Home Random walk-based similarity measure method for patterns in complex object
Article Open Access

Random walk-based similarity measure method for patterns in complex object

  • Shihu Liu EMAIL logo and Xiaozhou Chen
Published/Copyright: April 14, 2017
Download Article (PDF)
Open Physics
From the journal Open Physics Volume 15 Issue 1

Abstract

This paper discusses the similarity of the patterns in complex objects. The complex object is composed both of the attribute information of patterns and the relational information between patterns. Bearing in mind the specificity of complex object, a random walk-based similarity measurement method for patterns is constructed. In this method, the reachability of any two patterns with respect to the relational information is fully studied, and in the case of similarity of patterns with respect to the relational information can be calculated. On this bases, an integrated similarity measurement method is proposed, and algorithms 1 and 2 show the performed calculation procedure. One can find that this method makes full use of the attribute information and relational information. Finally, a synthetic example shows that our proposed similarity measurement method is validated.

Keywords: Complex object; Random walk; Reachability; Similarity measure
PACS: 02.90.+p

1 Introductory comments and Problem statement

Similarity measurement, as a tool to determine the similar between two patterns, is given special attention from its wide application in many fields, such as pattern recognition[1], machine learning[2], image processing[3–6], multimodal maps[7], supply chain network[8], dynamic systems[9], and others[10–15]. It is not hard to find that the data generated in similarity computing processes are almost interval numbers[16], fuzzy numbers[17–21], (interval-valued)intuitionistic fuzzy numbers[22, 23], or even a set[24]. Besides these, many similarity measure methods are applied, such as the cosine method, correlation coefficient method and the max-min method, amongst others.

No matter which representation the data has or what similarity measurement method is used, all the data are vector-based attribute information, to some extent. But, in practical problem solving, this is not enough. For example, if we want to detect the community structure, the research should be aimed at network data[25]. Therefore, the data takes not only the attribute information of patterns but also the relational information between patterns.

In view of the similarity problem of such data, a lot of studies have been done. For example, Rossi et al.[26] proposed a quantum algorithm to measure the similarity between a pair of unattributed graphs, and in which the theory of quantum Jensen-Shannon divergence constitutes the basis of theoretical analysis. Moreover, Rossi et al.[27] discussed the similarity between attributed graphs by means of the evolution of a continuous-time quantum walk. In [28], Cason et al. computed the low approximation of the graph similarity matrix. Brandes and Lerner [29] introduced the concept of structural similarity by relaxation of equitable partitions. Kpodjedo et al.[30] investigated heuristics for approximate graph matching. Maggini et al.[2] presented a neural networks model that could be used to learn a similarity measure for pairs of patterns. Grewenig, Zimmer and Weickert [31] studied the rotationally invariant similarity measures for non-local image denoising. Besides these studies, many other similarity measuring approaches are proposed in references [32–39], in this paper’s.

Taking the relational information of directly-linked patterns and indirectly-linked patterns into account, here we propose a random walk-based similarity measure method for patterns in complex object. Here, the “random walk” refers to the linking route between any two patterns, and the “complex object” refers to the data that it contains not only the attribute information of patterns but also the relational information between patterns. According to the corresponding relational information of any two patterns, firstly we propose the concept of reachability of patterns. On this basis, the so called random walk route between any two patterns is constructed. From this, the similarity value with respect to relational information can be obtained by weighting method. After that, the similarity value comes naturally. During the process of constructing the random walk route, we consider two cases: one is that the longest length of it is not limited; another is that the longest length of it is restricted.

The remainder of this paper is organized as follows. In Section 2, we make a discussion on the concept of complex object. In Section 3, the random walk-based similarity measurement method for patterns in complex object is discussed carefully. In Section 4, a synthetic example is simulated to illustrate the validity of our proposed algorithm. Finally, Section 5 concludes this paper.

2 The mathematical description of complex object

Mathematically, the complex object can be expressed as a tuple CO=(X, R), where

  1. X = {x1, x2, ⋯, xn} is a nonempty finite set and xi is a pattern, for i = 1, 2, ⋯, n;

  2. R = {rij | i, j = 1, 2, ⋯, n} is a set of relations and rij ∈ R represents the possible relational information between the patterns xi and xj.

Naturally, if xi ∈ X is nothing but a symbolic description of the ith pattern, then the information provided by R be used. If not, the pattern xi can be expressed as xi = (xi1, xi2, ⋯, xim), where xij represents the value of xi with respect to the attribution aj. To the best of our knowledge, the set X can be rewritten as:

X=x11x12⋯x1mx21x22⋯x2m⋮⋮⋱⋮xn1xn2⋯xnm.

Similarly, R can be expressed as

R=r11r12⋯r1nr21r22⋯r2n⋮⋮⋱⋮rn1rn2⋯rnn.

It is well known that the attribute information xij may be not a real number, sometimes it may be a set[24], an interval [16], or even a fuzzy number [17, 18]. Certainly, the foregoing proposed data representation formats are also suitable for the entries in the set R. Especially for some practical problems, the relationship between any two patterns xi and xj may be described by more than one relation, that is, R = {R1, R2, ⋯, Rk with k ≥ 1, where Ri ∈ R shows the ith relationship between patterns.

In what follows, we adhere to the hypotheses that for complex object CO = (X, R): R describes only one relationship, that is, rij ∈ [0, 1] for i, j = 1, 2, ⋯, n and xij is a real number for i = 1, 2, ⋯, n and j = 1, 2, ⋯, m.

3 Random walk-based similarity measure method for patterns in complex object

In this section, we pay attention to constructing the similarity measurement method from two aspects: one is that the length of the random walk route between xi to xj which is not limited, and another is that the length of the random walk route between xi and xj is restricted. Before doing this, at first we introduce some relative concepts.

3.1 Reachability of patterns

Definition 3.1

Suppose that CO = (X, R) is a complex object. If rij ≠ 0, then we say that the patterns xi and xj are one step reachable with respect to the relationship described by R, otherwise it is one step unreachable.

Obviously, for a complex object CO = (X, R), there holds rij = 0 and rij ≠ 0. Therefore, in this situation all patterns can be divided into two types: one step reachable and one step unreachable. Take the patterns in figure 1 for example, the patterns x1 and x2, x1 and x4, x5 and x7 are one step reachable, but the patterns x1 and x5, x5 and x6 are one step unreachable.

Figure 1 One complex object CO = (X, R)
Figure 1

One complex object CO = (X, R)

Definition 3.2

Let CO = (X, R) be a complex object. If rij = 0 and rik0, rk0k1, ⋯, rkℓ−1j ≠ 0 when xk0, xk1, ⋯, xkℓ-1 ∈ X, then we say that the patterns xi and xj are ℓ steps reachable with respect to the patterns xk0, xk1, ⋯, xkℓ-1. Moreover, xi → xk0 → xk1 → ⋯ → xkℓ-1 → xj is the possible random walk route between xi and xj.

