Density of excess modes below the first phonon mode in four-dimensional glasses

Glasses are known to possess low-frequency excess modes beyond the Debye prediction.For decades,it has been assumed that evolution of low-frequency density of excess modes D(ω) with frequency ω follows a power-law scaling:D(ω)~ω~γ.However,it remains debated on the value of γ at low frequencies below the first phonon-like mode in finitesize glasses.Early simulation studies reported γ=4 at low frequencies in two-(2D),three-(3D),and four-dimensional(4D)glasses,whereas recent observations in 2D and 3D glasses suggested γ=3.5 in a lower-frequency regime.It is uncertain whether the low-frequency scaling of D(ω)~ω^(3.5) could be generalized to 4D glasses.Here,we conduct numerical simulation studies of excess modes at frequencies below the first phonon-like mode in 4D model glasses.It is found that the system size dependence of D(ω) below the first phonon-like mode varies with spatial dimensions:D(ω) increases in2D glasses but decreases in 3D and 4D glasses as the system size increases.Furthermore,we demonstrate that the ω^(3.5)scaling,rather than the ω~4 scaling,works in the lowest-frequency regime accessed in 4D glasses,regardless of interaction potentials and system sizes examined.Therefore,our findings in 4D glasses,combined with previous results in 2D and 3D glasses,suggest a common low-frequency scaling of D(ω)~ ω^3.5) below the first phonon-like mode across different spatial dimensions,which would inspire further theoretical studies.

Evaluation of mitral chordae tendineae length using four-dimensional computed

BACKGROUND Mitral valvuloplasty using artificial chordae tendineae represents an effective surgical approach for treating mitral regurgitation.Achieving precise measurements of artificial chordae tendineae length(CL)is an important factor in the procedure;however,no objective index currently exists to facilitate this measurement.Therefore,preoperative assessment of CL is critical for surgical planning and support.Four-dimensional x-ray micro-computed tomography(4D-CT)may be useful for accurate CL measurement considering that it allows for dynamic three-dimensional(3D)evaluation compared to that with transthoracic echocardiography,a conventional inspection method.AIM To investigate the behavior and length of mitral chordae tendineae during systole using 4D-CT.METHODS Eleven adults aged>70 years without mitral valve disease were evaluated.A 64-slice CT scanner was used to capture 20 phases in the cardiac cycle in electrocardiographic synchronization.The length of the primary chordae tendineae was measured from early systole to early diastole using the 3D image.The primary chordae tendineae originating from the anterior papillary muscle and attached to the A1-2 region and those from the posterior papillary muscle and attached to the A2-3 region were designated as cA and cP,respectively.The behavior and maximum lengths[cA(ma),cP(max)]were compared,and the correlation with body surface area(BSA)was evaluated.RESULTS In all cases,the mitral anterior leaflet chordae tendineae could be measured.In most cases,the cA and cP chordae tendineae could be measured visually.The mean cA(max)and cP(max)were 20.2 mm±1.95 mm and 23.5 mm±4.06 mm,respectively.cP(max)was significantly longer.The correlation coefficients(r)with BSA were 0.60 and 0.78 for cA(max)and cP(max),respectively.Both cA and cP exhibited constant variation in CL during systole,with a maximum 1.16-fold increase in cA and a 1.23-fold increase in cP from early to mid-systole.For cP,CL reached a plateau at 15%and remained elongated until end-systole,whereas for cA,after peaking at 15%,CL shortened slightly and then moved toward its peak again as end-systole approached.CONCLUSION The study suggests that 4D-CT is a valuable tool for accurate measurement of both the length and behavior of chordae tendineae within the anterior leaflet of the mitral valve.

