scholarly journals On the Set Version of Selectively Star-CCC Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Ljubiša D. R. Kočinac ◽  
Sumit Singh
Keyword(s):  
Nonempty Subset ◽  
Topological Properties ◽  
Open Problems ◽  
The Relationship

A space X is said to be set selectively star-ccc if for each nonempty subset B of X , for each collection U of open sets in X such that B ¯ ⊂ ∪ U , and for each sequence A n : n ∈ ℕ of maximal cellular open families in X , there is a sequence A n : n ∈ ℕ such that, for each n ∈ ℕ , A n ∈ A n and B ⊂ St ∪ n ∈ ℕ A n , U . In this paper, we introduce set selectively star-ccc spaces and investigate the relationship between set selectively star-ccc and other related spaces. We also study the topological properties of set selectively star-ccc spaces. Some open problems are posed.

scholarly journals Remarks on neighborhood star-Lindelöf spaces II

Filomat ◽  
2013 ◽  
Vol 27 (5) ◽  
pp. 875-880
Author(s):  
Yan-Kui Song
Keyword(s):  
Open Cover ◽  
Countable Subset ◽  
Topological Properties ◽  
Pseudocompact Spaces ◽  
The Relationship

A space X is said to be neighborhood star-Lindel?f if for every open cover U of X there exists a countable subset A of X such that for every open O?A, X=St(O,U). In this paper, we continue to investigate the relationship between neighborhood star-Lindel?f spaces and related spaces, and study topological properties of neighborhood star-Lindel?f spaces in the classes of normal and pseudocompact spaces. .

scholarly journals Winding number selection on merons by Gaussian curvature’s sign

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Ricardo Gabriel Elías ◽  
Nicolás Vidal-Silva ◽  
Vagson L. Carvalho-Santos
Keyword(s):  
Gaussian Curvature ◽  
Domain Walls ◽  
Curved Surfaces ◽  
Two Dimensional ◽  
Winding Number ◽  
Direct Relation ◽  
Topological Properties ◽  
The Core ◽  
Magnetic Surfaces ◽  
The Relationship

Abstract We study the relationship between the winding number of magnetic merons and the Gaussian curvature of two-dimensional magnetic surfaces. We show that positive (negative) Gaussian curvatures privilege merons with positive (negative) winding number. As in the case of unidimensional domain walls, we found that chirality is connected to the polarity of the core. Both effects allow to predict the topological properties of metastable states knowing the geometry of the surface. These features are related with the recently predicted Dzyaloshinskii-Moriya emergent term of curved surfaces. The presented results are at our knowledge the first ones drawing attention about a direct relation between geometric properties of the surfaces and the topology of the hosted solitons.

Fixed Point Theorems for Maps With Local and Pointwise Contraction Properties

2018 ◽  
Vol 70 (3) ◽  
pp. 538-594 ◽  
Author(s):  
Krzysztof Chris Ciesielski ◽  
Jakub Jasinski
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Topological Properties ◽  
Open Problems ◽  
Local Contraction ◽  
Path Connectedness ◽  
Perfect Subset ◽  
Minimal Dynamical System ◽  
Comprehensive Study

AbstractThis paper constitutes a comprehensive study of ten classes of self-maps on metric spaces ⟨X, d⟩ with the pointwise (i.e., local radial) and local contraction properties. Each of these classes appeared previously in the literature in the context of fixed point theorems.We begin with an overview of these fixed point results, including concise self contained sketches of their proofs. Then we proceed with a discussion of the relations among the ten classes of self-maps with domains ⟨X, d⟩ having various topological properties that often appear in the theory of fixed point theorems: completeness, compactness, (path) connectedness, rectifiable-path connectedness, and d-convexity. The bulk of the results presented in this part consists of examples of maps that show non-reversibility of the previously established inclusions between these classes. Among these examples, the most striking is a differentiable auto-homeomorphism f of a compact perfect subset X of ℝ with f′ ≡ 0, which constitutes also a minimal dynamical system. We finish by discussing a few remaining open problems on whether the maps with specific pointwise contraction properties must have the fixed points.

scholarly journals Universal arrows to forgetful functors from categories of topological algebra

1993 ◽  
Vol 48 (2) ◽  
pp. 209-249 ◽  
Author(s):  
Vladimir G. Pestov
Keyword(s):  
Functional Analysis ◽  
Lie Algebras ◽  
Topological Algebra ◽  
Locally Convex Spaces ◽  
Topological Groups ◽  
Open Problems ◽  
Relationship Of ◽  
The Relationship ◽  
Locally Convex ◽  
Convex Spaces

We survey the present trends in theory of universal arrows to forgetful functors from various categories of topological algebra and functional analysis to categories of topology and topological algebra. Among them are free topological groups, free locally convex spaces, free Banach-Lie algebras, and more. An accent is put on the relationship of those constructions with other areas of mathematics and their possible applications. A number of open problems is discussed; some of them belong to universal arrow theory, and other may become amenable to the methods of this theory.

scholarly journals Application of Algorithmic Manifold to Exponential Time

2017 ◽  
Author(s):  
Takuya Yabu
Keyword(s):  
Turing Machine ◽  
Turing Machines ◽  
Topological Properties ◽  
Exponential Time ◽  
Polynomial Time Algorithms ◽  
Exponential Time Algorithms ◽  
Deterministic Turing Machine ◽  
The Relationship ◽  
Np Problem ◽  
Machine Problem

