Interaction of additive and quantization noises in digital PLLs

Phase-locked loops (PLLs) are a crucial component in modern communications systems. Comprising of a phase-detector, linear filter, and controllable oscillator, they are widely used in radio receivers to retrieve the information content from remote signals. As such, they are capable of signal demodulation, phase and carrier recovery, frequency synthesis, and clock synchronization. Continuous-time PLLs are a mature area of study, and have been covered in the literature since the early classical work by Viterbi [1] in the 1950s. With the rise of computing in recent decades, discrete-time digital PLLs (DPLLs) are a more recent discipline; most of the literature published dates from the 1990s onwards. Gardner [2] is a pioneer in this area. It is our aim in this work to address the difficulties encountered by Gardner [3] in his investigation of the DPLL output phase-jitter where additive noise to the input signal is combined with frequency quantization in the local oscillator. The model we use in our novel analysis of the system is also applicable to another of the cases looked at by Gardner, that is the DPLL with a delay element integrated in the loop. This gives us the opportunity to look at this system in more detail, our analysis providing some unique insights into the variance `dip' seen by Gardner in [3]. We initially provide background on the probability theory and stochastic processes. These branches of mathematics are the basis for the study of noisy analogue and digital PLLs. We give an overview of the classical analogue PLL theory as well as the background on both the digital PLL and circle map, referencing the model proposed by Teplinsky et al. [4, 5]. For our novel work, the case of the combined frequency quantization and noisy input from [3] is investigated first numerically, and then analytically as a Markov chain via its Chapman-Kolmogorov equation. The resulting delay equation for the steady-state jitter distribution is treated using two separate asymptotic analyses to obtain approximate solutions. It is shown how the variance obtained in each case matches well to the numerical results. Other properties of the output jitter, such as the mean, are also investigated. In this way, we arrive at a more complete understanding of the interaction between quantization and input noise in the first order DPLL than is possible using simulation alone. We also do an asymptotic analysis of a particular case of the noisy first-order DPLL with delay, previously investigated by Gardner [3]. We show a unique feature of the simulation results, namely the variance `dip' seen for certain levels of input noise, is explained by this analysis. Finally, we look at the second-order DPLL with additive noise, using numerical simulations to see the effects of low levels of noise on the limit cycles. We show how these effects are similar to those seen in the noise-free loop with non-zero initial conditions.

Self-organized vegetation patterning as a fingerprint of climate and human impact on semi-arid ecosystems

Spatially periodic vegetation patterns are well known in arid and semi-arid regions around the world. Mathematical models have been developed that attribute this phenomenon to a symmetry-breaking instability. Such models are based on the interplay between competitive and facilitative influences that the vegetation exerts on its own dynamics when it is constrained by arid conditions, but evidence for these predictions is still lacking. Moreover, not all models can account for the development of regularly spaced spots of bare ground in the absence of a soil prepattern. We applied Fourier analysis to high-resolution, remotely sensed data taken at either end of a 40-year interval in southern Niger. Statistical comparisons based on this textural characterization gave us broad-scale evidence that the decrease in rainfall over recent decades in the sub-Saharan Sahel has been accompanied by a detectable shift from homogeneous vegetation cover to spotted patterns marked by a spatial frequency of about 20 cycles km-1. Wood cutting and grazing by domestic animals have led to a much more marked transition in unprotected areas than in a protected reserve. Field measurements demonstrated that the dominant spatial frequency was endogenous rather than reflecting the spatial variation of any pre-existing heterogeneity in soil properties. All these results support the use of models that can account for periodic vegetation patterns without invoking substrate heterogeneity or anisotropy, and provide new elements for further developments, refinements and tests. This study underlines the potential of studying vegetation pattern properties for monitoring climatic and human impacts on the extensive fragile areas bordering hot deserts. Explicit consideration of vegetation self-patterning may also improve our understanding of vegetation and climate interactions in arid areas. © 2006 The Authors.

Low demographic variability in wild primate populations: fitness impacts of variation, covariation, and serial correlation in vital rates.

In a stochastic environment, long-term fitness can be influenced by variation, covariation, and serial correlation in vital rates (survival and fertility). Yet no study of an animal population has parsed the contributions of these three aspects of variability to long-term fitness. We do so using a unique database that includes complete life-history information for wild-living individuals of seven primate species that have been the subjects of long-term (22-45 years) behavioral studies. Overall, the estimated levels of vital rate variation had only minor effects on long-term fitness, and the effects of vital rate covariation and serial correlation were even weaker. To explore why, we compared estimated variances of adult survival in primates with values for other vertebrates in the literature and found that adult survival is significantly less variable in primates than it is in the other vertebrates. Finally, we tested the prediction that adult survival, because it more strongly influences fitness in a constant environment, will be less variable than newborn survival, and we found only mixed support for the prediction. Our results suggest that wild primates may be buffered against detrimental fitness effects of environmental stochasticity by their highly developed cognitive abilities, social networks, and broad, flexible diets.

