A functional decomposition theorem for the conformal representation

A Representation Theorem for Unique Decomposition Categories

Haghverdi introduced the notion of unique decomposition categories as a foundation for categorical study of Girard’s Geometry of Interaction (GoI). The execution formula in GoI provides a semantics of cut-elimination process, and we can capture the execution formula in every unique decomposition category: each hom-set of a unique decomposition category comes equipped with a partially defined co...

New Functional Representation for the Decomposition of Machine Learning Problems

The central idea in machine learning is to gather information from a given data set. This can be a very difficult task because practical databases are usually very large. To address this difficulty, the assumption of Occam’s Razor (simplest is best) and explicit domain knowledge are used to reduce the search space [3, 4]. Machine learning is not an exact methodology or formal theory of learning...

A non-renormalization theorem for conformal anomalies

We provide a non-renormalization theorem for the coefficients of the conformal anomaly associated with operators with vanishing anomalous dimensions. Such operators include conserved currents and chiral operators in superconformal field theories. We illustrate the theorem by computing the conformal anomaly of 2-point functions both by a computation in the conformal field theory and via the adS/...

A Decomposition Theorem for Domains

A domain constructor that generalizes the product is de ned. It is shown that with this constructor exactly the prime-algebraic coherent Scott-domains and the empty set can be generated from two-chains and boolean at domains. 3 List of Symbols I am identifying the symbols by the corresponding Latex(+Amssymb)-symbols. " uparrow # downarrow ! rightarrow ? bot > top leq geq 2 in W bigvee V bigwedg...

A Martingale Decomposition Theorem