Extremal asymmetric universal cloning machines

The trade-offs among various output fidelities of asymmetric universal cloning machines are investigated. First we find out all the attainable optimal output fidelities for the 1 to 3 asymmetric universal cloning machine and it turns out that there are two kinds of extremal asymmetric cloning machines which have to cooperate in order to achieve some of the optimal output fidelities. Second we construct a family of extremal cloning machines that includes the universal symmetric cloning machine as well as an asymmetric 1 to $1+N$ cloning machine for qudits with two different output fidelities such that the optimal trade-off between the measurement disturbance and state estimation is attained in the limit of infinite $N$.Comment: 4 pages 2 figure

Moderate deviations for the mildly stationary autoregressive models with dependent errors

In this paper, we consider the normalized least squares estimator of the parameter in a mildly stationary first-order autoregressive model with dependent errors which are modeled as a mildly stationary AR(1) process. By martingale methods, we establish the moderate deviations for the least squares estimators of the regressor and error, which can be applied to understand the near-integrated second order autoregressive processes. As an application, we obtain the moderate deviations for the Durbin-Watson statistic.Comment: Comments welcome. 28 page

Ternary system of pyrolytic lignin, mixed solvent, and water: phase diagram and implications

Bio-oil from biomass fast pyrolysis is considered to be an important feedstock for the production of renewable fuels and green chemicals. Fast pyrolysis bio-oil generally contains a water-soluble fraction (excluding water), a water-insoluble fraction (i.e., pyrolytic lignin, PL), and water in a single phase. However, phase separation can occur during bio-oil transport, storage, and processing. In this study, a mixed solvent (MS) is developed based on the compositions of various fast pyrolysis bio-oils produced from a wide range of feedstocks and reactor systems. Experiments are then carried out to investigate the phase behavior of the PL/MS/water ternary system. Several ternary phase diagrams are constructed for PL and its fractions, and the PL solubilities in various MS/water mixtures are also estimated. Under the experimental conditions, the PL solubility in the MS is high, i.e., ∼112 g per 100 g of MS. In the PL/MS/water system, an increase in water content to ∼17 wt % in the MS/water mixture leads to a slight increase in the PL solubility to a maximal value of ∼118 g per 100 g of MS/water mixture, followed by a gradual decrease in the PL solubility when the water content further increases. It is found that the phase stability of the PL/MS/ water system is strongly determined by the composition of the system. For example, the PL/MS/water system is always stable when the MS content is \u3e50 wt %, while the system is always phase-separated when the PL content is \u3e54 wt %. A comparison of the results for various PL fractions indicates that the molecular weight of PL can affect the ternary phase diagram, with the PL of a lower molecular weight having a higher solubility in the same MS/water mixture. The presence of free sugar (i.e., levoglucosan, present in bio-oil as solute) also influences the ternary phase diagram of the PL/MS/system, but only at a low water content (i.e., \u3c 20 wt %). The results suggest that such ternary diagrams may be potentially an important tool for predicting the phase separation of bio-oil, as a result of changes in the bio-oil chemistry in various processes (e.g., cold-water precipitation and aging). Please click Additional Files below to see the full abstract

Learning World Models with Identifiable Factorization

Extracting a stable and compact representation of the environment is crucial for efficient reinforcement learning in high-dimensional, noisy, and non-stationary environments. Different categories of information coexist in such environments -- how to effectively extract and disentangle these information remains a challenging problem. In this paper, we propose IFactor, a general framework to model four distinct categories of latent state variables that capture various aspects of information within the RL system, based on their interactions with actions and rewards. Our analysis establishes block-wise identifiability of these latent variables, which not only provides a stable and compact representation but also discloses that all reward-relevant factors are significant for policy learning. We further present a practical approach to learning the world model with identifiable blocks, ensuring the removal of redundants but retaining minimal and sufficient information for policy optimization. Experiments in synthetic worlds demonstrate that our method accurately identifies the ground-truth latent variables, substantiating our theoretical findings. Moreover, experiments in variants of the DeepMind Control Suite and RoboDesk showcase the superior performance of our approach over baselines