Transport Exponents of Sturmian Hamiltonians

We consider discrete Schr\"odinger operators with Sturmian potentials and study the transport exponents associated with them. Under suitable assumptions on the frequency, we establish upper and lower bounds for the upper transport exponents. As an application of these bounds, we identify the large coupling asymptotics of the upper transport exponents for frequencies of constant type. We also bound the large coupling asymptotics uniformly from above for Lebesgue-typical frequency. A particular consequence of these results is that for most frequencies of constant type, transport is faster than for Lebesgue almost every frequency. We also show quasi-ballistic transport for all coupling constants, generic frequencies, and suitable phases.Comment: 30 page

Quantification of the influence of drugs on zebrafish larvae swimming kinematics and energetics

The use of zebrafish larvae has aroused wide interest in the medical field for its potential role in the development of new therapies. The larvae grow extremely quickly and the embryos are nearly transparent which allows easy examination of its internal structures using fluorescent imaging techniques. Medical treatment of zebrafish larvae can directly influence its swimming behaviours. These behaviour changes are related to functional changes of central nervous system and transformations of the zebrafish body such as muscle mechanical power and force variation, which cannot be measured directly by pure experiment observation. To quantify the influence of drugs on zebrafish larvae swimming behaviours and energetics, we have developed a novel methodology to exploit intravital changes based on observed zebrafish locomotion. Specifically, by using an in-house MATLAB code to process the recorded live zebrafish swimming video, the kinematic locomotion equation of a 3D zebrafish larvae was obtained, and a customised Computational Fluid Dynamics tool was used to solve the fluid flow around the fish model which was geometrically the same as experimentally tested zebrafish. The developed methodology was firstly verified against experiment, and further applied to quantify the fish internal body force, torque and power consumption associated with a group of normal zebrafish larvae vs. those immersed in acetic acid and two neuroactive drugs. As indicated by our results, zebrafish larvae immersed in 0.01% acetic acid display approximately 30% higher hydrodynamic power and 10% higher cost of transport than control group. In addition, 500 μM diphenylhydantoin significantly decreases the locomotion activity for approximately 50% lower hydrodynamic power, whereas 100 mg/L yohimbine has not caused any significant influences on 5 dpf zebrafish larvae locomotion. The approach has potential to evaluate the influence of drugs on the aquatic animal’s behaviour changes and thus support the development of new analgesic and neuroactive drugs

BLISTER-regulated vegetative growth is dependent on the protein kinase domain of ER stress modulator IRE1A in Arabidopsis thaliana

The unfolded protein response (UPR) is required for protein homeostasis in the endoplasmic reticulum (ER) when plants are challenged by adverse environmental conditions. Inositol-requiring enzyme 1 (IRE1), the bifunctional protein kinase / ribonuclease, is an important UPR regulator in plants mediating cytoplasmic splicing of the mRNA encoding the transcription factor bZIP60. This activates the UPR signaling pathway and regulates canonical UPR genes. However, how the protein activity of IRE1 is controlled during plant growth and development is largely unknown. In the present study, we demonstrate that the nuclear and Golgi-localized protein BLISTER (BLI) negatively controls the activity of IRE1A/IRE1B under normal growth condition in Arabidopsis. Loss-of-function mutation of BLI results in chronic up-regulation of a set of both canonical UPR genes and non-canonical UPR downstream genes, leading to cell death and growth retardation. Genetic analysis indicates that BLI-regulated vegetative growth phenotype is dependent on IRE1A/IRE1B but not their canonical splicing target bZIP60. Genetic complementation with mutation analysis suggests that the D570/K572 residues in the ATP-binding pocket and N780 residue in the RNase domain of IRE1A are required for the activation of canonical UPR gene expression, in contrast, the D570/K572 residues and D590 residue in the protein kinase domain of IRE1A are important for the induction of non-canonical UPR downstream genes in the BLI mutant background, which correlates with the shoot growth phenotype. Hence, our results reveal the important role of IRE1A in plant growth and development, and BLI negatively controls IRE1A’s function under normal growth condition in plants