Four-Dimensional Mathematics Creates the Super Universe

In the common theory of the Universe, the redshift of the light wavelength from distant stars indicates the speed of the star. In this study, the model of the Universe is the surface volume of the four-dimensional sphere, and the shape of the Universe results in the most of the redshift of light wavelength. Therefore, there is no dark energy accelerating the Universe. The surface of the four-dimensional sphere is a volume, and this volume is a good model for the Universe. The surface volume of the four-dimensional sphere has been explained by a model of four-dimensional cube, within which the forming of surface volume can be easily shown. The model of four-dimensional cube containing six side cubes is ingenious for explaining the structure of the four-dimensional Universe, but it is not enough because the four-dimensional cube has not six side cubes, but eight side cubes. Therefore, in this study a better method has been created to construct the four-dimensional cube. Our three-dimensional Universe is the surface of the four-dimensional sphere Universe. The volume of our three-dimensional Universe is finite, and beneath it is the infinite volume four-dimensional Super Universe. Two important basic formulae have been derived: The surface volume of the four-dimensional sphere is π3R3 in which R is the radius of the sphere, and the fourth-power volume of the four-dimensional sphere is 1/4 π3R4. The volume of the Universe has been calculated π3R3 = 62 × 1030 ly3. Time as the fourth dimension of the space takes effect only near the speed of light, and therefore it has been ignored in this study.

Coupling Ensemble Kalman Filter with Four-dimensional Variational Data Assimilation

This study examines the performance of coupling the deterministic four-dimensional variational assimilation system （4DVAR） with an ensemble Kalman filter （EnKF） to produce a superior hybrid approach for data assimilation. The coupled assimilation scheme （E4DVAR） benefits from using the state-dependent uncertainty provided by EnKF while taking advantage of 4DVAR in preventing filter divergence： the 4DVAR analysis produces posterior maximum likelihood solutions through minimization of a cost function about which the ensemble perturbations are transformed, and the resulting ensemble analysis can be propagated forward both for the next assimilation cycle and as a basis for ensemble forecasting. The feasibility and effectiveness of this coupled approach are demonstrated in an idealized model with simulated observations. It is found that the E4DVAR is capable of outperforming both 4DVAR and the EnKF under both perfect- and imperfect-model scenarios. The performance of the coupled scheme is also less sensitive to either the ensemble size or the assimilation window length than those for standard EnKF or 4DVAR implementations.

Four-dimensional flow magnetic resonance imaging incirrhosis

Since its introduction in the 1970’s,magnetic resonance imaging(MRI)has become a standard imaging modality.With its broad and standardized application,it is firmly established in the clinical routine and an essential element in cardiovascular and abdominal imaging.In addition to sonography and computer tomography,MRI is a valuable tool for diagnosing cardiovascular and abdominal diseases,for determining disease severity,and for assessing therapeutic success.MRI techniques have improved over the last few decades,revealing not just morphologic information,but functional information about perfusion,diffusion and hemodynamics as well.Four-dimensional(4D)flow MRI,a time-resolved phase contrast-MRI with three-dimensional(3D)anatomic coverage and velocity encoding along all three flow directions has been used to comprehensively assess complex cardiovascular hemodynamics in multiple regions of the body.The technique enables visualization of 3D blood flow patterns and retrospective quantification of blood flow parameters in a region of interest.Over the last few years,4D flow MRI has been increasingly performed in the abdominal region.By applying different acceleration techniques,taking 4D flow MRI measurements has dropped to a reasonable scanning time of 8 to 12 min.These new developments have encouraged a growing number of patient studies in the literature validating the technique’s potential for enhanced evaluation of blood flow parameters within the liver’s complex vascular system.The purpose of this review article is to broaden our understanding of 4D flow MRI for the assessment of liver hemodynamics by providing insights into acquisition,data analysis,visualization and quantification.Furthermore,in this article we highlight its development,focussing on the clinical application of the technique.

