A Structural Entropy Measurement Principle of Propositional Formulas in Conjunctive Normal Form

The satisfiability (SAT) problem is a core problem in computer science. Existing studies have shown that most industrial SAT instances can be effectively solved by modern SAT solvers while random SAT instances cannot. It is believed that the structural characteristics of different SAT formula classes are the reasons behind this difference. In this paper, we study the structural properties of propositional formulas in conjunctive normal form (CNF) by the principle of structural entropy of formulas. First, we used structural entropy to measure the complex structure of a formula and found that the difficulty solving the formula is related to the structural entropy of the formula. The smaller the compressing information of a formula, the more difficult it is to solve the formula. Secondly, we proposed a λ-approximation strategy to approximate the structural entropy of large formulas. The experimental results showed that the proposed strategy can effectively approximate the structural entropy of the original formula and that the approximation ratio is more than 92%. Finally, we analyzed the structural properties of a formula in the solution process and found that a local search solver tends to select variables in different communities to perform the next round of searches during a search and that the structural entropy of a variable affects the probability of the variable being flipped. By using these conclusions, we also proposed an initial candidate solution generation strategy for a local search for SAT, and the experimental results showed that this strategy effectively improves the performance of the solvers CCAsat and Sparrow2011 when incorporated into these two solvers.     

Quantitative Analysis of Al in Flour Products by Laser-Induced Breakdown Spectroscopy Combined with Partial Least Squares

Journal of Applied Spectroscopy - Based on partial least squares (PLS) analysis, the effects of different smoothing points and different preprocessing methods on the accuracy and precision of the...     

Editorial to the Special Issue: Adsorption,Absorption and Thermochemical Transport Processes in Complex Porous Structures

Transport in Porous Media - The theme of coupling problems for adsorption, absorption and thermochemical transport in porous media is very important for engineering applications. Based on the...     

The single-polarization filter composed of gold-coated photonic crystal fiber

A single-polarization filter comprising a gold-coated photonic crystal fiber based on surface plasmon resonance is designed and investigated. The pattern matching and coupled polarization characteristics analyzed by the full-vector finite element method (FEM) and losses at 1,540 nm are achieved to 1,016.01739 dB/cm (x-pol core mode) and 33.81917 dB/cm (y-pol core mode). The crosstalk (CT) value of the 1,540 nm band is ?853.12653 dB for fiber length $L=1,000\mathrm{\mu }\text{m}$ and the bandwidth is 850 nm. The working wavelength of the filter ranges from 1,280 nm to 1,540 nm by varying the diameter of outer air holes ($d_1$), the diameter of inner air holes ($d_4$), the metal film thickness (t), as well as the liquid refractive index (n).     

Bimetallic Covalent Organic Frameworks for Constructing Multifunctional Electrocatalyst

Covalent organic frameworks (COFs) are a new class of crystalline porous polymers comprised mainly of carbon atoms, and are versatile for the integration of heteroatoms such as B, O, and N into the skeletons. The designable structure and abundant composition render COFs useful as precursors for heteroatom-doped porous carbons for energy storage and conversion. Herein, we describe a multifunctional electrochemical catalyst obtained through pyrolysis of a bimetallic COF. The catalyst possesses hierarchical pores and abundant iron and cobalt nanoparticles embedded with standing carbon layers. By integrating these features, the catalyst exhibits excellent electrochemical catalytic activity in the oxygen reduction reaction (ORR), with a 50 mV positive half-wave potential, a higher limited diffusion current density, and a much smaller Tafel slope than a Pt-C catalyst. Moreover, the catalyst displays superior electrochemical performance toward the hydrogen evolution reaction (HER), with overpotentials of −0.26 V and −0.33 V in acidic and alkaline aqueous solution, respectively, at a current density of 10 mA cm⁻². The overpotential in the catalysis of the oxygen evolution reaction (OER) was 1.59 V at the same current density.     

Comprehensive Profiling by Non-targeted Stable Isotope Tracing Capillary Electrophoresis-Mass Spectrometry: A New Tool Complementing Metabolomic Analyses of Polar Metabolites

Mass spectrometry (MS) driven metabolomics is a frequently used tool in various areas of life sciences; however, the analysis of polar metabolites is less commonly included. In general, metabolomic analyses lead to the detection of the total amount of all covered metabolites. This is currently a major limitation with respect to metabolites showing high turnover rates, but no changes in their concentration. Such metabolites and pathways could be crucial metabolic nodes (e.g., potential drug targets in cancer metabolism). A stable-isotope tracing capillary electrophoresis–mass spectrometry (CE-MS) metabolomic approach was developed to cover both polar metabolites and isotopologues in a non-targeted way. An in-house developed software enables high throughput processing of complex multidimensional data. The practicability is demonstrated analyzing [U-¹³C]-glucose exposed prostate cancer and non-cancer cells. This CE-MS-driven analytical strategy complements polar metabolite profiles through isotopologue labeling patterns, thereby improving not only the metabolomic coverage, but also the understanding of metabolism.     

A posteriori error estimation for a singularly perturbed Volterra integro-differential equation

Numerical Algorithms - A singularly perturbed Volterra integro-differential equation with an integrable singularity in the integral term is considered. The upwind difference method is used to...