Results 81 to 90 of about 165,625 (255)

On Sums Related to Central Binomial and Trinomial Coefficients [PDF]

, 2014
A generalized central trinomial coefficient $T_n(b,c)$ is the coefficient of $x^n$ in the expansion of $(x^2+bx+c)^n$ with $b,c\in\mathbb Z$. In this paper we investigate congruences and series for sums of terms related to central binomial coefficients and generalized central trinomial coefficients.
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Integral Representations of Catalan Numbers and Sums Involving Central Binomial Coefficients

, 2023
In the paper, the authors collect several integral representations of the Catalan numbers and central binomial coefficients, supply alternative proofs of two integral representations of the Catalan numbers, and apply these integral representations to alternatively prove several combinatorial identities for finite and infinite sums in which central ...
Guo, Bai-Ni, Lim, Dongkyu
openaire   +2 more sources

The Impact of Extreme Weather on Dengue Fever in Guangzhou, China: A Zero‐Inflated Negative Binomial Spatial Lag Analysis

GeoHealth
Climate change intensifies extreme weather, which in turn influences infectious disease transmission. As a dengue fever (DF) hotspot, Guangzhou lacks research on how extreme weather characteristics and spatial factors interact to shape DF patterns.
Xinqiu Ouyang, Fang Shi, Yang Qiu, Guangran Deng, Shujun Zhang   +4 more
doaj   +1 more source

Temporal Interference Stimulation Enhances Neural Regeneration

Advanced Science, EarlyView.
Temporal interference (TI) stimulation is proposed as a non‐invasive approach to enhance neural regeneration in the deep brain. Theta‐band TI modulation selectively promotes neural progenitor cell differentiation in vitro and augments hippocampal neurogenesis in amouse model of Alzheimer's disease‐like amyloidosis.
Sofia Peressott, Maria Garcia Garrido, Patrycja Dzialecka, Rachel Man Hoi Law, Roberto Portillo‐Lara, Bethany Geary, Elena Faillace, Shirine Merlo‐Nikpay Aslie, Marcelina Wojewska, Maria Otero‐Jimenez, Martina Genta, Luqiao Tan, Karen Duff, Javier Alegre‐Abarrategui, Rylie Green, Nir Grossmann   +15 more
wiley   +1 more source

PAIR: Reconstructing Single‐Cell Open‐Chromatin Landscapes for Transcription Factor Regulome Mapping

Advanced Science, EarlyView.
scATAC‐seq analysis is often constrained by limited sequencing depth, extreme sparsity, and pervasive technical missingness. PAIR is a probabilistic framework that restores scATAC‐seq accessibility profiles by directly modeling the native cell–peak bipartite structure of chromatin accessibility.
Yanchi Su, Qi Qi, Yi Fan, Yubo Wang, Gaoyang Hao, Ka‐Chun Wong, Yunhe Wang, Xiangtao Li   +7 more
wiley   +1 more source

Three combinatorial sums involving central binomial coefficients

We study three classes of combinatorial sums involving central binomial coefficients and harmonic numbers, odd harmonic numbers, and even indexed harmonic numbers, respectively. In each case we use summation by parts to derive recursive expressions for these sums.
Adegoke, Kunle, Frontczak, Robert
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Some $q$-congruences involving central $q$-binomial coefficients

, 2021
Suppose that $p$ is an odd prime and $m$ is an integer not divisible by $p$. Sun and Tauraso [Adv. in Appl. Math., 45(2010), 125--148] gave $\sum_{k=0}^{n-1}\binom{2k}{k+d}/m^k$ and $\sum_{k=0}^{n-1}\binom{2k}{k+d}/(km^k)$ modulo $p$ for all $d=0,1, \ldots n$ and $n= p^a$, where $a$ is a positive integer. In this paper, we present some $q$-analogues of
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SpaMode: A Broadly Applicable Framework for Deciphering Spatial Multi‐Omics Using Multimodal Mixture of Disentangled Experts

Advanced Science, EarlyView.
SpaMode introduces a versatile framework for spatial multi‐omics integration across vertical, horizontal, and mosaic scenarios. By disentangling modality‐invariant and variant features through a mixture‐of‐experts mechanism, it adaptively reconfigures spatially heterogeneous signals.
Xubin Zheng, Xinlei Huang, Xiang Zhou, Dian Meng, Ziyue Qiao, Zhiyuan Yuan, Lixin Cheng   +6 more
wiley   +1 more source

Agricultural Diversification at the Margin. Strategies and Determinants in Italian Mountain and Remote Areas

Agribusiness, EarlyView.
ABSTRACT This paper explores the convergence in on‐farm diversification strategies of agricultural holdings, between remote areas and more central ones. Using Italian farm‐level data, we explore the determinants of diversification strategies across farms.
Gianluca Grilli, Francesco Pagliacci, Paola Gatto   +2 more
wiley   +1 more source

On congruences related to central binomial coefficients, harmonic and Lucasnumbers

TURKISH JOURNAL OF MATHEMATICS, 2016
Summary: In this paper, using some combinatorial identities, we present new congruences involving central binomial coefficients and harmonic, Catalan, and Fibonacci numbers. For example, for an odd prime \(p\), we have \[\begin{aligned} \sum\limits_{k=1}^{\left( p-1\right) /2}\left( -1\right) ^{k}\binom{2k}{k} H_{k-1} &\equiv \frac{2^{p}}{p}\left( 2F_ ...
KOPARAL, SİBEL, ÖMÜR, NEŞE
openaire   +6 more sources