468 research outputs found
Continuum percolation for Cox point processes
We investigate continuum percolation for Cox point processes, that is,
Poisson point processes driven by random intensity measures. First, we derive
sufficient conditions for the existence of non-trivial sub- and super-critical
percolation regimes based on the notion of stabilization. Second, we give
asymptotic expressions for the percolation probability in large-radius,
high-density and coupled regimes. In some regimes, we find universality,
whereas in others, a sensitive dependence on the underlying random intensity
measure survives.Comment: 21 pages, 5 figure
Geospatial Tessellation in the Agent-In-Cell Model: A Framework for Agent-Based Modeling of Pandemic
Agent-based simulation is a versatile and potent computational modeling
technique employed to analyze intricate systems and phenomena spanning diverse
fields. However, due to their computational intensity, agent-based models
become more resource-demanding when geographic considerations are introduced.
This study delves into diverse strategies for crafting a series of Agent-Based
Models, named "agent-in-the-cell," which emulate a city. These models,
incorporating geographical attributes of the city and employing real-world
open-source mobility data from Safegraph's publicly available dataset, simulate
the dynamics of COVID spread under varying scenarios. The "agent-in-the-cell"
concept designates that our representative agents, called meta-agents, are
linked to specific home cells in the city's tessellation. We scrutinize
tessellations of the mobility map with varying complexities and experiment with
the agent density, ranging from matching the actual population to reducing the
number of (meta-) agents for computational efficiency. Our findings demonstrate
that tessellations constructed according to the Voronoi Diagram of specific
location types on the street network better preserve dynamics compared to
Census Block Group tessellations and better than Euclidean-based tessellations.
Furthermore, the Voronoi Diagram tessellation and also a hybrid -- Voronoi
Diagram - and Census Block Group - based -- tessellation require fewer
meta-agents to adequately approximate full-scale dynamics. Our analysis spans a
range of city sizes in the United States, encompassing small (Santa Fe, NM),
medium (Seattle, WA), and large (Chicago, IL) urban areas. This examination
also provides valuable insights into the effects of agent count reduction,
varying sensitivity metrics, and the influence of city-specific factors
Cluster-based reduced-order modelling of a mixing layer
We propose a novel cluster-based reduced-order modelling (CROM) strategy of
unsteady flows. CROM combines the cluster analysis pioneered in Gunzburger's
group (Burkardt et al. 2006) and and transition matrix models introduced in
fluid dynamics in Eckhardt's group (Schneider et al. 2007). CROM constitutes a
potential alternative to POD models and generalises the Ulam-Galerkin method
classically used in dynamical systems to determine a finite-rank approximation
of the Perron-Frobenius operator. The proposed strategy processes a
time-resolved sequence of flow snapshots in two steps. First, the snapshot data
are clustered into a small number of representative states, called centroids,
in the state space. These centroids partition the state space in complementary
non-overlapping regions (centroidal Voronoi cells). Departing from the standard
algorithm, the probabilities of the clusters are determined, and the states are
sorted by analysis of the transition matrix. Secondly, the transitions between
the states are dynamically modelled using a Markov process. Physical mechanisms
are then distilled by a refined analysis of the Markov process, e.g. using
finite-time Lyapunov exponent and entropic methods. This CROM framework is
applied to the Lorenz attractor (as illustrative example), to velocity fields
of the spatially evolving incompressible mixing layer and the three-dimensional
turbulent wake of a bluff body. For these examples, CROM is shown to identify
non-trivial quasi-attractors and transition processes in an unsupervised
manner. CROM has numerous potential applications for the systematic
identification of physical mechanisms of complex dynamics, for comparison of
flow evolution models, for the identification of precursors to desirable and
undesirable events, and for flow control applications exploiting nonlinear
actuation dynamics.Comment: 48 pages, 30 figures. Revised version with additional material.
