Tootfinder

Contextual Online Pricing with (Biased) Offline Data
Yixuan Zhang, Ruihao Zhu, Qiaomin Xie
https://arxiv.org/abs/2507.02762 https://a…

Contextual Online Pricing with (Biased) Offline Data
We study contextual online pricing with biased offline data. For the scalar price elasticity case, we identify the instance-dependent quantity $δ^2$ that measures how far the offline data lies from the (unknown) online optimum. We show that the time length $T$, bias bound $V$, size $N$ and dispersion $λ_{\min}(\hatΣ)$ of the offline data, and $δ^2$ jointly determine the statistical complexity. An Optimism-in-the-Face-of-Uncertainty (OFU) policy achieves a minimax-optimal, instance-dependent…

Entropic characterization of Tunneling and State Pairing in a Quasi-Exactly Solvable Sextic Potential
Angelina N. Mendoza Tavera, Adrian M. Escobar Ruiz, Robin P. Sagar
https://arxiv.org/abs/2506.22684

Entropic characterization of Tunneling and State Pairing in a Quasi-Exactly Solvable Sextic Potential
We analyze the (de)localization properties of a quasi-exactly solvable (QES) sextic potential $V_{\text{QES}}(x) = \frac{1}{2}(x^6 + 2x^4 - 2(2λ+ 1)x^2)$ as a function of the tunable parameter $λ\in [-\frac{3}{4}, 6]$. For $λ> -\frac{1}{2}$, the potential exhibits a symmetric double-well structure, with tunneling emerging for the ground state level at $λ\approx 0.732953$. {For the lowest energy states \( n = 0,1,2,3 \), we construct physically meaningful variational wavefunctions that $i)$ …

A Hot Jupiter with a Retrograde Orbit around a Sun-like Star and a Toy Model of Hot Jupiters in Wide Binary Star Systems
Steven Giacalone, Andrew W. Howard, Ryan A. Rubenzahl, Fei Dai, Luke B. Handley, Howard Isaacson, Samuel Halverson, Max Brodheim, Matt Brown, Theron W. Carmichael, William Deich, Benjamin J. Fulton, Steven R. Gibson, Grant M. Hill, Bradford Holden, Aaron Householder, Russ R. Laher, Kyle Lanclos, Joel Payne, Erik A. Petigura, Arpita Roy, Christian Schwab, Martin M. Si…

A Hot Jupiter with a Retrograde Orbit around a Sun-like Star and a Toy Model of Hot Jupiters in Wide Binary Star Systems
We report an observation of a transit of the hot Jupiter (HJ) KELT-23A b with the Keck Planet Finder spectrograph and a measurement of the sky-projected obliquity ($λ$) of its Sun-like ($T_{\rm eff} \approx 5900$ K) host star. We measured a projected stellar obliquity of $λ\approx 180^\circ$, indicating that the orbit of the HJ is retrograde relative to the direction of the stellar spin. Due to the slow sky-projected rotational velocity of the host star ($v \sin{i_\star} \approx 0.5$ km s$^{-…

Local laws and spectral properties of deformed sparse random matrices
Ji Oon Lee, Inyoung Yeo
https://arxiv.org/abs/2507.02298 https://

Local laws and spectral properties of deformed sparse random matrices
We consider deformed sparse random matrices of the form $H= W+ λV$, where $W$ is a real symmetric sparse random matrix, $V$ is a random or deterministic, real, diagonal matrix whose entries are independent of $W$, and $λ= O(1) $ is a coupling constant. Under mild assumptions on the matrix entries of $W$ and $V$, we prove local laws for $H$ that compares the empirical spectral measure of it with a refined version of the deformed semicircle law. By applying the local laws, we also prove several…

On sporadic symmetry breaking operators for principal series representations of the de Sitter and Lorentz groups
V\'ictor P\'erez-Vald\'es
https://arxiv.org/abs/2506.23064

On sporadic symmetry breaking operators for principal series representations of the de Sitter and Lorentz groups
In this paper, we construct and classify all differential symmetry breaking operators $\mathbb{D}_{λ, ν}^{N,m}: C^\infty(S^3, \mathcal{V}_λ^{2N+1})\rightarrow C^\infty(S^2, \mathcal{L}_{m, ν})$ between principal series representations with respect to the restriction $SO_0(4,1) \downarrow SO_0(3,1)$ when the parameters satisfy the condition $|m| > N$. In this case we also prove a localness theorem, namely, all symmetry breaking operators between the principal series representations…

An improvement toward global boundedness in a fully parabolic chemotaxis with singular sensitivity in any dimension
Minh Le
https://arxiv.org/abs/2506.19318

An improvement toward global boundedness in a fully parabolic chemotaxis with singular sensitivity in any dimension
We are concerned with the following chemotaxis system \begin{equation*} \begin{cases} u_t = Δu -χ\nabla \cdot \left ( \frac{u}{v} \nabla v\right ), v_t = Δv -u+ v, \end{cases} \end{equation*} in an open bounded domain with smooth boundary $Ω\subset \mathbb{R}^n$ with $n \geq 3$. It is known that solutions are globally bounded when $0<χ< \sqrt{ \frac{2}{n}}$. In this paper, by considering the following energy functional \begin{align*} F_λ(u,v)= \int_Ω\frac{u^p}{v^r} + λ\int_Ω\…

