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Mechanical forces are obviously important in the assembly of three-dimensional multicellular structures, but their detailed role is often unclear. We have used growing microcolonies of the bacterium \emph{Escherichia coli} to investigate the role of mechanical forces in the transition from two-dimensional growth (on t... |
The immune system protects the body against health-threatening entities, known as antigens, through very complex interactions involving the antigens and the system's own entities. One remarkable feature resulting from such interactions is the immune system's ability to improve its capability to fight antigens ... |
Tip growth in filamentous cells, such as root hairs, moss protonemata, and fungal hyphae, depends on coordinated cell wall extension driven by turgor pressure, wall mechanics, and exocytosis. We introduce a dual-configuration model that incorporates both turgid and unturgid states to describe cell wall growth as the c... |
Viral kinetics have been extensively studied in the past through the use of spatially well-mixed ordinary differential equations describing the time evolution of the diseased state. However, emerging spatial structures such as localized populations of dead cells might adversely affect the spread of infection, similar ... |
All life, including cells and artificial protocells, must integrate diverse molecules into a single unit in order to reproduce. Despite expected pressure to evolve a simple system with the fastest replication speed, the mechanism by which the use of the great variety of components, and the coexistence of diverse cell-... |
Cellular biology exists embedded in a world dominated by random dynamics and chance. Many vital molecules and pieces of cellular machinery diffuse within cells, moving along random trajectories as they collide with the other biomolecular inhabitants of the cell. |
A big challenge in current biology is to understand the exact self-organization mechanism underlying complex multi-physics coupling developmental processes. With multiscale computations of from subcellular gene expressions to cell population dynamics that is based on first principles, we show that cell cycles can self... |
The binding affinity between the T-cell receptors (TCRs) and antigenic peptides mainly determines immunological recognition. It is not a trivial task that T cells identify the digital sequences of peptide amino acids by simply relying on the integrated binding affinity between TCRs and antigenic peptides. |
This paper proposes an original theory of aging of multicellular organisms. The cells of multicellular organisms, in contrast to unicellular organisms, are burdened with a two- part genome: housekeeping and specialized (multicellular), responsible for ontogenesis and terminal differentiation. |
The behaviour of an organism often reflects a strategy for coping with its environment. Such behaviour in higher organisms can often be reduced to a few stereotyped modes of movement due to physiological limitations, but finding such modes in amoeboid cells is more difficult as they lack these constraints. |
Many complex systems obey allometric, or power, laws y=Yx^{a}. Here y is the measured value of some system attribute a, Y is a constant, and x is a stochastic variable. |
Wound healing assays are commonly used to study how populations of cells, initialised on a two-dimensional surface, act to close an artificial wound space. While real wounds have different shapes, standard wound healing assays often deal with just one simple wound shape, and it is unclear whether varying the wound sha... |
Angiogenesis, the development of new vasculature, is a critical process in the growth of new tumors. Driven by a goal to understand this aspect of cancer proliferation, I develop a discrete computationally optimized mathematical model of angiogenesis that specializes in intercellular interactions. |
Sperm cooperation has evolved in a variety of taxa and is often considered a response to sperm competition, yet the benefit of this form of collective movement remains unclear. Here we use fine-scale imaging and a minimal mathematical model to study sperm aggregation in the rodent genus $Peromyscus$. |
"Secrete-and-sense cells" can communicate by secreting a signaling molecule while also producing a receptor that detects the molecule. The cell can potentially "talk" to itself ("self-communication") or talk to neighboring cells with the same receptor ("neighbor-communication"). |
DNA replication in Xenopus laevis is extremely reliable, failing to complete before cell division no more than once in 10,000 times; yet replication origins sites are located and initiated stochastically. Using a model based on 1d theories of nucleation and growth and using concepts from extreme-value statistics, we d... |