Testing a Four-Dimensional Variational Data Assimilation Method Using an Improved Intermediate Coupled Model for ENSO Analysis and Prediction

A four-dimensional variational （4D-Var） data assimilation method is implemented in an improved intermediate coupled model （ICM） of the tropical Pacific. A twin experiment is designed to evaluate the impact of the 4D-Var data assimilation algorithm on ENSO analysis and prediction based on the ICM. The model error is assumed to arise only from the parameter uncertainty. The ＂observation＂ of the SST anomaly, which is sampled from a ＂truth＂ model simulation that takes default parameter values and has Gaussian noise added, is directly assimilated into the assimilation model with its parameters set erroneously. Results show that 4D-Var effectively reduces the error of ENSO analysis and therefore improves the prediction skill of ENSO events compared with the non-assimilation case. These results provide a promising way for the ICM to achieve better real-time ENSO prediction.

Generating one-,two-,three-and four-scroll attractors from a novel four-dimensional smooth autonomous chaotic system

A new four-dimensional quadratic smooth autonomous chaotic system is presented in this paper, which can exhibit periodic orbit and chaos under the conditions on the system parameters. Importantly, the system can generate one-, two-, three- and four-scroll chaotic attractors with appropriate choices of parameters. Interestingly, all the attractors are generated only by changing a single parameter. The dynamic analysis approach in the paper involves time series, phase portraits, Poincare maps, a bifurcation diagram, and Lyapunov exponents, to investigate some basic dynamical behaviours of the proposed four-dimensional system.

Four-Dimensional Variational Data Assimilation Experiments for a Heavy Rain Case During the 2002 IOP in China

A heavy rainfall event along the mei-yu front during 22-23 June 2002 was chosen for this study. To assess the impact of the routine and additional IOP (intensive observation period) radiosonde observations on the mesoscale heavy rainfall forecast, a series of four-dimensional variational (4DVAR) data assimilation and model simulation experiments was conducted using nonhydrostatic mesoscale model MM5 and the MM5 4DVAR system. The effects of the intensive observations in the different areas on the heavy rainfall forecast were also investigated. The results showed that improvement of the forecast skill for mesoscale heavy rainfall intensity was possible from the assimilation of the IOP radiosonde observations. However, the impact of the IOP observations on the forecast of the rainfall pattern was not significant. Initial conditions obtained through the 4DVAR experiments with a 12-h assimilation window were capable of improving the 24-h forecast. The simulated results after the assimilation showed that it would be best to perform the intensive radiosonde observations in the upstream of the rainfall area and in the moisture passageway area at the same time. Initial conditions created by the 4DVAR led to the low-level moisture convergence over the rainfall area, enhanced frontogenesis and upward motion within the mei-yu front, and intensified middle- and high-level unstable stratification in front of the mei-yu front. Consequently, the heavy rainfall forecast was improved.

Real-Time Four-Dimensional Trajectory Generation Based on Gain-Scheduling Control and a High-Fidelity Aircraft Model

Aircraft ground movement plays a key role in improving airport efficiency,as it acts as a link to all other ground operations.Finding novel approaches to coordinate the movements of a fleet of aircraft at an airport in order to improve system resilience to disruptions with increasing autonomy is at the center of many key studies for airport airside operations.Moreover,autonomous taxiing is envisioned as a key component in future digitalized airports.However,state-of-the-art routing and scheduling algorithms for airport ground movements do not consider high-fidelity aircraft models at both the proactive and reactive planning phases.The majority of such algorithms do not actively seek to optimize fuel efficiency and reduce harmful greenhouse gas emissions.This paper proposes a new approach for generating efficient four-dimensional trajectories(4DTs)on the basis of a high-fidelity aircraft model and gainscheduling control strategy.Working in conjunction with a routing and scheduling algorithm that determines the taxi route,waypoints,and time deadlines,the proposed approach generates fuel-efficient 4DTs in real time,while respecting operational constraints.The proposed approach can be used in two contexts:①as a reactive decision support tool to generate new trajectories that can resolve unprecedented events;and②as an autopilot system for both partial and fully autonomous taxiing.The proposed methodology is realistic and simple to implement.Moreover,simulation studies show that the proposed approach is capable of providing an up to 11%reduction in the fuel consumed during the taxiing of a large Boeing 747-100 jumbo jet.

