GIVEN an input sequence x 0,..., x n 1 and the
|
|
- Gerard Baker
- 5 years ago
- Views:
Transcription
1
2 1 Running Max/Min Filters using 1 + o(1) Comarisons er Samle Hao Yuan, Member, IEEE, and Mikhail J. Atallah, Fellow, IEEE Abstract A running max (or min) filter asks for the maximum or (minimum) elements within a fixed-length sliding window. The revious best deterministic algorithm (develoed by Gil and Kimmel, and refined by Coltuc) can comute the 1D max filter using o(1) comarisons er samle in the worst case. The best known algorithm for indeendent and identically distributed inut uses o(1) exected comarisons er samle(by Gil and Kimmel). In this work, we show that the number of comarisons can be reduced to 1 + o(1) comarisons er samle in the worst case. As a consequence of the new max/min filters, the oening (or closing) filter can also be comuted using 1 + o(1) comarisons er samle in the worst case, where the revious best work requires o(1) comarisons er samle (by Gil and Kimmel); and comuting the max and min filters simultaneously can be done in 2 + o(1) comarisons er samle in the worst case, where the revious best work (by Lemire) requires 3 comarisons er samle. Our imrovements over the revious work are asymtotic, that is, the number of comarisons is reduced only when the window size is large. Index Terms Mathematical morhology, erosion, dilation, oening, closing. 1 INTRODUCTION GIVEN an inut sequence x 0,..., x n 1 and the window size > 1, the 1D running max filter roblem is to comute the oututs y i = max 0 j< x i+j for 0 i n. The 1D running min filter roblem is defined in a similar way (by changing max to min). In the d-dimensional case, a d-dimensional cube is used as a window. Throughout this work, we assume that the dimension is one unless otherwise secified. Following revious work [6], [7], [14], the comutation model is the comarison model, i.e., only the number of comarisons for comaring inut elements is counted, and the comarisons between indices (e.g., as art of iterations) are not counted. This means that the inuts can be drawn from any totally ordered set, rather than a restricted universe like {0, 1,..., 255}. Usually, n is very large comared to, so the comlexity is measured by the number Portions of this work were suorted by a grant from City University of Hong Kong (Project No ); by National Science Foundation Grants CNS , CNS , Science and Technology Center CCF ; by an NPRP grant from the Qatar National Research Fund; by Grant FA from the Air Force Office of Scientific Research; by sonsors of the Center for Education and Research in Information Assurance and Security. The statements made herein are solely the resonsibility of the authors. Hao Yuan (the corresonding author) is with the Deartment of Comuter Science, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong, China. haoyuan@cityu.edu.hk Mikhail J. Atallah is with the Deartment of Comuter Science, Purdue University, West Lafayette, IN 47907, USA. mja@cs.urdue.edu of comarisons er outut (or sometimes called er samle) in terms of. Running max/min filters are fundamental oerators in morhological image rocessing [13]. The max filter corresonds to the dilation oerator over gray-scale images using a flat and linear structuring element, and the min filter corresonds to the erosion oerator. Because all the algorithms for the running max filter aly to the min filter, we will only discuss the running max filter. In this work, we also consider the oening and closing filters, which are two basic morhological image rocessing oerators [13]. The oening filter is obtained by first alying the min filter, and then alying the max filter to the result of the revious min filtering. Similarly, the closing filter is obtained by first alying the max filter, and then alying the min filter to the result of the revious max filtering. 1.1 Previous Work A naïve imlementation of the max filter requires 1 comarisons er samle. Pitas [11] gave an algorithm that uses O(log ) comarisons er samle for the max filter 1. An algorithm that does not deend on the window size was given by van Herk [14] and indeendently by Gil and Werman [6]. Their algorithm (HGW for short) requires 3 4/ comarisons er samle. Gevorkian, Astola and Atourian [5] considered indeendent and identically distributed (i.i.d.) inuts, and resented an algorithm that uses / + 1/ 2 exected comarisons er samle. The revious best known worst-case algorithm was due to Gil and Kimmel [7]. Their algorithm (GK for 1. Throughout this work, we use log to reresent log 2.
3 2 short) requires log + O( 1 ) comarisons er samle. The GK algorithm was further imroved by Coltuc [3]. Coltuc s algorithm saves about 1.5/( + 1) comarisons er samle comared to the GK algorithm, but the order is still log + O( 1 ). For i.i.d. inuts, Gil and Kimmel also resented an algorithm that requires log exected comarisons er samle. Note that the HGW algorithm can comute semigrou sums in a sliding window using 3 4/ semigrou oerations er samle. The semigrou case was imroved to 3 6/( + 1) oerations er samle by Coltuc [3]. For comuting both the maximum and minimum elements in the sliding window, Lemire [10] resented an algorithm that uses 3 comarisons er samle in the worst case, which is slightly better than running the GK algorithm twice. When the inut is i.i.d., Gil and Kimmel [7] resented an algorithm that uses log() exected comarisons er samle. The community of algorithm and theory studied a more general version of the roblem Range Minimum Query (RMQ). The RMQ roblem is to rerocess an inut array, such that the minimum element within any query window must be returned efficiently. A linear time and sace rerocessing algorithm for 1D RMQ to achieve constant-time query answering was first given by Gabow, Bentley and Tarjan [4], using a linear reduction to the Nearest Common Ancestor (NCA) roblem [9] on the Cartesian tree [15]. The Cartesian tree (defined by Vuillemin [15]) is built on to of the inut array to comletely cature the information necessary to determine the solution for any range minimum query on the original array. It was shown that any range minimum query can be translated to an NCA query on the recomuted Cartesian tree in constant time. The first constant-time NCA solution with linear rerocessing was given by Harel and Tarjan [9], and much effort was sent on simlifying the solution [1], [2], [12]. Multidimensional RMQ was studied by the authors [16]. Note that using the Cartesian tree aroach [15], the 1D max filter can be solved using at most 2 comarisons er samle. The d-dimensional max/min filter can be comuted by alying the 1D filter d times [6], using a structuring element decomosition aroach [8]. Therefore, the GK algorithm can be used to comute the 2D max (or min) filter by 3+o(1) comarisons er samle, and more generally d(1.5 + o(1)) comarisons er samle for d-dimensional cases. The revious best result for the 1D oening/closing filter was O( log2 ) by Gil and Kimmel [7]. They extended the result to the d-dimensional cases using (2d 1)(1.5 + o(1)) comarisons er samle. 1.2 Our Contribution In this work, we resent a simle imrovement based on the GK algorithm for 1D max filter. Our new algorithm achieves log + O( 1 ) comarisons er samle in the worst case, which imroves over the GK algorithm when 20, and over the Coltuc s algorithm when 24. As a consequence, the worstcase comlexity to comute both the maximum and minimum elements in a sliding window becomes log + O( 1 ) comarisons er samle, which imroves the solution of Lemire [10] when 37. This means that our imrovements over revious work are asymtotic, i.e., the number of comarisons is reduced only for large s. Based on our imrovement for the 1D max/min filter, the d-dimensional max (or min) filter can be comuted in d(1+o(1)) comarisons er samle in the worst case. Using the techniques of Gil and Kimmel [7], 1D oening (or closing) filter can be comuted in 1 + O( 1 ) comarisons er samle in the worst case, and the d-dimensional oening and closing can be comuted in (2d 1)(1 + o(1)) comarisons er samle in the worst case. We will first review the GK algorithm in Section 2, and then resent our result in Section 3. Section 4 resents an exerimental evaluation. Section 5 concludes. 2 GIL AND KIMMEL S ALGORITHM We will first review the HGW algorithm, on which the GK algorithm is built. All the given resentations are for the 1D max filter. The HGW algorithm slits the inut sequence into overlaing segments of length 2 1, where the segments are centered at ositions i 1 for 1 i n/. Consider a segment centered at osition c, i.e., x c +1, x c +2,..., x c,..., x c+ 2, x c+ 1. The HGW algorithm generates oututs y c +1, y c +2,..., y c in two stages a rerocessing stage and a merge stage. In the rerocessing stage, refix maximums and suffix maximums are comuted for each block. This consists of comuting P c (k) = max{x c, x c+1,..., x c+k }, S c (k) = max{x c, x c 1,..., x c k }, for 0 k 1. Then in the merge stage, 2 oututs can be obtained by merging the refix maximums and suffix maximums in the following way: for 1 k 2, y c +1+k = max{s c ( 1 k), P c (k)}. (1) We can get the remaining two oututs by y c +1 = S c ( 1), y c = P c ( 1).
