In this thesis we present a compendium of _ve works where discrete mathematics play a key role. The _rst three works describe di_erent developments and applications of the semigroup theory while the other two have more independent topics. First we present a result on semigroups and code e_ciency, where we introduce our results on the so-called Geil-Matsumoto bound and Lewittes' bound for algebraic geometry codes. Following that, we work on semigroup ideals and their relation with the Feng-Rao numbers; those numbers, in turn, are used to describe the Hamming weights which are used in a broad spectrum of applications, i.e. the wire-tap channel of type II or in the t-resilient functions used in cryptography. The third work presented describes the non-homogeneous patterns for semigroups, explains three di_erent scenarios where these patterns arise and gives some results on their admissibility. The last two works are not as related as the _rst three but still use discrete mathematics. One of them is a work on the applications of coding theory to _ngerprinting, where we give results on the traitor tracing problem and we bound the number of colluders in a colluder set trying to hack a _ngerprinting mark made with a Reed-Solomon code. And _nally in the last work we present our results on scientometrics and graphs, modeling the scienti_c community as a cocitation graph, where nodes represent authors and two nodes are connected if there is a paper citing both authors simultaneously. We use it to present three new indices to evaluate an author's impact in the community.

The Combined DNA Index System (CODIS) database is utilized in all 50 states for matching DNA evidence with criminal suspects. While each state administers CODIS, which ultimately feeds into a national database, little is understood about how citizens in states perceive the utility of such a database and how their perceptions and knowledge of DNA could impact state policy changes though voting. Research also suggests that the "CSI Effect" may impact how citizens perceive the role of a national DNA database. Grounded on Gerbner's cultivation theory, the purpose of this study was to determine if, in Alabama, there is a statistically significant relationship between the likelihood of providing DNA and the educational level and gender of study participants and perceptions concerning expanded support state participation in CODIS. Data were collected through an online survey administered to a random sample (n = 584) residents of Alabama that focused on examined the relationships between demographics variables of age, race or ethnicity, level of education and the CSI effect, and support of increased participation in in a standardized national DNA database. Findings indicate that there is not a statistically significant relationship between the CSI effect and support of participation in CODIS. However, data analysis revealed that level of education (p=.05) and gender (p=

Compilació i comparació dels codis deontològics de cadenes i corporacions televisives de diferents països: Estats Units (ABC, CBS i NBC), Canadà (SRC/CBC), Gran Bretanya (BBC i ITC), Itàlia (RAI), Brasil (ABERT) i Japó (NAB). L'estudi s'inscriu en una línia d'investigació que parteix del postulat que els codis deontològics contenen una part substancial dels valors i de les normes ètiques vigents per a la professió periodística. La metodologia seguida és la pròpia del Dret Comparat: s'ha elaborat un "tesaurus" que comprèn, amb ànim d'exhaustivitat, els diferents ítems que constitueixen el bagatge de problemes ètics que es plantegen en l'exercici del periodisme en general i, més particularment, en els mitjans audiovisuals. Per a cada ítem es presenta una exposició de l'estat de la qüestió sobre la matèria i, a continuació, es fa la relació i la comparació de les normes que hi ha establertes als diferents codis que constitueixen el corpus de la investigació. Aquesta tasca analítica està flanquejada per una reflexió teòrica sobre les bases de l'ètica periodística i s'alimenta també de l'experiència personal de l'autor de la tesi en el camp de la informació televisiva. / Compilación y comparación de los códigos deontològics de cadenas y corporaciones televisivas de diferentes países: Estados Unidos (ABC, CBS y NBC), Canadá (SRC/CBC), Gran Bretaña (BBC e ITC), Italia (RAI), Brasil (ABERT) y Japón (NAB). El estudio se inscribe en una línea de investigación que parte del postulado que los códigos deontològics contienen una parte sustancial de los valores y de las normas éticas vigentes para la profesión periodística. La metodología seguida es la propia del Derecho Comparado: se ha elaborado un "tesauro" que comprende, con ánimo de exhaustividad, los diferentes ítems que constituyen el bagaje de problemas éticos que se plantean en el ejercicio del periodismo en general y, más particularmente, en los medios audiovisuales. Para cada ítem se presenta una exposición del estado de la cuestión sobre la materia y, a continuación, se hace la relación y la comparación de las normas que hay establecidas en los diferentes códigos que constituyen el corpus de la investigación. Esta tarea analítica está flanqueada por una reflexión teórica sobre las bases de la ética periodística y se alimenta también de la experiencia personal del autor de la tesis en el campo de la información televisiva. / Compilation and comparison of the deontological codes of television broadcasting corporations and channels in different countries: United States (ABC, CBS and NBC), Canada (SRC/CBC), Great Britain (BBC and ITC), Italy (RAI), Brazil (ABERT) and Japan (NAB). The study is part of an investigative approach based on the hypothesis that deontological codes contain a substantial part of the ethical values and standards which apply to the journalism profession. The methodology used consisted of a Comparative Study: an exhaustive "thesaurus" was prepared of the different items constituting the baggage of ethical problems which arise in the exercise of journalism in general and more particularly in the audio-visual media. For each item is presented an explanation of the status of the question on the subject and afterwards a list is prepared and a comparison of the standards make up the different codes constituting the body of the research. This analytical task is surrounded by a theoretical reflection on the bases of journalistic ethics and is supplemented by the author's personal experience in the field of television reporting.

