Showing papers in "Natural Computing in 2016"

Emulating cellular automata in chemical reaction---diffusion networks

Abstract: Chemical reactions and diffusion can produce a wide variety of static or transient spatial patterns in the concentrations of chemical species. Little is known, however, about what dynamical patterns of concentrations can be reliably programmed into such reaction---diffusion systems. Here we show that given simple, periodic inputs, chemical reactions and diffusion can reliably emulate the dynamics of a deterministic cellular automaton, and can therefore be programmed to produce a wide range of complex, discrete dynamics. We describe a modular reaction---diffusion program that orchestrates each of the fundamental operations of a cellular automaton: storage of cell state, communication between neighboring cells, and calculation of cells' subsequent states. Starting from a pattern that encodes an automaton's initial state, the concentration of a "state" species evolves in space and time according to the automaton's specified rules. To show that the reaction---diffusion program we describe produces the target dynamics, we simulate the reaction---diffusion network for two simple one-dimensional cellular automata using coupled partial differential equations. Reaction---diffusion based cellular automata could potentially be built in vitro using networks of DNA molecules that interact via branch migration processes and could in principle perform universal computation, storing their state as a pattern of molecular concentrations, or deliver spatiotemporal instructions encoded in concentrations to direct the behavior of intelligent materials.

Classical, quantum and biological randomness as relative unpredictability

Abstract: We propose the thesis that randomness is unpredictability with respect to an intended theory and measurement. From this point of view we briefly discuss various forms of randomness that physics, mathematics and computing science have proposed. Computing science allows to discuss unpredictability in an abstract, yet very expressive way, which yields useful hierarchies of randomness and may help to relate its various forms in natural sciences. Finally we discuss biological randomness--its peculiar nature and role in ontogenesis and in evolutionary dynamics (phylogenesis). Randomness in biology has a positive character as it contributes to the organisms' and populations' structural stability by adaptation and diversity.

A new approach for solving set covering problem using jumping particle swarm optimization method

Abstract: The set covering problem (SCP) is a well known classic combinatorial NP-hard problem, having practical application in many fields. To optimize the objective function of the SCP, many heuristic, meta heuristic, greedy and approximation approaches have been proposed in the recent years. In the development of swarm intelligence, the particle swarm optimization is a nature inspired optimization technique for continuous problems and for discrete problems we have the well known discrete particle swarm optimization (DPSO) method. Aiming towards the best solution for discrete problems, we have the recent method called jumping particle swarm optimization (JPSO). In this DPSO the improved solution is based on the particles attraction caused by attractor. In this paper, a new approach based on JPSO is proposed to solve the SCP. The proposed approach works in three phases: for selecting attractor, refining the feasible solution given by the attractor in order to reach the optimality and for removing redundancy in the solution. The proposed approach has been tested on the benchmark instances of SCP and compared with best known methods. Computational results show that it produces high quality solution in very short running times when compared to other algorithms.

Probability 1 computation with chemical reaction networks

Abstract: The computational power of stochastic chemical reaction networks (CRNs) varies significantly with the output convention and whether or not error is permitted. Focusing on probability 1 computation, we demonstrate a striking difference between stable computation that converges to a state where the output cannot change, and the notion of limit-stable computation where the output eventually stops changing with probability 1. While stable computation is known to be restricted to semilinear predicates (essentially piecewise linear), we show that limit-stable computation encompasses the set of predicates $$\phi :{\mathbb {N}}\rightarrow \{0,1\}$$?:N?{0,1} in $$\Delta ^0_2$$Δ20 in the arithmetical hierarchy (a superset of Turing-computable). In finite time, our construction achieves an error-correction scheme for Turing universal computation. We show an analogous characterization of the functions $$f:{\mathbb {N}}\rightarrow {\mathbb {N}}$$f:N?N computable by CRNs with probability 1, which encode their output into the count of a certain species. This work refines our understanding of the tradeoffs between error and computational power in CRNs.

A bio inspired and trust based approach for clustering in WSN

Abstract: Wireless sensor network (WSN) is a special kind of ad-hoc network consists of battery powered low cost sensor nodes with limited computation and communication capabilities deployed densely in a target area. Clustering in WSN plays an important role because of its inherent energy saving capability and suitability for highly scalable network. This paper is an extended version of our previous work (Sahoo et al. 2013a). Although the clustering strategy presented in this paper is same as our previous work but here a light weight dynamic TRUST model along with honey bee mating algorithm is presented, which will only prevent malicious node to be a cluster head. The choice of light weight TRUST model makes our clustering method more secure and energy efficient, which are most pivotal issues for resource constrained sensor network. We have also introduced a priority scheme among the trust metrics which is more realistic. Furthermore, the use of honey bee mating algorithm finds most appropriate node as cluster head. Simulation results are also presented here to compare the performance of our algorithm with low energy adaptive clustering hierarchy and advertisement time-out driven bee mating approach to maintain fair energy level in sensor networks.

