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The study of fuzzy variational problems has received significant attention over the past decade due to its successful applications in numerous fields, such as image segmentation and optimal control theory. The fuzzy Euler-Lagrange equations provide the necessary optimality conditions for solving fuzzy variational problems explicitly and have been studied under several differentiability conditions. In this paper, we provide a systematic review to recap the history of variational principle in the calculus of variations and compare it with the existing techniques in the fuzzy setting. We begin with the preliminary concepts and definitions of fuzzy theory and scrutinize the Euler-Lagrange’s strategy via systematically searched studies concerning fuzzy variational problems to highlight the importance of improving the existing methods. Finally, we set up the main open problems regarding the limitations of the current approaches, shedding light on future directions.

We present a pursuit differential game for an infinite system of two-block differential equations in Hilbert space l2. The pursuer and evader control functions are subject to integral constraints. The differential game is said to be completed if the state of the system falls into the origin of l2 at some finite time. The purpose of the pursuer is to bring the state of the controlled system to the origin of the space l2, whereas the evader’s aim is to prevent this. For the optimal pursuit time, we obtain an equation and construct the optimal strategies for the players.

A pursuit differential game described by an infinite system of 2-systems is studied in Hilbert space l2. Geometric constraints are imposed on control parameters of pursuer and evader. The purpose of pursuer is to bring the state of the system to the origin of the Hilbert space l2 and the evader tries to prevent this. Differential game is completed if the state of the system reaches the origin of l2. The problem is to find a guaranteed pursuit and evasion times. We give an equation for the guaranteed pursuit time and propose an explicit strategy for the pursuer. Additionally, a guaranteed evasion time is found.

Background: Nonalcoholic fatty liver disease (NAFLD) is a major cause of liver-related morbidity in people with and without diabetes, but it is underdiagnosed, posing challenges for research and clinical management. Here, we determine if natural language processing (NLP) of data in the electronic health record (EHR) could identify undiagnosed patients with hepatic steatosis based on pathology and radiology reports., Methods: A rule-based NLP algorithm was built using a Linguamatics literature text mining tool to search 2.15 million pathology report and 2.7 million imaging reports in the Penn Medicine EHR from November 2014, through December 2020, for evidence of hepatic steatosis. For quality control, two independent physicians manually reviewed randomly chosen biopsy and imaging reports (n = 353, PPV 99.7%)., Findings: After exclusion of individuals with other causes of hepatic steatosis, 3007 patients with biopsy-proven NAFLD and 42,083 patients with imaging-proven NAFLD were identified. Interestingly, elevated ALT was not a sensitive predictor of the presence of steatosis, and only half of the biopsied patients with steatosis ever received an ICD diagnosis code for the presence of NAFLD/NASH. There was a robust association for PNPLA3 and TM6SF2 risk alleles and steatosis identified by NLP. We identified 234 disorders that were significantly over- or underrepresented in all subjects with steatosis and identified changes in serum markers (e.g., GGT) associated with presence of steatosis., Interpretation: This study demonstrates clear feasibility of NLP-based approaches to identify patients whose steatosis was indicated in imaging and pathology reports within a large healthcare system and uncovers undercoding of NAFLD in the general population. Identification of patients at risk could link them to improved care and outcomes., Funding: The study was funded by US and German funding sources that did provide financial support only and had no influence or control over the research process., Competing Interests: The authors declare no competing interests., (© 2023 The Author(s).)

Background: Pharmacogenomics (PGx) aims to utilize a patient's genetic data to enable safer and more effective prescribing of medications. The Clinical Pharmacogenetics Implementation Consortium (CPIC) provides guidelines with strong evidence for 24 genes that affect 72 medications. Despite strong evidence linking PGx alleles to drug response, there is a large gap in the implementation and return of actionable pharmacogenetic findings to patients in standard clinical practice. In this study, we evaluated opportunities for genetically guided medication prescribing in a diverse health system and determined the frequencies of actionable PGx alleles in an ancestrally diverse biobank population., Methods: A retrospective analysis of the Penn Medicine electronic health records (EHRs), which includes ~ 3.3 million patients between 2012 and 2020, provides a snapshot of the trends in prescriptions for drugs with genotype-based prescribing guidelines ('CPIC level A or B') in the Penn Medicine health system. The Penn Medicine BioBank (PMBB) consists of a diverse group of 43,359 participants whose EHRs are linked to genome-wide SNP array and whole exome sequencing (WES) data. We used the Pharmacogenomics Clinical Annotation Tool (PharmCAT), to annotate PGx alleles from PMBB variant call format (VCF) files and identify samples with actionable PGx alleles., Results: We identified ~ 316.000 unique patients that were prescribed at least 2 drugs with CPIC Level A or B guidelines. Genetic analysis in PMBB identified that 98.9% of participants carry one or more PGx actionable alleles where treatment modification would be recommended. After linking the genetic data with prescription data from the EHR, 14.2% of participants (n = 6157) were prescribed medications that could be impacted by their genotype (as indicated by their PharmCAT report). For example, 856 participants received clopidogrel who carried CYP2C19 reduced function alleles, placing them at increased risk for major adverse cardiovascular events. When we stratified by genetic ancestry, we found disparities in PGx allele frequencies and clinical burden. Clopidogrel users of Asian ancestry in PMBB had significantly higher rates of CYP2C19 actionable alleles than European ancestry users of clopidrogrel (p < 0.0001, OR = 3.68)., Conclusions: Clinically actionable PGx alleles are highly prevalent in our health system and many patients were prescribed medications that could be affected by PGx alleles. These results illustrate the potential utility of preemptive genotyping for tailoring of medications and implementation of PGx into routine clinical care., (© 2022. The Author(s).)

