Search results for: compressed vertex tables

Authors: Jefri Marzal, Hong Xie, Chun Che Fung

Abstract:

Vertex configuration for a vertex in an orthogonal pseudo-polyhedron is an identity of a vertex that is determined by the number of edges, dihedral angles, and non-manifold properties meeting at the vertex. There are up to sixteen vertex configurations for any orthogonal pseudo-polyhedron (OPP). Understanding the relationship between these vertex configurations will give us insight into the structure of an OPP and help us design better algorithms for many 3-dimensional geometric problems. In this paper, 16 vertex configurations for OPP are described first. This is followed by a number of formulas giving insight into the relationship between different vertex configurations in an OPP. These formulas will be useful as an extension of orthogonal polyhedra usefulness on pattern analysis in 3D-digital images.

Keywords: Orthogonal Pseudo Polyhedra, Vertex configuration

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Authors: S. Balaji, V. Swaminathan, K. Kannan

Abstract:

The Minimum Weighted Vertex Cover (MWVC) problem is a classic graph optimization NP - complete problem. Given an undirected graph G = (V, E) and weighting function defined on the vertex set, the minimum weighted vertex cover problem is to find a vertex set S V whose total weight is minimum subject to every edge of G has at least one end point in S. In this paper an effective algorithm, called Support Ratio Algorithm (SRA), is designed to find the minimum weighted vertex cover of a graph. Computational experiments are designed and conducted to study the performance of our proposed algorithm. Extensive simulation results show that the SRA can yield better solutions than other existing algorithms found in the literature for solving the minimum vertex cover problem.

Keywords: Weighted vertex cover, vertex support, approximation algorithms, NP-complete problem.

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Authors: S. Balaji, V. Swaminathan, K. Kannan

Abstract:

The Minimum Vertex Cover (MVC) problem is a classic graph optimization NP - complete problem. In this paper a competent algorithm, called Vertex Support Algorithm (VSA), is designed to find the smallest vertex cover of a graph. The VSA is tested on a large number of random graphs and DIMACS benchmark graphs. Comparative study of this algorithm with the other existing methods has been carried out. Extensive simulation results show that the VSA can yield better solutions than other existing algorithms found in the literature for solving the minimum vertex cover problem.

Keywords: vertex cover, vertex support, approximation algorithms, NP - complete problem.

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Authors: S. Mulholland

Abstract:

Octree compression techniques have been used for several years for compressing large three dimensional data sets into homogeneous regions. This compression technique is ideally suited to datasets which have similar values in clusters. Oil engineers represent reservoirs as a three dimensional grid where hydrocarbons occur naturally in clusters. This research looks at the efficiency of storing these grids using octree compression techniques where grid cells are broken into active and inactive regions. Initial experiments yielded high compression ratios as only active leaf nodes and their ancestor, header nodes are stored as a bitstream to file on disk. Savings in computational time and memory were possible at decompression, as only active leaf nodes are sent to the graphics card eliminating the need of reconstructing the original matrix. This results in a more compact vertex table, which can be loaded into the graphics card quicker and generating shorter refresh delay times.

Keywords: 3D visualisation, compressed vertex tables, octree compression techniques, oil reservoir grids.

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Authors: S. Balaji, V. Swaminathan, K. Kannan

Abstract:

The Maximum Weighted Independent Set (MWIS) problem is a classic graph optimization NP-hard problem. Given an undirected graph G = (V, E) and weighting function defined on the vertex set, the MWIS problem is to find a vertex set S V whose total weight is maximum subject to no two vertices in S are adjacent. This paper presents a novel approach to approximate the MWIS of a graph using minimum weighted vertex cover of the graph. Computational experiments are designed and conducted to study the performance of our proposed algorithm. Extensive simulation results show that the proposed algorithm can yield better solutions than other existing algorithms found in the literature for solving the MWIS.

Keywords: weighted independent set, vertex cover, vertex support, heuristic, NP - hard problem.

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Authors: Priyadarsini P. L. K, Hemalatha T.

