The central question of this thesis is: what is mathematics about? The answer arrived at by the thesis is an unsettling and unsatisfying one. By examining two of the most promising contemporary accounts of the nature of mathematics, I conclude that neither is as yet capable of giving us a conclusive answer to our question. The conclusion is arrived at by a combination of historical and conceptual analysis. It begins with the historical fact that, since the middle of the nineteenth century, mathematics has undergone a radical transformation. This transformation occurred in most branches of mathematics, but was perhaps most apparent in geometry. Earlier images of geometry understood it as the science of space. In the wake of the emergence of multiple distinct geometries and the realization that non-Euclidean geometries might lay claim to the description of physical space, the old picture of Euclidean geometry as the sole correct description of physical space was no longer tenable. The first chapter of the dissertation provides an historical account of some of the forces which led to the destabilization of the traditional picture of geometry. The second chapter examines the debate between Gottlob Frege and David Hilbert regarding the nature of geometry and axiomatics, ending with an argument suggesting that Hilbert’s views are ultimately unsatisfying. The third chapter continues to probe the work of Frege and, again, finds his explanations of the nature of mathematics troublingly unsatisfying. The end result of the first three chapters is that the Frege-Hilbert debate leaves us with an impasse: the traditional understanding of mathematics cannot hold, but neither can the two most promising modern accounts. The fourth and final chapter of the thesis investigates mathematical structuralism—a more recent development in the philosophy of mathematics—in order to see whether it can move us beyond the impasse of the Frege-Hilbert debate. Ultimately, it is argued that the contemporary debate between ‘assertoric’ structuralists and ‘algebraic’ structuralists recapitulates a form of the Frege-Hilbert impasse. The ultimate claim of the thesis, then, is that neither of the two most promising contemporary accounts can offer us a satisfying philosophical answer to the question ‘what is mathematics about?’.

Le ZX-Calculus est un langage graphique puissant et intuitif, issu de la théorie des catégories, et qui permet de raisonner et calculer en quantique. Les évolutions quantiques sont vues dans ce formalisme comme des graphes ouverts, ou diagrammes, qui peuvent être transformés localement selon un ensemble d’axiomes qui préservent le résultat du calcul. Un aspect des plus importants du langage est sa complétude : Étant donnés deux diagrammes qui représentent la même évolution quantique, puis-je transformer l’un en l’autre en utilisant seulement les règles graphiques permises par le langage ? Si c’est le cas, cela veut dire que le langage graphique capture entièrement la mécanique quantique. Le langage est connu comme étant complet pour une sous-classe (ou fragment) particulière d’évolutions quantiques, appelée Clifford. Malheureusement, celle-ci n’est pas universelle : on ne peut pas représenter, ni même approcher, certaines évolutions. Dans cette thèse, nous proposons d’élargir l’ensemble d’axiomes pour obtenir la complétude pour des fragments plus grands du langage, qui en particulier sont approximativement universels, voire universels. Pour ce faire, dans un premier temps nous utilisons la complétude d’un autre langage graphique et transportons ce résultat au ZX-Calculus. Afin de simplifier cette fastidieuse étape, nous introduisons un langage intermédiaire, intéressant en lui-même car il capture un fragment particulier mais universel de la mécanique quantique : Toffoli-Hadamard. Nous définissons ensuite la notion de diagramme linéaire, qui permet d’obtenir une preuve uniforme pour certains ensembles d’équations. Nous définissons également la notion de décomposition d’un diagramme en valeurs singuliaires, ce qui nous permet de nous épargner un grand nombre de calculs. Dans un second temps, nous définissons une forme normale qui a le mérite d’exister pour une infinité de fragments du langage, ainsi que pour le langage lui-même, sans restriction. Grâce à cela, nous reprouvons les résultats de complétude précédents, mais cette fois sans utiliser de langage tiers, et nous en dérivons de nouveaux, pour d’autres fragments. Les états contrôlés, utilisés pour la définition de forme normale, s’avèrent en outre utiles pour réaliser des opérations non-triviales telles que la somme, le produit terme-à-terme, ou la concaténation. / The ZX-Calculus is a powerful and intuitive graphical language, based on category theory, that allows for quantum reasoning and computing. Quantum evolutions are seen in this formalism as open graphs, or diagrams, that can be transformed locally according to a set of axioms that preserve the result of the computation. One of the most important aspects of language is its completeness: Given two diagrams that represent the same quantum evolution, can I transform one into the other using only the graphical rules allowed by the language? If this is the case, it means that the graphical language captures quantum mechanics entirely. The language is known to be complete for a particular subclass (or fragment) of quantum evolutions, called Clifford. Unfortunately, this one is not universal: we cannot represent, or even approach, certain quantum evolutions. In this thesis, we propose to extend the set of axioms to obtain completeness for larger fragments of the language, which in particular are approximately universal, or even universal. To do this, we first use the completeness of another graphical language and transport this result to the ZX-Calculus. In order to simplify this tedious step, we introduce an intermediate language, interesting in itself as it captures a particular but universal fragment of quantum mechanics: Toffoli-Hadamard. We then define the notion of a linear diagram, which provides a uniform proof for some sets of equations. We also define the notion of singular value decomposition of a diagram, which allows us to avoid a large number of calculations. In a second step, we define a normal form that exists for an infinite number of fragments of the language, as well as for the language itself, without restriction. Thanks to this, we reprove the previous completeness results, but this time without using any third party language, and we derive new ones for other fragments. The controlled states, used for the definition of the normal form, are also useful for performing non-trivial operations such as sum, term-to-term product, or concatenation.