Physarum in silicon: the Greek motorways study

Abstract: Physarum polycephalum has repeatedly, during the last decade, demonstrated that has unexpected computing abilities. While the plasmodium of P. polycephalum can effectively solve several geographical described problems, like evaluating human---made transport networks, a disadvantage of a biological computer, like the aforementioned is directly apparent; the great amount of time needed to provide results. Thus, the main focus of this paper is the enhancement of the time efficiency of the biological computer by using conventional computers or even digital circuitry. Cellular automata (CA) as a powerful computational tool has been selected to tackle with these difficulties and a software (Matlab) CA model is used to produce results in shorter time periods. While the duration of a laboratory experiment is occasionally from 3 to 5 days, the CA model, for a specific configuration, needs around 40 s. In order to achieve a further acceleration of the computation, a hardware implementation of the corresponding CA software based model is proposed here, taking full advantage of the CA inherent parallelism, uniformity and the locality of interconnections. Consequently, the digital circuit designed can be used as a massively parallel nature inspired computer for real---time applications. The hardware implementation of the model needs six orders of magnitude less time than the software representation. In this paper, in order to develop a proof of concept and depict the applicability of the proposed hardware oriented CA approach, the topology of Greece is used as an input of the biological computer. The network formed by the in vitro experiments, along with the one designed by the CA model and implemented in hardware are compared with the real motorways and the proximity graphs of the topology.

Development of firefly algorithm via chaotic sequence and population diversity to enhance the image contrast

Abstract: Nature-inspired algorithms have been applied in the optimization field including digital image processing like image enhancement or segmentation Firefly algorithm (FA) is one of the most powerful of them In this paper two different implementation of FA has been taken into consideration One of them is FA via levy flight where step length of levy flight has been taken from chaotic sequence Chaotic sequence shows ergodicity property which helps in better searching But in the second implementation chaotic sequence replaces levy flight to enhance the capability of FA Population of individuals has been created in every generation using the information of population diversity As an affect FA does not converges prematurely These two modified FA algorithms have been applied to optimize parameters of parameterized contrast stretching function Entropy, contrast and energy of the image have been used as objective criterion for measuring goodness of image enhancement Fitness criterion has been maximized in order to get enhanced image with better contrast From the experimental results it has been shown that FA with chaotic sequence and population diversity information outperforms the Particle swarm optimization and FA via levy flight

Monodirectional P systems

Abstract: We investigate the influence that the flow of information in membrane systems has on their computational complexity. In particular, we analyse the behaviour of P systems with active membranes where communication only happens from a membrane towards its parent, and never in the opposite direction. We prove that these "monodirectional P systems" are, when working in polynomial time and under standard complexity-theoretic assumptions, much less powerful than unrestricted ones: indeed, they characterise classes of problems defined by polynomial-time Turing machines with $${\mathbf{NP}}$$NP oracles, rather than the whole class $${\mathbf{PSPACE}}$$PSPACE of problems solvable in polynomial space.

Global memory schemes for dynamic optimization

Abstract: Nowadays, it is common to find research problems (in system biology, mobile applications, etc) that change over time, requiring algorithms which dynamically adapt the search to the new conditions In most of them, the utilization of some information from the past allows to quickly adapt after a change This is the idea underlining the use of memory in this field, what involves key design issues concerning the memory content, the process of update, and the process of retrieval In this article, we focus on global memory schemes, which are the most intuitive and popular ones, and perform an integral analysis of current design variants based on a comprehensive set of benchmarks Results show the benefits and drawbacks of each strategy, as well as the effect of the algorithm and problem features in the memory performance

