Natural forms, often characterized by irregularity and roughness, have a unique complexity that exhibit self-similarity across different spatial scales or levels of magnification. Our visual system is remarkably efficient in the processing of natural scenes and tuned to the multi-scale, fractal-like properties they possess. The fractal-like scaling characteristics are ubiquitous in many physical and biological domains, with recent research also highlighting their importance in aesthetic perception, particularly in the visual and, to some extent, auditory modalities. Given the (...) multitude of fractal-like scaling manifestations, we explore potential commonalities in the way they might affect aesthetic preference within and across different physical and sensory domains. We use a range of visual and tactile stimuli to explore the equivalence of fractal-scaling effects on aesthetic preferences within and across visual and tactile modalities. Our results suggest that, despite some superficial differences, the underlying dimensional structure mediating the preference across the two domains is remarkably similar. The qualitative nature of this dimensional structure as well as suggestions for future research are discussed. (shrink)

The finding of fractal scaling (FS) in behavioral sequences has raised a debate on whether FS is a pervasive property of the cognitive system or is the result of specific processes. Inferences about the origins of properties in time sequences are causal. That is, as opposed to correlational inferences reflecting instantaneous symmetrical relations, causal inferences concern asymmetric relations lagged in time. Here, I integrate Granger-causality with inferences about FS. Four simulations illustrate that causal analyses can isolate distinct FS (...) sources, whereas correlational techniques cannot. I then analyze three simultaneous sequences of responses from a database of word-naming trials. I find that two, or perhaps three, distinct sources account for the presence of FS in these sequences, but FS is not a general property of the system. This suggests that FS arises due to the properties of a limited number of identifiable psychological and/or neural processes. Finally, I reanalyze a previously published dataset of acoustic frequency spectra using the new tools. The causality/criticality combination introduced here offers a new important perspective in the study of cognition. (shrink)

The finding of fractal scaling (FS) in behavioral sequences has raised a debate on whether FS is a pervasive property of the cognitive system or is the result of specific processes. Inferences about the origins of properties in time sequences are causal. That is, as opposed to correlational inferences reflecting instantaneous symmetrical relations, causal inferences concern asymmetric relations lagged in time. Here, I integrate Granger‐causality with inferences about FS. Four simulations illustrate that causal analyses can isolate distinct FS (...) sources, whereas correlational techniques cannot. I then analyze three simultaneous sequences of responses from a database of word‐naming trials. I find that two, or perhaps three, distinct sources account for the presence of FS in these sequences, but FS is not a general property of the system. This suggests that FS arises due to the properties of a limited number of identifiable psychological and/or neural processes. Finally, I reanalyze a previously published dataset of acoustic frequency spectra using the new tools. The causality/criticality combination introduced here offers a new important perspective in the study of cognition. (shrink)

A (to our knowledge) novel Generalized Nonlinear Schrödinger equation based on the modifications of Nottale-Cresson’s fractal-scale calculus and resulting from the noncommutativity of the phase space coordinates is explicitly derived. The modifications to the ground state energy of a harmonic oscillator yields the observed value of the vacuum energy density. In the concluding remarks we discuss how nonlinear and nonlocal QM wave equations arise naturally from this fractal-scale calculus formalism which may have a key role in the final (...) formulation of Quantum Gravity. (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)

Using fractal analyses to study events allows us to capture the scale-independence of those events, that is, no matter at which level we study a phenomenon, we should get roughly the same results because events exhibit similar structure across scales. This is demonstrably true in mathematical fractals but is less assured in behavioral fractals. The current research directly tests the scale-independence hypothesis in the behavioral domain by exploring the fractal structure of aggression, a social phenomenon comprising events that (...) span temporal scales from minutes of face-to-face arguments to centuries of international armed conflicts. Using publicly available data, we examined the temporal fractal structure of four scales of aggression: wars, riots, violent crimes, and body movement during arguments. Our results lend mixed support to the scale-independence hypothesis and provide insight into the self-organization of human interactions. (shrink)

