Nonlinear internal models for output regulation

In this paper we show how nonlinear internal models can be effectively used in the design of output regulators for nonlinear systems. This result provides a significant enhancement of the non-equilibrium theory for output regulation, which we have presented in the recent paper entitled "Limit Sets, Zero Dynamics, and Internal Models in the Problem of Nonlinear Output Regulation"

Simultaneous stabilization and simultaneous pole placement by nonswitching dynamic compensation

The 'simultaneous stabilization problem' is defined and theorems are proposed for its solution. The problem consists in answering the question: given an r-tuple G sub 1(s), G sub r(s) of p x m proper transfer functions, does there exist a compensator K(s) such that the closed loop systems G sub 1(s) (I+K(s)G sub 1(s)) (-1), G sub r(s) (I+K(s) G sub r(s)) (-1) are (internally) stable. This question arises in reliability theory, where G sub 2(s), G sub r(s) represents a plant G sub 1(s) operating in various modes of failure and K(s) is a nonswitching stabilizing compensator. It is important in the stability analysis and design of a plant which can be switched into various operating modes. The simultaneous stabilization problem can also apply to the stabilization of a nonlinear system which is linearized at several equilibria. Conditions are defined for pole placement and the generalized Sylvestor matrix is discussed

Algebraic geometric methods for the stabilizability and reliability of multivariable and of multimode systems

The extent to which feedback can alter the dynamic characteristics (e.g., instability, oscillations) of a control system, possibly operating in one or more modes (e.g., failure versus nonfailure of one or more components) is examined

Local non-Gaussianity from inflation

The non-Gaussian distribution of primordial perturbations has the potential to reveal the physical processes at work in the very early Universe. Local models provide a well-defined class of non-Gaussian distributions that arise naturally from the non-linear evolution of density perturbations on super-Hubble scales starting from Gaussian field fluctuations during inflation. I describe the delta-N formalism used to calculate the primordial density perturbation on large scales and then review several models for the origin of local primordial non-Gaussianity, including the cuvaton, modulated reheating and ekpyrotic scenarios. I include an appendix with a table of sign conventions used in specific papers.Comment: 21 pages, 1 figure, invited review to appear in Classical and Quantum Gravity special issue on non-linear and non-Gaussian cosmological perturbation

Renormalization of QCD_2

The low energy infrared scaling of the multi-color 2-dimensional quantum chromodynamics is determined in the framework of its bosonized model by using the functional renormalization group method with gliding sharp cut-off k in momentum space in the local potential approximation. The model exhibits a single phase with a superuniversal effective potential.Comment: 15 pages, 3 figures, final versio

Functional renormalization group with a compactly supported smooth regulator function

The functional renormalization group equation with a compactly supported smooth (CSS) regulator function is considered. It is demonstrated that in an appropriate limit the CSS regulator recovers the optimized one and it has derivatives of all orders. The more generalized form of the CSS regulator is shown to reduce to all major type of regulator functions (exponential, power-law) in appropriate limits. The CSS regulator function is tested by studying the critical behavior of the bosonized two-dimensional quantum electrodynamics in the local potential approximation and the sine-Gordon scalar theory for d<2 dimensions beyond the local potential approximation. It is shown that a similar smoothing problem in nuclear physics has already been solved by introducing the so called Salamon-Vertse potential which can be related to the CSS regulator.Comment: JHEP style, 11 pages, 2 figures, proofs corrected, accepted for publication by JHE

RELEASE (REdressing Long-tErm Antidepressant uSE): protocol for a 3-arm pragmatic cluster randomised controlled trial effectiveness-implementation hybrid type-1 in general practice

