Tootfinder

Perceptual Rationality: An Evolutionary Game Theory of Perceptually Rational Decision-Making
Mohammad Salahshour
https://arxiv.org/abs/2506.17724 https://

Perceptual Rationality: An Evolutionary Game Theory of Perceptually Rational Decision-Making
Understanding how biological organisms make decisions is of fundamental importance in understanding behavior. Such an understanding within evolutionary game theory so far has been sought by appealing to bounded rationality. Here, we present a perceptual rationality framework in the context of group cooperative interactions, where individuals make rational decisions based on their evolvable perception of the environment. We show that a simple public goods game accounts for power law distributed …

Simultaneous multiplicative rational approximation to a real and a $p$-adic numbers
Yann Bugeaud, Bernard de Mathan
https://arxiv.org/abs/2507.16503 https:…

Simultaneous multiplicative rational approximation to a real and a $p$-adic numbers
We give new examples of pairs composed of a real and a $p$-adic numbers that satisfy a conjecture on simultaneous multiplicative approximation by rational numbers formulated by Einsiedler and Kleinbock in 2007.

Homological stability and Manin's conjecture for rational curves on quartic del Pezzo surfaces
Ronno Das, Brian Lehmann, Sho Tanimoto, Philip Tosteson
https://arxiv.org/abs/2506.17071

Homological stability and Manin's conjecture for rational curves on quartic del Pezzo surfaces
We prove a version of Manin's conjecture (over $\mathbb{F}_{q}$ for $q$ large) and the Cohen--Jones--Segal conjecture (over $\mathbb{C}$) for maps from rational curves to split quartic del Pezzo surfaces. The proofs share a common method which builds upon prior work of the first and fourth authors. The main ingredients of this method are (i) the construction of bar complexes formalizing the inclusion-exclusion principle and its point counting estimates, (ii) dimension estimates for spaces of ra…

The rational homotopy groups of virtual spheres for rank 1 compact Lie groups
J. P. C. Greenlees
https://arxiv.org/abs/2506.18085 https://

The rational homotopy groups of virtual spheres for rank 1 compact Lie groups
We calculate the rational representation-ring-graded stable stems for rank 1 groups, SU(2), SO(3), Pin (2), O(2), Spin(2) and SO(2), in the same spirit as the calculations for finite groups in arXiv:2205.02382 with J.D.Quigley. This illustrates the effectiveness of the algebraic models for these categories of G-spectra, and the way tom Dieck splitting fails for desuspensions.

Rational Motions of Minimal Quaternionic Degree with Prescribed Line Trajectories
Z\"ulal Derin Yaqub, Hans-Peter Schr\"ocker
https://arxiv.org/abs/2506.18029

Rational Motions of Minimal Quaternionic Degree with Prescribed Line Trajectories
In this paper, we study how to find rational motions that move a line along a given rational ruled surface. Our goal is to find motions with the lowest possible degree using dual quaternions. While similar problems for point trajectories are well known, the case of line trajectories is more complicated and has not been studied. We explain when such motions exist and how to compute them. Our method gives explicit formulas for constructing these motions and shows that, in many cases, the solution…

A Deep Convolutional Neural Network-Based Novel Class Balancing for Imbalance Data Segmentation
Atifa Kalsoom, M. A. Iftikhar, Amjad Ali, Zubair Shah, Shidin Balakrishnan, Hazrat Ali
https://arxiv.org/abs/2506.18474

A Deep Convolutional Neural Network-Based Novel Class Balancing for Imbalance Data Segmentation
Retinal fundus images provide valuable insights into the human eye's interior structure and crucial features, such as blood vessels, optic disk, macula, and fovea. However, accurate segmentation of retinal blood vessels can be challenging due to imbalanced data distribution and varying vessel thickness. In this paper, we propose BLCB-CNN, a novel pipeline based on deep learning and bi-level class balancing scheme to achieve vessel segmentation in retinal fundus images. The BLCB-CNN scheme uses …

Determinant formulas for finite Toeplitz plus Hankel matrices with rational symbols
Estelle Basor, Kent E. Morrison
https://arxiv.org/abs/2506.16613 https:…

Determinant formulas for finite Toeplitz plus Hankel matrices with rational symbols
In 1975 K. Michael Day produced an exact formula for the determinants of finite Toeplitz matrices whose symbols are rational. The answer is a sum that involves powers of the roots of the numerator of the symbol and whose coefficients depend on both the roots of the numerator and denominator. In this paper we prove an analogue of Day's formula for determinants of finite Toeplitz plus Hankel matrices with rational symbols. The key to the proof is an exact formula for the finite determinants that …

The spaces of rational curves on del Pezzo surfaces via conic bundles
Sho Tanimoto
https://arxiv.org/abs/2506.18239 https://arxiv.org…

The spaces of rational curves on del Pezzo surfaces via conic bundles
Using the homological sieve method developed by Das--Lehmann--Tosteson and the author, we prove Peyre's all height approach to Manin's conjecture for split quintic del Pezzo surfaces defined over $\mathbb F_q(t)$ assuming $q$ is sufficiently large. We also establish lower bounds of correct magnitude for the counting function of rational curves on split low degree del Pezzo surfaces defined over $\mathbb F_q$ assuming $q$ is large.

Effective bounds for polynomial systems defined over the rationals
Teresa Krick
https://arxiv.org/abs/2506.18144 https://arxiv.org/pd…

Effective bounds for polynomial systems defined over the rationals
This survey paper was primarily written as as the support for a course pesented at the JNCF2025: it aims to present some material that illustrates the kind of estimates one can obtain in effective algebraic geometry, for affine polynomial equation systems defined over the rational numbers Q, and focuses on the case of finite varieties.

Severi varieties on Enriques surfaces of base change type and on rational elliptic surfaces
Simone Pesatori
https://arxiv.org/abs/2506.18453 https://

Severi varieties on Enriques surfaces of base change type and on rational elliptic surfaces
If an irreducible curve on the very general Enriques surface splits in the K3 cover, its preimage consists of two linearly equivalent irreducible curves. We prove the nonemptiness of countable families of Severi varieties of curves of any genus on Enriques surfaces of base change type, whose members split in nonlinearly equivalent curves in the K3 cover. Our machinery leads us to provide examples of special superabundant logarithmic Severi varieties of curves of any genus on rational elliptic s…