Slopes for higher rank Artin-Schreier-Witt Towers

We fix a monic polynomial $\bar f(x) \in \mathbb{F}_q[x]$ over a finite field of characteristic $p$, and consider the $\mathbb{Z}_{p^{\ell}}$-Artin-Schreier-Witt tower defined by $\bar f(x)$; this is a tower of curves $\cdots \to C_m \to C_{m-1} \to \cdots \to C_0 =\mathbb{A}^1$, whose Galois group is canonically isomorphic to $\mathbb{Z}_{p^\ell}$, the degree $\ell$ unramified extension of $\mathbb{Z}_p$, which is abstractly isomorphic to $(\mathbb{Z}_p)^\ell$ as a topological group. We study the Newton slopes of zeta functions of this tower of curves. This reduces to the study of the Newton slopes of L-functions associated to characters of the Galois group of this tower. We prove that, when the conductor of the character is large enough, the Newton slopes of the L-function asymptotically form a finite union of arithmetic progressions. As a corollary, we prove the spectral halo property of the spectral variety associated to the $\mathbb{Z}_{p^{\ell}}$-Artin-Schreier-Witt tower. This extends the main result in [DWX] from rank one case $\ell=1$ to the higher rank case $\ell\geq 1$.Comment: 20 page

Parametric and economic analysis of high-temperature cascade organic Rankine cycle with a biphenyl and diphenyl oxide mixture

High-temperature organic Rankine cycle (ORC) systems have the potential to improve the heat-to-power conversion efficiency and expand the temperature range for heat recovery, heat battery and solar power generation. Restricted by the critical temperature of the commonly used organic working fluids, the current ORC technology has a maximum working temperature of around 300 °C. This paper proposes a high-temperature cascade organic Rankine cycle (CORC) system using a biphenyl and diphenyl oxide (BDO) mixture as the top cycle fluid and conventional organic fluids for the bottom cycle. The BDO mixture has excellent heat stability over a wide operation condition from 12 °C to 400 °C in single-phase and binary-phase states. However, at present a detailed study on the ORC using the mixture is lacking. In this paper, a parametric analysis of the high-temperature CORC system is conducted. A mathematical model based on the equivalent hot side temperature is built to simulate the ORC efficiency. The thermodynamic and exergetic performances of the novel CORC system under different bottom ORC working fluids, mixing chamber temperatures, evaporation temperatures, and condensation temperatures are investigated. The results show the maximum thermal efficiency of the CORC system is 38.74 % and 40.26 % at top ORC evaporation temperatures of 360 °C and 400 °C. The largest exergy destruction takes place in the heat exchanger between the top and bottom ORCs. Besides, the heat regenerators have a significant impact on the thermodynamic performance and can elevate the CORC efficiency by about 4 %. The proposed system has a higher efficiency and a lower equipment cost than conventional steam Rankine cycle at 400 °C while eliminating the challenges of wet steam turbines

Risk factors for surgical site infection of pilon fractures

OBJECTIVES: Pilon fracture is a complex injury that is often associated with severe soft tissue damage and high rates of surgical site infection. The goal of this study was to analyze and identify independent risk factors for surgical site infection among patients undergoing surgical fixation of a pilon fracture. METHODS: The medical records of all pilon fracture patients who underwent surgical fixation from January 2010 to October 2012 were reviewed to identify those who developed a surgical site infection. Then, we constructed univariate and multivariate logistic regressions to evaluate the independent associations of potential risk factors with surgical site infection in patients undergoing surgical fixation of a pilon fracture. RESULTS: A total of 519 patients were enrolled in the study from January 2010 to October 2012. A total of 12 of the 519 patients developed a surgical site infection, for an incidence of 2.3%. These patients were followed for 12 to 29 months, with an average follow-up period of 19.1 months. In the final regression model, open fracture, elevated postoperative glucose levels (≥125 mg/dL), and a surgery duration of more than 150 minutes were significant risk factors for surgical site infection following surgical fixation of a pilon fracture. CONCLUSIONS: Open fractures, elevated postoperative glucose levels (≥125 mg/dL), and a surgery duration of more than 150 minutes were related to an increased risk for surgical site infection following surgical fixation of a pilon fracture. Patients exhibiting the risk factors identified in this study should be counseled regarding the possible surgical site infection that may develop after surgical fixation

DiffMimic: Efficient Motion Mimicking with Differentiable Physics

Motion mimicking is a foundational task in physics-based character animation. However, most existing motion mimicking methods are built upon reinforcement learning (RL) and suffer from heavy reward engineering, high variance, and slow convergence with hard explorations. Specifically, they usually take tens of hours or even days of training to mimic a simple motion sequence, resulting in poor scalability. In this work, we leverage differentiable physics simulators (DPS) and propose an efficient motion mimicking method dubbed DiffMimic. Our key insight is that DPS casts a complex policy learning task to a much simpler state matching problem. In particular, DPS learns a stable policy by analytical gradients with ground-truth physical priors hence leading to significantly faster and stabler convergence than RL-based methods. Moreover, to escape from local optima, we utilize a Demonstration Replay mechanism to enable stable gradient backpropagation in a long horizon. Extensive experiments on standard benchmarks show that DiffMimic has a better sample efficiency and time efficiency than existing methods (e.g., DeepMimic). Notably, DiffMimic allows a physically simulated character to learn Backflip after 10 minutes of training and be able to cycle it after 3 hours of training, while the existing approach may require about a day of training to cycle Backflip. More importantly, we hope DiffMimic can benefit more differentiable animation systems with techniques like differentiable clothes simulation in future research.Comment: ICLR 2023 Code is at https://github.com/jiawei-ren/diffmimic Project page is at https://diffmimic.github.io