Nonuniform Dependence on the Initial Data for Solutions of Conservation Laws

In this paper,we study systems of conservation laws in one space dimension.We prove that for classical solutions in Sobolev spaces H^(s),with s>3/2,the data-to-solution map is not uniformly continuous.Our results apply to all nonlinear scalar conservation laws and to nonlinear hyperbolic systems of two equations.

BCCLR:A Skeleton-Based Action Recognition with Graph Convolutional Network Combining Behavior Dependence and Context Clues

In recent years,skeleton-based action recognition has made great achievements in Computer Vision.A graph convolutional network(GCN)is effective for action recognition,modelling the human skeleton as a spatio-temporal graph.Most GCNs define the graph topology by physical relations of the human joints.However,this predefined graph ignores the spatial relationship between non-adjacent joint pairs in special actions and the behavior dependence between joint pairs,resulting in a low recognition rate for specific actions with implicit correlation between joint pairs.In addition,existing methods ignore the trend correlation between adjacent frames within an action and context clues,leading to erroneous action recognition with similar poses.Therefore,this study proposes a learnable GCN based on behavior dependence,which considers implicit joint correlation by constructing a dynamic learnable graph with extraction of specific behavior dependence of joint pairs.By using the weight relationship between the joint pairs,an adaptive model is constructed.It also designs a self-attention module to obtain their inter-frame topological relationship for exploring the context of actions.Combining the shared topology and the multi-head self-attention map,the module obtains the context-based clue topology to update the dynamic graph convolution,achieving accurate recognition of different actions with similar poses.Detailed experiments on public datasets demonstrate that the proposed method achieves better results and realizes higher quality representation of actions under various evaluation protocols compared to state-of-the-art methods.

Understand anisotropy dependence of damage evolution and material removal during nanoscratch of MgF_(2) single crystals

To understand the anisotropy dependence of the damage evolution and material removal during the machining process of MgF_(2) single crystals,nanoscratch tests of MgF_(2) single crystals with different crystal planes and directions were systematically performed,and surface morphologies of the scratched grooves under different conditions were analyzed.The experimental results indicated that anisotropy considerably affected the damage evolution in the machining process of MgF_(2) single crystals.A stress field model induced by the scratch was developed by considering the anisotropy,which indicated that during the loading process,median cracks induced by the tensile stress initiated and propagated at the front of the indenter.Lateral cracks induced by tensile stress initiated and propagated on the subsurface during the unloading process.In addition,surface radial cracks induced by the tensile stress were easily generated during the unloading process.The stress change led to the deflection of the propagation direction of lateral cracks.Therefore,the lateral cracks propagated to the workpiece surface,resulting in brittle removal in the form of chunk chips.The plastic deformation parameter indicated that the more the slip systems were activated,the more easily the plastic deformation occurred.The cleavage fracture parameter indicated that the cracks propagated along the activated cleavage planes,and the brittle chunk removal was owing to the subsurface cleavage cracks propagating to the crystal surface.Under the same processing parameters,the scratch of the(001)crystal plane along the[100]crystal-orientation was found to be the most conducive to achieving plastic machining of MgF_(2) single crystals.The theoretical results agreed well with the experimental results,which will not only enhance the understanding of the anisotropy dependence of the damage evolution and removal process during the machining of MgF_(2) crystals,but also provide a theoretical foundation for achieving the high-efficiency and low-damage processing of anisotropic single crystals.

Assessment of Dependent Performance Shaping Factors in SPAR-H Based on Pearson Correlation Coefficient

With the improvement of equipment reliability,human factors have become the most uncertain part in the system.The standardized Plant Analysis of Risk-Human Reliability Analysis(SPAR-H)method is a reliable method in the field of human reliability analysis(HRA)to evaluate human reliability and assess risk in large complex systems.However,the classical SPAR-H method does not consider the dependencies among performance shaping factors(PSFs),whichmay cause overestimation or underestimation of the risk of the actual situation.To address this issue,this paper proposes a new method to deal with the dependencies among PSFs in SPAR-H based on the Pearson correlation coefficient.First,the dependence between every two PSFs is measured by the Pearson correlation coefficient.Second,the weights of the PSFs are obtained by considering the total dependence degree.Finally,PSFs’multipliers are modified based on the weights of corresponding PSFs,and then used in the calculating of human error probability(HEP).A case study is used to illustrate the procedure and effectiveness of the proposed method.

