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A Note on Extended Binomial Coefficients
J. Integer Seq., 2014 We study the distribution of the extended binomial coefficients by deriving a complete asymptotic expansion with uniform error terms. We obtain the expansion from a local central limit theorem and we state all coefficients explicitly as sums of Hermite polynomials and Bernoulli numbers.
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Advanced Science, EarlyView.In microglia, STAT3 upregulates TAB2, which promotes NF‐κB activation through its NZF domain‐mediated recognition of K63‐linked ubiquitin chains, leading to inflammatory cytokine release and subsequent neuronal injury. Lumacaftor suppresses TAB2 expression and directly binds the TAB2‐NZF domain to interrupt K63 ubiquitin recognition, thereby blocking ...
Yanhao Zhao +12 more
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Bernstein-type approximations of smooth functions
Statistica, 2007 The Bernstein-type approximation for smooth functions is proposed and studied. We propose the Bernstein-type approximation with definitions that directly apply the binomial distribution and the multivariate binomial distribution.
Andrea Pallini
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Sum of the Reciprocals of the Binomial Coefficients
European Journal of Combinatorics, 1993 Let \(S_ n=\sum^ n_{k=0}{1 \over {n \choose k}}\). It is shown that \(S_ n\) satisfies the recurrence \(S_ n={n+1 \over 2n}S_{n-1}+1\). The proof can be simplified by observing that \[ n!S_ n=\sum^ n_{k=0}k!(n-k)!=n!+\sum^{n-1}_{k=0}k!(n-k-1)!(n+1-k-1) =n!+(n+ 1)(n-1)!S_{n-1}-(n!S_ n-n!). \]
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Some divisibility properties of binomial and q -binomial coefficients
Journal of Number Theory, 2014 We first prove that if $a$ has a prime factor not dividing $b$ then there are infinitely many positive integers $n$ such that $\binom {an+bn} {an}$ is not divisible by $bn+1$. This confirms a recent conjecture of Z.-W. Sun. Moreover, we provide some new divisibility properties of binomial coefficients: for example, we prove that $\binom {12n} {3n}$ and
Krattenthaler, Christian +1 more
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Advanced Science, EarlyView.Ex‐spRandom is a spatial transcriptomics platform that synergizes random‐primed chemistry with iterative hydrogel expansion. By physically decrowding the dense FFPE matrix, this scalable technology shatters the traditional resolution‐sensitivity barrier.
Shunji Zhang +7 more
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DyProL: Dynamic Ensemble Representation Learning for Protein–Nucleic Acid Binding Site Prediction
Advanced Science, EarlyView.Protein function is represented as a dynamic conformational ensemble rather than a single static structure. A multi‐conformation geometric attention framework aligns, clusters, and learns representative states to capture residue‐ and ensemble‐level signals. Integrating structural dynamics improves interpretable protein‐NA binding prediction and reveals
Pengpai Li +3 more
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Advanced Science, EarlyView.Mesenchymal GSCs preferentially uptake palmitic acid, thereby promoting ZDHHC12‐mediated LDHA palmitoylation. This modification enhances LDHA enzymatic activity, drives glycolytic reprogramming, and facilitates exosomal LDHA‐mediated TAM regulation.
Zijie Gao +20 more
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Generalized Binomial Trees [PDF]
We consider the problem of consistently pricing new options given the prices of related options on the same stock. The Black-Scholes formula and standard binomial trees can only accommodate one related European option which then effectively specifies the
Jackwerth, Jens Carsten
core
A consistent estimator for the binomial distribution in the presence of “incidental parameters”: an application to patent data [PDF]
, 2003 In this paper a consistent estimator for the Binomial distribution in the presence of incidental parameters, or fixed effects, when the underlying probability is a logistic function is derived.
Machado, Matilde P.
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