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Fast detection of biological viruses in DNA sequence is very important for investigation of patients and overcome diseases. First, an intelligent algorithm to completely retrieve DNA sequence is presented. DNA codes that may be missed during the splitting process are retrieved by using Hopfield neural networks. Then, a new approach for fast detection of biological viruses like H1N1 and H1N5 in DNA sequence is presented. Such algorithm uses high speed time delay neural networks (HSTDNNs). The operation of these networks relies on performing cross correlation in the frequency domain between the input DNA sequence and the input weights of neural networks. It is proved mathematically and practically that the number of computation steps required for the presented HSTDNNs is less than that needed by conventional time delay neural networks (CTDNNs). Simulation results using MATLAB confirm the theoretical computations.
(IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, No. 11, November 2011 Fast Detection of H1N1 and H1N5 Viruses in DNA Sequence by using High Speed Time Delay Neural Networks Hazem M. El-Bakry Nikos Mastorakis Faculty of Computer Science & Information Systems, Technical University of Sofia, Mansoura University, EGYPT BULGARIA email@example.com Abstract—Fast detection of biological viruses in DNA sequence is very machinery the host cell would ordinarily use to reproduce its important for investigation of patients and overcome diseases. First, an own DNA. Then the host cell is forced to encapsulate this viral intelligent algorithm to completely retrieve DNA sequence is presented. DNA into new protein shells; the new viruses created are then DNA codes that may be missed during the splitting process are retrieved released, destroying the cell [32-35]. by using Hopfield neural networks. Then, a new approach for fast detection of biological viruses like H1N1 and H1N5 in DNA sequence is presented. Such algorithm uses high speed time delay All living things are susceptible to viral infections plants, neural networks (HSTDNNs). The operation of these networks animals, or bacteria can all be infected by a virus specific for relies on performing cross correlation in the frequency domain that type of organism. Moreover, within an individual species between the input DNA sequence and the input weights of neural there may be a hundred or more different viruses which can networks. It is proved mathematically and practically that the infect that species alone. There are viruses which infect only number of computation steps required for the presented humans (for example, smallpox), viruses which infect humans HSTDNNs is less than that needed by conventional time delay and one or two additional kinds of animals (for example, neural networks (CTDNNs). Simulation results using MATLAB influenza), viruses which infect only a certain kind of plant confirm the theoretical computations. (for example, the tobacco mosaic virus), and some viruses Keywords- High Speed Neural Networks; Cross Correlation; which infect only a particular species of bacteria (for example, Frequency Domain; H1N1 and H1N5 Detection the bacteriophage which infects E. coli) [32-35]. Sometimes when a virus reproduces, mutations occur. The I. INTRODUCTION offspring that have been changed by the mutation may no longer be infectious. But a virus replicates itself thousands of A virus is a tiny bundle of genetic material - either DNA or times, so there will usually be some offspring that are still RNA - carried in a shell called a viral coat, or capsid, which is infectious, but sufficiently different from the parent virus so made up of protein. Some viruses have an additional layer that vaccines no longer work to kill it. The influeza virus can around this coat called an envelope. When a virus particle do this, which is why flu vaccines for last year's flu don't work enters a cell and begins to reproduce itself, this is called a viral the next year. The common cold virus changes so quickly that infection. The virus is usually very, very small compared to vaccines are useless; the cold you have today will be a the size of a living cell. The information carried in the virus's different strain than the cold you had last