Pure Time Research Articles

Algorithm 1016

In this article, we introduce the Python framework PyMGRIT, which implements the multigrid-reduction-in-time (MGRIT) algorithm for solving (non-)linear systems arising from the discretization of time-dependent problems. The MGRIT algorithm is a reduction-based iterative method that allows parallel-in-time simulations, i.e., calculating multiple time steps simultaneously in a simulation, using a time-grid hierarchy. The PyMGRIT framework includes many different variants of the MGRIT algorithm, ranging from different multigrid cycle types and relaxation schemes, various coarsening strategies, including time-only and space-time coarsening, and the ability to utilize different time integrators on different levels in the multigrid hierachy. The comprehensive documentation with tutorials and many examples and the fully documented code allow an easy start into the work with the package. The functionality of the code is ensured by automated serial and parallel tests using continuous integration. PyMGRIT supports serial runs suitable for prototyping and testing of new approaches, as well as parallel runs using the Message Passing Interface (MPI). In this manuscript, we describe the implementation of the MGRIT algorithm in PyMGRIT and present the usage from both a user and a developer point of view. Three examples illustrate different aspects of the package itself, especially running tests with pure time parallelism, as well as space-time parallelism through the coupling of PyMGRIT with PETSc or Firedrake.

Joint tracking coefficients and the time delay of a nonstationary linear system, preceded by a static nonlinearity

SummaryThe paper considers a block‐oriented nonlinear Hammerstein system that consists of a linear block with real‐valued time‐varying unknown coefficients and a pure time delay, preceded by the static nonlinearity. The joint tracking of linear block coefficients and the time delay while processing observation samples is under consideration. The difficulty of the tracking process consists in the initial nonconvexity of the objective function to be minimized, in respect of the time delay. To obtain current estimates of the true coefficients and the time delay it is necessary to overcome the multiextremality of the objective function. A global optimization problem could be solved by changing a form of the nonconvex objective function into a convex one. The optimization problem has been subdivided into two problems that are analyzed in this article, as well. The first one consists of removal of the objective function multiextremality in respect of the time delay, while hunting for the global extremum. Therefore, the well‐known approach based on the method of corrective operators, which is used to transform the multiextremal criterion into a unimodal function for the nonstationary Wiener system, is developed here for the Hammerstein one. The other problem consists of the applicability of unified adaptive algorithms, used for Wiener systems in the case of Hammerstein systems. The recursive parametric identification technique, based on the adaptive algorithm procedures, is developed here for the nonstationary block‐oriented Hammerstein systems, too. The applicability of algorithms is supported by various simulation tests solved by computer for distinct inputs and for two static nonlinearities.

Can Low Retirement Savings Be Rationalized?

Simple presentations of the life cycle model often suggest a constant level of real consumption in retirement. Similarly, financial planners commonly suggest that people save for retirement in such a way as to enable them to maintain a level retirement standard of living equal to their standard of living while working. However, constant consumption with age is only optimal under the precise and unlikely condition that the subjective rate of time preference is equal to the real interest rate. Most people exhibit a positive rate of pure time preference, and additionally discount the future by both mortality and morbidity risks. In comparison, the real interest rate is roughly 0%—and the term structure of interest rates suggests this condition is likely to persist. These considerations suggest that optimal consumption in the life cycle model declines with age. This finding has major implications for optimal retirement saving. For instance, we find that for many, perhaps most, people in the bottom half of the lifetime earnings distribution, it is optimal to spend out their retirement wealth well before death and to live on Social Security alone after that. Very low earners may find it optimal to not engage in retirement saving at all. <b>TOPICS:</b>Long-term/retirement investing, portfolio theory <b>Key Findings</b> ▪ Under plausible assumptions, optimal consumption in the life cycle model declines with age. ▪ For many people in the bottom half of the lifetime earnings distribution, it is optimal to spend out retirement wealth well before death and live on Social Security alone after that. ▪ These results stand in contrast to standard financial planning advice that people save for retirement in such a way as to enable them to maintain a level retirement standard of living equal to their standard of living while working.

