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The purpose of this paper is to examine the possibility of biotic patterns. In economics, markets are thought to tend to equilibrium with random and unpredictable deviations. However, an explosion of empirical work searching for possible chaos show an enormous amount of unexplained nonlinear structure. These observations led the authors to examine the possibility of biotic patterns in economics.

Bios is defined as a causally generated creative process. It is the causal counterpart to random walk, just as chaos is the causal equivalent to randomness. Economic data consisting of time series from several categories, including banking, employment and population, and gross domestic product and components, were studied for diversification, recurrence, and predictability patterns characteristic of bios. Diversification was quantified as increased variance with embedding, recurrences were measured using newly developed computer programs, and predictability was measured with a nonlinear prediction method.

Dynamic analyses of the data show: episodic patterning and asymmetric statistical distribution, typical of bios; increase in variance with embedding (diversification), less recurrence than shuffled copies of the data (novelty), demonstrating creativity; consecutive recurrence; and patterning in the series of differences, indicating non‐random causation.

The demonstration of bios in empirical data indicates that the economy is non‐stationary, causal, and creative. This contradicts the notion that markets regulate themselves and tend to equilibrium, and the characterization of market variation as random or chaotic. Further economic crises may be avoided by acknowledging that financial markets are not bound within limits and can be modified into new forms by human action.

Aging is a continuous process of growth and decay, both of which start at birth and continue throughout life. Activity develops muscles and neurons; inactivity atrophies them. Here we propose lifelong creative activity as a method to deal with aging. Decreased creative and learning capacity is a self‐fulfilling prophecy. Changing personal perceptions and expectations can promote health care and productive behavior.

The physical universe is the embodiment of necessary mathematical forms by ever‐present flux. Interaction of these forms generates diversity, novelty, complexity, and higher levels of organization. Lattice order, group opposition, and topological transformation are generators necessary and sufficient to construct mathematics. Homologous cognitive structures generate human mental development. Process theory proposes that these mathematical generators also create nature. Lattice order is embodied as action, group opposition as two‐valued information, and topological transformation as spatial organization.

In this paper we report on a mathematical pattern that we call bios, and its generation by recursions of bipolar feedback. Bios is a newly found form of organization, that resembles chaos in its aperiodic pattern and its extreme sensitivity to initial conditions, but has additional properties (diversification, novelty, nonrandom complexity, life‐limited patterning, 1/f power spectrum) found in natural creative processes, and absent in chaos. The process equation A_t+1=A_t+g_tsin(A_t) generates convergence to π, a cascade of bifurcations, chaos, bios and infinitation, as the value of the feedback gain g_t increases. In the complex plane, series generated by orthogonal process equations display fractal organic patterns.

In our society, medical care and economic progress have improved the duration and quality of life, but aging is accelerated by social norms and their psychological introjection. Healthy aging involves the continuing pursuit of creative activity. Changes in self‐view and behavior will require and promote a change in social roles, and the emancipatory mobilization of senior adults of both sexes and all classes.

We describe a theory of creative activity through the development and use of mathematical tools in the analysis of time series. The time series analyzed include empirical series and biotic and chaotic series generated by recurrent functions. Embeddings are used to measure the dimensionality of a series, and analyses of isometries of Euclidean norms at various embeddings reveal the relatively simple processes that generate and combine with complex structures. These tools identify and measure diversity, novelty, and complexity in complex natural processes and in mathematical bios. The presence of these properties shows that creative processes result from deterministic interactions among relatively simple components, not only from random accident.

Mathematical bios and heartbeat series show an inverse relation between frequency and power; the time series of differences between successive terms of cardiac and mathematical chaos shows a direct relation between frequency and power. Other statistical analyses differentiate these biotic series from stochastically generated 1/f noise. The time series of complex biological and economic processes as well as mathematical bios show asymmetry, positive autocorrelation, and extended partial autocorrelation. Random, chaotic and stochastic models show symmetric statistical distributions, and no partial autocorrelation. The percentage of continuous proportions is high in cardiac, economic, and mathematical biotic series, and scarce in pink noise and chaos. These findings differentiate creative biotic processes from chaotic and stochastic series. We propose that the widespread 1/f power spectrum found in natural processes represents the integration of the fundamental relation between frequency and energy stated in Planck's law. Natural creativity emerges from determined interactions rather than from the accumulation of accidental random changes.

