1 – Institute for Frontier Areas of Psychology and Mental Health, Wilhelmstr. 3a, 79098 Freiburg, Germany 2 – Parmenides Center, Via Mellini 26-28, 57031 Capoliveri, Italy 3 – Department of Ophtalmology, University of Freiburg, Killianstr. 5, 79106 Freiburg, Germany 4 – Institute of Physics, University of Freiburg, Hermann- Herder -Str. 3, 79104 Freiburg, GermanyThe “Necker-Zeno model”, a model for bistable perception inspired by the quantum Zeno effect, was previously used to relate three basic time scales of cognitive relevance (...) to one another in a quantitative manner. In this paper, the model predictions are compared with experimental results obtained under discontinuous presentation of an ambiguous stimulus. In addition to earlier results for long inter-stimulus intervals, we show that the reversal dynamics according to the Necker-Zeno model is also in agreement with new results for short inter-stimulus intervals. Moreover, we refine the model in such a way that it accounts for the distribution of “dwell times”. Finally, we indicate applications concerning the modification of cognitive time scales under conditions of psychopathological impairments and meditationinduced modes of awareness. ∗Address correspondence to this author at the Theory Division of the Institute for Frontier Areas of Psychology, Wilhelmstr. 3a, D–79098 Freiburg, Germany; E-mail: [email protected]. (shrink)

My goal is to conceive how the reality would look like for hypothetical creatures that supposedly perceive on time scales much faster or much slower than that of us humans. To attain the goal, I propose modelling in two steps. At step one, we have to single out a unified parameter that sets time scale of perception. Changing substantially the value of the parameter would mean changing scale. I argue that the required parameter is duration of discrete (...) perceptive frames, or snapshots, whose sequencing constitutes perceptive process. I show that different standard durations of perceptive frames is the ground for differences in perceptive time scales of various animals. Abnormally changed duration of perceptive frames is the cause of the effect of distorted subjective time observed by humans under some conditions. Now comes step two of the modelling. By inserting some arbitrary duration of a perceptive frame, we set a hypothetical scale and thus emulate a viewpoint for virtual observation of the reality in a wider or narrower angle of embracing events in time. Like changing lenses of a microscope, viewing reality in different temporal scales makes certain features of reality manifested, others veiled. These are, in particular, features of life. If we observe an object in an inappropriate interval, we may not notice the very essence of a process it is undergoing. (shrink)

The concept of levels of organization, despite its widespread scientific currency, has recently been criticized by a number of philosophers of science. This paper diagnoses the main source of problems facing theories of levels. On this basis, the problems with the usual criteria for distinguishing levels are evaluated: compositional relations, organizational types, and spatial scales. Drawing on some work on hierarchies in ecology, I argue in favor of an alternative conception of levels defined by the criterion of rates or (...) time scales of processes. (shrink)

Our model integrates the nativist assumption of prespecified neural structures underpinning basic emotions with the constructionist view that emotions are assembled from psychological constituents. From a dynamic systems perspective, the nervous system self-organizes in different ways at different time scales, in relation to functions served by emotions. At the evolutionary scale, brain parts and their connections are specified by selective pressures. At the scale of development, connectivity is revised through synaptic shaping. At the scale of real time, (...) temporary networks of synchronized activity mediate responses to situations. To the degree that humans share common emotional functions, neural structuration is similar across scales, giving rise to “basic” emotions. However, unique developmental and situational factors select for neural configurations mediating emotional variants. (shrink)

This paper addresses the role of time scales in conceptualizing biological hierarchies. So far, the concept of hierarchies in philosophy of science has been dominated by the idea of composition and parthood, respectively. However, this view does not exhaust the diversity of hierarchical descriptions in the biosciences. Therefore, we highlight a type of hierarchy usually overlooked by philosophers of science. It distinguishes processes based on the different time scales (i.e. rates, frequencies, and rhythms) on which they (...) occur. These time scale hierarchies often are connected with assumptions defended in process ontology. Due to their ability to describe interlevel dynamics of various kinds, we call these hierarchies ‘dynamic hierarchies.’ In order to highlight and discuss their organization, explanatory roles, and epistemic virtues we focus on dynamic hierarchies in developmental biology and evolutionary developmental biology (evo-devo). In these fields, dynamic hierarchies offer crucial complementary information to descriptions of compositional hierarchies. (shrink)