Fast arithmetic in algorithmic self-assembly

Abstract: In this paper we consider the time complexity of adding two n-bit numbers together within the tile self-assembly model. The (abstract) tile assembly model is a mathematical model of self-assembly in which system components are square tiles with different glue types assigned to tile edges. Assembly is driven by the attachment of singleton tiles to a growing seed assembly when the net force of glue attraction for a tile exceeds some fixed threshold. Within this frame work, we examine the time complexity of computing the sum of two n-bit numbers, where the input numbers are encoded in an initial seed assembly, and the output sum is encoded in the final, terminal assembly of the system. We show that this problem, along with multiplication, has a worst case lower bound of $$\varOmega ( \sqrt{n} )$$Ω(n) in 2D assembly, and $$\varOmega (\root 3 \of {n})$$Ω(n3) in 3D assembly. We further design algorithms for both 2D and 3D that meet this bound with worst case run times of $$O(\sqrt{n})$$O(n) and $$O(\root 3 \of {n})$$O(n3) respectively, which beats the previous best known upper bound of O(n). Finally, we consider average case complexity of addition over uniformly distributed n-bit strings and show how we can achieve $$O(\log n)$$O(logn) average case time with a simultaneous $$O(\sqrt{n})$$O(n) worst case run time in 2D. As additional evidence for the speed of our algorithms, we implement our algorithms, along with the simpler O(n) time algorithm, into a probabilistic run-time simulator and compare the timing results.

Interactive computations: toward risk management in interactive intelligent systems

Abstract: Understanding the nature of interactions is regarded as one of the biggest challenges in projects related to complex adaptive systems. We discuss foundations for interactive computations in interactive intelligent systems (IIS), developed in the Wistech program and used for modeling complex systems. We emphasize the key role of risk management in problem solving by IIS. The considerations are based on experience gained in real-life projects concerning, e.g., medical diagnosis and therapy support, control of an unmanned helicopter, fraud detection algorithmic trading or fire commander decision support.

A multi-objective membrane algorithm guided by the skin membrane

Abstract: Multi-objective optimization problems exist widely in the field of engineering and science. Many nature-inspired methods, such as genetic algorithms, particle swarm optimization algorithms and membrane computing model based algorithms, were proposed to solve the problems. Among these methods, membrane computing model based algorithms, also termed membrane algorithms, are becoming a current research hotspot because the successful linkage of membrane computing and evolutionary algorithms. In the past years, a lot of effective multi-objective membrane algorithms have been designed, where the skin membrane was often only used as an archive to store good solutions. In this paper, we propose an effective multi-objective membrane algorithm guided by the skin membrane, named SMG-MOMA, where the information of solutions stored in the skin membrane is used to guide the evolution of internal membranes. A skin membrane guiding strategy is suggested by allocating the solutions in skin membrane to internal membranes. Experimental results on ZDT and DTLZ benchmark multi-objective problems show that the proposed algorithm outperforms the-state-of-the-art multi-objective optimization algorithms.

The computational capability of chemical reaction automata

Abstract: We propose a new computing model called chemical reaction automata (CRAs) as a simplified variant of reaction automata (RAs) studied in recent literature (Okubo in RAIRO Theor Inform Appl 48:23---38 2014; Okubo et al. in Theor Comput Sci 429:247---257 2012a, Theor Comput Sci 454:206---221 2012b). We show that CRAs in maximally parallel manner are computationally equivalent to Turing machines, while the computational power of CRAs in sequential manner coincides with that of the class of Petri nets, which is in marked contrast to the result that RAs (in both maximally parallel and sequential manners) have the computing power of Turing universality (Okubo 2014; Okubo et al. 2012a). Intuitively, CRAs are defined as RAs without inhibitor functioning in each reaction, providing an offline model of computing by chemical reaction networks (CRNs). Thus, the main results in this paper not only strengthen the previous result on Turing computability of RAs but also clarify the computing powers of inhibitors in RA computation.

An improved dynamic membrane evolutionary algorithm for constrained engineering design problems

Abstract: Constrained global optimization is a highly important and challenging task in the field of optimization, and is embedded in many science and engineering optimizations. In this paper, an improved dynamic membrane evolutionary algorithm based on particle swarm optimization and differential evolution (IDMEA-PSO/DE) is proposed to solve constrained engineering design problems. The method combines the dynamic membrane structure of P systems and the PSO/DE search strategy. The performance of IDMEA-PSO/DE is tested on several well-known engineering design problems. The results of the simulation experiments show that the proposed algorithm is effective and outperforms other state-of-the-art-algorithms.

