Non-Abelian statistics as a Berry phase in exactly solvable models

We demonstrate how to directly study non-Abelian statistics for a wide class of exactly solvable many-body quantum systems. By employing exact eigenstates to simulate the adiabatic transport of a model's quasiparticles, the resulting Berry phase provides a direct demonstration of their non-Abelian statistics. We apply this technique to Kitaev's honeycomb lattice model and explicitly demonstrate the existence of non-Abelian Ising anyons confirming the previous conjectures. Finally, we present the manipulations needed to transport and detect the statistics of these quasiparticles in the laboratory. Various physically realistic system sizes are considered and exact predictions for such experiments are provided.Comment: 10 pages, 3 figures. To appear in New Journal of Physic

Saddle point localization of molecular wavefunctions

The quantum mechanical description of isomerization is based on bound eigenstates of the molecular potential energy surface. For the near-minimum regions there is a textbook-based relationship between the potential and eigenenergies. Here we show how the saddle point region that connects the two minima is encoded in the eigenstates of the model quartic potential and in the energy levels of the [H, C, N] potential energy surface. We model the spacing of the eigenenergies with the energy dependent classical oscillation frequency decreasing to zero at the saddle point. The eigenstates with the smallest spacing are localized at the saddle point. The analysis of the HCN???HNC isomerization states shows that the eigenstates with small energy spacing relative to the effective (v1, v3, l) bending potentials are highly localized in the bending coordinate at the transition state. These spectroscopically detectable states represent a chemical marker of the transition state in the eigenenergy spectrum. The method developed here provides a basis for modeling characteristic patterns in the eigenenergy spectrum of bound states

Uncrewed Aerial Vehicle Fruit Picking with Perceptual Imitation Learning Trajectory Generation

This thesis studies the problem of Uncrewed Aerial Vehicle (UAV) path planning and manipulation in unmapped environments. This thesis the specific task of orange picking with a quadrotor UAV. Robotic fruit harvesting is a fitting example problem to tackle in this research, as there is a worldwide need for improved agricultural technologies. This task is difficult because it requires comprehending and navigating a complex, unknown environment. To accomplish this task, we present a novel visual servoing controller which fuses information from onboard camera images with odometry data. This was used to calculate the relative position of an orange and a safe approach angle. By following a series of reference trajectories to the computed goal location, the system was able to grasp an orange autonomously and remove it from the tree. This visual servoing method has several inherent limitations. It cannot search for an occluded orange or handle any paths that remove the orange from its view. To improve upon this approach, and correct these shortcomings, we develop a novel neural network architecture to perform the same task using a learned implicit visual encoding. In the next section, we present the design of a simulation of this same orange picking task, and a Model Predictive Control (MPC) method for computing optimal trajectories within it. We trained the neural network to imitate the MPC expert, validating the network structure and cost function. In the subsequent chapter, we trained the same architecture on a dataset derived from the visual servoing controller. These experiments led to useful innovations in the neural network architecture, but even with these efforts, no network was able to vastly improve on the baseline data. In the final chapter, we discuss the relative strengths and weaknesses of these algorithms. Each has areas where it exceeds the others, and we propose new avenues of research to improve them all

Boundaries can steer active Janus spheres

The advent of autonomous self-propulsion has instigated research towards making colloidal machines that can deliver mechanical work in the form of transport, and other functions such as sensing and cleaning. While much progress has been made in the last 10 years on various mechanisms to generate self-propulsion, the ability to steer self-propelled colloidal devices has so far been much more limited. A critical barrier in increasing the impact of such motors is in directing their motion against the Brownian rotation, which randomizes particle orientations. In this context, here we report directed motion of a specific class of catalytic motors when moving in close proximity to solid surfaces. This is achieved through active quenching of their Brownian rotation by constraining it in a rotational well, caused not by equilibrium, but by hydrodynamic effects. We demonstrate how combining these geometric constraints can be utilized to steer these active colloids along arbitrary trajectories

Monitoring neural activity with bioluminescence during natural behavior

Existing techniques for monitoring neural activity in awake, freely behaving vertebrates are invasive and difficult to target to genetically identified neurons. We used bioluminescence to non-invasively monitor the activity of genetically specified neurons in freely behaving zebrafish. Transgenic fish with the Ca^(2+)-sensitive photoprotein green fluorescent protein (GFP)-Aequorin in most neurons generated large and fast bioluminescent signals that were related to neural activity, neuroluminescence, which could be recorded continuously for many days. To test the limits of this technique, we specifically targeted GFP-Aequorin to the hypocretin-positive neurons of the hypothalamus. We found that neuroluminescence generated by this group of ~20 neurons was associated with periods of increased locomotor activity and identified two classes of neural activity corresponding to distinct swim latencies. Our neuroluminescence assay can report, with high temporal resolution and sensitivity, the activity of small subsets of neurons during unrestrained behavior

Brain Changes in Long-Term Zen Meditators Using Proton Magnetic Resonance Spectroscopy and Diffusion Tensor Imaging: A Controlled Study

