Differential Entropy Research Articles

Cumulative and relative cumulative residual information generating measures and associated properties

In this work, we propose cumulative residual information generating (CRIG) and relative cumulative residual information generating (RCRIG) measures and then establish some of their properties. A new divergence measure based on the CRIG function is proposed to measure the closeness between two survival functions as well as a cumulative residual Kullback-Leibler divergence. We also present Jensen-cumulative residual information generating function, whose derivatives generate some new cumulative information measures such as Jensen-cumulative residual Taneja entropy, Jensen-fractional cumulative residual entropy and Jensen-Gini mean difference measure. We further show that the Jensen-cumulative residual information generating function can be expressed as a mixture of two versions of the proposed new divergence measure.

Controlling the Entropy of a Single-Molecule Junction

Single molecules are nanoscale thermodynamic systems with few degrees of freedom. Thus, the knowledge of their entropy can reveal the presence of microscopic electron transfer dynamics that are difficult to observe otherwise. Here, we apply thermocurrent spectroscopy to directly measure the entropy of a single free radical molecule in a magnetic field. Our results allow us to uncover the presence of a singlet to triplet transition in one of the redox states of the molecule, not detected by conventional charge transport measurements. This highlights the power of thermoelectric measurements which can be used to determine the difference in configurational entropy between the redox states of a nanoscale system involved in conductance without any prior assumptions about its structure or microscopic dynamics.

Moisture Adsorption potentials and energy models of Gongronema latifolium leaves dried in separate environments.

Moisture adsorption isotherm potentials and energy models of Gongronema latifolium leaf grits were investigated. Fresh leaves were dried in sun; passive solar dryer and hot air oven, while proximate composition of the dried and fresh leaves were determined using standard laboratory procedure. Equilibrium moisture content (EMC) of the leaf grits was measured using gravimetric static method. Selected mathematical and statistical models were applied on the experimental data to evaluate data fitting. Energy calculations were done based on the mathematical models. The EMCs of the leaf grits directly increased with water activity (aW) at specific temperatures. Adsorption data was better represented by GAB model than others while differential enthalpy decreased as the EMC of the oven sample increased. Differential entropy of all the samples decreased as the EMC increased. The safest monolayer moisture content varied between 7.1036 and 8.0164 gH2O/100 g solid, below 40°C, within relative humidity of 10%–50%. Sun and oven leaf grits adsorbed more moisture than solar sample. Proximate contents of the dried leaves showed higher values for protein and ash. Overall results indicated that the leaf grits when properly packaged could be used as spice or tea powder to manage household nutrient security in addition to the use as therapeutic foods.

Design of combustion experiments using differential entropy

The aim of several combustion experiments is the determination of the rate coefficients of important elementary reactions. The experimental conditions are usually selected on the basis of local sensitivity analysis. Shock tube and tubular flow reactor experiments are often designed in such a way that only one reaction step is important at the investigated conditions. Sheen and Manion (J. Phys. Chem. A, 118 (2014) 4929–4941) suggested a method for the design of shock tube experiments based on differential entropy. Their method was modified and extended in this work. In the extended method, both the experimental and residual errors of the measurements are considered at the calculation of the posterior uncertainty of the determined rate parameters, the differential entropy matrix is calculated in an analytical way and the net information flux value is calculated for each suggested experimental point. In an iterative procedure, all investigated experimental points with negative net information flux values are discarded and the remaining experimental conditions are recommended for the measurements. The most valuable candidate experimental points can be determined based on the net information flux values. The method was used for the selection of experimental conditions for the determination of the rate coefficient of reaction NO2 + H = NO + OH at conditions similar to the tubular flow reactor experiments of Alzueta et al. (Energy Fuels, 15 (2001) 724–729). In these experiments, the oxidation of methanol was investigated with and without NO addition. Our method suggested a range of temperature, equivalence ratio and initial NO concentration, where the experimental data carry the most information on the rate coefficient of this elementary reaction.

Vigilance Estimating in SSVEP-Based BCI Using Multimodal Signals.

