Unbounded Processes Research Articles

Generalized Inversion of Electrochemical Impedance Data for Battery Systems

Electrochemical Impedance Spectroscopy (EIS) is a key technique for taking a snapshot of an electrochemical system near equilibrium conditions. Due to the richness of the complex-valued dataset and its simple experimental operation, it is currently being investigated as a test to diagnosis battery health and degradation details. Nevertheless, challenges with use of EIS is in interpreting the measured impedance. Current methods for analysis involving either fitting simplified equivalent circuit models or inverting distribution of relaxation times with a singular basis function. Because of these methods' simplifications, their results sometime fail to capture both the complex and heterogeneous underlying physics.Here, we present a novel algorithm for the inversion of EIS data for battery systems, which generalizes the inversion problem to any given linear equivalent circuit model, allowing for the analysis of complicated electrochemical systems. Importantly, this algorithm provides two clear benefits. First, it allows for the analysis of both bounded and unbounded processes, something quite common to battery systems and is vital in understanding non-obvious relationships in degraded batteries. Second, the distribution of independent processes, which can correspond to different physical phenomena, are also inverted by this algorithm. These distributions contain vital features in the identification and prediction of battery state-of-health. Overall, this tool will be indispensable in the analysis of degradation extent over battery aging, and provide an algorithmic framework for interpreting EIS measurements of complicated electrochemical systems.

Optimal DC pension investment with square-root factor processes under stochastic income and inflation risks

ABSTRACT This paper studies optimally defined contribution (DC) pension investment problems under the expected utility maximization framework with stochastic income and inflation risks. The member has access to a financial market consisting of a risk-free asset (money account), an inflation-indexed bond, and a stock. The market price of volatility risk is assumed to depend on an affine-form, Markovian, square-root factor process, while the return rate and the volatility of the stock are possibly given by general non-Markovian, unbounded stochastic processes. This financial framework recovers the Black–Scholes model, constant elasticity of variance (CEV) model, Heston model, 3/2 model, 4/2 model, and some non-Markovian models as exceptional cases. To tackle the potentially non-Markovian structures, we adopt a backward stochastic differential equation (BSDE) approach. By solving the associated BSDEs explicitly, closed-form expressions for the optimal investment strategies and optimal value functions are obtained for the power, logarithmic, and exponential utility functions. Moreover, explicit solutions to some special cases of our portfolio model are provided. Finally, numerical examples are provided to illustrate the effects of model parameters on the optimal investment strategies under the 4/2 model.

Reference tracking stochastic model predictive control over unreliable channels and bounded control actions

A stochastic model predictive control framework over unreliable Bernoulli communication channels, in the presence of unbounded process noise and under bounded control inputs, is presented for tracking a reference signal. The data losses in the control channel are compensated by a carefully designed transmission protocol, and those of the sensor channel by a dropout compensator. A class of saturated, disturbance feedback policies is proposed for control in the presence of noisy dropout compensation. A reference governor is employed to generate trackable reference trajectories and stability constraints are employed to ensure mean-square boundedness of the reference tracking error. The overall approach yields a computationally tractable quadratic program, which can be iteratively solved online.

Mapping COVID-19: How web-based maps contribute to the infodemic

A proliferation of web-based maps have appeared depicting many different aspects of the spread of the novel coronavirus (SARS-CoV-2). In this commentary, we consider the usage of web-based mapping during the COVID-19 pandemic and argue that web maps have been widely misused for delivering public information on this fast moving, epidemiologically complex, and geographically unbounded process.

The dimensionality of niche space allows bounded and unbounded processes to jointly influence diversification

There are two prominent and competing hypotheses that disagree about the effect of competition on diversification processes. The first, the bounded hypothesis, suggests that species diversity is limited (bounded) by competition between species for finite ecological niche space. The second, the unbounded hypothesis, proposes that innovations associated with evolution render competition unimportant over macroevolutionary timescales. Here we use phylogenetically structured niche modelling to show that processes consistent with both of these diversification models drive species accumulation in conifers. In agreement with the bounded hypothesis, niche competition constrained diversification, and in line with the unbounded hypothesis, niche evolution and partitioning promoted diversification. We then analyse niche traits to show that these diversification enhancing and inhibiting processes can occur simultaneously on different niche dimensions. Together these results suggest a new hypothesis for lineage diversification based on the multi-dimensional nature of ecological niches that can accommodate both bounded and unbounded evolutionary processes.

Deadlock analysis of unbounded process networks

Deadlock detection in concurrent programs that create networks with arbitrary numbers of nodes is extremely complex and solutions either give imprecise answers or do not scale. To enable the analysis of such programs, (1) we define an algorithm for detecting deadlocks of a basic model featuring recursion and fresh name generation: the lam programs, and (2) we design a type system for value-passing CCS that returns lam programs. We show the soundness of the type system, and develop a type inference algorithm for it. The resulting algorithm is able to check deadlock-freedom of programs that cannot be handled by previous analyses, such as those that build unbounded networks.

