A perfect separation of discrete sample points by four‐layered perceptron with localized representation

A procedure for deconvolution of multiple images of the same object with space-variant point-spread functions (PSFs) is presented. It is based on expressing deconvolution with inverse filtering as convolution with kernels corresponding to inverse PSFs. Sets of basis functions are made from these inverse PSFs, given at discrete sample points, through Karhunen-Loève (K-L) decomposition. The entire field of view can then be convolved with the K-L kernels. Coadding the results using continuous maps of expansion weights, interpolated for every pixel between the sample points, results in an image that is deconvolved with smoothly varying PSFs that match the discrete measurements. A demonstration data set is used to show how the transition between the grid points improves deconvolutions compared to piecewise deconvolution and mosaicking by avoiding the blending of discontinuities at the interfaces between adjacent subfields.

Optimizing spatial interpolation method and sampling number for predicting cadmium distribution in the largest shallow lake of North China

At present, problems related to data mining are aris-ing in various poorly formalizable areas of research(genetics, archaeology, medicine, etc.). Such problemsare characterized by insufficient knowledge about theobjects under study, which hampers the development ofmathematical models for them; by a large number ofmultitype (quantitative and qualitative) factors and arelatively small amount of data; and by the requirementthat analysis results be represented in a form clear toexperts in applied areas.A promising approach to solving such problems isbased on the class of logical decision functions. Theyare frequently represented in the form of a decisiontree. A detailed description of this class and referencescan be found in [1].The construction of decision functions with a mini-mal risk of erroneous predictions is an important task inmethods based on logical decision functions and inother data analysis techniques. It is well known that thecomplexity of the class of decision functions (thecapacity characteristic of the class [2]) is a importantfactor affecting the quality of decisions. To achieve thebest quality, we need a certain tradeoff between thecomplexity of the class and the accuracy of decisionsobtained on the training sample. Thus, the problemarises of choosing an optimal complexity of the class.In numerous applications, empirical data (trainingsample) are supplemented with expert knowledge,which is not tightly related to a distribution model(expert knowledge can be specified as upper bounds forthe risk; they can express constraints on the class of dis-tributions or the class of decision functions, specifypreference rules used in decision making, etc.). Whenan optimal complexity of the class is chosen, availableempirical data and expert knowledge have to be jointlytaken into account.This problem can be solved within the framework ofthe Bayesian learning theory. The idea behind thisapproach is to use a priori knowledge about the prob-lem in question so that each possible distribution (strat-egy, the state of nature) is assigned a certain weight.This weight reflects the expert’s intuitive confidence inwhether the unknown true distribution coincides withthat under consideration.In this paper, we propose a Bayesian recognitionmodel based on a finite set of events. The model is usedto develop and analyze methods for constructing logi-cal decision functions. While choosing an optimal com-plexity of the class, the model takes into account empir-ical data and expert knowledge.In pattern recognition, the task is to predict the pat-tern’s index for an arbitrary object of the populationdescribed by a set of variables. The prediction is madeby analyzing a training sample consisting of the valuesof these variables, together with the index of the corre-sponding pattern for each object. The variables can beof different types; i.e., some of them can be quantita-tive, while the others can be qualitative. As a rule, theproblem is solved in a class of decision functions inwhich an optimal function is sought according to agiven criterion. The class of logical decision functionsis defined on a set of partitions of the feature space intoa finite number of subdomains described by conjunc-tions of simple predicates. The number of subdomainsdetermines the degree of complexity of a logical func-tion.A Bayesian pattern recognition model on a finite setof events is defined by formulating certain statementsthat avoid the local metric properties of the featurespace (the transition from points of the space to events,where an event is understood as that of the original vari-ables taking values from a certain subdomain of thepartition). Moreover, the pattern recognition problem isconsidered on the values of a discrete unordered vari-able, the concept of a learning method (a mapping from

Multi-view clustering with adaptive anchor and bipartite graph learning

This paper presents a Sequential Approximate Optimization (SAO) procedure that uses the Radial Basis Function (RBF) network. If the objective and constraints are not known explicitly but can be evaluated through a computationally intensive numerical simulation, the response surface, which is often called meta-modeling, is an attractive method for finding an approximate global minimum with a small number of function evaluations. An RBF network is used to construct the response surface. The Gaussian function is employed as the basis function in this paper. In order to obtain the response surface with good approximation, the width of this Gaussian function should be adjusted. Therefore, we first examine the width. Through this examination, some sufficient conditions are introduced. Then, a simple method to determine the width of the Gaussian function is proposed. In addition, a new technique called the adaptive scaling technique is also proposed. The sufficient conditions for the width are satisfied by introducing this scaling technique. Second, the SAO algorithm is developed. The optimum of the response surface is taken as a new sampling point for local approximation. In addition, it is necessary to add new sampling points in the sparse region for global approximation. Thus, an important issue for SAO is to determine the sparse region among the sampling points. To achieve this, a new function called the density function is constructed using the RBF network. The global minimum of the density function is taken as the new sampling point. Through the sampling strategy proposed in this paper, the approximate global minimum can be found with a small number of function evaluations. Through numerical examples, the validities of the width and sampling strategy are examined in this paper.