A Hybrid Spatial Dependence Model Based on Radial Basis Function Neural Networks (RBFNN) and Random Forest (RF)

The majority of spatial data reveal some degree of spatial dependence. The term “spatial dependence” refers to the tendency for phenomena to be more similar when they occur close together than when they occur far apart in space. This property is ignored in machine learning (ML) for spatial domains of application. Most classical machine learning algorithms are generally inappropriate unless modified in some way to account for it. In this study, we proposed an approach that aimed to improve a ML model to detect the dependence without incorporating any spatial features in the learning process. To detect this dependence while also improving performance, a hybrid model was used based on two representative algorithms. In addition, cross-validation method was used to make the model stable. Furthermore, global moran’s I and local moran were used to capture the spatial dependence in the residuals. The results show that the HM has significant with a R2 of 99.91% performance compared to RBFNN and RF that have 74.22% and 82.26% as R2 respectively. With lower errors, the HM was able to achieve an average test error of 0.033% and a positive global moran’s of 0.12. We concluded that as the R2 value increases, the models become weaker in terms of capturing the dependence.

Trees species’ dispersal mode and habitat heterogeneity shape negative density dependence in a temperate forest

Conspecific negative density dependence(CNDD)is a potentially important mechanism in maintaining species diversity.While previous evidence showed habitat heterogeneity and species’dispersal modes affect the strength of CNDD at early life stages of trees(e.g.,seedlings),it remains unclear how they affect the strength of CNDD at later life stages.We examined the degree of spatial aggregation between saplings and trees for species dispersed by wind and gravity in four topographic habitats within a 25-ha temperate forest dynamic plot in the Qinling Mountains of central China.We used the replicated spatial point pattern(RSPP)analysis and bivariate paircorrelation function(PCF)to detect the spatial distribution of saplings around trees at two scales,15 and 50 m,respectively.Although the signal was not apparent across the whole study region(or 25-ha),it is distinct on isolated areas with specific characteristics,suggesting that these characteristics could be important factors in CNDD.Further,we found that the gravity-dispersed tree species experienced CNDD across habitats,while for wind-dispersed species CNDD was found in gully,terrace and low-ridge habitats.Our study suggests that neglecting the habitat heterogeneity and dispersal mode can distort the signal of CNDD and community assembly in temperate forests.

Estimating the Components of a Mixture of Extremal Distributions under Strong Dependence

In this paper, we provide a method based on quantiles to estimate the parameters of a finite mixture of Fréchet distributions, for a large sample of strongly dependent data. This is a situation that appears when dealing with environmental data and there was a real need of such method. We validate our approach by means of estimation and goodness-of-fit testing over simulated data, showing an accurate performance.

Optimization of extended warranty cost for multi-component systems with economic dependence based on group maintenance

During extended warranty(EW)period,maintenance events play a key role in controlling the product systems within normal operations.However,the modelling of failure process and maintenance optimization is complicated owing to the complex features of the product system,namely,components of the multi-component system are interdependent with each other in some form.For the purpose of optimizing the EW pricing decision of the multi-component system scientifically and rationally,taking the series multi-component system with economic dependence sold with EW policy as a research object,this paper optimizes the imperfect preventive maintenance(PM)strategy from the standpoint of EW cost.Taking into consideration adjusting the PM moments of the components in the system,a group maintenance model is developed,in which the system is repaired preventively in accordance with a specified PM base interval.In order to compare with the system EW cost before group maintenance,the system EW cost model before group maintenance is developed.Numerical example demonstrates that offering group maintenance programs can reduce EW cost of the system to a great extent,thereby reducing the EW price,which proves to be a win-win strategy to manufacturers and users.

