Tootfinder

This https://arxiv.org/abs/2505.15724 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

Gravitational Bremsstrahlung in Black-Hole Scattering at $\mathcal{O}(G^3)$: Quadratic-in-Spin Effects
We are employing a supersymmetric variant of the worldline quantum field theory (WQFT) formalism to compute the far-field momentum-space gravitational waveform emitted during the scattering of two spinning black holes at next-to-leading order (NLO) in the post-Minkowskian expansion. Our results are accurate up to quadratic-in-spin contributions, which means we report for the very first time the waveform observable at the order $\mathcal{O}(G^3\mathcal{S}^2)$. Our computation is based on mapping…

Efficient Optimization Accelerator Framework for Multistate Ising Problems
Chirag Garg, Sayeef Salahuddin
https://arxiv.org/abs/2505.20250 https://

Efficient Optimization Accelerator Framework for Multistate Ising Problems
Ising Machines are a prominent class of hardware architectures that aim to solve NP-hard combinatorial optimization problems. These machines consist of a network of interacting binary spins/neurons that evolve to represent the optimum ground state energy solution. Generally, combinatorial problems are transformed into quadratic unconstrained binary optimization (QUBO) form to harness the computational efficiency of these Ising machines. However, this transformation, especially for multi-state p…

This https://arxiv.org/abs/2503.17464 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Other Examples of Principal Ideal Domains that are not Euclidean Domains
It is a well-known and easily established fact that every Euclidean domain is also a principal ideal domain. However, the converse statement is not true, and this is usually shown by exhibiting as a counterexample the ring of algebraic integers in a certain, very specific quadratic field, and the proof that this works is quite unnatural and technical. In this article, we will present a family of counterexamples constructed using real closed fields.

Der Hexe Flug zu blanker Nacht
Ihr sichtlich diebisch Freude macht.

Nachbarin mäht schon wieder ihr Handtuch, obwohl alles dürr ist. Sie können und vor allem wollen es nicht verstehen. Alles muss ordentlich und praktisch-quadratisch sein. Nein, das ist eben nicht gut. Vielleicht auch purer Protest, weil wir die Wiese, auf die sie blicken stehen lassen. Von #MähfreierMai haben sie zwar gehört, ignorieren es aber ganz bewusst. Auch den Aufruf der Stadt

Gaps between quadratic forms
Siddharth Iyer
https://arxiv.org/abs/2505.23428 https://arxiv.org/pdf/2505.23428

Gaps between quadratic forms
Let $\triangle$ denote the integers represented by the quadratic form $x^2+xy+y^2$ and $\square_{2}$ denote the numbers represented as a sum of two squares. For a non-zero integer $a$, let $S(\triangle,\square_{2},a)$ be the set of integers $n$ such that $n \in \triangle$, and $n + a \in \square_{2}$. We conduct a census of $S(\triangle,\square_{2},a)$ in short intervals by showing that there exists a constant $H_{a} > 0$ with \begin{align*} \# S(\triangle,\square_{2},a)\cap [x,x+H_{a}\cdot x^{…

This https://arxiv.org/abs/2406.18322 has been replaced.
initial toot: https://mastoxiv.page/@…

A new quadrature for the generalized hydrodynamics equation and absence of shocks in the Lieb-Liniger model
In conventional fluids, it is well known that Euler-scale equations are plagued by ambiguities and instabilities. Smooth initial conditions may develop shocks, and weak solutions, such as for domain wall initial conditions (the paradigmatic Riemann problem of hydrodynamics), are not unique. The absence of shock formation experimentally observed in quasi-one-dimensional cold-atomic gases, which are described by the Lieb-Liniger model, provides perhaps the strongest pointer to a modification of t…

This https://arxiv.org/abs/2405.19380 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_sta…

Approximate Thompson Sampling for Learning Linear Quadratic Regulators with $O(\sqrt{T})$ Regret
We propose a novel Thompson sampling algorithm that learns linear quadratic regulators (LQR) with a Bayesian regret bound of $O(\sqrt{T})$. Our method leverages Langevin dynamics with a carefully designed preconditioner and incorporates a simple excitation mechanism. We show that the excitation signal drives the minimum eigenvalue of the preconditioner to grow over time, thereby accelerating the approximate posterior sampling process. Furthermore, we establish nontrivial concentration propertie…

Heute vor 16 Jahren: Am 25. Mai 2009 führte #Nordkorea seinen 2. #Atomtest durch. Die Explosion hatte etwa ein Drittel der Sprengkraft der Hiroshima-Bombe mit einer geschätzten Stärke von 2,35 Kilotonnen. Der Test löste weltweite Verurteilungen und schärfere UN-Sanktionen aus.

This https://arxiv.org/abs/2505.00493 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On the greatest prime factor and uniform equidistribution of quadratic polynomials
We show that the greatest prime factor of $n^2+h$ is at least $n^{1.312}$ infinitely often. This gives an unconditional proof for the range previously known under the Selberg eigenvalue conjecture. Furthermore, we get uniformity in $h \leq n^{1+o(1)}$ under a natural hypothesis on real characters. The same uniformity is obtained for the equidistribution of the roots of quadratic congruences modulo primes. We also prove a variant of the divisor problem for $ax^2+by^3$, which was used by the seco…