Sub-Hopf algebras of the Steenrod algebra and the Singer transfer

The Singer transfer provides an interesting connection between modular representation theory and the cohomology of the Steenrod algebra. We discuss a version of `Quillen stratification' theorem for the Singer transfer and its consequences.Comment: This is the version published by Geometry & Topology Monographs on 14 November 200

Strict partitions and discrete dynamical systems

AbstractWe prove that the set of partitions with distinct parts of a given positive integer under dominance ordering can be considered as a configuration space of a discrete dynamical model with two transition rules and with the initial configuration being the singleton partition. This allows us to characterize its lattice structure, fixed point, and longest chains as well as their length, using Chip Firing Game theory. Finally, we study the recursive structure of infinite extension of the lattice of strict partitions

StyleID: Identity Disentanglement for Anonymizing Faces

Privacy of machine learning models is one of the remaining challenges that hinder the broad adoption of Artificial Intelligent (AI). This paper considers this problem in the context of image datasets containing faces. Anonymization of such datasets is becoming increasingly important due to their central role in the training of autonomous cars, for example, and the vast amount of data generated by surveillance systems. While most prior work de-identifies facial images by modifying identity features in pixel space, we instead project the image onto the latent space of a Generative Adversarial Network (GAN) model, find the features that provide the biggest identity disentanglement, and then manipulate these features in latent space, pixel space, or both. The main contribution of the paper is the design of a feature-preserving anonymization framework, StyleID, which protects the individuals' identity, while preserving as many characteristics of the original faces in the image dataset as possible. As part of the contribution, we present a novel disentanglement metric, three complementing disentanglement methods, and new insights into identity disentanglement. StyleID provides tunable privacy, has low computational complexity, and is shown to outperform current state-of-the-art solutions.Comment: Accepted to Privacy Enhancing Technologies Symposium (PETS), July 2023. Will appear in Proceedings on Privacy Enhancing Technologies (PoPETs), volume 1, 2023. 15 pages including references and appendix, 16 figures, 5 table

Linear topological invariants of spaces of holomorphic functions in infinite dimension

It is shown that if $E$ is a Frechet space with the strong dual $E^*$ then $H_b(E^*)$, the space of holomorphic functions on $E^*$ which are bounded on every bounded set in $E^*$, has the property $(DN)$ when $E\in (DN)$ and that $H_b(E^*)\in(\Omega)$ when $E\in (\Omega)$ and either $E^*$ has an absolute basis or $E$ is a Hilbert-Frechet-Montel space. Moreover the complementness of ideals $J(V)$ consisting of holomorphic functions on $E^*$ which are equal to $0$ on $V$ in $H(E^*)$ for every nuclear Frechet space $E$ with $E\in (DN)\cap (\Omega)$ is stablished when $J(V)$ is finitely generated by continuous polynomials on $E^*$

VNINDEX INDEX: A VIEW FROM QUANTITATIVE ANALYSIS

The financial strategy towards 2030 in Decision no. 368/QD-TTg enacted on 21/3/2022 by the Vietnam Prime Minister had set developmental goals for the stock market to become a channel to promote mid-and-long term capital raising for the economy, to continue changing the structure to be more appropriate for the monetary, the capital, the stock, and the bonds market. In the past two years, the stock market in Vietnam has manifested impressive growth. A prime example is the active growth of private investors. However, many challenges and loopholes still exist in the stock market. The stock market is a special market as the fluctuation of the VN-index index is affected by many factors including the expectations of the investor. When the market shows trends of increases in points then investors expect the next session to grow as well, leading to a rise in sales even for stocks with inflating costs, thus the VNindex will increase and vice versa. The structure of the econometric is utilized to assess the impacts of the VN-index of the previous month on the index of the following month on the Vietnamese stock market in the period from January 2019 to May 2022. The conclusion of the quantitative analysis shows that if the VN-index of the previous month increases by 1% then the VNindex of the following month will increase by 0.965% or vice versa. From the results of the analysis, the research team has proposed a few discussion points intending to stabilize the stock market in the upcoming time and develop the market according to the financial strategy towards 2030 in Decision no. 368/QD-TTg by the Vietnam Prime Ministe

SOME GLYCOSIDES ISOLATED FROM DESMODIUM GANGETICUM (L.) DC. OF VIET NAM

From the methanol extract of the leaves of Desmodium gangeticum collected in Me Linh, Ha Noi, we isolated 5 compounds. In which, there are four glycosides including (6S,9R)-roseoside (1), kaempferol-3-O-rutinoside (nicotiflorin) (2),  quercetin-3-O-rutinoside (rutin) (3), β-sitosterol-3-O- β-D-glucopyranoside (4), and the other is protocatechuic acid (5). Kaempferol-3-O-rutinoside (2) was isolated from Desmodium gangeticum for the first time while (6S,9R)-roseoside (1) was isolated from the genus Desmodium for the first time. Their structures were determined by 1D and 2D NMR spectra

Impact of Capital Structure and Cash Holdings on Firm Value: Case of Firms Listed on the Ho Chi Minh Stock Exchange

This study analyses the impact of capital structure on cash holdings and the impact of capital structure and cash holdings on the value of firms listed on the Ho Chi Minh Stock Exchange (HOSE). With data from the financial statements of 105 firms listed on HOSE since 2009 – 2014 and using the GLS method, results show that cash holdings are positively related to the firm value; short - term debt is negatively related to firm value; the impact of long - term debt on the firm value is not statistically significant; short and long - term debt are negatively related to cash holdings. Keywords: Capital Structure, Cash Holdings, Firm Value JEL Classificaitons: G30, G31, G3