Matrix inverses along the core parts of three matrix decompositions

New characterizations for generalized inverses along the core parts of three matrix decompositions were investigated in this paper. Let $A_{1}$, $\hat{A}_{1}$ and $\tilde{A}_{1}$ be the core parts of the core-nilpotent decomposition, the core-EP decomposition and EP-nilpotent decomposition of $A\in \mathbb{C}^{n\times n}$, respectively, where EP denotes the EP matrix. A number of characterizations and different representations of the Drazin inverse, the weak group inverse and the core-EP inverse were given by using the core parts $A_{1}$, $\hat{A}_{1}$ and $\tilde{A}_{1}$. One can prove that, the Drazin inverse is the inverse along $A_{1}$, the weak group inverse is the inverse along $\hat{A}_{1}$ and the core-EP inverse is the inverse along $\tilde{A}_{1}$. A unified theory presented in this paper covers the Drazin inverse, the weak group inverse and the core-EP inverse based on the core parts of the core-nilpotent decomposition, the core-EP decomposition and EP-nilpotent decomposition of $A\in \mathbb{C}^{n\times n}$, respectively. In addition, we proved that the Drazin inverse of $A$ is the inverse of $A$ along $U$ and $A_{1}$ for any $U\in \{A_{1}, \hat{A}_{1}, \tilde{A}_{1}\}$; the weak group inverse of $A$ is the inverse of $A$ along $U$ and $\hat{A}_{1}$ for any $U\in \{A_{1}, \hat{A}_{1}, \tilde{A}_{1}\}$; the core-EP inverse of $A$ is the inverse of $A$ along $U$ and $\tilde{A}_{1}$ for any $U\in \{A_{1}, \hat{A}_{1}, \tilde{A}_{1}\}$. Let $X_{1}$, $X_{4}$ and $X_{7}$ be the generalized inverses along $A_{1}$, $\hat{A}_{1}$ and $\tilde{A}_{1}$, respectively. In the last section, some useful examples were given, which showed that the generalized inverses $X_{1}$, $X_{4}$ and $X_{7}$ were different generalized inverses. For a certain singular complex matrix, the Drazin inverse coincides with the weak group inverse, which is different from the core-EP inverse. Moreover, we showed that the Drazin inverse, the weak group inverse and the core-EP inverse can be the same for a certain singular complex matrix

Post-Quantum Public-key Authenticated Searchable Encryption with Forward Security: General Construction, Implementation, and Applications

Public-key encryption with keyword search was first proposed by Boneh et al. (EUROCRYPT 2004), achieving the ability to search for ciphertext files. Nevertheless, this scheme is vulnerable to inside keyword guessing attacks (IKGA). Public-key authenticated encryption with keyword search (PAEKS), introduced by Huang et al. (Inf. Sci. 2017), on the other hand, is secure against IKGA. Nonetheless, it is susceptible to quantum computing attacks. Liu et al. and Cheng et al. addressed this problem by reducing to the lattice hardness (AsiaCCS 2022, ESORICS 2022). Furthermore, several scholars pointed out that the threat of secret key exposure delegates a severe and realistic concern, potentially leading to privacy disclosure (EUROCRYPT 2003, Compt. J. 2022). As a result, research focusing on mitigating key exposure and resisting quantum attacks for the PAEKS primitive is significant and far-reaching. In this work, we present the first instantiation of post-quantum PAEKS primitive that is forward-secure and does not require trusted authorities, mitigating the secret key exposure while ensuring quantum-safe properties. We extended the scheme of Liu et al. (AsiaCCS 2022), and proposed a novel post-quantum PAEKS construction, namely FS-PAEKS. To begin with, we introduce the binary tree structure to represent the time periods, along with a lattice basis extension algorithm, and SamplePre algorithm to obtain the post-quantum one-way secret key evolution, allowing users to update their secret keys periodically. Furthermore, our scheme is proven to be IND-CKA, IND-IKGA, and IND-Multi-CKA in the quantum setting. In addition, we also compare the security of our primitive in terms of computational complexity and communication overhead with other top-tier schemes and provide implementation details of the ciphertext generation and test algorithms. The proposed FS-PAEKS is more efficient than the FS-PEKS scheme (IEEE TDSC 2021). Lastly, we demonstrate three potential application scenarios of FS-PAEKS

