11,684 research outputs found
Cut finite element discretizations of cell-by-cell EMI electrophysiology models
The EMI (Extracellular-Membrane-Intracellular) model describes electrical
activity in excitable tissue, where the extracellular and intracellular spaces
and cellular membrane are explicitly represented. The model couples a system of
partial differential equations in the intracellular and extracellular spaces
with a system of ordinary differential equations on the membrane. A key
challenge for the EMI model is the generation of high-quality meshes conforming
to the complex geometries of brain cells. To overcome this challenge, we
propose a novel cut finite element method (CutFEM) where the membrane geometry
can be represented independently of a structured and easy-to-generated
background mesh for the remaining computational domain.
Starting from a Godunov splitting scheme, the EMI model is split into
separate PDE and ODE parts. The resulting PDE part is a non-standard elliptic
interface problem, for which we devise two different CutFEM formulations: one
single-dimensional formulation with the intra/extracellular electrical
potentials as unknowns, and a multi-dimensional formulation that also
introduces the electrical current over the membrane as an additional unknown
leading to a penalized saddle point problem. Both formulations are augmented by
suitably designed ghost penalties to ensure stability and convergence
properties that are insensitive to how the membrane surface mesh cuts the
background mesh. For the ODE part, we introduce a new unfitted discretization
to solve the membrane bound ODEs on a membrane interface that is not aligned
with the background mesh. Finally, we perform extensive numerical experiments
to demonstrate that CutFEM is a promising approach to efficiently simulate
electrical activity in geometrically resolved brain cells.Comment: 25 pages, 7 figure
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An investigation into the cultural and legal factors influencing the differential prosecution rate for female genital mutilation in England and France
Female Genital Mutilation (FGM) is a problem that both England and France face. Both countries agree that FGM is a criminal offence and that it constitutes child abuse. Accordingly, each nation has taken its own distinct measures in law and policy against the practice. These approaches have produced significantly divergent outcomes, particularly in the prosecution rates of offenders, with France leading in that regard.
This thesis seeks to understand why criminal justice outcomes differ so significantly between the two nations, despite many parallels between the historical and contemporary contexts of these two Western European neighbours. In order to do this, it seeks to explore the overarching, systemic forces at play within both paradigms, what the author has termed âthe Mediumâ. Furthermore, given that FGM within both France and England is a product of migrant communities having transported cultural practices into their new context, particular attention is paid to approaches to multiculturalism as a key aspect of the Medium for the purposes of this study. However, alongside this examination of the Medium, the study also explores the role of individual activism, and the agency of particular campaigners, termed âthe Human Catalystâ. It addresses the complex interplay between the Medium and the Human Catalyst, as a means of understanding their combined influence on the divergent pictures in respect of prosecuting FGM
Improving Heterogeneous Graph Learning with Weighted Mixed-Curvature Product Manifold
In graph representation learning, it is important that the complex geometric
structure of the input graph, e.g. hidden relations among nodes, is well
captured in embedding space. However, standard Euclidean embedding spaces have
a limited capacity in representing graphs of varying structures. A promising
candidate for the faithful embedding of data with varying structure is product
manifolds of component spaces of different geometries (spherical, hyperbolic,
or euclidean). In this paper, we take a closer look at the structure of product
manifold embedding spaces and argue that each component space in a product
contributes differently to expressing structures in the input graph, hence
should be weighted accordingly. This is different from previous works which
consider the roles of different components equally. We then propose
WEIGHTED-PM, a data-driven method for learning embedding of heterogeneous
graphs in weighted product manifolds. Our method utilizes the topological
information of the input graph to automatically determine the weight of each
component in product spaces. Extensive experiments on synthetic and real-world
graph datasets demonstrate that WEIGHTED-PM is capable of learning better graph
representations with lower geometric distortion from input data, and performs
better on multiple downstream tasks, such as word similarity learning, top-
recommendation, and knowledge graph embedding
Beam scanning by liquid-crystal biasing in a modified SIW structure
A fixed-frequency beam-scanning 1D antenna based on Liquid Crystals (LCs) is designed for application in 2D scanning with lateral alignment. The 2D array environment imposes full decoupling of adjacent 1D antennas, which often conflicts with the LC requirement of DC biasing: the proposed design accommodates both. The LC medium is placed inside a Substrate Integrated Waveguide (SIW) modified to work as a Groove Gap Waveguide, with radiating slots etched on the upper broad wall, that radiates as a Leaky-Wave Antenna (LWA). This allows effective application of the DC bias voltage needed for tuning the LCs. At the same time, the RF field remains laterally confined, enabling the possibility to lay several antennas in parallel and achieve 2D beam scanning. The design is validated by simulation employing the actual properties of a commercial LC medium
Learning to Collaborate by Grouping: a Consensus-oriented Strategy for Multi-agent Reinforcement Learning
Multi-agent systems require effective coordination between groups and
individuals to achieve common goals. However, current multi-agent reinforcement
learning (MARL) methods primarily focus on improving individual policies and do
not adequately address group-level policies, which leads to weak cooperation.
