Entropy

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3 pages, 155 KiB

Open AccessEditorial

Information Theory and Symbolic Analysis: Theory and Applications

by Mariano Matilla-García and Manuel Ruiz Marín

Entropy 2021, 23(10), 1361; https://doi.org/10.3390/e23101361 - 19 Oct 2021

Cited by 1 | Viewed by 1461

Abstract

Symbolic analysis has been developed and used successfully in very diverse fields [...] Full article

(This article belongs to the Special Issue Information theory and Symbolic Analysis: Theory and Applications)

Research

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13 pages, 363 KiB

Open AccessEditor’s ChoiceArticle

Selection of Embedding Dimension and Delay Time in Phase Space Reconstruction via Symbolic Dynamics

by Mariano Matilla-García, Isidro Morales, Jose Miguel Rodríguez and Manuel Ruiz Marín

Entropy 2021, 23(2), 221; https://doi.org/10.3390/e23020221 - 11 Feb 2021

Cited by 34 | Viewed by 4178

Abstract

The modeling and prediction of chaotic time series require proper reconstruction of the state space from the available data in order to successfully estimate invariant properties of the embedded attractor. Thus, one must choose appropriate time delay

τ^{*}

and embedding dimension p [...] Read more.

The modeling and prediction of chaotic time series require proper reconstruction of the state space from the available data in order to successfully estimate invariant properties of the embedded attractor. Thus, one must choose appropriate time delay

τ^{*}

and embedding dimension p for phase space reconstruction. The value of

τ^{*}

can be estimated from the Mutual Information, but this method is rather cumbersome computationally. Additionally, some researchers have recommended that

τ^{*}

should be chosen to be dependent on the embedding dimension p by means of an appropriate value for the time delay

τ_{w} = (p - 1) τ^{*}

, which is the optimal time delay for independence of the time series. The C-C method, based on Correlation Integral, is a method simpler than Mutual Information and has been proposed to select optimally

τ_{w}

and

τ^{*}

. In this paper, we suggest a simple method for estimating

τ^{*}

and

τ_{w}

based on symbolic analysis and symbolic entropy. As in the C-C method,

τ^{*}

is estimated as the first local optimal time delay and

τ_{w}

as the time delay for independence of the time series. The method is applied to several chaotic time series that are the base of comparison for several techniques. The numerical simulations for these systems verify that the proposed symbolic-based method is useful for practitioners and, according to the studied models, has a better performance than the C-C method for the choice of the time delay and embedding dimension. In addition, the method is applied to EEG data in order to study and compare some dynamic characteristics of brain activity under epileptic episodes Full article

(This article belongs to the Special Issue Information theory and Symbolic Analysis: Theory and Applications)

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15 pages, 1035 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Entropy Ratio and Entropy Concentration Coefficient, with Application to the COVID-19 Pandemic

by Christoph Bandt

Entropy 2020, 22(11), 1315; https://doi.org/10.3390/e22111315 - 18 Nov 2020

Cited by 13 | Viewed by 3261

Abstract

In order to study the spread of an epidemic over a region as a function of time, we introduce an entropy ratio U describing the uniformity of infections over various states and their districts, and an entropy concentration coefficient [...] Read more.

In order to study the spread of an epidemic over a region as a function of time, we introduce an entropy ratio U describing the uniformity of infections over various states and their districts, and an entropy concentration coefficient

C = 1 - U .

The latter is a multiplicative version of the Kullback-Leibler distance, with values between 0 and 1. For product measures and self-similar phenomena, it does not depend on the measurement level. Hence, C is an alternative to Gini’s concentration coefficient for measures with variation on different levels. Simple examples concern population density and gross domestic product. Application to time series patterns is indicated with a Markov chain. For the Covid-19 pandemic, entropy ratios indicate a homogeneous distribution of infections and the potential of local action when compared to measures for a whole region. Full article

(This article belongs to the Special Issue Information theory and Symbolic Analysis: Theory and Applications)

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15 pages, 1093 KiB

Open AccessArticle

Classification of Actigraphy Records from Bipolar Disorder Patients Using Slope Entropy: A Feasibility Study

by David Cuesta-Frau, Jakub Schneider, Eduard Bakštein, Pavel Vostatek, Filip Spaniel and Daniel Novák

Entropy 2020, 22(11), 1243; https://doi.org/10.3390/e22111243 - 1 Nov 2020

Cited by 25 | Viewed by 3601

Abstract

Bipolar Disorder (BD) is an illness with high prevalence and a huge social and economic impact. It is recurrent, with a long-term evolution in most cases. Early treatment and continuous monitoring have proven to be very effective in mitigating the causes and consequences [...] Read more.

