Maskininlärning (eng: Machine Learning) har på senare tid blivit ett populärt ämne. En fråga som många användare ställer sig är hur mycket data det behövs för att få ett så korrekt svar som möjligt. Detta arbete undersöker relationen mellan inlärningsdata, mängd såväl som struktur, och hur väl algoritmen presterar. Fyra olika typer av datamängder (Iris, Digits, Symmetriskt och Dubbelsymetriskt) studerades med hjälp av tre olika algoritmer (Support Vector Classifier, K-Nearest Neighbor och Decision Tree Classifier). Arbetet fastställer att alla tre algoritmers prestation förbättras vid större mängd inlärningsdata upp till en viss gräns, men att denna gräns är olika för varje algoritm. Datainstansernas struktur påverkar också algoritmernas prestation där dubbelsymmetri ger starkare prestation än enkelsymmetri. / In recent years Machine Learning has become a popular subject. A challange that many users face is choosing the correct amount of training data. This study researches the relationship between the amount and structure of training data and the accuracy of the algorithm. Four different datasets (Iris, Digits, Symmetry and Double symmetry) were used with three different algorithms (Support Vector Classifier, K-Nearest Neighbor and Decision Tree Classifier). This study concludes that all algorithms perform better with more training data up to a certain limit, which is different for each algorithm. The structure of the dataset also affects the performance, where double symmetry gives greater performance than simple symmetry.

Indiana University-Purdue University Indianapolis (IUPUI) / Over the past two decades, open systems that are described by a non-Hermitian Hamiltonian have become a subject of intense research. These systems encompass classical wave systems with balanced gain and loss, semi-classical models with mode selective losses, and lossy quantum systems. The rapidly growing research on these systems has mainly focused on the wide range of novel functionalities they demonstrate. In this thesis, I intend to present some intriguing properties of a class of open systems which possess parity (P) and time-reversal (T) symmetry with a theoretical background, accompanied by the experimental platform these are realized on. These systems show distinct regions of broken and unbroken symmetries separated by a special phase boundary in the parameter space. This separating boundary is called the PT-breaking threshold or the PT transition threshold. We investigate non-Hermitian systems in two settings: tight binding lattice models, and electrical circuits, with the help of theoretical and numerical techniques. With lattice models, we explore the PT-symmetry breaking threshold in discrete realizations of systems with balanced gain and loss which is determined by the effective coupling between the gain and loss sites. In one-dimensional chains, this threshold is maximum when the two sites are closest to each other or the farthest. We investigate the fate of this threshold in the presence of parallel, strongly coupled, Hermitian (neutral) chains, and find that it is increased by a factor proportional to the number of neutral chains. These results provide a surprising way to engineer the PT threshold in experimentally accessible samples. In another example, we investigate the PT-threshold for a one-dimensional, finite Kitaev chain—a prototype for a p-wave superconductor— in the presence of a single pair of gain and loss potentials as a function of the superconducting order parameter, onsite potential, and the distance between the gain and loss sites. In addition to a robust, non-local threshold, we find a rich phase diagram for the threshold that can be qualitatively understood in terms of the band-structure of the Hermitian Kitaev model. Finally, with electrical circuits, we propose a protocol to study the properties of a PT-symmetric system in a single LC oscillator circuit which is contrary to the notion that these systems require a pair of spatially separated balanced gain and loss elements. With a dynamically tunable LC oscillator with synthetically constructed circuit elements, we demonstrate static and Floquet PT breaking transitions by tracking the energy of the circuit. Distinct from traditional mechanisms to implement gain and loss, our protocol enables parity-time symmetry in a minimal classical system.

An alternative approach to the problem of CP-violation is presented. It is based on the possibility of spontaneous CP-breakdown in models with two Higgs doublets. General features of the phenomenon such as stability of the vacuum and the existence of a light axion are discussed. We investigate the feasibility of spontaneously broken CP in the minimal supersymmetric models - the MSSM and NMSSM. The latter is shown to be experimentally viable. The phenomenological implications of the model such as CP-violating effects in the kaon systems and a nonzero neutron electric dipole moment are studied. / Ph. D.

