arXiv subjects

Hao Chang

Publications and source records attributed to Hao Chang.

43 records · Page 3Linked to original sources

arXiv2017

Skin cancer reorganization and classification with deep neural network

As one kind of skin cancer, melanoma is very dangerous. Dermoscopy based early detection and recarbonization strategy is critical for melanoma therapy. However, well-trained dermatologists dominant the diagnostic accuracy. In order to solve this problem, many effort focus on developing automatic image analysis systems. Here we report a novel strategy based on deep learning technique, and achieve very high skin lesion segmentation and melanoma diagnosis accuracy: 1) we build a segmentation neural network (skin_segnn), which achieved very high lesion boundary detection accuracy; 2) We build another very deep neural network based on Google inception v3 network (skin_recnn) and its well-trained weight. The novel designed transfer learning based deep neural network skin_inceptions_v3_nn helps to achieve a high prediction accuracy.

cs.CV↗

arXiv2016

Finite group schemes of $p$-rank $\leq1$

Let $\mathcal{G}$ be a finite group scheme over an algebraically closed field $k$ of characteristic ${\rm char}(k)=p\geq 3$. In generalization of the familiar notion from the modular representation theory of finite groups, we define the $p$-rank $\mathsf{rk}_p(\mathcal{G})$ of $\mathcal{G}$ and determine the structure of those group schemes of $p$-rank $1$, whose linearly reductive radical is trivial. The most difficult case concerns infinitesimal groups of height $1$, which correspond to restricted Lie algebras. Our results show that group schemes of $p$-rank $\leq 1$ are closely related to those being of finite or domestic representation type.

math.RT↗

arXiv2016

A note on the rank of a restricted Lie algebra

In this short note, we study the rank of a restricted Lie algebra $(\mathfrak{g},[p])$ and give some applications, which concerns the dimensions of non-trivial irreducible modules. We also compute the rank of the restricted contact algebra $K(n)$.

math.RA↗

arXiv2016

Toral stabilizers of restricted Lie algebras

This paper investigates the toral stabilizer of a finite-dimensional restricted Lie algebra $(\mathfrak{g},[p])$, defined over an algebraically closed field $k$ of positive characteristic. We compute the group of toral stabilizers of some simple Lie algebras and give a new characterization of the solvable restricted Lie algebras. Moreover, we determine the subalgebra structure of exceptional simple Lie algebras in good characteristic. We also provide applications, which concern the distribution of weight spaces.

math.RA↗

arXiv2014

Adjoint quotient maps for restricted Lie algebras Wn and Sn

We give an explicit description of adjoint quotient maps for Jacobson-Witt algebra Wn and special algebra Sn. An analogue of Kostant's differential criterion of regularity is given for Wn. Furthermore, we describe the fiber of adjoint quotient map for Sn and construct the analogs of Kostant's transverse slice. In addition, we analysis the nilpotent elements and generalize some Premet's results to Sn.

math.RA↗

arXiv2013

Nilpotent commuting varieties of the Witt algebra

Let $\mathfrak{g}$ be the $p$-dimensional Witt algebra over an algebraically closed field $k$ of characteristic $p>3$. Let $\mathscr{N}={x\in\ggg\mid x^{[p]}=0}$ be the nilpotent variety of $\mathfrak{g}$, and $\mathscr{C}(\mathscr{N}):=\{(x,y)\in \mathscr{N}\times\mathscr{N}\mid [x,y]=0\}$ the nilpotent commuting variety of $\mathfrak{g}$. As an analogue of Premet's result in the case of classical Lie algebras [A. Premet, Nilpotent commuting varieties of reductive Lie algebras. Invent. Math., 154, 653-683, 2003.], we show that the variety $\mathscr{C}(\mathscr{N})$ is reducible and equidimensional. Irreducible components of $\mathscr{C}(\mathscr{N})$ and their dimension are precisely given. Furthermore, the nilpotent commuting varieties of Borel subalgebras are also determined.

math.RT↗

arXiv2012

Borel subalgebras of the Witt algebra $W_1$

Let $\mathbb{F}$ be an algebraically closed field of characteristic $p>3$, and $\ggg$ the $p$-dimensional Witt algebra over $\mathbb{F}$. Let $\N$ be the nilpotent cone of $\ggg$. Explicit description of $\N$ is given, so that the conjugacy classes of Borel subalgebras of $\ggg$ under the automorphism group are determined. In contrast with only one conjugacy class of Borel subalgebras in a classical simple Lie algebra, there are two conjugacy classes of Borel subalgebras in $\ggg$. The representatives of conjugacy classes of Borel subalgebras, i.e., the so-called standard Borel subalgebras, are precisely given.

math.RT↗