Abstract: Asymptotic behaviors are often of particular interest when analyzing Boolean networks that represent biological systems such as signal transduction or gene regulatory networks. Methods based on a generalization of the steady state notion, the so-called trap spaces, can be exploited to investigate attractor properties as well as for model reduction techniques. In this paper, we propose a novel optimization-based method for computing all minimal and maximal trap spaces and motivate their use. In particular, we add a new result yielding a lower bound for the number of cyclic attractors and illustrate the methods with a study of a MAPK pathway model. To test the efficiency and scalability of the method, we compare the performance of the ILP solver gurobi with the ASP solver potassco in a benchmark of random networks.

Abstract: We design logic circuits based on the notion of zero forcing on graphs; each gate of the circuits is a gadget in which zero forcing is performed. We show that such circuits can evaluate every monotone Boolean function. By using two vertices to encode each logical bit, we obtain universal computation. We also highlight a phenomenon of "back forcing" as a property of each function. Such a phenomenon occurs in a circuit when the input of gates which have been already used at a given time step is further modified by a computation actually performed at a later stage. Finally, we show that zero forcing can be also used to implement reversible computation. The model introduced here provides a potentially new tool in the analysis of Boolean functions, with particular attention to monotonicity. Moreover, in the light of applications of zero forcing in quantum mechanics, the link with Boolean functions may suggest a new directions in quantum control theory and in the study of engineered quantum spin systems. It is an open technical problem to verify whether there is a link between zero forcing and computation with contact circuits.

Abstract: The 2-handed assembly model (2HAM) is a tile-based self-assembly model in which, typically beginning from single tiles, arbitrarily large aggregations of static tiles combine in pairs to form structures. The signal-passing tile assembly model (STAM) is an extension of the 2HAM in which the tiles are dynamically changing components which are able to alter their binding domains as they bind together. In this paper, we examine the $$\hbox {STAM}^+$$STAM+, a restriction of the STAM that does not allow glues to be turned "off", and prove that there exists a 3D tile set at temperature $$\tau >1$$?>1 in the 2HAM which is intrinsically universal for the class of all 2D $$\hbox {STAM}^+$$STAM+ systems at temperature $$\tau $$? for each $$\tau $$? (where the $$\hbox {STAM}^+$$STAM+ does not make use of the STAM's power of glue deactivation and assembly breaking, as the tile components of the 2HAM are static and unable to change or break bonds). This means that there is a single tile set $$U$$U in the 3D 2HAM which can, for an arbitrarily complex $$\hbox {STAM}^+$$STAM+ system $$S$$S, be configured with a single input configuration which causes $$U$$U to exactly simulate $$S$$S at a scale factor dependent upon $$S$$S. Furthermore, this simulation uses only two planes of the third dimension. This implies that there exists a 3D tile set at temperature $$2$$2 in the 2HAM which is intrinsically universal for the class of all 2D $$\hbox {STAM}^+$$STAM+ systems at temperature $$1$$1. Moreover, we also show that there exists an $$\hbox {STAM}^+$$STAM+ tile set for temperature $$\tau $$? which is intrinsically universal for the class of all 2D $$\hbox {STAM}^+$$STAM+ systems at temperature $$\tau $$?, including the case where $$\tau = 1$$?=1. To achieve these results, we also demonstrate useful techniques and transformations for converting an arbitrarily complex $$\hbox {STAM}^+$$STAM+ tile set into an $$\hbox {STAM}^+$$STAM+ tile set where every tile has a constant, low amount of complexity, in terms of the number and types of "signals" they can send, with a trade off in scale factor. While the first result is of more theoretical interest, showing the power of static tiles to simulate dynamic tiles when given one extra plane in 3D, the second result is of more practical interest for the experimental implementation of STAM tiles, since it provides potentially useful strategies for developing powerful STAM systems while keeping the complexity of individual tiles low, thus making them easier to physically implement.

