Searcharxiv⌕ Search

arXiv subjects

Hongyu He

Publications and source records attributed to Hongyu He.

At least 37 records · Page 2Linked to original sources
arXiv2020

OpenHI2 -- Open source histopathological image platform

Transition from conventional to digital pathology requires a new category of biomedical informatic infrastructure which could facilitate delicate pathological routine. Pathological diagnoses are sensitive to many external factors and is known to be subjective. Only systems that can meet strict requirements in pathology would be able to run along pathological routines and eventually digitized the study area, and the developed platform should comply with existing pathological routines and international standards. Currently, there are a number of available software tools which can perform histopathological tasks including virtual slide viewing, annotating, and basic image analysis, however, none of them can serve as a digital platform for pathology. Here we describe OpenHI2, an enhanced version Open Histopathological Image platform which is capable of supporting all basic pathological tasks and file formats; ready to be deployed in medical institutions on a standard server environment or cloud computing infrastructure. In this paper, we also describe the development decisions for the platform and propose solutions to overcome technical challenges so that OpenHI2 could be used as a platform for histopathological images. Further addition can be made to the platform since each component is modularized and fully documented. OpenHI2 is free, open-source, and available at https://gitlab.com/BioAI/OpenHI.

q-bio.QM↗
arXiv2019

Stochastic Channel-Based Federated Learning for Medical Data Privacy Preserving

Artificial neural network has achieved unprecedented success in the medical domain. This success depends on the availability of massive and representative datasets. However, data collection is often prevented by privacy concerns and people want to take control over their sensitive information during both training and using processes. To address this problem, we propose a privacy-preserving method for the distributed system, Stochastic Channel-Based Federated Learning (SCBF), which enables the participants to train a high-performance model cooperatively without sharing their inputs. Specifically, we design, implement and evaluate a channel-based update algorithm for the central server in a distributed system, which selects the channels with regard to the most active features in a training loop and uploads them as learned information from local datasets. A pruning process is applied to the algorithm based on the validation set, which serves as a model accelerator. In the experiment, our model presents better performances and higher saturating speed than the Federated Averaging method which reveals all the parameters of local models to the server when updating. We also demonstrate that the saturating rate of performance could be promoted by introducing a pruning process. And further improvement could be achieved by tuning the pruning rate. Our experiment shows that 57% of the time is saved by the pruning process with only a reduction of 0.0047 in AUCROC performance and a reduction of 0.0068 in AUCPR.

cs.LG↗
arXiv2017

Gan-Gross-Prasad Conjecture for U(p,q)

In this paper, we give a proof of the Gan-Gross-Prasad conjecture for the discrete series of U(p,q). Given a discrete series representation $D(λ)$ in terms of the Harish-Chandra parameter, the restriction of $D(λ)$ to U(p-1,q) contains $D(μ)$ as a subrepresentation if and only if $λ$ and $μ$ interlaces in a very special way.

math.RT↗
arXiv2015

On Matrix-Valued Square Integrable Positive Definite Functions

In this paper, we study matrix valued positive definite functions on a unimodular group. We generalize two important results of Godement on square integrable positive definite functions to matrix valued square integrable positive definite functions. We show that a matrix-valued continuous $L^2$ positive definite function can always be written as a convolution of a $L^2$ positive definite function with itself. We also prove that, given two $L^2$ matrix valued positive definite functions $Φ$ and $Ψ$, $\int_G Trace(Φ(g) \bar{Ψ(g)}^t) d g \geq 0$. In addition this integral equals zero if and only if $Φ* Ψ=0$. Our proofs are operator-theoretic and independent of the group.

math.OA↗
arXiv2015

Generalized matrix coefficients of Unitary Representations

This is an introductory note concerning the distribution vectors in a unitary representation of a Lie group. We discuss the definition of matrix coefficients associated with a pair of distributions and how one can compute them. Most of the results are known to some expert, but missing in the literature.

math.FA↗
arXiv2015

Orbits on Lagrangian Grassmanian

The purpose of this note is to give a classification of the orbital structure of certain reductive group actions on the Lagrangian Grassmanian. The groups under consideration are $Sp \times Sp$ and $GL$. The classification of $Sp \times Sp$ orbits is well-known and the classification of $GL$-orbits is not known. We also compute the isotropy group. Some of the results here will be used to analyze the representations of the universal covering of the symplectic group on the Shilov boundary.

