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(IJCSIS) International Journal of Computer Science and Information Security, Vol. 8, No. 6, September 2010 Information realization with statistical predictive inferences and coding form D.Mukherjee P.Chakrabarti* , A.Khanna , V.Gupta Sir Padampat Singhania University Sir Padampat Singhania University Udaipur-313601,Rajasthan,India Udaipur-313601,Rajasthan,India debasismukherjee1@gmail.com *prasun9999@rediffmail.com Abstract—The paper deals with information realization in case of grid topology. Nodal communication strategies with clusters has A also been cited. Information prediction has been pointed out with * - relevant statistical method, forward sensing, backward sensing and cumulative frequency form. Binary tree classifier theory has * - been applied for information grouping. The paper also deals with * - M rows (m- 1)paths comparison analysis of information coding. * - - - - - * * * * * B Keywords- grid topology ,forward sensing , backward sensing, binary tree classifier, information coding I. INFORMATION MERGING IN GRID IN * shows path of traversal DIAGONAL APPROACH N columns (n-1) paths In order to solve complex problems in artificial intelligence one needs both large amount of knowledge & some Fig1: Information merging in mesh/grid mechanisms for manipulating that knowledge to create solutions to new problems .Basically knowledge is a mapping The above concept can be realized in DDM(Distributed Data of different facts with help appropriate functions for e.g. Earth Mining) where large amount of geographically scattered is a planet. Can be realized as a function – planet (Earth). knowledge is merged & is mined to derive conclusions & make decisions for e.g. GIS i.e. the Geographical Information Information merging can be realized as combining different System which uses cartography(art of making maps) with pieces of information to arrive at a conclusion. The different various information elements(sources) to derive decision information elements can be related in different ways i.e. support results like which route to choose for a given either in hierarchy or in form of a graph or even a mesh. destination. Consider a mesh of size m X n i.e. m rows & n columns then if each intersection point has a information element placed on II. INFORMATION MERGING IN CLUSTER NETWORKS it then one way of merging element A with B can be covering a path of length (5XN) (here m= 8 & n=9). If weight of This section mainly focuses on the nodal communication covering each path is considered same then in case of diagonal between the farthest node in a N*N structure[1] and approach we can find a path of diagonal nature of length 5√2 information realization indicates nodal message . Let us and then travelling a length (N-5) in linear fashion thus finding assume each cluster to be consisting of 16 nodes and then try a shortest path the same can also be determined by graph to communicate between the source and the destination node algorithms like Dijkstra‟s or kruskal‟s algorithm for as described in the fig1.The point to be noted here is that to minimum spanning tree. If each path is considered to be of establish the communication link between the adjacent zero weight then interestingly there is no sense travelling a elements or units of the cluster we have to have the path from A to B i.e. we can directly merge the two points communication in just reverse order in the 2 adjacent i.e. we take point A &directly merge it with point B in such a elements. The order of the communication is case we need to have some stack like mechanism to determine the order in which the nodes arrive & are merged. 