The Role and Place of Artificial Neural Network Architectures Structural Redundancy in the Input Data Prototypes and Generalization Development

Neural Networks (NN) are the functional unit of Deep Learning and are known to mimic the behavior of the human brain to solve complex data-driven problems. Whenever we train our own neural networks, we need to take care of something called the generalization of the neural network. The performance of Artificial Neural Networks (ANN) mostly depends upon its generalization capability. In this paper, we propose an innovative approach to enhance the generalization capability of artificial neural networks (ANN) using structural redundancy. A novel perspective on handling input data prototypes and their impact on the development of generalization, which could improve to ANN architectures accuracy and reliability is described.

Generalization of PhaseNet in Shandong and its application to the Changqing M4.1 earthquake sequence

Waveforms of seismic events,extracted from January 2019 to December 2021 were used to construct a test dataset to investigate the generalizability of PhaseNet in the Shandong region.The results show that errors in the picking of seismic phases(P-and Swaves)had a broadly normal distribution,mainly concentrated in the ranges of−0.4–0.3 s and−0.4–0.8 s,respectively.These results were compared with those published in the original PhaseNet article and were found to be approximately 0.2–0.4 s larger.PhaseNet had a strong generalizability for P-and S-wave picking for epicentral distances of less than 120 km and 110 km,respectively.However,the phase recall rate decreased rapidly when these distances were exceeded.Furthermore,the generalizability of PhaseNet was essentially unaffected by magnitude.The M4.1 earthquake sequence in Changqing,Shandong province,China,that occurred on February 18,2020,was adopted as a case study.PhaseNet detected more than twice the number of earthquakes in the manually obtained catalog.This further verified that PhaseNet has strong generalizability in the Shandong region,and a high-precision earthquake catalog was constructed.According to these precise positioning results,two earthquake sequences occurred in the study area,and the southern cluster may have been triggered by the northern cluster.The focal mechanism solution,regional stress field,and the location results of the northern earthquake sequence indicated that the seismic force of the earthquake was consistent with the regional stress field.

Mathematical Definitions of Operators for Cartographic Generalization

This paper puts forword 11 cartographic generalization operator models and introduces their mathematical definitions,and thus a precise mathematical form and quantitative description has been given to these formerly limited qualitative concepts.The meaning of mathematical definition of operators for cartographic generalization and the application prospect in computer_aided cartography (CAC) is stated.ract The Jurassic strata in Jingyan of Sichuan containing the Mamenchinsaurus fauna are dealt with and divided in this paper. The Mamenchisaurus fossils contained there are compared in morphological features and stratigraphically with other types of the genus on by one. The comprehensive analysis show that the Mamenchisaurus fauna of Jingyan appeared in the early Late Jurassic and is primitive in morphology. The results of the morphological identification and stratigraphical study agree with each other. Their evolutionary processes in different apoches of the Late Jurassic also made clear. Key words Jingyan, Sichuan, Mamenchisaurus Fauna, stratigraphy, evolution

Using Entropy Penalty Term for Improving the Generalization Ability of Multilayer Feedfoward Networks *

Generalization ability is a major problem encountered when using neural networks to find the structures in noisy data sets. Controlling the network complexity is a common method to solve this problem. In this paper, however, a novel additive penalty term which represents the features extracted by hidden units is introduced to eliminate the overtraining of multilayer feedfoward networks. Computer simulations demonstrate that by using this unsupervised fashion penalty term, the generalization ability is greatly improved.

Generalization Capabilities of Feedforward Neural Networks for Pattern Recognition

This paper studies the generalization capability of feedforward neural networks (FNN).The mechanism of FNNs for classification is investigated from the geometric and probabilistic viewpoints. It is pointed out that the outputs of the output layer in the FNNs for classification correspond to the estimates of posteriori probability of the input pattern samples with desired outputs 1 or 0. The theorem for the generalized kernel function in the radial basis function networks (RBFN) is given. For an 2-layer perceptron network (2-LPN). an idea of using extended samples to improve generalization capability is proposed. Finally. the experimental results of radar target classification are given to verify the generaliztion capability of the RBFNs.

