Haruna Chiroma

Sameem Abdulkareem
email: sameem@um.edu.my

Adamu I Abubakar

Eka Novita Sari

Tutut Herawan

Abdulsalam Ya'u Gital

Hybridization of Haar Wavelet Decomposition and Computational Intelligent Algorithms for the Estimation of Climate Change Behavior

Keywords: Haar Wavelet Decomposition, Relevance Vector Machine, Adaptive Linear Neural Network, Climate Change

We propose a hybrid of haar wavelet decomposition, relevance vector machine, and adaptive linear neural network (HWD-RVMALNN) for the estimation of climate change behavior. The HWD-RVMALNN is able to improve estimation accuracy of climate change more than the approaches already discussed in the literature. Comparative simulation results show that the HWD-RVMALNN outperforms cyclical weight/bias rule, Levenberg-Marquardt, resilient back-propagation, support vector machine, and learning vector quantization neural networks in both estimation accuracy and computational efficiency. The model proposes in this study can provide future knowledge of climate change behavior. The future climate change behavior can be used by policy makers in formulating policies that can drastically reduce the negative impact of climate change, and be alert on possible consequences expected to occur in the future.

Introduction

In the last ten [START_REF] Hardle | Wavelets, Approximation, and Statistical Applications[END_REF] to fifteen (15) years, the greater portion of the world experiences an unprecedented change in the temperature of sea water. For instance, the ice covering the Arctic is dramatically vanishing; the glaciers and green ice cap are observed to be significantly melting; reduction in the volume of Antarctic ice sheets; unusual increase of sea level, and the seas are getting stormier; upsurge in the intensity, and frequency of rainfall due to precipitation variability; earlier occurrence of springtime, and high intensity of hurricane [START_REF] Hoegh-Guldberg | The impact of climate change on the world's marine ecosystems[END_REF]. In addition, the world is experiencing an extraordinary warming. These changes experience throughout the globe are consequences of the climate change [START_REF] Belkin | Rapid warming of Large Marine Ecosystems[END_REF]. There is a growing report of numerous natural disasters triggered by climate change [START_REF] Hans | Proactive systems for early warning of potential impacts of natural disasters on food safety: Climate-change-induced extreme events as case in point[END_REF]. Therefore, the future knowledge of climate change is required for proper planning in order avoid the negative impact of natural disasters expect to be caused by the behavior of climate change. In the literature, several studies have been conducted using neural networks to predict climate change. For example, [START_REF] Matouqa | The climate change implication on Jordan: A case study using GIS and Artificial Neural Networks for weather forecasting[END_REF] proposed a neural network to build a model for predicting weather in Jordan. Goyal et al. [START_REF] Goyal | Statistical downscaling of temperatures under climate change scenarios for Thames river basin[END_REF] uses neural network to develop a downscaled model for predicting maximum and minimum temperature across 14 stations in Upper Thames River Basin Ontario, Canada. Holmberg et al. [START_REF] Holmberg | An application of artificial neural networks to carbon, nitrogen and phosphorus concentrations in three boreal streams and impacts of climate change[END_REF] proposed neural network to model the concentration of organic carbon, Nitrogen and phosphorus in a runoff stream water collected from Finland. The model is then used to predict future fluxes under climatic change. Tripathi [START_REF] Tripathi | Nanjundiah Downscaling of precipitation for climate change scenarios: A support vector machine approach[END_REF] applied support vector machine (SVM) for statistical downscaling of precipitation. Subsequently, the SVM model is used to predict future climate changes in India. The results obtained from the SVM model was compared to the neural network and it was found that the SVM model performs better than the neural network. However, the studies are limited to the region where the research data were conducted. The studies in the literature for predicting climate change using computational intelligent techniques, mainly focus on individual intelligent technique (IITs) whereas it is well known that hybrid intelligent technique is superior to the IITs when properly design. Hybrid techniques capitalized on their strengths to eliminate their weaknesses to build a synergistic model for effective prediction. Haar wavelet decomposition (HWD) has the ability to project data into time scale domain, and perform multi scale analysis to unveil useful hidden patterns in the historical data [START_REF] Jammazi | Crude oil forecasting: experimental evidence from wavelet decomposition and neural network modeling[END_REF]. The sensitivity of the relevance vector machine (RVM) to parameters is less compared to the SVM, and RVM is faster than SVM [START_REF] Demir | Hyperspectral image classification using relevance vector machines[END_REF]. We propose to apply RVM to different scales coefficients produce by HWD to predict global climate change in order to reduce estimation bias that might be introduced by the HWD. Adaptive linear neural network (ALNN) will be used to ensemble the results produce by each RVMs to produce more accurate ensemble result than the results produce by individual RVMs. We intend to investigate whether the propose hybrid of HWD, RVM and ALNN can yield superior novel results than the approaches in the literature.

Essential Rudiments

Haar Wavelet Decomposition

The HWD can be considered on the basis of the real line ) (IR [START_REF] Hardle | Wavelets, Approximation, and Statistical Applications[END_REF]: Let consider

) ( 2 IR L
to be the space of complex value function

) ( f on IR in such a way that                dx x f f 2 ) ( . (1)
Eq. ( 1) is donated with scalar product, as such we have

       . ) ( ) ( , dx x g x f g f f (2)
where the complex conjugate of ) (x g is given by

) (x g . If 0 ) , (  g f then ) ( , 2 IR L g f 
can be definedl to each other, the functions can be define as

  ). ( , , 2 IR L k k k      (3)
Eq. ( 3) is referred to as an orthonormal system if Eq. ( 4) is satisfied

. ) ( ) ( jk j k dx x x      (4) where jk  and     k k ,



are Kronecker delta, and orthonormal basis in a subspace

V of ) ( 2 IR L if any function V f  has a depiction   ). ( ) ( x C x f k k  (5) The coefficient satisfy    k k C 2                  k k . , , ... 1 , 0 , 1 ..., (6)
The subspace

o V of ) ( 2 IR L is define as  f IR L f V o : ) ( , 2   which is constant on     k k k ], 1 , ( , therefore      ) ( ) ( 0 k x C x f V f k , (7)
where

   k k C 2
, the series converges in Eqs. ( 8) and ( 9)

) ( 2 IR L , (8)
                 1 , 0 , 1 1 , 0 , 0 1 , 0 ( ) ( x x x I x  , (9)
where

    k k x x ok ), ( ) (   in which   ok  is the orthonormal basis in o V , as such a new linear subspace of ) ( 2 IR L is defined as   o V f x f x h V    : ) 2 ( ) ( 1 , (10)
comprises of all functions in ) ( 2 IR L that are constant within the intervals of

         k k k , 2 1 , 2 . The 1 V V o  , orthonormal basis in 1 V is given by   k 1  where . ), 2 ( 2 ) ( 1     k k x x k  
This process continues and the space is generally defined as  .

: ) 2 ( ) ( o j j V f x f x h V    (11)
The

j V is a linear subspace of ) ( 2 IR L
with the orthonormal basis in Eqs. ( 12) and ( 13)

    k k x x j j jk ), 2 ( 2 ) ( 2   . ( 12
) ... ... 1     j o V V V ( 13
)
In a similar manner we define

j V for    j j , 0
to get the inclusions ... ...

1 1      V V V o ( 14
)
The process is infinitely continued until the entire space ) ( 2 IR L is approximated. The orthogonal sum decomposition of j V is expressed as

j j o w V IR L     0 2 ) ( (15)
where

j j j V V w   1 which is the orthogonal complement of j V in 1  j V . Eq. (15) indicates that each ) ( 2 IR L f  can be represented as series in the form        0 ) ( ) ( ) ( j k jk jk ok ok x x x f    (16)
where , ,

Adaptive Linear Neural Network

The ALNN can mathematically be defined as [START_REF] Hagan | Neural Network Design[END_REF]:

      m i i i b x w x f 1 ) (  . ( 17
           N j N j j j j x p x T x e N MSE 1 1 2 2 ) ( ) ( 2
1 ) ( 1 , (18)
where ), ( ), ( , x T x e N j j and ) (x p j are number of data points in the samples, error, target output, and network output. An adaptation of the weights and bias for multiple neurons can be defined as

). ( ) ( 2 ) ( ) 1 ( x T x e x w x w T     (19)
) ( 2 ) ( ) 1 ( x e x b x b     , ( 20
)
where  is the learning rate.

Relevance Vector Machine

The RVM is typically used for solving classification and regression problems. In this study, we present regression relevance vector machine algorithm for our problem is a

regression. Let   N i i i t X 1
,  be input-dethe datasetutput pairs of dataset. Each desired output i t assumed a normal distribution with mean ) ( i x y and uniform variance 2  of the noise  define as

) ), ( / ( ) / ( 2  x y t N x t p  (21)
The desired output is also assumed joint normal distribution expressed as  

 ,  N ,
where  and  are unknown variables which can be determined by the RVM [START_REF] Tipping | Sparse Bayesian learning and the relevance vector machine[END_REF].