4 3 Straightforward imlementation of the rerocessing stage uses 2( 1) comarisons (based on the fact that P c (k) = max{p c (k 1), x c+k } and S c (k) = max{s c (k 1), x c k }), and the merge stage uses 2 comarison. Therefore, the total number of comarisons is 3 4 for generating oututs. The GK algorithm imroves both the rerocessing and merge stages of the HGW algorithm. In the rerocessing stage, the saving of comarisons is achieved by considering the comutations of P c ( ) and S c+ ( ) together when rocessing the elements x c, x c+1,..., x c+. Let q = ( + 1)/2. The GK algorithm first comutes P c (k) for k = 0, 1,..., q 1 using q 1 comarisons, and then comutes S c+ (k) for k = 0, 1,..., q using q comarisons. If P c (q 1) S c+ ( q), then no element in {x c+j q j < } can be greater than P c (q 1). In such a case, we have P c (j) = P c (q 1) for q j < (note that no comarison is required), and only q 1 more comarisons are required to finish comuting S c+ (k) for q < k <. Similarly, if P c (q 1) S c+ ( q), we have S c+ (j) = S c+ ( q) for q < j <, and q more comarisons are required to finish the comutation of P c (k) for q k <. This GK imrovement reduces the total number of comarisons for the ( mod 2) 2. rerocessing stage to 1.5 For the merge stage, the GK algorithm reduces the number of comarisons emloying the following observation: In equation (1), there is an index k such that y c +1+k = S c ( 1 k) for all 1 k k and y c +1+k = P c (k) for all k < k 2. Therefore, a binary search for k using log( 1) comarisons is sufficient to do the merge. Combining the imrovements for the rerocessing stage and the merge stage, the amortized number of comarisons ( mod 2) for oututs is log( 1), which is equivalent to log + O( 1 ) er samle. 3 IMPROVED ALGORITHM Our imrovement is obtained by imroving the rerocessing stage of the GK algorithm. When considering the comutations of S c+ ( ) and P c ( ) together, the GK algorithm achieves saving of comarisons by dividing the sequence x c, x c+1,..., x c+ into two halves, and then comuting the refix maximums of the first half and suffix maximums of the second half. The half that has a smaller maximum will extend the maximum comutation into the other half by doing more comarisons to finish the comutation. The worst case for the GK algorithm haens when the maximum is at or near the boundaries of the sequence x c, x c+1,..., x c+, in which case many comarisons are redundant. For examle, if the maximum is located at x c+3 (assume that it is at the left half), then the refix maximum comutations for P c (i) (where 3 < i < q) cost too many comarisons. This rerocessing strategy can be refined by adatively advancing the refix/suffix maximum comutations, so that not many comarisons are done after the refix/suffix maximum touches the actual maximum of x c, x c+1,..., x c+. At the beginning, a current refix index i and a current suffix index j are both set to 0. The index i is used to track the rogress of refix maximum comutation, and its semantic meaning is that: P c (k) has already been comuted for 0 k i. Similarly, the index j is used to track the rogress of suffix maximum comutation, and it means that S c+ (k) has already been comuted for 0 k j. Note that initially, P c (0) = x c and S c+ (0) = x c+. Let s 1 be a default ste size (a arameter whose value will be fixed to 1 later). Our algorithm will adatively advance the value of i and j until i + j = + s 1. In each advancement (excet the last one), either i or j will be advanced by s. In the last advancement (right before i + j reaches + s 1), the ste size is s if ( 1) mod s = 0; or the ste size is ( 1) mod s if ( 1) mod s 0. More secifically, excet in the last advancement, if P c (i) S c+ (j), then P c (k) for i < k i + s will be comuted, and after that i will have increased by s. Similarly, if P c (i) > S c+ (j), then S c+ (k) for j < k j + s will be comuted, and after that j will have increased by s. In the last advancement, similar comutation is done excet that a different ste size ( 1) mod s may be used (see the beginning art of this aragrah). There are +s 1 s advancements. So the number of comarisons sent on determining whether to advance i or j (by comaring P c (i) to S c+ (j)) is +s 1 s. At each time when i (or j) is increased by δ, there are δ comarisons for comuting δ entries of P c ( ) (or S c+ ( )). Because i + j is 0 at the beginning, and is changed to + s 1 at the end, + s 1 comarisons are made other than the comarisons for determining whether to advance i or j. So the total number of comarisons so far is + s 1 + s 1 +. s After i + j = + s 1, no comarison is required and we will show that P c (k) = P c (i) for i < k <, (2) S c+ (k) = S c+ (j) for j < k <. (3) The rerocessing stage is finished, and the correctness is based on Lemma 1 (given below). The seudocode of this algorithm is given in Algorithm 1. Line 5 sets the δ to be the advancement ste size. Lines 7 to 10 advance the refix comutations, and lines 12 to 15 advance the suffix comutations. Note that in Algorithm 1, some secial boundary cases are considered when i or j reaches 1, but these cases do not affect the correctness and comlexity of the algorithm. Lemma 1: When i + j = + s 1, equations (2) and (3) hold.