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This paper proves that the problem of finding connected vertex cover in a 2-connected planar graph ( CVC-2 ) with maximum degree 4 is NP-complete. The motivation for proving this result is to give a shorter and simpler proof of NP-Completeness of TRA-MLC (the Top Right Access point Minimum-Length Corridor) problem [1], by finding the reduction from CVC-2. TRA-MLC has many applications in laying optical fibre cables for data communication and electrical wiring in floor plans.The problem of finding connected vertex cover in any planar graph ( CVC ) with maximum degree 4 is NP-complete [2]. We first show that CVC-2 belongs to NP and then we find a polynomial reduction from CVC to CVC-2. Let a graph G0 and an integer K form an instance of CVC, where G0 is a planar graph and K is an upper bound on the size of the connected vertex cover in G0. We construct a 2-connected planar graph, say G, by identifying the blocks and cut vertices of G0, and then finding the planar representation of all the blocks of G0, leading to a plane graph G1. We replace the cut vertices with cycles in such a way that the resultant graph G is a 2-connected planar graph with maximum degree 4. We consider L = K -2t+3 t i=1 di where t is the number of cut vertices in G1 and di is the number of blocks for which ith cut vertex is common. We prove that G will have a connected vertex cover with size less than or equal to L if and only if G0 has a connected vertex cover of size less than or equal to K.

Keywords: NP-complete, 2-Connected planar graph, block, cut vertex

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Authors: Nurdin

Abstract:

Suppose G(V,E) is a graph, a function f : V \cup E \to \{1, 2, 3, \cdots, k\} is called the total edge(vertex) irregular k-labelling for G such that for each two edges are different having distinct weights. The total edge(vertex) irregularity strength of G, denoted by tes(G)(tvs(G), is the smallest k positive integers such that G has a total edge(vertex) irregular k-labelling. In this paper, we determined the total edge(vertex) irregularity strength of an amalgamation of two isomorphic cycles. The total edge irregularity strength and the total vertex irregularity strength of two isomorphic cycles on n vertices are \lceil (2n+2)/3 \rceil and \lceil 2n/3 \rceil for n \geq 3, respectively.

Keywords: Amalgamation of graphs, irregular labelling, irregularity strength.

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Authors: Khidir R. Sharaf, Didar A. Ali

Abstract:

The nullity η(G) of a graph is the occurrence of zero as an eigenvalue in its spectra. A zero-sum weighting of a graph G is real valued function, say f from vertices of G to the set of real numbers, provided that for each vertex of G the summation of the weights f(w) over all neighborhood w of v is zero for each v in G.A high zero-sum weighting of G is one that uses maximum number of non-zero independent variables. If G is graph with an end vertex, and if H is an induced subgraph of G obtained by deleting this vertex together with the vertex adjacent to it, then, η(G)= η(H). In this paper, a high zero-sum weighting technique and the endvertex procedure are applied to evaluate the nullity of t-tupple and generalized t-tupple graphs are derived  and determined for some special types of graphs,

 Also, we introduce and prove some important results about the t-tupple coalescence, Cartesian and Kronecker products of nut graphs.

Keywords: Graph theory, Graph spectra, Nullity of graphs.

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Authors: Ruili Zhou, Yuesheng Zhu

Abstract:

In this paper, a new robust audio fingerprinting algorithm in MP3 compressed domain is proposed with high robustness to time scale modification (TSM). Instead of simply employing short-term information of the MP3 stream, the new algorithm extracts the long-term features in MP3 compressed domain by using the modulation frequency analysis. Our experiment has demonstrated that the proposed method can achieve a hit rate of above 95% in audio retrieval and resist the attack of 20% TSM. It has lower bit error rate (BER) performance compared to the other algorithms. The proposed algorithm can also be used in other compressed domains, such as AAC.

Keywords: Audio Fingerprinting, MP3, Modulation Frequency, TSM

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Authors: Hongzhi Wang, Jianzhong Li, Hong Gao

Abstract:

XML is an important standard of data exchange and representation. As a mature database system, using relational database to support XML data may bring some advantages. But storing XML in relational database has obvious redundancy that wastes disk space, bandwidth and disk I/O when querying XML data. For the efficiency of storage and query XML, it is necessary to use compressed XML data in relational database. In this paper, a compressed relational database technology supporting XML data is presented. Original relational storage structure is adaptive to XPath query process. The compression method keeps this feature. Besides traditional relational database techniques, additional query process technologies on compressed relations and for special structure for XML are presented. In this paper, technologies for XQuery process in compressed relational database are presented..

