scholarly journals A new continuous entropy function and its inverse

2011 ◽  
Vol 9 (1) ◽  
pp. 65-70
Author(s):  
Andrej Grebenc
Keyword(s):  
Differential Equation ◽  
Neural Networks ◽  
Economic Modeling ◽  
Integral Solution ◽  
Entropy Function ◽  
Lambert W Function ◽  
Logarithmic Function ◽  
Lebesgue Integral ◽  
Parametric Function ◽  
Exponential Form

A new continuous entropy function of the form h(x)=-k?p'(x)*ln(p(x)) is constructed based on Lebesgue integral. Solution of the integral is of the form h(x)=-k*p(x)*ln(e-1*p(x)). Inverse solution of this function in the form of p(x)=h(x)*W-1(h(x)* e-1) has been obtained and this is a novelty. The fact that the integral of a logarithmic function is also a logarithmic function has been exploited and used in a more general ansatz for a deliberate function. The solution of the differential equation ?(x)= g(x)'*ln(g(x)) for a deliberate function g(x) includes the Lambert W function. The solution is a parametric function g(x)=(s(x)+C)/W(e-1*(s(x)+C)). Parameter C has a minimal value and, consequently, an infimal function g(x) exists. This transform is of general use, and is particularly suitable for use in neural networks, the measurement of complex systems and economic modeling, since it can transform multivariate variables to exponential form.

Novel Lebesgue-integral-based approach to improved results for neural networks with additive time-varying delay components

2017 ◽  
Vol 354 (16) ◽  
pp. 7543-7565 ◽  
Author(s):  
Deqiang Zeng ◽  
Ruimei Zhang ◽  
Shouming Zhong ◽  
Guowu Yang ◽  
Yongbin Yu ◽  
...  
Keyword(s):  
Neural Networks ◽  
Time Varying ◽  
Lebesgue Integral ◽  
Time Varying Delay ◽  
Varying Delay

An integral solution of the electromagnetic seismograph equation

1960 ◽  
Vol 50 (3) ◽  
pp. 461-465
Author(s):  
R. E. Ingram
Keyword(s):  
Differential Equation ◽  
Green’S Function ◽  
Green's Function ◽  
Integral Solution ◽  
Ground Movement ◽  
Ground Movements ◽  
Angular Movement ◽  
Electromagnetic Seismograph

ABSTRACT In investigating the response of an electromagnetic seismograph to various ground movements it is advantageous to have the solution of the differential equation as an integral. This is done by finding the Green's function, f(s), for the particular instrument. The angular movement of the galvanometer is then θ(t)=q∫0tf(s)x″(t−s)ds where x(t) is the ground movement and prime stands for the operator d/dt. It is sufficient to find one function, F(s), with dF/ds = f(s), to give the response to a displacement test, a tapping test, or a ground movement.

Artificial Neural Network for Solving the Inventory Control Problem in Fuzzy Environments

2021 ◽  
pp. 126-143
Author(s):  
Mostafijur Rahaman ◽  
Sankar Prasad Mondal ◽  
Shariful Alam
Keyword(s):  
Neural Network ◽  
Differential Equation ◽  
Neural Networks ◽  
Artificial Neural Network ◽  
Artificial Neural Networks ◽  
Inventory Control ◽  
Solution Procedure ◽  
Control Problems ◽  
Fuzzy Environment ◽  
Artificial Neural

In this chapter, different inventory control problems are formulated in fuzzy environment and solved by artificial neural network. Due to present the non-linearity associated with the differential equation in fuzzy environment, the solution procedure may be very complicated. To avoid the situation, artificial neural networks play an important role. In this chapter, different inventory control problems are formulated in fuzzy environment and solved by artificial neural network. Due to present the non-linearity associated with the differential equation in fuzzy environment, the solution procedure may be very complicated. To avoid the situation, artificial neural networks play an important role.