We present a modelling framework for the dynamics of cells structured by the concentration of a micromolecule they contain. We derive general equations for the evolution of the cell population and of the extra-cellular concentration of the molecule and apply this approach to models of silicosis, quorum sensing in Gram... |
A multiscale model for glioma spread in brain tissue under the influence of vascularization and vascular endothelial growth factors is proposed. It accounts for the interplay between the different components of the neoplasm and the healthy tissue and it investigates and compares various therapy approaches. |
We propose a physical model for developmental process at cellular level to discuss the mechanism of epigenetic landscape. In our simplified model, a minimal model, the network of the interaction among cells generates the landscape epigenetically and the differentiation in developmental process is understood as a self-... |
Unstable angina is common clinical manifestation of atherosclerosis. However, the detailed pathogenesis of unstable angina is still not known. |
To understand cell migration, it is crucial to gain knowledge on how cells exert and integrate forces on/from their environment. A quantity of prime interest for biophysicists interested in cell movements modeling is the intracellular stresses. |
The proliferation and migration dichotomy of the tumor cell invasion is examined within a two-component continuous time random walk (CTRW) model. The balance equations for the cancer cells of two phenotypes with random switching between cell proliferation and migration are derived. |
We derive the main properties of adaptive Hagen-Poiseuille flows in elastic microchannel networks similar to biological veins found in organisms. We demonstrate that adaptive Hagen-Poiseuille flows effectively simulate key features of \textit{Physarum polycephalum} networks, replicating physiological out-of-equilibriu... |
The shoot apical meristem (SAM) is a dome-shaped collection of cells at the apex of growing plants from which all above-ground tissue ultimately derives. In Arabidopsis thaliana (thale cress), a small flowering weed of the Brassicaceae family (related to mustard and cabbage), the SAM typically contains some three to f... |
The purpose of the present study is to evaluate changes in chromatin of human buccal epithelium under the influence of stressing factor - dosed physical activity. Investigations were performed in a group of students (13 men) of age 19-23. |
A reaction-diffusion model of receptor-toxin-antibody (RTA) interaction is studied numerically. The protective properties of an antibody against a given toxin are evaluated for a spherical cell placed into a toxin-antibody solution. |
Guided movement in response to slowly diffusing polymeric trails provides a unique mechanism for self-organization of some microorganisms. To elucidate how this signaling route leads to microcolony formation, we experimentally probe the trajectory and orientation of Pseudomonas aeruginosa that propel themselves on a s... |
Despite simplicity, the synchronous cellular automaton [D.A. Young, Math. Biosci. 72, 51 (1984)] enables reconstructing basic features of patterns of skin. Our extended model allows studying the formatting of patterns and their temporal evolution also on the favourable and hostile environments. |
The different cell types in a living organism acquire their identity through the process of cell differentiation in which the multipotent progenitor cells differentiate into distinct cell types. Experimental evidence and analysis of large-scale microarray data establish the key role played by a two-gene motif in cell ... |
A novel trait-structured Keller-Segel model that explores the dynamics of a migrating cell population guided by chemotaxis in response to an external ligand concentration is derived and analysed. Unlike traditional Keller-Segel models, this framework introduces an explicit representation of ligand-receptor bindings on... |
Collective sensing by interacting cells is observed in a variety of biological systems, and yet a quantitative understanding of how sensory information is collectively encoded is lacking. Here we investigate the ATP-induced calcium dynamics of monolayers of fibroblast cells that communicate via gap junctions. |
Bismuth Ferrite (BFO) nanoparticles (BFO-NP) display interesting optical (nonlinear response) and magnetic properties which make them amenable for bio-oriented applications as intra- and extra membrane contrast agents. Due to the relatively recent availability of this material in well dispersed nanometric form, its bi... |
During angiogenesis, new blood vessels headed by a migrating endothelial tip cell sprout from pre-existing ones. This process is known to be regulated by two signaling pathways concurrently, vascular endothelial growth factor A (VEGFA) and Notch-Delta. |
