Theta liftings on double covers of orthogonal groups:

Thesis advisor: Solomon FriedbergWe study the generalized theta lifting between the double covers of split special orthogonal groups, which uses the non-minimal theta representations constructed by Bump, Friedberg and Ginzburg. We focus on the theta liftings of non-generic representations and make a conjecture that gives an upper bound of the first non-zero occurrence of the liftings, depending only on the unipotent orbit. We prove both global and local results that support the conjecture.Thesis (PhD) — Boston College, 2021.Submitted to: Boston College. Graduate School of Arts and Sciences.Discipline: Mathematics

Random organization and non-equilibrium hyperuniform fluids on a sphere

Random organizing hyperuniform fluid induced by reciprocal activation is a non-equilibrium fluid with vanishing density fluctuations at large length scales like crystals. Here we extend this new state of matter to a closed manifold, namely a spherical surface. We find that the random organization on a spherical surface behaves similar to that in two dimensional Euclidean space, and the absorbing transition on a sphere also belongs to the conserved directed percolation universality class. Moreover, the reciprocal activation can also induce a non-equilibrium hyperuniform fluid on a sphere. The spherical structure factor at the absorbing transition and the non-equilibrium hyperuniform fluid phases are scaled as $S(l \rightarrow 0) \sim (l/R)^{0.45}$ and $S(l \rightarrow 0) \sim l(l+1)/R^2$, respectively, which are both hyperuniform according to the definition of hyperuniformity on a sphere with $l$ the wave number and $R$ the radius of the spherical surface. We also consider the impact of inertia in realistic hyperuniform fluids, and it is found only adding an extra length-scale, above which hyperuniform scaling appears. Our finding suggests a new method for creating non-equilibrium hyperuniform fluids on closed manifolds to avoid boundary effects.Comment: Accepted in J. Chem. Phy

The Success of Cataract Surgery and the Preoperative Measurement of Retinal Function by Electrophysiological Techniques

Purpose. To study the effect of different electrophysiological methods to evaluate retinal function prior to cataract surgery. Methods. Cataract patients who had no significant other eye disease were chosen. VA, pattern visual evoked potential (PVEP), electroretinogram (ERG), and multifocal electroretinogram (mfERG) responses were measured from 150 cataract patients and 20 control subjects. Results. When the preoperative VA was more than 0.3 in cataract patients, the amplitude of PVEP was not significantly different between cataract and control subjects. The amplitude of central point mfERG was significantly lower in cataract patients compared with control group from HM to 0.8 of preoperative VA. The 95% confidence intervals (CIs) of the amplitudes of center point mfERG were calculated for a range of preoperative VA values. Most of the patients within 95% CI of the center point mfERG had a postoperative VA more than 0.5. Conclusions. The amplitude of central point mfERG in cataract patients was the most relevant parameter to the preoperative VA compared with PVEP and ERG. The 95% CI of the amplitude of central point mfERG for each level of VA could help to evaluate preoperative macular function which is used to predict the outcome of cataract surgery

Nonadiabatic simulation study of photoisomerization of azobenzene: Detailed mechanism and load-resisting capacity

Nonadiabatic dynamical simulations were carried out to study cis-to-trans isomerization of azobenzene under laser irradiation and/or external mechanical loads. We used a semiclassical electron-radiation-ion dynamics method that is able to describe the coevolution of the structural dynamics and the underlying electronic dynamics in a real-time manner. It is found that azobenzene photoisomerization occurs predominantly by an out-of-plane rotation mechanism even under a nontrivial resisting force of several tens of piconewtons. We have repeated the simulations systematically for a broad range of parameters for laser pulses, but could not find any photoisomerization event by a previously suggested in-plane inversion mechanism. The simulations found that the photoisomerization process can be held back by an external resisting force of 90 - 200 pN depending on the frequency and intensity of the lasers. This study also found that a pure mechanical isomerization is possible from the cis state if the azobenzene molecule is stretched by an external force of 1250 -1650 pN. Remarkably, the mechanical isomerization first proceeds through a mechanically activated inversion, and then is diverted to an ultrafast downhill rotation that accomplishes the isomerization. Implications of these findings to azobenzene-based nanomechanical devices are discussed.Comment: 9 printed page

Monitoring of the central blood pressure waveform via a conformal ultrasonic device.

Continuous monitoring of the central-blood-pressure waveform from deeply embedded vessels, such as the carotid artery and jugular vein, has clinical value for the prediction of all-cause cardiovascular mortality. However, existing non-invasive approaches, including photoplethysmography and tonometry, only enable access to the superficial peripheral vasculature. Although current ultrasonic technologies allow non-invasive deep-tissue observation, unstable coupling with the tissue surface resulting from the bulkiness and rigidity of conventional ultrasound probes introduces usability constraints. Here, we describe the design and operation of an ultrasonic device that is conformal to the skin and capable of capturing blood-pressure waveforms at deeply embedded arterial and venous sites. The wearable device is ultrathin (240 μm) and stretchable (with strains up to 60%), and enables the non-invasive, continuous and accurate monitoring of cardiovascular events from multiple body locations, which should facilitate its use in a variety of clinical environments

Exploring Universal Intrinsic Task Subspace via Prompt Tuning

Why can pre-trained language models (PLMs) learn universal representations and effectively adapt to broad NLP tasks differing a lot superficially? In this work, we empirically find evidence indicating that the adaptations of PLMs to various few-shot tasks can be reparameterized as optimizing only a few free parameters in a unified low-dimensional intrinsic task subspace, which may help us understand why PLMs could easily adapt to various NLP tasks with small-scale data. To find such a subspace and examine its universality, we propose an analysis pipeline called intrinsic prompt tuning (IPT). Specifically, we resort to the recent success of prompt tuning and decompose the soft prompts of multiple NLP tasks into the same low-dimensional nonlinear subspace, then we learn to adapt the PLM to unseen data or tasks by only tuning parameters in this subspace. In the experiments, we study diverse few-shot NLP tasks and surprisingly find that in a 250-dimensional subspace found with 100 tasks, by only tuning 250 free parameters, we can recover 97% and 83% of the full prompt tuning performance for 100 seen tasks (using different training data) and 20 unseen tasks, respectively, showing great generalization ability of the found intrinsic task subspace. Besides being an analysis tool, IPT could further bring practical benefits, such as improving the prompt tuning stability.Comment: Withdrawn from Findings of ACL 202