text:
A Tutorial on Reed-Solomon Coding for Fault-Tolerance in RAID-like Systems
- Caitlin Ball
- 2 years ago
- Views:
1 A Tutorial on Reed-olomon Coding for Fault-Tolerance in RAID-like ystems James lank Technical Report C Department of Computer cience University of Tennessee IMORTANT The information dispersal matrix A given in this paper does not have the desired properties lease see Technical Report C for a correction to this problem This technical report is available at plank/papers/c html This material is based upon work supported by the National cience Foundation under Grant No CCR , and by the ORAU Junior Faculty Enhancement Award
2 Abstract It is well-known that Reed-olomon codes may be used to provide error correction for multiple failures in RAIDlike systems The coding technique itself, however, is not as well-known To the coding theorist, this technique is a straightforward extension to a basic coding paradigm and needs no special mention However, to the systems programmer with no training in coding theory, the technique may be a mystery Currently, there are no references that describe how to perform this coding that do not assume that the reader is already well-versed in algebra and coding theory This paper is intended for the systems programmer It presents a complete specification of the coding algorithm plus details on how it may be implemented This specification assumes no prior knowledge of algebra or coding theory The goal of this paper is for a systems programmer to be able to implement Reed-olomon coding for reliability in RAID-like systems without needing to consult any external references roblem pecification Let there be storage devices,, each of which holds bytes These are called the Data Devices Let there be more storage devices, each of which also holds bytes These are called the Checksum Devices The contents of each checksum device will be calculated from the contents of the data devices The goal is to define the calculation of each such that if any of fail, then the contents of the failed devices can be reconstructed from the non-failed devices Introduction Error-correcting codes have been around for decades [1, 2, 3] However, the technique of distributing data among multiple storage devices to achieve high-bandwidth input and output, and using one or more error-correcting devices for failure recovery is relatively new It came to the fore with Redundant Arrays of Inexpensive Disks (RAID) where batteries of small, inexpensive disks combine high storage capacity, bandwidth, and reliability all at a low cost [4, 5, 6] ince then, the technique has been used to design multicomputer and network file systems with high reliability and bandwidth [, 8], and to design fast distributed checkpointing systems [9, 10, 11, 12] We call all such systems RAID-like systems The above problem is central to all RAID-like systems When storage is distributed among devices, the chances of one of these devices failing becomes significant To be specific, if the mean time before failure of one device is, then the mean time to failure of a system of devices is Thus in such systems, fault-tolerance must be taken into account For small values of and reasonably reliable devices, one checksum device is often sufficient for fault-tolerance This is the RAID Level 5 configuration, and the coding technique is called +1-parity [4, 5, 6] With +1-parity, the -th byte of the checksum device is calculated to be the bitwise exclusive-or (XOR) of the -th byte of each data device If any one of the +1 devices fails, it can be reconstructed as the XOR of the remaining devices +1-parity is attractive because of its simplicity It requires one extra storage device, and one extra write operation per write to any single device Its main disadvantage is that it cannot recover from more than one simultaneous failure 2
3 As grows, the ability to tolerate multiple failures becomes important [13] everal techniques have been developed for this [13, 14, 15, 16], the concentration being small values of The most general technique for tolerating simultaneous failures with exactly checksum devices is a technique based on Reed-olomon coding This fact is cited in almost all papers on RAID-like systems However, the technique itself is harder to come by The technique has an interesting history It was first presented in terms of secret sharing by Karnin [1], and then by Rabin [18] in terms of information dispersal reparata [19] then showed the relationship between Rabin s method and Reed-olomon codes, hence the labeling of the technique as Reed-olomon coding The technique has recently been discussed in varying levels of detail by Gibson [5], chwarz [20] and Burkhard [13], with citations of standard texts on error correcting codes [1, 2, 3, 21, 22] for completeness There is one problem with all the above discussions of this technique they require the reader to have a thorough knowledge of algebra and coding theory Any programmer with a bachelor s degree in computer science has the skills to implement this technique, however few such programmers have the background in algebra and coding theory to understand the presentations in these papers and books The goal of this paper is to provide a presentation that can be understood by any systems programmer No background in algebra or coding theory is assumed We give a complete specification of the technique plus implementation details A programmer should need no other references besides this paper to implement Reed-olomon coding for reliability from multiple device failures in RAID-like systems General trategy Formally, our failure model is that of an erasure When a device fails, it shuts down, and the system recognizes this shutting down This is as opposed to an error, in which a device failure is manifested by storing and retrieving incorrect values that can only be recognized by sort of embedded coding [2, 23] The calculation of the contents of each checksum device requires a function applied to all the data devices Figure 1 shows an example configuration using this technique (which we henceforth call R-Raid ) for and The contents of checksum devices and are computed by applying functions and respectively The R-Raid coding method breaks up each storage device into words The size of each word is bits, )(+*,- being chosen by the programmer (subject to some constraints) Thus, the storage devices contain!1! "#%'& 0/ words each The coding functions operate on a word-by-word basis, as in Figure 2, where represents the 5 -th word of device 6 To make the notation simpler, we assume that each device holds just one word and drop the extra subscript Thus we view our problem as consisting of data words and checksum words 8 8 which are computed from the data words in such a way that the loss of any words can be tolerated To compute a checksum word 8 for the checksum device, we apply function to the data words: 8 If a data word on device 4 is updated from 4 to :9 4, then each checksum word 8 is recomputed by applying a func- 3
4 8 8 8 D1 D2 D3 D4 D5 D6 D D8 C1 C2 "!#%#%#&%#'%#(%#)%#*%#+, Figure 1: roviding two-site fault tolerance with two checksum devices 1 1 I I -0/ -21/ 340/ 65894:;-0/ 4<=-21/ > C<D-21/ > -0/ -21/ 340/ 1E5894:;-0/ 1F<=-21/ 14> 3?1/ 1G5A"12:B-0/ 1H<D-21/ 14> -0/ -21/ 340/ IJ5894:;-0/ IH<=-21/ IC> 3?1/ IE5A"12:B-0/ I<D-21/ IC> - 0/ K - 1/ K 3 0/ K 5A9L:;- 0/ K <M- 1/ K > 3 1/ K 5N"12:B- 0/ K <D- 1/ K > Figure 2: Breaking the storage devices into words (,, 1 ) tion O 3 4 such that: 8 9 O When up to devices fail, we reconstruct the system as follows First, for each failed data device 4, we construct a function to restore the words in 4 from the words in the non-failed devices When that is completed, we recompute any failed checksum devices with For example, suppose Q We can describe +1-parity in the above terms There is one checksum device words consist of one bit ( R ) To compute each checksum word 8 If a word on data device 4 changes from 4 to :9 4, then 8 words: If a device 8 9 O T, we take the parity (XOR) of the data words: U, and is recalculated from the parity of its old value and the two data 8 4 fails, then each word may be restored as the parity of the corresponding words on the remaining devices: 4 4CV 4W
5 8 In such a way, the system is resilient to any single device failure To restate, our problem is defined as follows We are given data words all of size We define functions and O which we use to calculate and maintain the checksum words 8 8 We then describe how to reconstruct the words of any lost data device when up to devices fail Once the data words are reconstructed, the checksum words can be recomputed from the data words and Thus, the entire system is reconstructed Overview of the R-Raid Algorithm There are three main aspects of the R-Raid algorithm: using the Vandermonde matrix to calculate and maintain checksum words, using Gaussian Elimination to recover from failures, and using Galois Fields to perform arithmetic Each is detailed below: Calculating and Maintaining Checksum Words We define each function to be a linear combination of the data words: In other words, if we represent the data and checksum words as the vectors and, and the functions as rows of the matrix We define, then the state of the system adheres to the following equation: to be the Vandermonde matrix: / 0/ 0/ 1/ 1/ 1/ V, and thus the above equation becomes: / / 1 /! When one of the data words 4 changes to 9 4, then each of the checksum words must be changed as well This can be effected by subtracting out the portion of the checksum word that corresponds to 4, and adding the required amount for 9 4 Thus, O 3 4 is defined as follows: 8 9 O " 8 8 %& 3 4 4(' 9 4 Therefore, the calculation and maintenance of checksum words can be done by simple arithmetic (however, it is a special kind of arithmetic, as explained below) # # 1 # 5
6 9 Recovering From Failures To explain recovery from errors, we define the matrix and the vector as follows: we have the following equation :! 1 " 1 # # 1 #, and Then We can view each device in the system as having a corresponding row of the matrix and the vector When a device fails, we reflect the failure by deleting the device s row from and from What results a new matrix 9 and a new vector 9 that adhere to the equation: uppose exactly devices fail Then 9 is a 9 matrix Because matrix is defined to be a Vandermonde matrix, every subset of rows of matrix is guaranteed to be linearly independent Thus, the matrix 9 is non-singular, and the values of may be calculated from 9 9 using Gaussian Elimination Hence all data devices can be recovered Once the values of are obtained, the values of any failed may be recomputed from It should be obvious that if fewer than devices fail, the system may be recovered in the same manner, choosing any rows of 9 to perform the Gaussian Elimination Thus, the system can tolerate any number of device failures up to Arithmetic over Galois Fields A major concern of the R-Raid algorithm is that the domain and range of the computation are binary words of a fixed length Although the above algebra is guaranteed to be correct when all the elements are infinite precision real numbers, we must make sure that it is correct for these fixed-size words A common error in dealing with these codes is to perform all arithmetic over the integers modulo This does not work, as division is not defined for all pairs of elements (for example, is undefined modulo 4), rendering the Gaussian Elimination unsolvable in many cases Instead, we must perform addition and multiplication over a field with more than elements [2] Fields with elements are called Galois Fields (denoted O ), and are a fundamental topic in algebra (eg [3, 21, 24]) This section defines how to perform addition, subtraction, multiplication, and division efficiently over a Galois Field We give such a description without explaining Galois Fields in general Appendix A contains a more detailed description of Galois Fields, and provides justification for the arithmetic algorithms in this section The elements of O are the integers from zero to ' Addition and subtraction of elements of O are simple They are the XOR operation For example, in O : R" " R 6
7 Multiplication and division are more complex When length ' R" " R ', to facilitate multiplication These tables are gflog and gfilog: is small (16 or less), we use two logarithm tables, each of int gflog[]: This table is defined for the indices 1 to ', and maps the index to its logarithm in the Galois Field int gfilog[]: This table is defined for the indices 0 to ', and maps the index to its inverse logarithm in the Galois Field Obviously, gflog[gfilog[ ]], and int gfilog[gflog[ ]] With these two tables, we can multiply two elements of O by adding their logs and then taking the inverse log, which yields the product To divide two numbers, we instead subtract the logs Figure 3 shows an implementation in C: This implementation makes use of the fact that the inverse log of an integer is equal to the inverse log of ( ' ) This fact is explained in Appendix A As with regular logarithms, we must treat zero as a special case, as the logarithm of zero is ' #define NW (1 << w) /* In other words, NW equals 2 to the w-th power */ int mult(int a, int b) { int sum_log; if (a == 0 b == 0) return 0; sum_log = gflog[a] + gflog[b]; if (sum_log >= NW-1) sum_log -= NW-1; return gfilog[sum_log]; } int div(int a, int b) { int diff_log; if (a == 0) return 0; if (b == 0) return -1; /* Can t divide by 0 */ diff_log = gflog[a] - gflog[b]; if (diff_log < 0) diff_log += NW-1; return gfilog[diff_log]; } Figure 3: C code for multiplication and division over O (Note: NW ) Unlike regular logarithms, the log of any non-zero element of a Galois Field is an integer, allowing for exact multiplication and division of Galois Field elements using these logarithm tables An important step, therefore, once is chosen, is generating the logarithm tables for O the logarithm and inverse logarithm tables for any The algorithm to generate can be found in Appendix A; however the realization of this algorithm in C for, or is included here in Figure 4 We include the tables for O as generated by setup tables(4) in Table 1
8 unsigned int prim_poly_4 = 023; unsigned int prim_poly_8 = 0435; unsigned int prim_poly_16 = ; unsigned short *gflog, *gfilog; int setup_tables(int w) { unsigned int b, log, x_to_w, prim_poly; switch(w) { case 4: prim_poly = prim_poly_4; break; case 8: prim_poly = prim_poly_8; break; case 16: prim_poly = prim_poly_16; break; default: return -1; } x_to_w = 1 << w; gflog = (unsigned short *) malloc (sizeof(unsigned short) * x_to_w); gfilog = (unsigned short *) malloc (sizeof(unsigned short) * x_to_w); b = 1; for (log = 0; log < x_to_w-1; log++) { gflog[b] = (unsigned short) log; gfilog[log] = (unsigned short) b; b = b << 1; if (b & x_to_w) b = b ^ prim_poly; } return 0; } Figure 4: C code for generating the logarithm tables of O, O and O gflog[i] gfilog[i] Table 1: Logarithm tables for O For example, using the values in Table 1 the following is arithmetic in O : gfilog[gflog[3]+gflog[]] gfilog[4+10] gfilog[14] gfilog[gflog[13]+gflog[10]] gfilog[13+9] gfilog[] gfilog[gflog[13]-gflog[10]] gfilog[13-9] gfilog[4] gfilog[gflog[3]-gflog[]] gfilog[4-10] gfilog[9] Therefore, a multiplication or division requires one conditional, three table lookups (two logarithm table lookups and one inverse table lookup), an addition or subtraction, and a modulo operation For efficiency in Figure 3, we implement the modulo operation as a conditional and a subtraction or addition The Algorithm ummarized Given data devices and checksum devices, the R-Raid algorithm for making them fault-tolerant to up to failures is as follows 8
