Neighborhood Assignment Research Articles

Generic classes defined by neighborhoods assignments and stars

In this article we have a couple of mains. The first one is to make a generic exposure on the classes that are obtained by using neighborhood assignments or applying the star operator to a given topological property P. The second one is to perform an analysis on the classes defined in the first part of the work, for the numerability property.It is important to note that in Example 3.13 we present a Hausdorff weakly star countable space which is not feebly Lindelof, which gives a negative response to the Question 3.14 from [1].

The class C(ω1) and countable net weight

Hart and Kunen in [5] and, independently, Ríos-Herrejón in [14] defined and studied the class C(ω1) of topological spaces X having the property that for every neighborhood assignment {U(y):y∈Y} with Y∈[X]ω1 there is Z∈[Y]ω1 such thatZ⊂⋂{U(z):z∈Z}. It is obvious that spaces of countable net weight, i.e. having a countable network, belong to this class. In this paper we present several independence results concerning the relationships of these two and several other natural classes that are sandwiched between them, thus clarifying some of the main problems that were raised in [14].In particular, we prove that the continuum hypothesis, in fact a weaker combinatorial principle called super stick, implies that every regular space in C(ω1) has countable net weight, answering a question that was raised by Hart and Kunen in both [5] and [6].

On monotonically normal and transitively (linearly) dually discrete spaces

In this article, we show that if X is a monotonically normal space, then for any neighborhood assignment ϕ for X there exists a discrete subspace D of X such that X=(⋃{ϕ(d):d∈D})∪D‾ and D‾∖(⋃{ϕ(d):d∈D}) is left-separated. A space X is called weakly dually discrete if for any neighborhood assignment ϕ for X there exists a discrete subspace D of X such that X=(⋃{ϕ(d):d∈D})∪D‾ and D‾∖(⋃{ϕ(d):d∈D}) is a closed discrete subspace of X. We discuss some basic properties of weakly dually discrete spaces.In the last part of this article, we introduce the notions of linear dual discreteness and transitive dual discreteness. Some of their properties are discussed. We finally show that if a space X is discretely complete and X=⋃{Xn:n∈N} such that Xn is monotonically normal for each n∈N, then X is compact. If X is a monotonically normal space and Y is a compact T1-space, then X×Y is dually 2-scattered. We also discuss some properties of spaces which are dually scattered with finite rank.

Cardinal invariants of dually CCC spaces

We say that a space X is dually CCC (respectively, weakly Lindelöf, separable) if for any neighbourhood assignment ϕ on X, there is a CCC (respectively, weakly Lindelöf, separable) subspace Y⊂X such that ϕ(Y)={ϕ(y):y∈Y} covers X. In this paper, we mainly show that(1) A dually CCC first countable Hausdorff space has cardinality at most 2c and a dually weakly Lindelöf first countable normal space has cardinality at most 2c.(2) Let Y=∏{Yi:i≤n}, where Yi is a scattered monotonically normal space for any i=0,1,...,n. If a subspace X⊂Y is dually CCC then e(X)≤ω and a normal subspace X⊂Y is DCCC if and only if e(X)≤ω.(3) Assume 2<c=c. A normal dually CCC space X with χ(X)≤c has extent at most c.(4) A dually separable Hausdorff space X with a Gδ⁎-diagonal has extent at most c and a dually separable regular space X with a Gδ-diagonal has cardinality at most c.(5) A dually CCC Hausdorff space with a Gδ-diagonal has cellularity at most c.

The Distributional Consequences of Public School Choice

School choice systems aspire to delink residential location and school assignments by allowing children to apply to schools outside of their neighborhood. However, choice programs also affect incentives to live in certain neighborhoods, and this feedback may undermine the goals of choice. We investigate this possibility by developing a model of public school and residential choice. School choice narrows the range between the highest and lowest quality schools compared to neighborhood assignment rules, and these changes in school quality are capitalized into equilibrium housing prices. This compressed distribution generates an ends-against-the-middle trade-off with school choice compared to neighborhood assignment. Paradoxically, even when choice results in improvement in the lowest-performing schools, the lowest type residents need not benefit. (JEL H75, I21, I28, R23, R31)

Robust Structured Graph Clustering.

