With the usage of biometrics becoming commonly used in a variety of applications, keeping those biometrics private and secure is an important issue. Indeed, the convenience of using biometrics for authentication is counteracted by the fact that they cannot easily be modified or changed. This can have dire consequences to a person if their biometrics are leaked. In the past decades, various techniques have been proposed to solve this problem. Such techniques range from using and storing randomized templates, using homomorphic encryption, or using biometric encryption techniques such as fuzzy extractors. Fuzzy extractors are a construction that allows the extraction of cryptographic keys from noisy data like biometrics. The key can then be rebuilt from some helper data and another biometric, provided that it is similar enough to the biometrics used to generate the key. This can be achieved through various approaches like the use of a quantizer or an error correcting code. In this thesis, we consider specifically fuzzy extractors for facial images. The first part of this thesis focuses on improving the security, privacy and performance of the extractor for faces first proposed by Sutcu et al. Our improvements make their construction more resistant to partial and total leaks of secure information, as well as improve the performance in a biometric authentication setting. The second part looks at using low density lattice codes (LDLC) as a quantizer in the fuzzy extractor, instead of using component based quantization. Although LDLC have been proposed as a quantizer for a general fuzzy extractor, they have yet to be used or tested for continuous biometrics like face images. We present a construction for a fuzzy extractor scheme using LDLC and we analyze its performance on a publicly available data set of images. Using an LDLC quantizer on this data set has lower accuracy than the improved scheme from the first part of this thesis. On the other hand, the LDLC scheme performs better when the inputs have additive white Gaussian noise (AWGN), as we show through simulated data. As such, we expect it to perform well in general on data and biometrics with variance akin to a AWGN channel.

In modern technology exciting developments are related to the ability to understand and control interfaces. Particularly, magnetic interfaces revealing spindependent electron transport are of great interest for modern spintronic devices, such as random access memories and logic devices. From the technological point of view, spintronic devices based on magnetic interfaces enable manipulation of the magnetism via an electric field. Such ability is a result of the different quantum effects arising from the magnetic interfaces (for example, spin transfer torque or spin-orbit torque) and it can reduce the energy consumption as compared to the traditional semiconductor electronic devices. Despite many appealing characteristics of these materials, fundamental understanding of their microscopic properties and related phenomena needs to be established by thorough investigation. In this work we implement first principles calculations in order to study the structural, electric, and magnetic properties as well as related phenomena of two types of interfaces with large potential in spintronic applications: 1) interfaces between antiferromagnetic 3d-metal-oxides and ferromagnetic 3d-metals and 2) interfaces between non-magnetic 5d(4d)- and ferromagnetic 3d-metals. A major difficulty in studying such interfaces theoretically is the typically large lattice mismatch. By employing supercells with Moir e patterns, we eliminate the artificial strain that leads to doubtful results and are able to describe the dependence of the atomic density at the interfaces on the component materials and their thicknesses. After establishing understanding about the interface structures, we investigate the electronic and magnetic properties. A Moir e supercell with transition layer is found to reproduce the main experimental findings and thus turns out to be the appropriate model for simulating magnetic misfit interfaces. In addition, we systematically study the magnetic anisotropy and Rashba band splitting at non-magnetic 5d(4d) and ferromagnetic 3d-metal interfaces and their dependences on aspects such as interdiffusion, surface oxidation, thin film thickness and lattice mismatch. We find that changes of structural details strongly alter the electronic states, which in turn influences the magnetic properties and phenomena related to spin-orbit coupling. Since the interfaces studied in this work have complex electronic structures, a computational approach has been developed in order to estimate the strength of the Rashba band splitting below and at the Fermi level. We apply this approach to the interfaces between a Co monolayer and 4d (Tc, Ru, Rh, Pd, and Ag) or 5d (Re, Os, Ir, Pt, and Au) transition metals and find a clear correlation between the overall size of the band splitting and the charge transfer between the d-orbitals at the interface. Furthermore, we show that the spin splitting at the Fermi surface scales with the induced orbital moment weighted by the strength of the spin-orbit coupling.

We study various quotient maps between frames which are defined by stipulating that they satisfy certain conditions on the cozero parts of their domains and codomains. By way of example, we mention that C-quotient and C -quotient maps (as defined by Ball and Walters- Wayland [7]) are typical of the types of homomorphisms we consider in the initial parts of the thesis. To be little more precise, we study uplifting quotient maps, C1- and C2-quotient maps and show that these quotient maps possess some properties akin to those of a C-quotient maps. The study also focuses on R - and G - quotient maps and show, amongst other things, that these quotient maps coincide with the well known C - quotient maps in mildly normal frames. We also study quasi-F frames and give a ring-theoretic characterization that L is quasi-F precisely when the ring RL is quasi-B´ezout. We also show that quasi-F frames are preserved and reflected by dense coz-onto R -quotient maps. We characterize normality and some of its weaker forms in terms of some of these quotient maps. Normality is characterized in terms of uplifting quotient maps, -normally separated frames in terms of C1-quotient maps and mild normality in terms of R - and G -quotient maps. Finally we define cozero complemented frames and show that they are preserved and reflected by dense z#- quotient maps. We end by giving ring-theoretic characterizations of these frames. / Mathematical Science / D. Phil. (Mathematics)