Abstract: In order to define a new method for analyzing the immune system within the realm of Big Data, we bear on the metaphor provided by an extension of Parisi's model, based on a mean field approach. The novelty is the multilinearity of the couplings in the configurational variables. This peculiarity allows us to compare the partition function $$Z$$Z with a particular functor of topological field theory--the generating function of the Betti numbers of the state manifold of the system--which contains the same global information of the system configurations and of the data set representing them. The comparison between the Betti numbers of the model and the real Betti numbers obtained from the topological analysis of phenomenological data, is expected to discover hidden n-ary relations among idiotypes and anti-idiotypes. The data topological analysis will select global features, reducible neither to a mere subgraph nor to a metric or vector space. How the immune system reacts, how it evolves, how it responds to stimuli is the result of an interaction that took place among many entities constrained in specific configurations which are relational. Within this metaphor, the proposed method turns out to be a global topological application of the S[B] paradigm for modeling complex systems.

Abstract: This paper answers an open question of Chen et al. (DNA 2012: proceedings of the 18th international meeting on DNA computing and molecular programming, vol 7433 of lecture notes in computer science. Springer, Berlin, pp 25---42, 2012), who showed that a function $$f:\mathbb {N}^k\rightarrow \mathbb {N}^l$$f:Nk?Nl is deterministically computable by a stochastic chemical reaction network (CRN) if and only if the graph of $$f$$f is a semilinear subset of $$\mathbb {N}^{k+l}$$Nk+l. That construction crucially used "leaders": the ability to start in an initial configuration with constant but non-zero counts of species other than the $$k$$k species $$X_1,\ldots ,X_k$$X1,?,Xk representing the input to the function $$f$$f. The authors asked whether deterministic CRNs without a leader retain the same power. We answer this question affirmatively, showing that every semilinear function is deterministically computable by a CRN whose initial configuration contains only the input species $$X_1,\ldots ,X_k$$X1,?,Xk, and zero counts of every other species, so long as $$f({\bf 0})={\bf 0}$$f(0)=0. We show that this CRN completes in expected time $$O(n)$$O(n), where $$n$$n is the total number of input molecules. This time bound is slower than the $$O(\log ^5 n)$$O(log5n) achieved in Chen et al. (2012), but faster than the $$O(n \log n)$$O(nlogn) achieved by the direct construction of Chen et al. (2012).

Abstract: This paper focuses on the application of hp hierarchic genetic strategy (hp---HGS) for solution of a challenging problem, the inversion of 3D direct current (DC) resistivity logging measurements. The problem under consideration has been formulated as the global optimization one, for which the objective function (misfit between computed and reference data) exhibits multiple minima. In this paper, we consider the extension of the hp---HGS strategy, namely we couple the hp---HGS algorithm with a gradient based optimization method for a local search. Forward simulations are performed with a self-adaptive hp finite element method, hp---FEM. The computational cost of misfit evaluation by hp---FEM depends strongly on the assumed accuracy. This accuracy is adapted to the tree of populations generated by the hp---HGS algorithm, which makes the global phase significantly cheaper. Moreover, tree structure of demes as well as branch reduction and conditional sprouting mechanism reduces the number of expensive local searches up to the number of minima to be recognized. The common (direct and inverse) accuracy control, crucial for the hp---HGS efficiency, has been motivated by precise mathematical considerations. Numerical results demonstrate the suitability of the proposed method for the inversion of 3D DC resistivity logging measurements.

Abstract: P systems are a class of distributed and parallel computing models inspired by the structure and the functioning of a single cell and complexes of cells. The computational efficiency of P systems with active membranes has been investigated widely with the assumption that the application of rules is completed in exactly one time unit. However, in biological facts, different biological processes may take different times to complete, and the execution time of certain biological process could vary because of external uncontrollable conditions. With this biological motivation, in this work, we solve SAT problem by a family of P systems with active membranes in a time-free manner in the sense that the correctness of the solution does not depend on the precise timing of the involved rules. In such a solution, standard cell division rules for elementary membranes are applied: the newly generated membranes have the same label with their parent membrane. This result answers an open problem formulated in Song et al. (Theor Comput Sci 529:61---68, 2014).

