Vortices in Chern-Simons-Ginzburg-Landau Theory and the Fractional Quantum Hall Effect

Chern-Simons-Ginzburg-Landau (CSGL) theory is an attempt of a phenomenological description of the fractional quantum Hall effect. The CSGL theory is studied mainly without considering the direct applications of the results. Vortices in CSGL theory are believed to be the analogue of quasiparticles in the fractional quantum Hall effect. The details of the vortices are studied both analytically and numerically, and we compare the analytical results to the numerical ones. We show how the vortices may be understood as particles in Maxwell-Chern-Simons (MCS) theory. We solve the CSGL equations for a vortex numerically for a range of the dimensionless parameter, and show how the size and energy of a vortex depends on this parameter. We also study the connection between the CSGL theory and the GL and MCS theories numerically, and find support for our analytical results. Also studied are various extensions of the CSGL theory. These extensions are made by adding terms to the CSGL Lagrangian. The extended theories are mainly studied numerically. The first extension we study is the addition of a dynamical magnetic field. We show how the charge is no longer quantized when the magnetic field is made dynamical. We also show how the inclusion of a dynamical magnetic field changes the size, energy and charge of a vortex, and we find that the self-dual point of pure CSGL theory extends to a self-dual line. The second extension we study is the extension of the CSGL wave function to a two-component spinor. We show how this extension allows another kind of vortex solutions, known as skyrmions, and show how the size and spin of the skyrmions depend on the effective gyromagnetic ratio, and we reproduce qualitative results found by a different kind of study of a spin-dependent model for the fractional quantum Hall effect. Using our numerical results, we obtain a phase diagram for the spin dependent CSGL theory. The last part of the thesis is devoted to the duality between the CSGL theory and the MCS theory. We make a detailed derivation of the duality starting from the Lagrangian of CSGL theory. We attempt to use this duality to find a better description of the dynamics of vortices and a dispersion relation for a system with a gas of free vortices. We conclude that in this area there is still room for further study

Permutation branes and linear matrix factorisations

All the known rational boundary states for Gepner models can be regarded as permutation branes. On general grounds, one expects that topological branes in Gepner models can be encoded as matrix factorisations of the corresponding Landau-Ginzburg potentials. In this paper we identify the matrix factorisations associated to arbitrary B-type permutation branes.Comment: 43 pages. v2: References adde

Dynamics of self-sustained asynchronous-irregular activity in random networks of spiking neurons with strong synapses

Random networks of integrate-and-fire neurons with strong current-based synapses can, unlike previously believed, assume stable states of sustained asynchronous and irregular firing, even without external random background or pacemaker neurons. We analyze the mechanisms underlying the emergence, lifetime and irregularity of such self-sustained activity states. We first demonstrate how the competition between the mean and the variance of the synaptic input leads to a non-monotonic firing-rate transfer in the network. Thus, by increasing the synaptic coupling strength, the system can become bistable: In addition to the quiescent state, a second stable fixed-point at moderate firing rates can emerge by a saddle-node bifurcation. Inherently generated fluctuations of the population firing rate around this non-trivial fixed-point can trigger transitions into the quiescent state. Hence, the trade-off between the magnitude of the population-rate fluctuations and the size of the basin of attraction of the non-trivial rate fixed-point determines the onset and the lifetime of self-sustained activity states. During self-sustained activity, individual neuronal activity is moreover highly irregular, switching between long periods of low firing rate to short burst-like states. We show that this is an effect of the strong synaptic weights and the finite time constant of synaptic and neuronal integration, and can actually serve to stabilize the self-sustained state

Carotid Atherosclerosis is Associated with Middle Cerebral Artery Pulsatility Index

