An analytical study is performed to obtain the phase description of a network of Leaky Integrate-and-Fire (LIF) neurons. We start by discussing the behaviour of single LIF neuron in the presence of a constant current and then derive the corresponding phase oscillator model for some parameters setup. In the case of two identical LIF neurons where the interactions are ruled by the weak pulse input, we determine the analytical expression for the phase response curve. Next, we extend the phase reduction principles to a generic case of N networks of identical LIF neurons. The final model of so-called phase oscillators is widely used to study synchronization in many natural systems. Through numerical simulations, we find an agreement between the LIF neurons and the phase oscillators model.
Collective oscillations is typical phenomena observed in the systems biology including neurons. Investigating the mechanisms for which it occurs in neural networks evokes a significant interest among neuroscientists. From mathematical point of view, the coupling schemes rule the neuron’s behaviours ranging from microscopic to macroscopic scales. This paper aims to study the impacts of coupling schemes in a minimal network of two fully coupled identical oscillators (e.g., neurons). We proceed with the research by employing the numerical approach and time-series analysis. We consider both Kuramoto-like oscillator and Leaky integrate-and-fire neuron as the objects of study. In the former case, we found the phase of two oscillators are perfectly locked and stable if their frequency are identical, as stated by the main theorem. In the latter case, the membrane potentials of two neurons are perfectly synchronized, characterized by the same firing rate, due to the effect of excitatory delta pulses.
Curriculum organization is a part of arranging material teaching wich can teach the student or study experience wich want to reach a some purpose such as make student easier in studying material lesson also helping student in doing study activity until me purpose of studying can be reach by affective and optimum. The some procedure in curriculum organizing: studying procedure (book of lesson) procedure to learn other curriculum analisys of adult activity, procedure of social function, opinion survey, wrong studying procedure. Some manner wich should implemented in order education purpose can be reach such as: horizontal stucture is a shape of arranging material teaching for student; vertical structure wich has relation whit system problem, realization, implementation in school. Some component to iplement this curriculum: studying and teaching proces, guidance spread, supervision administration, cullicular means, and rating of student.
Abstrak: Geometri fraktal merupakan cabang matematika yang memfokuskan kajiannya pada objek-objek fraktal. SFI yaitu teknik yang dapat digunakan untuk memodelkan objek fraktal. Tulisan ini memaparkan bagaimana mengaplikasikan teorema Collage untuk mendesain SFI suatu himpunan K yang memiliki sifat self-similarity. Mendesain SFI suatu himpunan K berarti mencari sejumlah berhingga pemetaan kontraktif berupa transformasi affine:
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