month! [31-34] DNA allows it to take over the operation of the cell, For efficient treatment of patients in real-time, it is important converting it to a factory to make more copies of itself. For to detect biological viruses like H1N1 and H1N5. Recently, example, the polio virus can make over one million copies of time delay neural networks have shown very good results in itself inside a single, infected human intestinal cell [32-35]. different areas such as automatic control, speech recognition, All viruses only exist to make more viruses. With the possible blind equalization of time-varying channel and other exception of bacterial viruses, which can kill harmful bacteria, communication applications. The main objective of this all viruses are considered harmful, because their reproduction research is to reduce the response time of time delay neural causes the death of the cells which the viruses entered. If a networks. The purpose is to perform the testing process in the virus contains DNA, it inserts its genetic material into the host frequency domain instead of the time domain. Our approach cell's DNA. If the virus contains RNA, it must first turn its was successfully applied for fast detection of computer viruses RNA into DNA using the host cell's machinery, before as shown in . Sub-image detection by using fast neural inserting it into the host DNA. Once it has taken over the cell, networks (FNNs) was proposed in [5,6]. Furthermore, it was viral genes are then copied thousands of times, using the used for fast face detection [7,10,12], and fast iris detection (IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, No. 11, November 2011 . Another idea to further increase the speed of FNNs given even a poor photograph of that person we are quite good through image decomposition was suggested in . In at reconstructing the persons face quite accurately. This is very addition it was applied for fast prediction of new data as different from a traditional computer where specific facts are described in [1,3]. located in specific places in computer memory. If only partial information is available about this location, the fact or FNNs for detecting a certain code in one dimensional serial memory cannot be recalled at all [35-42]. stream of sequential data were described in [1,2,3,4,8,14,15,20,23,27,28,29]. Compared with conventional Theoretical physicists are an unusual lot, acting like neural networks, FNNs based on cross correlation between the gunslingers in the old West, anxious to prove themselves tested data and the input weights of neural networks in the against a really good problem. And there aren’t that many frequency domain showed a significant reduction in the really good problems that might be solvable. As soon as number of computation steps required for certain data Hopfield pointed out the connection between a new and detection [1-29]. Here, we make use of the theory of FNNs important problem (network models of brain function) and an implemented in the frequency domain to increase the speed of old and well-studied problem (the Ising model), many time delay neural networks for biological virus detection . physicists rode into town, so to speak, with the intention of The idea of moving the testing process from the time domain shooting the problem full of holes and then, the brain to the frequency domain is applied to time delay neural understood, riding off into the sunset looking for a newer, networks. Theoretical and practical results show that the tougher problem. (Who was that masked physicist?). proposed HSTDNNs are faster than CTDNNs. Retrieval of Hopfield made the portentous comment: ‘This case is missed DNA codes by using Hopfield neural networks is isomorphic with an Ising model,’ thereby allowing a deluge of introduced in section II. Section III presents HSTDNNs for physical theory (and physicists) to enter neural network detecting of biological viruses in DNA sequence. modeling. This flood of new participants transformed the field. Experimental results for fast biological virus detection by In 1974 Little and Shaw made a similar identification of neural using HSTDNNs are given in section IV. network dynamics with the Ising model, but for whatever reason, their idea was not widely picked up at the time. II. RETRIEVAL