Download - Academy Publisher

More documents

Recommendations

Info

Theorem 2: If the number of the element in A is n and the sum of the elements in A is S in the partition problem can be solved with O(n+(0.25S 2 +2.5S)) biological operations, O(2 n ) strands, the logest strands is O(n+S) and O(S) test tubes. Proof:. Algorithm 1 includes four main steps. From the algorithm, Line(1), it is very obvious that it takes n amplify operations, 2n append operations, n merge operations and three test tubes to construct sticker-based solution space. From the algorithm, Line(2), it takes n extract operations, n detect operations, S append operations, n merge operations, and three test tubes to construct sticker-based solution space for elements of 2 n possible subsets to a n-element set A. From the algorithm, Parallel_Searcher (T 01 , S/2), it takes S(S+2)/8 exact operations, S(S+2)/8 merge operations, one detect operation, one discard operation and S/2+2 test tubes. The length of a DNA strand has never been changed, is 15(n+S).In Line(4), it takes one detect operation and it takes one read operation in Line(5). Hence, from the statements mentioned above, it is at once inferred that the time complexity of Algorithm 1 is O(n+(0.25S 2 +2.5S).After Line(1) of Algorithm1, the solution is constructed and there is 2 n strands in it. Referring to the Michael’s algorithm [8, 9], the number of the tube used in Algorithm 1 is O(n). The longest strand in Algorithm 1 is O(n+S). Ⅳ . EXPERIMENTAL RESULTS BY SIMULATED DNAS COMPUTING Consider that a finite set A is {1, 2, 3 } as an example. S is denoted to represent the sum of the elements in A So S is 6. The partition problem is to find a subset of A in which the sum is one half of S. Table 1 shows the strands pool and every step in T 0 . After Line(4) in Table 1, we will get the full solution space of the partition problem above. The DNA strands are {x 1 0 x 2 0 x 3 0 y 1,1 0 y 2,1 0 y 2,2 0 y 3,1 0 y 3,2 0 y 3,3 0 ; x 1 0 x 2 0 x 3 1 y 1,1 0 y 2,1 0 y 2,2 0 y 3,1 1 y 3,2 1 y 3,3 1 ; x 1 0 x 2 1 x 3 0 y 1,1 0 y 2,1 1 y 2,2 1 y 3,1 0 y 3,2 0 y 3,3 0 ; x 1 0 x 2 1 x 3 1 y 1,1 0 y 2,1 1 y 2,2 1 y 3,1 1 y 3,2 1 y 3,3 1 ; x 1 1 x 2 0 x 3 0 y 1,1 1 y 2,1 0 y 2,2 0 y 3,1 0 y 3,2 0 , y 3,3 0 ; x 1 1 x 2 0 x 3 1 y 1,1 1 y 2,1 0 y 2,2 0 y 3,1 1 y 3,2 1 y 3,3 1 ; x 1 1 x 2 1 x 3 0 y 1,1 1 y 2,1 1 y 2,2 1 y 3,1 0 y 3,2 0 y 3,3 0 ; x 1 1 x 2 1 x 3 1 y 1,1 1 y 2,1 1 y 2,2 1 y 3,1 1 y 3,2 1 y 3,3 1 }. Searching the union of the DNA strands by the algorithm Parallel_Searcher(T 0, S/2) showing in Table 2, we will get the legal strands of the partition problem. Reading the DNA sequence in tube T 3, we could get the answer is {1, 2} and {3}. Table 1 Every steps of the improved algorithm based on DNA computing tube T 0 1 { x 0 1 x 0 2 x 0 3 ; x 0 1 x 0 2 x 1 3 ; x 0 1 x 1 2 x 0 3 ; x 0 1 x 1 2 x 1 3 ; x 1 1 x 0 2 x 0 3 ; x 1 1 x 0 2 x 1 3 ; x 1 1 x 1 2 x 0 3 ; x 1 1 x 1 1 2 x 3 . } 2 { x 1 0 x 2 0 x 3 0 y 1,1 0 ; x 1 0 x 2 0 x 3 1 y 1,1 0 ; x 1 0 x 2 1 x 3 0 y 1,1 0 ; x 1 0 x 2 1 x 3 1 y 1,1 0 ; x 1 1 x 2 0 x 3 0 y 1,1 0 ; x 1 1 x 2 0 x 3 1 y 1,1 0 ; x 1 1 x 2 1 