NET BUNDLES OVER POSETS AND K-THEORY

We continue studying net bundles over partially ordered sets (posets), defined as the analogues of ordinary fiber bundles. To this end, we analyze the connection between homotopy, net homology and net cohomology of a poset, giving versions of classical Hurewicz theorems. Focusing our attention on Hilbert net bundles, we define the K-theory of a poset and introduce functions over the homotopy groupoid satisfying the same formal properties as Chern classes. As when the given poset is a base for the topology of a space, our results apply to the category of locally constant bundles.

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Finding Minimal Infrequent Elements in Multi-Dimensional Data Defined over Partially Ordered Sets and its Applications

Rare Association Rule Mining and Knowledge Discovery ◽

10.4018/978-1-60566-754-6.ch007 ◽

2010 ◽

pp. 98-116

Author(s):

Khaled M. Elbassioni

Keyword(s):

Association Rules ◽

Partially Ordered Set ◽

Quantitative Data ◽

Partially Ordered Sets ◽

Threshold Value ◽

Ordered Sets ◽

Time Intervals ◽

Partially Ordered ◽

The Given ◽

Over Time

The authors consider databases in which each attribute takes values from a partially ordered set (poset). This allows one to model a number of interesting scenarios arising in different applications, including quantitative databases, taxonomies, and databases in which each attribute is an interval representing the duration of a certain event occurring over time. A natural problem that arises in such circumstances is the following: given a database D and a threshold value t, find all collections of “generalizations” of attributes which are “supported” by less than t transactions from D. They call such collections infrequent elements. Due to monotonicity, they can reduce the output size by considering only minimal infrequent elements. We study the complexity of finding all minimal infrequent elements for some interesting classes of posets. The authors show how this problem can be applied to mining association rules in different types of databases, and to finding “sparse regions” or “holes” in quantitative data or in databases recording the time intervals during which a re-occurring event appears over time. Their main focus will be on these applications rather than on the correctness or analysis of the given algorithms.

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To the spectral theory of partially ordered sets

Sibirskii matematicheskii zhurnal ◽

10.33048/smzh.2019.60.308 ◽

2018 ◽

Vol 60 (3) ◽

pp. 578-598

Author(s):

Yu. L. Ershov ◽

M. V. Schwidefsky

Keyword(s):

Spectral Theory ◽

Partially Ordered Sets ◽

Ordered Sets ◽

Partially Ordered

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Modelling Nondeterministic Concurrent Processes with Event Structures

Fundamenta Informaticae ◽

10.3233/fi-1991-14103 ◽

1991 ◽

Vol 14 (1) ◽

pp. 39-73

Author(s):

Rita Loogen ◽

Ursula Goltz

Keyword(s):

Dynamic Behaviour ◽

Partially Ordered Sets ◽

Parallel Composition ◽

Ordered Sets ◽

Communicating Sequential Processes ◽

Partially Ordered ◽

Event Structures ◽

Transition Relation ◽

Concurrent Processes ◽

Sequential Processes

We present a non-interleaving model for non deterministic concurrent processes that is based on labelled event structures. We define operators on labelled event structures like parallel composition, nondeterministic combination, choice, prefixing and hiding. These operators correspond to the operations of the “Theory of Communicating Sequential Processes” (TCSP). Infinite processes are defined using the metric approach. The dynamic behaviour of event structures is defined by a transition relation which describes the execution of partially ordered sets of actions, abstracting from internal events.

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Estimating the area under a receiver operating characteristic curve using partially ordered sets

The International Journal of Biostatistics ◽

10.1515/ijb-2019-0127 ◽

2020 ◽

Vol 0 (0) ◽

Author(s):

Ehsan Zamanzade ◽

Xinlei Wang

Keyword(s):

Roc Curve ◽

Characteristic Curve ◽

Partially Ordered Sets ◽

Sampling Technique ◽

Real Data ◽

Cost Effective ◽

Ordered Sets ◽

Operating Characteristics ◽

Partially Ordered ◽

Receiver Operating

AbstractRanked set sampling (RSS), known as a cost-effective sampling technique, requires that the ranker gives a complete ranking of the units in each set. Frey (2012) proposed a modification of RSS based on partially ordered sets, referred to as RSS-t in this paper, to allow the ranker to declare ties as much as he/she wishes. We consider the problem of estimating the area under a receiver operating characteristics (ROC) curve using RSS-t samples. The area under the ROC curve (AUC) is commonly used as a measure for the effectiveness of diagnostic markers. We develop six nonparametric estimators of the AUC with/without utilizing tie information based on different approaches. We then compare the estimators using a Monte Carlo simulation and an empirical study with real data from the National Health and Nutrition Examination Survey. The results show that utilizing tie information increases the efficiency of estimating the AUC. Suggestions about when to choose which estimator are also made available to practitioners.

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