Simplified Entropy Research Articles

Enhancing cognitive abilities through the POE teaching strategy in a virtual learning environment

With the introduction of information technology into education, the educational environment has undergone qualitative changes, that is, from a real learning environment to a digital learning environment. In a virtual learning environment (VLE), learners not only perceive themselves in new ways but also construct themselves in new ways. However, the POE (Prediction-Observation-Explanation) teaching strategy includes prediction, observation, and explanation. At the entry point of the learning strategy, the effective interaction between teachers and students can promote the development of cognitive ability. Therefore, this paper analyzed the perceptual entropy and matching degree through the radar target tracking algorithm, aiming at analyzing the current situation of the classroom and the advantages of POE teaching strategies. The findings of the study indicate that the POE teaching strategy greatly enhances students’ cognitive ability by teaching through prediction, observation, and interpretation. The research offers a novel contribution to the field of POE teaching strategy under a virtual cultural learning environment by expanding the comprehensive benefits of its students’ cognitive ability cultivation, exploring its impact on students’ academic performance, and offering practical recommendations for its implementation in the learning environment. The research demonstrates that POE strategies have positive effects on students’ academic performance and attitudes toward physics. Under the radar target tracking algorithm, the model matching degree and simplified entropy of the POE teaching strategy were both increasing. The mean of the model fit was 0.61, which was 0.40 higher than that of the first day, and the mean of the simplified entropy was 0.38, which was 0.12 higher than that of the first day. Finally, the cognitive ability and cognitive regulation ability of students under the POE teaching strategy were higher than those of the traditional teaching strategy. Compared with the traditional teaching strategy, cognitive ability was 9% higher, and cognitive regulation ability was 6% higher.

Edge Computing-Based SAT-Video Coding for Remote Sensing

This paper proposes an edge computing-based video coding implementation on an Earth observation satellite (SAT-video coding), which can encode video using limited resources and the power of mini/microsatellites. SAT-video coding proposes a hardware-related quantization (Q) function, hardware reduction of the motion estimation (ME) method, and simplified entropy coding (EC), which reduces the computation complexity. The hardware-related Q reduces hardware resource and power consumption by 72% and 55%, respectively, compared with traditional Q implementation. The hardware reduction of ME reduces resource use compared with regular ME implementation (59 % of lookup tables [LUTs] and 79% of Registers). The total number of LUTs used for the simplified EC function is also much lower than other EC hardware implementations. The SAT-video encoder IP uses fewer hardware resources, and the power consumption is estimated at 0.0894 W at a high working frequency (125 MHz). The SAT-video encoding speed is 18.95 frames per second for 2560×2560 video. Therefore, the proposed SAT-video coding is an edge computation suitable for micro/minisatellites. The coding efficiency records the highest compression ratio at 33.8, with a peak signal-to-noise ratio of 34.46 dB. With the important task of designing edge computing based on satellite video encoding, these are adequate values for remote sensing video.

Reduced-Complexity End-to-End Variational Autoencoder for on Board Satellite Image Compression

Recently, convolutional neural networks have been successfully applied to lossy image compression. End-to-end optimized autoencoders, possibly variational, are able to dramatically outperform traditional transform coding schemes in terms of rate-distortion trade-off; however, this is at the cost of a higher computational complexity. An intensive training step on huge databases allows autoencoders to learn jointly the image representation and its probability distribution, possibly using a non-parametric density model or a hyperprior auxiliary autoencoder to eliminate the need for prior knowledge. However, in the context of on board satellite compression, time and memory complexities are submitted to strong constraints. The aim of this paper is to design a complexity-reduced variational autoencoder in order to meet these constraints while maintaining the performance. Apart from a network dimension reduction that systematically targets each parameter of the analysis and synthesis transforms, we propose a simplified entropy model that preserves the adaptability to the input image. Indeed, a statistical analysis performed on satellite images shows that the Laplacian distribution fits most features of their representation. A complex non parametric distribution fitting or a cumbersome hyperprior auxiliary autoencoder can thus be replaced by a simple parametric estimation. The proposed complexity-reduced autoencoder outperforms the Consultative Committee for Space Data Systems standard (CCSDS 122.0-B) while maintaining a competitive performance, in terms of rate-distortion trade-off, in comparison with the state-of-the-art learned image compression schemes.