Using Additive manufacturing it is possible to manufacture complicated components, that cannot be manufactured using conventional methods. The typical example is the lattice structure. Fabrication of these structures is complicated, and it is different from the fabrication of bulk parts. Using numerical simulation which can reflect process parameters it is possible to analyze the thermal behaviour of vertical and inclined struts fabrication. Results show that the diameter of struts influences weld track width. This influence is caused by preheating the powder material by previous scanning paths. The final geometry of inclined struts is made in more scanning layers. In this work influence of the start and endpoint of trajectory is described.

My dissertation is an investigation into the basic Physics of phase separation fronts. Such phase-separation fronts occur in many practical applications, like the formation of immersion precipitation membranes, Temperature induced phase-separation of polymeric blends, or the formation of steel. Despite the fact that these phenomena are ubiquitous no generally acceptable theory of phase-separation front exists. I believe the reason lies in the complexity of many of these material systems where a large number of physical effects (like phase-separation, crystallization, hydrodynamics, etc) cooperate to generate these structures. As a Physicist, I was driven to develop an understanding of these systems, and we choose to start our investigation with the simplest system that would incorporate a phase-separation front. So we initially limited our study to systems with a purely diffusive dynamics. The phase-separation front is induced by a control-parameter front that is a simple step function advancing with a prescribed velocity. We investigated these systems numerically using a lattice Boltzmann method and also investigated them analytically as much as possible. Starting from a one-dimensional front moving with a constant velocity we then extended the complexity of the systems by increasing the number of dimensions, examining a variable front velocity, and finally by including hydrodynamics.

In this Doktorarbeit the Lattice Boltzmann scheme, a heuristic method for the simulation of flows in complicated boundaries, is investigated. Its theory is renewed by emphasizing the entropy maximization principle, and new means for the modelling of geometries (including moving boundaries) and the visual representation of evoluting flows are presented. An object oriented implemen- tation is given with communication between objects realized by an interpreter object and communication from outside realized via interprocess communica- tion. Within the new theoretical apprach the applicability of existing Lattice Boltzmann schemes to model thermal flows for arbitrary temperatures is reex- amined. / In dieser Doktorarbeit wird das Gitter-Boltzmann-Schema, eine heuristische Methode fuer die Simulation von Stroemungen innerhalb komplexer Raender, untersucht. Die zugrundeliegende Theorie wird unter neuen Gesichtspunkten, insbesondere dem Prinzip der Entropiemaximierung, betrachtet. Des weiteren werden neuartige Methoden fuer die Modellierung der Geometrie (einschl. beweglicher Raender) und der visuellen Darstellung aufgezeigt. Eine objektorientierte Implementierung wird vorgestellt, wobei die Kommunikation zwischen den Objekten über Interpreter-Objekte und die Kommunikation mit der Aussenwelt ueber Interprozess-Kommunikation gehandhabt wird. Mit dem neuen theoretischen Ansatz wird die Gueltigkeit bestehender Gitter-Boltzmann-Schemata fuer die Anwendung auf Stroemungen mit nicht konstanter Temperatur untersucht.

Lattice gauge theory is an important approach to understanding quantum chromodynamics (QCD) due to the large coupling constant in the theory at low energy. In this thesis, we report our study of the topological properties of the gauge fields and we calculate 𝘮_η and 𝘮_η' which are related to the topology of the gauge fields. We also develop two algorithms to speed up the inversion of the Dirac equation which is computationally demanding in lattice QCD calculations. The topology of lattice gauge fields is important but difficult to study because of the large local fluctuations of the gauge fields. In chapter 2, we probe the topological properties of the gauge fields through the measurement of closed quark loops, field strength and low-lying eigenvectors of the Shamir domain wall operator. The closed quark loops suggest the slow evolution of topological modes during the generation of QCD configurations. The chirality of the low-lying eigenvectors is studied and the lattice eigenvectors are compared to the eigenvectors in the continuous theory. The topological charges are calculated from the eigenvectors and the results agree with the topological charges calculated from the smoothed gauge fields. The fermion correlators are also obtained from the eigenvectors. The non-trivial topological properties of QCD gauge fields are important to the mass of the η and η', 𝘮_η and 𝘮_η'. Lattice QCD is an area where 𝘮_{\eta}$ and 𝘮_{\eta'}$ can be calculated by using gauge fields that are sampled over different topological sectors. We calculate 𝘮_η and 𝘮_η' in chapter 3 by including the fermion correlators and the topological charge density correlators. The errors of 𝘮_η and 𝘮_η' are reduced to the percent level and the mixing angle between the octet, singlet states in the SU(3) limit and the physical eigenstates is calculated. An algorithm that reduces communication and increases the usage of the local computational power is developed in chapter 4. The algorithm uses the multisplitting algorithm as a preconditioner in the preconditioned conjugate gradient method. It speeds up the inversion of the Dirac equation during the evolution phase. In chapter 5, we utilize two lattices, called the coarse lattice and the fine lattice, that lie on the renormalization group trajectory and have different lattice spacings. We find that the low-mode space of the coarse lattice corresponds to the low-mode space of the fine lattice. Because of the correspondence, the coarse lattice can be used to solve the low modes of the fine lattice. The coarse lattice is used in the restart algorithm and the preconditioned conjugate gradient algorithm where the latter is called the renormalization group based preconditioned conjugate gradient algorithm (RGPCG). By using the near-null vectors as the filter, RGPCG could reduce the operations of the matrix multiplications on the fine lattice by 33% to 44% for the inversion of Dirac equation. The algorithm works better than the conjugate gradient algorithm when multiple equations are solved.