It has long been appreciated that the brain is oscillatory 1. Early measurements of brain electrophysiology revealed rhythmic synchronization unifying large swaths of the brain. The study of neural oscillation has enveloped cognitive neuroscience and neural systems. The traditional belief that oscillations are epiphenomenal of neuron spiking is being challenged by intracellular oscillations and the theoretical backing that oscillatory activity is fundamental to physics. Subjective experience oscillates at three particular frequency bands in a cognitive triad: perception at 5 Hz, action (...) at 2 Hz, and attention at 0.1 Hz. This triad functions as a means of information flow across scales of magnitude in a biological fractal. The _Homunculus Solution _is proposed in which mental experience occurs at fixed scales of biology. The mind is composed of minds, perceived as "the voices in your head." Each voice has voices inside its head to increasingly microscopic scales, forming an interactive fractal of subjective experience. Normal 0 false false false EN-US X-NONE X-NONE. (shrink)

Habitat fragmentation produces isolated patches characterized by increased edge effects from an originally continuous habitat. The shapes of these patches often show a high degree of irregularity: their shapes deviate significantly from regular geometrical shapes such as rectangular and elliptical ones. In fractal theory, the geometry of patches created by a common landscape transformation process should be statistically similar, i.e. their fractal dimensions and their form factors should be equal. In this paper, we analyze 49 woodlot fragments (Pinus (...) sylvestris L.) in the Belgian Kempen region to study the direct relationship between a transformation process and the concomitant patch geometry. Although the fractal dimension of the woodlots is scattered (i.e. they are not statistically similar), the perimeter-area relation of the fragments is characterized by a single, ‘dimension-like’ exponent. This exponent suggests a certain shape homogeneity among the patches, which is confirmed by the absence of hierarchical levels associated with sharp increases of the fractal dimension at scale transitions. The interaction of different natural (soil factor, vegetation type) and anthropogenic (afforestation, urbanization) processes during patch development is assumed to have generated this feature. Comparison of the area and perimeter fractal dimension with an ecological index for habitat quality, the interior-to-edge ratio, shows that the fractal dimension is suitable for predicting interior habitat presence, which is more likely for patches with smooth perimeters and compact areas. The ratio of the area to the perimeter fractal dimension confirms this observation, with high values for high interior-to-edge ratios, characteristic for regularly shaped patches. (shrink)

Successful applications of hierarchical complexity to the behaviors of organisms, animals and humans, and social entities evidence the scaling properties of self-similarity, thus the bounded fractal characteristics of orders of hierarchical complexity. The theory specifies an identical sequence of discrete-state transition steps required from each stage of performance to the next. It repeats at all scales. Tasks nested within the step sequence evidence self-similarity with the orders of complexity. This model introduces questions about noise categories when system tasks (...) are fully accounted for, dependent, self-similar, and measurable. Ubiquitous transition steps are inherent dynamics of evolution. (shrink)

Drinking kills a significant proportion of individuals every year, particularly in low-income communities. An impulsive differential equation system is used to explore the effectiveness of activated charcoal in detoxifying the body after methanol poisoning. Our impression of activated charcoal is shaped by the fractional dynamics of the problem, which leads to speedy and low-cost first aid. The adsorption capacity of activated charcoal is investigated using impulsive differential equations. The ABC fractional operator’s findings paint a more realistic image of first aid (...) in public and primary health centers, which can assist to reduce methanol poisoning deaths. Numerical simulations are provided using generalized Adams–Bashforth–Moulton method. (shrink)