On {\lambda}-Cent-Dians and Generalized-Center for Network Design: Formulations and Algorithms
V\'ictor Bucarey, Natividad Gonz\'alez-Blanco, Martine Labb\'e, Juan A. Mesa
https://arxiv.org/abs/2506.14839

On λ-Cent-Dians and Generalized-Center for Network Design: Formulations and Algorithms
In this paper, we study the $λ$-centdian problem in the domain of Network Design. The focus is on designing a sub-network within a given underlying network while adhering to a budget constraint. This sub-network is intended to efficiently serve a collection of origin/destination demand pairs. We extend the work presented in \cite{bucarey2024on}, providing an algorithmic perspective on the generalized $λ$-centdian problem. In particular, we provide a mathematical formulation for $λ\geq 0$ and…

Charmed baryon decays: $SU(3)_F$ breaking and CP violation
Chang Yang, Xiao-Gang He, Chia-Wei Liu
https://arxiv.org/abs/2506.19005 https://

Charmed baryon decays: $SU(3)_F$ breaking and CP violation
We present a comprehensive study of anti-triplet charmed baryon decays into octet baryons and pseudoscalar mesons using the $SU(3)_F$ flavor symmetry framework. By decomposing the flavor structure, all decay amplitudes are parametrized with a minimal set of irreducible amplitudes, and the Körner-Pati-Woo theorem further reduces the number of independent parameters from the original 35 to 19 under exact symmetry when small terms proportional to $λ_b = V_{cb}^*V_{ub}$ are neglected. The indepen…

Lipschitz regularity of weakly coupled vectorial almost-minimizers for Alt-Caffarelli functionals in Orlicz spaces
Pedro Fellype Pontes, Jo\~ao Vitor da Silva, Minbo Yang
https://arxiv.org/abs/2506.17616

Lipschitz regularity of weakly coupled vectorial almost-minimizers for Alt-Caffarelli functionals in Orlicz spaces
For a fixed constant $λ> 0$ and a bounded Lipschitz domain $Ω\subset \mathbb{R}^n$ with $n \geq 2$, we establish that almost-minimizers (functions satisfying a sort of variational inequality) of the Alt-Caffarelli type functional \[ \mathcal{J}_G({\bf v};Ω) \coloneqq \int_Ω\left(\sum_{i=1}^mG\big(|\nabla v_i(x)|\big) + λχ_{\{|{\bf v}|>0\}}(x)\right) dx , \] where ${\bf v} = (v_1, \dots, v_m)$ and $m \in \mathbb{N}$, exhibit optimal Lipschitz continuity on compact subse…

An Isomorphism Theorem for Some Linear Elliptic Differential Operators on Quasi-Asymptotically Conical Manifolds
Mohamed Nouidha
https://arxiv.org/abs/2506.13069

An Isomorphism Theorem for Some Linear Elliptic Differential Operators on Quasi-Asymptotically Conical Manifolds
We study a linear elliptic differential operator of the form $\mathcal{P}=Δ+ V - λ$ on a quasi-asymptotically conical (\textbf{QAC}) manifold $(M, g)$, where $g$ is a polyhomogeneous metric and $V$ is a $b$-vector field that is unbounded with respect to the metric $g$.

Eigenvalue estimates for the Coulombic one-particle density matrix and the kinetic energy density matrix
Alexander V. Sobolev
https://arxiv.org/abs/2506.16178

Eigenvalue estimates for the Coulombic one-particle density matrix and the kinetic energy density matrix
Consider a bound state (an eigenfunction) $ψ$ of an atom with $N$ electrons. We study the spectra of the one-particle density matrix $γ$ and of the one-particle kinetic energy density matrix $τ$ associated with $ψ$. The paper contains two results. First, we obtain the bounds $λ_k(γ)\le C_1 k^{-8/3}$ and $λ_k(τ)\le C_2 k^{-2}$ with some positive constants $C_1, C_2$ that depend explicitly on the eigenfunction $ψ$. The sharpness of these bounds is confirmed by the asymptotic results obta…

This https://arxiv.org/abs/2503.21940 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Normalized vector solutions of nonlinear Schrödinger systems
Given $μ>0$ we look for solutions $ λ\in\mathbb{R}$ and $v_1,\dots,v_k\in H^1(\mathbb{R}^N)$ of the system \[ \begin{cases} \displaystyle -Δv_i+ λv_i+V_i(x)v_i = \sum_{\substack{j=1}}^kβ_{ij} v_iv_j^2 &\text{ in } \mathbb{R}^N, \text{ } i=1,\dots,k,\newline \displaystyle \int_{\mathbb{R}^N} \left(v_1^2+\dots+v_k^2 \right)\mathrm{d} x = μ, \end{cases}\] where $N=1,2,3$, $V_i:\mathbb R^N\to \mathbb R$ and $β_{ij}\in\mathbb{R}$ satisfy $β_{ij}=β_{ji}$ and $β_{ii}>0$. Under …