In this paper, we introduce a numerical treatment using generalized Euler method (GEM) for the non-linear programming problem which is governed by a system of fractional differential equations (FDEs). The appeared fra...In this paper, we introduce a numerical treatment using generalized Euler method (GEM) for the non-linear programming problem which is governed by a system of fractional differential equations (FDEs). The appeared fractional derivatives in these equations are in the Caputo sense. We compare our numerical solutions with those numerical solutions using RK4 method. The obtained numerical results of the optimization problem model show the simplicity and the efficiency of the proposed scheme.展开更多
In this paper, an efficient numerical method is considered for solving the fractional wave equation (FWE). The fractional derivative is described in the Caputo sense. The method is based on Laguerre approximations. Th...In this paper, an efficient numerical method is considered for solving the fractional wave equation (FWE). The fractional derivative is described in the Caputo sense. The method is based on Laguerre approximations. The properties of Laguerre polynomials are utilized to reduce FWE to a system of ordinary differential equations, which is solved by the finite difference method. An approximate formula of the fractional derivative is given. Special attention is given to study the convergence analysis and estimate an error upper bound of the presented formula. Numerical solutions of FWE are given and the results are compared with the exact solution.展开更多
Learning to associate a positive or negative experience with an unrelated cue after the presentation of a reward or a punishment defines associative learning.The ability to form associative memories has been reported ...Learning to associate a positive or negative experience with an unrelated cue after the presentation of a reward or a punishment defines associative learning.The ability to form associative memories has been reported in animal species as complex as humans and as simple as insects and sea slugs.Associative memory has even been reported in tardigrades[1],species that diverged from other animal phyla 500 million years ago.Understanding the mechanisms of memory formation is a fundamental goal of neuroscience research.In this article,we work on resolving the current contradictions between different Drosophila associative memory circuit models and propose an updated version of the circuit model that predicts known memory behaviors that current models do not.Finally,we propose a model for how dopamine may function as a reward prediction error signal in Drosophila,a dopamine function that is well-established in mammals but not in insects[2,3].展开更多
文摘In this paper, we introduce a numerical treatment using generalized Euler method (GEM) for the non-linear programming problem which is governed by a system of fractional differential equations (FDEs). The appeared fractional derivatives in these equations are in the Caputo sense. We compare our numerical solutions with those numerical solutions using RK4 method. The obtained numerical results of the optimization problem model show the simplicity and the efficiency of the proposed scheme.
文摘In this paper, an efficient numerical method is considered for solving the fractional wave equation (FWE). The fractional derivative is described in the Caputo sense. The method is based on Laguerre approximations. The properties of Laguerre polynomials are utilized to reduce FWE to a system of ordinary differential equations, which is solved by the finite difference method. An approximate formula of the fractional derivative is given. Special attention is given to study the convergence analysis and estimate an error upper bound of the presented formula. Numerical solutions of FWE are given and the results are compared with the exact solution.
文摘Learning to associate a positive or negative experience with an unrelated cue after the presentation of a reward or a punishment defines associative learning.The ability to form associative memories has been reported in animal species as complex as humans and as simple as insects and sea slugs.Associative memory has even been reported in tardigrades[1],species that diverged from other animal phyla 500 million years ago.Understanding the mechanisms of memory formation is a fundamental goal of neuroscience research.In this article,we work on resolving the current contradictions between different Drosophila associative memory circuit models and propose an updated version of the circuit model that predicts known memory behaviors that current models do not.Finally,we propose a model for how dopamine may function as a reward prediction error signal in Drosophila,a dopamine function that is well-established in mammals but not in insects[2,3].