Modular co-evolution of metabolic networks

The architecture of biological networks has been reported to exhibit high level of modularity, and to some extent, topological modules of networks overlap with known functional modules. However, how the modular topology of the molecular network affects the evolution of its member proteins remains unclear. In this work, the functional and evolutionary modularity of Homo sapiens (H. sapiens) metabolic network were investigated from a topological point of view. Network decomposition shows that the metabolic network is organized in a highly modular core-periphery way, in which the core modules are tightly linked together and perform basic metabolism functions, whereas the periphery modules only interact with few modules and accomplish relatively independent and specialized functions. Moreover, over half of the modules exhibit co-evolutionary feature and belong to specific evolutionary ages. Peripheral modules tend to evolve more cohesively and faster than core modules do. The correlation between functional, evolutionary and topological modularity suggests that the evolutionary history and functional requirements of metabolic systems have been imprinted in the architecture of metabolic networks. Such systems level analysis could demonstrate how the evolution of genes may be placed in a genome-scale network context, giving a novel perspective on molecular evolution.Comment: 26 pages, 7 figure

Huntingtin forms toxic NH2-terminal fragment complexes that are promoted by the age-dependent decrease in proteasome activity

Although NH2-terminal mutant huntingtin (htt) fragments cause neurological disorders in Huntington's disease (HD), it is unclear how toxic htt fragments are generated and contribute to the disease process. Here, we report that complex NH2-terminal mutant htt fragments smaller than the first 508 amino acids were generated in htt-transfected cells and HD knockin mouse brains. These fragments constituted neuronal nuclear inclusions and appeared before neurological symptoms. The accumulation and aggregation of these htt fragments were associated with an age-dependent decrease in proteasome activity and were promoted by inhibition of proteasome activity. These results suggest that decreased proteasome activity contributes to late onset htt toxicity and that restoring the ability to remove NH2-terminal fragments will provide a more effective therapy for HD than inhibiting their production

Paleotopography continues to drive surface to deep-layer interactions in a subtropical Critical Zone Observatory

This study was supported by the National Natural Science Foundation of China (grant No. 41571130051, No. 41771251 and No. 41977003), the National Key Research and Development Program of China (No. 2018YFE0107000) and the UK Natural Environmental Research Council (NE/N007611/1). We thank the individual authors of each study regarding critical zone research in the Red Soil CZO. We are grateful to Dong-Sheng Yu, Li-Gang Zhou, Shun-Hua Yang and Yue Zhao for their support in conducting the GPR survey. We are grateful to Qin-Bo Cheng for interpreting the radargram images. Data Availability: All radargram data, soil data and environmental predictors used in this study are available from the corresponding author upon request.Peer reviewedPostprin

Analysis of the factors affecting the occurrence of myopia in children with myopia

AIM: To analyze the electronic product use time, writing time, playing piano time and outdoor activity time and the distribution of myopia in 586 cases of school age children in our hospital. METHODS: A retrospective analysis of 586 cases of children aged 6 to 12 years old in the outpatient department was established. Personalized files were used to record the uncorrected visual acuity, optometry, slit lamp, fundus mirror and strabismus. The cumulative use time of electronic products(including computer, mobile phone, iPad), writing time, whether to play the piano and outdoor activities time with the eye situation were recorded. Statistical analysis of the age group of myopia, the cumulative use of electronic age in different age groups, writing time, whether playing piano and outdoor activities and the distribution of myopia occurred.RESULTS:(1)With the increasing of age, the distribution of uncorrected eyesight was in children mostly mild myopia, and the proportion of mild myopia was significantly higher than that of moderate and high myopia.(2)Electronic products use time distribution: the proportion of playing electronic products(including mobilephone, computers, iPad)accounted for 76.8%, of which 9 years old, 10 years old the cumulative use of electronic products with a long time was higher than other age groups.(3)Distribution of writing time: the proportion of write homework ≤1h was significantly lower than the proportion of writing homework> 1h(37.2% vs 62.8%), of which 9 and 10 years old children cumulative write time was higher than other age group.(4)Distribution of playing the piano: the proportion of playing piano time less than 1h was significantly higher than the proportion of playing piano time more than 1h(89.1% vs 10.9%).(5)Distribution of outdoor activities: the proportion of outdoor activities ≤1h in children at school age was significantly higher than that of outdoor activities > 1h(91.8% vs 8.9%). CONCLUSION: With the age exposure to electronic products becoming younger, heavy learning tasks and less outdoor activities, myopia occurred in advance of age. So health examination and eye guidance, reducing the amount of work appropriately, increasing outdoor activities will slow the development of early childhood myopia