Single cell receptive field dynamics characterized by highly complicated spatio-temporal activity distributions observable during sensory information processing transforms into much simpler spatio-temporal activity pattern at a population level, indicating a qualitative transformational step of time-variant processing from microscopic to mesoscopic levels. As these dynamics are subject to significant modifications during learning, dynamic information processing is in a permanent state of use-dependent fluctuations.

The recent renewed interest in the foundation of quantum statistical mechanics and in the dynamics of isolated quantum systems has led to a revival of the old approach by von Neumann to investigate the problem of thermalization only in terms of quantum dynamics in an isolated system [1, 2]. It has been demonstrated in some general or concrete settings that a pure initial state evolving under quantum dynamics indeed approaches an equilibrium state [3–9]. The underlying idea that a single pure (...) quantum state can fully describe thermal equilibrium has also become much more concrete [10–12]. (shrink)

This thesis seeks to extend the search for the moral implications inherent in the development, possession and threatened use of physical/astrophysical processes and in current understandings of the evolution of the physical universe. ;The nature of moral/theological discussion will not be a primary concern although clearly some residual position that such discussion is meaningful is presupposed. Neither is the nature of science or the scientific method at issue. It is assumed that both theology and science have long since negotiated the (...) confidence crises of adolescence and have mustered the requisite self-esteem regarding their respective disciplines. ;The aim of this work is to present the concept of time-scales as a relevant moral category. It will investigate the use of this concept and its relationship to the other categories developed in the relevant scientific literature. Similarly, the use of this concept will be explored and its influence sought in the analogous documentation from the Catholic tradition. In this investigation the question will be raised as to the validity of and the future of the concept of time-scales as a common moral ground for these two traditions, enhancing convergence and leading toward a more direct collaboration on the question of human survival. (shrink)

Because both emotional arousal and regulation are continuous, ongoing processes, it is difficult, if not impossible, to separate them. Thus, affective dynamics can reveal the regulation of emotion as it occurs in real time. One way that this can be done is through the examination of intra- and interpersonal flexibility or the transitions into and out of affective states. The present article reviews and then expands upon the Flex3 model of real-time dynamic and reactive flexibility, specifying the ways (...) in which individual differences in emotion regulation manifest as differences in flexibility. The differences in results at the real-time scale versus diurnal variability are also discussed within an emotion regulation framework. (shrink)

The construct of flexibility has been a focus for research and theory for over 100 years. However, flexibility has not been consistently or adequately defined, leading to obstacles in the interpretation of past research and progress toward enhanced theory. We present a model of socioemotional flexibility—and its counterpart rigidity—at three time scales using dynamic systems modeling. At the real-time scale (micro), moment-to-moment fluctuations in affect are identified as dynamic flexibility. At the next higher meso-time scale, adaptive (...) adjustments to changes in context are characterized as reactive flexibility. At the macro scale is flexibility that occurs across months or years, reflecting flexibility due to developmental or life transitions. Implications of the model and suggestions for future research are discussed. (shrink)

This article catalogs social processes contributing to construction of emotions across three time-scales, covering: natural selection; ontogenesis; and moment-by-moment transactions. During human evolution, genetic and cultural influences operate interdependently, not as separate forces working against each other. Further, leaving infants’ environment-open serves adaptive purposes. During ontogenesis, cultural socialization affects emotion development in various ways, not all of which depend on internalization of cultural meanings as emphasized in some earlier social constructionist accounts. Construction also operates over the moment-by-moment (...) class='Hi'>time-scale of real-time interpersonal interactions, as emotions adjust to the constraints and affordances of immediate cultural environments. Claims that emotions are constructed, and that social processes contribute to their construction, are no longer contestable. Now the project is to specify how these processes operate and what materials they use. (shrink)