From one of the most influential scientists of our time, a dazzling exploration of the hidden laws that govern the life cycle of everything from plants and animals to the cities we live in. The former head of the Sante Fe Institute, visionary physicist Geoffrey West is a pioneer in the field of complexity science, the science of emergent systems and networks. The term "complexity" can be misleading, however, because what makes West's discoveries so beautiful is that he has found (...) an underlying simplicity that unites the seemingly complex and diverse phenomena of living systems, including our bodies, our cities and our businesses. Fascinated by issues of aging and mortality, West applied the rigor of a physicist to the biological question of why we live as long as we do and no longer. The result was astonishing, and changed science, creating a new understanding of energy use and metabolism: West found that despite the riotous diversity in the sizes of mammals, they are all, to a large degree, scaled versions of each other. If you know the size of a mammal, you can use scaling laws to learn everything from how much food it eats per day, what its heart-rate is, how long it will take to mature, its lifespan, and so on. Furthermore, the efficiency of the mammal's circulatory systems scales up precisely based on weight: if you compare a mouse, a human and an elephant on a logarithmic graph, you find with every doubling of average weight, a species gets 25% more efficient--and lives 25% longer. This speaks to everything from how long we can expect to live to how many hours of sleep we need. Fundamentally, he has proven, the issue has to do with the fractal geometry of the networks that supply energy and remove waste from the organism's body. (shrink)

Theterm, fractal, coined by Benoit B. Mandelbrot, describes a shape or pattern within a greater pattern of which it is a scaling piece identical to the greater pattern and in which are reproduced an infinite number of parts or fragments which are also identical to it, thus, identical to the whole at all scales. In this paper, the author describes Hindu cosmology as it is replicated in the elements of the Bharata Natyam, drawing the analogy to fractal (...) patterning. (shrink)

This NATO Advanced Study Institute centered on large-scale molecular systems: Quantum mechanics, although providing a general framework for the description of matter, is not easily applicable to many concrete systems of interest; classical statistical methods, on the other hand, allow only a partial picture of the behaviour of large systems. The aim of the ASI was to present both aspects of the subject matter and to foster interaction between the scientists working in these important areas of theoretical physics and theoretical (...) chemistry. The quantum-mechanical part was mostly based on the operator-algebraic formulation of quantum mechanics and comprised quantum statistics of infinite systems with special em phasis on macroscopic observables, equilibrium conditions, irreversibility on the one hand, symmetry breaking for molecules in the radiation field and macroscopic quantum phenomena in the theory of superconductivity (BCS-theory) on the other hand. In addition, phase-space methods for many-body systems were also presented. Statistical physics was the main topic in the other lectures of the School; much emphasis was put on the statistical features of macros copic ("large") systems, the lectures dealt with mass and energy transport im polymers, in gels and in microemulsions, with aggregation and growth phenomena, with relaxation in complex, correlated systems, with conduction and optical properties of polymers, and with the means of describing disordered systems, above all fractals and related hierarchical models. (shrink)

Different summarized shape indices, like mean shape index (MSI) and area weighted mean shape index (AWMSI) can change over multiple size scales. This variation is important to describe scale heterogeneity of landscapes, but the exact mathematical form of the dependence is rarely known. In this paper, the use of fractal geometry (by the perimeter and area Hausdorff dimensions) made us able to describe the scale dependence of these indices. Moreover, we showed how fractal dimensions can be deducted from (...) existing MSI and AWMSI data. In this way, the equality of a multiscale tabulated MSI and AWMSI dataset and two scale-invariant fractal dimensions has been demonstrated. (shrink)

It is difficult to watch wild animals while they move, so often biologists analyse characteristics of animal movement paths. One common path characteristic used is tortuousity, measured using the fractal dimension (D). The typical method for estimating fractal D, the divider method, is biased and imprecise. The bias occurs because the path length is truncated. I present a method for minimising the truncation error. The imprecision occurs because sometimes the divider steps land inside the bends of curves, and (...) sometimes they miss the curves. I present three methods for minimising this variation and test the methods with simulated correlated random walks. The traditional divider method significantly overestimates fractal D when paths are short and the range of spatial scales is narrow. The best method to overcome these problems consists of walking the dividers forwards and backwards along the path, and then estimating the path length remaining at the end of the last divider step. (shrink)