A Priori Parameter Estimation for the Thermodynamically Constrained Averaging Theory: Species Transport in a Saturated Porous Medium

The thermodynamically constrained averaging theory (TCAT) has been used to develop a simplified entropy inequality (SEI) for several major classes of macroscale porous medium models in previous works. These expressions can be used to formulate hierarchies of models of varying sophistication and fidelity. A limitation of the TCAT approach is that the determination of model parameters has not been addressed other than the guidance that an inverse problem must be solved. In this work we show how a previously derived SEI for single-fluid-phase flow and transport in a porous medium system can be reduced for the specific instance of diffusion in a dilute system to guide model closure. We further show how the parameter in this closure relation can be reliably predicted, adapting a Green’s function approach used in the method of volume averaging. Parameters are estimated for a variety of both isotropic and anisotropic media based upon a specified microscale structure. The direct parameter evaluation method is verified by comparing to direct numerical simulation over a unit cell at the microscale. This extension of TCAT constitutes a useful advancement for certain classes of problems amenable to this estimation approach.

Simplified Entropy and Multidimensional Search for Test Points Selection

In order to meet the demand of test points selection on higher speed, a new test points selection algorithm based on simplified entropy and multidimensional search is proposed. With the proposed algorithm, statistic results, instead of the complex entropy calculation, are utilized to estimate the order of entropy. In addition, multidimensional search method is adopted to find potential test points sets that can isolate the potential faults. The proposed method is also adaptive to the complexity of fault dictionary. In each iteration of the proposed algorithm, the dimension of multidimensional search could be changed according to the complexity of fault dictionary. Statistical experiments have shown that the proposed algorithm is more efficient in finding local optimum sets of test points compared with other test points selection algorithms.

An Improved Fault Propagation Analysis Method Based on Small-world Algorithm for Large Scale Electronic Systems

Single source multipath fault propagation analysis has contributed much on system fault modeling, fault location, and fault diagnosis. Studies have shown that the electronic system has small world network features. In this study, a new model of small world was established to observe the rapidly fault propagation of the electronic systems. In order to meet the higher requirements of testability and reliability for complex electronic systems, an improved fault propagation analysis method based on small world algorithm was proposed. First, inspired by the idea of small-world networks, a small world algorithm was proposed to greatly improve the speed of getting the fault path compared with other evolutionary algorithm. In addition, calculating entropy was firstly introduced to distinguish the importance of different nodes in systems. Finally, the proposed method was applied to a radar transmitter system for fault propagation analysis. The result shows that the performance is improved a lot by introducing the small world characteristic and simplified entropy. Simulation results demonstrate the computation method. Also, fault propagation could be applied to large-scale systems, which is meaningful for test points selection and fault diagnosis.

Approximate von Neumann entropy for directed graphs.

In this paper, we develop an entropy measure for assessing the structural complexity of directed graphs. Although there are many existing alternative measures for quantifying the structural properties of undirected graphs, there are relatively few corresponding measures for directed graphs. To fill this gap in the literature, we explore an alternative technique that is applicable to directed graphs. We commence by using Chung's generalization of the Laplacian of a directed graph to extend the computation of von Neumann entropy from undirected to directed graphs. We provide a simplified form of the entropy which can be expressed in terms of simple node in-degree and out-degree statistics. Moreover, we find approximate forms of the von Neumann entropy that apply to both weakly and strongly directed graphs, and that can be used to characterize network structure. We illustrate the usefulness of these simplified entropy forms defined in this paper on both artificial and real-world data sets, including structures from protein databases and high energy physics theory citation networks.

