Showing papers in "Natural Computing in 2018"
TL;DR: This tutorial will review some of the most important fundamentals in multiobjective optimization and then introduce representative algorithms, illustrate their working principles, and discuss their application scope.
Abstract: In almost no other field of computer science, the idea of using bio-inspired search paradigms has been so useful as in solving multiobjective optimization problems. The idea of using a population of search agents that collectively approximate the Pareto front resonates well with processes in natural evolution, immune systems, and swarm intelligence. Methods such as NSGA-II, SPEA2, SMS-EMOA, MOPSO, and MOEA/D became standard solvers when it comes to solving multiobjective optimization problems. This tutorial will review some of the most important fundamentals in multiobjective optimization and then introduce representative algorithms, illustrate their working principles, and discuss their application scope. In addition, the tutorial will discuss statistical performance assessment. Finally, it highlights recent important trends and closely related research fields. The tutorial is intended for readers, who want to acquire basic knowledge on the mathematical foundations of multiobjective optimization and state-of-the-art methods in evolutionary multiobjective optimization. The aim is to provide a starting point for researching in this active area, and it should also help the advanced reader to identify open research topics.
413 citations
TL;DR: This work will examine existing challenges in building predictable large-scale circuits including modularity, context dependency and metabolic burden as well as tools and methods used to resolve them.
Abstract: Synthetic biology aims to engineer and redesign biological systems for useful real-world applications in biomanufacturing, biosensing and biotherapy following a typical design-build-test cycle. Inspired from computer science and electronics, synthetic gene circuits have been designed to exhibit control over the flow of information in biological systems. Two types are Boolean logic inspired TRUE or FALSE digital logic and graded analog computation. Key principles for gene circuit engineering include modularity, orthogonality, predictability and reliability. Initial circuits in the field were small and hampered by a lack of modular and orthogonal components, however in recent years the library of available parts has increased vastly. New tools for high throughput DNA assembly and characterization have been developed enabling rapid prototyping, systematic in situ characterization, as well as automated design and assembly of circuits. Recently implemented computing paradigms in circuit memory and distributed computing using cell consortia will also be discussed. Finally, we will examine existing challenges in building predictable large-scale circuits including modularity, context dependency and metabolic burden as well as tools and methods used to resolve them. These new trends and techniques have the potential to accelerate design of larger gene circuits and result in an increase in our basic understanding of circuit and host behaviour.
62 citations
TL;DR: The importance of searching strategies for relevant approximation spaces as the basic tools in achieving computational building blocks (granules or patterns) required for approximation of complex vague concepts is emphasized.
Abstract: Introduction of rough sets by Professor Zdzislaw Pawlak has completed 35 years. The theory has already attracted the attention of many researchers and practitioners, who have contributed essentially to its development, from all over the world. The methods, developed based on rough set theory alone or in combination with other approaches, found applications in many areas. In this article, we outline some selected past and present research directions of rough sets. In particular, we emphasize the importance of searching strategies for relevant approximation spaces as the basic tools in achieving computational building blocks (granules or patterns) required for approximation of complex vague concepts. We also discuss new challenges related to problem solving by intelligent systems (IS) or complex adaptive systems (CAS). The concern is to control problems using interactive granular computing, an extension of the rough set approach, for effective realization of computations realized in IS or CAS. These challenges are important for the development of natural computing too.
57 citations
TL;DR: Simulation results show that the competitive ratio of the universal coating algorithm may be better than linear in practice, and a linear lower bound on the competitive gap between fully local coating algorithms and coating algorithms that rely on global information is shown.
Abstract: Imagine coating buildings and bridges with smart particles (also coined smart paint) that monitor structural integrity and sense and report on traffic and wind loads, leading to technology that could do such inspection jobs faster and cheaper and increase safety at the same time. In this paper, we study the problem of uniformly coating objects of arbitrary shape in the context of self-organizing programmable matter, i.e., programmable matter which consists of simple computational elements called particles that can establish and release bonds and can actively move in a self-organized way. Particles are anonymous, have constant-size memory, and utilize only local interactions in order to coat an object. We continue the study of our universal coating algorithm by focusing on its runtime analysis, showing that our algorithm terminates within a linear number of rounds with high probability. We also present a matching linear lower bound that holds with high probability. We use this lower bound to show a linear lower bound on the competitive gap between fully local coating algorithms and coating algorithms that rely on global information, which implies that our algorithm is also optimal in a competitive sense. Simulation results show that the competitive ratio of our algorithm may be better than linear in practice.