215 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 8, No. 6, September 2010 The condition can be visually imagined as follows: nodes, i.e, f(x)=3+4+4;In case of 4*4 matrix to communicate between the farthest node we need 7 nodes, i.e, f(x)=3+4+4+4;In case of 16 elements in a ring , we can proceed as follows. Let us consider the case of 1*1 matrix to communicate between the farthest node we need 3 nodes, i.e, f(x)=7.In case of 2*2 matrix to communicate between the farthest node we need 7 nodes, i.e, f(x)=7+8;In case of 3*3 matrix to communicate between the farthest node we need 7 nodes, i.e, f(x)=7+8+8;In case of 4*4 matrix to communicate between the farthest node we need 7 nodes, i.e, Now let us first talk about the case when there is only one f(x)=7+8+8+8;Now the total number of nodes can be derived element i.e, 1*1.In this particular case if we want to by the general formula as (N/2-1)+(M-1)*(N/2) where N = communicate between the farthest node then there will be only number of nodes present in the unit or element, M = 1 node in between the source and the destination which can be dimension of the square matrix.The data can be represented in further visualized as follows: the tabular form as follows: No. of 1*1 2*2 3*3 4*4 nodes 4 1 3 5 7 8 3 7 11 15 16 7 15 23 31 If we denote it by using the function f(x)then the value of f(x)will be 1.f(x)=1; The intermediate node is ll. Now let us consider the case 2*2 matrix the value here will be 35 f(x)=1+2=3; The intermediate nodes are 1(2,3),2(4). 30 25 20 4 8 15 16 For the case for the 3*3 matrix the value of the function 10 f(x)=1+2+2=5; 5 0 1*1 2*2 3*3 4*4 Fig.2: Nodal communication in cluster The x-axis represents the M*M matrix where M varies from 1 to 3.The y-axis represents the number of optimum communication nodes required in the establishing the path between the source node and the farthest node. The number of nodes per element is indicated by the 3colors. Similarly for the 4*4 matrix we can get the value of f(x)=1+2+2+2. III. STATISTICAL INFERENCE OF FUTURISTIC Here in this case we were having only 4 elements in a ring VALUES .Suppose we have 8 elements in the ring in that case we have to compute the number of nodes required to communicate or In statistical inferences the input & output of a situation are establish the connection between the farthest nodes. related with a certain relation or function based on which we Justification - Let us consider the case of 1*1 matrix to infer futuristic values. Consider a real-time situation in which communicate between the farthest node we need 3 nodes, i.e, a given input parameter is observed over time between instants f(x)=3.In case of 2*2 matrix to communicate between the T1 & T2 given the relation [2] farthest node we need 7 nodes, i.e, f(x)=3+4;In case of 3*3 matrix to communicate between the farthest node we need 7 Mt = a.et then Mavg = √(Mt1 . Mt2 ) 216 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 8, No. 6, September 2010 C. Cumulative frequency based information sensing Case 1: OBSERVATIONS INFORMATION INVOLVED If we take observations at equal instants of time then g1 i1,i3,i4,i6 Mt1 = a.et1 g2 i3,i5 Mt2 = a.et1+k g3 i4,i5,i6 Mt3 = a.et1+2k g4 i2,i3,i5 General term Mtn = a.et1+(n-1)k i.e. the values of output M g5 i1,i2 forms a G.P. series of increasing order common ratio as ek . g6 i1,i2,i3,i6 Case 2: Table1 : Association of information against each observation If we take observation at unequal timing interval in that case Features Initial Count Value (Value)2 T1 = t1 => Mt1 = a.et1 value T2 = t1 + k1 => Mt2 = a.et1+k1 i1 0.1 3 0.3 0.09 T3 = t2 + k2 = t1 + (k1 + k2) => Mt2 = a.et2+k2 = Mt2 = i2 0.2 3 0.6 0.36 a.et1+k1+k2 i3 0.3 4 1.2 1.44 General term Tn = T1+(k1+k2+k3+…+kn) i4 0.4 2 0.8 0.64 Tn = tn-1 + kn-1 = t1 + (k1 + k2 + k3+…+kn-1) => Mtn = a.etn-1+kn-1 = Mtn = a.e(t1+k1+k2+k3+…+kn-1) = a.et1+Ktotal i.e. i5 0.5 3 1.5 2.25 now any futuristic value say at instant tn is i6 0.6 3 1.8 3.24 Mtn = a.et1.eKtotal (observed value) Given Mt = a.et , taking log on both sides we have, Table 2 : Determination of count and value ln(Mt) = ln(a) + t i.e. ln(Mtn) = ln(a) + tn Now CF = ( x , y , z ) ln(Mtn) = ln(a) + t1+k1+k2+k3+…+kn-1 where x = number of elements , y = linear sum