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Di Yang

Publications and source records attributed to Di Yang.

At least 91 records · Page 5Linked to original sources
arXiv2022

Grothendieck's Dessins d'Enfants in a Web of Dualities. III

We identify the dessin partition function with the partition function of the Laguerre unitary ensemble (LUE). Combined with the result due to Cunden et al on the relationship between the LUE correlators and strictly monotone Hurwitz numbers introduced by Goulden et al, we then establish connection of dessin counting to strictly monotone Hurwitz numbers. We also introduce a correction factor for the dessin/LUE partition function, which plays an important role in showing that the corrected dessin/LUE partition function is a tau-function of the Toda lattice hierarchy. As an application, we use the approach of Dubrovin and Zhang for the computation of the dessin correlators. In physicists' terminology, we establish dualities among dessin counting, generalized Penner model, and $\mathbb{P}^1$-topological sigma model.

math-ph↗
arXiv2022

Latent Image Animator: Learning to Animate Images via Latent Space Navigation

Due to the remarkable progress of deep generative models, animating images has become increasingly efficient, whereas associated results have become increasingly realistic. Current animation-approaches commonly exploit structure representation extracted from driving videos. Such structure representation is instrumental in transferring motion from driving videos to still images. However, such approaches fail in case the source image and driving video encompass large appearance variation. Moreover, the extraction of structure information requires additional modules that endow the animation-model with increased complexity. Deviating from such models, we here introduce the Latent Image Animator (LIA), a self-supervised autoencoder that evades need for structure representation. LIA is streamlined to animate images by linear navigation in the latent space. Specifically, motion in generated video is constructed by linear displacement of codes in the latent space. Towards this, we learn a set of orthogonal motion directions simultaneously, and use their linear combination, in order to represent any displacement in the latent space. Extensive quantitative and qualitative analysis suggests that our model systematically and significantly outperforms state-of-art methods on VoxCeleb, Taichi and TED-talk datasets w.r.t. generated quality.

cs.CV↗
arXiv2022

The matrix-resolvent method to tau-functions for the nonlinear Schrödinger hierarchy

We extend the matrix-resolvent method of computing logarithmic derivatives of tau-functions to the nonlinear Schrödinger (NLS) hierarchy. Based on this method we give a detailed proof of a theorem of Carlet, Dubrovin and Zhang regarding the relationship between the Toda lattice hierarchy and the NLS hierarchy. As an application, we give an improvement of an algorithm of computing correlators in hermitian matrix models.

nlin.SI↗
arXiv2022

On the Hodge-BGW correspondence

We establish an explicit relationship between the partition function of certain special cubic Hodge integrals and the generalized Brezin--Gross--Witten (BGW) partition function, which we refer to as the Hodge-BGW correspondence. As an application, we obtain an ELSV-like formula for generalized BGW correlators.

math.AG↗
arXiv2021

Gelfand--Dickey hierarchy, generalized BGW tau-function, and $W$-constraints

Let $r\geq 2$ be an integer. The generalized BGW tau-function for the Gelfand--Dickey hierarchy of $(r-1)$ dependent variables (aka the $r$-reduced KP hierarchy) is defined as a particular tau-function that depends on $(r-1)$ constant parameters $d_1,\dots,d_{r-1}$. In this paper we show that this tau-function satisfies a family of linear equations, called the $W$-constraints of the second kind. The operators giving rise to the linear equations also depend on $(r-1)$ constant parameters. We show that there is a one-to-one correspondence between the two sets of parameters.

math-ph↗
arXiv2021

Tau-functions for the Ablowitz--Ladik hierarchy: the matrix-resolvent method

We extend the matrix-resolvent method for computing logarithmic derivatives of tau-functions to the Ablowitz--Ladik hierarchy. In particular, we derive a formula for the generating series of the logarithmic derivatives of an arbitrary tau-function in terms of matrix resolvents. As an application, we provide a way of computing certain integrals over the unitary group.

math-ph↗
arXiv2021

The Virasoro-like Algebra of a Frobenius Manifold

For an arbitrary calibrated Frobenius manifold, we construct an infinite dimensional Lie algebra, called the Virasoro-like algebra, which is a deformation of the Virasoro algebra of the Frobenius manifold. By using the Virasoro-like algebra we give a family of quadratic PDEs that are satisfied by the genus-zero free energy of the Frobenius manifold. We also derive, under the semisimplicity assumption, the Virasoro constraints for the corresponding abstract Hodge partition function.

math-ph↗
arXiv2021

Analysis and computation of a pressure-robust method for the rotation form of the stationary incompressible Navier-Stokes equations by using high-order finite elements

In this work, we develop a high-order pressure-robust method for the rotation form of the stationary incompressible Navier-Stokes equations. The original idea is to change the velocity test functions in the discretization of trilinear and right hand side terms by using an H(div)-conforming velocity reconstruction operator. In order to match the rotation form and error analysis, a novel skew-symmetric discrete trilinear form containing the reconstruction operator is proposed, in which not only the velocity test function is changed. The corresponding well-posed discrete weak formulation stems straight from the classical inf-sup stable mixed conforming high-order finite elements, and it is proven to achieve the pressure-independent velocity errors. Optimal convergence rates of H1, L2-error for the velocity and L2-error for the Bernoulli pressure are completely established. Adequate numerical experiments are presented to demonstrate the theoretical results and the remarkable performance of the proposed method.