5 4 Algorithm 1: Imroved Prerocessing Stage Inut: x c, x c+1,..., x c+ and a arameter s Outut: P c (k) and S c+ (k) for 0 k 1 1 P c (0) x c 2 S c+ (0) x c+ 3 i 0, j 0 4 while i + j < + s 1 do 5 δ min{s, + s 1 i j} 6 if i < 1 and P c (i) S c+ (j) then 7 for k = i + 1 to min{i + δ, 1} do 8 P c (k) max{p c (k 1), x c+k } 9 end 10 i i + δ 11 else 12 for k = j + 1 to min{j + δ, 1} do 13 S c+ (k) max{s c+ (k 1), x c+ k } 14 end 15 j j + δ 16 end 17 end 18 while i < 1 do 19 i i P c (i) P c (i 1) 21 end 22 while j < 1 do 23 j j S c+ (j) S c+ (j 1) 25 end Proof: Without loss of generality, assume that all the inut elements are distinct (ties can be broken by considering their indices). After each advancement, let l be the index of the maximum element of {x k k [c, c+i] [c+ j, c+]} (the set of elements considered so far), then we must have either c + i s < l c + i or c + j l < c + j + s. In other words, l is within a distance of s 1 from either c + i or c + j. This is because the algorithm always advances i if the current refix maximum is smaller, or advances j if the current suffix maximum is smaller. When i+j = +s 1, because of c+i+1 c+ j, the x l is the maximum element of {x k k [c, c + ]}. According to the revious aragrah, l c + i or l < c + j + s. The latter inequality imlies that: l c + j + s 1 = c + ( + s 1 j) = c + i. Therefore, we always have l c + i. This means that no element in {x k k [c+i+1, c+)} can be greater than the current refix maximum, hence equation (2) holds. By a similar argument, equation (3) holds. If s = 1, then the total number of comarisons for the rerocessing stage is bounded by + s 1 + s 1 + s 1 = = Combining with the merge stage of the GK algorithm (which requires log( 1) comarisons by a binary search), the total amortized number of comarisons er samle of Algorithm 1 is bounded by C 1 = 1 ( log( 1) 1 ( log + 3) log ( ) 1 + O ( ) 1 = 1 + O = 1 + o(1). This establishes the following theorem: Theorem 1: The 1D running maximum (or minimum) filter can be comuted in 1 + o(1) comarisons er samle in the worst case by a deterministic algorithm. Note that the GK algorithm is very similar to ours when s = q 1 = ( 1)/2. It was shown that the d-dimensional max/min filter can be comuted by alying the 1D filter d times [6], using a structuring element decomosition aroach [8]. More secifically, the following lemma holds: Lemma 2: Let C 1 () be the number of comarisons er samle of an 1D filter for a 1D window of size, then a d-dimensional max/min filter with window size 1 2 d can be comuted by d i=1 C 1( i ) comarisons er samle. Based on Lemma 2, we have Corollary 1. Corollary 1: The d-dimensional maximum (or minimum) filter can be comuted deterministically using d(1 + o(1)) comarisons er samle in the worst case. Gil and Kimmel [7] showed that the oening/closing filter can be comuted using C 1 +O( log2 ) comarisons er samle. Therefore, the number of comarisons er samle for comuting the oening (or closing) filter is at most ( log 2 ) C 1 + O ( ) ( 1 log 2 ) =1 + O + O ( ) 1 =1 + O =1 + o(1). )
6 5 Exeriment Time in Seconds Algorithms YA GK HGW Window Size (i.e., ) Fig. 1: Exeriment result. So Corollary 2 is established. Corollary 2: The 1D oening (or closing) filter can be comuted deterministically using 1 + o(1) comarisons er samle in the worst case. Gil and Kimmel [7] shows that d-dimensional oening (or closing) can be comuted by running 1D min filter d 1 times, 1D max filter d 1 times, and 1D oening (or closing) filter once. So we have Corollary 3. Corollary 3: The d-dimensional oening (or closing) filter can be comuted deterministically using (2d 1)(1+o(1)) comarisons er samle in the worst case. 4 EXPERIMENTAL EVALUATION The comarison model does not cature other costs, like comarisons between indices, memory accesses, branch misredictions, etc. Therefore, we do not exect our algorithm to beat existing methods in actual imlementations even when the window size is large, unless the comarison between two inut elements is very exensive. So here, we only show the exeriment result for the case where the costs to comare inut elements are high. One such a case is when two 128-bit floating-oint numbers are comared in a 64- bit rocessor without hardware suorts for 128-bit floating-oint comutations. Note that for the cases when the comarisons of inut elements are chea, we do not observe that our algorithm outerforms revious ones even for large window sizes. We imlemented the 1D max filter using the HGW algorithm, GK algorithm, and our algorithm in C++. The exeriment is conducted on a lato comuter with an Intel Core i5-540m 2.53GHz rocessor and 2GB main memory. The oerating system is Ubuntu bit version, and the comiler is the GNU Comiler Collections (GCC) The comilation otion that we used is -O2. The comiled binary file is in the 64-bit mode. The data tye is the quadrule recision floating-oint number (e.g., float128 in the C++ of GCC), which has 128 bits. The comarisons for quadrule recision floating-oint numbers are very exensive, because they are currently imlemented using a software emulation. We generated 10 7 random inut numbers, and tested the three algorithms on the inut with window sizes from 2 to 100. The running times are shown in Figure 1. Our algorithm (denoted by YA in the figure) outerforms the GK algorithm when 33 in this exeriment. 5 CONCLUDING REMARKS In this work, we asymtotically imrove the state-ofthe-art for comuting running max/min filters. Some questions remain oen: Is it ossible to simultaneously comute the 1D maximum and minimum filters with less than 2C 1 (e.g., 2 or even 1.5) comarisons er samle? Is it ossible to comute the 2D maximum (or minimum) filter with less than 2C 1 (e.g., 2 or even 1.5) comarisons er samle? Can the 2D oening or closing be comuted by 3 or less comarisons er samle?
