Tootfinder

This https://arxiv.org/abs/2405.05727 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On Chen's theorem, Goldbach's conjecture and almost prime twins II
Let $N$ denote a sufficiently large even integer and $x$ denote a sufficiently large integer, we define $D_{1,2}(N)$ as the number of primes $p$ that such that $N - p$ has at most 2 prime factors. In this paper, we show that $D_{1,2}(N) \geqslant 1.9728 \frac{C(N) N}{(\log N)^2}$, which is rather near to the asymptotic constant $2$ in Hardy--Littlewood conjecture for Goldbach's conjecture. We also get similar results on twin prime problem and additive representations of integers. The proof comb…

Slicing Correspondences with High Degree Hypersurfaces
Ishan Banerjee
https://arxiv.org/abs/2506.02977 https://arxiv.org/pdf/2506.029…

Slicing Correspondences with High Degree Hypersurfaces
We approximately compute the correspondence degree (as defined by Lazarsfeld and Martin) between two unbalanced complete intersections. This is accomplished by showing that the procedure of taking a subvariety of a product $Y \times Y'$ and intersecting it with $X \times Y'$ (for $X$ a sufficiently ample smooth divisor in $Y$) induces a bijection between two sets of varieties. This may be of independent interest.

This https://arxiv.org/abs/2112.13738 has been replaced.
link: https://scholar.google.com/scholar?q=a

Evaluation of binary classifiers for asymptotically dependent and independent extremes
Machine learning classification methods usually assume that all possible classes are sufficiently present within the training set. Due to their inherent rarities, extreme events are always under-represented and classifiers tailored for predicting extremes need to be carefully designed to handle this under-representation. In this paper, we address the question of how to assess and compare classifiers with respect to their capacity to capture extreme occurrences. This is also related to the topic…

Enhancing Lyrics Transcription on Music Mixtures with Consistency Loss
Jiawen Huang, Felipe Sousa, Emir Demirel, Emmanouil Benetos, Igor Gadelha
https://arxiv.org/abs/2506.02339

Enhancing Lyrics Transcription on Music Mixtures with Consistency Loss
Automatic Lyrics Transcription (ALT) aims to recognize lyrics from singing voices, similar to Automatic Speech Recognition (ASR) for spoken language, but faces added complexity due to domain-specific properties of the singing voice. While foundation ASR models show robustness in various speech tasks, their performance degrades on singing voice, especially in the presence of musical accompaniment. This work focuses on this performance gap and explores Low-Rank Adaptation (LoRA) for ALT, investig…

Input-Power-to-State Stability of Time-Varying Systems
Hernan Haimovich, Shenyu Liu, Antonio Russo, Jose L. Mancilla-Aguilar
https://arxiv.org/abs/2505.24805

Input-Power-to-State Stability of Time-Varying Systems
When the state of a system may remain bounded even if both the input amplitude and energy are unbounded, then the state bounds given by the standard input-to-state stability (ISS) and integral-ISS (iISS) properties may provide no useful information. This paper considers an ISS-related concept suitable in such a case: input-power-to-state stability (IPSS). Necessary and sufficient conditions for IPSS are developed for time-varying systems under very mild assumptions on the dynamics. More precise…

This https://arxiv.org/abs/2401.07018 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_sta…

Least squares for cardinal paired comparisons data
Least square estimators for graphical models for cardinal paired comparison data with and without covariates are rigorously analyzed. Novel, graph--based, necessary and sufficient conditions that guarantee strong consistency, asymptotic normality and the exponential convergence of the estimated ranks are emphasized. A complete theory for models with covariates is laid out. In particular, conditions under which covariates can be safely omitted from the model are provided. The methodology is empl…

Can Large Language Models Trigger a Paradigm Shift in Travel Behavior Modeling? Experiences with Modeling Travel Satisfaction
Pengfei Xu, Donggen Wang
https://arxiv.org/abs/2505.23262

Can Large Language Models Trigger a Paradigm Shift in Travel Behavior Modeling? Experiences with Modeling Travel Satisfaction
As a specific domain of subjective well-being, travel satisfaction has attracted much research attention recently. Previous studies primarily use statistical models and, more recently, machine learning models to explore the determinants of travel satisfaction. Both approaches require data from sufficient sample sizes and correct prior statistical assumptions. The emergence of Large Language Models (LLMs) offers a new modeling approach that can overcome the shortcomings of the existing methods. …

This https://arxiv.org/abs/2405.07636 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Nonlinear Network Identifiability with Full Excitations
We derive conditions for the identifiability of nonlinear networks characterized by additive dynamics at the level of the edges when all the nodes are excited. In contrast to linear systems, we show that the measurement of all sinks is necessary and sufficient for the identifiability of directed acyclic graphs, under the assumption that dynamics are described by analytic functions without constant terms (i.e., $f(0)=0$). But if constant terms are present, then the identifiability is impossible …

The bi-Lipschitz constant of an isothermal coordinate chart
Matan Eilat
https://arxiv.org/abs/2505.23591 https://arxiv.org/pdf/2505.2…

The bi-Lipschitz constant of an isothermal coordinate chart
Let $M$ be a $C^{2}$-smooth Riemannian surface. A classical theorem in differential geometry states that the Gauss curvature function $K : M \to \mathbb{R}$ vanishes everywhere if and only if the surface is locally isometric to the Euclidean plane. We give an asymptotically sharp quantitative version of this theorem with respect to an isothermal coordinate chart. Roughly speaking, we show that if $B$ is a Riemannian disc of radius $δ> 0$ with $δ^{2}\sup_{B}|K| < \varepsilon$ for som…

This https://arxiv.org/abs/2405.07636 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Nonlinear Network Identifiability with Full Excitations
We derive conditions for the identifiability of nonlinear networks characterized by additive dynamics at the level of the edges when all the nodes are excited. In contrast to linear systems, we show that the measurement of all sinks is necessary and sufficient for the identifiability of directed acyclic graphs, under the assumption that dynamics are described by analytic functions without constant terms (i.e., $f(0)=0$). But if constant terms are present, then the identifiability is impossible …