Related papers: Some algorithms arising in the proof of the Kepler…
In this paper, we consider classic randomized low diameter decomposition procedures for planar graphs that obtain connected clusters which are cohesive in that close-by pairs of nodes are assigned to the same cluster with high probability.…
In this paper we study the computational feasibility of an algorithm to prove orbifold equivalence between potentials describing Landau-Ginzburg models. Through a comparison with leading results of Groebner basis computations in cryptology,…
We consider linear problems in the worst case setting. That is, given a linear operator and a pool of admissible linear measurements, we want to approximate the values of the operator uniformly on a convex and balanced set by means of…
We present a quantum algorithm for systems of (possibly inhomogeneous) linear ordinary differential equations with constant coefficients. The algorithm produces a quantum state that is proportional to the solution at a desired final time.…
Since simulating quantum computers requires exponentially more classical resources, efficient algorithms are extremely helpful. We analyze algorithms that create single qubit and specific controlled qubit matrix representations of gates.…
Contracting tensor networks is often computationally demanding. Well-designed contraction sequences can dramatically reduce the contraction cost. We explore the performance of simulated annealing and genetic algorithms, two common discrete…
We present a complexity reduction algorithm for a family of parameter-dependent linear systems when the system parameters belong to a compact semi-algebraic set. This algorithm potentially describes the underlying dynamical system with…
The pursue of what are properties that can be identified to permit an automated reasoning program to generate and find new and interesting theorems is an interesting research goal (pun intended). The automatic discovery of new theorems is a…
The modular decomposition is a technique that applies but is not restricted to graphs. The notion of module naturally appears in the proofs of many graph theoretical theorems. Computing the modular decomposition tree is an important…
We introduce an algorithm which, in the context of nonlinear regression on vector-valued explanatory variables, chooses those combinations of vector components that provide best prediction. The algorithm devotes particular attention to…
A simple mechanism for the emergence of complexity in cellular automata out of predictable dynamics is described. This leads to unfold the concept of conditional predictability for systems whose trajectory can only be piecewise known. The…
We extend recent computer-assisted design and analysis techniques for first-order optimization over structured functions--known as performance estimation--to apply to structured sets. We prove "interpolation theorems" for smooth and…
In this paper we consider a distributed optimization scenario in which a set of agents has to solve a convex optimization problem with separable cost function, local constraint sets and a coupling inequality constraint. We propose a novel…
Mathematical proof is undoubtedly the cornerstone of mathematics. The emergence, in the last years, of computing and reasoning tools, in particular automated geometry theorem provers, has enriched our experience with mathematics immensely.…
Most continuous mathematical formulations arising in science and engineering can only be solved numerically and therefore approximately. We shall always assume that we're dealing with a numerical approximation to the solution. There are two…
Optimization with constraints is a typical problem in quantum physics and quantum information science that becomes especially challenging for high-dimensional systems and complex architectures like tensor networks. Here we use ideas of…
We propose a new quantifier elimination algorithm for the theory of linear real arithmetic. This algorithm uses as subroutine satisfiability modulo this theory, a problem for which there are several implementations available. The quantifier…
In a previous work, we developed the idea to solve Kepler's equation with a CORDIC-like algorithm, which does not require any division, but still multiplications in each iteration. Here we overcome this major shortcoming and solve Kepler's…
Kinematics of rigid bodies can be analyzed in many different ways. The advantage of using Euler parameters is that the resulting equations are polynomials and hence computational algebra, in particular Gr\"obner bases, can be used to study…
Recovering the digital input of a time-discrete linear system from its (noisy) output is a significant challenge in the fields of data transmission, deconvolution, channel equalization, and inverse modeling. A variety of algorithms have…