Uncertainty analysis of flow velocity estimation by a simplified entropy model

The velocity field in a river flow cross-sectional area can be determined by applying entropy as done in 1978 by Chiu, who developed a two-dimensional model of flow velocity based on the knowledge of maximum velocity, umax, and the dimensionless entropic parameter, characteristic of the river site. This is appealing in the context of discharge monitoring, particularly for high floods, considering that umax occurs in the upper portion of flow area and can be easily sampled, unlike velocity in the lower portion of flow area. The simplified form of Chiu's entropy-based velocity model, proposed in 2004 by Moramarco et al., has been found to be reasonably accurate for determining mean flow velocity along each vertical sampled in the flow area, but no uncertainty analysis has been reported for this simplified entropy-based velocity model. This study, therefore, performed uncertainty analysis of the simplified model following a procedure proposed by Misirli et al. in 2003. The flow velocity measurements at the Rosciano River section along the Chiascio River, central Italy, carried out for a period spanning 20 years were used for this purpose. Results showed that the simplified entropy velocity model was able to provide satisfactory estimates of velocity profiles in the whole flow area and the 95% confidence bands for the computed estimated mean vertical velocity were quite representative of observed values. In addition, using these 95% confidence bands, it was possible to have an indication of the uncertainty in the determination of mean cross-sectional flow velocity as well. Copyright © 2012 John Wiley & Sons, Ltd.

Thermodynamically Constrained Averaging Theory Approach for Heat Transport in Single-Fluid-Phase Porous Medium Systems

The recently developed thermodynamically constrained averaging theory is briefly summarized as a tool for the building of rigorous macroscale models of transport phenomena in complex systems. The specific case of thermal transport in a single-fluid-phase porous medium system is considered. Key results from the application of this theory are used to develop a simplified entropy inequality, which is in turn used to guide the development of closure relations. The decomposition of exchange terms is considered, and closed models for internal energy are derived for the case of nonequilibrium and local thermal equilibrium conditions. Since all variables are expressed in terms of precisely defined averages of microscale quantities, the resultant models can be compared with highly resolved microscale simulations to determine the range of validity of the upscaled models.

Thermodynamically constrained averaging theory approach for modeling flow and transport phenomena in porous medium systems: 6. Two-fluid-phase flow

This work is the sixth in a series of papers on the thermodynamically constrained averaging theory (TCAT) approach for modeling flow and transport phenomena in multiscale porous medium systems. Building upon the general TCAT framework and the mathematical foundation presented in previous works, the limiting case of connected two-fluid-phase flow is considered. A constrained entropy inequality is developed based upon a set of primary restrictions. Formal approximations are introduced to deduce a general simplified entropy inequality (SEI). The SEI is used along with secondary restrictions and closure approximations consistent with the SEI to produce a general functional form of a two-phase-flow model. The general model is in turn simplified to yield a hierarchy of models by neglecting common curves and by neglecting both common curves and interfaces. The simplest case considered corresponds to a traditional two-phase-flow model. The more sophisticated models including interfaces and common curves are more physically realistic than traditional models. All models in the hierarchy are posed in terms of precisely defined variables that allow for a rigorous connection with the microscale. The explicit nature of the restrictions and approximations used in developing this hierarchy of models provides a clear means to both understand the limitations of traditional models and to build upon this work to produce more realistic models.

The sharp form of Oleĭnik’s entropy condition in several space variables

We investigate the conditions under which the Volpert-Kruzkov solution of a single conservation law in several space variables with flux F F will satisfy the simplified entropy condition div F ′ ( u ) ⩽ 1 / t \operatorname {div}\,F’(u) \leqslant 1/t , and when this condition guarantees uniqueness for given L ∞ {L^\infty } Cauchy data. We show that, when F F is C 1 {C^1} , our condition guarantees uniqueness iff F F is isotropic, and that, for such F F , the Volpert-Kruzkov solution always satisfies our condition.