As can be seen from definition 3.2, we have that for the one step unreachable patterns, it may be ℓ steps reachable for ℓ ≥ 2. For example, the patterns x2 and x7 in figure 1 are reachable because they have 6 random walk routes between them:

(a)x2→x1→x4→x6→x7;(b)x2→x1→x4→x5→x7;(c)x2→x3→x4→x6→x7;(d)x2→x3→x4→x5→x7;(e)x2→x1→x4→x7;(f)x2→x3→x4→x7.

Obviously, the length of such random walk routes is not equal. Especially, even the length is equal, the random walk route may not be the same. In order to avoid the unnecessary confusion, we make the following definition.

Definition 3.3

Let CO = (X, R) be a complex object. The patterns xi and xj are ℓ steps reachable if and only if they are ℓ-1 steps unreachable.

Certainly, for any two ℓ(ℓ ≥ 2) steps reachable patterns xi and xj in the complex object CO = (X, R), the random walk route may not be unique. Moreover, there exist one case that if X can be divided into two or more disjoint subsets(such as x1 and x2) in terms of R, then the patterns xi ∈ x1 and xj ∈ x2 are unreachable forever.

Definition 3.4

Let CO = (X, R) be a complex object and |X| = n. If the patterns xi and xj are n−1 steps unreachable, then we say that they are never reachable.

Through above analysis, one can find that for a complex object CO = (X, R) with n patterns, the reachability between any two patterns can fall into 4 types:

  1. – xi and xj are zero step reachable, that is, xi and xj are the same pattern;

  2. – xi and xj are one step reachable;

  3. – xi and xj are ℓ steps reachable, where 2 ≤ l ≤ n − 1;

  4. – xi and xj are never reachable.

It should be pointed out that if the patterns xi and xj are zero step reachable, then its similarity value is equal to 1, not only in aspect of attribute information, but also in aspect of relational information. In other words, it is trivial.

3.2 Similarity measure in aspect of relational information

Up to now, the reachability of any two different patterns in aspect of relational information has been proposed clearly: one step reachable, ℓ steps reachable for 2 ≤ ℓn − 1 and never reachable.

When the patterns xi and xj are one step reachable, such as the patterns x1 and x2 in figure 1, the corresponding relational information rij can be applied to calculate the similarity between them: if R describes the similarity between patterns, then SR(xi, xj) = rij; if R describes the distance between patterns, then SR(xi, xj) = 1 − rij, and so on. Therefore, the finial similarity value between patterns xi and xj can be determined by some weighted approaches, such as the following formula:

sij=SR(xi,xj)2+SX(xi,xj)2SR(xi,xj)+SX(xi,xj).(1)

When the patterns xi and xj are never reachable, one can find that during the process of similarity measurement, the relational information contributes nothing. In other words, only the attribute information takes part in the calculation. Hence, the finial similarity between patterns xi and xj is the same as that of attribute information, that is,

sij=SX(xi,xj).(2)

In the sequel, we discuss the situation when the patterns xi and xj are ℓ steps reachable for 2 ≤ ℓ ≤ |X| − 1. For this, equation (1) and equation (2) are invalid for calculation. Take patterns xi, xj and xk for example, where rij = 0 but rjk ≠ 0 and rik ≠ 0. If we only consider rij = 0, then the similarity of xi and xj, about relational information, is equal to 0, is it reasonable? Certainly, no!

As can be seen from the above subsection, there would have more than one random walk routes between two patterns, such as x2 → x1 → x4 → x7 and x2 → x3 → x4 → x7 in figure 1. Intuitively, different random walk route reflects different similar-degree between these two patterns. To this, we introduce the following approach to calculate the similarity between two ℓ steps reachable patterns xi and xj. Given that the patterns xi and xj are ℓ steps reachable, and there are more than one random walk routes between them. Then, the similarity value, in aspect of relational information, can be calculated by formula

SℓR(xi,xj)=maxτ∈ΓSR(xi,xk0)2+⋯+SR(xkℓ−1,xj)2SR(xi,xk0)+⋯+SR(xkℓ−1,xj),(3)

where

  1. –τ : xi → xk0 → ⋯ → xkℓ−1 is one possible random walk route between xi and xj;

  2. –Γ is the index set with respect to the random walk routes;

  3. –SR(xki, xki+1 represents the similarity between one step reachable patterns xki and xki+1.

So, the finial similarity value between the patterns xi and xj can be calculated by the weighted formula

sij=SℓR(xi,xj)2+SX(xi,xj)2SℓR(xi,xj)+SX(xi,xj).(4)

Naturally, if patterns xi and xj are zero step reachable, then SℓR(xi,xj)≡1.

3.3 Similarity algorithm construction

In above subsection, we discussed the similarity measure with respect to the relational information. Because the attribute information of patterns is represented as a vector xi = (xi1, xi2, ⋯, xin), the similarity between any two patterns with respect to attribute information is straightforward, such as the cosine measurement

SX(xi,xj)=∑k=1mxikxjk∑k=1mxik2∑k=1mxjk2(5)

can be used.

Bearing our research purpose in mind, the random walk-based similarity measure method can be summarized as following algorithm 1. Notice that for briefness, the sentence “random walk-based similarity measure method for patterns in complex object” is abbreviated into “RWSMM-PCO”.

Algorithm 1

RWSMM-PCO

fori = 1, 2, …, ndo

  1. Compute the similarity value SX(xi, xj) by equation (5);

  2. If xi and xj are zero step reachable, then sij ≡ 1;

  3. If xi and xj are one step reachable, then compute sij by equation (1);

  4. If xi and xj are ℓ steps reachable, then compute sij by equation (4);

  5. If xi and xj are never reachable, then compute sij by equation (2).

returnS = (sij)n×n

Obviously, the similarity of any two patterns in CO = (X, R) can be determined by algorithm 1. But, the possible random walk route between patterns xi and xj may be very long, especially in some practical problems.

Once the value of R in CO = (X, R) is given, the random walk routes between any two patterns can be determined. By considering the needs of the practical problem and especially the difficulty of computing the concrete random walk route, next we study the similarity measure between any two patterns when the longest length of corresponding random walk route is restricted. For convenience, we suppose that the length of random walk route between patterns xi and xj is ℓij, and the corresponding threshold is ϑij∗. On this hypothesis, the algorithm 1 can be rewritten as following algorithm 2. Similarly, here the sentence “length limited random walk-based similarity measure method for patterns in complex object” is abbreviated into “LLRWSMM-PCO” for short.

