A Spectral Convolutional Neural Network Model Based on Adaptive Fick’s Law for Hyperspectral Image Classification

Hyperspectral image classification stands as a pivotal task within the field of remote sensing,yet achieving highprecision classification remains a significant challenge.In response to this challenge,a Spectral Convolutional Neural Network model based on Adaptive Fick’s Law Algorithm(AFLA-SCNN)is proposed.The Adaptive Fick’s Law Algorithm(AFLA)constitutes a novel metaheuristic algorithm introduced herein,encompassing three new strategies:Adaptive weight factor,Gaussian mutation,and probability update policy.With adaptive weight factor,the algorithmcan adjust theweights according to the change in the number of iterations to improve the performance of the algorithm.Gaussianmutation helps the algorithm avoid falling into local optimal solutions and improves the searchability of the algorithm.The probability update strategy helps to improve the exploitability and adaptability of the algorithm.Within the AFLA-SCNN model,AFLA is employed to optimize two hyperparameters in the SCNN model,namely,“numEpochs”and“miniBatchSize”,to attain their optimal values.AFLA’s performance is initially validated across 28 functions in 10D,30D,and 50D for CEC2013 and 29 functions in 10D,30D,and 50D for CEC2017.Experimental results indicate AFLA’s marked performance superiority over nine other prominent optimization algorithms.Subsequently,the AFLA-SCNN model was compared with the Spectral Convolutional Neural Network model based on Fick’s Law Algorithm(FLA-SCNN),Spectral Convolutional Neural Network model based on Harris Hawks Optimization(HHO-SCNN),Spectral Convolutional Neural Network model based onDifferential Evolution(DE-SCNN),SpectralConvolutionalNeuralNetwork(SCNN)model,and SupportVector Machines(SVM)model using the Indian Pines dataset and PaviaUniversity dataset.The experimental results show that the AFLA-SCNN model outperforms other models in terms of Accuracy,Precision,Recall,and F1-score on Indian Pines and Pavia University.Among them,the Accuracy of the AFLA-SCNN model on Indian Pines reached 99.875%,and the Accuracy on PaviaUniversity reached 98.022%.In conclusion,our proposed AFLA-SCNN model is deemed to significantly enhance the precision of hyperspectral image classification.

Zipf’s Law, Benford’s Law, and Pareto Rule

From a basic probabilistic argumentation, the Zipfian distribution and Benford’s law are derived. It is argued that Zipf’s law fits to calculate the rank probabilities of identical indistinguishable objects and that Benford’s distribution fits to calculate the rank probabilities of distinguishable objects. i.e. in the distribution of words in long texts all the words in a given rank are identical, therefore, the rank distribution is Zipfian. In logarithmic tables, the objects with identical 1st digits are distinguishable as there are many different digits in the 2nd, 3rd… places, etc., and therefore the distribution is according to Benford’s law. Pareto 20 - 80 rule is shown to be an outcome of Benford’s distribution as when the number of ranks is about 10 the probability of 20% of the high probability ranks is equal to the probability of the rest of 80% low probability ranks. It is argued that all these distributions, including the central limit theorem, are outcomes of Planck’s law and are the result of the quantization of energy. This argumentation may be considered a physical origin of probability.

Zipf定律在科里奥利加速度刺激心率动力学分析中的应用

采用Zipf定律建立科里奥利加速度刺激心率动力学分析方法,为前庭功能适应性训练中自主神经响应实时评估需求提供技术手段。25名男性志愿者完成了试验。试验1:转椅180°/s旋转下左右摆头2 min;试验2:转椅180°/s旋转下俯仰头动2 min,诱发加速度刺激。应用Zipf定律分析Polar表记录心率的动力学模式。研究表明:8种心率模式出现频率最高,2项试验的心率模式差异为0.27%±0.05%;相比中年组,青年组具有更明显的迷走神经响应模式(P<0.006);相比曾参训组(0.15%±0.03%),初期参训组2项试验心率模式差别增大(0.43%±0.10%),具有更明显的迷走神经响应模式(P<0.05),训练经验加速度刺激下对心率模式的影响超过年龄因素;运动病症状评分与体温变化量负相关(r=-0.459,P<0.007),而体温变化量与最常出现的3种心率模式发生率正相关(r=0.396~0.459,P<0.03)。应用Zipf定律的心率动力学分析可揭示加速度刺激相关生理规律,应用于前庭自主神经响应动态变化判断。

