Tootfinder

Binomial Convolution of Sequences
Kunle Adegoke
https://arxiv.org/abs/2507.04179 https://arxiv.org/pdf/2507.04179

Binomial Convolution of Sequences
Given any two sequences of complex numbers, we establish simple relations between their binomial convolution and the binomial convolution of their individual binomial transforms. We employ these relations to derive new identities involving Fibonacci numbers, Bernoulli numbers, harmonic numbers, odd harmonic numbers and binomial coefficients.

Binomial edge ideals of crown graphs
Arvind Kumar, Joshua Pomeroy, Le Tran
https://arxiv.org/abs/2507.03889 https://arxiv.org/pdf/250…

Binomial edge ideals of crown graphs
In this article, we explore the class of graphs for which the projective dimension of the quotient of the binomial edge ideals matches the big height of that ideal. Additionally, we investigate the Vasconcelos number of binomial edge ideals for cycles and crown graphs. We also provide proof for [Conjecture 4.13, 3], which is related to the Vasconcelos number of binomial edge ideals for cycles.

Safe Bimanual Teleoperation with Language-Guided Collision Avoidance
Dionis Totsila, Clemente Donoso, Enrico Mingo Hoffman, Jean-Baptiste Mouret, Serena Ivaldi
https://arxiv.org/abs/2507.04791

Safe Bimanual Teleoperation with Language-Guided Collision Avoidance
Teleoperating precise bimanual manipulations in cluttered environments is challenging for operators, who often struggle with limited spatial perception and difficulty estimating distances between target objects, the robot's body, obstacles, and the surrounding environment. To address these challenges, local robot perception and control should assist the operator during teleoperation. In this work, we introduce a safe teleoperation system that enhances operator control by preventing collisions i…

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…

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A Statistical Framework for Co-Mediators of Zero-Inflated Single-Cell RNA-Seq Data
Seungjun Ahn, Zhigang Li
https://arxiv.org/abs/2507.06113 https://

A Statistical Framework for Co-Mediators of Zero-Inflated Single-Cell RNA-Seq Data
Single-cell RNA sequencing (scRNA-seq) has revolutionized the study of cellular heterogeneity, enabling detailed molecular profiling at the individual cell level. However, integrating high-dimensional single-cell data into causal mediation analysis remains challenging due to zero inflation and complex mediator structures. We propose a novel mediation framework leveraging zero-inflated negative binomial models to characterize cell-level mediator distributions and beta regression for zero-inflati…

Discrete Boltzmann distributions via multisets and their coefficients
Bart Jacobs
https://arxiv.org/abs/2507.05719 https://arxiv.org/…

Discrete Boltzmann distributions via multisets and their coefficients
This paper investigates the combinatorics that gives rise to the Boltzmann probability distribution. Despite being one of the most important distributions in physics and other fields of science, the mathematics of the underlying model of particles at different energy levels is underexplored. This paper gives a reconstruction, using multisets with fixed sums as mathematical representations. Counting (the coefficients of) such multisets gives a general description of binomial, trinomial, quadrino…

Kamer stuurt aan op forse trendbreuk in openbaar vervoer: provincies mogen het weer zelf gaan regelen | de *Volkskrant
https://www.volkskrant.nl/binnenland/kamer-stuurt-aan-op-forse-…

Characterizing circle graphs with binomial partial Petrial polynomials
Ruiqing Feng, Qi Yan, Xuan Zheng
https://arxiv.org/abs/2507.02421 https://

Characterizing circle graphs with binomial partial Petrial polynomials
The partial Petrial polynomial was first introduced by Gross, Mansour, and Tucker as a generating function that enumerates the Euler genera of all possible partial Petrials on a ribbon graph. Yan and Li later extended this polynomial invariant to circle graphs by utilizing the correspondence between circle graphs and bouquets. Their explicit computation demonstrated that paths produce binomial polynomials, specifically those containing exactly two non-zero terms. This discovery led them to pose…

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@… #politiek #debat