The continual increase in anterior cruciate ligament (ACL) injuries in sports makes it the most common ligament injury and leads the athlete down a difficult road with reconstruction surgery (ACLR) and months of rehabilitation. Specifically, females are at a greater risk of both primary and secondary ACL injuries compared to males. The purpose of this research was to understand the differences in movement and loading variability between ACLR and healthy athletes during unilateral and bilateral landings while utilizing limb symmetry to understand between group differences. It was hypothesized that females with an ACLR would have greater variability compared to males with an ACLR and healthy female athletes. 40 ACLR and 67 healthy athletes were asked to complete seven stop jumps and 25 ACLR and 30 healthy athletes completed seven single hop trials to assess intra-subject variability. The stop jump task utilized embedded force plates and motion capture technology while the single hop task used loadsol® in-shoe force sensors. The measures studied with the stop jump included posterior and vertical ground reaction force (GRF), knee/hip abduction/adduction angles, and loading rate. The single hop measures included peak force, loading rate, and impulse. To assess variability and limb symmetry, coefficient of variation (CV) and the limb symmetry index (LSI) were calculated for each of outcome measure. A linear mixed effects model was completed in JMP (SAS Institute Inc., Cary, NC) with p<0.05 to see the effects of group, sex, and limb. During the stop jump task, the ACLR athletes showed higher variability for both posterior GRF (p<0.001), posterior GRF LSI (p<0.001), and loading rate (p=0.027) compared to controls. Females with an ACLR had higher variability in vertical GRF (p<0.001) and vertical GRF symmetry (p=0.029) compared to HC females. Additionally, females with an ACLR had higher variability in the vertical GRF (p=0.033) when compared to males with an ACLR. Knee abduction angle (p=0.024) showed males with an ACLR to have higher variability compared to females with an ACLR. For the single hop task, there was a significant difference between sex for loading rate (p<0.001), loading rate LSI (p=0.004), impulse (p=0.006), and impulse LSI (p=0.001) with males producing a higher mean CV compared to females in all measures regardless of group. Overall, these results support the hypothesis that group and sex differences exist and that females with an ACLR will have higher variability and asymmetrical movements than male ACLR patients and healthy females during bilateral landings, which could lead to increased injury risk. In unilateral landings, the results suggest that females are landing with less variability compared to males. With increased variability on the surgical limb of an athlete with an ACLR, it is likely that the athlete will have a more successful return to sport as they can react and adapt to changes in landing during sports. Future work should report reinjury rates to investigate the potential role of movement variability in injury risk and potentially determine variability thresholds for injury risk. The evaluation of bilateral and unilateral landings revealed the need to include both landing tasks in return to sport testing as well as a limb symmetry metric to understand an athlete's functional readiness to react to changing conditions during sports related movement. / Master of Science / Anterior cruciate ligament (ACL) injuries continue to rise in all sports and result in athletes having to undergo reconstruction surgery (ACLR) and months of rehabilitation if they want to compete at a high level again. Specifically, females have a greater risk of suffering both a primary and secondary ACL injury compared to males. Movement differences have been previously researched in hopes of decreasing injury risk. Variability, or the differences between one trial to the next, is a way to visualize the athlete's ability to adapt following injury. The ideal level of adaptability is still unclear as too much variability can be seen as unstable while too little can be seen as unforgiving. The purpose of this project was to better understand movement and loading variability between ACLR and healthy athletes during one legged (unilateral) and two legged (bilateral) landings. Differences between limbs were analyzed to understand whether one leg was favored over the other. Every participant completed seven stop jump trials which required them to run forward, jump off one leg and landing with two legs followed by a maximum vertical jump; another different group completed a series of seven single leg hop tasks during which they started on one-leg and jumped forward as far as they could while maintaining their balance. The measures studied with the stop jump included peak vertical and posterior force, frontal plane knee and hip angles, and loading rate. The single hop measures included peak force, loading rate, and impulse. The loading rate is defined as the ratio of peak force divided by the time it takes the athlete to reach peak force following initial contact. Impulse is the area under the force time curve and provides insight into the athlete's ability to dissipate load. The force data from each trial performed were collected using force plate technology and loadsol® shoe inserts. Variability was calculated using the coefficient of variation (CV) which is the ratio between the standard deviation and the mean value across the trails. The limb symmetry index (LSI) was calculated as the ratio between the surgical/non-dominant and the non-surgical/dominant limbs. During a stop jump, female patients with an ACLR showed greater variability in peak force and force LSI revealing asymmetric landing compared to healthy females. Additionally, females with an ACLR had greater variability compared to males with an ACLR in peak force. The ACLR group had greater variability in posterior force, posterior force symmetry, and loading rate compared to the athletes in the healthy group. During a single hop, males had higher greater variability in loading rate, loading rate limb difference, impulse, and impulse limb difference compared to females. These results suggest that all females have a more unstable and asymmetrical landing compared to all males during bilateral landing. However, during a unilateral landing, females had a less forgiving landing compared to males, which could also indicate an increased injury risk. Future work should investigate reinjury rates to determine whether variability impacts injury risk and if differences in injury risk between males and females are associated with differences in variability.

