ESTIMATION OF AVERAGE DIFFERENTIAL ENTROPY FOR A STATIONARY ERGODIC SPACE-TIME RANDOM FIELD ON A BOUNDED AREA

In this paper,we mainly discuss a discrete estimation of the average differential entropy for a continuous time-stationary ergodic space-time random field.By estimating the probability value of a time-stationary random field in a small range,we give an entropy estimation and obtain the average entropy estimation formula in a certain bounded space region.It can be proven that the estimation of the average differential entropy converges to the theoretical value with a probability of 1.In addition,we also conducted numerical experiments for different parameters to verify the convergence result obtained in the theoretical proofs.

Robust Space-Time Adaptive Track-Before-Detect Algorithm Based on Persymmetry and Symmetric Spectrum

Underwater monopulse space-time adaptive track-before-detect method,which combines space-time adaptive detector(STAD)and the track-before-detect algorithm based on dynamic programming(DP-TBD),denoted as STAD-DP-TBD,can effectively detect low-speed weak targets.However,due to the complexity and variability of the underwater environment,it is difficult to obtain sufficient secondary data,resulting in a serious decline in the detection and tracking performance,and leading to poor robustness of the algorithm.In this paper,based on the adaptive matched filter(AMF)test and the RAO test,underwater monopulse AMF-DP-TBD algorithm and RAO-DP-TBD algorithm which incorporate persymmetry and symmetric spectrum,denoted as PSAMF-DP-TBD and PS-RAO-DP-TBD,are proposed and compared with the AMF-DP-TBD algorithm and RAO-DP-TBD algorithm based on persymmetry array,denoted as P-AMF-DP-TBD and P-RAO-DP-TBD.The simulation results show that the four methods can work normally with sufficient secondary data and slightly insufficient secondary data,but when the secondary data is severely insufficient,the P-AMF-DP-TBD and P-RAO-DP-TBD algorithms has failed while the PSAMF-DP-TBD and PS-RAO-DP-TBD algorithms still have good detection and tracking capabilities.

Curved Space-Time at the Planck Scale

This paper presents a physically plausible and somewhat illuminating first step in extending the fundamental principles of mechanical stress and strain to space-time. Here the geometry of space-time, encoded in the metric tensor, is considered to be made up of a dynamic lattice of extremely small, localized fields that form a perfectly elastic Lorentz symmetric space-time at the global (macroscopic) scale. This theoretical model of space-time at the Planck scale leads to a somewhat surprising result in which matter waves in curved space-time radiate thermal gravitational energy, as well as an equally intriguing relationship for the anomalous dispersion of light in a gravitational field.

Virtually coupled train set control subject to space-time separation:A distributed economic MPC approach with emergency braking configuration

The emerging virtual coupling technology aims to operate multiple train units in a Virtually Coupled Train Set(VCTS)at a minimal but safe distance.To guarantee collision avoidance,the safety distance should be calculated using the state-of-the-art space-time separation principle that separates the Emergency Braking(EB)trajectories of two successive units during the whole EB process.In this case,the minimal safety distance is usually numerically calculated without an analytic formulation.Thus,the constrained VCTS control problem is hard to address with space-time separation,which is still a gap in the existing literature.To solve this problem,we propose a Distributed Economic Model Predictive Control(DEMPC)approach with computation efficiency and theoretical guarantee.Specifically,to alleviate the computation burden,we transform implicit safety constraints into explicitly linear ones,such that the optimal control problem in DEMPC is a quadratic programming problem that can be solved efficiently.For theoretical analysis,sufficient conditions are derived to guarantee the recursive feasibility and stability of DEMPC,employing compatibility constraints,tube techniques and terminal ingredient tuning.Moreover,we extend our approach with globally optimal and distributed online EB configuration methods to shorten the minimal distance among VCTS.Finally,experimental results demonstrate the performance and advantages of the proposed approaches.

REAL PALEY-WIENER THEOREMS FOR THE SPACE-TIME FOURIER TRANSFORM

This paper presents an extension of certain forms of the real Paley-Wiener theorems to the Minkowski space-time algebra. Our emphasis is dedicated to determining the space-time valued functions whose space-time Fourier transforms(SFT) have compact support using the partial derivatives operator and the Dirac operator of higher order.