Accepted for publication in Journal of Fluid Mechanic
Alpha, Betti and the Megaparsec Universe: on the Topology of the Cosmic Web
We study the topology of the Megaparsec Cosmic Web in terms of the
scale-dependent Betti numbers, which formalize the topological information
content of the cosmic mass distribution. While the Betti numbers do not fully
quantify topology, they extend the information beyond conventional cosmological
studies of topology in terms of genus and Euler characteristic. The richer
information content of Betti numbers goes along the availability of fast
algorithms to compute them.
For continuous density fields, we determine the scale-dependence of Betti
numbers by invoking the cosmologically familiar filtration of sublevel or
superlevel sets defined by density thresholds. For the discrete galaxy
distribution, however, the analysis is based on the alpha shapes of the
particles. These simplicial complexes constitute an ordered sequence of nested
subsets of the Delaunay tessellation, a filtration defined by the scale
parameter, . As they are homotopy equivalent to the sublevel sets of
the distance field, they are an excellent tool for assessing the topological
structure of a discrete point distribution. In order to develop an intuitive
understanding for the behavior of Betti numbers as a function of , and
their relation to the morphological patterns in the Cosmic Web, we first study
them within the context of simple heuristic Voronoi clustering models.
Subsequently, we address the topology of structures emerging in the standard
LCDM scenario and in cosmological scenarios with alternative dark energy
content. The evolution and scale-dependence of the Betti numbers is shown to
reflect the hierarchical evolution of the Cosmic Web and yields a promising
measure of cosmological parameters. We also discuss the expected Betti numbers
as a function of the density threshold for superlevel sets of a Gaussian random
field.Comment: 42 pages, 14 figure
Decentralized Resource Allocation through Constrained Centroidal Voronoi Tessellations
The advancements in the fields of microelectronics facilitate incorporating team elements like coordination into engineering systems through advanced computing power. Such incorporation is useful since many engineering systems can be characterized as a collection of interacting subsystems each having access to local information, making local decisions, interacting with neighbors, and seeking to optimize local objectives that may well conflict with other subsystems, while also trying to optimize certain global objective. In this dissertation, we take advantage of such technological advancements to explore the problem of resource allocation through different aspects of the decentralized architecture like information structure in a team.
Introduced in 1968 as a toy example in the field of team decision theory to demonstrate the significance of information structure within a team, the Witsenhausen counterexample remained unsolved until the analytical person-by-person optimal solution was developed within the past decade. We develop a numerical method to implement the optimal laws and show that our laws coincide with the optimal affine laws. For the region where the optimal laws are non-linear, we show that our laws result in the lowest costs when compared with previously reported costs.
Recognizing that, in the framework of team decision theory, the difficulties arising from the non-classical information structure within a team currently limit its applicability in real-world applications, we move on to investigating Centroidal Voronoi Tessellations (CVTs) to solve the resource allocation problem. In one-dimensional spaces, a line communication network is sufficient to obtain CVTs in a decentralized manner, while being scalable to any number of agents in the team.