Keywords: XML, compression, query processing

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Authors: Thomas Odaker, Dieter Kranzlmueller, Jens Volkert

Abstract:

We present an approach to triangle mesh simplification designed to be executed on the GPU. We use a quadric error metric to calculate an error value for each vertex of the mesh and order all vertices based on this value. This step is followed by the parallel removal of a number of vertices with the lowest calculated error values. To allow for the parallel removal of multiple vertices we use a set of per-vertex boundaries that prevent mesh foldovers even when simplification operations are performed on neighbouring vertices. We execute multiple iterations of the calculation of the vertex errors, ordering of the error values and removal of vertices until either a desired number of vertices remains in the mesh or a minimum error value is reached. This parallel approach is used to speed up the simplification process while maintaining mesh topology and avoiding foldovers at every step of the simplification.

Keywords: Computer graphics, half edge collapse, mesh simplification, precomputed simplification, topology preserving.

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Authors: Sudhakara G, Hemanth Kumar A.R

Abstract:

In this paper, we define distance partition of vertex set of a graph G with reference to a vertex in it and with the help of the same, a graph with metric dimension two (i.e. β (G) = 2 ) is characterized. In the process, we develop a polynomial time algorithm that verifies if the metric dimension of a given graph G is two. The same algorithm explores all metric bases of graph G whenever β (G) = 2 . We also find a bound for cardinality of any distance partite set with reference to a given vertex, when ever β (G) = 2 . Also, in a graph G with β (G) = 2 , a bound for cardinality of any distance partite set as well as a bound for number of vertices in any sub graph H of G is obtained in terms of diam H .

Keywords: Metric basis, Distance partition, Metric dimension.

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Authors: S. Raja Balachandar, K.Kannan

Abstract:

A new Meta heuristic approach called "Randomized gravitational emulation search algorithm (RGES)" for solving vertex covering problems has been designed. This algorithm is found upon introducing randomization concept along with the two of the four primary parameters -velocity- and -gravity- in physics. A new heuristic operator is introduced in the domain of RGES to maintain feasibility specifically for the vertex covering problem to yield best solutions. The performance of this algorithm has been evaluated on a large set of benchmark problems from OR-library. Computational results showed that the randomized gravitational emulation search algorithm - based heuristic is capable of producing high quality solutions. The performance of this heuristic when compared with other existing heuristic algorithms is found to be excellent in terms of solution quality.

Keywords: Vertex covering Problem, Velocity, Gravitational Force, Newton's Law, Meta Heuristic, Combinatorial optimization.

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Authors: Ratchakit Sakuldee, Somkait Udomhunsakul

Abstract:

Measurement of the quality of image compression is important for image processing application. In this paper, we propose an objective image quality assessment to measure the quality of gray scale compressed image, which is correlation well with subjective quality measurement (MOS) and least time taken. The new objective image quality measurement is developed from a few fundamental of objective measurements to evaluate the compressed image quality based on JPEG and JPEG2000. The reliability between each fundamental objective measurement and subjective measurement (MOS) is found. From the experimental results, we found that the Maximum Difference measurement (MD) and a new proposed measurement, Structural Content Laplacian Mean Square Error (SCLMSE), are the suitable measurements that can be used to evaluate the quality of JPEG200 and JPEG compressed image, respectively. In addition, MD and SCLMSE measurements are scaled to make them equivalent to MOS, given the rate of compressed image quality from 1 to 5 (unacceptable to excellent quality).

Keywords: JPEG, JPEG2000, objective image quality measurement, subjective image quality measurement, correlation coefficients.

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Authors: Jihyung Kim, Taejin Kim, Sungho Park, Jun-Dong Cho

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A conventional binding method for low power in a high-level synthesis mainly focuses on finding an optimal binding for an assumed input data, and obtains only one binding table. In this paper, we show that a binding method which uses multiple binding tables gets better solution compared with the conventional methods which use a single binding table, and propose a dynamic bus binding scheme for low power using multiple binding tables. The proposed method finds multiple binding tables for the proper partitions of an input data, and switches binding tables dynamically to produce the minimum total switching activity. Experimental result shows that the proposed method obtains a binding solution having 12.6-28.9% smaller total switching activity compared with the conventional methods.