9 It is easiest to choose or, as words then fall directly on byte boundaries Note that with R, can be as large as 1 Choose a value of such that 2 et up the tables gflog and gfilog as described in Appendix A and implemented in Figure 4 3 et up the matrix to be the Vandermonde matrix: V multiplication is performed over O (for 5 ) where 4 Use the matrix to calculate and maintain each word of the checksum devices from the words of the data devices Again, all addition and multiplication is performed over O 5 If any number of devices up to fail, then they can be restored in the following manner Choose any of the remaining devices, and construct the matrix 9 and vector 9 as defined previously Then solve for in 9 9 This enables the data devices to be restored Once the data devices are restored, the failed checksum devices may be recalculated using the matrix An Example As an example, suppose we have three data devices and three checksum devices, each of which holds one megabyte Then, and We choose to be four, since, and since we can use the logarithm tables in Table 1 to illustrate multiplication Next, we set up gflog and gfilog to be as in Table 1 We construct to be a over O : Vandermonde matrix, defined Now, we can calculate each word of each checksum device using For example, suppose the first word of is, the first word of is, and the first word of is Then we use to calculate the first words of, and : " " " 9
10 V uppose we change to be Then sends the value ' " to each checksum device, which uses this value to recompute its checksum: uppose now that devices,, and to get 9 9 : " "" are lost Then we delete the rows of and corresponding to,, and By applying Gaussian elimination, we can invert 9 to yield the following equation: 9 9, or: From this, we get:? R? And then: Thus, the system is recovered Implementation and erformance Details We examine some implementation and performance details of R-Raid coding on two applications: a RAID controller, and a distributed checkpointing system Both are pictured in Figure 5 In a RAID controller, there is one central processing location that controls the multiple devices A distributed checkpointing system is more decentralized Each device is controlled by a distinct processing unit, and the processing units communicate by sending messages over a communication network RAID Controllers In RAID systems, a basic file system operation is when a process writes an entire stripe s worth of data to a file The file system must break up this data into blocks, one for each data device, calculate blocks worth of encoding information, and then write one block to each of the + devices The overhead of calculating 8 Block ' 10 XOR is
11 V GFmult W W V D D C C 1 n 1 m CU RAID controller D D C C 1 n 1 m CU CU CU CU network Checkpointing system Figure 5: RAID-like configurations whereblock is the size of a block and XOR is the rate of performing XOR This is because the first row of XOR is all ones and therefore there are no Galois Field multiplications in the calculation of 8 The overhead of calculating 8 where is: Block ' where GFmult is the rate of performing Galois Field multiplications This is because -1 of the data blocks must be multiplied by some 3 4 before being XOR d together Thus the overhead of calculating the checksum blocks is Block ' ' XOR GFmult The cost of writing an entire parity stripe is therefore the above figure plus the time to write one block to each of the disks 1 A second basic file system operation is overwriting a small number of bytes of a file This updates the information stored on one disk, and necessitates a recalculation of the encoding on each checksum disk To be specific, for each word of disk 4 that is changed from 4 to 9 4, the appropriate word of each checksum disk is changed from 8 to 8 & ' 4, where arithmetic is performed over the Galois Field The cost of computing 9 4 ' 4 is one XOR operation This needs to be performed just one time The cost of multiplying 9 4 ' 4 by 3 4 is zero if or 5R, and one Galois Field multiplication if and 5 Finally, the cost of adding ' 9 4 to 8 is one XOR operation for each value of Thus, the total cost of changing a word from 4 to 9 4 is: The cost of writing one word to disks XOR XOR GFmult if 5R otherwise The dominant portion of this cost is the cost of writing to the disks For this reason, Gibson defines the update penalty of an encoding strategy to be the number of disks that must be updated per word update [14] For R-Raid coding, the update penalty is disks, which is the minimum value for tolerating failures As in all RAID systems, the encoding information may be distributed among the disks to avoid having the checksum disks become hot spots [5, 26] The final operation of concern is recovery Here, we assume that failures have occurred and the system must recover the contents of the disks In the R-Raid algorithm, recovery consists of performing Gaussian Elimination of an equation 9 9 so that 9 is determined Then, the contents of all the failed disks may be calculated as a linear combination of the disks in 9 Thus, recovery has two parts: the Gaussian Elimination and the recalculation 1 We do not include any equations for the time to perform disk reads/writes because the complexity of disk operation precludes a simple encapsulation [25] 11
12 network XOR V ince at least ' rows of 9 are identity rows, the Gaussian Elimination takes steps As is likely to be small this should be very fast (ie milliseconds) The subsequent recalculation of the failed disks can be broken into parity stripes For each parity stripe, one block is read from each of the non-failed disks One block is then calculated for each of the failed disks, and then written to the proper replacement disk The cost of recovering one block is therefore: The cost of reading one The costs of writing one block from each of Note that the Block GFmult disks +Block ' XOR +Block GFmult term accounts for the fact that all the elements of 9 block to each of disks may be greater than one For more detailed information on other parameters that influence the performance of recovery in RAID systems, see Reference [26] Checkpointing ystems In distributed checkpointing systems, the usage of R-Raid encoding is slightly different from its usage in the RAID controller Here, there are two main operations, checkpointing and recovery With checkpointing, we assume that the data devices hold data, but that the checksum devices are uninitialized There are two basic approaches that can be taken to initializing the checksum devices: D1 D2 D1 D2 D1 D2 D3 D4 C1 D3 D4 C1 D3 D4 C1 D5 D6 C2 D5 D6 C2 D5 D6 C2 DN-1 DN Cm DN-1 DN Cm DN-1 DN Cm tep 1 tep 2 tep N Figure 6: The broadcast algorithm The Broadcast Algorithm (Figure 6): Each checksum device initializes its data to zero Then each data device 4 broadcasts its contents to every checksum device Upon receiving 4 s data, multiplies it by 3 4 and XOR s it into its device broadcast GFmult data space When this is done, all the checksum devices are initialized The time complexity of this method is Wheredevice is the size of the device and broadcast is the rate of message broadcasting This assumes that message-sending bandwidth dominates latency, and that the checksum devices do not overlap computation and communication significantly The Fan-in Algorithm (Figure ): This algorithm proceeds in steps one for each In step, each data device 4 multiplies its data by 3 4, and then the data devices perform a fan-in XOR of their data, sending the final result to time complexity of this method is device XOR 12 ' device GFmult The
13 D1 D2 D1 D2 D1 D2 D3 D4 C1 D3 D4 C1 D3 D4 C1 D5 D6 C2 D5 D6 C2 D5 D6 C2 DN-1 DN Cm DN-1 DN Cm DN-1 DN Cm tep 1 tep 2 tep m Figure : The Fan-in algorithm where network is the network bandwidth This takes into account the fact that no Galois Field multiplications are necessary to compute Moreover, this equation assumes that there is no contention for the network during the fan-in On a broadcast network like an Ethernet, where two sets of processors cannot exchange messages simultaneously, the terms become ' Obviously, the choice of algorithm is dictated by the characteristics of the network Recovery from failure is straightforward ince the Gaussian Elimination is fast, it should be performed redundantly in the CU s of each device (as opposed to performing the Gaussian Elimination with some sort of distributed algorithm) The recalculation of the failed devices can then be performed using either the broadcast or fan-in algorithm as described above The cost of recovery should thus be slightly greater than the cost of computing the checksum devices Other Coding Methods There are other coding methods that can be used for fault-tolerance in RAID-like systems Most are based on parity encodings, where each checksum device is computed to be the bitwise exclusive-or of some subset of the data devices: where 3 4 Although these methods can tolerate up to failures (for example, all the checksum devices can fail), they do not tolerate all combinations of failures For example, the well-known Hamming code can be adapted for RAID-like systems [5] With Hamming codes, ' checksum devices are employed, and all two-device failures may be tolerated One-dimensional parity [14] is another parity-based method that can tolerate certain classes of multiple-device failures With one-dimensional parity, the data devices are partitioned into groups,, and each checksum device 8 is computed to be the parity of the data devices in With one-dimensional parity, the system can tolerate one failure per group Note that when, this is simply +1-parity, and when, this is equivalent to device mirroring Two-dimensional parity [14] is an extension of one-dimensional parity that tolerates any two device failures With twodimensional parity, must be greater than or equal to, which can result in too much cost if devices are expensive Other strategies for parity-based encodings that tolerate two and three device failures are discussed in Reference [14] ince 13
14 C1 C2 C3 C4 D1 D2 D3 D4 D5 D6 D D8 D9 D10 D11 Hamming code,r, C1 C2 C3 D1 D2 D3 C4 C1 C2 C3 D4 D5 D6 D D8 D9 C5 C6 D1 D2 D3 D4 D5 D6 D D8 D9 D10 D11 D12 One-dimensional parity,, Figure 8: arity-based encodings Two-dimensional parity,, all of these schemes are based on parity, they show better performance than R-Raid coding for equivalent values of However, unlike R-Raid coding, these schemes do not have minimal device overhead In other words, there are some combinations of device failures that the system cannot tolerate An important coding technique for two device failures is EVENODD coding [15] This technique tolerates all two device failures with just two checksum devices, and all coding operations are XOR s Thus, it too is faster than R-Raid coding To the author s knowledge, there is no parity-based scheme that tolerates three or more device failures with minimal device overhead Conclusion This paper has presented a complete specification for implementing Reed-olomon coding for RAID-like systems With this coding, one can add checksum devices to data devices, and tolerate the failure of any devices This has application in disk arrays, network file systems and distributed checkpointing systems This paper does not claim that R-Raid coding is the best method for all applications in this domain For example, in the case where, EVENODD coding [15] solves the problem with better performance, and one-dimensional parity [14] solves a similar problem with even better performance However, R-Raid coding is the only general solution for all values of and The table-driven approach for multiplication and division over a Galois Field is just one way of performing these actions For values where, this is an efficient software solution that is easy to implement and does not consume much physical memory For larger values of, other approaches (hardware or software) may be necessary ee References [2], [2] and [28] for examples of other approaches 14
15 Acknowledgements The author thanks Joel Friedman, Kai Li, Michael uening, Norman Ramsey, Brad Vander Zanden and Michael Vose for their valuable comments and discussion concerning this paper References [1] E R Berlekamp Algebraic Coding Theory McGraw-Hill, New York, 1968 [2] W W eterson and E J Weldon, Jr Error-Correcting Codes, econd Edition The MIT ress, Cambridge, Massachusetts, 192 [3] FJ MacWilliams and NJA loane The Theory of Error-Correcting Codes, art I North-Holland ublishing Company, Amsterdam, New York, Oxford, 19 [4] D A atterson, G Gibson, and R H Katz A case for redundant arrays of inexpensive disks (RAID) In 1988 ACM Conference on Management of Data, pages , June 1988 [5] G A Gibson Redundant Disk Arrays: Reliable, arallel econdary torage The MIT ress, Cambridge, Massachusetts, 1992 [6] M Chen, E K Lee, G A Gibson, R H Katz, and D A atterson RAID: High-performance, reliable secondary storage ACM Computing urveys, 1994 [] J H Hartman and J K Ousterhout The zebra striped network file system Operating ystems Review 14th ACM ymposium on Operating ystem rinciples, 2(5):29 43, December 1993 [8] Cao, B Lim, Venkataraman, and J Wilkes The TickerTAI parallel RAID architecture ACM Transactions on Computer ystems, 12(3), 1994 [9] J lank and K Li Faster checkpointing with parity In 24th International ymposium on Fault-Tolerant Computing, pages , Austin, TX, June 1994 [10] J lank, Y Kim, and J Dongarra Algorithm-based diskless checkpointing for fault tolerant matrix operations In 25th International ymposium on Fault-Tolerant Computing, pages , asadena, CA, June 1995 [11] T Chiueh and Deng Efficient checkpoint mechanisms for massively parallel machines In 26th International ymposium on Fault-Tolerant Computing, endai, June 1996 [12] J lank Improving the performance of coordinated checkpointers on networks of workstations using RAID techniques In 15th ymposium on Reliable Distributed ystems, October 1996 [13] W A Burkhard and J Menon Disk array storage system reliability In 23rd International ymposium on Fault- Tolerant Computing, pages , Toulouse, France, June
16 [14] G A Gibson, L Hellerstein, R M Karp, R H Katz, and D A atterson Failure correction techniques for large disk arrays In Third International Conference on Architectural upport for rogramming Languages and Operating ystems, pages , Boston, MA, April 1989 [15] M Blaum, J Brady, J Bruck, and J Menon EVENODD: An optimal scheme for tolerating double disk failures in RAID architectures In 21st Annual International ymposium on Computer Architecture, pages , Chicago, IL, April 1994 [16] C-I ark Efficient placement of parity and data to tolerate two disk failures in disk array systems IEEE Transactions on arallel and Distributed ystems, 6(11): , November 1995 [1] E D Karnin, J W Greene, and M E Hellman On secret sharing systems IEEE Transactions on Information Theory, IT-29(1):35 41, January 1983 [18] M O Rabin Efficient dispersal of information for security, load balancing, and fault tolerance Journal of the Association for Computing Machinery, 36(2): , April 1989 [19] F reparata Holographic dispersal and recovery of information IEEE Transactions on Information Theory, 35(5): , eptember 1989 [20] T J E chwarz and W A Burkhard RAID organization and performance In roceedings of the 12th International Conference on Distributed Computing ystems, pages , Yokohama, June 1992 [21] J H van Lint Introduction to Coding Theory pringer-verlag, New York, 1982 [22] B Wicker and V K Bhargava Reed-olomon Codes and Their Applications IEEE ress, New York, 1994 [23] D Wiggert Codes for Error Control and ynchronization Artech House, Inc, Norwood, Massachusetts, 1988 [24] I N Herstein Topis in Algebra, econd Edition Xerox College ublishing, Lexington, Massachusetts, 195 [25] C Ruemmler and J Wilkes An introduction to disk drive modeling IEEE Computer, 2(3):1 29, March 1994 [26] M Holland, G A Gibson, and D iewiorek Fast, on-line failure recovery in redundant disk arrays In 23rd International ymposium on Fault-Tolerant Computing, pages , Toulouse, France, June 1993 [2] A Z Broder ome applications of Rabin s fingerprinting method In R Capocelli, A De antis, and U Vaccaro, editors, equences II pringer-verlag, New York, 1991 [28] D W Clark and L-J Weng Maximal and near-maximal shift register sequences: Efficient event counters and easy discrete logarithms IEEE Transactions on Computers, 43(5): ,