Mutations in AUTS2 are associated with autism, intellectual disability, and microcephaly. AUTS2 is expressed in the brain and interacts with polycomb proteins, yet it is still unclear how mutations in AUTS2 lead to neurodevelopmental phenotypes. Here we report that when neuronal differentiation is initiated, there is a shift in expression from a long isoform to a short AUTS2 isoform. Yeast two-hybrid screen identified the splicing factor SF3B1 as an interactor of both isoforms, whereas the polycomb group proteins, PCGF3 and PCGF5, were found to interact exclusively with the long AUTS2 isoform. Reporter assays showed that the first exons of the long AUTS2 isoform function as a transcription repressor, but the part that consist of the short isoform acts as a transcriptional activator, both influenced by the cellular context. The expression levels of PCGF3 influenced the ability of the long AUTS2 isoform to activate or repress transcription. Mouse embryonic stem cells (mESCs) with heterozygote mutations in Auts2 had an increase in cell death during in vitro corticogenesis, which was significantly rescued by overexpressing the human AUTS2 transcripts. mESCs with a truncated AUTS2 protein (missing exons 12-20) showed premature neuronal differentiation, whereas cells overexpressing AUTS2, especially the long transcript, showed increase in expression of pluripotency markers and delayed differentiation. Taken together, our data suggest that the precise expression of AUTS2 isoforms is essential for regulating transcription and the timing of neuronal differentiation.

The relationship between commonly occurring genetic variants (G1 and G2) in the APOL1 gene in African Americans and different disease traits, such as kidney disease, cardiovascular disease, and pre-eclampsia, remains the subject of controversy. Here we took a genotype-first approach, a phenome-wide association study, to define the spectrum of phenotypes associated with APOL1 high-risk variants in 1,837 African American participants of Penn Medicine Biobank and 4,742 African American participants of Vanderbilt BioVU. In the Penn Medicine Biobank, outpatient creatinine measurement-based estimated glomerular filtration rate and multivariable regression models were used to evaluate the association between high-risk APOL1 status and renal outcomes. In meta-analysis of both cohorts, the strongest phenome-wide association study associations were for the high-risk APOL1 variants and diagnoses codes were highly significant for "kidney dialysis" (odds ratio 3.75) and "end stage kidney disease" (odds ratio 3.42). A number of phenotypes were associated with APOL1 high-risk genotypes in an analysis adjusted only for demographic variables. However, no associations were detected with non-renal phenotypes after controlling for chronic/end stage kidney disease status. Using calculated estimated glomerular filtration rate -based phenotype analysis in the Penn Medicine Biobank, APOL1 high-risk status was associated with prevalent chronic/end stage kidney disease /kidney transplant (odds ratio 2.27, 95% confidence interval 1.67-3.08). In high-risk participants, the estimated glomerular filtration rate was 15.4 mL/min/1.73m 2 ; significantly lower than in low-risk participants. Thus, although APOL1 high-risk variants are associated with a range of phenotypes, the risks for other associated phenotypes appear much lower and in our dataset are driven by a primary effect on renal disease., (Copyright © 2020 International Society of Nephrology. Published by Elsevier Inc. All rights reserved.)