Impact of coverage-dependent marginal costs on optimal HPV vaccination strategies.

The effectiveness of vaccinating males against the human papillomavirus (HPV) remains a controversial subject. Many existing studies conclude that increasing female coverage is more effective than diverting resources into male vaccination. Recently, several empirical studies on HPV immunization have been published, providing evidence of the fact that marginal vaccination costs increase with coverage. In this study, we use a stochastic agent-based modeling framework to revisit the male vaccination debate in light of these new findings. Within this framework, we assess the impact of coverage-dependent marginal costs of vaccine distribution on optimal immunization strategies against HPV. Focusing on the two scenarios of ongoing and new vaccination programs, we analyze different resource allocation policies and their effects on overall disease burden. Our results suggest that if the costs associated with vaccinating males are relatively close to those associated with vaccinating females, then coverage-dependent, increasing marginal costs may favor vaccination strategies that entail immunization of both genders. In particular, this study emphasizes the necessity for further empirical research on the nature of coverage-dependent vaccination costs.

A COMPARISON OF MARKET CLEARING TOOLS IN ELECTRICITY SYSTEMS

To maintain a strict balance between demand and supply in the US power systems, the Independent System Operators (ISOs) schedule power plants and determine electricity prices using a market clearing model. This model determines for each time period and power plant, the times of startup, shutdown, the amount of power production, and the provisioning of spinning and non-spinning power generation reserves, etc. Such a deterministic optimization model takes as input the characteristics of all the generating units such as their power generation installed capacity, ramp rates, minimum up and down time requirements, and marginal costs for production, as well as the forecast of intermittent energy such as wind and solar, along with the minimum reserve requirement of the whole system. This reserve requirement is determined based on the likelihood of outages on the supply side and on the levels of error forecasts in demand and intermittent generation. With increased installed capacity of intermittent renewable energy, determining the appropriate level of reserve requirements has become harder. Stochastic market clearing models have been proposed as an alternative to deterministic market clearing models. Rather than using a fixed reserve targets as an input, stochastic market clearing models take different scenarios of wind power into consideration and determine reserves schedule as output. Using a scaled version of the power generation system of PJM, a regional transmission organization (RTO) that coordinates the movement of wholesale electricity in all or parts of 13 states and the District of Columbia, and wind scenarios generated from BPA (Bonneville Power Administration) data, this paper explores a comparison of the performance between a stochastic and deterministic model in market clearing. The two models are compared in their ability to contribute to the affordability, reliability and sustainability of the electricity system, measured in terms of total operational costs, load shedding and air emissions. The process of building the models and running for tests indicate that a fair comparison is difficult to obtain due to the multi-dimensional performance metrics considered here, and the difficulty in setting up the parameters of the models in a way that does not advantage or disadvantage one modeling framework. Along these lines, this study explores the effect that model assumptions such as reserve requirements, value of lost load (VOLL) and wind spillage costs have on the comparison of the performance of stochastic vs deterministic market clearing models.

Thermodynamic and dynamic contributions to future changes in regional precipitation variance: focus on the Southeastern United States

© 2014, Springer-Verlag Berlin Heidelberg.The frequency and severity of extreme events are tightly associated with the variance of precipitation. As climate warms, the acceleration in hydrological cycle is likely to enhance the variance of precipitation across the globe. However, due to the lack of an effective analysis method, the mechanisms responsible for the changes of precipitation variance are poorly understood, especially on regional scales. Our study fills this gap by formulating a variance partition algorithm, which explicitly quantifies the contributions of atmospheric thermodynamics (specific humidity) and dynamics (wind) to the changes in regional-scale precipitation variance. Taking Southeastern (SE) United States (US) summer precipitation as an example, the algorithm is applied to the simulations of current and future climate by phase 5 of Coupled Model Intercomparison Project (CMIP5) models. The analysis suggests that compared to observations, most CMIP5 models (~60 %) tend to underestimate the summer precipitation variance over the SE US during the 1950–1999, primarily due to the errors in the modeled dynamic processes (i.e. large-scale circulation). Among the 18 CMIP5 models analyzed in this study, six of them reasonably simulate SE US summer precipitation variance in the twentieth century and the underlying physical processes; these models are thus applied for mechanistic study of future changes in SE US summer precipitation variance. In the future, the six models collectively project an intensification of SE US summer precipitation variance, resulting from the combined effects of atmospheric thermodynamics and dynamics. Between them, the latter plays a more important role. Specifically, thermodynamics results in more frequent and intensified wet summers, but does not contribute to the projected increase in the frequency and intensity of dry summers. In contrast, atmospheric dynamics explains the projected enhancement in both wet and dry summers, indicating its importance in understanding future climate change over the SE US. The results suggest that the intensified SE US summer precipitation variance is not a purely thermodynamic response to greenhouse gases forcing, and cannot be explained without the contribution of atmospheric dynamics. Our analysis provides important insights to understand the mechanisms of SE US summer precipitation variance change. The algorithm formulated in this study can be easily applied to other regions and seasons to systematically explore the mechanisms responsible for the changes in precipitation extremes in a warming climate.

