Results 81 to 90 of about 7,070,887 (229)
More congruences for central binomial coefficients
Journal of Number Theory, 2010 Let \(p>5\) be a prime number. The author proves that \[ \sum_{k=1}^{p-1}\frac{1}{k^2}\binom{2k}{k}^{-1}\equiv\frac13 \frac{H(1)}{p}\pmod {p^3} \] and that \[ \sum_{k=1}^{p-1}\frac{(-1)^k}{k^3}\binom{2k}{k}^{-1}\equiv-\frac25 \frac{H(1)}{p^2}\pmod {p^3}, \] where \(H(1)=\sum_{k=1}^{p-1}\frac{1}{k}\).
openaire +3 more sources
Advanced Science, EarlyView.Pathological tissue rigidity mechanoprimes microglia by enhancing actin cytoskeleton–nucleus coupling and chromatin opening at rigidity‐responsive cis‐regulatory elements (mechanoCREs). Subsequent NF‐κB/p65 signaling converges on this permissive regulatory state to amplify inflammatory gene expression and microglial activation.
Yu Xuan Meng +15 more
wiley +1 more source
On a conjecture of Graham on the p$p$‐divisibility of central binomial coefficients
MathematikaAbstractLet be pairwise distinct primes. From a theorem of Kummer, each prime can divide at most times. We show that, for all , if are sufficiently large in terms of and , then there exist infinitely many positive integers such that each divides at most times.
Mousavi, Seyyed Hamed +2 more
openaire +3 more sources
Random Dynamics and Finance: Constructing Implied Binomial Trees from a Predetermined Stationary Den [PDF]
We introduce a general binomial model for asset prices based on the concept of random maps. The asymptotic stationary distribution for such model is studied using techniques from dynamical systems.
Silvia Mayoral +3 more
core
Advanced Science, EarlyView.KFO‐Atlas reveals how real‐world aromas are organized as structured mixtures rather than individual molecules. Building on these principles, KFO‐Gen, a generative AI framework, designs perceptually valid aroma formulations and reconstructs meat‐like aromas exclusively from plant‐derived odorants, providing a foundation for mixture‐level studies and AI ...
Jingzhi Zhang +5 more
wiley +1 more source
Neuropsychiatric Disease and Treatment, 2016 Honglei Yin,1,2 Lin Xu,3 Yechang Shao,2,4 Liping Li,5 Chengsong Wan2 1Department of Psychiatry, Nanfang Hospital, Southern Medical University, Guangzhou, People’s Republic of China; 2School of Public Health, Southern Medical University ...
Yin HL, Xu L, Shao YC, Li LP, Wan CS
doaj
Advanced Science, EarlyView.Grounded in real biological RNA‐seq data, the framework benchmarks ten differential transcript usage (DTU) methods across short‐read bulk, long‐read bulk, long‐read single‐cell, and long‐read spatial transcriptomics. By integrating reference transcript sets with ranked DTU results, the Transcript Set Enrichment Score (TSES) identifies data‐type ...
Chenxing Zhang +6 more
wiley +1 more source
Central's first homecoming; male students standing on street in single file line
, 1920 In Central Methodist University (formerly Central College)'s first homecoming parade, male students in costume stand in single file on an unpaved road in Fayette ...
Central Methodist University, Smiley Memorial Library
core +1 more source
Advanced Science, EarlyView.Coexisting DCIS and IDC samples are profiled using spatial transcriptomics, single‐cell RNA sequencing, and single‐cell DNA sequencing. Integrative multi‐omics analysis reveals distinct malignant epithelial and microenvironmental features between DCIS and IDC, which are further validated using Xenium and multiplex immunohistochemistry.
Ning Zhang +18 more
wiley +1 more source
Advanced Science, EarlyView.DUET‐seq is an open‐source droplet platform that jointly profiles chromatin accessibility and gene expression from the same nucleus. Dissolvable dual‐linker hydrogel beads and a one‐step intra‐droplet RT‐PCR co‐index both modalities in under 12 h at roughly $0.04 per cell.
Dong Cheng +16 more
wiley +1 more source