, models, and the heuristic search strategy. The result shows that the discrete dynamic system, together with the state transition function and heuristic search strategy, shows better performance in simulation efficiency and solution quality.

Evolution-in-Materio (EIM) is a method of using artificial evolution to exploit physical properties of materials for computation. It has previously been successfully used to evolve a multitude of different computational devices implemented in physical materials. One of the main problems has been the stability of solutions due to physical changes in the substrate materials, e.g. topological or electrical, leading to devices sensitive to the evolutionary history, i.e. instability. This paper presents stable linearly and non-linearly separable logic gates, and elementary cellular automata (CA) transition functions, successfully evolved in single-walled carbon nanotube (SWCNT) and polymer composite materials. The results herein show the feasibility of building stand-alone in-materio devices and outline a novel computational abstraction for EIM based on CA. This work is done within the European Project NASCENCE.

Logic gates form the basis of modern digital computers, and from a theoretical perspective they are the unit of computation since they are the fundamental discrete logic element. By creating circuits of interconnected logic gates, computers can calculate more complex operations, such as adders, multiplexers, flips-flops, and eventually processing and control units. Herein, we use a 3D-printed platform consisting of a rectangular 2D-array of interconnected cells containing the Belousov–Zhabotinsky (BZ) reaction. This reaction can be made to oscillate between two states to simulate the binary codification of digital electronics. Within the platform each cell contains a magnetic stirrer that can be individually stirred to control the local oscillations of the BZ reaction in that cell, but all the cells are also weakly interconnected through the common medium, and here we used the convolution of their individual oscillations to perform heterotic computations. Moreover, the 3D-printed vessel can be fabricated using different architectures, to for example define how the cells are connected, and thus controlling how the oscillations propagate between them. We took advantage of these features to simulate the ”AND”, ”OR, and ”XOR” logic gates. We also implemented a 2D Cellular Automata. To do so we defined the cells where the BZ reaction oscillates as “on”, and set the transition rule as the propagation of oscillations from the “on” cells towards “off” ones. These results pave the way towards the development of more sophisticated unconventional computers, which might potentially enhance future Artificial Life implementations more effectively than current silicon-based advancements.