Synthesis of one-dimensional binary scope-2 flexible cellular systems from initial final configuration pairs

A complete classification of the computational complexity of the fixed-point existence problem for Boolean dynamical systems, i.e., finite discrete dynamical systems over the domain {0, 1}, is presented. For function classes $${\mathcal{F}}$$ and graph classes $${\mathcal{G}}$$ , an ( $${\mathcal{F}},{\mathcal{G}}$$ )-system is a Boolean dynamical system such that all local transition functions lie in $${\mathcal{F}}$$ and the underlying graph lies in $${\mathcal{G}}$$ . Let $${\mathcal{F}}$$ be a class of Boolean functions which is closed under composition and let $${\mathcal{G}}$$ be a class of graphs which is closed under taking minors. The following dichotomy theorems are shown: (1) If $${\mathcal{F}}$$ contains the self-dual functions and $${\mathcal{G}}$$ contains the planar graphs, then the fixed-point existence problem for ( $${\mathcal{F}},{\mathcal{G}}$$ )-systems with local transition function given by truth-tables is NP-complete; otherwise, it is decidable in polynomial time. (2) If $${\mathcal{F}}$$ contains the self-dual functions and $${\mathcal{G}}$$ contains the graphs having vertex covers of size one, then the fixed-point existence problem for ( $${\mathcal{F}},{\mathcal{G}}$$ )-systems with local transition function given by formulas or circuits is NP-complete; otherwise, it is decidable in polynomial time.

We consider the problem of inferring the local transition functions of discrete dynamical systems from observed behavior. Our focus is on synchronous systems whose local transition functions are threshold functions. We assume that the topology of the system is known and that the goal is to infer a threshold value for each node so that the system produces the observed behavior. We show that some of these inference problems are efficiently solvable while others are NP-complete, even when the underlying graph of the dynamical system is a simple path. We also identify a fixed parameter tractable problem in this context.

A number-conserving cellular automaton (NCCA) is a cellular automaton whose states are integers and whose transition function keeps the sum of all cells constant throughout its evolution. It can be seen as a kind of modeling of the physical conservation laws of mass or energy. In this paper we show a construction method of radius 1/2 NCCAs. The local transition function is expressed via a single unary function which can be regarded as 'flows' of numbers. In spite of the strong constraint, we constructed radius 1/2 NCCAs that simulate any radius 1/2 cellular automata or any radius 1 NCCA. We also consider the state complexity of these non-splitting simulations (4n2 + 2n + 1 and 8n2 + 12n - 16, respectively). These results also imply existence of an intrinsically universal radius 1/2 NCCA.

A property of superposability is defined here for Treillis Automata as an equivalent of the linearity property of Cellular Automata. We take advantage of the binary local transition function of TAs, which enables us to use an infix notation for it, to study this property in an algebraic framework. We show that a TA is superposable iff its local transition function operates on its set of states as a commutative monoid law and that the general case of commutative monoids is reducible to the case of Abelian groups in which the space-time diagrams obtained are isomorphic to a superposition of figures representing the triangle of binomial coefficients (Pascal's triangle) modulo integers.KeywordsCellular AutomatonInitial ConfigurationNeutral ElementBinomial CoefficientCommutative MonoidThese 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.

Inverse rules of ECA with rule number 150

We study a simple triangular partitioned cellular automaton (TPCA), and clarify its complex behavior. It is a CA with triangular cells, each of which is divided into three parts. The next state of a cell is determined by the three adjacent parts of its neighbor cells. This framework makes it easy to design reversible triangular CAs. Among them, isotropic and eight-state (i.e., each part has only two states) TPCAs are called elementary TPCAs (ETPCAs). They are extremely simple, since each of their local transition functions is described by only four local rules. In this paper, we investigate a specific reversible ETPCA $$T_{0347}$$ , where 0347 is its identification number in the class of 256 ETPCAs. In spite of the simplicity of the local function and the constraint of reversibility, evolutions of configurations in $$T_{0347}$$ have very rich varieties. It is shown that a glider, which is a space-moving pattern, and glider guns exist in this cellular space We also show that the trajectory and the timing of a glider can be fully controlled by appropriately placing stable patterns called blocks. Furthermore, using gliders to represent signals, we can implement universal reversible logic gates in it. By this, computational universality of $$T_{0347}$$ is derived.