Graph-based clustering methods have achieved remarkable performance by partitioning the data samples into disjoint groups with the similarity graph that characterizes the sample relations. Nevertheless, their learning scheme still suffers from two important problems: 1) the similarity graph directly constructed from the raw features may be unreliable as real-world data always involves adverse noises, outliers, and irrelevant information and 2) most graph-based clustering methods adopt two-step learning strategy that separates the similarity graph construction and clustering into two independent processes. Under such circumstance, the generated graph is unstructured and fixed. It may suffer from a low-quality clustering structure and thus lead to suboptimal clustering performance. To alleviate these limitations, in this article we propose a robust structured graph clustering (RSGC) model. We formulate a novel learning framework to simultaneously learn a robust structured similarity graph and perform clustering. Specifically, the structured graph with proper probabilistic neighborhood assignment is adaptively learned on a robust latent representation that resists the noises and outliers. Furthermore, an explicit rank constraint is imposed on the Laplacian matrix to structurize the graph such that the number of the connected components is exactly equal to the ground-truth cluster number. To solve the challenging objective formulation, we propose to first transform it into an equivalent one that can be tackled more easily. An iterative solution based on the augmented Lagrangian multiplier is then derived to solve the model. In RSGC, the discrete cluster labels can be directly obtained by partitioning the learned similarity graph without reliance on label discretization strategy as most graph-based clustering methods. Experiments on both synthetic and real data sets demonstrate the superiority of the proposed method compared with the state-of-the-art clustering techniques.

Connected and/or topological group pd-examples

The pinning down number pd(X) of a topological space X is the smallest cardinal κ such that for every neighborhood assignment U on X there is a set of size κ that meets every member of U. Clearly, pd(X)≤d(X) and we call X a pd-example if pd(X)<d(X). We denote by S the class of all singular cardinals that are not strong limit. It was proved in [6] that TFAE:(1)S≠∅;(2)there is a 0-dimensional T2 pd-example;(3)there is a T2 pd-example.The aim of this paper is to produce pd-examples with further interesting topological properties like connectivity or being a topological group by presenting several constructions that transform given pd-examples into ones with these additional properties.We show that S≠∅ is also equivalent to the existence of a connected and locally connected T3 pd-example, as well as to the existence of an abelian T2 topological group pd-example.However, S≠∅ in itself is not sufficient to imply the existence of a connected T3.5 pd-example. But if there is μ∈S with μ≥c then there is an abelian T2 topological group (hence T3.5) pd-example which is also arcwise connected and locally arcwise connected. Finally, the same assumption S∖c≠∅ even implies that there is a locally convex topological vector space pd-example.

Weakly dually Lindelöf spaces

Given a topological property (or a class) P, the class $$P'$$ consists of spaces X such that for any neighbourhood assignment $$\phi $$ on X, there exists a subspace $$Y \subset X$$ with property P for which $$\phi (Y)=\bigcup \{\phi (y): y\in Y\}$$ is dense in X. The class $$P'$$ are called the weak dual ofP or weakly duallyP (with respect to neighbourhood assignments). In this paper, we make several observations on weakly dually Lindelof spaces. We prove that a Baire weakly dually Lindelof o-semimetrizable space is separable. There exists a large first countable Hausdorff space X having a countable subset A such that $$\phi (A)$$ is dense in X for any neighborhood assignment $$\phi $$ of X, which answers two questions asked by Alas et al. (Topol Proc 30:25–38, 2006). We also prove that a weakly dually Lindelof first countable normal space has cardinality at most $$2^{\mathfrak {c}}$$. Every Baire, weakly dually Lindelof space X with a symmetry g-function g such that $$\bigcap \{g^2(n,x): n\in \omega \}=\{x\}$$ for each $$x\in X$$ has cardinality at most $$\mathfrak {c}$$. Finally, we prove that every separated subset of a weakly dually Lindelof normal space with a $$G_\delta $$-diagonal has cardinality at most $$\mathfrak {c}$$. Some new questions are also posed.

On the Alster, Menger and D-type covering properties

In this paper we give new characterizations for almost Menger and weakly Menger spaces by neighborhood assignments and define a natural weakening of almost D-spaces and weakly D-spaces. We discuss the relationships among the properties “D-type”, “Menger”, “Alster”, and the weak versions of these properties in Lindelöf spaces.

A 0-dimensional, Lindelöf space that is not strongly D

A topological space X is strongly D if for any neighbourhood assignment {Ux:x∈X}, there is a D⊆X such that {Ux:x∈D} covers X and D is locally finite in the topology generated by {Ux:x∈X}. We prove that ⋄ implies that there is an HFCw space in 2ω1 (hence 0-dimensional, Hausdorff and hereditarily Lindelöf) which is not strongly D. We also show that any HFC space X is dually discrete and if additionally countable sets have Menger closure then X is a D-space.