As the result of the complexity inherent in nature, mathematical models employed in ecology are often governed by a large number of variables. For instance, in the study of population dynamics we often deal with models for structured populations in which individuals are classified regarding their age, size, activity or location, and this structuring of the population leads to high dimensional systems. In many instances, the dynamics of the system is controlled by processes whose time scales are very (...) different from each other. Aggregation techniques take advantage of this situation to build a low dimensional reduced system from which behavior we can approximate the dynamics of the complex original system.In this work we extend aggregation techniques to the case of time dependent discrete population models with two time scales where both the fast and the slow processes are allowed to change at their own characteristic time scale, generalizing the results of previous studies. We propose a non-autonomous model with two time scales, construct an aggregated model and give relationship between the variables governing the original and the reduced systems. We also explore how the properties of strong and weak ergodicity, regarding the capacity of the system to forget initial conditions, of the original system can be studied in terms of the reduced system. (shrink)

A critical discussion is provided of three central assumptions underlying Nunez's approach to modeling cortical activity. A plea is made for neurophysiologically realistic models involving nonlinearities, multiple time scales, and stochasticity.

ABSTRACTNegative emotion influences cognitive control, and more specifically conflict adaptation. However, discrepant results have often been reported in the literature. In this study, we broke down negative emotion into integral and incidental components using a modern motivation-based framework, and assessed whether the former could change conflict adaptation. In the first experiment, we manipulated the duration of the inter-trial-interval to assess the actual time-scale of this effect. Integral negative emotion was induced by using loss-related feedback contingent on task performance, and (...) measured at the subjective and physiological levels. Results showed that conflict-driven adaptive control was enhanced when integral negative emotion was elicited, compared to a control condition without changes in defensive motivation. Importantly, this effect was only found when a short, as opposed to long ITI was used, suggesting that it had a short time scale. In the second experiment, we controlled for effe... (shrink)

The time-scale dynamic equations play an important role in modeling complex dynamical processes. In this paper, the Mei symmetry and new conserved quantities of time-scale Birkhoff’s equations are studied. The definition and criterion of the Mei symmetry of the Birkhoffian system on time scales are given. The conditions and forms of new conserved quantities which are found from the Mei symmetry of the system are derived. As a special case, the Mei symmetry of time-scale Hamilton (...) canonical equations is discussed and new conserved quantities for the Hamiltonian system on time scales are derived. Two examples are given to illustrate the application of results. (shrink)

To emphasize the importance of “the social” for the construction of emotions, Parkinson distinguishes three time-scales: a phylogenetic one, an ontogenetic one, and a time-scale which focuses on real-time interactions. As far as the sociology of emotions is concerned, the last time-scale is of special interest. The following commentary deals with some questions of the sociology of emotions and draws special attention to the third time-scale Parkinson has suggested.

As a result of the complexity inherent in some natural systems, mathematical models employed in ecology are often governed by a large number of variables. For instance, in the study of population dynamics we often find multiregional models for structured populations in which individuals are classified regarding their age and their spatial location. Dealing with such structured populations leads to high dimensional models. Moreover, in many instances the dynamics of the system is controlled by processes whose time scales (...) are very different from each other. For example, in multiregional models migration is often a fast process in comparison to the growth of the population.Approximate reduction techniques take advantage of the presence of different time scales in a system to introduce approximations that allow one to transform the original system into a simpler low dimensional system. In this way, the dynamics of the original system can be approximated in terms of that of the reduced system. This work deals with the study of that approximation. In particular, we work with a non-autonomous discrete time model previously presented in the literature and obtain different bounds for the error we incur when we describe the dynamics of the original system in terms of the reduced one. (shrink)

Aggregation of variables allows to approximate a large scale dynamical system (the micro-system) involving many variables into a reduced system (the macro-system) described by a few number of global variables. Approximate aggregation can be performed when different time scales are involved in the dynamics of the micro-system. Perturbation methods enable to approximate the large micro-system by a macro-system going on at a slow time scale. Aggregation has been performed for systems of ordinary differential equations in which (...) class='Hi'>time is a continuous variable. In this contribution, we extend aggregation methods to time-discrete models of population dynamics. Time discrete micro-models with two time scales are presented. We use perturbation methods to obtain a slow macro-model. The asymptotic behaviours of the micro and macro-systems are characterized by the main eigenvalues and the associated eigenvectors. We compare the asymptotic behaviours of both systems which are shown to be similar to a certain order. (shrink)

