Motivated by the recent development of noise systems, we try to describe, for fixed persistence modules \(X\) and \(Y\), the set of all persistence modules that are extensions of \(X\) by \(Y\), as well as their sizes. We restrict ourselves to tame persistence modules indexed by nonnegative numbers, and our notion of size is \((p,C)\)-norms, which is a generalization of \(p\)-norms. We prove that when \(X\) is a single bar, there is a monotone bijection between a set of antichains in the barcode of \(Y\) and the mentioned set of all extensions. A corollary is that the antichain consisting of maximal elements corresponds to the extension with maximal norm. Without this assumption on \(X\), we can reuse the previous result to construct a surjection from a set of tuples of antichains to the set of all extensions. We also conjecture that, with regards to this surjection, the tuple consisting of maximal antichains is mapped to the extension with maximal norm. We also provide some experimental justification for this conjecture. / Med anledning av det nyligen utvecklade begreppet noise system, försöker vi, för givna \(X\) och \(Y\), beskriva mängden av alla persistensmoduler som är utvidgningar av \(X\) med \(Y\), liksom deras storlekar. Vi begränsar oss till fallet med tama persistensmoduler, och där vi med storlek avser \((p,C)\)-normen, vilket är en generalisering av \(p\)-normen. I fallet när \(X\) består av en enda bar, konstruerar vi en monoton bijektion mellan en mängd av antikedjor och den nämnda mängden av alla utvidgningar. Ett korollarium är att antikedjan som består av maximala element motsvarar utvidgningen med störst norm. Vi använder sedan den nämnda bijektionen för att i det generella fallet konstruera en surjektion från en mängd av tuplar av antikedjor till mängden av alla utvidgningar. Vi formulerar även ett experimentellt bestyrkt påstående, nämligen att tupeln bestående av maximala antikedjor avbildas på utvidgningen med störst norm, av den nämnda surjektionen.

In recent years there has been a desire to definitively catalogue the life on our planet. In light of the increasing extinction rates that are driven by human activities, it is unlikely that this will be achieved using traditional methods. Whilst most organisms which have a body size of more than 1cm have been described, the vast majority of animal life is smaller than this, collectively known as meiofauna, and is yet to be catalogued. Meiofaunal organisms present a range of problems for traditional taxonomy. Firstly they are microscopic, meaning that morphological features are often difficult to resolve. Secondly these creatures often exhibit cryptic diversity meaning that different species often look the same. Thirdly, it is often the case that the organisms are poorly described in the literature making it very difficult to confirm identification, assuming that someone has already described it. It is possible, however, to obtain DNA sequences from these organisms. DNA barcoding, the use of short sequences of DNA to identify individuals, is now commonly used in a wide range of applications. It has been proposed that a single target gene should be sufficient to describe all organisms this way. Barcodes can be acquired from individuals or from bulk extractions from environmental samples. In the latter case, many of the sequences obtained are novel and unlikely to ever have a type specimen associated with them. When this is the case, assessing the diversity of a sample becomes a computational exercise. However, as yet, there is no agreed standard method adopted for analyzing the barcodes produced. Indeed most methods currently employed lack objectivity. This thesis investigates the efficiency of a range of gene targets and analysis methods for DNA barcoding, with an emphasis on meiofaunal organisms (nematodes, tardigrades and thrips). DNA barcodes were generated for up to three genes for each specimen. Sequences for each gene were analysed using two programs, MOTU_define.pl and DOTUR. These programs use different methods to assign sequences to operational taxonomic units (OTU), which were then compared. An objective method for analysing sequences such as MOTU_define.pl, which relies on only the information contained in the sequences, was found to be most suitable for designating taxa. It does not attempt to apply evolutionary models to the data, and then infer taxa from the derived data. In addition to barcoding, some samples were pre-processed using video capture and editing (VCE). This creates a virtual slide of a specimen so that a sequence can be linked to a morphological identification. VCE proved to be an efficient method to preserve morphological data from specimens.

