Accelerated leap methods for simulating discrete stochastic chemical kinetics

Biologists are increasingly conscious of the critical role that noise plays in cellular functions such as genetic regulation, often in connection with fluctuations in small numbers of key regulatory molecules. This has inspired the development of models that capture this fundamentally discrete and stochastic nature of cellular biology - most notably the Gillespie stochastic simulation algorithm (SSA). The SSA simulates a temporally homogeneous, discrete-state, continuous-time Markov process, and of course the corresponding probabilities and numbers of each molecular species must all remain positive. While accurately serving this purpose, the SSA can be computationally inefficient due to very small time stepping so faster approximations such as the Poisson and Binomial τ-leap methods have been suggested. This work places these leap methods in the context of numerical methods for the solution of stochastic differential equations (SDEs) driven by Poisson noise. This allows analogues of Euler-Maruyuma, Milstein and even higher order methods to be developed through the Itô-Taylor expansions as well as similar derivative-free Runge-Kutta approaches. Numerical results demonstrate that these novel methods compare favourably with existing techniques for simulating biochemical reactions by more accurately capturing crucial properties such as the mean and variance than existing methods.

A comparison of linear forecasting models and neural networks:an application to Euro inflation and Euro Divisia

Linear models reach their limitations in applications with nonlinearities in the data. In this paper new empirical evidence is provided on the relative Euro inflation forecasting performance of linear and non-linear models. The well established and widely used univariate ARIMA and multivariate VAR models are used as linear forecasting models whereas neural networks (NN) are used as non-linear forecasting models. It is endeavoured to keep the level of subjectivity in the NN building process to a minimum in an attempt to exploit the full potentials of the NN. It is also investigated whether the historically poor performance of the theoretically superior measure of the monetary services flow, Divisia, relative to the traditional Simple Sum measure could be attributed to a certain extent to the evaluation of these indices within a linear framework. Results obtained suggest that non-linear models provide better within-sample and out-of-sample forecasts and linear models are simply a subset of them. The Divisia index also outperforms the Simple Sum index when evaluated in a non-linear framework. © 2005 Taylor & Francis Group Ltd.

Techniques to improve forecasting models: applications to energy demand and price

This thesis is a study of three techniques to improve performance of some standard fore-casting models, application to the energy demand and prices. We focus on forecasting demand and price one-day ahead. First, the wavelet transform was used as a pre-processing procedure with two approaches: multicomponent-forecasts and direct-forecasts. We have empirically compared these approaches and found that the former consistently outperformed the latter. Second, adaptive models were introduced to continuously update model parameters in the testing period by combining ?lters with standard forecasting methods. Among these adaptive models, the adaptive LR-GARCH model was proposed for the fi?rst time in the thesis. Third, with regard to noise distributions of the dependent variables in the forecasting models, we used either Gaussian or Student-t distributions. This thesis proposed a novel algorithm to infer parameters of Student-t noise models. The method is an extension of earlier work for models that are linear in parameters to the non-linear multilayer perceptron. Therefore, the proposed method broadens the range of models that can use a Student-t noise distribution. Because these techniques cannot stand alone, they must be combined with prediction models to improve their performance. We combined these techniques with some standard forecasting models: multilayer perceptron, radial basis functions, linear regression, and linear regression with GARCH. These techniques and forecasting models were applied to two datasets from the UK energy markets: daily electricity demand (which is stationary) and gas forward prices (non-stationary). The results showed that these techniques provided good improvement to prediction performance.

Loss fluctuations and temporal correlations in network queues

We consider data losses in a single node of a packet- switched Internet-like network. We employ two distinct models, one with discrete and the other with continuous one-dimensional random walks, representing the state of a queue in a router. Both models have a built-in critical behavior with a sharp transition from exponentially small to finite losses. It turns out that the finite capacity of a buffer and the packet-dropping procedure give rise to specific boundary conditions which lead to strong loss rate fluctuations at the critical point even in the absence of such fluctuations in the data arrival process.

