Natural Computing

We survey and extend the work on the paradigm called "computing by observing". Its central feature is that one considers the behavior of an evolving system as the result of a computation. To this purpose an external observer records this behavior. In this way, several computational trade-offs between the observer and the observed system can be determined. It has turned out that the observed behavior of computationally simple systems can be very complex, when an appropriate observer is used. For example, a restricted version of context-free grammars with regular observers suffices to obtain computational completeness. As a second instantiation presented here, we apply an observer to sticker systems, an abstract model of DNA computing. Finally, we introduce and investigate the case where the observers can read only one measure of the observed system (e.g., mass or temperature) modeling in this way, limitations in the observation of real physical systems. Finally a research perspective on the topic is presented.

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 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.

The model we consider are stateless counter machines which mix the features of one-head counter machines and special two-head Watson-Crick automata (WK-automata). These biologically motivated machines have reading heads that read the input starting from the two extremes. The reading process is finished when the heads meet. The machine is realtime or non-realtime depending on whether the heads are required to advance at each move. A counter machine is k-reversal if each counter makes at most k alternations between increasing mode and decreasing mode on any computation, and reversal bounded if it is k-reversal for some k. In this paper we concentrate on the properties of deterministic stateless realtime WK-automata with counters that are reversal bounded. We give examples and establish hierarchies with respect to counters and reversals. Even 1-counter stateless WK-automata turn out to be quite powerful.

Combining forecasts is a common practice in time series analysis. This technique involves weighing each estimate of different models in order to minimize the error between the resulting output and the target. This work presents a novel methodology, aiming to combine forecasts using genetic programming, a metaheuristic that searches for a nonlinear combination and selection of forecasters simultaneously. To present the method, the authors made three different tests comparing with the linear forecasting combination, evaluating both in terms of RMSE and MAPE. The statistical analysis shows that the genetic programming combination outperforms the linear combination in two of the three tests evaluated.

Modern computers allow a methodical search of possibly billions of experiments and the exploitation of interactions that are not known in advance. This enables a bottom-up process of design by assembling or configuring systems and testing the degree to which they fulfill the desired goal. We give two detailed examples of this process. One is referred to as Cartesian genetic programming and the other evolution-in-materio. In the former, evolutionary algorithms are used to exploit the interactions of software components representing mathematical, logical, or computational elements. In the latter, evolutionary algorithms are used to manipulate physical systems particularly at the electrical or electronic level. We compare and contrast both approaches and discuss possible new research directions by borrowing ideas from one and using them in the other.

A hybrid approach called Evolutionary Swarm Cooperative Algorithm (ESCA) based on the collaboration between a particle swarm optimization algorithm and an evolutionary algorithm is presented. ESCA is designed to deal with moving optima of optimization problems in dynamic environments. ESCA uses three populations of individuals: two EA populations and one Particle Swarm Population. The EA populations evolve by the rules of an evolutionary multimodal optimization algorithm being used to maintain the diversity of the search. The particle swarm confers precision to the search process. The efficiency of ESCA is evaluated by means of numerical experiments.

In this statement we provide some examples of transdisciplinaryjourneys, from one field to another, and back. In particular, thequantuminformaticendeavoris not just a matter of feedingphys-ical theory into the general field of natural computation, bu t alsoone of using high-level methods developed in Computer Scienceto improve on the quantum physical formalism itself, and theunderstanding thereof. We highlight a seemingly contradictoryphenomenon: passing to an abstract, categorical quantum infor-matic formalism leads directly to a simple and elegant graphicalformulation of quantum theory itself, which for example makesthe design of some importantquantuminformaticprotocolscom-pletely transparent. It turns out that essentially all of the quan-tum informatic machinery can be recovered from this graphicalcalculus. But in turn, this graphical formalism provides a bridgebetween methods of logic and computer science, and some of themost exciting developments in the mathematics of the past tw...

We define a new relation on words by a finite series of insertions and/or deletions of palindromic subwords. In particular we concentrate on insertion or deletion of Watson–Crick palindromes. We show that the new relation ∼θ is, in fact, an equivalence relation where θ is any arbitrary antimorphic involution that is not the identity on the letters of the alphabet. We also show that the set of all θ-palindromic free words defined in (Daley et al. in preparation) is ∼θ-independent. Using the relation we define a new subclass of primitive words which we call as ∼θ-primitive words and show that the class of all ∼θ-primitive words is closed under circular permutations. We also define ∼θ-conjugates and ∼θ-commutativity and study the properties of such words and show that they are similar to that of conjugate words and words that commute.