In order to improve the work efficiency and save resources in the process of laser cladding on the H13 steel surface, based on COMSOL, by combining computer simulation and experiment, a plane continuous heat source model was used to simulate and analyze the temperature and stress field. The optimal power and scanning speed were obtained. It is found in the simulation process that the thermal sampling points stress increases with the increase of laser power and scanning speed. Because of the existence of solid–liquid phase variation in the laser cladding process, there are two peaks in the maximum thermal stress cycle curve of the sample points located in the molten pool, and the starting and ending time of each sample point’s peak value is basically the same. When the sample point is outside the molten pool, because the metal at the corresponding location is not melted, so there is no obvious peak value in the thermal stress cycle curve. With the increase of cladding layer depth corresponding to each sample point, the variation range of the two alternating thermal stress peaks increases first and then decreases, while the duration increases. According to the peak value of alternating thermal stress at the sampling point, the molten pool depth can be predicted. The residual stress analysis of the cladding layer is carried out according to the analysis results of temperature field and stress field. Through the actual cladding experiment, it is found that the depth of molten pool in the simulation results is basically consistent with the experimental results. All simulation results are verified through actual cladding experiments.

Feedforward neural networks (FNN's) have been proposed to solve complex problems in pattern recognition and classification and function approximation. Despite the general success of learning methods for FNN's, such as the backpropagation (BP) algorithm, second-order optimization algorithms and layer-wise learning algorithms, several drawbacks remain to be overcome. In particular, two major drawbacks are convergence to a local minima and long learning time. In this paper we propose an efficient learning method for a FNN that combines the BP strategy and optimization layer by layer. More precisely, we construct the layer-wise optimization method using the Taylor series expansion of nonlinear operators describing a FNN and propose to update weights of each layer by the BP-based Kaczmarz iterative procedure. The experimental results show that the new learning algorithm is stable, it reduces the learning time and demonstrates improvement of generalization results in comparison with other well-known methods.

Mapping Of Problem Learning Problem Vocational School 3 Yogyakarta And Its Completion (Class Srata Review) . This study aims to uncover the mapping of students' learning problems at SMK Negeri 3 Yogyakarta and their resolution is reviewed from the classroom. Research on student learning problems was conducted using a qualitative approach with a survey method with a sample size of 292 for an error rate of 5%. The instrument used in uncovering student learning problems is a non-test instrument check list problem (DCM) and an open questionnaire for how to solve problems then analyzed with descriptive analysis. The results showed that students of SMK Negeri 3 Yogyakarta experienced learning problems with a process of more than 90% with class XII having the biggest learning problems with a process of 96%, class XI students at 95% and class X students at 92%. The factors that cause learning problems in SMKN 3 Yogyakarta students are the lack of students' ability to manage time, technological development so that learning time is spent playing games and social media, as well as the tight hours of study of SMK students. Learning problem solving by students of SMKN 3 Yogyakarta there are various styles of problem solving including; trying to solve problems, seek social support, with religion and unproductive solutions. Keywords: Problems, Learning, Settlement

Metamodel-based approaches are very often used for nonlinear optimization. The Successive Response Surface Method (SRSM) (Roux et al. in Int J Numer Methods Eng 42:517–534, 1998; Stander and Craig in Eng Comput 19:431–450, 2002) is one example for the application of such an approach. SRSM computes a smoothing approximation for each system response in each iteration based on a set of sample points generated in a defined domain around the current optimum. This domain is shifted and contracted in each iteration according to the resulting current best point. By default, a linear polynomial is used as the approximation function. A new Linear Interpolation Approach (LInA) has been developed to reduce the number of nonlinear analyses required during the optimization. In contrast to SRSM, LInA uses interpolating linear polynomials rather than regressions. Linear approximation is used to exclude artificial local minima between sample points. Due to the fact that no oversampling is required anymore, interpolation results in a lower number of nonlinear analyses without losing accuracy. A second reduction of the required analyses is achieved by avoiding a complete resampling in each iteration. It is assumed that the vectors defined from the current best point to the remaining sample points should be as orthogonal as possible. Therefore, LInA starts with initial sample points from a Koshal design of experiments (DOE) locally around the initial design point. After having computed the new best point based on the linear approximation, only a few existing sample points are deleted in each iteration and replaced by new ones. Complete QR decomposition is used to generate the new sample points in an orthogonal complementary subspace. First studies with two nonlinear structural optimization problems have shown that the LInA approach leads to a noteworthy reduction of the number of required nonlinear analyses in comparison to SRSM. Furthermore, LInA is compared to two kriging approaches using a subdomain similar as LInA does. LInA shows results comparable to kriging with respect to the number of analysis runs.