Experiments

Dataset

The global annual land-ocean temperature (GLOT) is chosen as the indicator of the climate change behavior because it significantly determines climate change more than other indicators such as atmospheric temperature, heat emanating from the sun, among others [START_REF] Richardson | Climate change: Global Risk, Challenges & decisions. The United Nations Framework on Climate Change Synthesis Report[END_REF]. The GLOT data are provided in degrees Celsius (degree C) extracted from the National Aeronautic and Space Administration (NASA) website (www.nasa.gov), Goddard Institute for Space, for a period from 1880 to 2012 on a yearly basis. The GLOT data is a global data that is not restricted to a particular region, and were not normalized as the data are already provided in approximately equal proportion within -1 to 1.

The Propose Ensemble HWD-RVMALNN Framework

The propose ensemble HWD-RVMALNN paradigm is in the flowchart illustrated in Fig. 1. The major components of the entire process composed of the following stages: The original GLOT time series data are decomposed using HWD into five scale coefficient. For each of the scale coefficient, the RVM is employed as an estimation technique to model the decomposed scale coefficient and estimate for each of the five scale coefficient. The estimation results produce by each of the RVMs (HWD-RVM1, HWD-RVM2, HWD-RVM3, HWD-RVM4, and HWD-RVM5) is integrated by ALNN to generate an ensemble estimate of the GLOT which can be viewed as the estimation result of the original GLOT time series data. The optimal parameters of RVM were obtained through initial experimentation. The methodology can be summarized as a hybrid ensemble approach comprising of HWD (Decomposition) -RVM (estimate) -ALNN (ensemble) referred to HWD-RVMALNN. To verify the effectiveness of the our approach, we compared the proposed HWD-RVMALNN with the popular approaches of prediction such as Levenberg-Marquardt (LMQ), resilient backpropagation (RBP), Cyclical weight/bias rule (CWB), learning vector quantization (LVQ), and SVM. These algorithms are used as the benchmarks since they are the popular approaches in the literature for the estimation of climate change, readers can refer to [START_REF] Matouqa | The climate change implication on Jordan: A case study using GIS and Artificial Neural Networks for weather forecasting[END_REF][START_REF] Goyal | Statistical downscaling of temperatures under climate change scenarios for Thames river basin[END_REF][START_REF] Holmberg | An application of artificial neural networks to carbon, nitrogen and phosphorus concentrations in three boreal streams and impacts of climate change[END_REF] for details. The algorithms are also applied to estimate the GLOT for the purpose of comparing with the results generated by our proposal. The decomposition contributed to an understanding of the time varying patterns in the GLOT data. Some useful information is revealed from the analysis, and interpretation of the GLOT data. The original GLOT data (Figure 2) and the extracted portion (Figure 3) is in degree Celsius. It is clear shown in Table 1 that the algorithms compared with our approach estimated GLOT with a good degree of accuracy as suggested by the simulated results. The SVM performs better than the LM, CBW, RBF, and LVQ in terms of R 2 , MSE and MAE. The results corroborate with the study conducted by [START_REF] Tripathi | Nanjundiah Downscaling of precipitation for climate change scenarios: A support vector machine approach[END_REF]. The possible reason for this performance exhibited by SVM could be attributed to the use of support vectors by the SVM due to its ability to improve performance. The worst performance exhibited by LVQ in terms of R 2 which is merely random could likely be caused by the non-zero differentiability of the LVQ. The runtime of LM and LVQ outperform SVM, CBW, and RBP in terms of computational speed. The poorest convergence speed is observed to be exhibited by the CBW. The likely cause of this poor convergence can best be attributed to the cyclical nature of the CBW to present inputs to the network which might have caused the delay. An algorithm that converges to the optimal solution within the shortest time is considered the most efficient. The propose HWD-RVMALNN as reported in Table 1 based on the performance metrics was able to improve on the performance of the approaches typically use in the estimation of climate change in the literature. They propose an approach performs better than the commonly used approaches in both accuracy and computational efficiency. The likely reason for the performance of HWD-RVMALNN could be attributed to the fact that the results of several experts are ensemble to produce superior output. Estimates of GLOT obtained from simulating the propose ensemble HWD-RVMALNN on the independent test dataset is plotted in Figure 5.

Conclusion

In this research, a hybrid of wavelet transform and computational intelligent algorithms has been proposed for the estimation of climate change behavior. Specifically HWD, RVM, and ALNN were hybridized to propose ensemble HWD-RVMALNN. A series of comparative simulations were performed and it was found that the propose HWD-RVMALNN performs better in both accuracy and computational speed. The propose HWD-RVMALNN can provide better understanding of the future knowledge of climate change behavior than the methods already proposed in the literature. The model can assist policy makers in formulating global response policy in tackling the negative impact espected to be cause by the behavior of climate change. We intend to further this research by developing the real life application of the propose HWD-RVMALNN model to help climate change experts and policy makers in the decision making process.



  are representation of coefficients of the expansion.

Fig. 1 .

 1 Fig. 1. The propose ensemble HWD-RVMALNN framework

Fig. 2 .Fig. 3 .Fig. 4 .

 234 Fig. 2. The original signal of the GLOT

Fig. 5 .

 5 Fig. 5. Performance of the propose HWD-RVMALNN on the test dataset

  , weights, number of input neurons, and activation function for computation in the ALNN neurons. The architecture of the ALNN comprised of only one layer. The activation function and learning algorithm are pure linear and Widrow-Hoff, respectively. The learning algorithm minimizes mean square error (MSE) to optimized weights and bias as defined in Eq. (18)

																		)
	where	x	( i		..., 3 , 2 , 1	), n	f	(	), x	, b	w	( i		,..., 3 , 2 , 1	), n	, m	and	) (  are the input variables,
		i									i
	output, bias

Table 1 .

 1 Performance metrics of the algorithms compared with the propose ensemble HWD-RVMALNN

	Algorithm	MSE	MAE	SSE	R 2	RT(sec.)
	LMQ	0.00413	0.0071	0.422	0.7047	2
	CBW	0.00828	0.01923	0.51193	0.87268	932
	RBP	0.015	0.0788	1.14	0.7932	3
	SVM	0.002911	0.019884	0.195	0.88626	5
	LVQ	0.091	0.234	8.07	0	2
	HWD-RVMALNN	0.00081	0.00721	0.00916	0.93087	0
	Mean absolute error (MAE), Sum of square error (SSE), Runtime (RT)

Acknowledgments. This work is supported by University of Malaya High Impact Research Grant no vote UM.C/625/HIR/MOHE/SC/13/2 from Ministry of Higher Education Malaysia.


Younes Saadi
email: younessaadi@gmail.com

Eka Novita

Tutut Herawan

An Improved Ant Colony Matching by using Discrete Curve Evolution

Keywords: Ant Colony Optimization, Quadratic assignment problem, Discrete curve evolution, Contour matching

In this paper we present an improved Ant Colony Optimization (ACO) for contour matching, which can be used to match 2D shapes. Discrete Curve Evolution (DCE) technique is used to simplify the extracted contour. In order to find the best correspondence between shapes, the match process is formulated as a Quadratic Assignment Problem (QAP) and resolved by using Ant Colony Optimization (ACO). The experimental results justify that Discrete Curve Evolution (DCE) performs better than the previous Constant Sampling (CS) technique which has been selected for the ACO matching.

Introduction

Nowadays, shape analysis has become an important topic in computer vision. It has been widely adopted in many applications of computer graphics. In particular, shape matching one of the fundamental techniques of shape analysis. It plays a primordial role in shape retrieval, recognition and classification, and medical registration [START_REF] Tsapanos | Shape matching using a binary search tree structure of weak classifiers[END_REF]. Shape matching has reached a state of maturity in which many real products based on shape matching are commercialized in different areas [START_REF] Aaron | Characterizing complex particle morphologies through shape matching: descriptors, applications, and algorithms[END_REF]. In the commercial domain, shape matching methods are being used to retrieve and classify images, for personal and institutional needs like security and military. In the medical domain, shape matching is used in radiology to diagnose and to assess medical images to determine the progress and the suitable treatment options. Shape matching is application dependent. Different applications may have different requirements on invariance and tolerance to noise, distortion, blur, transformation, scale and orientation. Thus, it is difficult to design a universal method which is suitable for all applications. Nowadays, many techniques have been proposed but most of them only focus on the applications where shape is invariant to transformation.

Based on the representation techniques, shape matching techniques can be classified into two categories: contour based matching and region based matching [START_REF] Luciano | Shape Classification and Analysis: Theory and Practice[END_REF]. This research is focusing on contour based matching techniques, in which only the information located on the shape contour is explored. Majority of the past researches have concentrated on how to achieve a meaningful correspondence. On the other hand, some researches focused on improving representation methods of a contour in such a way that the resulted contour could be used to extract meaningful information. This is called simplification, evolution or smoothing in some sources [START_REF] Luciano | Shape Classification and Analysis: Theory and Practice[END_REF] [4] [START_REF] Parvez | Polygonal approximation of digital planar curves through adaptive optimizations[END_REF] [6] [START_REF] Parvez | Polygonal Approximation of Planar Curves Using Triangular Suppression[END_REF].

However, challenges still remain. The first challenge is the invariance [8] [9]. Since shape in many applications is often discussed based on the property of invariance, shape matching is expected to be invariant to transformations such as example translation, scale and orientation. The second challenge is tolerance as noise, blur, crack and deformation are usually introduced when the shape of an object is extracted from an image [START_REF] Li | 3D Organic Shape Correspondence Using Spherical Conformal Mapping[END_REF]. In this case, a shape matching is required to be robust to these imperfections.

