Related papers: On the Method of Brackets
The structural characterization of high-dimensional mutually unbiased bases (MUBs) by classifying MUBs subsets remains a major open problem. The existing methods not only fail to conclude on the exact classification, but also are severely…
Mellin-Barnes integral representation of one-loop off-shell box massless diagram is five-fold by construction. On the other hand, it is known from the year 1992 that it may be reduced to certain two-fold Mellin-Barnes integral. We propose a…
Concept bottleneck models (CBMs) are a class of interpretable neural network models that predict the target response of a given input based on its high-level concepts. Unlike the standard end-to-end models, CBMs enable domain experts to…
In this work we present the relation between method of brackets and the master theorem of Ramanujan in the evaluation of multivariable integrals, in this case Feynman diagrams.
We develop an immersed boundary (IB) method for modeling flows around fixed or moving rigid bodies that is suitable for a broad range of Reynolds numbers, including steady Stokes flow. The spatio-temporal discretization of the fluid…
Multiple Mellin-Barnes integrals are often used for perturbative calculations in particle physics. In this context, the evaluation of such objects may be performed through residues calculations which lead to their expression as multiple…
In this paper, we propose a real-world benchmark for studying robotic learning in the context of functional manipulation: a robot needs to accomplish complex long-horizon behaviors by composing individual manipulation skills in functionally…
Motivated by classical vortex blob methods for the Euler equations, we develop a numerical blob method for the aggregation equation. This provides a counterpoint to existing literature on particle methods. By regularizing the velocity field…
In this article, we introduce the concept of model confidence bounds (MCB) for variable selection in the context of nested models. Similarly to the endpoints in the familiar confidence interval for parameter estimation, the MCB identifies…
A key prerequisite to optimal reasoning under uncertainty in intelligent systems is to start with good class probability estimates. This paper improves on the current best probability estimation trees (Bagged-PETs) and also presents a new…
We begin by introducing an algebraic structure with three constants and one ternary operation to which we call mobi algebra. This structure has been designed to capture the most relevant properties of the unit interval that are needed in…
In this paper, we consider the problem of minimizing a difference-of-convex objective over a nonlinear conic constraint, where the cone is closed, convex, pointed and has a nonempty interior. We assume that the support function of a compact…
A numerical tool relying on sharp Immersed Boundary Method (IBM) is developed for the analysis of aerospace applications. The method, which is conceived for application using segregated solvers relying on implicit time discretization, uses…
Multidimensional population balance models (PBMs) describe chemical and biological processes having a distribution over two or more intrinsic properties (such as size and age, or two independent spatial variables). The incorporation of…
Integrative modeling of macromolecular assemblies allows for structural characterization of large assemblies that are recalcitrant to direct experimental observation. A Bayesian inference approach facilitates combining data from…
The machine learning (ML) techniques to predict unitarity (UNI) and bounded from below (BFB) constraints in multi-scalar models is employed. The effectiveness of this approach is demonstrated by applying it to the two and three Higgs…
Multimarginal Optimal Transport (MOT) is the problem of linear programming over joint probability distributions with fixed marginals. A key issue in many applications is the complexity of solving MOT: the linear program has exponential size…
Prevailing machine-learned interatomic potential (MLIP) uncertainty-quantification methods rely on ensembles of independently trained backbones. These methods scale unfavorably with foundation-scale MLIPs, and their member-disagreement…
In this paper, we introduce Ballooning Multi-Armed Bandits (BL-MAB), a novel extension of the classical stochastic MAB model. In the BL-MAB model, the set of available arms grows (or balloons) over time. In contrast to the classical MAB…
The problem of machine learning with missing values is common in many areas. A simple approach is to first construct a dataset without missing values simply by discarding instances with missing entries or by imputing a fixed value for each…