Forecasting the UK/US exchange rate with divisia monetary models and neural networks

This paper compares the UK/US exchange rate forecasting performance of linear and nonlinear models based on monetary fundamentals, to a random walk (RW) model. Structural breaks are identified and taken into account. The exchange rate forecasting framework is also used for assessing the relative merits of the official Simple Sum and the weighted Divisia measures of money. Overall, there are four main findings. First, the majority of the models with fundamentals are able to beat the RW model in forecasting the UK/US exchange rate. Second, the most accurate forecasts of the UK/US exchange rate are obtained with a nonlinear model. Third, taking into account structural breaks reveals that the Divisia aggregate performs better than its Simple Sum counterpart. Finally, Divisia-based models provide more accurate forecasts than Simple Sum-based models provided they are constructed within a nonlinear framework.

New career models in UK professional service firms:from up-or-out to up-and-going-nowhere?

In this paper, we empirically examine how professional service firms are adapting their promotion and career models to new market and institutional pressures, without losing the benefits of the traditional up-or-out tournament. Based on an in-depth qualitative study of 10 large UK based law firms we find that most of these firms do not have a formal up-or-out policy but that the up-or-out rule operates in practice. We also find that most firms have introduced alternative roles and a novel career policy that offers a holistic learning and development deal to associates without any expectation that unsuccessful candidates for promotion to partner should quit the firm. While this policy and the new roles formally contradict the principle of up-or-out by creating permanent non-partner positions, in practice they coexist. We conclude that the motivational power of the up-or-out tournament remains intact, notwithstanding the changes to the internal labour market structure of these professional service firms.

Classification of Chenopodium Genus Populations and Species Based on Continuous and Categorical Variables

2000 Mathematics Subject Classification: 62P10, 62H30

Latent Space and Social Psychological Models of Diffusion

The problem of social diffusion has animated sociological thinking on topics ranging from the spread of an idea, an innovation or a disease, to the foundations of collective behavior and political polarization. While network diffusion has been a productive metaphor, the reality of diffusion processes is often muddier. Ideas and innovations diffuse differently from diseases, but, with a few exceptions, the diffusion of ideas and innovations has been modeled under the same assumptions as the diffusion of disease. In this dissertation, I develop two new diffusion models for "socially meaningful" contagions that address two of the most significant problems with current diffusion models: (1) that contagions can only spread along observed ties, and (2) that contagions do not change as they spread between people. I augment insights from these statistical and simulation models with an analysis of an empirical case of diffusion - the use of enterprise collaboration software in a large technology company. I focus the empirical study on when people abandon innovations, a crucial, and understudied aspect of the diffusion of innovations. Using timestamped posts, I analyze when people abandon software to a high degree of detail.

To address the first problem, I suggest a latent space diffusion model. Rather than treating ties as stable conduits for information, the latent space diffusion model treats ties as random draws from an underlying social space, and simulates diffusion over the social space. Theoretically, the social space model integrates both actor ties and attributes simultaneously in a single social plane, while incorporating schemas into diffusion processes gives an explicit form to the reciprocal influences that cognition and social environment have on each other. Practically, the latent space diffusion model produces statistically consistent diffusion estimates where using the network alone does not, and the diffusion with schemas model shows that introducing some cognitive processing into diffusion processes changes the rate and ultimate distribution of the spreading information. To address the second problem, I suggest a diffusion model with schemas. Rather than treating information as though it is spread without changes, the schema diffusion model allows people to modify information they receive to fit an underlying mental model of the information before they pass the information to others. Combining the latent space models with a schema notion for actors improves our models for social diffusion both theoretically and practically.

The empirical case study focuses on how the changing value of an innovation, introduced by the innovations' network externalities, influences when people abandon the innovation. In it, I find that people are least likely to abandon an innovation when other people in their neighborhood currently use the software as well. The effect is particularly pronounced for supervisors' current use and number of supervisory team members who currently use the software. This case study not only points to an important process in the diffusion of innovation, but also suggests a new approach -- computerized collaboration systems -- to collecting and analyzing data on organizational processes.