17 2 Appendix A: Galois Fields, as applied to this algorithm Galois Fields are a fundamental topic of algebra, and are given a full treatment in a number of texts [24, 3, 21]) This Appendix does not attempt to define and prove all the properties of Galois Fields necessary for this algorithm Instead, our goal is to give enough information about Galois Fields that anyone desiring to implement this algorithm will have a good intuition concerning the underlying theory A field O is a set of elements closed under addition and multiplication, for which every element has an additive and multiplicative inverse (except for the element which has no multiplicative inverse) For example, the field O can be represented as the set, where addition and multiplication are both performed modulo 2 (ie addition is XOR, and multiplication is the bit operator AND) imilarly, if is a prime number, then we can represent the field O to be the set ' where addition and multiplication are both performed modulo However, suppose is not a prime Then the set ' where addition and multiplication are both performed modulo is not a field For example, let be four Then the set is indeed closed under addition and multiplication modulo 4, however, the element has no multiplicative inverse (there is no such that mod ) Thus, we cannot perform our coding with binary words of size using addition and multiplication modulo Instead, we need to use Galois Fields To explain Galois Fields, we work with polynomials of 2 whose coefficients are in O This means, for example, that if 2 2, and 2) 2, then 2 2) This is because Moreover, we take such polynomials modulo other polynomials, using the following identity: If 2 2) 2, then 2 is a polynomial with a degree less than 2, and 2 2) 2) 2, where 2) is any polynomial of 2 Thus, for example, if 2 2 2, and 2) 2, then 2) 2 2 Let 2 be a primitive polynomial of degree whose coefficients are in O This means that 2 cannot be factored, and that the polynomial 2 can be considered a generator of O To see how 2 generates O, we start with the elements 0, 1, and 2, and then continue to enumerate the elements by multiplying the last element by 2 and taking the result modulo 2 if it has a degree This enumeration ends at elements the last element multiplied by 2 2) equals 1 For example, suppose = 2, and 2) 2 2 To enumerate O we start with the three elements 0, 1, and 2, then then continue with 2 mod 2 2 Thus we have four elements: 2 If we continue, we see that 2 2 mod mod 2, thus ending the enumeration The field O is constructed by finding a primitive polynomial 2 of degree over O, and then enumerating the elements (which are polynomials) with the generator 2 Addition in this field is performed using polynomial addition, and multiplication is performed using polynomial multiplication and taking the result modulo 2 uch a field is typically written O O 2 2) 1
18 4 Now, to use O in the R-Raid algorithm, we need to map the elements of O to binary words of size Let 2) be a polynomial in O Then we can map 2 to a binary word of size by setting the th bit of to the coefficient of 2 in 2) For example, in O O 2 2 Addition of binary elements of O Generated olynomial Binary Decimal Element Element Element Representation of of of of W , we get the following table: can be performed by bitwise exclusive-or Multiplication is a little more difficult One must convert the binary numbers to their polynomial elements, multiply the polynomials modulo 2, and then convert the answer back to binary This can be implemented, in a simple fashion, by using the two logarithm tables described earlier: one that maps from a binary element to power 5 such that 2 is equivalent to (this is the gflog table, and is referred to in the literature as a discrete logarithm ), and one that maps from a power 5 to its binary element Each table has ' elements (there is no 5 such that 2 4 ) Multiplication then consists of converting each binary element to its discrete logarithm, then adding the logarithms modulo ' (this is equivalent to multiplying the polynomials modulo 2 ) and converting the result back to a binary element Division is performed in the same manner, except the logarithms are subtracted instead of added Obviously, elements where must be treated as special cases Therefore, multiplication and division of two binary elements takes three table lookups and a modular addition Thus, to implement multiplication over O, we must first set up the tables gflog and gfilog To do this, we first need a primitive polynomial 2 of degree over O uch polynomials can be found in texts on error correcting codes [1, 2] We list examples for powers of two up to 64 below: R We then start with the element 2, and enumerate all non-zero polynomials over O by multiplying the last element by 2, and taking the result modulo 2 This is done in Table 2 below for O, where 2) 2 2 It should be clear now how the C code in Figure 4 generates the gflog and gfilog arrays for O, O and O 18
19 Generated olynomial Binary Decimal Element Element Element Element W W W W W W W W W 0111 W W W W W W W W Table 2: Enumeration of the elements of O 19
A Tutorial on Reed-Solomon Coding for Fault-Tolerance in RAID-like Systems
A Tutorial on Reed-Solomon Coding for Fault-Tolerance in RAID-like Systems James S Plank Department of Computer Science University of Tennessee February 19, 1999 Abstract It is well-known that Reed-SolomonMore information
Distributed Storage Networks and Computer Forensics
Distributed Storage Networks 5 Raid-6 Encoding Technical Faculty Winter Semester 2011/12 RAID Redundant Array of Independent Disks Patterson, Gibson, Katz, A Case for Redundant Array of Inexpensive Disks,More information
Algorithms and Methods for Distributed Storage Networks 5 Raid-6 Encoding Christian Schindelhauer
Algorithms and Methods for Distributed Storage Networks 5 Raid-6 Encoding Institut für Informatik Wintersemester 2007/08 RAID Redundant Array of Independent Disks Patterson, Gibson, Katz, A Case for RedundantMore information
Theoretical Aspects of Storage Systems Autumn 2009
Theoretical Aspects of Storage Systems Autumn 2009 Chapter 2: Double Disk Failures André Brinkmann Data Corruption in the Storage Stack What are Latent Sector Errors What is Silent Data Corruption ChecksumMore information
Towards High Security and Fault Tolerant Dispersed Storage System with Optimized Information Dispersal Algorithm
Towards High Security and Fault Tolerant Dispersed Storage System with Optimized Information Dispersal Algorithm I Hrishikesh Lahkar, II Manjunath C R I,II Jain University, School of Engineering and Technology,More information
Non-Redundant (RAID Level 0)
There are many types of RAID and some of the important ones are introduced below: Non-Redundant (RAID Level 0) A non-redundant disk array, or RAID level 0, has the lowest cost of any RAID organizationMore information
Note: Correction to the 1997 Tutorial on Reed-Solomon Coding
Note: Correction to the 1997 utorial on Reed-Solomon Coding James S Plank Ying Ding University of ennessee Knoxville, N 3799 [plank,ying]@csutkedu echnical Report U-CS-03-504 Department of Computer ScienceMore information
The mathematics of RAID-6
The mathematics of RAID-6 H. Peter Anvin 1 December 2004 RAID-6 supports losing any two drives. The way this is done is by computing two syndromes, generally referred P and Q. 1 A quickMore information
The mathematics of RAID-6
The mathematics of RAID-6 H. Peter Anvin First version 20 January 2004 Last updated 20 December 2011 RAID-6 supports losing any two drives. syndromes, generally referred P and Q. The wayMore information
200 Chapter 7. (This observation is reinforced and elaborated in Exercises 7.5 and 7.6, and the reader is urged to work through them.
200 Chapter 7 (This observation is reinforced and elaborated in Exercises 7.5 and 7.6, and the reader is urged to work through them.) 7.2 RAID Disks are potential bottlenecks for system performance andMore information
Data Storage - II: Efficient Usage & Errors
Data Storage - II: Efficient Usage & Errors Week 10, Spring 2005 Updated by M. Naci Akkøk, 27.02.2004, 03.03.2005 based upon slides by Pål Halvorsen, 12.3.2002. Contains slides from: Hector Garcia-MolinaMore information
A Reed-Solomon Code for Disk Storage, and Efficient Recovery Computations for Erasure-Coded Disk Storage
A Reed-Solomon Code for Disk Storage, and Efficient Recovery Computations for Erasure-Coded Disk Storage M. S. MANASSE Microsoft Research, Mountain View, California, USA C. A. THEKKATH Microsoft Research,More information
EMC CLARiiON RAID 6 Technology A Detailed Review
A Detailed Review Abstract This white paper discusses the EMC CLARiiON RAID 6 implementation available in FLARE 26 and later, including an overview of RAID 6 and the CLARiiON-specific implementation, whenMore information
o. rof. Dr. eter Brezany arallele and Verteilte Datenbanksysteme 1 ARALLEL I/O FOR HIGH ERFORMANCE COMUTING Skriptum zur Vorlesung eter Brezany Institut für Scientific Computing Universität Wien E-Mail:More information
SURVEY ON RAID Aishwarya Airen 1, Aarsh Pandit 2, Anshul Sogani 3 1,2,3 A.I.T.R, Indore. Abstract RAID stands for Redundant Array of Independent Disk that is a concept which provides an efficient way forMore information
Using RAID6 for Advanced Data Protection
Using RAI6 for Advanced ata Protection 2006 Infortrend Corporation. All rights reserved. Table of Contents The Challenge of Fault Tolerance... 3 A Compelling Technology: RAI6... 3 Parity... 4 Why Use RAI6...More information
Chapter 2 Data Storage
Chapter 2 22 CHAPTER 2. DATA STORAGE 2.1. THE MEMORY HIERARCHY 23 26 CHAPTER 2. DATA STORAGE main memory, yet is essentially random-access, with relatively small differences Figure 2.4: A typicalMore information
Cryptography and Network Security. Prof. D. Mukhopadhyay. Department of Computer Science and Engineering. Indian Institute of Technology, Kharagpur
Cryptography and Network Security Prof. D. Mukhopadhyay Department of Computer Science and Engineering Indian Institute of Technology, Kharagpur Module No. # 01 Lecture No. # 12 Block Cipher StandardsMore information
An Area-Efficient Architecture of Reed-Solomon Codec for Advanced RAID Systems Min-An Song, I-Feng Lan, and Sy-Yen Kuo
An Area-Efficient Architecture of Reed-olomon Codec for Advanced RAID ystems Min-An ong, I-Feng Lan, and y-yen Kuo Department of Electrical Engineering, National Taiwan University, Taipei, Taiwan E-mail:More information
Definition of RAID Levels
RAID The basic idea of RAID (Redundant Array of Independent Disks) is to combine multiple inexpensive disk drives into an array of disk drives to obtain performance, capacity and reliability that exceedsMore information
Fault Tolerance & Reliability CDA 5140. Chapter 3 RAID & Sample Commercial FT Systems
Fault Tolerance & Reliability CDA 5140 Chapter 3 RAID & Sample Commercial FT Systems - basic concept in these, as with codes, is redundancy to allow system to continue operation even if some componentsMore information
The finite field with 2 elements The simplest finite field is
The finite field with 2 elements The simplest finite field is GF (2) = F 2 = {0, 1} = Z/2 It has addition and multiplication + and defined to be 0 + 0 = 0 0 + 1 = 1 1 + 0 = 1 1 + 1 = 0 0 0 = 0 0 1 = 0More information
Operating Systems. RAID Redundant Array of Independent Disks. Submitted by Ankur Niyogi 2003EE20367
Operating Systems RAID Redundant Array of Independent Disks Submitted by Ankur Niyogi 2003EE20367 YOUR DATA IS LOST@#!! Do we have backups of all our data???? - The stuff we cannot afford to lose?? HowMore information
RAID: Redundant Arrays of Inexpensive Disks this discussion is based on the paper: on Management of Data (Chicago, IL), pp.109--116, 1988.
: Redundant Arrays of Inexpensive Disks this discussion is based on the paper:» A Case for Redundant Arrays of Inexpensive Disks (),» David A Patterson, Garth Gibson, and Randy H Katz,» In ProceedingsMore information
Lecture 36: Chapter 6
Lecture 36: Chapter 6 Today s topic RAID 1 RAID Redundant Array of Inexpensive (Independent) Disks Use multiple smaller disks (c.f. one large disk) Parallelism improves performance Plus extra disk(s) forMore information
ECE 842 Report Implementation of Elliptic Curve Cryptography
ECE 842 Report Implementation of Elliptic Curve Cryptography Wei-Yang Lin December 15, 2004 Abstract The aim of this report is to illustrate the issues in implementing a practical elliptic curve cryptographicMore information
RAID HARDWARE. On board SATA RAID controller. RAID drive caddy (hot swappable) SATA RAID controller card. Anne Watson 1
RAID HARDWARE On board SATA RAID controller SATA RAID controller card RAID drive caddy (hot swappable) Anne Watson 1 RAID The word redundant means an unnecessary repetition. The word array means a lineup.More information
Reliability and Fault Tolerance in Storage
Reliability and Fault Tolerance in Storage Dalit Naor/ Dima Sotnikov IBM Haifa Research Storage Systems 1 Advanced Topics on Storage Systems - Spring 2014, Tel-Aviv University http://www.eng.tau.ac.il/semcomMore information
Erasure Codes Made So Simple, You ll Really Like Them
Erasure Codes Made So Simple, You ll Really Like Them W. David Schwaderer August 7, 214 email@example.com Santa Clara, CA 1 Agenda Errors Versus Erasures HDD Bit Error Rate Implications RAID 4,More information
Filing Systems. Filing Systems
Filing Systems At the outset we identified long-term storage as desirable characteristic of an OS. EG: On-line storage for an MIS. Convenience of not having to re-write programs. Sharing of data in anMore information
technology brief RAID Levels March 1997 Introduction Characteristics of RAID Levels
technology brief RAID Levels March 1997 Introduction RAID is an acronym for Redundant Array of Independent Disks (originally Redundant Array of Inexpensive Disks) coined in a 1987 University of CaliforniaMore information
RAID. Storage-centric computing, cloud computing. Benefits:
RAID Storage-centric computing, cloud computing. Benefits: Improved reliability (via error correcting code, redundancy). Improved performance (via redundancy). Independent disks. RAID Level 0 ProvidesMore information
Christian Schindelhauer Technical Faculty Computer-Networks and Telematics University of Freiburg
DAAD Summerschool Curitiba 2011 Aspects of Large Scale High Speed Computing Building Blocks of a Cloud Storage Networks 2: Virtualization of Storage: RAID, SAN and Virtualization Christian SchindelhauerMore information
Notes on Factoring. MA 206 Kurt Bryan
The General Approach Notes on Factoring MA 26 Kurt Bryan Suppose I hand you n, a 2 digit integer and tell you that n is composite, with smallest prime factor around 5 digits. Finding a nontrivial factorMore information
1. LINEAR EQUATIONS. A linear equation in n unknowns x 1, x 2,, x n is an equation of the form
1. LINEAR EQUATIONS A linear equation in n unknowns x 1, x 2,, x n is an equation of the form a 1 x 1 + a 2 x 2 + + a n x n = b, where a 1, a 2,..., a n, b are given real numbers. For example, with x andMore information
CHAPTER 4 RAID. Section Goals. Upon completion of this section you should be able to:
HPTER 4 RI s it was originally proposed, the acronym RI stood for Redundant rray of Inexpensive isks. However, it has since come to be known as Redundant rray of Independent isks. RI was originally describedMore information
RAID Overview: Identifying What RAID Levels Best Meet Customer Needs. Diamond Series RAID Storage Array
ATTO Technology, Inc. Corporate Headquarters 155 Crosspoint Parkway Amherst, NY 14068 Phone: 716-691-1999 Fax: 716-691-9353 www.attotech.com firstname.lastname@example.com RAID Overview: Identifying What RAID LevelsMore information
Disk Array Data Organizations and RAID
Guest Lecture for 15-440 Disk Array Data Organizations and RAID October 2010, Greg Ganger 1 Plan for today Why have multiple disks? Storage capacity, performance capacity, reliability Load distributionMore information
Chapter 13. Chapter Outline. Disk Storage, Basic File Structures, and Hashing
Chapter 13 Disk Storage, Basic File Structures, and Hashing Copyright 2007 Ramez Elmasri and Shamkant B. Navathe Chapter Outline Disk Storage Devices Files of Records Operations on Files Unordered FilesMore information
Volume 2, No. 3, March 2011 Journal of Global Research in Computer Science RESEARCH PAPER Available Online at www.jgrcs.info IMPROVING PERFORMANCE OF RANDOMIZED SIGNATURE SORT USING HASHING AND BITWISEMore information
AN INTRODUCTION TO ERROR CORRECTING CODES Part 1
AN INTRODUCTION TO ERROR CORRECTING CODES Part 1 Jack Keil Wolf ECE 154C Spring 2008 Noisy Communications Noise in a communications channel can cause errors in the transmission of binary digits. Transmit:More information
Dependable Systems. 9. Redundant arrays of. Prof. Dr. Miroslaw Malek. Wintersemester 2004/05 www.informatik.hu-berlin.de/rok/zs
Dependable Systems 9. Redundant arrays of inexpensive disks (RAID) Prof. Dr. Miroslaw Malek Wintersemester 2004/05 www.informatik.hu-berlin.de/rok/zs Redundant Arrays of Inexpensive Disks (RAID) RAID isMore information