Theoretical characterization of the temperature-dependent saturation magnetization of magnetic metallic materials

Based on the force-heat equivalence energy density principle,a theoretical model for magnetic metallic materials is developed,which characterizes the temperature-dependent magnetic anisotropy energy by considering the equivalent relationship between magnetic anisotropy energy and heat energy;then the relationship between the magnetic anisotropy constant and saturation magnetization is considered.Finally,we formulate a temperature-dependent model for saturation magnetization,revealing the inherent relationship between temperature and saturation magnetization.Our model predicts the saturation magnetization for nine different magnetic metallic materials at different temperatures,exhibiting satisfactory agreement with experimental data.Additionally,the experimental data used as reference points are at or near room temperature.Compared to other phenomenological theoretical models,this model is considerably more accessible than the data required at 0 K.The index included in our model is set to a constant value,which is equal to 10/3 for materials other than Fe,Co,and Ni.For transition metals(Fe,Co,and Ni in this paper),the index is 6 in the range of 0 K to 0.65T_(cr)(T_(cr) is the critical temperature),and 3 in the range of 0.65T_(cr) to T_(cr),unlike other models where the adjustable parameters vary according to each material.In addition,our model provides a new way to design and evaluate magnetic metallic materials with superior magnetic properties over a wide range of temperatures.

IndRT-GCNets: Knowledge Reasoning with Independent Recurrent Temporal Graph Convolutional Representations

Due to the structural dependencies among concurrent events in the knowledge graph and the substantial amount of sequential correlation information carried by temporally adjacent events,we propose an Independent Recurrent Temporal Graph Convolution Networks(IndRT-GCNets)framework to efficiently and accurately capture event attribute information.The framework models the knowledge graph sequences to learn the evolutionary represen-tations of entities and relations within each period.Firstly,by utilizing the temporal graph convolution module in the evolutionary representation unit,the framework captures the structural dependency relationships within the knowledge graph in each period.Meanwhile,to achieve better event representation and establish effective correlations,an independent recurrent neural network is employed to implement auto-regressive modeling.Furthermore,static attributes of entities in the entity-relation events are constrained andmerged using a static graph constraint to obtain optimal entity representations.Finally,the evolution of entity and relation representations is utilized to predict events in the next subsequent step.On multiple real-world datasets such as Freebase13(FB13),Freebase 15k(FB15K),WordNet11(WN11),WordNet18(WN18),FB15K-237,WN18RR,YAGO3-10,and Nell-995,the results of multiple evaluation indicators show that our proposed IndRT-GCNets framework outperforms most existing models on knowledge reasoning tasks,which validates the effectiveness and robustness.

Learning Sequential and Structural Dependencies Between Nucleotides for RNA N6-Methyladenosine Site Identification

N6-methyladenosine(m6A)is an important RNA methylation modification involved in regulating diverse biological processes across multiple species.Hence,the identification of m6A modification sites provides valuable insight into the biological mechanisms of complex diseases at the post-transcriptional level.Although a variety of identification algorithms have been proposed recently,most of them capture the features of m6A modification sites by focusing on the sequential dependencies of nucleotides at different positions in RNA sequences,while ignoring the structural dependencies of nucleotides in their threedimensional structures.To overcome this issue,we propose a cross-species end-to-end deep learning model,namely CR-NSSD,which conduct a cross-domain representation learning process integrating nucleotide structural and sequential dependencies for RNA m6A site identification.Specifically,CR-NSSD first obtains the pre-coded representations of RNA sequences by incorporating the position information into single-nucleotide states with chaos game representation theory.It then constructs a crossdomain reconstruction encoder to learn the sequential and structural dependencies between nucleotides.By minimizing the reconstruction and binary cross-entropy losses,CR-NSSD is trained to complete the task of m6A site identification.Extensive experiments have demonstrated the promising performance of CR-NSSD by comparing it with several state-of-the-art m6A identification algorithms.Moreover,the results of cross-species prediction indicate that the integration of sequential and structural dependencies allows CR-NSSD to capture general features of m6A modification sites among different species,thus improving the accuracy of cross-species identification.