In this paper, a hybridization of Harmony Search Algorithm (HSA) with a greedy shuffle move is proposed for Nurse Rostering Problem (NRP). NRP is a combinatorial optimization problem that is tackled by assigning a set of nurses with different skills and contracts to different types of shifts, over a pre-determined scheduling period. HSA is a population-based method which mimics the improvisation process that has been successfully applied for a wide range of optimization problems. The performance of HSA is enhanced by hybridizing it with a greedy shuffle move. The proposed method is evaluated using a dataset defined in first International Nurse Rostering Competition (INRC2010). The hybrid HSA obtained the best results of the comparative methods in four datasets.

This paper is placed in a formal framework in which the interdisciplinary study of natural language is conducted by integrating linguistics, computer science and biology. It provides an overview of the field of research, conveying the main biological ideas that have influenced research in linguistics. Our work highlights the main methods of molecular computing that have been applied to the processing and study of the structure of natural language: DNA computing, membrane computing and networks of evolutionary processors. Moreover, some new challenges and lines of research for the future are pointed out, that can provide important improvements in the understanding of natural language as a structure and a human capacity.

Recently, money laundering is becoming more and more sophisticated, it seems to have moved from the personal gain to the cliché of drug trafficking and financing terrorism. This criminal activity poses a serious threat not only to financial institutions but also to the nation. Today, most international financial institutions have been implementing anti-money laundering solutions but traditional investigative techniques consume numerous man-hours. Besides, most of the existing commercial solutions are based on statistics such as means and standard deviations and therefore are not efficient enough, especially for detecting suspicious cases in investment activities. In this paper, we present a case study of applying a knowledge-based solution that combines data mining and natural computing techniques to detect money laundering patterns. This solution is a part of a collaboration project between our research group and an international investment bank.

Securitatea se pare că poate fi mult mai uşor înţeleasă în prezenţa unei ameninţări concrete şi directe. Faptul că Războiul Rece s-a sfârşit la începutul anilor '90 a dus la dispariţia unei asemenea ameninţări. Astfel, statele europene care s-au declarat neutre, majoritatea din cauza situaţiei lor geopolitice dintre Est şi Vest, se aflau în acea perioadă întro situaţie de reevaluare a politicii lor de neutralitate.

The world of finance is an exciting and challenging environment. Recent years have seen an explosion in the application of computational intelligence methodologies in finance. In this article we provide an overview of some of these applications concentrating on those employing an evolutionary computation approach.

This work is an attempt for a state-of-the-art survey of natural and life sciences with the goal to define the scope and address the central questions of an original research program. It is focused on the phenomena of emergence, adaptive dynamics and evolution of self-assembling, self-organizing, selfmaintaining and self-replicating biosynthetic systems viewed from a newly-arranged perspective and understanding of computation and communication in the living nature. The author regards this research as an integral part of the emerging discipline of nature-inspired or natural computation, i.e. computation inspired by or occurring in nature. Within this context, he is interested in studies which represent a significant departure from traditional theories about complex systems and selforganization, emergent phenomena and artificial biology. In particular, these include non-conventional approaches exploring the aggregation, composition, growth and development of physical forms and structures, autopoiesis along with the associated abstract information structures and processes.

This paper proposes a multiobjective formulation for variable selection in multivariate calibration problems in order to improve the generalization ability of the calibration model. The authors applied this proposed formulation in the multiobjective genetic algorithm NSGA-II. The formulation consists in two conflicting objectives: minimize the prediction error and minimize the number of selected variables for multiple linear regression. These objectives are conflicting because, when the number of variables is reduced the prediction error increases. As study of case is used the wheat data set obtained by NIR spectrometry with the objective for determining a variable subgroup with information about protein concentration. The results of traditional techniques of multivariate calibration as the partial least square and successive projection algorithm for multiple linear regression are presented for comparisons. The obtained results showed that the proposed approach obtained better resul...

The growing complexity of real-world problems has motivated computer scientists to search for efficient problem-solving methods. Evolutionary Computation and Swarm Intelligence metaheuristics are outstanding examples that nature has been an unending source of inspiration. The behavior of bees, bacteria, glowworms, fireflies, slime molds, cockroaches, mosquitoes and other organisms have inspired swarm intelligence researchers to devise new optimization algorithms. This tutorial highlights the most recent nature-based inspirations as metaphors for swarm intelligence metaheuristics. We describe the biological behaviors from which a number of computational algorithms were developed. Also, the most recent and important applications and the main features of such metaheuristics are reported.

