1,779 research outputs found
The stationary horizon as the central multi-type invariant measure in the KPZ universality class
The Kardar-Parisi-Zhang (KPZ) universality class describes a large class of
2-dimensional models of random growth, which exhibit universal scaling
exponents and limiting statistics. The last ten years has seen remarkable
progress in this area, with the formal construction of two interrelated
limiting objects, now termed the KPZ fixed point and the directed landscape
(DL). This dissertation focuses on a third central object, termed the
stationary horizon (SH). The SH was first introduced (and named) by Busani as
the scaling limit of the Busemann process in exponential last-passage
percolation. Shortly after, in the author's joint work with Sepp\"al\"ainen, it
was independently constructed in the context of Brownian last-passage
percolation. In this dissertation, we give an alternate construction of the SH,
directly from the description of its finite-dimensional distributions and
without reference to Busemann functions. From this description, we give several
exact distributional formulas for the SH. Next, we show the significance of the
SH as a key object in the KPZ universality class by showing that the SH is the
unique coupled invariant distribution for the DL. A major consequence of this
result is that the SH describes the Busemann process for the DL. From this
connection, we give a detailed description of the collection of semi-infinite
geodesics in the DL, from all initial points and in all directions. As a
further evidence of the universality of the SH, we show that it appears as the
scaling limit of the multi-species invariant measures for the totally
asymmetric simple exclusion process (TASEP). This dissertation is adapted from
two joint works with Sepp\"al\"ainen and two joint works with Busani and
Sepp\"al\"ainen.Comment: v2: minor typos corrected, PhD dissertation, University of
Wisconsin--Madison (2023). Contains material adapted from arXiv:2103.01172,
arXiv:2112.10729, arXiv:2203.13242 and arXiv:2211.04651. Chapter 3 gives an
alternate proof of the invariance of the SH shown in arXiv:2203.1324
Automatic and Accurate Performance Prediction in Distributed Systems
System performance is getting attention by industry as it affects
user experience, and much research focused on performance
evaluation approaches. Profiling is the most straightforward
approach to performance evaluation of software systems,
despite being limited to shallow analyses. Conversely,
software performance models excel in representing complex
interactions between components. Still, practitioners do not
integrate performance models in the software development
cycle, as the learning curve is too steep, and the approaches
do not adapt well to incremental development practices. In
this thesis, we propose three approaches towards automatic
learning of performance models. The first approach employs
a Recurrent Neural Network (RNN) to extract a full Queueing
Network (QN) model of the system; the second one calibrates
a Layered Queueing Network (LQN) using an RNN;
the third one presents ÎĽP, a framework that allows the user
to develop microservice systems and obtain the corresponding
LQN model from source code analysis. We considered
the microservices architecture as it is embraced by influential
players (e.g., Amazon, Netflix). Those approaches have
two advantages: i) minimal user intervention to flatten the
learning curve; ii) continuous synchronization between software
and performance model, such as each software development
iteration is reflected on the model. We validated our
approaches on several benchmarks taken from the literature.
The models we generate can be queried to predict the system
behavior under conditions significantly different from
the learning setting, and the results show sensible advancements
in the quality of the predictions
Modelling spread risk via time-change approach
The thesis considers two stochastic models for managing spread risk: i) the Duffie-Singleton model; ii) a model developed in the context of electricity spot price modelling, properly adapted to model spread risk, obtained by changing the Duffie-Singleton model with compound Poisson’s jumps with exponentially distributed jump size and a subordinated process as a random clock. The latter has a mean reverting jump component that leads to mean reversion in the level of credit spread in addition to the smooth mean reversion force. In order to calibrate the models the particle filtering technique is used, which allows for the estimate of real-world and risk-neutral probability distributions from time series of credit spread observations
Model-Predictive Control in Communication Networks
This dissertation consists of 8 papers, separated into 3 groups. The first 3 papers show, how model-predictive control can be applied to queueing networks and contain a detailed proof of throughput optimality. Additionally, numerous network examples are discussed, and a connection between the stability properties of assembly queues and random walks on quotient spaces is established. The next two papers develop algorithms, with which robust forecasts of delay can be obtained in queueing networks. To that end, a notion of robustness is proposed, and the network control policy is designed to meet this goal. For the last 3 papers, focus is shifted towards Age-of-Information. Two main contributions are the derivation of the distribution of the Age-of-Information values in networks with clocked working cycles and an algorithm for the exact numerical evaluation of the Age-of-Information state-space in a similar set-up
Energy-aware coordination of machine scheduling and support device recharging in production systems
Electricity generation from renewable energy sources is crucial for achieving climate targets, including greenhouse gas neutrality. Germany has made significant progress in increasing renewable energy generation. However, feed-in management actions have led to losses of renewable electricity in the past years, primarily from wind energy. These actions aim to maintain grid stability but result in excess renewable energy that goes unused. The lost electricity could have powered a multitude of households and saved CO2 emissions. Moreover, feed-in management actions incurred compensation claims of around 807 million Euros in 2021. Wind-abundant regions like Schleswig-Holstein are particularly affected by these actions, resulting in substantial losses of renewable electricity production. Expanding the power grid infrastructure is a costly and time-consuming solution to avoid feed-in management actions. An alternative approach is to increase local electricity consumption during peak renewable generation periods, which can help balance electricity supply and demand and reduce feed-in management actions. The dissertation focuses on energy-aware manufacturing decision-making, exploring ways to counteract feed-in management actions by increasing local industrial consumption during renewable generation peaks. The research proposes to guide production management decisions, synchronizing a company's energy consumption profile with renewable energy availability for more environmentally friendly production and improved grid stability
Statistical Modeling: Regression, Survival Analysis, and Time Series Analysis
Statistical Modeling provides an introduction to regression, survival analysis, and time series analysis for students who have completed calculus-based courses in probability and mathematical statistics. The book uses the R language to fit statistical models, conduct Monte Carlo simulation experiments and generate graphics. Over 300 exercises at the end of the chapters makes this an appropriate text for a class in statistical modeling.