Moreover, in contour based matching, the points along the contours as a bipartite graph can be figured out and formulated as a QA. This is considered as an NP-hard problem [START_REF] Ruberto | ACO contour matching: a dominant point approach[END_REF]. In order to find an acceptable solution, heuristic1s techniques are often used. The main idea is to compute the mapping between two contours by minimizing the global dissimilarity. Many research studies have been proposed. For example, Hungarian method uses the simple greedy matching [START_REF] Papadimitriou | Combinatorial Optimization: Algorithms and Complexity[END_REF], and COPAP [START_REF] Scott | Robust contour matching via the order-preserving assignment problem[END_REF] takes into account the order preserving. However, the main drawback of these techniques is the omission of proximity information measurement between feature points on the same shape contour. For this reason, Kaick [START_REF] Kaick | Contour CorrespondenceVia Ant Colony Optimization[END_REF] proposed an Ant Colony Optimization (ACO) approach based on incorporating proximity into an optimization framework. However, the huge number of points incorporated in the correspondence makes the matching more complex and less accurate [START_REF] Ruberto | ACO contour matching: a dominant point approach[END_REF]. A modified ACO matching approach has been proposed by Ruberto and Morgera [START_REF] Ruberto | ACO contour matching: a dominant point approach[END_REF] based on genetic algorithm; only dominant points are used instead of the sampling distribution of contour points, which improves the correspondence accuracy and reduces the complexity.

Generally, speaking a heuristic is a method that achieves good (but not necessarily optimal) results at low expense. However, which results are to be considered good heavily depends on the application at hand. Analysing contour matching we can figure out the points along the contour as a bipartite graph, which can be formulated as a Quadratic Assignment (QA). This is one of the NP-hard problems [START_REF] Zhu | Shape Matching Based on Ant Colony Optimization[END_REF]. Finding an optimal solution for such problem seems difficult by using conventional methods. Heuristics methods are used to find an acceptable solution for such cases.

It is important to mention the Hungarian method as one of the well-studied methods in this context. In fact it is based on solving the complexity which is a part of the combinatorial optimization solved by using Iterative Closest Point (ICP) scheme [START_REF] Rusinkiewicz | Efficient Variants of the ICP Algorithm.3-D Digital Imaging and Modeling[END_REF]. Following the requirements of the applications, many versions of heuristics approaches have been proposed. A review about correspondence introduced in [START_REF] Kaick | A survey on shape correspondence[END_REF] shows clearly the importance of heuristic methods to solve complexity related to shape matching issues.

In this paper, an improved ACO matching approach based on Discrete Curve Evolution (DCE) was proposed. In order to reduce the number of contour points incorporated in the correspondence, a polygonal approximation proposed previously by Latecki and Lakamper [START_REF] Latecki | Shape Similarity Measure Based on correspondence of visual parts[END_REF] was selected to simplify the extracted contour. Mainly, it simplifies the contour by neglecting distortions while at the same time preserving the perceptual appearance at a level sufficient for object recognition. To test the effectiveness of our approach, an MPEG-7 subset described by Ruberto and Morgera [START_REF] Ruberto | ACO contour matching: a dominant point approach[END_REF] was used to test shape retrieval considering noise and distortions effect. The results were also compared with the previous work of ACO matching by Ruberto and Morgera [START_REF] Ruberto | ACO contour matching: a dominant point approach[END_REF].

Proposed Method

The structure of the proposed method is shown in (Fig. 1). It operates into four stages. In the first stage the contour is traced by using a basic Matlab function. In the second stage the extracted contours are approximated by using Discrete Curve Evolution (DCE) which is proposed previously by Latecki and Lakamper [START_REF] Latecki | Shape Similarity Measure Based on correspondence of visual parts[END_REF]. After that, Ant Colony Optimization proposed previously [START_REF] Kaick | Contour CorrespondenceVia Ant Colony Optimization[END_REF] is used to compute the correspondence in the third stage. Finally in the fourth stage, the Euclidean distance has been selected to compute the dissimilarity between shapes according to the resulted matrix of correspondence. After analyzed the shortcoming of polygonal evolution methods, discrete curve evolution [START_REF] Latecki | Shape Similarity Measure Based on correspondence of visual parts[END_REF] has been selected to be used in our approach (See Figures 2, 3, and4). The main reason is that this method allows the user to control the degree of evolution according to the human judgment. In every iteration, a pair of consecutive line segments s1, s2 is replaced with a single line related to the endpoints of U . The substitution is calculated according to the relevance value K given by the following equation:

K( , ) = ( ) ( ) ( ) ( ) ( ) . ( 1
)
( ) is the turn angle at the common vertex between s 1 and s 2 . is the length function normalized with respect to the total length of a polygonal curve C. A new matching algorithm based on ant colony optimization is described previously [START_REF] Kaick | Contour CorrespondenceVia Ant Colony Optimization[END_REF]. It consists of taking in consideration the proximity measured between feature points on the same shape (Fig. 5). The matching is formulated as a two sets of points I and J where the ants cross these two sets doing a complete tour. All the movements produce a collection of possible paths between the two sets. During building of these paths Ants release the pheromone with different amounts for each possible path. A bigger amount of pheromone on a path means that it is more eligible in term of cost of correspondence. The traversing from a vertex to a vertex is given by the equation below [START_REF] Ruberto | ACO contour matching: a dominant point approach[END_REF].

Edge Probability

( ) ∑ , ( ) - (2)
The pheromone accumulated on the edge ( ) is quantified by , indicates the desirability (or probability) of traversing ( ) based on heuristic information, * ( ) + is the immediate neighbourhood of vertex . The parameter regulates the influence of pheromones over heuristic information. After a complete tour of the ants, an ACO iteration, the cost of solutions is computed as defined in second. Pheromones are updated at the end of ACO iteration. First, pheromones are evaporated at n constant pheromone rate [START_REF] Ruberto | ACO contour matching: a dominant point approach[END_REF] .

) 3
where is the pheromone evaporation rate and the new pheromone deposition on the edges that were traversed by the ants is regulated by pheromone deposition:

∑ , ( 4
)
where is the amount of pheromone that an ant has deposited on the edge ( ).

Cost Function

The formulation of the problem is done by a QAP. When augmenting the shape descriptor R with proximity information. The general objective function is in the form:

( ) ( -) ( ) ( ), (5)
where is used to control parameter between S and the proximity and the arguments I, J represents the two points sets, a mapping such that to a pint of I correspondents a point in J and R the set of shape descriptors. The form S and is detailed in [START_REF] Ruberto | ACO contour matching: a dominant point approach[END_REF].

Input data: Query shape and stored shapes: An ordered set of shape contours. Output data: Matrix of dissimilarity between the query shapes and all the stored shapes 1. for = 1 to M do {M number of query shapes} 2. Read a query shape 3.

Contour tracing of shape 4.

Apply DCE 5. end for 6. for = 1 to N do {N number of stored shapes} 7.

Read a stored shape 8.

Contour tracing of shape 9.

Apply DCE 10. End for 11. for = 1 to M do 12.

for = 1 to N do 13. Compute the best correspondence between and contours 14. Compute the degree of dissimilarity 14. end for 15. for each class sort the dissimilarity degree of each pairwise (query-stored)ascending where the first retrieved is the one with a min value.

Experimental Results

In order to test the effectiveness of our approach, which is based on DCE and ACO matching, an MPEG-7 subset (Fig. 6) is used to test shape retrieval and contour matching issues [START_REF] Ruberto | ACO contour matching: a dominant point approach[END_REF]. The database constitutes of 18 classes, each class contains 11 items plus 18 query shapes selected from each class. Basically this database assesses universal measures that are translation rotation and scaling invariant. However, in our scope we are not interested in rotation since we are using the classic shape context as a shape descriptor. For this reason we are using a set of parameters consist of 1 as number of ants and 100 as number of iterations each ants make in optimization process. The experiment is executed on a Matlab environment (Windows 32 OS) running on Intel Pentium 2.2 GHz. As stated in section 2, DCE reduce the number of points located on the contour. After the evolution, ACO is convoked to establish best possible correspondence between the approximated contours.

We compared our approach to retrieval similar objects by using Constant Sampling points (CS) [START_REF] Ruberto | ACO contour matching: a dominant point approach[END_REF]. It is important to mention that comparison is not possible with Dominant Points (DP) approach proposed by Ruberto and Morgera since it is based on rotational descriptor, which is not the case of our research. Table 1 shows the accuracy rate for each class of our method compared to the CS approach. In Table 1 we show the experiments made to MPEG-7 subset with CS and the proposed method. Table 1 also introduces a comparison with 18 classes for both CS and the proposed method.

It is important to notice the highly performance affected by DCE compared to CS as a result of the lower number of points incorporated in the matching. There is dependence between lower accuracy and the smoothing of the contour. However th distribution of dominant points along the contour plays an important role to preserve the orig-inal frame of the shape and thus increasing the matching accuracy. The results obtained with classes 5 and 7 as shown in Table 1 by constant points CS is due to the nature of CS simplification.