Abstract: Chemical self-replicators are of considerable interest in the field of nanomanufacturing and as a model for evolution. We introduce the problem of self-replication of rectangular two-dimensional patterns in the practically motivated signal tile assembly model (STAM) (Padilla et al. Asynchronous signal passing for tile self-assembly: fuel efficient computation and efficient assembly of shapes, 2013). The STAM is based on the tile assembly model (TAM) which is a mathematical model of self-assembly in which DNA tile monomers may attach to other DNA tile monomers in a programmable way. More abstractly, four-sided tiles are assigned glue types to each edge, and self-assembly occurs when singleton tiles bind to a growing assembly, if the glue types match and the glue binding strength exceeds some threshold. The signal tile extension of the TAM allows signals to be propagated across assemblies to activate glues or break apart assemblies. Here, we construct a pattern replicator that replicates a two-dimensional input pattern over some fixed alphabet of size $$\phi $$? with $$O(\phi )$$O(?) tile types, $$O(\phi )$$O(?) unique glues, and a signal complexity of $$O(1)$$O(1). Furthermore, we show that this replication system displays exponential growth in $$n$$n, the number of replicates of the initial patterned assembly.

Abstract: Building a structure using self-assembly of DNA molecules by origami folding requires finding a route for the scaffolding strand through the desired structure. When the target structure is a 1-complex (or the geometric realization of a graph), an optimal route corresponds to an Eulerian circuit through the graph with minimum turning cost. By showing that it leads to a solution to the 3-SAT problem, we prove that the general problem of finding an optimal route for a scaffolding strand for such structures is NP-hard. We then show that the problem may readily be transformed into a traveling salesman problem (TSP), so that machinery that has been developed for the TSP may be applied to find optimal routes for the scaffolding strand in a DNA origami self-assembly process. We give results for a few special cases, showing for example that the problem remains intractable for graphs with maximum degree 8, but is polynomial time for 4-regular plane graphs if the circuit is restricted to following faces. We conclude with some implications of these results for related problems, such as biomolecular computing and mill routing problems.

Abstract: Watson---Crick automata are finite automata working on double strands. Extensive research work has already been done on non-deterministic Watson---Crick automata and on deterministic Watson---Crick automata. State complexity of Watson---Crick automata has also been discussed. In this paper we analyze the state complexity of deterministic Watson---Crick automata with respect to non-deterministic block automata and non-deterministic finite automata. We also introduce new finite automata combining the properties of Watson---Crick automata and time varying automata. These automata have the unique property that the 1-limited stateless variant of these automata have the power to count. We further discuss the state complexity of time varying automata and time varying Watson---Crick automata.

Abstract: Guided by a polymath approach--encompassing neuroscience, philosophy, psychology and computer science, this article describes a novel `cognitive' computational mind framework for text comprehension in terms of Minsky's `Society of Mind' and `Emotion Machine' theories. Observing a top-down design method, we enumerate here the macrocosmic elements of the model--the `agencies' and memory constructs, followed by an elucidation on the working principles and synthesis concerns. Besides corroboration of results of a dry-run test by thoughts generated by random human subjects; the completeness of the conceptualized framework has been validated as a consequence of its total representation of `text understanding' functions of the human brain, types of human memory and emulation of the layers of the mind. A brief conceptual comparison, between the architecture and existing `conscious' agents, has been included as well. The framework, though observed here in its capacity as a text comprehender, is capable of understanding in general. A cognitive model of text comprehension, besides contributing to the `thinking machines' research enterprise, is envisioned to be strategic in the design of intelligent plagiarism checkers, literature genre-cataloguers, differential diagnosis systems, and educational aids for children with reading disorders. Turing's landmark 1950 article on computational intelligence is the principal motivator behind our research initiative.

Abstract: Complex Systems Modelling and Simulation (CoSMoS) was a 4 year EPSRC funded research project at the Universities of York and Kent in the UK. As part of that project, the research team developed the CoSMoS approach to assist the building and use of fit-for-purpose computational simulations of complex systems, and initiated a series of international workshops to disseminate best practice in CoSMoS. This special issue brings together several authors from the first six workshops.

