In this thesis we compute the Frobenius manifold of the Landau-Ginzburg A-model (FJRW theory) for certain polynomials. Specifically, our computations apply to polynomials that are sums of An and Dn singularities, paired with the corresponding maximal symmetry group. In particular this computation applies to several K3 surfaces. We compute the necessary correlators using reconstruction, the concavity axiom, and new techniques. We also compute the Frobenius manifold of the D3 singularity.

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In computer science, an ontology is a machine-processable representation of knowledge about some domain. Ontologies are encoded in ontology languages, such as the Web Ontology Language (OWL) based on Description Logics (DLs). An ontology is a set of logical statements, called axioms. Some axioms make universal statements, e.g. all fathers are men, while others record data, i.e. facts about specific individuals, e.g. Bob is a father. A set of universal statements is called TBox, as it encodes terminology, i.e. schema-level conceptual relationships, and a set of facts is called ABox, as it encodes instance-level assertions. Ontologies are extensively developed and widely used in domains such as biology and medicine. Manual engineering of a TBox is a difficult task that includes modelling conceptual relationships of the domain and encoding those relationships in the ontology language, e.g. OWL. Hence, it requires the knowledge of domain experts and skills of ontology engineers combined together. In order to assist engineering of TBoxes and potentially automate it, acquisition (or induction) of axioms from data has attracted research attention and is usually called Ontology Learning (OL). This thesis investigates the problem of OL from general principles. We formulate it as General Terminology Induction that aims at acquiring general, expressive TBox axioms (called general terminology) from data. The thesis addresses and investigates in depth two main questions: how to rigorously evaluate the quality of general TBox axioms and how to efficiently construct them. We design an approach for General Terminology Induction and implement it in an algorithm called DL-Miner. We extensively evaluate DL-Miner, compare it with other approaches, and run case studies together with domain experts to gain insight into its potential applications. The thesis should be of interest to ontology developers seeking automated means to facilitate building or enriching ontologies. In addition, as our experiments show, DL-Miner can deliver valuable insights into the data, i.e. can be useful for data analysis and debugging.

The aesthetic aspect of a functional product is growing to be an important reason for the consumers choice to buy the product. Despite this importance, aesthetics has not generally been incorporated into engineering design which makes much sense of functional and ergonomic designs. The study presented in this thesis aims to remedy this observed gap. The study focuses on the integration of aesthetic attributes with functional attributes of a product and on the quantification of the aesthetic principle from fine arts into design variables of the product. In particular, two hypotheses underlie this study: (1) design variables can be classified in terms of their relevance to functional, ergonomic, and aesthetic attributes, and (2) a particular aesthetic principle, namely visual balance, helps to achieve an improved aesthetic product.<p>The cell phone is used to ground this study. A statistic experiment using the cell phone product positively tests the first hypothesis, resulting in two design variable which are only related to the aesthetic attribute of the cell phone product. The study of the visual balance principle results in a more general formula which relates design variables to visual balance with consideration of both geometry and color of the cell phone product. Finally, another statistic experiment is designed, which positively tests the second hypothesis.<p>This study concludes: (1) the effective integration of aesthetics with function and ergonomics requires an analysis and classification of design variables, and (2) there is a potential to quantify all aesthetic principles from fine arts into design variables.

The aesthetic aspect of a functional product is growing to be an important reason for the consumers choice to buy the product. Despite this importance, aesthetics has not generally been incorporated into engineering design which makes much sense of functional and ergonomic designs. The study presented in this thesis aims to remedy this observed gap. The study focuses on the integration of aesthetic attributes with functional attributes of a product and on the quantification of the aesthetic principle from fine arts into design variables of the product. In particular, two hypotheses underlie this study: (1) design variables can be classified in terms of their relevance to functional, ergonomic, and aesthetic attributes, and (2) a particular aesthetic principle, namely visual balance, helps to achieve an improved aesthetic product.<p>The cell phone is used to ground this study. A statistic experiment using the cell phone product positively tests the first hypothesis, resulting in two design variable which are only related to the aesthetic attribute of the cell phone product. The study of the visual balance principle results in a more general formula which relates design variables to visual balance with consideration of both geometry and color of the cell phone product. Finally, another statistic experiment is designed, which positively tests the second hypothesis.<p>This study concludes: (1) the effective integration of aesthetics with function and ergonomics requires an analysis and classification of design variables, and (2) there is a potential to quantify all aesthetic principles from fine arts into design variables.