In the previous paper, I defined algorithmic manifolds simulating polynomial-time algorithms, and I showed topological properties for P problem and NP problem and that NP problem can be transformed into deterministic Turing machine problem.　In this paper, I define algorithmic manifolds simulating exponential-time algorithms and, I show topological properties for EXPTIME problem and NEXPTIME problem. I also discuss the relationship between NEXPTIME and deterministic Turing machines.

scholarly journals On star-K-Hurewicz spaces

Filomat ◽  
2017 ◽  
Vol 31 (5) ◽  
pp. 1279-1285 ◽  
Author(s):  
Yan-Kui Song
Keyword(s):  
Topological Properties ◽  
The Relationship ◽  
Compact Subsets

A space X is star-K-Hurewicz if for each sequence (Un : n ? N) of open covers of X there exists a sequence (Kn : n ? N) of compact subsets of X such that for each x ? X, x ? St(Kn,Un) for all but finitely many n. In this paper, we investigate the relationship between star-K-Hurewicz spaces and related spaces by giving some examples, and also study topological properties of star-K-Hurewicz spaces.

scholarly journals Understanding the Relationship between Interactions and Outcomes in Human-in-the-Loop Machine Learning

2021 ◽  
Author(s):  
Yuchen Cui ◽  
Pallavi Koppol ◽  
Henny Admoni ◽  
Scott Niekum ◽  
Reid Simmons ◽  
...  
Keyword(s):  
Machine Learning ◽  
Human Performance ◽  
Autonomous Agents ◽  
Training Data ◽  
Open Problems ◽  
Human In The Loop ◽  
Efficiency And Effectiveness ◽  
Interaction Types ◽  
The Relationship ◽  
And Training

Human-in-the-loop Machine Learning (HIL-ML) is a widely adopted paradigm for instilling human knowledge in autonomous agents. Many design choices influence the efficiency and effectiveness of such interactive learning processes, particularly the interaction type through which the human teacher may provide feedback. While different interaction types (demonstrations, preferences, etc.) have been proposed and evaluated in the HIL-ML literature, there has been little discussion of how these compare or how they should be selected to best address a particular learning problem. In this survey, we propose an organizing principle for HIL-ML that provides a way to analyze the effects of interaction types on human performance and training data. We also identify open problems in understanding the effects of interaction types.

On the relationship between histogram indexing and block-mass indexing

2014 ◽  
Vol 372 (2016) ◽  
pp. 20130132 ◽  
Author(s):  
Amihood Amir ◽  
Ayelet Butman ◽  
Ely Porat
Keyword(s):  
Pattern Matching ◽  
Linear Time ◽  
Matching Problem ◽  
Open Problems ◽  
Time Solution ◽  
Text Length ◽  
Active Research ◽  
Histogram Indexing ◽  
The Relationship ◽  
Mass Pattern

Histogram indexing , also known as jumbled pattern indexing and permutation indexing is one of the important current open problems in pattern matching. It was introduced about 6 years ago and has seen active research since. Yet, to date there is no algorithm that can preprocess a text T in time o (| T | 2 /polylog| T |) and achieve histogram indexing, even over a binary alphabet, in time independent of the text length. The pattern matching version of this problem has a simple linear-time solution. Block-mass pattern matching problem is a recently introduced problem, motivated by issues in mass-spectrometry. It is also an example of a pattern matching problem that has an efficient, almost linear-time solution but whose indexing version is daunting. However, for fixed finite alphabets, there has been progress made. In this paper, a strong connection between the histogram indexing problem and the block-mass pattern indexing problem is shown. The reduction we show between the two problems is amazingly simple. Its value lies in recognizing the connection between these two apparently disparate problems, rather than the complexity of the reduction. In addition, we show that for both these problems, even over unbounded alphabets, there are algorithms that preprocess a text T in time o (| T | 2 /polylog| T |) and enable answering indexing queries in time polynomial in the query length. The contributions of this paper are twofold: (i) we introduce the idea of allowing a trade-off between the preprocessing time and query time of various indexing problems that have been stumbling blocks in the literature. (ii) We take the first step in introducing a class of indexing problems that, we believe, cannot be pre-processed in time o (| T | 2 /polylog| T |) and enable linear-time query processing.

Thermodynamic, energetic, and topological properties of crystal packing of pyrazolo[1,5-a]pyrimidines governed by weak electrostatic intermolecular interactions

CrystEngComm ◽  
2015 ◽  
Vol 17 (23) ◽  
pp. 4325-4333 ◽  
Author(s):  
Clarissa P. Frizzo ◽  
Aniele Z. Tier ◽  
Izabelle M. Gindri ◽  
Alexandre R. Meyer ◽  
Gabrielle Black ◽  
...  
Keyword(s):  
Intermolecular Interactions ◽  
Thermodynamic Data ◽  
Crystal Packing ◽  
Topological Properties ◽  
The Relationship

The relationship between energetic and topological properties of crystals with weak electrostatic intermolecular interactions and thermodynamic data are presented.

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