Cellularautomata were first described by von Neumann in 1948 (see von Neumann and Burks, 1966). The CA describe the global evolution of a system in space and time based on a predefined set of local rules (transition rules). Cellular au- tomata are able to capture the essential features of complex self-organizing cooperative behaviour observed in real sys- tems (Ilachinski, 2001). The basic premise involved in CA modelling of natural systems is the assumption that any het- erogeneity in the material properties of a physical system is scale dependent and there exists a length scale for any sys- tem at which material properties become homogeneous (Hutt and Neff, 2001). This length scale characterizes the construc- tion of the spatial grid cells (elementary cells) or units of the system. There is no restriction on the shape or size of the cell with the only requirement being internal homogeneity in material properties in each cell. One can then recreate the spatial description of the entire system by simple repetitions of the elementary cells. The local transition rules are results of empirical observations and are not dependant on the scale of homogeneity in space and time. The basic assumption in traditional differential equation solutions is of continuity in space and time. The discretization in models based on tradi- tional numerical methods needs to be over grid spacing much smaller than the smallest length scale of the heterogeneous properties making solutions computationally very expensive. The CA approach is not limited by this requirement and is better suited to simulate spatially large systems at any res- olution, if the homogeneity criteria at elementary cell level are satisfied (Ilachinski, 2001; Parsons and Fonstad, 2007). In fact, in many highly non-linear physical systems such as those describing critical phase transitions in thermodynam- ics and the statistical mechanical theory of ferromagnetism, discrete schemes such as cellularautomata are the only sim- ulation procedures (Hoekstra et al., 2010).
Geospatial data and information availability has been increasing rapidly and has provided users with knowledge on entities change and movement in a system. Cellular Geography model applies CellularAutomata on Geographic data by defining transition rules to the data grid. This paper presents the techniques for extracting transition rule(s) from time series data grids, using multiple linear regression analysis. Clustering technique is applied to minimize the number of transition rules, which can be offered and chosen to change a new unknown grid. Each centroid of a cluster is associated with a transition rule and a grid of data. The chosen transition rule is associated with grid that has a minimum distance to the new data grid to be simulated. Validation of the model can be provided either quantitatively through an error measurement or qualitatively by visualizing the result of the simulation process. The visualization can also be more informative by adding the error information. Increasing number of cluster may give possibility to improve the simulation accuracy.
All cells within the tumor compete for oxygen, reduced organic compounds and space, so cancer can be viewed, from the standpoint of the complex system theory and artificial life disci- plines, as an ecological system in which cells with different mutations compete for survival. The interaction among cells generates an emergent behavior, that is, a behavior present in sys- tems whose elements interact locally, providing a global behavior which cannot be explained by studying the behavior of a single element, but rather the group interactions . CellularAutomata (CA) was the tool most employed in artificial life for studying and characterizing the emergent behavior  . A cellular automaton is defined by a set of rules that establishes the next state of each of the sites of a grid environment given the previous state of this site and the states of its defined neighborhood, where the states can be associated with the cell states in the intended simulations of tumor growth. Thus, although computationally there are different approaches to model cancer growth and the traditional approach was to use differential equa- tions to describe tumor growth , the approaches relying on cellularautomata models or agent-based models facilitate modeling at cellular level, where the state of each cell is described by its local environment.
Quantum Dot cellularAutomata is an outstanding nanotechnology which is used for its better performance than CMOS technology. We describe the basic building block of QCA cells in the previous section. A QCA cell is shown in figure 1. This figure is considered as a square with four dots as its corners. The cell is to consist of two extra electrons which can tunnel between cell dots [1, 15].
Rules are usually named using standard convention. A CA characterized by EXOR and/or EXNOR dependence is called an additive CA . If in a CA the neighbor- hood dependence is EXOR, then it is called a non comple- mented rule. For neighborhood dependence of EXNOR (where there is an inversion of the modulo-2 logic), the CA is called a complemented CA. The corresponding rule involving the EXNOR function is called a comple- mented rule. If in a CA same rule applies to all cells, then the CA is called a uniform CA; otherwise the CA is called a hybrid CA. There can be various boundary con- ditions; namely, null ( where extreme cells are connected to logic ‘0’), periodic ( extreme cells are adjacent ) etc . Nonuniform, or inhomogeneous, cellularautomata func- tion in the same way as uniform ones, the only difference being in the cellular rules that need not be identical for
CellularAutomata (CA) has been used for pseudoran- dom number generation in the past . They are also used to implement random number generators (RNGs) in cryptographic devices  and in Built-In-Self-Test (BIST) circuits. With the increase in the computational capabil- ities of computers, the demand of RNGs have likewise increased  to carry out more sophisticated simulations. Wolfram , in 1986, suggested that CA could be used for eﬃcient hardware implementation of random number generation due to their simplicity and regularity of de- sign.