Bipolar Disorder (BD) is an illness with high prevalence and a huge social and economic impact. It is recurrent, with a long-term evolution in most cases. Early treatment and continuous monitoring have proven to be very effective in mitigating the causes and consequences of BD. However, no tools are currently available for a massive and semi-automatic BD patient monitoring and control. Taking advantage of recent technological developments in the field of wearables, this paper studies the feasibility of a BD episodes classification analysis while using entropy measures, an approach successfully applied in a myriad of other physiological frameworks. This is a very difficult task, since actigraphy records are highly non-stationary and corrupted with artifacts (no activity). The method devised uses a preprocessing stage to extract epochs of activity, and then applies a quantification measure, Slope Entropy, recently proposed, which outperforms the most common entropy measures used in biomedical time series. The results confirm the feasibility of the approach proposed, since the three states that are involved in BD, depression, mania, and remission, can be significantly distinguished. Full article

(This article belongs to the Special Issue Information theory and Symbolic Analysis: Theory and Applications)

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18 pages, 6514 KiB

Open AccessArticle

A Symbolic Encapsulation Point as Tool for 5G Wideband Channel Cross-Layer Modeling

by Nenad Stefanovic, Marija Blagojevic, Ivan Pokrajac, Marian Greconici, Yigang Cen and Vladimir Mladenovic

Entropy 2020, 22(10), 1151; https://doi.org/10.3390/e22101151 - 14 Oct 2020

Cited by 3 | Viewed by 2265

Abstract

Considering that networks based on New Radio (NR) technology are oriented to provide services of desired quality (QoS), it becomes questionable how to model and predict targeted QoS values, especially if the physical channel is dynamically changing. In order to overcome mobility issues, [...] Read more.

Considering that networks based on New Radio (NR) technology are oriented to provide services of desired quality (QoS), it becomes questionable how to model and predict targeted QoS values, especially if the physical channel is dynamically changing. In order to overcome mobility issues, we aim to support the evaluation of second-order statistics of signal, namely level-crossing rate (LCR) and average fade duration (AFD) that is missing in general channel 5G models. Presenting results from our symbolic encapsulation point 5G (SEP5G) additional tool, we fill this gap and motivate further extensions on current general channel 5G. As a matter of contribution, we clearly propose: (i) anadditional tool for encapsulating different mobile 5G modeling approaches; (ii) extended, wideband, LCR, and AFD evaluation for optimal radio resource allocation modeling; and (iii) lower computational complexity and simulation time regarding analytical expression simulations in related scenario-specific 5G channel models. Using our deterministic channel model for selected scenarios and comparing it with stochastic models, we show steps towards higherlevel finite state Markov chain (FSMC) modeling, where mentioned QoS parameters become more feasible, placing symbolic encapsulation at the center of cross-layer design. Furthermore, we generate values within a specified 5G passband, indicating how it can be used for provisioningoptimal radio resource allocation. Full article

(This article belongs to the Special Issue Information theory and Symbolic Analysis: Theory and Applications)

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12 pages, 4187 KiB

Open AccessArticle

Neuronal Transmission of Subthreshold Periodic Stimuli Via Symbolic Spike Patterns

by Maria Masoliver and Cristina Masoller

Entropy 2020, 22(5), 524; https://doi.org/10.3390/e22050524 - 5 May 2020

Cited by 3 | Viewed by 2363

Abstract

We study how sensory neurons detect and transmit a weak external stimulus. We use the FitzHugh–Nagumo model to simulate the neuronal activity. We consider a sub-threshold stimulus, i.e., the stimulus is below the threshold needed for triggering action potentials (spikes). However, in the [...] Read more.

