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The Takahashi and Alexander (TA) model is a widely used framework for simulating private equity cash flows. However, its core shape parameter b, which governs the distribution timing, lacks a direct connection to investor-relevant metrics such as internal rate of return (IRR) and total value to paid-in capital (TVPI). This article introduces a reformulation of the TA model that replaces the opaque b-parameter with a more intuitive and analytically derived function of the investor’s performance goals. We define a dimensionless quantity d=log(M)/(G*L) where M is the desired TVPI, G the target IRR, and L, the fund’s life. We then derive the relationship b=exp(pi*d)/sqrt(2) offering a closed-form link between fund performance objectives and the TA model’s cash flow shape. This formulation simplifies calibration, enhances interpretability, and enables goal-driven simulation of capital calls and distributions. Numerical validation confirms the robustness of the approximation across a wide range of practical scenarios, making the TA model significantly more accessible and aligned with real-world decision-making.

Modern high-performance computing is being reshaped by novel hardware architectures, particularly those developed for AI, offering unprecedented performance. Effectively using these systems for scientific workloads, however, often requires redesigning the underlying physics, algorithms, and data structures, as well as adapting existing methods to better align with these architectures. In this talk, we present our efforts to apply emerging AI hardware to non-AI workloads, specifically quantum chemistry and electronic structure calculations, and showcase our significant performance gains.