Synthetic biology of cell signaling

Abstract: Synthetic biology often takes cues from complex natural networks and pathways to create novel biological systems. The design modalities used in synthetic systems generally follow the different classes of gene regulation in cells such as transcriptional, post-transcriptional and post-translational regulation. The latter class is most prominent in cell signaling pathways that operate via multitude of protein---protein interactions. Engineering signaling pathways is a relatively unexplored area. This review discussed the work toward signaling pathway engineering in diverse biological contexts including bacteria, yeast, vertebrate, and plant cells. While creating synthetic signaling cascades is perhaps one of the most challenging tasks in synthetic biology, potential implications can be far-reaching and include new tools for programming cells and tissues, artificial developmental processes, and therapeutic tools.

Detecting outliers in categorical data through rough clustering

Abstract: Outlier detection is an important data mining task with many contemporary applications. Clustering based methods for outlier detection try to identify the data objects that deviate from the normal data. However, the uncertainty regarding the cluster membership of an outlier object has to be handled appropriately during the clustering process. Additionally, carrying out the clustering process on data described using categorical attributes is challenging, due to the difficulty in defining requisite methods and measures dealing with such data. Addressing these issues, a novel algorithm for clustering categorical data aimed at outlier detection is proposed here by modifying the standard $$k$$k-modes algorithm. The uncertainty regarding the clustering process is addressed by considering a soft computing approach based on rough sets. Accordingly, the modified clustering algorithm incorporates the lower and upper approximation properties of rough sets. The efficacy of the proposed rough $$k$$k-modes clustering algorithm for outlier detection is demonstrated using various benchmark categorical data sets.

On string languages generated by sequential spiking neural P systems based on the number of spikes

Abstract: Spiking neural P systems (SN P systems, for short) are a class of distributed parallel computing devices inspired from the way neurons communicate by means of spikes. In this work, we consider SN P systems with the following restriction: at each step the active neuron with the maximum (or minimum) number of spikes among the neurons that can spike will fire [if there is a tie for the maximum (or minimum) number of spikes stored in the active neurons, only one of the neurons containing the maximum (or minimum) is chosen non-deterministically]. We investigate the computational power of such sequential SN P systems that are used as language generators. We prove that recursively enumerable languages can be characterized as projections of inverse-morphic images of languages generated by such sequential SN P systems. The relationships of the languages generated by these sequential SN P systems with finite and regular languages are also investigated.

Doubles and negatives are positive (in self-assembly)

Abstract: In the abstract Tile Assembly Model (aTAM), the phenomenon of cooperation occurs when the attachment of a new tile to a growing assembly requires it to bind to more than one tile already in the assembly. Often referred to as "temperature-2" systems, those which employ cooperation are known to be quite powerful (i.e. they are computationally universal and can build an enormous variety of shapes and structures). Conversely, aTAM systems which do not enforce cooperative behavior, a.k.a. "temperature-1" systems, are conjectured to be relatively very weak, likely to be unable to perform complex computations or algorithmically direct the process of self-assembly. Nonetheless, a variety of models based on slight modifications to the aTAM have been developed in which temperature-1 systems are in fact capable of Turing universal computation through a restricted notion of cooperation. Despite that power, though, several of those models have previously been proven to be unable to perform or simulate the stronger form of cooperation exhibited by temperature-2 aTAM systems. In this paper, we first prove that another model in which temperature-1 systems are computationally universal, namely the restricted glue TAM (rgTAM) in which tiles are allowed to have edges which exhibit repulsive forces, is also unable to simulate the strongly cooperative behavior of the temperature-2 aTAM. We then show that by combining the properties of two such models, the Dupled Tile Assembly Model (DTAM) and the rgTAM into the DrgTAM, we derive a model which is actually more powerful at temperature-1 than the aTAM at temperature-2. Specifically, the DrgTAM, at temperature-1, can simulate any aTAM system of any temperature, and it also contains systems which cannot be simulated by any system in the aTAM.

Anytime pack search

Abstract: Heuristic search is one of the fundamental problem solving techniques in artificial intelligence, which is used in general to efficiently solve computationally hard problems in various domains, especially in planning and optimization. In this paper, we present an anytime heuristic search algorithm called anytime pack search (APS) which produces good quality solutions quickly and improves upon them over time, by focusing the exploration on a limited set of most promising nodes in each iteration. We discuss the theoretical properties of APS and show that it is complete. We also present the complexity analysis of the proposed algorithm on a tree state-space model and show that it is asymptotically of the same order as that of A*, which is a widely applied best-first search method. Furthermore, we present a parallel formulation of the proposed algorithm, called parallel anytime pack search (PAPS), which is applicable for searching tree state-spaces. We theoretically prove the completeness of PAPS. Experimental results on the sliding-tile puzzle problem, traveling salesperson problem, and single machine scheduling problem depict that the proposed sequential algorithm produces much better anytime performance when compared to some of the existing methods. Also, the proposed parallel formulation achieves super-linear speedups over the sequential method.