Hermite approximation of a hyperbolic Fokker–Planck optimality system to control a piecewise-deterministic process

ABSTRACTThe Hermite spectral approximation of a hyperbolic Fokker–Planck (FP) optimality system arising in the control of an unbounded piecewise-deterministic process (PDP) is discussed. To control the probability density function (PDF) corresponding to the PDP process, an optimal control based on an FP strategy is considered. The resulting optimality system consists of a hyperbolic system with opposite-time orientation and an integral optimality condition equation. A Hermite spectral discretisation is investigated to approximate solutions to the optimality system in unbounded domains. It is proven that the proposed scheme satisfies the conservativity requirement of the PDFs. The spectral convergence rate of the discretisation scheme is proved and validated by numerical experiments.

Modelling Inflation Volatility

SummaryThis paper discusses estimation of US inflation volatility using time‐varying parameter models, in particular whether it should be modelled as a stationary or random walk stochastic process. Specifying inflation volatility as an unbounded process, as implied by the random walk, conflicts with priors beliefs, yet a stationary process cannot capture the low‐frequency behaviour commonly observed in estimates of volatility. We therefore propose an alternative model with a change‐point process in the volatility that allows for switches between stationary models to capture changes in the level and dynamics over the past 40 years. To accommodate the stationarity restriction, we develop a new representation that is equivalent to our model but is computationally more efficient. All models produce effectively identical estimates of volatility, but the change‐point model provides more information on the level and persistence of volatility and the probabilities of changes. For example, we find a few well‐defined switches in the volatility process and, interestingly, these switches line up well with economic slowdowns or changes of the Federal Reserve Chair. Moreover, a decomposition of inflation shocks into permanent and transitory components shows that a spike in volatility in the late 2000s was entirely on the transitory side and characterized by a rise above its long‐run mean level during a period of higher persistence. Copyright © 2015 John Wiley & Sons, Ltd.

Optimal investment–reinsurance strategy for mean–variance insurers with square-root factor process

This paper studies an optimal investment–reinsurance problem for an insurer with a surplus process represented by the Cramér–Lundberg model. The insurer is assumed to be a mean–variance optimizer. The financial market consists of one risk-free asset and one risky asset. The market price of risk depends on a Markovian, affine-form, square-root stochastic factor process, while the volatility and appreciation rate of the risky asset are given by non-Markovian, unbounded processes. The insurer faces the decision-making problem of choosing to purchase reinsurance, acquire new business and invest its surplus in the financial market such that the mean and variance of its terminal wealth is maximized and minimized simultaneously. We adopt a backward stochastic differential equation approach to solve the problem. Closed-form expressions for the efficient frontier and efficient strategy of the mean–variance problem are derived. Numerical examples are presented to illustrate our results in two special cases, the constant elasticity of variance model and Heston’s model.

(Re)Producing Nature in Pyrmont and Ultimo

AbstractUrban political ecology (UPE), as articulated by Heynen et al., is premised on the refusal to ontologically separate nature and society. The urban becomes representative of an unbounded process of ‘urbanisation’, a complex interplay between ecological, political, and economic processes that produce historically and geographically contingent outcomes. Importantly, it advances a historical conception of nature, and problems in and of nature, that necessarily encompasses the socio‐economic conditions of its production. This paper presents research into the formation of urban sustainability policy in Australia that draws on the theoretical insights offered by the UPE approach. Using one of Australia's largest urban regeneration projects as a focus, Pyrmont and Ultimo in Sydney, this paper discusses how the politics and economics of urban change and development framed possibilities of how urban environmental problems were firstly understood and, secondly, how they could be addressed. In doing so, this foreclosed alternative visions of urban policy that do not align with hegemonic forms of socio‐economic regulation.

Optimal convergence rates of high order Parzen windows with unbounded sampling

Abstract High order Parzen windows are considered with data drawn from unbounded sampling processes. Convergence analysis is established by imposing a moment hypothesis on the unbounded sampling outputs and some decay conditions on the marginal distributions. Our estimate of convergence rate is consistent with the previous result with bounded sampling.

Modelling Inflation Volatility

This paper discusses estimation of US inflation volatility using time varying parameter models, in particular whether it should be modelled as a stationary or random walk stochastic process. Specifying inflation volatility as an unbounded process, as implied by the random walk, conflicts with priors beliefs, yet a stationary process cannot capture the low frequency behaviour commonly observed in estimates of volatility. We therefore propose an alternative model with a change-point process in the volatility that allows for switches between stationary models to capture changes in the level and dynamics over the past forty years. To accommodate the stationarity restriction, we develop a new representation that is equivalent to our model but is computationally more efficient. All models produce effectively identical estimates of volatility, but the change-point model provides more information on the level and persistence of volatility and the probabilities of changes. For example, we find a few well defined switches in the volatility process and, interestingly, these switches line up well with economic slowdowns or changes of the Federal Reserve Chair. Moreover, a decomposition of inflation shocks into permanent and transitory components shows that a spike in volatility in the late 2000s was entirely on the transitory side and a characterized by a rise above its long run mean level during a period of higher persistence.