Part 1: RegressionChapter 1: Simple Linear Regression Chapter 2: Inference in Simple Linear Regression Chapter 3: Topics in RegressionPart II: Survival Analysis Chapter 4: Probability Models in Survival AnalysisChapter 5: Statistical Methods in Survival Analysis Chapter 6: Topics in Survival Analysis Part III: Time Series Analysis Chapter 7: Basic Methods in Time Series AnalysisChapter 8: Modeling in Time Series Analysis Chapter 9: Topics in Time Series Analysi
Investigating the Effectiveness of Supermarket Transmission Control Measures on the Spread of COVID-19 in the Presence of Super-Spreaders through Agent-Based Modelling
An examination of the effectiveness of transmission control measures for COVID-19 in a supermarket setting, factoring for the inclusion of Super-Spreaders, must extend beyond the direct effects the control measure has on transmission in order to account for the indirect effects changes in human movement dynamics have on the spread of disease. The analysis makes use of Agent-Based Modelling simulation techniques to model changes in customer movement and disease transmission dynamics resulting from the isolated and combined implementation of COVID-19 transmission control measures. The bottom-up approach of agent-based modelling allows for the inclusion of heterogeneous, individual-level chances of infectiousness, compliance, and consumer behaviours, allowing for a more realistic representation of real-world behaviours. The model used for analysis is built entirely in the NetLogo environment, designed to be interactive, adaptable to user-varied inputs, and visually engaging. This allows for the model to adapt to changes in disease parameters and easily communicate model effects in a manner accessible to users in and out of the field. Control measures considered include: Vaccinations, Capacity Limiting, Social Distancing, Staff COVID-19 Testing, and the use of Sanitizers. Results indicate high levels of effectiveness for the use of Vaccinations at reducing transmission with minimal impact on customer dynamics. The results also highlight the negative effects changes in customer dynamics can have on transmission, indicated by increased shop-queue transmissions resulting from the use of Capacity Limiting or other measures slowing customer entrance to the shop. The positive effects of interactions between control measures are highlighted by the additional implementation of Social Distancing in reducing these increases. The implications of these findings involve the need to factor for changes in human movement dynamics when assessing the effectiveness of transmission control measures implemented in any environment. The findings further reinforce the benefits of implementing social distancing practises in conjunction with mechanisms that reduce the flow of movement, as well as the benefits of increased vaccination coverage in the population. Lastly, the findings provide an effective comparison of the control measures considered, allowing for the direct assessment of their implementation and the resulting effects on transmission and customer dynamics
Applications of Molecular Dynamics simulations for biomolecular systems and improvements to density-based clustering in the analysis
Molecular Dynamics simulations provide a powerful tool to study biomolecular systems with atomistic detail. The key to better understand the function and behaviour of these molecules can often be found in their structural variability. Simulations can help to expose this information that is otherwise experimentally hard or impossible to attain. This work covers two application examples for which a sampling and a characterisation of the conformational ensemble could reveal the structural basis to answer a topical research question. For the fungal toxin phalloidin—a small bicyclic peptide—observed product ratios in different cyclisation reactions could be rationalised by assessing the conformational pre-organisation of precursor fragments. For the C-type lectin receptor langerin, conformational changes induced by different side-chain protonations could deliver an explanation
of the pH-dependency in the protein’s calcium-binding. The investigations were accompanied by the continued development of a density-based clustering protocol into a respective software package, which is generally well applicable for the use case of extracting conformational states from Molecular Dynamics data
Simulating The Impact of Emissions Control on Economic Productivity Using Particle Systems and Puff Dispersion Model
A simulation platform is developed for quantifying the change in productivity of an economy under passive and active emission control mechanisms. The program uses object-oriented programming to code a collection of objects resembling typical stakeholders in an economy. These objects include firms, markets, transportation hubs, and boids which are distributed over a 2D surface. Firms are connected using a modified Prim’s Minimum spanning tree algorithm, followed by implementation of an all-pair shortest path Floyd Warshall algorithm for navigation purposes. Firms use a non-linear production function for transformation of land, labor, and capital inputs to finished product. A GA-Vehicle Routing Problem with multiple pickups and drop-offs is implemented for efficient delivery of commodities across multiple nodes in the economy. Boids are autonomous agents which perform several functions in the economy including labor, consumption, renting, saving, and investing. Each boid is programmed with several microeconomic functions including intertemporal choice models, Hicksian and Marshallian demand function, and labor-leisure model. The simulation uses a Puff Dispersion model to simulate the advection and diffusion of emissions from point and mobile sources in the economy. A dose-response function is implemented to quantify depreciation of a Boid’s health upon contact with these emissions. The impact of emissions control on productivity and air quality is examined through a series of passive and active emission control scenarios. Passive control examines the impact of various shutdown times on economic productivity and rate of emissions exposure experienced by boids. The active control strategy examines the effects of acceptable levels of emissions exposure on economic productivity. The key findings on 7 different scenarios of passive and active emissions controls indicate that rate of productivity and consumption in an economy declines with increased scrutiny of emissions from point sources. In terms of exposure rates, the point sources may not be the primary source of average exposure rates, however they significantly impact the maximum exposure rate experienced by a boid. Tightening of emissions control also negatively impacts the transportation sector by reducing the asset utilization rate as well as reducing the total volume of goods transported across the economy
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