Results 31 to 40 of about 169 (169)
Disorder, entropy and harmonic functions [PDF]
The Annals of Probability, 2015 We study harmonic functions on random environments with particular emphasis on the case of the infinite cluster of supercritical percolation on $\mathbb{Z}^d$. We prove that the vector space of harmonic functions growing at most linearly is $(d+1)$-dimensional almost surely.
Itai Benjamini +3 more
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The Harmonicity of Slice Regular Functions [PDF]
The Journal of Geometric Analysis, 2020 AbstractIn this article, we investigate harmonicity, Laplacians, mean value theorems, and related topics in the context of quaternionic analysis. We observe that a Mean Value Formula for slice regular functions holds true and it is a consequence of the well-known Representation Formula for slice regular functions over $${\mathbb {H}}$$
Cinzia Bisi, Jörg Winkelmann
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FEBS Open Bio, EarlyView.We generated and characterized clear cell renal cell carcinoma models using the patient‐derived RCC243 cell line—including cell culture, orthotopic, and metastatic tumors—via single‐cell RNA‐sequencing for comparisons between models and patient tumor datasets.
Richard Huang +9 more
wiley +1 more source
Journal of Applied Clinical Medical Physics, EarlyView.Abstract Background The aim of this study was to thoroughly analyze the reproducibility of radiomics feature extraction across three Image Biomarker Standardization Initiative (IBSI)‐compliant platforms using a digital phantom for benchmarking. It uncovers high consistency among common features while also pointing out the necessity for standardization ...
Han‐Back Shin +5 more
wiley +1 more source
Multiply Harmonic Functions [PDF]
Nagoya Mathematical Journal, 1966 Let Ω and Ω′ be two locally compact, connected Hausdorff spaces having countable bases. On each of the spaces is defined a system of harmonic functions satisfying the axioms of M. Brelot [2]. The following is the description of such a system. To each open set of Ω is assigned a vector space of finite continuous functions, called the harmonic functions,
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On ratios of harmonic functions
Advances in Mathematics, 2015 Let $u$ and $v$ be harmonic in $ \subset \mathbb{R}^n$ functions with the same zero set $Z$. We show that the ratio $f$ of such functions is always well-defined and is real analytic. Moreover it satisfies the maximum and minimum principles. For $n=3$ we also prove the Harnack inequality and the gradient estimate for the ratios of harmonic functions ...
Alexander Logunov, Eugenia Malinnikova
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Journal of Applied Clinical Medical Physics, EarlyView.Abstract The establishment of guidelines and curriculum standards for medical physics residency training is a critical component of setting expectations and competencies for the profession. Since the last publication of these standards, residency training has become integrated into the eligibility criteria for most medical physics certification bodies.
Jonathon A. Nye +16 more
wiley +1 more source
Developing reference plans for evaluating global clinical trials credentialing and PSQA systems
Journal of Applied Clinical Medical Physics, EarlyView.Abstract Purpose To develop a practical framework for creating a diverse set of validated reference plans (varying in complexity) and implement a workflow to introduce beam modeling, calibration, and delivery errors into the reference cohort to test and compare various dosimetry audit methodologies.
Fre'Etta M. D. Brooks +13 more
wiley +1 more source
Annals of Clinical and Translational Neurology, EarlyView.ABSTRACT Objective Quantitative markers of cortical excitability may help identify responders to anti‐seizure medications (ASMs). We studied the relationship between ASM load and two electroencephalography (EEG) markers of cortical excitability in people with refractory epilepsy. Methods We included individuals with refractory focal epilepsy undergoing
Silvano R. Gefferie +7 more
wiley +1 more source
Clinical Trial Readiness in Limb Girdle Muscular Dystrophy R1 (LGMDR1): A GRASP Consortium Study
Annals of Clinical and Translational Neurology, EarlyView.ABSTRACT Objective Identifying functional measures that are both valid and reliable in the limb girdle muscular dystrophy (LGMD) population is critical for quantifying the level of functional impairment related to disease progression in order to establish clinical trial readiness in the context of anticipated therapeutic trials.
Stephanie M. Hunn +29 more
wiley +1 more source