New methods for movement technique development in cross-country skiing using mathematical models and simulation

This Licentiate Thesis is devoted to the presentation and discussion of some new contributions in applied mathematics directed towards scientific computing in sports engineering. It considers inverse problems of biomechanical simulations with rigid body musculoskeletal systems especially in cross-country skiing. This is a contrast to the main research on cross-country skiing biomechanics, which is based mainly on experimental testing alone. The thesis consists of an introduction and five papers. The introduction motivates the context of the papers and puts them into a more general framework. Two papers (D and E) consider studies of real questions in cross-country skiing, which are modelled and simulated. The results give some interesting indications, concerning these challenging questions, which can be used as a basis for further research. However, the measurements are not accurate enough to give the final answers. Paper C is a simulation study which is more extensive than paper D and E, and is compared to electromyography measurements in the literature. Validation in biomechanical simulations is difficult and reducing mathematical errors is one way of reaching closer to more realistic results. Paper A examines well-posedness for forward dynamics with full muscle dynamics. Moreover, paper B is a technical report which describes the problem formulation and mathematical models and simulation from paper A in more detail. Our new modelling together with the simulations enable new possibilities. This is similar to simulations of applications in other engineering fields, and need in the same way be handled with care in order to achieve reliable results. The results in this thesis indicate that it can be very useful to use mathematical modelling and numerical simulations when describing cross-country skiing biomechanics. Hence, this thesis contributes to the possibility of beginning to use and develop such modelling and simulation techniques also in this context.

Development and Application of Predictive Models for Survival, Growth, and Death of Enteric Pathogens in Leafy Greens Supply Chain

Leafy greens are essential part of a healthy diet. Because of their health benefits, production and consumption of leafy greens has increased considerably in the U.S. in the last few decades. However, leafy greens are also associated with a large number of foodborne disease outbreaks in the last few years. The overall goal of this dissertation was to use the current knowledge of predictive models and available data to understand the growth, survival, and death of enteric pathogens in leafy greens at pre- and post-harvest levels. Temperature plays a major role in the growth and death of bacteria in foods. A growth-death model was developed for Salmonella and Listeria monocytogenes in leafy greens for varying temperature conditions typically encountered during supply chain. The developed growth-death models were validated using experimental dynamic time-temperature profiles available in the literature. Furthermore, these growth-death models for Salmonella and Listeria monocytogenes and a similar model for E. coli O157:H7 were used to predict the growth of these pathogens in leafy greens during transportation without temperature control. Refrigeration of leafy greens meets the purposes of increasing their shelf-life and mitigating the bacterial growth, but at the same time, storage of foods at lower temperature increases the storage cost. Nonlinear programming was used to optimize the storage temperature of leafy greens during supply chain while minimizing the storage cost and maintaining the desired levels of sensory quality and microbial safety. Most of the outbreaks associated with consumption of leafy greens contaminated with E. coli O157:H7 have occurred during July-November in the U.S. A dynamic system model consisting of subsystems and inputs (soil, irrigation, cattle, wildlife, and rainfall) simulating a farm in a major leafy greens producing area in California was developed. The model was simulated incorporating the events of planting, irrigation, harvesting, ground preparation for the new crop, contamination of soil and plants, and survival of E. coli O157:H7. The predictions of this system model are in agreement with the seasonality of outbreaks. This dissertation utilized the growth, survival, and death models of enteric pathogens in leafy greens during production and supply chain.

A study of electrochemical transport and diffuse charge dynamics using a Langevin equation

This thesis aims to develop new numerical and computational tools to study electrochemical transport and diffuse charge dynamics at small scales. Previous efforts at modeling electrokinetic phenomena at scales where the noncontinuum effects become significant have included continuum models based on the Poisson-Nernst-Planck equations and atomic simulations using molecular dynamics algorithms. Neither of them is easy to use or conducive to electrokinetic transport modeling in strong confinement or over long time scales. This work introduces a new approach based on a Langevin equation for diffuse charge dynamics in nanofluidic devices, which incorporates features from both continuum and atomistic methods. The model is then extended to include steric effects resulting from finite ion size, and applied to the phenomenon of double layer charging in a symmetric binary electrolyte between parallel-plate blocking electrodes, between which a voltage is applied. Finally, the results of this approach are compared to those of the continuum model based on the Poisson-Nernst-Planck equations.

