Continuous Symmetries of Difference Equations

Lie group theory was originally created more than 100 years ago as a tool for solving ordinary and partial differential equations. In this article we review the results of a much more recent program: the use of Lie groups to study difference equations. We show that the mismatch between continuous symmetries and discrete equations can be resolved in at least two manners. One is to use generalized symmetries acting on solutions of difference equations, but leaving the lattice invariant. The other is to restrict to point symmetries, but to allow them to also transform the lattice.Comment: Review articl

Conceptualizing throughput legitimacy: procedural mechanisms of accountability, transparency, inclusiveness and openness in EU governance

This symposium demonstrates the potential for throughput legitimacy as a concept for shedding empirical light on the strengths and weaknesses of multi-level governance, as well as challenging the concept theoretically. This article introduces the symposium by conceptualizing throughput legitimacy as an ‘umbrella concept’, encompassing a constellation of normative criteria not necessarily empirically interrelated. It argues that in order to interrogate multi-level governance processes in all their complexity, it makes sense for us to develop normative standards that are not naïve about the empirical realities of how power is exercised within multilevel governance, or how it may interact with legitimacy. We argue that while throughput legitimacy has its normative limits, it can be substantively useful for these purposes. While being no replacement for input and output legitimacy, throughput legitimacy offers distinctive normative criteria— accountability, transparency, inclusiveness and openness— and points towards substantive institutional reforms.Published versio

Hyperdeterminants as integrable discrete systems

We give the basic definitions and some theoretical results about hyperdeterminants, introduced by A. Cayley in 1845. We prove integrability (understood as 4d-consistency) of a nonlinear difference equation defined by the 2x2x2-hyperdeterminant. This result gives rise to the following hypothesis: the difference equations defined by hyperdeterminants of any size are integrable. We show that this hypothesis already fails in the case of the 2x2x2x2-hyperdeterminant.Comment: Standard LaTeX, 11 pages. v2: corrected a small misprint in the abstrac

mgwr: a Python implementation of multiscale geographically weighted regression for investigating process spatial heterogeneity and scale

Geographically weighted regression (GWR) is a spatial statistical technique that recognizes that traditional ‘global’ regression models may be limited when spatial processes vary with spatial context. GWR captures process spatial heterogeneity by allowing effects to vary over space. To do this, GWR calibrates an ensemble of local linear models at any number of locations using ‘borrowed’ nearby data. This provides a surface of location-specific parameter estimates for each relationship in the model that is allowed to vary spatially, as well as a single bandwidth parameter that provides intuition about the geographic scale of the processes. A recent extension to this framework allows each relationship to vary according to a distinct spatial scale parameter, and is therefore known as multiscale (M)GWR. This paper introduces mgwr, a Python-based implementation of MGWR that explicitly focuses on the multiscale analysis of spatial heterogeneity. It provides novel functionality for inference and exploratory analysis of local spatial processes, new diagnostics unique to multi-scale local models, and drastic improvements to efficiency in estimation routines. We provide two case studies using mgwr, in addition to reviewing core concepts of local models. We present this in a literate programming style, providing an overview of the primary software functionality and demonstrations of suggested usage alongside the discussion of primary concepts and demonstration of the improvements made in mgwr

Quantitative methods I:The world we have lost – or where we started from

Although pioneering studies using statistical methods in geographical data analysis were published in the 1930s, it was only in the 1960s that their increasing use in human geography led to a claim that a ‘quantitative revolution’ had taken place. The widespread use of quantitative methods from then on was associated with changes in both disciplinary philosophy and substantive focus. The first decades of the ‘revolution’ saw quantitative analyses focused on the search for spatial order of a geometric form within an, often implicit, logical positivist framework. In the first of three reviews of the use of quantitative methods in human geography, this progress report uncovers their origin with regard to the underlying philosophy, the focus on spatial order, and the nature of the methods deployed. Subsequent reports will outline the changes in all three that occurred in later decades and will chart the contemporary situation.</jats:p

Reduction without reduction: Adding KK-monopoles to five dimensional stationary axisymmetric solutions