INTRODUCTION: ACL-reconstructed (ACL-R) patients exhibit side-to-side asymmetries in movement and loading patterns after surgery, some of which are predictive of a secondary ACL injury. These asymmetries have not been fully assessed in healthy athletes. PURPOSE: To quantify side-to-side symmetry in secondary injury predictors in healthy athletes and compare these metrics to those measured in previous cohorts of ACL-R patients, as well as to assess differences in these metrics between two landing tasks and between sexes. METHODS: 60 healthy recreational athletes performed seven trials of a stop-jump task and seven trials of a single-leg hop for distance on each limb. The kinematics and kinetics of the first landing of the stop-jump and the landing of the single-leg hop were analyzed with a 10-camera motion analysis system (240Hz) and 2 embedded force plates (1920Hz). Limb symmetry indices (LSIs) were calculated for each variable and compared between subject groups, tasks, and sexes with Wilcoxon Signed Rank tests (p<0.05). RESULTS: Control subjects exhibited asymmetry in hop distance (p=0.006). ACL-R subjects displayed greater asymmetry in knee flexion variables, peak forces, and peak knee extension moments during the bilateral landing (p<0.001) and in hop distance (p<0.001). Control subjects showed greater asymmetry in knee flexion variables during the single-leg hop (p<0.001). Males and females showed similar symmetry in both tasks. CONCLUSIONS: Symmetry cannot be assumed in control subjects in all metrics. Asymmetries are more prevalent in ACL-R athletes than in healthy controls. Future work will continue to examine the usefulness of each metric in assessing ACL-R rehabilitation. / Master of Science / Up to 200,000 ACL injuries occur in the US annually. Researchers have demonstrated that ACL-reconstructed (ACL-R) patients display differences in movements between their injured leg and their healthy leg during athletic activities. In some cases, these differences, or asymmetries, can increase a person’s risk of sustaining a second ACL injury. However, movement symmetry is not well understood in people who have not had an ACL injury. The goal of this work was to better understand asymmetries in healthy people so that we can better assess those who have suffered an ACL injury. We did this by assessing movement in healthy athletes during single- and double-leg landing activities that have been traditionally used to assess recovery in ACL-R patients. We found that the healthy athletes exhibited significant asymmetries in several metrics during both the single- and double-leg landings. These results indicate that movement symmetry should not be assumed in healthy control subjects. We also similarities and differences in symmetry profiles between single- and double-leg landing activities in a control population. The results of this study will enable researchers to better understand movement deficiencies in ACL-R patients when compared to healthy control subjects as we continue to work to minimize re-injury following return to sport in ACL patients.

The Q_weak Experiment ran for two and a half years at the Thomas Jefferson National Accelerator Facility in pursuit of Q_w^p, the neutral weak analog to the electric charge of the proton. Qweak measured the parity-violating asymmetry in elastic electron-proton scattering at an extreme forward angle (Q² = 0.0249 (GeV/c)² ). From the data gathered via the 1.16 GeV 180 μA longitudinally polarized electron beam scattering off the unpolarized photons in the liquid hydrogen target, a value of Q_w^p (PVES) = 0.0719 ± 0.0045 was determined. The Standard Model has a definite prediction of Q_w^p (SM) = 0.0708 ± 0.0003, consistent with the value determined by Q_weak which sets a limit on possible new physics up to 7.5 TeV. The theory behind the main measurement of the Q_weak Experiment is described in this document, along with the apparatus that made the measurement possible. Understanding the kinematics of the apparatus was a vital component to Qweak 's final measurement. An in-depth explanation of the tracking system responsible for benchmarking the momentum transfer and scattering angle simulations is included. The unblinded analysis of Q_weak's final result is outlined, as are additional physics results related to the N→ ∆ transition. During April 2012, an opportunity was seized to take ancillary data on the inelastic N→ ∆ transition at a different beam energy(877 MeV) than the nominal Q_weak data. This data, combined with the inelastic data taken at nominal beam energy and a previous measurement, determined a constraint on d_∆ , a low energy constant related to hadronic parity violation, of (3.8 ± 14.7)g_π . It also resulted in a measurement of the beam-normal single-spin asymmetry of the N→ ∆ transition of 149 ± 3 (stat) ± 72 (syst) ppm. This document includes both the longitudinal and transverse analysis of the 877 MeV data. / Doctor of Philosophy / The Q_weak Experiment, run at the Thomas Jefferson National Accelerator Facility, measured the weak charge, the weak force analog of the electric charge of the electromagnetic force, of the proton. Unlike the well-know Large Hadron Collider, which operates on the energy-frontier and directly searches for new particles, Q_weak operates by precisely measuring the results of scattering electrons off of protons. This approach is referred to as the precision frontier and is used to test the Standard Model, which has a well-defined prediction for the weak charge of the proton. Deviations from the Standard Model would suggest that there was new physics beyond the Standard Model affecting the results. However, the Q_weak measured weak charge of the proton, Q_w^p (PVES) = 0.0719 ± 0.0045, is in good agreement with the Standard Model predicted value. This provides a new limit, 7.5 TeV, on possible new physics beyond the Standard Model. The theoretical background and apparatus of the Qweak experiment will be explained in this document. A vital component of the final result was understanding the path and energy of the electron as it passed through the apparatus. This was done via simulation but benchmarked by the tracking system. The tracking system will be explained in detail. The final analysis of the Q_weak measurement of the weak charge will also be explained. A secondary result discussed here focuses on data taken using the Q_weak apparatus but at a different beam energy than the nominal Q_weak data. For this data, the electron scatter inelastically off the proton. The lost kinetic energy of the electron causes the proton to be excited into the first resonance state, the ∆, which quickly decays away. This transition grants access to a low energy constant, d_∆, and a measurement linked to the spins of the electrons being polarized perpendicular to the direction of the beam, B_n. The extraction of these values is covered in detail.

