Results 121 to 130 of about 1,299,040 (282)
A note on expansion in prime fields
, 2018 Let $β,ε\in (0,1]$, and $k \geq \exp(122 \max\{1/β,1/ε\})$. We prove that if $A,B$ are subsets of a prime field $\mathbb{Z}_{p}$, and $|B| \geq p^β$, then there exists a sum of the form $$S = a_{1}B \pm \ldots \pm a_{k}B, \qquad a_{1},\ldots,a_{k} \in A,$$ with $|S| \geq 2^{-12}p^{-ε}\min\{|A||B|,p\}$.
Orponen, Tuomas, Venieri, Laura
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Complementarity of Long‐Reads and Optical Mapping in Parkinson's Disease for Structural Variants
Annals of Clinical and Translational Neurology, EarlyView.ABSTRACT Objective Long‐read sequencing and optical genome mapping technologies have the ability to detect large and complex structural variants. This has led to the discovery of novel pathogenic variants in neurodegenerative movement disorders. Thus, we aimed to systematically compare the SV detection capabilities of OGM and ONT in Parkinson's disease.
André Fienemann +17 more
wiley +1 more source
Dihedral Congruence Primes and Class Fields of Real Quadratic Fields
Journal of Number Theory, 2002 The author characterizes the primes \(p\) such that the congruence \(f\equiv f\otimes\mod{\wp}\) holds for primitive cusp forms \(f\) of weight \(k\geq 2\) and quadratic nebentypus \(\chi=\chi_1\chi_2\), and a prime \(\wp\) of \(\overline{\mathbb Q}\) above \(p\), where \(\chi_1\) is even quadratic. Such primes are called dihedral. They are essentially
Brown, Alexander F., Ghate, Eknath P.
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Annals of Clinical and Translational Neurology, EarlyView.Epigenetic reprogramming in hematopoietic stem and progenitor cells (HSPCs) and downstream myeloid cells, mediated by H3.3 downregulation and endogenous retroelement (ERE) overexpression, contributes to the progression of multiple sclerosis (MS). ABSTRACT Background Skewed myelopoiesis in the bone marrow has been identified as a key driver of multiple ...
Li‐Mei Xiao +6 more
wiley +1 more source
Improvements to the number field sieve for non-prime finite fields
CoRR, 2014 We propose various strategies for improving the computation of discrete logarithms in non-prime fields of medium to large characteristic using the Number Field Sieve. This includes new methods for selecting the polynomials; the use of explicit automorphisms; explicit computations in the number fields; and prediction that some units have a zero virtual ...
Razvan Barbulescu +3 more
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The Role of Calcitonin Gene‐Related Peptide in High‐Altitude Headache: A Prospective Field Study
Annals of Clinical and Translational Neurology, EarlyView.ABSTRACT Objective High‐altitude headache (HAH) is a common neurological condition associated with rapid ascent to high altitude. The pathophysiological mechanisms underlying HAH remain incompletely understood. Calcitonin gene‐related peptide (CGRP), a neuropeptide implicated in migraine pathophysiology, may play a key role in the pathophysiology of ...
Roman Schniepp +4 more
wiley +1 more source
Annals of Clinical and Translational Neurology, EarlyView.ABSTRACT Chimeric antigen receptor (CAR) T‐cell therapy has been investigated in neurological diseases, encompassing both central nervous system malignancies and autoimmune disorders, thereby extending its application beyond hematological cancers.
Omar Alqaisi +5 more
wiley +1 more source
Investigating Schema-Free Encoding of Categorical Data Using Prime Numbers in a Geospatial Context
ISPRS International Journal of Geo-Information, 2019 Prime numbers are routinely used in a variety of applications, e.g., cryptography and hashing. A prime number can only be divided by one and the number itself.
Martin Sudmanns
doaj +1 more source
The smallest inert prime in a cyclic number field of prime degree [PDF]
Mathematical Research Letters, 2013 Fix an odd prime `. For each cyclic extension K/Q of degree `, let nK denote the least rational prime which is inert in K, and let rK be the least rational prime which splits completely in K. We show that nK possesses a finite mean value, where the average is taken over all such K ordered by conductor.
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Advanced Engineering Materials, Volume 27, Issue 6, March 2025.ErB4 and NdB4 nanostructured powders are produced by mechanochemical synthesis. 5 h mechanical alloying and 4 M HCl acid leaching are used in the production. ErB4 and NdB4 powders exhibit maximum magnetization of 0.4726 emu g−1 accompanied with an antiferromagnetic‐to‐paramagnetic phase transition at about TN = 18 K and 0.132 emu g−1 with a maximum at ...
Burçak Boztemur +5 more
wiley +1 more source