Space-time correlations of passive scalar in Kraichnan model

We consider the two-point,two-time(space-time)correlation of passive scalar R(r,τ)in the Kraichnan model under the assumption of homogeneity and isotropy.Using the fine-gird PDF method,we find that R(r,τ)satisfies a diffusion equation with constant diffusion coefficient determined by velocity variance and molecular diffusion.Itssolution can be expressed in terms of the two-point,one time correlation of passive scalar,i.e.,R(r,0).Moreover,the decorrelation o R(k,τ),which is the Fourier transform of R(r,τ),is determined byR(k,0)and a diffusion kernal.

Curved Spine:The Shape of Spine in Taoist Body Diagrams and Its Influence on Medical Body Diagrams

From the early Taoist diagrams of the human body to the end of the Qing dynasty and the beginning of the Republic of China,Taoists exaggerated and deformed the human spine in a shape-shifting manner.It is likely that medical practitioners were influenced by this style of representation,and there are also numerous diagrams of the human body with the curved spine in the lateral-view diagrams of viscera and Ming Tang Tu(明堂图Acupuncture and Moxibustion Chart),which constantly show the human torso in an elliptical“egg shape”.No later than the Ming dynasty,medical practitioners began to depict the actual physiological spinal curve of the human body.By the Qing dynasty,the depiction of the spinal curve in medical diagrams of the human figure showed a tendency to part ways with the Taoist freehand style of the previous generation.Although the representation of the curve of the spine was very crude,later medical images of the human body at least gradually straightened the spine and no longer depicted it in a shape-shifting manner.However,the curved spine in Taoist diagrams of the human body continued to exist,and the presentation of the curved spine never changed.This way of depicting its appearance,which is very different from reality,is shaped by Taoism's special way of perceiving and viewing the body,and may also contain another form of truth.

Coulomb Force, Charge, and Electric Properties under Collision Space-Time

We have recently published a series of papers on a theory we call collision space-time, that seems to unify gravity and quantum mechanics. In this theory, mass and energy are redefined. We have not so far demonstrated how to make it compatible with electric properties such as charge and the Coulomb force. The aim of this paper is to show how electric properties can be reformulated to make it consistent with collision space-time. It is shown that we need to incorporate the Planck scale into the electric constants to do so. This is also fully possible from a practical point of view, as it has recently been shown how to measure the Planck length independent of other constants and without the need for dimensional analysis.

Phase diagram and quench dynamics of a periodically drivenHaldane model

We investigate a periodically driven Haldane model subjected to a two-stage driving scheme in the form of a step function.By using the Floquet theory,we obtain the topological phase diagram of the system.We also find that anomalous Floquet topological phases exist in the system.Focusing on examining the quench dynamics among topological phases,we analyze the site distribution of the 0-mode and p-mode edge states in long-period evolution after a quench.The results demonstrate that,under certain conditions,the site distribution of the 0-mode can be confined at the edge even in long-period evolution.Additionally,both the 0-mode and p-mode can recover and become confined at the edge in long-period evolution when the post-quench parameters(T,M_(2) /M_(1))in the phase diagram cross away from the phase boundary (M_(2)/ M_(1))=(6√3t2)/ M_(1)−1.Furthermore,we conclude that whether the edge state is confined at the edge in the long-period evolution after a quench depends on the similarity of the edge states before and after the quench.Our findings reveal some new characteristics of quench dynamics in a periodically driven system.

Properties of the phase diagram from the Nambu-Jona-Lasino model with a scalar-vector interaction

We investigated the properties of the phase diagram of high-order susceptibilities,speed of sound,and polytropic index based on an extended Nambu-Jona-Lasinio model with an eight-quark scalar-vector interaction.Non-monotonic behavior was observed in all these quantities around the phase transition boundary,which also revealed the properties of the critical point.Further,this study indicated that the chiral phase transition boundary and critical point could vary depending on the scalarvector coupling constant G_(SV).At finite densities and temperatures,the negative G_(SV)term exhibited attractive interactions,which enhanced the critical point temperature and reduced the chemical potential.The G_(SV)term also affected the properties of the high-order susceptibilities,speed of sound,and polytropic index near the critical point.The non-monotonic(peak or dip)structures of these quantities shifted to a low baryon chemical potential(and high temperature)with a negative G_(SV).G_(SV)also changed the amplitude and range of the nonmonotonic regions.Therefore,the scalar-vector interaction was useful for locating the phase boundary and critical point in QCD phase diagram by comparing the experimental data.The study of the non-monotonic behavior of high-order susceptibilities,speed of sound,and polytropic index is of great interest,and further observations related to high-order susceptibilities,speed of sound,and polytropic index being found and applied to the search for critical points in heavy-ion collisions and the study of compact stars are eagerly awaited.