Although the descriptor used in our approach is not invariant to rotation, the global average shows that our method performs better than CS. Thus the advantage of incorporating DCE and proximity using ACO is demonstrated.

Conclusion

In this study, an improved ACO matching algorithm based on curve evolution has been introduced. The main challenge to the contour matching was to find the best correspondence between the huge numbers of points along the contours incorporated in the matching. Whenever the number of points participated in the matching increased, the complexity of matching also increased which directly affected the performance of the matching process. A solution based on dominant points has been proposed by Ruberto and Morgera [START_REF] Ruberto | ACO contour matching: a dominant point approach[END_REF]. The obtained results showed the efficiency of our approach. This research produced an improved ACO matching based on curve evolution. Before starting matching, a proposed DCE was applied in order to simplify the shape contour. This reduced the contour points incorporated along the contour. The DCE algorithmcan be personalized according to the number of iterations required. The iterations can be predefined to approximate the shape contour. Instead of the original ACO, the improved ACO matching as shown to be more accurate although the used descriptor is not invariant to rotation. This does not mean, that heuristics methods might be useful for all matching applications, but the applicability of such methods is only related to: firstly, the domain of application for example sometimes in image registration it is enough to get an approximated matching to obtain the abnormalities. Secondly the applicability depends the requirements of the matching for example in some cases considering proximity between the points along the contour is compulsory which allow the usage of heuristic methods as a key for the solution.

Fig. 1 .

 1 Fig. 1. Method structure

Fig. 2 .Fig. 3 . 4 .

 234 Fig. 2. A series of polygonal evolution

Fig. 5 .

 5 Fig. 5.ACO matching before DCE2.2 Pheromone Evaporation

Fig. 6 .

 6 Fig.6. MPEG-7 dataset[START_REF] Kolesnikov | ISE-bounded polygonal approximation of digital curves[END_REF]

Table 1 .

 1 Retrieval rates of different MPEG-7 CE-Shape-1 Part B data set[START_REF] Ruberto | ACO contour matching: a dominant point approach[END_REF]

		Class	Proposed	CS
			Method
		1	0.9166	0.6909
		2	1.0000	0.9273
		3	0.9166	0.8818
		4	0.8333	0.7273
	class	5	0.9166	0.9909
	each	6 7	1.0000 0.9266	1.0000 0.9909
	for	8	0.9100	0.8818
	accuracy Average	9 10 11 12 13	1.0000 1.0000 0.9166 1.0000 0.5000	0.9727 0.9455 1.0000 1.0000 0.6818
		14	1.0000	1.0000

Acknowledgments. This work is supported by University of Malaya High Impact Research Grant no vote UM.C/625/HIR/MOHE/SC/13/2 from Ministry of Higher Education Malaysia.


Haruna Chiroma

Sameem Abdulkareem

Eka Adamu I Abubakar

Novita Sari

Tutut Herawan

Eka Novita Sari

A Novel Approach to Gasoline Price Forecasting Based on Karhunen-Loève Transform and Network for Vector Quantization with Voronoid Polyhedral

Keywords: Vector quantization, Gasoline price, Karhunen-Loève Transform

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Gasoline is obtained from the refining of crude oil through a process called fractional distillation. The gasoline is highly utilized by the general public for daily activities. Shortage of gasoline can inflict pain on communities, especially in US where long queues of vehicles were typically experienced when the gasoline is scarce. Similarly, the shortage of gasoline causes cuts in motoring, reduction of work weeks, and threats of job cuts in automobile industries [START_REF] Hamilton | Historical oil shocks[END_REF]. Forecasting that is of low quality contributes to poor or inadequate investment which in turn might result in losses in welfare.

When forecasting is bias, it makes investors not to make a cost effective investment in the energy efficiency [START_REF] Anderson | Forecasting Gasoline Prices Using Consumer Surveys[END_REF]. There are studies in the literature that forecast gasoline price in order to provide advance knowledge of the price so that its negative impact can be reduced successfully. For example, asymmetric and symmetric models were applied to build a model for the forecasting of the gasoline price. It was found that the regression results emanated from the study suggested asymmetric model performs better than the symmetric in out of sample forecast accuracy [START_REF] Deltas | Retail gasoline price dynamics and local market power[END_REF]. The linear trend correlation error was used to build a model for the forecasting of gasoline price [START_REF] Borenstein | Do gasoline prices respond asymmetrically to crude oil price change?[END_REF]. Similarly, Autoregressive Integrated Moving Average (ARIMA) was used for the forecasting of gasoline price by [START_REF] Chinn | The predictive of energy futures: An update on petroleum, natural gas, heating oil and gasoline[END_REF]. Anderson et al. [START_REF] Anderson | Forecasting Gasoline Prices Using Consumer Surveys[END_REF] used the Michigan Consumers Survey data to forecast the price of Gasoline. The results indicated that the forecast accuracy outperform the Econometrics Auto Regressive Moving Average (ARMA). The studies in the literature mainly focus on statistics and econometric models for the forecasting of the gasoline price. However, those models assume linear distribution for input data, whereas gasoline price is nonlinear and volatile. Therefore, those models cannot provide effective solution to the problem of gasoline price forecasting. In addition, experimental evidence documented in the literature shows that artificial intelligence techniques such as neural network, fuzzy logic, expert systems, Genetic algorithms provide better solution for forecasting than statistical and econometric models. Though, there are very few instances in which statistical tools perform better the artificial intelligence methodologies [START_REF] Bahrammirzaee | comparative survey of artificial intelligence applications in finance: artificial neural networks, expert system and hybrid intelligent systems[END_REF]. Despite the significance of gasoline price, we have not found a reference in the literature that investigates the forecast of gasoline prices using artificial intelligence techniques. In this paper, we propose to forecast the price of gasoline based on the network for vector quantization with Voronoid Polyhedral, and Karhunen-Loève Transform (KL) to select the most relevant inputs and eliminate the irrelevant attributes to improve forecast accuracy. The rest of this paper is organized as follows. Section 2 describes the theoretical background of the study. Section 3 describes the experimentations. Section 4 describes results and discussion. Finally the conclusion of this work is described in Section 5.

Theoretical Background of the Study

Karhunen-Loève Transform

Suppose that the vector Y is for random variables V and the point of interest is covariance or correlation of V. The approach here is to find the most valuable subset of V (<< V) that have the most relevant information given by these variances and covariances or correlations. The KLT mainly concentrates on variants, although correlations and co-variances are not totally ignored. Let 1

x , 2

x , and 3 x be variables as given by equation (1)

 . , , , , 3 2 1 V x x x x X   (1) . 1 X  (2)
The linear function of X is given by Equation [START_REF] Anderson | Forecasting Gasoline Prices Using Consumer Surveys[END_REF]

         V i j j V V x x x x x X        (4)
.

1 2 2 3 23 2 22 1 21 2          V i j j V V x x x x x X        (5)
.

1 3 3 3 33 2 32 1 31 3          V i j j V V x x x x x X        (6)
Eqs. ( 1), ( 2) and ( 3) are uncorrelated having maximum variance up to Equation ( 7) so that in step kth a linear function given in Equation ( 8) with maximum variance subject to being uncorrelated with Equation (

.

X V  (7)
.

X k  (8) . , , , , 1 3 2 1 X X X k          (9)
The principal component kth is the Equation ( 8), as such the principal component can be found up to V principal components. In this way it is expected that the highest number of variations in X will account for m principal components, where m << V [START_REF] Jolliffe | Principal component analysis (2nd Edn)[END_REF][START_REF] Karhunen | Robust PCA methods for complete and missing data[END_REF].

Network for Vector Quantization

Vector quantization (VQ) methods encode a manifold such that sub manifold

D V   , use a finite set   n w w w w , , , 2 1   of reference (codebook) or cluster centers. D i w   , N i , , 1   vector of a data V  
can best be defined as the optimal matched or wining reference vector

) ( i w of w for ) , ( ) (  i w d
which is a distortion error, for instance, square error

2 ) (  i w 
is minimum as possible. The procedure further divides the V into smaller units of regions  

. 10) is referred to as voronoid polyhedral through which every data vector  corresponds to reference vector i w if probability of the data vectors over V is defined by ) ( p , then Equation ( 11) is the average of reconstruction error (distortion error)

j j i i w w V V          (10) Equation (
   . ) )( ( 2 i D w p d E    (11)
Equation ( 11) is optimized to the minimal by the optimum selection of the i w (reference vector).

V   , then       v i i i D w E w w k h p d , ) ))( , ( ( ) (      (12)     N j j j D w w k h p d E 1 2 , ) ))( , ( ( ) ( 2 1      (13) where ) , ( w k j  represent the number of reference vectors i w with j i w w      . By substituting i i w d    ) (
for ease we obtain

. ) ))( , ( ( ) (        v i i D i i w w k h p d R w E      (14)         N j i j j j D i w w k d w k h p d R 1 2 . ) , ( )) , ( ( ) ( 2 1      (15) The derivative of ) (  h is ) (  h N i ,..., 1   R i vanishes for ) , ( w k j  then     N i i j j d d w k 1 2 2 ). ( ) , (   (16)
Equation ( 16) is valid with the heavy-side step function

) (        0 , 1 0 , 0 ) ( x for x for x  . ( 17
) 0 0 ) (   x for x  . ( 18
)        v N l l j i i i D i d d d d w k h x p d R 1 2 2 2 ). ( )) , ( ( ) (    (19)        N j v i j i j j D d d d d w k h x p d 1 2 2 2 ) ( )) , ( ( ) (    . ( 20
)
The integral of the N integrands in the 2 nd term of Equation ( 20) is non-vanishing only for those in which .