Brain-computer interface (BCI) is a communication system that allows a direct connection between the human brain and external devices. With the application of BCI, it is important to estimate vigilance for BCI users. In order to investigate the vigilance changes of the subjects during BCI tasks and develop a multimodal method to estimate the vigilance level, a high-speed 4-target BCI system for cursor control was built based on steady-state visual evoked potential (SSVEP). 18 participants were recruited and underwent a 90-min continuous cursor-control BCI task, when electroencephalogram (EEG), electrooculogram (EOG), electrocardiography (ECG), and electrodermal activity (EDA) were recorded simultaneously. Then, we extracted features from the multimodal signals and applied regression models to estimate vigilance. Experimental results showed that the differential entropy (DE) feature could effectively reflect the change of vigilance. The vigilance estimation method, which integrates DE and EOG features into the support vector regression (SVR) model, achieved a better performance than the compared methods. These results demonstrate the feasibility of our methods for estimating vigilance levels in BCI.

Kidney tumor diffusion-weighted magnetic resonance imaging derived ADC histogram parameters combined with patient characteristics and tumor volume to discriminate oncocytoma from renal cell carcinoma

PurposeTo assess the ability to discriminate oncocytoma from RCC based on a model using whole tumor ADC histogram parameters with additional use of tumor volume and patient characteristics. MethodIn this prospective study, 39 patients (mean age 65 years, range 28–79; 9/39 (23%) female) with 39 renal tumors (32/39 (82%) RCC and 7/39 (18%) oncocytoma) underwent multiparametric MRI between November 2014 and June 2018. Two regions of interest (ROIs) were drawn to cover both the entire tumor volume and a part of healthy renal cortex. ROI ADC maps were calculated using a mono-exponential model and ADC histogram distribution parameters were calculated. A logistic regression model was created using ADC histogram parameters, radiographic and patient characteristics that were significantly different between oncocytoma and RCC. A ROC curve of the model was constructed and the AUC, sensitivity and specificity were calculated. Furthermore, differences in intra-patient ADC histogram parameters between renal tumor and healthy cortex were calculated. A separate ROC curve was constructed to differentiate oncocytoma from RCC using statistically significant intra-patient parameter differences. ResultsADC standard deviation (p = 0.008), entropy (p = 0.010), tumor volume (p = 0.012), and patient sex (p = 0.018) were significantly different between RCC and oncocytoma. The regression model of these parameters combined had an ROC-AUC of 0.91 with a sensitivity of 86% and specificity of 84%. Intra-patient difference in ADC 25th percentile (p < 0.01) and entropy (p = 0.030) combined had a ROC-AUC of 0.86 with a sensitivity and specificity of 86%, and 81%, respectively. ConclusionA model combining ADC standard deviation and entropy with tumor volume and patient sex has the highest diagnostic value for discrimination of oncocytoma. Although less accurate, intra-patient difference in ADC 25th percentile and entropy between renal tumor and healthy cortex can also be used. Although the results of this preliminary study do not yet justify clinical use of the model, it does stimulate further research using whole tumor ADC histogram parameters.

Differential Entropy: An Appropriate Analysis to Interpret the Shape Complexity of Self-Similar Organic Islands.

Differential entropy, along with fractal dimension, is herein employed to describe and interpret the shape complexity of self-similar organic islands. The islands are imaged with in situ Atomic Force Microscopy, following, step-by-step, the evolution of their shape while deposition proceeds. The fractal dimension shows a linear correlation with the film thickness, whereas the differential entropy presents an exponential plateau. Plotting differential entropy versus fractal dimension, a linear correlation can be found. This analysis enables one to discern the 6T growth on different surfaces, i.e., native SiOx or 6T layer, and suggests a more comprehensive interpretation of the shape evolution. Changes in fractal dimension reflect rougher variations of the island contour, whereas changes in differential entropy correlates with finer contour details. The computation of differential entropy therefore helps to obtain more physical information on the island shape dependence on the substrate, beyond the standard description obtained with the fractal dimension.

Ultra-Low-Power, High-Accuracy 434 MHz Indoor Positioning System for Smart Homes Leveraging Machine Learning Models