Cell spheroids are a widely used model to investigate cell-cell and cell-matrix interactions in a 3D microenvironment in vitro. Most research on cell spheroids has been focused on their response to various stimuli under static conditions. |
Cell migration is essential for regulating many biological processes in physiological or pathological conditions, including embryonic development and cancer invasion. In vitro and in silico studies suggest that collective cell migration is associated with some biomechanical particularities, such as restructuring of ex... |
Recently experiments showed that some adhesive receptor-ligand complexes increase their lifetimes when they are stretched by mechanical force, while the force increase beyond some thresholds their lifetimes decrease. Several specific chemical kinetic models have been developed to explain the intriguing transitions fro... |
The emergence of complex behaviors in cellular automata is an area that has been widely developed in recent years with the intention to generate and analyze automata that produce space-moving patterns or gliders that interact in a periodic background. Frequently, this type of automata has been found through either an ... |
We develop a lattice Boltzmann equation method for simulating multi-phase immiscible fluid flows with variation of density and viscosity, based on the model proposed by Gunstensen {\em et al} for two-component immiscible fluids. The numerical measurements of surface tension and viscosity agree well with theoretical pr... |
Reversible lattice dynamics embody basic features of physics that govern the time evolution of classical information. They have finite resolution in space and time, don't allow information to be erased, and easily accommodate other structural properties of microscopic physics, such as finite distinct state and loc... |
Cellular Automaton (CA) and an Integral Value Transformation (IVT) are two well established mathematical models which evolve in discrete time steps. Theoretically, studies on CA suggest that CA is capable of producing a great variety of evolution patterns. |
Larger than Life cellular automaton (LtL) is a class of cellular automata and is a generalization of the game of Life by extending its neighborhood radius. We have studied the three-dimensional extension of LtL. |
An exact characterization of the different dynamical behavior that exhibit the space phase of a reversible and conservative cellular automaton, the so called Q2R model, is shown in this paper. Q2R is a cellular automaton which is a dynamical variation of the Ising model in statistical physics and whose space of config... |
Reactive lattice gas automata provide a microscopic approachto the dynamics of spatially-distributed reacting systems. After introducing the subject within the wider framework of lattice gas automata (LGA) as a microscopic approach to the phenomenology of macroscopic systems, we describe the reactive LGA in terms of a... |
This paper examines the claim that cellular automata (CA) belonging to Class III (in Wolfram's classification) are capable of (Turing universal) computation. We explore some chaotic CA (believed to belong to Class III) reported over the course of the CA history, that may be candidates for universal computation, he... |
A general method for testing nonlinearity in time series is described and applied to measurements of different pressure data inside the draft tube surge of a real Francis turbine. Comparing the current original time series to an ensemble of surrogates time series, suitably constructed to mimic the linear properties of... |
We perform a Koopman spectral analysis of elementary cellular automata (ECA). By lifting the system dynamics using a one-hot representation of the system state, we derive a matrix representation of the Koopman operator as a transpose of the adjacency matrix of the state-transition network. |
From the striped coats of zebras to the ripples in windblown sand, the natural world abounds with locally banded patterns. Such patterns have been of great interest throughout history, and, in the last twenty years, scientists in a wide variety of fields have been studying the patterns formed in well-controlled experi... |
We demonstrate the advantages of feedforward loops using a Boolean network, which is one of the discrete dynamical models for transcriptional regulatory networks. After comparing the dynamical behaviors of network embedded feedback and feedforward loops, we found that feedforward loops can provide higher temporal orde... |
A kinetic flux-splitting procedure used in conjunction with local thermodynamic equilibrium in a finite volume allows us to investigate numerically discrete-velocity gas flows. The procedure, outlined for a general discrete-velocity gas, is used to simulate flows of the nine-velocity gas, a simple two dimensional mult... |
In 2005, Nagler and Claussen (Phys. Rev. E 71 (2005) 067103) investigated the time series of the elementary cellular automata (ECA) for possible (multi)fractal behavior. |
