Codes Andn-ary Relations

The aim of this thesis is to develop a general mechanism for the construction of codes and to extract general properties of classes of codes. This mechanism makes it unnecessary to study various classes of codes separately--at least to some extent--by different constructions and properties.;To achieve this goal, the mechanism of characterizing classes of languages by binary relations is studied. Some general properties related to binary relations and languages are obtained. Moreover, three new classes of codes, n-shuffle codes, solid codes, and intercodes are constructed. Solid codes and intercodes have the synchronous decoding property which is very useful in the design of circuits of coders and decoders.;The studies of codes, n-codes, and intercodes indicate that these three classes of codes cannot be characterized by binary relations. We introduce a more general mechanism, that is, to characterize classes of languages by finitary relations. This mechanism can be used to characterize more classes of languages, such as the classes of n-codes and intercodes. Sometimes, it is difficult to show inclusion relations between classes of codes and hierarchy properties of classes of codes. Results derived in this thesis provide a mechanism which can simplify this task

The Relationship Between Restoration and Furcation Involvement on Molar Teeth

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/141346/1/jper0302.pd

An EGFR and AKT Signaling Pathway was Identified with Mediation Model in Osteosarcomas Clinical Study

Identification of correlation pattern and signal pathway among biomarkers in patients has become increasingly interesting for its potential values in diagnosis, treatment and prognosis. EGFR and p-AKT signaling in osteosarcoma (OS) patients were analyzed for its relationship with cancer cell proliferation maker, Ki-67, using causal procedures and statistical tests. A total of 69 patients were collected who present to Vanderbilt University Medical Center with newly diagnosed, previously untreated osteosarcomas during the clinical study period 1994 through 2003. Tissue microarrays were constructed for EGFR, p-AKT and Ki-67. The mediation model was constructed with structural equation model (SEM) for the causal analysis of the three biomarkers in osteosarcoma patients. The results suggested a mediating effect of p-AKT for the causal relationship between EGFR and Ki-67. The study also found significant associations between EGFR and Ki-67 (p = 0.002), EGFR and p-AKT (p = 0.027), and p-AKT and Ki-67 controlling EGFR (p = 0.004). After the impact of EGFR on Ki-67 was accounted for by p-AKT, the relation between EGFR and Ki-67 was no longer significant (p = 0.381). The mediating effect was confirmed with Sobel test (p < 0.001) and Goodman (I) test (p < 0.001). The study indicated that a mediation model could be an approach to exploring the correlation pattern of EGFR and AKT signal pathway for cancer cell proliferation in OS patients in clinical study

COMPLETELY DISJUNCTIVE LANGUAGES

A language over a finite alphabet X is called disjunctive if the principal congruence PL determined by L is the equality. A dense language is a language which has non-empty intersection with any two-sided ideal of the free monoid X* generated by the alphabet X. We call an infinite language L completely disjunctive (completely dense) if every infinite subset of L is disjunctive (dense). For a language L, if every dense subset of L is disjunctive, then we call L quasi-completely disjunctive. In this paper, (for the case IXI ≥ 2) we show that every completely disjunctive language is completely dense and conversely. Characterizations of completely disjunctive languages and quasi-completely disjunctive languages were obtained. We also discuss some operations on the families of languages

Network-based stratification analysis of 13 major cancer types using mutations in panels of cancer genes.

BACKGROUND: Cancers are complex diseases with heterogeneous genetic causes and clinical outcomes. It is critical to classify patients into subtypes and associate the subtypes with clinical outcomes for better prognosis and treatment. Large-scale studies have comprehensively identified somatic mutations across multiple tumor types, providing rich datasets for classifying patients based on genomic mutations. One challenge associated with this task is that mutations are rarely shared across patients. Network-based stratification (NBS) approaches have been proposed to overcome this challenge and used to classify tumors based on exome-level mutations. In routine research and clinical applications, however, usually only a small panel of pre-selected genes is screened for mutations. It is unknown whether such small panels are effective in classifying patients into clinically meaningful subtypes. RESULTS: In this study, we applied NBS to 13 major cancer types with exome-level mutation data and compared the classification based on the full exome data with those focusing only on small sets of genes. Specifically, we investigated three panels, FoundationOne (240 genes), PanCan (127 genes) and TruSeq (48 genes). We showed that small panels not only are effective in clustering tumors but also often outperform full exome data for most cancer types. We further associated subtypes with clinical data and identified 5 tumor types (CRC-Colorectal carcinoma, HNSC-Head and neck squamous cell carcinoma, KIRC-Kidney renal clear cell carcinoma, LUAD-Lung adenocarcinoma and UCEC-Uterine corpus endometrial carcinoma) whose subtypes are significantly associated with overall survival, all based on small panels. CONCLUSION: Our analyses indicate that effective patient subtyping can be carried out using mutations detected in smaller gene panels, probably due to the enrichment of clinically important genes in such panels

The Influence of Molar Furcation Involvement and Mobility on Future Clinical Periodontal Attachment Loss

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/141720/1/jper0025.pd