<p>The objective of this study was to develop and validate a six Non-CODIS miniSTR genotyping system and to determine its suitability for forensic casework in South Africa. In Non-CODIS miniSTR genotyping systems, smaller PCR products are amplified and the primers are positioned as close as possible to the repeat region. For this reason, these systems can be valuable in a variety of scenarios including complex paternity cases, missing persons work, and mass fatality disasters.</p>

<p>The objective of this study was to develop and validate a six Non-CODIS miniSTR genotyping system and to determine its suitability for forensic casework in South Africa. In Non-CODIS miniSTR genotyping systems, smaller PCR products are amplified and the primers are positioned as close as possible to the repeat region. For this reason, these systems can be valuable in a variety of scenarios including complex paternity cases, missing persons work, and mass fatality disasters.</p>

The objective of this study was to develop and validate a six Non-CODIS miniSTR genotyping system and to determine its suitability for forensic casework in South Africa.In Non-CODIS miniSTR genotyping systems, smaller PCR products are amplified and the primers are positioned as close as possible to the repeat region. For this reason, these systems can be valuable in a variety of scenarios including complex paternity cases,missing persons work, and mass fatality disasters. After the successful implementation of the genotyping system in the laboratory, allele size range was determined for each of the loci and allelic ladders were constructed. The entire repeat regions of the six loci under investigation were successfully sequenced.Consequently, allele repeat number, structure and observed size were determined for each locus.An internal validation study of the six Non-CODIS miniSTR genotyping system was conducted following the SWGDAM guidelines. A comprehensive population study,covering five population groups from South Africa was also carried out.The genotyping system produced consistent, accurate and precise genetic profiles for low concentrations of template DNA. When analyzing mixed DNA samples, successful differentiation of minor and major DNA components was identifiable. Amplification products were observed in non-human DNA studies but in all instances complete genotype profiles were not obtained. Allele frequencies and forensic parameters were determined for the system in five South African population groups (i.e. Afrikaner, Asian-Indian, Mixed Ancestry, Xhosa and Cape Muslim). No deviation from Hardy-Weinberg equilibrium was observed in any of the populations. Furthermore, all populations displayed a high power of discrimination and a high power of exclusion.The six Non-CODIS miniSTR genotyping system has shown a good potential to aid in the analysis of degraded DNA samples. This system can be further improved by including additional loci. Even in its current form, it can certainly provide additional discrimination in complex paternity and/or missing person cases. / >Magister Scientiae - MSc

Magister Scientiae - MSc / The objective of this study was to develop and validate a six Non-CODIS miniSTR genotyping system and to determine its suitability for forensic casework in South Africa. In Non-CODIS miniSTR genotyping systems, smaller PCR products are amplified and the primers are positioned as close as possible to the repeat region. For this reason, these systems can be valuable in a variety of scenarios including complex paternity cases, missing persons work, and mass fatality disasters. / South Africa

<p>In many forensic cases, such as mass disasters reconstruction cases, the recovered DNA is highly degraded. In such incidences, typing of STR loci has become one of the most powerful tools for retrieving information from the degraded DNA. However, as DNA degradation proceeds, three phenomena occur consecutively: loci imbalance, allele dropout and no amplification. To solve the problem of degraded DNA, redesigned primer sets have been developed in which the primers were positioned as close as possible to the STR repeat region. These reduced primer sets were called Miniplexes. Unfortunately, a few of the CODIS STR loci cannot be made into smaller amplicons. For this reason non-CODIS miniSTRs have been developed. The present study was undertaken for the population genetic analysis of microsatellite variation in four South African populations / Afrikaner, Xhosa, Mixed Ancestry and Asian Indian using eight non-CODIS miniSTR loci. These miniSTRs loci were characterized within the populations by estimating the levels of diversity of the markers, estimating the population genetic parameters, and studying the inter-population relationships. All of the miniSTRs were amplified successfully and the genetic variability parameters across all loci in Afrikaner, Mixed Ancestry, Asian Indian and Xhosa were estimated to be in the range of 3 (D4S2364) to 12 (D9S2157) alleles, the total number of alleles over all loci ranged from 100 to 204, the allelic richness ranged from 3.612 to 10.307 and the heterozygosity ranged from 0.4360 to 0.8073. Genetic distance was least between Afrikaner and Asian Indian and highest between Xhosa and Mixed Ancestry. Deviations from Hardy-Weinberg equilibrium were not observed for most of the loci. The low mean FIS (-0.027) and FIT (-0.010) and FST (0.017) values across the populations indicated low level of inbreeding within (FIS) and among (FST) the populations. The Asian Indian population showed higher levels of the inbreeding coefficient, indicating less gene exchange between it and other populations. These 8 markers can be used for genetic investigations and assessing population structure. The study contributed to the knowledge and genetic characterization of four South African populations. In addition, these MiniSTRs prove to be useful in cases where more genetic information is needed.</p>

