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"Analysis Situs" is a seminal mathematics paper that Henri Poincaré published in 1895. [1] Poincaré published five supplements to the paper between 1899 and 1904. [2]These papers provided the first systematic treatment of topology and revolutionized the subject by using algebraic structures to distinguish between non-homeomorphic topological spaces, founding the field of algebraic topology. [3]
Analysis Situs is a book by the Princeton mathematician Oswald Veblen, published in 1922. It is based on his 1916 lectures at the Cambridge Colloquium of the American Mathematical Society . The book, which went into a second edition in 1931, was the first English-language textbook on topology , and served for many years as the standard ...
Analysis (pl.: analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (384–322 BC), though analysis as a formal concept is a relatively recent development.
Philosophical analysis is any of various techniques, typically used by philosophers in the analytic tradition, in order to "break down" (i.e. analyze) philosophical issues. Arguably the most prominent of these techniques is the analysis of concepts , known as conceptual analysis .
Citation analysis for legal documents is an approach to facilitate the understanding and analysis of inter-related regulatory compliance documents by exploration of the citations that connect provisions to other provisions within the same document or between different documents.
The paper introduced a new deep learning architecture known as the transformer, based on the attention mechanism proposed in 2014 by Bahdanau et al. [4] It is considered a foundational [5] paper in modern artificial intelligence, as the transformer approach has become the main architecture of large language models like those based on GPT.
Thematic analysis provides a flexible method of data analysis and allows for researchers with various methodological backgrounds to engage in this type of analysis. [1] For positivists, 'reliability' is a concern because of the numerous potential interpretations of data possible and the potential for researcher subjectivity to 'bias' or distort ...
A systematic review focuses on a specific research question to identify, appraise, select, and synthesize all high-quality research evidence and arguments relevant to that question. A meta-analysis is typically a systematic review using statistical methods to effectively combine the data used on all selected studies to produce a more reliable ...