We study how sensory neurons detect and transmit a weak external stimulus. We use the FitzHugh–Nagumo model to simulate the neuronal activity. We consider a sub-threshold stimulus, i.e., the stimulus is below the threshold needed for triggering action potentials (spikes). However, in the presence of noise the neuron that perceives the stimulus fires a sequence of action potentials (a spike train) that carries the stimulus’ information. To yield light on how the stimulus’ information can be encoded and transmitted, we consider the simplest case of two coupled neurons, such that one neuron (referred to as neuron 1) perceives a subthreshold periodic signal but the second neuron (neuron 2) does not perceive the signal. We show that, for appropriate coupling and noise strengths, both neurons fire spike trains that have symbolic patterns (defined by the temporal structure of the inter-spike intervals), whose frequencies of occurrence depend on the signal’s amplitude and period, and are similar for both neurons. In this way, the signal information encoded in the spike train of neuron 1 propagates to the spike train of neuron 2. Our results suggest that sensory neurons can exploit the presence of neural noise to fire spike trains where the information of a subthreshold stimulus is encoded in over expressed and/or in less expressed symbolic patterns. Full article

(This article belongs to the Special Issue Information theory and Symbolic Analysis: Theory and Applications)

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17 pages, 440 KiB

Open AccessArticle

Symbolic Analysis Applied to the Specification of Spatial Trends and Spatial Dependence

by Maryna Makeienko

Entropy 2020, 22(4), 466; https://doi.org/10.3390/e22040466 - 20 Apr 2020

Cited by 5 | Viewed by 2358

Abstract

This article provides symbolic analysis tools for specifying spatial econometric models. It firstly considers testing spatial dependence in the presence of potential leading deterministic spatial components (similar to time-series tests for unit roots in the presence of temporal drift and/or time-trend) and secondly [...] Read more.

This article provides symbolic analysis tools for specifying spatial econometric models. It firstly considers testing spatial dependence in the presence of potential leading deterministic spatial components (similar to time-series tests for unit roots in the presence of temporal drift and/or time-trend) and secondly considers how to econometrically model spatial economic relations that might contain unobserved spatial structure of unknown form. Hypothesis testing is conducted with a symbolic-entropy based non-parametric statistical procedure, recently proposed by Garcia-Cordoba, Matilla-Garcia, and Ruiz (2019), which does not rely on prior weight matrices assumptions. It is shown that the use of geographically restricted semiparametric spatial models is a promising modeling strategy for cross-sectional datasets that are compatible with some types of spatial dependence. The results state that models that merely incorporate space coordinates might be sufficient to capture space dependence. Hedonic models for Baltimore, Boston, and Toledo housing prices datasets are revisited, studied (with the new proposed procedures), and compared with standard spatial econometric methodologies. Full article

(This article belongs to the Special Issue Information theory and Symbolic Analysis: Theory and Applications)

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18 pages, 5195 KiB

Open AccessFeature PaperArticle

Musical Collaboration in Rhythmic Improvisation

by Shinnosuke Nakayama, Vrishin R. Soman and Maurizio Porfiri

Entropy 2020, 22(2), 233; https://doi.org/10.3390/e22020233 - 19 Feb 2020

Cited by 4 | Viewed by 4046

Abstract

Despite our intimate relationship with music in every-day life, we know little about how people create music. A particularly elusive area of study entails the spontaneous collaborative musical creation in the absence of rehearsals or scripts. Toward this aim, we designed an experiment [...] Read more.

Despite our intimate relationship with music in every-day life, we know little about how people create music. A particularly elusive area of study entails the spontaneous collaborative musical creation in the absence of rehearsals or scripts. Toward this aim, we designed an experiment in which pairs of players collaboratively created music in rhythmic improvisation. Rhythmic patterns and collaborative processes were investigated through symbolic-recurrence quantification and information theory, applied to the time series of the sound created by the players. Working with real data on collaborative rhythmic improvisation, we identified features of improvised music and elucidated underlying processes of collaboration. Players preferred certain patterns over others, and their musical experience drove musical collaboration when rhythmic improvisation started. These results unfold prevailing rhythmic features in collaborative music creation while informing the complex dynamics of the underlying processes. Full article

(This article belongs to the Special Issue Information theory and Symbolic Analysis: Theory and Applications)

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