Tootfinder

Relaxation of variational problems in the space of functions with bounded $\mathcal{B}$-variation: interaction with measures and lack of concentration phenomena
Lorenza D'Elia, Elvira Zappale
https://arxiv.org/abs/2507.18781

Relaxation of variational problems in the space of functions with bounded $\mathcal{B}$-variation: interaction with measures and lack of concentration phenomena
We prove an integral representation result for variational functionals in the space $BV^{\mathcal{B}}$ of functions with bounded $\mathcal{B}$-variation where $\mathcal{B}$ denotes a $k$-th order, $\mathbb{C}$-elliptic, linear homogeneous differential operator. This result has been used as a key tool to get an explicit representation of relaxed energies with linear growth which lead to limiting generic measures. According to the space dimension and the order of the operator, concentration pheno…

Families of Morse functions for manifolds with boundary
Maciej Borodzik, Weronika Buczy\'nska
https://arxiv.org/abs/2507.15847 https://arxiv.org/pdf/25…

Families of Morse functions for manifolds with boundary
We study 1-parameter families of Morse functions for manifolds with boundary. We list all degeneracies that may occur in generic 1-parameter families.

Bispectrum Islands
Claudia de Rham, Sadra Jazayeri, Andrew J. Tolley
https://arxiv.org/abs/2506.19198 https://arxiv.org/pdf/2506.1919…

Bispectrum Islands
Inspired by the amplitude bootstrap program, the spirit of this work is to constrain the space of consistent inflationary correlation functions - specifically, the bispectrum of curvature perturbations - using fundamental principles such as unitarity, locality, analyticity, and symmetries. To this end, we assume a setup for inflation in which de Sitter isometries are only mildly broken by the slow roll of the inflaton field, and study the bispectrum imprinted by a generic hidden sector during i…

Pseudorandomness of Expander Walks via Fourier Analysis on Groups
Fernando Granha Jeronimo, Tushant Mittal, Sourya Roy
https://arxiv.org/abs/2507.14445 htt…

Pseudorandomness of Expander Walks via Fourier Analysis on Groups
One approach to study the pseudorandomness properties of walks on expander graphs is to label the vertices of an expander with elements from an alphabet $Σ$, and study the mean of functions over $Σ^n$. We say expander walks $\varepsilon$-fool a function if, for any unbiased labeling of the vertices, the expander walk mean is $\varepsilon$-close to the true mean. We show that: - The class of symmetric functions is $O(|Σ|\cdotλ)$-fooled by expander walks over any generic $λ$-expa…

$L$-packets and the generic Arthur packet conjectures for even unitary similitude groups
Yeansu Kim, Muthu Krishnamurthy, Freydoon Shahidi
https://arxiv.org/abs/2506.00892

$L$-packets and the generic Arthur packet conjectures for even unitary similitude groups
We establish the generic local Langlands correspondence by showing the equality of the Langlands-Shahidi $L$-functions and Artin $L$-functions in the case of even unitary similitude groups. As an application, we prove both weak and strong versions of the generic Arthur packet conjectures in the cases of even unitary similitude groups and even unitary groups. We further describe (not necessarily generic) $L$-packets for even unitary similitude groups and establish their expected properties, incl…

Convolutive sequences, I: Through the lens of integer partition functions
Shane Chern, Dennis Eichhorn, Shishuo Fu, James A. Sellers
https://arxiv.org/abs/2507.10965

Convolutive sequences, I: Through the lens of integer partition functions
Motivated by the convolutive behavior of the counting function for partitions with designated summands in which all parts are odd, we consider coefficient sequences $(a_n)_{n\ge 0}$ of primitive eta-products that satisfy the generic convolutive property \begin{align*} \sum_{n\ge 0} a_{mn} q^n = \left(\sum_{n\ge 0} a_n q^n\right)^m \end{align*} for a specific positive integer $m$. Given the results of an exhaustive search of the Online Encyclopedia of Integer Sequences for such sequences…

The asymptotic Samuel functions and applications to resolution of singularities techniques
A. Benito, A. Bravo, S. Encinas
https://arxiv.org/abs/2506.14993

The asymptotic Samuel functions and applications to resolution of singularities techniques
We use the asymptotic Samuel function to define the Samuel slope of a Noetherian local ring, and we prove that it characterizes local regular excellent rings. In addition, we introduce a second invariant that refines the Samuel slope using generic linear cuts, the refined Samuel slope. We show that both, the Samuel slope and the refined Samuel slope, are connected to invariants coming from resolution of singularities.

Electroweak splitting functions in the Standard Model and beyond
Stefan Dittmaier, Max Reyer
https://arxiv.org/abs/2507.06568 https://

Electroweak splitting functions in the Standard Model and beyond
We derive quasi-collinear factorization formulas in generic spontaneously broken gauge theories with scalars, fermions, and vector bosons. Specifically, we obtain polarized leading-order splitting functions for all possible final-state and initial-state 1->2 processes in the considered gauge theory. The main complication lies in the presence of mass-singular terms in longitudinal polarization vectors, prohibiting the direct application of the usual factorization procedure known from Quantum Ele…

A Generic Branch-and-Bound Algorithm for $\ell_0$-Penalized Problems with Supplementary Material
Cl\'ement Elvira, Th\'eo Guyard, C\'edric Herzet
https://arxiv.org/abs/2506.03974

