arXiv subjects
Publications and source records attributed to Lucas Martin.
The tree-level type II superstring theory scattering amplitude of two dilatons and two dilatinos is explicitly calculated from the Kawai-Lewellen-Tye relations. The corresponding Regge behavior is obtained.
We calculate the glueball-fermion hard-scattering amplitude from the dilaton-dilatino closed string scattering amplitude in type IIB superstring theory, in the framework of the gauge/string theory duality. We investigate its high-energy scaling at fixed angle and also in the Regge limit. We derive the leading and sub-leading terms contributing to the scattering cross section. This dual calculation of the glueball-fermion scattering amplitude is particularly interesting since it involves the scattering of two different types of external states. We calculate explicitly some angular integrals for two scalar spherical harmonics and two spinor spherical harmonics on the five-sphere, leading to selection rules.
Large language models (LLMs) have shown remarkable progress in mathematical problem-solving, but evaluation has largely focused on problems that have exact analytical solutions or involve formal proofs, often overlooking approximation-based problems ubiquitous in applied science and engineering. To fill this gap, we build on prior work and present HARDMath2, a dataset of 211 original problems covering the core topics in an introductory graduate applied math class, including boundary-layer analysis, WKB methods, asymptotic solutions of nonlinear partial differential equations, and the asymptotics of oscillatory integrals. This dataset was designed and verified by the students and instructors of a core graduate applied mathematics course at Harvard. We build the dataset through a novel collaborative environment that challenges students to write and refine difficult problems consistent with the class syllabus, peer-validate solutions, test different models, and automatically check LLM-generated solutions against their own answers and numerical ground truths. Evaluation results show that leading frontier models still struggle with many of the problems in the dataset, highlighting a gap in the mathematical reasoning skills of current LLMs. Importantly, students identified strategies to create increasingly difficult problems by interacting with the models and exploiting common failure modes. This back-and-forth with the models not only resulted in a richer and more challenging benchmark but also led to qualitative improvements in the students' understanding of the course material, which is increasingly important as we enter an age where state-of-the-art language models can solve many challenging problems across a wide domain of fields.
An explicit derivation of the four-dilatino scattering amplitude from type II superstring theory is presented. This is obtained by using the Kawai-Lewellen-Tye relations for closed string scattering amplitudes in terms of the product of two open string scattering amplitudes. We also investigate its Regge limit.
We study high-energy scattering at fixed angle in the planar limit of non-Abelian gauge field theories from type IIB superstring theory scattering amplitudes. Firstly, we consider four-glueball scattering described in terms of the four-dilaton string theory scattering amplitude. We explicitly calculate some angular integrals of four scalar spherical harmonics on the five sphere leading to selection rules for several scattering processes. Then, we consider the high-energy limit of the four-dilatino scattering amplitude in type IIB superstring theory, which allows to describe four spin-1/2 fermions scattering in the dual gauge field theory. In both cases the partonic structure of the scattering cross sections is obtained. The Regge behavior is also obtained. In addition, we study certain related aspects by considering the effective action constructed from IIB supergravity.
The shared response model provides a simple but effective framework to analyse fMRI data of subjects exposed to naturalistic stimuli. However when the number of subjects or runs is large, fitting the model requires a large amount of memory and computational power, which limits its use in practice. In this work, we introduce the FastSRM algorithm that relies on an intermediate atlas-based representation. It provides considerable speed-up in time and memory usage, hence it allows easy and fast large-scale analysis of naturalistic-stimulus fMRI data. Using four different datasets, we show that our method matches the performance of the original SRM algorithm while being about 5x faster and 20x to 40x more memory efficient. Based on this contribution, we use FastSRM to predict age from movie watching data on the CamCAN sample. Besides delivering accurate predictions (mean absolute error of 7.5 years), FastSRM extracts topographic patterns that are predictive of age, demonstrating that brain activity during free perception reflects age.