Speeding up Training of Linear Predictors for Multi-Antenna Frequency-Selective Channels via Meta-Learning

An efficient data-driven prediction strategy for multi-antenna frequency-selective channels must operate based on a small number of pilot symbols. This paper proposes novel channel-prediction algorithms that address this goal by integrating transfer and meta-learning with a reduced-rank parametrization of the channel. The proposed methods optimize linear predictors by utilizing data from previous frames, which are generally characterized by distinct propagation characteristics, in order to enable fast training on the time slots of the current frame. The proposed predictors rely on a novel long short-term decomposition (LSTD) of the linear prediction model that leverages the disaggregation of the channel into long-term space-time signatures and fading amplitudes. We first develop predictors for single-antenna frequency-flat channels based on transfer/meta-learned quadratic regularization. Then, we introduce transfer and meta-learning algorithms for LSTD-based prediction models that build on equilibrium propagation (EP) and alternating least squares (ALS). Numerical results under the 3GPP 5G standard channel model demonstrate the impact of transfer and meta-learning on reducing the number of pilots for channel prediction, as well as the merits of the proposed LSTD parametrization.     

Comparison of Various K̄N Partial Wave Analyses in the Region 0–1400 MeV/c

A comprehensive comparative study of the available K̄N partial wave analyses is made with a view to bring out their similarities and disagreements and to point towards those momentum regions that require particular attention in all future analyses. The multichannel nature of the K̄N scattering is discussed along with the presently available scattering cross-section data for various channels. The parametrization of the various partial wave analyses is discussed and their amplitudes calculated and compared under the set of conventions proposed by Levi Setti.     

Classical Information Capacities of Some Single Qubit Quantum Noisy Channels

By using the Holevo-Schumacher-Westmoreland theorem and through solving eigenvalues of states out from the quantum noisy channels directly, or with the help of the Bloch sphere representation, or Stokes parametrization representation, we investigate the classical information capacities of some well-known quantum noisy channels.     

One-Dimensional Three-State Quantum Walk with Single-Point Phase Defects

In this paper, we study a three-state quantum walk with a phase defect at a designated position. The coin operator is a parametrization of the eigenvectors of the Grover matrix. We numerically investigate the properties of the proposed model via the position probability distribution, the position standard deviation, and the time-averaged probability at the designated position. It is shown that the localization effect can be governed by the phase defect’s position and strength, coin parameter and initial state.     

Four-Wave Semidiscrete Nonlinear Integrable System with PT-Symmetry

The new type of third-order spectral operator suitable to generate new multifield semidiscrete nonlinear systems with two coupling parameters in the framework of zero-curvature equation is proposed. The evolution operator corresponding to the first integrable system in an infinite hierarchy is explicitly recovered and the general form of first integrable system is isolated. The generalized procedure for the direct recursive development of infinite hierarchy of local conservation laws is presented and several lowest local conservation laws and local conserved densities are found. The reduction to the real field amplitudes in general system with unfixed sampling functions is made and the symmetric parametrization of field amplitudes allowing to exclude the redundant field function and to resolve the problem of sampling fixation for the particular realization of reduced integrable system is considered. This parametrization gives rise to the four field nonlinear model which in certain intervals of adjustable coupling parameter could serve as a semidiscrete analogy to the beam-plasma interaction system.     

Comments on the state densities and the transition rates in the pre-equilibrium exciton model

It is proposed to renormalize the exciton-state densities used in models for precompound decay such that the summed state densities agree with the expressions employed in equilibrium statistical models. In this way a close fit can be guaranteed between preequilibrium model calculations and the results of equilibrium statistical models for the evaporative stage of the reaction. The consequences of this proposal for the internal transition rates of the pre-equilibrium exciton model are analyzed. The matrix element for the residual interaction is obtained not from a phenomenological parametrization, but from the nucleon mean free path in nuclear matter. It is demonstrated that the proposed renormalization, from one-component Fermi-gas formulas to two-fermion expressions for the state densities, leads to strongly improved agreement of the effective exciton-model values for the nucleon mean free path in nuclear matter with realistic estimates. It is proved that the particle-hole state densities for a two-component Fermi gas, summed over the allowed exciton-state numbers, agree with the phenomenological state-density expressions used in statistical Hauser-Feshbach models.     