Relative Prices and Climate Policy: How the Scarcity of Nonmarket Goods Drives Policy Evaluation

Climate change not only impacts production and market consumption but also the relative scarcity of nonmarket goods, such as environmental amenities. We study fundamental drivers of the resulting relative price changes, their potential magnitude, and their implications for climate policy in Nordhaus’s Dynamic Integrated Climate-Economy (DICE) model, thereby addressing one of its key criticisms. We propose plausible ranges for these relative prices changes based on best available evidence. Our central calibration reveals that accounting for relative prices is equivalent to decreasing pure time preference by 0.6 percentage points and leads to a more than 50 percent higher social cost of carbon. (JEL D61, H43, Q51, Q54, Q58)

Utility Maximization When Shorting American Options

An investor initially shorts a divisible American option $f$ and dynamically trades stock $S$ to maximize her expected utility. The investor faces the uncertainty of the exercise time of $f$, yet by observing the exercise time she would adjust her dynamic trading strategy accordingly. We thus investigate the robust utility maximization problem $V(x)=\sup_{(H,c)}\inf_{\eta}\mathbb{E}[U(x+H\cdot S-c(\eta(f)-p))]$, where $H$ is the dynamic trading strategy for $S$, $c$ represents the amount of $f$ the investor initially shorts, $\eta$ is the liquidation strategy for $f$, and $p$ is the initial price of $f$. We mainly consider two cases: In the first case, the investor shorts a fixed amount of $f$; i.e., without loss of generality, $c=1$ and $p=0$; in the second case, she statically trades $f$; i.e., $c$ can be any nonnegative number. We first show that in both cases $V(x)=\sup_{(H,c)}\inf_{\tau}\mathbb{E}[U(x+H\cdot S-c(f_\tau-p))]=\inf_{\rho}\sup_{(H,c)}$ $\mathbb{E}[U(x+H\cdot S-c(f_\rho-p))]$, where $\tau$ is a pure stopping time, $\rho$ is a randomized stopping time, and $H$ satisfies a certain nonanticipation condition. Then in the first case (i.e., $c=1$), we show that when $U$ is exponential, $V(x)=\inf_{\tau}\sup_{H}\mathbb{E}[U(x+H\cdot S-f_\tau)]$; for general utility, this equality may fail, yet it can be recovered if we in addition let $\tau$ be adapted to $H$ in a certain sense. Finally, in the second case ($c\in[0,\infty)$) we obtain a duality result for the robust utility maximization on an enlarged space.

Theoretical and experimental results of determination of the peeler-bar parameters of corn-thresher

A new type corn-thresher was developed and tested for farms in Uzbekistan. Unlike to the existent threshers, this corn-thresher peels the husks of corn-cobs and threshes the kernel. At first parameters of the peeler-bars were researched theoretically, then three types of peeler bars were installed symmetrically on the surface of rotor of the corn-thresher and compared experimentally. The corn-thresher works qualitatively and it requires least metal and energy. The weight of corn-thresher is just 350 kg, consumes power amount is 5 KW and the work performance of the thresher in the pure time is 4600 kg/hour. During the theoretical research, the results were determined that, width of the peeler-bar should be bigger or equal than 4.8 cm (b p ≥ 4.8 cm). Also, the distance between peeler-bar and concave should be equal to 38 mm (S c = 38). While we researched experimentally the types of peeler bars, three type of them, namely straight tooth, sloped tooth and fluted bar were tested. Their surface was compared between 36-44 mm distance of peeler-bar and concave. When the distance between sloped tooth peeler-bar and concave was 38-40 mm, we achieved to peeling well the husk of corn-cob, threshing better the kernels than other peelers, the most important was that any grain had not damaged when we analyzed results.