Algorithm 2

LLRWSMM-PCO

fori = 1, 2, …, n and parameter ϑij∗ do

  1. Compute the similarity value SX(xi, xj) by equation (5);

  2. If xi and xj are zero step reachable, then sij ≡ 1;

  3. If xi and xj are one step reachable, then compute sij by equation (1);

  4. If ℓij ≤ ϑij∗, then compute sij by equation (4);

  5. If ℓij > ϑij∗, then compute sij by equation (2).

returnS = (sij)n×n

4 Experimental study

In this section, we introduce a synthetic example to illustrate the validity of the proposed similarity measure method for patterns in complex object. For the complex object CO = (X, R), the attribute information is listed in table 1 and the relational information is shown in figure 2. Hereinto, the relational information reflects the similarity between any two patterns.

Table 1

Attribute information of patterns.

x1x2x3x4x5x6x7x8x9
a15.14.66.66.47.73.53.13.02.2
a24.96.17.46.36.33.02.82.82.8
a34.76.47.96.16.43.22.92.82.6
Figure 2 Relational information of patterns in complex object
Figure 2

Relational information of patterns in complex object

As can be seen from figure 2, there is at least one random walk route from xi to xj.

Take the patterns x2 and x8 for example, they are 4 steps reachable patterns. With the aid of equation (5), we have that the similarity of x2 and x8 with respect to the attribute information is

SX(x2,x8)=0.986.(6)

Obviously, there are 2 random walk routes between x2 and x8, which are:

  1. τ1 : x2 → x1 → x4 → x7 → x8;

  2. τ2 : x2 → x3 → x4 → x7 → x8.

If the route τ1 is considered, then, we have that

Sτ1R(x2,x8)=0.633,(7)

while if we take route τ2 into account, then

Sτ2R(x2,x8)=0.627.(8)

Taking equation (7) and equation (8) into equation (3), we have that SR(x2, x8) = 0.633. Thus, the similarity of patterns x2 and x8 is s28 = 0.848. Similarity, if take patterns x2 and x4 for example, we have that the similarity with respect to the random walk route x2 → x1 → x4 is

Sτ1R(x2,x4)=0.456,(9)

and the similarity with respect to the random walk route x2 → x3 → x4 is

Sτ2R(x2,x4)=0.654.(10)

Therefore, the similarity of x2 and x4 is s24 = 0.855.

Obviously, if only the attribute information is considered, then the similarity value of x2 and x8 is 0.986, and the similarity value of x2 and x4 reaches up to 0.988. Certainly, if we only take the relational information into consideration, then the similarity of x2 and x8 is equal to 0, and the same as that of x2 and x4. For the similarity of any two patterns, it can be found in table 2.

Table 2

The similarity of patterns.

x1x2x3x4x5x6x7x8x9
x11.0000.9110.8500.9220.8650.8350.8300.8200.823
x20.9111.0000.9400.8550.8620.8460.8360.8480.840
x30.8500.9401.0000.9270.8720.8440.8290.8290.832
x40.9220.8550.9271.0000.9550.9300.9260.8240.835
x50.8650.8620.8720.9551.0000.8910.9210.8230.816
x60.8350.8460.8440.9300.8911.0000.9770.8970.872
x70.8300.8360.8290.9260.9210.9771.0000.9220.826
x80.8200.8480.8290.8240.8230.8970.9221.0000.925
x90.8230.8400.8320.8350.8160.8720.8260.9251.000

In above discussion, the longest length of a random walk route is not restricted. For example, x2 and x8 are 4 steps reachable patterns, and there have 2 possible random walk routes. If the longest length of random walk route is limited to 3, then they are unreachable. If so, according to the algorithm 2, only the attribute information is considered during the process of similarity measuring. But for patterns x2 and x4, because they are 2 steps reachable patterns, then ϑ24∗=3 has no effect on it.

5 Conclusion

Here, the problem of how to calculate the similarity of patterns in complex object is discussed carefully. Because the complex object is composed by two types of irrelative information (the vector-based attribute information and the relationship-based relational information), the similarity of patterns in such object is not a simple thing. To this, we proposed a random walk-based similarity measure method for patterns in complex object, where the reachability of any two patterns played a dominant role. On these bases, the similarity of patterns can be obtained by weighting the similarity with respect to the attribute information and the similarity with respect to the relational information. At the end of this paper, a synthetic example showed the validity of our proposed similarity measure algorithm.

Acknowledgement

This work is supported by the National Natural Science Foundation of China (No. 31460297), Yunnan Applied Basic Research Youth Projects(No.2015FD032) and the Natural Science Foundation of Shandong Province(ZR2016AP12).

References

[1] Li D.F., Cheng C.T., New similarity measure of intuitionistic fuzzy sets and application to pattern recognitions, Pattern Recogn. Lett., 2002, 23, 221-225.10.1016/S0167-8655(01)00110-6Search in Google Scholar

[2] Maggini M., Melacci S., Sarti L., Learning from pairwise constraints by similarity neural networks, Neural Networks, 2012, 26, 141-158.10.1016/j.neunet.2011.10.009Search in Google Scholar PubMed

[3] Bustince H., Barrenechea E., Pagola M., Image thresholding using restricted equivalence functions and maximizing the measures of similarity, Fuzzy Sets Syst., 2007, 158, 496-516.10.1016/j.fss.2006.09.012Search in Google Scholar

[4] Chambon S., Crouzil A., Similarity measures for image matching despite occlusions in stereo vision, Pattern Recogn., 2011, 44, 2063-2075.10.1016/j.patcog.2011.02.001Search in Google Scholar

[5] Yen C.Y., Cios K.J., Image recognition system based on novel measures of image similarity and cluster validity, Neurocomputing, 2008, 72, 401-412.10.1016/j.neucom.2007.12.018Search in Google Scholar

[6] Moghaddam B., Nastar C., Pentland A., A Bayesian similarity measure for deformable image matching, Image Vision Comput., 2001, 19, 235-244.10.1016/S0262-8856(00)00059-7Search in Google Scholar

[7] Amigó J.M., Giménez Á., Applications of the min-max symbols of multimodal maps, Appl.Math.Nonlinear Sci., 2016,1,87-98.10.21042/AMNS.2016.1.00008Search in Google Scholar

[8] Guo C.X., Liu X.L., Jin M.Z., Lv Z., The research on optimization of auto supply chain network robust model under macroeconomic fluctuations, Chaos Soliton. Fract., 2015, 89, 105-114.10.1016/j.chaos.2015.10.008Search in Google Scholar

[9] Guo C.X., Qiang G., Jin M.Z., Lv Z.H., Dynamic systems based on preference graph and distance, Discrete Cont. Dyn-S., 2015, 8, 1139-1154.10.3934/dcdss.2015.8.1139Search in Google Scholar

[10] de A.T.de Carvalho F., Lechevallier Y., de Melo F.M., Partitioning hard clustering algorithms based on multiple dissimilarity matrices, Pattern Recogn., 2012, 45, 447-464.10.1016/j.patcog.2011.05.016Search in Google Scholar

[11] Egghe L., Rousseau R., Lorenz theory of symmetric relative concentration and similarity, incorporating variable array length, Math. Comput. Model., 2006, 44, 628-639.10.1016/j.mcm.2006.02.001Search in Google Scholar

