Statistical Inference of Partially Linear Spatial Autoregressive Model Under Constraint Conditions

In many application fields of regression analysis,prior information about how explanatory variables affect response variable of interest is often available and can be formulated as constraints on regression coefficients.In this paper,the authors consider statistical inference of partially linear spatial autoregressive model under constraint conditions.By combining series approximation method,twostage least squares method and Lagrange multiplier method,the authors obtain constrained estimators of the parameters and function in the partially linear spatial autoregressive model and investigate their asymptotic properties.Furthermore,the authors propose a testing method to check whether the parameters in the parametric component of the partially linear spatial autoregressive model satisfy linear constraint conditions,and derive asymptotic distributions of the resulting test statistic under both null and alternative hypotheses.Simulation results show that the proposed constrained estimators have better finite sample performance than the unconstrained estimators and the proposed testing method performs well in finite samples.Furthermore,a real example is provided to illustrate the application of the proposed estimation and testing methods.

An intelligent automatic correlation method of oilbearing strata based on pattern constraints:An example of accretionary stratigraphy of Shishen 100 block in Shinan Oilfield of Bohai Bay Basin,East China

Aiming at the problem that the data-driven automatic correlation methods which are difficult to adapt to the automatic correlation of oil-bearing strata with large changes in lateral sedimentary facies and strata thickness,an intelligent automatic correlation method of oil-bearing strata based on pattern constraints is formed.We propose to introduce knowledge-driven in automatic correlation of oil-bearing strata,constraining the correlation process by stratigraphic sedimentary patterns and improving the similarity measuring machine and conditional constraint dynamic time warping algorithm to automate the correlation of marker layers and the interfaces of each stratum.The application in Shishen 100 block in the Shinan Oilfield of the Bohai Bay Basin shows that the coincidence rate of the marker layers identified by this method is over 95.00%,and the average coincidence rate of identified oil-bearing strata reaches 90.02% compared to artificial correlation results,which is about 17 percentage points higher than that of the existing automatic correlation methods.The accuracy of the automatic correlation of oil-bearing strata has been effectively improved.

Consistency Conditions and Constraints on Generalized f(R) Gravity with Arbitrary Geometry-Matter Coupling

We study the consistency conditions of the generalized f （ R） gravity by extending f （ R） gravity with non-minimal coupling to the generalized f（R） with arbitrary geometry-matter coupling. Specifically, we discuss the two particular models of generalized f（R） by means of consistency conditions. It is found that the second model is not physically viable so as to be ruled out. Moreover, we further constrain the first model using the Dolgov- Kawasaki stability criterion, and give the value ranges of the parameters in the first model It is worth stressing that our results include the ones in f（R） gravity with non-minimal coupling as the special case of Q（Lm） = Lm.

Energy Conditions and Constraints on the Generalized Non-Local Gravity Model

We study and derive the energy conditions in generalized non-local gravity, which is the modified theory of general relativity obtained by adding a term m2n-2R□-nRto the Einstein-Hilbert action. Moreover, to obtain some insight on the meaning of the energy conditions, we illustrate the evolutions of four energy conditions with the model parameter ε for different n. By analysis we give the constraints on the model parameters ε.

Effective data sampling strategies and boundary condition constraints of physics-informed neural networks for identifying material properties in solid mechanics

Material identification is critical for understanding the relationship between mechanical properties and the associated mechanical functions.However,material identification is a challenging task,especially when the characteristic of the material is highly nonlinear in nature,as is common in biological tissue.In this work,we identify unknown material properties in continuum solid mechanics via physics-informed neural networks(PINNs).To improve the accuracy and efficiency of PINNs,we develop efficient strategies to nonuniformly sample observational data.We also investigate different approaches to enforce Dirichlet-type boundary conditions(BCs)as soft or hard constraints.Finally,we apply the proposed methods to a diverse set of time-dependent and time-independent solid mechanic examples that span linear elastic and hyperelastic material space.The estimated material parameters achieve relative errors of less than 1%.As such,this work is relevant to diverse applications,including optimizing structural integrity and developing novel materials.

Constraint Stabilization and One-Step Correction Method for Dynamical Systems

A computational method of constraint stabilization and correction is introduced. The method is based on the Baumgart＇s one-step method. Constraint conditions are addressed to stabilize and correct the solution. Two examples are given to illustrate the results of the method.

Gait Recognition via Cross Walking Condition Constraint

Gait recognition is a biometric technique that captures human walking pattern using gait silhouettes as input and can be used for long-term recognition.Recently proposed video-based methods achieve high performance.However,gait covariates or walking conditions,i.e.,bag carrying and clothing,make the recognition of intra-class gait samples hard.Advanced methods simply use triplet loss for metric learning,which does not take the gait covariates into account.For alleviating the adverse influence of gait covariates,we propose cross walking condition constraint to explicitly consider the gait covariates.Specifically,this approach designs center-based and pair-wise loss functions to decrease discrepancy of intra-class gait samples under different walking conditions and enlarge the distance of inter-class gait samples under the same walking condition.Besides,we also propose a video-based strong baseline model of high performance by applying simple yet effective tricks,which have been validated in other individual recognition fields.With the proposed baseline model and loss functions,our method achieves the state-of-the-art performance.