2 2 i j d d  Those s   can be defined as          N l N l i l i l j j w k d d d d w k 1 1 2 2 2 2 ) , ( ) ( ) ( ) , (     . ( 21
)
Hence,

       v N l l i i i i D i d d d d w k h p d R 1 2 2 2 ) ( )) , ( ( ) (     . ( 22
)        v N j i j i i i D d d d d w k h p d 1 2 2 2 ) ( )) , ( ( ) (     . ( 23
)
R i vanishes N i , , 1    because ) ( ) ( x x     . If the priori of the data point distribution      p
is not given whereas stochastic sequence of input data points

), 1 (  t  ), 2 (  t 
… govern by P(x) drives the adaptation procedure, adjusting steps for the reference vectors or cluster centers i w is defined by

) ) ( )).( ( ( . i ii i w t t w       . ( 24
)
where  and ij  are the step size and Kronecker delta, respectively.

Due to Equation (11) having many local minima, soft max is introduced into the learning process to adjust the winning reference vector i(x) as shown in Equation (25) to prevent the network for vector quantization from being trapped in local minima.

) .( .

j i                 . ( 25
)        N i w D i p d E 1 ) ( min 2 ln ) ( 1       . ( 26
)
Equation ( 25) corresponds to stochastic gradient decent on the cost function. The cost function   min E as given in Equation ( 26) is equivalent to E of Equation ( 11) [START_REF] Martinetz | Neural-Gas" Network for Vector Quantization and its Application to Time-Series Prediction[END_REF].

Experiments

Dataset

The data of New York Harbor Conventional Gasoline Regular Sport Price FOB ($/Gallon) were collected from the Energy Information Administration of the US Department of Energy. The data are freely available through the official website of the organization. The data were collected on a daily frequency from 2 of Jun, 1986 to October 15, 12012. Fig. 1 depicted the window of the original gasoline price data clearly showing its nonlinearity and volatile nature. The dataset consist of 6639 observations within the period under study, weekends and other public holidays created empty spaces of which we have used imputation to fill in the empty spaces. The value of 0 was used to fill the empty spaces since the dataset were normalized within the range of -1 to 1. Therefore, adding zero to empty spaces cannot affect the results because they are approximately equal proportion. Future contract prices (price of gasoline agreed between two parties today, but payment to be made on a specific future date) determine the gasoline price as pointed out in [START_REF] Chinn | The predictive of energy futures: An update on petroleum, natural gas, heating oil and gasoline[END_REF]. Therefore, fifteen futures contract prices were collected as the independent attributes, whereas gasoline price is the dependent variable. Descriptive statistics of the time series are reported in Table 1 showing the minimum and maximum gasoline price for the period under study. The standard deviation suggests that the gasoline price data are in good agreement with the observations.

The Proposed Application of the Network for Vector Quantization

The KLT is applied to reduce the number of input attributes in order to eliminate irrelevant inputs and used only minimum and relevant attributes. Including irrelevant attributes in the modeling process could affect the model performance, accuracy and increase the complexity of the network. The data of the gasoline price are partitioned into training, validation and testing dataset in the ration of 80%: 10%: 10% after several trials, since there is no ideal way for determining the exact percentage ratio. In building an NVQ model, initial parameter selection is critical to the performance of the model. For our study, we conducted several initial experimentation for choosing the optimal values that can yield global or near global solution. Number of adaptation steps, i w , minimal distribution error 0 E , performance measure were all set at the beginning of our experimentations. The KLNVQ model builds in this study was used to forecast the prices of gasoline.

For the purpose of comparison, ARIMA, Multiple Linear Regression (MLR) and Vector Auto-regression (VAR) models were also used to forecast the gasoline price.

The entire process of building the KLNVQ model is presented in Fig. 2 and it was implemented in MATLAB (2013a) neural network ToolBox and SPSS version 16 on a machine (HP L1750 model, 4Gb RAM, 232.4 GB HDD, 32-bit OS, Intel (R) Core (TM)2 Duo CPU @ 3.00 GHz).

Results and Discussion

Analysis of the results

We use KLT for the selection of input attributes in order to reduce its dimension. The attributes selected for the study are future contract 1 = 21.7, future contract 2 = 16.31, future contract 3 = 11.61, futures contract 4 = 9.4, future contract 5 = 8.7, future contract 6 = 7.2, future contract 7 = 6.5, future contract 8 = 6.1, and future contract 8 = 5.55 accounts for 93.07% cumulative variance. Others were rejected for inclusion in the model, therefore, six attributes were not included. The KLNVQ model has nine (9) inputs neurons, four hidden layer neurons, one (1) output neuron, soft max is used during adaptation. Number of adaptation steps = 0.2, i w = 0.04, minimal distribution error 0 E = 0.0012. These are the optimal parameters for the KLNVQ model. The performance of the model for training, validation, test and complete datasets is presented in Fig. 3. The Mean Square Error (MSE) for training, validation and out of sample test are 0.006241, 0.006134, and 0.001284 respectively. For comparison purpose as earlier mentioned we also forecast the gasoline price using statistics and econometric models such as ARIMA, MLR, and VAR. The ARIMA model was first identified several models were tried in order to identify the best fit model. The models that were built and tested are ARIMA (1,0,0), ARIMA (2,1,0), ARIMA (2,2,2), ARIMA (1,0,3), ARIMA [START_REF] Hamilton | Historical oil shocks[END_REF][START_REF] Deltas | Retail gasoline price dynamics and local market power[END_REF][START_REF] Borenstein | Do gasoline prices respond asymmetrically to crude oil price change?[END_REF], ARIMA (3,0,0) and ARIMA (1,1,1). The model ARIMA (1,0.0) was identified as the best among other comparable models. Ljung-Box was used to validate the ARIMA (1,0,0) model and the results obtained are: R 2 = 0.74, statistics = 9.822, Sig. 0.341 and predictors = 5. The MSE of the gasoline price predicted by the ARIMA (1,0,0) and observed prices was completed and it was found to be 0.471101. MLR model was used for the forecasting of gasoline prices. The R 2 measurement of variability generated by the independent variables is 0.61522 and MSE is 0.83522. The R 2 adjusted value of 0.61522 was identical with the original R 2 showing how well the MLR models were able to generalize. This is because shrinkage was not found from the adjusted values. VAR model is also applied for the forecasting of gasoline price and the adjusted R 2 value obtained is 0.79137. The MSE measured for the forecasted and observed gasoline price values is 0.339014.

Comparing performances of the propose KLNVQ model with ARIMA, MLR, and VAR

From the simulation results of the models presented in section 4.1, it can be summarized that the forecast accuracy of KLNVQ is better than the ARIMA, MLR and VAR in terms of MSE and R 2 (see Fig. 3). Evidence from this research has suggested that the propose KLNVQ can be a substitute for the statistical and econometric models commonly use in the literature for forecasting gasoline price. This performance demonstrated by the propose KLNVQ model can best be attributed to the capability of the model to approximate any nonlinear function with acceptable accuracy as well as the use of Voronoid Polyhedral which likely makes it easier for the model to detect patterns in the historical data. The research will be extended to compare the accuracy of several attribute selection methods such as genetic algorithm, particle swarm optimization, and hybridization of genetic algorithms and wavelet transform.

Conclusion

In this paper, we have presented a novel approach for the forecasting of the gasoline price. The approach is modeled based on KLT and NVQ with Voronoid Polyhedral. The experimental data were collected from the Energy Information Administration of the US Department of the Energy. Our approach is effective, robust, and efficient more than the statistical and econometric models propose in the literature. Comparative analysis suggested that the propose KLNVQ model performs better than the ARIMA, MLR, and VAR. Accurate forecasting of gasoline price has implication for the formulation of policies related to sustainable economic development which might improve the economic standard. In addition, having future knowledge of gasoline price can significantly assist policy makers in taking decisions that might successfully deviate from hardship typically cause by shortage of gasoline.

Theorem 1 .

 1 For a set of reference vectors ) ,

Fig. 1 .

 1 Fig. 1. Window of the gasoline price

Fig. 2 .

 2 Fig. 2. The propose conceptual framework for the KLNVQ model

Fig. 3 .

 3 Fig. 3. Regression plots of the KLNVQ model

Table 1

 1 Descriptive statistics of the gasoline price

	Mean	SD

Acknowledgments. This work is supported by University of Malaya High Impact Research Grant no vote UM.C/625/HIR/MOHE/SC/13/2 from Ministry of Higher Education Malaysia.


On a Singular Solution in Higgs Field (III') -The Photoelectric Conversion of Gamma-ray from an Axion-like Pseudo Nambu-Goldstone Boson by

Multi-Excited Ur-SM Higgs Boson.

On a Singular Solution in Higgs Field (III') -The Photoelectric Conversion of Gamma-ray from an

Axion-like Pseudo Nambu-Goldstone Boson by Multi-Excited Ur-SM Higgs Boson.