The abstract of the diploma thesis "Positive Formulas for Some Substructural Logics" by Pavel Truhlar We will examine which distributive substructural logics, as defined in the book of Restall "An Introduction to Substructural Logics" have the same positive fragment with and without the weak excluded middle axiom. The main result of this diploma thesis is that some substructural logics have this property. We repeat the basic notions as described in the Restall's book, especially the consecution, natural deduction, frame semantics, Hilbert system. We will use the soundness and completeness theorems. We also will use the equivalence of natural deduction systems and Hilbert systems. All these important theorems are in the above mentioned Restall's book. We make the proof of our main result in the next part. We will use the semantics of frames, similarly as de Jongh and Zhao in the article "Positive Formulas in Intuitionistic and Minimal Logic". We will define the top model. After, we define the construction which converts a model to the top model. We define for each formula the positive part of it; this is the formula, which behaves the same way on the top models as the original formula. We use Hilbert type calculus to formulate our main theorem. We prove our main result using the deduction theorem for certain...

Conner and Spencer used ultrafilters to construct homomorphisms between fundamental groups that could not be induced by continuous functions between the underlying spaces. We use methods from Shelah and Pawlikowski to prove that Conner and Spencer could not have constructed these homomorphisms with a weak version of the Axiom of Choice. This led us to define and examine a class of pathological objects that cannot be constructed without a strong version of the Axiom of Choice, which we call the class of inscrutable objects. Objects that do not need a strong version of the Axiom of Choice are scrutable. We show that the scrutable homomorphisms from the fundamental group of a Peano continuum are exactly the homomorphisms induced by a continuous function.We suspect that any proposed theorem whose proof does not use a strong Axiom of Choice cannot have an inscrutable counterexample.

Probabilistic interpretations consist of a set of interpretations with a shared domain and a measure assigning a probability to each interpretation. Such structures can be obtained as results of repeated experiments, e.g., in biology, psychology, medicine, etc. A translation between probabilistic and crisp description logics is introduced and then utilised to reduce the construction of a base of general concept inclusions of a probabilistic interpretation to the crisp case for which a method for the axiomatisation of a base of GCIs is well-known.

Today's smartphones and tablets use different applications and software for all sorts of purposes: communication, entertainment, fitness, to share images with each other, to keep up to date with the news and lots of different daily tasks. With the heavy usage of all these apps, it is no wonder that it comes with a few issues. Private data is stored in large quantities both on the local device and on the app-creators' servers. It is no wonder that applications advertising user secrecy and transient storage of user data. One of these applications is Snapchat, with over 500 million downloads on Google Play store, at the time of writing. Snapchat is a communication application with the niched feature that the images and messages sent, disappear once opened or after 24 hours have passed. With the illusion of privacy behind Snapchats niche it has become a breeding ground for criminal activity. The niche itself translates to a troublesome hurdle for law enforcement trying to retrieve evidence from devices of Snapchat users. This paper is aimed to investigate these issues and perform a methodology to retrieve potential evidence on a device using Snapchat to send images and messages. By performing a physical acquisition on a test device and analyzing to find artifacts pertaining to Snapchat and the test-data that was created. The method is performed on a Samsung Galaxy S4 with Android 5.0.1 running Snapchat version 10.52.3.0. Test data such as different images and messages were created and attempted to be retrieved at three points in time. First one being right after data creation. Second one after a restart and 24 hours after the data was created. And the third with 48 hours passed and the Snapchat user logged out at the time of acquisition. The acquisition resulted in the extraction of several sent images and a full text conversation between the experimental device and another party. A full video which was uploaded by the receiving user was able to be extracted even though the experimental device never actually viewed the video. The second acquisition which was made when 24h had passed gave the same results as the first one. This meant that time at least up to a day after the initial creation of the data did not have any effect on the evidence. However, when the Snapchat user was logged out from the application, the data was then unobtainable and had disappeared. Presumably Snapchat has a function which deletes personal data about the user when logged out from the application. This function might become a hurdle in law enforcement investigations where the application Snapchat is involved.

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