In this paper, we formalize precisely the sense in which the application of a cellular automaton to partial configurations is a natural extension of its local transition function through the categorical notion of Kan extension. In fact, the two possible ways to do such an extension and the ingredients involved in their definition are related through Kan extensions in many ways. These relations provide additional links between computer science and category theory, and also give a new point of view on the famous Curtis–Hedlund theorem of cellular automata from the extended topological point of view provided by category theory. These links also allow to relatively easily generalize concepts pioneered by cellular automata to arbitrary kinds of possibly evolving spaces. No prior knowledge of category theory is assumed for the most part.

One of the major design, considerations in a cellular mobile radio system is the reduction of co-channel interference. A technique known as microzoning can reduce interference while maintaining system capacity and quality of service. Based on the worst-case mobile location at the edge of a microzone, narrowband, frequency-division multiple access cellular systems require seven-cell per cluster architectures in order to maintain a signal-to-noise ratio of 18 dB. This is contrary to the conclusion drawn from previously published work: that three-cell per cluster systems are sufficient. A three-cell per cluster architecture can maintain a signal-to-noise ratio of 15 dB.

The relay-assisted Orthogonal Frequency-Division Multiple Access (OFDMA) cellular system is one of the most promising technology thanks to the enhancements of the system capacity and coverage it provides. However, some special features may lower its positive aspects. In multiple relay case, the asymmetric link problem in the two stages forming the relaying process may result in important resource wastage. Such resource wastage can even be more serious than in the case where only a single relay is used in the system. Only few works consider this resource wastage problem. In this paper, we first define a new term, channel holes, to denote the potential resource wastage in single and multiple relay systems. Then based on this new concept, we propose a novel resource management scheme for multiple relay systems, i.e. channel-hole based cooperative scheduling in multiple relay systems. In order to evaluate the performances of such resource management schemes, we build a system model and propose the corresponding analytical derivation, which helps analyzing the average queue length and the average packet delay. Simulations are used to validate and reinforce our theoretical analysis. Then using simulations, we compare our proposed scheduling algorithm to other algorithms from the literature. Hence, we show that our proposed algorithm performs better than others. In addition we also observe that our proposed scheduling algorithm performs a resource-aware relay selection that is more efficient than the one obtained using the ideal relay selection scheme.

The bilayer lipid membrane (BLM) is a naturally occurring thin layer of phospholipid molecules that surrounds cellular systems. The membrane operates as a near-impermeable barrier allowing for the generation of membrane potentials across the layer through changes in ionic concentrations. This membrane is required for regular cell function ranging from storing energy to passing signals. Engineering advancements have allowed for the rapid creation of artificial bilayer membranes, and these membranes are currently considered for many biomimetic applications. The application of interest for this paper is the further development of these cellular systems for sensing applications. This will be accomplished through a combined fluid-bilayer model, allowing for study of the bilayer transduction properties at both high and low frequencies. Several approaches are discussed and applied to multiple cell systems with or without embedded voltage-dependent ion pores. Finally the results are studied and evidence is presented for the development of a new molecular model for cellular systems combining chemical, electrical, and mechanical stimuli.

