One-dimensional Rule Research Articles

Learning traps and change blindness in dynamic environments.

Learning traps arise when early experience leads to a false belief about the reward structure of the environment which, in turn, leads to avoidance of rewarding options. Previous work on the negative effects of such traps has focused on static learning environments. The current work examines an additional negative effect of learning traps in dynamic environments-blindness to change in the features that predict decision outcomes. In two experiments (N = 416), participants had to decide whether to approach members of two different categories, respectively associated with either gains or losses. Early in learning, a category rule involving two feature dimensions predicted category membership. Subsequently, there was a change in the feature composition of this rule. When outcome feedback was only provided when an item was approached, a substantial proportion of participants fell into the trap of using a simple one-dimensional rule to guide approach decisions. Most of these participants did not notice the subsequent rule change and never learned the new rule. Signaling the possibility of rule change (Experiment 2) had no effect on change blindness for those in the learning trap but did improve learning of the new rule for those who initially avoided the trap. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Filling Process Optimization through Modifications in Machine Settings

In this paper, a mathematical model is developed for the modified settings of an automatic filling machine to minimize the filling time of orders for different volumes of dairy product and flavors. The linear programming model is solved using the Simplex method to find an optimal solution to the optimization problem. The results of the model are used for sequencing the processing of orders using one-dimensional rules with the aim of obtaining an optimal sequence for the most valued performance measure. The comparative analysis of the one-dimensional rules showed that Shortest Processing Time (SPT) is better than the other rules for minimization of the average time past due. Additionally, the results of the model for the new machine settings, when compared with previous similar studies, yielded encouraging results.

Periodic Solutions of One-Dimensional Cellular Automata with Uniformly Chosen Random Rules


 
 
 We study cellular automata whose rules are selected uniformly at random. Our setting are two-neighbor one-dimensional rules with a large number $n$ of states. The main quantity we analyze is the asymptotic distribution, as $n \to \infty$, of the number of different periodic solutions with given spatial and temporal periods. The main tool we use is the Chen-Stein method for Poisson approximation, which establishes that the number of periodic solutions, with their spatial and temporal periods confined to a finite range, converges to a Poisson random variable with an explicitly given parameter. The limiting probability distribution of the smallest temporal period for a given spatial period is deduced as a corollary and relevant empirical simulations are presented.
 
 

Shift-equivalence of k-ary, one-dimensional cellular automata rules

Cellular automata are locally-defined, synchronous, homogeneous, fully discrete dynamical systems. In spite of their typically simple local behaviour, many are capable of showing complex emergent behaviour. When looking at their time-evolution, one may be interested in studying their qualitative dynamical behaviour. One way to group rules that display the same qualitative behaviour is by defining symmetries that map rules to others, the simplest way being by means of permutations in the set of state variables and reflections in their neighbourhood definitions, therefore defining equivalence classes. Here, we introduce the notion of shift-equivalence as another kind of symmetry, now relative to the concept of translation. After defining the notion and showing it indeed defines an equivalence relation, we extend the usual characterisation of dynamical equivalence and use it to partition some specific binary cellular automata rule spaces. Finally, we give a characterisation of the class of shift-equivalent rules in terms of the local transition functions of the cellular automata in the class, by providing an algorithm to compute the members of the class, for any k-ary, one-dimensional rule.

Non-intrusive uncertainty quantification using reduced cubature rules

For the purpose of uncertainty quantification with collocation, a method is proposed for generating families of one-dimensional nested quadrature rules with positive weights and symmetric nodes. This is achieved through a reduction procedure: we start with a high-degree quadrature rule with positive weights and remove nodes while preserving symmetry and positivity. This is shown to be always possible, by a lemma depending primarily on Carathéodory's theorem. The resulting one-dimensional rules can be used within a Smolyak procedure to produce sparse multi-dimensional rules, but weight positivity is lost then. As a remedy, the reduction procedure is directly applied to multi-dimensional tensor-product cubature rules. This allows to produce a family of sparse cubature rules with positive weights, competitive with Smolyak rules. Finally the positivity constraint is relaxed to allow more flexibility in the removal of nodes. This gives a second family of sparse cubature rules, in which iteratively as many nodes as possible are removed. The new quadrature and cubature rules are applied to test problems from mathematics and fluid dynamics. Their performance is compared with that of the tensor-product and standard Clenshaw–Curtis Smolyak cubature rule.

