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"Beck, Christian"
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Spatial resistance : literary and digital challenges to neoliberalism
\"This book uses literary analysis and digital humanities to show how social justice can be enacted in everyday actions through changing the way we think about lived spaces. As corporate and state powers increase, it is necessary to examine ways to democratize space based on the shared values of equality, liberty, and solidarity\"-- Provided by publisher.
Book
Machine Learning Approximation Algorithms for High-Dimensional Fully Nonlinear Partial Differential Equations and Second-order Backward Stochastic Differential Equations
High-dimensional partial differential equations (PDEs) appear in a number of models from the financial industry, such as in derivative pricing models, credit valuation adjustment models, or portfolio optimization models. The PDEs in such applications are high-dimensional as the dimension corresponds to the number of financial assets in a portfolio. Moreover, such PDEs are often fully nonlinear due to the need to incorporate certain nonlinear phenomena in the model such as default risks, transaction costs, volatility uncertainty (Knightian uncertainty), or trading constraints in the model. Such high-dimensional fully nonlinear PDEs are exceedingly difficult to solve as the computational effort for standard approximation methods grows exponentially with the dimension. In this work, we propose a new method for solving high-dimensional fully nonlinear second-order PDEs. Our method can in particular be used to sample from high-dimensional nonlinear expectations. The method is based on (1) a connection between fully nonlinear second-order PDEs and second-order backward stochastic differential equations (2BSDEs), (2) a merged formulation of the PDE and the 2BSDE problem, (3) a temporal forward discretization of the 2BSDE and a spatial approximation via deep neural nets, and (4) a stochastic gradient descent-type optimization procedure. Numerical results obtained using
TensorFlow
in
Python
illustrate the efficiency and the accuracy of the method in the cases of a 100-dimensional Black–Scholes–Barenblatt equation, a 100-dimensional Hamilton–Jacobi–Bellman equation, and a nonlinear expectation of a 100-dimensional
G
-Brownian motion.
Journal Article
Data-driven load profiles and the dynamics of residential electricity consumption
The dynamics of power consumption constitutes an essential building block for planning and operating sustainable energy systems. Whereas variations in the dynamics of renewable energy generation are reasonably well studied, a deeper understanding of the variations in consumption dynamics is still missing. Here, we analyse highly resolved residential electricity consumption data of Austrian, German and UK households and propose a generally applicable data-driven load model. Specifically, we disentangle the average demand profiles from the demand fluctuations based purely on time series data. We introduce a stochastic model to quantitatively capture the highly intermittent demand fluctuations. Thereby, we offer a better understanding of demand dynamics, in particular its fluctuations, and provide general tools for disentangling mean demand and fluctuations for any given system, going beyond the standard load profile (SLP). Our insights on the demand dynamics may support planning and operating future-compliant (micro) grids in maintaining supply-demand balance.
In modern power grids, knowing the required electric power demand and its variations is necessary to balance demand and supply. The authors propose a data-driven approach to create high-resolution load profiles and characterize their fluctuations, based on recorded data of electricity consumption.
Journal Article
The POVM Theorem in Bohmian Mechanics
The POVM theorem is a central result in Bohmian mechanics, grounding the measurement formalism of standard quantum mechanics in a statistical analysis based on the quantum equilibrium hypothesis (the Born rule for Bohmian particle positions). It states that the outcome statistics of an experiment are described by a positive operator-valued measure (POVM) acting on the Hilbert space of the measured system. In light of recent debates about the scope and status of this result, we provide a systematic presentation of the POVM theorem and its underlying assumptions with a focus on their conceptual foundations and physical justifications. We conclude with a brief discussion of the scope of the POVM theorem—especially the sense in which it does (and does not) place limits on what is “measurable” in Bohmian mechanics.
Journal Article
Spatial heterogeneity of air pollution statistics in Europe
Air pollution is one of the leading causes of death globally, and continues to have a detrimental effect on our health. In light of these impacts, an extensive range of statistical modelling approaches has been devised in order to better understand air pollution statistics. However, the time-varying statistics of different types of air pollutants are far from being fully understood. The observed probability density functions (PDFs) of concentrations depend very much on the spatial location and on the pollutant substance. In this paper, we analyse a large variety of data from 3544 different European monitoring sites and show that the PDFs of nitric oxide (
NO
), nitrogen dioxide (
N
O
2
) and particulate matter (
P
M
10
and
P
M
2.5
) concentrations generically exhibit heavy tails and are asymptotically well approximated by
q
-exponential distributions with a given width parameter
λ
. We observe that the power-law parameter
q
and the width parameter
λ
vary widely for the different spatial locations. For each substance, we find different patterns of parameter clouds in the
(
q
,
λ
)
plane. These depend on the type of pollutants and on the environmental characteristics (urban/suburban/rural/traffic/industrial/background). This means the effective statistical physics description of air pollution exhibits a strong degree of spatial heterogeneity.
