Energy levels and lifetimes of Gd IV and enhancement of the electron dipole moment

We have calculated energy levels and lifetimes of 4f7 and 4f6 5d configurations of Gd IV using Hartree-Fock and configuration interaction methods. This allows us to reduce significantly the uncertainty of the theoretical determination of the electron electric dipole moment (EDM) enhancement factor in this ion and, correspondingly, in gadolinium-containing garnets for which such measurements were recently proposed. Our new value for the EDM enhancement factor of Gd+3 is -2.2 +- 0.5. Calculations of energy levels and lifetimes for Eu~III are used to control the accuracy.Comment: Submitted to Phys. Rev. A 6 pages, 0 figures, 3 table

Communication-Computation Efficient Gradient Coding

This paper develops coding techniques to reduce the running time of distributed learning tasks. It characterizes the fundamental tradeoff to compute gradients (and more generally vector summations) in terms of three parameters: computation load, straggler tolerance and communication cost. It further gives an explicit coding scheme that achieves the optimal tradeoff based on recursive polynomial constructions, coding both across data subsets and vector components. As a result, the proposed scheme allows to minimize the running time for gradient computations. Implementations are made on Amazon EC2 clusters using Python with mpi4py package. Results show that the proposed scheme maintains the same generalization error while reducing the running time by $32\%$ compared to uncoded schemes and $23\%$ compared to prior coded schemes focusing only on stragglers (Tandon et al., ICML 2017)

Stationary phase corrections in the process of bosonization of multi-quark interactions

The functional integration over the auxiliary bosonic variables of cubic order related with the effective action of the Nambu -- Jona-Lasinio model with 't Hooft term has recently been obtained in the form of a loop expansion. Even numbers of loops contribute to the action, while odd numbers of loops are assigned to the measure. We consider the two-loop corrections and analyse their effect on the low-lying pseudoscalar and scalar mass spectra, quark condensates and weak decay constants. The results are compared to the leading order calculations and other approaches.Comment: 22 pages, LaTeX, to appear in European Physics Journal

Model Building and Phenomenology of Flux-Induced Supersymmetry Breaking on D3-branes

We study supersymmetry breaking effects induced on D3-branes at singularities by the presence of NSNS and RR 3-form fluxes. First, we discuss some local constructions of chiral models from D3-branes at singularities, as well as their global embedding in flux compactifications. The low energy spectrum of these constructions contains features of the supersymmetric Standard Model. In these models, both the soft SUSY parameters and the mu-term are generated by turning on the 3-form NSNS and RR fluxes. We then explore some model-independent phenomenological features as, e.g., the fine-tuning problem of electroweak symmetry breaking in flux compactifications. We also comment on other phenomenological features of this scenario.Comment: 41 pages, 10 figure