The discovery of a light scalar at the Large Hadron Collider is in basic agreement with the predictions of an elementary Higgs in the Standard Model (SM). Nonetheless, a light, fundamental scalar is difficult to accommodate in the SM because quantum corrections suggest its mass should be much higher than the scale of electroweak symmetry breaking (EWSB). A natural possibility is to replace the Higgs by a strongly coupled composite. Composite dynamics also gives a natural explanation to the origin of EWSB. Phenomenologically viable composite models of EWSB are constrained by experiment to feature approximate scale invariance. This behavior may follow from near conformal dynamics. At present, lattice gauge theory (LGT) provides the only quantitative method to study near conformal composite Higgs dynamics in a fully consistent strongly coupled relativistic quantum field theory. As a novel approach to the question of finding and studying near conformal theories, I will apply LGT to the study of a generalization of Quantum ChromoDynamics (QCD) with four chiral fermion flavors plus eight flavors of finite, tunable mass. By continuously varying the mass of the eight heavy flavors, I can tune between the four flavor chirally broken theory, which exhibits features similar to QCD, and the twelve flavor theory, which is known to have a conformal fixed point. This is the "4+8 Model" for directly studying near-conformal behavior. In this dissertation, I will review modern composite phenomenology, followed by outlining a study of the 4+8 Model over a range of heavy flavor masses. As a check of near-conformal behavior, I will measure the scale dependent coupling with the method of the Wilson Flow. After verifying the existence of controllable, approximate scale invariance, I will measure the low energy particle spectrum of the 4+8 Model. This includes a Higgs-like light composite scalar. Throughout this dissertation I will make reference to LGT measurement code I wrote and contributed to the software package FUEL.

In this thesis after recalling some basic definitions and theorems in category theory, lattice theory and topology we first introduce the so called Stone duality of the category of boolean lattices and the category of boolean topological spaces. Then we introduce its generalization, the so called Priestley duality of the category of bounded distributive lattices and the category of total order disconnected topological spaces. Then we introduce the M3[.] lattice construction and prove that for every bounded distributive lattice L there is an isomorphism from the lattice M3[L] to the lattice of all continuous monotone maps from the Priestley space of L to the lattice M3 with discrete topology. Finally we introduce the so called boolean power, which we generalize to the so called priestley power and we prove that for every natural number n ≥ 3 and every bounded distributive lattice L there is an isomorphism from the lattice Mn to the priestley power of the lattice Mn by the lattice L. 1

A cubic lattice with random parameters is reduced to a linear chain by the means of the projection technique. The continued fraction expansion (c.f.e.) approach is herein applied to the density of states. Coefficients of the c.f.e. are obtained numerically by the recursion procedure. Properties of the non-stationary second moments (correlations and dispersions) of their distribution are studied in a connection with the other evidences of transport in a one-dimensional Mori chain. The second moments and the spectral density are computed for the various degrees of disorder in the prototype lattice. The possible directions of the further development are outlined. The physical problem that is addressed in the dissertation is the possibility of the existence of a non-Anderson disorder of a specific type. More precisely, this type of a disorder in the one-dimensional case would result in a positive localization threshold. A specific type of such non-Anderson disorder was obtained by adopting a transformation procedure which assigns to the matrix expressing the physics of the multidimensional crystal a tridiagonal Hamiltonian. This Hamiltonian is then assigned to an equivalent one-dimensional tight-binding model. One of the benefits of this approach is that we are guaranteed to obtain a linear crystal with a positive localization threshold. The reason for this is the existence of a threshold in a prototype sample. The resulting linear model is found to be characterized by a correlated and a nonstationary disorder. The existence of such special disorder is associated with the absence of Anderson localization in specially constructed one-dimensional lattices, when the noise intensity is below the non-zero critical value. This work is an important step towards isolating the general properties of a non-Anderson noise. This gives a basis for understanding of the insulator to metal transition in a linear crystal with a subcritical noise.