8 papers
Glass-Box Analysis for Computer Systems: Transparency Index, Shapley Attribution, and Markov Models of Branch Prediction
Faruk Alpay, Hamdi Alakkad
We formalize glass-box analysis for computer systems and introduce three principled tools. First, the Glass-Box Transparency Index (GTI) quantifies the fraction of performance vari…
On the Fixed Point Property in Reflexive Banach Spaces
Faruk Alpay, Hamdi Alakkad
Fixed point theory studies conditions under which nonexpansive maps on Banach spaces have fixed points. This paper examines the open question of whether every reflexive Banach spac…
Quantization Errors, Human--AI Interaction, and Approximate Fixed Points in
Faruk Alpay, Hamdi Alakkad
We develop a rigorous measure-theoretic framework for the analysis of fixed points of nonexpansive maps in the space , with explicit consideration of quantization errors ar…
New Approaches to the Fixed Point Property in L^1 Spaces
Faruk Alpay, Hamdi Alakkad
This paper presents new approaches to the fixed point property for nonexpansive mappings in L^1 spaces. While it is well-known that L^1 fails the fixed point property in general, w…
Fixed-Point Theorems and the Ethics of Radical Transparency: A Logic-First Treatment
Faruk Alpay, Hamdi Alakkad
This paper establishes a formal framework, grounded in mathematical logic and order theory, to analyze the inherent limitations of radical transparency. We demonstrate that self-re…
Nonlinear Continuum of States and Intuitionistic Flows in a Cognitive Space
Faruk Alpay, Taylan Alpay
We construct a rigorous mathematical framework for an abstract continuous evolution of an internal state, inspired by the intuitive notion of a flowing thought sequence. Using tool…