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problem of scheduling tasks with precedence constraints and unit computation costs on two identical processors such that the schedule length is minimized If the two processors are uniformly heterogeneous, this changes to Q2|prec, pi = 1|Cmax Finally, P |tree, cij pmin , dup|Cmax denotes the problem of scheduling a task graph with tree structure, arbitrary computation costs, and communication costs that are smaller than or equal to the minimum computation cost (ie, the graph is coarse grained) on an unlimited number of identical processors Node duplication is allowed and the objective is again to minimize the schedule length Generalizations and Reductions The theory of NP-completeness implies that a general problem cannot be easier, complexity-wise, than any of its special cases Many of the previously de ned sub elds restrict the parameters of the task scheduling in some way, making it a subproblem of a general one In particular, many speci c graph structures are listed, which are also related to each other A fork graph, for instance, is a special form of a tree If it is proved that a particular scheduling problem is NP-complete for tree structured task graphs, then the scheduling problem is also NPcomplete for an arbitrary graph structure In face of this observation, it is interesting to realize the relations of the different graph structures de ned for the eld Figure 613 visualizes these relations Each arrow points in the direction of the more general structure: that is, the graph at its tail is a special case of the graph at its head The above observation is re ected in the way NP-completeness of a problem is usually proved A common step in such proofs is to reduce a known NP-complete problem in polynomial time to that problem, as is done in all NP-completeness proofs of this text This is particularly easy if the known problem is a special case, as, for example, in Theorem 62 hus, if NP-completeness is shown for a special case, the NP-completeness of all more general cases can be proved using such reductions As a consequence, Figure 613 can also be interpreted as a reduction graph (Brucker and Knust [29]), although not all task graph structures lead necessarily to an NP-complete scheduling problem.

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This study shows that in arm manipulator motion planning tasks, training has no signi cant effect on human performance, neither in terms of path length nor in he task completion time. In our tasks the subjects were unable to seriously improve their motion planning skills via training. This is no doubt very surprising. One would expect the opposite conclusion: We all know examples of tasks involving motion where, given enough training, humans become extremely adept; an acrobat on the trapeze is but one example. There is a big difference, however: The acrobat does a once-and-for-all learned motion, whereas our tasks require constant spatial reasoning. Our test protocols do not allow a subject to simply memorize a task. We want our subjects to learn how to do a class of tasks; we want them to improve their spatial reasoning skills, rather than memorize a speci c motion. Examples of positive effect of training in tasks that involve spatial reasoning are harder to come up with. Note that since. Barcode In .NET Framework Using Barcode generator for .NET .Related: Codabar Generating .NET , .NET ITF-14 Generating , Generate Interleaved 2 of 5 .NET

Example 14.4: The following CRC-32 generator polynomial s used to generate 32-bit CRC. The parameter L is the constraint length of the onvolutional code. Convolutional code is a special case of error-control code. Unlike a block code, a convolutional coder is a device with memory. Even though a convolutional coder accepts a xed number of information symbols and produces a xed number of code symbols, its computation depends not only on the current set of input symbols, but also on some of the previous input symbols. barcode generating in .net using barcode generator for rdlc .Related: Create EAN-8 .NET , Print UPC-E .NET , Printing ISBN .NET

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Example 14.7: Two Rayleigh fading models have been eveloped, one was proposed by Jackes . size, image with visual basic.net barcode sdk. . Using the primitive polynomial (1011), the generator polynomial s generated by MATLAB function rsgenpoly(7,3) provided in the Communication Toolbox. In this experiment, the primitive polynomial is p(x) = 1 + x + x 3 . The output of generation polynomial function rsgenpoly(7,3) is (1 3 1 2 3), which is in symbol format and can be converted to polynomial presentation using Table 14.2. Thus, the generator polynomial generated by rsgenpoly(7,3) is g(x) = x 4 + ( + 1)x 3 + x 2 + x + ( + 1), where is the root of p(x). Using MATLAB functions that support the Reed Solomon encoder rsenc( ), decoder rsdec( ), and Galois eld array creator gf( ), we can easily simulate a communication system. The MATLAB script is listed in Table 14.8. In this experiment, a 3-symbol array msg is encoded and a 7-symbol code.Related: Intelligent Mail Printing .NET

