New Planar P-time Computable Six-Vertex Models and a Complete Complexity Classification

We discover new P-time computable six-vertex models on planar graphs beyond Kasteleyn's algorithm for counting planar perfect matchings. We further prove that there are no more: Together, they exhaust all P-time computable six-vertex models on planar graphs, assuming #P is not P. This leads to the following exact complexity classification: For every parameter setting in ${\mathbb C}$ for the six-vertex model, the partition function is either (1) computable in P-time for every graph, or (2) #P-hard for general graphs but computable in P-time for planar graphs, or (3) #P-hard even for planar graphs. The classification has an explicit criterion. The new P-time cases in (2) provably cannot be subsumed by Kasteleyn's algorithm. They are obtained by a non-local connection to #CSP, defined in terms of a "loop space". This is the first substantive advance toward a planar Holant classification with not necessarily symmetric constraints. We introduce M\"obius transformation on ${\mathbb C}$ as a powerful new tool in hardness proofs for counting problems.Comment: 61 pages, 16 figures. An extended abstract appears in SODA 202

The application of non-orthogonal multiple access in wireless powered communication networks

This work investigates the application of non-orthogonal multiple access (NOMA) scheme for the uplink of wireless powered communication networks (WPCN). We maximize the sum rate by jointly designing of the time allocation, the downlink energy beamforming and receiver beamforming. To solve this nonconvex problem, a method of two stages optimization is proposed. In the first stage, we apply the series approximations to obtain the optimal energy beamforming and receive beamforming with fixed time allocation. In the second stage, one-dimensional search is considered to obtain the optimal time allocation. For the approximation part, successive convex approximation (SCA) method is used to convert a mixed integer non-linear program into its convex approximation problem. The numerical results illustrate that the proposed algorithm converges to the local optimum solution and the proposed scheme outperforms the fixed time allocation scheme and orthogonal multiple access (OMA)

Numerical simulation of clouds and precipitation depending on different relationships between aerosol and cloud droplet spectral dispersion

The aerosol effects on clouds and precipitation in deep convective cloud systems are investigated using the Weather Research and Forecast (WRF) model with the Morrison two-moment bulk microphysics scheme. Considering positive or negative relationships between the cloud droplet number concentration (Nc) and spectral dispersion (ɛ), a suite of sensitivity experiments are performed using an initial sounding data of the deep convective cloud system on 31 March 2005 in Beijing under either a maritime (‘clean’) or continental (‘polluted’) background. Numerical experiments in this study indicate that the sign of the surface precipitation response induced by aerosols is dependent on the ɛ−Nc relationships, which can influence the autoconversion processes from cloud droplets to rain drops. When the spectral dispersion ɛ is an increasing function of Nc, the domain-average cumulative precipitation increases with aerosol concentrations from maritime to continental background. That may be because the existence of large-sized rain drops can increase precipitation at high aerosol concentration. However, the surface precipitation is reduced with increasing concentrations of aerosol particles when ɛ is a decreasing function of Nc. For the ɛ−Nc negative relationships, smaller spectral dispersion suppresses the autoconversion processes, reduces the rain water content and eventually decreases the surface precipitation under polluted conditions. Although differences in the surface precipitation between polluted and clean backgrounds are small for all the ɛ−Nc relationships, additional simulations show that our findings are robust to small perturbations in the initial thermal conditions. Keywords: aerosol indirect effects, cloud droplet spectral dispersion, autoconversion parameterization, deep convective systems, two-moment bulk microphysics schem

Sensor Scheduling with Intelligent Optimization Algorithm Based on Quantum Theory

The particle swarm optimization (PSO) algorithm superiority exists in convergence rate, but it tends to get stuck in local optima. An improved PSO algorithm is proposed using a best dimension mutation technique based on quantum theory, and it was applied to sensor scheduling problem for target tracking. The dynamics of the target are assumed as linear Gaussian model, and the sensor measurements show a linear correlation with the state of the target. This paper discusses the single target tracking problem with multiple sensors using the proposed best dimension mutation particle swarm optimization (BDMPSO) algorithm for various cases. Our experimental results verify that the proposed algorithm is able to track the target more reliably and accurately than previous ones

(1E,4E)-1,5-Bis(2,4-dimethyl­phen­yl)penta-1,4-dien-3-one

In the title compound, C21H22O, a derivative of the biologically active compound curcumin, the dihedral angle between the aromatic ring planes is 20.57 (11)°

Raman piezospectroscopic evaluation of intergrowth ferroelectric polycrystalline ceramic in biaxial bending configuration

The piezospectroscopic (PS) effect was studied in an intergrowth bismuth layer-structure ferroelectricceramicBi₅TiNbWO₁₅ according to a micro-Raman spectroscopic evaluation. By using a ball-on-ring flexure configuration, a biaxial stress was generated in a Bi₅TiNbWO₁₅ plate-like specimen and in situ collected Raman spectra were acquired and analyzed under several loading conditions. As the observed spectral line contained signals arising from the whole illuminated in-depth region, the laser probe information was deconvoluted (by means of an in-depth probe response function obtained according to the defocusing method) in order to deduce biaxial PS coefficients for the three Raman bands of Bi₅TiNbWO₁₅ located at 763, 857, and 886 cm−1, respectively. The biaxial PS coefficients of these bands were derived to be −1.74±0.16, −2.51±0.16, and −2.64±0.31 cm⁻¹/GPa, respectively, and should be referred to the c axis of the Bi5TiNbWO15 crystal

From Holant to Quantum Entanglement and Back

Holant problems are intimately connected with quantum theory as tensor networks. We first use techniques from Holant theory to derive new and improved results for quantum entanglement theory. We discover two particular entangled states |??? of 6 qubits and |??? of 8 qubits respectively, that have extraordinary closure properties in terms of the Bell property. Then we use entanglement properties of constraint functions to derive a new complexity dichotomy for all real-valued Holant problems containing a signature of odd arity. The signatures need not be symmetric, and no auxiliary signatures are assumed