Housing choices, sorting, and the distribution of educational benefits under deferred acceptance

AbstractI study the welfare and distributional consequences of introducing the student‐proposing deferred acceptance in a model where schools have exogenous qualities and the benefit from attending a school is supermodular in school quality and student type. Unlike neighborhood assignment, deferred acceptance induces nonpositive assortative matching where higher type students do not necessarily choose neighborhoods with better schools. Student types are more heterogeneous within neighborhoods under deferred acceptance. Assuming an elastic housing supply, deferred acceptance benefits residents in lower quality neighborhoods with more access to higher quality schools. Moreover, more parents will “vote with their feet” for deferred acceptance, other things equal, than for neighborhood assignment.

Weak duals and neighbourhood assignments

Given a topological property (or a class) P, the class P′ consists of spaces X such that for any neighbourhood assignment ϕ on X, there exists a subspace Y⊂X with property P for which ϕ(Y)=⋃{ϕ(y):y∈Y} is dense in X. The class P′ are called the weak dual of P or weakly dually P (with respect to neighbourhood assignments). We establish that DCCC is weakly self-dual in the class of weakly regular spaces. If P∈{weakly Lindelöf,CCC,separable}, then P is weakly self-dual in the class of Baire developable spaces. By using Erdös–Radó's theorem, we also prove that: (1) If X is a Baire, weakly dually CCC Hausdorff space with a rank 2-diagonal, then X has cardinality at most 2ω; (2) If X is a Baire, weakly dually DCCC Hausdorff space with a rank 3-diagonal, then X has cardinality at most 2ω; (3) If X is a weakly dually DCCC Hausdorff space with a rank 4-diagonal, then X has cardinality at most 2ω.

A study of chain conditions and dually properties

In this paper, we make some observations on chain conditions and dually properties. In particular, we show that:(1) A subspace X⊂ω1ω is dually CCC then e(X)≤ω and a normal subspace X⊂ω1ω is DCCC if and only if e(X)≤ω;(2) There is a Tychonoff pseudocompact subspace X⊂(ω1+1)2 which is not dually CCC;(3) In the class of o-semimetrizable spaces, dually separable is self-dual with respect to neighbourhood assignments. As an application, we obtain an example of a CCC normal Moore space which is not dually separable under MA+¬CH;(4) There exists an example of a large normal CCC semi-stratifiable space, which answers a question of Xuan and Song (2018) [21, Question 4.11];(5) Every dually separable and monotonically monolithic space is Lindelöf, which gives a partial answer to a question of Alas, Junqueira, van Mill, Tkachuk and Wilson (2011) [2, Question 2.1];(6) A dually separable Hausdorff space with a strong rank 1-diagonal has cardinality at most 2c. The conclusion is also true for regular spaces if we replace “strong rank 1-diagonal” with “Gδ-diagonal”;(7) A dually separable ω-monolithic Hausdorff space with a Gδ-diagonal has cardinality at most c.

Dually properties and cardinal inequalities

In this paper, we prove that DCCC is self-dual with respect to neighborhood assignments. Some related results on dually CCC (or dually DCCC) spaces are also obtained. Moreover, we prove that the cardinality of a dually CCC space X is at most 2ω if X satisfies one of the following conditions: (1) X has a rank 2-diagonal; (2) X is first countable and has a Gδ-diagonal; (3) X is first countable and perfect. Finally, we prove that the extent of a first countable dually CCC space is at most 2ω.

A new cardinal function on topological spaces

&lt;p&gt;Using neighbourhood assignments, we introduce and study a new cardinal function, namely GCI(X), for every topological space X. We shall mainly investigate the spaces X with finite GCI(X). Some properties of this cardinal in connection with special types of mappings are also proved.&lt;/p&gt;

A modified DIRECT algorithm for hidden constraints in an LNG process optimization

Optimization for process design in the chemical engineering industry has been important for energy efficiency and economic feasibility. Because many industries perform optimization with a commercial process simulator such as the Aspen HYSYS, an optimization methodology for expensive black-box functions is needed. Thus, the development of derivative free optimization algorithms has long been studied and the deterministic global search algorithm DIRECT (DIviding a hyper-RECTangle) was suggested. In this paper, a modified DIRECT algorithm with a sub-dividing step for considering hidden constraints is proposed. The effectiveness of the algorithm is exemplified by its application to a cryogenic mixed refrigerant process using a single mixed refrigerant for natural gas liquefaction and its comparison with a well-known stochastic algorithm (GA, PSO, SA), and model based search algorithm (SNOBFIT), local solver (GPS, GSS, MADS, active-set, interior-point, SQP), and other hidden constraint handling methods, including the barrier approach and the neighborhood assignment strategy. Optimal solution calculated by the proposed algorithms decreases the specific power required for natural gas liquefaction to 18.9% compared to the base case.

