Information entropy analysis of discrete aiming movements

Fitts studied the problem of information capacity and transfer in the speed–accuracy motor paradigm using a theoretical approach developed from Shannon and Weaver’s information theory. The information processing (bit/s) estimated in Fitts’ study is calculated from the movement time required to achieve the required task index of difficulty but is essentially different from Shannon’s information entropy. Thus, we estimated the information entropy of multiple human movement trajectories and the mutual information among trajectories for the continuous aiming task in Fitts’ paradigm. Further, we estimated the information processing moment by moment. Two methods were considered: (1) encoded values encompassing the coordinates of the three dimensions and (2) coordinate values associated with each direction in the three dimensions. Information entropy indicates the magnitude of variation at each time point, and the structure of this variation varies with the index of difficulty. The ratio of entropy to mutual information was examined, and it was found that information was processed from the first half of the trajectory in difficult tasks. In addition, since these values calculated from the encoded method were higher than those from the conventional method, this method may be able to estimate these values successfully.

Information sharing among cryptocurrencies: Evidence from mutual information and approximate entropy during COVID-19

Editorial| July 2023 Anesthesia and the Merry-go-round of Information in the Brain Jamie W. Sleigh, M.D.; Jamie W. Sleigh, M.D. 1Department of Anaesthesiology, Waikato Clinical Campus, Faculty of Medical and Health Sciences, University of Auckland, Hamilton, New Zealand. Search for other works by this author on: This Site PubMed Google Scholar Logan Voss, Ph.D. Logan Voss, Ph.D. 2Department of Anaesthesiology, Waikato Clinical Campus, Faculty of Medical and Health Sciences, University of Auckland, Hamilton, New Zealand. Search for other works by this author on: This Site PubMed Google Scholar Author and Article Information This editorial accompanies the article on p. 49. Accepted for publication March 30, 2023. Address correspondence to Dr. Sleigh: jamie.sleigh@waikatodhb.health.nz Anesthesiology July 2023, Vol. 139, 4–5. https://doi.org/10.1097/ALN.0000000000004571 Connected Content Article: Measures of Information Content during Anesthesia and Emergence in the Caenorhabditis elegans Nervous System Views Icon Views Article contents Figures & tables Video Audio Supplementary Data Peer Review Share Icon Share Facebook Twitter LinkedIn Email Cite Icon Cite Get Permissions Search Site Citation Jamie W. Sleigh, Logan Voss; Anesthesia and the Merry-go-round of Information in the Brain. Anesthesiology 2023; 139:4–5 doi: https://doi.org/10.1097/ALN.0000000000004571 Download citation file: Ris (Zotero) Reference Manager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentAll PublicationsAnesthesiology Search Advanced Search Topics: brain It is widely believed that anesthesia is a syndrome caused by drug-induced disruption of coordination within and between neuronal networks. The underlying teleological assumption is that normal function of the central nervous system requires precise electrical and chemical communication between neurons, and communication implies flow of “information.” In this issue of Anesthesiology is an article by Chang et al.1 in which isoflurane was given to a nematode (Caenorhabditis elegans), and the resultant real-time changes in activity of about half of its 302 neurons were visualized using high-resolution calcium fluorescence imaging. In this study, the authors focused on how anesthesia alters interneuronal coupling by measuring the entropy of the calcium transients in the imaged neurons. The meaning of the word “entropy” is intuitively difficult. It is often used as a synonym for disorder, uncertainty, or unpredictability. To take the extreme examples: if a neuron has no activity (a... You do not currently have access to this content.

ABSTRACTPreviously, we have shown that discrete and continuous rapid aiming tasks are governed by distinct visuomotor control mechanisms by assessing the combined visual illusion effects on the perceived and effective index of difficulty (ID). All participants were perceptually biased by the combined visual illusion before they performed the rapid aiming tasks. In the current study, the authors manipulated the order of performing perceptual and motor tasks to examine whether perceptual or motor experience with the illusory visual target would influence the subsequent perceived and effective ID in discrete and continuous tapping tasks. The results supported our hypothesis showing that perceptual experience with the illusory visual target in the discrete condition reduced the effective ID in the subsequent discrete tapping task, and motor experience with the illusory visual target in the continuous condition reduced the illusion effects on the perceived ID in the subsequent perceptual judgment task. The study demonstrates the coinfluence of perception and action, and suggests that perception and action influence one another with different magnitude depending on the spatial frame of reference used to perform the perceptuomotor task.

A privacy-preserving adversarial network (PPAN) was recently proposed as an information-theoretical framework to address the issue of privacy in data sharing. The main idea of this model was to use mutual information as the privacy measure and adversarial training of two deep neural networks, one as the mechanism and another as the adversary. The performance of the PPAN model for the discrete synthetic data, MNIST handwritten digits, and continuous Gaussian data was evaluated and compared to the analytically optimal trade-off. In this study, we evaluate the PPAN model for continuous non-Gaussian data, i.e. smart meters data, where lower and upper bounds of the privacy-preserving problem are used. These bounds include the Kraskov (KSG) estimation of entropy and mutual information that is based on the k-th nearest neighbor. In addition to the synthetic data sets, a practical case for hiding the actual electricity consumption from smart meter readings is examined. The results show that for continuous non-Gaussian data, the PPAN model performs within the determined optimal ranges and close to the lower bound.

