Cell Growth Problems

1967 ◽  
Vol 19 ◽  
pp. 851-863 ◽  
Author(s):  
David A. Klarner
Keyword(s):  
Cell Growth ◽  
Equivalence Class ◽  
Equivalence Classes ◽  
Lattice Points ◽  
The Other ◽  
Square Lattice ◽  
Cut Set ◽  
Point Set ◽  
Infinite Set ◽  
Interior Points

The square lattice is the set of all points of the plane whose Cartesian coordinates are integers. A cell of the square lattice is a point-set consisting of the boundary and interior points of a unit square having its vertices at lattice points. An n-omino is a union of n cells which is connected and has no finite cut set.The set of all n-ominoes, Rn is an infinite set for each n; however, we are interested in the elements of two finite sets of equivalence classes, Sn and Tn, which are defined on the elements of Rn as follows: Two elements of Rn belong to the same equivalence class (i) in Sn, or (ii) in Tn, if one can be transformed into the other by (i) a translation or (ii) by a translation, rotation, and reflection of the plane.

Regent Results in Comma-Free Codes

1963 ◽  
Vol 15 ◽  
pp. 178-187 ◽  
Author(s):  
B. H. Jiggs
Keyword(s):  
Equivalence Class ◽  
Cyclic Permutation ◽  
Equivalence Classes ◽  
The Other ◽  
Complete Class

A set D of k-letter words is called a comma-free dictionary (2), if whenever (a1a2 . . . ak) and (b1b2 . . . bk) are in D, the "overlaps" (a2a3 . . . akb1), (a3a4 . . . akb1b2), . . . , (akb1 . . . bk-1) are not in D. We say that two k-letter words are in the same equivalence class if one is a cyclic permutation of the other. An equivalence class is called complete if it contains k distinct members. Comma-freedom is violated if we choose words from incomplete equivalence classes, or if more than one word is chosen from the same complete class.

Densely methylated DNA islands in mammalian chromosomal replication origins

1994 ◽  
Vol 14 (9) ◽  
pp. 5636-5644
Author(s):  
E S Tasheva ◽  
D J Roufa
Keyword(s):  
Cell Growth ◽  
Dna Sequence ◽  
Chemical Method ◽  
Chinese Hamster ◽  
Chinese Hamster Cell ◽  
The Other ◽  
Replication Origins ◽  
Chromosomal Replication ◽  
Cpg Dinucleotides ◽  
Methylated Dna

Densely methylated DNA sequence islands, designated DMIs, have been observed in two Chinese hamster cell chromosomal replication origins by using a PCR-based chemical method of detection. One of the origins, oriS14, is located within or adjacent to the coding sequence for ribosomal protein S14 on chromosome 2q, and the other, ori-beta, is approximately 17 kbp downstream of the dhfr (dihydrofolic acid reductase) locus on chromosome 2p. The DMI in oriS14 is 127 bp long, and the DMI in ori-beta is 516 bp long. Both DMIs are bilaterally methylated (i.e., all dCs are modified to 5-methyl dC) only in cells that are replicating their DNA. When cell growth and DNA replication are arrested, methylation of CpA, CpT, and CpC dinucleotides is lost and the sequence islands display only a subset of their originally methylated CpG dinucleotides. Several possible roles for DMI-mediated regulation of mammalian chromosomal origins are considered.

A pseudohedron

2004 ◽  
Vol 88 (512) ◽  
pp. 226-229
Author(s):  
H. Martyn Cundy
Keyword(s):  
The Other ◽  
Regular Polygons ◽  
Spherical Trigonometry ◽  
Equilateral Triangles ◽  
Infinite Set

The other day I received a long tube from a Canadian stranger containing a large poster featuring over a hundred polyhedra, including ‘all 92 Johnson polyhedra’. This term, though probably unfamiliar this side of the pond, was not completely unknown to me; it means convex polyhedra, excluding the regular and Archimedean ones, all of whose faces are regular polygons. Of course, as usual, we have to exclude those naughty polyhedra whose faces go around in pairs collecting squares (prisms) or equilateral triangles (antiprisms) and don’t know when to stop. The word convex is vital, otherwise there would be another infinite set. A lot of them are rather trivial, like sticking pyramids on the faces of a dodecahedron, but they include the deltahedra and many other interesting members. But they have at least one imitator who didn't quite make the grade. Trying to discover why, and how to coach him so that he would, I found that my spherical trigonometry was getting rather rusty so I set out to make one and see what was happening. I thought perhaps other readers would like to share this piece of antiresearch.