CAD and mesh repair with Radial Basis Functions

In this paper we present a process that includes both model/mesh repair and mesh generation. The repair algorithm is based on an initial mesh that may be either an initial mesh of a dirty CAD model or STL triangulation with many errors such as gaps, overlaps and T-junctions. This initial mesh is then remeshed by computing a discrete parametrization with Radial Basis Functions (RBF’s).We showed in [1] that a discrete parametrization can be computed by solving Partial Differential Equations (PDE’s) on an initial correct mesh using finite elements. Paradoxically, the meshless character of the RBF’s makes it an attractive numerical method for solving the PDE’s for the parametrization in the case where the initial mesh contains errors or holes. In this work, we implement the Orthogonal Gradients method to be described in [2], as a RBF solution method for solving PDE’s on arbitrary surfaces.Different examples show that the presented method is able to deal with errors such as gaps, overlaps, T-junctions and that the resulting meshes are of high quality. Moreover, the presented algorithm can be used as a hole-filling algorithm to repair meshes with undesirable holes. The overall procedure is implemented in the open-source mesh generator Gmsh [3].     

“Orthogonalized” sparsity enhanced mismatch models for wireless heterogeneous networks

Performance of MIMO precoder for heterogeneous networks can be hindered by a lack of accurate channel state information. The sparsity enhanced mismatch model (SEMM) has been proposed recently to account for the channel estimate mismatch problem by exploiting the inherent sparse characteristics of MIMO interference channels. When (single user-MIMO) SU-MIMO precoder design takes into account the SEMM, it was shown to have better transmission performance compared to the conventional norm ball mismatch model (NBMM) in a single-user multi-victims scenario. However, when communicating and interference channels are highly correlated, which can happen frequently in ultra-dense heterogeneous networks, performance of the SEMM precoder degrades and in some cases, underperforms the NBMM precoder. An “orthogonalized” SEMM (OSEMM) is proposed herein to modify the SEMM such that it is better suited for correlated channels. The concept of orthogonalization of channels is not new but this work uses it to enhance the SEMM, which creates synergy between transmission performance and robustness toward channel mismatch error. Two variants of the OSEMM are proposed, namely the OSEMM-LQ and OSEMM-SVD, to modify the basis expansion model that is an integral part of the SEMM. The resulting mismatch model influences the design of the SU-MIMO precoder that aims to maximize certain transmission criterion. Even though SU-MIMO precoding is considered, a new channel correlation definition, which acts as a metric for the OSEMM, is given that allows for user selection in a multiuser scenario such that optimal performance can be attained for the targeted user. Analytical and simulation results are given that highlight the difference in performance between the two variants of the OSEMM.     

Growth of linear matter perturbations and current observational constraints

We discuss, using a recently proposed parametrization for the growth index of linear matter perturbations, the observational constraints on the wCDM model and the Dvali—Gabadadze—Porrati (DGP) model with all current growth factor data. We find that the wCDM model is allowed by the observations at the 1$\sigma$ confidence level, while the DGP model is only consistent with observations at 2$\sigma$ confidence level.     

Parametrizing the lepton mixing matrix in terms of charged lepton corrections

We consider a parametrization of the lepton mixing matrix in which the deviations from maximal atmospheric mixing and vanishing reactor mixing are obtained in terms of small corrections from the charged lepton sector. Relatively large deviations for the reactor mixing angle from zero as indicated by T2K experiment can be obtained in this parametrization. We are able to further reduce the number of complex phases, thus, simplifying the analysis. In addition, we have obtained the sides of unitarity triangles and the vacuum oscillation probabilities in this parametrization. The Jarlskog rephasing invariant measure of CP violation at the leading order has a single phase difference which can be identified as Dirac-type CP violating phase in this parametrization.     

Soft Parametrization of Renormalized Field Theory and Kadanoff Scaling

The soft renormalization procedure, proposed by Gomes, Lowenstein and Zimmermann, is applied to the construction of a pre-scaling (soft) parametrization of renormalized perturbation theory. The global pre-scaling parameters are directly incorporated into the Lagrangian; resummation problems and subsidiary condition are completely avoided. For the A⁴-theory with linear symmetry breaking and the spontaneous limit we give a detailed structural investigation in terms of partial differential equations to all orders of perturbation theory. In the second part the scaling structure and “marginal” corrections to scaling are reconsidered in terms of the soft parametrization. The pre-scaling parametrization represents a powerful tool in dealing with the field theoretical aspects of critical phenomena.     

