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IBIS: Inverse BInomial sum Solver
Paul A. J. W. van Hoegaerden, Coenraad B. Marinissen, Wouter J. Waalewijn
https://arxiv.org/abs/2506.19904 https://

IBIS: Inverse BInomial sum Solver
In higher-loop calculations, Mellin-Barnes representations are used to simplify the denominators encountered in Feynman parameter integrals. The contour integral of these representations yield sums over residues. We extend the classes of such sums that can be calculated, to include those involving inverse binomials. Our results are expressed in terms of so-called $S$-sums, where the dependence on the upper limit of the sum is analytic. This is accomplished by deriving several new recursion rela…

Inference for Error-Prone Count Data: Estimation under a Binomial Convolution Framework
Yuqiu Yang, Christina Vu, Cornelis J. Potgieter, Xinlei Wang, Akihito Kamata
https://arxiv.org/abs/2506.20596

Inference for Error-Prone Count Data: Estimation under a Binomial Convolution Framework
Measurement error in count data is common but underexplored in the literature, particularly in contexts where observed scores are bounded and arise from discrete scoring processes. Motivated by applications in oral reading fluency assessment, we propose a binomial convolution framework that extends binary misclassification models to settings where only the aggregate number of correct responses is observed, and errors may involve both overcounting and undercounting the number of events. The mode…

Boosting Binomial Exotic Option Pricing with Tensor Networks
Maarten van Damme, Rishi Sreedhar, Martin Ganahl
https://arxiv.org/abs/2505.17033 https://

Boosting Binomial Exotic Option Pricing with Tensor Networks
Pricing of exotic financial derivatives, such as Asian and multi-asset American basket options, poses significant challenges for standard numerical methods such as binomial trees or Monte Carlo methods. While the former often scales exponentially with the parameters of interest, the latter often requires expensive simulations to obtain sufficient statistical convergence. This work combines the binomial pricing method for options with tensor network techniques, specifically Matrix Product States…

SViP: Sequencing Bimanual Visuomotor Policies with Object-Centric Motion Primitives
Yizhou Chen, Hang Xu, Dongjie Yu, Zeqing Zhang, Yi Ren, Jia Pan
https://arxiv.org/abs/2506.18825

SViP: Sequencing Bimanual Visuomotor Policies with Object-Centric Motion Primitives
Imitation learning (IL), particularly when leveraging high-dimensional visual inputs for policy training, has proven intuitive and effective in complex bimanual manipulation tasks. Nonetheless, the generalization capability of visuomotor policies remains limited, especially when small demonstration datasets are available. Accumulated errors in visuomotor policies significantly hinder their ability to complete long-horizon tasks. To address these limitations, we propose SViP, a framework that se…

Bulls vs Bears: a Trinomial Model of a Financial Asset
Nahuel I. Arca
https://arxiv.org/abs/2505.18723 https://arxiv.org/pdf/2505.187…

Bulls vs Bears: a Trinomial Model of a Financial Asset
We present a variation of the well-known binomial model of asset prices. This variation incorporates a bound to short-selling, inspired by a model from Gunduz Caginalp[2]. We formalize this model and prove a formula for all the moments of the logarithmic returns. We also derive a formula for the case with infinitely many investors. As an application of the model, we show how to compute parameters in order to approximate given moments, enabling the modeling of skewness and excess kurtosis. Final…

Asymptotic behaviors of fractional binomial distributions derived from the generalized binomial theorem
Masanori Hino, Ryuya Namba
https://arxiv.org/abs/2506.10438

Asymptotic behaviors of fractional binomial distributions derived from the generalized binomial theorem
A fractional binomial distribution, introduced by Hino and Namba (2024) via the generalized binomial theorem, is a fractional variant of the classical binomial distribution. Building upon previous work that established limit theorems, such as the weak law of large numbers and the central limit theorem, for fractional binomial distributions, this paper further investigates their asymptotic behaviors. Specifically, we derive the large and moderate deviation principles and a Berry--Esseen type est…

On Differential and Boomerang Properties of a Class of Binomials over Finite Fields of Odd Characteristic
Namhun Koo, Soonhak Kwon
https://arxiv.org/abs/2506.11486

On Differential and Boomerang Properties of a Class of Binomials over Finite Fields of Odd Characteristic
In this paper, we investigate the differential and boomerang properties of a class of binomial $F_{r,u}(x) = x^r(1 + uχ(x))$ over the finite field $\mathbb{F}_{p^n}$, where $r = \frac{p^n+1}{4}$, $p^n \equiv 3 \pmod{4}$, and $χ(x) = x^{\frac{p^n -1}{2}}$ is the quadratic character in $\mathbb{F}_{p^n}$. We show that $F_{r,\pm1}$ is locally-PN with boomerang uniformity $0$ when $p^n \equiv 3 \pmod{8}$. To the best of our knowledge, the second known non-PN function class with boomerang uniformi…

A quadratic Abramovich-Bertram formula
Erwan Brugall\'e, Kirsten Wickelgren
https://arxiv.org/abs/2506.17854 https://arxiv.org/pd…

A quadratic Abramovich-Bertram formula
Quadratic Gromov--Witten invariants allow one to obtain an arithmetically meaningful count of curves satisfying constraints over a field $k$ without assuming that $k$ is the field of complex or real numbers. This paper studies the behavior of quadratic genus $0$ Gromov--Witten invariants during an algebraic analogue of surgery on del Pezzo surfaces. For this, we define and study (twisted) binomial coefficients in the Grothendieck--Witt group, building on work of Serre. We obtain a formula expre…

Nicotinesticks met smaakjes zijn nu nog toegestaan, maar bevatten 18 keer meer nicotine dan goed is voor het hart | Binnenland | #gelderlander