Computing Modulo-n by Composing Cellular Automata Rules

The understanding of how predefined computations can be attained by means of individ- ual cellular automata rules, their spatial arrangements or their temporal sequences, is a key concep- tual underpinning in the general notion of emergent computation. In this context, here we construct a solution to the MODn problem, which is the determination of whether the number of 1-bits in a cyclic binary string is perfectly divisible by the integer n > 1. Our solution is given for any lattice size N that is co-prime to n, and relies upon a set of one-dimensional rules, with maximum radius of n 1, organised in a temporal sequence. Although the simpler cases of the problem for n = 2 and n = 3 have been addressed in the literature, this is the first account on the general case, for arbitraryn.

Multidimensional paperfolding systems

Algorithms for constructing aperiodic structures produce templates for the nanofabrication of arrays for applications in photonics, phononics and plasmonics. Here a general multidimensional recursion rule is presented for the regular paperfolding structure by straightforward generalization of the one-dimensional rule. As an illustrative example the two-dimensional version of the paperfolding structure is explicitly constructed, its symbolic complexity referred to rectangles computed and its Fourier transform shown. The paperfolding structures readily yield novel 'paperfolding' tilings. Explicit formulas are put forward to count the number of folds in any dimension. Finally, possible generalizations of the dragon curve are discussed.

A study on learning robustness using asynchronous 1D cellular automata rules

Numerous studies can be found in literature concerning the idea of learning cellular automata (CA) rules that perform a given task by means of machine learning methods. Among these methods, genetic algorithms (GAs) have often been used with excellent results. Nevertheless, few attention has been dedicated so far to the generality and robustness of the learned rules. In this paper, we show that when GAs are used to evolve asynchronous one-dimensional CA rules, they are able to find more general and robust solutions compared to the more usual case of evolving synchronous CA rules.

The impact of category separation on unsupervised categorization

Most previous research on unsupervised categorization has used unconstrained tasks in which no instructions are provided about the underlying category structure or in which the stimuli are not clustered into categories. Few studies have investigated constrained tasks in which the goal is to learn predefined stimulus clusters in the absence of feedback. These studies have generally reported good performance when the stimulus clusters could be separated by a one-dimensional rule. In the present study, we investigated the limits of this ability. Results suggest that even when two stimulus clusters are as widely separated, as in previous studies, performance is poor if within-category variance on the relevant dimension is nonnegligible. In fact, under these conditions, many participants failed even to identify the single relevant stimulus dimension. This poor performance is generally incompatible with all current models of unsupervised category learning.

Learning and transfer of category knowledge in an indirect categorization task

Knowledge representations acquired during category learning experiments are 'tuned' to the task goal. A useful paradigm to study category representations is indirect category learning. In the present article, we propose a new indirect categorization task called the "same"-"different" categorization task. The same-different categorization task is a regular same-different task, but the question asked to the participants is about the stimulus category membership instead of stimulus identity. Experiment 1 explores the possibility of indirectly learning rule-based and information-integration category structures using the new paradigm. The results suggest that there is little learning about the category structures resulting from an indirect categorization task unless the categories can be separated by a one-dimensional rule. Experiment 2 explores whether a category representation learned indirectly can be used in a direct classification task (and vice versa). The results suggest that previous categorical knowledge acquired during a direct classification task can be expressed in the same-different categorization task only when the categories can be separated by a rule that is easily verbalized. Implications of these results for categorization research are discussed.

Strategy-proof voting rules on a multidimensional policy space for a continuum of voters with elliptic preferences

We consider voting rules on a multidimensional policy space for a continuum of voters with elliptic preferences. Assuming continuity, γ-strategy-proofness—meaning that coalitions of size smaller or equal to a small number γ cannot manipulate—and unanimity, we show that such rules are decomposable into one-dimensional rules. Requiring, additionally, anonymity leads to an impossibility result. The paper can be seen as an extension of the model of Border and Jordan (1983) to a continuum of voters. Contrary, however, to their finite case where single voters are atoms, in our model with nonatomic voters even a small amount of strategy-proofness leads to an impossibility.

