This paper focuses on the low-order nonconforming rectangular and quadrilateral finite elements approximation of incompressible flow. Beyond the previous research works [9, 8, 4], we propose a general strategy to construct the basis functions. Under several specific constraints, the optimal error estimates are obtained, i.e. the first order accuracy of the velocities in H-norm and the pressure ...

Voxel Coloring has become a popular technique for reconstructing a 3D scene from a set of 2D images. While many different variants of this technique exist, all rely on a test to determine if each voxel is projecting to regions of consistent color in all views of that voxel. A number of color consistency tests can be used and the specific choice has a large influence on the quality of the recons...

We consider the non-convex quadratic maximization problem subject to the `1 unit ball constraint. The nature of the l1 norm structure makes this problem extremely hard to analyze, and as a consequence, the same difficulties are encountered when trying to build suitable approximations for this problem by some tractable convex counterpart formulations. We explore some properties of this problem, ...

We identify the integrable stopping time τ∗ with minimal L1-distance from the lastpassage time γz associated with a given level z > 0, for an arbitrary nonnegative time-homogeneous transient diffusion X. We demonstrate that τ∗ is in fact the first time that X assumes a value outside a half-open interval [0, r∗). The upper boundary r∗ > z of this interval is characterized either as the solution ...

We establish general moment estimates for the discrete and continuous exit times of a general Itô process in terms of the distance to the boundary. These estimates serve as intermediate steps to obtain strong convergence results for the approximation of a continuous exit time by a discrete counterpart, computed on a grid. In particular, we prove that the discrete exit time of the Euler scheme o...

In multi-agent systems norms are an important influence that can engender cooperation by constraining actions and binding groups together. A key question is how to establish suitable norms in a decentralised population of self-interested agents, especially where individual agents might not adhere to the rules of the system. It is desirable, in certain situations, to establish multiple co-existi...

For many human machine interaction systems, techniques for continuously estimating the vigilance of operators are highly desirable to ensure work safety. Up to now, various signals are studied for vigilance analysis. Among them, electroencephalogram (EEG) is the most commonly used signal. In this paper, extreme learning machine (ELM) and its modifications with L1 norm and L2 norm penalties are ...

It is well known that quantile regression model minimizes the portfolio extreme risk, whenever the attention is placed on the estimation of the response variable left quantiles. We show that, by considering the entire conditional distribution of the dependent variable, it is possible to optimize different risk and performance indicators. In particular, we introduce a risk-adjusted profitability...

A heuristic improvement technique referred to as multi-dimensional heuristics is presented. Instead of only applying the heuristic between two states X 1 and X 2 , when a distance esti­ mate of X 1 X 2 is needed, this technique uses a reference state R and applies the heuristic func­ tion to {X 1 ,R) and (X' 2 ,R) and compares the resulting values. If two states are close to each other, then th...

To categorize the convergence properties of mesh-based approximations to manifolds and surfaces, this paper defines these approximations as “Wk,p-manifolds” and “Wk,psurfaces.” In particular, this paper examines the importance of these classifications in the convergence in L1-norm of interpolants, built on the approximate manifold or surface, of functions defined on the approximated manifold or...