This research proposes a modified metaheuristic optimization algorithm, named as improved stochastic fractal search, which is formed based on the integration of the quasiopposition-based learning and chaotic local search schemes into the original SFS algorithm for solving the optimal capacitor placement in radial distribution networks. The test problem involves the determination of the optimal number, location, and size of fixed and switched capacitors at different loading conditions so that the network total yearly cost is minimized with simultaneous fulfillment of (...) operating constraints. Also, the hourly on/off scheduling plans of switched shunt capacitors considering a modified cost objective function are obtained. The proposed ISFS algorithm has been tested on two IEEE 69-bus and 119-bus RDNs and a practical 152-bus RDN. For clarifying the effectiveness and validation of the ISFS, the simulated results have been compared with those of other previously utilized solution approaches in the literature as well as the original SFS. From result comparison, the proposed ISFS outperforms other previous approaches regarding solution quality and statistical performance for the compared cases, especially in the complex and large-scale networks. Notably, compared with the original SFS, the proposed ISFS shows a significantly better performance in all the tested cases. (shrink)

We have demonstrated, using the Cantor dust method, that the statistical distribution of appearance and disappearance of rodents species (Arvicolid rodent radiation in Europe) follows power laws strengthening the evidence for a fractal structure set. Self-similar laws have been used as model for the description of a huge number of biological systems. With Nottale we have shown that log-periodic behaviors of acceleration or deceleration can be applied to branching macroevolution, to the time sequences of major evolutionary leaps (global life (...) tree, sauropod and theropod dinosaurs postural structures, North American fossil equids, rodents, primates and echinoderms clades and human ontogeny). The Scale-Relativity Theory has others biological applications from linear with fractal behavior to non-linear and from classical mechanics to quantum mechanics. (shrink)

This paper shows how the republican model of Cicero has been transmitted fragmentarily, through the Italian civic humanist tradition (Maquiavelo), the English republican humanism of XVI, XVII and XVIII centuries, and the republicanism of the American patriots, ("neo-republicanism"). The proposals of Pettit and Brugger are analyzed, and a great variety of positions that some consider "republican" are summarily reckoned. Finally, it is maintained that the classic republican model is present in a very fragmented way in contemporary political theories, for these (...) theories are incapable to accept some strong anthropological, ethical and metaphysical theses. Cicero's model of republicanism appears to us like in a large scale copy or replica, precisely in the political and legal reality of the contemporary world, in its practices and institutions, and in the political function of its theoretical reflections. (shrink)

Climate dynamics and trends have significant environmental and socioeconomic impacts; however, in the Benin Republic, they are generally studied with diverse statistical methods ignoring the nonstationarity, nonlinearity, and self-similarity characteristics contained in precipitation time series. This can lead to erroneous conclusions and an unclear understanding of climatic dynamics. Based on daily precipitation data observed in the six synoptic stations of Benin Republic, in the period from 1951 to 2010, we have proposed determining the local trends of precipitations, investigating precipitation nonlinear (...) dynamics, and assessing climatic shift in the study period by Ensemble Empirical Mode Decomposition and Multifractal Detrended Fluctuation Analysis method. To overcome the detrending issue in the standard MFDFA method, the EEMD algorithm is embedded into the MFDFA. The study period is subdivided into three subperiods: 1951–1970, 1971–1990, and 1991–2010. Intrinsic Mode Functions are obtained according to the climatic region in which the stations are located. Results show that precipitation variation is significantly governed by the five first IMFs, in which oscillation periods vary from 1 to 25 days. The trend curves decrease at all the synoptic stations, and their slope values vary accordingly to the subperiods. Referring to the values of the multifractal spectrum parameters, α 0, and the width of the spectrum w, consistent changes are observed regardless of the subperiods and the concerned stations. The spatial and temporal variability of precipitation indicates that the multifractal properties are good indicators for assessing changes in precipitation dynamics, and the changes in their features could be explained by the global change than by the local climate variation. Despite the observed differences in multifractal spectra properties from the three subperiods, it is not possible to verify the subdivision of 1951–2010 in three subperiods as it is done by previous studies in West Africa. Our findings can be used in the validation of global and regional climate models since a valid model should explain empirically detected scaling properties in observed data. (shrink)