Novel four-dimensional autonomous chaotic system generating one-,two-,three- and four-wing attractors

In this paper, we propose a novel four-dimensional autonomous chaotic system. Of particular interest is that this novel system can generate one-, two, three- and four-wing chaotic attractors with the variation of a single parameter, and the multi-wing type of the chaotic attractors can be displayed in all directions. The system is simple with a large positive Lyapunov exponent and can exhibit some interesting and complicated dynamical behaviours. Basic dynamical properties of the four-dimensional chaotic system, such as equilibrium points, the Poincare map, the bifurcation diagram and the Lyapunov exponents are investigated by using either theoretical analysis or numerical method. Finally, a circuit is designed for the implementation of the multi-wing chaotic attractors. The electronic workbench observations axe in good agreement with the numerical simulation results.

The Role of Cultural Compatibility in Effective Management The Application of Cultural Four-dimensional Model in Transnational Corporations

Cross-cultural management is often regarded as a discipline of international management focusing on cultural encounters between the organization and the nation-state, and providing tools to tackle cultural difl＇erences seen as sources of conflict, friction or misunderstanding. Based on Greet Hofstede＇ s Cultural Model, this paper attempts to shed some light on effective corporation management through cultural analysis of the difl＇erences between China and western countries. The paper puts more emphasis on the impact of cultural compatibility on effective corporation man- agement through the case study of China, Japan, Germany and America. The author argues that managers and employ- ees involved in companies with diverse cultural backgrounds should be integrated and developed into a specific local context through interlocking their cultural identifications and the organizational practices.

Deep Volatiles as the Key for Energy and Environments of the Four-Dimensional Earth System

Carbon, hydrogen, oxygen, nitrogen, sulfur, and their compounds are volatile components that dominate the thin and fragile atmosphere, hydrosphere, and biosphere on Earth’s habitable surface. However, the vast majority of these volatiles are hidden in the deep interior, where the high pressure–temperature conditions drastically and categorically alter the physics and chemistry of the volatiles. Like the bloodstream of an organism, the circulations and interactions of volatiles in the deep Earth modulate climate, resources, energy, natural hazards, and other factors that define the Earth as a unique living and changing planet.

Rainfall Assimilation Using a New Four-Dimensional Variational Method:A Single-Point Observation Experiment

Accurate forecast of rainstorms associated with the mei-yu front has been an important issue for the Chinese economy and society. In July 1998 a heavy rainstorm hit the Yangzi River valley and received widespread attention from the public because it caused catastrophic damage in China. Several numerical studies have shown that many forecast models, including Pennsylvania State University National Center for Atmospheric Research’s fifth-generation mesoscale model （MM5）, failed to simulate the heavy precipitation over the Yangzi River valley. This study demonstrates that with the optimal initial conditions from the dimension-reduced projection four-dimensional variational data assimilation （DRP-4DVar） system, MM5 can successfully reproduce these observed rainfall amounts and can capture many important mesoscale features, including the southwestward shear line and the low-level jet stream. The study also indicates that the failure of previous forecasts can be mainly attributed to the lack of mesoscale details in the initial conditions of the models.

OPERATOR NORM AND LOWER BOUND OF FOUR-DIMENSIONAL GENERALIZED HAUSDORFF MATRICES

The problem addressed is the exact determination of the operator norm and lower bound of four-dimensional generalized Hausdorff matrices on the double sequence spaces L_(p).A Hardy type formulae is found as an exact value for their operator norm and a Copson type formulae is established as a lower estimate for their lower bound.Further,exact values are found for the operator norm and lower bound of the transpose of generalized Hausdorff matrices.