O presente trabalho inicia-se com uma breve história sobre a evolução da Teoria dos Números, destacando os estudiosos que tiveram grande importância para o reconhecimento dessa parte da Matemática. Logo após, é feita uma fundamentação teórica dos principais tópicos da Teoria dos Números, ressaltando alguns teoremas e apresentando exemplos de aplicações em várias áreas da Matemática. É apresentado um estudo a respeito dos diversos sistemas de codificação que fazem o uso do dígito verificador, com o objetivo de motivar o aluno a entender um pouco sobre o conceito de aritmética modular, de maneira fácil, rápida e simples. Para finalizar são apresentados relatos de atividades realizadas com alunos do ensino básico, envolvendo códigos de barras, visando ressaltar a importância de entender a aplicabilidade das congruências nos dias de hoje. / His work starts by describing a brief history on the development of Numbers Theory, highlighting the ones who had great importance for the recognition of this part of Mathematics. Next, a theoretical framework of the main topics of Numbers Theory is made, emphasizing some theorems and presenting examples of applications in several areas of Mathematics. A survey is done about several coding systems that use check digit, in order to motivate the student to understand the concept of modular arithmetic, in an easy, fast and simple way. Finally, we present reports of activities carried out with students of basic education, involving bar codes, in order to highlight the importance of understanding the applicability of congruences nowadays.

<p>The most common method for identifying merchandise in the commerce is by barcodes. Symbian OS is an advanced operating system aimed at cell phones and the most commonly used in smart phones. Opportunities to a full range of new services are given through barcode recognition in a Symbian OS based device. Therefore the purpose of this degree project was to create an application which would contribute to a future solution aimed at shopping where the cell phone constitutes a reader of itemsʼ identification numbers. Available barcode decoders have been evaluated and three were chosen for testing. The decoder that fared best was ZXing. It was subsequently incorporated into a Symbian OS-based mobile phone. The decoder was written in the Java language but sufficient Java APIs for controlling the camera's autofocus were missing, something that was necessary to decode the barcode. On the other hand the APIs were offered in C++. Therefore, the solution was split into two applications, one server application written in Java and responsible for the decoding and one client application written in C++ containing the GUI, camera controlling facilities and connections to two price comparison services. A procedure for communication between applications and an interface for various lookup services were defined. Finally, the information security was evaluated and the most relevant threat would be a third party that collects information about user behavior patterns for extortion purposes. It was concluded that the application that was created had the ability to scan barcodes, it is possible to extend and thereby fulfill the purpose.</p>

This thesis investigates species diversity and patterns of molecular evolution in Arachnida through DNA barcoding. The first chapter assesses mite species richness through comprehensive sampling at a subarctic location in Canada. Barcode analysis of 6279 specimens revealed nearly 900 presumptive species with high rates of turnover between major habitat types, demonstrating the utility of DNA barcoding for biodiversity surveys of understudied taxa. The second chapter explores nucleotide composition, indel occurrence, and rates of amino acid evolution in Arachnida. The results suggest a significant shift in nucleotide composition in the arachnid subclasses of Pulmonata (GC = 37.0%) and Apulmonata (GC = 34.2%). Indels were detected in five apulmonate orders, with deletions being much more common than insertions. Finally, rates of amino acid evolution were detected among the orders, and were negatively correlated with generation length, suggesting that generation time is a significant contributor to variation in molecular rates of evolution in arachnids.

O presente trabalho inicia-se com uma breve história sobre a evolução da Teoria dos Números, destacando os estudiosos que tiveram grande importância para o reconhecimento dessa parte da Matemática. Logo após, é feita uma fundamentação teórica dos principais tópicos da Teoria dos Números, ressaltando alguns teoremas e apresentando exemplos de aplicações em várias áreas da Matemática. É apresentado um estudo a respeito dos diversos sistemas de codificação que fazem o uso do dígito verificador, com o objetivo de motivar o aluno a entender um pouco sobre o conceito de aritmética modular, de maneira fácil, rápida e simples. Para finalizar são apresentados relatos de atividades realizadas com alunos do ensino básico, envolvendo códigos de barras, visando ressaltar a importância de entender a aplicabilidade das congruências nos dias de hoje. / His work starts by describing a brief history on the development of Numbers Theory, highlighting the ones who had great importance for the recognition of this part of Mathematics. Next, a theoretical framework of the main topics of Numbers Theory is made, emphasizing some theorems and presenting examples of applications in several areas of Mathematics. A survey is done about several coding systems that use check digit, in order to motivate the student to understand the concept of modular arithmetic, in an easy, fast and simple way. Finally, we present reports of activities carried out with students of basic education, involving bar codes, in order to highlight the importance of understanding the applicability of congruences nowadays.

