Number Of Linear Regions Research Articles

Learning and Meshing from Deep Implicit Surface Networks Using an Efficient Implementation of Analytic Marching.

Reconstruction of object or scene surfaces has tremendous applications in computer vision, computer graphics, and robotics. In this paper, we study a fundamental problem in this context about recovering a surface mesh from an implicit field function whose zero-level set captures the underlying surface. Given that an MLP with activations of Rectified Linear Unit (ReLU) partitions its input space into a number of linear regions, we are motivated to connect this local linearity with a same property owned by the desired result of polygon mesh. More specifically, we identify from the linear regions, partitioned by an MLP based implicit function, the analytic cells and analytic faces that are associated with the function's zero-level isosurface. We prove that under mild conditions, the identified analytic faces are guaranteed to connect and form a closed, piecewise planar surface. Based on the theorem, we propose an algorithm of analytic marching, which marches among analytic cells to exactly recover the mesh captured by an implicit surface network. We also show that our theory and algorithm are equally applicable to advanced MLPs with shortcut connections and max pooling. Extensive experiments demonstrate our advantages over existing methods in terms of both meshing accuracy and efficiency.

Retracted] An Artificial Intelligent Virtual Reality Interactive Model for Distance Education

Information and communication technologies play an important role in education. This fact was emphasized even more due to the significant upheavals, globally, caused by the pandemic of COVID‐19 and because distance education uses tools of modern technology that prove to be significantly important. Particularly, virtual reality immersion systems, which may include 3D spatial representations, multisensory interaction channels, and real‐time intuitive physical interaction, can extend the learning process by providing learners with stimuli that represent a real advanced training environment. In the present work, based on the most modern technologies of computational intelligence, virtual and augmented reality, wireless communications, and space‐sensitive positioning applications, an Artificial Intelligent Virtual Reality (AI‐VR) interactive model for distance education is presented. This is a case study of escape‐room‐type educational application, wherewith appropriate practices and methodologies promote individual and collective participation, enhance the active role of the learner, personalize the educational experience, and upgrade the process of participation in distance education, strengthening and assisting role of the educator. Specifically, a Newton polynomial is used for max‐polynomials arising from the stereoscopic problem of augmented reality used to indirectly indicate the number of linear regions in order to optimize the problem. The proposed application is related to the training course of agricultural education and methods of modernization of crops, including additional sound, 3D graphics, and short film projection. The history‐space‐objects relationship takes and evolves with various versions such as the parts of the story to be unlocked as the trainee moves from one tool to the next or the story to guide the trainee to explore the space‐time continuum, giving a new dimension to the technological development of agricultural education and the methods of modernization of crops. This finding shows that they learn best when they receive information in a style that incorporates visual, auditory, and kinetic stimuli so that learning improves when learners can examine an idea or concept using a multidimensional approach.

Sparsest Univariate Learning Models Under Lipschitz Constraint

Beside the minimizationof the prediction error, two of the most desirable properties of a regression scheme are <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">stability</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">interpretability</i> . Driven by these principles, we propose continuous-domain formulations for one-dimensional regression problems. In our first approach, we use the Lipschitz constant as a regularizer, which results in an implicit tuning of the overall robustness of the learned mapping. In our second approach, we control the Lipschitz constant explicitly using a user-defined upper-bound and make use of a sparsity-promoting regularizer to favor simpler (and, hence, more interpretable) solutions. The theoretical study of the latter formulation is motivated in part by its equivalence, which we prove, with the training of a Lipschitz-constrained two-layer univariate neural network with rectified linear unit (ReLU) activations and weight decay. By proving representer theorems, we show that both problems admit global minimizers that are continuous and piecewise-linear (CPWL) functions. Moreover, we propose efficient algorithms that find the sparsest solution of each problem: the CPWL mapping with the least number of linear regions. Finally, we illustrate numerically the outcome of our formulations.

Computational Approach for Predicting Common Epitopes in the VP1 Structural Protein of Enterovirus Serotypes EV-D68, EV-D70, and EV-A71

The three human Enterovirus serotypes D-68, D-70, and A-71, are common pathogens that are transmitted by fecal-oral and aerosol routes. These positive RNA viruses were known to exhibit high levels of genetic diversity and variability. Currently, no vaccines are available to protect humans from these three serotypes. Therefore, efforts are needed for the development of a vaccine directed against heterologous viruses. In our study, an immunoinformatics approach is used to identify T- and B-cell epitopes that may help for the generation of a universal vaccine against EV-D70, EV-A71, and EV-D68. B and T cell epitopes were selected based on their length. As a result, 5 B cell epitopes and 18 T cell epitopes were predicted. Our B cell epitope prediction results showed that there are a number of linear regions. Position 150-170 was found to be the most immunogenic for the different strains. Regarding the epitopes of the T lymphocytes, the result of the interactions shows that 95% of the predicted epitopes are common between the 3 sequences and the 5 methods used. These results demonstrate the great immunogenic potential of these sequences and their capacities to trigger immune reactions in people with different HLA alleles. The “VFYDGFAGF” epitope is the most important and most immunogenic for triggering an immune response. Our study results allowed us to identify epitopes to be used in the development of cross-protection vaccines against the three Enterovirus serotypes. However, in vivo and in vitro studies are needed to assess the potential of the epitopes predicted by our study.

