相关论文: Q-systems, Heaps, Paths and Cluster Positivity

Machine learning is becoming an increasingly valuable tool in mathematics, enabling one to identify subtle patterns across collections of examples so vast that they would be impossible for a single researcher to feasibly review and analyze.…

We provide a homomorphism of algebras from the quantum group $\mathbf{U}^+_v(\mathfrak{g})$ to the corresponding quantum cluster algebra $\mathcal {A}_q$ with principal coefficients. As a by-product, we show that the quantum cluster…

This paper proposes a hybrid quantum-classical algorithm that learns a suitable quantum feature map that separates unlabelled data that is originally non linearly separable in the classical space using a Variational quantum feature map and…

We present a novel approach for finding and evaluating structural models of small metallic nanoparticles. Rather than fitting a single model with many degrees of freedom, the approach algorithmically builds libraries of nanoparticle…

Clustering algorithms are of fundamental importance when dealing with large unstructured datasets and discovering new patterns and correlations therein, with applications ranging from scientific research to medical imaging and marketing…

A {\em cyclic graph} is a graph with at each vertex a cyclic order of the edges incident with it specified. We characterize which real-valued functions on the collection of cubic cyclic graphs are partition functions of a real vertex model…

Quantum periodic cluster methods for strongly correlated electron systems are reformulated and developed. The reformulation and development are based on a canonical transformation which periodizes the fermions in the cluster space. The…

Let $\FF$ be a finite field and $(Q,\bfd)$ an acyclic valued quiver with associated exchange matrix $\tilde{B}$. We follow Hubery's approach \cite{hub1} to prove our main conjecture of \cite{rupel}: the quantum cluster character gives a…

We introduce the notion of a lower bound cluster algebra generated by projective cluster variables as a polynomial ring over the initial cluster variables and the so-called projective cluster variables. We show that under an acyclicity…

We provide evidence that it is computationally difficult to approximate the partition function of the ferromagnetic q-state Potts model when q>2. Specifically we show that the partition function is hard for the complexity class #RHPi_1…

We obtain restrictions on the rational homotopy types of mapping spaces and of classifying spaces of homotopy automorphisms by means of the theory of positive weight decompositions. The theory applies, in particular, to connected components…

The objective of the present paper is to prove cluster multiplication theorem in the quantum cluster algebra of type $A_{2}^{(2)}$. As corollaries, we obtain bar-invariant $\mathbb{Z}[q^{\pm\frac{1}{2}}]$-bases established in [6], and…

We investigate nuclear matter at finite temperature and density, including the formation of light clusters up to the alpha particle The novel feature of this work is to include the formation of clusters as well as their dissolution due to…

We introduce a new method for performing clustering with the aim of fitting clusters with different scatters and weights. It is designed by allowing to handle a proportion $\alpha$ of contaminating data to guarantee the robustness of the…

A natural way to characterize the cluster structure of a dataset is by finding regions containing a high density of data. This can be done in a nonparametric way with a kernel density estimate, whose modes and hence clusters can be found…

A factor-graph representation of quantum-mechanical probabilities (involving any number of measurements) is proposed. Unlike standard statistical models, the proposed representation uses auxiliary variables (state variables) that are not…

The clustering of a data set is one of the core tasks in data analytics. Many clustering algorithms exhibit a strong contrast between a favorable performance in practice and bad theoretical worst-cases. Prime examples are least-squares…

This note introduces a novel clustering preserving transformation of cluster sets obtained from $k$-means algorithm. This transformation may be used to generate new labeled data{}sets from existent ones. It is more flexible that Kleinberg…

This is the last part of a series of three papers on the subject. In the first part we have considered the duality of algebraic quantum groups. In that paper, we use the term algebraic quantum group for a regular multiplier Hopf algebra…

A particular choice of renormalization, within the simplifications provided by the non-perturbative property of Effective Locality, leads to a completely finite, renormalized theory of QCD, in which all correlation functions can, in…