OF MISSED DNA CODES BY USING Unfortunately, the problem of brain function turned out to be HOPFIELD NEURAL NETWORKS more difficult than expected, and it is still unsolved, although a number of interesting results about Hopfield nets were One of the most important functions of our brain is the laying proved. At present, many of the traveling theoreticians have down and recall of memories. It is difficult to imagine how we traveled on . could function without both short and long term memory. The absence of short term memory would render most tasks The Hopfield neural network is a simple artificial network extremely difficult if not impossible - life would be punctuated which is able to store certain memories or patterns in a manner by a series of one time images with no logical connection rather similar to the brain - the full pattern can be recovered if between them. Equally, the absence of any means of long term the network is presented with only partial information. memory would ensure that we could not learn by past Furthermore there is a degree of stability in the system - if just experience. Indeed, much of our impression of self depends on a few of the connections between nodes (neurons) are severed, remembering our past history [36-40]. the recalled memory is not too badly corrupted - the network can respond with a "best guess". Of course, a similar Our memories function in what is called an associative or phenomenon is observed with the brain - during an average content-addressable fashion. That is, a memory does not exist lifetime many neurons will die but we do not suffer a in some isolated fashion, located in a particular set of neurons. catastrophic loss of individual memories - our brains are quite All memories are in some sense strings of memories - you robust in this respect (by the time we die we may have lost 20 remember someone in a variety of ways - by the color of their percent of our original neurons) [44-57]. hair or eyes, the shape of their nose, their height, the sound of their voice, or perhaps by the smell of a favorite perfume. The nodes in the network are vast simplifications of real Thus memories are stored in association with one another. neurons - they can only exist in one of two possible "states" - These different sensory units lie in completely separate parts firing or not firing. Every node is connected to every other of the brain, so it is clear that the memory of the person must node with some strength. At any instant of time a node will be distributed throughout the brain in some fashion. Indeed, change its state (i.e start or stop firing) depending on the PET scans reveal that during memory recall there is a pattern inputs it receives from the other nodes [44-57]. of brain activity in many widely different parts of the brain If we start the system off with a any general pattern of firing [36-43]. and non-firing nodes then this pattern will in general change Notice also that it is possible to access the full memory (all with time. To see this think of starting the network with just aspects of the person's description for example) by initially one firing node. This will send a signal to all the other nodes remembering just one or two of these characteristic features. via its connections so that a short time later some of these We access the memory by its contents not by where it is stored other nodes will fire. These new firing nodes will then excite in the neural pathways of the brain. This is very powerful; others after a further short time interval and a whole cascade (IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, No. 11, November 2011 of different firing patterns will occur. One might imagine that • Activation function on each neuron i is: the firing pattern of the network would change in a complicated perhaps random way with time. The crucial ⎧ 1 if net > 0 ⎫ property of the Hopfield network which renders it useful for f(net) = sgn(net) = ⎨ ⎬ (1) simulating memory recall is the following: we are guaranteed ⎩- 1 if net < 0 ⎭ that the pattern will settle down after a long enough time to where: some fixed pattern. Certain nodes will be always "on" and neti = Σwij xj (2) others "off". Furthermore, it is possible to arrange that these • If net = 0, then the output is the same as