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In binary classification, kernel-free quadratic support vector machines are proposed to avoid difficulties such as finding appropriate kernel functions or tuning their hyper-parameters. Furthermore, Universum data points, which do not belong to any class, can be exploited to embed prior knowledge into the corresponding models to improve the general performance. This paper designs novel kernel-free Universum quadratic surface support vector machine models. Further, this paper proposes the ℓ 1 norm regularized version that is beneficial for detecting potential sparsity patterns in the Hessian of the quadratic surface and reducing to the standard linear models if the data points are (almost) linearly separable. The proposed models are convex, so standard numerical solvers can be utilized to solve them. Moreover, a least squares version of the ℓ 1 norm regularized model is proposed. We also design an effective tailored algorithm that only requires solving one linear system. Several theoretical properties of these models are then reported and proved as well. The numerical results show that the least squares version of the proposed model achieves the highest mean accuracy scores with promising computational efficiency on some artificial and public benchmark data sets. Some statistical tests are conducted to show the competitiveness of the proposed models. [ABSTRACT FROM AUTHOR]

Numerical studies on internal fire whirls (IFW) generated in a vertical shaft model with a single corner gap were reported in this paper. The generation of IFW, burning rate of fuel and temperature were studied experimentally first. Numerical simulations on medium-scale IFW were carried out using a fully-coupled large eddy simulation incorporating subgrid scale turbulence and a fire source with heat release rates compiled from experimental results. Typical transient flame shape was studied and then simulated numerically by using temperature. The dynamic phenomena of generation and development of IFW were simulated and then compared with experimental results. The predicted results were validated by comparing with experimental data, which demonstrated that an IFW can be simulated by Computational Fluid Dynamics. Numerical results for flame surface, temperature, and flame length agreed well with the experimental results. The IFW flame region and intermittent region were longer than those for an ordinary pool fire. The modified empirical formula for centerline temperature was derived. Variations of vertical and tangential velocity in axial and radial directions were also shown. The vortex core radius was found to be determined by the fuel bed size. Velocity field was not measured extensively due to resources limitation. Comparing measured temperature distribution with predictions is acceptable because temperature is related to the heat release rate, air flow and pressure gradient. [ABSTRACT FROM AUTHOR]

We suggest a new greedy strategy for convex optimization in Banach spaces and prove its convergence rates under a suitable behavior of the modulus of uniform smoothness of the objective function. We show that this algorithm is a generalization of the recently discovered Rescaled Pure Greedy Algorithm for approximation in Hilbert spaces. [ABSTRACT FROM AUTHOR]