Cognitive Beamforming for Multiple Secondary Data Streams With Individual SNR Constraints

In this paper, we consider cognitive beamforming for multiple secondary data streams subject to individual signal-to-noise ratio (SNR) requirements for each secondary data stream. In such a cognitive radio system, the secondary user is permitted to use the spectrum allocated to the primary user as long as the caused interference at the primary receiver is tolerable. With both secondary SNR constraint and primary interference power constraint, we aim to minimize the secondary transmit power consumption. By exploiting the individual SNR requirements, we formulate this cognitive beamforming problem as an optimization problem on the Stiefel manifold. Both zero forcing beamforming (ZFB) and nonzero forcing beamforming (NFB) are considered. For the ZFB case, we derive a closed form beamforming solution. For the NFB case, we prove that the strong duality holds for the nonconvex primal problem and thus the optimal solution can be easily obtained by solving the dual problem. Finally, numerical results are presented to illustrate the performance of the proposed cognitive beamforming solutions.Comment: This is the longer version of a paper to appear in the IEEE Transactions on Signal Processin

Late Silurian trace fossils from the Melbourne Formation, Studley Park, Victoria, southeastern Australia

An ichnoassemblage of 10 ichnospecies is described for the first time from the Late Silurian Melbourne Formation at Studley Park, Victoria, southeastern Australia. The ichnofauna is preserved in a typical deep-water turbidite succession of alternating thin- to thick-bedded sandstone and thin- to medium-bedded mudrocks. Trace fossils observed within the study site have been assigned to three main ichnofacies. Ichnofacies 1 is best developed on the linguoid-rippled upper surface of thin sandstone beds and includes Laevicyclus, Aulichnites, Nereites, Helminthoidichnites, small Chondrites and possible Zoophycos. Ichnofacies 2 is very similar to Ichnofacies 1 in ichnospecies composition but instead contains large forms of Chondrites together with other thin burrow types usually poorly preserved and in very low abundance compared with Ichnofacies 1. Ichnofacies 3 is preserved mainly as casts on the underside of medium- to thick-bedded turbiditic sandstones, and has a very low diversity, with Planolites being the most common trace. A detailed analysis of the ichnofabrics and tiering structures of these ichnofacies suggest that Ichnofacies 1 and 3 represent &quot;simple tiering&rsquo;, in contrast to Ichnofacies 2, which is more characteristic of \u27complex tiering&rsquo;. Despite the differences in ichnospecies composition and ichnofabrics between the three recognized ichnofacies, the collective ichnoassemblage from the study site can be assigned confidently to the Nereites ichnofacies and is, therefore, interpreted to have formed in a distal submarine fan environment of lower bathyal to abyssal depth. Further, it is possible to recognize two main subenvironments within this deep-sea setting to account for the differences between the ichnofacies. Ichnofacies 1 and 2 are interpreted to represent a typical Nereites ichnofacies located on a level basin floor subenvironment of relatively low energy conditions at the distal end of a submarine fan deposit. In comparison, Ichnofacies 3 is dominated by Planolites with rare other facies-crossing trace fossil forms, and lacks Nereites. It is, therefore, best interpreted as representing a relatively high-energy environment, possibly a distributary channel near the distal end of the submarine fan system.<br /

Stochastic method with low mode substitution for nucleon isovector matrix elements

We introduce a stochastic sandwich method with low-mode substitution to evaluate the connected three-point functions. The isovector matrix elements of the nucleon for the axial-vector coupling $g_A^3$, scalar couplings $g_S^3$ and the quark momentum fraction $\langle x\rangle_{u -d}$ are calculated with overlap fermion on 2+1 flavor domain-wall configurations on a $24^3 \times 64$ lattice at $m_{\pi} = 330$ MeV with lattice spacing $a = 0.114$ fm.Comment: 15 pages, 13 figures, the version accepted by PR

Strange and Charm Quark Spins from Anomalous Ward Identity

We present a calculation of the strange and charm quark contributions to the nucleon spin from the anomalous Ward identity (AWI). It is performed with overlap valence quarks on 2+1-flavor domain-wall fermion gauge configurations on a $24^3 \times 64$ lattice with the light sea mass at $m_{\pi} = 330$ MeV. To satisfy the AWI, the overlap fermion for the pseudoscalar density and the overlap Dirac operator for the topological density, which do not have multiplicative renormalization, are used to normalize the form factor of the local axial-vector current at finite $q^2$. For the charm quark, we find that the negative pseudoscalar term almost cancels the positive topological term. For the strange quark, the pseudoscalar term is less negative than that of the charm. By imposing the AWI, the strange $g_A(q^2)$ at $q^2 =0$ is obtained by a global fit of the pseudoscalar and the topological form factors, together with $g_A(q^2)$ and the induced pseudoscalar form factor $h_A(q^2)$ at finite $q^2$. The chiral extrapolation to the physical pion mass gives $\Delta s + \Delta {\bar{s}} = -0.0403(44)(78)$.Comment: 8 pages, 9 figures. Updated version where a sign error is correcte

Diquark mass differences from unquenched lattice QCD

We calculate diquark correlation functions in the Landau gauge on the lattice using overlap valence quarks and 2+1-flavor domain wall fermion configurations. Quark masses are extracted from the scalar part of quark propagators in the Landau gauge. Scalar diquark quark mass difference and axial vector scalar diquark mass difference are obtained for diquarks composed of two light quarks and of a strange and a light quark. Light sea quark mass dependence of the results is examined. Two lattice spacings are used to check the discretization effects. The coarse and fine lattices are of sizes $24^3\times64$ and $32^3\times64$ with inverse spacings $1/a=1.75(4) {\rm~GeV}$ and $2.33(5) {\rm~GeV}$, respectively.Comment: 9 figure

Optimization of SM4 Encryption Algorithm for Power Metering Data Transmission

This study focuses on enhancing the security of the SM4 encryption algorithm for power metering data transmission by employing hybrid algorithms to optimize its substitution box (S-box). A multi-objective fitness function is constructed to evaluate the S-box structure, aiming to identify design solutions that satisfy differential probability, linear probability, and non-linearity balance. To achieve global optimization and local search for the S-box, a hybrid algorithm model that combines genetic algorithm and simulated annealing is introduced. This approach yields significant improvements in optimization effects and increased non-linearity. Experimental results demonstrate that the optimized S-box significantly reduces differential probability and linear probability while increasing non-linearity to 112. Furthermore, a comparison of the ciphertext entropy demonstrates enhanced encryption security with the optimized S-box. This research provides an effective method for improving the performance of the SM4 encryption algorithm

RI/MOM and RI/SMOM renormalization of overlap quark bilinears on domain wall fermion configurations

Renormalization constants (RCs) of overlap quark bilinear operators on 2+1-flavor domain wall fermion configurations are calculated by using the RI/MOM and RI/SMOM schemes. The scale independent RC for the axial vector current is computed by using a Ward identity. Then the RCs for the quark field and the vector, tensor, scalar and pseudoscalar operators are calculated in both the RI/MOM and RI/SMOM schemes. The RCs are converted to the $\overline{\rm MS}$ scheme and we compare the numerical results from using the two intermediate schemes. The lattice size is $48^3\times96$ and the inverse spacing $1/a = 1.730(4) {\rm~GeV}$.Comment: Minor changes and updates of Figure 10 and 15 to be more clea