Multi-level, Multi-stage and Stochastic Optimization Models for Energy Conservation in Buildings for Federal, State and Local Agencies

Energy Conservation Measure (ECM) project selection is made difficult given real-world constraints, limited resources to implement savings retrofits, various suppliers in the market and project financing alternatives. Many of these energy efficient retrofit projects should be viewed as a series of investments with annual returns for these traditionally risk-averse agencies. Given a list of ECMs available, federal, state and local agencies must determine how to implement projects at lowest costs. The most common methods of implementation planning are suboptimal relative to cost. Federal, state and local agencies can obtain greater returns on their energy conservation investment over traditional methods, regardless of the implementing organization. This dissertation outlines several approaches to improve the traditional energy conservations models. Any public buildings in regions with similar energy conservation goals in the United States or internationally can also benefit greatly from this research. Additionally, many private owners of buildings are under mandates to conserve energy e.g., Local Law 85 of the New York City Energy Conservation Code requires any building, public or private, to meet the most current energy code for any alteration or renovation. Thus, both public and private stakeholders can benefit from this research. The research in this dissertation advances and presents models that decision-makers can use to optimize the selection of ECM projects with respect to the total cost of implementation. A practical application of a two-level mathematical program with equilibrium constraints (MPEC) improves the current best practice for agencies concerned with making the most cost-effective selection leveraging energy services companies or utilities. The two-level model maximizes savings to the agency and profit to the energy services companies (Chapter 2). An additional model presented leverages a single congressional appropriation to implement ECM projects (Chapter 3). Returns from implemented ECM projects are used to fund additional ECM projects. In these cases, fluctuations in energy costs and uncertainty in the estimated savings severely influence ECM project selection and the amount of the appropriation requested. A risk aversion method proposed imposes a minimum on the number of “of projects completed in each stage. A comparative method using Conditional Value at Risk is analyzed. Time consistency was addressed in this chapter. This work demonstrates how a risk-based, stochastic, multi-stage model with binary decision variables at each stage provides a much more accurate estimate for planning than the agency’s traditional approach and deterministic models. Finally, in Chapter 4, a rolling-horizon model allows for subadditivity and superadditivity of the energy savings to simulate interactive effects between ECM projects. The approach makes use of inequalities (McCormick, 1976) to re-express constraints that involve the product of binary variables with an exact linearization (related to the convex hull of those constraints). This model additionally shows the benefits of learning between stages while remaining consistent with the single congressional appropriations framework.

Amazon forest structure generates diurnal and seasonal variability in light utilization.

The complex three-dimensional (3-D) structure of tropical forests generates a diversity of light environments for canopy and understory trees. Understanding diurnal and seasonal changes in light availability is critical for interpreting measurements of net ecosystem exchange and improving ecosystem models. Here, we used the Discrete Anisotropic Radiative Transfer (DART) model to simulate leaf absorption of photosynthetically active radiation (lAPAR) for an Amazon forest. The 3-D model scene was developed from airborne lidar data, and local measurements of leaf reflectance, aerosols, and PAR were used to model lAPAR under direct and diffuse illumination conditions. Simulated lAPAR under clear-sky and cloudy conditions was corrected for light saturation effects to estimate light utilization, the fraction of lAPAR available for photosynthesis. Although the fraction of incoming PAR absorbed by leaves was consistent throughout the year (0.80?0.82), light utilization varied seasonally (0.67?0.74), with minimum values during the Amazon dry season. Shadowing and light saturation effects moderated potential gains in forest productivity from increasing PAR during dry-season months when the diffuse fraction from clouds and aerosols was low. Comparisons between DART and other models highlighted the role of 3-D forest structure to account for seasonal changes in light utilization. Our findings highlight how directional illumination and forest 3-D structure combine to influence diurnal and seasonal variability in light utilization, independent of further changes in leaf area, leaf age, or environmental controls on canopy photosynthesis. Changing illumination geometry constitutes an alternative biophysical explanation for observed seasonality in Amazon forest productivity without changes in canopy phenology.