Pattern recognition is the study of automatic processing and interpretation of patterns using computers through mathematical techniques, where the environment and the objects are collectively referred to as “patterns”. It studies the problem of classifying samples by their attributes using computational methods. The main research directions of pattern recognition are computer vision, image processing, and natural language processing. In this paper, we discuss the application of a variant of reinforcement meta-learning, which combines experience replay and meta-learning in reinforcement learning, to the problem of continuous learning in pattern recognition. It also compares its accuracy with current solutions such as online learning for the continuous learning problem in pattern recognition. It mainly consists of reinforcement learning, reptilian meta-learning and experience replay in SGDM optimizer. It is finally concluded that for the problem of continuous learning in pattern recognition, its ability to preserve past learned knowledge with rapid learning of current knowledge is higher than the current online learning. Based on this, the effect of different parameters on the performance of this variant of reinforcement meta-learning is explored.

In many countries, population growth, rapid urbanization, industrialization, and the irrational use of fertilizers and pesticides are severely disrupting natural environments, leading to an imbalance in ecosystems and generating physico-chemical and biological pollutants in receiving aquatic environments, and changing their uses, such as drinking water collection, livestock watering, and bathing. The objective of our study is to analyze the spatial and temporal variations in the physicochemical properties of Lake Kankossa waters. The study is based on four sampling campaigns conducted over a two-year period, between 2017 and 2021, covering seven representative sampling points: Exploitation, ElVak, ElHakem, Essak, Harth Ewlad Emin, ElHachya, and ElBir. The parameters analyzed are: pH, temperature, turbidity, suspended solids, conductivity, major ions, calcium, magnesium, sodium, potassium, nitrate, nitrite, sulfate, and chloride. Recorded temperatures range from 24 to 25.1 °C in March and October, and from 32 to 38.7°C in September and April. The pH is slightly neutral to very alkaline, varying between 7.28 and 10.93, sometimes reaching 11. Recorded conductivity values fluctuate between 158 and 460 μS/cm during humid periods and decrease to between 210 and 377 μS/cm during dry periods. Average turbidity and suspended solids (SS) levels peak during winter (134–148 mg/L and 317.5 NTU).

Chemical reactions can be very complex and frequently produce undesired side products within short time spans. Investigation of such reactions necessitates in-situ measurements for analysis. We present a novel micro-reactor design enabling non-invasive and spatially highly resolved in-situ reaction analysis using Raman spectroscopy. The reactor consists of a stainless steel base containing milled channels covered with anodically bonded pyrex glass. The educt flow rate is finely controlled by a motor-driven feed pump. Monitoring of an exemplary test reaction by Raman spectroscopic means was achieved by recording spectra at various discrete sampling points along the reaction channel. The glass window allows visual observation of the channels by optical microscopy and does not affect, in contrast to infrared spectroscopy, the Raman spectroscopic signal. Taking Raman spectra along the reaction channel at different loci enabled us to determine the reaction kinetics of a fast chemical reaction.

Smoothed Particle Hydrodynamics (SPH) is a grid-free numerical particle method for the simulation of the compressible flow of gases and fluids. The SPH-Method provides a numerical algorithm for solving a system of coupled partial differential equations for continuous field magnitudes. The method transfers this system of equations to a system of coupled common differential equations for magnitudes at discrete sampling points, the locations of the SPH-particles.

Under the premise of predicting the dynamic obstacles, a UAV path planning strategy of variable rolling window combined with potential flows is proposed. By using an autoregressive model, the expression of prediction for dynamic obstacles between discrete sampling points is given. The rolling window is designed to a triangle, also with adaptive function based on speed and angle of incidence of the dynamic obstacles. Potential flows method is used in the rolling windows to plan the obstacle avoidance route. At last the whole route is smoothed to satisfy the UAV constraints of maximum turning angle. The problem solution implementation is described along with several simulation results demonstrating the effectiveness of the method.KeywordsUAVdynamic environmentautoregressive predictionon-line path planning

Flow prediction of heterogeneous nanoporous media based on physical information neural network