Modified DS np Chart Using Generalized Multiple Dependent State Sampling under Time Truncated Life Test

This study presents the design of a modified attributed control chart based on a double sampling(DS)np chart applied in combination with generalized multiple dependent state(GMDS)sampling to monitor the mean life of the product based on the time truncated life test employing theWeibull distribution.The control chart developed supports the examination of the mean lifespan variation for a particular product in the process of manufacturing.Three control limit levels are used:the warning control limit,inner control limit,and outer control limit.Together,they enhance the capability for variation detection.A genetic algorithm can be used for optimization during the in-control process,whereby the optimal parameters can be established for the proposed control chart.The control chart performance is assessed using the average run length,while the influence of the model parameters upon the control chart solution is assessed via sensitivity analysis based on an orthogonal experimental design withmultiple linear regression.A comparative study was conducted based on the out-of-control average run length,in which the developed control chart offered greater sensitivity in the detection of process shifts while making use of smaller samples on average than is the case for existing control charts.Finally,to exhibit the utility of the developed control chart,this paper presents its application using simulated data with parameters drawn from the real set of data.

TRADE DEPENDENCIES AND TRANSACTION COSTS: THE OC-CUPATION OF DECELEA HIGHLIGHTS BOTH THE BENEFITS AND THE DRAWBACKS OF A MARITIME ECONOMY

Thucydides asserts that the occupation of Decelea by the Spartans in 413 BC made the grain supply for Athens costly by forcing the transport from land onto the sea.This calls into question the well-established consensus that sea transport was far cheaper than land transport.This paper contends that the cost of protecting supply lines-specifically the expenses associated with the warships which escorted the supply ships-rendered the grain transported on the new route exceptionally costly.In this paper,the benefits and drawbacks of a maritime economy,including transaction costs,trade dependencies,and the capabilities of warships and supply ships are discussed.

Path-dependent speciation in dynamic fitness landscapes

Species is a fundamental concept in evolutionary biology and biodiversity.However,existing species definitions are often influenced by artificial factors or are challenging in practical application,leading to confusion in species classification.Due to uncertain environmental changes and random genetic drift,the fitness expectations of a population may shift,causing species to evolve to a new evolutionary state based on their current instantaneous fitness within a dynamic fitness landscape.This contrasts with the classic static fitness landscape,where fitness expectations are constant.In a dynamic fitness landscape,speciation may exhibit path dependence,where the evolution of traits follows a probabilistic path,creating feedback that shapes evolutionary trajectories.The path-dependent evolutionary mechanism suggests that species survival within an ecosystem is not directly determined by their fitness but by the probability of their evolutionary pathways.This model also indicates that species can coexist with varying probabilities under limited environmental pressures.Consequently,new species,cryptic species,or sympatric species may emerge via path-dependent evolutionary processes.Within this framework,we developed a mathematical species concept,which may guide future species classification methodologies.

Fuzzy Inventory Model under Selling Price Dependent Demand and Variable Deterioration with Fully Backlogged Shortages

The objective is to develop a model considering demand dependent on selling price and deterioration occurs after a certain period of time, which follows two-parameter Weibull distribution. Shortages are allowed and fully backlogged. Fuzzy optimal solution is obtained by considering hexagonal fuzzy numbers and for defuzzification Graded Mean Integration Representation Method. A numerical example is provided for the illustration of crisp and fuzzy, both models. To observe the effect of changes in parameters, sensitivity analysis is carried out.

Effect of Brisk Walking on Self-Care Agency or Care Dependency among Colorectal Cancer Patients with Permanent Stoma

Objective:The purpose of this study was to determine the effectiveness of brisk walking as an intervention for self-care agency and care dependency in patients with permanent colorectal cancer stoma.Method:This study adopted a quasi-experimental research design,specifically a non-equivalent control group pre-test and post-test design.Utilizing the Exercise of Self-Care Agency Scale(ESCA)and Care Dependency Scale(CDS),a survey was administered to 64 patients from a hospital in Shandong Province.The statistical methods used for analyzing data included frequency,mean,standard deviation(SD),independent t-test,P-value calculation,and dependent t-test.Result:After two months of a brisk walking exercise program,participants in the experimental group had a higher level of self-care agency than before the experiment(P<0.05),and their level of care dependency was significantly reduced(P<0.05).Participants in the control group also showed higher levels of self-care agency(P<0.05)and lower levels of care dependency(P<0.05)after two months compared to their levels before the two months.Conclusion:The brisk walking program had a positive impact on patients’self-care agency and reduced their care dependency.