A novel optical encryption method is proposed in this paper to achieve 3-D image encryption. This proposed encryption algorithm combines the use of computational integral imaging (CII) and linear-complemented maximum- length cellularautomata (LC-MLCA) to encrypt a 3D image. In the encryption process, the 2-D elemental image array (EIA) recorded by light rays of the 3-D image are mapped inversely through the lenslet array according the ray tracing theory. Next, the 2-D EIA is encrypted by LC-MLCA algorithm. When decrypting the encrypted image, the 2-D EIA is recovered by the LC-MLCA. Using the computational integral imaging reconstruction (CIIR) technique and a 3-D object is subsequently reconstructed on the output plane from the 2-D recovered EIA. Because the 2-D EIA is composed of a number of elemental images having their own perspectives of a 3-D image, even if the encrypted image is seriously harmed, the 3-D image can be successfully reconstructed only with partial data. To verify the usefulness of the proposed algorithm, we perform computational experiments and present the experimental results for various attacks. The experiments demonstrate that the proposed encryption method is valid and exhibits strong robustness and security.
CellularAutomata (CA) is also used for deforestation modelling due to its high accuracy in spatial modelling and its compatibility with Geographic Information System . The role of CA modelling especially in land use simulation in recent decades can not be ignored (Li and Yeh 2000, White and Engelen 1993, Wu and Webster,1998, Wu 1998b, White et al. 2000, Soares-Filho, 2002). This model also, has been widely applied in urban development simulation (Wolfram, 1984, White and Engelen, 1993, Clarke et al., 1997, Batty et al., 1999, Almeida, 2008, Alimohammadi et al., 2010)
Quantum-Dot CellularAutomata (QCA) is among the promising emerging nan- otechnologies that aim to solve the challenges faced by CMOS. The QCA operation principle takes advantage of the quantum mechanical phenomena to transport the infor- mation and perform logic operations without electric current ﬂow, which implies in a low power consumption (LENT et al., 1993). A very high packing density may be achieved, since each cell is in the range of a few nanometers. However, QCA has to overcome several challenges before its consolidation (SAHNI, 2008). Undoubtedly, the most worrisome one is the extremely diﬃcult physical implementation. High-resolution lithography techniques has been developed in order to eventually enable the fabrication of molecular QCA (HU et al., 2005). Prototypes of Metal-Island QCA and NML (Nanomagnetic Logic) devices have been successfully implemented as reported in (TóTH; LENT, 1999) and in (ALAM, 2010). However, none of the QCA realizations surpassed the performance of their CMOS counterparts so far.
In Section 2 we give a description of the 2D FSSP and review some basic results on 2D FSSP algo- rithms. Section 3 defines the recursive-halving marking on 1D arrays and gives some preliminary lemmas for the construction of 2D FSSP algorithms. In Sections 4, 5, and 6 we present a new 2D FSSP algorithm based on the recursive-halving marking and several multi-dimensional expansions. Two implementations in terms of 2D cellularautomata are also presented for the optimum-time FSSP algorithms. Most of the descriptions of the multi-dimensional FSSP algorithms are based on the 2D FSSP algorithms. Some expanded and generalized theorems for multi-dimensional arrays are given without proofs.
In the following, it seems hierarchical CellularAutomata is an appropriate structure for designing these types of algorithms, which can provide a better view of the whole conditions of the Grid System. In addition, the usage of Fuzzy Logic which leads to accuracy of decision-making in uncertain environments can be used to improve the efficiency of parallel algorithms. The combination of Fuzzy Logic and CellularAutomata can be a good technique for a lot of parallel algorithms.