47 citations
TL;DR: A historical perspective on computation by biological systems, with a focus on switches and clocks is presented, and parallels between biology and computing are discussed, and the vision for the future of biological computing is outlined.
Abstract: The complex dynamics of biological systems is primarily driven by molecular interactions that underpin the regulatory networks of cells. These networks typically contain positive and negative feedback loops, which are responsible for switch-like and oscillatory dynamics, respectively. Many computing systems rely on switches and clocks as computational modules. While the combination of such modules in biological systems leads to a variety of dynamical behaviours, it is also driving development of new computing algorithms. Here we present a historical perspective on computation by biological systems, with a focus on switches and clocks, and discuss parallels between biology and computing. We also outline our vision for the future of biological computing.
43 citations
TL;DR: A novel semi-automatic seeded image segmentation method, based on a cellular automata model, for MRI brain cancer detection and delineation is proposed, called GTVcut, which employs an adaptive seed selection strategy and helps to segment the GTV, by identifying the target volume to be treated using the Gamma Knife device.
Abstract: Despite of the development of advanced segmentation techniques, achieving accurate and reproducible gross tumor volume (GTV) segmentation results is still an important challenge in neuro-radiosurgery. Nowadays, magnetic resonance imaging (MRI) is the most prominent modality in radiation therapy for soft-tissue anatomical districts. Gamma Knife stereotactic neuro-radiosurgery is a minimally invasive technology for dealing with inaccessible or insufficiently treated tumors with traditional surgery or radiotherapy. During a treatment planning phase, the GTV is generally contoured by experienced neurosurgeons and radiation oncologists using fully manual segmentation procedures on MR images. Unfortunately, this operative methodology is definitely time-expensive and operator-dependent. Delineation result repeatability, in terms of both intra- and inter-operator reliability, can be achieved only by using computer-assisted approaches. In this paper a novel semi-automatic seeded image segmentation method, based on a cellular automata model, for MRI brain cancer detection and delineation is proposed. This approach, called GTVcut, employs an adaptive seed selection strategy and helps to segment the GTV, by identifying the target volume to be treated using the Gamma Knife device. The accuracy of GTVcut was evaluated on a dataset composed of 32 brain cancers, using both spatial overlap-based and distance-based metrics. The achieved experimental results are very reproducible, showing the effectiveness and the clinical feasibility of the proposed approach.
36 citations
TL;DR: This paper provides novel CRN designs for the construction of asynchronous logic, arithmetic and control flow elements based on a bi-molecular reaction motif with catalytic reactions and uniform reaction rates using Microsoft's GEC tool and the probabilistic model checker PRISM.
Abstract: Chemical reaction networks (CRNs) are a versatile language for describing the dynamical behaviour of chemical kinetics, capable of modelling a variety of digital and analogue processes. While CRN designs for synchronous sequential logic circuits have been proposed and their implementation in DNA demonstrated, a physical realisation of these devices is difficult because of their reliance on a clock. Asynchronous sequential logic, on the other hand, does not require a clock, and instead relies on handshaking protocols to ensure the temporal ordering of different phases of the computation. This paper provides novel CRN designs for the construction of asynchronous logic, arithmetic and control flow elements based on a bi-molecular reaction motif with uniform reaction rates. We model and validate the designs using Microsoft’s GEC tool.
32 citations
TL;DR: How thermodynamics determines both the overall potential of molecular networks, and the minute details of design is discussed, and it is argued that the need to understand molecular systems is helping to drive the development of theories of thermodynamics at the microscopic scale.
Abstract: Improved understanding of molecular systems has only emphasised the sophistication of networks within the cell. Simultaneously, the advance of nucleic acid nanotechnology, a platform within which reactions can be exquisitely controlled, has made the development of artificial architectures and devices possible. Vital to this progress has been a solid foundation in the thermodynamics of molecular systems. In this pedagogical review and perspective, we discuss how thermodynamics determines both the overall potential of molecular networks, and the minute details of design. We then argue that, in turn, the need to understand molecular systems is helping to drive the development of theories of thermodynamics at the microscopic scale.
