Higher-dimensional Chen-Lee-Liu equation and asymmetric peakon soliton

Integrable systems play a crucial role in physics and mathematics.In particular,the traditional(1+1)-dimensional and(2+1)-dimensional integrable systems have received significant attention due to the rarity of integrable systems in higher dimensions.Recent studies have shown that abundant higher-dimensional integrable systems can be constructed from(1+1)-dimensional integrable systems by using a deformation algorithm.Here we establish a new(2+1)-dimensional Chen-Lee-Liu(C-L-L)equation using the deformation algorithm from the(1+1)-dimensional C-L-L equation.The new system is integrable with its Lax pair obtained by applying the deformation algorithm to that of the(1+1)-dimension.It is challenging to obtain the exact solutions for the new integrable system because the new system combines both the original C-L-L equation and its reciprocal transformation.The traveling wave solutions are derived in implicit function expression,and some asymmetry peakon solutions are found.

3-Dimensional Kinematic Comparison of Arm Movements between an Individual with NGLY1 Deficiency and a Neurotypical Individual

NGLY1 Deficiency is an ultra-rare autosomal recessively inherited disorder. Characteristic symptoms include among others, developmental delays, movement disorders, liver function abnormalities, seizures, and problems with tear formation. Movements are hyperkinetic and may include dysmetric, choreo-athetoid, myoclonic and dystonic movement elements. To date, there have been no quantitative reports describing arm movements of individuals with NGLY1 Deficiency. This report provides quantitative information about a series of arm movements performed by an individual with NGLY1 Deficiency and an aged-matched neurotypical participant. Three categories of arm movements were tested: 1) open ended reaches without specific end point targets;2) goal-directed reaches that included grasping an object;3) picking up small objects from a table placed in front of the participants. Arm movement kinematics were obtained with a camera-based motion analysis system and “initiation” and “maintenance” phases were identified for each movement. The combination of the two phases was labeled as a “complete” movement. Three-dimensional analysis techniques were used to quantify the movements and included hand trajectory pathlength, joint motion area, as well as hand trajectory and joint jerk cost. These techniques were required to fully characterize the movements because the NGLY1 individual was unable to perform movements only in the primary plane of progression instead producing motion across all three planes of movement. The individual with NGLY1 Deficiency was unable to pick up objects from a table or effectively complete movements requiring crossing the midline. The successfully completed movements were analyzed using the above techniques and the results of the two participants were compared statistically. Almost all comparisons revealed significant differences between the two participants, with a notable exception of the 3D initiation area as a percentage of the complete movement. The statistical tests of these measures revealed no significant differences between the two participants, possibly suggesting a common underlying motor control strategy. The 3D techniques used in this report effectively characterized arm movements of an individual with NGLY1 deficiency and can be used to provide information to evaluate the effectiveness of genetic, pharmacological, or physical rehabilitation therapies.

Study on creep deformation and energy development of underground surrounding rock under four‐dimensional support

There is an urgent need to develop optimal solutions for deformation control of deep high‐stress roadways,one of the critical problems in underground engineering.The previously proposed four‐dimensional support(hereinafter 4D support),as a new support technology,can set the roadway surrounding rock under three‐dimensional pressure in the new balanced structure,and prevent instability of surrounding rock in underground engineering.However,the influence of roadway depth and creep deformation on the surrounding rock supported by 4D support is still unknown.This study investigated the influence of roadway depth and creep deformation time on the instability of surrounding rock by analyzing the energy development.The elastic strain energy was analyzed using the program redeveloped in FLAC3D.The numerical simulation results indicate that the combined support mode of 4D roof supports and conventional side supports is highly applicable to the stability control of surrounding rock with a roadway depth exceeding 520 m.With the increase of roadway depth,4D support can effectively restrain the area and depth of plastic deformation in the surrounding rock.Further,4D support limits the accumulation range and rate of elastic strain energy as the creep deformation time increases.4D support can effectively reduce the plastic deformation of roadway surrounding rock and maintain the stability for a long deformation period of 6 months.As confirmed by in situ monitoring results,4D support is more effective for the long‐term stability control of surrounding rock than conventional support.