before, by stable firing patterns of the network correspond to the desired convention. memories we wish to store! [44-57]. • There are no separate thresholds or biases. However, these could be represented by units that have all weights = The reason for this is somewhat technical but we can proceed 0 and thus never change their output. by analogy. Imagine a ball rolling on some bumpy surface. We imagine the position of the ball at any instant to represent the • The energy function is defined as: activity of the nodes in the network. Memories will be E(y1, y2, …, yn) = - Σ Σ wij yiyj (3) represented by special patterns of node activity corresponding to wells in the surface. Thus, if the ball is let go, it will execute where (y1, y2, …, yn) is outputs, wij is the weight neuron i, some complicated motion but we are certain that eventually it and the double sum is over i and j. will end up in one of the wells of the surface. We can think of the height of the surface as representing the energy of the ball. Different DNA patterns are stored in Hopfield neural network. We know that the ball will seek to minimize its energy by In the testing process, the missed codes (if any) are retrieved. seeking out the lowest spots on the surface -- the wells. Furthermore, the well it ends up in will usually be the one it III. FAST BIOLOGICAL VIRUS DETECTION BY USING started off closest to. In the language of memory recall, if we HSTDNNS start the network off with a pattern of firing which approximates one of the "stable firing patterns" (memories) it Finding a biological virus like H1N1 or H1N5 in DNA will "under its own steam" end up in the nearby well in the sequence is a searching problem. First neural networks are energy surface thereby recalling the original perfect memory. trained to classify codes which contain viruses from others The smart thing about the Hopfield network is that there exists that do not and this is done in time domain. In biological virus a rather simple way of setting up the connections between detection phase, each position in the DNA sequence is tested nodes in such a way that any desired set of patterns can be for presence or absence of biological virus code. At each made "stable firing patterns". Thus any set of memories can be position in the input DNA one dimensional matrix, each sub- burned into the network at the beginning. Then if we kick the matrix is multiplied by a window of weights, which has the network off with any old set of node activity we are same size as the sub-matrix. The outputs of neurons in the guaranteed that a "memory" will be recalled. Not too hidden layer are multiplied by the weights of the output layer. surprisingly, the memory that is recalled is the one which is When the final output is 10, this means that the sub-matrix "closest" to the starting pattern. In other words, we can give under test contains H1N1. When the final output is 01 this the network a corrupted image or memory and the network means that H1N5 is detected. Otherwise, there is no virus. will "all by itself" try to reconstruct the perfect image. Of Thus, we may conclude that this searching problem is a cross course, if the input image is sufficiently poor, it may recall the correlation between the incoming serial data and the weights incorrect memory - the network can become "confused" - just of neurons in the hidden layer. like the human brain. We know that when we try to remember The convolution theorem in mathematical analysis says that a someone's telephone number we will sometimes produce the convolution of f with h is identical to the result of the wrong one! Notice also that the network is reasonably robust - following steps: let F and H be the results of the Fourier if we change a few connection strengths just a little the Transformation of f and h in the frequency domain. Multiply F recalled images are "roughly right". We don't lose any of the and H* in the frequency domain point by point and then images completely [44-57]. transform this product into the spatial domain via the inverse As with the Linear Associative Memory, the “stored patterns” Fourier Transform. As a result, these cross correlations can be are represented by the weights. To be effective, the patterns represented by a product in the frequency domain. Thus, by