30 citations
TL;DR: This paper focuses on Boolean automata networks and the updatings of automata states in these networks and study how synchronous updates impact on the global behaviour of a network.
Abstract: This paper focuses on Boolean automata networks and the updatings of automata states in these networks. More specifically, we study how synchronous updates impact on the global behaviour of a network. On this basis, we define different types of network sensitivity to synchronism, which are effectively satisfied by some networks. We also relate this synchronism-sensitivity to some properties of the structure of networks and to their underlying mechanisms.
27 citations
TL;DR: This paper improves on and complement previous computational completeness results for matrix insertion-deletion systems, and generates non-semilinear languages using matrices of length three with context-free insertion and deletion rules.
Abstract: Matrix insertion-deletion systems combine the idea of matrix control (a control mechanism well established in regulated rewriting) with that of insertion and deletion (as opposed to replacements). Given a matrix insertion-deletion system, the size of such a system is given by a septuple of integers $$(k;n,i',i'';m,j',j'')$$
. The first integer k denotes the maximum number of rules in (length of) any matrix. The next three parameters $$n,i',i''$$
denote the maximal length of the insertion string, the maximal length of the left context, and the maximal length of the right context of insertion rules, respectively. The last three parameters $$m,j',j''$$
are similarly understood for deletion rules. In this paper, we improve on and complement previous computational completeness results for such systems, showing that matrix insertion-deletion systems of size (1) (3; 1, 0, 1; 1, 0, 1), (3; 1, 0, 1; 1, 1, 0), (3; 1, 1, 1; 1, 0, 0) and (3; 1, 0, 0; 1, 1, 1) (2) (2; 1, 0, 1; 2, 0, 0), (2; 2, 0, 0; 1, 0, 1), (2; 1, 1, 1; 1, 1, 0) and (2; 1, 1, 0; 1, 1, 1), are computationally complete. Further, we also discuss linear and metalinear languages and we show how to simulate grammars characterizing them by matrix insertion-deletion systems of size (3; 1, 1, 0; 1, 0, 0), (3; 1, 0, 1; 1, 0, 0), (2; 2, 1, 0; 1, 0, 0) and (2; 2, 0, 1; 1, 0, 0). We also generate non-semilinear languages using matrices of length three with context-free insertion and deletion rules.
18 citations
TL;DR: A specific computational approach to systems biology, based on the so-called process calculi, a formalism for describing concurrent systems, is surveyed, and some suggestions on the most suitable frameworks for dealing with specific cases of interest are derived.
Abstract: Systems biology is a research area devoted to developing computational frameworks for modeling biological systems in a holistic fashion. Within this approach, the typical advantages of using computer systems and formal methodologies are applicable. Experiments can indeed be carried on in silico that turn out to be much quicker and less expensive than wet-lab experiments. This paper surveys a specific computational approach to systems biology, based on the so-called process calculi, a formalism for describing concurrent systems. After a gentle, intuitive introduction to both fields, we present the most successful process calculi designed and used for this purpose. We start from a basic process calculus that is then extended with increasingly expressive features to better reflect the biological aspects of interest. We then compare the expressive power of the resulting calculi, mentioning if they are supported by software tools. From this comparison we derive some suggestions on the most suitable frameworks for dealing with specific cases of interest, with the help of three relevant case studies.
TL;DR: This work rigorously analyze the proposed algorithm for “shortcut bridging”, and shows it achieves a near-optimal balance between the competing factors of path length and bridge cost, and exhibits a dependence on the angle of the gap being “ shortcut” similar to that of the ant bridges.