A comprehensive revisit of the ρ meson with improved Monte-Carlo based QCD sum rules

We improve the Monte-Carlo based QCD sum rules by introducing the rigorous H¨older-inequalitydetermined sum rule window and a Breit-Wigner type parametrization for the phenomenological spectral function.In this improved sum rule analysis methodology, the sum rule analysis window can be determined without any assumptions on OPE convergence or the QCD continuum. Therefore, an unbiased prediction can be obtained for the phenomenological parameters(the hadronic mass and width etc.). We test the new approach in the ρ meson channel with re-examination and inclusion of α_s corrections to dimension-4 condensates in the OPE. We obtain results highly consistent with experimental values. We also discuss the possible extension of this method to some other channels.     

No Approximate Complex Fermion Coherent States

Whereas boson coherent states with complex parametrization provide an elegant, and intuitive representation, there is no counterpart for fermions using complex parametrization. However, a complex parametrization provides a valuable way to describe amplitude and phase of a coherent beam. Thus we pose the question of whether a fermionic beam can be described, even approximately, by a complex-parametrized coherent state and define, in a natural way, approximate complex-parametrized fermion coherent states. Then we identify four appealing properties of boson coherent states (eigenstate of annihilation operator, displaced vacuum state, preservation of product states under linear coupling, and factorization of correlators) and show that these approximate complex fermion coherent states fail all four criteria. The inapplicability of complex parametrization supports the use of Grassman algebras as an appropriate alternative.      

No Approximate Complex Fermion Coherent States

Whereas boson coherent states with complex parametrization provide an elegant, and intuitive representation, there is no counterpart for fermions using complex parametrization. However, a complex parametrization provides a valuable way to describe amplitude and phase of a coherent beam. Thus we pose the question of whether a fermionic beam can be described, even approximately, by a complex-parametrized coherent state and define, in a natural way, approximate complex-parametrized fermion coherent states. Then we identify four appealing properties of boson coherent states (eigenstate of annihilation operator, displaced vacuum state, preservation of product states under linear coupling, and factorization of correlators) and show that these approximate complex fermion coherent states fail all four criteria. The inapplicability of complex parametrization supports the use of Grassman algebras as an appropriate alternative.      

Soft and hard Pomeron in the structure function of the proton at low x and low Q^2

We study inclusive electroproduction on the proton at low x and low using a soft and a hard Pomeron. The contribution of the soft Pomeron is based on the Stochastic Vacuum Model, in which a nonperturbative dipole-dipole cross section can be calculated by means of a gauge invariant gluon field strength correlator. To model the hard Pomeron exchange we phenomenologically extend the leading order evolution of a power-behaved structure function, , proposed by López and Ynduráin. This extension allows to consider both the case and the region of higher on the basis of the same parametrization. A good simultaneous fit to the data on and on the cross section of real photoproduction is obtained for . With four parameters we achieve a for 222 data points. In addition, we use our model of the inclusive interaction to compute the longitudinal structure function . Received: 6 December 1998 / Revised version: 19 April 1999 / Published online: 18 June 1999     

Leptogenesis and bi-unitary parametrization of neutrino Yukawa matrix

We analyze the neutrino Yukawa matrix by considering three constraints: the out-of-equilibrium condition of the lepton number-violating process responsible for leptogenesis, the upper bound of the branching ratio of the lepton flavor violating decay, and the prediction of large mixing angles using the see-saw mechanism. In a certain parametrization with a bi-unitary transformation, it is shown that the structure which satisfies the constraints can be characterized by only seven types of Yukawa matrices. The constraint of the branching ratio of LFV turns out to be redundant after applying the other two constraints. We propose that this parametrization can be the framework in which the CP asymmetry of a lepton number-violating process can be predicted in terms of observable neutrino parameters at low energy, if necessary, under assumptions following from a theory with additional symmetries. There is an appealing model of the neutrino Yukawa matrix considering the CP asymmetry for leptogenesis, giving a theoretical motivation to reduce the number of free parameters.Arrival of the final proofs: 24 June 2003     

Decomposition kinetics in Fe–Cu dilute alloys. Monte Carlo simulation using concentration-dependent interactions

A generalization of the statistical (Monte Carlo) simulation technique for determining the structure of alloys is proposed. It takes into account the dependence of effective interactions between the atoms of a dissolved chemical element on their local concentration. Using the ab initio parametrization of the model, the decomposition of the bcc Fe–Cu alloy accompanied by the formation of Cu nanoprecipitates is studied. It is shown that the concentration dependence of effective interactions significantly affects the decomposition kinetics by displacing its onset to longer times in agreement with the experiment.