The complex-systems approach to cognitive science seeks to move beyond the formalism of information exchange and to situate cognition within the broader formalism of energy flow. Changes in cognitive performance exhibit a fractal (i.e., power-law) relationship between size and time scale. These fractal fluctuations reflect the flow of energy at all scales governing cognition. Information transfer, as traditionally understood in the cognitive sciences, may be a subset of this multiscale energy flow. The cognitive system exhibits not just a single power-law (...) relationship between fluctuation size and time scale but actually exhibits many power-law relationships, whether over time or space. This change in fractal scaling, that is, multifractality, provides new insights into changes in energy flow through the cognitive system. We survey recent findings demonstrating the role of multifractality in (a) understanding atypical developmental outcomes, and (b) predicting cognitive change. We propose that multifractality provides insights into energy flows driving the emergence of cognitive structure. (shrink)

We investigate the cross-correlations of return-volume relationship of the Bitcoin market. In particular, we select eight exchange rates whose trading volume accounts for more than 98% market shares to synthesize Bitcoin indexes. The empirical results based on multifractal detrended cross-correlation analysis reveal that the nonlinear dependencies and power-law cross-correlations in return-volume relationship are found; all cross-correlations are multifractal, and there are antipersistent behaviors of cross-correlation for q=2; the price of small fluctuations is more persistent than that of the volume, while (...) the volume of larger fluctuations is more antipersistent; and the rolling window method shows that the cross-correlations of return-volume are antipersistent in the entire sample period. (shrink)

The joint multifractal analysis is usually conducted in two different variables for their cross-correlations but rarely used for two records of one variable collected at two different places. It is important for the detection of change in multifractality in space. Besides, the cross-correlations in two analyzed series make the analysis of sources of joint multifractality difficult. There are few studies on the source of joint multifractality. We focus on the two issues for two level records at pairs of adjacent sites (...) along one river and carry out an extension of our previous work which is about the single multifractality of one record with the same data set. The data set is collected from 10 observation stations of a northern China river and contains about two million high-frequency river level records. Results of joint multifractal analysis via multifractal detrended cross-correlation analysis show that the change in joint multifractality at pairs of adjacent sites caused by weak cross-correlations can be detected by comparing the single generalized Hurst exponent with the joint scaling exponent function and reveal the effects of human activities on joint multifractality. This analysis provides an approach for detecting the change in multifractality. Following the idea of our previous work, two robust hypothesis tests via a set of pairs of surrogate series are proposed for the source testing of joint multifractality. The analysis of the effects of cross-correlations is carried out via a proposed simultaneously half-shifting technique which can both minimize the cross-correlations between original series and make full use of records. Results of source analysis show not only the effects of autocorrelations in series and probability distribution of river levels but also the effects of cross-correlations between series. (shrink)

Critical phenomena in stock exchange are regularly occurring and difficult to predict events, often leading to disastrous consequences. The presented paper is devoted to the search and research of early warning signals of critical transitions in stock exchange based on the results of a multifractal analysis of a series of transactions in shares of public companies. We have proposed and justified the use of certain features of behavior of multifractal spectrum shape parameters such as signals. As model time series, on (...) which methods of multifractal analysis were tested, we used a series of the number of unstable sites of the sandpile automaton on the random Erdős–Rényi graph, self-organizing into critical and bistable states. It was found that the early warning signals for both cellular automata and stock exchanges are an increase in the magnitude of the maximum position, a decrease in the width, and a decrease, followed by a sharp increase, in the value of the spectrum asymmetry parameter. (shrink)

Electromechanical actuators are more and more widely used as actuation devices in flight control system of aircrafts and helicopters. The reliability of EMAs is vital because it will cause serious accidents if the malfunction of EMAs occurs, so it is significant to detect and diagnose the fault of EMAs timely. However, EMAs often run under variable conditions in realistic environment, and the vibration signals of EMAs are nonlinear and nonstationary, which make it difficult to effectively achieve fault diagnosis. This paper (...) proposed a fault diagnosis method of electromechanical actuators based on variational mode decomposition multifractal detrended fluctuation analysis and probabilistic neural network. First, the vibration signals were decomposed by VMD into a number of intrinsic mode functions. Second, the multifractal features hidden in IMFs were extracted by using MFDFA, and the generalized Hurst exponents were selected as the feature vectors. Then, the principal component analysis was introduced to realize dimension reduction of the extracted feature vectors. Finally, the probabilistic neural network was utilized to classify the fault modes. The experimental results show that this method can effectively achieve the fault diagnosis of EMAs even under diffident working conditions. Simultaneously, the diagnosis performance of the proposed method in this paper has an advantage over that of EMD-MFDFA method for feature extraction. (shrink)

After more than 15 years of study, the 1/f noise or complex-systems approach to cognitive science has delivered promises of progress, colorful verbiage, and statistical analyses of phenomena whose relevance for cognition remains unclear. What the complex-systems approach has arguably failed to deliver are concrete insights about how people perceive, think, decide, and act. Without formal models that implement the proposed abstract concepts, the complex-systems approach to cognitive science runs the danger of becoming a philosophical exercise in futility. The complex-systems (...) approach can be informative and innovative, but only if it is implemented as a formal model that allows concrete prediction, falsification, and comparison against more traditional approaches. (shrink)

A recent set of experiments of ours supported the notion of a transition in experience from readiness-to-hand to unreadiness-tohand proposed by phenomenological philosopher Martin Heidegger. They were also an experimental demonstration of an extended cognitive system. We generated and then temporarily disrupted an interaction- dominant system that spans a human participant, a computer mouse, and a task performed on the computer screen. Our claim that this system was interaction dominant was based on the detection of 1/f noise at the hand-tool (...) interface. The inference from the presence of 1/f noise to the presence of an interaction-dominant system is occasionally disputed. Increasing evidence suggests that inference from multifractality to interaction dominance is more certain than 1/f- like scaling alone. In this paper, we reanalyze the data using the wavelet transform modulus maxima method, showing that the human-mouse system displays multifractality. This reinforces our claims that the system is interaction dominant. (shrink)

