Results 41 to 50 of about 19,998 (234)
On Sums Related to Central Binomial and Trinomial Coefficients [PDF]
, 2014 54 pages, final published ...
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Identities for squared central binomial coefficients
, 2021 We prove four identities for the squared central binomial coefficients. The first three of them reflect certain transformation properties of the complete elliptic integrals of the first and the second kind, while the last one is based on properties of the Lagrange polynomials.
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stMixer for Scalable Mosaic Integration and Label Transfer in Spatial Histology and Multi‐Omics
Advanced Science, EarlyView.stMixer is an unsupervised framework for scalable integration and label transfer across spatial histology and multi‐slide multi‐omics data with incomplete modality overlap. It combines self‐looped cross‐attention, multimodal metric learning, and graph‐guided cluster voting to align heterogeneous sections, correct batch effects, and propagate ...
Qixing Yang +3 more
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Advanced Science, EarlyView.SPADE integrates spatial transcriptomics with single‐cell RNA sequencing by using cell–cell communications (CCC) as a guide for spatial mapping. It improves cell‐type localization, enhances sparse gene‐expression signals, and reveals CCC programs at single‐spot resolution.
Xinyi Li, Ning Zhang, Zijie Jin
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A short derivation of an elegant sum involving central binomial coefficients due to László via a hypergeometric series approach [PDF]
Contributions to Mathematics, 2022 Dongkyu Lim, Arjun K. Rathie
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Advanced Science, EarlyView.Decoupling biological signals from unwanted variation in multi‑condition single‑cell RNA sequencing data remains challenging. CAPER disentangles condition‑associated biological effects from sample heterogeneity through matrix factorization, producing interpretable latent factors and a batch‑corrected expression matrix.
Ye Li +6 more
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Advanced Science, EarlyView.Caspofungin heteroresistance is prevalent in clinical Candida glabrata isolates and depends on calcineurin‐mediated stress adaptation. This transient phenotype serves as a reservoir for resistance evolution, enabling the emergence of stable resistant descendants under prolonged drug pressure.
Yanyu Su +7 more
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Sums of Reciprocals of the Central Binomial Coefficients
, 2006 We consider a set of combinatorial sums involving the reciprocals of the central binomial coefficients and try to solve (or close) them by means of generating functions. We obtain a number of results for infinite sums, in some of which the golden ratio ! appears.
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On congruences related to central binomial coefficients, harmonic and Lucasnumbers
TURKISH JOURNAL OF MATHEMATICS, 2016 Summary: In this paper, using some combinatorial identities, we present new congruences involving central binomial coefficients and harmonic, Catalan, and Fibonacci numbers. For example, for an odd prime \(p\), we have \[\begin{aligned} \sum\limits_{k=1}^{\left( p-1\right) /2}\left( -1\right) ^{k}\binom{2k}{k} H_{k-1} &\equiv \frac{2^{p}}{p}\left( 2F_ ...
KOPARAL, SİBEL, ÖMÜR, NEŞE
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Advanced Science, EarlyView.Population‐scale EDC–hormone association mapping among 4255 participants across demographic subgroups identifies phthalate metabolites as the most consistent signals associated with lower testosterone‐related markers in males. Integrative mechanistic validation prioritizes MCPP as a key phthalate metabolite linked to CYP17A1‐centered disruption of ...
Yanling Chen +14 more
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