Related papers: Geometric properties of reliability polynomials
The theory of multidimensional persistence captures the topology of a multifiltration -- a multiparameter family of increasing spaces. Multifiltrations arise naturally in the topological analysis of scientific data. In this paper, we give a…
An overview of computational methods to describe high-dimensional potential energy surfaces suitable for atomistic simulations is given. Particular emphasis is put on accuracy, computability, transferability and extensibility of the methods…
Many statistical models are algebraic in that they are defined by polynomial constraints or by parameterizations that are polynomial or rational maps. This opens the door for tools from computational algebraic geometry. These tools can be…
In this paper we use Euler-Seidel matrices method to find out some properties of exponential and geometric polynomials and numbers. Some known results are reproved and some new results are obtained.
A Geometric programming (GP) is a type of mathematical problem characterized by objective and constraint functions that have a special form. Many methods have been developed to solve large scale engineering design GP problems. In this paper…
In this paper I present a kind of proof for classical Euclidean geometric problems which relies on both synthetic and analytic geometry. Using the elementary tools of polynomial algebra and multivariate calculus we manage to reduce the…
It is known that a graph isomorphism testing algorithm is polynomially equivalent to a detecting of a graph non-trivial automorphism algorithm. The polynomiality of the latter algorithm, is obtained by consideration of symmetry properties…
Techniques for the evaluation of complex polynomials with one and two variables are introduced. Polynomials arise in may areas such as control systems, image and signal processing, coding theory, electrical networks, etc., and their…
Multi-homogeneous polynomial systems arise in many applications. We provide bit complexity estimates for solving them which, up to a few extra other factors, are quadratic in the number of solutions and linear in the height of the input…
Extending the thoroughly studied theory of group stability, we study Ulam stability type problems for associative and Lie algebras; namely, we investigate obstacles to rank-approximation of almost solutions by exact solutions for systems of…
Robust estimation is much more challenging in high dimensions than it is in one dimension: Most techniques either lead to intractable optimization problems or estimators that can tolerate only a tiny fraction of errors. Recent work in…
Geometric programming problem is a powerful tool for solving some special type non-linear programming problems. It has a wide range of applications in optimization and engineering for solving some complex optimization problems. Many…
Formal methods for verification of programs are extended to testing of programs. Their combination is intended to lead to benefits in reliable program development, testing, and evolution. Our geometric theory of testing is intended to serve…
In this paper, we present a geometric approach for computing the controlled invariant set of a continuous-time control system. While the problem is well studied for in the ellipsoidal case, this family is quite conservative for constrained…
This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…
Aiming for accurate estimation of system reliability of load-sharing systems, a flexible model for such systems is constructed by approximating the cumulative hazard functions of component lifetimes using piecewise linear functions. The…
The ongoing evolution of the electric power systems brings about the need to cope with increasingly complex interactions of technical components and relevant actors. In order to integrate a more comprehensive spectrum of different aspects…
Engineering and applied sciences use models of increasing complexity to simulate the behaviour of manufactured and physical systems. Propagation of uncertainties from the input to a response quantity of interest through such models may…
A class of parametric functions formed by alternating compositions of multivariate polynomials and rectification style monomial maps is studied (the layer-wise exponents are treated as fixed hyperparameters and are not optimized). For this…
This paper presents a framework for abstracting uncertain or non-polynomial components of dynamical systems using polynomial constraints. This enables the application of polynomial-based analysis tools, such as sum-of-squares programming,…