Study on eigenvalue space of hyperchaotic canonical four-dimensional Chua's circuit

The eigenvalue space of the canonical four-dimensional Chua＇s circuit which can realize every eigenvalue for fourdimensional system is studied in this paper. First, the analytical relations between the circuit parameters and the eigenvalues of the system are established, and therefore all the circuit parameters can be determined explicitly by any given set of eigenvalues. Then, the eigenvalue space of the circuit is investigated in two cases by the nonlinear elements used. According to the types of the eigenvalues, some novel hyperchaotic attractors are presented. Further, the dynamic behaviours of the circuit are studied by the bifurcation diagrams and the Lyapunov spectra of the eigenvalues.

Study and application of an improved four-dimensional variational assimilation system based on the physical-space statistical analysis for the South China Sea

The four-dimensional variational assimilation(4D-Var)has been widely used in meteorological and oceanographic data assimilation.This method is usually implemented in the model space,known as primal approach(P4D-Var).Alternatively,physical space analysis system(4D-PSAS)is proposed to reduce the computation cost,in which the 4D-Var problem is solved in physical space(i.e.,observation space).In this study,the conjugate gradient(CG)algorithm,implemented in the 4D-PSAS system is evaluated and it is found that the non-monotonic change of the gradient norm of 4D-PSAS cost function causes artificial oscillations of cost function in the iteration process.The reason of non-monotonic variation of gradient norm in 4D-PSAS is then analyzed.In order to overcome the non-monotonic variation of gradient norm,a new algorithm,Minimum Residual(MINRES)algorithm,is implemented in the process of assimilation iteration in this study.Our experimental results show that the improved 4D-PSAS with the MINRES algorithm guarantees the monotonic reduction of gradient norm of cost function,greatly improves the convergence properties of 4D-PSAS as well,and significantly restrains the numerical noises associated with the traditional 4D-PSAS system.

A Four-Dimensional Variational System for Skillful Operational Prediction of Convective Storms

Forecasting convective storms using NWP models is an important goal and a highly active area of ongoing research. Skillful and reliable NWP of convective storms could allow for severe weather warnings with longer lead times, as opera- tional forecasters begin to incorporate convective-scale fore- casts into severe weather forecast operations （Stensrud et al., 2009, 2013）. This would then provide vulnerable individuals and industries with more time to seek shelter and/or mitigate the impact of severe weather hazards.

Stability of Dirac Equation in Four-Dimensional Gravity

We introduce the Dirac equation in four-dimensional gravity which is a generally covariant form. We choose the suitable variable and solve the corresponding equation. To solve such equation and to obtain the corresponding bispinor, we employ the factorization method which introduces the associated Laguerre polynomial. The asso- ciated Laguerre polynomials help us to write the Dirac equation of four-dimensional gravity in the form of the shape invariance equation. Thus we write the shape invariance condition with respect to the secondary quantum number. Finally, we obtain the spinor wave function and achieve the corresponding stability of condition for the four-dimensional gravity system.

Application value of four-dimensional spatiotemporal image correlation and tomographic ultrasound imaging in screening fetal congenital heart disease