We present a rigorous derivation of the flow at arbitrary time in a deterministic cellular automaton model of traffic flow. The derivation employs regularities in preimages of blocks of zeros, reducing the problem of preimage enumeration to a well known lattice path counting problem. |
An exact solution for a high speed deterministic traffic model with open boundaries and synchronous update rule is presented. Because of the strong correlations in the model, the qualitative structure of the stationary state can be described for general values of the maximum speed. |
We compare several definitions for number-conserving cellular automata that we prove to be equivalent. A necessary and sufficient condition for \cas to be number-conserving is proved. |
Recent work with Lenia, a continuously-valued cellular automata (CA) framework, has yielded $\sim$100s of compelling, bioreminiscent and mobile patterns. Lenia can be viewed as a continuously-valued generalization of the Game of Life, a seminal cellular automaton developed by John Conway that exhibits complex and univ... |
A hybrid approach, incorporating concepts of nonlinear dynamics in artificial neural networks (ANN), is proposed to model time series generated by complex dynamic systems. We introduce well known features used in the study of dynamic systems - time delay $\tau$ and embedding dimension $d$ - for ANN modelling of time s... |
Cellular automata can simulate many complex physical phenomena using the power of simple rules. The presented methodological platform expresses the concept of programmable matter in which Newtons laws of motion are one of examples. |
John H. Conway's Game of Life, as well as cellular automata in the larger family of Life-like CA, are discrete: the cells have a binary state space and the birth and survival transition rules are 9-bits apiece. Inspired by Life, several projects have developed continuously-valued cellular automata frameworks in 2 ... |
Controllability is one of the central concepts of modern control theory that allows a good understanding of a system's behaviour. It consists in constraining a system to reach the desired state from an initial state within a given time interval. |
The problem `human and work' in a model working group is investigated by means of cellular automata technique. Attitude of members of a group towards work is measured by an indicator of loyalty to the group (the number of agents who carry out their tasks), and lack of loyalty (the number of agents, who give their ... |
We study the classification of cellular-automaton update rules into Wolfram's four classes. We start with the notion of the input entropy of a spatiotemporal block in the evolution of a cellular automaton, and build on it by introducing two novel entropy measures, one that is also based on inputs to the cells, the... |
Cellular automata have been useful artificial models for exploring how relatively simple rules combined with spatial memory can give rise to complex emergent patterns. Moreover, studying the dynamics of how rules emerge under artificial selection for function has recently become a powerful tool for understanding how e... |
We introduce our GraftalLace Cellular Automaton in short GLCA which is a new one-dimensional cellular automaton on the regular square lattice. It makes a monochromatic infinite directed graph otherwise an octal number triangle or number trapezoid by partly influences the states of the neighbour cells with bit operatio... |
Emergent processes in complex systems such as cellular automata can perform computations of increasing complexity, and could possibly lead to artificial evolution. Such a feat would require scaling up current simulation sizes to allow for enough computational capacity. |
We study a modified version of the stochastic susceptible-infected-refractory-susceptible (SIRS) model by employing a nonlinear (exponential) reinforcement in the contagion rate and no diffusion. We run simulations for complete and random graphs as well as d-dimensional hypercubic lattices (for d=3,2,1). |
Four different kinds of laminar flows between two parallel plates are investigated using the Lattice Boltzmann Method (LBM). The LBM accuracy is estimated in two cases using numerical fits of the parabolic velocity profiles and the kinetic energy decay curves, respectively. |
In this paper, we come back on the notion of local simulation allowing to transform a cellular automaton into a closely related one with different local encoding of information. This notion is used to explore solutions of the Firing Squad Synchronization Problem that are minimal both in time (2n -- 2 for n cells) and,... |
Based on complex network theory, we propose a computational methodology that addresses the spatial distribution of fuel breaks for the inhibition of the spread and size of wildland fires on heterogeneous landscapes. This is a two-tire approach where the dynamics of fire spread are modeled as a random Markov field proc... |