x 3 0 y 1,1 0 ; x 1 1 x 2 1 x 3 1 y 1,1 0 . } 3 4 { x 1 0 x 2 0 x 3 0 y 1,1 0 y 2,1 0 y 2,2 0 ; x 1 0 x 2 0 x 3 1 y 1,1 0 y 2,1 0 y 2,2 0 ; x 1 0 x 2 1 x 3 0 y 1,1 0 y 2,1 1 y 2,2 1 ; x 1 0 x 2 1 x 3 1 y 1,1 0 y 2,1 1 y 2,2 1 ; x 1 1 x 2 0 x 3 0 y 1,1 0 y 2,1 0 y 2,2 0 ; x 1 1 x 2 0 x 3 1 y 1,1 0 y 2,1 0 y 2,2 0 ; x 1 1 x 2 1 x 3 0 y 1,1 0 y 2,1 1 y 2,2 1 ; x 1 1 x 2 1 x 3 1 y 1,1 0 y 2,1 1 y 2,2 1 . } 0 0 0 0 0 0 {x 1 x 2 x 3 y 1,1 y 2,1 y 2,2 y 0 3,1 y 0 3,2 y 0 3,3 ; x 0 1 x 0 2 x 1 3 y 0 1,1 y 0 2,1 y 0 2,2 y 1 3,1 y 1 3,2 y 1 3,3 ; x 0 1 x 1 2 x 0 3 y 0 1,1 y 1 1 0 0 2,1 y 2,2 y 3,1 y 3,2 y 0 3,3 ; x 0 1 x 1 2 x 1 3 y 0 1,1 y 1 2,1 y 1 2,2 y 1 3,1 y 1 3,2 y 1 3,3 ; x 1 1 x 0 2 x 0 3 y 1 1,1 y 0 2,1 y 0 2,2 y 0 3,1 y 0 3,2 , y 0 3,3 ; x 1 1 x 0 2 x 1 1 3 y 1,1 y 0 0 1 1 2,1 y 2,2 y 3,1 y 3,2 y 1 3,3 ; x 1 1 x 1 2 x 0 3 y 1 1,1 y 1 2,1 y 1 2,2 y 0 0 3,1 y 3,2 y 0 3,3 ; x 1 1 x 1 2 x 1 3 y 1 1,1 y 1 2,1 y 1 2,2 y 1 3,1 y 1 3,2 y 1 3,3 . } Table 2 Search the solution space of the element Tube T 0 T 1 T 2 T 3 T 4 Inital pool 1 000000;000111 011000;011111 100000;100111 111000;111111 000000;000111 011000;011111 100000;100111 ; 111000; 111111 2 000000;000111 100000;100111 ; 011000;011111 111000; 111111 3 000000;000111 100000;100111 011000; 011111 111000; 111111 4 000000 100000;000111 011000;100111 111000 111000; 011111 111111 5 100000 011000; 000111 111000; 100111 011111;100111 ; 111111 6 011000 000111; 111000 52
Ⅴ.CONCLUSION REMARKS DNA computer’s power of parallel, high density computation by molecules in solution allows itself to solve hard computational problems such as NP-complete problems in polynomial increasing time. In this paper, we introduce an improved DNA algorithm for the partition problem, which is a classical NP-complete problem. Our algorithm could solve the partition problem effectivily and easily. Now, it is also very hard to say that whether the molecular computers will have a bright future. In the future molecular computers may be the clear and good choice for performing massively parallel computations. To reach a free stage in using DNA computers, just as using classical digital computers, there are still many technical difficulties to overcome before it becomes real. ACKNOWLEDGEMENT This research is supported by the key Project of National Natural Science Foundation of China under grant No.60533010, Natural Science Foundation of Zhejiang province under grant Y1090264, Natural Science Foundation of Hunan province under grant 07JJ6109. REFERENCES [1] L. Adleman, Molecular computation of solutions to combinatorial problems. Science, 1994, 266(5187): 1021– 1024 [2] R. S. Braich, N. chelyapov, C. Johnson, Solution of a 20-variable 3-SAT problem on a DNA computer. Science, 2002, 296(19): 499-502 [3] R. J. Lipton, DNA solution of hard computational problems. Science, 1995, 268(28): 542–545 [4] D. Faulhammer, A. R. Cukras, R.J. Lipton, et al., Molecular computation: RNA solutions to chess problems, Proc. Natl. Acad. Sci., 2000, U.S.A. 97: 1385-1389. [5] Q. Quyang, P. D. Kaplan, S. Liu, A. Libchaber, 1997. DNA solution of the maximal clique problem. Science, 