• Journal of the Chungcheong Mathematical Society
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• v.34 no.3
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• pp.259-269
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• 2021

We shall study the following. Let 𝜙 be an expansive flow on a compact TVS-cone metric space (X, d). First, we give some equivalent ways of defining expansiveness. Second, we show that expansiveness is conjugate invariance. Finally, we prove that lim sup ${\frac{1}{t}}$ log v(t) ≤ h(𝜙), where v(t) denotes the number of closed orbits of 𝜙 with a period 𝜏 ∈ [0, t] and h(𝜙) denotes the topological entropy. Remark that in 1972, R. Bowen and P. Walters had proved this three statements for an expansive flow on a compact metric space [?].

• The Pure and Applied Mathematics
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• v.19 no.1
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• pp.73-86
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• 2012

This is a survey on the volume entropy and its rigidity of various metric spaces. This survey is aimed to summarize recent results as well as remaining open questions and possible directions on this subject.

• Journal of Computing Science and Engineering
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• v.4 no.3
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• pp.225-239
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• 2010

This paper introduces a new approach to modeling relative distance among nodes under a variety of communication rates, due to node's mobility in Mobile Ad-hoc Networks (MANETs). When mobile nodes move to another location, the relative distance of communicating nodes will directly affect the data rate of transmission. The larger the distance between two communicating nodes is, the lower the rate that they can use for transferring data will be. The connection certainty of a link also changes because a node may move closer to or farther away out of the communication range of other nodes. Therefore, the stability of a route is related to connection entropy. Taking into account these issues, this paper proposes a new routing metric for MANETs. The new metric considers both link weight and route stability based on connection entropy. The problem of determining the best route is subsequently formulated as the minimization of an object function formed as a linear combination of the link weight and the connection uncertainty of that link. The simulation results show that the proposed routing metric improves end-to-end throughput and reduces the percentage of link breakages and route reparations.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.3
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• pp.377-384
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• 2015

It is well known that the entropy map is upper semi-continuous for expansive homeomorphisms on a compact metric space. Recently, Morales [3] introduced the notion of measure expansiveness which is general than that of expansiveness. In this paper, we prove that the entropy map is upper semi-continuous for measure expansive homeomorphisms.

• Journal of The Korean Association of Information Education
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• v.2 no.2
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• pp.260-268
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• 1998

In this paper, I propose a metric model for measuring complexity of Web documentations which are wrote by HTML and XML. The complexity of Web documentation has effect on documentation understandability which is an important metric in maintenance and reusing of Web documentation. The understandable documents have more effect on WEI. The proposed metric uses the entropy to represent the degree of information flows between Web documentations. The proposed documentation complexity measures the information flows in a Web document based on the information passing relationship between Web document files. I evaluate the proposed metric by using the complexity properties proposed by Weyuker, and measure the document complexity. I show effectiveness of analyzing the correlation between the number of document file and document complexity.

• International Journal of Advanced Culture Technology
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• v.1 no.2
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• pp.1-6
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• 2013

In this paper, we evaluate performance of existing similarity measurement metric and propose a novel method using user's preferences information entropy to reduce MAE in memory-based collaborative recommender systems. The proposed method applies a similarity of individual inclination to traditional similarity measurement methods. We experiment on various similarity metrics under different conditions, which include an amount of data and significance weighting from n/10 to n/60, to verify the proposed method. As a result, we confirm the proposed method is robust and efficient from the viewpoint of a sparse data set, applying existing various similarity measurement methods and Significance Weighting.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.4
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• pp.647-651
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• 2015

Let (X, d) be a compact metric space, and let $f:X{\rightarrow}X$ be a continuous map. We consider that if a positively continuum-wise expansiveness continuous map f has the positively shadowing property in the nonwandering set, then the topological entropy is positive.

• Proceedings of the IEEK Conference
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• 2007.07a
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• pp.59-60
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• 2007

Entropy, one of leading metrics on anomalous traffic, attracts researcher's attention since a packet sampling and a traffic volume impact little on entropy value. In this paper, we apply the entropy metric to a domestic network traffic trace which has real anomalous traffics. We used source IP address/port and destination IP address/port that are important attributes of a packet as entropy variable We found that entropy value of multiple-port DoS attack shows something related to a staircase fashion. Also, we show a Possibility of detection of anomalous traffic on small time scale.

• Journal of the Korean Mathematical Society
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• v.55 no.5
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• pp.1157-1175
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• 2018

For a switched system with constraint on switching sequences, which is also called a subshift action, on a metric space not necessarily compact, two kinds of topological entropies, average topological entropy and maximal topological entropy, are introduced. Then we give some properties of those topological entropies and estimate the bounds of them for some special systems, such as subshift actions generated by finite smooth maps on p-dimensional Riemannian manifold and by a family of surjective endomorphisms on a compact metrizable group. In particular, for linear switched systems on ${\mathbb{R}}^p$, we obtain a better upper bound, by joint spectral radius, which is sharper than that by Wang et al. in [42,43].

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.3 no.4
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• pp.366-375
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• 2009

In collaborative filtering, many neighbors are needed to improve the quality and stability of the recommendation. The quality may not be good mainly due to the high similarity between two users not guaranteeing the same preference for products considered for recommendation. This paper proposes a consistency definition, rather than similarity, based on information entropy between two users to improve the recommendation. This kind of consistency between two users is then employed as a trust metric in collaborative filtering methods that select neighbors based on the metric. Empirical studies show that such collaborative filtering reduces the number of neighbors required to make the recommendation quality stable. Recommendation quality is also significantly improved.