Variability in rhythmic physiological systems is of great interest, especially with regard to identifying deterministic variability. Algorithms have been proposed to quantify nonlinear variability, but the results can be difficult to interpret. Proper interpretation of traditional statistical methods depends on a knowledge of the underlying distribution (e.g. Gaussian). Measures of nonlinear variability must also be interpreted in the context of the particular characteristics of the system being analyzed [1]. Analysis methods are often first developed in the context of a particular application and then popularized as a general technique. For example, approximate entropy was developed to analyze the electrocardiogram [2,3] and is now used extensively in other areas. Though various algorithms may be well understood, parameter selection is typically based on tradition [1]. Additionally, proper interpretation requires the use of surrogate data analysis. However, surrogate data is often poorly understood by experimentalists with regard to the algorithms used and the data that is generated [4]. Information measures such as sample entropy and mutual information have recently been applied to the neural generation of respiratory rhythms [5]. Here we investigate two aspects of applying information measures to periodic patterns such as those found in respiration. First, the use of surrogate data analysis is critical for interpretation of results from information measures. Here we evaluate its application to the testing of hypotheses in respiratory control. Second, information measures do not necessarily distinguish between stochastic and deterministic sources of variability in a system. Here we use both experimental and simulated data to study the relative effects of stochastic and deterministic sources of variability on sample entropy and mutual information algorithms.

The lower visual field (loVF) has been hypothesized to demonstrate specialization for skilled, visually guided action. According to Danckert and Goodale, this visual field asymmetry indirectly suggests that the loVF has privileged connections to visuomotor networks within the dorsal visual pathway. Here we attempted to replicate the loVF advantage during the execution of a discrete aiming movement to targets of various widths (index of difficulty ranging from 1.5 to 5 bits). In addition, we employed trials in which vision of the target object was available or unavailable during the reaching movement to determine whether or not the purported visual field asymmetry reflects enhanced central planning (i.e., feedforward) or online control (i.e., feedback) processes. Reaching trajectories were examined for indicators of online amendments, and movement times and endpoint characteristics were examined to quantify possible visual field asymmetries in relative speed/accuracy trade-offs. In terms of reaching kinematics, it was found that vision of the target during the reaching movement resulted in greater online control of the reaching trajectory; however, no significant main effects or interactions involving visual field were observed. In other words, fixating in the upper or the lower region of peripersonal space did not influence the nature of reaching control (i.e., feedback vs. feedforward). Most importantly, our movement time and endpoint accuracy data elicited a robust speed/accuracy trade-off in both upper and lower regions of working space. Thus, and contrary to previous findings (such as those reported by Danckert and Goodale), the indices of difficulty coupled with the discrete aiming task used here did not elicit a lower visual field advantage for visually guided action.

Calculations of entropy of a signal or mutual information between two variables are valuable analytical tools in the field of neuroscience. They can be applied to all types of data, capture non-linear interactions and are model independent. Yet the limited size and number of recordings one can collect in a series of experiments makes their calculation highly prone to sampling bias. Mathematical methods to overcome this so-called “sampling disaster” exist, but require significant expertise, great time and computational costs. As such, there is a need for a simple, unbiased and computationally efficient tool for estimating the level of entropy and mutual information. In this article, we propose that application of entropy-encoding compression algorithms widely used in text and image compression fulfill these requirements. By simply saving the signal in PNG picture format and measuring the size of the file on the hard drive, we can estimate entropy changes through different conditions. Furthermore, with some simple modifications of the PNG file, we can also estimate the evolution of mutual information between a stimulus and the observed responses through different conditions. We first demonstrate the applicability of this method using white-noise-like signals. Then, while this method can be used in all kind of experimental conditions, we provide examples of its application in patch-clamp recordings, detection of place cells and histological data. Although this method does not give an absolute value of entropy or mutual information, it is mathematically correct, and its simplicity and broad use make it a powerful tool for their estimation through experiments.

Attribute selection in an information system is one of the important applications of rough set theory. This paper studies attribute selection for heterogeneous data based on information entropy. We first define information entropy in an information system with heterogeneous data and then put forward the notions of joint information entropy, conditional information entropy and mutual information entropy in a decision information system with heterogeneous data. We apply information entropy to perform attribute selection in a decision information system with heterogeneous data. We propose two attribute selection algorithms based on information entropy. Finally, we make experimental analysis and comparisons to illustrate the feasibility and efficiency of the proposed algorithms.