Resumen: Este artículo plantea la tesis que la complejidad humana es directamente proporcional a la consideración y estudio de múltiples temporalidades, todas las cuales tienen una base común la biología. Esta tesis se articula en dos argumentos. El primero sostiene que la complejidad en general es el tiempo mismo, lo cual significa directa e inmediatamente que el tiempo no es simplemente una variable. El segundo afirma la necesidad y la importancia de una epistemología del tiempo. Este segundo argumento emerge como (...) una subtesis, relativamente a la tesis principal. Al final se concluyen dos cosas: a) que la base material de la ciencia no es hoy ya la física, sino la biología; sin embargo, biología y cultura constituyen una sólida unidad, algo que es evidente gracias a la epigenética; b) que los actos humanos pueden explicarse a partir de temporalidades diferentes anteriores al segundo, las cuales se proyectan a escalas más amplias y densas. Las ciencias sociales y humanas pueden enriquecerse enormemente a partir de un cuadro semejante.: This paper claims that human complexity is directly proportional to considering and studying various times, all of which have a common ground in biology. The claim brought out entails a twofold argument. One says that complexity in general is time, which means straightforwardly that time is not a sheer variable. The second argument argues about the need for and importance of an epistemology of time. The latter argument emerges a second claim vis-à-vis the main one. At the end two clear cut conclusions are drawn, thus: a) the material ground for science is nowadays not physics any more but biology; however, biology and culture make a solid unity, something that is made evident thanks to epigenetics; b) human actions can be explained by virtue of different times prior to a second, all of which are projected onto larger and more dense time scales. The human and social sciences can benefit enormously from such a depicted frame. (shrink)

In this work we deal with a general class of spatially distributed periodic SIS epidemic models with two time scales. We let susceptible and infected individuals migrate between patches with periodic time dependent migration rates. The existence of two time scales in the system allows to describe certain features of the asymptotic behavior of its solutions with the help of a less dimensional, aggregated, system. We derive global reproduction numbers governing the general spatially distributed nonautonomous (...) system through the aggregated system. We apply this result when the mass action law and the frequency dependent transmission law are considered. Comparing these global reproductive numbers to their non spatially distributed counterparts yields the following: adequate periodic migration rates allow global persistence or eradication of epidemics where locally, in absence of migrations, the contrary is expected. (shrink)

The purpose of this work is reviewing some reduction results to deal with systems of nonautonomous ordinary differential equations with two time scales. They could be included among the so-called approximate aggregation methods. The existence of different time scales in a system, together with some long-term features, are used to build up a simpler system governed by a lesser number of state variables. The asymptotic behavior of the latter system is then used to describe the asymptotic (...) behaviour of the former one. The reduction results are stated in two particular but important cases: periodic systems and asymptotically autonomous systems. The reduction results are illustrated with the help of simple spatial SIS epidemic models including either periodic or asymptotically autonomous terms. (shrink)

This article takes as its point of departure the view that the discovery of the mathematical formalism of quantum mechanics (QM) was not merely a discovery of a new mathematical way of dealing with physical, and specifically quantum, processes in nature. It was also a discovery of a general mathematical formalism (in part discovered in mathematics itself earlier), which, supplemented by certain additional rules, consistently described the processing of incomplete information about certain events and contexts in which these events occur. (...) This article proposes a quantum-like (QL) model of the functioning of the brain based on the (Hilbert-space) formalism of quantum mechanics, but now used as part of a QL mathematical model of neural processes in the brain, rather than for describing quantum physical processes. This model is, thus, fundamentally different from the (reductionist) quantum model of the brain and consciousness, according to which cognition arises by virtue of physical quantum processes in the brain. In the present view, the brain is an advanced biological system that developed the ability to create a QL representation of contexts, which, thus, allows one to describe a significant part of its functioning by the QM mathematical formalism. The possibility of such a description has nothing to do with the constitution and workings of the brain as a quantum system (composed of photons, electrons, protons, and so forth). The QL model offered here is based instead on conventional neurophysiological model of the functioning of the brain, even though the brain, the article suggests, does use the QL rule (given by von Neumann trace formula, used in QM) for the calculation of approximate averages for mental functions. The QL model developed in this article has a temporal basis, based on a (hypothetical) argument that cognitive processes are based on at least two time scales: a (very fine) subcognitive one and a (much coarser) cognitive one. (shrink)