math.GR↗
arXiv2015

Wave Front Sets of Reductive Lie Group Representations

If $G$ is a Lie group, $H\subset G$ is a closed subgroup, and $τ$ is a unitary representation of $H$, then the authors give a sufficient condition on $ξ\in i\mathfrak{g}^*$ to be in the wave front set of $\operatorname{Ind}_H^Gτ$. In the special case where $τ$ is the trivial representation, this result was conjectured by Howe. If $G$ is a real, reductive algebraic group and $π$ is a unitary representation of $G$ that is weakly contained in the regular representation, then the authors give a geometric description of $\operatorname{WF}(π)$ in terms of the direct integral decomposition of $π$ into irreducibles. Special cases of this result were previously obtained by Kashiwara-Vergne, Howe, and Rossmann. The authors give applications to harmonic analysis problems and branching problems.

math.RT↗
arXiv2013

The Continuous Spectrum in Discrete Series Branching Laws

If $G$ is a reductive Lie group of Harish-Chandra class, $H$ is a symmetric subgroup, and $π$ is a discrete series representation of $G$, the authors give a condition on the pair $(G,H)$ which guarantees that the direct integral decomposition of $π|_H$ contains each irreducible representation of $H$ with finite multiplicity. In addition, if $G$ is a reductive Lie group of Harish-Chandra class, and $H\subset G$ is a closed, reductive subgroup of Harish-Chandra class, the authors show that the multiplicity function in the direct integral decomposition of $π|_H$ is constant along `continuous parameters'. In obtaining these results, the authors develop a new technique for studying multiplicities in the restriction $π|_H$ via convolution with Harish-Chandra characters. This technique has the advantage of being useful for studying the continuous spectrum as well as the discrete spectrum.

math.RT↗
arXiv2013

Certain Unitary Langlands-Vogan Parameters for Special Orthogonal Groups I

A Langlands parameter, in the Langlands dual group, can be decomposed into a product of a tempered parameter and a positive quasi-character. Fixing a tempered parameter, Arthur conjectured that positive quasi-characters corresponding to certain weighted Dynkin diagrams for the centralizer of the tempered parameter will yield unitary representations. In this paper, we treat one basic case in Arthur's conjecture for the special orthogonal groups. We establish the unitarity for a class of Langlands-Vogan parameters in Arthur's packet.

math.RT↗
arXiv2011

Symmetric Subgroup Actions on Isotropic Grassmannians

Let G be the group preserving a nondegenerate sesquilinear form on a vector space V, and H a symmetric subgroup of G of the type G1 x G2. We explicitly parameterize the H-orbits in the Grassmannian of r-dimensional isotropic subspaces of V by a complete set of H-invariants. We describe the Bruhat order in terms of the majorization relationship over a diagram of these H-invariants. The inclusion order, the stabilizer, the orbit dimension, the open H-orbits, the decompositions of an H orbit into H\cap G_0 and H_0 orbits are also explicitly described.

math.RT↗
arXiv2011

Unitary Representations and Heisenberg Parabolic Subgroup

In this paper, we study the restriction of an irreducible unitary representation $π$ of the universal covering $\widetilde{Sp}_{2n}(\mb R)$ to a Heisenberg maximal parabolic group $\tilde P$. We prove that if $π|_{\tilde P}$ is irreducible, then $π$ must be a highest weight module or a lowest weight module. This is in sharp constrast with the $GL_n(\mathbb R)$ case. In addition, we show that for a unitary highest or lowest weight module, $π|_{\tilde P}$ decomposes discretely. We also treat the groups $U(p,q)$ and $O^*(2n)$.

math.RT↗
arXiv2006

Eigenvectors and Reconstruction

In this paper, I study the simple eigenvectors of two hypomorphic matrices using linear algebra. I give new proofs of results of Godsil and MaKay.

math.CO↗
arXiv2006

Reconstruction and Higher Dimensional Geometry

In this paper, we give a new proof on a Theorem of Tutte which says that the determinants of the adjacency matrices of two hypomorphic graphs are the same. We also study the lowest eigenvectors.

math.CO↗
arXiv2005

Theta Correspondence and Quantum Induction

In his article "Transcending Classical Invariant Theory" (J.A.M.S., 1989, Vol 2), Roger Howe established a correspondence between representations of a dual pair of reductive groups. This correspondence is known as Howe's correspondence or local theta correspondence. In my paper "Unitary Representations and Theta Correspondence for Classical Group of Type I"(to appear in J. Func. Anal.), we proved that theta correspondence over the real field preserves unitarity under certain restrictions, generalizing some results of Jian-Shu Li (Invent. Math., Vol 97, 1989). In this paper, we study the compositions of theta correspondences. Under certain favorable conditions, we prove that the composition of theta correspodence yields unitary representations. We call this process quantum induction. Quantum induction resembles parabolic induction in various ways. Some results in this paper were announced at ICM-2002.

math.RT↗