[12] Gao W., Farahani M.R., Degree-based indices computation for special chemical molecular structures using edge dividing method, Appl. Math. Nonlinear Sci., 2016, 1, 99-122.10.21042/AMNS.2016.1.00009Search in Google Scholar

[13] Liu S.H., Yu F.S., Hesitation degree-based similarity measures for intuitionistic fuzzy sets, Int. J. Information and Communication Technology, 2014, 6, 7-22.10.1504/IJICT.2014.057969Search in Google Scholar

[14] Wu H.L., Zhao B., Overview of current techniques in remote data auditing, Appl. Math. Nonlinear Sci., 2016, 1, 145-158.10.21042/AMNS.2016.1.00011Search in Google Scholar

[15] Ramane H.S., Jummannaver R.B., Note on forgotten topological index of chemical structure in drugs, Applied Mathematics and Nonlinear Sciences, 2016, 1, 369-374.10.21042/AMNS.2016.2.00032Search in Google Scholar

[16] Qian Y.H., Liang J.Y., Dang C.Y., Interval ordered information systems, Comput. Math. Appl., 2008, 56, 1994-2009.10.1016/j.camwa.2008.04.021Search in Google Scholar

[17] Dubois D., Prade H., Gradualness, uncertainty and bipolarity: making sense of fuzzy sets, Fuzzy Sets Syst., 2012, 192, 3-24.10.1016/j.fss.2010.11.007Search in Google Scholar

[18] Ban A., Coroianu L., Grzegorzewski P., Trapezoidal approximation and aggregation, Fuzzy Sets Syst., 2011, 177, 45-59.10.1016/j.fss.2011.02.016Search in Google Scholar

[19] de Campos Ibáñez L.M., González Muñoz A., A subjective approach for ranking fuzzy numbers, Fuzzy Sets Syst., 1989, 29, 145-153.10.1016/0165-0114(89)90188-7Search in Google Scholar

[20] Zadeh L.A., Fuzzy sets, Information and Control, 1965, 8, 338-353.10.21236/AD0608981Search in Google Scholar

[21] Bortolan G., Degani R., A review of some methods for ranking fuzzy subsets, Fuzzy Sets Syst., 1985, 15, 1-19.10.1016/B978-1-4832-1450-4.50016-XSearch in Google Scholar

[22] Zhang Q.S., Jiang S.Y., Jia B.G., Luo S.H., Some information measures for interval-valued intuitionistic fuzzy sets, Inform. Sciences, 2010, 180, 5130-5145.10.1016/j.ins.2010.08.038Search in Google Scholar

[23] Atanassov K.T., Intuitionistic fuzzy sets, Fuzzy Sets Syst., 1986, 20, 87-96.10.1016/S0165-0114(86)80034-3Search in Google Scholar

[24] Qian Y.H., Liang J.Y., Song P., Dang C.Y., On dominance relations in disjunctive set-valued ordered information systems, Int. J. Inf. Tech. Decis., 2010, 9, 9-33.10.1142/S0219622010003646Search in Google Scholar

[25] Newman M.E.J., Detecting community structure in networks, Eur. Phys.J.B., 2004, 38, 321-330.10.1140/epjb/e2004-00124-ySearch in Google Scholar

[26] Rossi L., Torsello A., Hancock E.R., Measuring graph similarity through continuous-time quantum walks and the quantum Jensen-Shannon divergence, Phys. Rev. E., 2015, 91, 12 pages.10.1103/PhysRevE.91.022815Search in Google Scholar PubMed

[27] Rossi L., Torsello A., Andrea E.R., Attributed graph similarity from the quantum Jensen-Shannon divergence, Lecture Notes in Comput. Sci., 2013, 7953, 204-218.10.1007/978-3-642-39140-8_14Search in Google Scholar

[28] Cason T.P., Absil P.A., Van Dooren P., Iterative methods for low rank approximation of graph similarity matrices, Linear Algebra Appl., 2013, 438, 1863-1882.10.1016/j.laa.2011.12.004Search in Google Scholar

[29] Brandes U., Lerner J., Structural Similarity in Graphs(a relaxation approach for role assignment), Lecture Notes in Comput. Sci., 2005, 3341, 184-195.10.1007/978-3-540-30551-4_18Search in Google Scholar

[30] Kpodjedo S., Galinier P., Antoniol G., Using local similarity measures to efficiently address approximate graph matching, Discrete Appl. Math., 2014, 164, part 1, 161-177.10.1016/j.dam.2012.01.019Search in Google Scholar

[31] Grewenig S., Zimmer S., Weickert J., Rotationally invariant similarity measures for nonlocal image denoising, J.Vis. Commun. Image. R., 2011, 22, 117-130.10.1016/j.jvcir.2010.11.001Search in Google Scholar

[32] Hosamani S.M., Correlation of domination parameters with physicochemical properties of octane isomers, Applied Mathematics and Nonlinear Sciences, 2016, 1, 346-352.10.21042/AMNS.2016.2.00029Search in Google Scholar

[33] Fernandez M.L., Valiente G., A graph distance metric combining maximum common subgraph and minimum common supergraph, Pattern Recogn. Lett., 2001, 22, 753-758.10.1016/S0167-8655(01)00017-4Search in Google Scholar

[34] Bunke H., Shearer K., A graph distance metric based on the maximal common sub-graph, Pattern Recogn. Lett., 1998, 19, 255-259.10.1016/S0167-8655(97)00179-7Search in Google Scholar

[35] Chen J., Safro I., A measure of the local connectivity between graph vertices, Procedia Comput. Sci., 2011, 4, 96-205.10.1016/j.procs.2011.04.021Search in Google Scholar

[36] Dehmer M., Emmert-Streib F., Kilian J., A similarity measure for graphs with low computational complexity, Appl. Math. Comput., 2006, 182, 447-459.10.1016/j.amc.2006.04.006Search in Google Scholar

[37] Hidovic D., Pelillo M., Metrics for attributed graphs based on the maximal similarity common subgraph, Int. J. Pattern Recogn., 2004, 18, 299-313.10.1142/S0218001404003216Search in Google Scholar

[38] Rupp M., Proschak A.E., Schneider G., Kernel approach to molecular similarity based on iterative graph similarity, J. Chem. Inf. Model., 2007, 47, 2280-2286.10.1021/ci700274rSearch in Google Scholar PubMed

[39] Zager L.A., Verghese G.C., Graph similarity scoring and matching, Appl. Math. Lett., 2008, 21, 86-94.10.1016/j.aml.2007.01.006Search in Google Scholar