Neural Networks in Agent-Based Economic Modeling

2002 ◽  
pp. 97-111
Author(s):  
Herbert Dawid ◽  
Karl Doerner ◽  
Richard F. Hartl ◽  
Marc Reimann ◽  
Georg Dorffner ◽  
...  
Keyword(s):  
Neural Networks ◽  
Economic Modeling ◽  
Agent Based

scholarly journals Nonindependent Session Recommendation Based on Ordinary Differential Equation

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Zhenyu Yang ◽  
Mingge Zhang ◽  
Guojing Liu ◽  
Mingyu Li
Keyword(s):  
Neural Network ◽  
Differential Equation ◽  
Neural Networks ◽  
Ordinary Differential Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Deep Neural Networks ◽  
Semantic Information ◽  
User Behavior ◽  
User Behaviors

The recommendation method based on user sessions is mainly to model sessions as sequences in the assumption that user behaviors are independent and identically distributed, and then to use deep semantic information mining through Deep Neural Networks. Nevertheless, user behaviors may be a nonindependent intention at irregular points in time. For example, users may buy painkillers, books, or clothes for different reasons at different times. However, this has not been taken seriously in previous studies. Therefore, we propose a session recommendation method based on Neural Differential Equations in an attempt to predict user behavior forward or backward from any point in time. We used Ordinary Differential Equations to train the Graph Neural Network and could predict forward or backward at any point in time to model the user's nonindependent sessions. We tested for four real datasets and found that our model achieved the expected results and was superior to the existing session-based recommendations.

GIẢI PHƯƠNG TRÌNH ĐẠO HÀM RIÊNG SỬ DỤNG MẠNG NEURAL NHÂN TẠO

2020 ◽  
Vol 45 (03) ◽  
Author(s):  
HO DAC QUAN ◽  
HUYNH TRUNG HIEU
Keyword(s):  
Neural Network ◽  
Differential Equation ◽  
Neural Networks ◽  
Partial Differential Equation ◽  
Partial Differential ◽  
Neural Network Method ◽  
Network Method ◽  
Hidden Layer

Phương trình đạo hàm riêng đã được ứng dụng rộng rãi trong các lĩnh vực khác nhau của đời sống như vật lý, hóa học, kinh tế, xử lý ảnh vv. Trong bài báo này chúng tôi trình bày một phương pháp giải phương trình đạo hàm riêng (partial differential equation - PDE) thoả điều kiện biên Dirichlete sửdụng mạng neural truyền thẳng một lớp ẩn (single-hidden layer feedfordward neural networks - SLFN) gọi là phương pháp mạng neural (neural network method – NNM). Các tham số của mạng neural được xác định dựa trên thuật toán huấn luyện mạng lan truyền ngược (backpropagation - BP). Kết quả nghiệm PDE thu được bằng phương pháp NNM chính xác hơn so với nghiệm PDE giải bằng phương pháp sai phân hữu hạn.

P Wave Propagation in the Functionally Graded Materials

2013 ◽  
Vol 706-708 ◽  
pp. 1685-1688
Author(s):  
Li Gang Zhang ◽  
Hong Zhu ◽  
Hong Biao Xie ◽  
Lin Yuan
Keyword(s):  
Differential Equation ◽  
Wave Propagation ◽  
Functionally Graded Materials ◽  
Wave Motion ◽  
Mass Density ◽  
Functionally Graded ◽  
P Wave ◽  
Exponential Form ◽  
Graded Materials ◽  
P Wave Velocity

The P wave propagation in the functionally graded materials (FGM) is studied. The differential equation with varied-coefficient of wave motion in the FGM is established. By using of the WKBJ approximation method, the differential equation with varied-coefficient is solved, and the closed-analytical solutions of displacement in the FGM are obtained. The properties of the FGM whose shear modulus and mass density are gradually varying in exponential form are calculated; the curves of P wave velocity and amplitude, and the general properties of the P wave in the FGM are analyzed.

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