A Dynamical System Approach to Sign Language

At present in ecologies for mathematical models use the systems of chaotic maps. Presence deterministic (dynamic) chaos in such systems define with positions of the global largest Lyapunov exponent λ_1. The chaos is present when λ_1>0 (when execution of some additional conditions). When performing the studies for finding of the spectrum global and local Lyapunov exponent was used QR-method. Using QR-method were organized studies of the large number of chaotic maps however in article as example are considered only two such maps. When undertaking the studies was found that als such chaotic maps possible to refer to two classes (the class I and class II). Systems from class I have a positive largest global Lyapunov exponent. Herewith local largest Lyapunov exponents can take zero and negative values. The systems from class II also have a positive global largest Lyapunov exponent. However chaotic maps from class II have only positive values for local largist Lyapunov exponents. The study of the large number of the chaotic maps from class I and from class II has shown that majority maps from class II it is impossible adequately forecast with the help of the known presently methods of the forecasting (even on one point ahead). That is to say if ecological model is based on chaotic maps from class II that forecast in most cases not possible. For possibility of the adequate forecast it is necessary to use the ecological models built on base of the chaotic maps from class I. The purpose of the undertaking the scientific studies. The purpose of the studies consisted in creation to principal new categ0rizatiom of the chaotic maps. The purpose of the studies consisted in that to show that exists two classes of such chaotic maps (the class I and II), from which maps of the class II it is impossible forecast when use known an present time methods of the forecasting.

The Lyapunov exponents are calculated from numerically simulated and measured time series. The existing algorithms for the estimation of Lyapunov spectra have free parameters. Hence, their influence is analysed on various chaotic and quasi-periodic simulated signals. Furthermore, the exponents of a blood flow signal, measured on a healthy subject, are calculated over a wide range of parameter values. For the embedding dimension d ≥ 10, two typical spectra are observed for both the global and the local Lyapunov exponents. There are either 4 paired and 1 zero, or 5 paired exponents. At least one exponent equals zero within the calculation error.

Local Lyapunov exponents associated with regularitiesof the transition of the zero and positive conditional Lyapunov exponents in the region of negative values are studied. Local conditional Lyapunov exponents are introduced separately for laminar and turbulent phases. It is shown that the negative nature of these conditional Lyapunov exponents is a manifestation of the synchronismobserved at certain time intervals near the boundaries of synchronous regime onset, where synchronous regime has not been established completely.

It is the aim of this paper to further the use of Lyapunov and local Lyapunov exponent methods for analyzing phenomena involving nonlinear vessel dynamics. Lyapunov exponents represent a means to measure the rate of convergence or divergence of nearby trajectories thus denoting chaos and possibly leading to the onset of conditions that produce capsize. The work developed here makes use of Lyapunov exponent methodologies to study capsize and chaotic behavior in vessels both experimentally and numerically using a multi-degree of freedom computational model. Since, the Lyapunov exponent is defined in the limit as time approaches infinity, one encounters fundamental difficulties using Lyapunov exponents on the capsize problem, which is inherently limited to a finite time. This work also incorporates the use of local Lyapunov exponents, which do not require an infinite time series, to demonstrate their usefulness in analyzing finite time chaotic vessel phenomena. The objective is to demonstrate the value of the Lyapunov exponent and local Lyapunov exponent as a predictive tool with which to indicate regions with crucial sensitivity to initial conditions. Through the intelligent use of Lyapunov exponents in vessel analysis to indicate specific regions of questionable stability, one may significantly reduce the volume of costly simulation and experimentation.

We explore a simple example of a chaotic thermostated harmonic-oscillator system which exhibits qualitatively different local Lyapunov exponents for simple scale-model constant-volume transformations of its coordinate q and momentum p : { q,p } --> { (Q/s),(sP) } . The time-dependent thermostat variable zeta(t) is unchanged by such scaling. The original (q,p,zeta) motion and the scale-model (Q,P,zeta) version of the motion are physically identical. But both the local Gram-Schmidt Lyapunov exponents and the related local exponents change with the change of scale. Thus this model furnishes a clearcut chaotic time-reversible example showing how and why both the local Lyapunov exponents and covariant exponents vary with the scale factor s .

We explore a simple example of a chaotic thermostated harmonic-oscillator system which exhibits qualitatively different local Lyapunov exponents for simple scale-model constant-volume transformations of its coordinateq and momen- tum p: {q,p} ! {(Q/s),(sP)}. The time-dependent thermostat variable ζ(t) is unchanged by such scaling. The original (qpζ) motion and the scale-model (QPζ) version of the motion are physically identical. But both the local Gram-Schmidt Lyapunov exponents and the related local exponents change with the change of scale. Thus this model fur- nishes a clearcut chaotic time-reversible example showing how and why both the local Lyapunov exponents and covariant exponents vary with the scale factor s.