CONSERVATION FEATURES IN BINARY COLLISIONS FOR RULE 110 CELLULAR AUTOMATON

This paper investigates collisions of gliders generated by one-dimensional Rule 110 cellular automaton. A specific value associated with each glider and an algebraic equation that describes the collision between two gliders were found. Because the products of the collision between two gliders may result in no gliders or one, two or more gliders, this equation states that the total sum of the associated values corresponding to colliding gliders equals the sum of the values of the gliders which are products of the collision. Moreover, an analogy is proposed between the glider collisions and the collisions of physical particles with the equation corresponding to colliding gliders being similar to the equation of energy conservation in physics. In this scheme, even without carrying out the temporal evolution for a collision, it can be determined if a possible combination of resulting gliders accomplishes the equation corresponding to that collision.

Some Investigations About Synchronization and Density Classification Tasks in One-dimensional and Two-dimensional Cellular Automata Rule Spaces

The study of computational aspects of cellular automata (CA) is a recurrent theme being that the investigation of specific tasks to be solved by CA rules a common and widely-known approach. We investigated two of the most-studied computational tasks: synchronization (ST) and density classification (DCT). Different specifications of CA rule space were analyzed for both tasks: one-dimensional rules with radius 1 and 2, and two-dimensional rules with von Neumann and Moore neighborhoods. We also analyzed different lattice sizes when trying to execute these tasks. Several evolutionary experiments were performed to characterize ST and DCT on these different scenarios. Some interesting results have been occurred from these experiments as the adequacy of the tasks to be solved in two-dimensional spaces instead of 1D even using rules with the same length and the dependency to the parity of the lattice size related to good rules for DCT in 1D and 2D spaces.

Novelty and conflict in the categorization of complex stimuli.

We manipulated categorical typicality and the presence of conflicting information as participants categorized multifeatured artificial animals. In Experiment 1, rule-irrelevant features were correlated with particular categories during training. In the test phase, participants applied a one-dimensional rule to stimuli with rule-irrelevant features that were category-congruent, category-incongruent, or novel. Category-incongruent and novel features delayed RT and P3 latency, but had no effect on the N2. Experiment 2 used a two-dimensional rule to create conflict between rule-relevant features. Conflict resulted in prolonged RTs and larger amplitudes of a prefrontal positive component, but had no impact on the N2. Stimuli with novel features did elicit a larger N2 than those with frequent features. These results suggest limitations on the generality of the N2's sensitivity to conflicting information while confirming its sensitivity to attended visual novelty.

Real-Time Implementation of Modified Fuzzy Logic Controller for a Non-Linear Quasi-Resonant DC-DC Converter

This paper describes the design and implementation of Modified Fuzzy Logic Controller (MFLC) for a non-linear quasi-resonant converter (QRC). It is shown that the two-dimensional rule table of conventional FLCs (CFLCs) used in power converters can be reduced to one-dimensional rule table using MFLC. The proposed MFLC reduces the memory space and computing time of the fuzzy algorithm. The tuning of scaling factors and the generation of fuzzy rules is also easier when compared with CFLC. As a result, realizing MFLC in a Microcontroller or Digital Signal Processor is made simple. The proposed controller structure is universal and it can be directly applied to any of the dc-dc converter topologies. In this paper, the application of MFLC is successfully verified for the voltage control of Extended Period (EP)-ZCS/ZVS-QRC through simulation and experimental studies using TMS320F2407A Processor. The ability of MFLC compared to CFLC, to achieve good transient response for load variations and supply disturbances are demonstrated.

Single-input fuzzy-like moving sliding surface approach to the sliding mode control

A new approach to the sliding mode control of second-order nonlinear systems is introduced in continuous-time. A single-input fuzzy logic controller is used to continuously compute the slope of the sliding surface, with the result that the sliding surface is rotated in such a direction that tracking performance of the system under control is improved. The proposed fuzzy moving sliding surface approach with a one-dimensional rule base (FMSS-1D) reduces huge number of linguistic fuzzy rules significantly. However, it is shown that the input/output relation of the single-input fuzzy rule base is very close to the input/output relation of a straight line. Therefore, a single-input fuzzy-like moving sliding surface (FLMSS) approach using an approximate line function is then proposed. It is shown that the proposed control approaches have better tracking performance than the conventional sliding mode control with fixed sliding surface. The proposed moving sliding surface approaches are applied to balance an inverted pendulum on a cart. Computer simulations are presented to show the effectiveness of the proposed methods and to make a quantitative comparison with the classical sliding-mode controller with fixed sliding surface method existing in literature.

