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Universal Infinite Partially Ordered Sets [PDF]

Proceedings of the American Mathematical Society, 1956
Introduction. The purpose of this paper is to construct for each infinite cardinal X an M-universal partially ordered set in which every partially ordered set of cardinality N can be embedded. An R-universal partially ordered set of cardinality 2H is constructed for every infinite cardinal N.
openaire   +1 more source

The role and implications of mammalian cellular circadian entrainment

FEBS Letters, EarlyView.
At their most fundamental level, mammalian circadian rhythms occur inside every individual cell. To tell the correct time, cells must align (or ‘entrain’) their circadian rhythm to the external environment. In this review, we highlight how cells entrain to the major circadian cues of light, feeding and temperature, and the implications this has for our
Priya Crosby
wiley   +1 more source

Ramsey numbers of partial order graphs (comparability graphs) and implications in ring theory

Open Mathematics, 2020
For a partially ordered set (A,≤)(A,\le ), let GA{G}_{A} be the simple, undirected graph with vertex set A such that two vertices a≠b∈Aa\ne b\in A are adjacent if either a≤ba\le b or b≤ab\le a.
Badawi Ayman, Rissner Roswitha
doaj   +1 more source

Pattern Avoidance in Poset Permutations

, 2015
We extend the concept of pattern avoidance in permutations on a totally ordered set to pattern avoidance in permutations on partially ordered sets. The number of permutations on $P$ that avoid the pattern $\pi$ is denoted $Av_P(\pi)$.
A Godbole, C Krattenthaler, C Savage, D Richards, DE Knuth, DE Knuth, GR Brightwell, J Bloom, M Bóna, M Klazar, MD Atkinson, MH Albert, Morgan Weiler, N Alon, P Brändén, R Simion, S Elizalde, S Heubach, S Kitaev, Sam Hopkins   +19 more
core   +1 more source

Molecular bases of circadian magnesium rhythms across eukaryotes

FEBS Letters, EarlyView.
Circadian rhythms in intracellular [Mg2+] exist across eukaryotic kingdoms. Central roles for Mg2+ in metabolism suggest that Mg2+ rhythms could regulate daily cellular energy and metabolism. In this Perspective paper, we propose that ancestral prokaryotic transport proteins could be responsible for mediating Mg2+ rhythms and posit a feedback model ...
Helen K. Feord, Gerben van Ooijen
wiley   +1 more source

A technique of tripled coincidence points for solving a system of nonlinear integral equations in POCML spaces

Journal of Inequalities and Applications, 2020
This manuscript aims to initiate some recent theoretical consequences related to tripled coincidence points for non-self mappings via the notion of C-type functions in partially ordered complete metric-like space (for short, POCML space).
Hasanen A. Hammad, Manuel De La Sen
doaj   +1 more source

Interplay between circadian and other transcription factors—Implications for cycling transcriptome reprogramming

FEBS Letters, EarlyView.
This perspective highlights emerging insights into how the circadian transcription factor CLOCK:BMAL1 regulates chromatin architecture, cooperates with other transcription factors, and coordinates enhancer dynamics. We propose an updated framework for how circadian transcription factors operate within dynamic and multifactorial chromatin landscapes ...
Xinyu Y. Nie, Jerome S. Menet
wiley   +1 more source

Liquid Crystal Phases of Quantum Hall Systems

, 1998
Mean-field calculations for the two dimensional electron gas (2DEG) in a large magnetic field with a partially filled Landau level with index $N\geq 2$ consistently yield ``stripe-ordered'' charge-density wave ground-states, for much the same reason that
A. P. Young, B. I. Halperin, D. R. Nelson, Eduardo Fradkin, J. M. Tranquada, J. M. Tranquada, K. Yamada, L. Bonsall, M. M. Fogler, M. M. Fogler, M. P. Lilly, M. Stone, P. G. de Gennes, R. L. Willett, R. Moessner, S-W. Cheong, S. A. Kivelson, S. A. Kivelson, Steven A. Kivelson, T. E. Mason, T. R. Thurston, V. J. Emery, X-G. Wen   +22 more
core   +1 more source

Disordered but rhythmic—the role of intrinsic protein disorder in eukaryotic circadian timing

FEBS Letters, EarlyView.
Unstructured domains known as intrinsically disordered regions (IDRs) are present in nearly every part of the eukaryotic core circadian oscillator. IDRs enable many diverse inter‐ and intramolecular interactions that support clock function. IDR conformations are highly tunable by post‐translational modifications and environmental conditions, which ...
Emery T. Usher, Jacqueline F. Pelham
wiley   +1 more source

Key Assignment Scheme with Authenticated Encryption

IACR Transactions on Symmetric Cryptology, 2018
The Key Assignment Scheme (KAS) is a well-studied cryptographic primitive used for hierarchical access control (HAC) in a multilevel organisation where the classes of people with higher privileges can access files of those with lower ones.
Suyash Kandele, Souradyuti Paul
doaj   +1 more source