Related papers: Cluster Estimates for Modular Structures
Several perspectives of the cluster Gutzwiller method are briefly discussed. I show that the cluster mean-field method can be used for large inhomogeneous lattices, for computing local excitations, and for the time evolution of correlated…
We construct "quantum theta bases," extending the set of quantum cluster monomials, for various versions of skew-symmetric quantum cluster algebras. These bases consist precisely of the indecomposable universally positive elements of the…
The microscopic quantum field theory origins of warm inflation dynamics are reviewed. The warm inflation scenario is first described along with its results, predictions and comparison with the standard cold inflation scenario. The basics of…
These notes present an application of the geometric Satake equivalence to the description of characters of indecomposable tilting modules for reductive algebraic groups over fields of positive characteristic, obtained in joint work with G.…
Model selection in clustering requires (i) to specify a suitable clustering principle and (ii) to control the model order complexity by choosing an appropriate number of clusters depending on the noise level in the data. We advocate an…
These lecture notes provide an introduction to quantum cluster methods for strongly correlated systems. Cluster Perturbation Theory (CPT), the Variational Cluster Approximation (VCA) and Cellular Dynamical Mean Field Theory (CDMFT) are…
In the theory of generalized cluster algebras, we build the so-called cluster formula and $D$-matrix pattern. Then as applications, some fundamental conjectures of generalized cluster algebras are solved affirmatively.
Clusters of galaxies are used in a variety of ways to do cosmology. Some of them are presented here. Their X-ray emitting gas allows us to determine the baryon fraction, dark matter distribution and the matter density $\Omega_{m}$ of the…
Nonequilibrium quantum field theory is often used to derive an approximation for the evolution of number densities and asymmetries in astroparticle models when a more precise treatment of quantum thermal effects is required. This work…
We review recent experimental and theoretical progress in understanding the microscopic details of clustering in light nuclei. We discuss recent experimental results on $\alpha$-conjugate systems, molecular structures in neutron-rich…
Combining conservation of energy throughout nearly-spherical collapse of galaxy clusters with the virial theorem, we derive the mass-temperature relation for X-ray clusters of galaxies $T=CM^{2/3}$. The normalization factor $C$ and the…
We review clustering as an analysis tool and the underlying concepts from an introductory perspective. What is clustering and how can clusterings be realised programmatically? How can data be represented and prepared for a clustering task?…
The clustering ensemble technique aims to combine multiple clusterings into a probably better and more robust clustering and has been receiving an increasing attention in recent years. There are mainly two aspects of limitations in the…
We discuss the derivation of a ``cluster sum rule'' from the Gellmann-Goldberger-Thirring (GGT) sum rule as an alternative to the Thomas-Reiche-Kuhn (TRK) sum rule, which was used as the basis up to now. We compare differences in the…
The module theorem by Janhunen et al. demonstrates how to provide a modular structure in answer set programming, where each module has a well-defined input/output interface which can be used to establish the compositionality of answer sets.…
Light clusters (mass number $A \leq 4$) in nuclear matter at subsaturation densities are described using a quantum statistical approach. In addition to self-energy and Pauli-blocking, effects of continuum correlations are taken into account…
An approach for explicit consideration of cluster effects in nuclear systems and accurate ab initio calculations of cluster characteristics of nuclei is devised. The essential block of the approach is a construction of a basis which…
We study the stabilities of quantum states of macroscopic systems, against noises, against perturbations from environments, and against local measurements. We show that the stabilities are closely related to the cluster property, which…
In the present paper we examine the relationship between several type $A$ cluster theories and structures. We define a 2D geometric model of a cluster theory, which generalizes cluster algebras from surfaces, and encode several existing…
We discuss the evolution of the cluster temperature function (TF) in different scenarios for structure formation. We use the commonly adopted procedure of fitting the model parameters to the local TF data, finding the best fit values and,…