Three projective problems on Finsler surfaces

Two Finsler metrics on the same manifold are called projectively equivalent, if they have the same unparametrized, oriented geodesics. A vector field on the manifold is called projective for a Finsler metric, if its flow takes geodesics to geodesics as unparametrized curves. In this dissertation, after an introduction to the general theory of Finsler metrics and its projective aspects, results to three projective problems on Finsler metrics on surfaces are presented: Firstly. Inspired by a problem posed by Sophus Lie, it is proven that every Finsler metric, admitting three independent projective vector fields, is projectively equivalent to a Randers metric. An explicit list of such metrics is given, complete up to isometry and projective equivalence. Secondly. The problem of local, fiber-global projective metrization asks whether a given system of unparametrized, oriented curves describes the geodesics of some fiber-globally defined Finsler metric - and if yes, how unique this metric is. It is shown that the set of such metrizations is, up to the trivial freedom, in 1-to-1 correspondence with measures on the space of prescribed curves, satisfying a certain equilibrium property. Thirdly. It is proven that on surfaces of negative Euler characteristic, two real-analytic Finsler metrics can only be trivially projectively related: they are projectively equivalent, if and only if they differ by multiplication with a positive number and addition of a closed 1-form

Gauge-Symmetry Protection Using Single-Body Terms

Quantum-simulator hardware promises new insights into problems from particle and nuclear physics. A major challenge is to reproduce gauge invariance, as violations of this quintessential property of lattice gauge theories can have dramatic consequences, e.g., the generation of a photon mass in quantum electrodynamics. Here, we introduce an experimentally friendly method to protect gauge invariance in $\mathrm{U}(1)$ lattice gauge theories against coherent errors in a controllable way. Our method employs only single-body energy-penalty terms, thus enabling practical implementations. As we derive analytically, some sets of penalty coefficients render undesired gauge sectors inaccessible by unitary dynamics for exponentially long times, and, for few-body error terms, with resources independent of system size. These findings constitute an exponential improvement over previously known results from energy-gap protection or perturbative treatments. In our method, the gauge-invariant subspace is protected by an emergent global symmetry, meaning it can be immediately applied to other symmetries. In our numerical benchmarks for continuous-time and digital quantum simulations, gauge protection holds for all calculated evolution times (up to $t>10^{10}/J$ for continuous time, with $J$ the relevant energy scale). Crucially, our gauge-protection technique is simpler to realize than the associated ideal gauge theory, and can thus be readily implemented in current ultracold-atom analog simulators as well as digital noisy intermediate scale quantum (NISQ) devices.Comment: 19 pages, 12 figures, journal articl

Glutathione and morbidity in a community-based sample of elderly

This study examined the association of blood glutathione level, a potential marker of physiological/functional aging, with a number of biomedical/psychological traits in a subgroup (N = 33) of a representative sample of community-based elderly. Higher glutathione levels were associated with fewer number of illnesses (p p p < 0.05), lower body mass index, and lower blood pressures. Subjects with diagnoses of arthritis, diabetes, or heart disease (as assessed by physicians) had at least marginally significant lower glutathione levels than those who were disease free. Glutathione, together with age and a measure of suppressed anger, accounted for 39% of the variance of an index of morbidity. Glutathione, by itself, accounted for 24% of the variance. To our knowledge, this is the first evidence of an association of higher glutathione levels with higher levels of physical health in a sample of community-based elderly. Further studies in large samples are needed to investigate glutathione as a potential overall health risk factor for morbidity among the elderly.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/31377/1/0000290.pd

Distribution of genuine high-dimensional entanglement over 10.2 km of noisy metropolitan atmosphere

In a recent quantum key distribution experiment, high-dimensional protocols were used to show an improved noise resistance over a 10.2 km free-space channel. One of the unresolved questions in this context is whether the communicating parties actually shared genuine high-dimensional entanglement. In this letter we introduce an improved discretisation and entanglement certification scheme for high-dimensional time-bin setups and apply it to the data obtained during the experiment. Our analysis answers the aforementioned question affirmatively and thus the experiment constitutes the first transmission of genuine high-dimensional entanglement in a single degree of freedom over a long-range free-space channel.Comment: 6 pages, 3 figure

Gümnaasiumi-õpetajate I kongress :3., 4. ja 5. aprillil 1929. a. Tallinnas

Digiteeritud Euroopa Regionaalarengu Fondi rahastusel, projekti "Eesti teadus- ja õppekirjandus" (2014-2020.12.03.21-0848) raames.https://www.ester.ee/record=b1400823*es

Preoperative Assessment of Language Dominance through Combined Resting-State and Task-Based Functional Magnetic Resonance Imaging

Brain lesions in language-related cortical areas remain a challenge in the clinical routine. In recent years, the resting-state fMRI (RS-fMRI) was shown to be a feasible method for preoperative language assessment. The aim of this study was to examine whether language-related resting-state components, which have been obtained using a data-driven independent-component-based identification algorithm, can be supportive in determining language dominance in the left or right hemisphere. Twenty patients suffering from brain lesions close to supposed language-relevant cortical areas were included. RS-fMRI and task-based (TB-fMRI) were performed for the purpose of preoperative language assessment. TB-fMRI included a verb generation task with an appropriate control condition (a syllable switching task) to decompose language-critical and language-supportive processes. Subsequently, the best fitting ICA component for the resting-state language network (RSLN) referential to general linear models (GLMs) of the TB-fMRI (including models with and without linguistic control conditions) was identified using an algorithm based on the Dice index. Thereby, the RSLNs associated with GLMs using a linguistic control condition led to significantly higher laterality indices than GLM baseline contrasts. LIs derived from GLM contrasts with and without control conditions alone did not differ significantly. In general, the results suggest that determining language dominance in the human brain is feasible both with TB-fMRI and RS-fMRI, and in particular, the combination of both approaches yields a higher specificity in preoperative language assessment. Moreover, we can conclude that the choice of the language mapping paradigm is crucial for the mentioned benefits