Multiple Parton Interactions Studies at CMS

This paper summarizes the Multiple Parton Interactions studies in CMS, focusing on the already performed low pT QCD measurements up to highest centre of mass energies of 7 TeV and discussing the plans for the direct measurement of the multiple high-pT scatterings. The underlying event in pp interactions is studied measuring the charged multiplicity density and the charged energy density in the transverse region, which is defined considering the azimuthal distance of the reconstructed tracks with respect to the leading track-jet of the event, defined from tracks according to a jet clustering algorithms. In addition, we present the measurement of the underlying event using the jet-area/median approach, demonstrating its sensitivity to different underlying event scenarios. Observations in the central region are complemented by the mea- surement of the energy flow in the forward direction for minimum bias and central di-jet events. We compare our underlying event and forward results with the predictions from different Monte Carlo event generators and tunes, aiming to best parametrize the multiple parton interaction energy de- pendence starting from the Monte Carlo tunes developed to best fit the charged particle spectra measured at central rapidities. Finally we discuss the strategy to directly measure the multiple particle interactions rate focusing on the topologies with two hard scatterings in the same event

Time-dependent trading strategies in a continuous double auction

We model a continuous double auction with heterogenous agents and compute approximate optimal trading strategies using evolution strategies. Agents privately know their values and costs and have a limited time to transact. We focus on equilibrium strategies that are developed taking into account the number of traders that submitted orders previously, as well as the number of who will submit subsequently. We find that it is optimal to place increasingly aggressive orders, according to a roughly linear schedule, and test the resulting equilibrium for robustness and accuracy.Continuous double auction, equilibrium trading strategies, evolution strategies.

The density matrix renormalization group method. Application to the PPP model of a cyclic polyene chain

The density matrix renormalization group (DMRG) method introduced by White for the study of strongly interacting electron systems is reviewed; the method is variational and considers a system of localized electrons as the union of two adjacent fragments A, B. A density matrix rho is introduced, whose eigenvectors corresponding to the largest eigenvalues are the most significant, the most probable states of A in the presence of B; these states are retained, while states corresponding to small eigenvalues of rho are neglected. It is conjectured that the decreasing behaviour of the eigenvalues is gaussian. The DMRG method is tested on the Pariser-Parr-Pople Hamiltonian of a cyclic polyene (CH)_N up to N=34. A Hilbert space of dimension 5 x 10^+18 is explored. The ground state energy is 10^-3 eV within the full CI value in the case N=18. The DMRG method compares favourably also with coupled cluster approximations. The unrestricted Hartree-Fock solution (which presents spin density waves) is briefly reviewed, and a comparison is made with the DMRG energy values. Finally, the spin-spin and density-density correlation functions are computed; the results suggest that the antiferromagnetic order of the exact solution does not extend up to large distances but exists locally. No charge density waves are present.Comment: 8 pages, RevTex, 2 figures, to be published in the Journal of Chemical Physic

Generalized biodiversity assessment by Bayesian nested random effects models with spyke-and-slab priors

We analyze variations in alpha-diversity of benthic macroinvertebrate communities in an Italian lagoon system using Bayesian hierarchical models with nested random effects. Our aim is to understand how spatial scales influence microhabitat definition. Tsallis entropy measures diversity and spike-and-slab regression selects predictors

The Hubbard model on a complete graph: Exact Analytical results

We derive the analytical expression of the ground state of the Hubbard model with unconstrained hopping at half filling and for arbitrary lattice sites.Comment: Email:[email protected]

Siegert pseudostate perturbation theory: one- and two-threshold cases

Perturbation theory for the Siegert pseudostates (SPS) [Phys.Rev.A 58, 2077 (1998) and Phys.Rev.A 67, 032714 (2003)] is studied for the case of two energetically separated thresholds. The perturbation formulas for the one-threshold case are derived as a limiting case whereby we reconstruct More's theory for the decaying states [Phys.Rev.A 3,1217(1971)] and amend an error. The perturbation formulas for the two-threshold case have additional terms due to the non-standard orthogonality relationship of the Siegert Pseudostates. We apply the theory to a 2-channel model problem, and find the rate of convergence of the perturbation expansion should be examined with the aide of the variance $D= ||E-\sum_{n}\lambda^n E^{(n)}||$ instead of the real and imaginary parts of the perturbation energy individually