scholarly journals On the finiteness of the derived equivalence classes of some stable endomorphism rings

2020 ◽  
Vol 296 (3-4) ◽  
pp. 1157-1183 ◽  
Author(s):  
Jenny August
Keyword(s):  
Equivalence Class ◽  
Minimal Model ◽  
Equivalence Classes ◽  
Finite Dimensional Algebra ◽  
Derived Equivalence ◽  
Endomorphism Rings ◽  
Dimensional Algebra ◽  
Rigid Objects ◽  
Finite Dimensional ◽  
Frobenius Category

Abstract We prove that the stable endomorphism rings of rigid objects in a suitable Frobenius category have only finitely many basic algebras in their derived equivalence class and that these are precisely the stable endomorphism rings of objects obtained by iterated mutation. The main application is to the Homological Minimal Model Programme. For a 3-fold flopping contraction $$f :X \rightarrow {\mathrm{Spec}\;}\,R$$ f : X → Spec R , where X has only Gorenstein terminal singularities, there is an associated finite dimensional algebra $$A_{{\text {con}}}$$ A con known as the contraction algebra. As a corollary of our main result, there are only finitely many basic algebras in the derived equivalence class of $$A_{\text {con}}$$ A con and these are precisely the contraction algebras of maps obtained by a sequence of iterated flops from f. This provides evidence towards a key conjecture in the area.

Scalable l-Diversity

2019 ◽  
Vol 14 (2) ◽  
pp. 27-40
Author(s):  
Udai Pratap Rao ◽  
Brijesh B. Mehta ◽  
Nikhil Kumar
Keyword(s):  
Equivalence Class ◽  
Information Loss ◽  
Equivalence Classes ◽  
Data Publishing ◽  
Programming Paradigm ◽  
Research Areas ◽  
Complete Dataset ◽  
Input Dataset ◽  
Privacy Preserving Data Publishing ◽  
Cost Penalty

Privacy preserving data publishing is one of the most demanding research areas in the recent few years. There are more than billions of devices capable to collect the data from various sources. To preserve the privacy while publishing data, algorithms for equivalence class generation and scalable anonymization with k-anonymity and l-diversity using MapReduce programming paradigm are proposed in this article. Equivalence class generation algorithms divide the datasets into equivalence classes for Scalable k-Anonymity (SKA) and Scalable l-Diversity (SLD) separately. These equivalence classes are finally fed to the anonymization algorithm that calculates the Gross Cost Penalty (GCP) for the complete dataset. The value of GCP gives information loss in input dataset after anonymization.

scholarly journals Bipolar Fuzzy Relations

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1044 ◽  
Author(s):  
Jeong-Gon Lee ◽  
Kul Hur
Keyword(s):  
Equivalence Class ◽  
Level Set ◽  
Equivalence Relation ◽  
Level Sets ◽  
Equivalence Classes ◽  
Fuzzy Relation ◽  
Fuzzy Relations ◽  
Transitive Relation ◽  
Fuzzy Partition

We introduce the concepts of a bipolar fuzzy reflexive, symmetric, and transitive relation. We study bipolar fuzzy analogues of many results concerning relationships between ordinary reflexive, symmetric, and transitive relations. Next, we define the concepts of a bipolar fuzzy equivalence class and a bipolar fuzzy partition, and we prove that the set of all bipolar fuzzy equivalence classes is a bipolar fuzzy partition and that the bipolar fuzzy equivalence relation is induced by a bipolar fuzzy partition. Finally, we define an ( a , b ) -level set of a bipolar fuzzy relation and investigate some relationships between bipolar fuzzy relations and their ( a , b ) -level sets.

scholarly journals The binomial equivalence classes of finite words

2020 ◽  
Vol 30 (07) ◽  
pp. 1375-1397
Author(s):  
Marie Lejeune ◽  
Michel Rigo ◽  
Matthieu Rosenfeld
Keyword(s):  
Nilpotent Group ◽  
Equivalence Class ◽  
Free Monoid ◽  
Equivalence Classes ◽  
Single Element ◽  
Free Nilpotent Group ◽  
Context Free ◽  
Abelian Equivalence