BACKGROUND AND PURPOSE Pulsatility index (PI) in the middle cerebral artery (MCA) is considered a measure of peripheral vascular resistance. Several established cardiovascular risk factors are common for both MCA PI and carotid atherosclerosis. Accordingly, in the present study we hypothesized an association between ultrasound‐derived indices of carotid atherosclerosis and MCA PI. METHODS All residents in Akershus County, born in 1950, were invited to a cardiovascular examination, The Akershus Cardiac Examination (ACE) 1950 Study (2012‐2015). A thorough ultrasound examination was performed to assess indices of atherosclerosis in the carotid arteries, and PI in the MCAs. In all, 3154 (85.1%) had adequate transcranial and carotid data. Associations between indices of carotid atherosclerosis and MCA PI were assessed by regression analyses adjusted for established cardiovascular risk factors. RESULTS Mean age was 64 (standard deviation [SD]: .6) years, and 1,357 (43%) were women. Mean MCA PI was .97 (SD: .17). Participants in the upper quartile of MCA PI had higher pulse pressure, more frequently hypertension, diabetes mellitus, and a history of coronary artery disease. Both carotid plaque score (B .007 [95% CI: .003‐.010]) and carotid intimamedia thickness (B .173 [95% CI: .120‐.226]) were significantly associated with MCA PI in adjusted analysis. The model R 2 was .055. CONCLUSION In a population‐based sample of middle‐aged adults, ultrasound‐derived indices of carotid atherosclerosis were independently associated with MCA PI. However, the overall explained variance of MCA PI was low, suggesting other factors than atherosclerosis and cardiovascular risk factors to play an important role for MCA PI

Blood pressure at age 40 predicts carotid atherosclerosis two decades later: Data from the Akershus Cardiac Examination 1950 Study

Objective: We assessed the impact of a single time-point measurement of SBP, DBP and pulse pressure at the age of 40, on carotid plaque burden, echolucent plaques and carotid intima–media thickness late midlife. Methods: Individuals participating in two separate studies, 23 years apart, defined our cohort (n = 2714). ‘The Age 40 Program’, a nationwide Norwegian cardiovascular screening survey, performed 1985–1999, assessed cardiovascular risk factors and lifestyle variables at age 40. ‘The ACE 1950 Study’, a population-based cohort study on individuals born in 1950, performed 2012–2015, included ultrasound examinations of the carotid arteries. Blood pressure (BP) determinants of carotid atherosclerosis were assessed by regression models adjusted for cardiovascular risk factors at age 40, and late midlife BP. Results: The participants, 50.3% women, had a mean age of 40 (SD 0.3) years in the first study, and 64 (SD 0.6) years in the second. At age 40, mean SBP was 128 (SD 14) mmHg, mean DBP was 78 (SD 10) mmHg and mean pulse pressure was 50 (SD 9) mmHg. SBP and DBP at age 40 predicted carotid plaque burden in late midlife. Only DBP predicted echolucent plaques, and none of the BP components predicted carotid intima–media thickness. Conclusion: A single time-point measurement of SBP and DBP at age 40 is associated with carotid plaque burden late midlife, also after adjustment for other cardiovascular risk factors at age 40, and of late midlife BP. Our findings emphasize the strong association between BP and atherosclerosis

Prevalence of carotid plaque in a 63- to 65-Year-Old Norwegian cohort from the general population: The ACE (Akershus Cardiac Examination) 1950 study

Background New data on extracranial carotid atherosclerosis are needed, as improved ultrasound techniques may detect more atherosclerosis, the definition of plaque has changed over the years, and better cardiovascular risk control in the population may have changed patterns of carotid arterial wall disease and actual prevalence of established cardiovascular disease. We investigated the prevalence of atherosclerotic carotid plaques and carotid intima–media thickness (cIMT) and their relation to cardiovascular risk factors in a middle‐aged cohort from the general population. Methods and Results We performed carotid ultrasound in 3683 participants who were born in 1950 and included in a population‐based Norwegian study. Carotid plaque and cIMT were assessed according to the Mannheim Carotid Intima–Media Thickness and Plaque Consensus, and a carotid plaque score was used to calculate atherosclerotic burden. The participants were aged 63 to 65 years, and 49% were women. The prevalence of established cardiovascular disease was low (10%), but 62% had hypertension, 53% had hypercholesterolemia, 11% had diabetes mellitus, and 23% were obese. Mean cIMT was 0.73±0.11 mm, and atherosclerotic carotid plaques were present in 87% of the participants (median plaque score: 2; interquartile range: 3). Most of the cardiovascular risk factors, with the exception of diabetes mellitus, obesity and waist–hip ratio, were independently associated with the plaque score. In contrast, only sex, hypertension, obesity, current smoking, and cerebrovascular disease were associated with cIMT. Conclusions We found very high prevalence of carotid plaque in this middle‐aged population, and our data support a greater association between cardiovascular risk factors and plaque burden, compared with cIMT