The physical behaviour of a class of mesoscopic models for multiphase flows is analyzed in details near interfaces. In particular, an extended pseudo-potential method is developed, which permits to tune the equation of state and surface tension independently of each other. |
Inspired by the approach of kinetic theory of gases, a three-level description (microscopic, mesoscopic and macroscopic) of cellular automaton is presented. To provide an analytical treatment a simple domino cellular automaton with avalanches was constructed. |
We investigate the totally asymmetric simple exclusion process (TASEP) in the presence of a bottleneck, i.e. a sequence of consecutive defect sites with reduced hopping rate. The influence of such a bottleneck on the phase diagram is studied by computer simulations and a novel analytical approach. |
We analyze global stability properties of birhythmicity in a self-sustained system with random excitations. The model is a multi-limit cycles variation of the van der Pol oscillatorintroduced to analyze enzymatic substrate reactions in brain waves. |
Periodic orbit theory allows calculations of long time properties of chaotic systems from traces, dynamical zeta functions and spectral determinants of deterministic evolution operators, which are in turn evaluated in terms of periodic orbits. For the case of stochastic dynamics a direct numerical evaluation of the tr... |
We present a characterization of short-term stability of random Boolean networks under \emph{arbitrary} distributions of transfer functions. Given any distribution of transfer functions for a random Boolean network, we present a formula that decides whether short-term chaos (damage spreading) will happen. |
Mean value and cross-covariance function of chaotic binary sequences are evaluated for chaotic maps with specific properties. We also take into account the effect of fixed- and floating-point representations on statistical properties of chaotic generators. |
High implementation complexity of multi-scroll circuit is a bottleneck problem in real chaos-based communication. Especially, in multi-scroll Chua's circuit, the simplified implementation of piecewise-linear resistors with multiple segments is difficult due to their intricate irregular breakpoints and slopes. |
We suggest a "minimal model" for the 3D turbulent energy spectra in superfluids, based on their two-fluid description. We start from the Navier-Stokes equation for the normal fluid and from the coarse-grained hydrodynamic equation for the superfluid component (obtained from the Euler equation for the superflui... |
This article describes a numerical procedure designed to tune the parameters of periodically-driven dynamical systems to a state in which they exhibit rich dynamical behavior. This is achieved by maximizing the diversity of subharmonic solutions available to the system within a range of the parameters that define the ... |
Homogeneous shear flows (with constant strainrate du/dy) are generated with the Doll's and Sllod algorithms and compared to corresponding inhomogeneous boundary-driven flows. We use one-, two-, and three-dimensional smooth-particle weight functions for computing instantaneous spatial averages. |
Dynamical systems, whether continuous or discrete, are used by physicists in order to study non-linear phenomena. In the case of discrete dynamical systems, one of the most used is the quadratic map depending on a parameter. |
We scrutinize the reliability of covariant and Gram-Schmidt Lyapunov vectors for capturing hydrodynamic Lyapunov modes (HLMs) in one-dimensional Hamiltonian lattices. We show that,in contrast with previous claims, HLMs do exist for any energy density, so that strong chaos is not essential for the appearance of genuine... |
The literature is rich with studies, analyses, and examples on parameter estimation for describing the evolution of chaotic dynamical systems based on measurements, even when only partial information is available through observations. <br>However, parameter estimation alone does not resolve prediction challenges, part... |
We study the effect of homogeneous noise on the escape rate of strongly chaotic area-preserving maps with a small opening. While in the noiseless dynamics the escape rate analytically depends on the instability of the shortest periodic orbit inside the hole, adding noise overall enhances escape, which, however, exhibi... |
Classical, self-consistent theory of statistical mechanics was developed for the thermodynamic and conservative Hamiltonian systems. Later there were many attempts (Sinai-Bowen-Ruelle's temperature, Tsallis' non-extensive theory) to apply similar formalism to non-Hamiltonian dynamical systems. |
