Related papers: Spectral sum rules and Selberg's integral
In this article, the logic rule ensembles approach to supervised learning is applied to the unsupervised or semi-supervised clustering. Logic rules which were obtained by combining simple conjunctive rules are used to partition the input…
We present a set of sum rules relating the low-energy light-by-light scattering to integrals of \gamma\gamma-fusion cross sections and use them to study the hadronic contributions.
In this work, we give a formula for coefficients of orthogonal polynomials on the unit circle. By using this formula, a new and computable approach is provided for sum rules which applying to a spectral gem problem proposed by Barry Simon…
We outline our approach to understand the family structure through the idea of a SM-like chiral fermion spectrum, one that is derivable from anomaly cancellation conditions in the same way as the one family SM, under an extended symmetry,…
In this work, we perform the one-loop calculation of the scalar and pseudoscalar form factors in the framework of U(3) chiral perturbation theory with explicit tree level exchanges of resonances. The meson-meson scattering calculation from…
Supersymmetric $SO(10)$ grand unified models with renormalizable Yukawa couplings involving only ${\bf 10}$ and $\overline{\bf 126}$ Higgs fields have been shown to realize the fermion masses and mixings economically. In previous works, the…
We propose new quantum algorithms for estimating spectral sums of positive semi-definite (PSD) matrices. The spectral sum of an PSD matrix $A$, for a function $f$, is defined as $ \text{Tr}[f(A)] = \sum_j f(\lambda_j)$, where $\lambda_j$…
Four different neutrino mass sum-rules have been analyzed: these frequently arise in flavor symmetry models based on the groups A_4, S_4 or T', which are often constructed to generate tri-bimaximal mixing. In general, neutrino mass can be…
The present paper is a report on joint work with Alessandro Languasco and Alberto Perelli on our recent investigations on the Selberg integral and its connections to Montgomery's pair-correlation function. We introduce a more general form…
We calculate a general spectral correlation function of products and ratios of characteristic polynomials for a $N\times N$ random matrix taken from the chiral Gaussian Unitary Ensemble (chGUE). Our derivation is based upon finding an…
In this note we report about a method to deal with finite energy sum rules. With a reasonable knowledge of the main resonances of the spectrum, the method guarantees that we can find a nice duality matching between the low energy hadronic…
We investigate the spectral distribution of random matrix ensembles with correlated entries. We consider symmetric matrices with real valued entries and stochastically independent diagonals. Along the diagonals the entries may be…
We propose a closed-form spectral framework for relative log-density estimation in linearly parameterized probabilistic models, including unnormalized and conditional models. This is achieved by representing the Kullback-Leibler (KL)…
The history and present status of several sum rules for deep-inelastic lepton scattering are reviewed, with particular attention to the discovery of scaling, partons, quarks and QCD. Two outstanding issues are then discussed in more detail:…
The neutrino mixing sum rule $\theta_{12} - \theta_{13}\cos(\delta) \approx \theta^\nu_{12}$ provides a possibility to explore the structure of the neutrino mass matrix in the presence of charged lepton corrections, since it relates the 1-2…
We introduce kernel estimators for the semicircle law. In this first part of our general theory on the estimators, we prove the consistency and conduct simulation study to show the performance of the estimators. We also point out that…
The statistics of chiral matrix ensembles with uncorrelated but multivariate Gaussian distributed elements is intuitively expected to be driven by many parameters. Contrary to intuition, however, our theoretical analysis reveals the…
We propose a new definition of effective formulas for problems in enumerative combinatorics. We outline the proof of the fact that every linear recurrence sequence of integers has such a formula. It follows from a lower bound that can be…
The Drell-Hearn-Gerasimov sum rule for the deuteron is studied in nuclear effective field theory. The low-energy theorem for the spin-dependent Compton amplitude $f_1(\omega)$ is derived to the next-to-leading order in low-energy expansion.…
Analytical expressions are derived for sums of matrix elements and their squared moduli over many-body states with given total spin --- the states built from spin and spatial wavefunctions belonging to multidimensional irreducible…