scholarly journals Strong Euler well-composedness

2021 ◽  
Author(s):  
Nicolas Boutry ◽  
Rocio Gonzalez-Diaz ◽  
Maria-Jose Jimenez ◽  
Eduardo Paluzo-Hildago
Keyword(s):  
Euler Characteristic ◽  
General Setting ◽  
Cell Complex ◽  
Cubical Complexes ◽  
Cell Complexes ◽  
Boundary Cell ◽  
Dimensional Ball ◽  
Regular Cell Complex

AbstractIn this paper, we define a new flavour of well-composedness, called strong Euler well-composedness. In the general setting of regular cell complexes, a regular cell complex of dimension n is strongly Euler well-composed if the Euler characteristic of the link of each boundary cell is 1, which is the Euler characteristic of an $$(n-1)$$ ( n - 1 ) -dimensional ball. Working in the particular setting of cubical complexes canonically associated with $$n$$ n D pictures, we formally prove in this paper that strong Euler well-composedness implies digital well-composedness in any dimension $$n\ge 2$$ n ≥ 2 and that the converse is not true when $$n\ge 4$$ n ≥ 4 .

scholarly journals Identification of a 107-kD glycoprotein that mediates adhesion between stromal cells and hematolymphoid cells.

1991 ◽  
Vol 173 (2) ◽  
pp. 373-381 ◽  
Author(s):  
T Kina ◽  
A S Majumdar ◽  
S Heimfeld ◽  
H Kaneshima ◽  
B Holzmann ◽  
...  
Keyword(s):  
Bone Marrow ◽  
Complex Formation ◽  
Stromal Cells ◽  
Stromal Cell ◽  
Cell Clone ◽  
Cell Interaction ◽  
Cell Complex ◽  
Cell Complexes ◽  
Initial Stage ◽  
Sds Page

The mechanism of cell complex formation between lymphocytes and stromal cells was investigated. We found that lymphoid lines of both T and B lineages could form cell complexes with stromal cells from the thymus as well as bone marrow but not with macrophages or typical fibroblast lines. Formation of these cell complexes is temperature dependent and requires the presence of Mg2+, active cellular metabolism, and microfilament assembly of cytoskeleton. We raised an antiserum against a thymic stromal cell clone (BATE-2) in rats and found that, after absorption, this serum could effectively block cell complex formation between lymphocytes and stromal cells from both thymus and bone marrow. An efficient blocking was obtained only when the antiserum was added at the initial stage of cell interaction. From the blocking experiments and the SDS-PAGE analysis of immunoprecipitated materials from the stromal cell surface, we identified a unique 107-kD glycoprotein on the stromal cells as a molecule for mediating stromal cell-lymphocyte interaction. This is further supported by the findings that an antiserum raised in hamsters against the excised gel band corresponding to 107 kD, which specifically immunoprecipitated the 107-kD molecule, effectively blocked the lymphocyte-stromal cell interaction. The possible function of this molecule in hematolymphoid development is discussed.

THE VISIBILITY COMPLEX

1996 ◽  
Vol 06 (03) ◽  
pp. 279-308 ◽  
Author(s):  
MICHEL POCCHIOLA ◽  
GERT VEGTER
Keyword(s):  
Pairwise Disjoint ◽  
Free Space ◽  
Cell Complex ◽  
Combinatorial Complexity ◽  
Working Space ◽  
Visibility Complex ◽  
Disjoint Convex ◽  
Regular Cell Complex

We introduce the visibility complex (a 2-dimensional regular cell complex) of a collection of n pairwise disjoint convex obstacles in the plane. It can be considered as a subdivision of the set of free rays (i.e., rays whose origins lie in free space, the complement of the obstacles). Its cells correspond to collections of rays with the same backward and forward views. The combinatorial complexity of the visibility complex is proportional to the number k of free bitangents of the collection of obstacles. We give an O(n log n+k) time and O(k) working space algorithm for its construction. Furthermore we show how the visibility complex can be used to compute the visibility polygon from a point in O(m log n) time, where m is the size of the visibility polygon. Our method is based on the notions of pseudotriangle and pseudo-triangulation, introduced in this paper.

scholarly journals Min-Max Theory for Cell Complexes

2020 ◽  
Vol 27 (03) ◽  
pp. 447-454
Author(s):  
Lacey Johnson ◽  
Kevin Knudson
Keyword(s):  
Morse Function ◽  
Critical Values ◽  
Discrete Version ◽  
Mountain Pass Lemma ◽  
Smooth Functions ◽  
Alternate Proof ◽  
Cell Complexes ◽  
Lusternik Schnirelmann ◽  
Regular Cell Complex ◽  
Discrete Morse Function

In the study of smooth functions on manifolds, min-max theory provides a mechanism for identifying critical values of a function. We introduce a discretized version of this theory associated to a discrete Morse function on a (regular) cell complex. As applications we prove a discrete version of the mountain pass lemma and give an alternate proof of a discrete Lusternik–Schnirelmann theorem.

Covering diagrams over surface-knot diagrams

2018 ◽  
Vol 27 (06) ◽  
pp. 1850042
Author(s):  
Tsukasa Yashiro
Keyword(s):  
Lower Bound ◽  
Triple Point ◽  
Orthogonal Projection ◽  
Cell Complex ◽  
Rectangular Cell ◽  
Oriented Surface ◽  
Cell Complexes ◽  
Projected Image ◽  
Knot Diagrams ◽  
Closed Oriented Surface

A surface-knot is a closed oriented surface smoothly embedded in 4-space and a surface-knot diagram is a projected image of a surface-knot under the orthogonal projection in 3-space with crossing information. Every surface-knot diagram induces a rectangular-cell complex. In this paper, we introduce a covering diagram over a surface-knot diagram. the covering map induces a covering of the rectangular-cell complexes. As an application, a lower bound of triple point numbers for a family of surface-knots is obtained.

A Note about the Definition of CW-Complexes

1971 ◽  
Vol 14 (4) ◽  
pp. 559-559
Author(s):  
Marcel Déruaz ◽  
Mary O'Keefe
Keyword(s):  
Weak Topology ◽  
Cell Complex ◽  
Cell Complexes ◽  
The Family ◽  
Cw Complexes ◽  
Definition Of ◽  
Finite Cell

In [1] Whitehead defined a CW-complex as a closure finite cell complex with the weak topology (i.e. a topology coherent with the family of closed cells, in Spanier's terminology). The purpose of this note is to show that these two conditions imposed on cell complexes can be replaced by a single one.

scholarly journals Coxeter-like complexes

2004 ◽  
Vol Vol. 6 no. 2 ◽  
Author(s):  
Eric Babson ◽  
Victor Reiner
Keyword(s):  
Symmetric Group ◽  
Type A ◽  
Cell Complex ◽  
Coxeter System ◽  
Coxeter Complex ◽  
Homology Groups ◽  
Finite Set ◽  
International Audience ◽  
Regular Cell Complex ◽  
Chessboard Complexes

International audience Motivated by the Coxeter complex associated to a Coxeter system (W,S), we introduce a simplicial regular cell complex Δ (G,S) with a G-action associated to any pair (G,S) where G is a group and S is a finite set of generators for G which is minimal with respect to inclusion. We examine the topology of Δ (G,S), and in particular the representations of G on its homology groups. We look closely at the case of the symmetric group S_n minimally generated by (not necessarily adjacent) transpositions, and their type-selected subcomplexes. These include not only the Coxeter complexes of type A, but also the well-studied chessboard complexes.

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