We first solve the static resource allocation problem where the amount of resource is fixed. Using such static allocation solution as an initialization step, we solve the dynamic resource allocation problem in a truly decentralized manner. Furthermore, we allow for flexibility in agents\u27 embedding their local preferences through what we call a civility model. We end the dissertation by revisiting the application of Demand-response in smart grids and demonstrate the developed decentralized dynamic resource allocation method to solve the problem of power allocation in a group of building loads
Cooperation among cancer cells as public goods games on Voronoi networks
Cancer cells produce growth factors that diffuse and sustain tumor proliferation, a form of cooperation among cancer cells that can be studied using mathematical models of public goods in the framework of evolutionary game theory. Cell populations, however, form heterogeneous networks that cannot be described by regular lattices or scale-free networks, the types of graphs generally used in the study of cooperation. To describe the dynamics of growth factor production in populations of cancer cells, I study public goods games on Voronoi networks, using a range of non-linear benefits that account for the known properties of growth factors, and different types of diffusion gradients. e results are surprisingly similar to those obtained on regular graphs and different from results on scale-free networks, revealing that network heterogeneity per se does not promote cooperation when public goods diffuse beyond one-step neighbours. e exact shape of the diffusion gradient is not crucial, however, whereas the type of non-linear benefit is an essential determinant of the dynamics. Public goods games on Voronoi networks can shed light on intra-tumor heterogeneity, the evolution of resistance to therapies that target growth factors, and new types of cell therapy
Graph Sphere: From Nodes to Supernodes in Graphical Models
High-dimensional data analysis typically focuses on low-dimensional
structure, often to aid interpretation and computational efficiency. Graphical
models provide a powerful methodology for learning the conditional independence
structure in multivariate data by representing variables as nodes and
dependencies as edges. Inference is often focused on individual edges in the
latent graph. Nonetheless, there is increasing interest in determining more
complex structures, such as communities of nodes, for multiple reasons,
including more effective information retrieval and better interpretability. In
this work, we propose a multilayer graphical model where we first cluster nodes
and then, at the second layer, investigate the relationships among groups of
nodes. Specifically, nodes are partitioned into "supernodes" with a
data-coherent size-biased tessellation prior which combines ideas from Bayesian
nonparametrics and Voronoi tessellations. This construct allows accounting also
for dependence of nodes within supernodes. At the second layer, dependence
structure among supernodes is modelled through a Gaussian graphical model,
where the focus of inference is on "superedges". We provide theoretical
justification for our modelling choices. We design tailored Markov chain Monte
Carlo schemes, which also enable parallel computations. We demonstrate the
effectiveness of our approach for large-scale structure learning in simulations
and a transcriptomics application.Comment: 71 pages, 18 figure
Automated Discovery of porous molecular materials facilitated by characterization of molecular porosity
Porous materials are critical to many industrial sectors, including petrochemicals, energy and water. Traditional porous polymers and zeolites are currently most widely employed within membranes, as adsorbents for separations and storage, and as heterogeneous catalysts. The emerging advanced porous materials, e.g. extended framework materials and molecular porous materials, can boost performance and energy-efficiency of the current technologies because of the unprecedented level of control of their structure and function. The enormous possibilities for tuning these materials by changing their building blocks mean that, in principle, optimally performing materials for a variety of applications can be systematically designed. However, the process of finding a set of optimal structures for a given application could take decades using the traditional materials development approaches. These is a substantial payoff for developing tools and approaches that can accelerate this process. Among advanced porous materials, porous molecular materials are one of the most recent members though they have already attracted significant interest......Programa de Doctorado en Ciencia e Ingeniería de Materiales por la Universidad Carlos III de MadridPresidente: Germán Ignacio Sastre Navarro.- Secretario: Javier Carrasco Rodríguez.- Vocal: Andreas Mavrantonaki
On the influence of spatial sampling on climate networks
Peer reviewedPublisher PD
Mathematical modeling of Lynch syndrome carcinogenesis
Cancer is one of the leading causes of disease-related death worldwide. In recent years, large amounts of data on cancer genetics and molecular characteristics have become available and accumulated with increasing speed. However, the current understanding of cancer as a disease is still limited by the lack of suitable models that allow interpreting these data in proper ways. Thus, the highly interdisciplinary research field of mathematical oncology has evolved to use mathematics, modeling, and simulations to study cancer with the overall goal to improve clinical patient care.
This dissertation aims at developing mathematical models and tools for different spatial scales of cancer development at the example of colorectal cancer in Lynch syndrome, the most common inherited colorectal cancer predisposition syndrome. We derive model-driven approaches for carcinogenesis at the DNA, cell, and crypt level, as well as data-driven methods for cancer-immune interactions at the DNA level and for the evaluation of diagnostic procedures at the Lynch syndrome population level. The developed models present an important step toward an improved understanding of hereditary cancer as a disease aiming at rapid implementation into clinical management guidelines and into the development of novel, innovative approaches for prevention and treatment
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