Kullback–Leibler Divergence Based Composite Prior Modeling for Bayesian Super-Resolution

This paper proposes to adaptively combine the known total variation model and more recent Frobenius norm regularization for multi-frame image super-resolution (SR). In contrast to existing literature, in this paper both the composite prior modeling and posterior variational optimization are achieved in the Bayesian framework by utilizing the Kullback–Leibler divergence, and hyper-parameters related to the composite prior and noise statistics are all determined automatically, resulting in a spatially adaptive SR reconstruction method. Experimental results demonstrate that the new approach can generate a super-resolved image with higher signal-to-noise ratio and better visual perception, not only image details better preserved but also staircase effects better suppressed.     

Optimal Kullback–Leibler approximation of Markov chains via nuclear norm regularisation

This paper is concerned with model reduction for Markov chain models. The goal is to obtain a low-rank approximation to the original Markov chain. The Kullback–Leibler divergence rate is used to measure the similarity between two Markov chains; the nuclear norm is used to approximate the rank function. A nuclear-norm regularised optimisation problem is formulated to approximately find the optimal low-rank approximation. The proposed regularised problem is analysed and performance bounds are obtained through the convex analysis. An iterative fixed point algorithm is developed based on the proximal splitting technique to compute the optimal solutions. The effectiveness of this approach is illustrated via numerical examples.     

Annealed Kullback–Leibler divergence minimization for generalized TSP,spot identification and gene sorting

This work explores learning LCGM (lattice-connected Gaussian mixture) models by annealed Kullback–Leibler (KL) divergence minimization for a hybrid of topological and statistical pattern analysis. The KL divergence measures the general criteria of learning an LCGM model that is composed of a lattice of multivariate Gaussian units. A planar lattice emulates topological order of cortex-like neighboring relations and built-in parameters of connected Gaussian units represent statistical features of unsupervised data. Learning an LCGM model involves collateral optimization tasks of resolving mixture combinatorics and extracting geometric features from high-dimensional patterns. Under assumption that mixture combinatorics encoded by Potts variables obey the Boltzmann distribution, approximating their joint probability by the product of individual probabilities is qualified by the KL divergence whose minimization under physical-like deterministic annealing faithfully optimizes involved mixture combinatorics and geometric features. Numerical simulations show the proposed annealed KL divergence minimization is effective and reliable for solving generalized TSP, spot identification, self-organization and visualization and sorting of yeast gene expressions.     

Kullback–Leibler average,consensus on probability densities,and distributed state estimation with guaranteed stability

This paper addresses distributed state estimation over a sensor network wherein each node–equipped with processing, communication and sensing capabilities–repeatedly fuses local information with information from the neighbors. Estimation is cast in a Bayesian framework and an information-theoretic approach to data fusion is adopted by formulating a consensus problem on the Kullback–Leibler average of the local probability density functions (PDFs) to be fused. Exploiting such a consensus on local posterior PDFs, a novel distributed state estimator is derived. It is shown that, for a linear system, the proposed estimator guarantees stability, i.e. mean-square boundedness of the state estimation error in all network nodes, under the minimal requirements of network connectivity and system observability, and for any number of consensus steps. Finally, simulation experiments demonstrate the validity of the proposed approach.     

基于Kullback信息测度的长输管线的泄漏检测

长输管线泄漏检测的一类方法需要测量其端点甚至中间的流量信号,这是实际中所不希望的.本文提出了一种基于 Kullback 信息测度的长输管线泄漏检测方法,它通过对管线两个端点附近的压力梯度所构成的时间序列进行分析,从而检测出泄漏.这种方法只需要测量两个端点附近的四个压力信号,计算量又小,在实际中容易实现.该方法在一条长120米,内径10毫米的液体管线上进行了实验,结果表明,这是一种很有实用价值的检测方法.     

The integrated production–inventory–distribution–routing problem

The integration of production and distribution decisions presents a challenging problem for manufacturers trying to optimize their supply chain. At the planning level, the immediate goal is to coordinate production, inventory, and delivery to meet customer demand so that the corresponding costs are minimized. Achieving this goal provides the foundations for streamlining the logistics network and for integrating other operational and financial components of the system. In this paper, a model is presented that includes a single production facility, a set of customers with time varying demand, a finite planning horizon, and a fleet of vehicles for making the deliveries. Demand can be satisfied from either inventory held at the customer sites or from daily product distribution. In the most restrictive case, a vehicle routing problem must be solved for each time period. The decision to visit a customer on a particular day could be to restock inventory, meet that day’s demand or both. In a less restrictive case, the routing component of the model is replaced with an allocation component only. A procedure centering on reactive tabu search is developed for solving the full problem. After a solution is found, path relinking is applied to improve the results. A novel feature of the methodology is the use of an allocation model in the form of a mixed integer program to find good feasible solutions that serve as starting points for the tabu search. Lower bounds on the optimum are obtained by solving a modified version of the allocation model. Computational testing on a set of 90 benchmark instances with up to 200 customers and 20 time periods demonstrates the effectiveness of the approach. In all cases, improvements ranging from 10–20% were realized when compared to those obtained from an existing greedy randomized adaptive search procedure (GRASP). This often came at a three- to five-fold increase in runtime, however.     