Energy Model for UAV Communications:Experimental Validation and Model Generalization

Wireless communication involving unmanned aerial vehicles(UAVs)is expected to play an important role in future wireless networks.However,different from conventional terrestrial communication systems,UAVs typically have rather limited onboard energy on one hand,and require additional flying energy consumption on the other hand.This renders energy-efficient UAV communication with smart energy expenditure of paramount importance.In this paper,via extensive flight experiments,we aim to firstly validate the recently derived theoretical energy model for rotary-wing UAVs,and then develop a general model for those complicated flight scenarios where rigorous theoretical model derivation is quite challenging,if not impossible.Specifically,we first investigate how UAV power consumption varies with its flying speed for the simplest straight-and-level flight.With about 12,000 valid power-speed data points collected,we first apply the model-based curve fitting to obtain the modelling parameters based on the theoretical closed-form energy model in the existing literature.In addition,in order to exclude the potential bias caused by the theoretical energy model,the obtained measurement data is also trained using a model-free deep neural network.It is found that the obtained curve from both methods can match quite well with the theoretical energy model.Next,we further extend the study to arbitrary 2-dimensional(2-D)flight,where,to our best knowledge,no rigorous theoretical derivation is available for the closed-form energy model as a function of its flying speed,direction,and acceleration.To fill the gap,we first propose a heuristic energy model for these more complicated cases,and then provide experimental validation based on the measurement results for circular level flight.

Generalization of Results of Computations and Natural Experiments at Steel Parts Quenching

Complicated changes occur inside the steel parts during quenching process. A three dimensional nonlinear mathematical model for quenching process has been established and the numerical simulation on temperature field, microstructure and stress field has been realized. The alternative technique for the formation of high-strength materials has been developed on the basis of intensification of heat transfer at phase transformations. The technology for the achievement of maximum compressive residual stresses on the hard surface is introduced. It has been shown that there is an optimal depth of hard layer providing the maximum compression stresses on the surface. It has also been established that in the surface hard layer additional strengthening (superstrengthening) of the material is observed. The generalized formula for the determination of the time of reaching maximum compressive stresses on the surface has been proposed.

SYSTEM FOR AUTOMATIC GENERALIZATION OF TOPOGRAPHIC MAPS

With the construction of spatial data infi＇astructure, automated topographic map generalization becomes an indispensable component in the community of cartography and geographic information science. This paper describes a topographic map generalization system recently developed by the authors. The system has the following characteristics： 1） taking advantage of three levels of automation, i.e. fully automated generalization, batch generalization, and interactive generalization, to undertake two types of processes, i.e. intelligent inference process and repetitive operation process in generalization; 2） making use of two kinds of sources for generalizing rule library, i.e. written specifications and cartographers＇ experiences, to define a six-element structure to describe the rules; 3） employing a hierarchical structure for map databases, logically and physically; 4） employing a grid indexing technique and undo/redo operation to improve database retrieval and object generalization efficiency. Two examples of topographic map generalization are given to demonstrate the system. It reveals that the system works well. In fact, this system has been used for a number of projects and it has been found that a great improvement in efficiency compared with traditional map general- ization process can be achieved.

Generalization Rough Set Theory

In order to avoid the discretization in the classical rough set theory, a generlization rough set theory is proposed. At first, the degree of general importance of an attribute and attribute subsets are presented. Then, depending on the degree of general importance of attribute, the space distance can be measured with weighted method. At last, a generalization rough set theory based on the general near neighborhood relation is proposed. The proposed theory partitions the universe into the tolerant modules, and forms lower approximation and upper approximation of the set under general near neighborhood relationship, which avoids the discretization in Pawlak's rough set theory.

