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Mathematics, Volume 12, Issue 11

June-1 2024 - 166 articles

Cover Story: Topic modeling is a widely used tool in text analysis, aiming to extract meaningful 'topics' from a collection of documents. This paper investigates the optimal statistical guarantees for estimating a topic model. The authors introduce a new normalized word count matrix and provide a sharp entry-wise eigenvector analysis for this matrix. These results are used to enhance an existing spectral algorithm, Topic-SCORE, for topic modeling. The authors demonstrate that the error rate of the enhanced algorithm is minimax optimal across the entire parameter regime of interest. Compared to existing results, the improvement is particularly significant in the challenging regime where all documents are short. View this paper
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Articles (166)

  • Article
  • Open Access
1,404 Views
13 Pages

6 June 2024

The discrete Legendre transform is a powerful tool for analyzing the properties of convex lattice sets. In this paper, for t>0, we study a class of convex lattice sets and establish a relationship between vertices of the polar of convex lattice se...

  • Article
  • Open Access
1 Citations
1,461 Views
12 Pages

An Efficient Iterative Approach for Hermitian Matrices Having a Fourth-Order Convergence Rate to Find the Geometric Mean

  • Tao Liu,
  • Ting Li,
  • Malik Zaka Ullah,
  • Abdullah Khamis Alzahrani and
  • Stanford Shateyi

6 June 2024

The target of this work is to present a multiplication-based iterative method for two Hermitian positive definite matrices to find the geometric mean. The method is constructed via the application of the matrix sign function. It is theoretically inve...

  • Article
  • Open Access
1,362 Views
20 Pages

6 June 2024

Due to the Jacobian matrix rank reduction near singularities, applying numerical methods to study PMs’ motion stability at singularities is quite difficult. As a result, there is a scarcity of literature on the investigation of PMs’ dynam...

  • Article
  • Open Access
1,396 Views
20 Pages

6 June 2024

This paper investigates the existence of common fixed points for mappings satisfying generalized rational type contractive conditions in the framework of bicomplex valued metric spaces. Our findings extend well-established results in the existing lit...

  • Feature Paper
  • Article
  • Open Access
1 Citations
2,288 Views
14 Pages

Flexible and Compact MLWE-Based KEM

  • Wenqi Liang,
  • Zhaoman Liu,
  • Xuyang Zhao,
  • Yafang Yang and
  • Zhichuang Liang

6 June 2024

In order to resist the security risks caused by quantum computing, post-quantum cryptography (PQC) has been a research focus. Constructing a key encapsulation mechanism (KEM) based on lattices is one of the promising PQC routines. The algebraically s...

  • Article
  • Open Access
1 Citations
3,553 Views
25 Pages

Typology and Design of Parametric Cat-in-a-Box and Cat-in-a-Grid Triggers for Tropical Cyclone Risk Transfer

  • Guillermo Franco,
  • Laura Lemke-Verderame,
  • Roberto Guidotti,
  • Ye Yuan,
  • Gianbattista Bussi,
  • Dag Lohmann and
  • Paolo Bazzurro

6 June 2024

The insurance industry has used parametric solutions to transfer catastrophe risks since the 1990s. Instead of relying on a lengthy process to assess a claim, these products pay the insured a pre-agreed amount if the physical characteristics of the e...

  • Article
  • Open Access
13 Citations
2,316 Views
16 Pages

Robust Adaptive Fault-Tolerant Control of Quadrotor Unmanned Aerial Vehicles

  • Imil Hamda Imran,
  • Nezar M. Alyazidi,
  • Ahmed Eltayeb and
  • Gamil Ahmed

6 June 2024

The paper introduces a robust adaptive fault-tolerant control system for the six-degree-of-freedom (six-DOF) dynamics of quadrotor unmanned aerial vehicles (UAVs), incorporating disturbances and abrupt actuator faults to represent real-world conditio...

  • Article
  • Open Access
3 Citations
1,030 Views
11 Pages

6 June 2024

This paper focuses on a system of differential inclusions expressing hemivariational inequalities driven by competing operators constructed with p-Laplacians that involve two real parameters. The existence of a generalized solution is shown by means...

  • Article
  • Open Access
4 Citations
1,176 Views
15 Pages

Dynamic Binary-Medium Model for Jointed Rock Subjected to Cyclic Loading

  • Mingxing Liu,
  • Enlong Liu,
  • Xingyan Liu and
  • Qingsong Zheng

6 June 2024

Revealing the damage mechanism of jointed rocks under a cyclic loading and formulating the corresponding dynamic constitutive model to meet the requirements for the evaluation of anti-vibration safety for critical engineering construction and operati...

  • Article
  • Open Access
4 Citations
1,557 Views
16 Pages

Stability Analysis of the Credit Market in Supply Chain Finance Based on Stochastic Evolutionary Game Theory

  • Chunsheng Wang,
  • Jiatong Weng,
  • Jingshi He,
  • Xiaopin Wang,
  • Hong Ding and
  • Quanxin Zhu

6 June 2024

The rapid development of supply chain finance (SCF) has significantly alleviated the financing difficulties of small and medium-sized enterprises (SMEs). However, it is important to recognize that within the accounts receivable financing segment of t...

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Mathematics - ISSN 2227-7390