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A second important technique in error-control coding is that of convolutional coding [1 6] In this type of coding the encoder output is not in block form, but is in the form of an encoded sequence generated from an input information sequence The encoded output sequence is generated from present and previous message input elements, in a continuous encoding process that creates redundancy relationships in the encoded sequence of elements A given message sequence generates a particular encoded sequence The redundancy in the encoded sequence is used by the corresponding decoder to infer the message sequence by performing error correction The whole set of encoded sequences form a convolutional code Cconv , where there exists a bijective (one-to-one) relationship between message sequences and encoded sequences From this point of view, a sequence can also be considered as a vector.

Having determined the rule and action(s), the third and last step in creation of an alert is determining the recipient(s). The alert configuration tool within the dashboard must allow an easy selection of alert recipients. The selection interface must facilitate inclusion of individuals and user groups defined within the dashboard framework. For example, if an alert is defined to appear in the event that Region 1 sales drop below 10% of the monthly target for the region, then the alert may be configured to initiate an action, an e-mail to the Region 1 user group, as well as the VP of Sales. In other words, all users defined within the Region 1 user group would receive the alert. Effective recipient selection interface facilitates user search and easy navigation of the users list when the dashboard deployment is across a large user base. It also allows the selection of several user groups across different hierarchies as recipients of an alert action. Depending on the scope of recipients, alerts may be divided into two categories: (1) personal and (2) public alerts.

Then, message sequences belong to a message vector space, and encoded sequences belong to a code vector space Message sequence vectors are shorter than code sequence vectors, and so there are potentially many more possible code sequences than message sequences, which permits the selection of code sequences containing redundancy, thus allowing errors to be corrected The set of selected sequences in the code vector space is the convolutional code A suitable decoding algorithm can allow us to determine the message sequence as a function of the received sequence, which is the code sequence affected by the errors on the channel In general terms, convolutional encoding is designed so that its decoding can be performed in some structured and simpli ed way One of the design assumptions that simpli es decoding is linearity of the code For this reason, linear convolutional codes are preferred.

The source alphabet is taken from a nite eld or Galois eld GF(q) The message sequence is a sequence of segments of k elements that are simultaneously input to the encoder For each segment of k elements that belongs to the extended vector space [GF(q)]k , the encoder generates a segment of n elements, n > k, which belongs to the extended vector space [GF(q)]n Unlike in block coding, the n elements that form the encoded segment do not depend only on the segment of k elements that are input at a given instant i, but also on the previous segments input at instants i 1, i 2, , i K , where K is the memory of the encoder The higher the level of memory, the higher the complexity of the convolutional decoder, and the stronger the errorcorrection capability of the convolutional code.

APPENDIX C: SPSS MACRO AND REGRESSION CODE FOR MULTIPLE IMPUTATION Note: This code automates the process of standardizing items, computing new scales, and performing the regression analysis for the 20 imputed data sets. However, the immediate results of this macro are not readable by NORM. For these analyses, we used the utility NORMSPSS to read the SPSS Regression output, create the NORM-readable data set, and create a partial MI Inference data set (NORMSPSS.OUT) automatically. The NORMSPSS utility and related les can be obtained at our web site: http://methcenter.psu.edu. DEFINE !NORMIMP() . *** modify the following statement (number of imputed datasets) as needed *** . !DO !I = 1 !TO 20 . *** modify the /FILE = line (shown as jan06 ) as needed *** . *** modify the /VARIABLES = statements as needed *** . *** NOTE that the format given behind each variables appears to be necessary, but arbitrary *** . *** That is, it appears that F2.2 may be used for all numeric variables *** . GET DATA /TYPE = TXT /FILE = !CONCAT ( jan06_ , !I , .IMP ) /DELCASE = LINE /DELIMITERS = /ARRANGEMENT = DELIMITED /FIRSTCASE = 1 /IMPORTCASE = ALL /VARIABLES = relig F2.2 female F2.2 introvrt F2.2 alcsep F2.2 alcnov F2.2

Linear convolutional codes are a subspace of dimension k of the vector space [GF(q)]n de ned over GF(q) Linear convolutional codes.