结合Cannikin’s Law的离线数据增广方法研究

数据增广是提升深度学习模型性能的有效方法之一。针对多类别目标检测任务中检测性能不平衡问题,提出一种针对“短板类别”(检测性能远低于模型平均检测性能的类别)的离线数据增广方法。受Cannikin’s Law的启发,采用基于复制粘贴(copy-paste)机制的场景多样性增广方法。随机采集训练集中“短板类别”实例区域,通过相似性度量机制选取训练集中增广目标样本进行随机粘贴。为了降低随机粘贴导致的遮挡问题,采用基于自遮挡(cut-replace)机制的增广方法提升模型遮挡表达能力。通过截取样本自身区域,对特征表达最显著区域进行遮挡。实验表明,FCOS目标检测框架在PASCAL VOC数据上的平均检测精度(mean average precision,mAP)从79.10%提升到83.90%,其中短板类别更为显著,提升了20.8个百分点。在MS-COCO数据上平均检测精度提升了0.9个百分点。

A Darcy-Law Based Model for Heat and Moisture Transfer in a Hill Cave

A hill can be regarded as an environmental carrier of heat.Water,rocks and the internal moisture naturally pre-sent in such environment constitute a natural heat accumulator.In the present study,the heat and moisture trans-fer characteristics in a representative hill cave have been simulated via a method relying on the Darcy’s law.The simulations have been conducted for both steady and unsteady conditions to discern the influence of permeability and geometric parameters on the thermal and moisture transfer processes.The reliability of the simulation has been verified through comparison of the numerical results with the annual observation data.As revealed by the numericalfindings,the internal temperature of the hill accumulator is proportional to the permeability,outside surface temperature,overground height,underground constant temperature layer depth,and underground tem-perature of the hill,and it is inversely proportional to the horizontal size of the hill.Moreover,in the considered case,the order of magnitude of the permeability of the hill is contained in the range 10-15–10-13,and displays a certain sensitivity to the rainwater seepage.

Broader applicability of the metacoupling framework than Tobler’s first law of geography for global sustainability:A systematic review

Complex sustainability issues in the Anthropocene,with rapid globalization and global environmental changes,are increasingly interlinked between not only nearby systems but also distant systems.Tobler’s first law of geog-raphy(TFL)states“near things are more related than distant things”.Evidence suggests that TFL is not infallible for sustainability issues.Recently,the integrated framework of metacoupling(MCF;human-nature interactions within as well as between adjacent and distant systems)has been applied to analyze the interactions between nearby and distant coupled human and natural systems simultaneously.However,previous work has been scat-tered and fragmented.It is crucial to understand the extent to which TFL and MCF apply across pressing issues in sustainability.Therefore,we reviewed and synthesized sustainability literature that used TFL and MCF across seven major topics:land change,species migration,tourism,trade,agricultural development,conservation,and governance.Results indicate MCF had a much broader applicability than TFL for these topics.The literature using MCF generally did not or likely did not obey TFL,especially in trade,governance,and agricultural de-velopment.In the TFL literature,most topics obeyed TFL,except for species migration and trade.The findings suggest the need to rethink and further test TFL’s relevance to sustainability issues,and highlight the potential of MCF to address complex interactions between both adjacent and distant systems across the world for global sustainability.

Determination of the Henry’s Law Constant of Hexane in High-Viscosity Polymer Systems

The Henry’s law constant of volatiles in polymer systems is a crucial parameter reflecting the gas-liquid equilibrium,which is very important for devolatilization.In this research,polyolefin elastomer(POE)-cyclohexane and polydimethylsiloxane(PDMS)-hexane systems were studied,and the Henry’s law constant was obtained by measuring the gas phase equilibrium partial pressure when polymer solutions containing different mass fractions of volatiles reached a saturated state.The effects of temperature,type of volatiles,and polymer viscosity on the gas phase equilibrium partial pressure and Henry’s law constant of the volatiles were investigated.The results indicate that,with the increase of temperature and polymer viscosity,the gas phase equilibrium partial pressure and Henry’s law constant of volatiles increase.As temperature increases,the solubility of gas in liquid decreases.The relationship between the Henry’s law constant and temperature is consistent with the Arrhenius law.In the PDMS-hexane system,the gas phase equilibrium partial pressure and Henry’s law constant of n-hexane are higher than those of cyclohexane.The obtained Henry’s law constants can be used as a reference for perfecting the devolatilization process and improving the devolatilization effect.

