http://bura.brunel.ac.uk/handle/2438/8627 2026-06-21T04:14:38Z http://bura.brunel.ac.uk/handle/2438/33442 Title: Convergent Lifted Lasserre Hierarchy of SDPs for Minimizing Expectation of Piecewise Polynomial Loss over Wasserstein Balls Authors: Dizon, NDV; Huang, QY; Chuong, TD; Li, G; Jeyakumar, V Abstract: This paper investigates the minimization of the expectation of piecewise polynomial loss functions over Wasserstein balls. This optimization problem often appears as a key sub-problem of distributionally robust optimization problems. We establish the asymptotic convergence of a hierarchy of semi-definite programming (SDP) relaxations, providing a framework for approximating the optimal values of these inherently infinite-dimensional optimization problems. A central foundational contribution is the development of a new lifted positivity certificate: we demonstrate that piecewise polynomials positive over Archimedean basic semi-algebraic sets admit a structured system of sum-of-squares (SOS) representations. Furthermore, we prove that the proposed hierarchy achieves finite convergence under suitable conditions when the defining polynomials are convex. The practical utility and versatility of this approach are demonstrated via numerical experiments in revenue estimation and portfolio optimization. Description: Data Availability: All data generated and analyzed in this study are provided within the article. The data used in the numerical experiments were generated randomly, and we have clearly described the procedure for reproducing them. 2026-05-08T00:00:00Z http://bura.brunel.ac.uk/handle/2438/33237 Title: Higher mode filtering: optimum attenuation in a continuum of exceptional points Authors: Lawrie, JB; Afzal, M Abstract: ... Description: ... 2026-01-01T00:00:00Z http://bura.brunel.ac.uk/handle/2438/33226 Title: Mixed topics on geometry of varieties of Fano type Authors: Jiao, Dongchen Abstract: In this thesis, we investigate the deformation properties of Fano threefolds and the birational ge-ometry of foliations. First, we try to find compactification of several families of Fano threefolds. Then we give a description of the connections between foliated minimal models. Finally, we will discuss geometric properties of Fano foliations. This thesis contains results of (1), (26), (19) and some recent independent work. Description: This thesis was submitted for the award of Doctor of Philosophy and was awarded by Brunel University London 2025-01-01T00:00:00Z http://bura.brunel.ac.uk/handle/2438/32954 Title: Jiangfeng Wang, Keming Yu and Rong Jiang's contribution to the Discussion of ‘Augmented balancing weights as linear regression’ by Bruns-Smith et al Authors: Wang, J; Yu, K; Jiang, R Abstract: This is an interesting and well-executed paper that makes a substantial contribution to the literature on semiparametric causal inference, elegantly bridging the seemingly distinct fields of balancing weights and regression adjustment. ... Description: Discussion Paper Contribution. 2026-01-13T00:00:00Z