A Study of Radiation-Induced Telomere Instability Using Multiplex Ligation-Dependent Probe Amplification (MLPA)

The integrity of the chromosomes for two WIL2-derived lymphoblastoid cell lines (TK6 and WTK1) in the presence and absence of ionizing radiation was analyzed by Multiplex Ligation-Dependent Probe Amplification (MLPA). The TK6 cell line has the native p53 tumor-suppressor gene, whereas WTK1 cells contain a p53 mutation. Each cell line was isolated pre- and post-irradiation (2 and 3 Gy) and analyzed by MLPA. The impact of irradiation on these two cell lines was investigated using probes that target specific regions on chromosomes associated with subtelomeric regions. Results indicate that WTK1 and TK6 are impacted differently after irradiation, and that each cell line presents its own unique MLPA profile. The most notable differences are the appearance of a number of probes in the post-irradiated MLPA profile that are not present in the controls, and two unique probe signals only seen in WTK1 cells. These results build on our previous studies that indicate how different human cell lines can be affected by radiation in significantly different ways depending on the presence or absence of wild type p53.

Inverse Spectral Problem for Sturm-Liouville Operator with Boundary and Jump Conditions Dependent on the Spectral Parameter

In this paper, the inverse spectral problem of Sturm-Liouville operator with boundary conditions and jump conditions dependent on the spectral parameter is investigated. Firstly, the self-adjointness of the problem and the eigenvalue properties are given, then the asymptotic formulas of eigenvalues and eigenfunctions are presented. Finally, the uniqueness theorems of the corresponding inverse problems are given by Weyl function theory and inverse spectral data approach.

Molecular dynamics study on temperature and strain rate dependences of mechanical tensile properties of ultrathin nickel nanowires

Based on the EAM potential, a molecular dynamics study on the tensile properties of ultrathin nickel nanowires in the （100〉 orientation with diameters of 3.94, 4.95 and 5.99 nm was presented at different temperatures and strain rates. The temperature and strain rate dependences of tensile properties were investigated. The simulation results show that the elastic modulus and the yield strength are gradually decreasing with the increase of temperature, while with the increase of the strain rate, the stress--strain curves fluctuate more intensely and the ultrathin nickel nanowires rupture at one smaller and smaller strain. At an ideal temperature of 0.01 K, the yield strength of the nanowires drops rapidly with the increase of strain rate, and at other temperatures the strain rate has a little influence on the elastic modulus and the yield strength. Finally, the effects of size on the tensile properties of ultrathin nickel nanowires were briefly discussed.

Thermomechanical Dynamics (TMD) and Bifurcation-Integration Solutions in Nonlinear Differential Equations with Time-Dependent Coefficients

The new independent solutions of the nonlinear differential equation with time-dependent coefficients (NDE-TC) are discussed, for the first time, by employing experimental device called a drinking bird whose simple back-and-forth motion develops into water drinking motion. The solution to a drinking bird equation of motion manifests itself the transition from thermodynamic equilibrium to nonequilibrium irreversible states. The independent solution signifying a nonequilibrium thermal state seems to be constructed as if two independent bifurcation solutions are synthesized, and so, the solution is tentatively termed as the bifurcation-integration solution. The bifurcation-integration solution expresses the transition from mechanical and thermodynamic equilibrium to a nonequilibrium irreversible state, which is explicitly shown by the nonlinear differential equation with time-dependent coefficients (NDE-TC). The analysis established a new theoretical approach to nonequilibrium irreversible states, thermomechanical dynamics (TMD). The TMD method enables one to obtain thermodynamically consistent and time-dependent progresses of thermodynamic quantities, by employing the bifurcation-integration solutions of NDE-TC. We hope that the basic properties of bifurcation-integration solutions will be studied and investigated further in mathematics, physics, chemistry and nonlinear sciences in general.