Approximate Recovery and Relative Entropy I: General von Neumann Subalgebras

We prove the existence of a universal recovery channel that approximately recovers states on a von Neumann subalgebra when the change in relative entropy, with respect to a fixed reference state, is small. Our result is a generalization of previous results that applied to type-I von Neumann algebras by Junge at al. [arXiv:1509.07127]. We broadly follow their proof strategy but consider here arbitrary von Neumann algebras, where qualitatively new issues arise. Our results hinge on the construction of certain analytic vectors and computations/estimations of their Araki–Masuda $$L_p$$ L p norms. We comment on applications to the quantum null energy condition.

High precision phase estimation with controllable sensitivity and dynamic range

High precision phase estimation is at the core of modern physics and practical applications. We investigate a method for high precision phase estimation via inserting a reference state which enables weak measurement technique to be used in wide dynamic range. A reference phase is introduced artificially to offset the time delay between preselection state and reference state. The sensitivity of measured phase and the linear dynamic range are controllable by adjusting reference phase. Moreover, an arbitrary postselection in measurement is applicable by choosing appropriate reference phase. This method has merits of controllable sensitivity and wide dynamic range, which shows great potential practical applications in high precision phase measurement.

Asymptotic properties of a class of linearly implicit schemes for weakly compressible Euler equations

In this paper we derive and analyse a class of linearly implicit schemes which includes the one of Feistauer and Kučera (J Comput Phys 224:208–221, 2007) as well as the class of RS-IMEX schemes (Schütz and Noelle in J Sci Comp 64:522–540, 2015; Kaiser et al. in J Sci Comput 70:1390–1407, 2017; Bispen et al. in Commun Comput Phys 16:307–347, 2014; Zakerzadeh in ESAIM Math Model Numer Anal 53:893–924, 2019). The implicit part is based on a Jacobian matrix which is evaluated at a reference state. This state can be either the solution at the old time level as in Feistauer and Kučera (2007), or a numerical approximation of the incompressible limit equations as in Zeifang et al. (Commun Comput Phys 27:292–320, 2020), or possibly another state. Subsequently, it is shown that this class of methods is asymptotically preserving under the assumption of a discrete Hilbert expansion. For a one-dimensional setting with some limitations on the reference state, the existence of a discrete Hilbert expansion is shown.

Complete model-free siding mode control (CMFSMC)

This study presents a complete model-free sliding mode control (CMFSMC) framework for the control of continuous-time non-affine nonlinear dynamic systems with unknown models. The novelty lies in the introduction of two equalities to assign the derivative of the sliding functions, which generally bridges the designs of those model-based SMC and model-free SMC. The study includes a double SMC (DSMC) design, state observer design, and desired reference state vector design (whole system performance), which all do not require plant nominal models. The preconditions required in the CMFSMC are the plant dynamic order and the boundedness of plant and disturbances. U-model based control (U-control) is incorporated to configure the whole control system, that is (1) taking model-free double SMC as a robust dynamic inverter to cancel simultaneously both nonlinearity and dynamics of the underlying plants, (2) taking a model-free state observer to estimate the state vector, (3) taking invariant controller to specify the whole control system performance in a linear output feedback control and to provide desired reference state vector. The related properties are studied to support the concept/configuration development and the analytical formulations. Simulated case studies demonstrate the developed framework and show off the transparent design procedure for applications and expansions.

Model Predictive Control-Based Integrated Path Tracking and Velocity Control for Autonomous Vehicle with Four-Wheel Independent Steering and Driving

This paper presents an MPC-based integrated control algorithm for an autonomous vehicle equipped with four-wheel independent steering and driving systems. The objective of this research is to improve the performance of the path and velocity tracking controllers by distributing the control effort to the multiple actuators. The proposed algorithm has two modules: reference state decision and MPC-based vehicle motion controller. Reference state decision module determines reference state profiles consisting of yaw rate and velocity in order to overcome the limitation of the error dynamics-based path tracking controller, which requires several assumptions on the reference path. The MPC-based vehicle motion controller is designed with a linear time-varying vehicle model in order to optimally allocate the control effort to each actuator. A linear time-varying MPC is adopted to reduce computational burden caused by using a non-linear one. The effectiveness of the proposed algorithm is validated via simulation on MATLAB/Simulink and CarSim. The simulation results show that the proposed algorithm improves the reference tracking performance by effectively distributing the control effort to the steering angle and driving force of each actuator.

Complete Model-Free Siding Mode Control (CMFSMC)

This study presents a Complete Model-Free Sliding Mode Control (CMFSMC) framework for the control of continuous-time nonaffine nonlinear dynamic systems with unknown models. The novelty lies in the introduction of two equalities to assign the derivative of the sliding functions, which generally bridges the designs of those model-based SMC and model-free SMC. The study includes a double SMC (DSMC) design, state observer design, and desired reference state vector design (whole system performance), which all do not require plant nominal models. The preconditions required in the CMFSMC are the plant dynamic order and the boundedness of plant and disturbances. U-model based control (U-control) is incorporated to configure the whole control system, that is 1) taking model-free double SMC as a robust dynamic inverter to cancel simultaneously both nonlinearity and dynamics of the underlying plants, 2) taking a model-free state observer to estimate the state vector, 3) taking invariant controller to specify the whole control system performance in a linear output feedback control and to provide desired reference state vector. The related properties are studied to support the concept/configuration development and the analytical formulations. Simulated case studies demonstrate the developed framework and show off the transparent design procedure for applications and expansions.

Statistical potentials from the Gaussian scaling behaviour of chain fragments buried within protein globules

Knowledge-based approaches use the statistics collected from protein data-bank structures to estimate effective interaction potentials between amino acid pairs. Empirical relations are typically employed that are based on the crucial choice of a reference state associated to the null interaction case. Despite their significant effectiveness, the physical interpretation of knowledge-based potentials has been repeatedly questioned, with no consensus on the choice of the reference state. Here we use the fact that the Flory theorem, originally derived for chains in a dense polymer melt, holds also for chain fragments within the core of globular proteins, if the average over buried fragments collected from different non-redundant native structures is considered. After verifying that the ensuing Gaussian statistics, a hallmark of effectively non-interacting polymer chains, holds for a wide range of fragment lengths, we use it to define a `bona fide' reference state. Notably, despite the latter does depend on fragment length, deviations from it do not. This allows to estimate an effective interaction potential which is not biased by the presence of correlations due to the connectivity of the protein chain. We show how different sequence-independent effective statistical potentials can be derived using this approach by coarse-graining the protein representation at varying levels. The possibility of defining sequence-dependent potentials is explored.

SARS CoV 2 Nsp5 Protein Causes Acute Lung Inflammation, a Dynamical Mathematical Model

In the present work we propose a dynamical mathematical model of the lung cells inflammation process in response to SARS-CoV-2 infection. In this scenario, our model suggests that the main protease Nsp5 enhances the inflammatory process by increasing the levels of NF κB, IL-6, Cox2, and PGE2 with respect to a reference state without the virus. This overstimulated immune state becomes autonomous of the signals from other immune cells, and does not shut down by itself neither when the external signals are turned off. Our model suggests that Nsp5 is effectively the switch to start inflammation, the consequent overproduction of the ACE2 receptor, and an important underlying cause of the most severe cases of COVID19.