Introduction: This work aimed to determine whether 1H magnetic resonance imaging (MRI), magnetic resonance spectroscopy (MRS), diffusion-weighted imaging (DWI) and diffusion tensor imaging (DTI) are correlated with years of meditation and psychological variables in long-term Zen meditators compared to healthy non-meditator controls. Materials and Methods: Design. Controlled, cross-sectional study. Sample. Meditators were recruited from a Zen Buddhist monastery. The control group was recruited from hospital staff. Meditators were administered questionnaires on anxiety, depression, cognitive impairment and mindfulness. 1H-MRS (1.5 T) of the brain was carried out by exploring four areas: both thalami, both hippocampi, the posterior superior parietal lobule (PSPL) and posterior cingulate gyrus. Predefined areas of the brain were measured for diffusivity (ADC) and fractional anisotropy (FA) by MR-DTI. Results: Myo-inositol (mI) was increased in the posterior cingulate gyrus and Glutamate (Glu), N-acetyl-aspartate (NAA) and N-acetyl-aspartate/Creatine (NAA/Cr) was reduced in the left thalamus in meditators. We found a significant positive correlation between mI in the posterior cingulate and years of meditation (r = 0.518; p = .019). We also found significant negative correlations between Glu (r =20.452; p = .045), NAA (r =20.617; p = .003) and NAA/Cr (r =20.448; P = .047) in the left thalamus and years of meditation. Meditators showed a lower Apparent Diffusion Coefficient (ADC) in the left posterior parietal white matter than did controls, and the ADC was negatively correlated with years of meditation (r =20.4850, p = .0066). Conclusions: The results are consistent with the view that mI, Glu and NAA are the most important altered metabolites. This study provides evidence of subtle abnormalities in neuronal function in regions of the white matter in meditators

Molecular psychiatry of zebrafish

Due to their well-characterized neural development and high genetic homology to mammals, zebrafish (Danio rerio) have emerged as a powerful model organism in the field of biological psychiatry. Here, we discuss the molecular psychiatry of zebrafish, and its implications for translational neuroscience research and modeling central nervous system (CNS) disorders. In particular, we outline recent genetic and technological developments allowing for in vivo examinations, high-throughput screening and whole-brain analyses in larval and adult zebrafish. We also summarize the application of these molecular techniques to the understanding of neuropsychiatric disease, outlining the potential of zebrafish for modeling complex brain disorders, including attention-deficit/hyperactivity disorder (ADHD), aggression, post-traumatic stress and substance abuse. Critically evaluating the advantages and limitations of larval and adult fish tests, we suggest that zebrafish models become a rapidly emerging new field in modern molecular psychiatry research

Anisotropic Instabilities in Trapped Spinor Bose-Einstein Condensates

We theoretically investigate the effect of an anisotropic trap on the instability of the polar $(m_F=0)$ phase of a spin-1 Bose-Einstein condensate. By considering rigorously the spatial quantization, we show that the growth of the nascent ferromagnetic phase at short times becomes anisotropic with stronger oscillations in the magnetization correlation function along the unconfined direction.Comment: 8 pages, 6 figure

The genesis of cerebellar interneurons and the prevention of neural DNA damage require XRCC1

Defective responses to DNA single strand breaks underlie various neurodegenerative diseases. However, the exact role of this repair pathway during the development and maintenance of the nervous system is unclear. Using murine neural-specific inactivation of Xrcc1, a factor that is critical for the repair of DNA single strand breaks, we found a profound neuropathology that is characterized by the loss of cerebellar interneurons. This cell loss was linked to p53-dependent cell cycle arrest and occurred as interneuron progenitors commenced differentiation. Loss of Xrcc1 also led to the persistence of DNA strand breaks throughout the nervous system and abnormal hippocampal function. Collectively, these data detail the in vivo link between DNA single strand break repair and neurogenesis and highlight the diverse consequences of specific types of genotoxic stress in the nervous system

4-Aminopyridine-induced epileptogenesis depends on activation of mitogen-activated protein kinase ERK

Extracellular signal-regulated kinases such as ERK1 [p44 mitogen-activated protein kinase (MAPK)] and ERK2 (p42 MAPK) are activated in the CNS under physiological and pathological conditions such as ischemia and epilepsy. Here, we studied the activation state of ERK1/2 in rat hippocampal slices during application of the K+ channel blocker 4-aminopyridine (4AP, 50 lM), a procedure that enhances synaptic transmission and leads to the appearance of epileptiform activity. Hippocampal slices superfused with 4AP-containing medium exhibited a marked activation of ERK1/2 phosphorylation that peaked within about 20 min. These effects were not accompanied by changes in the activation state of c-Jun N-terminal kinase (JNK), another member of the MAP kinase superfamily. 4AP-induced ERK1/2 activation was inhibited by the voltage-gated Na+ channel blocker tetrodotoxin (1 lM). We also found that application of the ERK pathway inhibitors U0126 (50 lM) or PD98059 (100 lM) markedly reduced 4AP-induced epileptiform synchronization, thus abolishing ictal discharges in the CA3 area. The effects induced by U0126 or PD98059 were not associated with changes in the amplitude and latency of the field potentials recorded in the CA3 area following electrical stimuli delivered in the dentate hylus. These data demonstrate that activation of ERK1/2 accompanies the appearance of epileptiform activity induced by 4AP and suggest a cause-effect relationship between the ERK pathway and epileptiform synchronization