7 6 ACKNOWLEDGMENTS We would like to thank the referees for their helful comments and suggestions. REFERENCES [1] S. Alstru, C. Gavoille, H. Kalan, and T. Rauhe, Nearest common ancestors: a survey and a new distributed algorithm, in SPAA 02: Proceedings of the fourteenth annual ACM symosium on Parallel algorithms and architectures. New York, NY, USA: ACM, 2002, [2] M. A. Bender, M. Farach-Colton, G. Pemmasani, S. Skiena, and P. Sumazin, Lowest common ancestors in trees and directed acyclic grahs, Journal of Algorithms, vol. 57, no. 2, , [3] D. Coltuc, Mathematical comlexity of running filters on semi-grous and related roblems, Signal Processing, IEEE Transactions on, vol. 56, no. 7, , jul [4] H. N. Gabow, J. L. Bentley, and R. E. Tarjan, Scaling and related techniques for geometry roblems, in STOC 84: Proceedings of the sixteenth annual ACM symosium on Theory of comuting. New York, NY, USA: ACM, 1984, [5] D. Gevorkian, J. Astola, and S. Atourian, Imroving gilwerman algorithm for running min and max filters, Pattern Analysis and Machine Intelligence, IEEE Transactions on, vol. 19, no. 5, , may [6] J. Gil and M. Werman, Comuting 2-d min, median, and max filters, Pattern Analysis and Machine Intelligence, IEEE Transactions on, vol. 15, no. 5, , may [7] J. Gil and R. Kimmel, Efficient dilation, erosion, oening, and closing algorithms, Pattern Analysis and Machine Intelligence, IEEE Transactions on, vol. 24, no. 12, , dec [8] R. M. Haralick, S. R. Sternberg, and X. Zhuang, Image analysis using mathematical morhology, Pattern Analysis and Machine Intelligence, IEEE Transactions on, vol. PAMI-9, no. 4, , jul [9] D. Harel and R. E. Tarjan, Fast algorithms for finding nearest common ancestors, SIAM Journal of Comuting, vol. 13, no. 2, , [10] D. Lemire, Streaming maximum-minimum filter using no more than three comarisons er element, Nordic Journal of Comuting, vol. 13, no. 4, , [11] I. Pitas, Fast algorithms for running ordering and max/min calculation, Circuits and Systems, IEEE Transactions on, vol. 36, no. 6, , jun [12] B. Schieber and U. Vishkin, On finding lowest common ancestors: simlification and arallelization, SIAM Journal on Comuting, vol. 17, no. 6, , [13] P. Soille, Morhological Image Analysis: Princiles and Alications. Secaucus, NJ, USA: Sringer-Verlag New York, Inc., [14] M. van Herk, A fast algorithm for local minimum and maximum filters on rectangular and octagonal kernels, Pattern Recognition Letters, vol. 13, no. 7, , [Online]. Available: htt:// B6V15-48N559B-18/2/1b976a6102acf3d50831ad0e75a481e2 [15] J. Vuillemin, A unifying look at data structures, Communications of the ACM, vol. 23, no. 4, , [16] H. Yuan and M. J. Atallah, Data structures for range minimum queries in multidimensional arrays, in Proceedings of the Twenty-First Annual ACM-SIAM Symosium on Discrete Algorithms (SODA 2010), 2010,
Topic: Lower Bounds on Randomized Algorithms Date: September 22, 2004 Scribe: Srinath Sridhar
15-859(M): Randomized Algorithms Lecturer: Anuam Guta Toic: Lower Bounds on Randomized Algorithms Date: Setember 22, 2004 Scribe: Srinath Sridhar 4.1 Introduction In this lecture, we will first consider
More informationComputer arithmetic. Intensive Computation. Annalisa Massini 2017/2018
Comuter arithmetic Intensive Comutation Annalisa Massini 7/8 Intensive Comutation - 7/8 References Comuter Architecture - A Quantitative Aroach Hennessy Patterson Aendix J Intensive Comutation - 7/8 3
More informationMODELING THE RELIABILITY OF C4ISR SYSTEMS HARDWARE/SOFTWARE COMPONENTS USING AN IMPROVED MARKOV MODEL
Technical Sciences and Alied Mathematics MODELING THE RELIABILITY OF CISR SYSTEMS HARDWARE/SOFTWARE COMPONENTS USING AN IMPROVED MARKOV MODEL Cezar VASILESCU Regional Deartment of Defense Resources Management
More informationApproximating min-max k-clustering
Aroximating min-max k-clustering Asaf Levin July 24, 2007 Abstract We consider the roblems of set artitioning into k clusters with minimum total cost and minimum of the maximum cost of a cluster. The cost
More informationData Structures for Range Minimum Queries in Multidimensional Arrays
Data Structures for Range Minimum Queries in Multidimensional Arrays Hao Yuan Mikhail J. Atallah Abstract Given a d-dimensional array A with N entries, the Range Minimum Query (RMQ) asks for the minimum
More informationA Parallel Algorithm for Minimization of Finite Automata
A Parallel Algorithm for Minimization of Finite Automata B. Ravikumar X. Xiong Deartment of Comuter Science University of Rhode Island Kingston, RI 02881 E-mail: fravi,xiongg@cs.uri.edu Abstract In this
More informationThe Knuth-Yao Quadrangle-Inequality Speedup is a Consequence of Total-Monotonicity
The Knuth-Yao Quadrangle-Ineuality Seedu is a Conseuence of Total-Monotonicity Wolfgang W. Bein Mordecai J. Golin Lawrence L. Larmore Yan Zhang Abstract There exist several general techniues in the literature
More informationImproved Capacity Bounds for the Binary Energy Harvesting Channel
Imroved Caacity Bounds for the Binary Energy Harvesting Channel Kaya Tutuncuoglu 1, Omur Ozel 2, Aylin Yener 1, and Sennur Ulukus 2 1 Deartment of Electrical Engineering, The Pennsylvania State University,
More informationShadow Computing: An Energy-Aware Fault Tolerant Computing Model
Shadow Comuting: An Energy-Aware Fault Tolerant Comuting Model Bryan Mills, Taieb Znati, Rami Melhem Deartment of Comuter Science University of Pittsburgh (bmills, znati, melhem)@cs.itt.edu Index Terms
More informationThe Graph Accessibility Problem and the Universality of the Collision CRCW Conflict Resolution Rule
The Grah Accessibility Problem and the Universality of the Collision CRCW Conflict Resolution Rule STEFAN D. BRUDA Deartment of Comuter Science Bisho s University Lennoxville, Quebec J1M 1Z7 CANADA bruda@cs.ubishos.ca
More informationMATH 2710: NOTES FOR ANALYSIS
MATH 270: NOTES FOR ANALYSIS The main ideas we will learn from analysis center around the idea of a limit. Limits occurs in several settings. We will start with finite limits of sequences, then cover infinite
More informationFor q 0; 1; : : : ; `? 1, we have m 0; 1; : : : ; q? 1. The set fh j(x) : j 0; 1; ; : : : ; `? 1g forms a basis for the tness functions dened on the i
Comuting with Haar Functions Sami Khuri Deartment of Mathematics and Comuter Science San Jose State University One Washington Square San Jose, CA 9519-0103, USA khuri@juiter.sjsu.edu Fax: (40)94-500 Keywords:
More informationUniversal Finite Memory Coding of Binary Sequences
Deartment of Electrical Engineering Systems Universal Finite Memory Coding of Binary Sequences Thesis submitted towards the degree of Master of Science in Electrical and Electronic Engineering in Tel-Aviv
More informationThe inverse Goldbach problem
1 The inverse Goldbach roblem by Christian Elsholtz Submission Setember 7, 2000 (this version includes galley corrections). Aeared in Mathematika 2001. Abstract We imrove the uer and lower bounds of the
More informationOn Line Parameter Estimation of Electric Systems using the Bacterial Foraging Algorithm
On Line Parameter Estimation of Electric Systems using the Bacterial Foraging Algorithm Gabriel Noriega, José Restreo, Víctor Guzmán, Maribel Giménez and José Aller Universidad Simón Bolívar Valle de Sartenejas,
More informationAn Introduction To Range Searching
An Introduction To Range Searching Jan Vahrenhold eartment of Comuter Science Westfälische Wilhelms-Universität Münster, Germany. Overview 1. Introduction: Problem Statement, Lower Bounds 2. Range Searching
More informationPositive decomposition of transfer functions with multiple poles
Positive decomosition of transfer functions with multile oles Béla Nagy 1, Máté Matolcsi 2, and Márta Szilvási 1 Deartment of Analysis, Technical University of Budaest (BME), H-1111, Budaest, Egry J. u.