278: 446–449. [6] Y. Li, C. Fang, Q. OuYang. Genetic algorithm in DNA Computing: A solution to the maximal clique problem. Chinese Science Bulletin, 2004, 49(9): 967-971 [7] E. Bach, A. Condon, E. Glaser, C. Tanguay, DNA models and algorithms for NP-complete problems. In: Proceedings of the 11th Annual Conference on Structure in Complexity Theory, 1996, 290–299 [8] Q. Huiqin, L. Mingming, Z. Hong. Solve maximum clique problem by sticker model in DNA computing. Progress in Nature Science. 2004, 14(12): 1116- 1121 [9] W. L. Chang, M. Guo, H. Michael. Fast Parallel Molecular Algorithms for DNA-Based Computation. IEEE Transactions on Nanobioscience, 2005, 4(2): 133- 163 [10] W. L. Chang, M.Guo. Molecular solutions for the subset-sum problem on DNA-based supercomputing. BioSystems, 2004, 73: 117–130 [11] D. F. Li, X. R. Li, H.T. Huang, Scalability of the surface-based DNA algorithm for 3-SAT. BioSystems, 2006, 85:95–98 [12] E. Horowitz, S. Sahni. Computing partitions with applications to the knapsack problem. Journal of ACM, 1974, 21(2): 277-292 [13] Ho. Michael, W.L. Chang, M. Guo. Fast parallel solution for Set-Packing and Clique Problems by DNA- Based Computing. IEICE Transactions on Information and System, 2004, E87-D(7): 1782– 1788 [14] Ho. Michael. Fast parallel molecular solutions for DNA-based supercomputing: the subset-product problem. BioSystems, 2005, 80: 233-250 [15] K. H Zimmermann, Efficient DNA sticker algorithms for NP-complete graph problems. Computer Physics Communications , 144 (2002) 297–309 [16] K. L. Li, F.J. Yao, J. Xu, Improved Molecular Solutions for the Knapsack Problem on DNA-based Supercomputing. Chinese Journal of Computer Research and Development, 2007, 44(6):1063-1070 [17] M. R. Garey, D. S. Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness, Freeman, San Francisco, 1979 [18] J. Xu, S.P. Li, Y.F. Dong, Sticker DNA computer model-Part I: Theory. Chinese Science Bulletin, 2004, 49(3): 205-212 [19] K. L. Li, F.J. Yao, J. Xu, Improved Molecular Solutions for the Knapsack Problem on DNA-based Supercomputing. Chinese Journal of Computer Research and Development, 2007, 44(6):1063-1070 53
Page 1 and 2:
Proceedings The Second Internationa
Page 3 and 4:
Table of Contents Message from the
Page 5 and 6:
Zuming Xiao, Zhan Guo, Bin Tan, and
Page 7 and 8:
Message from the Symposium Chairs T
Page 9 and 10:
Second International Symposium on N
Page 11 and 12: ISBN 978-952-5726-09-1 (Print) Proc
Page 13 and 14: model that can deal with time serie
Page 17 and 18: training for the Wushu competition
Page 21 and 22: information, called weak uncertain
Page 23 and 24: Student side Student side Student s
Page 27 and 28: If we define element of student as
Page 31 and 32: QoS, each frame data is divided int
Page 35 and 36: for Imaging Two and Three Phase Flo
Page 39 and 40: A. Profiling&following control algo
Page 41 and 42: Research and Realization about Conv
Page 43 and 44: PDF document structure is a tree st
Page 47 and 48: support 10 Mb / s. But ENC28J60 onl
Page 51 and 52: condition the first byte output of
Page 55 and 56: According to maximum membership deg