Journal Article
3D lattice distortions and defect structures in ion-implanted nano-crystals
Focussed Ion Beam (FIB) milling is a mainstay of nano-scale machining. By manipulating a tightly focussed beam of energetic ions, often gallium (Ga
+
), FIB can sculpt nanostructures via localised sputtering. This ability to cut solid matter on the nano-scale revolutionised sample preparation across the life, earth and materials sciences. Despite its widespread usage, detailed understanding of the FIB-induced structural damage, intrinsic to the technique, remains elusive. Here we examine the defects caused by FIB in initially pristine objects. Using Bragg Coherent X-ray Diffraction Imaging (BCDI), we are able to spatially-resolve the full lattice strain tensor in FIB-milled gold nano-crystals. We find that
every
use of FIB causes large lattice distortions. Even very low ion doses, typical of FIB imaging and previously thought negligible, have a dramatic effect. Our results are consistent with a damage microstructure dominated by vacancies, highlighting the importance of free-surfaces in determining which defects are retained. At larger ion fluences, used during FIB-milling, we observe an extended dislocation network that causes stresses far beyond the bulk tensile strength of gold. These observations provide new fundamental insight into the nature of the damage created and the defects that lead to a surprisingly inhomogeneous morphology.
Journal Article
Relativistic Consistency of Nonlocal Quantum Correlations
What guarantees the “peaceful coexistence” of quantum nonlocality and special relativity? The tension arises because entanglement leads to locally inexplicable correlations between distant events that have no absolute temporal order in relativistic spacetime. This paper identifies a relativistic consistency condition that is weaker than Bell locality but stronger than the no-signaling condition meant to exclude superluminal communication. While justifications for the no-signaling condition often rely on anthropocentric arguments, relativistic consistency is simply the requirement that joint outcome distributions for spacelike separated measurements (or measurement-like processes) must be independent of their temporal order. This is necessary to obtain consistent statistical predictions across different Lorentz frames. We first consider ideal quantum measurements, derive the relevant consistency condition on the level of probability distributions, and show that it implies no-signaling (but not vice versa). We then extend the results to general quantum operations and derive corresponding operator conditions. This will allow us to clarify the relationships between relativistic consistency, no-signaling, and local commutativity. We argue that relativistic consistency is the basic physical principle that ensures the compatibility of quantum statistics and relativistic spacetime structure, while no-signaling and local commutativity can be justified on this basis.
Journal Article
Statistical characterization of airplane delays
The aviation industry is of great importance for a globally connected economy. Customer satisfaction with airlines and airport performance is considerably influenced by how much flights are delayed. But how should the delay be quantified with thousands of flights for each airport and airline? Here, we present a statistical analysis of arrival delays at several UK airports between 2018 and 2020. We establish a procedure to compare both mean delay and extreme events among airlines and airports, identifying a power-law decay of large delays. Furthermore, we note drastic changes in plane delay statistics during the COVID-19 pandemic. Finally, we find that delays are described by a superposition of simple distributions, leading to a superstatistics.
Journal Article
Weak correlation between fluctuations in protein diffusion inside bacteria
A weak correlation between the diffusion-exponent fluctuations and the temperature fluctuations is discussed based on recent experimental observations for protein diffusion inside bacteria. Its existence is shown to be essential for describing the statistical properties of the fluctuations. It is also quantified how largely the fluctuations are modulated by the weak correlation.
Journal Article
Analyzing spatio-temporal dynamics of dissolved oxygen for the River Thames using superstatistical methods and machine learning
By employing superstatistical methods and machine learning, we analyze time series data of water quality indicators for the River Thames (UK). The indicators analyzed include dissolved oxygen, temperature, electrical conductivity, pH, ammonium, turbidity, and rainfall, with a specific focus on the dynamics of dissolved oxygen. After detrending, the probability density functions of dissolved oxygen fluctuations exhibit heavy tails that are effectively modeled using
q
-Gaussian distributions. Our findings indicate that the multiplicative Empirical Mode Decomposition method stands out as the most effective detrending technique, yielding the highest log-likelihood in nearly all fittings. We also observe that the optimally fitted width parameter of the
q
-Gaussian shows a negative correlation with the distance to the sea, highlighting the influence of geographical factors on water quality dynamics. In the context of same-time prediction of dissolved oxygen, regression analysis incorporating various water quality indicators and temporal features identify the Light Gradient Boosting Machine as the best model. SHapley Additive exPlanations reveal that temperature, pH, and time of year play crucial roles in the predictions. Furthermore, we use the Transformer, a state-of-the-art machine learning model, to forecast dissolved oxygen concentrations. For long-term forecasting, the Informer model consistently delivers superior performance, achieving the lowest Mean Absolute Error (0.15) and Symmetric Mean Absolute Percentage Error (21.96%) with the 192 historical time steps that we used. This performance is attributed to the Informer’s ProbSparse self-attention mechanism, which allows it to capture long-range dependencies in time-series data more effectively than other machine learning models. It effectively recognizes the half-life cycle of dissolved oxygen, with particular attention to critical periods such as morning to early afternoon, late evening to early morning, and key intervals between the 16th and 26th quarter-hours of the previous half-day. Our findings provide valuable insights for policymakers involved in ecological health assessments, aiding in accurate predictions of river water quality and the maintenance of healthy aquatic ecosystems.
Journal Article