A Dimensional Reduction Approach Based on Essential Constraints in Linear Programming

This paper presents a new dimension reduction strategy for medium and large-scale linear programming problems. The proposed method uses a subset of the original constraints and combines two algorithms: the weighted average and the cosine simplex algorithm. The first approach identifies binding constraints by using the weighted average of each constraint, whereas the second algorithm is based on the cosine similarity between the vector of the objective function and the constraints. These two approaches are complementary, and when used together, they locate the essential subset of initial constraints required for solving medium and large-scale linear programming problems. After reducing the dimension of the linear programming problem using the subset of the essential constraints, the solution method can be chosen from any suitable method for linear programming. The proposed approach was applied to a set of well-known benchmarks as well as more than 2000 random medium and large-scale linear programming problems. The results are promising, indicating that the new approach contributes to the reduction of both the size of the problems and the total number of iterations required. A tree-based classification model also confirmed the need for combining the two approaches. A detailed numerical example, the general numerical results, and the statistical analysis for the decision tree procedure are presented.

Three-Dimensional N-Doped Carbon Nanotube/Graphene Composite Aerogel Anode to Develop High-Power Microbial Fuel Cell

Optimizing the structure of electrode materials is one of the most effective strategies for designing high-power microbial fuel cells(MFCs).However,electrode materials currently suffer from a series of shortcomings that limit the output of MFCs,such as high intrinsic resistance,poor electrolyte wettability,and low microbial load capacity.Here,a three-dimensional(3D)nitrogen-doped multiwalled carbon nanotube/graphene(N-MWCNT/GA)composite aerogel is synthesized as the anode for MFCs.Comparing nitrogen-doped GA,MWCNT/GA,and N-MWCNT/GA,the macroporous hydrophilic N-MWCNT/GA electrode with an average pore size of 4.24μm enables high-density loading of the microbes and facilitates extracellular electron transfer with low intrinsic resistance.Consequently,the hydrophilic surface of N-MWCNT can generate high charge mobility,enabling a high-power output performance of the MFC.In consequence,the MFC system based on N-MWCNT/GA anode exhibits a peak power density and output voltage of 2977.8 mW m^(−2)and 0.654 V,which are 1.83 times and 16.3%higher than those obtained with MWCNT/GA,respectively.These results demonstrate that 3D N-MWCNT/GA anodes can be developed for high-power MFCs in different environments by optimizing their chemical and microstructures.

Hyper Catastrophe on 4-Dimensional Canards

When discovering the potential of canards flying in 4-dimensional slow-fast system with a bifurcation parameter, the key notion “symmetry” plays an important role. It is of one parameter on slow vector field. Then, it should be determined to introduce parameters to all slow/fast vectors. It is, however, there might be no way to explore for another potential in this system, because the geometrical structure is quite different from the system with one parameter. Even in this system, the “symmetry” is also useful to obtain the potentials classified by R. Thom. In this paper, via the coordinates changing, the possible way to explore for the potential will be shown. As it is analyzed on “hyper finite time line”, or done by using “non-standard analysis”, it is called “Hyper Catastrophe”. In the slow-fast system which includes a very small parameter , it is difficult to do precise analysis. Thus, it is useful to get the orbits as a singular limit. When trying to do simulations, it is also faced with difficulty due to singularity. Using very small time intervals corresponding small , we shall overcome the difficulty, because the difference equation on the small time interval adopts the standard differential equation. These small intervals are defined on hyper finite number N, which is nonstandard. As and the intervals are linked to use 1/N, the simulation should be done exactly.

Optimal Estimation of High-Dimensional Covariance Matrices with Missing and Noisy Data

The estimation of covariance matrices is very important in many fields, such as statistics. In real applications, data are frequently influenced by high dimensions and noise. However, most relevant studies are based on complete data. This paper studies the optimal estimation of high-dimensional covariance matrices based on missing and noisy sample under the norm. First, the model with sub-Gaussian additive noise is presented. The generalized sample covariance is then modified to define a hard thresholding estimator , and the minimax upper bound is derived. After that, the minimax lower bound is derived, and it is concluded that the estimator presented in this article is rate-optimal. Finally, numerical simulation analysis is performed. The result shows that for missing samples with sub-Gaussian noise, if the true covariance matrix is sparse, the hard thresholding estimator outperforms the traditional estimate method.