Received: 2016-9-10
Accepted: 2016-9-26
Published Online: 2017-4-14

© 2017 Shihu Liu and Xiaozhou Chen

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Articles in the same Issue

  1. Regular Articles
  2. Analysis of a New Fractional Model for Damped Bergers’ Equation
  3. Regular Articles
  4. Optimal homotopy perturbation method for nonlinear differential equations governing MHD Jeffery-Hamel flow with heat transfer problem
  5. Regular Articles
  6. Semi- analytic numerical method for solution of time-space fractional heat and wave type equations with variable coefficients
  7. Regular Articles
  8. Investigation of a curve using Frenet frame in the lightlike cone
  9. Regular Articles
  10. Construction of complex networks from time series based on the cross correlation interval
  11. Regular Articles
  12. Nonlinear Schrödinger approach to European option pricing
  13. Regular Articles
  14. A modified cubic B-spline differential quadrature method for three-dimensional non-linear diffusion equations
  15. Regular Articles
  16. A new miniaturized negative-index meta-atom for tri-band applications
  17. Regular Articles
  18. Seismic stability of the survey areas of potential sites for the deep geological repository of the spent nuclear fuel
  19. Regular Articles
  20. Distributed containment control of heterogeneous fractional-order multi-agent systems with communication delays
  21. Regular Articles
  22. Sensitivity analysis and economic optimization studies of inverted five-spot gas cycling in gas condensate reservoir
  23. Regular Articles
  24. Quantum mechanics with geometric constraints of Friedmann type
  25. Regular Articles
  26. Modeling and Simulation for an 8 kW Three-Phase Grid-Connected Photo-Voltaic Power System
  27. Regular Articles
  28. Application of the optimal homotopy asymptotic method to nonlinear Bingham fluid dampers
  29. Regular Articles
  30. Analysis of Drude model using fractional derivatives without singular kernels
  31. Regular Articles
  32. An unsteady MHD Maxwell nanofluid flow with convective boundary conditions using spectral local linearization method
  33. Regular Articles
  34. New analytical solutions for conformable fractional PDEs arising in mathematical physics by exp-function method
  35. Regular Articles
  36. Quantum mechanical calculation of electron spin
  37. Regular Articles
  38. CO2 capture by polymeric membranes composed of hyper-branched polymers with dense poly(oxyethylene) comb and poly(amidoamine)
  39. Regular Articles
  40. Chain on a cone
  41. Regular Articles
  42. Multi-task feature learning by using trace norm regularization
  43. Regular Articles
  44. Superluminal tunneling of a relativistic half-integer spin particle through a potential barrier
  45. Regular Articles
  46. Neutrosophic triplet normed space
  47. Regular Articles
  48. Lie algebraic discussion for affinity based information diffusion in social networks
  49. Regular Articles
  50. Radiation dose and cancer risk estimates in helical CT for pulmonary tuberculosis infections
  51. Regular Articles
  52. A comparison study of steady-state vibrations with single fractional-order and distributed-order derivatives
  53. Regular Articles
  54. Some new remarks on MHD Jeffery-Hamel fluid flow problem
  55. Regular Articles
  56. Numerical investigation of magnetohydrodynamic slip flow of power-law nanofluid with temperature dependent viscosity and thermal conductivity over a permeable surface
  57. Regular Articles
  58. Charge conservation in a gravitational field in the scalar ether theory
  59. Regular Articles
  60. Measurement problem and local hidden variables with entangled photons
  61. Regular Articles
  62. Compression of hyper-spectral images using an accelerated nonnegative tensor decomposition
  63. Regular Articles
  64. Fabrication and application of coaxial polyvinyl alcohol/chitosan nanofiber membranes
  65. Regular Articles
  66. Calculating degree-based topological indices of dominating David derived networks
  67. Regular Articles
  68. The structure and conductivity of polyelectrolyte based on MEH-PPV and potassium iodide (KI) for dye-sensitized solar cells
  69. Regular Articles
  70. Chiral symmetry restoration and the critical end point in QCD
  71. Regular Articles
  72. Numerical solution for fractional Bratu’s initial value problem
  73. Regular Articles
  74. Structure and optical properties of TiO2 thin films deposited by ALD method
  75. Regular Articles
  76. Quadruple multi-wavelength conversion for access network scalability based on cross-phase modulation in an SOA-MZI
  77. Regular Articles
  78. Application of ANNs approach for wave-like and heat-like equations
  79. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  80. Study on node importance evaluation of the high-speed passenger traffic complex network based on the Structural Hole Theory
  81. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  82. A mathematical/physics model to measure the role of information and communication technology in some economies: the Chinese case
  83. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  84. Numerical modeling of the thermoelectric cooler with a complementary equation for heat circulation in air gaps
  85. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  86. On the libration collinear points in the restricted three – body problem
  87. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  88. Research on Critical Nodes Algorithm in Social Complex Networks
  89. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  90. A simulation based research on chance constrained programming in robust facility location problem
  91. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  92. A mathematical/physics carbon emission reduction strategy for building supply chain network based on carbon tax policy
  93. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  94. Mathematical analysis of the impact mechanism of information platform on agro-product supply chain and agro-product competitiveness
  95. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  96. A real negative selection algorithm with evolutionary preference for anomaly detection
  97. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  98. A privacy-preserving parallel and homomorphic encryption scheme
  99. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  100. Random walk-based similarity measure method for patterns in complex object
  101. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  102. A Mathematical Study of Accessibility and Cohesion Degree in a High-Speed Rail Station Connected to an Urban Bus Transport Network
  103. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  104. Design and Simulation of the Integrated Navigation System based on Extended Kalman Filter
  105. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  106. Oil exploration oriented multi-sensor image fusion algorithm
  107. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  108. Analysis of Product Distribution Strategy in Digital Publishing Industry Based on Game-Theory
  109. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  110. Expanded Study on the accumulation effect of tourism under the constraint of structure
  111. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  112. Unstructured P2P Network Load Balance Strategy Based on Multilevel Partitioning of Hypergraph
  113. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  114. Research on the method of information system risk state estimation based on clustering particle filter
  115. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  116. Demand forecasting and information platform in tourism
  117. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  118. Physical-chemical properties studying of molecular structures via topological index calculating
  119. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  120. Local kernel nonparametric discriminant analysis for adaptive extraction of complex structures
  121. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  122. City traffic flow breakdown prediction based on fuzzy rough set
  123. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  124. Conservation laws for a strongly damped wave equation
  125. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  126. Blending type approximation by Stancu-Kantorovich operators based on Pólya-Eggenberger distribution
  127. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  128. Computing the Ediz eccentric connectivity index of discrete dynamic structures
  129. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  130. A discrete epidemic model for bovine Babesiosis disease and tick populations
  131. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  132. Study on maintaining formations during satellite formation flying based on SDRE and LQR
  133. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  134. Relationship between solitary pulmonary nodule lung cancer and CT image features based on gradual clustering
  135. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  136. A novel fast target tracking method for UAV aerial image
  137. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  138. Fuzzy comprehensive evaluation model of interuniversity collaborative learning based on network
  139. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  140. Conservation laws, classical symmetries and exact solutions of the generalized KdV-Burgers-Kuramoto equation
  141. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  142. After notes on self-similarity exponent for fractal structures
  143. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  144. Excitation probability and effective temperature in the stationary regime of conductivity for Coulomb Glasses
  145. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  146. Comparisons of feature extraction algorithm based on unmanned aerial vehicle image
  147. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  148. Research on identification method of heavy vehicle rollover based on hidden Markov model
  149. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  150. Classifying BCI signals from novice users with extreme learning machine