Hilbert Space Valued Signal Plus Noise Models: Analysis of Structural Breaks under High Dimensionality and Temporal Dependence

This thesis is concerned with change point analysis for time series, i.e. with detection of structural breaks in time-ordered, random data. This long-standing research field regained popularity over the last few years and is still undergoing, as statistical analysis in general, a transformation to high-dimensional problems. We focus on the fundamental »change in the mean« problem and provide extensions of the classical non-parametric Darling-Erdős-type cumulative sum (CUSUM) testing and estimation theory within highdimensional Hilbert space settings. In the first part we contribute to (long run) principal component based testing methods for Hilbert space valued time series under a rather broad (abrupt, epidemic, gradual, multiple) change setting and under dependence. For the dependence structure we consider either traditional m-dependence assumptions or more recently developed m-approximability conditions which cover, e.g., MA, AR and ARCH models. We derive Gumbel and Brownian bridge type approximations of the distribution of the test statistic under the null hypothesis of no change and consistency conditions under the alternative. A new formulation of the test statistic using projections on subspaces allows us to simplify the standard proof techniques and to weaken common assumptions on the covariance structure. Furthermore, we propose to adjust the principal components by an implicit estimation of a (possible) change direction. This approach adds flexibility to projection based methods, weakens typical technical conditions and provides better consistency properties under the alternative. In the second part we contribute to estimation methods for common changes in the means of panels of Hilbert space valued time series. We analyze weighted CUSUM estimates within a recently proposed »high-dimensional low sample size (HDLSS)« framework, where the sample size is fixed but the number of panels increases. We derive sharp conditions on »pointwise asymptotic accuracy« or »uniform asymptotic accuracy« of those estimates in terms of the weighting function. Particularly, we prove that a covariance-based correction of Darling-Erdős-type CUSUM estimates is required to guarantee uniform asymptotic accuracy under moderate dependence conditions within panels and that these conditions are fulfilled, e.g., by any MA(1) time series. As a counterexample we show that for AR(1) time series, close to the non-stationary case, the dependence is too strong and uniform asymptotic accuracy cannot be ensured. Finally, we conduct simulations to demonstrate that our results are practically applicable and that our methodological suggestions are advantageous.

Data surveillance for infectious diseases: models, complex networks and machine learning

In this thesis, we investigate the role of applied physics in epidemiological surveillance through the application of mathematical models, network science and machine learning. The spread of a communicable disease depends on many biological, social, and health factors. The large masses of data available make it possible, on the one hand, to monitor the evolution and spread of pathogenic organisms; on the other hand, to study the behavior of people, their opinions and habits. Presented here are three lines of research in which an attempt was made to solve real epidemiological problems through data analysis and the use of statistical and mathematical models. In Chapter 1, we applied language-inspired Deep Learning models to transform influenza protein sequences into vectors encoding their information content. We then attempted to reconstruct the antigenic properties of different viral strains using regression models and to identify the mutations responsible for vaccine escape. In Chapter 2, we constructed a compartmental model to describe the spread of a bacterium within a hospital ward. The model was informed and validated on time series of clinical measurements, and a sensitivity analysis was used to assess the impact of different control measures. Finally (Chapter 3) we reconstructed the network of retweets among COVID-19 themed Twitter users in the early months of the SARS-CoV-2 pandemic. By means of community detection algorithms and centrality measures, we characterized users’ attention shifts in the network, showing that scientific communities, initially the most retweeted, lost influence over time to national political communities. In the Conclusion, we highlighted the importance of the work done in light of the main contemporary challenges for epidemiological surveillance. In particular, we present reflections on the importance of nowcasting and forecasting, the relationship between data and scientific research, and the need to unite the different scales of epidemiological surveillance.