Securing Cloud Data Storage
IOSR Journal of Computer Engineering (IOSRJCE) ISSN: 2278-0661 Volume 1, Issue 6 (July-Aug. 2012), PP 43-49 Securing Cloud Data Storage S. P. Jaikar 1, M. V. Nimbalkar 2 1,2 (Department of InformationMore information
3PAR Fast RAID: High Performance Without Compromise
3PAR Fast RAID: High Performance Without Compromise Karl L. Swartz Document Abstract: 3PAR Fast RAID allows the 3PAR InServ Storage Server to deliver higher performance with less hardware, reducing storageMore information
Mathematics Course 111: Algebra I Part IV: Vector Spaces
Mathematics Course 111: Algebra I Part IV: Vector Spaces D. R. Wilkins Academic Year 1996-7 9 Vector Spaces A vector space over some field K is an algebraic structure consisting of a set V on which areMore information
CS 153 Design of Operating Systems Spring 2015
CS 153 Design of Operating Systems Spring 2015 Lecture 22: File system optimizations Physical Disk Structure Disk components Platters Surfaces Tracks Arm Track Sector Surface Sectors Cylinders Arm HeadsMore information
STAR : An Efficient Coding Scheme for Correcting Triple Storage Node Failures
STAR : An Efficient Coding Scheme for Correcting Triple Storage Node Failures Cheng Huang, Member, IEEE, and Lihao Xu, Senior Member, IEEE Abstract Proper data placement schemes based on erasure correctingMore information
RAID Level Descriptions. RAID 0 (Striping)
RAID Level Descriptions RAID 0 (Striping) Offers low cost and maximum performance, but offers no fault tolerance; a single disk failure results in TOTAL data loss. Businesses use RAID 0 mainly for tasksMore information
The Essentials of Computer Organization and Architecture. Linda Null and Julia Lobur Jones and Bartlett Publishers, 2003
The Essentials of Computer Organization and Architecture Linda Null and Julia Lobur Jones and Bartlett Publishers, 2003 Chapter 2 Instructor's Manual Chapter Objectives Chapter 2, Data Representation,More information
Theoretical Aspects of Storage Systems Autumn 2009
Theoretical Aspects of Storage Systems Autumn 2009 Chapter 1: RAID André Brinkmann University of Paderborn Personnel Students: ~13.500 students Professors: ~230 Other staff: ~600 scientific, ~630 non-scientificMore information
Guide to SATA Hard Disks Installation and RAID Configuration
Guide to SATA Hard Disks Installation and RAID Configuration 1. Guide to SATA Hard Disks Installation... 2 1.1 Serial ATA (SATA) Hard Disks Installation... 2 2. Guide to RAID Configurations... 3 2.1 IntroductionMore information
Surviving Two Disk Failures. Introducing Various RAID 6 Implementations
Surviving Two Failures Introducing Various RAID 6 Implementations Notices The information in this document is subject to change without notice. While every effort has been made to ensure that all informationMore information
Binary search tree with SIMD bandwidth optimization using SSE
Binary search tree with SIMD bandwidth optimization using SSE Bowen Zhang, Xinwei Li 1.ABSTRACT In-memory tree structured index search is a fundamental database operation. Modern processors provide tremendousMore information
Copyright 2007 Ramez Elmasri and Shamkant B. Navathe. Slide 13-1
Slide 13-1 Chapter 13 Disk Storage, Basic File Structures, and Hashing Chapter Outline Disk Storage Devices Files of Records Operations on Files Unordered Files Ordered Files Hashed Files Dynamic and ExtendibleMore information
Operation Count; Numerical Linear Algebra
10 Operation Count; Numerical Linear Algebra 10.1 Introduction Many computations are limited simply by the sheer number of required additions, multiplications, or function evaluations. If floating-pointMore information
DELL RAID PRIMER DELL PERC RAID CONTROLLERS. Joe H. Trickey III. Dell Storage RAID Product Marketing. John Seward. Dell Storage RAID Engineering
DELL RAID PRIMER DELL PERC RAID CONTROLLERS Joe H. Trickey III Dell Storage RAID Product Marketing John Seward Dell Storage RAID Engineering http://www.dell.com/content/topics/topic.aspx/global/products/pvaul/topMore information
Linear Codes. Chapter 3. 3.1 Basics
Chapter 3 Linear Codes In order to define codes that we can encode and decode efficiently, we add more structure to the codespace. We shall be mainly interested in linear codes. A linear code of lengthMore information
Homework 5 Solutions
Homework 5 Solutions 4.2: 2: a. 321 = 256 + 64 + 1 = (01000001) 2 b. 1023 = 512 + 256 + 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = (1111111111) 2. Note that this is 1 less than the next power of 2, 1024, whichMore information
Three-Dimensional Redundancy Codes for Archival Storage
Three-Dimensional Redundancy Codes for Archival Storage Jehan-François Pâris Darrell D. E. Long Witold Litwin Department of Computer Science University of Houston Houston, T, USA firstname.lastname@example.com DepartmentMore information
A Tutorial on RAID Storage Systems
A Tutorial on RAID Storage Systems Sameshan Perumal and Pieter Kritzinger CS04-05-00 May 6, 2004 Data Network Architectures Group Department of Computer Science University of Cape Town Private Bag, RONDEBOSCHMore information
Mathematics of Cryptography
CHAPTER 2 Mathematics of Cryptography Part I: Modular Arithmetic, Congruence, and Matrices Objectives This chapter is intended to prepare the reader for the next few chapters in cryptography. The chapterMore information
Chapter 13 Disk Storage, Basic File Structures, and Hashing.
Chapter 13 Disk Storage, Basic File Structures, and Hashing. Copyright 2004 Pearson Education, Inc. Chapter Outline Disk Storage Devices Files of Records Operations on Files Unordered Files Ordered FilesMore information
CS 61C: Great Ideas in Computer Architecture. Dependability: Parity, RAID, ECC
CS 61C: Great Ideas in Computer Architecture Dependability: Parity, RAID, ECC Instructor: Justin Hsia 8/08/2013 Summer 2013 Lecture #27 1 Review of Last Lecture MapReduce Data Level Parallelism FrameworkMore information
Review. Lecture 21: Reliable, High Performance Storage. Overview. Basic Disk & File System properties CSC 468 / CSC 2204 11/23/2006
S 468 / S 2204 Review Lecture 2: Reliable, High Performance Storage S 469HF Fall 2006 ngela emke rown We ve looked at fault tolerance via server replication ontinue operating with up to f failures RecoveryMore information
RAID. Contents. Definition and Use of the Different RAID Levels. The different RAID levels: Definition Cost / Efficiency Reliability Performance
RAID Definition and Use of the Different RAID Levels Contents The different RAID levels: Definition Cost / Efficiency Reliability Performance Further High Availability Aspects Performance OptimizationMore information
December 4, 2013 MATH 171 BASIC LINEAR ALGEBRA B. KITCHENS
December 4, 2013 MATH 171 BASIC LINEAR ALGEBRA B KITCHENS The equation 1 Lines in two-dimensional space (1) 2x y = 3 describes a line in two-dimensional space The coefficients of x and y in the equationMore information
RN-Codings: New Insights and Some Applications
RN-Codings: New Insights and Some Applications Abstract During any composite computation there is a constant need for rounding intermediate results before they can participate in further processing. RecentlyMore information
a 11 x 1 + a 12 x 2 + + a 1n x n = b 1 a 21 x 1 + a 22 x 2 + + a 2n x n = b 2.
Chapter 1 LINEAR EQUATIONS 1.1 Introduction to linear equations A linear equation in n unknowns x 1, x,, x n is an equation of the form a 1 x 1 + a x + + a n x n = b, where a 1, a,..., a n, b are givenMore information
CS161: Operating Systems
CS161: Operating Systems Matt Welsh firstname.lastname@example.com Lecture 18: RAID April 19, 2007 2007 Matt Welsh Harvard University 1 RAID Redundant Arrays of Inexpensive Disks Invented in 1986-1987 by David PattersonMore information
Linear Dependence Tests
Linear Dependence Tests The book omits a few key tests for checking the linear dependence of vectors. These short notes discuss these tests, as well as the reasoning behind them. Our first test checksMore information
CSE 120 Principles of Operating Systems
CSE 120 Principles of Operating Systems Fall 2004 Lecture 13: FFS, LFS, RAID Geoffrey M. Voelker Overview We ve looked at disks and file systems generically Now we re going to look at some example fileMore information
Big Data & Scripting storage networks and distributed file systems
Big Data & Scripting storage networks and distributed file systems 1, 2, in the remainder we use networks of computing nodes to enable computations on even larger datasets for a computation, each nodeMore information
Storing Data: Disks and Files
Storing Data: Disks and Files (From Chapter 9 of textbook) Storing and Retrieving Data Database Management Systems need to: Store large volumes of data Store data reliably (so that data is not lost!) RetrieveMore information
This Unit: Floating Point Arithmetic. CIS 371 Computer Organization and Design. Readings. Floating Point (FP) Numbers
This Unit: Floating Point Arithmetic CIS 371 Computer Organization and Design Unit 7: Floating Point App App App System software Mem CPU I/O Formats Precision and range IEEE 754 standard Operations AdditionMore information
Applications of Linear Algebra to Coding Theory. Presented by:- Prof.Surjeet kaur Dept of Mathematics SIES College.Sion(W)
Applications of Linear Algebra to Coding Theory Presented by:- Prof.Surjeet kaur Dept of Mathematics SIES College.Sion(W) Outline Introduction AIM Coding Theory Vs Cryptography Coding Theory Binary SymmetricMore information
Why disk arrays? CPUs speeds increase faster than disks. - Time won t really help workloads where disk in bottleneck
1/19 Why disk arrays? CPUs speeds increase faster than disks - Time won t really help workloads where disk in bottleneck Some applications (audio/video) require big files Disk arrays - make one logicalMore information
Impact of Stripe Unit Size on Performance and Endurance of SSD-Based RAID Arrays
1 Impact of Stripe Unit Size on Performance and Endurance of SSD-Based RAID Arrays Farzaneh Rajaei Salmasi Hossein Asadi Majid GhasemiGol email@example.com firstname.lastname@example.com firstname.lastname@example.com information
DNA Data and Program Representation. Alexandre David 1.2.05 firstname.lastname@example.com
DNA Data and Program Representation Alexandre David 1.2.05 firstname.lastname@example.com Introduction Very important to understand how data is represented. operations limits precision Digital logic built on 2-valuedMore information
Summer Student Project Report
Summer Student Project Report Dimitris Kalimeris National and Kapodistrian University of Athens June September 2014 Abstract This report will outline two projects that were done as part of a three monthsMore information
Elementary Number Theory We begin with a bit of elementary number theory, which is concerned
CONSTRUCTION OF THE FINITE FIELDS Z p S. R. DOTY Elementary Number Theory We begin with a bit of elementary number theory, which is concerned solely with questions about the set of integers Z = {0, ±1,More information
Reliable Adaptable Network RAM
Reliable Adaptable Network RAM Tia Newhall, Daniel Amato, Alexandr Pshenichkin Computer Science Department, Swarthmore College Swarthmore, PA 19081, USA Abstract We present reliability solutions for adaptableMore information
Hill Cipher Project K80TTQ1EP-??,VO.L,XU0H5BY,_71ZVPKOE678_X,N2Y-8HI4VS,,6Z28DDW5N7ADY013 Directions: Answer all numbered questions completely. Show non-trivial work in the space provided. Non-computationalMore information
A simple and fast algorithm for computing exponentials of power series
A simple and fast algorithm for computing exponentials of power series Alin Bostan Algorithms Project, INRIA Paris-Rocquencourt 7815 Le Chesnay Cedex France and Éric Schost ORCCA and Computer Science Department,More information
Guide to SATA Hard Disks Installation and RAID Configuration
Guide to SATA Hard Disks Installation and RAID Configuration 1. Guide to SATA Hard Disks Installation...2 1.1 Serial ATA (SATA) Hard Disks Installation...2 2. Guide to RAID Configurations...3 2.1 IntroductionMore information
Algorithms and Methods for Distributed Storage Networks 4: Volume Manager and RAID Christian Schindelhauer
Algorithms and Methods for Distributed Storage Networks 4: Volume Manager and RAID Institut für Informatik Wintersemester 2007/08 RAID Redundant Array of Independent Disks Patterson, Gibson, Katz, A CaseMore information
Introduction. What is RAID? The Array and RAID Controller Concept. Click here to print this article. Re-Printed From SLCentral
Click here to print this article. Re-Printed From SLCentral RAID: An In-Depth Guide To RAID Technology Author: Tom Solinap Date Posted: January 24th, 2001 URL: http://www.slcentral.com/articles/01/1/raidMore information
An Efficient and Secure Key Management Scheme for Hierarchical Access Control Based on ECC
An Efficient and Secure Key Management Scheme for Hierarchical Access Control Based on ECC Laxminath Tripathy 1 Nayan Ranjan Paul 2 1Department of Information technology, Eastern Academy of Science andMore information
Physical Data Organization
Physical Data Organization Database design using logical model of the database - appropriate level for users to focus on - user independence from implementation details Performance - other major factorMore information
RAID Technology. RAID Overview
Technology In the 1980s, hard-disk drive capacities were limited and large drives commanded a premium price. As an alternative to costly, high-capacity individual drives, storage system developers beganMore information
IBM ^ xseries ServeRAID Technology
IBM ^ xseries ServeRAID Technology Reliability through RAID technology Executive Summary: t long ago, business-critical computing on industry-standard platforms was unheard of. Proprietary systems wereMore information
Input / Ouput devices. I/O Chapter 8. Goals & Constraints. Measures of Performance. Anatomy of a Disk Drive. Introduction - 8.1
Introduction - 8.1 I/O Chapter 8 Disk Storage and Dependability 8.2 Buses and other connectors 8.4 I/O performance measures 8.6 Input / Ouput devices keyboard, mouse, printer, game controllers, hard drive,More information
Mathematics of Cryptography Modular Arithmetic, Congruence, and Matrices. A Biswas, IT, BESU SHIBPUR
Mathematics of Cryptography Modular Arithmetic, Congruence, and Matrices A Biswas, IT, BESU SHIBPUR McGraw-Hill The McGraw-Hill Companies, Inc., 2000 Set of Integers The set of integers, denoted by Z,More information
A Cost-based Heterogeneous Recovery Scheme for Distributed Storage Systems with RAID-6 Codes
A Cost-based Heterogeneous Recovery Scheme for Distributed Storage Systems with RAID-6 Codes Yunfeng Zhu, Patrick P. C. Lee, Liping Xiang, Yinlong Xu, Lingling Gao School of Computer Science and Technology,More information
HP Smart Array Controllers and basic RAID performance factors
Technical white paper HP Smart Array Controllers and basic RAID performance factors Technology brief Table of contents Abstract 2 Benefits of drive arrays 2 Factors that affect performance 2 HP Smart ArrayMore information
Levent EREN email@example.com A-306 Office Phone:488-9882 INTRODUCTION TO DIGITAL LOGIC
Levent EREN firstname.lastname@example.com A-306 Office Phone:488-9882 1 Number Systems Representation Positive radix, positional number systems A number with radix r is represented by a string of digits: A nMore information
PYTHAGOREAN TRIPLES KEITH CONRAD 1. Introduction A Pythagorean triple is a triple of positive integers (a, b, c) where a + b = c. Examples include (3, 4, 5), (5, 1, 13), and (8, 15, 17). Below is an ancientMore information
Disk drives are an integral part of any computing system. Disk drives are usually where the operating system and all of an enterprise or individual s data are stored. They are also one of the weakest linksMore information
RAID Triple Parity. Peter Corbett. Atul Goel ABSTRACT. Categories and Subject Descriptors. General Terms. Keywords
RAID Triple Parity Atul Goel NetApp Inc firstname.lastname@example.com Peter Corbett NetApp Inc firstname.lastname@example.com ABSTRACT RAID triple parity (RTP) is a new algorithm for protecting against three-disk failures.More information
Chapter 13. Disk Storage, Basic File Structures, and Hashing
Chapter 13 Disk Storage, Basic File Structures, and Hashing Chapter Outline Disk Storage Devices Files of Records Operations on Files Unordered Files Ordered Files Hashed Files Dynamic and Extendible HashingMore information