New Planck’s Law

In quantum mechanics, there are two very famous formulas. One is the energy formula of the bose particle, called Planck’s law. The other is the wavelength formula, which is called the de Broy wavelength. According to Einstein’s mass-energy equation, we have studied Planck’s law and De Bloy’s wavelength, and generalized it to the De Bloy’s wavelength formula from low speed to light speed. Then, on this basis, the smallest particle is defined as mass quantum. The new wavelength formula is obtained from the mass quantum and converted into the frequency formula. The generalized Planck’s law is obtained.

Revisiting the Curie-Von Schweidler Law for Dielectric Relaxation and Derivation of Distribution Function for Relaxation Rates as Zipf’s Power Law and Manifestation of Fractional Differential Equation for Capacitor

The classical power law relaxation, i.e. relaxation of current with inverse of power of time for a step-voltage excitation to dielectric—as popularly known as Curie-von Schweidler law is empirically derived and is observed in several relaxation experiments on various dielectrics studies since late 19th Century. This relaxation law is also regarded as “universal-law” for dielectric relaxations;and is also termed as power law. This empirical Curie-von Schewidler relaxation law is then used to derive fractional differential equations describing constituent expression for capacitor. In this paper, we give simple mathematical treatment to derive the distribution of relaxation rates of this Curie-von Schweidler law, and show that the relaxation rate follows Zipf’s power law distribution. We also show the method developed here give Zipfian power law distribution for relaxing time constants. Then we will show however mathematically correct this may be, but physical interpretation from the obtained time constants distribution are contradictory to the Zipfian rate relaxation distribution. In this paper, we develop possible explanation that as to why Zipfian distribution of relaxation rates appears for Curie-von Schweidler Law, and relate this law to time variant rate of relaxation. In this paper, we derive appearance of fractional derivative while using Zipfian power law distribution that gives notion of scale dependent relaxation rate function for Curie-von Schweidler relaxation phenomena. This paper gives analytical approach to get insight of a non-Debye relaxation and gives a new treatment to especially much used empirical Curie-von Schweidler (universal) relaxation law.

Not Athenian or a Stranger:The Veiled Critique of Aristotle in Plato’s Laws

Plato’s last dialogue,the Laws,occupies an anomalous position within his larger body of work.An individual identified as the“Athenian stranger”replaces Socrates and reverses key Socratic teachings,most notably by endorsing tyranny.Scholars conclude that Plato abandoned his earlier political recommendations in favor of a more pragmatic vision.In that case,the Laws should be treated as Plato’s definitive work,the ultimate statement of his thought,when in fact,much more attention is paid to earlier dialogues,particularly the Republic.The problem is resolved and the true significance of the Laws revealed when the text is read as Plato’s ironic critique of his brilliant-but-rebellious student,Aristotle.Reasoning from Aristotelian premises,the Athenian stranger arrives at conclusions that Platonists and Aristotelians alike would find unpalatable or absurd.The alleged rupture between Plato’s earlier and later work disappears.The esoteric writings that are thought to have been the product of Aristotle’s later career are shown to have emerged from ideas that Plato himself was familiar with and rejected.

Motion State Modification of Coulomb’s Law and Dynamic Gravitation

As we know, Coulomb’s law describes the interaction between static charges. In this paper, the modified formula of Coulomb’s law in the state of charge motion is given. Based on this formula, Ampere’s law and Lorentz’s law of force are derived by pure mathematics. According to the similarity between the formula of universal gravitation and Coulomb’s law, the correction of the formula of universal gravitation under the state of motion is assumed boldly, and some inferences are made on the motion law of celestial bodies.