GEVA is an open source implementation of Grammatical Evolution in Java developed at UCD's Natural Computing Research & Applications group. As well as providing the characteristic genotype-phenotype mapper of GE a search algorithm engine and a simple GUI are also provided. A number of sample problems and tutorials on how to use and adapt GEVA have been developed.

We view Digital Ecosystems to be the digital counterparts of biological ecosystems. Here, we are concerned with the creation of these Digital Ecosystems, exploiting the self-organising properties of biological ecosystems to evolve high-level software applications. Therefore, we created the Digital Ecosystem, a novel optimisation technique inspired by biological ecosystems, where the optimisation works at two levels: a first optimisation, migration of agents which are distributed in a decentralised peer-to-peer network, operating continuously in time; this process feeds a second optimisation based on evolutionary computing that operates locally on single peers and is aimed at finding solutions to satisfy locally relevant constraints. The Digital Ecosystem was then measured experimentally through simulations, with measures originating from theoretical ecology, evaluating its likeness to biological ecosystems. This included its responsiveness to requests for applications from the user base, as a measure of the ecological succession (ecosystem maturity). Overall, we have advanced the understanding of Digital Ecosystems, creating Ecosystem-Oriented Architectures (EOA) where the word ecosystem is more than just a metaphor.

We define two accepting devices inspired by peptide computing called string binding-blocking automata and rewriting binding-blocking automata. In both the devices there is an option to mark some symbols -in one case, it is used to postpone reading of marked symbols to a later part of processing and in other case, it is used to store some information. These ideas are inherited from peptide computing. We show a nice hierarchy between these two systems and the previous model, the binding-blocking automaton. ⋆ A very short and preliminary version of this paper appeared in [1]. Language Theory in Biocomputing 1 UC'07 -Kingston, Canada

Meta-heuristic optimization algorithms have become popular choice for solving complex and intricate problems which are otherwise difficult to solve by traditional methods. In the present study an attempt is made to review the one main algorithm is a well known meta-heuristic; Particle Swarm Optimization (PSO). PSO, in its present form, has been in existence for roughly a decade, a relatively short time compared with some of the other natural computing paradigms such as artificial neural networks and evolutionary computation. However, in that short period, PSO has gained widespread appeal amongst researchers and has been shown to offer good performance in a variety of application domains, with potential for hybridization and specialization, and demonstration of some interesting emergent behavior. This study comprises a snapshot of particle swarm optimization from the authors' perspective, including variations in the algorithm, modifications and refinements introduced to prevent swarm stagnation and hybridization of PSO with other heuristic algorithms.

This paper deals with the spontaneous emergence of glider guns in cellular automata. An evolutionary search for glider guns with different parameters is described and other search techniques are also presented to provide a benchmark. We demonstrate the spontaneous emergence of an important number of novel glider guns discovered by an evolutionary algorithm. An automatic process to identify guns leads to a classification of glider guns that takes into account the number of emitted gliders of a specific type. We also show it is possible to discover guns for many other types of gliders. Significantly, all the found automata can be candidate to an automatic search for collision-based universal cellular automata simulating Turing machines in their space-time dynamics using gliders and glider guns.

We experimentally demonstrate that computation of spanning trees and implementation of general purpose storage-modification machines can be executed by a vegetative state of the slime mold Physarum polycephalum. We advance theory and practice of reaction-diffusion computing by studying a biological model of reaction-diffusion encapsulated in a membrane.

The increased interactivity and connectivity of computational devices along with the spreading of computational tools and computational thinking across the fields, has changed our understanding of the nature of computing. In the course of this development computing models have been extended from the initial abstract symbol manipulating mechanisms of stand-alone, discrete sequential machines, to the models of natural computing in the physical world, generally concurrent asynchronous processes capable of modelling living systems, their informational structures and dynamics on both symbolic and sub-symbolic information processing levels. Present account of models of computation highlights several topics of importance for the development of new understanding of computing and its role: natural computation and the relationship between the model and physical implementation, interactivity as fundamental for computational modelling of concurrent information processing systems such as living organisms and their networks, and the new developments in logic needed to support this generalized framework. Computing understood as information processing is closely related to natural sciences; it helps us recognize connections between sciences, and provides a unified approach for modeling and simulating of both living and non-living systems.