Statistical analysis of the moving least-squares method with unbounded sampling

Moving least-squares method is investigated with samples drawn from unbounded sampling processes. Convergence analysis is established by imposing incremental conditions on moments of sample output and window width. Satisfied convergence rates are derived by means of projection operator and some concentration inequalities.

Modelling Inflation Volatility

This paper discusses estimation of US inflation volatility using time varying parameter models, in particular whether it should be modelled as a stationary or random walk stochastic process. Specifying inflation volatility as an unbounded process, as implied by the random walk, conflicts with priors beliefs, yet a stationary process cannot capture the low frequency behaviour commonly observed in estimates of volatility. We therefore propose an alternative model with a change-point process in the volatility that allows for switches between stationary models to capture changes in the level and dynamics over the past forty years. To accommodate the stationarity restriction, we develop a new representation that is equivalent to our model but is computationally more efficient. All models produce effectively identical estimates of volatility, but the change-point model provides more information on the level and persistence of volatility and the probabilities of changes. For example, we find a few well defined switches in the volatility process and, interestingly, these switches line up well with economic slowdowns or changes of the Federal Reserve Chair. Moreover, a decomposition of inflation shocks into permanent and transitory components shows that a spike in volatility in the late 2000s was entirely on the transitory side and a characterized by a rise above its long run mean level during a period of higher persistence.

CONVERGENCE ANALYSIS OF COEFFICIENT-BASED REGULARIZATION UNDER MOMENT INCREMENTAL CONDITION

In this paper, we investigate coefficient-based regularized least squares regression problem in a data dependent hypothesis space. The learning algorithm is implemented with samples drawn by unbounded sampling processes and the error analysis is performed by a stepping-stone technique. A new error decomposition technique is proposed for the error analysis. The regularization parameters in our setting provide much more flexibility and adaptivity. Sharp learning rates are addressed by means of l2-empirical covering numbers under a moment hypothesis condition.

Tensed and non-tensed nominalization of the infinitive in Portuguese

This text presents an analysis of three types of nominalization of the infinitive in European Portuguese, characterized by distinct syntactic and semantic properties but all indicated by the presence of a determiner to the left of the infinitive. In the nominal infinitive, which has more nominal than verbal properties, a process is denoted, which is why culmination verbs are forbidden in most cases. In the literature it has also been stated that transitive verbs cannot be used as nominal infinitives. However, the presence of some aspectual modifiers that force a durative and unbounded process reading may allow the occurrence of these verbs. There is also the possibility of nominalizing a full infinitival clause, denoting a fact. Since this contains verbal and tensed properties, it may contain the inflected infinitive and in most cases involves the so called Aux-to-Comp movement, it is thus analyzed here as the nominalization of CP.

Coefficient-Based Regression with Non-Identical Unbounded Sampling

We investigate a coefficient-based least squares regression problem with indefinite kernels from non-identical unbounded sampling processes. Here non-identical unbounded sampling means the samples are drawn independently but not identically from unbounded sampling processes. The kernel is not necessarily symmetric or positive semi-definite. This leads to additional difficulty in the error analysis. By introducing a suitable reproducing kernel Hilbert space (RKHS) and a suitable intermediate integral operator, elaborate analysis is presented by means of a novel technique for the sample error. This leads to satisfactory results.

Observer-Based Quantized Feedback Control via Noisy Communication Channels

This paper investigates the input and output quantized control problem for stochastic linear systems with unbounded and possibly non-Gaussian process disturbance, where sensors, controllers and plants are connected by a noisy digital communication channel. Due to the unbounded process disturbance, a dynamic, logarithmic quantization scheme is proposed. An observer-based control policy is presented to stabilize the unstable plant in the mean square sense. Simulation results show the validity of the proposed quantization and control policy.

Quantized Feedback Control under Dynamic Logarithmic Quantization Schemes

This paper addresses the quantized feedback stabilization problem for networked control systems with unbounded process disturbance, where sensors, controllers and plants are connected by digital communication channels. A dynamic logarithmic quantization policy is proposed to stabilize the unstable plant. It is derived that the quantization policy can maintain stabilization in the presence of unbounded and possibly non-Gaussian process disturbance. Simulation results show the validity of the proposed scheme.

Fig-Frugivore Interactions Follow a Constrained Brownian Motion Model of Evolution in an Important Bird Area, West Africa

Understanding how ecosystems function is critical in order to shed light on processes that lead to species coexistence. Ficus species provide highly specialized niches for frugivores in tropical forests, but little is known about how Ficus-hugivore interactions evolve over time. Here we applied three approaches to investigate these interactions based on key parameters. We tested for a model of evolution that could explain interaction patterns, evaluated the phylogenetic signal, and assessed the evolutionary rate of niches generated by Ficus species. We showed that interactions are best explained by a Brownian motion model, indicating a random walk. However, the signal observed is lower than expected under this model, and at the same time the evolutionary rate provides evidence for niche conservatism. Such findings are incompatible with an unbounded Brownian process. We therefore propose that a random walk constrained by ecological forces towards a stabilizing selection could better explain fig-frugivore i...