The most common method for identifying merchandise in the commerce is by barcodes. Symbian OS is an advanced operating system aimed at cell phones and the most commonly used in smart phones. Opportunities to a full range of new services are given through barcode recognition in a Symbian OS based device. Therefore the purpose of this degree project was to create an application which would contribute to a future solution aimed at shopping where the cell phone constitutes a reader of itemsʼ identification numbers. Available barcode decoders have been evaluated and three were chosen for testing. The decoder that fared best was ZXing. It was subsequently incorporated into a Symbian OS-based mobile phone. The decoder was written in the Java language but sufficient Java APIs for controlling the camera's autofocus were missing, something that was necessary to decode the barcode. On the other hand the APIs were offered in C++. Therefore, the solution was split into two applications, one server application written in Java and responsible for the decoding and one client application written in C++ containing the GUI, camera controlling facilities and connections to two price comparison services. A procedure for communication between applications and an interface for various lookup services were defined. Finally, the information security was evaluated and the most relevant threat would be a third party that collects information about user behavior patterns for extortion purposes. It was concluded that the application that was created had the ability to scan barcodes, it is possible to extend and thereby fulfill the purpose.

Master thesis is focused on retrieval of multimedia information based on location of mobile device. Paper describes mobile platforms technology and technology behind location sensing and two-dimensional barcode recognition. There is also included design of client-server architecture for information retrieval of location based multimedia data. Master thesis includes report of system testing and some ideas about new features for implemented location based information distribution system.

This master thesis project is interdisciplinary between the fields of biology, visualization, and astrophysics. The project was conducted at the American Museum of Natural History in New York in collaboration with researchers from Basel, Switzerland. The goal of the project was to, with the help of OpenSpace, visualize and map the relation- ship between animal species by looking closely at their DNA and commuting the informa- tion to the general public. First, Openspace and the software’s existing functionality were examined to visualize the datasets used during the project. The two datasets explored in OpenSpace were: a cloud-based dataset known as The Barcode of Life Data (BOLD) Sys- tem, which contains 1.1 million DNA barcodes, and a dataset containing differences in human DNA to track human emigration. This project is the first time Openspace has been used to visualize fields other than space. As a starting point, the group of primates from the BOLD dataset was visualized. With the help of researchers in Switzerland, the indi- vidual DNA barcodes in the datasets were converted into three-dimensional positions that represent the relationship between species. This was achieved by applying dimensional- ity reduction techniques. In addition, various features were added to the dataset during the project, such as lineage, mutations, consensus sequences, endangered species, human emigration, and measures of polymorphism within species. With the help of Openspace, different visualization techniques could be investigated to visualize the different features in the two datasets and combine these visualizations into a story. The result is a story that highlights information from the dataset. The relationships between species are visualized using colors, glyphs, and volumes. The story takes an audience on a journey from the closest human relatives to the whole group of primates. The results were evaluated through interviews with four people to determine how the visualizations were interpreted. Further development of the project is to add other animal species in the visualizations to compare with the primates in the three-dimensional information space. A future goal of the project is to create a show about the subject of biology at the Hayden Planetarium at the Natural History Museum, which today has shows about space. / <p>Examensarbetet är utfört vid Institutionen för teknik och naturvetenskap (ITN) vid Tekniska fakulteten, Linköpings universitet</p>

Master´s thesis analyses current methods and procedures of storing and marking of goods of Disk obchod & technika, spol. s.r.o. company. It includes the proposal of goods identification which leads to the optimizing of continuous flows from the point of view of both simplification and acceleration of work and simpler and more accurate ways of goods identification. The proposal is related to the choice of appropriate method of goods identification and the selection of particular type of barcodes, including the necessary hardware.