Many recent advances have been made in understanding the functional implications of the global topological properties of biological networks through the application of complex network theory, particularly in the area of small-world and scalefree topologies. Computational studies which attempt to understand the structure-function relationship usually proceed by defining a representation of cells and an affinity measure to describe their interactions. We show that this necessarily restricts the topology of the networks that can arise-furthermore, we show that although simple topologies can be produced via representation and affinity measures common in the literature, it is unclear how to select measures which result in complex topologies, for example, exhibiting scalefree functionality. In this paper, we introduce the concept of the potential network as a method in which abstract network topologies can be directly studied, bypassing any definition of shape-space and affinity function. We illustrate the benefit of the approach by studying the evolution of idiotypic networks on a selection of scale-free and regular topologies, finding that a key immunological property-tolerance-is promoted by bipartite and heterogeneous topologies. The approach, however, is applicable to the study of any network and thus has implications for both immunology and artificial immune systems.

The vehicle routing problem is a classical combinatorial optimization problem. This work is about a variant of the vehicle routing problem with dynamically changing orders and time windows. In real-world applications often the demands change during operation time. New orders occur and others are canceled. In this case new schedules need to be generated on-the-fly. Online optimization algorithms for dynamical vehicle routing address this problem but so far they do not consider time windows. Moreover, to match the scenarios found in real-world problems adaptations of benchmarks are required. In this paper, a practical problem is modeled based on the procedure of daily routing of a delivery company. New orders by customers are introduced dynamically during the working day and need to be integrated into the schedule. A multiple ant colony algorithm combined with powerful local search procedures is proposed to solve the dynamic vehicle routing problem with time windows. The performance is tested on a new benchmark based on simulations of a working day. The problems are taken from Solomon's benchmarks but a certain percentage of the orders are only revealed to the algorithm during operation time. Different versions of the MACS algorithm are tested and a high performing variant is identified. Finally, the algorithm is tested in situ: In a field study, the algorithm schedules a fleet of cars for a surveillance company. We compare the performance of the algorithm to that of the procedure used by the company and we summarize insights gained from the implementation of the real-world study. The results show that the multiple ant colony algorithm can get a much better solution on the academic benchmark problem and also can be integrated in a real-world environment. Keywords Ant colony optimization Á Vehicle routing problem Á Dynamic vehicle routing problem with time windows Á Pilot study A conference version van Veen et al. (2013) containing the theoretical part of this paper appeared under the title ''Ant Colony Algorithms for the Dynamic Vehicle Routing Problem with Time Windows'' in the conference IWINAC 2013.

This paper proposes a multiobjective formulation for variable selection in multivariate calibration problems in order to improve the generalization ability of the calibration model. The authors applied this proposed formulation in the multiobjective genetic algorithm NSGA-II. The formulation consists in two conflicting objectives: minimize the prediction error and minimize the number of selected variables for multiple linear regression. These objectives are conflicting because, when the number of variables is reduced the prediction error increases. As study of case is used the wheat data set obtained by NIR spectrometry with the objective for determining a variable subgroup with information about protein concentration. The results of traditional techniques of multivariate calibration as the partial least square and successive projection algorithm for multiple linear regression are presented for comparisons. The obtained results showed that the proposed approach obtained better resul...

Bat Algorithm (BA) is a simple and effective global optimization algorithm which has been applied to a wide range of real-world optimisation problems. Various extensions to Bat algorithm have been proposed in the past; prominent amongst them being ShBAT. ShBAT is a hybrid between BA and Shuffled Frog Leaping Algorithm-SFLA; a memetic algorithm based on food search behavior of frogs. ShBAT integrates the shuffling and reorganization technique of SFLA to enhance the exploitation capabilities of BAT. This paper proposes Enhanced Shuffled Bat algorithm (EShBAT) an extension to ShBAT. In ShBAT, different memeplexes evolve independently, with different cultures. EShBAT improves the exploitation capabilities of ShBAT by grouping together the best of each memeplex to form a super-memeplex. This super-memeplex evolves independently to further exploit the best solutions. The performance of EShBAT is verified over 30 well-known benchmark functions. Experimental results indicate a significant improvement of EShBAT over BA and ShBAT.