A Feature Fusion Based Indicator for Training-Free Neural Architecture Search

Neural Architecture Search Without Training (NASWOT) has been proposed recently to replace the conventional Neural Architecture Search (NAS). Pioneer works only deploy one or two indicator(s) to search. Nevertheless, the quantitative assessment for indicators is not fully studied and evaluated. In this paper, we first review several indicators, which are used to evaluate the network in a training-free manner, including the correlation of Jacobian, the output sensitivity, the number of linear regions, and the condition number of the neural tangent kernel. Our observation is that each indicator is responsible for characterizing a network in a specific aspect and there is no single indicator that achieves good performance in all cases, e.g. highly correlated with the test accuracy. This motivated us to develop a novel indicator where all properties of a network are taken into account. To obtain better indicator that can consider various characteristics of networks in a harmonized form, we propose a Fusion Indicator (FI). Specifically, the proposed FI is formed by combining multiple indicators in a weighted sum manner. We minimize the mean squared error loss between the predicted and actual accuracy of networks to acquire the weights. Moreover, as the conventional training-free NAS researches used limited metrics to evaluate the quality of indicators, we introduce more desirable metrics that can evaluate the quality of training-free NAS indicator in terms of fidelity, correlation and rank-order similarity between the predicted quality value and actual accuracy of networks. That is, we introduce the Pearson Linear Coefficient Correlation (PLCC), the Root Mean Square Error (RMSE), the Spearman Rank-Order Correlation Coefficient (SROCC), and Kendall Rank-Order Correlation Coefficient (KROCC). Extensive experiments on NAS-Bench-101 and NAS-Bench-201 demonstrate the effectiveness of our FI, outperforming existing methods by a large margin.

FINDING ALL SOLUTIONS OF PIECEWISE-LINEAR RESISTIVE CIRCUITS WITH HIGH APPROXIMATION ACCURACY

An efficient algorithm is proposed for finding all solutions of piecewise-linear (PWL) resistive circuits with high approximation accuracy, namely, circuits where the characteristics of PWL resistors are approximated by PWL functions with a very large number of segments. This algorithm is based on the LP test using the dual simplex method, the contraction method, and a special technique that makes the algorithm not require large memory space and not require copying tableaus. By numerical examples, it is shown that the proposed algorithm could find all solutions of a circuit where the number of PWL resistors is 4000 and the number of linear regions is 10 0004000.

Finding all solutions of piecewise-linear resistive circuits using the simplex method

Recently, an efficient algorithm was proposed for finding all solutions of piecewise-linear (PWL) resistive circuits using the simplex method, which could solve a problem where the number of PWL resistors is 200 and the number of linear regions is 10/sup 200/. In this work, an improved version of this algorithm is proposed, which can be applied to a broader class of PWL resistive circuits and could solve problems where the number of PWL resistors is 500 and the number of linear regions is 10/sup 500/ in practical computation time.

Finding all solutions of piecewise‐linear resistive circuits using the dual simplex method

AbstractAn efficient algorithm is proposed for finding all solutions of piecewise‐linear (PWL) resistive circuits using linear programming (LP). This algorithm is based on a simple test (termed the LP test) for non‐existence of a solution to a system of PWL equations in a given region. In the conventional LP test, the system of PWL equations is transformed into an LP problem, to which the simplex method is applied. However, this algorithm requires a very large number of pivotings because the simplex method is applied on many regions. In this paper, we introduce the dual simplex method to the LP test, which makes the average number of pivotings per region much smaller (less than one, for example) and makes the algorithm very efficient. By numerical examples, it is shown that the proposed algorithm could find all solutions of large‐scale problems, including those where the number of variables is 300 and the number of linear regions is 10300, in practical computation time. Copyright © 2002 John Wiley &amp; Sons, Ltd.

Improvement of the contraction‐type LP test algorithm for finding all solutions of piecewise‐linear resistive circuits

AbstractIn this letter, an effective technique is proposed for improving the computational efficiency of the contraction‐type LP test algorithm, which is an algorithm for finding all solutions of piecewise‐linear resistive circuits. Using the proposed technique, all solutions of a large‐scale problem, where the number of variables is 100 and the number of linear regions is 10100, could be found in less than 10 min using a 360 MHz computer. Copyright 2001 John Wiley &amp; Sons, Ltd.

