相关论文: A cluster version of the GGT sum rule

Increasing inhomogeneity due to gravitational clumping reflects increasing gravitational entropy in a time evolving universe. Starting from an ensemble of uniformly distributed particles it is demonstrated that gravitational clustering is…

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…

We provide a far reaching derived equivalence classification of the cluster-tilted algebras of Dynkin type D and suggest standard forms for the derived equivalence classes. We believe that the classification is complete, but some subtle…

We use renormalization group summed perturbation theory (RGSPT) to improve perturbation series in quantum chromodynamics in the determination of some of the standard model parameters.

Various applications of quantum algebraic techniques in nuclear structure physics and in molecular physics are briefly reviewed and a recent application of these techniques to the structure of atomic clusters is discussed in more detail.

Various theories of quantum gravity predict the existence of a minimum length scale, which implies the Planck-scale modifications of the Heisenberg uncertainty principle to a so-called generalized uncertainty principle (GUP). Previous…

An analytical understanding of the strongly nonlinear regime of gravitational collapse has been difficult to achieve. The only insight has been the stable clustering hypothesis, which assumes that the number of neighbors for objects…

The validity of the Luttinger sum rule is considered for finite systems of interacting electrons, where the Fermi volume is determined by location of zeroes of Green's function. It is shown that the sum rule in the paramagnetic state is…

The development on relativistic nuclear many-body theories is reviewed. The second order self-energies of hadrons are calculated from $\hat{S}_2$ matrix, and then an effective method to solve nuclear many-body problems, sum rules on quantum…

A univariate clustering criterion for stationary processes satisfying a $\beta$-mixing condition is proposed extending the work of \cite{KB2} to the dependent setup. The approach is characterized by an alternative sample criterion function…

We generalise the work of Sarnak-Tsimerman to twisted sums of Kloosterman sums and thus give evidence towards the twisted Linnik-Selberg Conjecture.

We re-examine the estimates of the higher twist contributions to the integral of $g_1$, the polarised structure function of the nucleon, based on QCD sum rules. By including corrections both to the perturbative contribution and to the low…

We present recent results from Jefferson Lab on sum rules related to the spin structure of the nucleon. We then discuss how the Bjorken sum rule, with its connection to the Gerasimov-Drell-Hearn sum, allows us to conveniently define an…

We derive a sum rule which establishes a linear relation between a particle's anomalous magnetic moment and a quantity connected to the photoabsorption cross-section. This quantity cannot be measured directly. However, it can be computed…

Clustering mixtures of Gaussian distributions is a fundamental and challenging problem that is ubiquitous in various high-dimensional data processing tasks. While state-of-the-art work on learning Gaussian mixture models has focused…

A new method for hierarchical clustering is presented. It combines treelets, a particular multiscale decomposition of data, with a projection on a reproducing kernel Hilbert space. The proposed approach, called kernel treelets (KT),…

We develop a general theory for estimating the probability that a galaxy cluster of a given shape exists. The theory is based on the observed result that the distribution of galaxies is very close to quasi-equilibrium, in both its linear…

Fluctuation theorem is derived for a quantum current system around a nonequilibrium steady state. It is demonstrated that the fluctuation theorem can be a part of the generalized Green-Kubo formula or a nonlinear response theory of an…

We formulate a general setting for the cluster expansion method and we discuss sufficient criteria for its convergence. We apply the results to systems of classical and quantum particles with stable interactions.

We revisit the $(f,g)$-clustering problem that we introduced in a recent work [SODA'25], and which subsumes fundamental clustering problems such as $k$-Center, $k$-Median, Min-Sum of Radii, and Min-Load $k$-Clustering. This problem assigns…