Abstract: During the last 10 years, many-objective optimization problems, i.e. optimization problems with more than three objectives, are getting more and more important in the area of multi-objective optimization. Many real-world optimization problems consist of more than three mutually dependent subproblems, that have to be considered in parallel. Furthermore, the objectives have different levels of importance. For this, priorities have to be assigned to the objectives. In this paper we present a new model for many-objective optimization called Prio-?-Preferred, where the objectives can have different levels of priorities or user preferences. This relation is used for ranking a set of solutions such that an ordering of the solutions is determined. Prio-?-Preferred is controlled by a parameter ?, that is problem specific and has to be adjusted experimentally by the developer. Therefore we also present an extension called Adapted-?-Preferred (AEP), that determines the ? values automatically without any user interaction. To demonstrate the efficiency of our approach, experiments are performed. The method based on Prio-?-Preferred is used to guide the search of an Evolutionary Algorithm. As optimization problem a very complex scheduling problem, i.e. a utilization planning in a hospital is used. The considered benchmarks consist of 2 up to 90 optimization objectives. First, Prio-?-Preferred where ? is set "by hand", is compared to the basic method NSGA-II. It is shown that Prio-?-Preferred clearly outperforms NSGA-II. Furthermore, it turns out that the results obtained by AEP are as good as if ? is adjusted manually.

Abstract: Previous work by Demaine et al. (Nat Comput 6937:100---114, 2012) developed a strong connection between smallest context-free grammars and staged self-assembly systems for one-dimensional strings and assemblies. We extend this work to two-dimensional polyominoes and assemblies, comparing staged self-assembly systems to a natural generalization of context-free grammars we call polyomino context-free grammars (PCFGs). We achieve nearly optimal bounds on the largest ratios of the smallest PCFG and staged self-assembly system for a given polyomino with $$n$$n cells. For the ratio of PCFGs over assembly systems, we show that the smallest PCFG can be an $$\varOmega (n/\log ^3{n})$$Ω(n/log3n)-factor larger than the smallest staged assembly system, even when restricted to square polyominoes. For the ratio of assembly systems over PCFGs, we show that the smallest staged assembly system is never more than a $$O(\log {n})$$O(logn)-factor larger than the smallest PCFG and is sometimes an $$\varOmega (\log {n}/\log \log {n})$$Ω(logn/loglogn)-factor larger.

Abstract: The evaluation of the emergent behaviour in complex systems requires an analytical framework which allows the observation of different phenomena that take place at different levels. In order to observe the dynamics of complex systems, it is necessary to perform simulations so that both local and the emergent behaviour can be observed. To this end, the way in which complex system simulators are built must be examined so that it will be feasible to model large scale scenarios. In this paper, the use of Model Driven Engineering methodology is proposed to deal with this issue. Among other benefits, it is shown that this methodology allows the representation and simulation of a complex system providing support for the analysis. This analysis is supported by a metamodel which describes the system components that are under study. The application of this methodology to the development of large scale simulators is explored through a case study. This case study analyses a complex socio-technical system: a power grid.

Abstract: The problem of patterned self-assembly tile set synthesis (Pats) is to find a minimal tile set which uniquely self-assembles into a given pattern. Czeizler and Popa proved the $$\mathrm {NP}$$NP-completeness of Pats and Seki showed that the Pats problem is already $$\mathrm {NP}$$NP-complete for patterns with 60 colors. In search for the minimal number of colors such that Pats remains $$\mathrm {NP}$$NP-complete, we introduce multiple bound Pats (mbPats) where we allow bounds for the numbers of tile types of each color. We show that mbPats is $$\mathrm {NP}$$NP-complete for patterns with just three colors and, as a byproduct of this result, we also obtain a novel proof for the $$\mathrm {NP}$$NP-completeness of Pats which is more concise than the previous proofs.

Abstract: Modelling and simulation of complex systems can create scientific research tools that allow the inaccessible dynamic aspects of systems to be explored in ways that are not possible in live systems. In some scientific contexts, there is a need to be able to create and use such simulations to explore and generate hypotheses alongside conventional laboratory research. The principled complex systems modelling and simulation (CoSMoS) approach was created to support these activities, as a response to a perceived gap in the software engineering development process for simulation. The article presents some of the software engineering motivation for CoSMoS, by exploring this perceived gap. Following from this analysis, the article considers the validation of complex systems simulators, especially where these are to be used in ongoing research.

