Tootfinder

A relative trace formula and counting geodesic arcs in the hyperbolic plane
Dimitrios Lekkas, Yiannis Petridis
https://arxiv.org/abs/2509.12902 https://arx…

A relative trace formula and counting geodesic arcs in the hyperbolic plane
We study a modification of the hyperbolic circle problem: instead of all elements of a Fuchsian group $Γ$, we consider the double cosets by two hyperbolic subgroups. This has a geometric interpretation in terms of the number of common perpendiculars between two closed geodesics for $Γ\backslash\mathbb{H}$. We prove an explicit relative trace formula, which is flexible for the counting problem. Using a large sieve inequality developed by the first author and Voskou, we prove a new bound in mea…

A note on helices in the Euclidean space and in the hyperbolic space
Rafael L\'opez
https://arxiv.org/abs/2507.12861 https://arxi…

A note on helices in the Euclidean space and in the hyperbolic space
We prove that general helices in Euclidean space for Killing vector fields associated to rotations are helices, that is, curves with constant curvature and constant torsion. In hyperbolic space $\h^3$, we obtain the parametrization of helices for the Killing vector fields associated to hyperbolic rotations, spherical rotations and parabolic rotations. It is proved that these helices are geodesics in suitable surfaces of $\h^3$.

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HANS-Net: Hyperbolic Convolution and Adaptive Temporal Attention for Accurate and Generalizable Liver and Tumor Segmentation in CT Imaging
Arefin Ittesafun Abian, Ripon Kumar Debnath, Md. Abdur Rahman, Mohaimenul Azam Khan Raiaan, Md Rafiqul Islam, Asif Karim, Reem E. Mohamed, Sami Azam
https://arxiv.org/abs/2507.11325

HANS-Net: Hyperbolic Convolution and Adaptive Temporal Attention for Accurate and Generalizable Liver and Tumor Segmentation in CT Imaging
Accurate liver and tumor segmentation on abdominal CT images is critical for reliable diagnosis and treatment planning, but remains challenging due to complex anatomical structures, variability in tumor appearance, and limited annotated data. To address these issues, we introduce Hyperbolic-convolutions Adaptive-temporal-attention with Neural-representation and Synaptic-plasticity Network (HANS-Net), a novel segmentation framework that synergistically combines hyperbolic convolutions for hierar…

Analysis of a parabolic-hyperbolic hybrid population model: an integrated semigroup approach
Qihua Huang, Minglong Wang, Yixiang Wu
https://arxiv.org/abs/2507.12833

Analysis of a parabolic-hyperbolic hybrid population model: an integrated semigroup approach
This paper is concerned with the global dynamics of a hybrid parabolic-hyperbolic model describing populations with distinct dispersal and sedentary stages. We first establish the global well-posedness of solutions, prove a comparison principle, and demonstrate the asymptotic smoothness of the solution semiflow. Through the spectral analysis of the linearized system, we derive and characterize the net reproductive rate $\mathcal{R}_{0}$. Furthermore, an explicit relationship between $\mathcal{R…

The Complexity of Generalized HyperLTL with Stuttering and Contexts
Ga\"etan Regaud (ENS Rennes), Martin Zimmermann (Aalborg University)
https://arxiv.org/abs/2509.14095 ht…

The Complexity of Generalized HyperLTL with Stuttering and Contexts
We settle the complexity of satisfiability and model-checking for generalized HyperLTL with stuttering and contexts, an expressive logic for the specification of asynchronous hyperproperties. Such properties cannot be specified in HyperLTL, as it is restricted to synchronous hyperproperties. Nevertheless, we prove that satisfiability is $Σ_1^1$-complete and thus not harder than for HyperLTL. On the other hand, we prove that model-checking is equivalent to truth in second-order arithmetic, and …

The End of Hyperbolic Growth in Human Population and CO$_2$ Emissions
Victor M. Yakovenko
https://arxiv.org/abs/2508.11038 https://arxiv.org/pdf/2508.11038…

The End of Hyperbolic Growth in Human Population and CO$_2$ Emissions
Using current empirical data from 10,000 BCE to 2023 CE, we re-examine a hyperbolic pattern of human population growth, which was identified by von Foerster et al. in 1960 with a predicted singularity in 2026. We find that human population initially grew exponentially in time as $N(t)\propto e^{t/T}$ with $T$=2080 years. This growth then gradually evolved to be super-exponential with a form similar to the Bose function in statistical physics. Around 1700, population growth further accelerated, …

Quadratic Volatility from the P\"oschl-Teller Potential and Hyperbolic Geometry
Joel Saucedo
https://arxiv.org/abs/2507.12501 https://arxiv.org/pdf/25…

Quadratic Volatility from the Pöschl-Teller Potential and Hyperbolic Geometry
This investigation establishes a formal equivalence between the generalized Black-Scholes equation under a Quadratic Normal Volatility (QNV) specification and the stationary Schrödinger equation for a hyperbolic Pöschl-Teller potential. A sequence of canonical transformations maps the financial pricing operator to a quantum Hamiltonian, revealing the volatility smile as a direct manifestation of diffusion on a hyperbolic manifold whose geometry is classified by the discriminant of the QNV pol…

“What if AI Doesn’t Get Much Better Than This?” – a pretty good summary for those who don't want to read Gary Marcus’s rather… elaborate… treatizes.
> I think it’s safe, at least for now, to turn your attention away from the tech titans’ increasingly hyperbolic claims
🧘‍♂️
https://ca…

What if AI Doesn’t Get Much Better Than This? - Cal Newport
In the years since ChatGPT’s launch in late 2022, it’s been hard not to get swept up in feelings of euphoria or dread about the ... Read more

Blow-up exponents and a semilinear elliptic equation for the fractional Laplacian on hyperbolic spaces
Tommaso Bruno, Effie Papageorgiou
https://arxiv.org/abs/2509.12349 https:/…

Blow-up exponents and a semilinear elliptic equation for the fractional Laplacian on hyperbolic spaces
Let $\mathbb{H}^n$ be the $n$-dimensional real hyperbolic space, $Δ$ its nonnegative Laplace--Beltrami operator whose bottom of the spectrum we denote by $λ_{0}$, and $σ\in (0,1)$. The aim of this paper is twofold. On the one hand, we determine the Fujita exponent for the fractional heat equation \[\partial_{t} u + Δ^σu = e^{βt}|u|^{γ-1}u,\] by proving that nontrivial positive global solutions exist if and only if $γ\geq 1 + β/ λ_{0}^σ$. On the other hand, we prove the ex…