text:
Log In to Schoolconnects
Register In to Schoolconnects
Select a role
what is the country you seek admission? (Proof of human entry)
Admission Enquiry form
I am seeking admission for my child in South Delhi , My child will completed 3 yrs on Jan, 2017 . Can i know the details about best schools in South Delhi
I m going shift to delhi from Mumbai, so would like to know good CBSE schools in west delhi for admission for an Nursery. What age group they take as it seems there is difference in Mumbai & Delhi for school age limit. Looking forward to support from parents.
Hi Frds,
My Child going to complete 3.8 yrs on June, I need to know best board is it CBSE or ICSE?
Due to recent transfer in Delhi, I have to find a school in Delhi for my daughter .She is in UKG. Please advise.
Anush Raj.
I m trying to get admission for 2017-18 for an that i m trying KIIT World School bt i heard that this school dnt have nursery wing. If no means let me know best schools near to Pitampura area becoz all schools in Pitampura are so good. bt can i know which one is best.
Hi Frds,
I'm shifting from New York on Nov Month near to Dwarka. My Child Age will be 3yrs on Mar'17. Whether my child is eligible for Nursery or Pre-Nursery ah. I need to know best IB schools in Dwarka means it also so useful for ready my child base upon schools. Thanks in so advance.
Search in Chennai
SchoolConnects.in is a free service to providing the latest updates on School admission details for schools across the city. A dedicated team reaches school across the city and updates the portal as frequently as daily.
About Us | Terms of Use | Privacy Policy | Contact Us
Our mission is to save the parents from the stress for chasing the schools themselves to seek admission information, and also improve the productivity of our community overall but avoiding multiple parents calling multiple schools multiple times with same queries.

