相关论文: Counting components of an integral lamination
A recently developed numerical method for the calculation of derivatives of functions of general complex matrices, which can also be combined with implicit matrix function approximations such as Krylov-Ritz type algorithms, is presented. An…
We count subrings of small index of $\mathbb{Z}^n$, where the addition and multiplication are defined componentwise. Let $f_n(k)$ denote the number of subrings of index $k$. For any $n$, we give a formula for this quantity for all integers…
We introduce an image based algorithmic tool for analyzing multi-component shapes here. Due to the generic concept of multi-component shapes, our method can be applied to the analysis of a wide spectrum of applications where real objects…
We give an algorithm for reversion of formal power series, based on an efficient way to implement the Lagrange inversion formula. Our algorithm requires $O(n^{1/2}(M(n) + MM(n^{1/2})))$ operations where $M(n)$ and $MM(n)$ are the costs of…
This paper presents a method for expressing the determinant of an N {\times} N complex block matrix in terms of its constituent blocks. The result allows one to reduce the determinant of a matrix with N^2 blocks to the product of the…
We refine the bit complexity analysis of an algorithm for the computation of at least one point per connected component of a smooth real algebraic set, yielding exponential speedup (with respect to the number of variables) compared to prior…
The computation of determinants plays a central role in diagrammatic Monte Carlo algorithms for strongly correlated systems. The evaluation of large numbers of determinants can often be the limiting computational factor determining the…
For a positive integer $d$, the $d$-dimensional Chebyshev-Frolov lattice is the $\mathbb{Z}$-lattice in $\mathbb{R}^d$ generated by the Vandermonde matrix associated to the roots of the $d$-dimensional Chebyshev polynomial. It is important…
We propose approximate and accurate formulas for the number of electron configurations in hot plasmas. Such a quantity is an ingredient of algorithms devoted to the generation of configurations or superconfigurations, which is a…
The negative dimensional integration method (NDIM) is a technique where several difficulties concerning loop integration can be overcome. From usual covariant gauges to complicated Coulomb gauge integrals, and even the trickiest light-cone…
Motivated by finding analogues of elliptic curve point counting techniques, we introduce one deterministic and two new Monte Carlo randomized algorithms to compute the characteristic polynomial of a finite rank-two Drinfeld module. We…
We introduce a novel method for encoding integers using smooth real-valued functions whose integral properties implicitly reflect discrete quantities. In contrast to classical representations, where the integer appears as an explicit…
We present a method for the calculation of electronic structure of systems that contain tens of thousands of atoms. The method is based on the division of the system into mutually overlapping fragments and the representation of the…
A numerical program is presented which facilitates the computation of the full set of one-gluon loop diagrams (including ghost loop contributions), with M attached external gluon lines in all possible ways. The feasibility of such a task…
The computation of eigenvalues of large-scale matrices arising from finite element discretizations has gained significant interest in the last decade. Here we present a new algorithm based on slicing the spectrum that takes advantage of the…
For the investigation of higher order Feynman integrals, potentially with tensor structure, it is highly desirable to have numerical methods and automated tools for dedicated, but sufficiently 'simple' numerical approaches. We elaborate two…
We present a detailed description of the recent idea for a direct decomposition of Feynman integrals onto a basis of master integrals by projections, as well as a direct derivation of the differential equations satisfied by the master…
The integer complexity $f(n)$ of a positive integer $n$ is defined as the minimum number of 1's needed to represent $n$, using additions, multiplications and parentheses. We present two simple and faster algorithms for computing the integer…
We suggest an efficient scheme for quantum computation with linear optical elements utilizing "linked" photon states. The linked states are designed according to the particular quantum circuit one wishes to process. Once a linked-state has…
We present a new program package for calculating one-loop Feynman integrals, based on a new method avoiding Feynman parametrization and the contraction due to Passarino and Veltman. The package is calculating one-, two- and three-point…