Sign languages used by deaf communities around the world possess the same structural and organizational properties as spoken languages: In particular, they are richly expressive and also tightly grammatically constrained. They therefore offer the opportunity to investigate the extent to which the neural organization for language is modality independent, as well as to identify ways in which modality influences this organization. The fact that sign languages share the visual-manual modality with a nonlinguistic symbolic communicative system-gesture-further allows us to investigate where the boundaries lie between language and symbolic communication more generally. In the present study, we had three goals: to investigate the neural processing of linguistic structure in American Sign Language (using verbs of motion classifier constructions, which may lie at the boundary between language and gesture); to determine whether we could dissociate the brain systems involved in deriving meaning from symbolic communication (including both language and gesture) from those specifically engaged by linguistically structured content (sign language); and to assess whether sign language experience influences the neural systems used for understanding nonlinguistic gesture. The results demonstrated that even sign language constructions that appear on the surface to be similar to gesture are processed within the left-lateralized frontal-temporal network used for spoken languages-supporting claims that these constructions are linguistically structured. Moreover, although nonsigners engage regions involved in human action perception to process communicative, symbolic gestures, signers instead engage parts of the language-processing network-demonstrating an influence of experience on the perception of nonlinguistic stimuli.

or much of her life, Sarah M. was an accomplished artist, skilled in painting and the precise brush strokes required to decorate eggshells and ceramics with elaborate designs. The delicate, gentle-looking woman, now 71 years old, was born deaf and communicates with the hand symbols and motions of sign language. Tragically, her mastery of paint and canvas was blotted out by a stroke that caused massive damage to the right side of her brain. A few discouraging attempts at painting and drawing consisted of haphazard lines and disorganized figures. The right-brain damage disturbed her left-eye perception, and the left side of her drawings was often left blank. Artistic ability, quite literally, abandoned her. However, to the astonishment of scientists at the Salk Institute for Biological Sciences in San Diego, Sarah M. continues to use sign language flawlessly and in total disregard of the assumption by many scientists that the brain's right hemisphere controls all visual and spatial tasks. Furthermore, her comprehension of American Sign Language, in which a complex grammar is conveyed through hand and arm motions, is good. A stark contrast is provided by 38-yearold Gail D., also deaf from birth and fluent in sign language. Much of the front part of her left brain hemisphere, including areas thought to control spoken language, was devastated by a stroke. Although no artist, she can still accurately copy simple drawings and abstract figures. But her sign language is now limited to basic nouns and verbs, with none of the shifts in movement and positioning that link signs into sentences or subtly change the meaning of individual signs. S arah M., Gail D. and four other deaf people with stroke-induced damage to a cerebral hemisphere have provided neuropsychologists Howard Poizner and Ursula Bellugi and linguist Edward S. Klima with intriguing insights into the organization of language in the brain. The scientists describe their work in What The Hands Reveal About The Brain (Bradford Books/MIT Press, 1987). Three signers with right-hemisphere damage, including Sarah M., have few problems with sign language or written English, report the researchers, but show severe impairment on visual and spatial tasks outside the realm of language. Examples are the ability to assemble colored blocks into preset patterns and to draw and describe with signs the layout of objects in a familiar room. The three signers with left-side damage do well on these tasks, but each displays a different pattern of sign language breakdown. Gail D. is reduced to the labored production of simple words; Paul D., who has a smaller lesion, is more adept at sign language, but his communication often becomes a salad,' with overly complex sentences and bizarre word substitutions; and Karen L., with damage to the parietal region next to the frontal lobe, engages in animated and grammatically correct signed conversations but often fails to specify whom or what she is referring to and has difficulty understanding the signed communication of others. In each case, problems in written English mirror sign-language deficits.

We develop methods for determining local Lyapunov exponents from observations of a scalar data set. Using average mutual information and the method of false neighbors, we reconstruct a multivariate time series, and then use local polynomial neighborhood-to-neighborhood maps to determine the phase space partial derivatives required to compute Lyapunov exponents. In several examples we demonstrate that the methods allow one to accurately reproduce results determined when the dynamics is known beforehand. We present a new recursive QR decomposition method for finding the eigenvalues of products of matrices when that product is severely ill conditioned, and we give an argument to show that local Lyapunov exponents are ambiguous up to order 1/L in the number of steps due to the choice of coordinate system. Local Lyapunov exponents are the critical element in determining the practical predictability of a chaotic system, so the results here will be of some general use.

EDITORIAL article Front. Psychol., 16 February 2015Sec. Language Sciences Volume 6 - 2015 | https://doi.org/10.3389/fpsyg.2015.00078

SUMMARY When a deterministic mechanism gives rise to an erratic time series, then under certain conditions the series is said to exhibit chaos. The catalogue of statistical methods for the analysis of time series is being augmented currently by methods for the detection and quantification of deterministic chaos. A hallmark of chaos is the tendency of nearby trajectories to diverge in the short term. A measure of the average rate of exponential divergence exhibited by a chaotic system is given by the Lyapunov exponents of that system; the values of such exponents can suggest the presence of chaos. In this paper, we give a brief exposition of a finite time version of the Lyapunov exponent which is state dependent, and to which we attach the epithet ‘local'. The local Lyapunov exponent is shown to be able to detect non-linearity in some cases, and to have other qualitative features. As defined, its success is limited, but this does not preclude its usefulness as a diagnostic tool.