Decreased gait symmetry has been correlated with an increased fall risk, abnormal joint loading and decreased functional outcomes. Therefore, symmetry is focused on in the rehabilitation of many patient populations. Currently, load based symmetry is collected using expensive and immobile devices that are not clinically accessible, but there is a clinical need for an objective measure of loading symmetry during daily tasks like walking. Therefore, the purpose of this dissertation was to 1) assess the validity and reliability of the loadsol® to capture ground reaction force data, 2) use the loadsol® to determine the differences in symmetry between adults with a TKA and their healthy peers and 3) explore the potential of a commercially available biofeedback system to acutely improve gait symmetry in adults. The results of this work indicate that the loadsol® is a valid and reliable method of collecting loading measures during walking in both young and older adults. TKA patients who are 12-24 months post-TKA have lower symmetry in the weight acceptance peak force, propulsive peak force and impulse when compared to their healthy peers. Finally, a case study with four asymmetric adults demonstrated that a 10-minute biofeedback intervention with the loadsol® resulted in an acute improvement in symmetry. Future work is needed to determine the potential of this intervention to improve symmetry in patient populations and to determine whether the acute response is retained following the completion of the intervention. / Doctor of Philosophy / Symmetry during walking is a valuable attribute as asymmetry has been correlated with an increased fall risk and decreased mobility. Currently, load based symmetry is collected using expensive and immobile devices that are not clinically accessible. As a result, there is a critical need for a system that can objectively measure load and loading symmetry during rehabilitation and everyday tasks in a variety of settings. A new device has been developed (loadsol®) that could potentially fill this need. Before it can be used to assess and treat patients, the loadsol® needed to be assessed for accuracy and reliability in both older and younger adults and at various speeds. Then we needed to determine if the loadsol® can be used to look at the levels of symmetry in patients who have had a knee replacement compared to their healthy peers. Finally, we tested a visual biofeedback intervention with the loadsol® to see if this intervention was able to improve symmetry. We found that the loadsol® is accurate and reliable. Patients with a knee replacement were less symmetric than their age matched peers. Finally, in a small study, the visual biofeedback intervention improved symmetry during walking in a group of people with less than 90% symmetry. Future work is needed to explore the potential of this biofeedback intervention to improve symmetry in various patient populations and to determine the extent to which patients are able to retain these improvements.

Architecture is a translation of an idea. An ordering idea is vital to make architecture. A building that is symmetrical about two axis, with some necessary exceptions, is an example of such an idea. / Master of Architecture

The project is a columbarium and crematorium complex. It is located on the Eastern peripherie of Blacksburg, Virginia. The site slopes downward to the South East. The project is organized in an axial arrangement following the direction of the slope. The program of the building does not follow any religious ritual and is culturally determined only in so far as cremation is an acceptable form of disposal of the deceased. In this sense the building itself becomes a memorial of the dead. With the exclusion of formal ritual as a guiding principle for an architectural expression of the contemplation of death simple geometric figures are meant to evoke a general sense of proper emotional and intellectual response to the phenomenon of death, perhaps to dying. This approach hopes to allow for individual contemplation of the ending and the end of human life. / Master of Architecture

This dissertation is a collection of works studying selected condensed matter systems from the high energy theory point of view. We use the effective field theories of systems that spontaneously break Lorentz symmetry in order to investigate a number of questions, puzzles, and their consequences, such as apparent superluminality, and scattering amplitude properties of a system with unstable asymptotic states. In the process, we highlight the interplay between condensed matter physics and high energy theory, with Lorentz invariance violation as a common denominator.