Multiplier Hopf Algebras and Duality

In this thesis, we study and apprehend Hopf algebras, multiplier Hopf algebras, and their dualities. A Hopf algebra A is a unital algebra with an comutiplication (A tensor A) &rarr A, which is the reverse of multiplication, and other structures. In the finite-dimensional case, we can construct the dual A\u27 of A, which is also a Hopf algebra, and prove that A is isomorphic to its bidual A\u27\u27. If we drop the assumption that A is unital and allow the comultiplication to have values in the multiplier algebra of (A tensor A), we end with a multiplier Hopf algebra. If the coopposite algebra of A is also a multiplier Hopf algebra, we say that A is regular, for which we can involve non-zero left (right) invariant linear functionals, called left (right) integrals. It is proved that if left (right) integrals exist, they are faithful and unique up to a scalar. For a regular multiplier Hopf algebra A with integrals, we can construct its dual A^ with the help of integrals. In this case, A^ is again a regular multiplier Hopf algebra, on which integrals can also be constructed, and it turns out that the bidual A^^ is canonically isomorphic to A

Towards Better Fairness-Utility Trade-off: A Comprehensive Measurement-Based Reinforcement Learning Framework

Machine learning is widely used to make decisions with societal impact such as bank loan approving, criminal sentencing, and resume filtering. How to ensure its fairness while maintaining utility is a challenging but crucial issue. Fairness is a complex and context-dependent concept with over 70 different measurement metrics. Since existing regulations are often vague in terms of which metric to use and different organizations may prefer different fairness metrics, it is important to have means of improving fairness comprehensively. Existing mitigation techniques often target at one specific fairness metric and have limitations in improving multiple notions of fairness simultaneously. In this work, we propose CFU (Comprehensive Fairness-Utility), a reinforcement learning-based framework, to efficiently improve the fairness-utility trade-off in machine learning classifiers. A comprehensive measurement that can simultaneously consider multiple fairness notions as well as utility is established, and new metrics are proposed based on an in-depth analysis of the relationship between different fairness metrics. The reward function of CFU is constructed with comprehensive measurement and new metrics. We conduct extensive experiments to evaluate CFU on 6 tasks, 3 machine learning models, and 15 fairness-utility measurements. The results demonstrate that CFU can improve the classifier on multiple fairness metrics without sacrificing its utility. It outperforms all state-of-the-art techniques and has witnessed a 37.5% improvement on average

Frequent copy number variations of PI3K/AKT pathway and aberrant protein expressions of PI3K subunits are associated with inferior survival in diffuse large B cell lymphoma

BACKGROUND: It has been reported that the PI3K/AKT signaling pathway is activated in diffuse large B-cell lymphoma (DLBCL), PI3K constitutive activation plays a crucial role in PI3K/AKT pathway. However, the copy number variations (CNVs) of PI3K subunits on gene level remain unknown in DLBCL. Therefore, the aim of the study is to investigate the CNV of PI3K subunits and their relationship with clinicopathological features exploring the possible mechanism underlying of PI3K activation in DLBCL. METHODS: CNV of 12 genes in the PI3K/AKT pathway was detected by NanoString nCounter in 60 de novo DLBCLs and 10 reactive hyperplasia specimens as controls. Meanwhile, immunohistochemistry (IHC) was performed to examine the expression of p110α, p110β, p110γ, p110δ, and pAKT on DLBCL tissue microarrays. RESULTS: All PI3K and AKT subunits, except for PIK3R1, had various CNVs in the form of copy number amplifications and copy number losses. Their rates were in the range of 8.3–20.0%. Of them PIK3CA and PIK3CB gene CNVs were significantly associated with decreased overall survival (P = 0.029 and P = 0.019, respectively). IHC showed that the frequency of strong positive expression of p110α, p110β, p110γ, and p110δ were 26.7%, 25.0%, 18.3%, and 25.0% respectively, and they were found to be associated with decreased survival (P = 0.022, P = 0.015, P = 0.015, and P = 0.008, respectively). Expression of p110α was not only significantly associated with CNVs of PIK3CA (P = 0.002) but also positively correlated with strong positive expression of pAKT (P = 0.026). CONCLUSIONS: CNV of PIK3CA is highly associated with aberrant p110α protein expression and subsequent activation of PI3K/AKT pathway. CNVs of PIK3CA and PIK3CB, and aberrant protein expression of p110 isoforms are of great important value for predicting inferior prognosis in DLBCL. Frequent CNVs of PI3K/AKT subunits may play an important role in the tumorigenesis of DLBCL