Thermodynamic assessment of the Si–Zn,Mn–Si,Mg–Si–Zn and Mg–Mn–Si systems

The binary Si–Zn and Mn–Si systems have been critically evaluated based upon available phase equilibrium and thermodynamic data, and optimized model parameters have been obtained giving the Gibbs energies of all phases as functions of temperature and composition. The liquid solution has been modeled with the Modified Quasichemical Model (MQM) to account for the short-range-ordering. The results have been combined with those of our previous optimizations of the Mg–Si, Mg–Zn and Mg–Mn systems to predict the phase diagrams of the Mg–Si–Zn and Mg–Mn–Si systems. The predictions have been compared with available data.     

Thermodynamic modeling of the Al–Bi,Al–Sb,Mg–Al–Bi and Mg–Al–Sb systems

All available thermodynamic and phase diagram data of the binary Al–Bi and Al–Sb systems and ternary Mg–Al–Bi and Mg–Al–Sb systems were critically evaluated, and all reliable data were used simultaneously to obtain the best set of the model parameters for each ternary system. The Modified Quasichemical Model used for the liquid solution shows a high predictive capacity for the ternary systems. The ternary liquid miscibility gaps in the Mg–Al–Bi and Mg–Al–Sb systems resulting from the ordering behaviour of the liquid solutions can be well reproduced with one additional ternary parameter. Using the optimized model parameters, the experimentally unexplored portions of the Mg–Al–Bi and Mg–Al–Sb ternary phase diagrams were more reasonably predicted. All calculations were performed using the FactSage thermochemical software package.     

Single-phase Ce3+–Mn2+–Tb3+ tri–codoped barium–yttrium–silicate phosphors

Ce³⁺–Mn²⁺–Tb³⁺ cooperative barium–yttrium-orthosilicate phosphors composed of Ba_{9-3m/2-n-3p/2}Ce_mMn_nTb_pY₂Si₆O₂₄ (m = 0.005–0.4, n = 0–0.5, p = 0–0.5) were prepared using a solid-state reaction. The X-ray diffraction patterns of the resultant phosphors were examined to index the peak positions. The photoluminescence (PL) excitation and emission spectra of the Ce³⁺–Mn²⁺–Tb³⁺ activated phosphors were clearly monitored. The dependence of the luminescent intensity of the Mn²⁺–Tb³⁺ co-doped Ba_9-3m/2Ce_mY₂Si₆O₂₄ host lattices on Ce³⁺ content (m = 0.025, 0.1) was also investigated. Co-doping Mn²⁺ into the Ce³⁺–Tb³⁺ co-doped host structure enabled energy transfer from Ce³⁺ to Mn²⁺; this energy transfer mechanism is discussed. The phosphors of Ce³⁺–Mn²⁺–Tb³⁺ doped Ba₉Y₂Si₆O₂₄ host lattice were prepared for efficient white-light emission under NUV excitation. With these phosphors, the desired CIE values including white region of the emission spectra were achieved.     

Dimension–Adaptive Tensor–Product Quadrature

We consider the numerical integration of multivariate functions defined over the unit hypercube. Here, we especially address the high–dimensional case, where in general the curse of dimension is encountered. Due to the concentration of measure phenomenon, such functions can often be well approximated by sums of lower–dimensional terms. The problem, however, is to find a good expansion given little knowledge of the integrand itself. The dimension–adaptive quadrature method which is developed and presented in this paper aims to find such an expansion automatically. It is based on the sparse grid method which has been shown to give good results for low- and moderate–dimensional problems. The dimension–adaptive quadrature method tries to find important dimensions and adaptively refines in this respect guided by suitable error estimators. This leads to an approach which is based on generalized sparse grid index sets. We propose efficient data structures for the storage and traversal of the index sets and discuss an efficient implementation of the algorithm. The performance of the method is illustrated by several numerical examples from computational physics and finance where dimension reduction is obtained from the Brownian bridge discretization of the underlying stochastic process.     

Numerical investigation of homogenized Stokes–Nernst–Planck–Poisson systems

We consider charged transport within a porous medium, which at the pore scale can be described by the non-stationary Stokes–Nernst–Planck–Poisson (SNPP) system. We state three different homogenization results using the method of two-scale convergence. In addition to the averaged macroscopic equations, auxiliary cell problems are solved in order to provide closed-form expressions for effective coefficients. Our aim is to study numerically the convergence of the models for vanishing microstructure, i. e., the behavior for $\varepsilon \rightarrow 0$ ε → 0 , where $\varepsilon $ ε is the characteristic ratio between pore diameter and size of the porous medium. To this end, we propose a numerical scheme capable of solving the fully coupled microscopic SNPP system and also the corresponding averaged systems. The discretization is performed fully implicitly in time using mixed finite elements in two space dimensions. The averaged models are evaluated using simulation results and their approximation errors in terms of $\varepsilon $ ε are estimated numerically.     

