scholarly journals On Multiset Minimal Structure Topological Space

2022 ◽  
Author(s):  
Binod Chandra TRİPATHY ◽  
Rakhal DAS ◽  
Suman DAS
Keyword(s):  
Topological Space ◽  
Minimal Structure

The Spatial Dimensions of Social Networks

2020 ◽  
pp. 367-383
Author(s):  
Zachary P. Neal
Keyword(s):  
Social Networks ◽  
Topological Space ◽  
Network Science ◽  
Spatial Dimensions

The first law of geography holds that everything is related to everything else, but near things are more related than distant things, where distance refers to topographical space. If a first law of network science exists, it would similarly hold that everything is related to everything else, but near things are more related than distant things, but where distance refers to topological space. Frequently these two laws collide, together holding that everything is related to everything else, but topographically and topologically near things are more related than topographically and topologically distant things. The focus of the spatial study of social networks lies in exploring a series of questions embedded in this combined law of geography and networks. This chapter explores the questions that have been asked and the answers that have been offered at the intersection of geography and networks.

On a topological construction of Juhasz and Shelah

1992 ◽  
Vol 57 (1) ◽  
pp. 166-171
Author(s):  
Dan Velleman
Keyword(s):  
Topological Space ◽  
Additional Structure ◽  
Homogeneous Set ◽  
Stationary Set ◽  
Topological Construction

In [2], Juhasz and Shelah use a forcing argument to show that it is consistent with GCH that there is a 0-dimensional T2 topological space X of cardinality ℵ3 such that every partition of the triples of X into countably many pieces has a nondiscrete (in the topology) homogeneous set. In this paper we will show how to construct such a space using a simplified (ω2, 1)-morass with certain additional structure added to it. The additional structure will be a slight strengthening of a built-in ◊ sequence, analogous to the strengthening of ordinary ◊k to ◊S for a stationary set S ⊆ k.Suppose 〈〈θα∣ ∝ ≤ ω2〉, 〈∝β∣α < β ≤ ω2〉〉 is a neat simplified (ω2, 1)-morass (see [3]). Let ℒ be a language with countably many symbols of all types, and suppose that for each α < ω2, α is an ℒ-structure with universe θα. The sequence 〈α∣α < ω2 is called a built-in ◊ sequence for the morass if for every ℒ-structure with universe ω3 there is some α < ω2 and some f ∈αω2 such that f(α) ≺ , where f(α) is the ℒ-structure isomorphic to α under the isomorphism f. We can strengthen this slightly by assuming that α is only defined for α ∈ S, for some stationary set S ⊆ ω2. We will then say that is a built-in ◊ sequence on levels in S if for every ℒ-structure with universe ω3 there is some α ∈ S and some f ∈ αω2 such that f(α) ≺ .

scholarly journals Antisymmetry of the Stochastical Order on all Ordered Topological Spaces

2019 ◽  
Vol 7 (1) ◽  
pp. 250-252 ◽  
Author(s):  
Tobias Fritz
Keyword(s):  
Topological Space ◽  
General Result ◽  
Elementary Proof ◽  
Short Note ◽  
Stochastic Order ◽  
Topological Spaces ◽  
Probability Measures ◽  
Ordered Topological Space ◽  
Special Cases

Abstract In this short note, we prove that the stochastic order of Radon probability measures on any ordered topological space is antisymmetric. This has been known before in various special cases. We give a simple and elementary proof of the general result.

scholarly journals Exploring the “minimal” structure of a functional ADAMTS13 by mutagenesis and small-angle X-ray scattering

Blood ◽  
2019 ◽  
Vol 133 (17) ◽  
pp. 1909-1918 ◽  
Author(s):  
Jian Zhu ◽  
Joshua Muia ◽  
Garima Gupta ◽  
Lisa A. Westfield ◽  
Karen Vanhoorelbeke ◽  
...  
Keyword(s):  
Small Angle ◽  
Columba Livia ◽  
Allosteric Activation ◽  
Complement Components ◽  
X Ray ◽  
X Ray Scattering ◽  
Morphogenetic Protein ◽  
Minimal Structure ◽  
Von Willebrand ◽  
Ray Scattering

Abstract Human ADAMTS13 is a multidomain protein with metalloprotease (M), disintegrin-like (D), thrombospondin-1 (T), Cys-rich (C), and spacer (S) domains, followed by 7 additional T domains and 2 CUB (complement components C1r and C1s, sea urchin protein Uegf, and bone morphogenetic protein-1) domains. ADAMTS13 inhibits the growth of von Willebrand factor (VWF)–platelet aggregates by cleaving the cryptic Tyr1605-Met1606 bond in the VWF A2 domain. ADAMTS13 is regulated by substrate-induced allosteric activation; without shear stress, the distal T8-CUB domains markedly inhibit VWF cleavage, and binding of VWF domain D4 or selected monoclonal antibodies (MAbs) to distal ADAMTS13 domains relieves this autoinhibition. By small angle X-ray scattering (SAXS), ADAMTS13 adopts a hairpin-like conformation with distal T7-CUB domains close to the proximal MDTCS domains and a hinge point between T4 and T5. The hairpin projects like a handle away from the core MDTCS and T7-CUB complex and contains distal T domains that are dispensable for allosteric regulation. Truncated constructs that lack the T8-CUB domains are not autoinhibited and cannot be activated by VWF D4 but retain the hairpin fold. Allosteric activation by VWF D4 requires T7, T8, and the 58–amino acid residue linker between T8 and CUB1. Deletion of T3 to T6 produced the smallest construct (delT3-6) examined that could be activated by MAbs and VWF D4. Columba livia (pigeon) ADAMTS13 (pADAMTS13) resembles human delT3-6, retains normal activation by VWF D4, and has a SAXS envelope consistent with amputation of the hairpin containing the dispensable T domains of human ADAMTS13. Our findings suggest that human delT3-6 and pADAMTS13 approach a “minimal” structure for allosterically regulated ADAMTS13.

Sign in / Sign up

Export Citation Format

Share Document