Abstract: Motivated by an interest to understand how information is organized within genomes, and how genes communicate between each other in the transcription process, in this paper we propose a novel network based methodology for genomic sequence analysis, specifically applied to three organisms: Nanoarchaeum equitans, Escherichia coli, and Saccaromyces cerevisiae. A dictionary based approach previously introduced is here continued through a repeat analysis in genic and intergenic regions. Key results of this work have been found in a biological and computational analysis of novel parametrized gene networks, defined by means of motifs of fixed length occurring inside multiple genes. Cliques emerge as groups of genes sharing a long repeat with a clear biological interpretation, while a (complete, paralog) cluster analysis has outlined some unexpected regularity. Repeat sharing gene networks may be applied in contexts of comparative genomics, as an investigation methodology for a comprehension of evolutional and functional properties of genes.

Abstract: It has become popular to describe the behaviour of certain systems as "undergoing a tipping point". This is normally used as a description of a system that has rapidly changed from an apparently stable state to a new state with little or no warning. A wide range of complex systems can display tipping point behaviour, from climate systems to populations of people. Here we present preliminary work of using the British banking sector from 1559 to 2012 as a case study for the modelling of complex systems that show tipping point behaviour. Currently implemented in a highly abstracted form, we present a description of a conceptual model of the British banking system that is able to reproduce the general features of the changing population of British banks. However, to do so requires interventions in the system, rather than emergent properties. We discuss what future alterations to the model could be made to overcome this limitation.

Abstract: Self-organized regularities in terms of patient arrivals and wait times have been discovered in real-world healthcare services. What remains to be a challenge is how to characterize those regularities by taking into account the underlying patients' or hospitals' behaviors with respect to various impact factors. This paper presents a case study to address such a challenge. Specifically, it models and simulates the cardiac surgery services in Ontario, Canada, based on the methodology of Autonomy-Oriented Computing (AOC). The developed AOC-based cardiac surgery service model (AOC-CSS model) pays a special attention to how individuals' (e.g., patients and hospitals) behaviors and interactions with respect to some key factors (i.e., geographic accessibility to services, hospital resourcefulness, and wait times) affect the dynamics and relevant patterns of patient arrivals and wait times. By experimenting with the AOC-CSS model, we observe that certain regularities in patient arrivals and wait times emerge from the simulation, which are similar to those discovered from the real world. It reveals that patients' hospital-selection behaviors, hospitals' service-adjustment behaviors, and their interactions via wait times may potentially account for the self-organized regularities of wait times in cardiac surgery services.

Abstract: Particle swarm optimization is an optimization method based on a simulated social behavior displayed by artificial particles in a swarm, inspired from bird flocks and fish schools. An underlying component that influences the exchange of information between particles in a swarm, is its topological structure. Therefore, this property has a great influence on the comportment of the optimization method. In this study, we propose DCluster: a dynamic topology, based on a combination of two well-known topologies viz. Four-cluster and Fitness. The proposed topology is analyzed, and compared to six other topologies used in the standard PSO algorithm using a set of benchmark test functions and several well-known constrained and unconstrained engineering design problems. Our comparisons demonstrate that DCluster outperforms the other tested topologies and leads to satisfactory performance while avoiding the problem of premature convergence.

Abstract: Computational and mathematical modelling approaches are increasingly being adopted in attempts to further our understanding of complex biological systems This approach can be subjected to strong criticism as substantial aspects of the biological system being captured are not currently known, meaning assumptions need to be made that could have a critical impact on simulation response We have utilised the CoSMoS process in the development of an agent-based simulation of the formation of Peyer's patches (PP), gut-associated lymphoid organs that have a key role in the initiation of adaptive immune responses to infection Although the use of genetic tools, imaging technologies and ex vivo culture systems has provided significant insight into the cellular components and associated pathways involved in PP development, interesting questions remain that cannot be addressed using these approaches, and as such well justified assumptions have been introduced into our model to counter this Here we focus not on the development of the model itself, but instead demonstrate how the resultant simulation can be used to assess how these assumptions impact the simulation response For example, we consider the impact of our assumption that the migration rate of lymphoid tissue cells into the gut remains constant throughout PP development We demonstrate that an analysis of the assumptions made in the construction of the domain model may either increase confidence in the model as a representation of the biological system it captures, or may suggest areas where further biological experimentation is required