We present a general method to add KK-monopole charge to any asymptotically flat stationary axisymmetric solution of five dimensional General Relativity. The technique exploits the underlying SL(3,R) invariance of the system by identifying a particular element of the symmetry group which changes the asymptotic boundary condition and adds KK-monopole charge. Furthermore, we develop a set of technical tools which allow us to apply the SL(3,R) transformations to solutions produced by the Inverse Scattering method. As an example of our methods, we construct the exact solution describing a static black ring carrying KK-monopole charge.Comment: 36 pages, 3 figures, LaTeX, minor typos fixe

Superconducting 2D system with lifted spin degeneracy: Mixed singlet-triplet state

Motivated by recent experimental findings, we have developed a theory of the superconducting state for 2D metals without inversion symmetry modeling the geometry of a surface superconducting layer in a field-effect-transistor or near the boundary doped by adsorbed ions. In such systems the two-fold spin degeneracy is lifted by spin-orbit interaction, and singlet and triplet pairings are mixed in the wave function of the Cooper pairs. As a result, spin magnetic susceptibility becomes anisotropic and Knight shift retains finite and rather high value at T=0.Comment: 5 pages, no figure

Unconventional MBE Strategies from Computer Simulations for Optimized Growth Conditions

We investigate the influence of step edge diffusion (SED) and desorption on Molecular Beam Epitaxy (MBE) using kinetic Monte-Carlo simulations of the solid-on-solid (SOS) model. Based on these investigations we propose two strategies to optimize MBE growth. The strategies are applicable in different growth regimes: During layer-by-layer growth one can exploit the presence of desorption in order to achieve smooth surfaces. By additional short high flux pulses of particles one can increase the growth rate and assist layer-by-layer growth. If, however, mounds are formed (non-layer-by-layer growth) the SED can be used to control size and shape of the three-dimensional structures. By controlled reduction of the flux with time we achieve a fast coarsening together with smooth step edges.Comment: 19 pages, 7 figures, submitted to Phys. Rev.

spopt: a python package for solving spatial optimization problems in PySAL

Spatial optimization is a major spatial analytical tool in management and planning, the significance of which cannot be overstated. Spatial optimization models play an important role in designing and managing effective and efficient service systems such as transportation, education, public health, environmental protection, and commercial investment among others. To this end, spopt (spatial optimization) is under active development for the inclusion of newly proposed models and methods for regionalization, facility location, and transportation-oriented solutions (Feng et al., 2021). Spopt is a submodule in the open-source spatial analysis library PySAL (Python Spatial Analysis Library) founded by Dr. Sergio J. Rey and Dr. Luc Anselin in 2005 (Rey et al., 2015, 2021; Rey &amp; Anselin, 2007). The goal of developing spopt is to provide management and decision-making support to all relevant practitioners and to further promote the appropriate and meaningful application of spatial optimization models in practice

Systemic versus localized coagulation activation contributing to organ failure in critically ill patients

In the pathogenesis of sepsis, inflammation and coagulation play a pivotal role. Increasing evidence points to an extensive cross-talk between these two systems, whereby inflammation not only leads to activation of coagulation but coagulation also considerably affects inflammatory activity. The intricate relationship between inflammation and coagulation may not only be relevant for vascular atherothrombotic disease in general but has in certain clinical settings considerable consequences, for example in the pathogenesis of microvascular failure and subsequent multiple organ failure, as a result of severe infection and the associated systemic inflammatory response. Molecular pathways that contribute to inflammation-induced activation of coagulation have been precisely identified. Pro-inflammatory cytokines and other mediators are capable of activating the coagulation system and downregulating important physiological anticoagulant pathways. Activation of the coagulation system and ensuing thrombin generation is dependent on an interleukin-6-induced expression of tissue factor on activated mononuclear cells and endothelial cells and is insufficiently counteracted by physiological anticoagulant mechanisms and endogenous fibrinolysis. Interestingly, apart from the overall systemic responses, a differential local response in various vascular beds related to specific organs may occur