Abstract: In a self-organizing particle system, an abstraction of programmable matter, simple computational elements called particles with limited memory and communication self-organize to solve system-wide problems of movement, coordination, and configuration. In this paper, we consider a stochastic, distributed, local, asynchronous algorithm for “shortcut bridging”, in which particles self-assemble bridges over gaps that simultaneously balance minimizing the length and cost of the bridge. Army ants of the genus Eciton have been observed exhibiting a similar behavior in their foraging trails, dynamically adjusting their bridges to satisfy an efficiency trade-off using local interactions. Using techniques from Markov chain analysis, we rigorously analyze our algorithm, show it achieves a near-optimal balance between the competing factors of path length and bridge cost, and prove that it exhibits a dependence on the angle of the gap being “shortcut” similar to that of the ant bridges. We also present simulation results that qualitatively compare our algorithm with the army ant bridging behavior. Our work gives a plausible explanation of how convergence to globally optimal configurations can be achieved via local interactions by simple organisms (e.g., ants) with some limited computational power and access to random bits. The proposed algorithm also demonstrates the robustness of the stochastic approach to algorithms for programmable matter, as it is a surprisingly simple extension of our previous stochastic algorithm for compression.
TL;DR: This work considers extended spiking neural P systems with the additional possibility of so-called “white hole rules”, which send the complete contents of a neuron to other neurons, and proves that this extension of the original model can easily simulate register machines.
Abstract: We consider extended spiking neural P systems with the additional possibility of so-called "white hole rules", which send the complete contents of a neuron to other neurons, and we prove that this extension of the original model can easily simulate register machines. Based on this proof, we then define red-green variants of these extended spiking neural P systems with white hole rules and show how to go beyond Turing with these red-green systems. We also discuss the number of actor neurons needed, and the relation of this model to some special variants of Lindenmayer systems.
TL;DR: A calculus to compute on distributions that is complete for finite support distributions, and can be compiled to a restricted class of CRNs that at steady state realize those distributions.
Abstract: We explore the range of probabilistic behaviours that can be engineered with Chemical Reaction Networks (CRNs). We give methods to "program" CRNs so that their steady state is chosen from some desired target distribution that has finite support in [Formula: see text], with [Formula: see text]. Moreover, any distribution with countable infinite support can be approximated with arbitrarily small error under the [Formula: see text] norm. We also give optimized schemes for special distributions, including the uniform distribution. Finally, we formulate a calculus to compute on distributions that is complete for finite support distributions, and can be compiled to a restricted class of CRNs that at steady state realize those distributions.
TL;DR: A nondeterministic OS (NOS) that chooses an assignment of Boolean values nondeterministically and evaluates a logical formula on the assignment and enables proving the coNP-hardness of deciding, given two NOSs, if there exists no conformation that one of them folds but the other does not.
Abstract: The oritatami system (OS) is a model of computation by cotranscriptional folding, being inspired by the recent experimental succeess of RNA origami to self-assemble an RNA tile cotranscriptionally. The OSs implemented so far, including binary counter and Turing machine simulator, are deterministic, that is, uniquely fold into one conformation, while nondeterminism is intrinsic in biomolecular folding. We introduce nondeterminism to OS (NOS) and propose an NOS that chooses an assignment of Boolean values nondeterministically and evaluates a logical formula on the assignment. This NOS is seedless in the sense that it does not require any initial conformation to begin with like the RNA origami. The NOS allows to prove the co-NP hardness of deciding, given two NOSs, if there exists no conformation that one of them folds into but the other does not.
TL;DR: Linear diversity index (LDI) measures the individual density around the center-point individual in coding space, which is characterized by itself linearity, and control the search-region ranges of diversity and intensification subpopulations by using negative and positive perturbations, respectively.
Abstract: How to rationally inject randomness to control population diversity is still a difficult problem in evolutionary algorithms We propose balanced-evolution genetic algorithm (BEGA) as a case study of this problem Similarity guide matrix (SGM) is a two-dimensional matrix to express the population (or subpopulation) distribution in coding space Different from binary-coding similarity indexes, SGM is able to be suitable for binary-coding and symbol-coding problems, simultaneously In BEGA, opposite-direction and forward-direction regions are defined by using two SGMs as reference points, respectively In opposite-direction region, diversity subpopulation always tries to increase Hamming distances between themselves and the current population In forward-direction region, intensification subpopulation always tries to decrease Hamming distances between themselves and the current elitism population Thus, diversity subpopulation is more suitable for injecting randomness Linear diversity index (LDI) measures the individual density around the center-point individual in coding space, which is characterized by itself linearity According to LDI, we control the search-region ranges of diversity and intensification subpopulations by using negative and positive perturbations, respectively Thus, the search efforts between exploration and exploitation are balanced We compared BEGA with CHC, dual-population genetic algorithm, variable dissortative mating genetic algorithm, quantum-inspired evolutionary algorithm, and greedy genetic algorithm for 12 benchmarks Experimental results were acceptable In addition, it is worth noting that BEGA is able to directly solve bounded knapsack problem (ie symbol-coding problem) as one EA-based solver, and does not transform bounded knapsack problem into an equivalent binary knapsack problem
TL;DR: This work uses a 2D vertex model of circular cross-sections of cell monolayers to investigate how cell mechanical properties and proliferation affect the shape of in-silico growing tissues and shows that increasing the cells’ contractility and the intercellular adhesion reduces tissue buckling.