Finding all solutions of piecewise‐linear circuits by using linear programming

AbstractAn efficient algorithm is proposed for finding all solutions of piecewise‐linear (PWL) resistive circuits using linear programming (LP). This algorithm is based on a simple test (termed the LP test) for nonexistence of a solution to a system of PWL equations of the form Pg(x) + Qx – s = 0 in a given region. In the LP test, the system of PWL equations is transformed into an LP problem, to which the simplex method is applied. Such an LP problem is obtained by surrounding the PWL functions by rectangles. In this paper, it is shown that the LP test can be performed very efficiently mostly by Phase II of the simplex method. Using the proposed techniques, the number of pivotings in the LP test becomes much smaller, which makes the algorithm very efficient. By numerical examples, it is shown that the proposed algorithm could find all solutions of relatively large scale circuits (including those where the number of variables is 200 and the number of linear regions is 10200) in practical computation time. © 2001 Scripta Technica, Electron Comm Jpn Pt 3, 84(7): 1–11, 2001

Performance evaluation of the LP test algorithm for finding all solutions of piecewise-linear resistive circuits

In this letter, the performance of the LP test algorithm, which is an algorithm for finding all solutions of piecewise-linear resistive circuits, is evaluated by numerical experiments. It is shown that the algorithm could find all solutions of large-scale problems (including those where the number of variables is 200-300 and the number of linear regions is 10 200 -10 300 ) in practical computation time.

An efficient piecewise‐linear DC analysis method for general non‐linear circuits

The convergence problems of conventional DC analysis can be partly avoided by using piecewise-linear analysis. This paper proposes a piecewise-linear DC analysis method that can efficiently handle arbitrary couplings between non-linear circuit elements. Piecewise-linear modelling of the non-linear circuit elements is automatically performed during simulation, using simplicial subdivisions. The number of linear regions, and thereby iterations, is considerably reduced by combining the common parts of separate simplicial subdivisions. Due to these reasons and since the method is formulated with the commonly used modified nodal approach, it has been possible to implement the method in the general-purpose circuit simulator APLAC. The correct operation of the method is demonstrated with three examples. Copyright © 1999 John Wiley & Sons, Ltd.

An efficient piecewise-linear DC analysis method for general non-linear circuits

The convergence problems of conventional DC analysis can be partly avoided by using piecewise-linear analysis. This paper proposes a piecewise-linear DC analysis method that can efficiently handle arbitrary couplings between non-linear circuit elements. Piecewise-linear modelling of the non-linear circuit elements is automatically performed during simulation, using simplicial subdivisions. The number of linear regions, and thereby iterations, is considerably reduced by combining the common parts of separate simplicial subdivisions. Due to these reasons and since the method is formulated with the commonly used modified nodal approach, it has been possible to implement the method in the general-purpose circuit simulator APLAC. The correct operation of the method is demonstrated with three examples. Copyright © 1999 John Wiley & Sons, Ltd.

Immunity in the connective tissue diseases. The humoral side of the coin.

Clinicians who care for patients with various connective tissue diseases frequently employ measurements of autoantibodies such as rheumatoid factors (RFs), anti-Sm antibodies, or anti-neutrophil cytoplasmic antibodies (cANCA) as a method to follow patients. Although the primary specificity of RFs appears to be directed against the Fc portion (C gamma 3 and C gamma 2 domains) of IgG, epitope mapping studies have now also demonstrated that many RFs also react with linear regions on beta 2-microglobulin and Class I HLA molecules. Cross reacting regions of IgG, beta 2m, and HLA Class I frequently show immunodominant tyrosines, trytophanes, valines, leucines, glutamic acids, aspartic acids, and threonines. Immunodominant linear epitopes on Sm antigen may be limited to regions expressing the PPPGMRPP or PPPGIRGP motifs. A number of linear regions of Proteinase 3 reacting with IgG antibodies in the sera of patients with Wegener's granulomatosis have now been identified. However, affinity purified rabbit antibodies to two of these major PR3 antigenic sties (ATVQLPQ and RVGAHDP) linked to Sepharose to form affinity columns, absorbed equal amounts of a mixture of many serum proteins from both Wegener's patients and normal controls. Continued study of this interface between autoantibody production, disease, and normal immune modulation is necessary.

PIECEWISE-LINEAR ANALYSIS FOR CHUA'S CIRCUIT FAMILY, INCLUDING THE COMPUTATION OF LYAPUNOV EXPONENTS

A special purpose program has been developed to compute the time-domain solutions and the Lyapunov exponents for Chua's circuit family. Advantage has been taken of the piecewise-linear nature of the circuits and the small number of linear regions in order to obtain fast and accurate computations. Examples are given to illustrate the capabilities of the program, in particular, to illustrate the calculation of the Lyapunov exponents.