FRAMEWORKS FOR GENERALIZATION CONSTRAINTS AND OPERATIONS BASED ON OBJECT-ORIENTED DATA STRUCTURE IN DATABASE GENERALIZATION

The constraints and the operations play an important role in database generalization.They guide and govern database generalization.The constraints are translation of the required conditions that should take into account not only the objects and relationships among objects but also spatial data schema (classification and aggregation hierarchy) associated with the final existing database.The operations perform the actions of generalization in support of data reduction in the database.The constraints in database generalization are still lack of research.There is still the lack of frameworks to express the constraints and the operations on the basis of object_oriented data structure in database generalization.This paper focuses on the frameworks for generalization operations and constraints on the basis of object_oriented data structure in database generalization.The constraints as the attributes of the object and the operations as the methods of the object can be encapsulated in classes.They have the inheritance and polymorphism property.So the framework of the constraints and the operations which are based on object_oriented data structure can be easily understood and implemented.The constraint and the operations based on object_oriented database are proposed based on object_oriented database.The frameworks for generalization operations,constraints and relations among objects based on object_oriented data structure in database generalization are designed.The categorical database generalization is concentrated on in this paper.

Internal Defects Detection Method of the Railway Track Based on Generalization Features Cluster Under Ultrasonic Images

There may be several internal defects in railway track work that have different shapes and distribution rules,and these defects affect the safety of high-speed trains.Establishing reliable detection models and methods for these internal defects remains a challenging task.To address this challenge,in this study,an intelligent detection method based on a generalization feature cluster is proposed for internal defects of railway tracks.First,the defects are classified and counted according to their shape and location features.Then,generalized features of the internal defects are extracted and formulated based on the maximum difference between different types of defects and the maximum tolerance among same defects’types.Finally,the extracted generalized features are expressed by function constraints,and formulated as generalization feature clusters to classify and identify internal defects in the railway track.Furthermore,to improve the detection reliability and speed,a reduced-dimension method of the generalization feature clusters is presented in this paper.Based on this reduced-dimension feature and strongly constrained generalized features,the K-means clustering algorithm is developed for defect clustering,and good clustering results are achieved.Regarding the defects in the rail head region,the clustering accuracy is over 95%,and the Davies-Bouldin index(DBI)index is negligible,which indicates the validation of the proposed generalization features with strong constraints.Experimental results prove that the accuracy of the proposed method based on generalization feature clusters is up to 97.55%,and the average detection time is 0.12 s/frame,which indicates that it performs well in adaptability,high accuracy,and detection speed under complex working environments.The proposed algorithm can effectively detect internal defects in railway tracks using an established generalization feature cluster model.

Categorical Database Generalization

This paper focuses on the issues of categorical database gen-eralization and emphasizes the roles ofsupporting data model, integrated datamodel, spatial analysis and semanticanalysis in database generalization.The framework contents of categoricaldatabase generalization transformationare defined. This paper presents an in-tegrated spatial supporting data struc-ture, a semantic supporting model andsimilarity model for the categorical da-tabase generalization. The concept oftransformation unit is proposed in generalization.

Schematic Road Network Map Progressive Generalization Based on Multiple Constraints

Multiple constraints for schematic road network map cartographic design are analyzed and summarized. Based on this, a set of quantitative criteria are set up and a new road network generalization method including progressive selection and displacement is proposed. Furthermore, topological checking methods for road networks are researched. Based on these constraints, the points in a road network are classified, and a satisfactory and effective schematic map is designed in a con- crete experiment while maintaining topological consistency of the road network between the original and the schematic map

Multi-linear Variable Separation Approach to Solve a (2+1)-DimensionalGeneralization of Nonlinear Schroedinger System

By using a Baecklund transformation and the multi-linear variable separationapproach, we find a new general solution of a (2+1)-dimensional generalization of the nonlinearSchroedinger system. The new 'universal' formula is defined, and then, rich coherent structures canbe found by selecting corresponding functions appropriately.