should be reasonably orthogonal. The basic Hopfield model using cross correlation in the frequency domain, speed up in can be described as follows : an order of magnitude can be achieved during the detection process [1-29]. Assume that the size of the biological virus • N neurons, fully connected in a cyclic fashion: code is 1xn. In biological virus detection phase, a sub matrix I • Values are +1, -1. of size 1xn (sliding window) is extracted from the tested • Each neuron has a weighted input from all other neurons. matrix, which has a size of 1xN. Such sub matrix, which may • The weight matrix w is symmetric (wij=wji) and diagonal be biological virus code, is fed to the neural network. Let Wi terms (self-weights wii = 0). be the matrix of weights between the input sub-matrix and the (IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, No. 11, November 2011 hidden layer. This vector has a size of 1xn and can be required for computing the 1D-FFT of the weight matrix at represented as 1xn matrix. The output of hidden neurons h(i) each neuron in the hidden layer. can be calculated as follows [1-7]: 2- At each neuron in the hidden layer, the inverse 1D-FFT is computed. Therefore, q backward and (1+q) forward ⎛ n ⎞ hi = g⎜ ∑ Wi (k)I(k) + bi ⎟ (4) transforms have to be computed. Therefore, for a given matrix ⎜ ⎟ under test, the total number of operations required to compute ⎝ k =1 ⎠ the 1D-FFT is (2q+1)Nlog2N. where g is the activation function and b(i) is the bias of each 3- The number of computation steps required by HSTDNNs is hidden neuron (i). Equation 4 represents the output of each complex and must be converted into a real version. It is known hidden neuron for a particular sub-matrix I. It can be obtained that, the one dimensional Fast Fourier Transform requires to the whole input matrix Z as follows [1-6]: (N/2)log2N complex multiplications and Nlog2N complex ⎛ n/2 ⎞ additions . Every complex multiplication is realized by six hi(u)=g⎜ ∑ Wi(k) Z(u + k) +b i ⎟ ⎜ ⎟ (5) real floating point operations and every complex addition is ⎜k= − n/2 ⎟ implemented by two real floating point operations. Therefore, ⎝ ⎠ the total number of computation steps required to obtain the Eq.5 represents a cross correlation operation. Given any two 1D-FFT of a 1xN matrix is: functions f and d, their cross correlation can be obtained by ρ=6((N/2)log2N) + 2(Nlog2N) (10) : ⎛ ∞ ⎞ which may be simplified to: d(x)⊗ f(x) = ⎜ ∑f(x + n)d(n)⎟ ⎜ n= − ∞ ⎟ (6) ρ=5Nlog2N (11) ⎝ ⎠ Therefore, Eq. 5 may be written as follows [1-7]: 4- Both the input and the weight matrices should be dot ( ) multiplied in the frequency domain. Thus, a number of h i = g Wi ⊗ Z + b i (7) complex computation steps equal to qN should be considered. This means 6qN real operations will be added to the number where hi is the output of the hidden neuron (i) and hi (u) is the of computation steps required by HSTDNNs. activity of the hidden unit (i) when the sliding window is 5- In order to perform cross correlation in the frequency located at position (u) and (u) ∈ [N-n+1]. domain, the weight matrix must be extended to have the same size as the input matrix. So, a number of zeros = (N-n) must be Now, the above cross correlation can be expressed in terms of added to the weight matrix. This requires a total real number one dimensional Fast Fourier Transform as follows [1-7]: of computation steps = q(N-n) for all neurons. Moreover, after ( Wi ⊗ Z = F −1 F(Z)• F * Wi ( )) (8) computing the FFT for the weight matrix, the conjugate of this matrix must be obtained. As a result, a real number of Hence, by evaluating this cross correlation, a speed up ratio computation steps = qN should be added in order to obtain the can be obtained comparable to conventional neural networks. conjugate of the weight matrix for all neurons. Also, a Also, the final output of the neural network can be evaluated number of real computation steps equal to N is required to as follows: create butterflies complex numbers (e-jk(2Πn/N)), where 0<K<L. These (N/2) complex numbers are multiplied by the elements ⎛ q ⎞ of the input matrix or by previous complex numbers during the O(u) = g⎜ ∑ Wo (i) h i (u ) + b o ⎟ ⎜ ⎟ (9) computation of FFT. To create a complex number requires two ⎝ i=1 ⎠ real floating point operations. Thus, the