Related papers: Numerical generation of vector potentials from spe…
In this review many of the well known tools for the analysis of Complex systems are used in order to study the global coupling of the turbulent convection zone with the solar atmosphere where the magnetic energy is dissipated explosively.…
Properties of the magnetic translation operators for a charged particle moving in a crystalline potential and a uniform magnetic field show that it is necessary to consider all inequivalent irreducible projective representations of the the…
We deal with direct and inverse problems of the calculus of variations on arbitrary time scales. Firstly, using the Euler-Lagrange equation and the strengthened Legendre condition, we give a general form for a variational functional to…
The toric code can be constructed as a gauge theory of finite groups on oriented two dimensional lattices. Here we construct analogous models with the gauge fields belonging to groupoids, which are categories where every morphism has an…
We review various approaches to approximating general relativistic effects in hydrodynamic simulations of stellar core collapse and post-bounce evolution. Different formulations of a modified Newtonian gravitational potential are presented.…
In this paper, we present a new class of invertible transformations with an application to flow-based generative models. We indicate that many well-known invertible transformations in reversible logic and reversible neural networks could be…
Representing vector fields by potentials can be a challenging task in domains with cavities or tunnels, due to the presence of harmonic fields which are both irrotational and solenoidal but may have no scalar or vector potentials. For…
Rydberg atom arrays have emerged as a powerful platform to simulate a number of exotic quantum ground states and phase transitions. To verify these capabilities numerically, we develop a versatile quantum Monte Carlo sampling technique…
The generic problem of extracting information on intrinsic particle properties from the whole class of interacting magnetic fine particle systems is a long standing and difficult inverse problem. As an example, the Switching Field…
Despite extensive research efforts, few quantum algorithms for classical optimization demonstrate realizable quantum advantage. The utility of many quantum algorithms is limited by high requisite circuit depth and nonconvex optimization…
We present a novel class of methods to compute functions of matrices or their action on vectors that are suitable for parallel programming. Solving appropriate simple linear systems of equations in parallel (or computing the inverse of…
Generating graph structures is a challenging problem due to the diverse representations and complex dependencies among nodes. In this paper, we introduce Graph Variational Recurrent Neural Network (GraphVRNN), a probabilistic autoregressive…
The inversion of nabla Laplace transform, corresponding to a causal sequence, is considered. Two classical methods, i.e., residual calculation method and partial fraction method are developed to perform the inverse nabla Laplace transform.…
Despite recent advances, goal-directed generation of structured discrete data remains challenging. For problems such as program synthesis (generating source code) and materials design (generating molecules), finding examples which satisfy…
Although machine-learning potentials have recently had substantial impact on molecular simulations, the construction of a robust training set can still become a limiting factor, especially due to the requirement of a reference ab initio…
The field of molecular programming allows for the programming of the structure and behavior of matter at the molecular level, even to the point of encoding arbitrary computation. However, current approaches tend to be wasteful in terms of…
Vector data is prevalent across business and scientific applications, and its popularity is growing with the proliferation of learned embeddings. Vector data collections often reach billions of vectors with thousands of dimensions, thus,…
We develop an approach for building quantum models based on the exponentially growing orthonormal basis of Hartley kernel functions. First, we design a differentiable Hartley feature map parametrized by real-valued argument that enables…
The ideal Magnetohydrodynamics (MHD) equations are challenging because one needs to maintain the divergence free condition, $\nabla \cdot \Bv = 0$. Many numerical methods have been developed to enforce this condition. In this work, we…
Spin wave computing device where an algorithm can be encoded by recording a corresponding magnetization pattern onto a hard magnetic material was previously proposed1 and a particular implementation of a vector-matrix algorithm was…