Anomalous Forms in Computer Music

Anomalous Forms in Computer Music

Quantum quench dynamics in the transverse-field Ising model: A numerical expansion in linked rectangular clusters

We study quantum quenches in the transverse-field Ising model defined on different lattice geometries such as chains, two- and three-leg ladders, and two-dimensional square lattices. Starting from fully polarized initial states, we consider the dynamics of the transverse and the longitudinal magnetization for quenches to weak, strong, and critical values of the transverse field. To this end, we rely on an efficient combination of numerical linked cluster expansions (NLCEs) and a forward propagation of pure states in real time. As a main result, we demonstrate that NLCEs comprising solely rectangular clusters provide a promising approach to study the real-time dynamics of two-dimensional quantum many-body systems directly in the thermodynamic limit. By comparing to existing data from the literature, we unveil that NLCEs yield converged results on time scales which are competitive to other state-of-the-art numerical methods.

Data-Driven Modeling of Wireless Power Transfer Systems With Multiple Transmitters

This article develops a new method of data-driven modeling for a class of multiple-transmitter single-receiver wireless power transfer (WPT) systems. A continuous-time multiple-input single-output (MISO) model with pure time delays is used to characterize the input–output behavior of the system, where the transfer functions associated with each input channel are not constrained to have the same denominator. Moreover, the time delays are allowed to be a fraction of the sampling interval in order to account for the delay effects that stem from circuit components and wireless communication, which are, by nature, often a fraction of the sampling interval. An optimal refined instrumental variable method is proposed to estimate the parameters and time delays of the MISO model based on sampled input–output data. In contrast to the conventional circuit-theory-based modeling methods that rely on circuit parameters and result in models which are often complex, the proposed data-based method yields parsimonious models, whose parameters are directly estimated from input–output data. Due to the easy availability of sampled data in control engineering applications, the proposed method is clearly more user-friendly, having a broad prospect for efficient operation of WPT systems, such as prediction, optimization, and control. Numerical and experimental results are presented to validate the effectiveness and merit of the proposed method.

Data-Driven Modeling of Wireless Power Transfer Systems With Slowly Time-Varying Parameters

This article considers the data-driven modeling of a class of phase-controlled wireless power transfer (WPT) systems, where the load may vary slowly with respect to time. The dominant mode analysis suggests that a model of the Hammerstein type, which consists of a static nonlinearity function, followed by a linear time-varying model with a pure time delay, is the best structure to describe the input–output relationship of the system. On this basis, we derive a small-signal model that is linear in the variables in order to aid control design and allow the associated model parameters to be estimated from sampled input–output data using the standard refined instrumental variable (RIV) method. In the presence of a time-varying load, however, the plant model parameters may not be correctly estimated if the load response is not removed. In order to address this problem, a new recursive RIV method is proposed, in which an effective technique is introduced to track the load response, so allowing the parameters and time delay of the time-varying model to be accurately estimated. The effectiveness of the proposed method is verified by applying it to both a simulation model and a laboratory system.

Testing monetary exchange rate models with the Westerlund panel cointegration test

Time series testing of long-run monetary models of exchange rate determination in most cases fails to support the conjectures of the theory. The empirical literature increasingly uses the panel technique when testing monetary exchange rate models because the power of the panel unit root and panel cointegration tests seems higher than the pure time series tests. In this paper we examine the validity of the monetary exchange rate models over the period 1996Q1-2011Q4 for US dollar exchange rates of 15 OECD countries using Westerlund’s 2007 panel cointegration tests. We found moderate empirical support for monetary exchange rate models.

