Destabilizing Different Strengths of Fear Memories Requires Different Degrees of Prediction Error During Retrieval

Reactivation of consolidated memories can induce a labile period, in which these reactivated memories might be susceptible to change and need reconsolidation. Prediction error (PE) has been recognized as a necessary boundary condition for memory destabilization. Moreover, memory strength is also widely accepted as an essential boundary condition to destabilize fear memory. This study investigated whether different strengths of conditioned fear memories require different degrees of PE during memory reactivation in order for the memories to become destabilized. Here, we assessed the fear-potentiated startle and skin conductance response, using the post-retrieval extinction procedure. A violation of expectancy (PE) was induced during retrieval to reactivate enhanced (unpredictable-shock) or ordinary (predictable-shock) fear memories that were established the day before. Results showed that a PE retrieval before extinction can prevent the return of predictable-shock fear memory but cannot prevent the return of unpredictable-shock fear memory, indicating that a single PE is insufficient to destabilize enhanced fear memory. Therefore, we further investigated whether increasing the degree of PE could destabilize enhanced fear memory using different retrieval strategies (multiple PE retrieval and unreinforced CS retrieval). We found that spontaneous recovery of enhanced fear memory was prevented in both retrieval strategies, but reinstatement was only prevented in the multiple PE retrieval group, suggesting that a larger amount of PE is needed to destabilize enhanced fear memory. The findings suggest that behavioral updating during destabilization requires PE, and the degree of PE needed to induce memory destabilization during memory retrieval depends on the strength of fear memory. The study indicates that memory reconsolidation inference can be used to destabilize stronger memories, and the findings shed lights on the treatment of posttraumatic stress disorders and anxiety disorders.

Element-Free Galerkin method for dynamic boundary flow problems

This paper focuses on the study of dynamic boundary flow problems based on the Element-Free Galerkin method. First, Navier–Stokes equation is discretized with the Galerkin method. The inertial term in the equation is discretized with the method of the speed term and direct deduction, respectively. The penalty function method is used to deal with the pressure and the essential boundary condition in the equation, and the discretization of two-dimensional N–S equation based on the EFG method is established. However, irregular changes in boundary conditions are often encountered in practical fluid problems. For example, the motion of flapping-foil is not uniform relative to the flow. In this paper, numerical experiments are carried out for the flow problems with non-uniform boundary motions. The problem which a plate with non-uniform drag movement above a rectangular tank filled with water is studied with the EFG method. The feasibility of the proposed algorithm is verified by comparison with the FEM method. Then, the procession of the water in the tank is stimulated. In the end, the influence of different calculation time steps on the accuracy of the solution is discussed.

Solving the Problem of Constraints Due to Dirichlet Boundary Conditions in the Context of the Mini Element Method

In this work, we propose a new boundary condition called CA;B to remedy the problems of constraints due to the Dirichlet boundary conditions. We consider the 2D-linear elasticity equation of Navier-Lam´e with the condition CA;B. The latter allows to have a total insertion of the essential boundary condition in the linear system obtained without going through a numerical method like the lagrange multiplier method, this resulted in a non-extended linear system easy to reverse. We have developed the mixed finite element method using the mini element space (P1 + bubble, P1). Finally we have shown the efficiency and the feasibility of the limited condition CA;B.

Group discrimination, intergroup contact, and ethnic minority members’ reactions toward the majority

This study expands research on how intergroup contact makes ethnic minority members less prejudiced toward the majority group. Specifically, we propose that perceived group discrimination may serve as an essential boundary condition of the friendship‒prejudice relationship. Accordingly, analyses show that: (a) cross-group friendship predicts less prejudice, (b) perceived group discrimination relates to greater prejudice only among noncontacted ethnic minority members, and (c) greater perceived group discrimination enhances the ability of cross-group friendship to predict reduced prejudice toward majority members. The enhancing effect is inconsistent with previous research. Moreover, we show that perceived personal discrimination does not moderate the friendship‒prejudice relationship. Finally, analyses confirm the unique qualities of cross-group friendship, as perceived group discrimination does not predict greater prejudice when this type of contact is most intense. Analyses are performed on an unusually rich, national probability sample of ethnic minority members fielded in 2017 including 1211 respondents from Denmark. We conclude with discussion of the implications of our findings.

