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In this article we study the problem of recovering the unknown solution of a linear ill-posed problem, via iterative regularization methods. We review the problem of projection-regularization from a statistical point of view. A basic…
We develop a commuting vector field method for a general class of radiating spacetimes. The metrics considered are certain long range perturbations of Minkowski space including those constructed from global stability problems in general…
The basic arguments underlying the symplectic projector method are presented. By this method, local free coordinates on the constrait surface can be obtained for a broader class of constrained systems. Some interesting examples are…
Recent works have developed new projection-free first-order methods based on utilizing linesearches and normal vector computations to maintain feasibility. These oracles can be cheaper than orthogonal projection or linear optimization…
Random projections (RP) are a popular tool for reducing dimensionality while preserving local geometry. In many applications the data set to be projected is given to us in advance, yet the current RP techniques do not make use of…
The estimation of periodicity is a fundamental task in many scientific areas of study. Existing methods rely on theoretical assumptions that the observation times have equal or i.i.d. spacings, and that common estimators, such as the…
A planar integral point set is a set of non-collinear points in plane such that for any pair of the points the Euclidean distance between the points is integral. We discuss the classification of planar integral point sets and provide…
Partially ordered sets (posets) play a universal role as an abstract structure in many areas of mathematics. For finite posets, an explicit enumeration of distinct partial orders on a set of unlabelled elements is known only up to a…
The localization spread gives a criterion to decide between metallic versus insulating behaviour of a material. It is defined as the second moment cumulant of the many-body position operator, divided by the number of electrons. Different…
Localised radial patterns have been observed in the vegetation of semi-arid ecosystems, often as localised patches of vegetation or in the form of `fairy circles'. We consider stationary localised radial solutions to a reduced model for…
A reaction--diffusion replicator equation is studied. A novel method to apply the principle of global regulation is used to write down the model with explicit spatial structure. Properties of stationary solutions together with their…
Spatial designs for monitoring stream networks, especially ephemeral systems, are typically non-standard, `sparse' and can be very complex, reflecting the complexity of the ecosystem being monitored, the scale of the population, and the…
Conformal prediction is a general distribution-free approach for constructing prediction sets combined with any machine learning algorithm that achieve valid marginal or conditional coverage in finite samples. Ordinal classification is…
The effectiveness of projection methods for solving systems of linear inequalities is investigated. It is shown that they have a computational advantage over some alternatives and that this makes them successful in real-world applications.…
The paper studies differentially positive systems, that is, systems whose linearization along an arbitrary trajectory is positive. We illustrate the use of differential positivity on compact forward invariant sets for the characterization…
We present an approach for the study and design of reflectors with rotational or translational symmetry that redirect light from a point source into any desired radiant intensity distribution. This method is based on a simple conformal map…
Local navigation is one of the fundamental problems in robot navigation, and numerous approaches have been proposed over the years, including methods such as the Dynamic Window Approach, Model Predictive Control, and more recently, Control…
We investigate the relevance of time ordering in the definition of off-diagonal parton distributions in terms of products of fields. The method we use easily allows determination of their support properties and provides a link to their…
The basic tool for solving problems in metric geometry and isotonic regression is the metric projection onto closed convex cones. Isotonicity of these projections with respect to a given order relation can facilitate finding the solutions…
We provide criteria for deciding whether a given planar curve is an image of a given spatial curve, obtained by a central or a parallel projection with unknown parameters. These criteria reduce the projection problem to a certain…