1332 papers
Mathematics often feels like a fortress of abstract symbols, yet at its core, it is the language describing the very fabric of our reality. This collection explores the "It" of mathematics: the computational power, the logical structures, and the algorithmic foundations that drive modern technology and scientific discovery. Here, we move beyond dry equations to see how pure math shapes the digital tools and physical models we rely on every day.
Every new preprint in this category arrives directly from arXiv, the premier archive for cutting-edge research. Gist.Science processes each of these fresh submissions to provide two distinct pathways for understanding: a clear, plain-language overview for the curious mind and a detailed technical summary for those seeking deeper rigor. Below are the latest papers in mathematics, curated to help you navigate the newest breakthroughs with confidence.
This paper surveys the 3GPP evolution from Release 19 to Release 20 regarding Integrated Sensing and Communication (ISAC) for 6G, detailing current requirements, technical studies across physical and system layers, and unresolved challenges to provide a standards-centric roadmap for practical ISAC deployment.
The paper introduces CORAL, a constrained oblique rotation method that achieves exact decorrelation of multivariate systems while preserving high source-variable identity through anchored loadings, significantly outperforming traditional PCA in maintaining fidelity across various datasets.
This paper proposes two novel separable channel approximations—the Kullback-Leibler divergence-enabled model and a moment matching method—to overcome the analytical complexity of the non-separable Weichselberger MIMO channel model, with the latter offering a robust, closed-form ergodic capacity estimate that outperforms conventional Kronecker models across all SNR regimes.
This paper refutes Titov's conjecture by proving that the analogue of the Barmpalias-Lewis-Pye Limit Theorem, which establishes the convergence of approximation ratios for Solovay reducibility, does not hold for S2a-reducibility in the context of Martin-Löf random reals.
This paper presents a reinforcement learning framework using Proximal Policy Optimization to co-design Bivariate Bicycle quantum error correcting codes and their decoders, optimizing the code generation process to maximize decoder performance under depolarizing noise.
This paper introduces a unified family of geodesic quantum -divergences interpolating between standard and maximal relative modular operators, establishing their data-processing inequalities, characterizing their equality conditions and associated quantum Markov chains, and analyzing their monotonicity, continuity, and information-theoretic interpretations.
This paper presents a construction of list-decodable codes that achieve capacity with deterministic time and space complexity of and respectively, while maintaining a constant output list size and alphabet size.
This paper establishes a central limit theorem in Rényi divergence for independent and identically distributed lattice random variables, proving that the divergence converges to zero if and only if it is finite at some level and the variables satisfy a strict sub-Gaussian condition, while also providing an arbitrary-order Edgeworth-type asymptotic expansion.
This paper introduces quantized maximal correlation, a cardinality-constrained extension of maximal correlation, and derives dimension-free upper bounds for product distributions by linking it to MMSE distortion and leveraging rate-distortion techniques, thereby improving bounds on isoperimetric constants for reversible Markov chains.
This paper proposes an efficiently estimable metric for quantifying the economic value of prompts given to Large Language Models by defining it as algorithmic mutual information based on a novel LLM-relative probabilistic Levin–Kolmogorov complexity ($pKt$), which captures how much a prompt reduces the computational effort or increases the probability of generating a target artifact.