Results 61 to 70 of about 100,720 (284)
p-adic valuations of some sums of multinomial coefficients
, 2011 Let $m$ and $n>0$ be integers. Suppose that $p$ is a prime dividing $m-4$ but not dividing $m$. We show that $\nu_p(\sum_{k=0}^{n-1}\frac{\binom{2k}k}{m^k})$ and $\nu_p(\sum_{k=0}^{n-1}\binom{n-1}{k}(-1)^k\frac{\binom{2k}k}{m^k})$ are at least $\nu_p(n)$,
Sun, Zhi-Wei
core +1 more source
Molecular Oncology, EarlyView.To integrate multiple transcriptomics data with severe batch effects for identifying MB subtypes, we developed a novel and accurate computational method named RaMBat, which leveraged subtype‐specific gene expression ranking information instead of absolute gene expression levels to address batch effects of diverse data sources.
Mengtao Sun, Jieqiong Wang, Shibiao Wan
wiley +1 more source
Congruences for central binomial sums and finite polylogarithms [PDF]
, 2011 We prove congruences, modulo a power of a prime p, for certain finite sums involving central binomial coefficients $\binom{2k}{k}$
Mattarei, Sandro, Tauraso, Roberto
core
Shared Genetic Effects and Antagonistic Pleiotropy Between Multiple Sclerosis and Common Cancers
Annals of Clinical and Translational Neurology, EarlyView.ABSTRACT Objective Epidemiologic studies have reported inconsistent altered cancer risk in individuals with multiple sclerosis (MS). Factors such as immune dysregulation, comorbidities, and disease‐modifying therapies may contribute to this variability.
Asli Buyukkurt +5 more
wiley +1 more source
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
Polynomial Triangles Revisited [PDF]
, 2012 A polynomial triangle is an array whose inputs are the coefficients in integral powers of a polynomial. Although polynomial coefficients have appeared in several works, there is no systematic treatise on this topic. In this paper we plan to fill this gap.
Mohammedia Morocco, Nour-eddine Fahssi
core
Annals of Clinical and Translational Neurology, EarlyView.ABSTRACT Objective Glioma recurrence severely impacts patient prognosis, with current treatments showing limited efficacy. Traditional methods struggle to analyze recurrence mechanisms due to challenges in assessing tumor heterogeneity, spatial dynamics, and gene networks.
Lei Qiu +10 more
wiley +1 more source
Lucas' theorem: its generalizations, extensions and applications (1878--2014) [PDF]
, 2014 In 1878 \'E. Lucas proved a remarkable result which provides a simple way to compute the binomial coefficient ${n\choose m}$ modulo a prime $p$ in terms of the binomial coefficients of the base-$p$ digits of $n$ and $m$: {\it If $p$ is a prime, $n=n_0 ...
Meštrović, Romeo
core
, 2017 We study the dependence of the normalized moments of the net-proton multiplicity distributions on the definition of centrality in relativistic nuclear collisions at a beam energy of $\sqrt{s_{\mathrm{NN}}}= 7.7$ GeV.
Bleicher, M. +5 more
core +1 more source