This paper aims to explain, first of all, signal modeling steps using Poincaré, and then considering the occurred events, concept of information applying Poincaré section and information approach, the brain pattern variations in autism spectrum disorder (ASD) cases will be diagnosed. A kind of representation of electroencephalogram (EEG) signal, namely, complementary plot, in which the main characteristic is special attention to asymmetry and symmetry coexist in natural and human processes, is introduced. In this paper, a new model is provided whose variations of patterns are similar to EEG’s when the transformation parameter is changed. A significant difference between ASD and healthy cases was also observed, which could be used to distinguish between various types of systems.

Complementary plot method is one of the most proper representations for Poincaré section of complex dynamics, because, as it was said about its characteristics, it has a qualitative approach toward signal (Sabelli, 2000, 2001, 2003, 2008, 2005, Sabelli et al., 2011). Considering the special conditions of this representation, here, intersection with a circle y² + x² = r² will be used; the important fact is, on the contrary to previous representations in which circular section had energy concept, here circular section considers phases. For finding trajectory intersection points, after calculating the sin and cosine of each term of EEG, plotting them in XY plane and drawing a chord between successive points of presentation transitions, then its intersections with the assumed circle are determined. But considering the sampling frequency, chords and Poincaré section, in this space, a minimum error – as the threshold – should be assumed in the program.

Natural and human processes are biotic (life-like) and creative (Sabelli and Galilei), and studying coexisting opposites by calculating the sine and cosine of each term in heartbeat intervals, weather variables and integer biotic series or random walk reveals an astonishingly regular mandala pattern; these patterns are not generated by random, periodic or chaotic series (Sabelli, 2005). This paper shows that in EEG of ASD children, mandala-like patterns of concentric rings are emergent in all situations (baseline – watching animation with voice and without voice) and electrode site (C3 and C4), but not in healthy individuals. The authors take the relation between sine and cosine functions as a mathematical model for complementary opposition, because it involves reciprocity and orthogonality sine and cosine are natural models for information. In fact, trigonometric analyses of empirical data to be described in this paper suggest expanding the concept of co-creative opposition to include uncorrelated opposites and partial opposites, i.e. partial agonists and partial antagonists that are neither linear nor orthogonal. Using Poincaré sections, it is shown that the difference in information and creativity of the data is the distinctive characteristic in ASD and healthy cases. Creation is the generation of novelty, diversity and complexity in complex systems.

This paper is an original paper based on cybernetic approaches for studying the variations of ASD children.

Explains the need for quality educational technology in our schools and notes the contributions of existing technology in improving education. Describes the potential that telecommunications network technology holds for revitalizing American education. Out‐lines the major federal programs that provide policy guidance and funding assistance for educational institutions to access and contribute to the evolving National Information Infrastructure (NII), and summarizes federal activities to date. In particular, describes the relevant experiences of the first year of the Telecommunications and Information Infrastructure Assistance Program (TIIAP) which is part of the National Telecommunications and Information Administration (NTIA) at the Department of Commerce. Contact information for all federal programs is provided as well.

Identity exploration is a central mechanism for identity formation that has been found to be associated with intense engagement, positive coping, openness to change, flexible cognition, and meaningful learning. Moreover, identity exploration in school has been associated with adaptive motivation for learning the academic material. Particularly in the fast-changing environment of contemporary society, confidence and skills in identity exploration and self-construction seems to be increasingly important. Therefore, promoting students’ identity exploration in school within the curriculum and in relation to the academic content should be adopted as an important educational goal. The purpose of this paper is to describe a conceptual framework for interventions to promote students’ identity exploration within the curriculum. The framework involves the application of four interrelated principles: (1) promoting self-relevance; (2) triggering exploration; (3) facilitating a sense of safety; and (4) scaffolding exploratory actions.

We begin the paper with a conceptual review of identity exploration. We follow by specifying the conceptual framework for interventions. We then present a methodological-intervention approach for applying this framework and describe three such interventions in middle-school contexts, in the domains of environmental education, literature, and mathematics.

In each intervention, applying the principles contributed to students’ adaptive motivation and engagement in the academic material and also contributed to students’ identity exploration, though not among all students. The findings highlight the contextual, dynamic, and indeterminate nature of identity exploration among early adolescents in educational settings, and the utility of the conceptual framework and approach for conceptualizing and intervening to promote identity exploration among students.

This paper contributes to the conceptual understanding of identity exploration in educational settings, highlights the benefits and the challenges in intervening to promote identity exploration among students, and discusses the future directions in theory, research, and practice concerned with the promotion of identity exploration in educational settings.