Potentially Functional Variants of PLCE1 Identified by GWASs Contribute to Gastric Adenocarcinoma Susceptibility in an Eastern Chinese Population

BACKGROUND: Recent genome-wide association studies (GWAS) have found a single nucleotide polymorphism (SNP, rs2274223 A>G) in PLCE1 to be associated with risk of gastric adenocarcinoma. In the present study, we validated this finding and also explored the risk associated with another unreported potentially functional SNP (rs11187870 G>C) of PLCE1 in a hospital-based case-control study of 1059 patients with pathologically confirmed gastric adenocarcinoma and 1240 frequency-matched healthy controls. METHODOLOGY/PRINCIPAL FINDINGS: We determined genotypes of these two SNPs by the Taqman assay and used logistic regression models to estimate odds ratios (ORs) and 95% confidence intervals (95% CI). We found that a significant higher gastric adenocarcinoma risk was associated with rs2274223 variant G allele (adjusted OR = 1.35, 95% CI = 1.14-1.60 for AG+GG vs. AA) and rs11187870 variant C allele (adjusted OR = 1.26, 95% CI = 1.05-1.50 for CG+CC vs. GG). We also found that the number of combined risk alleles (i.e., rs2274223G and rs11187870C) was associated with risk of gastric adenocarcinoma in an allele-dose effect manner (P(trend) = 0.0002). Stratification analysis indicated that the combined effect of rs2274223G and rs11187870C variant alleles was more evident in subgroups of males, non-smokers, non-drinkers and patients with gastric cardia adenocarcinoma. Further real-time PCR results showed that expression levels of PLCE1 mRNA were significantly lower in tumors than in adjacent noncancerous tissues (0.019±0.002 vs. 0.008±0.001, P<0.05). CONCLUSIONS/SIGNIFICANCES: Our results further confirmed that genetic variations in PLCE1 may contribute to gastric adenocarcinoma risk in an eastern Chinese population

Methylation of the candidate biomarker TCF21 is very frequent across a spectrum of early-stage nonsmall cell lung cancers

The transcription factor TCF21 is involved in mesenchymal-to-epithelial differentiation and was shown to be aberrantly hypermethylated in lung and head and neck cancers. Because of its reported high frequency of hypermethylation in lung cancer, we sought to characterize the stages and types of non-small cell lung cancer (NSCLC) that are hypermethylated and to define the frequency of hypermethylation and associated “second hits”

Whole exome sequencing identifies frequent somatic mutations in cell-cell adhesion genes in chinese patients with lung squamous cell carcinoma

Lung squamous cell carcinoma (SQCC) accounts for about 30% of all lung cancer cases. Understanding of mutational landscape for this subtype of lung cancer in Chinese patients is currently limited. We performed whole exome sequencing in samples from 100 patients with lung SQCCs to search for somatic mutations and the subsequent target capture sequencing in another 98 samples for validation. We identified 20 significantly mutated genes, including TP53, CDH10, NFE2L2 and PTEN. Pathways with frequently mutated genes included those of cell-cell adhesion/Wnt/Hippo in 76%, oxidative stress response in 21%, and phosphatidylinositol-3-OH kinase in 36% of the tested tumor samples. Mutations of Chromatin regulatory factor genes were identified at a lower frequency. In functional assays, we observed that knockdown of CDH10 promoted cell proliferation, soft-agar colony formation, cell migration and cell invasion, and overexpression of CDH10 inhibited cell proliferation. This mutational landscape of lung SQCC in Chinese patients improves our current understanding of lung carcinogenesis, early diagnosis and personalized therapy

Nano-titanium dioxide exacerbates the harmful effects of perfluorooctanoic acid on the health of mussels

