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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…

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…

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…

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…

Limiting distributions of ratios of Binomial random variables
Adriel Barretto, Zachary Lubberts
https://arxiv.org/abs/2506.13071 https://

Limiting distributions of ratios of Binomial random variables
We consider the limiting distribution of the quantity $X^s/(X+Y)^r$, where $X$ and $Y$ are two independent Binomial random variables with a common success probability and a number of trials $n$ and $m$, respectively, and $r,s$ are positive real numbers. Under several settings, we prove that this converges to a Normal distribution with a given mean and variance, and demonstrate these theoretical results through simulations.

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BiAssemble: Learning Collaborative Affordance for Bimanual Geometric Assembly
Yan Shen, Ruihai Wu, Yubin Ke, Xinyuan Song, Zeyi Li, Xiaoqi Li, Hongwei Fan, Haoran Lu, Hao dong
https://arxiv.org/abs/2506.06221

BiAssemble: Learning Collaborative Affordance for Bimanual Geometric Assembly
Shape assembly, the process of combining parts into a complete whole, is a crucial robotic skill with broad real-world applications. Among various assembly tasks, geometric assembly--where broken parts are reassembled into their original form (e.g., reconstructing a shattered bowl)--is particularly challenging. This requires the robot to recognize geometric cues for grasping, assembly, and subsequent bimanual collaborative manipulation on varied fragments. In this paper, we exploit the geometri…