Very Original Proofs of Two Famous Problems: “Are There Any Odd Perfect Numbers?” (Unsolved until to Date) and “Fermat’s Last Theorem: A New Proof of Theorem (Less than One and a Half Pages) and Its Generalization”

This article presents very original and relatively brief or very brief proofs about of two famous problems: 1) Are there any odd perfect numbers? and 2) “Fermat’s last theorem: A new proof of theorem and its generalization”. They are achieved with elementary mathematics. This is why these proofs can be easily understood by any mathematician or anyone who knows basic mathematics. Note that, in both problems, proof by contradiction was used as a method of proof. The first of the two problems to date has not been resolved. Its proof is completely original and was not based on the work of other researchers. On the contrary, it was based on a simple observation that all natural divisors of a positive integer appear in pairs. The aim of the first work is to solve one of the unsolved, for many years, problems of the mathematics which belong to the field of number theory. I believe that if the present proof is recognized by the mathematical community, it may signal a different way of solving unsolved problems. For the second problem, it is very important the fact that it is generalized to an arbitrarily large number of variables. This generalization is essentially a new theorem in the field of the number theory. To the classical problem, two solutions are given, which are presented in the chronological order in which they were achieved. Note that the second solution is very short and does not exceed one and a half pages. This leads me to believe that Fermat, as a great mathematician was not lying and that he had probably solved the problem, as he stated in his historic its letter, with a correspondingly brief solution. To win the bet on the question of whether Fermat was telling truth or lying, go immediately to the end of this article before the General Conclusions.

Changes of Word Meaning in English-Generalization/Specialization and Pejoration/Amelioration

Changes of word meanings in English are often achieved by the processes of generalization/specialization and pejoration/amelioration.By generalization or specialization,the literal meanings of a word are broadened or narrowed.While by pejoration or amelioration,the associations of a word go downhill or rise.Trough supplying certain examples,a brief picture about meaning changes of words in English is drawn.

Overlay Generalization of Polygons Based on Fuzzy-Voronoi

The analysis of an overlaid map with different attributes has a very important function in GIS. In an overlaid map, approximately half of the constructed polygons are tiny and only account for less than 5% of the total area. In subsequent analysis of an overlaid map, a tiny polygon may require the same amount of computing time and memory space as any large one. In addition, in most cases it is meaningless to treat such polygons as distinct analysis units. So eliminating the tiny polygons is useful to improve efficiency. Now we often use the methods of “boundary comparison” and “fuzzy discriminance” to merge tiny polygons. But in the boundary comparison method, a polygon may be merged into a neighbor of quite different attribute values. In the second method, when the fuzzy grades of two boundary lines are almost the same and their lengths are different, this can lead to large error. In this paper, the partition principle of fuzzy Voronoi (F V) is proposed based on the characteristic of fuzzy boundary and the contiguity of Voronoi diagram. The bigger tiny polygons are divided by Voronoi diagram, and then are merged to neighbor polygon according to contiguity. The F V principle and arithmetic are presented in detail. In the end, an experiment is given; the result has proved that error in the F V method, compared with the two other methods, is only about 30%.

Point Set Generalization Based on the Kohonen Net

Point set generalization is one of the essential problems in map generalization. On the demands analysis of point set generalization, this paper proposes a method to generalize point sets based on the Kohonen Net model; the standard SOM algorithm has been improved so as to preserve the spatial distribution properties of the original point set. Examples illustrate that this method suits the generalization of point sets.

APPLICATIONS OF STAIR MATRICES AND THEIR GENERALIZATIONS TO ITERATIVE METHODS

Stair matrices and their generalizations are introduced. The definitions and some properties of the matrices were first given by Lu Hao. This class of matrices provide bases of matrix splittings for iterative methods. The remarkable feature of iterative methods based on the new class of matrices is that the methods are easily implemented for parallel computation. In particular, a generalization of the accelerated overrelaxation method （GAOR） is introduced. Some theories of the AOR method are extended to the generalized method to include a wide class of matrices. The convergence of the new method is derived for Hermitian positive definite matrices. Finally, some examples are given in order to show the superiority of the new method.

Generalization of vdW Type of Equations of State

The importance of equations of state (EOS) has brought about the proliferation of hundreds of EOS. Nearly all prevailing cubic EOS could be regarded as the results of reforming the original vdW EOS. However, the accuracy of the vdW EOS is so low. In view of this, a new general equation is proposed that could be used to value or compare vdW type of EOS, and consequently develop a better vdW type of EOS.