Bellman optimality principle for the stochastic dynamic system on time scales is derived, which includes the continuous time and discrete time as special cases. At the same time, the Hamilton–Jacobi–Bellman equation on time scales is obtained. Finally, an example is employed to illustrate our main results.

In this paper we will show how “weighted path integral” proposed by Mensky and Kent can emerge out of Ghirardi Rimini Weber model.

Time preference reversals refers to systematic inconsistencies between preferences and valuations in intertemporal choice. When faced with a pair of intertemporal options, people preferred the smaller-sooner option but assign a higher price to the larger-later one. Different hypotheses postulate that the differences in evaluation scale or output format between the choice and the bid tasks cause the preference reversal. However, these hypotheses have not been distinguished. In the present study, we conducted a hybrid task, which shares the same evaluation (...) scale with the bid task and shares the same output format with the choice task. By comparing these three tasks, we can figure out the key reason for time preference reversal. The eye-tracking measures reflecting attention allocation, cognitive effort and information search pattern were examined. Results showed that participants' time preference and eye-tracking measures in the hybrid task were similar to those in the choice task, but different from those in the bid task. Our findings suggest that the output format is the core reason for time preference reversal and may deepen our understanding of the mechanisms that underlie time preference reversal. (shrink)

In the first part of this contribution, we review the development of the theory of scale relativity and its geometric framework constructed in terms of a fractal and nondifferentiable continuous space-time. This theory leads (i) to a generalization of possible physically relevant fractal laws, written as partial differential equation acting in the space of scales, and (ii) to a new geometric foundation of quantum mechanics and gauge field theories and their possible generalisations. In the second part, we discuss (...) some examples of application of the theory to various sciences, in particular in cases when the theoretical predictions have been validated by new or updated observational and experimental data. This includes predictions in physics and cosmology (value of the QCD coupling and of the cosmological constant), to astrophysics and gravitational structure formation (distances of extrasolar planets to their stars, of Kuiper belt objects, value of solar and solar-like star cycles), to sciences of life (log-periodic law for species punctuated evolution, human development and society evolution), to Earth sciences (log-periodic deceleration of the rate of California earthquakes and of Sichuan earthquake replicas, critical law for the arctic sea ice extent) and tentative applications to systems biology. (shrink)

It is argued that the `problem of time' in quantum gravity necessitates a refinement of the local inertial structure of the world, demanding a replacement of the usual Minkowski line element by a 4+2n dimensional pseudo-Euclidean line element, with the extra 2n being the number of internal phase space dimensions of the observed system. In the refined structure, the inverse of the Planck time takes over the role of observer-independent conversion factor usually played by the speed of light, (...) which now emerges as an invariant but derivative quantity. In the relativistic theory based on the refined structure, energies and momenta turn out to be invariantly bounded from above, and lengths and durations similarly bounded from below, by their respective Planck scale values. Along the external timelike world-lines, the theory naturally captures the `flow of time' as a genuinely structural attribute of the world. The theory also predicts expected deviations---suppressed quadratically by the Planck energy---from the dispersion relations for free fields in the vacuum. The deviations from the special relativistic Doppler shifts predicted by the theory are also suppressed quadratically by the Planck energy. Nonetheless, in order to estimate the precision required to distinguish the theory from special relativity, an experiment with a binary pulsar emitting TeV range gamma-rays is considered in the context of the predicted deviations from the second-order shifts. (shrink)