Recension of boron nitride phase diagram based on high-pressure and high-temperature experiments

Cubic boron nitride and hexagonal boron nitride are the two predominant crystalline structures of boron nitride.They can interconvert under varying pressure and temperature conditions.However,this transformation requires overcoming significant potential barriers in dynamics,which poses great difficulty in determining the c-BN/h-BN phase boundary.This study used high-pressure in situ differential thermal measurements to ascertain the temperature of h-BN/c-BN conversion within the commonly used pressure range(3-6 GPa)for the industrial synthesis of c-BN to constrain the P-T phase boundary of h-BN/c-BN in the pressure-temperature range as much as possible.Based on the analysis of the experimental data,it is determined that the relationship between pressure and temperature conforms to the following equation:P=a+1/bT.Here,P denotes the pressure(GPa)and T is the temperature(K).The coefficients are a=-3.8±0.8 GPa and b=229.8±17.1 GPa/K.These findings call into question existing high-pressure and high-temperature phase diagrams of boron nitride,which seem to overstate the phase boundary temperature between c-BN and h-BN.The BN phase diagram obtained from this study can provide critical temperature and pressure condition guidance for the industrial synthesis of c-BN,thus optimizing synthesis efficiency and product performance.

A Future Life of Binary Phase Diagrams

The article raises the question of what to do with one of the main achievements of metal science in recent years—binary phase diagrams. These diagrams play a key role in the science of alloys and therefore their reliability must be complete. However, the discovery of the “ordering-separation” phase transition, which showed that in binary alloys at certain temperatures the sign of the chemical interatomic interaction changes (and, consequently, the microstructure changes), forces us to reconsider our ideas about those areas. Currently, these areas are designated on diagrams as areas of a “disordered solid solution.” This article proposes, using transmission electron microscopy, to study all the so-called solid solution regions, and apply the results obtained to the studied regions of the phase diagram.

Relativistic Velocity Addition on a Space-Time Diagram

We derive the addition of velocities in special relativity from the Minkowski’s space-time diagram. We only need to draw some world lines on the diagram, measure the lengths and divide the two lengths for obtaining the velocity. We also give the theoretical background for this method. This method is so simple that it is worth for undergraduate students to acquire the addition of velocities in special relativity.

From rectangle to parallelogram:an area-weighted method to make time-space diagrams incorporate traffic waves

A time-space(TS)traffic diagram is one of the most important tools for traffic visualization and analysis.Recently,it has been empirically shown that using parallelogram cells to construct a TS diagram outperforms using rectangular cells due to its incorporation of traffic wave speed.However,it is not realistic to immediately change the fundamental method of TS diagram construction that has been well embedded in various systems.To quickly make the existing TS diagram incorporate traffic wave speed and exhibit more realistic traffic patterns,the paper proposes an area-weighted transformation method that directly transforms rectangular-cell-based TS(rTS)diagrams into parallelogram-cell-based TS(pTS)diagrams,avoiding tracing back the raw data of speed to make the transformation.Two five-hour trajectory datasets from Japanese highway segments are used to demonstrate the effectiveness of the proposed methods.The travel time-based comparison involves assessing the disparities between actual travel times and those computed using rTS diagrams,as well as travel times derived directly from pTS diagrams based on rTS diagrams.The results show that travel times calculated from pTS diagrams converted from rTS diagrams are closer to the actual values,especially in congested conditions,demonstrating superior performance in parallelogram representation.The proposed transformation method has promising prospects for practical applications,making the widely-existing TS diagrams show more realistic traffic patterns.