Some sufficiency conditions for D-spaces, dually discrete and its applications

In this note, we obtain some sufficiency conditions for D-spaces, dually discrete, and dually scattered of rank≤2. As an application, we show that if a space X has a chain (F) point network W={W(x):x∈X} such that W(x) is a chain and is a closure-preserving family of subsets of X for each x∈X then X is a paracompact D-space. If a space X has an ω1-sheltering chain (F) point network W={W(x):x∈X} such that W(x) is a chain and is a weak ω-closure-preserving family of subsets of X for each x∈X, then X is a paracompact D-space.If X is a chain neighborhood (F) space, then for each neighborhood assignment ϕ for X there is an open neighborhood Vx of x for each x∈X such that x∈Vx⊂ϕ(x) and for each closed discrete subspace F1 of X and for each closed subset A of X, there exists a closed discrete subspace D of X such that D⊂A∩{z∈X∖ϕ(F1):Vz∩F1≠∅} and A∩{z∈X∖ϕ(F1):Vz∩F1≠∅}⊂ϕ(D). By the above conclusion and a sufficiency condition for D-spaces in this note, we can get a known conclusion that every chain neighborhood (F) space is a D-space [8].

Pinning down versus density

The pinning down number pd(X) of a topological space X is the smallest cardinal κ such that for any neighborhood assignment U: X → τX there is a set A ∈ [X]κ with A ∩ U(x) ≠ O for all x ∈ X. Clearly, c(X) ≤ pd(X) ≤ d(X).

On Gradient Descriptor Distribution-based Dimensionality Reduction Analysis: A Case of Recognizing Plastic Surgery Sample Faces

Objectives: To analyze the influence of the sparseness distribution characteristics of gradient-based descriptor data on reduction of high-dimensional data, this paper presents experimental analysis on learned samples of gradient descriptor data. Method: In order to draw valid inferences, a single gradient descriptor, the Edge based Gabor Magnitude (EGM) facial descriptor, is used. The descriptor data is learned using various linear subspace dimensionality reduction methods. The subspace models are the Principle Component Analysis plus Linear Discriminant Analysis (PCA plus LDA), supervised Locality Preserving Projection (sLPP) and Locality Sensitive Discriminant Analysis (LSDA) under the LGE and OLGE general framework (which in the present is used to aid the characterization of the data geometric properties). Findings: Using the plastic surgery data set, the following observations were made. The global based linear subspace model (PCA plus LDA) which do not require complex neighborhood assignment performs favorably well in relation to the graph embedding models. This may be due to the fact that it only works on the basis of class information. The LSDA is observed to be more affected by the nature of the descriptor data influenced by the complexity of plastic surgery because in all its identification rates, a below 60% is achieved. On the other hand, the sLPP show to be a best fit model for the sparse nature of the descriptor data. This can be attributed to its data preserving property by which it is able to preserve the local structures of a sparse data (gradient-based) and so outperformed the PCA plus LDA and most importantly, the LSDA. Applications/Improvements: Understanding the best fit model for certain descriptor data is as important as optimizing recognition rates, an important observation for the face recognition research community.

Incremental Semi-Supervised Clustering Method Using Neighbourhood Assignment

Semi-supervised considering so as to cluster expects to enhance clustering execution client supervision as pair wise imperatives. In this paper, we contemplate the dynamic learning issue of selecting pair wise must-connect and can't interface imperatives for semi supervised clustering. We consider dynamic learning in an iterative way where in every emphasis questions are chosen in light of the current clustering arrangement and the current requirement set. We apply a general system that expands on the idea of Neighbourhood, where Neighbourhoods contain named samples of distinctive bunches as indicated by the pair wise imperatives. Our dynamic learning strategy extends the areas by selecting educational focuses and questioning their association with the areas. Under this system, we expand on the fantastic vulnerability based rule and present a novel methodology for figuring the instability related with every information point. We further present a determination foundation that exchanges off the measure of vulnerability of every information point with the expected number of inquiries (the expense) needed to determine this instability. This permits us to choose questions that have the most astounding data rate. We assess the proposed strategy on the benchmark information sets and the outcomes show predictable and significant upgrades over the current cutting edge.