Posts

The Independence of the Axiom of Choice From Zermelo-Fraenkel Set Theory (ZF)

 Here is the link to my blog post.   This week we will finish discussing the prerequisite set theory necessary to understanding the Banach-Tarski Theorem.

Implications of the Axiom of Choice Within Set Theory

Here is the link to this week's blog post! I did not have the time to write about everything I planned to this week, but hopefully next week I can finish the discussion of set theory and move on to the geometry of the Banach-Tarski theorem.

The Incompleteness Theorems and Their Relevance to Axiomatic Indeterminance

Here is the link to the Google Document for this week's blog post. Unfortunately I am still unable to upload to Blogger due to the lack of support for mathematical notation. 

Research Proposal For the Study of Transinfinant Sets as They Relate to the Banach-Tarski Theorem

Unfortunately, Blogger is making it very difficult for me to retain the formatting of the mathematical notation in my writing when using their client. Due to this I will be hosting my blogpost for this week on Google Docs at this link while I work to find a longterm solution to this issue. I have enabled commenting on the document. I apologize for any inconvenience. 

Designing a Research Project to Facilitate Further Understanding of the Development of Melanocytes in Relation to Delocalized Cytoplasmic Pirin

Throughout the course of the last several months I have utilized several biology databases and much scientific literature to investigate the novel protein pirin and the PIR gene that encodes it. This week will be the apotheosis of my efforts, in which I will design a research project to conduct upon pirin that will, hopefully, help us to develop a better understanding of the protein. The question as to what type of experiment to design for pirin is an extremely broad one; over the course of this blog I have discussed pirin’s role as a transcriptional cofactor, its correlation with the maturation of myeloid hematopoietic cells and thereby its possible role in the development of leukemia, the potential for pirin to play a role in programmed cell death, and many other aspects of the protein that warrant further research ( The UniProt Consortium, 2021) . However, the research I wish to engage in revolves around pirin's potential to contribute to melanoma when decentralized from the cel...

The Repeat Masker Tool Within the UCSC Genome Browser

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This week I will continue to utilize the UCSC Genome Browser ( http://genome.ucsc.edu/ ), this time using the Repeat Masker track to research the repeat elements of the PIR gene (Kent, Sugnet, Furey, et al., 2002). Repeat elements are sections of the genome that repeat themselves within the genome. The Screen Masker track is capable of displaying 10 separate classes of repeats: SINE, LINE, LTR, DNA, Simple, Low Complexity, Satellite, RNA, Others, and Unknown. Within each of these classes, areas of the PIR gene are shaded from a light grey to a very dark grey to indicate how many “Base mismatches, base deletions, and base insertions [are] associated with a repeat element,” with a higher number of these being indicated by light shading, while a lower number is indicated by darker shading.  Utilizing this knowledge we can see that classes such as LINE and LTR have relatively high concentrations of repeats and classes such as LINE and DNA contain longer repeats. Understan...

Using the ORegAnno Track in The UCSC Genome Browser to Research PIR' Regulatory Elements

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This week I will continue to utilize the UCSC Genome Browser ( http://genome.ucsc.edu ) to investigate the PIR gene; particularly, I will be using the ORegAnno track within the database (Kent, Sugnet, Furey, et al., 2002). ORegAnno, short for Open Regulatory Annotation, seeks to document curated information concerning the regulatory factors of genes (Operators and operands, silencers, repressor proteins, transcription factors and cofactors, etc.). Previously in this blog I discussed the redox-sensitive nature of pirin, and how said redox-sensitivity may contribute to pirin acting as a transcriptional cofactor by allowing pirin to interact allosterically with transcription factors in redox-specific environments. Conversely, this week I will be focusing on the regulatory factors involved in the expression of the PIR (Pirin encoding) gene, rather than what regulations PIR expression may itself contribute towards.  Navigating to the ORegAnno track for PIR on the Genome Browser retu...