DEVELOPMENT OF SIMPLE FUZZY LOGIC CONTROLLER FOR EXTENDED PERIOD-ZCS/ZVS-QUASI RESONANT CONVERTER: DESIGN, SIMULATION, AND EXPERIMENTATION

This paper describes the design and implementation of simple fuzzy logic controller (SFLC) for a nonlinear quasi-resonant converter (QRC). It is shown that the two-dimensional rule table of conventional FLCs (CFLCs) used in power converters can be reduced to one-dimensional rule table using SFLC. The proposed SFLC reduces the memory space and computing time of the fuzzy algorithm. The tuning of scaling factors and the generation of fuzzy rules are also easier when compared with CFLC. As a result, realizing SFLC in a Microcontroller or Digital Signal Processor (DSP) is made simple. The proposed controller structure is universal and it can be directly applied to any of the dc–dc converter topologies. In this paper, the application of SFLC is successfully verified for the voltage control of Extended Period (EP)-ZCS/ZVS-QRC through simulation and experimental studies using TMS320F2407A Processor. The ability of SFLC, compared to CFLC, to achieve good transient response for load variations and supply disturbances is demonstrated.

Eyetracking and selective attention in category learning

An eyetracking version of the classic Shepard, Hovland, and Jenkins (1961) experiment was conducted. Forty years of research has assumed that category learning often involves learning to selectively attend to only those stimulus dimensions useful for classification. We confirmed that participants learned to allocate their attention optimally. We also found that learners tend to fixate all stimulus dimensions early in learning. This result obtained despite evidence that participants were also testing one-dimensional rules during this period. Finally, the restriction of eye movements to only relevant dimensions tended to occur only after errors were largely (or completely) eliminated. We interpret these findings as consistent with multiple-systems theories of learning which maximize information input in order to maximize the number of learning modules involved, and which focus solely on relevant information only after one module has solved the learning problem.

Evolutionary Design of one-dimensional Rule Changing cellular automata using genetic algorithms.

In this paper we propose a new method to obtain transition rules of one-dimensional two-state cellular automata (CAs) using genetic algorithms (GAs). CAs have the advantages of producing complex systems from the interaction of simple elements, and have attracted increased research interest. However, the difficulty of designing CAs' transition rules to perform a particular task has severely limited their applications. The evolutionary design of CA rules has been studied by the EVCA group in detail. A GA was used to evolve CAs for two tasks: density classification and synchronization problems. That GA was shown to have discovered rules that gave rise to sophisticated emergent computational strategies. Sipper has studied a cellular programming algorithm for 2-state non-uniform CAs, in which each cell may contain a different rule. Meanwhile, Land and Belew proved that the perfect two-state rule for performing the density classification task does not exist. However, Fuks´ showed that a pair of human written rules performs the task perfectly when the size of neighborhood is one. In this paper, we consider a pair of rules and the number of rule iterations as a chromosome, whereas the EVCA group considers a rule as a chromosome. The present method is meant to reduce the complexity of a given problem by dividing the problem into smaller ones and assigning a distinct rule to each one. Experimental results for the two tasks prove that our method is more efficient than a conventional method. Some of the obtained rules agree with the human written rules shown by Fuks´. We also grouped 1000 rules with high fitness into 4 classes according to the Langton's λ parameter. The rules obtained by the proposed method belong to Class- I, II, III or IV, whereas most of the rules by the conventional method belong to Class-IV only. This result shows that the combination of simple rules can perform complex tasks.

On the canonical projection method for one-dimensional quasicrystals and invertible substitution rules

We show that if a quasiperiodic two-symbol sequence obtained by the canonical projection method has an infinite number of predecessors with respect to a substitution rule , then is an invertible substitution rule. Vice versa, we show that every quasiperiodic two-symbol sequence that has an infinite number of predecessors with respect to a non-trivial invertible substitution rule can be obtained by the canonical projection method.