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Quantum block Krylov subspace projector algorithm for computing low-lying eigenenergies
Maria Gabriela Jord\~ao Oliveira, Nina Glaser
https://arxiv.org/abs/2506.09971

Quantum block Krylov subspace projector algorithm for computing low-lying eigenenergies
Determining eigenvalues is a computationally expensive task that is crucial for countless applications in natural sciences. Toward this end, we introduce the quantum block Krylov subspace projector (QBKSP) algorithm, a multireference quantum variant of the Lanczos algorithm designed to accurately compute low-lying eigenvalues, including degenerate states. We present three different compact quantum circuits to evaluate the required expectation values, each suited to different problem settings. T…

Replaced article(s) found for math.NA. https://arxiv.org/list/math.NA/new
[1/1]:
Generalized Gearhart-Koshy acceleration is a Krylov subspace method

Krylov Complexity in Lifshitz-type Dirac Field Theories
Hamid R. Imani, K. Babaei Velni, M. Reza Mohammadi Mozaffar
https://arxiv.org/abs/2506.08765 https:…

Krylov Complexity in Lifshitz-type Dirac Field Theories
We study Krylov complexity in Lifshitz-type Dirac field theories with a generic dynamical critical exponent z. By computing the Lanczos coefficients for massless and massive cases, we analyze the growth and saturation behavior of K-complexity in different regimes. We incorporate a hard UV cutoff and investigate the effects of lattice discretization, revealing fundamental differences between continuum and lattice models. In the presence of a UV cutoff, Krylov complexity exhibits an initial expon…

LiveCodeBench Pro: How Do Olympiad Medalists Judge LLMs in Competitive Programming?
Zihan Zheng, Zerui Cheng, Zeyu Shen, Shang Zhou, Kaiyuan Liu, Hansen He, Dongruixuan Li, Stanley Wei, Hangyi Hao, Jianzhu Yao, Peiyao Sheng, Zixuan Wang, Wenhao Chai, Aleksandra Korolova, Peter Henderson, Sanjeev Arora, Pramod Viswanath, Jingbo Shang, Saining Xie
http…

LiveCodeBench Pro: How Do Olympiad Medalists Judge LLMs in Competitive Programming?
Recent reports claim that large language models (LLMs) now outperform elite humans in competitive programming. Drawing on knowledge from a group of medalists in international algorithmic contests, we revisit this claim, examining how LLMs differ from human experts and where limitations still remain. We introduce LiveCodeBench Pro, a benchmark composed of problems from Codeforces, ICPC, and IOI that are continuously updated to reduce the likelihood of data contamination. A team of Olympiad medal…

Global Hypoellipticity for Systems in Time-Periodic Gelfand-Shilov Spaces
Fernando de \'Avila Silva, Marco Cappiello, Alexandre Kirilov
https://arxiv.org/abs/2506.12178

Global Hypoellipticity for Systems in Time-Periodic Gelfand-Shilov Spaces
We investigate the global hypoellipticity of a class of overdetermined systems with coefficients depending both on time and space variables in the setting of time-periodic Gelfand-Shilov spaces. Our main result provides necessary and sufficient conditions for the global hypoellipticity of this class of systems, stated in terms of Diophantine-type estimates and sign-changing behavior of the imaginary parts of the coefficients. Through a reduction to a normal form and detailed construction of sin…

Accelerating Large-Scale Regularized High-Order Tensor Recovery
Wenjin Qin, Hailin Wang, Jingyao Hou, Jianjun Wang
https://arxiv.org/abs/2506.09594 https:/…

Accelerating Large-Scale Regularized High-Order Tensor Recovery
Currently, existing tensor recovery methods fail to recognize the impact of tensor scale variations on their structural characteristics. Furthermore, existing studies face prohibitive computational costs when dealing with large-scale high-order tensor data. To alleviate these issue, assisted by the Krylov subspace iteration, block Lanczos bidiagonalization process, and random projection strategies, this article first devises two fast and accurate randomized algorithms for low-rank tensor approx…

The Holography of Spread Complexity: A Story of Observers
Zhehan Li, Jia Tian
https://arxiv.org/abs/2506.13481 https://arxiv.org/pdf/…

The Holography of Spread Complexity: A Story of Observers
We propose a holographic description of spread complexity and its rate in 2D CFTs, building on the pioneering work \cite{Caputa:2024sux}. By exploiting the $SL(2,\mathbb{R})$ symmetry, we construct the Krylov basis and demonstrate that its non-uniqueness gives rise to ambiguities analogous to those in quantum complexity. Within the AdS/CFT correspondence, we identify the spread complexity as the energy measured by a bulk observer, with its rate corresponding to the radial momentum. These result…

Senior State Department staffer Darren Beattie,
a passionate Putin supporter behind the move to dismantle a key agency fighting Russian propaganda,
is married to a Russian woman whose uncle is a longtime Kremlin ally, according to The Telegraph.
Yulia Kirillova grew up in Moscow, studied abroad in North America, and married Beattie in 2021 in Florida.
She moved to D.C. in January.
Her uncle Sergei Cherniko is a drinks magnate who had an estimated net worth of $1…

Trump Official Behind Controversial Russia Decision Has Kremlin Ties
Darren Beattie dismantled a key agency fighting Russian propaganda. There’s a reason why.

Graham positivity of triple Schubert calculus
Yibo Gao, Rui Xiong
https://arxiv.org/abs/2506.09421 https://arxiv.org/pdf/2506.09421…

Graham positivity of triple Schubert calculus
We prove Samuel's conjecture on certain Graham positivity of the expansion coefficient of two double Schubert polynomials in three sets of variables by establishing a refined version of Graham's positivity theorem. As a corollary, we prove Kirillov's conjecture on the positivity of skew divided difference operators applied to Schubert polynomials.

Adultification Bias in LLMs and Text-to-Image Models
Jane Castleman, Aleksandra Korolova
https://arxiv.org/abs/2506.07282 https://arx…

Adultification Bias in LLMs and Text-to-Image Models
The rapid adoption of generative AI models in domains such as education, policing, and social media raises significant concerns about potential bias and safety issues, particularly along protected attributes, such as race and gender, and when interacting with minors. Given the urgency of facilitating safe interactions with AI systems, we study bias along axes of race and gender in young girls. More specifically, we focus on "adultification bias," a phenomenon in which Black girls are presumed t…