subset: commoncrawl


text:
Click Image for Additional Pictures
Code: toiletbrush
Bathroom Accessories: Blomus Sento Wall Mounted Toilet Brush
Finish is High-Grade Stainless Steel
Blomus, imported from Germany.
Special: $75.59 instead of $81.29
Say goodbye to the old toilet brush. This elegant wall mounted toilet brush is a customer favorite!
Its clean lines and durable German-made construction compliment any type of bathroom design.
This stylish wall mount toilet brush by Blomus is a space saving and sanitary solution for any bathroom!
The Sento toilet brush from Blomus features a high-grade stainless steel construction
and space-efficient wall-mounted storage. Its elegant stainless steel cylinder stylishly
conceals its contents. This toilet brush mounts off the floor for an uncluttered look. Plus, it makes cleaning the bathroom so much easier.
It's stainless steel construction makes cleaning a breeze. Features a high gloss white plastic cover lid to keep the toilet brush out of view.
The Blomus Sento wall-mounted toilet brush is a necessity for any residential- or commercial bathroom.
A handy option for any bathroom design and to create a clean and sleek modern appearance.
The Blomus Sento toilet brush is made and imported from Germany.
Mounting hardware is included.
Blomus design accessories are made in Germany for unsurpassed precision-made quality.
The aim of Blomus is to harmonize form and function and to create special
products for everyday life. By creating accessories that combine simplicity of function with the beauty of the material,
Blomus has created an impressive design catalog that includes
bathroom accessories, shower accessories, kitchen accessories, fireplace tools, mailboxes, laundry bins and outdoor furniture.
Keep your bathroom looking neat, organized and beautiful with award-winning bath design accessories from
Dimensions: 16.9"H x 5.1"DIA
Material: stainless steel.
110% Lowest Price Guarantee on this product.
Free shipping, includes insurance and tracking.
Plus: sign up for 'super saver' & get 10% off towards future purchase!
In stock, usually ships in 2 business day.
Let's Save you some money!
Feature this product on your Facebook, Twitter, Pinterest or Tumblr Page.
And we will reward you with an Instant 10% Discount Coupon Code!


text: Posted February 5, 2011 · Report post I am living in Bali, Indonesia. I"ve tried to register for Premiere Package, but I didnt find my country (Indonesia) on the list. Is that mean that we are in Indonesia can not join tor Fans Club Bungalow B? Share this post Link to post Share on other sites


text:
Author Affiliations: Department of Medicine, Johns Hopkins University, Baltimore, Md (Dr Weisfeldt); and Section of Emergency Medicine, Department of Medicine, University of Chicago, Chicago, Ill (Dr Becker).
Despite 40 years of cardiopulmonary resuscitation (CPR) therapies, overall
survival rates after cardiac arrest remain poor. Recent data suggest that
the death toll in the United States is greater than previously believed—possibly
450 000 sudden deaths each year—yet the average survival rate remains
lower than 5%.1 In contrast, the article by
Cobb et al2 in this issue of THE JOURNAL suggests
a lower incidence rate, about 184 000 cardiac arrests per year, as well
as a decreasing proportion of cardiac arrests with ventricular fibrillation
(VF) as the first identified rhythm.
Weisfeldt ML, Becker LB. Resuscitation After Cardiac ArrestA 3-Phase Time-Sensitive Model. JAMA. 2002;288(23):3035-3038. doi:10.1001/jama.288.23.3035
© 2017


text:
Build a Website - 21/11/2016 07:20 EST
Budżet $10-30 USD
i want to build a good website
63 freelancerów złożyło ofertę na średnią kwotę w wysokości $163 do tego projektu.
For the proposed cost we assure you * 90 days free support & maintenance (After sales service) * Unlimited* design revisions * Website with bootstrap resposnive design * Double tested by quality analyst which is b Więcej
yes, let's clarify the requirement in details also if you want us to share our skill and previous work let us know.. hope to hear you soon.. Thanks & Regards PROMITI
Hi, I am Retheesh and i have more than 7 yrs of exp and can very well do your project as per the project description given. Portfolio: http://webzersolutions.com/projects/ Completed projects: http://ww Więcej
Hello,I can complete your project on time and within your budget.I read through the job details extremely carefully and I am absolutely sure that I can do the project very well. I will give you our best work with our Więcej
I am Yogesh sanwal, 5+ years experienced inwebsite and e-commerce development using PHP/MySQL. Take a look to my last work: https://www.solomonbrothers.com http://charleskrypell.com/ http://ounati.com/ http://ww Więcej
Hi, I just read the job description and would like to chat with you to understand your requirement that you want in the site. Let me know what exact features you need for this site ? I have good skills in web de Więcej
Dear Client, Thank you for looking at my candidature. As per your given brief you are looking for an web application, am glad to say that i have prior experience in the field of development. I can fulfil you Więcej
Hi, I have a few questions about your project. Please send me a message so that we can discuss more. Just went through your project description, I understand your requirement for Build a Website I have done Więcej
Hello, Thanks for reviewing my proposal ! I have gone through your requirement to Develop Responsive Website, So I'm perfectly able to do this Job in less than anticipating time. Here are Responsive Sites rece Więcej
Hi there , i will provide you 100% resposive design and all device compatible i will make the same as you need also provide you the complete admin panel so from there you are able to manage your complete website lik Więcej