Keywords: low power, bus binding, switching activity, multiplebinding tables

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Authors: Guo Wenyu, Qu Youli

Abstract:

A practical and simple self-indexing data structure, Partitioned Elias-Fano (PEF) - Compressed Suffix Arrays (CSA), is built in linear time for the CSA based on PEF indexes. Moreover, the PEF-CSA is compared with two classical compressed indexing methods, Ferragina and Manzini implementation (FMI) and Sad-CSA on different type and size files in Pizza & Chili. The PEF-CSA performs better on the existing data in terms of the compression ratio, count, and locates time except for the evenly distributed data such as proteins data. The observations of the experiments are that the distribution of the φ is more important than the alphabet size on the compression ratio. Unevenly distributed data φ makes better compression effect, and the larger the size of the hit counts, the longer the count and locate time.

Keywords: Compressed suffix array, self-indexing, partitioned Elias-Fano, PEF-CSA.

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Authors: Brahim Hamid, Bertrand Le Saec, Mohamed Mosbah

Abstract:

The vertex connectivity of a graph is the smallest number of vertices whose deletion separates the graph or makes it trivial. This work is devoted to the problem of vertex connectivity test of graphs in a distributed environment based on a general and a constructive approach. The contribution of this paper is threefold. First, using a preconstructed spanning tree of the considered graph, we present a protocol to test whether a given graph is 2-connected using only local knowledge. Second, we present an encoding of this protocol using graph relabeling systems. The last contribution is the implementation of this protocol in the message passing model. For a given graph G, where M is the number of its edges, N the number of its nodes and Δ is its degree, our algorithms need the following requirements: The first one uses O(Δ×N2) steps and O(Δ×logΔ) bits per node. The second one uses O(Δ×N2) messages, O(N2) time and O(Δ × logΔ) bits per node. Furthermore, the studied network is semi-anonymous: Only the root of the pre-constructed spanning tree needs to be identified.

Keywords: Distributed computing, fault-tolerance, graph relabeling systems, local computations, local knowledge, message passing system, networks, vertex connectivity.

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Authors: Wichan Lertlop, Boonyarat Chaleephay

Abstract:

The objective of this research was to study the appropriate thermal level and time for dabbing customers with the massage compressed pack reported from their perception. The investigation was conducted by comparing different angles of tilted heads done by the customers together with their perception before and after the dabbing. The variables included different temperature of the compressed packs and different dabbing duration. Samples in this study included volunteers who got massage therapy and dabbing with hot compressed packs by traditional Thai medical students. The experiment was conducted during January to June 2013. The research tool consisted of angle meters, stop watches, thermometers, and massage compressed packs. The customers were interviewed for their perceptions before and after the dabbing. The results showed that:

1. There was a difference of the average angles of tilted heads before and after the dabbing.
2. There was no difference of the average angles at different temperatures but constant duration.
3. There was no difference of the average angles at different durations.
4. The customers reported relaxation no matter what the various temperatures and various dabbing durations were. However, they reported too hot at the temperature 70^oC and over.

Keywords: Massage, Therapy, Therapeutic Systems and Technologies.

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Authors: Bharat Raj Singh, Onkar Singh

Abstract:

This paper details a new concept of using compressed air as a potential zero pollution power source for motorbikes. In place of an internal combustion engine, the motorbike is equipped with an air turbine transforms the energy of the compressed air into shaft work. The mathematical modeling and performance evaluation of a small capacity compressed air driven vaned type novel air turbine is presented in this paper. The effect of isobaric admission and adiabatic expansion of high pressure air for different rotor diameters, casing diameters and ratio of rotor to casing diameters of the turbine have been considered and analyzed. It is concluded that the work output is found optimum for some typical values of rotor / casing diameter ratios. In this study, the maximum power works out to 3.825 kW (5.20 HP) for casing diameter of 200 mm and rotor to casing diameter ratio of 0.65 to 0.60 which is sufficient to run motorbike.

Keywords: zero pollution, compressed air, air turbine, injectionangle, rotor / casing diameter ratio.

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Authors: K. Ratan Singh, P. K. Das

Abstract:

An induced graphoidal cover of a graph G is a collection ψ of (not necessarily open) paths in G such that every path in ψ has at least two vertices, every vertex of G is an internal vertex of at most one path in ψ, every edge of G is in exactly one path in ψ and every member of ψ is an induced cycle or an induced path. The minimum cardinality of an induced graphoidal cover of G is called the induced graphoidal covering number of G and is denoted by ηi(G) or ηi. Here we find induced graphoidal cover for some classes of graphs.

Keywords: Graphoidal cover, Induced graphoidal cover, Induced graphoidal covering number.