More informationMatching Partition a Linked List and Its Optimization
Matching Partition a Linked List and Its Otimization Yijie Han Deartment of Comuter Science University of Kentucky Lexington, KY 40506 ABSTRACT We show the curve O( n log i + log (i) n + log i) for the
More informationOn the capacity of the general trapdoor channel with feedback
On the caacity of the general tradoor channel with feedback Jui Wu and Achilleas Anastasooulos Electrical Engineering and Comuter Science Deartment University of Michigan Ann Arbor, MI, 48109-1 email:
More informationNew Schedulability Test Conditions for Non-preemptive Scheduling on Multiprocessor Platforms
New Schedulability Test Conditions for Non-reemtive Scheduling on Multirocessor Platforms Technical Reort May 2008 Nan Guan 1, Wang Yi 2, Zonghua Gu 3 and Ge Yu 1 1 Northeastern University, Shenyang, China
More informationTests for Two Proportions in a Stratified Design (Cochran/Mantel-Haenszel Test)
Chater 225 Tests for Two Proortions in a Stratified Design (Cochran/Mantel-Haenszel Test) Introduction In a stratified design, the subects are selected from two or more strata which are formed from imortant
More informationAnalysis of execution time for parallel algorithm to dertmine if it is worth the effort to code and debug in parallel
Performance Analysis Introduction Analysis of execution time for arallel algorithm to dertmine if it is worth the effort to code and debug in arallel Understanding barriers to high erformance and redict
More informationState Estimation with ARMarkov Models
Deartment of Mechanical and Aerosace Engineering Technical Reort No. 3046, October 1998. Princeton University, Princeton, NJ. State Estimation with ARMarkov Models Ryoung K. Lim 1 Columbia University,
More informationElliptic Curves and Cryptography
Ellitic Curves and Crytograhy Background in Ellitic Curves We'll now turn to the fascinating theory of ellitic curves. For simlicity, we'll restrict our discussion to ellitic curves over Z, where is a
More informationUsing a Computational Intelligence Hybrid Approach to Recognize the Faults of Variance Shifts for a Manufacturing Process
Journal of Industrial and Intelligent Information Vol. 4, No. 2, March 26 Using a Comutational Intelligence Hybrid Aroach to Recognize the Faults of Variance hifts for a Manufacturing Process Yuehjen E.
More informationVerifying Two Conjectures on Generalized Elite Primes
1 2 3 47 6 23 11 Journal of Integer Sequences, Vol. 12 (2009), Article 09.4.7 Verifying Two Conjectures on Generalized Elite Primes Xiaoqin Li 1 Mathematics Deartment Anhui Normal University Wuhu 241000,
More informationUnit 1 - Computer Arithmetic
FIXD-POINT (FX) ARITHMTIC Unit 1 - Comuter Arithmetic INTGR NUMBRS n bit number: b n 1 b n 2 b 0 Decimal Value Range of values UNSIGND n 1 SIGND D = b i 2 i D = 2 n 1 b n 1 + b i 2 i n 2 i=0 i=0 [0, 2
More informationUncorrelated Multilinear Principal Component Analysis for Unsupervised Multilinear Subspace Learning
TNN-2009-P-1186.R2 1 Uncorrelated Multilinear Princial Comonent Analysis for Unsuervised Multilinear Subsace Learning Haiing Lu, K. N. Plataniotis and A. N. Venetsanooulos The Edward S. Rogers Sr. Deartment
More informationSAT based Abstraction-Refinement using ILP and Machine Learning Techniques
SAT based Abstraction-Refinement using ILP and Machine Learning Techniques 1 SAT based Abstraction-Refinement using ILP and Machine Learning Techniques Edmund Clarke James Kukula Anubhav Guta Ofer Strichman
More information1-way quantum finite automata: strengths, weaknesses and generalizations
1-way quantum finite automata: strengths, weaknesses and generalizations arxiv:quant-h/9802062v3 30 Se 1998 Andris Ambainis UC Berkeley Abstract Rūsiņš Freivalds University of Latvia We study 1-way quantum
More informationAn Ant Colony Optimization Approach to the Probabilistic Traveling Salesman Problem
An Ant Colony Otimization Aroach to the Probabilistic Traveling Salesman Problem Leonora Bianchi 1, Luca Maria Gambardella 1, and Marco Dorigo 2 1 IDSIA, Strada Cantonale Galleria 2, CH-6928 Manno, Switzerland
More informationSystem Reliability Estimation and Confidence Regions from Subsystem and Full System Tests
009 American Control Conference Hyatt Regency Riverfront, St. Louis, MO, USA June 0-, 009 FrB4. System Reliability Estimation and Confidence Regions from Subsystem and Full System Tests James C. Sall Abstract
More informationMATHEMATICAL MODELLING OF THE WIRELESS COMMUNICATION NETWORK
Comuter Modelling and ew Technologies, 5, Vol.9, o., 3-39 Transort and Telecommunication Institute, Lomonosov, LV-9, Riga, Latvia MATHEMATICAL MODELLIG OF THE WIRELESS COMMUICATIO ETWORK M. KOPEETSK Deartment
More informationJohn Weatherwax. Analysis of Parallel Depth First Search Algorithms
Sulementary Discussions and Solutions to Selected Problems in: Introduction to Parallel Comuting by Viin Kumar, Ananth Grama, Anshul Guta, & George Karyis John Weatherwax Chater 8 Analysis of Parallel
More informationPreconditioning techniques for Newton s method for the incompressible Navier Stokes equations
Preconditioning techniques for Newton s method for the incomressible Navier Stokes equations H. C. ELMAN 1, D. LOGHIN 2 and A. J. WATHEN 3 1 Deartment of Comuter Science, University of Maryland, College
More informationLinear diophantine equations for discrete tomography
Journal of X-Ray Science and Technology 10 001 59 66 59 IOS Press Linear diohantine euations for discrete tomograhy Yangbo Ye a,gewang b and Jiehua Zhu a a Deartment of Mathematics, The University of Iowa,
More informationCombining Logistic Regression with Kriging for Mapping the Risk of Occurrence of Unexploded Ordnance (UXO)
Combining Logistic Regression with Kriging for Maing the Risk of Occurrence of Unexloded Ordnance (UXO) H. Saito (), P. Goovaerts (), S. A. McKenna (2) Environmental and Water Resources Engineering, Deartment
More informationMulti-Operation Multi-Machine Scheduling
Multi-Oeration Multi-Machine Scheduling Weizhen Mao he College of William and Mary, Williamsburg VA 3185, USA Abstract. In the multi-oeration scheduling that arises in industrial engineering, each job
More informationA generalization of Amdahl's law and relative conditions of parallelism
A generalization of Amdahl's law and relative conditions of arallelism Author: Gianluca Argentini, New Technologies and Models, Riello Grou, Legnago (VR), Italy. E-mail: gianluca.argentini@riellogrou.com
More information2-D Analysis for Iterative Learning Controller for Discrete-Time Systems With Variable Initial Conditions Yong FANG 1, and Tommy W. S.