This work presents a discussion about the relationship between the contributions of Alan Turing the centenary of whose birth is celebrated in 2012to the field of artificial neural networks and modern unorganized machines: reservoir computing (RC) approaches and extreme learning machines (ELMs). Firstly, we review Turing's connectionist proposals and also expose the fundamentals of the main RC paradigmsecho state networks and liquid state machines -, as well as of the design and training of ELMs. Throughout this exposition, the main points of contact between Turing's ideas and these modern perspectives are outlined, being, then, duly summarized in the second and final part of the work. We hope this paper be useful in offering a distinct appreciation of Turing's pioneering contributions to the field of neural networks and also in indicating some perspectives for the future development of the field that may arise from the synergy between these views.

To date, a number of researchers are seeking for and/or designing novel molecules which function as arithmetic molecular engines. Biomolecules such as deoxyribonucleic acid (DNA) and proteins are examples of promising candidate molecules. In the present article, we showed our view that DNA-based molecules could be used as a novel class of platforms for discrete mathematical operations or tools for natural computation. Here, we report on a novel molecular logic circuit combining exclusive disjunction (XOR) gate and conjunction (AND) gate implemented on a single DNA molecule performing arithmetic operations with simple binary numbers through polymerase chain reactions (PCR); which was inspired by previously developed protein-based computing model allowing simple polynomial algebra over fields through algebraic representation of cyclic inter-conversions in the catalytic modes of a plant enzyme as a cyclic additive group. In addition, we showed that DNA can be used as the platform for image coding and processing leading to DNA-coded animation by using novel PCR-based protocols. Lastly, we discussed the significance of recent attempts in the stream of natural computing and synthetic biological research, by handling DNA and related biomolecules as the media for discrete mathematical operations.

This paper reports the hybridization of the artificial bee colony (ABC) and a genetic algorithm (GA), ina hierarchical topology, a step ahead of a previous work. We used this parallel approach for solving theprotein structure prediction problem using the three-dimensional hydrophobic-polar model with side-chains(3DHP-SC). The proposed method was run in a parallel processing environment (Beowulf cluster), andseveral aspects of the modeling and implementation are presented and discussed. The performance of thehybrid-hierarchical ABC-GA approach was compared with a hybrid-hierarchical ABC-only approach forfour benchmark instances. Results show that the hybridization of the ABC with the GA improves the qualityof solutions caused by the coevolution effect between them and their search behavior. Copyright © 2011John Wiley & Sons, Ltd.

The capability to establish adaptive relationships with the environment is an essential characteristic of living cells. Both bacterial computing and bacterial intelligence are two general traits manifested along adaptive behaviors that respond to surrounding environmental conditions. These two traits have generated a variety of theoretical and applied approaches. Since the different systems of bacterial signaling and the different ways of genetic change are better known and more carefully explored, the whole adaptive possibilities of bacteria may be studied under new angles. For instance, there appear instances of molecular "learning" along the mechanisms of evolution. More in concrete, and looking specifically at the time dimension, the bacterial mechanisms of learning and evolution appear as two different and related mechanisms for adaptation to the environment; in somatic time the former and in evolutionary time the latter. In the present chapter it will be reviewed the...

Meta-heuristic optimization algorithms have become popular choice for solving complex and intricate problems which are otherwise difficult to solve by traditional methods. In the present study an attempt is made to review the one main algorithm is a well known meta-heuristic; Particle Swarm Optimization (PSO). PSO, in its present form, has been in existence for roughly a decade, a relatively short time compared with some of the other natural computing paradigms such as artificial neural networks and evolutionary computation. However, in that short period, PSO has gained widespread appeal amongst researchers and has been shown to offer good performance in a variety of application domains, with potential for hybridization and specialization, and demonstration of some interesting emergent behavior. This study comprises a snapshot of particle swarm optimization from the authors' perspective, including variations in the algorithm, modifications and refinements introduced to prevent swarm stagnation and hybridization of PSO with other heuristic algorithms.

This paper provides an overview of existing approaches to encoding information on DNA strands for biocomputing, with a focus on the notion of Watson-Crick (WK) palindromes. We obtain a closed form for, as well as several properties of WK palindromes: The set of WK-palindromes is dense, context-free, but not regular, and is in general not closed under catenation and insertion. We obtain some properties that link the WK palindromes to classical notions such as that of primitive words. For example we show that the set of WK-palindromic words that cannot be written as the product of two nonempty WK-palindromes equals the set of primitive WK-palindromes. We also investigate various simultaneous Watson-Crick conjugate equations of words and show that the equations have, in most cases, only Watson-Crick palindromic solutions. Our results hold for more general functions, such as arbitrary morphic and antimorphic involutions.