  151. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  152. Topics on data transmission problem in software definition network
  153. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  154. Statistical inferences with jointly type-II censored samples from two Pareto distributions
  155. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  156. Estimation for coefficient of variation of an extension of the exponential distribution under type-II censoring scheme
  157. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  158. Analysis on trust influencing factors and trust model from multiple perspectives of online Auction
  159. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  160. Coupling of two-phase flow in fractured-vuggy reservoir with filling medium
  161. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  162. Production decline type curves analysis of a finite conductivity fractured well in coalbed methane reservoirs
  163. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  164. Flow Characteristic and Heat Transfer for Non-Newtonian Nanofluid in Rectangular Microchannels with Teardrop Dimples/Protrusions
  165. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  166. The size prediction of potential inclusions embedded in the sub-surface of fused silica by damage morphology
  167. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  168. Research on carbonate reservoir interwell connectivity based on a modified diffusivity filter model
  169. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  170. The method of the spatial locating of macroscopic throats based-on the inversion of dynamic interwell connectivity
  171. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  172. Unsteady mixed convection flow through a permeable stretching flat surface with partial slip effects through MHD nanofluid using spectral relaxation method
  173. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  174. A volumetric ablation model of EPDM considering complex physicochemical process in porous structure of char layer
  175. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  176. Numerical simulation on ferrofluid flow in fractured porous media based on discrete-fracture model
  177. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  178. Macroscopic lattice Boltzmann model for heat and moisture transfer process with phase transformation in unsaturated porous media during freezing process
  179. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  180. Modelling of intermittent microwave convective drying: parameter sensitivity
  181. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  182. Simulating gas-water relative permeabilities for nanoscale porous media with interfacial effects
  183. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  184. Simulation of counter-current imbibition in water-wet fractured reservoirs based on discrete-fracture model
  185. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  186. Investigation effect of wettability and heterogeneity in water flooding and on microscopic residual oil distribution in tight sandstone cores with NMR technique
  187. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  188. Analytical modeling of coupled flow and geomechanics for vertical fractured well in tight gas reservoirs
  189. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  190. Special Issue: Ever New "Loopholes" in Bell’s Argument and Experimental Tests
  191. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  192. The ultimate loophole in Bell’s theorem: The inequality is identically satisfied by data sets composed of ±1′s assuming merely that they exist
  193. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  194. Erratum to: The ultimate loophole in Bell’s theorem: The inequality is identically satisfied by data sets composed of ±1′s assuming merely that they exist
  195. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  196. Rhetoric, logic, and experiment in the quantum nonlocality debate
  197. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  198. What If Quantum Theory Violates All Mathematics?
  199. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  200. Relativity, anomalies and objectivity loophole in recent tests of local realism
  201. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  202. The photon identification loophole in EPRB experiments: computer models with single-wing selection
  203. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  204. Bohr against Bell: complementarity versus nonlocality
  205. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  206. Is Einsteinian no-signalling violated in Bell tests?
  207. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  208. Bell’s “Theorem”: loopholes vs. conceptual flaws
  209. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  210. Nonrecurrence and Bell-like inequalities
  211. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  212. Three-dimensional computer models of electrospinning systems
  213. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  214. Electric field computation and measurements in the electroporation of inhomogeneous samples
  215. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  216. Modelling of magnetostriction of transformer magnetic core for vibration analysis
  217. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  218. Comparison of the fractional power motor with cores made of various magnetic materials
  219. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  220. Dynamics of the line-start reluctance motor with rotor made of SMC material
  221. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  222. Inhomogeneous dielectrics: conformal mapping and finite-element models
  223. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  224. Topology optimization of induction heating model using sequential linear programming based on move limit with adaptive relaxation
  225. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  226. Detection of inter-turn short-circuit at start-up of induction machine based on torque analysis
  227. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  228. Current superimposition variable flux reluctance motor with 8 salient poles
  229. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  230. Modelling axial vibration in windings of power transformers
  231. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  232. Field analysis & eddy current losses calculation in five-phase tubular actuator
  233. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  234. Hybrid excited claw pole generator with skewed and non-skewed permanent magnets
  235. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  236. Electromagnetic phenomena analysis in brushless DC motor with speed control using PWM method
  237. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  238. Field-circuit analysis and measurements of a single-phase self-excited induction generator
  239. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  240. A comparative analysis between classical and modified approach of description of the electrical machine windings by means of T0 method
  241. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  242. Field-based optimal-design of an electric motor: a new sensitivity formulation
  243. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  244. Application of the parametric proper generalized decomposition to the frequency-dependent calculation of the impedance of an AC line with rectangular conductors
  245. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  246. Virtual reality as a new trend in mechanical and electrical engineering education
  247. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  248. Holonomicity analysis of electromechanical systems
  249. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  250. An accurate reactive power control study in virtual flux droop control
  251. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  252. Localized probability of improvement for kriging based multi-objective optimization
  253. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  254. Research of influence of open-winding faults on properties of brushless permanent magnets motor
  255. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  256. Optimal design of the rotor geometry of line-start permanent magnet synchronous motor using the bat algorithm
  257. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  258. Model of depositing layer on cylindrical surface produced by induction-assisted laser cladding process
  259. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  260. Detection of inter-turn faults in transformer winding using the capacitor discharge method
  261. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  262. A novel hybrid genetic algorithm for optimal design of IPM machines for electric vehicle
  263. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  264. Lamination effects on a 3D model of the magnetic core of power transformers
  265. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  266. Detection of vertical disparity in three-dimensional visualizations
  267. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  268. Calculations of magnetic field in dynamo sheets taking into account their texture
  269. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  270. 3-dimensional computer model of electrospinning multicapillary unit used for electrostatic field analysis
  271. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  272. Optimization of wearable microwave antenna with simplified electromagnetic model of the human body
  273. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  274. Induction heating process of ferromagnetic filled carbon nanotubes based on 3-D model
  275. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  276. Speed control of an induction motor by 6-switched 3-level inverter
https://doi.org/10.1515/phys-2017-0016
Keywords for this article
Complex object; Random walk; Reachability; Similarity measure
Creative Commons
BY-NC-ND 3.0