-D Analysis for Iterative Learning Controller for Discrete-ime Systems With Variable Initial Conditions Yong FANG, and ommy W. S. Chow Abstract In this aer, an iterative learning controller alying to linear
More informationEstimation of the large covariance matrix with two-step monotone missing data
Estimation of the large covariance matrix with two-ste monotone missing data Masashi Hyodo, Nobumichi Shutoh 2, Takashi Seo, and Tatjana Pavlenko 3 Deartment of Mathematical Information Science, Tokyo
More informationUse of Transformations and the Repeated Statement in PROC GLM in SAS Ed Stanek
Use of Transformations and the Reeated Statement in PROC GLM in SAS Ed Stanek Introduction We describe how the Reeated Statement in PROC GLM in SAS transforms the data to rovide tests of hyotheses of interest.
More informationProbability Estimates for Multi-class Classification by Pairwise Coupling
Probability Estimates for Multi-class Classification by Pairwise Couling Ting-Fan Wu Chih-Jen Lin Deartment of Comuter Science National Taiwan University Taiei 06, Taiwan Ruby C. Weng Deartment of Statistics
More informationA randomized sorting algorithm on the BSP model
A randomized sorting algorithm on the BSP model Alexandros V. Gerbessiotis a, Constantinos J. Siniolakis b a CS Deartment, New Jersey Institute of Technology, Newark, NJ 07102, USA b The American College
More informationRecursive Estimation of the Preisach Density function for a Smart Actuator
Recursive Estimation of the Preisach Density function for a Smart Actuator Ram V. Iyer Deartment of Mathematics and Statistics, Texas Tech University, Lubbock, TX 7949-142. ABSTRACT The Preisach oerator
More informationarxiv:cond-mat/ v2 25 Sep 2002
Energy fluctuations at the multicritical oint in two-dimensional sin glasses arxiv:cond-mat/0207694 v2 25 Se 2002 1. Introduction Hidetoshi Nishimori, Cyril Falvo and Yukiyasu Ozeki Deartment of Physics,
More informationCubic Sieve Congruence of the Discrete Logarithm Problem, and Fractional Part Sequences
Cubic Sieve Congruence of the Discrete Logarithm Problem, and Fractional Part Sequences Srinivas Vivek University of Luxembourg, Luxembourg C. E. Veni Madhavan Deartment of Comuter Science and Automation,
More informationA New Method of DDB Logical Structure Synthesis Using Distributed Tabu Search
A New Method of DDB Logical Structure Synthesis Using Distributed Tabu Search Eduard Babkin and Margarita Karunina 2, National Research University Higher School of Economics Det of nformation Systems and
More informationGeneralized Coiflets: A New Family of Orthonormal Wavelets
Generalized Coiflets A New Family of Orthonormal Wavelets Dong Wei, Alan C Bovik, and Brian L Evans Laboratory for Image and Video Engineering Deartment of Electrical and Comuter Engineering The University
More informationOn Wald-Type Optimal Stopping for Brownian Motion
J Al Probab Vol 34, No 1, 1997, (66-73) Prerint Ser No 1, 1994, Math Inst Aarhus On Wald-Tye Otimal Stoing for Brownian Motion S RAVRSN and PSKIR The solution is resented to all otimal stoing roblems of
More informationModeling and Estimation of Full-Chip Leakage Current Considering Within-Die Correlation
6.3 Modeling and Estimation of Full-Chi Leaage Current Considering Within-Die Correlation Khaled R. eloue, Navid Azizi, Farid N. Najm Deartment of ECE, University of Toronto,Toronto, Ontario, Canada {haled,nazizi,najm}@eecg.utoronto.ca
More informationAdditive results for the generalized Drazin inverse in a Banach algebra
Additive results for the generalized Drazin inverse in a Banach algebra Dragana S. Cvetković-Ilić Dragan S. Djordjević and Yimin Wei* Abstract In this aer we investigate additive roerties of the generalized
More information16. Binary Search Trees
Dictionary imlementation 16. Binary Search Trees [Ottman/Widmayer, Ka..1, Cormen et al, Ka. 1.1-1.] Hashing: imlementation of dictionaries with exected very fast access times. Disadvantages of hashing:
More informationAn Adaptive Three-bus Power System Equivalent for Estimating Voltage Stability Margin from Synchronized Phasor Measurements
An Adative Three-bus Power System Equivalent for Estimating oltage Stability argin from Synchronized Phasor easurements Fengkai Hu, Kai Sun University of Tennessee Knoxville, TN, USA fengkaihu@utk.edu
More informationOn split sample and randomized confidence intervals for binomial proportions
On slit samle and randomized confidence intervals for binomial roortions Måns Thulin Deartment of Mathematics, Usala University arxiv:1402.6536v1 [stat.me] 26 Feb 2014 Abstract Slit samle methods have
More informationCERIAS Tech Report The period of the Bell numbers modulo a prime by Peter Montgomery, Sangil Nahm, Samuel Wagstaff Jr Center for Education
CERIAS Tech Reort 2010-01 The eriod of the Bell numbers modulo a rime by Peter Montgomery, Sangil Nahm, Samuel Wagstaff Jr Center for Education and Research Information Assurance and Security Purdue University,
More informationFeedback-error control
Chater 4 Feedback-error control 4.1 Introduction This chater exlains the feedback-error (FBE) control scheme originally described by Kawato [, 87, 8]. FBE is a widely used neural network based controller
More information16. Binary Search Trees
Dictionary imlementation 16. Binary Search Trees [Ottman/Widmayer, Ka..1, Cormen et al, Ka. 12.1-12.] Hashing: imlementation of dictionaries with exected very fast access times. Disadvantages of hashing:
More informationA New Perspective on Learning Linear Separators with Large L q L p Margins
A New Persective on Learning Linear Searators with Large L q L Margins Maria-Florina Balcan Georgia Institute of Technology Christoher Berlind Georgia Institute of Technology Abstract We give theoretical
More informationParallelism and Locality in Priority Queues. A. Ranade S. Cheng E. Deprit J. Jones S. Shih. University of California. Berkeley, CA 94720