Philosophiae Doctor - PhD / In this thesis, we describe linear codes over prime fields obtained from incidence designs of iterated line graphs of complete graphs Li(Kn) where i = 1,2. In the binary case, results are extended to codes from neighbourhood designs of the line graphs Li+l(Kn) using certain elementary relations. Codes from incidence designs of complete graphs, Kn' and neighbourhood designs of their line graphs, £1(Kn) (the so-called triangular graphs), have been considered elsewhere by others. We consider codes from incidence designs of Ll(Kn) and L2(Kn), and neighbourhood designs of L2(Kn) and L3(Kn). In each case, the basic parameters of the codes are determined. Further, we introduce a family of vertex-transitive graphs Rn that are embeddable into the strong product Ll(Kn) ~ K2' of triangular graphs and K2' a class that at first sight may seem unnatural but, on closer look, is a repository of graphs rich with combinatorial structures. For instance, unlike most regular graphs considered here and elsewhere that only come with incidence and neighbourhood designs, Rn also has what we have termed as 6-cycle designs. These are designs in which the point set contains vertices of the graph and every block contains vertices of a 6-cycle in the graph. Also, binary codes from incidence matrices of these graphs have other minimum words in addition to incidence vectors of the blocks. In addition, these graphs have induced subgraphs isomorphic to the family Hn of complete porcupines (see Definition 4.11). We describe codes from incidence matrices of Rn and Hn and determine their parameters. The discussion is concluded with a look at complements of Rn and Hn, respectively denoted by Rn and Hn. Among others, the complements rn are contained in the union of the categorical product Ll(Kn) x Kn' and the categorical product £1(Kn) x Kn (where £1(Kn) is the complement of the iii triangular graph £1(Kn)). As with the other graphs, we have also considered codes from the span of incidence matrices of Rn and Hn and determined some of their properties. In each case, automorphisms of the graphs, designs and codes have been determined. For the codes from incidence designs of triangular graphs, embeddings of Ll(Kn) x K2 and complements of complete porcupines, we have exhibited permutation decoding sets (PD-sets) for correcting up to terrors where t is the full error-correcting capacity of the codes. For the remaining codes, we have only been able to determine PD-sets for which it is possible to correct a fraction of t-errors (partial permutation decoding). For these codes, we have also determined the number of errors that can be corrected by permutation decoding in the worst-case.

The constraint satisfaction problem (CSP) over a structure A with a finite relational signature, denoted by CSP(A), is the problem of deciding whether a given finite structure B with the same signature as A has a homomorphism to A. Using concepts and techniques from universal algebra, Bulatov and Zhuk proved independently that if A is finite, then the CSP over A is always in P or NP-complete. Following this result, it is a natural question to ask when and how this dichotomy can be generalized for infinite structures. The infinite-domain CSP dichotomy conjecture (originally formulated by Bodirsky and Pinsker [BPP14]) states that the same complexity dichotomy holds for first-order reducts of finitely bounded homogeneous structures. This conjecture has been solved for many special classes of structures. In this thesis we are developing new techniques involving canonical polymorphisms to attack this conjecture. Using these techniques we prove a new CSP dichotomy result, namely we show that the CSP over every finitely related ω-categorical monadically stable structure is in P or NP-complete.

A Monte Carlo simulation study on class enumeration with latent class regression models. / Latent class regression (LCR) is a statistical method used to identify qualitatively different groups or latent classes within a heterogeneous population and commonly used in the behavioural, health, and social sciences. Despite the vast applications, an agreed fit index to correctly determine the number of latent classes is hotly debated. To add, there are also conflicting views on whether covariates should or should not be included into the class enumeration process. We conduct a simulation study to determine the impact of covariates on the class enumeration accuracy as well as study the performance of several commonly used fit indices under different population models and modelling conditions. Our results indicate that of the eight fit indices considered, the aBIC and BLRT proved to be the best performing fit indices for class enumeration. Furthermore, we found that covariates should not be included into the enumeration procedure. Our results illustrate that an unconditional LCA model can enumerate equivalently as well as a conditional LCA model with its true covariate specification. Even with the presence of large covariate effects in the population, the unconditional model is capable of enumerating with high accuracy. As noted by Nylund and Gibson (2016), a misspecified covariate specification can easily lead to an overestimation of latent classes. Therefore, we recommend to perform class enumeration without covariates and determine a set of candidate latent class models with the aBIC. Once that is determined, the BLRT can be utilized on the set of candidate models and confirm whether results obtained by the BLRT match the results of the aBIC. By separating the enumeration procedure of the BLRT, it still allows one to use the BLRT but reduce the heavy computational burden that is associated with this fit index. Subsequent analysis can then be pursued accordingly after the number of latent classes is determined. / Thesis / Master of Science (MSc)