A population model of folate-mediated one-carbon metabolism.

BACKGROUND: Previous mathematical models for hepatic and tissue one-carbon metabolism have been combined and extended to include a blood plasma compartment. We use this model to study how the concentrations of metabolites that can be measured in the plasma are related to their respective intracellular concentrations. METHODS: The model consists of a set of ordinary differential equations, one for each metabolite in each compartment, and kinetic equations for metabolism and for transport between compartments. The model was validated by comparison to a variety of experimental data such as the methionine load test and variation in folate intake. We further extended this model by introducing random and systematic variation in enzyme activity. OUTCOMES AND CONCLUSIONS: A database of 10,000 virtual individuals was generated, each with a quantitatively different one-carbon metabolism. Our population has distributions of folate and homocysteine in the plasma and tissues that are similar to those found in the NHANES data. The model reproduces many other sets of clinical data. We show that tissue and plasma folate is highly correlated, but liver and plasma folate much less so. Oxidative stress increases the plasma S-adenosylmethionine/S-adenosylhomocysteine (SAM/SAH) ratio. We show that many relationships among variables are nonlinear and in many cases we provide explanations. Sampling of subpopulations produces dramatically different apparent associations among variables. The model can be used to simulate populations with polymorphisms in genes for folate metabolism and variations in dietary input.

The role of evacuation and fire modelling in the development of safer air travel

Computer based mathematical models describing the aircraft evacuation process and aircraft fire have a role to play in the design and development of safer aircraft, in the implementaion of safer and more rigorous certification criteria and in post mortuum accident investigation. As the cost and risk involved in performing large-scale fire/evacuation experiments for the next generation 'Very Large Aircraft' (VLA) are expected to be high, the development and use of these modelling tools may become essential if these aircraft are to prove a viable reality. By describing the present capabililties and limitations of the EXODUS evacuation model and associated fire models, this paper will examine the future development and data requirements of these models.

The airEXODUS evacuation model and its application to evacuation certification, crew training and accident investigation.

Computer based mathematical models describing the aircraft evacuation process have a vital role to play in the design and development of safer aircraft, in the implementation of safer and more rigorous certification criteria, cabin crew training and in post mortuum accident investigation. As the risk of personal injury and costs involved in performing large-scale evacuation experiments for the next generation 'Ultra High Capacity Aircraft' (UHCA) are expected to be high, the development and use of these evacuation modelling tools may become essential if these aircraft are to prove a viable reality. In this paper the capabilities and limitations of the airEXODUS evacuation model are described. Its successful application to the prediction of a recent certification trial, prior to the actual trial taking place, is described. Also described is a newly defined parameter known as OPS which can be used as a measure of evacuation trial optimality. In addition, sample evacuation simulations in the presence of fire atmospheres are described. Finally, the data requiremnets of the airEXODUS evacuation model is discussed along with several projects currently underway at the the Univesity of Greenwich designed to obtain this data. Included in this discussion is a description of the AASK - Aircraft Accident Statistics and Knowledge - data base which contains detailed information from aircraft accident survivors.

The numerical simulation of aircraft evacuation and its application to aircraft design and certification

Computer based mathematical models describing the aircraft evacuation process have a vital role to play in the design and development of safer aircraft, in the implementation of safer and more rigorous certification criteria and in cabin crew training and post mortuum accident investigation. As the risk of personal injury and costs involved in performing large-scale evacuation experiments for the next generation `Ultra High Capacity Aircraft' (UHCA) are expected to be high, the development and use of these evacuation modelling tools may become essential if these aircraft are to prove a viable reality. This paper describes the capabilities and limitations of the airEXODUS evacuation model and some attempts at validation, including its successful application to the prediction of a recent certification trial, prior to the actual trial taking place, is described. Also described is a newly defined parameter known as OPS which can be used as a measure of evacuation trial optimality. In addition, sample evacuation simulations in the presence of fire atmospheres are described.

