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Background: Social support (SS) and social isolation (SI) are social determinants of health (SDOH) associated with psychiatric outcomes. In electronic health records (EHRs), individual-level SS/SI is typically documented as narrative clinical notes rather than structured coded data. Natural language processing (NLP) algorithms can automate the otherwise labor-intensive process of data extraction. Data and Methods: Psychiatric encounter notes from Mount Sinai Health System (MSHS, n=300) and Weill Cornell Medicine (WCM, n=225) were annotated and established a gold standard corpus. A rule-based system (RBS) involving lexicons and a large language model (LLM) using FLAN-T5-XL were developed to identify mentions of SS and SI and their subcategories (e.g., social network, instrumental support, and loneliness). Results: For extracting SS/SI, the RBS obtained higher macro-averaged f-scores than the LLM at both MSHS (0.89 vs. 0.65) and WCM (0.85 vs. 0.82). For extracting subcategories, the RBS also outperformed the LLM at both MSHS (0.90 vs. 0.62) and WCM (0.82 vs. 0.81). Discussion and Conclusion: Unexpectedly, the RBS outperformed the LLMs across all metrics. Intensive review demonstrates that this finding is due to the divergent approach taken by the RBS and LLM. The RBS were designed and refined to follow the same specific rules as the gold standard annotations. Conversely, the LLM were more inclusive with categorization and conformed to common English-language understanding. Both approaches offer advantages and are made available open-source for future testing., Comment: 2 figures, 3 tables

Entropic uncertainty relations place nontrivial lower bounds to the sum of Shannon information entropies for noncommuting observables. Here we obtain a novel lower bound on the entropy sum for general pairs of observables in finite-dimensional Hilbert space, which improves on the best bound known to date [Maassen and Uffink, Phys. Rev. Lett. 60, 1103 (1988)] for a wide class of observables. This result follows from another formulation of the uncertainty principle, the Landau-Pollak inequality, whose relationship to the Maassen-Uffink entropic uncertainty relation is discussed., Comment: 11 pages, 1 Postscript figure

The position and momentum information entropies of $D$-dimensional quantum systems with central potentials, such as the isotropic harmonic oscillator and the hydrogen atom, depend on the entropies of the (hyper)spherical harmonics. In turn, these entropies are expressed in terms of the entropies of the Gegenbauer (ultraspherical) polynomials $C_n^{(\lambda)}(x)$, the parameter $\lambda$ being either an integer or a half-integer number. Up to now, however, the exact analytical expression of the entropy of Gegenbauer polynomials of arbitrary degree $n$ has only been obtained for the particular values of the parameter $\lambda=0,1,2$. Here we present a novel approach to the evaluation of the information entropy of Gegenbauer polynomials, which makes use of trigonometric representations for these polynomials and complex integration techniques. Using this method, we are able to find the analytical expression of the entropy for arbitrary values of both $n$ and $\lambda\in\mathbb{N}$., Comment: 19 pages, 1 Postscript figure

We obtain a collection of necessary (sufficient) conditions for a bipartite system of qubits to be separable (entangled), which are based on the Landau-Pollak formulation of the uncertainty principle. These conditions are tested, and compared with previously stated criteria, by applying them to states whose separability limits are already known. Our results are also extended to multipartite and higher-dimensional systems., Comment: 20 pages