A chaotic dynamical system is characterized by a positive averaged exponential separation of two neighboring trajectories over a chaotic attractor. Knowledge of the Largest Lyapunov Exponent λ1 of a dynamical system over a bounded attractor is necessary and sufficient for determining whether it is chaotic (λ1＞0) or not (λ1≤0). We intended in this work to elaborate the connection between Local Lyapunov Exponents and the Largest Lyapunov Exponent where an altemative method to calculate λ1has emerged. Finally, we investigated some characteristics of the fixed points and periodic orbits embedded within a chaotic attractor which led to the conclusion of the existence of chaotic attractors that may not embed in any fixed point or periodic orbit within it.

The deterministic equations describing the dynamics of the atmosphere (and of the climate system) are known to display the property of sensitivity to initial conditions. In the ergodic theory of chaos, this property is usually quantified by computing the Lyapunov exponents. In this review, these quantifiers computed in a hierarchy of atmospheric models (coupled or not to an ocean) are analyzed, together with their local counterparts known as the local or finite-time Lyapunov exponents. It is shown in particular that the variability of the local Lyapunov exponents (corresponding to the dominant Lyapunov exponent) decreases when the model resolution increases. The dynamics of (finite-amplitude) initial condition errors in these models is also reviewed, and in general found to display a complicated growth far from the asymptotic estimates provided by the Lyapunov exponents. The implications of these results for operational (high resolution) atmospheric and climate modelling are also discussed.

This paper explores the relationship between memory, language, and embodied cognition by analyzing how sign languages encode the concept of memory through bodily referents. While memory is often associated with the brain from a neurological perspective (Baddeley [1974]; Cann & Ross [1989]; Ackerman [1992]), different languages metaphorically locate memory in various parts of the body, such as the heart, muscles, or even the environment. Sentences like “This is etched on my heart” (English) refer to something that has made a big impression on me, making it easy for me to remember. Other languages refer to memory as residing in various places in the body, such as the ventral area of the body or the environment itself (in Japanese culture, for instance). Sign languages provide an opportunity to examine this phenomenon visually and spatially, offering insights into how bodily experience influences linguistic representation. Drawing on theories of embodiment, including work from neuroscience, psycholinguistics, and sign linguistics, this study investigates the bodily locations used to express memory across five sign languages: Italian Sign Language (LIS), Brazilian Sign Language (LIBRAS), American Sign Language (ASL), British Sign Language (BSL), and Japanese Sign Language (JSL). Using data from Spreadthesign and other linguistic resources, the study identifies commonalities in how these languages position memory-related signs primarily around the head, supporting the idea that cognitive and linguistic structures align with physical and cultural perceptions of memory storage. The research is grounded in conceptual metaphor theory (Lakoff & Johnson [1981]), which posits that abstract concepts are understood through embodied experiences and incorporates reflections on the semantic approach to sign language studies (Cuxac [2004]). Findings suggest that while spoken languages may metaphorically associate memory with different body parts, sign languages provide a more direct visual and spatial representation of these associations. By analyzing the lexicon of “memory” across different sign languages, the study offers evidence of a shared cognitive and bodily foundation in language structure, supporting the hypothesis that linguistic meaning is deeply embedded in human perception and bodily experience. Furthermore, this work contributes to ongoing discussions about the relationship between sign and spoken languages. While sign languages have often been studied in relation to their spoken counterparts, they offer unique insights into how language interacts with cognition and physicality. This study also aligns with previous research on iconicity in sign language (Cuxac [2000a, 2000b]; Wilcox [2000]; Taub [2001]), emphasizing the role of the body in structuring linguistic meaning. The findings challenge traditional distinctions between phonology and morphology in linguistic theory, reinforcing the need for models that account for the multimodal and spatial dimensions of sign language. By bridging linguistic, cognitive, and neurological perspectives, this paper underscores the importance of embodied cognition in understanding language development and meaning construction. The analysis of memory-related lexicon in sign languages not only highlights the influence of bodily experience in linguistic representation but also opens new avenues for exploring how language reflects fundamental cognitive processes across different modalities.

Even though research in sign language is a special field of language research it has contributed with new knowledge about human language because of the visuospatial nature. The article introduces to different issues in sign language research from a cognitive and neuropsychological view. These issues are sign language linguistic, sign aphasia, the neural organization of sign language, signed short-term memory, and the study of speech errors in sign language. The overall purpose of the article is to examine the structure and organization of sign language in comparison to oral language. What linguistics, neural and cognitive similarities and differences are there between signed and oral languages? The article demonstrates that the linguistic, cognitive and neural basis for signed languages overall is similar to oral languages. The similarity of signed and oral languages indicates an amodal cognitive organization of human language.