Related papers: Graded cluster expansion for lattice systems
Clustering is a powerful and extensively used data science tool. While clustering is generally thought of as an unsupervised learning technique, there are also supervised variations such as Spath's clusterwise regression that attempt to…
The short-range attraction and long-range repulsion (SALR) between nanoparticles or macromolecules can lead to spontaneous pattern formation on solid surfaces, fluid interfaces or membranes. In order to study the self-assembly in such…
We introduce a generic scheme to perform non-perturbative linked cluster expansions in long-range ordered quantum phases. Clusters are considered to be surrounded by an ordered reference state leading to effective edge-fields in the exact…
In this thesis we investigate the Renormalization Group (RG) approach in finite-dimensional glassy systems, whose critical features are still not well-established, or simply unknown. We focus on spin and structural-glass models built on…
In this technical note, cluster consensus of discrete-time linear multi-agent systems is investigated. A set of stochastic matrices $\mathcal{P}$ is said to be a cluster consensus set if the system achieves cluster consensus for any initial…
We consider the rigidity and global rigidity of bar-joint frameworks in Euclidean $d$-space under additional dilation constraints in specified coordinate directions. In this setting we obtain a complete characterisation of generic rigidity.…
We study domain growth properties of two species of particles executing biased diffusion on a half-filled square lattice, consisting of just two lanes. Driven in opposite directions by an external ``electric'' field, the particles form…
Distributed signal processing for wireless sensor networks enables that different devices cooperate to solve different signal processing tasks. A crucial first step is to answer the question: who observes what? Recently, several distributed…
Under quite general conditions critical phenomena can be described with high order linked cluster expansions. The coefficients of the series admit a graphical expansion that is generated with the aid of computers. Our generalization of…
We revisit homogenisation theory for Friedrichs systems. In particular, we show that $G$-compactness can be obtained under severely weaker assumptions than in the original work of Burazin and Vrdoljak (2014). In this way we extend the…
The harmonic Frenkel-Kontorova model is used to illustrate with an exactly solvable example a general technique of mapping a coherently strained epitaxial system with continuous atomic displacements onto a lattice gas model (LGM) with only…
This article concerns a class of generalized linear mixed models for clustered data, where the random effects are mapped uniquely onto the grouping structure and are independent between groups. We derive necessary and sufficient conditions…
The purpose of this paper is to extend standard finite mixture models in the context of multinomial mixtures for spatial data, in order to cluster geographical units according to demographic characteristics. The spatial information is…
Loss-based clustering methods, such as k-means and its variants, are standard tools for finding groups in data. However, the lack of quantification of uncertainty in the estimated clusters is a disadvantage. Model-based clustering based on…
The lensing information provided by multiple images, arclets, and statistical distortions can all be formulated as linear constraints on the arrival-time surface, and hence on the mass distribution. This reduces cluster lens reconstruction…
We give a general constructive proof for hierarchical coordinatizations (Lagrange Decompositions) of permutation groups. The generalization originates from the investigation of how the subgroup chains of finite permutation groups yield…
With the inflation of the data, clustering analysis, as a branch of unsupervised learning, lacks unified understanding and application of its mathematical law. Based on the view of fixed point, this paper restates the model-based clustering…
Crystalline alloys and related mixed systems make up a large family of materials with high tunability which have been proposed as the solution to a large number of energy related materials design problems. Due to the presence of chemical…
In this paper, we investigate the polyhedral structure of two submodular sets with generalized upper bound (GUB) constraints, which arise as important substructures in various real-world applications. We derive a class of strong valid…
Generalised bi-adjoint scalar amplitudes, obtained from integrations over moduli space of punctured $\mathbb{CP}^{k-1}$, are novel extensions of the CHY formalism. These amplitudes have realisations in terms of Grassmannian cluster…