The dilemma between eliminating dominance-resistant solutions and preserving boundary solutions of extremely convex Pareto fronts

It has been acknowledged that dominance-resistant solutions (DRSs) extensively exist in the feasible region of multi-objective optimization problems. Recent studies show that DRSs can cause serious performance degradation of many multi-objective evolutionary algorithms (MOEAs). Thereafter, various strategies (e.g., the $$\epsilon $$ ϵ -dominance and the modified objective calculation) to eliminate DRSs have been proposed. However, these strategies may in turn cause algorithm inefficiency in other aspects. We argue that these coping strategies prevent the algorithm from obtaining some boundary solutions of an extremely convex Pareto front (ECPF). That is, there is a dilemma between eliminating DRSs and preserving boundary solutions of the ECPF. To illustrate such a dilemma, we propose a new multi-objective optimization test problem with the ECPF as well as DRSs. Using this test problem, we investigate the performance of six representative MOEAs in terms of boundary solutions preservation and DRS elimination. The results reveal that it is quite challenging to distinguish between DRSs and boundary solutions of the ECPF.

Insider trading in Brazil's stock market

How much insider trading happens in Brazil’s stock market? Previous research has used the model proposed by Easley et al. [1996] to estimate the probability of insider trading (PIN) for different stocks in Brazil. Those estimates have a number of problems: i) they are based on a factorization that biases the PIN downward, especially for high-activity stocks; ii) they fail to account for boundary solutions, which biases most PIN estimates upward (and a few of them downward); and iii) they are a decade old and therefore based on a very different market (for instance, the number of retail investors grew from 600 thousand in 2011 to 3.5 million in 2021). In this paper I address those three problems and estimate the probability of insider trading for 431 different stocks in the Brazilian stock market, for each quarter from October 2019 to March 2021.

On Monotonic Pattern in Periodic Boundary Solutions of Cylindrical and Spherical Kortweg–De Vries–Burgers Equations

We studied, for the Kortweg–de Vries–Burgers equations on cylindrical and spherical waves, the development of a regular profile starting from an equilibrium under a periodic perturbation at the boundary. The regular profile at the vicinity of perturbation looks like a periodical chain of shock fronts with decreasing amplitudes. Further on, shock fronts become decaying smooth quasi-periodic oscillations. After the oscillations cease, the wave develops as a monotonic convex wave, terminated by a head shock of a constant height and equal velocity. This velocity depends on integral characteristics of a boundary condition and on spatial dimensions. In this paper the explicit asymptotic formulas for the monotonic part, the head shock and a median of the oscillating part are found.

Meshless Analysis of Nonlocal Boundary Value Problems in Anisotropic and Inhomogeneous Media

In this work, meshless methods based on a radial basis function (RBF) are applied for the solution of two-dimensional steady-state heat conduction problems with nonlocal multi-point boundary conditions (NMBC). These meshless procedures are based on the multiquadric (MQ) RBF and its modified version (i.e., integrated MQ RBF). The meshless method is extended to the NMBC and compared with the standard collocation method (i.e., Kansa’s method). In extended methods, the interior and the boundary solutions are approximated with a sum of RBF series, while in Kansa’s method, a single series of RBF is considered. Three different sorts of solution domains are considered in which Dirichlet or Neumann boundary conditions are specified on some part of the boundary while the unknown function values of the remaining portion of the boundary are related to a discrete set of interior points. The influences of NMBC on the accuracy and condition number of the system matrix associated with the proposed methods are investigated. The sensitivity of the shape parameter is also analyzed in the proposed methods. The performance of the proposed approaches in terms of accuracy and efficiency is confirmed on the benchmark problems.

On Some Classes of Correct Problems in the Membrane Theory of Convex Shells

On the basis of the theory of the modified Riemann-Hilbert problem for generalized analytic functions, a geometric description is given of a fairly wide family of correct by I. N. Vekua of boundary value problems of the membrane theory of convex hulls with a piecewise smooth boundary. Solutions to the corresponding Riemann-Hilbert problem for an elliptic system of equilibrium equations are found in the classes of N.I. Muskhelishvili and realize a state of tense equilibrium under the condition of stress concentration in corner points. An effective formula is given for calculating the index of the boundary condition, which allows us to formulate the results in a visible form. Families of shells are found for which the solvability picture of the main boundary-value problem coincides with the solvability picture of the Vekua problem for shells with a smooth border.