A modern, 'S7'-based foundation for survey analysis spanning both probability and non-probability samples. Probability sample designs include Taylor series linearization, replicate weights (BRR, Fay, jackknife, bootstrap), and two-phase estimation, following 'Lumley' (2004) &lt;<a href="https://doi.org/10.18637%2Fjss.v009.i08" target="_top">doi:10.18637/jss.v009.i08</a>&gt;. Non-probability sample designs support bootstrap and jackknife variance estimation for opt-in panels and convenience samples. Provides a unified estimator interface for means, frequencies, totals, quantiles, ratios, correlations, regression, and t-tests, with weighted 'polychoric' and 'polyserial' correlation following 'Mannan' (2025) &lt;<a href="https://doi.org/10.2139%2Fssrn.6580480" target="_top">doi:10.2139/ssrn.6580480</a>&gt;. A metadata system preserves 'haven'-style variable labels, value labels, and question-preface attributes through all operations, alongside dataset-level metadata that records the survey name, the fielding vendor, and the field period. Uses a 'tidyselect' interface throughout.

A detailed introduction to Lipschitz-free spaces, from linearization and compact reduction to the absence of c₀ in the free space over a real Hilbert space.

arXiv abstract link

Kevin Paramero-Arias, Alejandro P. Riascos We study synchronization in network-coupled oscillators subject to stochastic resetting of a subset of nodes. We show that resetting can induce collective coherence in oscillators that are never directly reset, through the interplay of network structure, frequency heterogeneity, and the organization of the reset subsystem. In the infinite-resetting-rate limit, the reset nodes become effectively pinned to a reference phase, and linearization near synchronization maps the dynamics of the remaining subsystem onto a grounded-Laplacian problem. This formulation yields an analytical relation between the synchronization level and the reset parameters, providing an estimate of the coupling strength required to achieve a prescribed degree of coherence. Beyond the linear regime, we develop a mean-field description in which the reset subsystem acts as an effective ordering field for the remaining oscillators. Numerical simulations across different network topologies confirm these predictions and show that synchronization is enhanced by increasing both the reset fraction and network connectivity. In heterogeneous networks, the placement of reset nodes can strongly influence the synchronization response. For frequency distributions with nonzero mean, resetting competes with the intrinsic collective rotation and can drive the system from a rotating synchronized state to a phase-locked state. These results establish subsystem resetting as a mechanism for inducing and controlling collective synchronization in complex networks. Read the full article at: arxiv.org

Nonlinear differential equations play a crucial role in modeling a wide range of phenomena, yet their solutions remain notoriously difficult to obtain. With the rapid development of quantum computing, quantum algorithms for efficiently solving such equations are actively being explored. One promisin

This is a portal to these repositories from neutral aspect, as plainly a collection of texts and code to teach an AI. - tambetvali/LaegnaDocumentation