<p>In many forensic cases, such as mass disasters reconstruction cases, the recovered DNA is highly degraded. In such incidences, typing of STR loci has become one of the most powerful tools for retrieving information from the degraded DNA. However, as DNA degradation proceeds, three phenomena occur consecutively: loci imbalance, allele dropout and no amplification. To solve the problem of degraded DNA, redesigned primer sets have been developed in which the primers were positioned as close as possible to the STR repeat region. These reduced primer sets were called Miniplexes. Unfortunately, a few of the CODIS STR loci cannot be made into smaller amplicons. For this reason non-CODIS miniSTRs have been developed. The present study was undertaken for the population genetic analysis of microsatellite variation in four South African populations / Afrikaner, Xhosa, Mixed Ancestry and Asian Indian using eight non-CODIS miniSTR loci. These miniSTRs loci were characterized within the populations by estimating the levels of diversity of the markers, estimating the population genetic parameters, and studying the inter-population relationships. All of the miniSTRs were amplified successfully and the genetic variability parameters across all loci in Afrikaner, Mixed Ancestry, Asian Indian and Xhosa were estimated to be in the range of 3 (D4S2364) to 12 (D9S2157) alleles, the total number of alleles over all loci ranged from 100 to 204, the allelic richness ranged from 3.612 to 10.307 and the heterozygosity ranged from 0.4360 to 0.8073. Genetic distance was least between Afrikaner and Asian Indian and highest between Xhosa and Mixed Ancestry. Deviations from Hardy-Weinberg equilibrium were not observed for most of the loci. The low mean FIS (-0.027) and FIT (-0.010) and FST (0.017) values across the populations indicated low level of inbreeding within (FIS) and among (FST) the populations. The Asian Indian population showed higher levels of the inbreeding coefficient, indicating less gene exchange between it and other populations. These 8 markers can be used for genetic investigations and assessing population structure. The study contributed to the knowledge and genetic characterization of four South African populations. In addition, these MiniSTRs prove to be useful in cases where more genetic information is needed.</p>

Magister Scientiae - MSc / In many forensic cases, such as mass disasters reconstruction cases, the recovered DNA is highly degraded. In such incidences, typing of STR loci has become one of the most powerful tools for retrieving information from the degraded DNA. However, as DNA degradation proceeds, three phenomena occur consecutively: loci imbalance, allele dropout and no amplification. To solve the problem of degraded DNA, redesigned primer sets have been developed in which the primers were positioned as close as possible to the STR repeat region. These reduced primer sets were called Miniplexes. Unfortunately, a few of the CODIS STR loci cannot be made into smaller amplicons. For this reason non-CODIS miniSTRs have been developed. The present study was undertaken for the population genetic analysis of microsatellite variation in four South African populations; Afrikaner, Xhosa, Mixed Ancestry and Asian Indian using eight non-CODIS miniSTR loci. These miniSTRs loci were characterized within the populations by estimating the levels of diversity of the markers, estimating the population genetic parameters, and studying the inter-population relationships. All of the miniSTRs were amplified successfully and the genetic variability parameters across all loci in Afrikaner, Mixed Ancestry, Asian Indian and Xhosa were estimated to be in the range of 3 (D4S2364) to 12 (D9S2157) alleles, the total number of alleles over all loci ranged from 100 to 204, the allelic richness ranged from 3.612 to 10.307 and the heterozygosity ranged from 0.4360 to 0.8073. Genetic distance was least between Afrikaner and Asian Indian and highest between Xhosa and Mixed Ancestry. Deviations from Hardy-Weinberg equilibrium were not observed for most of the loci. The low mean FIS (-0.027) and FIT (-0.010) and FST (0.017) values across the populations indicated low level of inbreeding within (FIS) and among (FST) the populations. The Asian Indian population showed higher levels of the inbreeding coefficient, indicating less gene exchange between it and other populations. These 8 markers can be used for genetic investigations and assessing population structure. The study contributed to the knowledge and genetic characterization of four South African populations. In addition, these MiniSTRs prove to be useful in cases where more genetic information is needed. / South Africa