On orthogonal tensors and best rank-one approximation ratio

As is well known, the smallest possible ratio between the spectral norm and the Frobenius norm of an $m \times n$ matrix with $m \le n$ is $1/\sqrt{m}$ and is (up to scalar scaling) attained only by matrices having pairwise orthonormal rows. In the present paper, the smallest possible ratio between spectral and Frobenius norms of $n_1 \times \dots \times n_d$ tensors of order $d$, also called the best rank-one approximation ratio in the literature, is investigated. The exact value is not known for most configurations of $n_1 \le \dots \le n_d$. Using a natural definition of orthogonal tensors over the real field (resp., unitary tensors over the complex field), it is shown that the obvious lower bound $1/\sqrt{n_1 \cdots n_{d-1}}$ is attained if and only if a tensor is orthogonal (resp., unitary) up to scaling. Whether or not orthogonal or unitary tensors exist depends on the dimensions $n_1,\dots,n_d$ and the field. A connection between the (non)existence of real orthogonal tensors of order three and the classical Hurwitz problem on composition algebras can be established: existence of orthogonal tensors of size $\ell \times m \times n$ is equivalent to the admissibility of the triple $[\ell,m,n]$ to the Hurwitz problem. Some implications for higher-order tensors are then given. For instance, real orthogonal $n \times \dots \times n$ tensors of order $d \ge 3$ do exist, but only when $n = 1,2,4,8$. In the complex case, the situation is more drastic: unitary tensors of size $\ell \times m \times n$ with $\ell \le m \le n$ exist only when $\ell m \le n$. Finally, some numerical illustrations for spectral norm computation are presented

VIBE: Topic-Driven Temporal Adaptation for Twitter Classification

Language features are evolving in real-world social media, resulting in the deteriorating performance of text classification in dynamics. To address this challenge, we study temporal adaptation, where models trained on past data are tested in the future. Most prior work focused on continued pretraining or knowledge updating, which may compromise their performance on noisy social media data. To tackle this issue, we reflect feature change via modeling latent topic evolution and propose a novel model, VIBE: Variational Information Bottleneck for Evolutions. Concretely, we first employ two Information Bottleneck (IB) regularizers to distinguish past and future topics. Then, the distinguished topics work as adaptive features via multi-task training with timestamp and class label prediction. In adaptive learning, VIBE utilizes retrieved unlabeled data from online streams created posterior to training data time. Substantial Twitter experiments on three classification tasks show that our model, with only 3% of data, significantly outperforms previous state-of-the-art continued-pretraining methods.Comment: accepted by EMNLP 202

Global dynamics for a class of infection-age model with nonlinear incidence

In this paper, we propose an HBV viral infection model with continuous age structure and nonlinear incidence rate. Asymptotic smoothness of the semi-flow generated by the model is studied. Then we caculate the basic reproduction number and prove that it is a sharp threshold determining whether the infection dies out or not. We give a rigorous mathematical analysis on uniform persistence by reformulating the system as a system of Volterra integral equations. The global dynamics of the model is established by using suitable Lyapunov functionals and LaSalle's invariance principle. We further investigate the global behaviors of the HBV viral infection model with saturation incidence through numerical simulations

High-pressure and high-temperature synthesis of heavy lanthanide sesquisulfides Ln2S3 ( Ln=Yb and Lu)

Detailed pressure-temperature phase diagrams of heavy lanthanide sesquisulfides Ln2S3 (Ln = Yb and Lu) have been investigated by in-situ x-ray diffraction experiments under high pressure and high temperature using synchrotron radiation and multi-anvil press. Based on the results of the in-situ observation, the single γ-phase (Th3P4-type structure, I3d) samples of Ln2S3 (Ln = Yb and Lu) have been synthesized under high pressure. The physical properties of the compounds were studied by electrical resistivity, specific heat, and magnetic susceptibility measurements between 2 K and 300 K

Recent advances on Schr\"odinger equations with dissipative nonlinearities

We give a survey on recent developments on nonlinear Schr\"odinger equations with dissipative structure based on the authors' recent works.Comment: 15 pages. arXiv admin note: text overlap with arXiv:2204.0732

Large time asymptotics for a cubic nonlinear Schr\"odinger system in one space dimension, II

This is a sequel to the paper "Large time asymptotics for a cubic nonlinear Schr\"odinger system in one space dimension" by the same authors. We continue to study the Cauchy problem for the two-component system of cubic nonlinear Schr\"odinger equations in one space dimension. We provide criteria for large time decay or non-decay in $L^2$ of the small amplitude solutions in terms of the Fourier transforms of the initial data.Comment: 6 page

Multi-Body Interactions of D-Particles in Supergravity and Matrix Theory

We present detailed analyses of the 3-body interactions of D-particles from both sides of 11 dimensional supergravity and Matrix theory. In supergravity, we derive a complete expression for the classical bosonic effective action for D-particles including 2-and 3-body interaction terms. In Matrix theory, we compute 1-particle irreducible contributions to the eikonal phase shift in the two-loop approximation. The results precisely agree with the predictions from supergravity and thus provide a strong support to the discrete light-cone interpretation of the Matrix-theory conjecture as a possible nonperturbative definition of M-theory.Comment: 38 pages, no figures, a few minor typos are correcte

The noncanonical BMP signaling pathway plays an important role in club cell regeneration

The bronchiole is a major site for the development of several life‐threatening disorders, including chronic obstructive pulmonary disease and lung adenocarcinomas. The bronchiolar epithelium is composed of club cells and ciliated epithelial cells, with club cells serving as progenitor cells. Presently, the identity of the cells involved in regeneration of bronchiolar epithelium and the underlying mechanisms remain incompletely understood. Here, we show that Prrx1, a homeobox transcription factor, can mark club cells in adult mice during homeostasis and regeneration. We further show that the noncanonical signaling pathway of BMPs, BMPR1A‐Tak1‐p38MAPK, plays a critical role in club cell regeneration. Ablation of Bmpr1a, Tak1, or Mapk14 (encoding p38α) in Prrx1+ club cells caused minimal effect on bronchiolar epithelium homeostasis, yet it resulted in severe defects in club cell regeneration and bronchiole repair in adult mice. We further show that this pathway supports proliferation and expansion of the regenerating club cells. Our findings thus identify a marker for club cells and reveal a critical role for the BMP noncanonical pathway in club cell regeneration.Schematic representation of our results showing the critical roles of the noncanonical signaling pathway of BMPs, (BMPR1A‐Tak1‐p38MAPK) in club cell regeneration. Naphthalene (NA) is metabolized by CYP‐2F2, which is expressed exclusively in club cells, generating cytotoxic epoxide that kills the club cells within 1.5 days after NA exposure. Under normal conditions, hyperplastic growth occurs at day 3 and the bronchiolar epithelium is restored at day 7. We show that ablation of Bmpr1a, Tak1, or Mapk14 (encoding p38α) in club cells resulted in severe defects in regeneration and bronchiole repair in adult mice.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/154263/1/stem3125_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/154263/2/stem3125.pd