Articles in the same Issue

  1. Regular Articles
  2. Analysis of a New Fractional Model for Damped Bergers’ Equation
  3. Regular Articles
  4. Optimal homotopy perturbation method for nonlinear differential equations governing MHD Jeffery-Hamel flow with heat transfer problem
  5. Regular Articles
  6. Semi- analytic numerical method for solution of time-space fractional heat and wave type equations with variable coefficients
  7. Regular Articles
  8. Investigation of a curve using Frenet frame in the lightlike cone
  9. Regular Articles
  10. Construction of complex networks from time series based on the cross correlation interval
  11. Regular Articles
  12. Nonlinear Schrödinger approach to European option pricing
  13. Regular Articles
  14. A modified cubic B-spline differential quadrature method for three-dimensional non-linear diffusion equations
  15. Regular Articles
  16. A new miniaturized negative-index meta-atom for tri-band applications
  17. Regular Articles
  18. Seismic stability of the survey areas of potential sites for the deep geological repository of the spent nuclear fuel
  19. Regular Articles
  20. Distributed containment control of heterogeneous fractional-order multi-agent systems with communication delays
  21. Regular Articles
  22. Sensitivity analysis and economic optimization studies of inverted five-spot gas cycling in gas condensate reservoir
  23. Regular Articles
  24. Quantum mechanics with geometric constraints of Friedmann type
  25. Regular Articles
  26. Modeling and Simulation for an 8 kW Three-Phase Grid-Connected Photo-Voltaic Power System
  27. Regular Articles
  28. Application of the optimal homotopy asymptotic method to nonlinear Bingham fluid dampers
  29. Regular Articles
  30. Analysis of Drude model using fractional derivatives without singular kernels
  31. Regular Articles
  32. An unsteady MHD Maxwell nanofluid flow with convective boundary conditions using spectral local linearization method
  33. Regular Articles
  34. New analytical solutions for conformable fractional PDEs arising in mathematical physics by exp-function method
  35. Regular Articles
  36. Quantum mechanical calculation of electron spin
  37. Regular Articles
  38. CO2 capture by polymeric membranes composed of hyper-branched polymers with dense poly(oxyethylene) comb and poly(amidoamine)
  39. Regular Articles
  40. Chain on a cone
  41. Regular Articles
  42. Multi-task feature learning by using trace norm regularization
  43. Regular Articles
  44. Superluminal tunneling of a relativistic half-integer spin particle through a potential barrier
  45. Regular Articles
  46. Neutrosophic triplet normed space
  47. Regular Articles
  48. Lie algebraic discussion for affinity based information diffusion in social networks
  49. Regular Articles
  50. Radiation dose and cancer risk estimates in helical CT for pulmonary tuberculosis infections
  51. Regular Articles
  52. A comparison study of steady-state vibrations with single fractional-order and distributed-order derivatives
  53. Regular Articles
  54. Some new remarks on MHD Jeffery-Hamel fluid flow problem
  55. Regular Articles
  56. Numerical investigation of magnetohydrodynamic slip flow of power-law nanofluid with temperature dependent viscosity and thermal conductivity over a permeable surface
  57. Regular Articles
  58. Charge conservation in a gravitational field in the scalar ether theory
  59. Regular Articles
  60. Measurement problem and local hidden variables with entangled photons
  61. Regular Articles
  62. Compression of hyper-spectral images using an accelerated nonnegative tensor decomposition
  63. Regular Articles
  64. Fabrication and application of coaxial polyvinyl alcohol/chitosan nanofiber membranes
  65. Regular Articles
  66. Calculating degree-based topological indices of dominating David derived networks
  67. Regular Articles
  68. The structure and conductivity of polyelectrolyte based on MEH-PPV and potassium iodide (KI) for dye-sensitized solar cells
  69. Regular Articles
  70. Chiral symmetry restoration and the critical end point in QCD
  71. Regular Articles
  72. Numerical solution for fractional Bratu’s initial value problem
  73. Regular Articles
  74. Structure and optical properties of TiO2 thin films deposited by ALD method
  75. Regular Articles
  76. Quadruple multi-wavelength conversion for access network scalability based on cross-phase modulation in an SOA-MZI
  77. Regular Articles
  78. Application of ANNs approach for wave-like and heat-like equations
  79. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  80. Study on node importance evaluation of the high-speed passenger traffic complex network based on the Structural Hole Theory
  81. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  82. A mathematical/physics model to measure the role of information and communication technology in some economies: the Chinese case
  83. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  84. Numerical modeling of the thermoelectric cooler with a complementary equation for heat circulation in air gaps
  85. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  86. On the libration collinear points in the restricted three – body problem
  87. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  88. Research on Critical Nodes Algorithm in Social Complex Networks
  89. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  90. A simulation based research on chance constrained programming in robust facility location problem
  91. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  92. A mathematical/physics carbon emission reduction strategy for building supply chain network based on carbon tax policy
  93. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  94. Mathematical analysis of the impact mechanism of information platform on agro-product supply chain and agro-product competitiveness
  95. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  96. A real negative selection algorithm with evolutionary preference for anomaly detection
  97. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  98. A privacy-preserving parallel and homomorphic encryption scheme
  99. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  100. Random walk-based similarity measure method for patterns in complex object
  101. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  102. A Mathematical Study of Accessibility and Cohesion Degree in a High-Speed Rail Station Connected to an Urban Bus Transport Network
  103. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  104. Design and Simulation of the Integrated Navigation System based on Extended Kalman Filter
  105. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  106. Oil exploration oriented multi-sensor image fusion algorithm
  107. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  108. Analysis of Product Distribution Strategy in Digital Publishing Industry Based on Game-Theory
  109. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  110. Expanded Study on the accumulation effect of tourism under the constraint of structure
  111. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  112. Unstructured P2P Network Load Balance Strategy Based on Multilevel Partitioning of Hypergraph
  113. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  114. Research on the method of information system risk state estimation based on clustering particle filter
  115. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  116. Demand forecasting and information platform in tourism
  117. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  118. Physical-chemical properties studying of molecular structures via topological index calculating
  119. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  120. Local kernel nonparametric discriminant analysis for adaptive extraction of complex structures
  121. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  122. City traffic flow breakdown prediction based on fuzzy rough set
  123. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  124. Conservation laws for a strongly damped wave equation
  125. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  126. Blending type approximation by Stancu-Kantorovich operators based on Pólya-Eggenberger distribution
  127. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  128. Computing the Ediz eccentric connectivity index of discrete dynamic structures
  129. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  130. A discrete epidemic model for bovine Babesiosis disease and tick populations
  131. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  132. Study on maintaining formations during satellite formation flying based on SDRE and LQR
  133. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  134. Relationship between solitary pulmonary nodule lung cancer and CT image features based on gradual clustering
  135. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  136. A novel fast target tracking method for UAV aerial image
  137. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  138. Fuzzy comprehensive evaluation model of interuniversity collaborative learning based on network
  139. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  140. Conservation laws, classical symmetries and exact solutions of the generalized KdV-Burgers-Kuramoto equation
  141. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  142. After notes on self-similarity exponent for fractal structures
  143. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  144. Excitation probability and effective temperature in the stationary regime of conductivity for Coulomb Glasses
  145. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  146. Comparisons of feature extraction algorithm based on unmanned aerial vehicle image
  147. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  148. Research on identification method of heavy vehicle rollover based on hidden Markov model
  149. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  150. Classifying BCI signals from novice users with extreme learning machine
  151. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  152. Topics on data transmission problem in software definition network