To address this issue, we propose a novel Consensus-oriented Strategy (CoS)
that emphasizes group and individual policies simultaneously. Specifically, CoS
comprises two main components: (a) the vector quantized group consensus module,
which extracts discrete latent embeddings that represent the stable and
discriminative group consensus, and (b) the group consensus-oriented strategy,
which integrates the group policy using a hypernet and the individual policies
using the group consensus, thereby promoting coordination at both the group and
individual levels. Through empirical experiments on cooperative navigation
tasks with both discrete and continuous spaces, as well as Google research
football, we demonstrate that CoS outperforms state-of-the-art MARL algorithms
and achieves better collaboration, thus providing a promising solution for
achieving effective coordination in multi-agent systems
Collective variables between large-scale states in turbulent convection
The dynamics in a confined turbulent convection flow is dominated by multiple
long-lived macroscopic circulation states, which are visited subsequently by
the system in a Markov-type hopping process. In the present work, we analyze
the short transition paths between these subsequent macroscopic system states
by a data-driven learning algorithm that extracts the low-dimensional
transition manifold and the related new coordinates, which we term collective
variables, in the state space of the complex turbulent flow. We therefore
transfer and extend concepts for conformation transitions in stochastic
microscopic systems, such as in the dynamics of macromolecules, to a
deterministic macroscopic flow. Our analysis is based on long-term direct
numerical simulation trajectories of turbulent convection in a closed cubic
cell at a Prandtl number and Rayleigh numbers and
for a time lag of convective free-fall time units. The simulations
resolve vortices and plumes of all physically relevant scales resulting in a
state space spanned by more than 3.5 million degrees of freedom. The transition
dynamics between the large-scale circulation states can be captured by the
transition manifold analysis with only two collective variables which implies a
reduction of the data dimension by a factor of more than a million. Our method
demonstrates that cessations and subsequent reversals of the large-scale flow
are unlikely in the present setup and thus paves the way to the development of
efficient reduced-order models of the macroscopic complex nonlinear dynamical
system.Comment: 24 pages, 12 Figures, 1 tabl
An anatomically detailed arterial-venous network model. Cerebral and coronary circulation
In recent years, several works have addressed the problem of modeling blood flow phenomena in veins, as a response to increasing interest in modeling pathological conditions occurring in the venous network and their connection with the rest of the circulatory system. In this context, one-dimensional models have proven to be extremely efficient in delivering predictions in agreement with in-vivo observations. Pursuing the increase of anatomical accuracy and its connection to physiological principles in haemodynamics simulations, the main aim of this work is to describe a novel closed-loop Anatomically-Detailed Arterial-Venous Network (ADAVN) model. An extremely refined description of the arterial network consisting of 2,185 arterial vessels is coupled to a novel venous network featuring high level of anatomical detail in cerebral and coronary vascular territories. The entire venous network comprises 189 venous vessels, 79 of which drain the brain and 14 are coronary veins. Fundamental physiological mechanisms accounting for the interaction of brain blood flow with the cerebro-spinal fluid and of the coronary circulation with the cardiac mechanics are considered. Several issues related to the coupling of arterial and venous vessels at the microcirculation level are discussed in detail. Numerical simulations are compared to patient records published in the literature to show the descriptive capabilities of the model. Furthermore, a local sensitivity analysis is performed, evidencing the high impact of the venous circulation on main cardiovascular variables
Unstable Periodic Orbits: a language to interpret the complexity of chaotic systems
Unstable periodic orbits (UPOs), exact periodic solutions of the evolution equation, offer a very
powerful framework for studying chaotic dynamical systems, as they allow one to dissect their
dynamical structure. UPOs can be considered the skeleton of chaotic dynamics, its essential
building blocks. In fact, it is possible to prove that in a chaotic system, UPOs are dense in
the attractor, meaning that it is always possible to find a UPO arbitrarily near any chaotic
trajectory. We can thus think of the chaotic trajectory as being approximated by different
UPOs as it evolves in time, jumping from one UPO to another as a result of their instability.
