Related papers: Valuations and Boolean Models
We aim to completely formalize the rough topological analysis of integrable Hamiltonian systems admitting analytical solutions such that the initial phase variables along with the time derivatives of the auxiliary variables are expressed as…
Differential equations (DEs) are commonly used to describe dynamic systems evolving in one (ordinary differential equations or ODEs) or in more than one dimensions (partial differential equations or PDEs). In real data applications the…
We show that the natural "convolution" on the space of smooth, even, translation-invariant convex valuations on a euclidean space $V$, obtained by intertwining the product and the duality transform of S. Alesker, may be expressed in terms…
Functions with uniform sublevel sets can represent orders, preference relations or other binary relations and thus turn out to be a tool for scalarization that can be used in multicriteria optimization, decision theory, mathematical…
We propose a representation of boolean bent functions by bent rectangles, that is, by special matrices with restrictions on rows and columns. Using this representation, we exhibit new classes of bent functions, give an algorithm to…
Random tessellations are a prominent class of models in stochastic geometry. In this chapter, we give an overview of mechanisms that have been used to formulate random tessellation models. First, the notion of a random tessellation and…
The geometric and algebraic theory of valuations on cones is applied to understand identities involving summing certain rational functions over the set of linear extensions of a poset.
A complete classification of all zonal, continuous, and translation invariant valuations on convex bodies is established. The valuations obtained are expressed as principal value integrals with respect to the area measures. The convergence…
Substitute valuations (in some contexts called gross substitute valuations) are prominent in combinatorial auction theory. An algorithm is given in this paper for generating a substitute valuation through Monte Carlo simulation. In…
We generalize Taylor's theorem by introducing a stochastic formulation based on an underlying Poisson point process model. We utilize this approach to propose a novel non-linear regression framework and perform statistical inference of the…
We introduce the concepts of a pair of valuations and a good generating set and show how they can be used to prove geometric properties of soluble groups.
This paper describes valuation-based systems for representing and solving discrete optimization problems. In valuation-based systems, we represent information in an optimization problem using variables, sample spaces of variables, a set of…
We present a new method for performing Boolean operations on volumes represented as triangle meshes. In contrast to existing methods which treat meshes as 3D polyhedra and try to partition the faces at their exact intersection curves, we…
Gaussian Process (GP) models are often used as mathematical approximations of computationally expensive experiments. Provided that its kernel is suitably chosen and that enough data is available to obtain a reasonable fit of the simulator,…
Generalized additive models (GAMs) provide a way to blend parametric and non-parametric (function approximation) techniques together, making them flexible tools suitable for many modeling problems. For instance, GAMs can be used to…
Stochastic processes are considered on free loop spaces, geometric loop and diffeomorphism groups of real and complex manifolds. They are used for investigations of Wiener differentiable quasi-invariant measures on such groups relative to…
We study dually epi-translation invariant valuations on cones of convex functions containing the space of finite-valued convex functions. The existence of a homogeneous decomposition is used to associate a distribution to every valuation of…
We prove a generalized version of Rogers' mean value formula in the space $X_n$ of unimodular lattices in $R^n$, which gives the mean value of a multiple sum over a lattice $L$ and its dual $L^*$. As an application, we prove that for $L$…
We express the mean and variance terms in a double exponential regression model as additive functions of the predictors and use Bayesian variable selection to determine which predictors enter the model, and whether they enter linearly or…
In this paper, we study the value distributions of perfect nonlinear functions, i.e., we investigate the sizes of image and preimage sets. Using purely combinatorial tools, we develop a framework that deals with perfect nonlinear functions…