Space-Time Diagrams Lead to False Paradoxes

This paper provides a clear analysis of how hypothetical concepts not allowed in Special Relativity should be treated and exposes hidden assumptions in space-time diagrams used on YouTube, where some prominent physicists have taken to publishing on popular topics that may not survive peer review. Such casual graphical treatment conceals the fact that space-time diagrams provide only for the Einstein synchronization convention for all observers, not the many other valid synchronization protocols, and also obscure that relativity’s equality of reference frames is rebutted if concepts outside relativity, such as instant communication, are introduced. These omissions of unconscious assumptions have been used to “prove” the existence of block time and time travel or time paradoxes. We will show the contradictory assumptions amount to assuming time travel, rather than the more mundane need to adjust synchronization conventions. We further show a new result that the use of the space-time diagrams as proposed by these “explainers” leads to discontinuities in which a differential change in communication speed leads to a sudden jump from present to long-past arrival time, strongly suggesting invalidity of the method.

Scalable transcoding for video transmission over space-time OFDM systems

A new scheme combining a scalable transcoder with space time block codes （STBC） for an orthogonal frequency division multiplexing （OFDM） system is proposed for robust video transmission in dispersive fading channels. The target application for such a scalable transcoder is to provide successful access to the pre-encoded high quality video MPEG-2 from mobile wireless terminals. In the scalable transcoder, besides outputting the MPEG-4 fine granular scalability （FGS） bitstream, both the size of video frames and the bit rate are reduced. And an array processing algorithm of layer interference suppression is used at the receiver which makes the system structure provide different levels of protection to different layers. Furthermore, by considering the important level of scalable bitstream, the different bitstreams can be given different level protection by the system structure and channel coding. With the proposed system, the concurrent large diversity gain characteristic of STBC and alleviation of the frequency-selective fading effect of OFDM can be achieved. The simulation results show that the proposed schemes integrating scalable transcoding can provide a basic quality of video transmission and outperform the conventional single layer transcoding transmitted under the random and bursty error channel conditions.

EM-based detection scheme for differential unitary space-time modulation

The performance loss of an approximately 3 dB signal-to-noise ratio is always paid with conventional differential detection compared to the related coherent detection. A new detection scheme consisting of two steps is proposed for the differential unitary space-time modulation （DUSTM） system. In the first step, the data sequence is estimated by conventional unitary space-time demodulation （DUSTD） and differentially encoded again to produce an initial estimate of the transmitted symbol stream. In the second step, the initial estimate of the symbol stream is utilized to initialize an expectation maximization （EM）-based iterative detector. In each iteration, the most recent detected symbol stream is employed to estimate the channel, which is then used to implement coherent sequence detection to refine the symbol stream. Simulation results show that the proposed detection scheme performs much better than the conventional DUSTD after several iterations.

基于space-time的二叉树表示动态环境中的路径规划

研究具有空间和时间的三维动态环境下的机器人路径规划分析了四叉树表示二维空间的搜索算法,在此基础上,提出采space-time,用二叉树表示二维空间的方法时间信息中增加加速度利用二叉树遍历方法和算法设计一个在动态障碍物环境下进行路径规划的新算法并,,A*,,在足球机器人系统中进行仿真,实现了较好的路径规划。

Design of super-orthogonal space-time trellis codes based on trace criterion

A design of super-orthogonal space-time trellis codes （SOSTTCs） based on the trace criterion （TC） is proposed for improving the design of SOSTTCs. The shortcomings of the rank and determinant criteria based design and the advantages of the TC-based design are analyzed. The optimization principle of four factors is presented, which includes the space-time block coding （STBC） scheme, set partitioning, trellis structure, and the assignment of signal subsets and STBC schemes in the trellis. According to this principle, systematical and handcrafted design steps are given in detail. By constellation expansion, the code performance can be further improved. The code design results are given, and the new codes outperform others in the simulation.

Method of combining space-time block coding with adaptive beamforming

A method of space-time block coding （STBC） system based on adaptive beamforming of cyclostationarity signal algorithm is proposed.The method uses cyclostationarity of signals to achieve adaptive beamforming,then constructs a pair of low correlated transmit beams based on beamform estimation of multiple component signals of uplink.Using these two selected transmit beams,signals encoded by STBC are transmitted to achieve diversity gain and beamforming gain at the same time,and increase the signal to noise ratio （SNR） of downlink.With simple computation and fast convergence performance,the proposed scheme is applicable for time division multiple access （TDMA） wireless communication operated in a complex interference environment.Simulation results show that the proposed scheme has better performance than conventional STBC,and can obtain a gain of about 5 dB when the bit error ratio （BER） is 10-4.