Testing and selecting cosmological models with ultra-compact radio quasars

In this paper, we place constraints on four alternative cosmological models under the assumption of the spatial flatness of the Universe: CPL, EDE, GCG and MPC. A new compilation of 120 compact radio quasars observed by very-long-baseline interferometry, which represents a type of new cosmological standard rulers, are used to test these cosmological models. Our results show that the fits on CPL obtained from the quasar sample are well consistent with those obtained from BAO. For other cosmological models considered, quasars provide constraints in agreement with those derived with other standard probes at $1\sigma$ confidence level. Moreover, the results obtained from other statistical methods including Figure of Merit, $Om(z)$ and statefinder diagnostics indicate that: (1) Radio quasar standard ruler could provide better statistical constraints than BAO for all cosmological models considered, which suggests its potential to act as a powerful complementary probe to BAO and galaxy clusters. (2) Turning to $Om(z)$ diagnostics, CPL, GCG and EDE models can not be distinguished from each other at the present epoch. (3) In the framework of statefinder diagnostics, MPC and EDE will deviate from $\rm{\Lambda}$CDM model in the near future, while GCG model cannot be distinguished from $\rm{\Lambda}$CDM model unless much higher precision observations are available.Comment: 12 pages, 8 figures, 1 tabl

Online Control with Adversarial Disturbance for Continuous-time Linear Systems

We study online control for continuous-time linear systems with finite sampling rates, where the objective is to design an online procedure that learns under non-stochastic noise and performs comparably to a fixed optimal linear controller. We present a novel two-level online algorithm, by integrating a higher-level learning strategy and a lower-level feedback control strategy. This method offers a practical and robust solution for online control, which achieves sublinear regret. Our work provides one of the first nonasymptotic results for controlling continuous-time linear systems a with finite number of interactions with the system

Neural Network Weights Do Not Converge to Stationary Points: An Invariant Measure Perspective

This work examines the deep disconnect between existing theoretical analyses of gradient-based algorithms and the practice of training deep neural networks. Specifically, we provide numerical evidence that in large-scale neural network training (e.g., ImageNet + ResNet101, and WT103 + TransformerXL models), the neural network's weights do not converge to stationary points where the gradient of the loss is zero. Remarkably, however, we observe that even though the weights do not converge to stationary points, the progress in minimizing the loss function halts and training loss stabilizes. Inspired by this observation, we propose a new perspective based on ergodic theory of dynamical systems to explain it. Rather than studying the evolution of weights, we study the evolution of the distribution of weights. We prove convergence of the distribution of weights to an approximate invariant measure, thereby explaining how the training loss can stabilize without weights necessarily converging to stationary points. We further discuss how this perspective can better align optimization theory with empirical observations in machine learning practice

Iteratively Learn Diverse Strategies with State Distance Information

In complex reinforcement learning (RL) problems, policies with similar rewards may have substantially different behaviors. It remains a fundamental challenge to optimize rewards while also discovering as many diverse strategies as possible, which can be crucial in many practical applications. Our study examines two design choices for tackling this challenge, i.e., diversity measure and computation framework. First, we find that with existing diversity measures, visually indistinguishable policies can still yield high diversity scores. To accurately capture the behavioral difference, we propose to incorporate the state-space distance information into the diversity measure. In addition, we examine two common computation frameworks for this problem, i.e., population-based training (PBT) and iterative learning (ITR). We show that although PBT is the precise problem formulation, ITR can achieve comparable diversity scores with higher computation efficiency, leading to improved solution quality in practice. Based on our analysis, we further combine ITR with two tractable realizations of the state-distance-based diversity measures and develop a novel diversity-driven RL algorithm, State-based Intrinsic-reward Policy Optimization (SIPO), with provable convergence properties. We empirically examine SIPO across three domains from robot locomotion to multi-agent games. In all of our testing environments, SIPO consistently produces strategically diverse and human-interpretable policies that cannot be discovered by existing baselines

Direct test of the FLRW metric from strongly lensed gravitational wave observations

The assumptions of large-scale homogeneity and isotropy underly the familiar Friedmann-Lemaître- Robertson-Walker (FLRW) metric that appears to be an accurate description of our Universe. In this paper, we propose a new strategy of testing the validity of the FLRW metric, based on the galactic-scale lensing systems where strongly lensed gravitational waves and their electromagnetic counterparts can be simultaneously detected. Each strong lensing system creates opportunity to infer the curvature parameter of the Universe. Consequently, combined analysis of many such systems will provide a model-independent tool to test the validity of the FLRW metric. Our study demonstrates that the thirdgeneration ground based GW detectors, like the Einstein Telescope (ET) and space-based detectors, like the Big Bang Observer (BBO), are promising concerning determination of the curvature parameter or possible detection of deviation from the FLRW metric. Such accurate measurements of the FLRW metric can become a milestone in precision GW cosmology

Early Identification and Diagnosis of Adrenal Crisis after Retroperitoneal Laparoscopic Unilateral Adrenalectomy

The occurrence of adrenal crisis after retroperitoneal laparoscopic unilateral adrenalectomy is usually concealed. If not timely diagnosis and treatment,it may cause shock, and even lead to death. It is very difficult to distinguish the clinical manifestations of adrenal crisis from nausea, vomiting, fatigue,gas separation from the lower diaphragm, abdominal pain, hypotension, hypertension, fever and hypothermia after operation. This makes it very difficult to identify and diagnose adrenal crisis early. This article mainly discusses the early recognition, diagnosis and treatment of adrenal crisis after unilateral adrenalectomy by retroperitoneoscope

In Situ Measurements of the Mechanical Properties of Electrochemically Deposited Li₂CO₃ and Li₂O Nanorods

Solid-electrolyte interface (SEI) is “the most important but least understood (component) in rechargeable Li-ion batteries”. The ideal SEI requires high elastic strength and can resist the penetration of a Li dendrite mechanically, which is vital for inhibiting the dendrite growth in lithium batteries. Even though Li$_{2}$CO$_{3}$ and Li$_{2}$O are identified as the major components of SEI, their mechanical properties are not well understood. Herein, SEI-related materials such as Li$_{2}$CO$_{3}$ and Li$_{2}$O were electrochemically deposited using an environmental transmission electron microscopy (ETEM), and their mechanical properties were assessed by in situ atomic force microscopy (AFM) and inverse finite element simulations. Both Li$_{2}$CO$_{3}$ and Li$_{2}$O exhibit nanocrystalline structures and good plasticity. The ultimate strength of Li$_{2}$CO$_{3}$ ranges from 192 to 330 MPa, while that of Li$_{2}$O is less than 100 MPa. These results provide a new understanding of the SEI and its related dendritic problems in lithium batteries