Using a very simple cellularautomata model of the immune repertoire dynamics we show that, although the usual regimes (stable and chaotic) attained by this automata, are not interesting from the biological point of view, the transition region, at the edge of chaos, is very appropriate to describe such dynamics. In this region we have obtained a functional connected network involving 10–20% of the lymphocytes available in the repertoire, as suggested by Jerne and others. The model also reproduces the immune system signature, the ensemble of different lymphocytes that each individual expresses in his immune repertoire, which varies from one individual to another. We show how the immune memory comes out as a consequence of the dynamics of the system. From our results we confirm and present evidence that the chaotic regime corresponds to a sort of non-healthy state, as has been suggested previously.
different model types might be chosen, again relating to further constraints on model complexity/development such as budget/time: (1) if there are many constraints at this point the suggestion is the use of dispersal kernels or cellularautomata – which sim- plify the known complexity of the dispersal events and mechanisms, or (2) if there are few constraints then a mechanistic approach may be taken such as individual-based modelling, gaussian plumes or trajectory models, all of which can better represent the complexity of the dispersal mechanisms. The other option for seasonal pest forecast- ing, if the first constraint cannot be met (i.e. the modeller is required to assume highly simplified behaviour such as limited dispersal pathways within defined areas), then the modeller can make the assumption of a more limited mode of dispersal that allows for such constraints. This leads to a different approach where the preferred option (if there are further constraints relating to e.g. model development time and budget) would be potential distribution models; however if a more dynamic approach is feasible by fewer constraints at this point (e.g. as there is good data availability about movement pathways) then network models/metapopulation models may be more appropriate.
The Prisoner’s Dilemma (PD) is one of the most popular games of the Game Theory due to the emergence of cooperation among competitive rational players. In this paper, we present the PD played in cells of one- dimension cellularautomata, where the number of possible neighbors that each cell interacts, z, can vary. This makes possible to retrieve results obtained previously in regular lattices. Exhaustive exploration of the parame- ters space is presented. We show that the ﬁnal state of the system is governed mainly by the number of neighbors z and there is a drastic difference if it is even or odd.
This motivation has led to the use of cellu- lar automata as a technique for simulation of urban and regional growth. Cellularautomata (CA) are very simple dynamic spatial systems in which the state of each cell in an array de- pends on the previous state of the cells within a neighborhood of the cell, according to a set of transition rules. CA are very efficient com- putationally because they are discrete, iterative systems that involve interactions only within local regions rather than between all pairs of cells. The good spatial resolution that can thus be attained is an important advantage when modeling land use dynamics, especially for planning and policy applications (White & En- gelen, 1997).
The development of conventional, silicon-based computers has several limitations, including some related to the Heisenberg uncertainty principle and the von Neumann “bottleneck”. Biomolecular computers based on DNA and proteins are largely free of these disadvantages and, along with quantum computers, are reasonable alternatives to their conventional counterparts in some applications. The idea of a DNA computer proposed by Ehud Shapiro’s group at the Weizmann Institute of Science was developed using one restriction enzyme as hardware and DNA frag- ments (the transition molecules) as software and input/output signals. This computer represented a two-state two-symbol finite automaton that was subsequently extended by using two restriction enzymes. In this paper, we pro- pose the idea of a multistate biomolecular computer with multiple commercially available restriction enzymes as hardware. Additionally, an algorithmic method for the construction of transition molecules in the DNA computer based on the use of multiple restriction enzymes is presented. We use this method to construct multistate, biomolecular, nondeterministic finite automata with four commercially available restriction enzymes as hardware. We also describe an experimental applicaton of this theoretical model to a biomolecular finite automaton made of four endonucleases.
Typically, non-degenerated uterine leiomyomas appear on MR imaging as well-circumscribed masses of homogeneously decreased signal intensity compared to that in the outer myometrium on T2-weighted images and of intermediate signal on T1-weighted images. Cellular leiomyomas, which are composed of compact smooth muscle cells with little or no collagen, can have relatively higher intensity signal on T2-weighted images and demonstrate enhancement on contrast enhanced images .
Eight well studied and documented changes in cellular physiology are considered hallmarks of all types of cancer: self- sufficiency in growth signals (proliferation without external stimuli); insensitivity to growth-inhibitory signals (lack of response to molecules that inhibit cell proliferation by inactivation of tumor suppressor genes); altered cell metabolism (metabolic conversion to anaerobic glycolysis); evasion of apoptosis (resistance to programmed cell death); unlimited replication potential (protection against cell senescence and mitotic catastrophe); induction of angiogenesis; tissue invasion and metastasis (malignancy, involves degradation of the interstitial matrix mediated by proteolytic enzymes, such as metalloproteinases and cathepsins); and evasion of the immune response (4) .