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Beamforming design for extremely large-scale multiple-input multiple-output (XL-MIMO) systems is challenging due to prohibitive computational complexity and complex near-field propagation effects. To address this, this paper introduces a…
We present higher order polynomial algebras which are the dynamical symmetry algebras of a wide class of multi-mode boson systems in non-linear optics. We construct their unitary representations and the corresponding single-variable…
Line features are valid complements for point features in man-made environments. 3D-2D constraints provided by line features have been widely used in Visual Odometry (VO) and Structure-from-Motion (SfM) systems. However, how to accurately…
We employ the (dynamical) density matrix renormalization group technique to investigate the ground-state properties of the Bose-Hubbard model with nearest-neighbor transfer amplitudes t and local two-body and three-body repulsion of…
This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…
Regularization method and Bayesian inverse method are two dominating ways for solving inverse problems generated from various fields, e.g., seismic exploration and medical imaging. The two methods are related with each other by the MAP…
Generalized linear mixed models are useful in studying hierarchical data with possibly non-Gaussian responses. However, the intractability of likelihood functions poses challenges for estimation. We develop a new method suitable for this…
The size of datasets has been increasing rapidly both in terms of number of variables and number of events. As a result, the empty space phenomenon and the curse of dimensionality complicate the extraction of useful information. But, in…
A Bose-Hubbard model, describing bosons in a harmonic trap with a superimposed optical lattice, is studied using a fast and accurate variational technique (MF+NRG): the Gutzwiller mean-field (MF) ansatz is combined with a Numerical…
We consider the Wess-Zumino-Witten theory to obtain the functional integral bosonization of the Thirring-Wess model with an arbitrary regularization parameter. Proceeding a systematic of decomposing the Bose field algebra into…
We study Lefschetz fixed point formulas for constructible sheaves with higher-dimensional fixed point sets. Under fairly weak assumptions, we prove that the local contributions from them are expressed by some constructible functions…
In this article, we outline a version of a balayage formula in probabilistic potential theory adapted to measure-preserving dynamical systems. This balayage identity generalizes the property that induced maps preserve the restriction of the…
We propose an accurate and interpretable fine-grained cross-view localization method that estimates the 3 Degrees of Freedom (DoF) pose of a ground-level image by matching its local features with a reference aerial image. Unlike prior…
We prove the local well-posedness of the 3D free-boundary incompressible elastodynamics with surface tension describing the motion of an elastic medium in a periodic domain with a moving graphical surface. The deformation tensor is assumed…
Monocular 3D human pose and shape estimation is an ill-posed problem since multiple 3D solutions can explain a 2D image of a subject. Recent approaches predict a probability distribution over plausible 3D pose and shape parameters…
In the rapidly evolving field of computer vision, the task of accurately estimating the poses of multiple individuals from various viewpoints presents a formidable challenge, especially if the estimations should be reliable as well. This…
We establish a sharp asymptotic formula for the number of rational points up to a given height and within a given distance from a hypersurface. Our main innovation is a bootstrap method that relies on the synthesis of Poisson summation,…
We present a new method for stochastic shape optimisation of engineering structures. The method generalises an existing deterministic scheme, in which the structure is represented and evolved by a level-set method coupled with mathematical…
Bayesian optimization (BO) is a popular technique for sequential black-box function optimization, with applications including parameter tuning, robotics, environmental monitoring, and more. One of the most important challenges in BO is the…
A three-parameter integrable deformation of $\mathbb{Z}_4$ permutation supercosets is constructed. These supercosets are of the form $ {\widehat{F}} / {F_0}$ where $F_0$ is the bosonic diagonal subgroup of the product supergroup…