Structural Engineering of Hierarchical Aerogels Comprised of Multi-dimensional Gradient Carbon Nanoarchitectures for Highly Efficient Microwave Absorption

Recently,multilevel structural carbon aerogels are deemed as attractive candidates for microwave absorbing materials.Nevertheless,excessive stack and agglomeration for low-dimension carbon nanomaterials inducing impedance mismatch are significant challenges.Herein,the delicate“3D helix-2D sheet-1D fiber-0D dot”hierarchical aerogels have been successfully synthesized,for the first time,by sequential processes of hydrothermal self-assembly and in-situ chemical vapor deposition method.Particularly,the graphene sheets are uniformly intercalated by 3D helical carbon nanocoils,which give a feasible solution to the mentioned problem and endows the as-obtained aerogel with abundant porous structures and better dielectric properties.Moreover,by adjusting the content of 0D core-shell structured particles and the parameters for growth of the 1D carbon nanofibers,tunable electromagnetic properties and excellent impedance matching are achieved,which plays a vital role in the microwave absorption performance.As expected,the optimized aerogels harvest excellent performance,including broad effective bandwidth and strong reflection loss at low filling ratio and thin thickness.This work gives valuable guidance and inspiration for the design of hierarchical materials comprised of dimensional gradient structures,which holds great application potential for electromagnetic wave attenuation.

A Dimension-Splitting Variational Multiscale Element-Free Galerkin Method for Three-Dimensional Singularly Perturbed Convection-Diffusion Problems

By introducing the dimensional splitting(DS)method into the multiscale interpolating element-free Galerkin(VMIEFG)method,a dimension-splitting multiscale interpolating element-free Galerkin(DS-VMIEFG)method is proposed for three-dimensional(3D)singular perturbed convection-diffusion(SPCD)problems.In the DSVMIEFG method,the 3D problem is decomposed into a series of 2D problems by the DS method,and the discrete equations on the 2D splitting surface are obtained by the VMIEFG method.The improved interpolation-type moving least squares(IIMLS)method is used to construct shape functions in the weak form and to combine 2D discrete equations into a global system of discrete equations for the three-dimensional SPCD problems.The solved numerical example verifies the effectiveness of the method in this paper for the 3D SPCD problems.The numerical solution will gradually converge to the analytical solution with the increase in the number of nodes.For extremely small singular diffusion coefficients,the numerical solution will avoid numerical oscillation and has high computational stability.

Theoretical model of radiation heat wave in two-dimensional cylinder with sleeve

A semi-analytical model is constructed to investigate two-dimensional radiation heat waves(Marshak waves)in a low-Z foam cylinder with a sleeve made of high-Z material.In this model,the energy loss to the high-Z wall is regarded as the primary two-dimensional effect and is taken into account via an indirect approach in which the energy loss is subtracted from the drive source and the wall loss is ignored.The interdependent Marshak waves in the low-Z foam and high-Z wall are used to estimate the energy loss.The energies and the heat front position calculated using the model under typical inertial confinement fusion conditions are verified by simulations.The validated model provides a theoretical tool for studying two-dimensional Marshak waves and should be helpful in providing further understanding of radiation transport.

The Microparticles SiOx Loaded on PAN-C Nanofiber as Three-Dimensional Anode Material for High-Performance Lithium-Ion Batteries

Three-dimensional C/SiOx nanofiber anode was prepared by polydimethylsiloxane(PDMS)and polyacrylonitrile(PAN)as precursors via electrospinning and freeze-drying successfully.In contrast to conventional carbon cover-ing Si-based anode materials,the C/SiOx structure is made up of PAN-C,a 3D carbon substance,and SiOx load-ing steadily on PAN-C.The PAN carbon nanofibers and loaded SiOx from pyrolyzed PDMS give increased conductivity and a stable complex structure.When employed as lithium-ion batteries(LIBs)anode materials,C/SiOx-1%composites were discovered to have an extremely high lithium storage capacity and good cycle per-formance.At a current density of 100 mA/g,its reversible capacity remained at 761 mA/h after 50 charge-dis-charge cycles and at 670 mA/h after 200 cycles.The C/SiOx-1%composite aerogel is a particularly intriguing anode candidate for high-performance LIBs due to these appealing qualities.

