School of Mathematics and Statistics - Research Publications
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ItemNo Preview AvailableBenchmarking algorithm portfolio construction methods(Association for Computing Machinery, 2022-07-09)A portfolio is a set of algorithms, which run concurrently or interchangeably, whose aim is to improve performance by avoiding a bad selection of a single algorithm. Despite its high error tolerance, a carefully constructed portfolio, i.e., the smallest set of complementary algorithms, is expected to perform better than an arbitrarily constructed one. In this paper, we benchmark five algorithm portfolio construction methods, using as benchmark problems the ASLib scenarios, under a cross-validation regime. We examine the performance of each portfolio in terms of its riskiness, i.e., the existence of unsolved problems on the test set, and its robustness, i.e., the existence of an algorithm that solves most instances. The results demonstrate that two of these methods produce portfolios with the lowest risk, albeit with different levels of robustness.
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ItemNo Preview AvailableMaximum Spatial Perturbation Consistency for Unpaired Image-to-Image Translation(IEEE COMPUTER SOC, 2022)
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ItemNo Preview AvailableOff-lattice and parallel implementations of the pivot algorithm(IOP Publishing, 2021-12-09)Abstract The pivot algorithm is the most efficient known method for sampling polymer configurations for self-avoiding walks and related models. Here we introduce two recent improvements to an efficient binary tree implementation of the pivot algorithm: an extension to an off-lattice model, and a parallel implementation.
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ItemSemiglobal Practical Stability of a Class of Parameterized Networked Control Systems(IEEE, 2012-01-01)This paper studies a class of parameterized networked control systems that are designed via an emulation procedure. In the first step, a controller is designed ignoring network so that semiglobal practical stability is achieved for the closed-loop. In the second step, it is shown that if the same controller is emulated and implemented over a large class of networks, then the networked control system is also semiglobally practically asymptotically stable; in this case, the controller parameter needs to be sufficiently small and communication bandwidth sufficiently high.
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ItemDifferential operators on modular forms mod p(RIMS, 2019)We give a survey of recent work on the construction of differential operators on various types of modular forms (mod p) . We also discuss a framework for determining the effect of such operators on the mod p Galois representations attached to Hecke eigenforms.
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ItemAnalytic evaluation of Hecke eigenvalues for Siegel modular forms of degree two(Mathematical Sciences Publishers, 2019)The standard approach to evaluate Hecke eigenvalues of a Siegel modular eigenform F is to determine a large number of Fourier coefficients of F and then compute the Hecke action on those coefficients. We present a new method based on the numerical evaluation of F at explicit points in the upper half-space and of its image under the Hecke operators. The approach is more efficient than the standard method and has the potential for further optimization by identifying good candidates for the points of evaluation, or finding ways of lowering the truncation bound. A limitation of the algorithm is that it returns floating point numbers for the eigenvalues; however, the working precision can be adjusted at will to yield as close an approximation as needed.
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ItemLogic and the 2-Simplicial Transformer(International Conference on Learning Representations, 2020)We introduce the 2-simplicial Transformer, an extension of the Transformer which includes a form of higher-dimensional attention generalising the dot-product attention, and uses this attention to update entity representations with tensor products of value vectors. We show that this architecture is a useful inductive bias for logical reasoning in the context of deep reinforcement learning.
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ItemData-Driven Approach to Multiple-Source Domain Adaptation(PMLR, 2019)A key problem in domain adaptation is determining what to transfer across different domains. We propose a data-driven method to represent these changes across multiple source domains and perform unsupervised domain adaptation. We assume that the joint distributions follow a specific generating process and have a small number of identifiable changing parameters, and develop a data-driven method to identify the changing parameters by learning low-dimensional representations of the changing class-conditional distributions across multiple source domains. The learned low-dimensional representations enable us to reconstruct the target-domain joint distribution from unlabeled target-domain data, and further enable predicting the labels in the target domain. We demonstrate the efficacy of this method by conducting experiments on synthetic and real datasets.
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ItemGeometry-Consistent Generative Adversarial Networks for One-Sided Unsupervised Domain Mapping(IEEE, 2019)Unsupervised domain mapping aims to learn a function to translate domain X to Y by a function GXY in the absence of paired examples. Finding the optimal GXY without paired data is an ill-posed problem, so appropriate constraints are required to obtain reasonable solutions. One of the most prominent constraints is cycle consistency, which enforces the translated image by GXY to be translated back to the input image by an inverse mapping GYX. While cycle consistency requires the simultaneous training of GXY and GY X, recent studies have shown that one-sided domain mapping can be achieved by preserving pairwise distances between images. Although cycle consistency and distance preservation successfully constrain the solution space, they overlook the special properties that simple geometric transformations do not change the semantic structure of images. Based on this special property, we develop a geometry-consistent generative adversarial network (GcGAN), which enables one-sided unsupervised domain mapping. GcGAN takes the original image and its counterpart image transformed by a predefined geometric transformation as inputs and generates two images in the new domain coupled with the corresponding geometry-consistency constraint. The geometry-consistency constraint reduces the space of possible solutions while keep the correct solutions in the search space. Quantitative and qualitative comparisons with the baseline (GAN alone) and the state-of-the-art methods including CycleGAN and DistanceGAN demonstrate the effectiveness of our method.