Objective: Plasma levels of high-density lipoprotein cholesterol (HDL-C) are strongly inversely associated with coronary artery disease (CAD), and high HDL-C is generally associated with reduced risk of CAD. Extremely high HDL-C with CAD is an unusual phenotype, and we hypothesized that the HDL in such individuals may have an altered composition and reduced function when compared with controls with similarly high HDL-C and no CAD., Approach and Results: Fifty-five subjects with very high HDL-C (mean, 86 mg/dL) and onset of CAD at the age of ≈ 60 years with no known risk factors for CAD (cases) were identified through systematic recruitment. A total of 120 control subjects without CAD, matched for race, sex, and HDL-C level (controls), were identified. In all subjects, HDL composition was analyzed and HDL cholesterol efflux capacity was assessed. HDL phospholipid composition was significantly lower in cases (92 ± 37 mg/dL) than in controls (109 ± 43 mg/dL; P=0.0095). HDL cholesterol efflux capacity was significantly lower in cases (1.96 ± 0.39) than in controls (2.11 ± 0.43; P=0.04)., Conclusions: In people with very high HDL-C, reduced HDL phospholipid content and cholesterol efflux capacity are associated with the paradoxical development of CAD., (© 2015 American Heart Association, Inc.)

Background: Exome sequencing is a promising tool for gene mapping in Mendelian disorders. We used this technique in an attempt to identify novel genes underlying monogenic dyslipidemias., Methods and Results: We performed exome sequencing on 213 selected family members from 41 kindreds with suspected Mendelian inheritance of extreme levels of low-density lipoprotein cholesterol (after candidate gene sequencing excluded known genetic causes for high low-density lipoprotein cholesterol families) or high-density lipoprotein cholesterol. We used standard analytic approaches to identify candidate variants and also assigned a polygenic score to each individual to account for their burden of common genetic variants known to influence lipid levels. In 9 families, we identified likely pathogenic variants in known lipid genes (ABCA1, APOB, APOE, LDLR, LIPA, and PCSK9); however, we were unable to identify obvious genetic etiologies in the remaining 32 families, despite follow-up analyses. We identified 3 factors that limited novel gene discovery: (1) imperfect sequencing coverage across the exome hid potentially causal variants; (2) large numbers of shared rare alleles within families obfuscated causal variant identification; and (3) individuals from 15% of families carried a significant burden of common lipid-related alleles, suggesting complex inheritance can masquerade as monogenic disease., Conclusions: We identified the genetic basis of disease in 9 of 41 families; however, none of these represented novel gene discoveries. Our results highlight the promise and limitations of exome sequencing as a discovery technique in suspected monogenic dyslipidemias. Considering the confounders identified may inform the design of future exome sequencing studies., (© 2015 American Heart Association, Inc.)

Our understanding of protein evolution would greatly benefit from mapping of binding landscapes, i.e., changes in protein-protein binding affinity due to all single mutations. However, experimental generation of such landscapes is a tedious task due to a large number of possible mutations. Here, we use a simple computational protocol to map the binding landscape for two homologous high-affinity complexes, involving a snake toxin fasciculin and acetylcholinesterase from two different species. To verify our computational predictions, we experimentally measure binding between 25 Fas mutants and the 2 enzymes. Both computational and experimental results demonstrate that the Fas sequence is close to the optimum when interacting with its targets, yet a few mutations could further improve Kd, kon, and koff. Our computational predictions agree well with experimental results and generate distributions similar to those observed in other high-affinity PPIs, demonstrating the potential of simple computational protocols in capturing realistic binding landscapes., (Copyright © 2014 Elsevier Ltd. All rights reserved.)

Previous genetic studies of idiopathic talipes equinovarus (ITEV) suggest an environmental and genetic component to the etiology of ITEV. The present study was undertaken to assess the role of causal factors in the development of ITEV. A total of 285 propositi were ascertained, with detailed family history information available in 173 cases and medical records on the remaining 112 propositi. Information was collected on specific prenatal, parental, and demographic factors. No racial heterogeneity was noted among any of the factors. The overall ratio of affected males to females was 2.5:1. The incidence of twinning among all propositi was significantly increased (P=0.006) above the expected population frequency. A family history of ITEV was noted in 24.4% of all propositi studied. These findings, in addition to the detailed analysis of 53 pedigrees with ITEV history, suggest the potential role of a gene or genes operating in high-risk families to produce this foot deformity.

"Idiopathic" talipes equinovarus (ITEV) is a nonsyndromal congenital anomaly of one or both feet. Casting and surgery are often necessary to obtain correct foot alignment. In spite of treatment, residual deformities of the feet occur and calf muscles may be hypoplastic. The cause of ITEV is unknown but genetic factors have been postulated. Complex segregation analysis was performed on 173 ITEV families including 93 Caucasian and 48 Hispanic families. The recessive mixed model was the best fitting model and no differences were found based on ethnicity. These results confirm previous studies suggesting that there is a genetic component to the development of ITEV.