THUDosePD:a three-dimensional Monte Carlo platform for phantom dose assessment

Monte Carlo simulations are frequently utilized in radiation dose assessments.However,many researchers find the prevailing computing platforms to be intricate.This highlights a pressing need for a specialized framework for phantom dose evalua-tion.To address this gap,we developed a user-friendly radiation dose assessment platform using the Monte Carlo toolkit,Geant4.The Tsinghua University Phantom Dose(THUDosePD)augments the flexibility of Monte Carlo simulations in dosi-metric research.Originating from THUDose,a code with generic,functional,and application layers,THUDosePD focuses predominantly on anatomical phantom dose assessment.Additionally,it enables medical exposure simulation,intricate geometry creation,and supports both three-dimensional radiation dose analysis and phantom format transformations.The system operates on a multi-threaded parallel CPU architecture,with some modules enhanced for GPU parallel computing.Benchmark tests on the ICRP reference male illustrated the capabilities of THUDosePD in phantom dose assessment,covering the effective dose,three-dimensional dose distribution,and three-dimensional organ dose.We also conducted a voxelization conversion on the polygon mesh phantom,demonstrating the method’s efficiency and consistency.Extended applications based on THUDosePD further underline its broad adaptability.This intuitive,three-dimensional platform stands out as a valuable tool for phantom radiation dosimetry research.

Dimensionality reduction model based on integer planning for the analysis of key indicators affecting life expectancy

Purpose:Exploring a dimensionality reduction model that can adeptly eliminate outliers and select the appropriate number of clusters is of profound theoretical and practical importance.Additionally,the interpretability of these models presents a persistent challenge.Design/methodology/approach:This paper proposes two innovative dimensionality reduction models based on integer programming(DRMBIP).These models assess compactness through the correlation of each indicator with its class center,while separation is evaluated by the correlation between different class centers.In contrast to DRMBIP-p,the DRMBIP-v considers the threshold parameter as a variable aiming to optimally balances both compactness and separation.Findings:This study,getting data from the Global Health Observatory(GHO),investigates 141 indicators that influence life expectancy.The findings reveal that DRMBIP-p effectively reduces the dimensionality of data,ensuring compactness.It also maintains compatibility with other models.Additionally,DRMBIP-v finds the optimal result,showing exceptional separation.Visualization of the results reveals that all classes have a high compactness.Research limitations:The DRMBIP-p requires the input of the correlation threshold parameter,which plays a pivotal role in the effectiveness of the final dimensionality reduction results.In the DRMBIP-v,modifying the threshold parameter to variable potentially emphasizes either separation or compactness.This necessitates an artificial adjustment to the overflow component within the objective function.Practical implications:The DRMBIP presented in this paper is adept at uncovering the primary geometric structures within high-dimensional indicators.Validated by life expectancy data,this paper demonstrates potential to assist data miners with the reduction of data dimensions.Originality/value:To our knowledge,this is the first time that integer programming has been used to build a dimensionality reduction model with indicator filtering.It not only has applications in life expectancy,but also has obvious advantages in data mining work that requires precise class centers.

Dimensionality regulation in tin halide perovskite solar cells: Toward high performance and stability

Tin halide perovskites(THPs)have received extensive attention due to their low toxicity and excellent optoelectronic properties,and are considered to be the most promising alternatives to develop efficient lead-free perovskite solar cells.However,due to the unique and inherent characteristics of Sn^(2+)being easily oxidized to Sn^(4+)and fast crystallization,tin perovskite solar cells(TPSCs)show relatively poor performance and stability,compared to the lead counterparts.Recently,the introduction of bulky organic spacers into three-dimensional(3D)THPs for dimensional regulation can not only prevent the intrusion of water and oxygen,but also inhibit the self-doping effect and ion migration.In this review,we will detail how dimensional regulation enables TPSCs with high performance and superior stability.First,we summarize the intrinsic properties of THPs and analyze the root causes of their poor performance and instability.Next,we discuss the specific structure and types of the dimensional regulation strategy.Then,the mechanism of dimensional regulation is discussed in detail,mainly from inhibiting the Sn^(2+)oxidation,optimizing crystallization,passivating defects,and improving energy level alignment.Finally,future challenges and prospects for dimensional regulation are elaborated to help researchers develop more efficient and stable TPSCs.

