Results 41 to 50 of about 101,155 (259)
Weighted Lattice Paths Enumeration by Gaussian Polynomials
, 2017 The Gaussian polynomial in variable $q$ is defined as the $q$-analog of the binomial coefficient. In addition to remarkable implications of these polynomials to abstract algebra, matrix theory and quantum computing, there is also a combinatorial ...
Martinjak, Ivica, Zubac, Ivana
core +1 more source
Odd Euler Sums and Harmonic Series with Cubic Central Binomial Coefficients in Denominators
AxiomsBy means of the coefficient extraction method, we examine a transformation of a classical hypergeometric series. Three classes of infinite series (of convergence rate “1/4”) with harmonic numbers in numerators and cubic central binomial coefficients in ...
Chunli Li, Wenchang Chu
doaj +1 more source
Divisibility of binomial coefficients by powers of two
, 2017 For nonnegative integers $j$ and $n$ let $\Theta(j,n)$ be the number of entries in the $n$-th row of Pascal's triangle that are not divisible by $2^{j+1}$. In this paper we prove that the family $j\mapsto\Theta(j,n)$ usually follows a normal distribution.
Spiegelhofer, Lukas, Wallner, Michael
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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
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
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
Relationship Between Neurologic Symptoms and Signs and FMR1 Genotype in Premutation Carriers
Annals of Clinical and Translational Neurology, EarlyView.ABSTRACT Background and Objectives Fragile X‐associated Tremor/Ataxia Syndrome (FXTAS) is the most severe late‐onset condition caused by a premutation in the FMR1 gene, characterized by expanded CGG triplet repeats of 55–200. Clinical presentations of FXTAS, including gait ataxia, kinetic tremor, cognitive decline, and rare Parkinsonism, are linked to ...
Flora Tassone +8 more
wiley +1 more source
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 High‐resolution MRI enables detailed assessment of intracranial vessel wall pathology in moyamoya vasculopathy. We aimed to classify adult moyamoya vasculopathy etiologies using high‐resolution MRI and to examine subtype‐specific associations between high‐resolution MRI features and ischemic infarction.
Guangsong Han +8 more
wiley +1 more source