Global navigation satellite systems have been used for reliable location-based services in outdoor environments. However, satellite-based systems are not suitable for indoor positioning due to low signal power inside buildings and low accuracy of 5 m. Future smart homes demand low-cost, high-accuracy and low-power indoor positioning systems that can provide accuracy of less than 5 m and enable battery operation for mobility and long-term use. We propose and implement an intelligent, highly accurate and low-power indoor positioning system for smart homes leveraging Gaussian Process Regression (GPR) model using information-theoretic gain based on reduction in differential entropy. The system is based on Time Difference of Arrival (TDOA) and uses ultra-low-power radio transceivers working at 434 MHz. The system has been deployed and tested using indoor measurements for two-dimensional (2D) positioning. In addition, the proposed system provides dual functionality with the same wireless links used for receiving telemetry data, with configurable data rates of up to 600 Kbauds. The implemented system integrates the time difference pulses obtained from the differential circuitry to determine the radio frequency (RF) transmitter node positions. The implemented system provides a high positioning accuracy of 0.68 m and 1.08 m for outdoor and indoor localization, respectively, when using GPR machine learning models, and provides telemetry data reception of 250 Kbauds. The system enables low-power battery operation with consumption of <200 mW power with ultra-low-power CC1101 radio transceivers and additional circuits with a differential amplifier. The proposed system provides low-cost, low-power and high-accuracy indoor localization and is an essential element of public well-being in future smart homes.

Dimensional stability of a metastable FCC high entropy alloy

In this work, a metastable face-centered cubic High Entropy Alloy (HEA) Fe35.0Co28.7Ni24.8Cr1.1Al1.3V4.5Ti1.2Nb2.8Si0.6 was found to exhibit significantly suppressed thermal expansion coefficient (6.0 ppm/K) and stable Young's modulus over a wide temperature range. Experimental and theoretical analyses suggest that both Invar and Elinvar effects were present; in addition, the metastability of this alloy with respect to the first-order phase transition and the magnetic second-order phase transition led to abrupt changes in thermal expansion behavior. The first-order phase transition was associated with the formation of a plate-like D019 phase. The magnetic second-order phase transition decreased the Invar effect and the Elinvar effect and resulted in a significant magnetic entropy difference (−3.12 J kg−1 K−1) in this HEA of interest.

A process-oriented probabilistic linguistic decision-making model with unknown attribute weights

As an effective tool to describe qualitative evaluations, probabilistic linguistic term set (PLTS) can identify the different preference degrees for the possible linguistic evaluations. For the multi-attribute decision making (MADM) problems based on the PLTSs, making decisions is not instantaneous behavior but needs some time to complete information processing. Considering the dynamic nature of decision-making behavior, this study aims to develop a process-oriented probabilistic linguistic decision-making framework. First, we introduce the parameters in the probabilistic linguistic multi-alternative decision field theory (PLMDFT) model. An improved decision rule for selecting the optimal alternative(s) is also presented. Then, a deviation entropy-based model is developed to determine attribute weights. Furthermore, we construct a probabilistic linguistic decision-making framework based on the PLMDFT and deviation entropy. Finally, the constructed framework is applied to solve emergency scheme selection problem. Some discussion and comparative analysis is complemented to demonstrate the validity of the proposed framework.

Electroencephalogram Emotion Recognition Based on 3D Feature Fusion and Convolutional Autoencoder.

As one of the key technologies of emotion computing, emotion recognition has received great attention. Electroencephalogram (EEG) signals are spontaneous and difficult to camouflage, so they are used for emotion recognition in academic and industrial circles. In order to overcome the disadvantage that traditional machine learning based emotion recognition technology relies too much on a manual feature extraction, we propose an EEG emotion recognition algorithm based on 3D feature fusion and convolutional autoencoder (CAE). First, the differential entropy (DE) features of different frequency bands of EEG signals are fused to construct the 3D features of EEG signals, which retain the spatial information between channels. Then, the constructed 3D features are input into the CAE constructed in this paper for emotion recognition. In this paper, many experiments are carried out on the open DEAP dataset, and the recognition accuracy of valence and arousal dimensions are 89.49 and 90.76%, respectively. Therefore, the proposed method is suitable for emotion recognition tasks.

AdS graviton stars and differential configurational entropy

AdS graviton stars are studied in the differential configurational entropy setup, as solutions of the effective Einstein field equations that backreact to compactification. With the critical central density of AdS graviton stars, the differential configurational entropy is derived and computed, presenting global minima for a wide range of stellar mass magnitude orders. It indicates insular domains of configurational stability for AdS graviton stars near astrophysical neutron star densities. Other relevant features are also reported.

Predicting T and N Staging of Resectable Gastric Cancer According to Whole Tumor Histogram Analysis About a Non-Cartesian k-Space Acquisition DCE-MRI: A Feasibility Study.

