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A linear-time algorithm is presented for the construction of the Gibbs distribution of configurations in the Ising model, on a quantum computer. The algorithm is designed so that each run provides one configuration with a quantum…
How can complexity theory and algorithms benefit from practical advances in computing? We give a short overview of some prior work using practical computing to attack problems in computational complexity and algorithms, informally describe…
The geometric approach to mechanics based on the Jacobi metric allows to easily construct natural mechanical systems which are integrable (actually separable) at a fixed value of the energy. The aim of the present paper is to investigate…
This paper is devoted to constructing and studying exactly solvable dynamical systems in discrete time obtained from some algebraic operations on matrices, to reductions of such systems leading to classical field theory models in…
A set of algorithms is presented for efficient numerical calculation of the time evolution of classical dynamical systems. Starting with a first approximation for solving the differential equations that has a "reversible" character, we show…
In robotics, simulation has the potential to reduce design time and costs, and lead to a more robust engineered solution and a safer development process. However, the use of simulators is predicated on the availability of good models. This…
The design and analysis of systems that combine computational behaviour with physical processes' continuous dynamics - such as movement, velocity, and voltage - is a famous, challenging task. Several theoretical results from programming…
A cellular automaton is a deterministic and exactly computable dynamical system which mimics certain fundamental aspects of physical dynamics such as spatial locality and finite entropy. CA systems can be constructed which have additional…
Mathematics has many useful properties for developing of complex software systems. One is that it can exactly describe a physical situation of the object or outcome of an action. Mathematics support abstraction and this is an excellent…
This draft suggests a new counterexample guided abstraction refinement (CEGAR) framework that uses the combination of numerical simulation for nonlinear differential equations with linear programming for linear hybrid automata (LHA) to…
The difficulty of assessing the state lies in a little predictable change in the dimension of a dynamic system under the influence of internal changes and environmental parameters. In the work, the state of such a system is estimated by the…
This paper presents a novel numerical optimisation method for infinite dimensional optimisation. The functional optimisation makes minimal assumptions about the functional and without any specific knowledge on the derivative of the…
In this paper we propose a new approach to the study of integrable cases based on intensive computer methods' application. We make a new investigation of Kovalevskaya and Goryachev-Chaplygin cases of Euler-Poisson equations and obtain many…
This paper is devoted to the study of symplectic manifolds and their connection with Hamiltonian dynamical systems. We review some properties and operations on these manifolds and see how they intervene when studying the complete…
A simple yet efficient computational algorithm for computing the continuous optimal experimental design for linear models is proposed. An alternative proof the monotonic convergence for $D$-optimal criterion on continuous design spaces are…
This paper presents a methodology for constructing iterative schemes of any order of convergence for solving nonlinear systems of equations. It also provides formulas for the order of convergence of any iterative schemes constructed using…
We consider optimization algorithms that are open systems, that is, with external inputs and outputs. Such algorithms arise for instance, when analyzing the effect of noise or disturbance on an algorithm, or when an algorithm is part of…
Hybrid systems with both discrete and continuous dynamics are an important model for real-world cyber-physical systems. The key challenge is to ensure their correct functioning w.r.t. safety requirements. Promising techniques to ensure…
The representation of polynomials by arithmetic circuits evaluating them is an alternative data structure which allowed considerable progress in polynomial equation solving in the last fifteen years. We present a circuit based computation…
The high-performance scalable parallel algorithm for rigorous calculation of partition function of lattice systems with finite number Ising spins was developed. The parallel calculations run by C++ code with using of Message Passing…