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Symbolic stochastic dynamical systems viewed as binary N-step Markov chains.

A theory of systems with long-range correlations based on the consideration of binary N-step Markov chains is developed. In the model, the conditional probability that the ith symbol in the chain equals zero (or unity) is a linear function of the number of unities among the preceding N symbols. The correlation and distribution functions as well as the variance of the number of symbols in the words of arbitrary length L are obtained analytically and numerically. A self-similarity of the studied stochastic process is revealed and the similarity group transformation of the chain parameters is presented. The diffusion Fokker-Planck equation governing the distribution function of the L words is explored. If the persistent correlations are not extremely strong, the distribution function is shown to be the Gaussian with the variance being nonlinearly dependent on L. The applicability of the developed theory to the coarse-grained written and DNA texts is discussed.

Journal Article↗

Topographic voltage and coherence mapping of brain potentials by means of the symbolic resonance analysis.

We apply the recently developed symbolic resonance analysis to electroencephalographic measurements of event-related brain potentials (ERPs) in a language processing experiment by using a three-symbol static encoding with varying thresholds for analyzing the ERP epochs, followed by a spin-flip transformation as a nonlinear filter. We compute an estimator of the signal-to-noise ratio (SNR) for the symbolic dynamics measuring the coherence of threshold-crossing events. Hence, we utilize the inherent noise of the EEG for sweeping the underlying ERP components beyond the encoding thresholds. Plotting the SNR computed within the time window of a particular ERP component (the N400) against the encoding thresholds, we find different resonance curves for the experimental conditions. The maximal differences of the SNR lead to the estimation of optimal encoding thresholds. We show that topographic brain maps of the optimal threshold voltages and of their associated coherence differences are able to dissociate the underlying physiological processes, while corresponding maps gained from the customary voltage averaging technique are unable to do so.

Algorithms↗

Validity of threshold-crossing analysis of symbolic dynamics from chaotic time series

A practical and popular technique to extract the symbolic dynamics from experimentally measured chaotic time series is the threshold-crossing method, by which an arbitrary partition is utilized for determining the symbols. We address to what extent the symbolic dynamics so obtained can faithfully represent the phase-space dynamics. Our principal result is that such a practice can lead to a severe misrepresentation of the dynamical system. The measured topological entropy is a Devil's staircase-like, but surprisingly nonmonotone, function of a parameter characterizing the amount of misplacement of the partition.

Journal Article↗

Symbolic dynamics of coupled map lattices.

We present a method to reduce the [FORMULA: SEE TEXT] dynamics of coupled map lattices (CMLs) of N invertibly coupled unimodal maps to a sequence of N-bit symbols. We claim that the symbolic description is complete and provides for the identification of all fixed points, periodic orbits, and dense orbits as well as an efficient representation for studying pattern formation in CMLs. We give our results for CMLs in terms of symbolic dynamical concepts well known for one-dimensional chaotic maps, including generating partitions, Gray orderings, and kneading sequences. An example utilizing coupled quadratic maps is given.

Journal Article↗

Periodic intensity distribution (PID) of mica polytypes: symbolism, structural model orientation and axial settings.

Following a preliminary revisitation of the nomenclatures in use for mica polytypes, the properties of the periodic intensity distribution (PID) function, which represents the Fourier transform of the stacking sequence, are analysed. On the basis of the relative rotations of neighbouring layers, mica polytypes are classified into three types; for each type, the PID exists in different subspaces of the reciprocal space. A revised procedure to compute the PID, in which further restrictions on the structural model orientation are introduced, is presented. A unifying terminology based upon the most common symbols used to describe mica polytypes (RTW, Z and TS) is derived; these symbols represent the geometrical basis for the computation of the PID. Results are presented for up to four layer polytypes and are compared with the reflection conditions derived by means of Zvyagin's functions. Both the PID values and the reflection conditions are expressed in suitable axial settings and compared with previous partial reports, revealing some errors in previous analyses. A computer program to compute PID from the stacking symbols is available.

Journal Article↗

Symbol recognition with kernel density matching.

We propose a novel approach to similarity assessment for graphic symbols. Symbols are represented as 2D kernel densities and their similarity is measured by the Kullback-Leibler divergence. Symbol orientation is found by gradient-based angle searching or independent component analysis. Experimental results show the outstanding performance of this approach in various situations.

Algorithms↗

Biohazards symbol: development of a biological hazards warning signal.

The need for a symbol to warn of potential infection hazards became apparent during Public Health Service contract work on the development of containment facilities for virus-leukemia research. A program of direct inquiry and a search of the literature revealed that there was no universally used signal and that scientific and safety organizations concurred in the need for one. Criteria for symbol design were established, and final selection was based on "uniqueness" and "memorability." The National Institutes of Health is recommending use of the symbol as a warning of biological hazard.

Accident Prevention↗

Symbolic communication between two chimpanzees (Pan troglodytes).