Hubble Tension Explanation from This Cosmological Model AΛΩ (Slow Bang Model, SB)

In this article we present a model of Hubble-Lemaître law using the notions of a transmitter (galaxy) and a receiver (MW) coupled to a model of the universe (Slow Bang Model, SB), based on a quantum approach of the evolution of space-time as well as an equation of state that retains all the infinitesimal terms. We find an explanation of the Hubble tension H0. Indeed, we have seen that this constant depends on the transceiver pair which can vary from the lowest observable value, from photons of the CMB (theoretical [km/s/Mpc]) to increasingly higher values depending on the earlier origin of the formation of the observed galaxy or cluster (ETG ~0.3 [Gy], ~74 [km/s/Mpc]). We have produced a theoretical table of the values of the constant according to the possible pairs of transmitter/receiver in the case where these galaxies follow the Hubble flow without large disturbance. The calculated theoretical values of the constant are in the order of magnitude of all values mentioned in past studies. Subsequently, we applied the models to 9 galaxies and COMA cluster and found that the models predict acceptable values of their distances and Hubble constant since these galaxies mainly follow the Hubble flow rather than the effects of a galaxy cluster or a group of clusters. In conclusion, we affirm that this Hubble tension does not really exist and it is rather the understanding of the meaning of this constant that is questioned.

Non-Darcy Flow in Molding Sands

Darcy’s law is widely used to describe the flow in porous media in which there is a linear relationship between fluid velocity and pressure gradient. However, it has been found that for high numbers of Reynolds this law ceases to be valid. In this work, the Ergun equation is employed to consider the non-linearity of air velocity with the pressure gradient in casting sands. The contribution of non-linearity to the total flow in terms of a variable defined as a non-Darcy flow fraction is numerically quantified. In addition, the influence of the shape factor of the sand grains on the non-linear flow fraction is analyzed. It is found that for values of the Reynolds number less or equal than 1, the contribution of non-linearity for spherical particles is around 1.15%.

Habits on Social Networks at Workplace: A Survey of Motivations and Behaviour

This article explores the use of social networks by workers in Abidjan, Côte d’Ivoire, with particular emphasis on a descriptive or quantitative analysis aimed at understanding motivations and methods of use. More than five hundred and fifty questionnaires were distributed, highlighting workers’ preferred digital channels and platforms. The results indicate that the majority use social media through their mobile phones, with WhatsApp being the most popular app, followed by Facebook and LinkedIn. The study reveals that workers use social media for entertainment purposes and to develop professional and social relationships, with 55% unable to live without social media at work for recreational activities. In addition, 35% spend on average 1 to 2 hours on social networks, mainly between 12 p.m. and 2 p.m. It also appears that 46% believe that social networks moderately improve their productivity. These findings can guide marketing strategies, training, technology development and government policies related to the use of social media in the workplace.

Physical Mathematical Evaluation of the Cardiac Dynamic Applying the Zipf-Mandelbrot Law

Introduction: The law of Zipf-Mandelbrot is a power law, which has been observed in natural languages. A mathematical diagnosis of fetal cardiac dynamics has been developed with this law. Objective: To develop a methodology for diagnostic aid to assess the degree of complexity of adult cardiac dynamics by Zipf-Mandelbrot law. Methodology: A mathematical induction was done for this;two groups of Holter recordings were selected: 11 with normal diagnosis and 11 with acute disease of each group, one Holter of each group was chosen for the induction, the law of Zipf-Mandelbrot was applied to evaluate the degree of complexity of each Holter, searching similarities or differences between the dynamics. A blind study was done with 20 Holters calculating sensitivity, specificity and the coefficient kappa. Results: The complexity grade of a normal cardiac dynamics varied between 0.9483 and 0.7046, and for an acute dynamic between 0.6707 and 0.4228. Conclusions: A new physical mathematical methodology for diagnostic aid was developed;it showed that the degree of complexity of normal cardiac dynamics was higher than those with acute disease, showing quantitatively how cardiac dynamics can evolve to acute state.