Non-ideal teleportation of tripartite entanglement: Einstein–Podolsky–Rosen versus Greenberger–Horne–Zeilinger schemes

Channels composed by Einstein–Podolsky–Rosen (EPR) pairs are capable of teleporting arbitrary multipartite states. The question arises whether EPR channels are also optimal against imperfections. In particular, the teleportation of Greenberger–Horne–Zeilinger states (GHZ) requires three EPR states as the channel and full measurements in the Bell basis. We show that, by using two GHZ states as the channel, it is possible to transport any unknown three-qubit state of the form \(c_0|000\rangle +c_1|111\rangle \). The teleportation is made through measurements in the GHZ basis, and, to obtain deterministic results, in most of the investigated scenarios, four out of the eight elements of the basis need to be unambiguously distinguished. Most importantly, we show that when both systematic errors and noise are considered, the fidelity of the teleportation protocol is higher when a GHZ channel is used in comparison with that of a channel composed by EPR pairs.     

A real–integer–discrete-coded differential evolution

The successful application of the real-coded differential evolution (DE) to a wide range of real-valued problems has motivated researchers to investigate its potentiality to integer and discrete valued problems. In most of such works, a real-valued solution is converted into a desired integer-valued solution by applying some posterior decoding mechanisms. Only a limited number of works are found, in which attempts are made for developing an actual integer-coded DE. In this article, such a DE is presented which can work directly with real, integer and discrete variables of a problem without any conversion. In the computational experiments carried out with a set of test problems taken from literature, the DE improved several previously known best solutions, as well as outperformed some similar proposals in most of the cases.     

Systematic search of low melting point alloys in the Fe–Cr–Mn–Mo–C system

In ternary systems, the liquidus surface is usually represented by a group of constant temperature contours projected onto a composition plane, i.e. the liquidus projection. The liquidus univariant lines indicate the conditions under which two solid phases coexist with the liquid phase. Those lines intersect at eutectics and peritectics. The univariant lines can also be projected onto a temperature vs. composition plane; this diagram allows easy identification of the lowest liquidus temperature on the system, covering the whole composition range of each component. This type of representation can also be used in quaternary and multicomponent systems, as a systematic tool to identify low melting point alloys as well as the solid phases involved at that temperature. This approach has been used in the present work to search low melting point alloys in the Fe–Cr–Mn–Mo–C system, using univariant line projections calculated with Thermo-Calc software and selected thermodynamic databases. The analysis covered the whole quinary system as well as the related binaries, ternaries and quaternaries. Some selected alloys of this system were prepared by mixing the elemental powders; the liquidus temperature was checked using calorimetric methods. The agreement between calculations and experiments is satisfactory.     

Decomposed fuzzy proportional–integral–derivative controllers

In this paper, several types of decomposed proportional–integral–derivative fuzzy logic controllers (PID FLCs) are tested and compared. An important feature of decomposed PID FLCs are their simple structures. In its simplest version, the decomposed PID FLC uses three one-input one-output inferences with three separate rule bases. Behaviours of proportional, integral and derivative PID FLC parts are defined with simple rules in proportional rule base, integral rule base and derivative rule base. The proposed decomposed PID FLC has been compared with several PID FLCs structures. All PID FLCs have been realised by the same hardware and software tools and have been applied as a real-time controller to a simple magnetic suspension system.     

Critical evaluation and thermodynamic modeling of the Fe–V–O (FeO–Fe2O3–VO–V2O3–VO2–V2O5) system

Critical evaluation and optimization of the Fe–V–O ternary oxide system was carried out based on all the available phase equilibria and thermodynamic property data at 1 atm total pressure. The Fe₃O₄–FeV₂O₄ spinel solid solution was described within the framework of Compound Energy Formalism considering the cation distribution between tetrahedral and octahedral sites. The wüstite phase, corundum phase, and VO₂ solid solution were described using a simple random mixing model. The Modified Quasichemical Model was used to describe liquid oxide solution in consideration of all multivalence states of Fe and V (Fe²⁺, Fe³⁺, V²⁺, V³⁺, V⁴⁺ and V⁵⁺). The variation of phase equilibria depending on the oxygen partial pressures and thermodynamic data in the system were well reproduced in the present study.     

Thermodynamic reassessments of the Ti–Si–C/Ti–Si–N systems and thermodynamic calculations of CVD TiSiCN hard-coating based on the Ti–Si–C–N quaternary system

The Ti–Si–C and Ti–Si–N systems were thermodynamically reassessed by using the CALculation of PHAse Diagram (CALPHAD) approach. A more suitable Gibbs energies expression of Ti₃SiC₂ was obtained to fit better with heat capacity data in the Ti–Si–C system. The thermodynamic parameters of the Ti–Si–N system were adjusted based on the revised Ti–Si system. A self-consistent thermodynamic database of the quaternary Ti–Si–C–N system was established. The calculated thermodynamic data and phase diagrams agree well with the experimental data. The CVD (Chemical Vapor Deposition) process for TiSiCN coatings was simulated using the newly evaluated thermodynamic parameters of the Ti–Si–C–N system. A good agreement between the predicted coating composition and the experimental ones was achieved, verifying the reliability of the thermodynamic database obtained in the present work.