Kazuyoshi KITAZAWA, Mitsui Chemicals FAX: 03-6253-4244, E-mail: Kazuyoshi.Kitazawa@misui-chem.co.jp

The possibility that a photon of 492 MeV which would be radiated from the tightly bound fermion (top quark)-antifermion (top quark_bar) coupling during condensing to ur-SM Higgs boson (fullerene type quasicrystal of 240 Glueballs) converts to a pseudo Nambu-Goldstone boson (axion-like particle: ALP) under certain color magnetic field, is suggested by the latest gamma-ray observing data of supernova remnant-Cassiopeia A . We show then the produced ALP, after decayed into two photons, elementarily excites an ur-SM Higgs boson by their multi-exciton actions and becomes itself 2*240 electron pairs; on the other hand, the SM Higgs boson may finally transform to an aggregate of pseudo-scalar mesons (spin 0) in truncated-octahedron. As the existence of this 'heavy' ALP could solve CP invariance problem in strong force (= naturalness of minimum theta), to confirm this by observation is to be surely expected. We will also discuss about the predictable respective state of superconductivity in two processes above.

1.Introduction

In preceding paper [START_REF] Kitazawa | On a Singular Solution in Higgs Field[END_REF] the author discussed the mass and the basic structure of SM Higgs boson with reference to bound top quark-pair by obtaining asymptotic solution for their equation of motion of nonlinear Klein-Gordon type-PDE via 'mass triangle method'. Where we saw that SM Higgs boson (H 0 ) will consist of a number of mesons each of which is composed of two gluons (glueball: GB), after emitting a photon of 492 MeV. The GB mass value calculated of ground state is around at 502.55 MeV/c 2 which is expected as f 0 (600) meson's mass. [START_REF] Nakamura | [END_REF] In this paper we at first show that our calculated mass values of f 0 (1370), f 0 (1500) and f 0 (1710) are within each f 0 meson's mass from experiment and they also crystallize into respective fullerene structure as well as f 0 (600). Then we propose each mass-expression for H 0 of f 0 -meson with several light pseudoscalar mesons such as 0

 , 0 K , 0 K , K
 ,π ± ,π 0 and GB. All of ur-SM Higgs boson and its relatives of fullerene structure will finally transit to SM Higgs boson (H 0 ) of truncated-octahedron (tr-O), after excited by two gamma-rays originated from an ALP which was produced from the one photon of 492 MeV.

2.Analysis and the Result 2.1 Equation for f 0 Meson Mass We have discussed in preceding paper (III) [START_REF] Kitazawa | On a Singular Solution in Higgs Field[END_REF] the relation between GB mass (M GB ) and the SM Higgs boson mass (M H 0 ). The general formula of f 0 meson mass is to be expressed as

0 ( ) GB H o f i i i M M N M   , ( 1
)
where N i : the number of vertex for (f 0 ) i meson in fullerene structure and i  : GB-inclusion ratio. From eq.( 1), calculated f 0 mesons' masses are well consistent with (or at least within) experimental values as shown in Table 1. Here we adopted 90, 80, 70

N N N    (2)
for f 0 (1370), f 0 (1500) and f 0 (1710) respectively. And M H 0 =120.611 GeV/c 2 which was obtained in preceding paper (I) [START_REF] Kitazawa | On a Singular Solution in Higgs Field[END_REF] . Hence the total number of GB which is included in H 0 is computed by eq.( 4) since we let regarding GB-inclusion ratio to obey eq.( 3), adding to (1). .

GB i i N N    (4) Table 1 f 0 mesons' mass values 2 MeV/c     .
Actually over three decades ago, Rossi and Veneziano 3) , also Igarashi et al [START_REF] Igarashi | Constituent Rearrangement Model and Hadron Reactions[END_REF] Therefore we shall apply this junction type to be able to describe H 0 with f 0 -mesons of the fullerene structure. For H 0 with f 0 (1500) of pure GB's we may construct it as an aggregation of 12 units of 10 0 S and 30 units of 12 0 S . For H 0 with f 0 (1370) or with f 0 (1710) we must construct it as mixed one from a GB and several certain light pseudo-scalar mesons, because f 0 (1370) and f 0 (1710) have both been interpreted that they are not consisted only of GB's. We propose their massstructure formulae as

Our calculation

Experiment

which give mass values of 1723.0 and 1340.1MeV/c 2 respectively, reproducing the calculated values in Table 1 which have been obtained from eq.( 1). Here we should remind that H 0 would be constructed by 70* f 0 (1710)-or 90* f 0 (1370)-fullerene of eq.( 2). So the factor (70/90) for K 0 or K  in eq.( 6) is considered. While the factor (1/3) in eq.( 5) is expected from that 3*[fullerene number of H 0 with f 0 (1500) of pure GB] = 240. Because, H 0 with f 0 (1500) might have resonant mass of 3*(mass of GB for ground state) at each 80 vertexes. [START_REF] Kitazawa | On a Singular Solution in Higgs Field[END_REF] 2.2 Axion-like Pseudo Nambu-Goldstone Boson It is widely believed [START_REF] Pecci | The Strong CP Problem and Axions[END_REF] that strong CP invariant problem (or 'the naturalness of minimum theta') is to be solved by the existence of axion. We shall hereafter study on certain 'heavy' axion-like particle (ALP), although up to now rather light axions have been comprehensively searched both theoretically and experimentally.

In astrophysics, Cassiopeia A (Cas A) has been well recognized as a gamma-ray emitting supernova remnant which has young neutron star at the center. [START_REF] Ho | A neutron star with a carbon atmosphere in the Cassiopeia A supernova remnant[END_REF] Recently, Giannotti et al [START_REF] Giannotti | New constraints for heavy axion-like particles from supernovae[END_REF] derived new constraints on the coupling of heavy pseudo-scalar ALP's to photons, based on the gamma-ray flux expected from the decay of these particles into photons, from the data of Cas A, etc.. Hence we here point out the possibility that a photon of our 492 MeV which would be radiated from the tightly bound top quark_anti-top quark coupling during condensing to ur-SM Higgs boson (fullerene type quasicrystal of 240 Glueballs) converts to a pseudo Nambu-Goldstone boson (ALP) under certain color magnetic field around the shell of GB fullerene. Then the produced ALP, after it decayed into two photons, elementarily excites an ur-SM Higgs boson by their multi-exciton actions and becomes itself 2*240 electron pairs. These processes are described as

  * 00
, where H condenses to GB fullerene.

Eqs.(8-1) and (8-2) express respective conversions both by Primakoff effect [START_REF] Primakoff | Photo-production of neutral mesons in nuclear electric fields and the mean life of the neutral meson[END_REF] at impinging inward and re-impinging outward to color magnetic field around ur-H 0 as shown in Fig. 2. In the last stage, two gamma-rays are to be converted to twice of 240*(e + e -)-pairs by multi-exciton, after elementarily exciting each 240 GB-vertexes of ur-H 0 in color magnetic field. Then next time, fragmentation to {GB and light pseudo-scalar mesons}-fullerenes of 'lower' number may happen. We consider fragmentation of ur-H 0 to {f 0 (1370), f 0 (1500), f 0 (1710)}-fullerenes in sec.2.1 is one of major pattern of it. The excess of energy:

        2
is understood as necessary 'margin' to initiate the elementary excitation, which is to be energy of the produced axion (ALP). Gianotti et al [START_REF] Giannotti | New constraints for heavy axion-like particles from supernovae[END_REF] described exclusion plot for ALP models with mass up to 1 GeV/c 2 , and Peccei-Quinn (PQ) constant f a > 10 12 GeV, considering PQ mechanism. We expect similar mechanism in the color magnetic field around ur-H 0 of fullerene also, since 'our ALP' of 490.56 MeV/c 2 falls within the not excluded mass region. To produce such a heavy ALP mass within short distance of femto-meter scale fromγ-ray that high magnetic flux density will be needed. We estimate that it is up to order of 10 10 Gauss.

2.3 Possible Superconductivities in ur-H 0 and in H 0 of tr-O Fukushima et al [START_REF] Fukushima | Color superconducting matter in a magnetic field[END_REF] investigated color superconducting quark matter in a magnetic field, and pointed out the possibility of the 2SCds phase in the interior of the neutron star with extremely strong magnetic field (magnetar). It is now under investigation to reconstruct ur-H 0 from a standpoint of that ur-H 0 is to be consisted of gluons in the crystalline color superconducting phase of QCD. Also, that H 0 of tr-O to whom ur-H 0 would be finally decayed, has superconductivity is anticipated. <Details are to be explained at talk> 3.References

  have described gauge invariant junction type baryonium j, i and m denote respective number of junction, junction-pair (equivalent to GB) and quark-pair (meson) , as shown in Fig.1. Recently, Csörgó et al[START_REF] Csörgó | Buckyballs and gluon junction networks on the femtometre scale[END_REF] showed gluon junction networks of truncated-polyhedrons.