of the elements Thus we have obtained a log linear model for the above and z = sum of the square of the elements[3] function Mt = a.et using which we can calculate or predict the futuristic values for increased ranges. Y = m.X + C V. BINARY TREE BASED GAIN CLASSIFIER If we try to minimize the value of Ktotal we can do so by making k1=k2=k3=…=kn-1 which is same as Case 1. In this section information represents gain analysis. A search[4] can be formed based on the initial search term and IV. PROJECTION OF SENSED INFORMATION its gradual sub term while the process of matching. Thereby the level is increased, in initial search term is the root and the Let I= {i1,i2,…in} be the set of sensed information. In the final term fully matching with the context of the users‟ desire process of feature appropriate observation, forward selection , is a leaf node. backward elimination and decision based induction methods are applied. G0 LEVEL 0 A. Forward selection based information sensing G1,1 G1,2 LEVEL 1 Let I= {i1 , i2,….,in}be the set of information estimates of various trends noted after observation in respective timing G2,1 G2,2 G2,3 G2,4 LEVEL 2 instants Y = {y1,y2,…yn}. The accuracy measurement is to be calculated first based on comparison analysis. The minimum deviation reflects high accuracy level of prediction and that LEVEL 3 information will be selected. In this manner, { } , {best G3,1 G3,2 G3,3 G3,4 G3,5 G3,6 G3,7 G3,8 information},{first two}….will be selected. Fig3: Binary tree based gain classifier B. Backward elimination based information sensing In the above figure, G0 is the root that is initial search term. If Using backward elimination , in each stage each information is a user wants to analyze further gain classification, then eliminated and thereby after the final screening stage the identify each search term as a binary code and by giving the projected set reveals the final optimum information space. code number he can analyze the position of gain estimate in the model . The concept of coding is as follows: 217 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 8, No. 6, September 2010 Value = 0 if the search term is a left child of parent node C3 = { 10 } = 1 otherwise C4 = { 11 } N For p3: Theorem: In the process of coding, ∑ 1/2Li =1, where Class ijk False True i=1 C1 000 p1,p2,p3 - Li is the length of code of ith leaf node in the tree, N is total C2 001 p1,p2 p3 number of leaf nodes and 1<i<N. C3 010 p1,p3 p2 C4 011 p1 p2,p3 Proof: C5 100 p2,p3 p1 C6 101 p2 p1,p3 From fig.3 codes of leaf nodes are as follows: C7 110 p3 p1,p2 C8 111 - p1,p2,p3 Nodes Respective code G3,1 000 In the initial stage, classes are C1, C2 based on the parameter G3,2 001 p1. In the second stage, the classes are C1,C2,C3 based on p2. G3,3 010 In the last stage, classes are C1,C2...C8 based on p3.This G3,4 011 means that if we assume that „n‟ is the number of parameters G3,5 100 involved in the system for examination purpose. Then, the G3,6 101 maximum length of code word for a particular class is „n‟. The G3,7 110 number of classes is 2n, provided that the classes are distinct in G3,8 111 nature. So, N=8. Each leaf node has identical code length i.e. 3. VI. CODED INFORMATION SENSING Therefore, 1/2Li =1/2=1/8, 1/2= 1/8, …1/2=1/8 Let original message is “FATHER”. For the first alphabet, We now design a binary tree based classifier taking some µvalue = 1/((position of that)+ π /100). Hence it‟s offset value = parameters for examination purpose and represent each point ceiling of (the product of µvalue and 10). The weight is given by on the basis of a code generated by arithmetic coding. Finally, its position in alphabet string[5]. represent the same on the basis of set theory .We assume that Therefore total_value = offset value * weight. From the next the gain set available is G ={ g1,g2,g3,g4 }.The parameters character onwards, µvalue_next = 1/(mod value of (position of based on which the examination is to be carried