Abstract For any A=A 1+A 2 j∈Q n×n and η∈i, j, k, denote A η H =−η A H η. If A η H =A, A is called an $\eta$-Hermitian matrix. If A η H =−A, A is called an η-anti-Hermitian matrix. Denote η-Hermitian matrices and η-anti-Hermitian matrices by η HQ n×n and η AQ n×n , respectively. By using the complex representation of quaternion matrices, the Moore–Penrose generalized inverse and the Kronecker product of matrices, we derive the expressions of the least-squares solution with the least norm for the quaternion matrix equation AXB+CYD=E over X∈η HQ n×n and Y∈η AQ n×n . Keywords: matrix equationleast-squares solutionMoore–Penrose generalized inverseKronecker productη-Hermitian matrices 2010 AMS Subject Classifications:: 65F0565H1015B33 Acknowledgements The authors thank the referees very much for their valuable suggestions and comments, which resulted in a great improvement of the original manuscript. This work is supported by the Natural Science Foundation of China (11171205, 60672160), Natural Science Foundation of Shanghai (11ZR1412500), PhD Programs Foundation of Ministry of Education of China (20093108110001), the Key Project of Scientific Research Innovation Foundation of Shanghai Municipal Education Commission (13ZZ080), the Discipline Project at the corresponding level of Shanghai (A. 13-0101-12-005), Shanghai Leading Academic Discipline Project (J50101), Guangdong Natural Science Fund of China (No. 10452902001005845), and Program for Guangdong Excellent Talents in University, Guangdong Education Ministry, China (LYM10128), Science and Technology Project of Jiangmen City, China (No. 201215628).
321 Objectives Vesicular acetylcholine transporter (VAChT) plays an important role in mediating cholinergic transmission, and it is considered a specific biomarker for neurodegenerative diseases. Compound (-)-TZ6-59 showed high in vitro binding potency and selectivity towards VAChT (Ki-VAChT = 0.78 nM, Ki-σ1 = 990 nM, and Ki- σ2 >10,000 nM). Here, we report the radiosynthesis and in vivo evaluation of (-)-[11C]TZ6-59 to image VAChT. Methods The synthesis of (-)-[11C]TZ6-59 was accomplished by alkylating the Boc protected aniline precursor with [11C]CH3I, followed by the removal of the protective group. Biodistribution studies were performed in male SD rats (300-360 g). Rats were injected with ~300-400 µCi/150 µL of (-)-[11C]TZ6-59 and euthanized at 5, 30 and 60 min post injection; the uptake (%ID/g) in each organ of interest was calculated. Blocking study was performed in rats pretreated with cold TZ4-3-76, a potent VAChT ligand at 2 mg/kg. Dynamic microPET imaging studies were performed in cynomolgus monkeys. Results (-)-[11C]TZ6-59 was synthesized in high chemical (>95%) and radiochemical (>99%) purities, and high specific activity (>0.5 Ci/µmol, EOB) with a yield of 20-25%. Biodistribution studies revealed that (-)-[11C]TZ6-59 is able to cross the rat BBB and specifically accumulate in the VAChT-enriched striatal area; at 60 min, the uptake ratio of striatum vs. cerebellum reached ~5.5-fold. Pretreated with unlabeled TZ4-3-76, striatum uptake of labeled (-)-[11C]TZ6-59 was reduced by ~48%. MicroPET imaging of monkey brains demonstrated that the highest uptake occurs in the striatal area with sufficient contrast ratios vs. reference regions. Conclusions (-)-[11C]TZ6-59 is a promising PET tracer for imaging VAChT in the brain. Further evaluations will be performed prior to seeking IND and RDRC approval for translational clinical validation in human beings. Research Support 1R21NS061025-01A2 & 1R01NS075527-01.