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Authors: Sizhong Zhou, Hongxia Liu

Abstract:

Abstract–Let k ≥ 3 be an integer, and let G be a graph of order n with n ≥ 9k +3- 42(k - 1)2 + 2. Then a spanning subgraph F of G is called a k-factor if dF (x) = k for each x ∈ V (G). A fractional k-factor is a way of assigning weights to the edges of a graph G (with all weights between 0 and 1) such that for each vertex the sum of the weights of the edges incident with that vertex is k. A graph G is a fractional k-deleted graph if there exists a fractional k-factor after deleting any edge of G. In this paper, it is proved that G is a fractional k-deleted graph if G satisfies δ(G) ≥ k + 1 and |NG(x) ∪ NG(y)| ≥ 1 2 (n + k - 2) for each pair of nonadjacent vertices x, y of G.

Keywords: Graph, minimum degree, neighborhood union, fractional k-factor, fractional k-deleted graph.

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Authors: R. Anitha, R. S. Lekshmi

Abstract:

Graph decompositions are vital in the study of combinatorial design theory. A decomposition of a graph G is a partition of its edge set. An n-sun graph is a cycle Cn with an edge terminating in a vertex of degree one attached to each vertex. In this paper, we define n-sun decomposition of some even order graphs with a perfect matching. We have proved that the complete graph K2n, complete bipartite graph K2n, 2n and the Harary graph H4, 2n have n-sun decompositions. A labeling scheme is used to construct the n-suns.

Keywords: Decomposition, Hamilton cycle, n-sun graph, perfect matching, spanning tree.

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Authors: Leila Kazemi, Akram Pourmohammad, Zargham OstadiAsl, Maryam Jahandideh, Ahadollah Azami

Abstract:

Due to its geographical location, Iran is considered one of the earthquake-prone areas where the best way to decrease earthquake effects is supposed to be strengthening the buildings. Even though, one idea suggests that the use of adobe in constructing buildings be prohibited for its weak function especially in earthquake-prone areas, however, regarding ecological considerations, sustainability and other local skills, another idea pays special attention to adobe as one of the construction technologies which is popular among people. From the architectural and technological point of view, as strong sustainable building construction materials, compressed adobe construction materials make most of the construction in urban or rural areas ranging from small to big industrial buildings used to replace common earth blocks in traditional systems and strengthen traditional adobe buildings especially against earthquake. Mentioning efficient construction using compressed adobe system as a reliable replacement for traditional soil construction materials , this article focuses on the experiences of India in the fields of sustainable development of compressed adobe systems in the form of system in which the compressed soil is combined with cement, load bearing building with brick/solid concrete block system, brick system using rat trap bond, metal system with adobe infill and finally emphasizes on the use of these systems in the earthquake-struck city of Bam in Iran.

Keywords: Local Materials, Compressed Earth Blocks, Sustainable Construction, Retrofitting

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Authors: Bharat Raj Singh, Onkar Singh

Abstract:

This paper deals with new concept of using compressed atmospheric air as a zero pollution power source for running motorbikes. The motorbike is equipped with an air turbine in place of an internal combustion engine, and transforms the energy of the compressed air into shaft work. The mathematical modeling and performance evaluation of a small capacity compressed air driven vaned type novel air turbine is presented in this paper. The effect of isobaric admission and adiabatic expansion of high pressure air for different rotor to casing diameter ratios with respect to different vane angles (number of vanes) have been considered and analyzed. It is found that the shaft work output is optimum for some typical values of rotor / casing diameter ratios at a particular value of vane angle (no. of vanes). In this study, the maximum power is obtained as 4.5kW - 5.3kW (5.5-6.25 HP) when casing diameter is taken 100 mm, and rotor to casing diameter ratios are kept from 0.65 to 0.55. This value of output is sufficient to run motorbike.

Keywords: zero pollution, compressed air, air turbine, vane angle, rotor / casing diameter ratio

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Authors: M. Hamdi, R. Rhouma, S. Belghith

Abstract:

Generating random numbers are mainly used to create secret keys or random sequences. It can be carried out by various techniques. In this paper we present a very simple and efficient pseudo random number generator (PRNG) based on chaotic maps and S-Box tables. This technique adopted two main operations one to generate chaotic values using two logistic maps and the second to transform them into binary words using random S-Box tables. The simulation analysis indicates that our PRNG possessing excellent statistical and cryptographic properties.

Keywords: Chaotic map, Cryptography, Random Numbers, Statistical tests, S-box.