Decoupling Adaptive Smith Prediction Model of Flatness Closed-Loop Control and Its Application

Flatness control system is characterized by multi-parameters, strong coupling, pure time delay, which complicate the establishment of an accurate mathematical model. Therefore, a control scheme that combines dynamic decoupling, PI (Proportion and Integral) control and adaptive Smith predictive compensation is proposed. To this end, a dynamic matrix is used to decouple the control system. A multivariable coupled pure time-delay system is transformed into several independent generalized single-loop pure time-delay systems. Then, a PI-adaptive Smith predictive controller is constructed for the decoupled generalized single-loop pure time-delay system. Simulations show that the scheme has a simple and feasible structure, and good control performance. When the mathematical model of the control system is inaccurate, the control performance of adaptive Smith control method is evidently better than that of the ordinary Smith control method. The model is successfully applied to the cold rolling production site through LabVIEW, and the control accuracy is within 5I. This study reveals a new solution to the problem of coupled pure time-delay in flatness control system.

Approximate and exact stability analysis of 1-DOF and 2-DOF single-actuator real-time hybrid substructuring

This paper presents approximate and exact stability analysis to determine the critical time delays of one and two degree of freedom (DOF) single-actuator real-time hybrid substructuring (RTHS). The approximate stability analysis is based on applying the Routh-Hurwitz stability criterion using a first-order Taylor expansion of the actuator dynamics represented by a constant gain and pure time delay. The exact stability analysis involves solving the critical frequencies first by canceling the exponential delay term of the closed-loop characteristic equation through multiplication by its complex conjugate. The exact critical time delays are then found using the phase of the closed-loop characteristic equation evaluated at the critical frequencies. These stability analysis techniques are applied to several 1-DOF and 2-DOF mass-spring configurations of single-actuator RTHS. Results show that the critical time delays are highly dependent on the mass, stiffness, and damping partitioning of the physical and numerical substructures as well as the actuator gain. This information provides useful insight into the stability behavior of a particular substructure partitioning configuration to evaluate the feasibility of conducting RTHS tests of these systems.

Negative weights in network time model

Time does not go backward. A negative duration, such as “time period” at first sight is difficult to interpret. Previous network techniques (CPM/PERT/PDM) did not support negative parameters and/or loops (potentially necessitating recursive calculations) in the model because of the limited computing and data storage capabilities of early computers. Monsieur Roy and John Fondahl implicitly introduced negative weights into network techniques to represent activities with fixed or estimated durations (MPM/PDM). Subsequently, the introduction of negative lead and/or lag times by software developers (IBM) apparently overcome the limitation of not allowing negative time parameters in time model. Referring to general digraph (Event on Node) representation where activities are represented by pairs of nodes and pairwise relative time restrictions are represented by weighted arrows, we can release most restraints in constructing the graph structure (incorporating the dynamic model of the inner logic of time plan), and a surprisingly flexible and handy network model can be developed that provides all the advantages of the abovementioned techniques. This paper aims to review the theoretical possibilities and technical interpretations (and use) of negative weights in network time models and discuss approximately 20 types of time-based restrictions among the activities of construction projects. We focus on pure relative time models, without considering other restrictions (such as calendar data, time-cost trade-off, resource allocation or other constraints).

Quantum walks as mathematical foundation for quantum gates

It is demonstrated that in gate-based quantum computing architectures quantum walk is a natural mathematical description of quantum gates. It originates from field-matter interaction driving the system, but is not attached to specific qubit designs and can be formulated for very general field-matter interactions. It is shown that, most generally, gates are described by a set of coined quantum walks. Rotating wave and resonant approximations for field-matter interaction simplify the walks, factorizing the coin, and leading to pure continuous time quantum walk description. The walks reside on a graph formed by the Hilbert space of all involved qubits and auxiliary states, if present. Physical interactions between different parts of the system necessary to propagate entanglement through such graph---quantum network---enter via reduction of symmetries in graph edges. Description for several single- and two-qubit gates are given as examples.