Derivation of a Revised Tsiolkovsky Rocket Equation That Predicts Combustion Oscillations

Our study identifies a subtle deviation from Newton’s third law in the derivation of the ideal rocket equation, also known as the Tsiolkovsky Rocket Equation (TRE). TRE can be derived using a 1D elastic collision model of the momentum exchange between the differential propellant mass element (dm) and the rocket final mass (m1), in which dm initially travels forward to collide with m1 and rebounds to exit through the exhaust nozzle with a velocity that is known as the effective exhaust velocity ve. We observe that such a model does not explain how dm was able to acquire its initial forward velocity without the support of a reactive mass traveling in the opposite direction. We show instead that the initial kinetic energy of dm is generated from dm itself by a process of self-combustion and expansion. In our ideal rocket with a single particle dm confined inside a hollow tube with one closed end, we show that the process of self-combustion and expansion of dm will result in a pair of differential particles each with a mass dm/2, and each traveling away from one another along the tube axis, from the center of combustion. These two identical particles represent the active and reactive sub-components of dm, co-generated in compliance with Newton’s third law of equal action and reaction. Building on this model, we derive a linear momentum ODE of the system, the solution of which yields what we call the Revised Tsiolkovsky Rocket Equation (RTRE). We show that RTRE has a mathematical form that is similar to TRE, with the exception of the effective exhaust velocity (ve) term. The ve term in TRE is replaced in RTRE by the average of two distinct exhaust velocities that we refer to as fast-jet, vx1, and slow-jet, vx2. These two velocities correspond, respectively, to the velocities of the detonation pressure wave that is vectored directly towards the exhaust nozzle, and the retonation wave that is initially vectored in the direction of rocket propagation, but subsequently becomes reflected from the thrust surface of the combustion chamber to exit through the exhaust nozzle with a time lag behind the detonation wave. The detonation-retonation phenomenon is supported by experimental evidence in the published literature. Finally, we use a convolution model to simulate the composite exhaust pressure wave, highlighting the frequency spectrum of the pressure perturbations that are generated by the mutual interference between the fast-jet and slow-jet components. Our analysis offers insights into the origin of combustion oscillations in rocket engines, with possible extensions beyond rocket engineering into other fields of combustion engineering.

The Magnetic Longitudinal (P-) Wave’s Propagation and Energy Models Underlying the Mechanisms of Its Capacity to Absorb Free Energy

The longitudinal wave term within Faraday’s law of electromagnetic induction (Faraday’s law) underwent recovery to ensure its suitability for theoretical derivation of the equation governing longitudinal electromagnetic (LEM) waves. The revised Maxwell’s equations include the crucial parameters being the attenuation time constants of magnetic vortex potential and electric vortex potential generated by external electromagnetic field within the propagation medium. Specific expressions for them are obtained through theoretical analysis. Subsequently, a model for propagating magnetic P-wave generated by the superposition of a left-handed photo and a right-handed photon in a vacuum is formulated based on reevaluated total current law and revised Faraday’s law, covering wave equations, energy equation, as well as propagation mode involving mutual induction and conversion between scalar magnetic field and vortex electric field. Furthermore, through theoretical derivations centered around magnetic P-wave, evidence was presented regarding its ability to absorb huge free energy through the entangled interaction between zero-point vacuum energy field and the torsion field produced by the vortex electric field.

EXPERIMENTAL STUDY ON DARCY′S LAW IN HELE-SHAW CELLS

The basic physics of unsteady Hele-Shaw flow at high Reynolds numbers is mainly studied by an experimental measurement. In order to confirm the Darcy′s law in Hele-Shaw cell, since there is an analogy between flow in cells and that in porous media, progressive water waves are utilized to build an unsteady flow in a Hele-Shaw cell, and which complex wave number is measured by a wave height gauge. Meanwhile, theoretical analyses are used to compare with experimental data. Result shows Darcy′s Law is not exactly correct for unsteady Hele-Shaw flows, and it is expected to conduct a modified Darcy′s Law.

幂律思考系列文章4——论Heaps律与Zipf律等价的条件

在词频服从拟幂律分布并满足致密性的条件下,证明了Zipf律和Heaps律相互等价,并且讨论了词频序号为2时的临界行为。

Benford’s Law在煤矿安全数据真实性判定中的应用和优化研究

首先阐述了对煤矿安全数据进行真实性判定的重要性.然后,提出了基于Benford’s Law的煤矿安全数据真实性的判定方法,并通过对淮南地矿井安全数据的分析,证明了该方法的科学性和有效性.最后,对该方法进行优化,使得优化后的方法在煤矿安全数据的真实性判定上,不仅区分度高而且运算量小.