Creating Identification Numbers

Although the set theory concepts presented in the first section of this chapter are not crucial to understanding the process of creating an identification number, they are necessary for investigating functions and permutations, two topics that are motivated through the material presented next. 

Preliminary Activity. Suppose that the State of New York decides to change the identification number system that it cuirently uses to identify drivers. The new method will create a drivers license number using a person s name and birth dale. Listed below are the names and birth dates of four drivers and what their driver s license number will be under this new system. Use this information to determine what system New York State will be using to assign driver s license numbers. 

The reason identifications numbers are created is so that the information they represent can be more easily stored, retrieved, and transmitted. Recall the 12-digit Version A UPC codes discussed in Chapter 2. In a 12-digit UPC 01-0203040506-070809010011- 12. the first digit oi, which is the number system character, identifies the type of product (the values are given in Table 2.1). The second set of numbers 0203040506 identifies the manufacturer. The third set of numbers 070809010011 identifies the product, and the last digit oi2 is the check digit. Through the UPC, stores can track inventory and identify which types and brands of products are the best (and worst) sellers. 

The process of creating an identification number is called hashing. 

Definition 3.2.2. A hash or hashing function is the actual pwce.ss that transforms the information into an identification number. 

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The protocol should specify what should be recorded directly into the CRF and what will also be recorded in the medical records. The CRF will contain all the pertinent data associated specifically with the clinical trial but some will be repeated in the medical records, for example, the protocol identification number, date of consent, date of commencement of the study, key baseline medical findings, visit dates, start and finish dates of the study drug/placebo or treatment, concurrent medication, adverse events and key efficacy and any unscheduled or scheduled actions or interventions (such as escape medication). Additional information obtained from biopsy reports, radiographs and similar documents will provide confirmation that the data in the CRF are recorded correctly. Monitors, QA auditors and inspectors need to see all the medical records available to the investigator. It is not appropriate to create copies of data from CRFs or checklists derived from medical records and claim that these are source documents. 

To make sure these numbers are transmitted correctly, it adds a fourth digit (the check digit) 04 to each product number, creating the four-digit identification number 01020304. To do this, the first three digits of the number are added. 

Each computer on campus will have a five-digit aia2asa4a5 computer number (CN) associated with it. The sixth digit ag will be the check digit and will be appended to the end of the CN to create a six-digit identification number aia2a3a4a5n6. 

Definition 2.4.1. Let aia2a3a4a5a6Ardigit document number associated with a US postal tnoney order. The check digit uu, which is appended to this number to create the ll-digit identification number 010303 4 isuearogagaioai 1. is determined by... 

Recall that the goal for any check digit scheme is to catch all the errors listed in Table 1.2. At the very least, a scheme should catch all the single-digit and transposition-of-adjacent-digits errors. Consider the valid money order identification number that was just created. Listed below are two different single-digit errors. 

Since airline ticket numbers are large, the exercise will be completed with much smaller four-digit numbers, ai 020304. The scheme works in the same manner. The check digit 04 is appended to the three-digit number 010303 to create the identification number 01030304 such that 04 satisfies the equation 04 = 010303 (mod 7). These numbers are easier to work with, but the mathematical concept is the same. 

Once the 11-digit product number of an item is created, this system is used to generate the check digit. Consider the product identification number 5-02003-91562. The check digit C will be appended to this number to create the UPC 5-02(X)3-91562-C, such that C satisfies the equation (3,1,3,1,3,1,3,1,3,1,3,1) (5,0,2,0,0,3,9,1,5,6,2,C) = 0 (mod 10). To find C, this equation is solved ... 

For each check digit scheme discussed in Chapter 2, the emphasis was on how the scheme caught errors when a number was transmitted. However, there is another important issue to consider hov identification numbers are created. Recall that an identification number is a suing of digits, letters, symbols, or a combination of them that is used to identify a specific product, account, document, individual, and so on. The process used to create a UPC for a product and an ISBN for a book has already been discussed. 

Before investigating identification numbers, it is necessary to discuss the mathematical concept of a set. This is important because the process of creating a single identification number to identify an item motivates a discussion of functions and permutations, which requires a firm knowledge of sets. Furthermore, permutations will be used to create check digit schemes more sophisticated than the ones presented in Chapter 2. One of these schemes, devel( )ed by IBM. is presented in this chapter. 

Now consider the specific hashing function used by the State of Washington and the Province of Manitoba to create driver s license numbers [5]. The hashing function uses the driver s name and date of birth to generate a 12-character identification number 01020304050 070909010011012 ... 

This hashing function would create the following driver s license identification numbers for these three individuals. The tenth position, which contains the check digit, will be left as aio for now. Note that the second person has no middle name, and the third surname has only three letters. 

Now suppose that the identification number created above for Joseph Marshall Pollan is already in the system. In creating an identification number for Joseph s twin brother John Michael, we would u.se the alternative month code to avoid a collision (assuming... 

Listed below are five individuals, their dates of birth, cities of residence, and an identification number associated with each person. Use the personal information given to determine the hashing function used to create the identification numbers. 

Besides having different domains and ranges, other characteristics differentiate functions from one another. To motivate one of them, recall the work done in the previous section on hashing functions and the Washington State driver s license identification numbers. The hashing function created a correspondence between the drivers in the state and a set of identification numbers. This correspondence was clearly a function, because each driver was assigned his or her own number. However, one problem that was unavoidable was that two different drivers could be assigned (could correspond to) the same driver s license number. 

Example 5.4.4. Consider the five-digit number 27163 that has been generated to identify a certain item. The Verhoeff scheme will be used to append a check digit K to the number 27163 to create the identification number 27163/f. 

One question still remains Why do many identification number systems still use check digit schemes that do not catch all of the errors listed in Table 1.2 This is a good question for which I have no answer. However, it does motivate the need to adjust current schemes and to create new ones. All of the concepts introduced in this book can be applied to create sophisticated schemes that will catch most errors. This was demonstrated by the Verhoeff scheme. With the birth of new identification number systems and the existence of old and ineffective check digit schemes, innovative schemes must be developed to ensure that data and information continue to flow error-free. 

Requirements for multiple EPA identification numbers for a single campus create an unnecessary administrative burden. 

There are many examples. The National Highway Traffic Safety Administration (NHTSA) works with auto manufacturers to establish vehicle recalls for safety issues. A huge recall involving many manufacturers and vehicle brands and models dealt with an air bag issue. The model of the device that automatically inflates an air bag sometimes created shrapnel that could injure or kill a driver or passenger. Individuals could look up their vehicle by vehicle identification number (VIN) to determine if the list includes their vehicles in the recall. NHTSA offered the database on its web site. 

Another aspect of LIMSs is their flexibility and ability of configuration, This means that the LIMS functions and the user interface can be adapted to the requirements of the laboratory. Such flexibility is necessary because tasks can change and new demands can arise. Mainly new definitions, fields, algorithms, screen layouts, and reports then have to be created, but sometimes it occurs that the structure of the data or keys (identification numbers) must be changed. This is a serious intervention in a LIMS and should not be done, or only seldom. 

It is known that multivalued adiabatic electronic manifolds create topological effects [23,25,45]. Since the newly introduced D matrix contains the information relevant for this manifold (the number of functions that flip sign and their identification) we shall define it as the Topological Matrix. Accordingly, K will be defined as the Topological Number. Since D is dependent on the contour F the same applies to K thus K = f(F),... 

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