The numerical simulation of aircraft evacuation and its application to aircraft design and certification

Computer based mathematical models describing the aircraft evacuation process have a vital role to play in the design and development of safer aircraft, the implementation of safer and more rigorous certification criteria, in cabin crew training and post-mortem accident investigation. As the risk of personal injury and the costs involved in performing large-scale evacuation experiments for the next generation ultra high capacity aircraft (UHCA) are expected to be high, the development and use of these evacuation modelling tools may become essential if these aircraft are to prove a viable reality. This paper describes the capabilities and limitations of the airEXODUS evacuation model and some attempts at validation, including its successful application to the prediction of a recent certification trial, prior to the actual trial taking place. Also described is a newly defined performance parameter known as OPS that can be used as a measure of evacuation trial optimality. In addition, sample evacuation simulations in the presence of fire atmospheres are described.

The role of evacuation modelling in the development of safer air travel

Computer based mathematical models describing the aircraft evacuation process have a vital role to play in the design and development of safer aircraft, in the implementation of safer and more rigorous certification criteria and in post mortuuum accident investigation. As the risk of personal injury and costs involved in performing large-scale evacuation experiments for the next generation 'Ultra High Capacity Aircraft' (UHCA) are expected to be high, the development and use of these evacuation modelling tools may become essential if these aircraft are to prove a viable reality. In this paper the capabilities and limitation of the air-EXODUS evacuation model are described. Its successful application to the prediction of a recent certificaiton trial, prior to the actual trial taking place, is described. Also described is a newly defined parameter known as OPS which can be used as a measure of evacuation trial optimality. Finally, the data requirements of aircraft evacuation models is discussed along with several projects currently underway at the University of Greenwich designed to obtain this data. Included in this discussion is a description of the AASK - Aircraft Accident Statistics and Knowledge - data base which contains detailed information from aircraft accident survivors.

An aircraft accident database of human experience in evacuation derived from aviation accident reports

Computer based mathematical models describing the aircraft evacuation process have a vital role to play in aviation safety. However, such models have a heavy dependency on real evacuation data. The Fire Safety Engineering Group of the University of Greenwich is undertaking a large data extraction exercise in order to address this issue. This paper describes the extraction and application of data from aviation accident reports. To aid in the storage and analysis of the raw data, a computer database known as AASK (Aircraft Accident Statistics and Knowledge) is under development. AASK is being developed to store human observational and anecdotal data contained in accident reports and interview transcripts. AASK currently contains information from 25 survivable aviation accidents covering the period 04/04/77 to 06/08/95, involving some 2415 passengers, 2210 survivors, 205 fatalities and accounts from 669 people. Copyright © 1999 John Wiley & Sons, Ltd.

The airEXODUS evacuation model and its application to aircraft safety

Computer based mathematical models describing the aircraft evacuation process have a vital role to play in the design and development of safer aircraft, the implementation of safer and more rigorous certification criteria, in cabin crew training and post-mortem accident investigation. As the risk of personal injury and the costs involved in performing full-scale certification trials are high, the development and use of these evacuation modelling tools are essential. Furthermore, evacuation models provide insight into the evacuation process that is impossible to derive from a single certification trial. The airEXODUS evacuation model has been under development since 1989 with support from the UK CAA and the aviation industry. In addition to describing the capabilities of the airEXODUS evacuation model, this paper describes the findings of a recent CAA project aimed at investigating model accuracy in predicting past certification trials. Furthermore, airEXODUS is used to examine issues related to the Blended Wing Body (BWB) and Very Large Transport Aircraft (VLTA). These radical new aircraft concepts pose considerable challenges to designers, operators and certification authorities. BWB concepts involving one or two decks with possibly four or more aisles offer even greater challenges. Can the largest exits currently available cope with passenger flow arising from four or five aisles? Do we need to consider new concepts in exit design? Should the main aisle be made wider to accommodate more passengers? In this paper we discuss various issues evacuation related issues associated VLTA and BWB aircraft and demonstrate how computer based evacuation models can be used to investigage these issues through examination of aisle/exit configurations for BWB cabin layouts.

Single machine scheduling and due date assignment with positionally dependent processing times

We consider single machine scheduling and due date assignment problems in which the processing time of a job depends on its position in a processing sequence. The objective functions include the cost of changing the due dates, the total cost of discarded jobs that cannot be completed by their due dates and, possibly, the total earliness of the scheduled jobs. We present polynomial-time dynamic programming algorithms in the case of two popular due date assignment methods: CON and SLK. The considered problems are related to mathematical models of cooperation between the manufacturer and the customer in supply chain scheduling.