Exposing marine organisms to contemporary contaminants, such as perfluorooctanoic acid (PFOA) and nano-titanium dioxide (nano-TiO2), can induce multifaceted physiological consequences. Our investigation centered on the responses of the mussel, Mytilus coruscus, to these agents. We discerned pronounced disruptions in gill filament connections, pivotal structures for aquatic respiration, suggesting compromised oxygen uptake capabilities. Concurrently, the respiratory rate exhibited a marked decline, indicating a respiratory distress. Furthermore, the mussels' clearance rate, a metric of their filtration efficacy, diminished, suggesting the potential for bioaccumulation of deleterious substances. Notably, the co-exposure of PFOA and nano-TiO2 exhibits interactive effects on the physiological performance of the mussels. The mussels' digestive performance waned in the face of heightened PFOA and nano-TiO2 concentrations, possibly hampering nutrient assimilation and energy accrual. This was mirrored in the noticeable contraction of their energy budget, suggesting long-term growth repercussions. Additionally, the dysregulation of the gut microbiota and the reduction in its diversity further confirm alterations in intestinal homeostasis, subsequently impacting its physiological functions and health. Collectively, these findings underscore the perils posed by escalated PFOA and nano-TiO2 levels to marine mussels, accentuating the need for a deeper understanding of nanoparticle-pollutant synergies in marine ecosystems

The P38α rs3804451 Variant Predicts Chemotherapy Response and Survival of Patients with Non–Small Cell Lung Cancer Treated with Platinum-Based Chemotherapy

The JNK and P38α pathways play an important role in the sensitivity and outcomes of chemotherapy. We hypothesize that functional single nucleotide polymorphisms (SNPs) of genes of these pathways modulate outcomes of patients with advanced non–small cell lung cancer (NSCLC) treated with first-line platinum-based chemotherapy (PBC). We selectively genotyped 11 independent, potentially functional SNPs of 9 genes in the JNK and P38α pathways first in a discovery group of 355 patients with advanced NSCLC treated with PBC, and we evaluated their associations with progression-free survival (PFS) and overall survival (OS) by Cox proportional hazards regression analysis. Then, resultant significant SNPs were further validated in a replication group of 355 patients. In both discovery and validation groups as well as their combined analysis, the MAPK14 rs3804451GA/AA genotypes showed a strong association with a reduced PFS (adjusted hazards ratio [HR] = 1.39; 95% confidence interval [CI] = 1.16–1.66; P = .0003) and OS (adjusted HR = 1.41; 95% CI = 1.11-1.80; P = .005) compared with the wild-type GG genotype. In contrast, patients with or without the MAPK14 rs3804451A allele had no significant difference in OS in response to tyrosine-kinase inhibitor treatment (adjusted HR = 0.86; 95% CI = 0.56-1.33; P = .505). The present study provides evidence that the MAPK14 rs3804451 G>A variant may modulate survival outcomes in patients with advanced NSCLC treated with PBC. Larger studies of additional patient populations are needed to validate our findings

Calcium Phosphate Ceramics and Synergistic Bioactive Agents for Osteogenesis in Implant Dentistry

Implant-supported dental prosthetics are widely used in dental practice. Sufficient peri-implant bone tissue is a crucial prerequisite for the long-term success of this treatment, as insufficient peri-implant bone volume hampers dental implant installation and negatively influences dental implant stability. However, due to tooth extraction, bone metabolism diseases, and trauma, bone defects in the jaw are common in patients, particularly in the elderly and those suffering from underlying conditions. If this is the case, the alveolar ridge has to be augmented for reliable implant placement. Various biomaterials, growth factors (GFs) or GF-based products, and trace elements have been tested and used for alveolar ridge augmentation. Among those biomaterials, calcium phosphates (CaPs) are the most popular due to their promising biocompatibility, great osteoconductivity, and distinguishing osteogenesis. Combining CaPs with GFs or trace elements can further favor bone defect repair. This review mainly focuses on applying artificial CaP biomaterials and their combination with bioactive agents to repair bone defects in implant dentistry