SMALLEST g-SUPERSOLUTION WITH CONSTRAINT

In this paper the existence and uniqueness of the smallest g-supersolution for BSDE is discussed in the case without Lipschitz condition imposing on both constraint function and drift coefficient in the different method from the one with Lipschitz condition.Then by considering (ξ,g) as a parameter of BSDE,and ( ξ α,g α) as a class of parameters for BSDE,where α belongs to a set A,for every α ∈A there exists a pair of solution { Y α,Z α } for the BSDE,the properties of sup α ∈A{ Y α } which is also a solution for some BSDE is studied.This result may be used to discuss optimal problems with recursive utility.

Coherence destruction of tunneling in a quantum-dot molecule with bias

This paper studies the constraint conditions for coherence destruction in tunneling by using perturbation theory and numerical simulation for an AC-field with bias and Coulomb interaction between electrons in a quantum dot molecule. Such conditions can be described by using the roots of a Bessel function Jn（x）, where n is determined by both the bias and the Coulomb interactions, and x is the ratio of the amplitude to the frequency of the AC-field. Under such conditions, a coherent suppression of tunneling occurs between localized electronic states, which results from the dynamical localization phenomenon. All the conditions are verified with numerical simulations.

A REASONABLE METHOD FOR CONSTRACTING GENERAL ELEMENT DM4 OF THICK AND THIN PLATE WITH EFFECTUAL AND REALIABLE NUMERICAL SOLUTIONS

In this thesis, the interal relations between about shear looking, zero energy mode and patch test are studied, and a reasonable method provided for building general element of thick and thin plate with effectual and realiable numerical solution.

New initial condition of the new agegraphic dark energy model

The initial condition Ωde（zini）=n^2（1＋zini）^-2/4 at zini = 2000,widely used to solve the differential equation of the density of the new agegraphic dark energy（NADE） Ωde,makes the NADE model a single-parameter dark-energy cosmological model.However,we find that this initial condition is only applicable in a flat universe with only dark energy and pressureless matter.In fact,in order to obtain more information from current observational data,such as the cosmic microwave background（CMB） and the baryon acoustic oscillations（BAO）,we need to consider the contribution of radiation.For this situation,the initial condition mentioned above becomes invalid.To overcome this shortcoming,we investigate the evolutions of dark energy in matter-dominated and radiation-dominated epochs,and obtain a new initial condition de（zini）=n2（1＋zini）-2（1＋F（zini））2/4 at z ini = 2000,where F（z）≡Ωr0（1＋z）/[Ωm0＋Ωr0（1＋z）] with Ωr0 and Ωm0 being the current density parameters of radiation and pressureless matter,respectively.This revised initial condition is applicable for the differential equation of Ωde obtained in the standard Friedmann-Robertson-Walker（FRW） universe with dark energy,pressureless matter,radiation,and even spatial curvature,and can still keep the NADE model as a single-parameter model.With the revised initial condition and the observational data of type Ia supernova（SNIa）,CMB,and BAO,we finally constrain the NADE model.The results show that the single free parameter n of the NADE model can be constrained tightly.

Dynamic Effect Research of Cable-Lead-In Rod on Towed System

This paper aims to research the cable-lead-in rod effect on a towed system through mathematical modeling and numerical simulations.The rod dynamics,as a key part of this study,is modeled using the combination of cable node governing equations and kinematic constraint conditions.As the first attempt to analyze such a problem,the rod is simply treated as an elastic cable segment so as to be incorporated into the dynamics of the cable,and a set of algorithm is then proposed based on the kinematic constraint conditions to fully describe its motions.Meanwhile,the cable and the underwater vehicle are modeled by the traditional lumped mass method and the 6 degree-of-freedom maneuverability equations for submarines respectively;the coupling boundary conditions besides the rod dynamics are also given to form the whole system's model.Several numerical cases are performed to investigate the rod effect on the system in different maneuver situations.Some meaningful conclusions are drawn through comparative analysis.

ELASTIC CALCULATION OF STRESSES IN RINGS USING AIRY STRESS FUNCTION

Stress calculation formulae for a ring have been obtained by using Airy stress function of the plane strain field with the decomposition of the solutions for normal stresses of Airy biharmonic equation into two parts when it is loaded under two opposite inside forces along a diameter. One part should fulfill a constraint condition about normal stress distribution along the circumference at an energy valley to do the minimum work. Other part is a stress residue constant. In order to verify these formulae and the computed results, the computed contour lines of equi-maximal shear stresses were plotted and quite compared with that of photo-elasticity test results. This constraint condition about normal stress distribution along circumference is confirmed by using Greens’ theorem. An additional compression exists along the circumference of the loaded ring, explaining the divorcement and displacement of singularity points at inner and outer boundaries.

On Some Aspects of Perturbation Analysis for Matrix Cone Optimization Induced by Spectral Norm

In this paper,we consider a cone problem of matrix optimization induced by spectral norm(MOSN).By Schur complement,MOSN can be reformulated as a nonlinear semidefinite programming(NLSDP)problem.Then we discuss the constraint nondegeneracy conditions and strong second-order sufficient conditions of MOSN and its SDP reformulation,and obtain that the constraint nondegeneracy condition of MOSN is not always equivalent to that of NLSDP.However,the strong second-order sufficient conditions of these two problems are equivalent without any assumption.Finally,a sufficient condition is given to ensure the nonsingularity of the Clarke’s generalized Jacobian of the KKT system for MOSN.