Gestures and speech are clearly synchronized in many ways. However, previous studies have shown that the semantic similarity between gestures and speech breaks down as people approach transitions in understanding. Explanations for these gesture–speech mismatches, which focus on gestures and speech expressing different cognitive strategies, have been criticized for disregarding gestures’ and speech's integration and synchronization. In the current study, we applied three different perspectives to investigate gesture–speech synchronization in an easy and a difficult task: temporal alignment, semantic similarity, and (...) complexity matching. Participants engaged in a simple cognitive task and were assigned to either an easy or a difficult condition. We automatically measured pointing gestures, and we coded participant's speech, to determine the temporal alignment and semantic similarity between gestures and speech. Multifractal detrended fluctuation analysis was used to determine the extent of complexity matching between gestures and speech. We found that task difficulty indeed influenced gesture–speech synchronization in all three domains. We thereby extended the phenomenon of gesture–speech mismatches to difficult tasks in general. Furthermore, we investigated how temporal alignment, semantic similarity, and complexity matching were related in each condition, and how they predicted participants’ task performance. Our study illustrates how combining multiple perspectives, originating from different research areas (i.e., coordination dynamics, complexity science, cognitive psychology), provides novel understanding about cognitive concepts in general and about gesture–speech synchronization and task difficulty in particular. (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)

Resumen: Este artículo sostiene que la regla en el mundo social es el cambio, en todas las escalas de tiempo, sin ciclos ni periodicidades. Por consiguiente, el tema que emerge inmediatamente es la irregularidad del mundo. Si esto es cierto, deben ser posibles unas ciencias sociales irregulares. El mejor antecedente para una idea semejante se encuentra en la comprensión del propio Mandelbrot acerca de los fractales y multifractales. Las ciencias sociales tratan radicalmente, de fenómenos irrepetibles, singulares. Estos han sido llamados (...) como eventos raros. De esta suerte, una nueva epistemología emerge y es posible. Al final se muestra que existen nexos fuertes entre las ciencias sociales con la biología y la ecología. Pero en ese punto, el texto termina abierto.: This paper claims that change is the rule in the social world, in all scales of time, without cycles or periodic dynamics. Hereafter, the topic that immediately arises is the irregularity of the world. If this is true, then irregular social sciences are to be possible. The best antecedent of such an idea is to be found in Mandelbrot’s own understanding of fractals and multifractals. Thus, the social sciences radically deal with phenomena that are in no way repeated, for they are singular. Such events have been called as rare events. In thus tenure, a brand-new epistemology arises and is possible. At the end, some connections between the social sciences and biology and ecology are depicted. That, however, is where this text ends and remains open. (shrink)

We empirically analyze the impact of economic uncertainty due to the COVID-19 pandemic on the trading volume of each sector in the S&P 500 index. Wavelet coherence analysis is carried out using economic policy uncertainty data and the trading volume of each sector in the S&P 500 index from July 2004 to September 2020. Furthermore, we apply multifractal detrended fluctuation analysis to the trading volume series of all sectors. The wavelet coherence analysis shows that the COVID-19 pandemic has substantially influenced (...) trading volume in all sectors. However, the impact of the pandemic is different from that during the global financial crisis in some sectors, such as information technology, consumer discretionary, and communication services. Because of the lockdown taken to suppress COVID-19, increased remote working and remote learning are the main reasons for these results. Additionally, according to the MF-DFA analysis, the trading volume of all the sectors has clear multifractal characteristics, and they are all nonpersistent. Specifically, trading volumes of the real estate and materials sector are highly correlated, whereas the trading volumes of industry and information technology sectors are comparatively less correlated. (shrink)

The related fields of fractal image encoding and fractal image analysis have blossomed in recent years. This book, originating from a NATO Advanced Study Institute held in 1995, presents work by leading researchers. It is developing the subjects at an introductory level, but it also has some recent and exciting results in both fields. The book contains a thorough discussion of fractal image compression and decompression, including both continuous and discrete formulations, vector space and hierarchical methods, and algorithmic optimizations. The (...) book also discusses multifractal approaches to image analysis, segmentation, and recognition, including medical applications. (shrink)

Entropy is one of the physical bases for the fractal dimension definition, and the generalized fractal dimension was defined by Renyi entropy. Using the fractal dimension, we can describe urban growth and form and characterize spatial complexity. A number of fractal models and measurements have been proposed for urban studies. However, the precondition for fractal dimension application is to find scaling relations in cities. In the absence of the scaling property, we can make use of the entropy function and measurements. (...) This paper is devoted to researching how to describe urban growth by using spatial entropy. By analogy with fractal dimension growth models of cities, a pair of entropy increase models can be derived, and a set of entropy-based measurements can be constructed to describe urban growing process and patterns. First, logistic function and Boltzmann equation are utilized to model the entropy increase curves of urban growth. Second, a series of indexes based on spatial entropy are used to characterize urban form. Furthermore, multifractal dimension spectra are generalized to spatial entropy spectra. Conclusions are drawn as follows. Entropy and fractal dimension have both intersection and different spheres of application to urban research. Thus, for a given spatial measurement scale, fractal dimension can often be replaced by spatial entropy for simplicity. The models and measurements presented in this work are significant for integrating entropy and fractal dimension into the same framework of urban spatial analysis and understanding spatial complexity of cities. (shrink)