are the next - position of previous ) + π/100). Hence total_value is elements of the set P = { p1,p2,p3 }.The result of the calculated in similar manner. Now, bias value will be equal to examination are denoted in the form of Boolean variables such total number of characters in the message.Compute net_value that the outputs are denoted as: as (total_value_first char + total _value_last char)- (bias value) NO = 0 and let it be x (say). YES = 1 Mode Operation At the initial timing instant, the parameter p1 is applied for testing purpose. Hence, in the initial stage, there will be at 0≤x<100 Reverse the message. least one class while a maximum of two classes. In the second 100≤x<150 Circular left shift of message by n/2 bits level, the parameter p2 is applied and accordingly the classes where n= bias value. are defined. In the final stage, the parameters p3 is applied. 150≤x<200 Circular right shift of message by n/2 bits If we assume the classifier as a binary tree representation, we can apply arithmetic coding to each class such that a „NO‟ of a Iteration 1: µF = 1/((position of „F‟ in alphabet list) + π /100) = particular exam is denoted by „0‟ and a „YES‟ is denoted by 1/((6)+ π /100) = 0.165798547. Offset value = ceiling of „1‟.In the initial stage, the class which contains the elements (0.165798547*10) = 2. Weight = position of „F‟ in alphabet list for negative supply of p1 is C1 ={ d1,d2}, while, C2 = { d2,d4 = 6. Thus, total_value = 2*6 =12. }. In this manner, the tree is to be constructed such that the code word for each class is denoted by ijk where i Є { 0,1 } , j Iteration 2: µA= 1/(|(position of „A‟ – position of „F‟)|+ π/100) Є { 0,1 } and k Є { 0,1 }. = 1/(|(1-6)|+ π/100) = 1/5.031415927 = 0.198751209. Offset value = ceiling of (0.198751209*10) = 2. Weight = 1. Thus, For p1: total_value = 2*1 = 2. C1 = { d1,d2 } Iteration 3: µT = 1/(|(position of „T‟ – position of „A‟)|+ π/100) C2 = { d2,d4 } = 1/(|(20-1)|+ π/100) = 1/19.03141593 = 0.052544697. Offset For p2: value = ceiling of (0.052544697*10) = 1. Weight = 20. Thus, C1 = { 00 } total_value = 1*20 = 20. C2 = { 01 } 218 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 8, No. 6, September 2010 REFERENCES Comparator [1] A.Kumar , P.Chakrabarti , P.Saini , V.Gupta ,“Proposed techniques of random walk, statistical and cluster based node realization” communicated to IEEE conf. Advances in Computer Science ACS 2010 , India , Dec10 - Encryption Output [2] P.Chakrabarti , S.K.De , S.C.Sikdar , “Statistical Quantification of Gain system Cipher Analysis in Strategic Management” published in IJCSNS ,Korea , Vol 9 No11 ,pp.315-318, 2009 [3]P.Chakrabarti, “Data mining- A Mathematical Realization and cryptic + application using variable key” published in International journal , Advances wb in Information Mining , Vol 2 No 1, pp-18-22,2010 [4] P.Chakrabarti, P.S.Goswami, “Approach towards realizing resource * mining and secured information transfer” published in international journal of IJCSNS, Korea , Vol 8 No.7, pp345-350, 2008 * * wn [5] P.Chakrabarti , “Attacking Attackers in Relevant to Information Security” cn Proceedings of RIMT-IET, Mandi Gobindgarh. pp 69-71, March 29, 2008 w1 C1 About authors: W2 C2 Ci = offset value for i = 1 to n , wi = weight , wb = bias value Fig 4: Coding Model Iteration 4: µH = 1/(|(position of „H‟ – position of „T‟)|+ π/100) = 1/(|(8-20)|+ π/100) = 1/12.03141593 = 0.083115736. Offset Debasis Mukherjee (20/08/80) is pursuing Ph.D. from USIT, value = ceiling of (0.083115736*10) = 1. Weight = 8. Thus, GGSIPU, Delhi, India from2010. He received the M. Tech. total_value = 1*8 = 8. degree in VLSI Design from CDAC Noida in 2008 and Iteration 5: µE = 1/(|(position of „E‟ – position of „H‟)|+ π/100) bachelor degree in Electronics and Instrumentation = 1/(|(5-8)|+ π/100) = 1/3.031415927 = 0.32987885. Offset Engineering from BUIE, Bankura, West Bengal, India in value = ceiling of (0.32987885*10) = 4. Weight = 5. Thus, 2003.He