  153. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  154. Statistical inferences with jointly type-II censored samples from two Pareto distributions
  155. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  156. Estimation for coefficient of variation of an extension of the exponential distribution under type-II censoring scheme
  157. Special issue on Nonlinear Dynamics in General and Dynamical Systems in particular
  158. Analysis on trust influencing factors and trust model from multiple perspectives of online Auction
  159. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  160. Coupling of two-phase flow in fractured-vuggy reservoir with filling medium
  161. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  162. Production decline type curves analysis of a finite conductivity fractured well in coalbed methane reservoirs
  163. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  164. Flow Characteristic and Heat Transfer for Non-Newtonian Nanofluid in Rectangular Microchannels with Teardrop Dimples/Protrusions
  165. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  166. The size prediction of potential inclusions embedded in the sub-surface of fused silica by damage morphology
  167. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  168. Research on carbonate reservoir interwell connectivity based on a modified diffusivity filter model
  169. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  170. The method of the spatial locating of macroscopic throats based-on the inversion of dynamic interwell connectivity
  171. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  172. Unsteady mixed convection flow through a permeable stretching flat surface with partial slip effects through MHD nanofluid using spectral relaxation method
  173. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  174. A volumetric ablation model of EPDM considering complex physicochemical process in porous structure of char layer
  175. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  176. Numerical simulation on ferrofluid flow in fractured porous media based on discrete-fracture model
  177. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  178. Macroscopic lattice Boltzmann model for heat and moisture transfer process with phase transformation in unsaturated porous media during freezing process
  179. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  180. Modelling of intermittent microwave convective drying: parameter sensitivity
  181. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  182. Simulating gas-water relative permeabilities for nanoscale porous media with interfacial effects
  183. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  184. Simulation of counter-current imbibition in water-wet fractured reservoirs based on discrete-fracture model
  185. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  186. Investigation effect of wettability and heterogeneity in water flooding and on microscopic residual oil distribution in tight sandstone cores with NMR technique
  187. Special Issue on Advances on Modelling of Flowing and Transport in Porous Media
  188. Analytical modeling of coupled flow and geomechanics for vertical fractured well in tight gas reservoirs
  189. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  190. Special Issue: Ever New "Loopholes" in Bell’s Argument and Experimental Tests
  191. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  192. The ultimate loophole in Bell’s theorem: The inequality is identically satisfied by data sets composed of ±1′s assuming merely that they exist
  193. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  194. Erratum to: The ultimate loophole in Bell’s theorem: The inequality is identically satisfied by data sets composed of ±1′s assuming merely that they exist
  195. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  196. Rhetoric, logic, and experiment in the quantum nonlocality debate
  197. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  198. What If Quantum Theory Violates All Mathematics?
  199. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  200. Relativity, anomalies and objectivity loophole in recent tests of local realism
  201. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  202. The photon identification loophole in EPRB experiments: computer models with single-wing selection
  203. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  204. Bohr against Bell: complementarity versus nonlocality
  205. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  206. Is Einsteinian no-signalling violated in Bell tests?
  207. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  208. Bell’s “Theorem”: loopholes vs. conceptual flaws
  209. Special Issue on Ever-New "Loopholes" in Bell’s Argument and Experimental Tests
  210. Nonrecurrence and Bell-like inequalities
  211. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  212. Three-dimensional computer models of electrospinning systems
  213. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  214. Electric field computation and measurements in the electroporation of inhomogeneous samples
  215. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  216. Modelling of magnetostriction of transformer magnetic core for vibration analysis
  217. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  218. Comparison of the fractional power motor with cores made of various magnetic materials
  219. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  220. Dynamics of the line-start reluctance motor with rotor made of SMC material
  221. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  222. Inhomogeneous dielectrics: conformal mapping and finite-element models
  223. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  224. Topology optimization of induction heating model using sequential linear programming based on move limit with adaptive relaxation
  225. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  226. Detection of inter-turn short-circuit at start-up of induction machine based on torque analysis
  227. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  228. Current superimposition variable flux reluctance motor with 8 salient poles
  229. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  230. Modelling axial vibration in windings of power transformers
  231. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  232. Field analysis & eddy current losses calculation in five-phase tubular actuator
  233. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  234. Hybrid excited claw pole generator with skewed and non-skewed permanent magnets
  235. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  236. Electromagnetic phenomena analysis in brushless DC motor with speed control using PWM method
  237. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  238. Field-circuit analysis and measurements of a single-phase self-excited induction generator
  239. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  240. A comparative analysis between classical and modified approach of description of the electrical machine windings by means of T0 method
  241. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  242. Field-based optimal-design of an electric motor: a new sensitivity formulation
  243. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  244. Application of the parametric proper generalized decomposition to the frequency-dependent calculation of the impedance of an AC line with rectangular conductors
  245. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  246. Virtual reality as a new trend in mechanical and electrical engineering education
  247. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  248. Holonomicity analysis of electromechanical systems
  249. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  250. An accurate reactive power control study in virtual flux droop control
  251. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  252. Localized probability of improvement for kriging based multi-objective optimization
  253. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  254. Research of influence of open-winding faults on properties of brushless permanent magnets motor
  255. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  256. Optimal design of the rotor geometry of line-start permanent magnet synchronous motor using the bat algorithm
  257. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  258. Model of depositing layer on cylindrical surface produced by induction-assisted laser cladding process
  259. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  260. Detection of inter-turn faults in transformer winding using the capacitor discharge method
  261. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  262. A novel hybrid genetic algorithm for optimal design of IPM machines for electric vehicle
  263. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  264. Lamination effects on a 3D model of the magnetic core of power transformers
  265. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  266. Detection of vertical disparity in three-dimensional visualizations
  267. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  268. Calculations of magnetic field in dynamo sheets taking into account their texture
  269. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  270. 3-dimensional computer model of electrospinning multicapillary unit used for electrostatic field analysis
  271. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  272. Optimization of wearable microwave antenna with simplified electromagnetic model of the human body
  273. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  274. Induction heating process of ferromagnetic filled carbon nanotubes based on 3-D model
  275. Special Issue: The 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering ISEF 2017
  276. Speed control of an induction motor by 6-switched 3-level inverter
Sign up now to receive a 20% welcome discount
Institutional Access
How does access work?
Have an idea on how to improve our website?
Please write us.
© 2025 De Gruyter Brill
Downloaded on 8.9.2025 from https://www.degruyterbrill.com/document/doi/10.1515/phys-2017-0016/html
Scroll to top button