Gene expression and protein---protein interaction data for identification of colon cancer related genes using f-information measures

Abstract: One of the most important and challenging problems in functional genomics is how to select the disease genes. In this regard, the paper presents a new computational method to identify disease genes. It judiciously integrates the information of gene expression profiles and shortest path analysis of protein---protein interaction networks. While the $$f$$f-information based maximum relevance-maximum significance framework is used to select differentially expressed genes as disease genes using gene expression profiles, the functional protein association network is used to study the mechanism of diseases. An important finding is that some $$f$$f-information measures are shown to be effective for selecting relevant and significant genes from microarray data. Extensive experimental study on colorectal cancer establishes the fact that the genes identified by the integrated method have more colorectal cancer genes than the genes identified from the gene expression profiles alone, irrespective of any gene selection algorithm. Also, these genes have greater functional similarity with the reported colorectal cancer genes than the genes identified from the gene expression profiles alone. The enrichment analysis of the obtained genes reveals to be associated with some of the important KEGG pathways. All these results indicate that the integrated method is quite promising and may become a useful tool for identifying disease genes.

A quantum particle swarm optimization for the 0---1 generalized knapsack sharing problem

Abstract: This study proposes a new hybrid heuristic approach that combines the quantum particle swarm optimization (QPSO) technique with a local search phase to solve the binary generalized knapsack sharing problem (GKSP). The approach also incorporates a heuristic repair operator that uses problem-specific knowledge instead of the penalty function technique commonly used for constrained problems. This study is the first to report on the application of the QPSO method to the GKSP. The efficiency of our proposed approach was tested on a large set of instances, and the results were compared to those produced by the commercial mixed integer programming solver CPLEX 12.5 of IBM-ILOG. The Experimental results demonstrated the good performance of the QPSO in solving the GKSP.

An improved multi-objective evolutionary algorithm for simultaneously detecting separated and overlapping communities

Abstract: In our previous work, a multi-objective evolutionary algorithm (MEA_CDPs) was proposed for detecting separated and overlapping communities simultaneously. However, MEA_CDPs has a couple of defects, like individuals cannot be transformed to community structure by the decoder when the quality of community structure is lower certain thresholds, many vertices with weak overlapping nature are identified as overlapping nodes, and the objective functions can not control the ratio of separated nodes to overlapping nodes. Therefore, in this paper, to overcome these defects, we improve MEA_CDPs by designing more efficient objective functions. We also extend MEA_CDPs' capability in detecting hierarchical community structures. The improved algorithm is named as iMEA_CDPs. In the experiments, a set of computer-generated networks are first used to test the effect of parameters in iMEA_CDPs, and then four real-world networks are used to validate the performance of iMEA_CDPs. The experimental results show that iMEA_CDPs outperforms MEA_CDPs. Moreover, compared with MEA_CDPs, iMEA_CDPs can detect various kinds of overlapping and hierarchical community structures.

More on quantum, stochastic, and pseudo stochastic languages with few states

Abstract: Stochastic languages are the languages recognized by probabilistic finite automata (PFAs) with cutpoint over the field of real numbers More general computational models over the same field such as generalized finite automata (GFAs) and quantum finite automata (QFAs) define the same class In 1963, Rabin proved the set of stochastic languages to be uncountable presenting a single 2-state PFA over the binary alphabet recognizing uncountably many languages depending on the cutpoint In this paper, we show the same result for unary stochastic languages Namely, we exhibit a 2-state unary GFA, a 2-state unary QFA, and a family of 3-state unary PFAs recognizing uncountably many languages; all these numbers of states are optimal After this, we completely characterize the class of languages recognized by 1-state GFAs, which is the only nontrivial class of languages recognized by 1-state automata Finally, we consider the variations of PFAs, QFAs, and GFAs based on the notion of inclusive/exclusive cutpoint, and present some results on their expressive power

Evolution of new algorithms for the binary knapsack problem

Abstract: Due to its NP-hard nature, it is still difficult to find an optimal solution for instances of the binary knapsack problem as small as 100 variables. In this paper, we developed a three-level hyper-heuristic framework to generate algorithms for the problem. From elementary components and multiple sets of problem instances, algorithms are generated. The best algorithms are selected to go through a second step process, where they are evaluated with problem instances that differ in size and difficulty. The problem instances are generated according to methods that are found in the literature. In all of the larger problem instances, the generated algorithms have less than 1 % error with respect to the optimal solution. Additionally, generated algorithms are efficient, taking on average fractions of a second to find a solution for any instance, with a standard deviation of 1 s. In terms of structure, hyper-heuristic algorithms are compact in size compared with those in the literature, allowing an in-depth analysis of their structure and their presentation to the scientific world.