total number of where q is the number of neurons in the hidden layer. O(u) is computation steps required for HSTDNNs becomes: the output 2D matrix (corresponding to two output neurons) of σ=(2q+1)(5Nlog2N)+6qN+q(N-n)+qN+N (12) the neural network when the sliding window located at the position (u) in the input matrix Z. Wo is the weight matrix which can be reformulated as: between hidden and output layer. σ=(2q+1)(5Nlog2N)+q(8N-n)+N (13) IV. COMPLEXITY ANALYSIS OF HSTDNNS FOR 6- Using sliding window of size 1xn for the same matrix of BIOLOGICAL VIRUS DETECTION 1xN pixels, q(2n-1)(N-n+1) computation steps are required when using CTDNNs for biological virus detection or The complexity of cross correlation in the frequency domain processing (n) input data. The theoretical speed up factor η can be analyzed as follows: can be evaluated as follows: 1- For a tested matrix of 1xN elements, the 1D-FFT requires a number equal to Nlog2N of complex computation steps . q(2n - 1)(N- n + 1) η= (14) Also, the same number of complex computation steps is (2q + 1)(5Nlog2 N) + q(8N- n) + N (IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, No. 11, November 2011 CTDNNs and HSTDNNs are shown in Figures 1 and 2  Hazem M. El-Bakry, "New Fast Principal Component Analysis For Real- Time Face Detection," MG&V Journal, vol. 18, no.4, 2009, pp. 405-426. respectively.  Hazem M. El-bakry, and Mohamed Hamada “High speed time delay Neural Networks for Detecting DNA Coding Regions,” Springer, Lecture Time delay neural networks accept serial input data with fixed Notes on Artificial Intelligence (LNAI 5711), 2009, pp. 334-342. size (n). Therefore, the number of input neurons equals to (n).  Hazem M. El-Bakry, "New Faster Normalized Neural Networks for Sub- Instead of treating (n) inputs, the proposed new approach is to Matrix Detection using Cross Correlation in the Frequency Domain and collect all the incoming data together in a long vector (for Matrix Decomposition, " Applied Soft Computing journal, vol. 8, issue 2, March 2008, pp. 1131-1149. example 100xn). Then the input data is tested by time delay  Hazem M. El-Bakry, "Face detection using fast neural networks and neural networks as a single pattern with length L (L=100xn). image decomposition," Neurocomputing Journal, vol. 48, 2002, pp. 1039- Such a test is performed in the frequency domain as described 1046. before.  Hazem M. El-Bakry, "Human Iris Detection Using Fast Cooperative Modular Neural Nets and Image Decomposition," Machine Graphics & The theoretical speed up ratio for searching short successive Vision Journal (MG&V), vol. 11, no. 4, 2002, pp. 498-512. (n) code in a long input vector (L) using time delay neural  Hazem M. El-Bakry, "Automatic Human Face Recognition Using networks is listed in tables I, II, and III. Also, the practical Modular Neural Networks," Machine Graphics & Vision Journal (MG&V), vol. 10, no. 1, 2001, pp. 47-73. speed up ratio for manipulating matrices of different sizes (L)  Hazem M. El-Bakry, "A New Neural Design for Faster Pattern Detection and different sized weight matrices (n) using a 2.7 GHz Using Cross Correlation and Matrix Decomposition," Neural World processor and MATLAB is shown in table IV. journal, Neural World Journal, 2009, vol. 19, no. 2, pp. 131-164.  Hazem M. El-Bakry, and H. Stoyan, "FNNs for Code Detection in An interesting point is that the memory capacity is reduced Sequential Data Using Neural Networks for Communication when using HSTDNN. This is because the number of variables Applications," Proc. of the First International Conference on Cybernetics and Information Technologies, Systems and Applications: CITSA 2004, is reduced compared with CTDNN. 21-25.  Hazem M. El-Bakry, "New High speed time delay Neural Networks V. CONCLUSION Using Cross Correlation Performed in the Frequency Domain," Neurocomputing Journal, vol. 69, October 2006, pp. 2360-2363. To facilitate investigation of patients and overcome diseases, fast  Hazem M. El-Bakry, "A New High Speed Neural Model For Character detection of biological viruses in DNA sequence has been presented. Recognition Using Cross Correlation and Matrix Decomposition," International Journal of Signal Processing, vol.2, no.3, 2005, pp. 183-202. Missed DNA codes have been retrieved by using Hopfield neural  Hazem M. El-Bakry, "New High Speed Normalized Neural Networks for networks. After that a new approach for fast detection of Fast Pattern Discovery on Web Pages," International Journal of Computer biological viruses like H1N1 and H1N5 in DNA sequence has Science and Network Security, vol.6, No. 2A, February 2006, pp.142- been introduced. Such strategy has been realized by using our 152.  