BACKGROUND: Many people experience withdrawal symptoms when they attempt to stop antidepressants. Withdrawal symptoms are readily misconstrued for relapse or ongoing need for medication, contributing to long-term use (> 12 months). Long-term antidepressant use is increasing internationally yet is not recommended for most people. Long-term use is associated with adverse effects including weight gain, sexual dysfunction, lethargy, emotional numbing and increased risk of falls and fractures. This study aims to determine the effectiveness of two multi-strategy interventions (RELEASE and RELEASE+) in supporting the safe cessation of long-term antidepressants, estimate cost-effectiveness, and evaluate implementation strategies. METHODS: DESIGN: 3-arm pragmatic cluster randomised controlled trial effectiveness-implementation hybrid type-1. SETTING: primary care general practices in southeast Queensland, Australia. POPULATION: adults 18 years or older taking antidepressants for longer than 1 year. Practices will be randomised on a 1.5:1:1 ratio of Usual care:RELEASE:RELEASE+. INTERVENTION: RELEASE for patients includes evidence-based information and resources and an invitation to medication review; RELEASE for GPs includes education, training and printable resources via practice management software. RELEASE+ includes additional internet support for patients and prescribing support including audit and feedback for GPs. OUTCOME MEASURES: the primary outcome is antidepressant use at 12 months self-reported by patients. Cessation is defined as 0 mg antidepressant maintained for at least 2 weeks. SECONDARY OUTCOMES: at 6 and 12 months are health-related quality of life, antidepressant side effects, well-being, withdrawal symptoms, emotional numbing, beliefs about antidepressants, depressive symptoms, and anxiety symptoms; and at 12 months 75% reduction in antidepressant dose; aggregated practice level antidepressant prescribing, and health service utilisation for costs. SAMPLE SIZE: 653 patients from 28 practices. A concurrent evaluation of implementation will be through mixed methods including interviews with up to 40 patients and primary care general practitioners, brief e-surveys, and study administrative data to assess implementation outcomes (adoption and fidelity). DISCUSSION: The RELEASE study will develop new knowledge applicable internationally on the effectiveness, cost-effectiveness, and implementation of two multi-strategy interventions in supporting the safe cessation of long-term antidepressants to improve primary health care and outcomes for patients. TRIAL REGISTRATION: ANZCTR, ACTRN12622001379707p. Registered on 27 October 2022

On the divergences of inflationary superhorizon perturbations

We discuss the infrared divergences that appear to plague cosmological perturbation theory. We show that within the stochastic framework they are regulated by eternal inflation so that the theory predicts finite fluctuations. Using the $\Delta N$ formalism to one loop, we demonstrate that the infrared modes can be absorbed into additive constants and the coefficients of the diagrammatic expansion for the connected parts of two and three-point functions of the curvature perturbation. As a result, the use of any infrared cutoff below the scale of eternal inflation is permitted, provided that the background fields are appropriately redefined. The natural choice for the infrared cutoff would of course be the present horizon; other choices manifest themselves in the running of the correlators. We also demonstrate that it is possible to define observables that are renormalization group invariant. As an example, we derive a non-perturbative, infrared finite and renormalization point independent relation between the two-point correlators of the curvature perturbation for the case of the free single field.Comment: 12 page

Infrared effects in inflationary correlation functions

In this article, I briefly review the status of infrared effects which occur when using inflationary models to calculate initial conditions for a subsequent hot, dense plasma phase. Three types of divergence have been identified in the literature: secular, "time-dependent" logarithms, which grow with time spent outside the horizon; "box-cutoff" logarithms, which encode a dependence on the infrared cutoff when calculating in a finite-sized box; and "quantum" logarithms, which depend on the ratio of a scale characterizing new physics to the scale of whatever process is under consideration, and whose interpretation is the same as conventional field theory. I review the calculations in which these divergences appear, and discuss the methods which have been developed to deal with them.Comment: Invited review for focus section of Classical & Quantum Gravity on nonlinear and nongaussian perturbation theory. Some improvements compared to version which will appear in CQG, especially in Sec. 2.3. 30 pages + references

Quantum Simulation of Tunneling in Small Systems

A number of quantum algorithms have been performed on small quantum computers; these include Shor's prime factorization algorithm, error correction, Grover's search algorithm and a number of analog and digital quantum simulations. Because of the number of gates and qubits necessary, however, digital quantum particle simulations remain untested. A contributing factor to the system size required is the number of ancillary qubits needed to implement matrix exponentials of the potential operator. Here, we show that a set of tunneling problems may be investigated with no ancillary qubits and a cost of one single-qubit operator per time step for the potential evolution. We show that physically interesting simulations of tunneling using 2 qubits (i.e. on 4 lattice point grids) may be performed with 40 single and two-qubit gates. Approximately 70 to 140 gates are needed to see interesting tunneling dynamics in three-qubit (8 lattice point) simulations.Comment: 4 pages, 2 figure