Parallel simulation of Population Dynamics P systems: updates and roadmap

Abstract: Population Dynamics P systems are a type of multienvironment P systems that serve as a formal modeling framework for real ecosystems. The accurate simulation of these probabilistic models, e.g. with Direct distribution based on Consistent Blocks Algorithm, entails large run times. Hence, parallel platforms such as GPUs have been employed to speedup the simulation. In 2012, the first GPU simulator of PDP systems was presented. However, it was able to run only randomly generated PDP systems. In this paper, we present current updates made on this simulator, involving an input modu le for binary files and an output module for CSV files. Finally, the simulator has been experimentally validated with a real ecosystem model, and its performance has been tested with two high-end GPUs: Tesla C1060 and K40.

A class of restricted P colonies with string environment

Abstract: In this paper we continue the study of variants of P colonies, called APCol systems, where the environment is given as a string and the model is an accepting system. We develop the concept by introducing the notion of the generating working mode. We then compare the power of a special subclass of APCol systems working in the generating mode to the power of register machines and context-free matrix grammars without appearance checking.

Levy distributed parameter control in differential evolution for numerical optimization

Abstract: Differential evolution (DE) algorithm is a population based stochastic search technique widely applied in scientific and engineering fields for global optimization over real parameter space. The performance of DE algorithm highly depends on the selection of values of the associated control parameters. Therefore, finding suitable values of control parameters is a challenging task and researchers have already proposed several adaptive and self-adaptive variants of DE. In the paper control parameters are adapted by levy distribution, named as Levy distributed DE (LdDE) which efficiently handles exploration and exploitation dilemma in the search space. In order to assure a fair comparison with existing parameter controlled DE algorithms, we apply the proposed method on number of well-known unimodal, basic and expanded multimodal and hybrid composite benchmark optimization functions having different dimensions. The empirical study shows that the proposed LdDE algorithm exhibits an overall better performance in terms of accuracy and convergence speed compared to five prominent adaptive DE algorithms.

Adaptive niche quantum-inspired immune clonal algorithm

Abstract: The adaptive niche quantum-inspired immune clonal algorithm (ANQICA) is proposed by combining the quantum coding, immune clone and niche mechanism together to solve the multi-modal function optimization more effectively and make the function converge to as many as possible extreme value points. The quantum coding can better explore the solution space, the niche mechanism ensures the algorithm to converge to multi-extremum and the adaptive mechanism is introduced according to the characteristics of each procedure of the algorithm to improve the effect of the algorithm. Example analysis shows that the ANQICA is better in exploration and convergence. Therefore, the ANQICA can be used to solve the problem of multi-modal function optimization effectively.

On decidability and closure properties of language classes with respect to bio-operations

Abstract: We present general results that are useful in showing closure and decidable properties of large classes of languages with respect to biologically-inspired operations. We use these results to prove new decidability results and closure properties of some classes of languages under bio-operations such hairpin-inversion, the recently studied operation of pseudo-inversion, and other bio-operations. We also provide techniques for proving undecidability results. In particular, we give a new approach for proving the undecidability of problems for which the usual method of reduction to the undecidability of the Post Correspondence Problem seems hard to apply. Our closure and decidability results strengthen or generalize previous results.

Projections onto convex sets parameter estimation through harmony search and its application for image restoration

Abstract: Image restoration is a research field that attempts to recover a blurred and noisy image. Although we have one-step algorithms that are often fast for image restoration, iterative formulations allow a better control of the trade-off between the enhancement of high frequencies (image details) and noise amplification. Projections onto convex sets (POCS) is an iterative--and parametric-based approach that employs a priori knowledge about the blurred image to guide the restoration process, with promising results in different application domains. However, a proper choice of its parameters is a high computational burden task, since they are continuous-valued and there are an infinity of possible values to be checked. In this paper, we propose to optimize POCS parameters by means of harmony search-based techniques, since they provide elegant and simple formulations for optimization problems. The proposed approach has been validated in synthetic and real images, being able to select suitable parameters in a reasonable amount of time.