BackgroundThe opportunistic pathogen Naegleria fowleri establishes infection in the human brain, killing almost invariably within 2 weeks. The amoeba performs piece-meal ingestion, or trogocytosis, of brain material causing direct tissue damage and massive inflammation. The cellular basis distinguishing N. fowleri from other Naegleria species, which are all non-pathogenic, is not known. Yet, with the geographic range of N. fowleri advancing, potentially due to climate change, understanding how this pathogen invades and kills is both important and timely.ResultsHere, we report an -omics approach to understanding N. fowleri biology and infection at the system level. We sequenced two new strains of N. fowleri and performed a transcriptomic analysis of low- versus high-pathogenicity N. fowleri cultured in a mouse infection model. Comparative analysis provides an in-depth assessment of encoded protein complement between strains, finding high conservation. Molecular evolutionary analyses of multiple diverse cellular systems demonstrate that the N. fowleri genome encodes a similarly complete cellular repertoire to that found in free-living N. gruberi. From transcriptomics, neither stress responses nor traits conferred from lateral gene transfer are suggested as critical for pathogenicity. By contrast, cellular systems such as proteases, lysosomal machinery, and motility, together with metabolic reprogramming and novel N. fowleri proteins, are all implicated in facilitating pathogenicity within the host. Upregulation in mouse-passaged N. fowleri of genes associated with glutamate metabolism and ammonia transport suggests adaptation to available carbon sources in the central nervous system.ConclusionsIn-depth analysis of Naegleria genomes and transcriptomes provides a model of cellular systems involved in opportunistic pathogenicity, uncovering new angles to understanding the biology of a rare but highly fatal pathogen.

Deployment of relay nodes (RNs) in cellular orthogonal frequency division multiple access (OFDMA) systems provides an effective solution to increase high data rate coverage and improve cell throughput. However, a challenging issue is that additional interferences caused by RNs may substantially compromise the performance gain if no measure is taken. In this study, the authors address the problem of interference coordination in relay-aided cellular OFDMA systems, aiming at exploiting the benefits of RNs while minimising the negative effects of interferences introduced. The authors first analyse the possible interference scenarios in multi-cell systems. Based on the insights into their analysis, the authors propose resource allocation with interference coordination (RAIC) scheme for cellular OFDMA systems. RAIC selectively perform one of three resource allocation algorithms according to the offered traffic load in the system, to mitigate interferences and thus enhance system throughput. The authors conduct intensive simulation experiments based on the model with realistic broadband channel propagation conditions. Numerical results demonstrate that their proposed RAIC can effectively improve system throughput compared with the resource allocation schemes without appropriate interference coordination.

RAC/ROP GTPases: ‘hubs’ for signal integration and diversification in plants

This paper investigates the problem of designing cellular manufacturing systems with multi-period production planning, dynamic system reconfiguration, operation sequence, duplicate machines, machine capacity and machine procurement. An important aspect of this problem is the introduction of routing flexibility in the system by the formation of alternate contingency process routings in addition to alternate main process routings for all part types. Contingency routings serve as backups so as to effectively address the reality of part process routing disruptions (in the main routings) owing to machine breakdowns and allow the cellular manufacturing system to operate in a continuous manner even in the event of such breakdowns. The paper also provides in-depth discussions on the trade-off between the increased flexibility obtained versus the additional cost to be incurred through the formation of contingency routings for all parts. Some sensitivity analysis is also performed on some of the model parameters. The problem is modelled and solved through a comprehensive mixed integer programming formulation. Computational results presented by solving some numerical examples show that the routing and process flexibilities can be incorporated within the cellular manufacturing system design without significant increase in the system cost.

We study the localization transition in three typical one-dimensional systems by means of geometric discord. For the slowly varying potential model, the geometric discord exhibits a sharp transition between the extended states and the localized ones and it is independent on the system size L in the extended states. In the Aubry-Andre model, the geometric discord drop fast and show an inflexion around the boundary between the extended states and the localized ones. For the exponential hopping model, although there is an energy dependent mobility edges, the geometric discord characterize the boundary between the localized states and the extended ones exactly, which is similar with the traditional method. All these features show that the geometric discord can be good quantity to detect localization transition in these one-dimensional systems.