Related papers: Complex Formulation of Lensing Theory and Applicat…
We explore various combinatorial problems mostly borrowed from physics, that share the property of being continuously or discretely integrable, a feature that guarantees the existence of conservation laws that often make the problems…
It is well-known that the equations for a simple fluid can be cast into what is called their Lagrange formulation. We introduce a notion of a generalized Lagrange formulation, which is applicable to a wide variety of systems of partial…
Linear approximations to the decision boundary of a complex model have become one of the most popular tools for interpreting predictions. In this paper, we study such linear explanations produced either post-hoc by a few recent methods or…
Spin glasses are magnetic systems exhibiting both quenched disorder and frustration, and have often been cited as examples of `complex systems.' In this talk I review some of the basic notions of spin glass physics, and discuss how some of…
A new simple geometrical interpretation of complex numbers is presented. It differs from their usual interpretation as points in the complex plane. From the new point of view the complex numbers are rather operations on vectors than points.…
Euler used intrinsic equations expressing the radius of curvature as a function of the angle of inclination to find curves similar to their evolutes. We interpret the evolute of a plane curve optically, as the caustic (envelope) of light…
Strong gravitational lensing is an important tool to probe the universe. In the theoretical analysis of gravitational lensing, it is assumed that continuous density profile can correctly describe the lens galaxy. But in fact this assumption…
In this geometrical approach to gravitational lensing theory, we apply the Gauss-Bonnet theorem to the optical metric of a lens, modelled as a static, spherically symmetric, perfect non-relativistic fluid, in the weak deflection limit. We…
Arclets in clusters of galaxies can be used to determine the lens mapping and not only to constrain the mass density of the cluster. Multiply imaged arclets are therefore easily identified without further modelling.
Recent studies showed that hardness, a complex property, can be calculated using very simple approaches or even analytical formulae. These form the basis for evaluating controversial experimental results (as we illustrate for…
When light from a distant source object, like a galaxy or a supernova, travels towards us, it is deflected by massive objects that lie on its path. When the mass density of the deflecting object exceeds a certain threshold, multiple, highly…
In a previous paper [Adcock & Huybrechs, 2019] we described the numerical approximation of functions using redundant sets and frames. Redundancy in the function representation offers enormous flexibility compared to using a basis, but…
As a first application of a very old theorem, known as Herschel's theorem, we provide direct elementary proofs of several explicit expressions for some numbers and polynomials that are known in combinatorics. The second application deals…
We give a generalization of the random matrix ensembles, including all lassical ensembles. Then we derive the joint density function of the generalized ensemble by one simple formula, which give a direct and unified way to compute the…
The distribution function of quasars with respect to apparent brightness is given, found under the assumption that quasars are, at least partially, the gravitationally enhanced images of the active nuclei of distant galaxies. A Schechter…
The analysis of the shear induced by a single cluster on the images of a large number of background galaxies is all centered around the curl-free character of a well-known vector field that can be derived from the data. Such basic property…
Drawing appropriate defeasible inferences has been proven to be one of the most pervasive puzzles of natural language processing and a recurrent problem in pragmatics. This paper provides a theoretical framework, called ``stratified…
Explicit formulas for the mean and variance of linear stochastic differential equations are derived in terms of an exponential matrix. This result improved a previous one by means of which the mean and variance are expressed in terms of a…
Kinematic weak lensing describes the distortion of a galaxy's projected velocity field due to lensing shear, an effect recently reported for the first time by Gurri et al. based on a sample of 18 galaxies at $z \sim 0.1$. In this paper, we…
We illustrate the use of intersection types as a semantic tool for showing properties of the lattice of lambda theories. Relying on the notion of easy intersection type theory we successfully build a filter model in which the interpretation…