Results 111 to 120 of about 160,421 (323)
The design of the entire paper. Green part represents the bioinformatics analysis approach. Yellow part represents the ideas of animal experiment. Abstract Background Chronic obstructive pulmonary disease (COPD) is a type of chronic respiratory disease.
Xuejing Luan +5 more
wiley +1 more source
On the Relation between Inverse Factorial Series and Binomial Coefficient Series [PDF]
W. L. Ferrar
openalex +1 more source
Depression Polygenicity and Disease Activity and Disability Worsening in Multiple Sclerosis
Objective A better understanding of factors associated with multiple sclerosis (MS) disease activity and disability is needed. Given the strong link between comorbid depression and MS disease activity and disability, we aimed to determine whether the depression genetic burden, as modelled using its polygenic score, is associated with MS disease ...
Ali Manouchehrinia +24 more
wiley +1 more source
On the Relation between Bernoulli's Numbers and the Binomial Coefficients [PDF]
J.K. Hammond
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Objective The objective of this study was to compare the long‐term safety profiles of ocrelizumab and rituximab in persons with multiple sclerosis (MS). Methods Using retrospective data from the University of California (UC) Health System, we simulated a target clinical trial. The primary cohort from UC San Francisco (UCSF) and a validation cohort from
Gabriel Cerono +3 more
wiley +1 more source
Objective Tumornecrosis factor inhibitors (TNFi) have significantly improved rheumatoid arthritis (RA) management, yet variability in patient response remains a substantial challenge, with approximately 40% of patients discontinuing TNFi due to nonresponse or adverse effects.
Chuan Fu Yap +12 more
wiley +1 more source
Triple Symmetric Sums of Circular Binomial Products
By employing the generating function approach, 16 triple sums for circular binomial products of binomial coefficients are examined. Recurrence relations and generating functions are explicitly determined.
Marta Na Chen, Wenchang Chu
doaj +1 more source
Series associated with harmonic numbers, Fibonacci numbers and central binomial coefficients $binom{2n}{n}$ [PDF]
We find various series that involve the central binomial coefficients $binom{2n}{n}$, harmonic numbers and Fibonacci numbers. Contrary to the traditional hypergeometric function _pF_q approach, our method utilizes a straightforward transformation to ...
Segun Olofin Akerele +1 more
doaj +1 more source
Remark on a conjecture of Erdős on binomial coefficients [PDF]
Andrzej Mạkowski
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On sums of binomial coefficients and their applications
In this paper we study recurrences concerning the combinatorial sum $[n,r]_m=\sum_{k\equiv r (mod m)}\binom {n}{k}$ and the alternate sum $\sum_{k\equiv r (mod m)}(-1)^{(k-r)/m}\binom{n}{k}$, where m>0, $n\ge 0$ and r are integers. For example, we show that if $n\ge m-1$ then $$\sum_{i=0}^{\lfloor(m-1)/2\rfloor}(-1)^i\binom{m-1-i}i [n-2i,r-i]_m=2^{n-
openaire +3 more sources