With regional socio-economic development, the gap between water use demand and available water resources in arid and humid semi-arid areas becomes increasingly serious. In this study, the size of regional water use in the Guanzhong region and Shiyang river basin in northwest China are analyzed to identify important factors affecting it, with the aim of providing better and optimal development planning for the region. Information entropy is used to measure and characterize the diversity of regional water use. Agricultural development and meteorological factors are found to be the main issues affecting regional water use in both regions. A multiple-linear regression (MLR) model was built by applying correlation coefficient (R) and mutual information (MI) scores in the process. Results show that the low value of information entropy of water use in the Shiyang river basin is due to the high proportion of agriculture water use. Using input factors chosen by MI score was found to be the best model to simulate the change of regional water use in both regions. A method using an MLR model together with MI is shown to be able to quantify the relationship between the influencing factors and water use diversity with limited available data.

Aiming at the problem that the high computational complexity of calculating information entropy and mutual information of a neighborhood rough set, a fast calculation method based on data sorting was proposed to estimate neighborhood mutual information speedily. This method can reduce the computational complexity of neighborhood entropy from O(n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) to O(nlogn). Under this premise, the method can calculate the approximation of the joint neighborhood entropy by infinite-norm-calculated neighborhood relation, thus to estimate the neighborhood mutual information quickly. For the reason that the method is based on neighborhood entropy, it is also effective for mixed data. Experimental results show that this method can significantly shorten the computational time of neighborhood mutual information and ensure high approximation quality when using large-scale data sets.

Damage detection of mechanical structures such as bridges is an important research problem in civil engineering. Using spatially distributed sensor time series data collected from a recent experiment on a local bridge in Upper State New York, we study noninvasive damage detection using information-theoretical methods. Several findings are in order. First, the time series data, which represent accelerations measured at the sensors, more closely follow Laplace distribution than normal distribution, allowing us to develop parameter estimators for various information-theoretic measures such as entropy and mutual information. Second, as damage is introduced by the removal of bolts of the first diaphragm connection, the interaction between spatially nearby sensors as measured by mutual information becomes weaker, suggesting that the bridge is "loosened." Finally, using a proposed optimal mutual information interaction procedure to prune away indirect interactions, we found that the primary direction of interaction or influence aligns with the traffic direction on the bridge even after damaging the bridge.

Measures of relevance between features play an important role in classification and regression analysis. Mutual information has been proved to be an effective measure for categorical features. However, there is a limitation in computing relevance between numerical features with mutual information. In this work, we generalize Shannon's information entropy to neighborhood information entropy and propose a measure of neighborhood mutual information. It is shown that the new measure is a natural extension of classical mutual information which reduces to the classical one if features are discrete; thus the new measure can also be used to compute the relevance between discrete variables. In experiment, we show that neighborhood mutual information produces the nearly same outputs as mutual information. However, unlike mutual information, no discretization is required in computing relevance when used the proposed algorithm.

Conscious activity is generally consistent with a deterministic mode of action, however some activities demand randomness. The goal of this study was to find whether mind can produce randomness. We asked various human subjects, aged between 21 and 57, to produce sequences of random integers. The non-repetition of the terms in the series was the "algorithm" generally used by all the subjects. The series were analyzed by using spectral analysis (SA), detrended fluctuation analysis (DFA), information (I2) and approximate entropy (AE) and correlation dimension analysis (CDA). SA of the series revealed 1/fβ(-0.4&lt;β&lt;1) types of spectra. The α scaling exponent resulting from DFA ranged between 0.2 and 1.1. The maximum of the distribution of α was centered at about 0.62. This is equivalent to a quarter power law in spectral terms. A significant percentage of subjects were able to produce random series. I2 of mental series revealed short-range correlation for pairs of successive numbers in the series. The correlation decreased gradually and it disappeared at a delay step of about 7 which is the characteristic number of short memory. AE had a minimum value at α=1 and a maximum value at α=0.5 for mental and random series, respectively. CDA showed no presence of attractors in the series, therefore none of the randomness produced by the subjects was of deterministic origin. A comparison of the scaling exponents revealed that the mental series have a certain long-range characteristic which is common to the human language as evident in the literature writings.

Metaphor is to express another thing through one thing, it is not only a rhetorical means, but also embodies a kind of analogical cognition and way of thinking of people. In recent years, metaphors have made more and more progress in Chinese language recognition, so their status has gradually risen. Chinese language sentiment analysis is a relatively difficult problem in language processing. Chinese language semantics is ambiguous and complex, so it is a great challenge to construct Chinese Emotion structure. In this paper, Chinese nouns and Chinese verbs are used as test samples to conduct metaphor test calculation. The test results of mutual information and information entropy show that for the sample metaphor calculation, the correct rate of individual words is less than 70%. The ratio between the macro-average of gerund words and the baseline fluctuates relatively large. The metaphor recognition of nouns is about 20% higher than the original test results and about 10% higher for verbs. It shows that under the action of mutual information and information entropy, the metaphor recognition performance of the basic structure of Chinese Emotion constructed from the perspective of metaphor is improved, and further illustrates the feasibility of mutual information and information entropy algorithm for building the basic structure.