Abstract:
This talk is the first part
of a series of lectures on the sparse
representation and dictionary learning with applications to image processing. This lecture will cover the
following topics:
(1) Sparse
representation problem
(2) Alternating
direction method of multipliers
(3) Application
to signal denoising
(4) Sparse
dictionary learning problem
(5)
Solving
sparse
dictionary learning problem
Abstract：
Categorification is the process
of finding hidden higher level structure. In this talk, I will introduce a new
class of algebra, which is called the shifted q=0 affine algebra. Our
motivation comes from the categorification of quantum groups and their actions
on categories. Then I will explain how the shifted q=0 affine algebra acts on
categories by using the language of Fourier-Mukai transformations. The kernels
are induced by natural correspondences on the bounded derived categories of
coherent sheaves on Grassmannians or partial flag varieties. Finally, if time
permits, I may discuss some further directions.
Abstract：
深度學習的生成模型，近年有許多長足的進展，適合用來生成圖片。對於點陣字體，也能達到一定的效果。 但向量字型多數是由 Bézier curve 描述外框，與一般圖片有許多不同特性。而在產業應用上，對於品質的要求，以及問題的重點也會有所不同。 這次會分享會先簡單介紹一下先關背景以及在產業應用上的困難點， 然後會介紹如何利用不同技術，處理中文字型變化、點陣字、向量字的一些經驗。包含一些早期的結果、常見的方式與最近的案例的一些不同處理方式的想法。
Abstract：
Today, the field of microswimmers
covers an extremely wide panel of systems going from prokaryotic and eukaryotic
microorganisms (such as bacteria, algae, leukocytes, and so on) to artificial
microswimmers. A prototypical example of the latter is a Janus-like particle,
named after the two-faced Roman god; their motion originates from the asymmetry
of their surface properties. Here, by contrast, we focus on the
diffusiophoretic system without such an anisotropic restriction. To investigate
the dynamics of the diffusiophoretic particles, we first proposed a simple and
efficient class of direct solvers for Poisson equation in finite or infinite
domains related to spherical geometry. The solver was developed based on
truncated spherical harmonics expansion, where the differential mode equations
were solved by second-order finite difference method without handling
coordinate singularities. We then applied the solver to study the fluid flow
and solute coupled nonlinear system. Numerical experiments suggested that the
particle can achieve a spontaneous symmetry-breaking unidirectional motion at
moderate Peclet numbers, whereas the particle motion becomes chaotic in high
Peclet number regimes. The statistical analysis illustrates the
run-and-tumble-like nature at short times and diffusive nature at long times
without any source of noise. Such results show evidence that the complicated
motions may already be hidden in purely isotropic media due to the intrinsic
nonlinearities of the problem.
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