We consider the parity problem in one-dimensional, binary, circular cellular automata: if the initial configuration contains an odd number of 1s, the lattice should converge to all 1s; otherwise, it should converge to all 0s. It is easy to see that the problem is ill-defined for even-sized lattices (which, by definition, would never be able to converge to 1). We then consider only odd lattices.

We propose certain non-Turing models of computation, but our intent is not to advocate models that surpass the power of Turing Machines (TMs), but to defend the need for models with orthogonal notions of power. We review the nature of models and argue that they are relative to a domain of application and are ill-suited to use outside that domain. Hence we review the presuppositions and context of the TM model and show that it is unsuited to natural computation (computation occurring in or inspired by nature). Therefore we must consider an expanded definition of computation that includes alternative (especially analog) models as well as the TM. Finally we present an alternative model, of continuous computation, more suited to natural computation. We conclude with remarks on the expressivity of formal mathematics.

In this paper, Parallel Evolutionary Algorithms for integer weight neural network training are presented. To this end, each processor is assigned a subpopulation of potential solutions. The subpopulations are independently evolved in parallel and occasional migration is employed to allow cooperation between them. The proposed algorithms are applied to train neural networks using threshold activation functions and weight values confined to a narrow band of integers. We constrain the weights and biases in the range [-3, 3], thus they can be represented by just 3 bits. Such neural networks are better suited for hardware implementation than the real weight ones. These algorithms have been designed keeping in mind that the resulting integer weights require less bits to be stored and the digital arithmetic operations between them are easier to be implemented in hardware. Another advantage of the proposed evolutionary strategies is that they are capable of continuing the training process "on-chip", if needed. Our intention is to present results of parallel evolutionary algorithms on this difficult task. Based on the application of the proposed class of methods on classical neural network problems, our experience is that these methods are effective and reliable.

When noise dominates an information system, like in nano-electronic systems of the foreseeable future, a natural question occurs: Can we perhaps utilize the noise as information carrier? Another question is: Can a deterministic logic scheme be constructed that may explain how the brain efficiently processes information, with random neural spike trains of less than 100 Hz frequency, and with a similar number of human brain neurons as the number of transistors in a 16 GB Flash dive? The answers to these questions are yes. Related developments indicate reduced power consumption with noise-based deterministic Boolean logic gates and the more powerful multivalued logic versions with an arbitrary number of logic values. Similar schemes as the Hilbert space of quantum informatics can also be constructed with noise-based logic by utilizing the noise-bits and their multidimensional hyperspace without the limitations of quantum-collapse of wavefunctions. A noise-based string search algorithm faster than Grover’s quantum search algorithm can be obtained, with the same hardware complexity class as the quantum engine. This logic hyperspace scheme has also been utilized to construct the noise-based neuro-bits and a deterministic multivalued logic scheme for the brain. Some of the corresponding circuitry of neurons is shown. Some questions and answers about a chip realization of such a random spike based deterministic multivalued logic scheme are presented.

Classification is an important task in time series mining. It is often reported in the literature that nearest neighbor classifiers perform quite well in time series classification, especially if the distance measure properly deals with invariances required by the domain. Complexity invariance was recently introduced, aiming to compensate from a bias towards classes with simple time series representatives in nearest neighbor classification. To this end, a complexity correcting factor based on the ratio of the more complex to the simpler series was proposed. The original formulation uses the length of the rectified time series to estimate its complexity. In this paper we investigate an alternative complexity estimate, based on fractal dimension. Results show that this alternative is very competitive with the original proposal, and has a broader application as it does neither depend on the number of points in the series nor on a previous normalization. Furthermore, these results also verify, using a different formulation, the validity of complexity invariance in time series classification.

Today's software applications increasingly feature a great deal of openness, dynamism and unpredictable behav- ior, forcing to shift design and engineering from traditional, centralized approaches to nature-inspired, self-organizing tech- niques. Among the others, biology has been adopted as a source of inspiration to solve some of the issues proper of nowadays systems by self-organizing techniques, usually exploited in an ad-hoc

It has been argued that neural networks and other forms of analog computation may transcend the limits of Turing-machine computation; proofs have been offered on both sides, subject to differing assumptions. In this article I argue that the important comparisons between the two models of computation are not so much mathematical as epistemological. The Turing-machine model makes assumptions about information representation and processing that are badly matched to the realities of natural computation (information representation and processing in or inspired by natural systems). This points to the need for new models of computation addressing issues orthogonal to those that have occupied the traditional theory of computation.