This paper is devoted to the problem of synchronization between fractional-order chaotic systems with Gaussian fluctuation by the method of fractional-order sliding mode control. A fractional integral (FI) sliding surface is proposed for synchronizing the uncertain fractional-order system, and then the sliding mode co... |
The basins of convergence, associated with the roots (attractors) of a complex equation, are revealed in the Hill problem with oblateness and radiation, using a large variety of numerical methods. Three cases are investigated, regarding the values of the oblateness and radiation. |
We study the asymptotic long-time behavior of open quantum maps and relate the decays to the eigenvalues of a coarse-grained superoperator. In specific ranges of coarse graining, and for chaotic maps, these decay rates are given by the Ruelle-Pollicott resonances of the classical map. |
A shell model can be considered as a chain of triads, where each triad can be interpreted as a nonlinear oscillator that can be mapped to a spinning top. Investigating the relation between phase dynamics and intermittency in a such a chain of nonlinear oscillators, it is found that synchronization is linked to increas... |
We describe ideal incompressible hydrodynamics on the hyperbolic plane which is an infinite surface of constant negative curvature. We derive equations of motion, general symmetries and conservation laws, and then consider turbulence with the energy density linearly increasing with time due to action of small-scale fo... |
In this work we introduce a deterministic scheme of synchronization of linear and nonlinear cellular automata (CA) with complex behavior, connected through a master-slave coupling. By using a definition of Boolean derivative, we use the linear approximation of the automata to determine a function of coupling that prom... |
The mechanism of synchronization of oscillations in two identical coupled flow systems has beenstudied. The time (past the coupling onset) during which a synchronous oscillation regime is establisheddepends on the oscillation phase difference between the subsystems. |
The mechanism of synchronization in the random Zaslavsky map is investigated. <br>From the error dynamics of two particles, the structure of phase space was analyzed, and a transcritical bifurcation between a saddle and a stable fixed point was found. |
While extensive research has been conducted on chaos emerging from a dynamical system's temporal dynamics, our research examines extreme sensitivity to initial conditions in discrete-time dynamical systems from a geometrical perspective. Specifically, we develop methods of detecting, classifying, and quantifying g... |
We present experimental results on statistics of polymer orientation angles relatively to shear plane and tumbling times in shear flow with thermal noise. Strong deviation of probability distribution functions (PDF) of these parameters from Gaussian was observed and a good accord with theory was found. |
We consider a perturbation of the Anosov-type system, which leads to the appearance of a hierarchical set of islands-around-islands. We demonstrate by simulation that the boundaries of the islands are sticky to trajectories. |
Experiments are carried out with a globally coupled, externally forced population of limit-cycle electrochemical oscillators with an approximately unimodal distribution of heterogeneities. Global coupling induces mutually entrained (at frequency $\omega_{1}$) states; periodic forcing produces forced-entrained ($\omega... |
We present a calculation of defect--defect correlation functions in the defect turbulence regime of the complex Ginzburg--Landau equation. Our results do not agree with the predictions of generic scale invariance. |
We investigate the high dimensional Hamiltonian chaotic dynamics in $N$ coupled area-preserving maps. We show the existence of an enhanced trapping regime caused by trajectories performing a random walk {\em inside} the area corresponding to regular islands of the uncoupled maps. |
We reduce the dynamics of an ensemble of mean-coupled Stuart-Landau oscillators close to the synchronized solution. In particular, we map the system onto the center manifold of the Benjamin-Feir instability, the bifurcation destabilizing the synchronized oscillation. |
Computing with networks of synchronous oscillators has attracted wide-spread attention as novel materials and device topologies have enabled realization of compact, scalable and low-power coupled oscillatory systems. Of particular interest are compact and low-power relaxation oscillators that have been recently demons... |
We introduce the reader to the "global flow reconstruction method". The purpose of the method is to see if a given temporal sequence has been generated by a low dimensional dynamics, and to determine that dimension and other properties of the dynamics. |
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