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SHIFT REGISTERS net Framework code-128c generator for vb Using Barcode Control SDK for None Control to generate, create, read, scan barcode image in one applications For example, a 3-stage LFSR with connection olynomial C ( x ) = 1 x2 will generate a sequence of period length seven for any nonzero initial fill In general, if C ( x )is a primitive polynomial [43], then the resulting LFSR will yield m-sequences for all nonzero initial fills While m-sequences have many nice statistical properties [59],they would be poor choices for keystream generators Suppose we have a 32-bit key and we decide to use a stream cipher that consists of a 32-stage LFSR, with the connection polynomial chosen so that the resulting keystream is an msequence.

Then if Trudy is able to obtain just 64 consecutive keystream bits, she can use the Berlekamp-Massey Algorithm to determine the entire keystream, which is of length 232 - 1 Recall that with a stream cipher, known plaintext reveals the keystrearn, so for this example, a very small amount of known plaintext completely breaks the cipher Consequently, a single shift register that generates an m-sequences would be an extremely poor stream cipher, in spite of its excellent statistical properties and long period length In a sense, m-sequences are among the worst keystream sequences However, it is possible to combine m-sequences to generate usable keystreams We give examples of such keystream generators in the next section This discussion of rn-sequences highlights the fact that, as a consequence of the Berlekamp-Massey Algorithm, a cryptographically strong keystream must have a high linear complexity.

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But is this sufficient' That is, if we have a sequence with a high linear complexity, can we be certain that it is a cryptographically strong keystream In fact, it easy to see that this is not the case, since any sequence of the formRelated: .

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ERASURE CODES in NET Generator QR Code in NET ERASURE ODESNET Control to generate, create, read, scan barcode image in NET framework applications For example, a typical value is 4 However, a imited stretch factor limits in practice the applicability of Tornado codes Another drawback related to the stretch factor is that, when using RS code or another kind of erasure code at the last stage, the stretch factor must be predetermined before encoding takes place Hence, researchers need to estimate, in advance, the loss probability of the channel to determine the amount of redundancy to put into the data For most Internet applications, the loss probability varies widely over time Thus, in practice, the loss rate has to be overestimated, making the codes slower to decode and far less ef cient in transmitting information If the loss probability is underestimated instead, the code fails 43.

3 LT Codes With Luby-Transform codes (LT codes for short) it is no longer necessary to tune the encoding process over the loss characteristics of the transmission channel LT codes do not rely on a xed rate to add redundancy to the data to send out; rather, they are said to be rateless codes They were rst devised in 1998 and can de nitely be considered the rst full realization of the concept of digital fountains [28] Let a symbol be an l-bit string Encoding is performed over k input symbols and has the potential to generate a limitless number of encoded symbols Each encoded symbol is produced, on average, by O(ln(k/ )) symbol operations, being 0 < 1.

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The original input symbols can k be reconstructed with probability (1 ) from any set of k + O( kln2 (k/ )) encoded symbols out of the total number of encoded symbols produced The total number of operations needed to recover the original k symbols is about O(k ln(k/ )) Hence, encoding and decoding times depend on the ingress data length independent of how many encoded symbols are generated and sent by the decoder The same relations hold for the encoder and decoder memory usage Therefore, given the reduced overall costs of LT codes with respect to the other aforementioned erasure codes, encoding can be performed over bigger chunks of data than those used in RS codes and Tornado codes, or even over the entire le at once.

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Luby-Transform codes are similar in construction and properties to Tornado codes because they also rely on a graph and the encoded symbols are obtained by XOR-ing over other initial (or previously encoded) symbols (see Figure 48) However, the graph construction for LT codes is quite different fromRelated: .

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