Related papers: Automatic code generator for higher order integrat…
The sine(sinh)-Gordon hierarchy of integrable Hamiltonian systems is described in detail, and all dynamic variables are expressed in terms of the $\wp$-functions that uniformize the associated spectral curve. Quasi-periodic solutions to the…
We present an equation generator algorithm that utilizes second-quantized operators in normal order with respect to a correlated or non-correlated reference and the corresponding Wick theorem. The algorithm proposed here, written with…
We revisit the idea of numerically integrating the differential form of Feynman integrals. With a novel approach for the treatment of branch cuts, we develop an integrator capable of evaluating a basis of master integrals in double and…
We propose a project for automatic representation and evaluation of helicity amplitudes we started to develop and explain it's main functioning principles.
Dependable numerical results from long-time simulations require stable numerical integration schemes. For Hamiltonian systems, this is achieved with symplectic integrators, which conserve the symplectic condition and exactly solve for the…
This paper had no abstract originally. A second-order symplectic integration algorithm for guiding center motion is presented. The algorithm is based on the Poincar\'e (mid-point) generating function.
Pipelined algorithms implemented in field programmable gate arrays are being extensively used for hardware triggers in the modern experimental high energy physics field and the complexity of such algorithms are increases rapidly. For…
This overview is devoted to splitting methods, a class of numerical integrators intended for differential equations that can be subdivided into different problems easier to solve than the original system. Closely connected with this class…
We introduce an algebraic methodology for designing exactly-solvable Lie model Hamiltonians. The idea consists in looking at the algebra generated by bond operators. We illustrate how this method can be applied to solve numerous problems of…
We consider the problem of generating automatic code given sample input-output pairs. We train a neural network to map from the current state and the outputs to the program's next statement. The neural network optimizes multiple tasks…
Numerical methods that preserve geometric invariants of the system, such as energy, momentum or the symplectic form, are called geometric integrators. In this paper we present a method to construct symplectic-momentum integrators for…
We present a universal quantum Monte Carlo algorithm for simulating arbitrary high-spin (spin greater than 1/2) Hamiltonians, based on the recently developed permutation matrix representation (PMR) framework. Our approach extends a…
In earlier work, we developed an approach for automatic complexity analysis of integer programs, based on an alternating modular inference of upper runtime and size bounds for program parts. In this paper, we show how recent techniques to…
Recent advancements in natural language processing \cite{gpt2} \cite{BERT} have led to near-human performance in multiple natural language tasks. In this paper, we seek to understand whether similar techniques can be applied to a highly…
We present a new class of exponential integrators for ordinary differential equations. They are locally exact, i.e., they preserve the linearization of the original system at every point. Their construction consists in modifying existing…
We reconsider the variational derivation of symplectic partitioned Runge-Kutta schemes. Such type of variational integrators are of great importance since they integrate mechanical systems with high order accuracy while preserving the…
We introduce the use of high order automatic differentiation, implemented via the algebra of truncated Taylor polynomials, in genetic programming. Using the Cartesian Genetic Programming encoding we obtain a high-order Taylor representation…
We study efficiency of higher order integrator schemes for the hybrid Monte Carlo (HMC) algorithm. Numerical tests are performed for Quantum Chromo Dynamics (QCD) with two flavors of Wilson fermions. We compare 2nd, 4th and 6th order…
Modular arithmetic is widely used in crytography and symbolic computation. This paper presents a vectorized Montgomery algorithm for modular multiplication, the key to fast modular arithmetic, that fully utilizes the SIMD instructions. We…
The existence of explicit symplectic integrators for general nonseparable Hamiltonian systems is an open and important problem in both numerical analysis and computing in science and engineering, as explicit integrators are usually more…