Aim: MicroRNAs (miRNAs), pivotal regulators in various biological processes, are closely linked to human diseases. This study aims to propose a computational model, SIDMF, for predicting miRNA-disease associations. Background: Computational methods have proven efficient in predicting miRNA-disease associations, leveraging functional similarity and network-based inference. Machine learning techniques, including support vector machines, semi-supervised algorithms, and deep learning models, have gained prominence in this domain. Objective: Develop a computational model that integrates disease semantic similarity and miRNA functional similarity within a deep matrix factorization framework to predict potential associations between miRNAs and diseases accurately. Methods: SIDMF, introduced in this study, integrates disease semantic similarity and miRNA functional similarity within a deep matrix factorization framework. Through the reconstruction of the miRNA-disease association matrix, SIDMF predicts potential associations between miRNAs and diseases. Results: The performance of SIDMF was evaluated using global Leave-One-Out Cross-Validation (LOOCV) and local LOOCV, achieving high Area Under the Curve (AUC) values of 0.9536 and 0.9404, respectively. Comparative analysis against other methods demonstrated the superior performance of SIDMF. Case studies on breast cancer, esophageal cancer, and prostate cancer further validated SIDMF's predictive accuracy, with a substantial percentage of the top 50 predicted miRNAs confirmed in relevant databases. Conclusion: SIDMF emerges as a promising computational model for predicting potential associations between miRNAs and diseases. Its robust performance in global and local evaluations, along with successful case studies, underscores its potential contributions to disease prevention, diagnosis, and treatment.
Top- $k$ proximity query in large graphs is a fundamental problem with a wide range of applications. Various random walk based measures have been proposed to measure the proximity between different nodes. Although these measures are effective, efficiently computing them on large graphs is a challenging task. In this paper, we develop an efficient and exact local search method, FLoS (Fast Local Search), for top- $k$ proximity query in large graphs. FLoS guarantees the exactness of the solution. Moreover, it can be applied to a variety of commonly used proximity measures. FLoS is based on the no local optimum property of proximity measures. We show that many measures have no local optimum. Utilizing this property, we introduce several operations to manipulate transition probabilities and develop tight lower and upper bounds on the proximity values. The lower and upper bounds monotonically converge to the exact proximity value when more nodes are visited. We further extend FLoS to measures having local optimum by utilizing relationship among different measures. We perform comprehensive experiments on real and synthetic large graphs to evaluate the efficiency and effectiveness of the proposed method.
Multiple functional and hard-to-quantify sensorial product attributes that can be satisfied by a large number of cosmetic ingredients are required in the design of cosmetics. To overcome this challenge, a new optimization-based approach for expediting cosmetic formulation is presented. It exploits the use of a hierarchy of models in an iterative manner to refine the search for creating the highest-quality cosmetic product. First, a systematic procedure is proposed for optimization problem formulation, where the cosmetic formulation problem is defined, design variables are specified, and a set of models for sensorial perception and desired product properties are identified. Then, a solution strategy that involves iterative model adoption and two numerical techniques (i.e., generalized disjunctive programming reformulation and model substitution) is applied to improve the efficiency of solving the optimization problem and to find better solutions. The applicability of the proposed procedure and solution strategy is illustrated with a perfume formulation example.
The prediction of molecular properties remains a challenging task in the field of drug design and development. Recently, there has been a growing interest in the analysis of biological images. Molecular images, as a novel representation, have proven to be competitive, yet they lack explicit information and detailed semantic richness. Conversely, semantic information in SMILES sequences is explicit but lacks spatial structural details. Therefore, in this study, we focus on and explore the relationship between these two types of representations, proposing a novel multimodal architecture named ISMol. ISMol relies on a cross-attention mechanism to extract information representations of molecules from both images and SMILES strings, thereby predicting molecular properties. Evaluation results on 14 small molecule ADMET datasets indicate that ISMol outperforms machine learning (ML) and deep learning (DL) models based on single-modal representations. In addition, we analyze our method through a large number of experiments to test the superiority, interpretability and generalizability of the method. In summary, ISMol offers a powerful deep learning toolbox for drug discovery in a variety of molecular properties.
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