Fuzzy Sliding Mode Predictive Control of Air Flow Rate for a High-Speed High-Temperature Heat-Airflow Test System

To solve the problem of accurate control of air flow rate of a high-speed high-temperature heat-airflow test system, this paper introduces the working principle, establishes the mathematical model and analyzes the characteristics of the air supply subsystem. According to the characteristics of the air supply subsystem, such as time-varying parameters, time delay and disturbance, which are difficult to control accurately, a new fuzzy sliding mode predictive control algorithm is proposed based on fuzzy sliding mode control and Smith predictor. On this basis, the proposed control algorithm is simulated and studied. The results show that the proposed fuzzy sliding mode predictive control algorithm has good control performance. It can not only achieve high-performance tracking of step, slope, square wave and sinusoidal signals, but also can overcome the influence on the system caused by pure time delay, time-varying parameter and external disturbance.

Basic examination of two substructuring schemes for shake table tests

This study examines two basic substructuring schemes for shake table tests where the dynamics of the table is significantly affected by a specimen. The hybrid simulation (HS) scheme, commonly adopted in substructuring experiments, directly uses the output of a numerical substructure as an input signal to a physical substructure. The dynamical substructuring system (DSS) scheme, developed long after HS, uses feedforward and feedback controllers to minimise the control error produced by the outputs of numerical and physical substructures. Before examining these two schemes, this study introduces a systematic formulation for dividing a multi-degree-of-freedom emulate system into a numerical substructure and a physical substructure with a shake table. Then, controller designs for HS and DSS are discussed for the substructures. The two schemes with basic control approaches were numerically examined through substructuring tests for a linear 3DOF emulate system. DSS with stability was powerful even under a control condition with a pure time delay and inaccurate estimation of the table dynamics, whereas these factors degraded the HS performance. In additional simulations in which nonlinear characteristics were considered, the performance of DSS (HS) was degraded mainly by the nonlinear (inaccurate estimation of the table dynamics). It was found that the stability of substructures with nonlinear characteristics could be roughly assessed by the Nyquist stability criterion. These simulations with/without nonlinear characteristics clarified the performances of the HS and DSS schemes through basic control approaches and stability analysis under practical conditions.

Dynamics of a Predator–Prey-Competition System with Pure Delays

This paper deals with the non-autonomous Lotka–Volterra type one prey-two competitive predator systems with pure time delays. Based on the the comparison method and construction of the multiple Lyapunov functional, some new sufficient conditions on the boundedness, permanence, extinction and global attractivity of the system are established. In addition, two examples with numerical simulations are presented to illustrate the obtained theoretical results.

Integrating superfluids with superconducting qubit systems

Superfluid helium's low-loss dielectric properties, excellent thermal conductivity, and unique collective excitations make it an attractive candidate to incorporate into superconducting qubit systems. We controllably immerse a three-dimensional superconducting transmon qubit in superfluid helium-4 and measure the spectroscopic and coherence properties of the system. We find that the cavity, the qubit, and their coupling are all modified by the superfluid, which we analyze within the framework of circuit quantum electrodynamics (cQED). At at temperatures relevant to quantum computing experiments, the energy relaxation time of the qubit is not significantly changed by the presence of the superfluid, while the pure dephasing time modestly increases, which we attribute to improved thermalization of the microwave environment via the superfluid.

Tracking coefficients of a nonstationary system, followed by static nonlinearity jointly with the time delay

SummaryThis paper considers a block‐oriented nonlinear Wiener system that consists of a linear block with real time‐varying unknown coefficients and pure time delay followed by a static invertible nonlinearity. Consideration is concentrated on the joint linear block coefficients and time delay tracking by processing observation samples. Two problems are analyzed. The first one is the avoidance of mean‐squares prediction error function multiextremality for time delay while seeking the global minimum. The other problem consists of the applicability of unified adaptive algorithms, based on the schema with corrective operators for the Wiener system. An approach used to transform the multiextremal criterion into a unimodal function for a nonstationary linear system, in respect of the time delay, is developed and analyzed for a block‐oriented nonlinear Wiener system with time‐varying coefficients and a time delay. The recursive parametric identification approach, based on the method of corrective operators, is developed for the nonstationary dynamic Wiener system. Applicability of algorithms is supported by various simulation tests solved by a computer.