Abstract: Tissue folding is a frequently observed phenomenon, from the cerebral cortex gyrification, to the gut villi formation and even the crocodile head scales development. Although its causes are not yet well understood, some hypotheses suggest that it is related to the physical properties of the tissue and its growth under mechanical constraints. In order to study the underlying mechanisms affecting tissue folding, experimental models are developed where epithelium monolayers are cultured inside hydrogel microcapsules. In this work, we use a 2D vertex model of circular cross-sections of cell monolayers to investigate how cell mechanical properties and proliferation affect the shape of in-silico growing tissues. We observe that increasing the cells’ contractility and the intercellular adhesion reduces tissue buckling. This is found to coincide with smaller and thicker cross-sections that are characterized by shorter relaxation times following cell division. Finally, we show that the smooth or folded morphology of the simulated monolayers also depends on the combination of the cell proliferation rate and the tissue size.
TL;DR: It is shown that an infinite family of unary regular languages can be recognized by 2-state affine automata, whereas the number of inner states of quantum and probabilistic automata cannot be bounded.
Abstract: In this work we study a non-linear generalization based on affine transformations of probabilistic and quantum automata proposed recently by Diaz-Caro and Yakaryilmaz (in: Computer science—theory and applications, LNCS, vol 9691. Springer, pp 1–15, 2016. ArXiv:1602.04732
) referred to as affine automata. First, we present efficient simulations of probabilistic and quantum automata by means of affine automata which characterizes the class of exclusive stochastic languages. Then we initiate a study on the succintness of affine automata. In particular, we show that an infinite family of unary regular languages can be recognized by 2-state affine automata, whereas the number of inner states of quantum and probabilistic automata cannot be bounded. Finally, we present a characterization of all (regular) unary languages recognized by two-state affine automata.
TL;DR: It is proved that there exist 3D2HAM systems that only assemble infinite aperiodic shapes, and that this model is Turing universal, overcoming undesired growth by breaking apart undesired computation assembly via repulsive forces.
Abstract: We consider problems in variations of the two-handed abstract Tile Assembly Model (2HAM), a generalization of Erik Winfree’s abstract Tile Assembly Model (aTAM). In the latter, tiles attach one-at-a-time to a seed-containing assembly. In the former, tiles aggregate into supertiles that then further combine to form larger supertiles; hence, constructions must be robust to the choice of seed (nucleation) tiles. We obtain three distinct results in two 2HAM variants whose aTAM siblings are well-studied.
TL;DR: Based on comparative judgment, an improved particle swarm optimization (IPSO) is proposed and a new search equation is developed by considering individual experience, social experience and the integration of individual and social experience, which can be used to improve the convergence speed of the algorithm.
Abstract: Particle swarm optimization (PSO) algorithm is one of the most effective and popular swarm intelligence algorithms. In this paper, based on comparative judgment, an improved particle swarm optimization (IPSO) is proposed. Firstly, a new search equation is developed by considering individual experience, social experience and the integration of individual and social experience, which can be used to improve the convergence speed of the algorithm. Secondly, in order to avoid falling into a local optima, a location abandoned mechanism is proposed; meanwhile, a new equation to generate a new position for the corresponding particle is proposed. The experimental results show that IPSO algorithm has excellent solution quality and convergence characteristic comparing to basic PSO algorithm and performs better than some state-of-the-art algorithms on almost all tested functions.
TL;DR: It is shown that linear CA are equivalent to linear cyclic codes, and a formula is derived from which the Walsh spectrum of CA induced by permutive local rules is derived, from which a formula for the nonlinearity of such CA is derived.