We present a model for genome evolution, comprising biologically plausible events such as transpositions inside the genome and insertions of exogenous sequences. This model attempts to formulate a minimal proposition accounting for key statistical properties of genomes, avoiding, as far as possible, unsupportable hypotheses for the remote evolutionary past. The statistical properties that are observed in genomic sequences and are reproduced by the proposed model are: (i) deviations from randomness at different length scales, measured by suitable algorithms, (ii) a special (...) form of size distribution (power law distribution) characterising different levels of genome organisation in the non‐coding, and (iii) extensive resemblance in the alternation of coding and non‐coding regions at several length scales (self‐similarity) in long genomic sequences of higher eukaryotes. BioEssays 23:647–656, 2001. © 2001 John Wiley & Sons, Inc. (shrink)

Human neural and behavioral activities have been reported to exhibit fractal dynamics known as 1/f noise, which is more aptly named 1/f scaling. Some argue that 1/f scaling is a general and pervasive property of the dynamical substrate from which cognitive functions are formed. Others argue that it is an idiosyncratic property of domain‐specific processes. An experiment was conducted to investigate whether 1/f scaling pervades the intrinsic fluctuations of a spoken word. Ten participants each repeated the (...) word bucket over 1,000 times, and fluctuations in acoustic measurements across repetitions generally followed the 1/f scaling relation, including numerous parallel yet distinct series of 1/f fluctuations. On the basis of work showing that 1/f scaling is a universal earmark of metastability, it is proposed that the observed pervasiveness of 1/f fluctuations in speech reflects the fact that cognitive functions are formed as metastable patterns of activity in brain, body, and environment. (shrink)

Our families are our first and most important ethical training grounds. But what is the family? And what are our ethical commitments to our family members and to the broader moral community? After a brief introductory chapter on basic ethical concepts and theories, the essays in this volume provide readers with ethical analyses of issues ranging from same-sex marriage to a controversial proposal to "license" parents. The chapters cover love, sex, marriage, parents and children, the relationship between the family and (...) the larger moral community, and the influence of emerging technologies on the ethical issues inherent in family life. The volume is intended to open up this exciting territory in applied ethics to those interested in philosophy, family studies, social work, and to anyone who wants a deeper understanding of the ethical forces at work in this most basic social institution. (shrink)

Irecently admitted a 93-year-old Spanish-speaking woman with bilateral flank pain. A thorough history revealed her pain was due to constipation and intense straining with each bowel movement, but a language barrier, a mild troponin elevation, and "new atrial fibrillation" on her EKG triggered the Emergency Department physician to admit her for observation. When I went to see her, she mentioned her pain was worse since she was told we would need to monitor her heart overnight. She asked, "Is everything ok (...) with my heart?"To assess that question, I prepared to perform a bedside ultrasound, also known as point-of-care ultrasound. We moved from a hallway in the ED to a room for more privacy, and the patient... (shrink)

Critical discussion of Quine's concepts of purely referential occurrence/position. It is argued from the perspective of a Russellian view of truth that existential generalization and substitutivity of identity are non-equivalent tests for referential occurrence/position, and that the former rather than the latter is the appropriate test.

Critical discussion of Quine's concepts of purely referential occurrence/position. It is argued from the perspective of a Russellian view of truth that existential generalization and substitutivity of identity are non-equivalent tests for referential occurrence/position, and that the former rather than the latter is the appropriate test.

Human–Human and Human–Robot Interaction are known to be influenced by a variety of modalities and parameters. Nevertheless, it remains a challenge to anticipate how a given mobile robot’s navigation and appearance will impact how it is perceived by humans. Drawing a parallel with vocal prosody, we introduce the notion of movement prosody, which encompasses spatio-temporal and appearance dimensions which are involved in a person’s perceptual experience of interacting with a mobile robot. We design a novel robot motion corpus, encompassing variables (...) related to the kinematics, gaze, and appearance of the robot, which we hypothesize are involved in movement prosody. Initial results of three perception experiments suggest that these variables have significant influences on participants’ perceptions of robot socio-affects and physical attributes. (shrink)