相关论文: Can fusion coefficients be calculated from the dep…
Single image depth estimation is a foundational task in computer vision and generative modeling. However, prevailing depth estimation models grapple with accommodating the increasing resolutions commonplace in today's consumer cameras and…
We investigate the depth of the tensor product of finitely generated modules over local rings. One of the main ingredients of our approach is a lifting construction introduced by Huneke, Jorgensen, and Wiegand. We recover a result of…
Classical complexity theory measures the cost of computing a function, but many computational tasks require committing to one valid output among several. We introduce determination depth -- the minimum number of sequential layers of…
Recent advances in end-to-end unsupervised learning has significantly improved the performance of monocular depth prediction and alleviated the requirement of ground truth depth. Although a plethora of work has been done in enforcing…
Projective Norms are a class of tensor norms that map on the input and output spaces. These norms are useful for providing a measure of entanglement. Calculating the projective norms is an NP-hard problem, which creates challenges in…
The best way to combine the results of deep learning with standard 3D reconstruction pipelines remains an open problem. While systems that pass the output of traditional multi-view stereo approaches to a network for regularisation or…
Since its inception, Benders Decomposition (BD) has been successfully applied to a wide range of large-scale mixed-integer (linear) problems. The key element of BD is the derivation of Benders cuts, which are often not unique. In this…
Product formulae are a popular class of digital quantum simulation algorithms due to their conceptual simplicity, low overhead, and performance which often exceeds theoretical expectations. Recently, Richardson extrapolation and polynomial…
As a series of work about 5D (spacetime) topological orders, here we employ the path-integral formalism of 5D topological quantum field theory (TQFT) established in Zhang and Ye, JHEP 04 (2022) 138 to explore non-Abelian fusion rules,…
The design of fusion devices is typically based on computationally expensive simulations. This can be alleviated using high aspect ratio models that employ a reduced number of free parameters, especially in the case of stellarator…
We prove upper and lower bounds for certain sums of products of fractional parts by using majoring and minorizing functions from Fourier analysis. In special cases the upper bounds are sharp if there exist counterexamples to the Littlewood…
Period finding and phase estimation are fundamental in quantum computing. Prior work has established lower bounds on their success probabilities. Such quantum algorithms measure a state $|\hat\ell\rangle$ in an $n$-qubit computational…
The concept of data depth in non-parametric multivariate descriptive statistics is the generalization of the univariate rank method to multivariate data. Halfspace depth is a measure of data depth. Given a set S of points and a point p, the…
This paper looks to apply the mathematical framework of the Theory of Functional Connections to the solution of boundary-value problems arising from hybrid systems. The Theory of Functional Connections is a technique to derive constrained…
The aim of this paper is to introduce a method for computing Hilbert decompositions (and consequently the Hilbert depth) of a finitely generated multigraded module $M$ over the polynomial ring $K[X_1,..., X_n]$ by reducing the problem to…
To define a minimal mathematical framework for isolating some of the characteristic properties of quantum entanglement, we introduce a generalization of the tensor product of graphs. Inspired by the notion of a density matrix, the…
A compression algorithm is introduced for multi-determinant wave functions which can greatly reduce the number of determinants that need to be evaluated in quantum Monte Carlo calculations. We have devised an algorithm with three levels of…
We show that Inner Product in $2n$ variables, $\mathbf{IP}_n(x, y) = x_1y_1 \oplus \ldots \oplus x_ny_n$, can be computed by depth-3 bottom fan-in 2 circuits of size $\mathsf{poly}(n)\cdot (9/5)^n$, matching the lower bound of G\"o\"os,…
A product quadrature rule, based on the filtered de la Vall\'ee Poussin polynomial approximation, is proposed for evaluating the finite Hilbert transform in [-1; 1]. Convergence results are stated in weighted uniform norm for functions…
The contribution of the hadronic continuum in the QCD sum rule calculation of the parameters entering in pseudoscalar meson mixing is evaluated by making use of simple integration kernels tailored in order to practically eliminate the…