Non-simple systoles on random hyperbolic surfaces for large genus

In this paper, we investigate the asymptotic behavior of the non-simple systole, which is the length of a shortest non-simple closed geodesic, on a random closed hyperbolic surface on the moduli space $\mathcal{M}_g$ of Riemann surfaces of genus $g$ endowed with the Weil-Petersson measure. We show that as the genus $g$ goes to infinity, the non-simple systole of a generic hyperbolic surface in $\mathcal{M}_g$ behaves exactly like $\log g$.Comment: 47 pages, 11 figures. Comments welcom

Two dimensional vertex-decorated Lieb lattice with exact mobility edges and robust flat bands

The mobility edge (ME) that marks the energy separating extended and localized states is a central concept in understanding the metal-insulator transition induced by disordered or quasiperiodic potentials. MEs have been extensively studied in three dimensional disorder systems and one-dimensional quasiperiodic systems. However, the studies of MEs in two dimensional (2D) systems are rare. Here we propose a class of 2D vertex-decorated Lieb lattice models with quasiperiodic potentials only acting on the vertices of a (extended) Lieb lattice. By mapping these models to the 2D Aubry-Andr\'{e} model, we obtain exact expressions of MEs and the localization lengths of localized states, and further demonstrate that the flat bands remain unaffected by the quasiperiodic potentials. Finally, we propose a highly feasible scheme to experimentally realize our model in a quantum dot array. Our results open the door to studying and realizing exact MEs and robust flat bands in 2D systems

Color-Perception-Guided Display Power Reduction for Virtual Reality

Battery life is an increasingly urgent challenge for today's untethered VR and AR devices. However, the power efficiency of head-mounted displays is naturally at odds with growing computational requirements driven by better resolution, refresh rate, and dynamic ranges, all of which reduce the sustained usage time of untethered AR/VR devices. For instance, the Oculus Quest 2, under a fully-charged battery, can sustain only 2 to 3 hours of operation time. Prior display power reduction techniques mostly target smartphone displays. Directly applying smartphone display power reduction techniques, however, degrades the visual perception in AR/VR with noticeable artifacts. For instance, the "power-saving mode" on smartphones uniformly lowers the pixel luminance across the display and, as a result, presents an overall darkened visual perception to users if directly applied to VR content. Our key insight is that VR display power reduction must be cognizant of the gaze-contingent nature of high field-of-view VR displays. To that end, we present a gaze-contingent system that, without degrading luminance, minimizes the display power consumption while preserving high visual fidelity when users actively view immersive video sequences. This is enabled by constructing a gaze-contingent color discrimination model through psychophysical studies, and a display power model (with respect to pixel color) through real-device measurements. Critically, due to the careful design decisions made in constructing the two models, our algorithm is cast as a constrained optimization problem with a closed-form solution, which can be implemented as a real-time, image-space shader. We evaluate our system using a series of psychophysical studies and large-scale analyses on natural images. Experiment results show that our system reduces the display power by as much as 24% with little to no perceptual fidelity degradation

Confidant: Customizing Transformer-based LLMs via Collaborative Edge Training

Transformer-based large language models (LLMs) have demonstrated impressive capabilities in a variety of natural language processing (NLP) tasks. Nonetheless, it is challenging to deploy and fine-tune LLMs on mobile edge devices with limited computing, memory, and energy budgets. In this paper, we propose Confidant, a multi-backend collaborative training framework for customizing state-of-the-art LLMs on commodity mobile devices like smartphones. Confidant partitions an LLM into several sub-models so that each fits into a mobile device's memory. A pipeline parallel training mechanism is further developed to ensure fast and efficient distributed training. In addition, we propose a novel backend scheduler to allocate different attention heads to heterogeneous compute hardware, including mobile CPU and GPUs, to maximize the compute resource utilization on each edge device. Our preliminary experimental results show that Confidant achieves at most 45.3% memory reduction and 8.03x inference speedup in practical settings.Comment: 6 pages, 7 figures; Submitted to HotMobile 202