ObjectiveTo explore the feasibility of the whole tumor histogram analysis parameters derived from dynamic contrast-enhanced MRI (DCE-MRI) based on stack-of stars (StarVIBE) to predict T and N staging of resectable gastric cancer (GC).MethodsEighty-seven patients confirmed as GC by histopathology were enrolled in this prospective study. DCE-MRI were performed before surgery, and quantitative DCE parameters (Ktrans, Kep, Ve) and histogram metrics (Skewness, Kurtosis and Entropy) were measured by Omni-Kinetics software. Intraclass correlation coefficient (ICC) testing was used to determine the consistency of Ktrans, Kep and Ve values and histogram metrics values between two radiologists using Bland–Altman analysis. The quantitative DCE parameters or histogram metrics values between T stage or N stage were compared using ANOVA or Kruskal–Wallis testing. Receiver operating characteristic (ROC) analyses was performed to find out the best parameters for identifying T and N staging.ResultsThere was statistical difference in Ktrans, Kep, Ve and entropy to identify T staging (P=0.015, 0.033, <0.001, and 0.007, respectively), and in pairwise comparisons of Ve values showed statistically difference between T1+2 and T3 group (P<0.001), T1+2 and T4 group (P<0.001). There were statistical differences in Ve to identify N staging (P=0.041). In ROC analysis, Ve was the best parameter for identifying T staging (AUC: 0.788, the sensitivity and specificity was 0.929 and 0.578, respectively) and N staging (AUC: 0.590, the sensitivity and specificity was 0.714 and 0.899, respectively).ConclusionThe whole tumor histogram analysis parameters derived from StarVIBE DCE-MRI may be able to quantitatively evaluate T and N staging of GC, so as to help clinical treatment decision optimization.

Configurational entropy of heavy-quark QCD exotica

The mass spectroscopy of exotic meson states is scrutinized in the AdS/QCD paradigm. The differential configurational entropy is then used to study, derive, and analyze the mass spectrum of excited exotic vector meson resonances, whose configurational stability is also addressed. For it the hadronic molecule, the hadrocharmonium, and the hybrid description of heavy-quark exotic mesonic states are employed to more precisely match experimental data in the Particle Data Group and also to predict the next generations of heavy-quark QCD exotica in the $Z_c$, $Y$, $\pi_1$, and $Z_b$ exotic meson families.

Robust pole placement and random disturbance rejection for linear polytopic systems with application to grid-connected converters

This paper deals with an application of robust state feedback pole placement for discrete-time polytopic systems with stochastic disturbance attenuation. A set of stochastic signals is described using differential entropy functional. In the paper the parameter-independent robust state-feedback controller design procedure for linear discrete-time polytopic systems with theoretic-information constraints on the set of external random disturbances is proposed. Such additional constraints allow to find a tradeoff between H2 and H∞ control with better control energy consumption and improved robustness against random disturbances. This approach is applied to PWM inverters with LCL filters connected to the grid under uncertain parameters. Simulation results indicates that proposed controller allows to improve frequency and transient responses with better performance than existing ones.

Quantum watermarking based on threshold segmentation using quantum informational entropy

We propose a new quantum watermarking scheme based on threshold selection using informational entropy of quantum image. The core idea of this scheme is to embed information into object and background of cover image in different ways. First, a threshold method adopting the quantum informational entropy is employed to determine a threshold value. The threshold value can then be further used for segmenting the cover image to a binary image, which is an authentication key for embedding and extraction information. By a careful analysis of the quantum circuits of the scheme, that is, translating into the basic gate sequences which show the low complexity of the scheme. One of the simulation-based experimental results is entropy difference which measures the similarity of two images by calculating the difference in quantum image informational entropy between watermarked image and cover image. Furthermore, the analyses of peak signal-to-noise ratio, histogram and capacity of the scheme are also provided.

Three-dimensional Yang-Mills-Chern-Simons theory from a D3-brane background with D-instantons

By constructing the configuration of D3-branes with D(-1)-branes as D-instantons, we study the three-dimensional Yang-Mills Chern-Simons theory in holography. Due to the presence of the D-instantons, the D7-branes with discrepant embedding functions are able to be introduced in order to include the fundamental fermions (as flavors) and the Chern-Simons term (at very low energy) in the dual theory. The vacuum structure at zero temperature is studied in the soliton background and it illustrates the topological phase transition in the presence of instantons. Moreover, since the confinement/deconfinement phase transition could be holographically identified as the Hawking-Page transition in the bulk, we accordingly calculate the critical temperature of the deconfinement phase transition by collecting the bulk onshell action as the thermodynamical free energy. On the other hand, we evaluate the difference of the entanglement entropy in slab configuration by using the RT formula since the confinement may also be characterized by the entanglement entropy. Altogether we find the behavior of the critical temperature is in qualitative agreement with the behavior of the critical length determined by the entanglement entropy which implies the entanglement entropy could indeed be a character of the confinement in our setup and the D3-D(-1) system would be a remarkable approach to study the three-dimensional gauge theory.

