相关论文: Recent mathematical advances in coupled cluster th…

Count data is becoming more and more ubiquitous in a wide range of applications, with datasets growing both in size and in dimension. In this context, an increasing amount of work is dedicated to the construction of statistical models…

In this work clustering schemes for uncertain and structured data are considered relying on the notion of Wasserstein barycenters, accompanied by appropriate clustering indices based on the intrinsic geometry of the Wasserstein space where…

This review paper highlights research findings from the authors' participation in the SUMMIT-P project, which studied how to build and sustain multi-institutional interdisciplinary partnerships to design and implement curricular change in…

We develop and numerically analyze an algebraic-geometric framework for spin-adapted coupled-cluster (CC) theory. Since the electronic Hamiltonian is SU(2)-invariant, physically relevant quantum states lie in the spin singlet sector. We…

A new approach has been recently developed to study the arithmetic of hyperelliptic curves $y^2=f(x)$ over local fields of odd residue characteristic via combinatorial data associated to the roots of $f$. Since its introduction, numerous…

Divergence measures play a central role and become increasingly essential in deep learning, yet efficient measures for multiple (more than two) distributions are rarely explored. This becomes particularly crucial in areas where the…

Graph clustering is a central topic in unsupervised learning with a multitude of practical applications. In recent years, multi-view graph clustering has gained a lot of attention for its applicability to real-world instances where one has…

Hierarchical clustering is one of the most powerful solutions to the problem of clustering, on the grounds that it performs a multi scale organization of the data. In recent years, research on hierarchical clustering methods has attracted…

The paper deals with a comprehensive theory of mappings, whose local behavior can be described by means of linear subspaces, contained in the graphs of two (primal and dual) generalized derivatives. This class of mappings includes the…

Local general depth ($LGD$) functions are used for describing the local geometric features and mode(s) in multivariate distributions. In this paper, we undertake a rigorous systematic study of $LGD$ and establish several analytical and…

In 2010, Shiffman and Zelditch proved a central limit theorem (CLT) for smooth statistics of Gaussian random zeros in codimension one over compact K\"ahler manifolds. They raised the question of whether this result admits a two-fold…

A multiple-perspective co-citation analysis method is introduced for characterizing and interpreting the structure and dynamics of co-citation clusters. The method facilitates analytic and sense making tasks by integrating network…

We propose a modified coupled cluster Monte Carlo algorithm that stochastically samples connected terms within the truncated Baker--Campbell--Hausdorff expansion of the similarity transformed Hamiltonian by construction of coupled cluster…

We present a spin-free, size-extensive, and size-consistent coupled cluster method based on a generalised normal ordered exponential ansatz. This approach is a natural generalisation of single-reference coupled cluster theory for arbitrary…

Real-world networks often come with side information that can help to improve the performance of network analysis tasks such as clustering. Despite a large number of empirical and theoretical studies conducted on network clustering methods…

The tailored coupled cluster (TCC) approach is a promising ansatz that preserves the simplicity of single-reference coupled cluster theory, while incorporating a multi-reference wave function through amplitudes obtained from a preceding…

The investigation and classification of non-unique factorization phenomena has attracted some interest in recent literature. For finitely generated monoids, S.T. Chapman and P.A. Garc\'ia-S\'anchez, together with several co-authors, derived…

This work provides a quantum-computing-first derivation of the Unitary Coupled Cluster ansatz, showing that its structure emerges naturally from fermionic algebra under unitary constraints. By explicitly connecting second quantization,…

In online clustering problems, there is often a large amount of uncertainty over possible cluster assignments that cannot be resolved until more data are observed. This difficulty is compounded when clusters follow complex distributions, as…

In the cluster algebra literature, the notion of a graded cluster algebra has been implicit since the origin of the subject. In this work, we wish to bring this aspect of cluster algebra theory to the foreground and promote its study. We…