Abstract: We describe an algorithm which automates the generation of appropriate shift and coin operators for a discrete time quantum walk, given the adjacency matrix of the graph over which the walk is run This gives researchers the freedom to numerically investigate any discrete time quantum walk over graphs of a computationally tractable size by greatly reducing the time required to initialise a given walk We then describe one application in which the swift initialisation of walks has enabled systematic investigations of walks over a large number of structures New results concerning this application, which is to formal language recognition, are described The reliability of these results, as well as the general suitability of numerical analysis as a tool for investigating discrete time quantum walks, are briefly discussed We also mention specific Python packages which facilitate our simulations and analysis, motivating the use of high level programming languages in this context

Abstract: We present a holography based optical architecture that computes Kronecker product of two given binary matrices in a single (configuration) step. We demonstrate the use of the holography capability to enlarge the input of size $$n$$n into the size $$n^2$$n2 in one step, in contrast to the traditional optical copying techniques that duplicate the input by a fixed constant factor in a single step.

Abstract: We consider certain types of discretization schemes for differential equations with quadratic nonlinearities, which were introduced by Kahan, and considered in a broader setting by Mickens. These methods have the property that they preserve important structural features of the original systems, such as the behaviour of solutions near to fixed points, and also, where appropriate (e.g. for certain mechanical systems), the property of being volume-preserving, or preserving a symplectic/Poisson structure. Here we focus on the application of Kahan's method to models of biological systems, in particular to reaction kinetics governed by the Law of Mass Action, and present a general approach to birational discretization, which is applied to population dynamics of Lotka---Volterra type.

Abstract: Clustering is one of the most well known activities in scientific investigation and the object of research in many disciplines, ranging from Statistics to Computer Science. In this beautiful area, one of the most difficult challenges is a particular instance of the model selection problem, i.e., the identification of the correct number of clusters in a dataset. In what follows, for ease of reference, we refer to that instance still as model selection. It is an important part of any statistical analysis. The techniques used for solving it are mainly either Bayesian or data-driven, and are both based on internal knowledge. That is, they use information obtained by processing the input data. Although both techniques have been evaluated in the realm of microarray data analysis, their merits (relative to each other) has not been assessed. Here we will fill this gap in the literature by comparing three Bayesians versus several state of the art data-driven model selection methods. Our results show that, although in some cases Bayesian methods guarantee good results, they are not able to compete in terms of ability to predict the correct number of clusters in a dataset with the data-driven methods.

Abstract: Reduction of the search space to the feasible region with global optimum is one of the approaches that can significantly improve the efficiency of a GA. This study focuses on the modelling of a GA with dynamical adjustment of a search space size to analytically establish the setting of a parameter k, which specifies a ratio of narrowing the boundaries of a search space. A general form of real valued version of one-max problem, which is a general linear pseudo-Boolean function with positive coefficients, is applied to analyse a GA with an adjustment of a search space size. The paper assesses an influence of a parameter k to an accuracy and velocity of the convergence of GA to an optimal solution.

Abstract: Metabolic P systems are a modeling framework for metabolic, regulatory and signaling processes. The key point of MP systems are flux regulation functions, which determine the evolution of a system from a given initial state. This paper presents important improvements to a technique, based on genetic algorithms and multiple linear regression, for inferring regulation functions that reproduce observed behaviors (time series datasets). An accurate analysis of three case studies, namely the mitotic oscillator in early amphibian embryos, the Lodka---Volterra predator-prey model and the chaotic logistic map show that this methodology can provide, from observed data, significant knowledge about the regulation mechanisms underlying biological processes.

Abstract: In this paper, we provide a new optical model for computation, which is named filter machine. Filter machine consists of optical filters as data storage and imaging operation for computation. Each filter is a long optical sensitive sheet, divided into cells. Filter cells may represent different patterns of opaque and transparent cells which are constructed by emitting light to some cells and made them opaque. The computation in filter machines starts from basic filters with basic patterns of opaque and transparent cells. We provide an algorithm that, given a Boolean circuit, produces a filter machine generating output of the circuit for all possible inputs. Thus, we show that the filter machine is able to generate every Boolean function. Indeed, the number of required cells in each filter is exponential according to the number of variables in the given Boolean function. In order to show the efficiency of the model in solving combinatorial problems, we provide a solution for the k-clique problem on graphs by filter machines, which requires polynomial time and number of filters but exponential number of cells in each filter.