Results 51 to 60 of about 923 (213)

Binary Representations and Theta Function

Integers, 2018
See the abstract in the attached pdf.
George E. Andrews, David Newman
openaire   +3 more sources

Elevated Connectivity During Language Processing Is Associated With Cognitive Performance in SeLECTS

Annals of Clinical and Translational Neurology, EarlyView.
ABSTRACT Objective Self‐Limited Epilepsy with Centrotemporal Spikes (SeLECTS) is associated with language impairments despite seizures originating in the motor cortex, suggesting aberrant cross‐network interactions. Here we tested whether functional connectivity in SeLECTS during language tasks predicts language performance.
Wendy Qi, Katharine Lee, Kerry C. Nix, Miguel Menchaca, Xiwei Shé, Lorelei Santa Maria, Wei Wu, Zihuai He, Fiona M. Baumer   +8 more
wiley   +1 more source

Theta function identities involving fourth power [PDF]

Notes on Number Theory and Discrete Mathematics
On page 241 of his Second Notebook, Ramanujan recorded one of his theta function identity, which involves the ratio of the fourth power of theta functions with respect to ψ(q). In this article, we give a new proof for this theta function identity.
Praveenkumar, Siddaraju, R. Rangarajan
doaj   +1 more source

Unraveling 4‐Phenylbutyrate's Therapeutic Role in SLC6A1 Disorders: Pharmacochaperoning Over HDAC Inhibition

Annals of Clinical and Translational Neurology, EarlyView.
ABSTRACT Objective Variants in SLC6A1, encoding the GABA transporter 1 (GAT‐1), cause epilepsy, autism spectrum disorder, and developmental delay via loss of GABA uptake, impaired trafficking, and ER retention. We previously found that 4‐Phenylbutyrate (PBA), an FDA‐approved drug, restores GABA uptake and reduces seizures in SLC6A1‐related disorders ...
Melissa B. DeLeeuw, Karishma Randhave, Ekta Anand, Ziang (Debbie) Song, Wangzhen Shen, Jing‐Qiong Kang   +5 more
wiley   +1 more source

T1 Over Squared Proton Density Ratio to Characterize Multiple Sclerosis Lesions

Annals of Clinical and Translational Neurology, EarlyView.
ABSTRACT Objective Differentiating remyelinated from demyelinated lesions in MS remains challenging without histological confirmation. This study introduces the T1‐to‐PD2 ratio (TPR) imaging approach and evaluates its ability to characterize MS lesions alongside other quantitative MRI (qMRI) metrics. Methods Thirty individuals with MS (mean age: 47.5 ± 
Sarah J. Wright, Scotty G. McKay, Jean Ramos Bou, Fen Bao, Vivian B. Truong, Chenyang Li, Li Jiang, Anza B. Memon, E. Mark Haacke, Yulin Ge, Yongsheng Chen   +10 more
wiley   +1 more source

Temporal Interference Stimulation of Centromedian‐Parafascicular Complex in Disorders of Consciousness: A Pilot Study

Annals of Clinical and Translational Neurology, EarlyView.
ABSTRACT Objective Treatment of disorders of consciousness (DoC) remains a major clinical challenge, and noninvasive, targeted modulation of deep brain structures has emerged as a promising therapeutic strategy. We aimed to evaluate the feasibility/safety and preliminary effects of thalamic temporal interference stimulation (TIS) targeting centromedian‐
Gengyao Hu, Changgeng Song, Dianwei Wu, Xiaoqian Niu, Jianmin Hao, Lijuan Liu, Xiaogang Kang, Wen Jiang   +7 more
wiley   +1 more source

Mock theta functions and Appell–Lerch sums

Journal of Inequalities and Applications, 2018
Recently, Mortenson (Proc. Edinb. Math. Soc. 4:1–13, 2015) explored the bilateral series in terms of Appell–Lerch sums for the universal mock theta function g2(x,q) $g_{2}{(x,q)}$.
Bin Chen
doaj   +1 more source

A Q‐Learning Algorithm to Solve the Two‐Player Zero‐Sum Game Problem for Nonlinear Systems

International Journal of Adaptive Control and Signal Processing, Volume 39, Issue 3, Page 566-581, March 2025.
A Q‐learning algorithm to solve the two‐player zero‐sum game problem for nonlinear systems. ABSTRACT This paper deals with the two‐player zero‐sum game problem, which is a bounded L2$$ {L}_2 $$‐gain robust control problem. Finding an analytical solution to the complex Hamilton‐Jacobi‐Issacs (HJI) equation is a challenging task.
Afreen Islam, Anthony Siming Chen, Guido Herrmann   +2 more
wiley   +1 more source

MOCK THETA FUNCTIONS AND QUANTUM MODULAR FORMS

Forum of Mathematics, Pi, 2013
Ramanujan’s last letter to Hardy concerns the asymptotic properties of modular forms and his ‘mock theta functions’. For the mock theta function $f(q)$, Ramanujan claims that as $q$ approaches an even-order $2k$ root of unity, we have $$\begin{eqnarray ...
AMANDA FOLSOM, KEN ONO, ROBERT C. RHOADES   +2 more
doaj   +1 more source

Adaptive Observer for Coupled Wave PDE and Infinite ODE With Sampled Data and Unknown Input: Application to Brain Hemodynamics Estimation

International Journal of Adaptive Control and Signal Processing, EarlyView.
This article proposes a convergent adaptive observer for a damped wave PDE and an infinite‐dimensional ODE coupled in cascade using sampled‐in‐space ODE state measurements. The proposed observer estimates the distributed states of the PDE and ODE along with unknown PDE parameters and spatial input.
Zehor Belkhatir, Sarah Mechhoud, Taous‐Meriem Laleg‐Kirati   +2 more
wiley   +1 more source