arXiv research

Multi-dimensional state-integrals of products of Faddeev's quantum dilogarithms arise frequently in Quantum Topology, quantum Teichmüller theory and complex Chern--Simons theory. Using the quasi-periodicity property of the quantum dilogarithm, we evaluate 1-dimensional state-integrals at rational points and express the…

This paper deals with the evaluation of double line integrals of the squared exponential covariance function. We propose a new approach in which the double integral is reduced to a single integral using the error function. This single integral is then computed with efficiently implemented numerical techniques. The perf…

The paper evaluates integrals of planes and their relation to convex set angles.

We give a purely combinatorial formula for evaluating closed decorated foams. Our evaluation gives an integral polynomial and is directly connected to an integral equivariant version of the $\mathfrak{sl}_N$ link homology categorifying the $\mathfrak{sl}_N$ link polynomial. We also provide connections to the equivarian…

A new method combines AIS and SMCI for efficient evaluation of Ising models.

The paper evaluates integrals for fBm with various Hurst indices.

Researchers calculate the Ray-Singer Torsion for $S^{1}$ bundles.

The paper addresses numerical integration issues in SV models, proposing a fast regime switching algorithm.

Derives integral representations for a Lévy process and its extremum, hitting time, with fast evaluation.

Paper uses Sugeno integral for binary classification with ordinal data.

We propose a Bayesian optimization algorithm for objective functions that are sums or integrals of expensive-to-evaluate functions, allowing noisy evaluations. These objective functions arise in multi-task Bayesian optimization for tuning machine learning hyperparameters, optimization via simulation, and sequential des…

We introduce a "minimal" Kontsevich integral that generates the original Kontsevich integral while at the same time producing ribbons whose boundaries are the braids on which the minimal Kontsevich integral is evaluated. We generalize the definition of the Kontsevich integral to that of graphs in R^3 and study the beha…

Q-NETs use neural networks to estimate integrals of low-dimensional functions efficiently.

Extends integrability to cosymplectic manifolds.

In this paper I develop a new computational method for pricing path dependent options. Using the path integral representation of the option price, I show that in general it is possible to perform analytically a partial averaging over the underlying risk-neutral diffusion process. This result greatly eases the computati…

The paper calculates the full asymptotics of analytic torsions for compact orbifolds.

3D BF theory on certain 3-manifolds evaluated via residues and large k limits.

We discuss several aspects of Mellin transform, including distributional Mellin transform and inversion of multiple Mellin-Barnes integrals in $\mathbb{C}^n$ and its connection to residue expansion or evaluation of Laplace integrals. These mathematical concepts are demonstrated on several option-pricing models. This in…

In this paper we analytically study the problem of pricing an arithmetically averaged Asian option in the path integral formalism. By a trick about the Dirac delta function, the measure of the path integral is defined by an effective action functional whose potential term is an exponential function. This path integral …

Study topological twists of massive SQCD with gauge group SU(2) and 3 or fewer fundamental hypermultiplets.

Proposes a diagnostic method to evaluate factor models using cap-axis integrals.

Proposes a diagnostic method to evaluate factor models using cap-axis integrals.

Gaussian process is a very promising novel technology that has been applied to both the regression problem and the classification problem. While for the regression problem it yields simple exact solutions, this is not the case for the classification problem, because we encounter intractable integrals. In this paper we …

A new method calculates fractional moments using the moment-generating function.

On asymptotically flat and asymptotically hyperbolic manifolds, by evaluating the total mass via the Ricci tensor, we show that the limits of certain Brown-York type and Hawking type quasi-local mass integrals equal the total mass of the manifold in all dimensions.

The purpose of this paper is to extend the explicit geometric evaluation of semisimple orbital integrals for smooth kernels for the Casimir operator obtained by the first author to the case of kernels for arbitrary elements in the center of the enveloping algebra.

Recommendation systems have been integrated into the majority of large online systems to filter and rank information according to user profiles. It thus influences the way users interact with the system and, as a consequence, bias the evaluation of the performance of a recommendation algorithm computed using historical…

Real-world applications often involve domain-specific and task-based performance objectives that are not captured by the standard machine learning losses, but are critical for decision making. A key challenge for direct integration of more meaningful domain and task-based evaluation criteria into an end-to-end gradient…

In many fields of science, high-dimensional integration is required. Numerical methods have been developed to evaluate these complex integrals. We introduce the code i-flow, a python package that performs high-dimensional numerical integration utilizing normalizing flows. Normalizing flows are machine-learned, bijectiv…

Bayesian quadrature improves integration on Riemannian manifolds.

Recommendation systems have been integrated into the majority of large online systems to filter and rank information according to user profiles. It thus influences the way users interact with the system and, as a consequence, bias the evaluation of the performance of a recommendation algorithm computed using historical…

Recommendation systems have been integrated into the majority of large online systems. They tailor those systems to individual users by filtering and ranking information according to user profiles. This adaptation process influences the way users interact with the system and, as a consequence, increases the difficulty …

Combines experimental and historical data for robust policy evaluation.

Efficiently approximates integrals using a subset of samples from a target distribution in RKHS.

We introduce a method for evaluating integrals in geometric calculus without introducing coordinates, based on using the fundamental theorem of calculus repeatedly and cutting the resulting manifolds so as to create a boundary and allow for the existence of an antiderivative at each step. The method is a direct general…

A new test evaluates risk estimation accuracy using probability integral transform.

Enhanced visual feature attribution via adaptive baseline weighting.

We construct cohomology classes in the space of knots by considering a bundle over this space and "integrating along the fiber" classes coming from the cohomology of configuration spaces using a Pontrjagin-Thom construction. The bundle we consider is essentially the one considered by Bott and Taubes, who integrated dif…

We establish an efficient compatibility criterion for a system of generalized complete intersection type in terms of certain multi-brackets of differential operators. These multi-brackets generalize the higher Jacobi-Mayer brackets, important in the study of evolutionary equations and the integrability problem. We also…

Improves accuracy of SMCI estimators without expanding sum regions.

Paper uses LightGBM for mobile user credit assessment.

GRETEL unifies GCE evaluation across various settings.

The path integral generalization of the Casson invariant as developed by Rozansky and Witten is investigated. The path integral for various three manifolds is explicitly evaluated. A new class of topological observables is introduced that may allow for more effective invariants. Finally it is shown how the dimensional …

We study finite-dimensional integrals in a way that elucidates the mathematical meaning behind the formal manipulations of path integrals occurring in quantum field theory. This involves a proper understanding of how Wick's theorem allows one to evaluate integrals perturbatively, i.e., as a series expansion in a formal…

The contribution of reducible connections to the U(N) Chern-Simons invariant of a Seifert manifold $M$ can be expressed in some cases in terms of matrix integrals. We show that the U(N) evaluation of the LMO invariant of any rational homology sphere admits a matrix model representation which agrees with the Chern-Simon…

The paper introduces ESE scores for farmers to assess climate change risks.

We use a path integral approach for solving the stochastic equations underlying the financial markets, and we show the equivalence between the path integral and the usual SDE and PDE methods. We analyze both the one-dimensional and the multi-dimensional cases, with point dependent drift and volatility, and describe a c…

Integrality of FJRW invariants for Lie algebras A_l, D_l, and E_6.