Fig. 1

 1 Fig.1Junction type of baryonium.[START_REF] Igarashi | Constituent Rearrangement Model and Hadron Reactions[END_REF]

  photoelectric ur

Fig. 2

 2 Fig. 2 Gamma-ray and Color Magnetic Field around Ur-H 0 .

  photon


Bens Pardamean
email: bpardamean@binus.edu

Teddy Suparyanto

Eryadi Masli

Jerome Donovan

Enhancing the Use of Digital Model with Team-Based Learning Approach in Science Teaching

Keywords: Team-Based Learning, TBL, digital model, science teaching

This study describes the introduction of digital models and team-based learning (TBL) for teaching science; in this case, the teaching of the magnetic induction portion of a physics class. This new approach required students' active construction of knowledge as both an individual and team. Students were asked to begin their studies through the viewing of digital models in videos through an online learning portal. Camtasia Studio was utilized in creating video contains class material and experiments along with the teacher's audio explanation. The TBL approach was implemented as the instructional strategy during in-class sessions. A portion of the classroom time was spent ensuring that students master the class material and a vast majority of class time was used for team assignments that focused on problem-based learning and simulating complex questions that the student would face as the course developed. The utilization of digital models and TBL improved the students' ability to learn independently and to present their ideas coherently, transforming them into more engaged, independent learners, not just in science learning but also in their overall academic experience.

Introduction

The latest data indicates that the development of secondary education, especially in the science and mathematics, in Indonesia experienced a declining trend, in comparison with other countries. The TIMSS (Trends International in Mathematics and Science Study) report showed that in 2007, Indonesian was ranked 35 (out of 49 countries) in eighth grade science. However, four years later, its rank went down to 40 (from 42 countries). Realizing that science (and technology) plays significant role in shaping the future of the country, the Indonesian government is putting efforts to improve the quality of education through National Education Standard (NES). One of the issues that impede the government's endeavor is the practice of learning and teaching, especially in science.

Currently, the teaching of science-related courses at primary as well as secondary school level in Indonesia is based on a relatively traditional teaching method; the instructor imparts knowledge to students in the classroom, explaining various concepts, facts, and other learning contents [START_REF] Hasil | IPA dan Matematika di Sekolah Dasar[END_REF]. As teaching time is limited, the students listens to, absorbs, and memorizes what the teacher has said while activities, such as homework and material review would then complement the teaching activities. This renders the students to be more of a group of passive participants in the learning process. Furthermore, students rely on textbooks as a primary information source; they are urged to read the text but in reality, many do not do so. As a result, the teacher spends more time organizing and clarifying the text's information for the students. In this more traditional method of teaching, students are not maximally engaged in the learning process and do not reach their maximum potential in mastering the content material. (The Content Standard of the NES is the minimum criteria in the Indonesian educational system; thus, mastering the material is essential). Furthermore, in the traditional teaching method, there is a lack of opportunity for students to develop the attitudes necessary for scientific inquiry [START_REF] Taraban | Effects of Active-Learning Experiences on Achievement, Attitudes, and Behaviors in High School Biology[END_REF]. In the traditional curriculum, the science is taught as proven facts and absolute truth, which is treated as a static body of knowledge [3]. Thus, we believe that an effective teaching method should involve the students' active participation in the learning process. The focus of instruction would be learning how to apply the concepts and ideas substantially instead of merely learning about them theoretically. [START_REF] Marx | Inquiry-Based Science in the Middle Grades: Assessment of Learning in Urban Systemic Reform[END_REF] argue that learning science should be active and constructive [START_REF] Marx | Inquiry-Based Science in the Middle Grades: Assessment of Learning in Urban Systemic Reform[END_REF]. In this studentcentered teaching method, a different kind of instructional strategies to teach science is employed. It includes using digital models as well as putting students in groups for them to collaborate as an effective team.

The use of models and analogies in the pedagogy of science teaching was directed to assist students to gain understanding of the subject [START_REF] Coll | The Role of Models and Analogies in Science Education: Implications from Research[END_REF]. However, the advances in Information and Communication Technology (ICT) within the past three decades which positively impact on the teaching and learning in science [START_REF] Linn | Technology and Science Education: Starting Points, Research Programs, and Trends[END_REF] have provided the opportunities for some educators to employ the digital models in the teaching and learning activities, especially for science-related subjects. Many digital models and applications have been developed to address students' difficulties in understanding the concept. However, the students' grasping of a concept does not depend solely on the model; there should be a learning process that ensures the model can help students optimally in their learning activities. This problem is often exacerbated by the fact that the students are not accustomed to working in groups. [START_REF] Coll | The Role of Models and Analogies in Science Education: Implications from Research[END_REF] suggest that the collaborative work and peer discussion are important factors to enhance students' cognitive thinking skills, which are crucial in the understanding of science-related subjects [START_REF] Coll | The Role of Models and Analogies in Science Education: Implications from Research[END_REF]. Thus, the aim of the paper is to present a method of science teaching with digital models that requires students to actively construct knowledge in both an independent and group setting. This method is currently employed in the Grade 9 in one of public junior high schools in Jakarta, Indonesia. The students learnt about magnetic induction in their physics class in. Students were asked to examine digital models in the form of instructional videos through an online learning portal. The video content consisted of class materials and experiments, along with the teacher's narration, which was created using Camtasia Studio.

In learning science-related subjects, it is not enough just to study the concepts; the Indonesian Ministry of National Education in its science curriculum policy expect that students to develop their domain knowledge as well as cognitive process [START_REF] Pkbpdpdpn | Naskah Akademik Kajian Kebijakan Kurikulum Mata Pelajaran IPA[END_REF]. As students learn from cognitive processes of their peers [START_REF] Brindley | Peer Assessment in Undergraduate Programmes[END_REF], during classroom activities, the Team-Based Learning (TBL) would be employed as the instructional strategy. In this method, the students would learn about magnetic induction concepts and its applications through individual and group activities.

Models In Science Teaching and Learning

Learning is defined as any relatively permanent change in behavior that occurs as a result of practice or experience [START_REF] Morgan | Introduction to Psychology[END_REF]. This definition consists of two important concepts, "change in behavior" and "a result of practice or experience". Thus, a teaching method should aim to achieve these two ideas in learning. For science, models can be one of the tools for shaping the students' learning experience.

Models are defined as intended physical, computational, or mental representations of a more concrete entity, set of concepts, or phenomena [START_REF] Rapp | Models and Modeling in Science Learning, Encyclopedia of the Sciences of Learning[END_REF]. There are three different types of model in science education [START_REF] Ornek | Models in Science Education: Applications of Models in Learning and Teaching Science[END_REF]: conceptual, mental, and physical models.

Conceptual models are external representations. They are precise, complete, and consistent with the shared scientific knowledge specifically created to facilitate the comprehension or the teaching of systems in the world [START_REF] Greca | Mental models, conceptual models, and modeling[END_REF]. Mental models are internal and cognitive representations of familiar objects and concepts [START_REF] Rapp | Models and Modeling in Science Learning, Encyclopedia of the Sciences of Learning[END_REF][START_REF] Buckley | Model-based teaching and learning with BioLogica: What do they learn? How do they learn? How do we know[END_REF]. They are psychological representations of real or imaginary situations [START_REF] Ornek | Models in Science Education: Applications of Models in Learning and Teaching Science[END_REF]. Lastly, physical models are considered by the science-education community as a simplified and/or idealized version of a more complex physical system or phenomenon [START_REF] Ornek | Models in Science Education: Applications of Models in Learning and Teaching Science[END_REF].

The conceptual models consists of mathematical, computer, and physical models. [START_REF] Ornek | Models in Science Education: Applications of Models in Learning and Teaching Science[END_REF] states that the definitions of each conceptual model are as follows [START_REF] Ornek | Models in Science Education: Applications of Models in Learning and Teaching Science[END_REF]:

-A mathematical model is the use of mathematical language to describe the behavior of a system.

-A computer model has a program that attempts to simulate the behavior of a particular system. The program was created through the use of a mathematical model to find analytical solutions to problems, enabling the prediction of a complex system's behavior via a set of parameters and initial conditions.

-Physical models in the science-education community are considered to be tangible representations that can be carried, touched, or held.

ICT for Science Teaching and Learning

With computer technology's rapid advancement as well as widespread use of the Internet, teaching and learning with communication/information processing technologies have become a current, popular interest among researchers and educators [START_REF] Hsien | Students' Concept Learning in Digital Learning Context -Atom and Molecule[END_REF]. The implementation of Information and Communication Technology (ICT) influenced the teaching methodology and teaching material. For the science teaching and learning, ICT could provide digital contents and a deliver mechanism to the students. Due to difference with a traditional class, the students must "adjust" their concept cognition to reap the benefits of conceptual change learning [START_REF] Hsien | Students' Concept Learning in Digital Learning Context -Atom and Molecule[END_REF].

Digital Model

A digital model is created and delivered via ICT, with the ability to incorporate not only a computer model, but also a mathematical or physical model. The resulting digital data can range from videos to interactive games to virtual simulation. This research addressed the use of digital video presentations. The instructor/teacher created the video with Camtasia, a computer software that captures both the computer's screen and teacher's voice. With this software, the teacher recorded his power point presentation then added with his own explanation in synch with the presentation's progress.

Webblog

A web blog (blog) was used to deliver the digital model. From an educational point of view, weblogs are the development of traditional learning logs for students and teachers, whether as a complement to traditional lectures or as an e-learning tool [START_REF] Luján-Mora | The Use of Weblogs in Higher Education: Benefits and Barriers[END_REF].