text:
Like ex-athletes and ice-cream cakes, tattoos rarely retain their original appearance after 10 years. Bid a graceful goodbye to body art with today's Groupon to Creative Laser Tattoo Removal Clinic in Waxahachie. Choose from the following options:
- For $49, you get one tattoo-removal treatment for up to 7 square inches (a $150 value).
- For $129, you get three tattoo-removal treatments for up to 7 square inches (a $450 value).
- For $99, you get one tattoo-removal treatment for an area of 7–10 square inches (a $250 value).
- For $279, you get three tattoo-removal treatments for an area of 7–10 square inches (a $750 value).
The expert technicians at Creative Laser Tattoo Removal Clinic erase all hues of skin art with short pulses of concentrated, solid-state laser light. Customers first make an appointment for a free consultation to assess their skin type, discuss any medical concerns, and answer the question of whether lasers can remove wine stains from clothing. Armed with the Nd:YAG Q-switched laser, a technician will target the tattooed pigments of the skin and leave innocent skin and body-hair bystanders unharmed. Journeying through the top layer of the skin, the laser is absorbed by tattooed pigments, breaking down inky invaders and removing them through the immune system with no scarring. Each session takes approximately 15 minutes, after which skin will be thoroughly bandaged and treated with antibacterial ointment. Tattoo removal may require anywhere from five to 12 laser-treatment sessions, depending on several factors including size, location, age of the tattoo, and the depth of one's emblazoned devotion to Mom.
Creative Laser Tattoo Removal Clinic LLC
In a charming, Victorian–style building, staffers blast away unwanted tattoos, encroaching toe fungus, and skin blemishes such as age spots and stretch marks using state of the art Nd:Yag Q-switched lasers. During free consultations, certified laser technicians assess the proper course of treatment, discuss any medical concerns, and answer the question of whether lasers can remove wine stains from clothing. In addition to wielding lasers, technicians also harness ultrasound technology to fend off cellulite, and they knead the abdomen using chi nei tsang, a specialized massage meant to stimulate the lymphatic and circulatory systems.


text:
Beware! Space Pandas! | Audio
By Will Ross
Website http://prefacesandasides.blogspot.com
Will Ross is a writer/poet from Omaha, Nebraska. He's been writing and podcasting for nearly five years now. He lives at home with three terriers, a roommate, and about thirty Arizona Iced tea empties.
I think the greatest environmental threat to the human race is if super smart pandas had lasers and they came down from space where aliens trained them to be smart, but also shoot lasers. This would be a drastic change of environment. Because it would be a bear, which is harder to shoot than a person, but it would also have a laser, which is better than a gun. So as you can see the space pandas are each worth like... four army dudes. Not the ones from Call of Duty with the Javelins or nothing. Like regular just want to go to college not die fighting space panda type dudes.
So like, also, they're coming from Space. Sun Tzu once said "Shoot arrows from up there, they'll go farther." So like, a third thing is that with their Jet-Packs (how they're getting down from space) their lasers are firing DOWN so they'll go twice as far as the bullets from the army dudes, which will go half as far. What that means is mathematically at that altitude each space panda with a laser is worth EIGHT army dudes.
Now, on top of that, remember how I said the aliens trained them to be super smart? So the soldiers don't get to go to college until they fight space pandas in the army. So they won't understand leading and trajectories like the space pandas will; or Shakespeare as well. So now we're up to like NINE OR TEN DUDES, for one panda from space.
So now, imagine there are like a hundred of them? They could take out an army base easy. And our army is all spread out so they could laser through like Strat-Com and junk. So with all our nuclear missiles down... the mother-ship is in play!
So the mother-ship drops out of space, right? Cause regulars SAMs and junk wont penetrate it, and our nukes were surgically removed by space pandas. And it's got like, tons of little ships that fly out also, so even if all the worlds air force teamed up, forget about it. Not gonna happen.
So all the army dudes and like cops and maybe security guards that fight back get lasered plus also those dudes that have bumper-stickers that say "You can take my gun out my cold dead hands" but they're hands are always sweaty and kind of gross; like they rub your palm with their thumb and it's probably by accident but he really likes cleaning that gun. Those guys get lasered.
A resistance forms but with the mother-ship in the sky there's no way to stop them. Then someone asks this guy. And I say, "just put a bunch of nukes in some catapults and you can hit the side of it rendering it exploded." And I got the idea because there was a show on catapults at that exact moment and I pull my sunglasses off and say what I already said I said.
So like the army guys that are left roll all these catapults out that we had in the Smithsonian from the War of 1812 and all these suitcases. And they give me this like handful of ropes attached to the triggers of the catapults. And they're like "Pull it Bobby, your the only one who's got the moves." And so I John Woo it and the suitcases look like they arn't going to make it but they do and they blow the crap out of mothership which probably will land on the school, so unfortunately none of us will really see the ending but me, but trust me, from that day forth I have no problems with the ladies.
This is not an appropriate Earth Day essay. Please write another essay over the weekend and turn it in on Monday.
-Mr. Thompkins
Why? It won't be Earth Day on Monday, no one will care about the environment then.
Detention it is.
-Mr. Thompkins


text:
News By Tag
Industry News
News By Place
Industry News
Free Online Astrology Compatibility Love Report
Renewing love life and find the life partner is just a click away!
Bello Jewels, an Indian based jewelry store and an international supplier of gemstones, has taken up the service of providing free online Astrology consultation and Vedic astrology consultation to better people's lives. The free online astrology compatibility love report that can be generated at this site has improved the lives of many. When two absolute strangers would try to make a living under one roof, it is obvious to find differences however if they are compatible in love then all these difference are minute and can be easily succumbed. Astrology helps to acquire this greater strength by making a few changes that can enhance love life and even find a perfect match. It is an ancient belief that when a person is born, their better-half is also born somewhere and destiny unites them. This belief becomes a reality in most cases however in some cases; it has to be made possible.
Indian astrology and Vedic consultation with a reliable Jyotish provided by Bello Jewels would help to find the right match and settle with the right person. The match is found according to the birth chart calculation and in order to mend a broken relationship, there are gemstones and precious stones that are predicted through free gemstone recommendation software online. This free gemstone consultancy would enable people to effective match making as the report would provide some in-depth information on bettering relationships. The influence of the Rashis and the role played by precious stones like Pukhraj, Panna, planetary gemstones, nine gems, Manik and Rashi ratna are incomparable. Get the free compatibility love report through http://astrology.bellojewelsonline.com/
Follow us on:
Facebook- http://www.facebook.com/
Twitter- http://twitter.com/
LinkedIn- http://www.linkedin.com/
Media Contact:
Free Online Astrology Compatibility Love Report
+(91)-9555149149 (India)
Account Email Address Account Phone Number Disclaimer Report Abuse


text:
A regulated professional firm of farmland and agribusiness investment specialists with a proven track record since 1993. Delivering solutions for landowners, managers and investors in all aspects of agricultural business, farmland and property matters.
Contributing proactive and practical support that adds value to our clients, whether large or small, farmer or institution. We focus on growth for our clients through a range of solution based services, tailored to your requirements. Typically we are instructed by institutional investors, family offices, international farming corporations, individual farmers, individual investors and funds.
We have both a successful agricultural business consultancy practice, rooted in the detail of day to day farming and business decisions; and a land agency/brokerage division offering a full range of valuation, agency and farmland investment services for property and land across the UK, USA, CEE and CIS. To find out more link to our About page or browse the website at your leisure.
For details relating to Agricultural Asset Management, a Brown & Co and Dexion joint venture, please visit the AAM website here….
The acquisition of a large scale operating Agricultural entity can be a complex process. Additionally there is usually a short time frame given in which to accurately assess a business,…Read more
Our international agency and brokerage team are farmland investment specialists in large scale agriculture worldwide, offering; • since 2003 advice in the acquisition, marketing or sale of over…Read more
Brown & co are a leading consultancy service provider. We work with farming businesses of all sizes throughout the CEEC and are very proud of our long established, experience based…Read more
We act as a fiduciary for the absentee agricultural investor. By definition, the fiduciary duty is the highest standard of care. The fiduciary relationship is highlighted by good faith, loyalty…Read more
Over 20 years of international experience
Quality management systems
Regulated by the RICS
Proven track record
High standards of reporting
Professional Indemnity
Brown & Co together with Dexion Capital have formed
to find out more see press releases or visit the bespoke AAM website…
Our latest
is available to Download, providing an insight into active markets across the region..
looking at the impact of the climate and environment on property and agriculture - Download
For past Brown & Co publications and research please visit our reports page…
Aug, 2015
Yesterday, Russian media reported a lifting of sanctions against 29 New Zealand dairy companies. 'The market has yet to react to this opening but certainly any boost in demand across the sector should help to reduce the glut in supply …Read more
Mar, 2015
In Brown & Co's latest CEE land market brief; Wojtek Behnke reports on the Polish farmland market… Poland's farmland land market has gone through a period of sustained growth over the past five years. The most marked increases in value have …Read more
Feb, 2015
In Brown & Co's recent CEE land market brief – Stephen Hall reports on the Romanian farmland market…. The concept of quality can not be understated in Romania, however it stretches far beyond the basics of soil type and classification. …Read more
Jan, 2015
The European Union has voted to allow individual member States to decide on their own policy relating to GM crops. The vote, which was passed with a 480-159 majority on Tuesday 13 January opens the possibility for GM crops to …Read more