Through use of learned symbols, two chimpanzees accurately specified 11 foods by name to one another when the food item's identity was known by only one. They could not do this when denied use of the symbols. The chimpanzees then spontaneously requested specific foods of one another by name. Requests resulted in cooperative and reciprocal symbolically mediated food exchange.

Animal Communication↗

Comparing Yin-Yang, the Chinese symbol of creation, with Ouroboros of Greek alchemy.

The universe was early divided into Earth below and Heaven above. These, two as one, gave the idea of opposites but forming a unity. Each opposite was assumed to be powerful and so was their final unity. For creation of the universe they projected reproduction to conceive creation. Now reproduction results in the union of two opposites as male and female. Correspondingly, the Chinese believed Light and Darkness, as the ideal opposites, when united, yielded creative energy. The two opposites were further conceived as matter and energy which became dual-natured but as one. The two opposites were yin-yang and their unity was called Chhi. Yin-Yang was treated separately in Chinese cosmology which consisted of five cosmic elements. Since Chinese alchemy did reach Alexandria probably the symbol Yin-Yang, as dual-natured, responsible for creation, was transformed into a symbol called Ouroboros. It is a snake and as such as symbol of soul. Its head and anterior portion is red, being the colour of blood as soul; its tail and posterior half is dark, representing body. Ouroboros here is depicted white and black, as soul and body, the two as "one which is all." It is cosmic soul, the source of all creation. Ouroboros is normally depicted with its anterior half as black but it should be the reverse as shown here. With the name Chemeia taken to Kim-Iya, the last word would take Ouroboros to Yin-Yang.

Alchemy↗

Symbolic dynamics of heart rate variability: a probe to investigate cardiac autonomic modulation.

BACKGROUND: Sympathetic and parasympathetic systems are considered the principal rapidly reacting systems that control heart rate. METHODS AND RESULTS: We propose a symbolic analysis series to quantify the prevalence of sympathetic or parasympathetic cardiac modulation. This analysis decomposes the heart rate variability series in patterns lasting 3 beats and classifies them into 3 categories: nonvariable, variable, and very variable patterns referred to as 0V, 1V, and 2V patterns. First, we applied this method to experimental and pharmacological conditions characterized by sympathetic activation (tilt test, handgrip, nitroprusside, and high-dose atropine administration) or parasympathetic activation (phenylephrine and low-dose atropine administration) in 60 healthy subjects. An increase in sympathetic modulation and a vagal withdrawal elicited a significant increase in 0V patterns and a decrease in 2V patterns, whereas parasympathetic dominance induced the opposite, reflecting a reciprocal sympathovagal balance. The second part of the study considered a series of 300 beats before the onset of major arrhythmic events in patients with an implantable cardioverter-defibrillator. Symbolic analysis detected an increase in the percentage of 0V patterns before the onset of major arrhythmias compared with baseline (41.6+/-3.9% and 24.4+/-2.9%, respectively; P<0.01), indicating a sympathetic prevalence. On the other hand, the 2V patterns did not decrease before major arrhythmias, suggesting the presence of nonreciprocal autonomic modulations. CONCLUSIONS: Symbolic analysis of 3 beat sequences takes into account the different time course of sympathetic and parasympathetic cardiac modulations and seems appropriate for elucidating the neural pathophysiological mechanisms occurring during the short periods that precede acute cardiac events.

Adult↗

A machine learning method for extracting symbolic knowledge from recurrent neural networks.

Neural networks do not readily provide an explanation of the knowledge stored in their weights as part of their information processing. Until recently, neural networks were considered to be black boxes, with the knowledge stored in their weights not readily accessible. Since then, research has resulted in a number of algorithms for extracting knowledge in symbolic form from trained neural networks. This article addresses the extraction of knowledge in symbolic form from recurrent neural networks trained to behave like deterministic finite-state automata (DFAs). To date, methods used to extract knowledge from such networks have relied on the hypothesis that networks' states tend to cluster and that clusters of network states correspond to DFA states. The computational complexity of such a cluster analysis has led to heuristics that either limit the number of clusters that may form during training or limit the exploration of the space of hidden recurrent state neurons. These limitations, while necessary, may lead to decreased fidelity, in which the extracted knowledge may not model the true behavior of a trained network, perhaps not even for the training set. The method proposed here uses a polynomial time, symbolic learning algorithm to infer DFAs solely from the observation of a trained network's input-output behavior. Thus, this method has the potential to increase the fidelity of the extracted knowledge.

Algorithms↗

The symbolic self in evolutionary context.

We propose that the capacity for a symbolic self(a flexible and multifaceted cognitive representation of an organism's own attributes) in humans is a product of evolution. In pursuing this argument, we note that some primates possess rudimentary elements of a self (an objectified self) and that the symbolic self (a) is a trait that is widely shared among humans, (6) serves adaptive functions, and (c) could have evolved in response to environmental pressures, with ecological and social pressures being of particular relevance. We suggest that these two environmental pressures caused the symbolic self to emerge in the Pleistocene epoch as an adaptation for Homo erectus, and we review the possible functions served by such an adaptation.