Page 59 and 60: ubber according to the mass ratio o
Page 61: Ⅲ. AN IMPROVED DNA ALGORITHM FOR
Page 65 and 66: its first child q 1 on the left, th
Page 67 and 68: chains can greatly improve efficien
Page 69 and 70: II. RELATED WORK A. Mobile Service
Page 71 and 72: special services. SOAP is used to b
Page 73 and 74: detection methods of DDoS attacks m
Page 75 and 76: Step4 calculate the new subordinate
Page 77 and 78: Figure 1. An analysis of the partit
Page 81 and 82: The preceding three formulas can be
Page 85 and 86: And the decay speed of buffer seque
Page 89 and 90: distance of view point. Given that
Page 93 and 94: Ⅳ. EVALUATION OF BLENDED LEARNING
Page 97 and 98: symmetric with respect to the origi
Page 101 and 102: each sample belongs to each categor
Page 105 and 106: A. Data Preparing To generate our t
Page 109 and 110: oth α and β . determination of Qu
Page 113 and 114:
Strong earthquake 0.1< M L
Page 115 and 116:
ISBN 978-952-5726-09-1 (Print) Proc
Page 117 and 118:
indirect causes, and the logical re
Page 119 and 120:
egression. Granger causality test i
Page 121 and 122:
B. Evaluation We have evaluated thi
Page 123 and 124:
used as a source and neighboring ce
Page 125 and 126:
Figure 3. Drainage networks generat
Page 127 and 128:
Combinational logic unit failures i
Page 129 and 130:
Tabal.1 Combinational fault logic t
Page 131 and 132:
under the endorsement of both the m
Page 133 and 134:
TABLE I. DESCRIPTION OF PROPOSITION
Page 135 and 136:
Figure 2. The process of the invers
Page 137 and 138:
Figure 9. (a)the original image.(b)
Page 139 and 140:
ISBN 978-952-5726-09-1 (Print) Proc
Page 141 and 142:
In order to reduce to the number of
Page 143 and 144:
ISBN 978-952-5726-09-1 (Print) Proc
Page 145 and 146:
that studying being going to be to
Page 147 and 148:
Reference[10] analyzed the evolutio
Page 149 and 150:
module, communication module, apper
Page 151 and 152:
After the comprehensive performance
Page 153 and 154:
system testing can be seen that the
Page 155 and 156:
III. AUTONOMIC RESOURCE ALLOCATION
Page 157 and 158:
The QoE i (T i ) is the ith user’
Page 159 and 160:
ISBN 978-952-5726-09-1 (Print) Proc
Page 161 and 162:
nodes will be formed one cluster, t
Page 163 and 164:
ISBN 978-952-5726-09-1 (Print) Proc
Page 165 and 166:
Where n is the number of data point
Page 167 and 168:
ISBN 978-952-5726-09-1 (Print) Proc
Page 169 and 170:
Keyboard event Application User mod
Page 171 and 172:
ISBN 978-952-5726-09-1 (Print) Proc
Page 173 and 174:
SQL Azure will eventually include a
Page 175 and 176:
ISBN 978-952-5726-09-1 (Print) Proc
Page 177 and 178:
The nodes in the suffix tree are dr
Page 179 and 180:
[3] Y. Li, S. M. Chung, and J. D. H
Page 181 and 182:
some drilling fluid produces hydrog
Page 183 and 184:
"normalization", whose membership b
Page 185 and 186:
and minimum structural elements in
Page 187 and 188:
esults of the spatial transform par
Page 189 and 190:
B. Research on protocol actions Com
Page 191 and 192:
ACKNOWLEDGMENT This work is funded
Page 193 and 194:
A. Problem Description In a small b
Page 195 and 196:
[4] Huang, Hung, and J. Y. jen Hsu.