Parallelism and Locality in Priority Queues A. Ranade S. Cheng E. Derit J. Jones S. Shih Comuter Science Division University of California Berkeley, CA 94720 Abstract We exlore two ways of incororating
More informationarxiv: v1 [physics.data-an] 26 Oct 2012
Constraints on Yield Parameters in Extended Maximum Likelihood Fits Till Moritz Karbach a, Maximilian Schlu b a TU Dortmund, Germany, moritz.karbach@cern.ch b TU Dortmund, Germany, maximilian.schlu@cern.ch
More information1. INTRODUCTION. Fn 2 = F j F j+1 (1.1)
CERTAIN CLASSES OF FINITE SUMS THAT INVOLVE GENERALIZED FIBONACCI AND LUCAS NUMBERS The beautiful identity R.S. Melham Deartment of Mathematical Sciences, University of Technology, Sydney PO Box 23, Broadway,
More informationEnd-to-End Delay Minimization in Thermally Constrained Distributed Systems
End-to-End Delay Minimization in Thermally Constrained Distributed Systems Pratyush Kumar, Lothar Thiele Comuter Engineering and Networks Laboratory (TIK) ETH Zürich, Switzerland {ratyush.kumar, lothar.thiele}@tik.ee.ethz.ch
More informationUncertainty Modeling with Interval Type-2 Fuzzy Logic Systems in Mobile Robotics
Uncertainty Modeling with Interval Tye-2 Fuzzy Logic Systems in Mobile Robotics Ondrej Linda, Student Member, IEEE, Milos Manic, Senior Member, IEEE bstract Interval Tye-2 Fuzzy Logic Systems (IT2 FLSs)
More informationAn Investigation on the Numerical Ill-conditioning of Hybrid State Estimators
An Investigation on the Numerical Ill-conditioning of Hybrid State Estimators S. K. Mallik, Student Member, IEEE, S. Chakrabarti, Senior Member, IEEE, S. N. Singh, Senior Member, IEEE Deartment of Electrical
More informationq-ary Symmetric Channel for Large q
List-Message Passing Achieves Caacity on the q-ary Symmetric Channel for Large q Fan Zhang and Henry D Pfister Deartment of Electrical and Comuter Engineering, Texas A&M University {fanzhang,hfister}@tamuedu
More informationA Comparison between Biased and Unbiased Estimators in Ordinary Least Squares Regression
Journal of Modern Alied Statistical Methods Volume Issue Article 7 --03 A Comarison between Biased and Unbiased Estimators in Ordinary Least Squares Regression Ghadban Khalaf King Khalid University, Saudi
More informationGOOD MODELS FOR CUBIC SURFACES. 1. Introduction
GOOD MODELS FOR CUBIC SURFACES ANDREAS-STEPHAN ELSENHANS Abstract. This article describes an algorithm for finding a model of a hyersurface with small coefficients. It is shown that the aroach works in
More informationarxiv: v2 [quant-ph] 2 Aug 2012
Qcomiler: quantum comilation with CSD method Y. G. Chen a, J. B. Wang a, a School of Physics, The University of Western Australia, Crawley WA 6009 arxiv:208.094v2 [quant-h] 2 Aug 202 Abstract In this aer,
More informationE-companion to A risk- and ambiguity-averse extension of the max-min newsvendor order formula
e-comanion to Han Du and Zuluaga: Etension of Scarf s ma-min order formula ec E-comanion to A risk- and ambiguity-averse etension of the ma-min newsvendor order formula Qiaoming Han School of Mathematics
More informationHomework Set #3 Rates definitions, Channel Coding, Source-Channel coding
Homework Set # Rates definitions, Channel Coding, Source-Channel coding. Rates (a) Channels coding Rate: Assuming you are sending 4 different messages using usages of a channel. What is the rate (in bits
More informationRUN-TO-RUN CONTROL AND PERFORMANCE MONITORING OF OVERLAY IN SEMICONDUCTOR MANUFACTURING. 3 Department of Chemical Engineering
Coyright 2002 IFAC 15th Triennial World Congress, Barcelona, Sain RUN-TO-RUN CONTROL AND PERFORMANCE MONITORING OF OVERLAY IN SEMICONDUCTOR MANUFACTURING C.A. Bode 1, B.S. Ko 2, and T.F. Edgar 3 1 Advanced
More informationHotelling s Two- Sample T 2
Chater 600 Hotelling s Two- Samle T Introduction This module calculates ower for the Hotelling s two-grou, T-squared (T) test statistic. Hotelling s T is an extension of the univariate two-samle t-test
More informationsubstantial literature on emirical likelihood indicating that it is widely viewed as a desirable and natural aroach to statistical inference in a vari
Condence tubes for multile quantile lots via emirical likelihood John H.J. Einmahl Eindhoven University of Technology Ian W. McKeague Florida State University May 7, 998 Abstract The nonarametric emirical
More informationA Qualitative Event-based Approach to Multiple Fault Diagnosis in Continuous Systems using Structural Model Decomposition
A Qualitative Event-based Aroach to Multile Fault Diagnosis in Continuous Systems using Structural Model Decomosition Matthew J. Daigle a,,, Anibal Bregon b,, Xenofon Koutsoukos c, Gautam Biswas c, Belarmino
More informationHENSEL S LEMMA KEITH CONRAD
HENSEL S LEMMA KEITH CONRAD 1. Introduction In the -adic integers, congruences are aroximations: for a and b in Z, a b mod n is the same as a b 1/ n. Turning information modulo one ower of into similar
More informationRobust Predictive Control of Input Constraints and Interference Suppression for Semi-Trailer System
Vol.7, No.7 (4),.37-38 htt://dx.doi.org/.457/ica.4.7.7.3 Robust Predictive Control of Inut Constraints and Interference Suression for Semi-Trailer System Zhao, Yang Electronic and Information Technology
More informationInformation collection on a graph
Information collection on a grah Ilya O. Ryzhov Warren Powell February 10, 2010 Abstract We derive a knowledge gradient olicy for an otimal learning roblem on a grah, in which we use sequential measurements
More informationModel checking, verification of CTL. One must verify or expel... doubts, and convert them into the certainty of YES [Thomas Carlyle]
Chater 5 Model checking, verification of CTL One must verify or exel... doubts, and convert them into the certainty of YES or NO. [Thomas Carlyle] 5. The verification setting Page 66 We introduce linear
More informationEnergy-aware optimisation for run-time reconfiguration