Imaging the next Cascadia earthquake: optimal design for a seafloor GNSS-A network

SUMMARY The Cascadia subduction zone in the Pacific Northwest of the United States of America capable of producing magnitude ∼9 earthquakes, likely often accompanied by tsunamis. An outstanding question in this region is the degree and spatial extent of interseismic strain accumulation on the subduction megathrust. Seafloor geodetic methods combining GNSS and underwater acoustic ranging (GNSS-A) are capable of imaging this strain accumulation on the offshore portion of the subduction zone and therefore anticipating the potential size and rupture pattern of a future earthquake. However, the high cost of seafloor geodesy means that only a limited number of stations may be deployed and monitored. To facilitate expansion of current geodetic networks offshore, we develop a quantitative recommendation of optimal locations for future seafloor geodetic observations, based on the amount of new information provided by that observation. The optimal network depends on the problem that one is trying to solve with those observations (mapping subduction locking rates, coupling rates, constraining total moment rate, etc.), and on a number of modelling and data uncertainty assumptions. In particular, data uncertainty assumptions will change over time, as more position observations reduce velocity uncertainties. We find that near-trench observations on the megathrust hangingwall, distributed along-strike, consistently provide significant reduction in differential entropy over a large suite of assumptions, and that a well-placed seafloor observation can provide up to ∼30 times the information gain of the most optimal onshore observation.

Grey Relational Entropy Calculation and Fractional Prediction of Water and Economy in the Beijing-Tianjin-Hebei Region

The implementation of the Beijing-Tianjin-Hebei coordinated development strategy promotes the rapid development of the regional economy, but the consequent water shortage has become a major concern. How to optimize the allocation of water resources, promote the cooperation of water resources among various water-using departments, and maximize the water efficiency of the limited water resources in the region has become the main issue of research. Thus, this paper mainly studies the entropy value and the entropy difference of the grey relational entropy between water resources and economic systems. First, use the grey correlation entropy method to calculate the existing data to explore the relationship between the two systems, then use the FGM(1, 1) model to predict the grey correlation entropy value of Beijing-Tianjin-Hebei in 2020–2024, and finally, calculate the entropy difference of the grey relation entropy for the region from 2015 to 2024. The results show the following: (i) The connection between the water resources system and the economic system in the Beijing-Tianjin-Hebei region is poor, the entropy value between the two will continue to decrease from 2015 to 2024, and the degree of coordination has shown a decreasing trend. (ii) The entropy change value between the water resources system and the economic system in the Beijing-Tianjin-Hebei region reflects a gradual and orderly change trend. The research results can provide reasonable suggestions for improving the correlation between water resources and economic systems for government departments, local residents, and industrial enterprises in the Beijing-Tianjin-Hebei region, ultimately realizing the sustainable development of water resources and economic systems.

Postural Stability Challenges in Narrow Walking after Traumatic Brain Injury

The aim of this study was to evaluate the predictability and complexity of gait under preferred and narrow walking conditions for groups of TBI and age matched control subjects in order to determine if non-linear measures may be appropriate for identifying gait deviations not detected with more routine techniques. Ten participants from each group walked at preferred gait and with a narrow base of support. Center of mass motion was calculated from marker motion recorded with motion capture. Measures of predictability and complexity of center of mass motion were calculated with Recurrence Quantification Analysis. Walking with a narrow base of support resulted in a less predictable center of mass motion (reduced %Determinism) for TBI and control groups (p=0.0019 and p=0.0008, respectively), but no difference was found between groups. For the TBI group, there was a significant decrease in complexity of center of mass motion (lower Entropy, p=0.0038) with narrow base of support compared to preferred walking, but no difference in Entropy was found between groups. These results suggest non-linear measures determined using techniques such as Recurrence Quantification Analysis might have potential to be valid and reliable measurement techniques for predicting gait deviations in future studies.