In-situ assembly of TiO2 with high exposure of(001)facets on three-dimensional porous graphene aerogel for lithium-sulfur battery

Resulting from the development of electric vehicles,high energy-density Li-S batteries have recently attracted ever-increasing attentions worldwide.However,continuous dissolution of cathodic sulfur and followed shuttle effect of polysulfides lead to very limited service lifetime for currently-applied Li-S batteries.Herein,a 3 D porous graphene aerogel(GA)decorated with high exposure of anatase TiO2(001)nanoplatelets is proposed as robust host to immobilize cathodic sulfur.Compared with commonly used TiO2(101)nanoparticles,the Ti O2(001)nanoplatelets have highly matched lattices with graphene(002)nanosheets,thus facilitating the electronic transfer.The in-site assembled TiO2@GA host exhibits superior sulfur-immobilized capability,which cannot only entrap sulfur by physical confinement,but also capture dissoluble sulfurous species by chemical bonding.The fabricated S@TiO2@GA cathode shows excellent electrochemical performance with high discharge capacity,superior rate capability,and durable cycling stability as well,supposed to be a promising cathode for high-performance Li-S battery applications.

Metric Basis of Four-Dimensional Klein Bottle

The Metric of a graph plays an essential role in the arrangement of different dimensional structures and finding their basis in various terms.The metric dimension of a graph is the selection of the minimum possible number of vertices so that each vertex of the graph is distinctively defined by its vector of distances to the set of selected vertices.This set of selected vertices is known as the metric basis of a graph.In applied mathematics or computer science,the topic of metric basis is considered as locating number or locating set,and it has applications in robot navigation and finding a beacon set of a computer network.Due to the vast applications of this concept in computer science,optimization problems,and also in chemistry enormous research has been conducted.To extend this research to a four-dimensional structure,we studied the metric basis of the Klein bottle and proved that the Klein bottle has a constant metric dimension for the variation of all its parameters.Although the metric basis is variying in 3 and 4 values when the values of its parameter change,it remains constant and unchanged concerning its order or number of vertices.The methodology of determining the metric basis or locating set is based on the distances of a graph.Therefore,we proved the main theorems in distance forms.

Theoretical Predition of Two-dimensional SiGeP_(2)by the Global Optimization Method

The well-developed particle-swarm optimization method together with density functional theory calculations were employed to search lowest-energy geometric structures of two-dimensional(2D)SiGeP_(2).Two newly found structures(P3m1 and Pmm2)are predicted.The unbiased global search reveals that the two lowest-energy structures are honeycomb lattices with robust dynamical stabilities.A more accurate Heyd-Scuseria-Ernzerhof(HSE06)hybrid functional is used to estimate the band structures of SiGeP_(2),which indicates that both the structures are semiconductors with indirect band-gap energies 1.80 e V for P3m1 and1.93 e V for Pmm^(2),respectively.Using the deformation potential theory,the P3m1-SiGeP_(2)is predicted to have high electron mobilities(6.4×10^(4)along zigzag direction and 2.9×10^(3)cm^(2)·V^(-1)·s^(-1)along armchair direction,respectively)and hole electron mobilities(1.0×10^(3)along zigzag direction and 2.5×10^(3)cm^(2)·V^(-1)·s^(-1)along armchair direction,respectively),which can be comparable with that of phosphorene and show anisotropic character in-plane.In addition,to estimate the elastic limit of SiGeP_(2),we also calculated the surface tension of SiGeP_(2)as a function of tensile strain.Our results show that the 2D SiGeP_(2)may be good candidaticates for applications in nanoelectronic devices.