Objective:To explore the value of four-dimensional spatiotemporal image correlation and tomographic ultrasound imaging in screening fetal congenital heart disease.Methods: A total of 671 pregnant women at 22-24 gestational weeks from January 2018 to December 2018 were examined by two-dimensional ultrasound and four-dimensional spatiotemporal image correlation and tomographic ultrasound imaging to observe the development of fetal cardiovascular structure and to compare the two methods in terms of diagnostic accuracy, examination time, image quality and new physician training cycle.Results: Cardiac malformations were found in 12 of the 671 fetuses, among which 11 cases were detected by four-dimensional spatiotemporal image correlation and tomographic ultrasound imaging and 1 case was missed. Postnatal echocardiographic reexamination and autopsy confirmed 12 cases of children with cardiac malformation, including 1 case of atrial septal defect (missed diagnosis by four-dimensional spatiotemporal image correlation and tomographic ultrasound imaging), 4 cases of tetralogy of Fallot's disease, 1 case of right ventricular double outlet, 3 cases of left ventricular dysplasia, 2 cases of complete transposition of the great artery and 1 case of tricuspid valve descending malformation. There was no statistically significant difference between four-dimensional spatiotemporal image correlation and tomographic ultrasound imaging and conventional two-dimensional color echocardiography or/and autopsy (P>0.05). In terms of examination time and new physician training, the four-dimensional spatiotemporal image correlation and tomographic ultrasound imaging technique was superior to conventional color ultrasound screening. No statistically significant difference in image quality.Conclusions:The four-dimensional spatiotemporal image correlation and tomographic ultrasound imaging can rapidly and accurately display fetal heart development, and can be used as the main screening method for fetal congenital heart disease in clinical practice.

Clinical effect of four-dimensional therapy on patients with cervical hypertension

Objective:To research the effect of four-dimensional therapy on the clinical effect (symptoms, blood pressure, and pain degree), the changes of blood rheology and arterial (left vertebral artery (LVA), right vertebral artery (RVA), and basal artery (BA)) hemodynamics (average cerebral blood flow (Vm), resistance index (RI), pulsatility index (PI)) on patients with cervical hypertension. Method: Selecting 120 patients (Department of Orthopaedics, the second Affiliated Hospital to Liaoning University of Chinese Medicine, 2012.6-2018.10) with cervical hypertension, then they were divided into observation group (n=60) and control group (n=60). The control group were given enalapril meleate (amlodipine besylate) +conventional therapy (acupuncture treatment and massage), the observation group were given four-dimensional therapy on the basic of control group, they were treated 3 weeks. The primary endpoints were the changes from baseline to week 3 in the symptoms and function were scored using the Evaluation Scale for Cervical Vertigo, the secondary endpoints were changes from baseline to month 3 in the artery hemodynamics (Vm, RI, and PI) in the BA, LVA, blood rheology, and RVA. At last, assessing the pain degree through visual analog scale (VAS), measuring the blood pressure, and accessing the clinical effect.Results:The score of vertigo in the two groups had no statistical significance before treatment, the score of vertigo in the two groups were higher than pretherapy, and had statistical significance, and the score in the observation group were higher than control group, and had statistical significance. The hemodynamics (Vm, RI, and PI) in the artery (BA, LVA, and RVA) had no statistical significance in the two groups before treatment, and the hemodynamics (Vm) in the artery (BA, LVA, and RVA) were higher than pretherapy, and had statistical significance, the hemodynamics (Vm) in the artery (BA, LVA, and RVA) of observation group were higher than control group, and had statistical significance. The hemodynamics (RI and PI) in the artery (BA, LVA, and RVA) were lower than pretherapy, and had statistical significance, the the hemodynamics (Vm) in the artery (BA, LVA, and RVA) of observation group were lower than control group, and had statistical significance. The blood rheology had no statistical significance in the two groups before treatment, the blood rheology were lower than pretherapy, and had statistical significance, the blood rheology of observation group were lower than control group, and had statistical significance. The degree of VAS had no statistical significance in the two groups before treatment, the degree of VAS was lower than pretherapy, and had statistical significance, the degree of VAS of observation group were lower than control group, and had statistical significance. The blood pressure (systolic pressure and diastolic pressure) had no statistical significance in the two groups before treatment, the blood pressure (systolic pressure and diastolic pressure) were lower than pretherapy, and had statistical significance, the blood pressure (systolic pressure and diastolic pressure) of observation group were lower than control group, and had statistical significance, the clinical effect in the observation group were higher than control group, and had statistical significance.Conclusions:Giving four-dimensional therapy can improve the blood pressure and relieve the pain through improving blood rheology and hemodynamics in the artery in the patients with cervical hypertension.