Hazem M. El-Bakry "Fast Iris Detection for Personal Verification Using design for HSTDNNs. Theoretical computations have shown Modular Neural Networks," Lecture Notes in Computer Science, that HSTDNNs require fewer computation steps than Springer, vol. 2206, October 2001, pp. 269-283. conventional ones. This has been achieved by applying cross  Hazem M. El-Bakry, and Qiangfu Zhao, "Fast Normalized Neural correlation in the frequency domain between the input data and Processors For Pattern Detection Based on Cross Correlation Implemented in the Frequency Domain," Journal of Research and Practice the weights of neural networks. Simulation results have in Information Technology, Vol. 38, No.2, May 2006, pp. 151-170. confirmed this proof by using MATLAB. The proposed  Hazem M. El-Bakry, and Qiangfu Zhao, "High speed time delay Neural algorithm can be applied to detect other biological viruses in Networks," International Journal of Neural Systems, vol. 15, no.6, DNA sequence perfectly. December 2005, pp.445-455.  Hazem M. 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Schonfeld, “On the Hysteresis and Robustness of Hopfiled Neural Networks,” IEEE Transactions on Circuits and Systems – II : Analog and Digital Signal Processing, vol. 2, pp. 745–748, November 1993. I1 I2 Output Layer O/P1 O/P2 In-1 Hidden Layer In Cross correlation in time domain Input between the (n) input data and Layer weights of the hidden layer. Serial input data 1:N in groups of (n) elements shifted by a step of one element each time. IN Figure 1. CTDNNs. (IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, No. 11, November 2011 I1 I2 Output Layer O/P1 O/P2 IN-1 Hidden Layer IN Cross correlation in the frequency domain between the total (N) input data and the weights of the hidden layer. Figure 2. HSTDNNs. TABLE I: THE THEORETICAL SPEED UP RATIO FOR DETECTING H1N1 OR H1N5 (LENGTH OF BIOLOGICAL VIRUS CODE=400). Length of Number of computation steps required for Number of computation steps required Speed up serial data CTDNNs for HSTDNNs ratio 10000 2.3014e+008 4.2926e+007 5.3613 40000 0.9493e+009 1.9614e+008 4.8397 90000 2.1478e+009 4.7344e+008 4.5365 160000 3.8257e+009 8.8219e+008 4.3366 250000 5.9830e+009 1.4275e+009 4.1912 360000 8.6195e+009 2.1134e+009 4.0786 490000 1.1735e+010 2.9430e+009 3.9876 640000 1.5331e+010 3.9192e+009 3.9119 TABLE II: THE THEORETICAL SPEED UP RATIO FOR DETECTING H1N1 OR H1N5 (LENGTH OF BIOLOGICAL VIRUS CODE=625). Length of Number of computation steps required for Number of computation steps required Speed up serial data CTDNNs for HSTDNNs ratio 10000 3.5132e+008 4.2919e+007 8.1857 40000 1.4754e+009 1.9613e+008 7.5226 90000 3.3489e+009 4.7343e+008 7.0737 160000 0.5972e+010 8.8218e+008 6.7694 250000 0.9344e+010 1.4275e+009 6.5458 360000 1.3466e+010 2.1134e+009 6.3717 490000 1.8337e+010 2.9430e+009 6.2306 640000 2.3958e+010 3.9192e+009 6.1129 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 9, No. 11, November 2011 TABLE III: THE THEORETICAL SPEED UP RATIO FOR DETECTING H1N1 OR H1N5 (LENGTH OF BIOLOGICAL VIRUS CODE=900). Length of Number of computation steps required for Number of computation steps required Speed up serial data CTDNNs for HSTDNNs ratio 10000 4.9115e+008 4.2911e+007 11.4467 40000 2.1103e+009 1.9612e+008 10.7600 90000 4.8088e+009 4.7343e+008 10.1575 160000 0.8587e+010 8.8217e+008 9.7336 250000 1.3444e+010 1.4275e+009 9.4178 360000 1.9381e+010 2.1134e+009 9.1705 490000 2.6397e+010 2.9430e+009 8.9693 640000 3.4493e+010 3.9192e+009 8.8009 TABLE IV: PRACTICAL SPEED UP RATIO FOR DETECTING H1N1 OR H1N5. Length of serial data Speed up ratio (n=400) Speed up ratio (n=625) Speed up ratio (n=900) 10000 8.94 12.97 17.61 40000 8.60 12.56 17.22 90000 8.33 12.28 16.80 160000 8.07 12.07 16.53 250000 7.95 17.92 16.30 360000 7.79 11.62 16.14 490000 7.64 11.44 16.00 640000 7.04 11.27 15.89
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