math.NA↗
arXiv2021

UNIK: A Unified Framework for Real-world Skeleton-based Action Recognition

Action recognition based on skeleton data has recently witnessed increasing attention and progress. State-of-the-art approaches adopting Graph Convolutional networks (GCNs) can effectively extract features on human skeletons relying on the pre-defined human topology. Despite associated progress, GCN-based methods have difficulties to generalize across domains, especially with different human topological structures. In this context, we introduce UNIK, a novel skeleton-based action recognition method that is not only effective to learn spatio-temporal features on human skeleton sequences but also able to generalize across datasets. This is achieved by learning an optimal dependency matrix from the uniform distribution based on a multi-head attention mechanism. Subsequently, to study the cross-domain generalizability of skeleton-based action recognition in real-world videos, we re-evaluate state-of-the-art approaches as well as the proposed UNIK in light of a novel Posetics dataset. This dataset is created from Kinetics-400 videos by estimating, refining and filtering poses. We provide an analysis on how much performance improves on smaller benchmark datasets after pre-training on Posetics for the action classification task. Experimental results show that the proposed UNIK, with pre-training on Posetics, generalizes well and outperforms state-of-the-art when transferred onto four target action classification datasets: Toyota Smarthome, Penn Action, NTU-RGB+D 60 and NTU-RGB+D 120.

cs.CV↗
arXiv2021

On the spectral problem of the quantum KdV hierarchy

The spectral problem for the quantum dispersionless Korteweg-de Vries (KdV) hierarchy, aka the quantum Hopf hierarchy, is solved by Dubrovin. In this article, following Dubrovin, we study Buryak-Rossi's quantum KdV hierarchy. In particular, we prove a symmetry property and a non-degeneracy property for the quantum KdV Hamiltonians. On the basis of this we construct a complete set of common eigenvectors. The analysis underlying this spectral problem implies certain vanishing identities for combinations of characters of the symmetric group. We also comment on the geometry of the spectral curves of the quantum KdV hierarchy and we give a representation of the quantum dispersionless KdV Hamiltonians in terms of multiplication operators in the class algebra of the symmetric group.

math-ph↗
arXiv2021

On an extension of the generalized BGW tau-function

For an arbitrary solution to the Burgers--KdV hierarchy, we define the tau-tuple $(τ_1,τ_2)$ of the solution. We show that the product $τ_1τ_2$ admits Buryak's residue formula. Therefore, according to Alexandrov's theorem, $τ_1τ_2$ is a tau-function of the KP hierarchy. We then derive a formula for the affine coordinates for the point of the Sato Grassmannian corresponding to the tau-function $τ_1τ_2$ explicitly in terms of those for $τ_1$. Applications to the analogous open extension of the generalized BGW tau-function and to the open partition function are given.

math-ph↗
arXiv2021

VPN++: Rethinking Video-Pose embeddings for understanding Activities of Daily Living

Many attempts have been made towards combining RGB and 3D poses for the recognition of Activities of Daily Living (ADL). ADL may look very similar and often necessitate to model fine-grained details to distinguish them. Because the recent 3D ConvNets are too rigid to capture the subtle visual patterns across an action, this research direction is dominated by methods combining RGB and 3D Poses. But the cost of computing 3D poses from RGB stream is high in the absence of appropriate sensors. This limits the usage of aforementioned approaches in real-world applications requiring low latency. Then, how to best take advantage of 3D Poses for recognizing ADL? To this end, we propose an extension of a pose driven attention mechanism: Video-Pose Network (VPN), exploring two distinct directions. One is to transfer the Pose knowledge into RGB through a feature-level distillation and the other towards mimicking pose driven attention through an attention-level distillation. Finally, these two approaches are integrated into a single model, we call VPN++. We show that VPN++ is not only effective but also provides a high speed up and high resilience to noisy Poses. VPN++, with or without 3D Poses, outperforms the representative baselines on 4 public datasets. Code is available at https://github.com/srijandas07/vpnplusplus.

cs.CV↗
arXiv2021

On tau-functions for the KdV hierarchy

For an arbitrary solution to the KdV hierarchy, the generating series of logarithmic derivatives of the tau-function of the solution can be expressed by the basic matrix resolvent via algebraic manipulations. Based on this we develop in this paper two new formulae for the generating series by introducing a pair of wave functions of the solution. Applications to the Witten--Kontsevich tau-function, to the generalized Brézin--Gross--Witten (BGW) tau-function, as well as to a modular deformation of the generalized BGW tau-function which we call the Lamé tau-function are also given.

math-ph↗
arXiv2020

A discontinuous Galerkin method by patch reconstruction for convection-diffusion-reaction problems over polytopic meshes

In this article, using the weighted discrete least-squares, we propose a patch reconstruction finite element space with only one degree of freedom per element. As the approximation space, it is applied to the discontinuous Galerkin methods with the upwind scheme for the steady-state convection-diffusion-reaction problems over polytopic meshes. The optimal error estimates are provided in both diffusion-dominated and convection-dominated regimes. Furthermore, several numerical experiments are presented to verify the theoretical error estimates, and to well approximate boundary layers and/or internal layers.

math.NA↗
arXiv2020

The Loop Equation for Special Cubic Hodge Integrals

As the first step of proving the Hodge-FVH correspondence recently proposed in [19], we derive the Virasoro constraints and the Dubrovin--Zhang loop equation for special cubic Hodge integrals. We show that this loop equation has a unique solution, and provide a new algorithm for the computation of these Hodge integrals. We also observe the gap phenomenon for certain special cubic Hodge free energies.

math.AG↗
arXiv2020

On the solution of the coupled steady-state dual-porosity-Navier-Stokes fluid flow model with the Beavers-Joseph-Saffman interface condition

In this work, we propose a new analysis strategy to establish an a priori estimate of the weak solutions to the coupled steady-state dual-porosity-Navier-Stokes fluid flow model with the Beavers-Joseph-Saffman interface condition. The most advantage of our proposed method is that the a priori estimate and the existence result are independent of small data and the large viscosity restriction. Therefore the global uniqueness of the weak solution is naturally obtained.

math.AP↗