ENHANCED MESHFREE RPIM WITH NURBS BASIS FUNCTION FOR ANALYSIS OF IRREGULAR BOUNDARY DOMAIN

Radial Point Interpolation Method (RPIM) has become a powerful tool to numerical analysis due to its ability to provide a higher-order approximation function with the Kronecker delta property, by which the field nodes can be fitted exactly. However, one of the major drawbacks of RPIM is the inefficiency in handling irregular domain problems. This paper presents an enhanced RPIM formulation that employs Non-Uniform Rational B-Splines (NURBS) basis functions to represent the exact geometry of the boundary domain. The NURBS is a mathematical model which provides an efficient and numerically stable algorithm to exactly represent all conic sections in engineering modelling. Taking advantage of the flexibility and adaptivity of RPIM approximation and the accuracy of geometric representations by NURBS, this new method is able to improve geometry accuracy and flexibility in numerical analysis, thus providing a better and more rational approach to analyze irregular domain problems. Numerical problem of steady heat transfer considering curved beam is presented to verify the validity and accuracy of the developed method. The essential boundary condition can simply be imposed using direct imposition as in Finite Element Method (FEM). The result shows that the RPIM/NURBS achieved the converged solution much faster than conventional RPIM and FEM, with the number of nodes required only less than 200 for an error of less than 0.01%. This shows the potential of the developed method as a powerful numerical technique for future development.

Sensitivity analysis based multi-scale methods of coupled path-dependent problems

In the paper, a generalized essential boundary condition sensitivity analysis based implementation of $$\text {FE}^2$$FE2 and mesh-in-element (MIEL) multi-scale methods is derived as an alternative to standard implementations of multi-scale analysis, where the calculation of Schur complement of the microscopic tangent matrix is needed for bridging the scales. The paper presents a unified approach to the development of an arbitrary MIEL or $$\text {FE}^2$$FE2 computational scheme for an arbitrary path-dependent material model. Implementation is based on efficient first and second order analytical sensitivity analysis, for which automatic-differentiation-based formulation of essential boundary condition sensitivity analysis is derived. A fully consistently linearized two-level path-following algorithm is introduced as a solution algorithm for the multi-scale modeling. Sensitivity analysis allows each macro step to be followed by an arbitrary number of micro substeps while retaining quadratic convergence of the overall solution algorithm.

Penalty method with Crouzeix–Raviart approximation for the Stokes equations under slip boundary condition

The Stokes equations subject to non-homogeneous slip boundary conditions are considered in a smooth domain Ω ⊂ ℝN (N = 2,3). We propose a finite element scheme based on the nonconforming P1/P0 approximation (Crouzeix–Raviart approximation) combined with a penalty formulation and with reduced-order numerical integration in order to address the essential boundary condition u · n∂Ω = g on ∂Ω. Because the original domain Ω must be approximated by a polygonal (or polyhedral) domain Ωh before applying the finite element method, we need to take into account the errors owing to the discrepancy Ω ≠ Ωh, that is, the issues of domain perturbation. In particular, the approximation of n∂Ω by n∂Ωh makes it non-trivial whether we have a discrete counterpart of a lifting theorem, i.e., continuous right inverse of the normal trace operator H1 (Ω)N → H1/2(∂Ω); u ↦ u⋅n∂Ω. In this paper we indeed prove such a discrete lifting theorem, taking advantage of the nonconforming approximation, and consequently we establish the error estimates O(hα + ε) and O(h2α + ε) for the velocity in the H1- and L2-norms respectively, where α = 1 if N = 2 and α = 1/2 if N = 3. This improves the previous result [T. Kashiwabara et al., Numer. Math. 134 (2016) 705–740] obtained for the conforming approximation in the sense that there appears no reciprocal of the penalty parameter ϵ in the estimates.

Numerical Simulation of Nonlinear Flow Based on Element-Free Galerkin Method

This paper focuses on the studying on some flow problems of nonlinear based on the Element Free Galerkin method. First the Navier-Stokes equation is discretized with the Galerkin method. The inertial term in the equation is discretized with the method of the speed term and direct deduction respectively. And the penalty function method is used to deal with the pressure and the essential boundary condition in the equation, and the discretization of two-dimensional N-S equation based on the EFG method is established. Then the flow problem of stationary nonlinear is studied. The flow problem of water in the rectangular domain squeezed by the two plates distributed above and below the calculated domain is studied with the method of EFG. The accuracy of the direct linear alternating interation method is shown by contrast with the analytical solution. Then the flow problem of unsteady nonlinear is studied. The θ-weighted method is used to discrete the time term of the N-S equation and the unsteady nonlinear solution matrix of EFG is established. The flow problem of flow around the square column is studied with the method of EFG and the flows under a series of low Reynolds are stimulated.

Numerical Analysis of a Semi-Infinite Solid with Temperature Dependent Thermal Conductivity using Truly Meshfree Method

This article presents Meshless Local Petrov-Galerkin (MLPG) method to obtain the numerical solution of linear and non-linear heat conduction in a semi-infinite solid object with specific heat flux. Moving least square approximants are used to approximate the unknown function of temperature T(x) with Th(x). These approximants are constructed by using a linear basis, a weight function and a set of non-constant coefficients. Essential boundary condition is imposed by the penalty function method. A predictor-corrector scheme based on direct substitution iteration has been applied to address the non-linearity and two-level  method for temporal discretization. The accuracy of MLPG method is verified by comparing the results for the simplified versions of the present model with the exact solutions. Once the accuracy of MLPG method is established, the method is further extended to investigate the effects of temperature-dependent properties.