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Authors: C.Natarajan, S.K.Ayyaswamy

Abstract:

Let G be a fuzzy graph. Then D Ôèå V is said to be a strong (weak) fuzzy dominating set of G if every vertex v ∈ V -D is strongly (weakly) dominated by some vertex u in D. We denote a strong (weak) fuzzy dominating set by sfd-set (wfd-set). The minimum scalar cardinality of a sfd-set (wfd-set) is called the strong (weak) fuzzy domination number of G and it is denoted by γsf (G)γwf (G). In this paper we introduce the concept of strong (weak) domination in fuzzy graphs and obtain some interesting results for this new parameter in fuzzy graphs.

Keywords: Fuzzy graphs, fuzzy domination, strong (weak) fuzzy domination number.

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Authors: Seiya Teshima, Kazushige Magatani

Abstract:

Currently, many types of no-reversible compressed sound source, represented by MP3 (MPEG Audio Layer-3) are popular in the world and they are widely used to make the music file size smaller. The sound data created in this way has less information as compared to pre-compressed data. The objective of this study is by analyzing EEG to determine if people can recognize such difference as differences in sound. A measurement system that can measure and analyze EEG when a subject listens to music were experimentally developed. And ten subjects were studied with this system. In this experiment, a WAVE formatted music data and a MP3 compressed music data that is made from the WAVE formatted data were prepared. Each subject was made to hear these music sources at the same volume. From the results of this experiment, clear differences were confirmed between two wound sources.

Keywords: EEG, Biological signal , Sound , MP3

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Authors: K. Ratan Singh, P. K. Das

Abstract:

An induced acyclic graphoidal cover of a graph G is a collection ψ of open paths in G such that every path in ψ has atleast two vertices, every vertex of G is an internal vertex of at most one path in ψ, every edge of G is in exactly one path in ψ and every member of ψ is an induced path. The minimum cardinality of an induced acyclic graphoidal cover of G is called the induced acyclic graphoidal covering number of G and is denoted by ηia(G) or ηia. Here we find induced acyclic graphoidal cover for some classes of graphs.

Keywords: Graphoidal cover, Induced acyclic graphoidal cover, Induced acyclic graphoidal covering number.

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Authors: Yohei Saika, Yuji Haraguchi

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We constructed a method of noise reduction for JPEG-compressed image based on Bayesian inference using the maximizer of the posterior marginal (MPM) estimate. In this method, we tried the MPM estimate using two kinds of likelihood, both of which enhance grayscale images converted into the JPEG-compressed image through the lossy JPEG image compression. One is the deterministic model of the likelihood and the other is the probabilistic one expressed by the Gaussian distribution. Then, using the Monte Carlo simulation for grayscale images, such as the 256-grayscale standard image “Lena" with 256 × 256 pixels, we examined the performance of the MPM estimate based on the performance measure using the mean square error. We clarified that the MPM estimate via the Gaussian probabilistic model of the likelihood is effective for reducing noises, such as the blocking artifacts and the mosquito noise, if we set parameters appropriately. On the other hand, we found that the MPM estimate via the deterministic model of the likelihood is not effective for noise reduction due to the low acceptance ratio of the Metropolis algorithm.

Keywords: Noise reduction, JPEG-compressed image, Bayesian inference, the maximizer of the posterior marginal estimate

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Authors: Wongsakorn Charoenpanitseri

Abstract:

The total chromatic number χ"(G) of a graph G is the minimum number of colors needed to color the elements (vertices and edges) of G such that no incident or adjacent pair of elements receive the same color Let G be a graph with maximum degree Δ(G). Considering a total coloring of G and focusing on a vertex with maximum degree. A vertex with maximum degree needs a color and all Δ(G) edges incident to this vertex need more Δ(G) + 1 distinct colors. To color all vertices and all edges of G, it requires at least Δ(G) + 1 colors. That is, χ"(G) is at least Δ(G) + 1. However, no one can find a graph G with the total chromatic number which is greater than Δ(G) + 2. The Total Coloring Conjecture states that for every graph G, χ"(G) is at most Δ(G) + 2. In this paper, we prove that the Total Coloring Conjectur for a Δ-claw-free 3-degenerated graph. That is, we prove that the total chromatic number of every Δ-claw-free 3-degenerated graph is at most Δ(G) + 2.

Keywords: Total colorings, the total chromatic number, 3-degenerated.

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