Abstract: Cellular Automata (CA) have widely been studied to design cryptographic primitives such as stream ciphers and pseudorandom number generators, focusing in particular on the properties of the underlying local rules. On the other hand, there have been comparatively fewer works concerning the applications of CA to the design of S-boxes and block ciphers, a task that calls for a study of CA global rules in terms of vectorial boolean functions. The aim of this paper is to analyze some of the most basic cryptographic criteria of the global rules of CA. We start by observing that the algebraic degree of a CA global rule equals the degree of its local rule. Then, we characterize the Walsh spectrum of CA induced by permutive local rules, from which we derive a formula for the nonlinearity of such CA. Additionally, we prove that the 1-resiliency property of bipermutive local rules transfers to the corresponding global rules. This result leads us to consider CA global rules from a coding-theoretic point of view: in particular, we show that linear CA are equivalent to linear cyclic codes, observing that the syndrome computation process corresponds to the application of the CA global rule, while the error-correction capability of the code is related to the resiliency order of the global rule.
TL;DR: This article aims to illustrate some of the key developments in the design and characterisation of self-assembling 3D nanostructures based on wireframe polyhedral models, in sufficient detail so that the reader can achieve a general understanding of the main concepts and approaches.
Abstract: The field of structural DNA nanotechnology aims at the systematic development of self-assembling nanostructures using DNA as the construction material. Research in this area is progressing rapidly, and the controlled, computer-aided design of increasingly complex structures is becoming feasible. One thread of this endeavour is the design and characterisation of self-assembling 3D nanostructures based on wireframe polyhedral models. This article aims to illustrate some of the key developments in this direction, in sufficient detail so that the reader can achieve a general understanding of the main concepts and approaches. The emphasis is on the design principles rather than experimental methodology, and the role of computer science and computational tools is set forth.
TL;DR: In this paper, the authors address the problem of regional controllability of cellular automata via boundary actions, i.e., they investigate the characteristics of a cellular automaton so that it can be controlled inside a given region only acting on the value of sites at its boundaries.
Abstract: An important question to be addressed regarding system control on a time interval [0, T] is whether some particular target state in the configuration space is reachable from a given initial state. When the target of interest refers only to a portion of the spatial domain, we speak about regional analysis. Cellular automata approach have been recently promoted for the study of control problems on spatially extended systems for which the classical approaches cannot be used. An interesting problem concerns the situation where the subregion of interest is not interior to the domain but a portion of its boundary . In this paper we address the problem of regional controllability of cellular automata via boundary actions, i.e., we investigate the characteristics of a cellular automaton so that it can be controlled inside a given region only acting on the value of sites at its boundaries.
TL;DR: A unified definition of classification problem for one-dimensional, binary cellular automata is proposed, from which various known problems are couched in and novel ones are defined, and the solvability of the new problems is analysed.
Abstract: Decision problems addressed by cellular automata have been historically expressed either as determining whether initial configurations would belong to a given language, or as classifying the initial configurations according to a property in them. Unlike traditional approaches in language recognition, classification problems have typically relied upon cyclic configurations and fully paralell (two-way) update of the cells, which render the action of the cellular automaton relatively less controllable and difficult to analyse. Although the notion of cyclic languages have been studied in the wider realm of formal languages, only recently a more systematic attempt has come into play in respect to cellular automata with fully parallel update. With the goal of contributing to this effort, we propose a unified definition of classification problem for one-dimensional, binary cellular automata, from which various known problems are couched in and novel ones are defined, and analyse the solvability of the new problems. Such a unified perspective aims at increasing existing knowledge about classification problems by cellular automata over cyclic configurations and parallel update.
TL;DR: In this article, the authors present a high-level overview of tile-based self-assembling systems capable of producing complex, infinite, aperiodic structures known as discrete self-similar fractals.
Abstract: In this extended abstract, we present high-level overviews of tile-based self-assembling systems capable of producing complex, infinite, aperiodic structures known as discrete self-similar fractals. Fractals have a variety of interesting mathematical and structural properties, and by utilizing the bottom-up growth paradigm of self-assembly to create them we not only learn important techniques for building such complex structures, we also gain insight into how similar structural complexity arises in natural self-assembling systems. Our results fundamentally leverage hierarchical assembly processes, and use as our building blocks square “tile” components which are capable of activating and deactivating their binding “glues” a constant number of times each, based only on local interactions. We provide the first constructions capable of building arbitrary discrete self-similar fractals at scale factor 1, and many at temperature 1 (i.e. “non-cooperatively”), including the Sierpinski triangle.
