Related papers: Syzygies Probing Scattering Amplitudes
Efficient sampling from a classical Gibbs distribution is an important computational problem with applications ranging from statistical physics over Monte Carlo and optimization algorithms to machine learning. We introduce a family of…
In recent years, the problem of fuzzy clustering has been widely concerned. The membership iteration of existing methods is mostly considered globally, which has considerable problems in noisy environments, and iterative calculations for…
We study linear relations between color-ordered all-plus amplitudes at one loop in Yang--Mills theory. We show that on general grounds, there are $(n-1)!/2-2$ relations for $n\ge 5$, leaving only two independent color-ordered amplitudes. We…
The speed of quantum random number generators is a major concern for practical quantum applications. However, the bit extraction process limits the final bit rate due to lack of comparably fast electronics. Here we introduce optical…
In these proceedings, we discuss the recent approach of Ref. [1] for the construction of compact Ans\"atze for scattering amplitudes. The method builds powerful constraints on the analytic structure of the rational functions in amplitudes…
A wide variety of problems in machine learning, including exemplar clustering, document summarization, and sensor placement, can be cast as constrained submodular maximization problems. A lot of recent effort has been devoted to developing…
We use massive spinor helicity formalism to study scattering amplitudes in $\mathcal{N}=2^*$ super-Yang-Mills theory in four dimensions. We compute the amplitudes at an arbitrary point in the Coulomb branch of this theory. We compute…
As we have shown in previous work, the high energy limit of scattering amplitudes in N=4 supersymmetric Yang-Mills theory corresponds to the infrared limit of the 1-dimensional quantum integrable system that solves minimal area problems in…
Two minimal generating sets of the first syzygies of a monomial ideal are produced, given the minimal generating set of the ideal.
Synthetic Data Generation (SDG), leveraging Large Language Models (LLMs), has recently been recognized and broadly adopted as an effective approach to improve the performance of smaller but more resource and compute efficient LLMs through…
The scattering theory of the integrable statistical models can be generalized to the case of systems with extended lines of defect. This is done by adding the reflection and transmission amplitudes for the interactions with the line of…
The distributed subgradient method (DSG) is a widely discussed algorithm to cope with large-scale distributed optimization problems in the arising machine learning applications. Most exisiting works on DSG focus on ideal communication…
The major problem in information theoretic analysis of neural responses and other biological data is the reliable estimation of entropy--like quantities from small samples. We apply a recently introduced Bayesian entropy estimator to…
We describe a self calibrating optical technique that allows to perform absolute measurements of scattering cross sections for the light scattered at extremely small angles. Very good performances are obtained by using a very simple optical…
In cluster analysis interest lies in probabilistically capturing partitions of individuals, items or observations into groups, such that those belonging to the same group share similar attributes or relational profiles. Bayesian posterior…
Scattering amplitudes are both a wonderful playground to discover novel ideas in Quantum Field Theory and simultaneously of immense phenomenological importance to make precision predictions for e.g.~particle collider observables and more…
We study the geometry underlying the Wilson loop diagram approach to calculating scattering amplitudes in the gauge theory of Supersymmetric Yang Mills (SYM) $N=4$. By applying the tools developed to study total positivity in the real…
This chapter introduces the foundational elements of scattering amplitudes. It is meant to be accessible to readers with only a basic understanding of quantum field theory. Topics covered include: the four-dimensional spinor-helicity…
We characterise possible identities among the two-loop partial amplitudes of gluon scattering in Yang-Mills theory. We use known amplitudes in an exhaustive search to identify potential new relations. We find two candidate relations which…
Maximum entropy modeling is a flexible and popular framework for formulating statistical models given partial knowledge. In this paper, rather than the traditional method of optimizing over the continuous density directly, we learn a smooth…