In this thesis we provide a contribution towards the use of UPOs as a tool to understand and
distill the dynamical structure of chaotic dynamical systems. We will focus on two models,
characterised by different properties, the Lorenz-63 and Lorenz-96 model.
The process of approximation of a chaotic trajectory in terms of UPOs will play a central role
in our investigation. In fact, we will use this tool to explore the properties of the attractor of
the system under the lens of its UPOs.
In the first part of the thesis we consider the Lorenz-63 model with the classic parametersâ value.
We investigate how a chaotic trajectory can be approximated using a complete set of UPOs
up to symbolic dynamicsâ period 14. At each instant in time, we rank the UPOs according to
their proximity to the position of the orbit in the phase space. We study this process from
two different perspectives. First, we find that longer period UPOs overwhelmingly provide the
best local approximation to the trajectory. Second, we construct a finite-state Markov chain
by studying the scattering of the trajectory between the neighbourhood of the various UPOs.
Each UPO and its neighbourhood are taken as a possible state of the system. Through the
analysis of the subdominant eigenvectors of the corresponding stochastic matrix we provide a
different interpretation of the mixing processes occurring in the system by taking advantage of
the concept of quasi-invariant sets.
In the second part of the thesis we provide an extensive numerical investigation of the variability
of the dynamical properties across the attractor of the much studied Lorenz â96 dynamical
system. By combining the Lyapunov analysis of the tangent space with the study of the
shadowing of the chaotic trajectory performed by a very large set of unstable periodic orbits,
we show that the observed variability in the number of unstable dimensions, which shows a
serious breakdown of hyperbolicity, is associated with the presence of a substantial number of
finite-time Lyapunov exponents that fluctuate about zero also when very long averaging times
are considered
Fracture prediction of fully clamped circular brittle plates subjected to impulsive loadings
When a high explosive detonates at some distance from the structure, the generated hot gas with high magnitude pressure and temperature expand rapidly and force the surrounding air out of the volume it occupies. As a consequence, a high pressure shock discontinuity namely a shock wave is produced. As this shock propagates away from the charge, it may inflict widespread damage to any structure that it impacts on. It is the challenge of structural engineers to improve the blast-resistant performance of the vulnerable structures and design adequate and efficient protective engineering systems against such extreme loading.
Most of studies on the response of plate subjected to blast loadings focus on the transient or permanent deformation without any failure occur. Available methods in the literature for predicting failure response only works for one specific load distribution while distribution of blast loadings could be significantly due to various scenarios. Predictive method are therefore required that can predict the failure response of plates under loading with arbitrary distribution and intensity that are fast to run and accurate.
Conducting the experimental research dealing with blast loads needs to consider both cost and safety issues. Besides, numerical analysis requires a high computational time. Therefore, the given analytical approach provides an alternative for failure response investigation.
This thesis proposes an analytical method to predict failure response of plates under more than one specific loading distribution. Besides, this thesis provides dimensionless I â K diagrams that could quickly determine the potential failure modes a plate will suffer under the given blast loading.
The results of this thesis should be used to guide analytical approach development for the prediction of failure response of plates subjected to blast loadings. The simple method developed in this thesis can be employed for design purposes, especially, at the early stages requiring an understanding of the structural failure response and help to rapid evaluation of the likely damage a structure will sustain in the event of blast
Large deviations for hyperbolic -nearest neighbor balls
We prove a large deviation principle for the point process of large Poisson
-nearest neighbor balls in hyperbolic space. More precisely, we consider a
stationary Poisson point process of unit intensity in a growing sampling window
in hyperbolic space. We further take a growing sequence of thresholds such that
there is a diverging expected number of Poisson points whose -nearest
neighbor ball has a volume exceeding this threshold. Then, the point process of
exceedances satisfies a large deviation principle whose rate function is
described in terms of a relative entropy. The proof relies on a fine
coarse-graining technique such that inside the resulting blocks the exceedances
are approximated by independent Poisson point processes.Comment: 18 page
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