Team-Based Learning (TBL)

The primary learning objective in TBL is to go beyond simply covering content, shifting more focus to ensuring that students have the opportunity to practice course concepts via problem solving. Thus, TBL is designed to provide students with both conceptual and procedural knowledge [START_REF] Michaelsen | The Essential Elements of Team-Based Learning, New Directions for Teaching and Learning[END_REF]. Although a portion of the classroom time is still spent ensuring that students master the course content, the vast majority of class time is used for team assignments that focus on problem-based learning, simulating complex questions that the student will face as the course develops.

Figure 1 outlines a general scheme of how a TBL course is organized. Students are strategically organized into permanent groups for the term, and the course content is organized into major units-typically five to seven. Before any in-class content work, students must study assigned materials since each unit begins with the readiness assurance process (RAP), which consists of a short test on the key ideas from the readings that students complete as individuals. Subsequently, the students would work on the test as a team, coming to consensus on team answers. Immediate feedback is given on the team test, allowing the opportunity to write evidence-based appeals and valid arguments for incorrect responses. The final step in the RAP is short and specific lecture to clarify any common misunderstandings found within the team test and appeals. Upon the completion of the RAP, the majority remainder of learning unit is spent on in-class activities and assignments that require students to practice using the course content.

TBL Structure

Shifting from simply familiarizing students with course concepts to requiring that students use those concepts to solve problems is no small task [START_REF] Michaelsen | The Essential Elements of Team-Based Learning, New Directions for Teaching and Learning[END_REF]. The realization of this shift requires changes in the roles of both instructor and students. The instructor's primary role shifts from dispensing information to designing and managing the overall instructional process. On the other hand, the students' role shifts from being passive recipients of information to actively responding to initial exposure to the course content during the process of preparing for in-class teamwork. Changes of this magnitude do not happen automatically and may even seem improbable. They are, however, achievable when the four essential elements of TBL are implemented successfully [START_REF] Michaelsen | The Essential Elements of Team-Based Learning, New Directions for Teaching and Learning[END_REF]:

 Teams: groups of students must be properly formed and managed  Accountability: students must be accountable for the quality of their individual and group work  Feedback: instructors must provide frequent and timely feedback to students  Assignment design: group questions must promote both learning and team development When these four elements are implemented in a course, the stage is set for student groups to evolve into cohesive learning teams [START_REF] Michaelsen | The Essential Elements of Team-Based Learning, New Directions for Teaching and Learning[END_REF].

Advantages of TBL

Forming student teams for group work, even in a casual manner, produces benefits that cannot be achieved with students's being in a strictly passive learning role. While even the casual use of teams is beneficial, it must be stressed that team-based learning allows the achievement and maintenance of important outcomes only through consistent utilization of the method. Some of these benefits include [START_REF] Michaelsen | The Essential Elements of Team-Based Learning, New Directions for Teaching and Learning[END_REF]: 1) developing students' higher level cognitive skills in large classes, 2) providing social support for "at-risk" students, 3) promoting the development of interpersonal and team skills, and 4) building and maintaining faculty members' enthusiasm for their teaching role.

Methods

This study was conducted to implement digital models and Team Based Learning (TBL) approach in the magnetic induction portion of a physics class. This research was done in a group consisting of 36 Grade 9 students at a public junior high school in Jakarta, Indonesia.

Magnetic induction is a part of Indonesia's physics curriculum for the junior high school level. This material is chosen because of students' difficulty in grasping the concept of induction with prior utilization of direct classroom demonstration. Some animations or digital models had been created but garnered no significant result, presumably because of the passive role that the students still assumed. Thus, TBL was applied as an attempt to make students construct knowledge actively. This research conducted a blended learning model; that is, the course taught magnetic induction with part traditional (in-person) lectures and part modern ICT over internet [START_REF] Nedelko | Participant Characteristics for E-learning[END_REF]. This course consisted of three stages: online learning, first in-person, and second in-person sessions. Fig. 1 shows the research design's stages. During the online learning stage, students learned the material by watching digital models that were uploaded onto the teacher's blog. The 'video presentation' materials consisted of presentation slides on Magnetic Induction along with the teacher's audio explanation, generated with Camtasia Studio. Every student could to study this video's contents independently, one week prior to the implementation of the next learning stage. They could access video presentation multiple times until they achieved good understanding on the topic.

At in-person stages, students completed a test and collaborated in a small group. The first in-person meeting had the students perform an RAP (Readiness Assurance Process) test individually for 10 minutes. The RAP gauged a student's comprehension of the concept through 10 multiple-choice questions, each of which had four answer choices. Students must distribute a total of 4 points to each question. This way, the students could receive partial credit based on their point distributions on the questions. An RAP test has a maximum possible score of 40. After the individual RAP testing, students split into nine groups (four students per group) with systematic grouping to ensure uniform distribution of genders and comprehension levels. Teachers checked the individual students' RAP tests while the students discussed the questions within their groups. The groups RAP's worksheet was a scratched paper. The students could scratch their group answer for every question. If they got a star in the first scratch, they would get 4 point for one question. For the second scratch, they got 2 point and 1 point for third scratch. From the individual and group RAP answers, the teacher compiled the wrong answers as basis for reviewing the RAP worksheet. At the end of the review, students could ask for a more in-depth explanation if confusion still remained. This first in-person meeting would last for approximately 80 minutes.

In the second in-person meeting, the students completed the Application Concept Test (ACT), which consisted of two essay questions. The student wrote out explanations to their answers individually then discussed those explanations with their team. This session also lasted for 80 minutes. The discourse among the team members is the key characteristic feature of students' engagement in their learning.

Discussions

The most important preparation for this research was to the creation of the video presentation and their subsequent uploading to the teacher's blog. The magnetic induction presentation consisted of fifteen power point slides. The details of each slide's content are shown in Table 1. All slides were synched with the recorded explanations with Camtasia Recorder version 3.0. The video's duration was 12:38.

The video presentation was saved in mpeg format with 720-pixel frame width and 576-pixel frame height. This screen resolution size produced a video that was difficult to see. However, higher resolutions led to data size that was too large. The total data size of the final video was 300 MB, which was too large for internet uploads in Indonesia. Thus, the file was split into three parts for easier uploads and downloads. Fig. 2 shows a screen capture of video presentation. The RAP test consisted of ten conceptual questions, all of which were based on the video presentation. The questions covered definitions, examples, and tools for creating magnetic induction. This test also covered how magnetic induction could be created as well as factors that influenced EMF.

The entire study was completed within two weeks; the first week was spent on Stage 1 while the second week was split between Stages 2 and 3. The following details the results from each step:

Stage 1: Online Learning Students had the opportunity to learn independently during in Stage 1 at their own convenience since virtually, the blog can be accessed anytime after school for the number of times the students needed until adequate comprehension was achieved. Half of the research participants repeated the video more than three times. By doing this repetition, students have well understanding about the topics.

Stage 2: First In-person Class Session

For the first ten minutes of class, students took the RAP test individually. Students can earn partial credit through point allocations for each question. For example, if a student is confident that the correct choice is "A", all 4 points would be assigned to "A". However, if a student is fairly certain of the answer "A", but is hesitant to rule out "C", they could allot 3 points to "A" and 1 to "C". After students had completed the RAP test individually, the teacher collected the worksheets and had the students discuss and decide on their group answers. They seemed happy to work in groups. They can evaluate their own answers. If they do not find "star" in the first scratch, they discuss their answers again to find the correct answer.

Based on the individual and group RAP worksheets, most of mistakes came from the question on factors that influenced EMF. After the individual and group RAP test were completed, the teacher gave explanations on common mistakes. The teacher also replayed parts of the video presentation that covered concepts that most of the students missed. This session concluded with a question and answer session.

Stage 3: Second In-person Class Session

This session begins with individual ACT that lasted for twenty minutes. After this test, the students returned to their groups to discuss and prepare a presentation on their ACT answers. Students were allowed to present with a flip chart or power point. During the presentation, the class was allowed to ask questions to the presenters.

Conclusion

TBL can be a solution to improve the use of digital media in teaching and learning processes. TBL helps students to self-evaluate their learning outcomes through small groups. The use of digital models without strict control can lead to misconceptions about student comprehension of course materials. Additionally, TBL can help teachers provide a quick feedback mechanism to student learning outcomes. Moreover, TBL improves students' ability to learn independently and to present their ideas coherently. This ability is important to transform students into independent learners, one of key features for engaging students in not just science learning but in their overall academic experience.

Fig 1 .

 1 Fig 1.Research Design[START_REF] Michaelsen | The Essential Elements of Team-Based Learning, New Directions for Teaching and Learning[END_REF]

Table 1 .

 1 Power Point Presentation's Description

	Slide Number	Description
	Slide 1	Introduction and definition of magnetic induction
	Slide 2	Animation about galvanometer when a wire was moved be-tween magnetic poles
	Slide 3-5	Animation about how to create electromagnetic induction in AC and DC powers
	Slide 6-8	Animation about the direction of Induced Electromotive Force (EMF)
	Slide 9-11	Animation about factors affecting EMF
	Slide 12-15	Animation about tools that uses the working principle of electromagnetic induction

Fig 2. Screen Capture of Video Presentation