Related papers: Cluster mechanisms in the fully frustrated Ising m…
A disordered spin glass model where both static and dynamical properties depend on macroscopic magnetizations is presented. These magnetizations interact via random couplings and, therefore, the typical quenched realization of the system…
A new approach to clustering, based on the physical properties of inhomogeneous coupled chaotic maps, is presented. A chaotic map is assigned to each data-point and short range couplings are introduced. The stationary regime of the system…
Frustration, that is, the impossibility of satisfying the energetic preferences between all spin pairs simultaneously, underlies the complexity of many fundamental properties in spin systems, including the computational difficulty in…
As a kind of basic machine learning method, clustering algorithms group data points into different categories based on their similarity or distribution. We present a clustering algorithm by finding hyper-planes to distinguish the data…
In this paper, we report new results on a novel Ising machine technology for solving combinatorial optimization problems using networks of coupled self-sustaining oscillators. Specifically, we present several working hardware prototypes…
In many statistical linear inverse problems, one needs to recover classes of similar curves from their noisy images under an operator that does not have a bounded inverse. Problems of this kind appear in many areas of application.…
Clustering is often used for discovering structure in data. Clustering systems differ in the objective function used to evaluate clustering quality and the control strategy used to search the space of clusterings. Ideally, the search…
We present a procedure to solve the inverse Ising problem, that is to find the interactions between a set of binary variables from the measure of their equilibrium correlations. The method consists in constructing and selecting specific…
A systematic study of both classical and quantum geometric frustrated Ising models with a competing ordering mechanism is reported in this paper. The ordering comes in the classical case from a coupling of 2D layers and in the quantum model…
In this paper we propose a novel method to study critical systems numerically by a combined collective-mode algorithm and Renormalization Group on the lattice. This method is an improved version of MCRG in the sense that it has all the…
Usual formulations of the clustering coefficient can be shown to be insufficient in the task of describing the local topology of very simple networks. Motivated by this, we review some alternatives in order to present an extension, the…
The size distribution of geometrical spin clusters is exactly found for the one dimensional Ising model of finite extent. For the values of lattice constant $\beta$ above some "critical value" $\beta_c$ the found size distribution…
The emergence of specialized optimization hardware such as CMOS annealers and adiabatic quantum computers carries the promise of solving hard combinatorial optimization problems more efficiently in hardware. Recent work has focused on…
Given the ubiquity of lattice models in physics, it is imperative for researchers to possess robust methods for quantifying clusters on the lattice --- whether they be Ising spins or clumps of molecules. Inspired by biophysical studies, we…
Unsupervised learning is widely recognized as one of the most important challenges facing machine learning nowa- days. However, in spite of hundreds of papers on the topic being published every year, current theoretical understanding and…
We study the design of interactive clustering algorithms for data sets satisfying natural stability assumptions. Our algorithms start with any initial clustering and only make local changes in each step; both are desirable features in many…
The structure of defect clusters formed in a displacement cascade plays a significant role in the micro-structural evolution during irradiation. Molecular dynamics simulations have been widely used to study collision cascades and subsequent…
A recently introduced model describing the folding of the triangular lattice is generalized allowing for defects in the lattice and written as an Ising model with nearest-neighbor and plaquette interactions on the honeycomb lattice. Its…
The paper tackles the problem of clustering multiple networks, directed or not, that do not share the same set of vertices, into groups of networks with similar topology. A statistical model-based approach based on a finite mixture of…
One of the most prominent challenges in clustering is "the user's dilemma," which is the problem of selecting an appropriate clustering algorithm for a specific task. A formal approach for addressing this problem relies on the…