achieved first place in district in “Science Talent total_value = 4*5 = 20. Search Test” 1991. He has some publications of repute in IEEE conferences. Iteration 6: µR = 1/(|(position of „R‟ – position of „E‟)|+ π/100) = 1/(|(18-5)|+ π/100) = 1/13.03141593 = 0.076737632. Offset value = ceiling of (0.076737632*10) = 1. Weight = 18. Thus, total_value = 1*18 = 18. Now, wb= bias value = number of bits in FATHER= 6. So net_value= accumulated sum of all total_value – wb = (12+2+20+8+20+18) - 6 = 74. It falls in the range 0≤x<100. So, “FATHER” is reversed. Therefore resultant cipher is “REHTAF”. Dr.P.Chakrabarti(09/03/81) is currently serving as Associate VII. CONCLUSION Professor in the department of Computer Science and Engineering of Sir Padampat Singhania University,Udaipur. The paper points out information merging in grid and cluster Previously he worked at Bengal Institute of Technology and network models. Statistical means of information prediction as Management , Oriental Institute of Science and Technology, well as forward, backward and cumulative frequency based Dr.B.C.Roy Engineering College, Heritage Institute of schemes have been analyzed . Binary tree based information Technology, Sammilani College. He obtained his Ph.D(Engg) classification and coded information have been justified with degree from Jadavpur University in Sep09,did M.E. in relevant mathematical analysis. Computer Science and Engineering in 2005,Executive MBA in 2008and B.Tech in Computer Science and Engineering in 2003.He is a life member of Indian Science Congress Association , Calcutta Mathematical Society , Calcutta 219 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 8, No. 6, September 2010 Statistical Association , Indian Society for Technical Education , Cryptology Research Society of India, IAENG(HongKong), CSTA(USA), annual member of Computer Society of India, VLSI Society of India , IEEE(USA), senior member of IACSIT(Singapore) and selected member of The IAENG Society of Artificial Intelligence , Computer Science , Data Mining. He is a Reviewer of International journal of Information Processing and Management (Elsevier) , International Journal of Computers and Applications , Canada and International Journal of Computer Science and Information Security(IJCSIS,USA), editorial board member of International Journal of Engineering and Technology, Singapore and International Journal of Computer and Electrical Engineering. He has about 100 papers in national and international journals and conferences in his credit and two patents(filed). He has several visiting assignments at BHU Varanasi , IIT Kharagpur , Amity University,Kolkata , et al. A.Khanna and V.Gupta are the third year students of Information Technology and Computer Science & Engg. branch respectively of Sir Padampat Singhania University. 220 http://sites.google.com/site/ijcsis/ ISSN 1947-5500

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IJCSIS is an open access publishing venue for research in general computer science and information security.
Target Audience: IT academics, university IT faculties; industry IT departments; government departments; the mobile industry and computing industry.
Coverage includes: security infrastructures, network security: Internet security, content protection, cryptography, steganography and formal methods in information security; computer science, computer applications, multimedia systems, software, information systems, intelligent systems, web services, data mining, wireless communication, networking and technologies, innovation technology and management.
The average paper acceptance rate for IJCSIS issues is kept at 25-30% with an aim to provide selective research work of quality in the areas of computer science and engineering. Thanks for your contributions in September 2010 issue and we are grateful to the experienced team of reviewers for providing valuable comments.

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