相关论文: BFACF-style algorithms for polygons in the body-ce…

We study the problem of enumerating Tarski fixed points on finite lattices. We derive query complexity lower bounds for finding three or more Tarski fixed points of isotone maps and the subclasses of increasing and decreasing isotone maps.…

The popular BFGS quasi-Newton minimization algorithm under reasonable conditions converges globally on smooth convex functions. This result was proved by Powell in 1976: we consider its implications for functions that are not smooth. In…

In recent work [arXiv:2003.06939v2] a novel fermion to qubit mapping -- called the compact encoding -- was introduced which outperforms all previous local mappings in both the qubit to mode ratio, and the locality of mapped operators. There…

In order to achieve error rates necessary for advantageous quantum algorithms, Quantum Error Correction (QEC) will need to be employed, improving logical qubit fidelity beyond what can be achieved physically. As today's devices begin to…

In a recent paper by the same authors, we provided a theoretical foundation for the component-by-component (CBC) construction of lattice algorithms for multivariate $L_2$ approximation in the worst case setting, for functions in a periodic…

Collapse modes in compressed simple cubic (SC) and body-centered cubic (BCC) periodic arrangements of elastic frictionless beads were studied numerically using the discrete element method. Under pure hydrostatic compression, the SC…

Much of the past work on asynchronous approximate Byzantine consensus has assumed scalar inputs at the nodes [3, 7]. Recent work has yielded approximate Byzantine consensus algorithms for the case when the input at each node is a…

We study the Back and Forth Error Compensation and Correction (BFECC) method for linear hyperbolic PDE systems. The BFECC method has been applied to schemes for advection equations to improve their stability and order of accuracy. Similar…

We discuss the possibility of the existence of finite algorithms that may give distinct knot classes. In particular we present two attempts for such algorithms which seem promising, one based on knot projections on a plane, the other on…

We develop a variational method to obtain many-body ground states of the Bose-Hubbard model using feedforward artificial neural networks. A fully-connected network with a single hidden layer works better than a fully-connected network with…

Lagrange coded computation (LCC) is essential to solving problems about matrix polynomials in a coded distributed fashion; nevertheless, it can only solve the problems that are representable as matrix polynomials. In this paper, we propose…

This paper provides the theoretical foundation for the construction of lattice algorithms for multivariate $L_2$ approximation in the worst case setting, for functions in a periodic space with general weight parameters. Our construction…

Recent advances in the study of conformally invariant discrete random processes have lead to increasing interest in the study of discrete analogues to holomorphic functions. Of particular interest are results which provide conditions under…

Materials science and the study of the electronic properties of solids are a major field of interest in both physics and engineering. The starting point for all such calculations is single-electron, or non-interacting, band structure…

We introduce one-center method in spherical coordinates to carry out Hartree-Fock calculations. Both the radial wave function and the angular wave function are expanded by B-splines, and the radial knots and angular knots are adjusted to…

The Riesz potential $f_s(r)=r^{-s}$ is known to be an important building block of many interactions, including Lennard-Jones type potentials $f_{n,m}^{\rm{LJ}}(r):=a r^{-n}-b r^{-m}$, $n>m$ that are widely used in Molecular Simulations. In…

Many machine learning tasks, such as principal component analysis and low-rank matrix completion, give rise to manifold optimization problems. Although there is a large body of work studying the design and analysis of algorithms for…

Fracton order is a new kind of quantum order characterized by topological excitations that exhibit remarkable mobility restrictions and a robust ground state degeneracy (GSD) which can increase exponentially with system size. In this paper,…

The Embedded-Atom Model (EAM) provides a phenomenological description of atomic arrangements in metallic systems. It consists of a configurational energy depending on atomic positions and featuring the interplay of two-body atomic…

Quadratic programming over orthogonal matrices encompasses a broad class of hard optimization problems that do not have an efficient quantum representation. Such problems are instances of the little noncommutative Grothendieck problem…