TL;DR: It is shown that networks of polarized splicing processors (NPSP) of size 2 are computationally complete, which immediately settles the question of designing computationallycomplete NPSPs of minimal size and it is proved that NPSP of size 4 can accept all languages in NP in polynomial time.
Abstract: In this paper, we consider the computational power of a new variant of networks of splicing processors in which each processor as well as the data navigating throughout the network are now considered to be polarized. While the polarization of every processor is predefined (negative, neutral, positive), the polarization of data is dynamically computed by means of a valuation mapping. Consequently, the protocol of communication is naturally defined by means of this polarization. We show that networks of polarized splicing processors (NPSP) of size 2 are computationally complete, which immediately settles the question of designing computationally complete NPSPs of minimal size. With two more nodes we can simulate every nondeterministic Turing machine without increasing the time complexity. Particularly, we prove that NPSP of size 4 can accept all languages in NP in polynomial time. Furthermore, another computational model that is universal, namely the 2-tag system, can be simulated by NPSP of size 3 preserving the time complexity. All these results can be obtained with NPSPs with valuations in the set \(\{-1,0,1\}\) as well. We finally show that Turing machines can simulate a variant of NPSPs and discuss the time complexity of this simulation.
TL;DR: A coarse-grained model is derived that captures the temporal evolution of DNA nanotube length distribution during growth experiments and can handle time varying concentration of tiles, and it is foresee that it will be useful to model dynamic behaviors in other types of biomolecular polymers.
Abstract: We derive a coarse-grained model that captures the temporal evolution of DNA nanotube length distribution during growth experiments. The model takes into account nucleation, polymerization, joining, and fragmentation processes in the nanotube population. The continuous length distribution is segmented, and the time evolution of the nanotube concentration in each length bin is modeled using ordinary differential equations. The binning choice determines the level of coarse graining. This model can handle time varying concentration of tiles, and we foresee that it will be useful to model dynamic behaviors in other types of biomolecular polymers.
TL;DR: This work automatically identifies leakage transitions in DNA walker circuits, which allows for a detailed qualitative and quantitative assessment of circuit designs, design comparison, and design optimisation.
Abstract: We consider localised DNA computation, where a DNA strand walks along a binary decision graph to compute a binary function. One of the challenges for the design of reliable walker circuits consists in leakage transitions, which occur when a walker jumps into another branch of the decision graph. We automatically identify leakage transitions, which allows for a detailed qualitative and quantitative assessment of circuit designs, design comparison, and design optimisation. The ability to identify leakage transitions is an important step in the process of optimising DNA circuit layouts where the aim is to minimise the computational error inherent in a circuit while minimising the area of the circuit. Our 2D modelling approach of DNA walker circuits relies on coloured stochastic Petri nets which enable functionality, topology and dimensionality all to be integrated in one two-dimensional model. Our modelling and analysis approach can be easily extended to 3-dimensional walker systems.
TL;DR: In this article, the reachability problem for rate-independent continuous chemical reaction networks (CCRNs) was investigated, and it was shown that deciding reachability and constructing a path if there is one is computable in polynomial time.
Abstract: Chemical reaction networks (CRNs) model the behavior of molecules in a well-mixed solution. The emerging field of molecular programming uses CRNs not only as a descriptive tool, but as a programming language for chemical computation. Recently, Chen, Doty and Soloveichik introduced rate-independent continuous CRNs (CCRNs) to study the chemical computation of continuous functions. A fundamental question for any CRN model is reachability, the question whether a given target state is reachable from a given start state via a sequence of reactions (a path) in the network. In this paper, we investigate CCRN-REACH, the reachability problem for rate-independent continuous chemical reaction networks. Our main theorem is that, for CCRNs, deciding reachability—and constructing a path if there is one—is computable in polynomial time. This contrasts sharply with the known exponential space hardness of the reachability problem for discrete CRNs. We also prove that the related problem Sub-CCRN-REACH, which asks about reachability in a CCRN using only a given number of its reactions, is NP-complete.