Related papers: On the probability of Boolean functions of events …
Euclidean functions with values in an arbitrary well-ordered set were first considered in a 1949 work of Motzkin and studied in more detail in work of Fletcher, Samuel and Nagata in the 1970's and 1980's. Here these results are revisited,…
We study algorithmic problems on subsets of Euclidean space of low fractal dimension. These spaces are the subject of intensive study in various branches of mathematics, including geometry, topology, and measure theory. There are several…
Parity functions are fundamental Boolean operations with critical applications across machine learning, cryptography, and error correction. Yet, learning high-dimensional parity functions poses significant challenges: in a general setting,…
A general theory is provided delivering convergence of maximal cyclically monotone mappings containing the supports of coupling measures of sequences of pairs of possibly random probability measures on Euclidean space. The theory is based…
This paper offers an overview of the mobile Boolean stochastic geometric model which is a time-dependent version of the ordinary Boolean model in a Euclidean space of dimension $d$. The main question asked is that of obtaining the law of…
In [C. Mouhot and L. Pareschi, "Fast algorithms for computing the Boltzmann collision operator," Math. Comp., to appear; C. Mouhot and L. Pareschi, C. R. Math. Acad. Sci. Paris, 339 (2004), pp. 71-76], fast deterministic algorithms based on…
This study presents a novel algorithm for identifying the set of extreme points that constitute the exact convex hull of a point set in high-dimensional Euclidean space. The proposed method iteratively solves a sequence of dynamically…
A family of maximally superintegrable systems containing the Coulomb atom as a special case is constructed in N-dimensional Euclidean space. Two different sets of N commuting second order operators are found, overlapping in the Hamiltonian…
Bayesian optimization has proven to be a highly effective methodology for the global optimization of unknown, expensive and multimodal functions. The ability to accurately model distributions over functions is critical to the effectiveness…
We present new algorithms to compute fundamental properties of a Boolean function given in truth-table form. Specifically, we give an O(N^2.322 log N) algorithm for block sensitivity, an O(N^1.585 log N) algorithm for `tree decomposition,'…
Mapping functions on bits to Hamiltonians acting on qubits has many applications in quantum computing. In particular, Hamiltonians representing Boolean functions are required for applications of quantum annealing or the quantum approximate…
A disordered medium is often constructed by $N$ points independently and identically distributed in a $d$-dimensional hyperspace. Characteristics related to the statistics of this system is known as the random point problem. As $d \to…
Contact Boolean algebras are one of the main algebraic tools in region-based theory of space. T. Ivanova provided strong motivations for the study of merely semilattices with a contact relation. Another significant motivation for…
The present paper develops two concepts of pointwise differentiability of higher order for arbitrary subsets of Euclidean space defined by comparing their distance functions to those of smooth submanifolds. Results include that…
We develop data structures for dynamic closest pair problems with arbitrary distance functions, that do not necessarily come from any geometric structure on the objects. Based on a technique previously used by the author for Euclidean…
Various applications involve assigning discrete label values to a collection of objects based on some pairwise noisy data. Due to the discrete---and hence nonconvex---structure of the problem, computing the optimal assignment (e.g.~maximum…
A fast method of an arbitrary high order for approximating volume potentials is proposed, which is effective also in high dimensional cases. Basis functions introduced in the theory of approximate approximations are used. Results of…
We study numerical integration of functions depending on an infinite number of variables. We provide lower error bounds for general deterministic linear algorithms and provide matching upper error bounds with the help of suitable multilevel…
We study stochastic optimization problems with objective function given by the expectation of the maximum of two linear functions defined on the component random variables of a multivariate Gaussian distribution. We consider random…
We consider the problem of numerically integrating functions with hyperplane discontinuities over the entire Euclidean space in many dimensions. We describe a simple process through which the Euclidean space is partitioned into simplices on…