Two finite words [Formula: see text] and [Formula: see text] are [Formula: see text]-binomially equivalent if, for each word [Formula: see text] of length at most [Formula: see text], [Formula: see text] appears the same number of times as a subsequence (i.e., as a scattered subword) of both [Formula: see text] and [Formula: see text]. This notion generalizes abelian equivalence. In this paper, we study the equivalence classes induced by the [Formula: see text]-binomial equivalence. We provide an algorithm generating the [Formula: see text]-binomial equivalence class of a word. For [Formula: see text] and alphabet of [Formula: see text] or more symbols, the language made of lexicographically least elements of every [Formula: see text]-binomial equivalence class and the language of singletons, i.e., the words whose [Formula: see text]-binomial equivalence class is restricted to a single element, are shown to be non-context-free. As a consequence of our discussions, we also prove that the submonoid generated by the generators of the free nil-[Formula: see text] group (also called free nilpotent group of class [Formula: see text]) on [Formula: see text] generators is isomorphic to the quotient of the free monoid [Formula: see text] by the [Formula: see text]-binomial equivalence.

scholarly journals Lattice points in a random parallelogram

1990 ◽  
Vol 22 (2) ◽  
pp. 484-485 ◽  
Author(s):  
Philip Holgate
Keyword(s):  
Fourier Series ◽  
Lattice Points ◽  
Square Lattice ◽  
Fixed Angle

A Fourier series is obtained for the variance of the number of points lying in a parallelogram thrown randomly on to a square lattice at a fixed angle.

Transfer of Social Attributions in Stimulus Equivalence Classes by Preschool Children

1997 ◽  
Vol 80 (1) ◽  
pp. 3-21 ◽  
Author(s):  
Mark Egli ◽  
Beth Joseph ◽  
Travis Thompson
Keyword(s):  
Preschool Children ◽  
Antisocial Behavior ◽  
Equivalence Class ◽  
Stimulus Equivalence ◽  
Computer Game ◽  
Equivalence Classes ◽  
Antisocial Behaviors ◽  
Conditional Discriminations ◽  
Response Options ◽  
Social Attributions

The transfer of social attributions within stimulus-equivalence classes comprised of photographs of children was examined. Five children (mean age: 4 yr., 2 mo.) were taught conditional discriminations sufficient for the emergence of two 3-member equivalence classes (A1-B1-C1 and A2-B2-C2). Social attributions were established by using two photographs to identify fictional children who could facilitate (B1) or prevent (B2) the participant's reinforcement on a computer game. Transfer of attribution was assessed by asking the participants questions regarding predicted social behaviors by children in all six photographs. One set of questions pertained explicitly to the response-options of the computer game; a second set referred to other prosocial and antisocial behaviors. Three children chose photographs in response to questions consistent with their experience with members B1 and B2 of the shared equivalence class when the questions pertained to the computer game. One subject also selected photographs in response to questions about predicted prosocial and antisocial behavior which reflected her experience with the B1 and B2 photographs.

Environmental effects on acidic lipids of thylakoid membranes

2000 ◽  
Vol 28 (6) ◽  
pp. 912-914 ◽  
Author(s):  
N. Sato ◽  
M. Hagio ◽  
H. Wada ◽  
M. Tsuzuki
Keyword(s):  
Cell Growth ◽  
Environmental Effects ◽  
Thylakoid Membranes ◽  
The Other ◽  
Chloroplast Membranes ◽  
Temperature Stresses ◽  
Acidic Lipid ◽  
Phosphorus Source ◽  
Source Limitation ◽  
Acidic Lipids

The contents of the chloroplast acidic lipids, SQDG (sulphoquinovosyldiacylglycerol) and PG (phosphatidylglycerol), were reduced in the cells of Chlamydomonas reinhartdtii with exposure to sulphur- or phosphorus-source limitation, respectively. The decrease in the content of one acidic lipid was accompanied by an increase in the content of the other acidic lipid, which resulted in the maintenance of a certain level of total acidic lipids of chloroplast membranes. On the other hand, the content of each acidic lipid was little affected by temperature stresses during cell growth.

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