text:
There's nothing new about bullying. However, what is new, is the rise of technology as a tool. What is equally sad, is our failure to use the same technology to beat the bully.
Bullying in childhood used to be confined within a specific group – usually a bunch of school bullies, or the classic big bully from the next street. However, today's children are exposed to a much wider, public circle.
Understandably, many parents are worried about bullying and fear for their children. It is important to discuss this subject with your children. Bullying is a subject I have dealt with in my own writing and I wrote this story called 'The Tree Hugger' about a girl being bullied in school. For various reasons children often don't tell when they are being bullied and reading stories that raise the subject of bullying can help a child open up.
Social networking sites provide not only a sharp and incisive tool for the bully but also an easy way for them to spread their venom to a much wider audience. This way, the idea that the 'whole world hates me' is easily perpetuated, sometimes with fatal results.
It is such a pity the networking sites are not as willing to take responsibility particularly as they make huge profits. They might even find their profits rise. Internet technology is increasingly being used to fight crime – why can't it be used to defeat bullies rather than enable? Providers should forward details of all bullying sites to the police voluntarily as well as banning their users for being accomplices. Surely this action would enhance their image?
An image of network providers as responsible, caring business people who defend human rights would surely be a better one to have than that of a faceless bureaucracy who far from caring about bullying actually defend the rights of those who seek to use the Internet to abuse others – because… well, why exactly? Some sense of freedom? Freedom to hurt others?
It's not all about bullying in childhood either. Adults, whether consciously or not, are condoning bullying behaviour by enjoying watching it on television. Matters aren't helped by the replacement of much quality television drama by reality television. Here is an arena where bullying is encouraged and applauded. Millionaire celebrity 'experts' showering their unfortunate trainees with drool as they shout and swear at them is considered funny and entertaining.
Some shows provide no end of bullying opportunities for their participants. People on 'Big Brother' and 'I'm A Celebrity Get Me Out Of Here' who 'fail' their tasks are letting down their 'team' or 'side' of fellow inmates or housemates who might even be deprived of food as a result of this 'failure.' A lot of these shows are simply all about bullying. Picture the participants on reality shows who 'fail' to win popularity while being deprived of everything considered normal in life being booed by a happily baying and boisterous mob.
However, I am not blaming television and the Internet for bullying; they are just tools. Bullying has always been with us and no doubt always will. This does not excuse our lack of intervention and support for the bullied. Alongside the rise of technology comes a rise in knowledge. We have the knowledge. We know how to stop bullying but we either don't have time to make the effort, or we prefer not to. I am not sure which. Perhaps a bit of both! I do remember one or two teachers in my own school adding some of their own brand of 'teacheristic' and sarcastic sneering to the misery of one particular girl who was always being bullied.
Many years later, when I used to teach creative writing myself, I heard first hand how little help a severely handicapped student of mine received when his able-bodied classmates viciously bullied him. I was even more shocked to hear that his teacher advised him to stop being such a goody-goody and do something bad so he would 'fit in.'
Perhaps we should be educating our children and teachers to learn that being ourselves is a goal worth achieving, whereas 'fitting in' is a goal more worthy of a sheep. I wrote my children's story 'The Tree Hugger' because I felt so strongly that we should be encouraging and celebrating individuality instead of the 'herd mentality' and I felt driven to tell a story about a girl who just wanted to 'be herself.'
Like many of us I have experienced bullying on a personal level myself. In fact, I am sure there are very few of us who have not been bullied at some time – especially us writers – since a lot of us were quiet and introverted growing up. I have shared my experiences and written specifically about how bullying influences us writers in this post.
If you have any comments or questions about bullying or any other subject on the site – don't forget I'd love to hear from you.
More from my writer's diary here.


text:
Listen to free music by Galagen
Blip.fm is internet radio made social. It's easy to search for, play, and discover free music recommended by real people. Join today to create your own free station.
Artists Like Galagen
Blip.fm DJs who play Galagen
Friends: MerchantCircle | Charity Blossom | Website Load Testing


text:
5 in 1 Camping Outdoor Survival Bracelet
5 tools in 1 - in this custom versatile Camping Outdoors Bracelet.
- Flint / Fire starter
- Compas
- Whistle
- Scraper can be used as knife
- Unravel the paracord and you have rope for tying down camping equipment, gear, climb walls, or build your shelter. There is a total of 10.5 ft of rescue cord woven into the bracelet.
Elegant bracelet for daily wear as well as a great accessory for camping, fishing, hiking, climbing and other outdoors activity.
Material: High quality parachute cord, Nylon
Length: approx. 9.84"
Width: approx. 0.79"
This product has FREE Shipping from our international warehouse. Please allow 2-4 weeks for your order to arrive.
This awesome product has FREE US Shipping from our international warehouse - only for a limited time. Please allow 2-4 weeks for US delivery. International add one week.


text:
If you have a business, you'll need to know something about taxes, the IRS, and tax deductions. Learn about the most valuable deductions -- car expenses, business-related travel and entertainment, Section 179 expensing. Also find out how to avoid problems with the IRS.
Deducting "Ordinary and Necessary" Business Expenses
How tax savvy a businessperson you are has a great effect on how much money remains in your pocket at the end of the year. Knowing how to maximize your deductible "ordinary and necessary" business expenses lowers your taxable income, which means you pay less to the IRS at the end of the year. But watch out: the IRS scrutinizes these deductions to make sure you don't include any purely personal (nondeductible) expenses.
Tax rules cover not only what expenses can be deducted but also when -- in what year -- they can be deducted.


text:
From WikiFur, the furry encyclopedia.
Kaedal is a male amateur furry writer who lives in Denmark. Kaedal used to be an active member in the DKFurs forum.
Kaedal's fursona, and namesake, is a grey Wolf with orange markings.
External links[edit]
|This person is a WikiFur user:
- Kaedal on Fur Affinity
- Kaedal on SoFurry
|This stub about a person could be expanded.


text:
My name is Nina Gabriel and I am a junior studying Fashion Merchandising at the University of South Carolina. I was born and raised in North Myrtle Beach, SC so naturally I'm a lover of the ocean, and would definitely say my happy place is sitting in a beach chair with my toes in the sand! Lover of chocolate, Harry Potter, anything snakeskin or leopard, and reading fashion blogs. Follow along with my CollegeFashionista posts to see what's trending here at USC!
Nina Gabriel
my bio


text:
Dull skin can definitely create an unattractive look, which is the substantial worry point amongst all the females of the world. Blame it on pollution, the unhealthy lifestyle or simply the not so good ability to choose the right products for your skin, the ultimate result is , you are going to end up with a flawed skin and a rather dull look. Here is what you can do to bring up that extra glow back to your skin in easy steps.
1) Use a gentle facewash
You can get if from here: Pond's white beauty facewash
2) Use a moisturizer
Vaseline healthy white moisturizer


text:
By martbaz
- 285 views
- Find their other images
A few baits I did over the weekend ..not perfect yet but it's getting better
0 Comments
There are no comments to display.
Create an account or sign in to comment
You need to be a member in order to leave a comment
Create an account
Sign up for a new account in our community. It's easy!
Register a new account
Sign in
Already have an account? Sign in here.
Sign In Now


text:
Insight Editions LLC is an art book publisher.
- The Art of StarCraft II: Wings of Liberty (2010)
- The Art of Blizzard Entertainment (2013)
- StarCraft Tech Manual (2015)
Insight Editions intended to publish The Cinematic Art of StarCraft II: The Terrans, but the product was canceled. They still intend to release another StarCraft art book, though after the release of Legacy of the Void.[1]
- ↑ 2009-05-22, The Cinematic Art of StarCraft II: Terrans Leaked?. Blizzplanet. Accessed on 2009-05-23


text:
What are the three types of plate margins?
Destructive Plate Margins
Constructive Margins
Conservative Margins
What is the Earth's surface serperated into?
The centre of the earth
The Mantle
The crust
Whats floats on the mantle?
What are the two types of plates?
Continental crust
Oceanic Crust
How are the plates moving?
What are the places called where plates meet?


text:
Chris is an astronaut in the Jupiter 16 Spacecraft in the 1967 film You Only Live Twice. He was portrayed by Norman Jones.
Film biography
Orbiting over the Earth is Jupiter 16, a US space capsule manned by two astronauts. As they maintain radio contact with bases in Hawaii and Houston, Chris ventures outside to make routine repairs, when radar picks up another spacecraft closing fast. Radio contact is lost and the spacecraft opens up and swallows Jupiter 16, in the process severing Chris's lifeline and leaving him to die in space.


text:
Charming Apartment Ocean View Boa Viagem, Recife
Daire, Bütün alan - Boa Viagem, Brezilya
With only 50 steps from the most attractive beach in Recife, good trip, you will find this wonderful apartment of 250m². Great location.
Come and have your perfect holiday on the beach of Good trip, with wonderful views of the sea in a secure apartment, comfortable, charming and clean and enjoy the hospitality of a superhost hostess.
One apartment per floor, tastefully decorated, lit with spectacular views of the Sea Good trip. Cable TV + HBO, Apple TV HD, Netiflix.
Large living room with four complete rooms, balcony with a wonderful view of the sea. full kitchen, laundry area.
Only 1 km from Guararapes International Airport. Near the American School of Recife.
Located on the eight floor of a building with elevator and 24 hour doorman. 3 bedrooms, 2 full suites, 1 bedroom with double sofa bed + an air mattress.
Party room on the top floor with stunning views of the beach Good trip.
Several bars, pubs and restaurants just a few meters from the apartment and lots of fun. Gym with Pilates, RPG and beauty salon in front of the apartment.
Private parking next to the Dona Lindu Park and its main attractions and close to everything you need!
There are two good supermarkets close to the apartment, several bakeries, cafes, bars, restaurants, pubs.
We offer several types of games for you to enjoy and movies.
Great for those who come for tourism, study or work. To drink a cup of tea or a glass of wine on the balcony and enjoy the sea view is wonderful.
Our proposal is to offer a sustained package of 4 pillars: Excellent Location + Safety + Comfort + Tranquility.
-------------------------------------------------- --------------------------------
-Suite 1 - With a queen size bed or two single beds / box and private bathroom, air conditioning, ceiling fan, TV, Chromecast, Netiflix, DVD, Wifi, Wardrobe, iPod connector, bed linen and bath.
suite bathroom: spacious sink, hot / cold shower. All clad in travertine marble and ceramics.
- Suite 2 - With a double bed / box and private bathroom, air conditioning, ceiling fan, TV, TV Aplle, Netiflix, DVD, Wifi, wardrobes, new furniture. Bed linen soft bath. Bathroom suite: spacious sink. hot / cold shower. All clad in travertine marble and ceramics.
- Room 3 - Room with a sofa double bed + 1 inflatable mattress, TV, TV Aplle, Netflix, ceiling fan, desk, wifi, clock.
- 1 Toilet - All travertine marble dresses.
Note: We have 2 suites and 1 room available for guests, one bedroom (4 room property) is used to deposit, then, is closed during the stay.
-------------------------------------------------- ---------------------------------
Approximately 60 meters from the apartment (about five minutes) the Dona Lindu Park, cultural space with a beautiful architecture of the famous architect Oscar Niemeyer, cultural attractions such as concerts, plays, art exhibits and more. There you will also find a tourist information booth very useful on urban bus schedules and routes, as well as general information on tourist attractions populares.Próximo to supermarkets, bakeries, deli, bank, restaurants, bars.
10 minutes from Boa Public Market Travel with its kiosks fruits, typical foods and crafts, and of good trip square with its beautiful church and crafts fair.
The Shopping Center Recife is 2.6km. Several bus lines pass in front of the apartment on the beach, toward the malls (Recife, Rio Mar and Tacaruna), the center of the city, Old Recife and Olinda.
Thirty minutes south, you will find several famous beaches.
Super close to point to wait for access to all places of interest.
- Sigara içilebilir
- Mutfak
- Duş / küvet
- Balkon
- Buzdolabı / dondurucu
- Bahçe
- Aile/çocuk için uygun
- Asansör
- Klima
- Eşcinsel dostu
- İnternet
- Ücretsiz park
- Portaria 24hrs
- Private Bathroom
- Suite Completa
- TV a Cabo
- Vista Panoramica do mar
- Çamaşır makinası
- WiFi
- Panoramik manzara
- Denize yakın mülk
- Kablo TV
- Kurutma makinesi
- Saç kurutma makinesi
- Demir
- çaydanlık
- Kilitlenebilir oda
- Mikrodalga
- Şampuan
- Havlu