Related papers: Automated proving in planar geometry based on the …
A visualized graph is a powerful tool for data analysis and synthesis tasks. In this case, the task of visualization constitutes not only in displaying vertices and edges according to the graph representation, but also in ensuring that the…
Let $X$ be an integral projective variety of codimension two, degree $d$ and dimension $r$ and $Y$ be its general hyperplane section. The problem of lifting generators of minimal degree $\sigma$ from the homogeneous ideal of $Y$ to the…
We present a novel algorithm 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. The motivation comes from the problem of establishing a…
In this article, we establish a class of new accelerated modulus-based iteration methods for solving the linear complementarity problem. When the system matrix is an $H_+$-matrix, we present appropriate criteria for the convergence…
This work proposes Isogeometric Analysis as an alternative to classical finite elements for simulating electric machines. Through the spline-based Isogeometric discretization it is possible to parametrize the circular arcs exactly, thereby…
Computer Algebra systems are widely spread because of some of their remarkable features such as their ease of use and performance. Nonetheless, this focus on performance sometimes leads to unwanted consequences: algorithms and computations…
This paper discusses a new method to solve definite integrals using artificial neural networks. The objective is to build a neural network that would be a novel alternative to pre-established numerical methods and with the help of a…
We present the first algorithm for computing class groups and unit groups of arbitrary number fields that provably runs in probabilistic subexponential time, assuming the Extended Riemann Hypothesis (ERH). Previous subexponential algorithms…
Computing the real solutions to a system of polynomial equations is a challenging problem, particularly verifying that all solutions have been computed. We describe an approach that combines numerical algebraic geometry and sums of squares…
Even competent programmers make mistakes. Automatic verification can detect errors, but leaves the frustrating task of finding the erroneous line of code to the user. This paper presents an automatic approach for identifying potential error…
Checking two probabilistic automata for equivalence has been shown to be a key problem for efficiently establishing various behavioural and anonymity properties of probabilistic systems. In recent experiments a randomised equivalence test…
We propose a new method for simplification of Gaussian process (GP) models by projecting the information contained in the full encompassing model and selecting a reduced number of variables based on their predictive relevance. Our results…
The Numerical Assembly Technique is extended to investigate arbitrary planar frame structures with the focus on the computation of natural frequencies. This allows us to obtain highly accurate results without resorting to spatial…
We consider a generic algorithmic paradigm that we call progressive exploration, which can be used to develop simple and efficient parameterized graph algorithms. We identify two model-theoretic properties that lead to efficient progressive…
In this paper we develop a general method to prove independence of algebraic monodromy groups in compatible systems of representations, and we apply it to deduce independence results for compatible systems both in automorphic and in…
We prove a complete complexity classification theorem for the planar eight-vertex model. For every parameter setting in ${\mathbb C}$ for the eight-vertex model, the partition function is either (1) computable in P-time for every graph, or…
Automated theorem proving in Euclidean geometry, particularly for International Mathematical Olympiad (IMO) level problems, remains a major challenge and an important research focus in Artificial Intelligence. In this paper, we present a…
The core challenge in designing an effective static program analysis is to find a good program abstraction -- one that retains only details relevant to a given query. In this paper, we present a new approach for automatically finding such…
In this paper we apply for the first time a new method for multivariate equation solving which was developed in \cite{gh1}, \cite{gh2}, \cite{gh3} for complex root determination to the {\em real} case. Our main result concerns the problem…
In this paper a deterministic preprocessing algorithm is presented, whose output can be given as input to most state-of-the-art epipolar geometry estimation algorithms, improving their results considerably. They are now able to succeed on…