This dissertation develops virtual reality modules to capture individuals’ learning abilities and systems thinking skills in dynamic environments. In the first chapter, an immersive queuing theory teaching module is developed using virtual reality technology. The objective of the study is to present systems engineering concepts in a more sophisticated environment and measure students learning abilities. Furthermore, the study explores the performance gaps between male and female students in manufacturing systems concepts. To investigate the gender biases toward the performance of developed VR module, three efficacy measures (simulation sickness questionnaire, systems usability scale, and presence questionnaire) and two effectiveness measures (NASA TLX assessment and post-motivation questionnaire) were used. The second and third chapter aims to assess individuals’ systems thinking skills when they engage in complex multidimensional problems. A modern complex system comprises many interrelated subsystems and various dynamic attributes. Understanding and handling large complex problems requires holistic critical thinkers in modern workplaces. Systems Thinking (ST) is an interdisciplinary domain that offers different ways to better understand the behavior and structure of a complex system. The developed scenario-based instrument measures students’ cognitive tendency for complexity, change, and interaction when making decisions in a turbulent environment. The proposed complex systems scenarios are developed based on an established systems thinking instrument that can measure important aspects of systems thinking skills. The systems scenarios are built in a virtual environment that facilitate students to react to real-world situations and make decisions. The construct validity of the VR scenarios is assessed by comparing the high systematic scores between ST instrument and developed VR scenarios. Furthermore, the efficacy of the VR scenarios is investigated using the simulation sickness questionnaire, systems usability scale, presence questionnaire, and NASA TLX assessment.

The purpose of this study was to determine if East Tennessee State University provides its employees appropriate financial planning services. In particular, it is unknown to what degree employees of East Tennessee State University have actively engaged in financial planning. The research was conducted during June and July, 2005. Data were gathered by surveying faculty, staff, and retirees of the university. Ten percent of the population responded to the study. The survey instrument covered the areas of retirement, other financial planning services, and attitudes toward financial planning. The results of the data analysis gave insight into what degree employees of East Tennessee State University have actively engaged in financial planning. For example, over 20% of the respondents encouraged employees to start early in order to achieve the benefit of time value of money. Fifteen percent of the respondents suggested financial planning workshops be offered on a more frequent basis. Approximately 10% of the respondents preferred an instructor to be independent, instead of a financial salesperson. The study provided an increase in the body of knowledge on financial planning for the ETSU employee and established a historical database for the various programs offered within the ETSU system.

The possible effects of the General Data Protections Regulations (GDPR) have been widely discussed among policymakers, stakeholders and ordinary people who are the objective for data collection. The purpose of GDPR is to protect people’s integrity and increase transparency for how personal data is used. Up until May 25th, 2018 personal data could be sampled and used without consent from users. Many argue that the introduction of GDPR is good, others are reluctant and argue that GDPR may harm data-driven companies. The report aims to answer how GDPR affects sales at the flight search engine Flygresor.se. By examining how and to what extent these regulations impact revenue, it is hoped for that these findings will lead to a deeper understanding of how these regulations affect businesses. Multiple linear regression analysis was used as the framework to answer the research question. Numerous models were constructed based on data provided by Flygresor.se. The models mostly included categorical variables representing time indicators such as month, weekday, etc. After carefully performing data modifications, variable selections and model evaluation tests three final models were obtained. After performing statistical inference tests and multicollinearity diagnostics on the models it could be concluded that an effect from GDPR could not be statistically proven. However, this does not mean that an actual effect of GDPR did not occur, only that it could not be isolated and proven. Thus, the extent of the effect of GDPR is statistically inconclusive. / De möjliga följderna av införandet av General Data Protections Regulations (GDPR) har varit väl omdiskuterat bland beslutsfattare, intressenter och människor som är målet för datainsamlingen. Syftet med GDPR är att skydda människors integritet samt öka insynen för hur personlig data används. Fram tills den 25 maj 2018 har det varit möjligt att samla in och använda personuppgifter utan samtyckte från användare. Många menar att införandet av GDPR är nödvändigt medans andra är mer kritiska och menar att GDPR kan skada lönsamheten för data beroende verksamheter. Denna rapport syftar till att svara på huruvida GDPR har påverkat försäljningen på flygsökmotorn Flygresor.se. Genom att undersöka om och i vilken utsträckning dessa regler påverkat intäkterna, är förhoppningen att dessa resultat kan leda till en djupare förståelse för hur GDPR påverkar företag. Multipel linjär regressionsanalys användes som ramverk för att svara på frågeställningen. Flera modeller utformades baserat på data som tillhandahölls av Flygresor.se. Modellerna var främst baserade på kategoriska variabler som representerade tidsaspekter så som månad, veckodag etc. Efter ett grundligt genomförande av data modifieringar, variabelselektion och modellutvärdering kunde tre modeller konstateras. Efter att ha genomfört signifikanstester och korrelationstester på modellerna kunde det fastställas att en effekt från GDPR inte kunde statistiskt säkerställas. Dock betyder detta inte att GDPR inte har haft en faktisk effekt, utan att en effekt inte kunde isoleras och bevisas.