Journal Article↗

[Information, attitudes, perceptions, and symbolic representations of AIDS risk and prevention among poor adolescents in Rio de Janeiro, Brazil].

Four hundred and sixteen poor adolescents of both sexes in Rio de Janeiro were interviewed to study both their level of information and symbolic representations concerning AIDS risk and prevention. The most common source of information on HIV/AIDS was the mass media, particularly television broadcasts. There were doubts and lack of trust regarding official government information on HIV/AIDS. Nearly 70% of the adolescents interviewed believe in HIV transmission through mosquito bites and some 40% through casual contact with wounds or scars or sharing of bathroom utensils. Men seemed to show a greater awareness and autonomy vis- -vis taking initiatives in sex encounters. Attitudes of segregation and exclusion of people with AIDS persist. Lack of prevention was attributed to the impossibility of predicting sexual encounters. The study of symbolic aspects concerning causes of HIV/AIDS displayed broad variability: 80% of the interviewees associated AIDS with excesses in sexual behavior and 40% with homosexual practices. Causal images vary from the predominant view of AIDS as unfair punishment to the less frequent stance considering AIDS as fair punishment (due to sinful behavior). An ambiguous attitude towards transgression (taking as its sterotype the figure of Rio's "malandro", or "streetwise dude") may influence perception of risk and prevention. The paper calls attention to the need for implementing clearer and more direct educational programs. This could be useful for the implementation of culturally sensitive control measures through a reshaping of AIDS symbols. The author recommends a better understanding of the social and economic determinants of disease and reinforcement of the kinds of discourse which empower and raise the self-esteem of poor adolescents by endorsing their civil rights.

English Abstract↗

Symbolic representation of cleft lip and palate.

Since the introduction of symbolic representations of cleft lip and palate anomalies in 1964, they have served the clinician as a quick and easy method of recording these disorders. This paper reviews the evolution of the schematic classification systems and evaluates them. It then presents a new scheme that synthesizes what the authors feel are the most advanced of the existing symbolic representations. This proposed new symbolic representation scheme also specifically provides for ratings of severity (including the documentation of microforms) and facilitates computerized data storage and analysis.

Cleft Lip↗

Treatment versus non-treatment in reduction of symbol reversals by first grade children.

A correcting program for symbol reversals by first grade children (n = 38) did not significantly reduce symbol reversals below those of a non-treated control group (n = 39). There were significant reductions in reversals within both groups. The practice of remediating reversals and the use of directionality to explain symbol reversals are both questioned. The possibility that maturation plays a role seems plausible as an explanation of the changes.

Child↗

Interactions among affect, cognition, and visuomotor coordination as measured in words and symbols.

The associative frequencies of responses to stimulus words during free and controlled forced-choice word-association tests correlate well with each other and with assessments of the affective character (emotional content) of the stimulus words for the test subjects (Osgood Index) for three samples of volunteer French undergraduate students (ns = 200, 64, and 72). These indices correlate negatively with the subjects' performance on Digit Symbol Substitution tests. Neisser's theory of schemata and Edelman's theory of neuronal group selection may provide insight into this relationship. If the associative frequency of a subject's response decreased, the affective content of the word stimulus (as perceived by the subject) diminished as well. This relationship was associated with a relatively higher score on Digit Symbol Substitution. Conversely, it was observed that subjects whose responses were characterized by high associative frequencies (whether the response was spontaneous or forced-choice) rated the stimulus words as having a relatively stronger affective content or emotional character and performed less well on Digit Symbol Substitution.

Adult↗

Oxygen parameters of blood: definitions and symbols.

Definitions and symbols for relevant parameters of the oxygen status of arterial blood are recommended. The recommendations are as simple as possible, easy to understand, and devoid of misinterpretations and double meanings. The authors propose no new definitions for limited new methods, no combination of symbols and methods, and no association between definition, symbol and commercial name.

Abbreviations as Topic↗

The assessment of symbolic play in young children: a prototype test.

In this paper it is argued that assessing symbolic play (defined as one object substituting for another, a property being attributed to an object which it does not have or an absent object being referred to as if present) is particularly useful for young children in whom language and/or play is not developing normally. A new test of symbolic play is described which assesses the child's ability to substitute her- or himself, a teddy or a non-representational object such as a piece of material for another object, to attribute a property to her- or himself or a teddy, and to refer to an absent object used by her- or himself or a teddy. The play may be modelled or instructed or the child may produce examples of her or his own. Some preliminary results from a group of 43 children are reported. It is concluded that this new test of symbolic play will provide clinicians working with children whose language and/or play is impaired with information of value in reaching a diagnosis and in understanding immediate treatment needs.

Child↗