Tootfinder

This https://arxiv.org/abs/2412.16740 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Hilbert's tenth problem for systems of diagonal quadratic forms, and Büchi's problem
In this paper we complete Büchi's proof that there is no decision algorithm for the solubility in integers of arbitrary systems of diagonal quadratic form equations, by proving the assertion that whenever $x_1^2, \cdots, x_5^2$ are five squares such that the second differences satisfy \[x_{k+2}^2 - 2 x_{k+1}^2 + x_k^2 = 2\] for $k = 1,2,3$, then they must be consecutive. This answers a question of J.~Richard~Büchi.

Renormalization of bosonic quadratic Hamiltonians involving rank-one perturbations
Thomas Gamet (UMPA-ENSL)
https://arxiv.org/abs/2506.08590 https://

Renormalization of bosonic quadratic Hamiltonians involving rank-one perturbations
In this article, we study the renormalization of a bosonic quadratic Hamiltonian with an ultraviolet divergence. The Hamiltonian is composed of the sum of a free energy and the square of the smeared field operator. We explicitly diagonalize the Hamiltonian via Bogoliubov transformations, and the diagonalized Hamiltonian is easier to study. We show a renormalization of both the energy and the coupling constant depending on the form factor of the interaction.

This https://arxiv.org/abs/2502.16212 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

Clustering-Based Sub-QUBO Extraction for Hybrid QUBO Solvers
Quantum Approximate Optimization Algorithm (QAOA) can be used to solve quadratic unconstrained binary optimization (QUBO) problems. However, the size of the solvable problem is limited by the number of qubits. To leverage noisy intermediate-scale quantum (NISQ) devices to solve large-scale QUBO problems, one possible way is to decompose the full problem into multiple sub-problems, which we refer to as the Sub-QUBO Formalism. In this work, we enhance this formalism by proposing a sub-QUBO extrac…

This https://arxiv.org/abs/2303.17475 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLG_…

Learning distributed representations with efficient SoftMax normalization
Learning distributed representations, or embeddings, that encode the relational similarity patterns among objects is a relevant task in machine learning. A popular method to learn the embedding matrices $X, Y$ is optimizing a loss function of the term ${\rm SoftMax}(XY^T)$. The complexity required to calculate this term, however, runs quadratically with the problem size, making it a computationally heavy solution. In this article, we propose a linear-time heuristic approximation to compute the …

Quantum transduction via generalized continuous-variable teleportation
Quntao Zhuang
https://arxiv.org/abs/2506.06899 https://arxiv.o…

Quantum transduction via generalized continuous-variable teleportation
Quantum transduction converts quantum states between different frequencies. Similarly, quantum teleportation transfers quantum states between different systems. While often appreciated for quantum communication between distant locations, teleportation can also operate between different frequencies. In terms of bosonic modes, quantum teleportation relies on two-mode squeezing -- squeezed on the balanced Einstein-Podolsky-Rosen (EPR) quadratures -- for entanglement and a balanced beamsplitter plu…

Hopf actions on Poisson algebras
Awn Alqahtani, Jason Gaddis, Xingting Wang
https://arxiv.org/abs/2506.06135 https://arxiv.org/pdf/25…

Hopf actions on Poisson algebras
We study finite-dimensional Hopf actions on Poisson algebras and explore the phenomenon of quantum rigidity in this context. Our main focus is on filtered (and especially quadratic) Poisson algebras, including the Weyl Poisson algebra in $2n$ variables and certain Poisson algebras in two variables. In particular, we show that any finite-dimensional Hopf algebra acting inner faithfully on these Poisson algebras must necessarily factor through a group algebra-mirroring well-known rigidity theorem…

AFP: Russen nahmen im Mai viel Territorium ein
Die russischen Streitkräfte haben im Mai ihren Vormarsch in der Ukraine beschleunigen können. Dies geht aus Berechnungen der Nachrichtenagentur AFP mit Bezug auf Daten des in den USA ansässigen Instituts für Kriegsstudien (ISW) hervor. Demnach besetzte Russland im vergangenen Monat 507 Quadratkilometer. Alleine in der ostukrainischen Region Donezk sollen es fast 400 Quadratkilome…
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Ukraine-Liveblog: ++ Wadephul: Müssen Druck aufrechterhalten ++
Bundesaußenminister Wadephul hat nach einem Treffen mit US-Senator Graham eine gemeinsame harte Linie gegenüber Russlands Präsidenten Putin betont. Friedensforscher mahnen eine Verteidigungsstrategie für Europa an.

This https://arxiv.org/abs/2503.09977 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csIT_…

Quadratic Transform for Fractional Programming in Signal Processing and Machine Learning
Fractional programming (FP) is a branch of mathematical optimization that deals with the optimization of ratios. It is an invaluable tool for signal processing and machine learning, because many key metrics in these fields are fractionally structured, e.g., the signal-to-interference-plus-noise ratio (SINR) in wireless communications, the Cramér-Rao bound (CRB) in radar sensing, the normalized cut in graph clustering, and the margin in support vector machine (SVM). This article provides a comp…

On the quadratic 8-edge case of the Brown-Erd\H{o}s-S\'os problem
Oleg Pikhurko, Shumin Sun
https://arxiv.org/abs/2506.01739 https://

On the quadratic 8-edge case of the Brown-Erdős-Sós problem
Let $f^{(r)}(n;s,k)$ be the maximum number of edges in an $n$-vertex $r$-uniform hypergraph containing no $k$ edges on at most $s$ vertices. Brown, Erdős and Sós conjectured in 1973 that the limit $\lim_{n\rightarrow \infty}n^{-2}f^{(3)}(n;k+2,k)$ exists for all $k$. Recently, Delcourt and Postle settled the conjecture and their approach was generalised by Shangguan to every uniformity $r\ge 4$: the limit $\lim_{n\rightarrow \infty}n^{-2}f^{(r)}(n;rk-2k+2,k)$ exists for all $r\ge 3$ and $k\ge…

This https://arxiv.org/abs/2505.16529 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Modular forms of CM type mod $\ell$
We say that a normalized modular form without complex multiplication is of CM type modulo $\ell$ by an imaginary quadratic field $K$ if its Fourier coefficients $a_p$ are $0$ modulo a prime ideal dividing $\ell$ for every prime $p$ inert in $K$. In this paper, we address the following problem: Given a weight 2 cuspidal Hecke eigenform $f$ without CM which is of CM type modulo $\ell$ by an imaginary quadratic field $K$, does there exist a congruence modulo $\ell$ between $f$ and a genuine CM m…