Augmented Industrial Data-Driven Modeling Under the Curse of Dimensionality

The curse of dimensionality refers to the problem o increased sparsity and computational complexity when dealing with high-dimensional data.In recent years,the types and vari ables of industrial data have increased significantly,making data driven models more challenging to develop.To address this prob lem,data augmentation technology has been introduced as an effective tool to solve the sparsity problem of high-dimensiona industrial data.This paper systematically explores and discusses the necessity,feasibility,and effectiveness of augmented indus trial data-driven modeling in the context of the curse of dimen sionality and virtual big data.Then,the process of data augmen tation modeling is analyzed,and the concept of data boosting augmentation is proposed.The data boosting augmentation involves designing the reliability weight and actual-virtual weigh functions,and developing a double weighted partial least squares model to optimize the three stages of data generation,data fusion and modeling.This approach significantly improves the inter pretability,effectiveness,and practicality of data augmentation in the industrial modeling.Finally,the proposed method is verified using practical examples of fault diagnosis systems and virtua measurement systems in the industry.The results demonstrate the effectiveness of the proposed approach in improving the accu racy and robustness of data-driven models,making them more suitable for real-world industrial applications.

Earth Pressure of the Trapdoor Problem Using Three-Dimensional Discrete Element Method

Load transformation from the yielding part of the soil to the adjacent part is known as the soil arching effect,which plays an important role in the design of various geotechnical infrastructures.Terzaghi’s trapdoor test was an importantmilestone in the development of theories on soil arching.The research on earth pressure of the trapdoor problem is presented in this paper using the three-dimensional(3D)discrete element method(DEM).Five 3D trapdoor models with different heights are established by 3DDEMsoftware PFC 3D.The variation of earth pressure on the trapdoor with the downward movement of the trapdoor,the distribution of vertical earth pressure along the horizontal direction,the distribution of vertical earth pressure along the vertical direction,the distribution of lateral earth pressure coefficient along the depth direction,the magnitude and direction of contact force chain are studied,respectively.Related research results show that the earth pressure on the trapdoor decreases rapidly after the downward movement of the trapdoor,and then reaches the minimum earth pressure.After that,the earth’s pressure will rise slightly,and whether this phenomenon occurs depends on the depth ratio.For the bottom soil,due to the stress transfer caused by the soil arching effect,the ratio of earth pressure in the loose area decreases,while the ratio of earth pressure in the stable area increases.With the trapdoor moving down,the vertical earth pressure along the depth in the stable zone is basically consistent with the initial state,which shows an approximate linear distribution.After the trapdoor moves down,the distribution of earth pressure along with the depth in the loose area changes,which is far less than the theoretical value of vertical earth pressure of its self-weight.Because of the compression of the soil on both sides,the lateral earth pressure coefficient of most areas on the central axis of the loose zone is close to the passive earth pressure coefficient Kp.The existence of a‘soil arch’can be observed intuitively from the distribution diagram of the contact force chain in the loose zone.

Dimensionality Reduction Using Optimized Self-Organized Map Technique for Hyperspectral Image Classification

The high dimensionalhyperspectral image classification is a challenging task due to the spectral feature vectors.The high correlation between these features and the noises greatly affects the classification performances.To overcome this,dimensionality reduction techniques are widely used.Traditional image processing applications recently propose numerous deep learning models.However,in hyperspectral image classification,the features of deep learning models are less explored.Thus,for efficient hyperspectral image classification,a depth-wise convolutional neural network is presented in this research work.To handle the dimensionality issue in the classification process,an optimized self-organized map model is employed using a water strider optimization algorithm.The network parameters of the self-organized map are optimized by the water strider optimization which reduces the dimensionality issues and enhances the classification performances.Standard datasets such as Indian Pines and the University of Pavia(UP)are considered for experimental analysis.Existing dimensionality reduction methods like Enhanced Hybrid-Graph Discriminant Learning(EHGDL),local geometric structure Fisher analysis(LGSFA),Discriminant Hyper-Laplacian projection(DHLP),Group-based tensor model(GBTM),and Lower rank tensor approximation(LRTA)methods are compared with proposed optimized SOM model.Results confirm the superior performance of the proposed model of 98.22%accuracy for the Indian pines dataset and 98.21%accuracy for the University of Pavia dataset over the existing maximum likelihood classifier,and Support vector machine(SVM).