Related papers: A cluster version of the GGT sum rule

In this paper, we define a parametric variant of generalized Euler sums and call them the (alternating) parametric Euler $T$-sums. By using the contour integration method and residue theorem, we establish several explicit formulae for the…

Let $k$ be a real abelian number field and $p$ an odd prime not dividing $[k:\mathbb{Q}]$. For a natural number $d$, let $E_d$ denote the group of units of $k$ congruent to $1$ modulo $d$, $C_d$ the subgroup of $d$-circular units of $E_d$,…

A cluster expansion is proposed, that applies to both continuous and discrete systems. The assumption for its convergence involves an extension of the neat Kotecky-Preiss criterion. Expressions and estimates for correlation functions are…

I extend the well-known photonuclear sum rule that relates the strength of the photoexcitation of the giant dipole resonance in a nucleus to the number of elementary scatterers-nucleons to the case of virtual photons. The new sum rule…

We describe various expansion schemes that can be used to study gravitational clustering. Obtained from the equations of motion or their path-integral formulation, they provide several perturbative expansions that are organized in different…

We use commutativity of null-integrated operators on the same null plane to construct dispersive CFT sum rules for spinning operators. The contribution of heavy blocks to these sum rules is dominated by a saddle configuration that we call…

Dark matter halos are the building blocks of the universe as they host galaxies and clusters. The knowledge of the clustering properties of halos is therefore essential for the understanding of the galaxy statistical properties. We derive…

Goodwillie's rational isomorphism between relative algebraic K-theory and relative cyclic homology, together with the lambda decomposition of cyclic homology, illustrates the close relationships among algebraic K-theory, cyclic homology,…

We study the polarized Bjorken sum rule at low momentum transfer squared Q2<3GeV2 in the twist-two approximation and to the next-to-next-to-leading order accuracy.

We construct a framework for studying clustering algorithms, which includes two key ideas: persistence and functoriality. The first encodes the idea that the output of a clustering scheme should carry a multiresolution structure, the second…

Sum rules are elegant formulas that relate entropy functionals to coefficients associated with orthogonal polynomials [Sim11]. In a series of paper (see for example [GNR16], [GNR17], [BSZ18a], [BSZ18b]), interesting connections have been…

A special linear Grassmann variety SGr(k,n) is the complement to the zero section of the determinant of the tautological vector bundle over Gr(k,n). For a representable ring cohomology theory A(-) with a special linear orientation and…

We derive Born's rule and the density-operator formalism for quantum systems with Hilbert spaces of dimension two or larger. Our extension of Gleason's theorem only relies upon the consistent assignment of probabilities to the outcomes of…

This paper investigates the validity of Kleinberg's axioms for clustering functions with respect to the quite popular clustering algorithm called $k$-means. While Kleinberg's axioms have been discussed heavily in the past, we concentrate…

A clustering algorithm based on the Hausdorff distance is introduced and compared to the single and complete linkage. The three clustering procedures are applied to a toy example and to the time series of financial data. The dendrograms are…

In this paper we consider several generalizations of the Borsuk-Ulam theorem for G-spaces and apply these results to Tucker type lemmas for G-simplicial complexes and PL-manifolds.

The cluster multiplication formulas for a generalized quantum cluster algebra of Kronecker type are explicitly given. Furthermore, a positive bar-invariant $\mathbb{Z}[q^{\pm\frac{1}{2}}]$-basis of this algebra is constructed.

This is the continuation of a previous article, in which the Bjorken and Voloshin sum rules were interpreted as statements of conservation of probability and energy. Here the formalism is extended to higher moments of the Hamiltonian…

The cluster category is a triangulated category introduced for its combinatorial similarities with cluster algebras. We prove that a cluster algebra A of finite type can be realized as a Hall algebra, called the exceptional Hall algebra, of…

We study cluster algebras with principal coefficient systems that are associated to unpunctured surfaces. We give a direct formula for the Laurent polynomial expansion of cluster variables in these cluster algebras in terms of perfect…