A Generic Branch-and-Bound Algorithm for $\ell_0$-Penalized Problems with Supplementary Material
We present a generic Branch-and-Bound procedure designed to solve L0-penalized optimization problems. Existing approaches primarily focus on quadratic losses and construct relaxations using "Big-M" constraints and/or L2-norm penalties. In contrast, our method accommodates a broader class of loss functions and allows greater flexibility in relaxation design through a general penalty term, encompassing existing techniques as special cases. We establish theoretical results ensuring that all key qu…

Optimal T depth quantum circuits for implementing arbitrary Boolean functions
Suman Dutta, Anik Basu Bhaumik, Anupam Chattopadhyay, Subhamoy Maitra
https://arxiv.org/abs/2506.01542

Optimal T depth quantum circuits for implementing arbitrary Boolean functions
In this paper we present a generic construction to obtain an optimal T depth quantum circuit for any arbitrary $n$-input $m$-output Boolean function $f: \{0,1\}^n \rightarrow \{0,1\}^m$ having algebraic degree $k\leq n$, and it achieves an exact Toffoli (and T) depth of $\lceil \log_2 k \rceil$. This is a broader generalization of the recent result establishing the optimal Toffoli (and consequently T) depth for multi-controlled Toffoli decompositions (Dutta et al., Phys. Rev. A, 2025). We achie…

Nonlinear projection for ballistic correlation functions: a formula in terms of minimal connected covers
Benjamin Doyon
https://arxiv.org/abs/2506.05266 ht…

Nonlinear projection for ballistic correlation functions: a formula in terms of minimal connected covers
In many-body systems, the dynamics is governed, at large scales of space and time, by the hydrodynamic principle of projection onto the conserved densities admitted by the model. This is formalised as local relaxation of fluctuations in the ballistic macroscopic fluctuation theory, a nonlinear Boltzmann-Gibbs principle. We use it to derive a projection formula, expressing n-point connected correlation functions (cumulants) of generic observables at different space-time points, in terms of those…

Stealth black hole solutions in higher-order Maxwell-Einstein theories
Masato Minamitsuji
https://arxiv.org/abs/2506.11353 https://ar…

Stealth black hole solutions in higher-order Maxwell-Einstein theories
We study static and spherically symmetric black hole solutions in higher-order Maxwell-Einstein theories. We do not particularly focus on the degenerate classes of theories. For several specific choices of the coupling functions, we show that in the presence of the ordinary Maxwell kinetic term the Reissner-Nordström-(anti-)de Sitter solution in the pure Maxwell-Einstein theory can also be a solution in generic classes of higher-order Maxwell-Einstein theories, and in the absence of the ordina…

Towards Large-Scale Condensed Phase Simulations using Machine Learned Energy Functions
Eric D. Boittier, Silvan K\"aser, Markus Meuwly
https://arxiv.org/abs/2506.23272

Towards Large-Scale Condensed Phase Simulations using Machine Learned Energy Functions
Accurate, yet computationally efficient energy functions are essential for state-of-the art molecular dynamics (MD) studies of condensed phase systems. Here, a generic workflow based on a combination of machine learning-based and empirical representations of intra- and intermolecular interactions is presented. The total energy is decomposed into internal contributions, and electrostatic and van der Waals interactions between monomers. The monomer potential energy surface is described using a ne…

This https://arxiv.org/abs/2309.04540 has been replaced.
initial toot: https://mastoxiv.page/@…

Inhomogeneous Quantum Quenches of Conformal Field Theory with Boundaries
We develop a method to calculate generic time-dependent correlation functions for inhomogeneous quantum quenches in (1+1)-dimensional conformal field theory (CFT) induced by sudden Hamiltonian deformations that modulate the energy density inhomogeneously. Our work particularly focuses on the effects of spatial boundaries, which have remained unresolved by previous analytical methods. For generic post-quench Hamiltonian, we develop a generic method to calculate the correlations by mirroring the …

Generic orbits, normal bases, and generation degree for fields of rational invariants
Ben Blum-Smith, Harm Derksen
https://arxiv.org/abs/2506.05650 https:/…

Generic orbits, normal bases, and generation degree for fields of rational invariants
For a linear representation of a finite group in coprime characteristic, we bound the degrees of the invariant polynomials needed to generate the field of rational invariants as a field, in terms of the degrees of the polynomials needed to span the field of rational functions as a vector space over the invariant field. This provides a far-reaching generalization of a recent result of Edidin and Katz.

Counting geodesics on prime-order $k$-differentials
Juliet Aygun
https://arxiv.org/abs/2506.24084 https://arxiv.org/pdf/2506.24084

Counting geodesics on prime-order $k$-differentials
We determine weak asymptotics of counting functions on generic surfaces in a component of a stratum of $k$-differentials when $k$ is prime and genus is greater than $2$. In order to do so, we classify the $GL^+(2,\mathbb{R})$-orbit closure of holonomy covers of components and apply Eskin-Mirzakhani-Mohammadi generalized to translation surfaces. We show that the $GL^+(2,\mathbb{R})$-orbit closure of these holonomy covers is generically a component of a stratum of translation surfaces or a hypere…

The Ising model and random fields of scales
Ricardo G\'omez A\'iza
https://arxiv.org/abs/2507.00071 https://arxiv.org/pdf/250…

The Ising model and random fields of scales
Random fields of scales result when the class of musical scales is thought as a set of sites, and a site can be in one of two possible states (or spins): On or Off. We present a flexible simulated annealing model that produces generic configurations arising from equilibrium states (or Gibbs measures) associated to hamiltonian energy functions defined in terms of musical interactions with parameters that can be manipulated to customize properties of the scales. The starting point is to think of …