Energy-aware otimisation for run-time reconfiguration Tobias Becker and Wayne Luk Deartment of Comuting Imerial College London, UK eter Y. K. Cheung Deartment of Electrical and Electronic Engineering Imerial
More informationEstimation of component redundancy in optimal age maintenance
EURO MAINTENANCE 2012, Belgrade 14-16 May 2012 Proceedings of the 21 st International Congress on Maintenance and Asset Management Estimation of comonent redundancy in otimal age maintenance Jorge ioa
More informationSolving Cyclotomic Polynomials by Radical Expressions Andreas Weber and Michael Keckeisen
Solving Cyclotomic Polynomials by Radical Exressions Andreas Weber and Michael Keckeisen Abstract: We describe a Male ackage that allows the solution of cyclotomic olynomials by radical exressions. We
More informationA Network-Flow Based Cell Sizing Algorithm
A Networ-Flow Based Cell Sizing Algorithm Huan Ren and Shantanu Dutt Det. of ECE, University of Illinois-Chicago Abstract We roose a networ flow based algorithm for the area-constrained timing-driven discrete
More informationON POLYNOMIAL SELECTION FOR THE GENERAL NUMBER FIELD SIEVE
MATHEMATICS OF COMPUTATIO Volume 75, umber 256, October 26, Pages 237 247 S 25-5718(6)187-9 Article electronically ublished on June 28, 26 O POLYOMIAL SELECTIO FOR THE GEERAL UMBER FIELD SIEVE THORSTE
More information#A64 INTEGERS 18 (2018) APPLYING MODULAR ARITHMETIC TO DIOPHANTINE EQUATIONS
#A64 INTEGERS 18 (2018) APPLYING MODULAR ARITHMETIC TO DIOPHANTINE EQUATIONS Ramy F. Taki ElDin Physics and Engineering Mathematics Deartment, Faculty of Engineering, Ain Shams University, Cairo, Egyt
More information2 K. ENTACHER 2 Generalized Haar function systems In the following we x an arbitrary integer base b 2. For the notations and denitions of generalized
BIT 38 :2 (998), 283{292. QUASI-MONTE CARLO METHODS FOR NUMERICAL INTEGRATION OF MULTIVARIATE HAAR SERIES II KARL ENTACHER y Deartment of Mathematics, University of Salzburg, Hellbrunnerstr. 34 A-52 Salzburg,
More informationResearch of PMU Optimal Placement in Power Systems
Proceedings of the 5th WSEAS/IASME Int. Conf. on SYSTEMS THEORY and SCIENTIFIC COMPUTATION, Malta, Setember 15-17, 2005 (38-43) Research of PMU Otimal Placement in Power Systems TIAN-TIAN CAI, QIAN AI
More informationON THE LEAST SIGNIFICANT p ADIC DIGITS OF CERTAIN LUCAS NUMBERS
#A13 INTEGERS 14 (014) ON THE LEAST SIGNIFICANT ADIC DIGITS OF CERTAIN LUCAS NUMBERS Tamás Lengyel Deartment of Mathematics, Occidental College, Los Angeles, California lengyel@oxy.edu Received: 6/13/13,
More informationAn Improved Calibration Method for a Chopped Pyrgeometer
96 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 17 An Imroved Calibration Method for a Choed Pyrgeometer FRIEDRICH FERGG OtoLab, Ingenieurbüro, Munich, Germany PETER WENDLING Deutsches Forschungszentrum
More informationTheoretically Optimal and Empirically Efficient R-trees with Strong Parallelizability
Theoretically Otimal and Emirically Efficient R-trees with Strong Parallelizability Jianzhong Qi, Yufei Tao, Yanchuan Chang, Rui Zhang School of Comuting and Information Systems, The University of Melbourne
More informationPrinciples of Computed Tomography (CT)
Page 298 Princiles of Comuted Tomograhy (CT) The theoretical foundation of CT dates back to Johann Radon, a mathematician from Vienna who derived a method in 1907 for rojecting a 2-D object along arallel
More information4. Score normalization technical details We now discuss the technical details of the score normalization method.
SMT SCORING SYSTEM This document describes the scoring system for the Stanford Math Tournament We begin by giving an overview of the changes to scoring and a non-technical descrition of the scoring rules
More informationUncorrelated Multilinear Discriminant Analysis with Regularization and Aggregation for Tensor Object Recognition
TNN-2007-P-0332.R1 1 Uncorrelated Multilinear Discriminant Analysis with Regularization and Aggregation for Tensor Object Recognition Haiing Lu, K.N. Plataniotis and A.N. Venetsanooulos The Edward S. Rogers
More informationWolfgang POESSNECKER and Ulrich GROSS*
Proceedings of the Asian Thermohysical Proerties onference -4 August, 007, Fukuoka, Jaan Paer No. 0 A QUASI-STEADY YLINDER METHOD FOR THE SIMULTANEOUS DETERMINATION OF HEAT APAITY, THERMAL ONDUTIVITY AND
More informationDimension Characterizations of Complexity Classes
Dimension Characterizations of Comlexity Classes Xiaoyang Gu Jack H. Lutz Abstract We use derandomization to show that sequences of ositive sace-dimension in fact, even ositive k-dimension for suitable
More information2 Asymptotic density and Dirichlet density
8.785: Analytic Number Theory, MIT, sring 2007 (K.S. Kedlaya) Primes in arithmetic rogressions In this unit, we first rove Dirichlet s theorem on rimes in arithmetic rogressions. We then rove the rime
More information2 Asymptotic density and Dirichlet density
8.785: Analytic Number Theory, MIT, sring 2007 (K.S. Kedlaya) Primes in arithmetic rogressions In this unit, we first rove Dirichlet s theorem on rimes in arithmetic rogressions. We then rove the rime
More informationMetrics Performance Evaluation: Application to Face Recognition
Metrics Performance Evaluation: Alication to Face Recognition Naser Zaeri, Abeer AlSadeq, and Abdallah Cherri Electrical Engineering Det., Kuwait University, P.O. Box 5969, Safat 6, Kuwait {zaery, abeer,
More informationarxiv:cond-mat/ v1 [cond-mat.stat-mech] 5 Jul 1998
arxiv:cond-mat/98773v1 [cond-mat.stat-mech] 5 Jul 1998 Floy modes and the free energy: Rigidity and connectivity ercolation on Bethe Lattices P.M. Duxbury, D.J. Jacobs, M.F. Thore Deartment of Physics
More informationElementary Analysis in Q p
Elementary Analysis in Q Hannah Hutter, May Szedlák, Phili Wirth November 17, 2011 This reort follows very closely the book of Svetlana Katok 1. 1 Sequences and Series In this section we will see some
More information