Machine learning methods can be used for solving important binary classification tasks in domains such as display advertising and recommender systems. In many of these domains categorical features are common and often of high cardinality. Using one-hot encoding in such circumstances lead to very high dimensional vector representations, causing memory and computability concerns for machine learning models. This thesis investigated the viability of a binary encoding scheme in which categorical values were mapped to integers that were then encoded in a binary format. This binary scheme allowed for representing categorical features using log2(d)-dimensional vectors, where d is the dimension associated with a one-hot encoding. To evaluate the performance of the binary encoding, it was compared against one-hot and feature hashed representations with the use of linear logistic regression and neural networks based models. These models were trained and evaluated using data from two publicly available datasets: Criteo and Census. The results showed that a one-hot encoding with a linear logistic regression model gave the best performance according to the PR-AUC metric. This was, however, at the expense of using 118 and 65,953 dimensional vector representations for Census and Criteo respectively. A binary encoding led to a lower performance but used only 35 and 316 dimensions respectively. For Criteo, binary encoding suffered significantly in performance and feature hashing was perceived as a more viable alternative. It was also found that employing a neural network helped mitigate any loss in performance associated with using binary and feature hashed representations. / Maskininlärningsmetoder kan användas för att lösa viktiga binära klassificeringsuppgifter i domäner som displayannonsering och rekommendationssystem. I många av dessa domäner är kategoriska variabler vanliga och ofta av hög kardinalitet. Användning av one-hot-kodning under sådana omständigheter leder till väldigt högdimensionella vektorrepresentationer. Detta orsakar minnesoch beräkningsproblem för maskininlärningsmodeller. Denna uppsats undersökte användbarheten för ett binärt kodningsschema där kategoriska värden var avbildade på heltalvärden som sedan kodades i ett binärt format. Detta binära system tillät att representera kategoriska värden med hjälp av log2(d) -dimensionella vektorer, där d är dimensionen förknippad med en one-hot kodning. För att utvärdera prestandan för den binära kodningen jämfördes den mot one-hot och en hashbaserad kodning. En linjär logistikregression och ett neuralt nätverk tränades med hjälp av data från två offentligt tillgängliga dataset: Criteo och Census, och den slutliga prestandan jämfördes. Resultaten visade att en one-hot kodning med en linjär logistisk regressionsmodell gav den bästa prestandan enligt PR-AUC måttet. Denna metod använde dock 118 och 65,953 dimensionella vektorrepresentationer för Census respektive Criteo. En binär kodning ledde till en lägre prestanda generellt, men använde endast 35 respektive 316 dimensioner. Den binära kodningen presterade väsentligt sämre specifikt för Criteo datan, istället var hashbaserade kodningen en mer attraktiv lösning. Försämringen i prestationen associerad med binär och hashbaserad kodning kunde mildras av att använda ett neuralt nätverk.

This research investigates the use of data mining methods for malware (malicious programs) detection and proposed a framework as an alternative to the traditional signature detection methods. The traditional approaches using signatures to detect malicious programs fails for the new and unknown malwares case, where signatures are not available. We present a data mining framework to detect malicious programs. We collected, analyzed and processed several thousand malicious and clean programs to find out the best features and build models that can classify a given program into a malware or a clean class. Our research is closely related to information retrieval and classification techniques and borrows a number of ideas from the field. We used a vector space model to represent the programs in our collection. Our data mining framework includes two separate and distinct classes of experiments. The first are the supervised learning experiments that used a dataset, consisting of several thousand malicious and clean program samples to train, validate and test, an array of classifiers. In the second class of experiments, we proposed using sequential association analysis for feature selection and automatic signature extraction. With our experiments, we were able to achieve as high as 98.4% detection rate and as low as 1.9% false positive rate on novel malwares.