Multi-interest Diversification for End-to-end Sequential Recommendation

Sequential recommenders capture dynamic aspects of users’ interests by modeling sequential behavior. Previous studies on sequential recommendations mostly aim to identify users’ main recent interests to optimize the recommendation accuracy; they often neglect the fact that users display multiple interests over extended periods of time, which could be used to improve the diversity of lists of recommended items. Existing work related to diversified recommendation typically assumes that users’ preferences are static and depend on post-processing the candidate list of recommended items. However, those conditions are not suitable when applied to sequential recommendations. We tackle sequential recommendation as a list generation process and propose a unified approach to take accuracy as well as diversity into consideration, called multi-interest, diversified, sequential recommendation . Particularly, an implicit interest mining module is first used to mine users’ multiple interests, which are reflected in users’ sequential behavior. Then an interest-aware, diversity promoting decoder is designed to produce recommendations that cover those interests. For training, we introduce an interest-aware, diversity promoting loss function that can supervise the model to learn to recommend accurate as well as diversified items. We conduct comprehensive experiments on four public datasets and the results show that our proposal outperforms state-of-the-art methods regarding diversity while producing comparable or better accuracy for sequential recommendation.

Simulation of crack propagation based on eigenerosion in brittle and ductile materials subject to finite strains

In this paper, a framework for the simulation of crack propagation in brittle and ductile materials is proposed. The framework is derived by extending the eigenerosion approach of Pandolfi and Ortiz (Int J Numer Methods Eng 92(8):694–714, 2012. 10.1002/nme.4352) to finite strains and by connecting it with a generalized energy-based, Griffith-type failure criterion for ductile fracture. To model the elasto-plastic response, a classical finite strain formulation is extended by viscous regularization to account for the shear band localization prior to fracture. The compression–tension asymmetry, which becomes particularly important during crack propagation under cyclic loading, is incorporated by splitting the strain energy density into a tensile and compression part. In a comparative study based on benchmark problems, it is shown that the unified approach is indeed able to represent brittle and ductile fracture at finite strains and to ensure converging, mesh-independent solutions. Furthermore, the proposed approach is analyzed for cyclic loading, and it is shown that classical Wöhler curves can be represented.

Unified Convergence Analysis of Chebyshev–Halley Methods for Multiple Polynomial Zeros

In this paper, we establish two local convergence theorems that provide initial conditions and error estimates to guarantee the Q-convergence of an extended version of Chebyshev–Halley family of iterative methods for multiple polynomial zeros due to Osada (J. Comput. Appl. Math. 2008, 216, 585–599). Our results unify and complement earlier local convergence results about Halley, Chebyshev and Super–Halley methods for multiple polynomial zeros. To the best of our knowledge, the results about the Osada’s method for multiple polynomial zeros are the first of their kind in the literature. Moreover, our unified approach allows us to compare the convergence domains and error estimates of the mentioned famous methods and several new randomly generated methods.