Page 197 and 198:
Further by calculating, the followi
Page 199 and 200:
TABLE II. THE CONCENTRATION BETWEEN
Page 201 and 202:
private key that obtained by using
Page 203 and 204:
ISBN 978-952-5726-09-1 (Print) Proc
Page 205 and 206:
ontology, and the domain dictionary
Page 207 and 208:
ISBN 978-952-5726-09-1 (Print) Proc
Page 209 and 210:
Eq.4 is NP-hard and can be solved b
Page 211 and 212:
ISBN 978-952-5726-09-1 (Print) Proc
Page 213 and 214:
Where: G i is the selection field o
Page 215 and 216:
If there is X j in a generation, wh
Page 217 and 218:
Theorem 2.4([10]). Let L 1 and L 2
Page 219 and 220:
The relation between the lattice im
Page 221 and 222:
Figure 2. Example of single-step de
Page 223 and 224:
evocation and the fourth group stor
Page 225 and 226:
focused mainly on rule-based forms
Page 227 and 228:
Ⅵ. CONCLUSION Figure 6. The Flask
Page 229 and 230:
EDCF in comparison with DCF, has so
Page 231 and 232:
B. Simulation results and analysis
Page 233 and 234:
ISBN 978-952-5726-09-1 (Print) Proc
Page 235 and 236:
in routing table. When search resou
Page 237 and 238:
ISBN 978-952-5726-09-1 (Print) Proc
Page 239 and 240:
others through the selective emotio
Page 241 and 242:
such as weather information, techno
Page 243 and 244:
the opening window, a related page
Page 245 and 246:
1) Process context storage areas. I
Page 247 and 248:
V. CONCLUSION In this thesis, sCPU-
Page 249 and 250:
main types of horizontal search env
Page 251 and 252:
Enterprise Portal security provides
Page 253 and 254:
() t = [ S () t S () t ] T N S ,...
Page 255 and 256:
[2] Kumaravel, N., and Kavitha, V.,
Page 257 and 258:
output, so BP network has been wide
Page 259 and 260:
input to the artificial neural netw
Page 261 and 262:
(2) In a process (tokens from outsi
Page 263 and 264:
The reduction process consists of t
Page 265 and 266:
all eight normal vectors are identi
Page 267 and 268:
is B object , and the number of emp
Page 269 and 270:
xi, j y' = εα ( (1 + tanh( )) −
Page 271 and 272:
Error 8000 7000 6000 5000 4000 3000
Page 273 and 274:
Architecture (AMBA) a new bus archi
Page 275 and 276:
In order to ensure the smooth proce
Page 277 and 278:
ISBN 978-952-5726-09-1 (Print) Proc
Page 279 and 280:
In this paper, we adopt two Sobel o
Page 281 and 282:
ISBN 978-952-5726-09-1 (Print) Proc
Page 283 and 284:
four layers.The far right of the gr
Page 285 and 286:
ISBN 978-952-5726-09-1 (Print) Proc
Page 287 and 288:
TABLE II. OPERATIONAL EMPLOYEE TABL
Page 289 and 290:
A. Object-relational Type To audit
Page 291 and 292:
to execution time. Also, DBA would
Page 293 and 294:
Liping Chen .......................
show all

Download - Academy Publisher

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?