1190 papers
This collection explores the fascinating intersection of mathematics and data science, where rigorous theory meets real-world application. From developing new algorithms to refining statistical models, these papers tackle how we organize, interpret, and predict patterns in an increasingly complex digital world. Whether you are a researcher or simply curious about the logic driving modern technology, this field offers a deep dive into the tools shaping our future.
Every entry here originates from arXiv, the premier repository for scientific preprints. At Gist.Science, we process each new submission in this category to provide both accessible plain-language summaries and detailed technical overviews, ensuring that groundbreaking research is understandable to everyone. Below are the latest papers in this dynamic category, ready to help you grasp the latest mathematical breakthroughs without the usual barriers.
This paper establishes two rigidity results for Laplace-isospectral deformations of generic Liouville metrics on the two-dimensional torus, proving that affine deformations are trivial and analytic deformations with trigonometric polynomial coefficients are merely componentwise rearrangements of the original metric.
This paper proves the Lagrange stability and existence of quasi-periodic solutions for reversible Duffing equations with quasi-periodic coefficients by constructing a finite normal-form procedure that yields codimension-one KAM tori accumulating at infinity under a specific degree condition.
This paper establishes that for a surjective upper semi-continuous set-valued map on a compact metric space, the shadowing property and various forms of transitivity are equivalent between the map, its inverse, and their associated generalized inverse limits, thereby strengthening previous results that required stronger continuity and openness assumptions.
This paper positively resolves Owings's sumsets question by proving that for any 2-coloring of the natural numbers, there exists an infinite subset such that the sumset is monochromatic, while also presenting weighted generalizations of this result.
This paper derives a single delay differential equation for the order parameter of an all-to-all coupled theta-neuron network with distributed delays, analyzing the stability and bifurcations of two distinct equilibrium families to demonstrate how delay kernels influence multistability, stability switching, and the emergence of periodic dynamics.
This paper provides an elementary proof of power Fourier decay for Patterson-Sullivan measures of convex co-compact Schottky groups with dimension , establishing an explicit decay exponent while replacing advanced techniques like sum-product estimates and renewal theory with oscillatory integral estimates, hyperbolic geometry, and a duality argument.
This paper presents a non-smooth ordinary differential equation model of dengue transmission that integrates finite hospital capacity and threshold-triggered fogging interventions, revealing how these state-dependent constraints and control policies generate complex dynamics like oscillatory outbreaks and bifurcations to guide the design of effective, resource-aware intervention strategies.
This paper introduces a machine learning framework that establishes a "universal dynamical clock" by mapping arbitrary oscillatory systems to uniform rotation via a Ptolemy-inspired equant, enabling the discovery of new physical laws, the resolution of long-standing biological scaling problems, and the prediction of critical transitions in complex networks.
This paper introduces a space of framed decorated polynomial trees as the dynamical tropicalization of ramification strata in polynomial parameter spaces by constructing a proper toroidal compactification via rigidified framed Hurwitz spaces, thereby establishing an isomorphism between this tree space and the associated Berkovich skeleton while providing a new compactification for polynomial moduli.
This paper establishes sufficient and necessary conditions for random Blaschke products to exhibit synchronization, chaos, or a unique random fixed point attractor, while specifically analyzing the critical transition between order and chaos in two-map cocycles.