本文選題：能量地貌與環(huán)流 + 神經(jīng)網(wǎng)絡(luò)�。� 參考：《吉林大學(xué)》2016年博士論文

【摘要】：理解人類大腦的功能一直都是當(dāng)今科學(xué)界的一大重要目標(biāo)。最近幾年,人們在理論和實(shí)驗(yàn)神經(jīng)科學(xué)領(lǐng)域都取得了巨大的成績。盡管人們已經(jīng)做了很多有意義的工作,關(guān)于大腦行為與功能的全局和物理角度的理解對于我們?nèi)允蔷薮蟮奶魬?zhàn)。在本文中,為了面對這一挑戰(zhàn),我們構(gòu)建了普適的非平衡態(tài)神經(jīng)網(wǎng)絡(luò)地貌與環(huán)流理論進(jìn)一步建立起理論預(yù)測結(jié)果與實(shí)驗(yàn)觀測結(jié)果之間的聯(lián)系。在之前的研究工作中,大腦的記憶與學(xué)習(xí)過程通過對稱連接神經(jīng)網(wǎng)絡(luò)中所構(gòu)建的平衡態(tài)能量來定量描述。各個能量的吸引子存儲著不同的記憶,記憶檢索的動力學(xué)過程是由能量的梯度力決定的。然而在真實(shí)的神經(jīng)網(wǎng)絡(luò)中,神經(jīng)元之間通常都是非對稱連接的,而且與生理韻律調(diào)控相關(guān)的振蕩行為在對稱的神經(jīng)網(wǎng)絡(luò)中也并不會出現(xiàn)。這里我們首先為普通的神經(jīng)網(wǎng)絡(luò)系統(tǒng)發(fā)展了一套普適的非平衡態(tài)地貌與環(huán)流理論。為量化網(wǎng)絡(luò)系統(tǒng)的全局穩(wěn)定性和功能,我們定量求解出了與系統(tǒng)穩(wěn)態(tài)概率分布相關(guān)的勢能地貌和相應(yīng)的Lyapunov函數(shù)。我們發(fā)現(xiàn)大腦中的神經(jīng)元振蕩活動不僅由地貌的梯度力決定同時也由環(huán)流所決定。我們發(fā)現(xiàn)回旋環(huán)流源自于網(wǎng)絡(luò)的非對稱連接部分。神經(jīng)振蕩的地貌展現(xiàn)出了一個閉合環(huán)狀吸引子的拓?fù)湫螤�。在被勢能地貌的梯度力吸引到環(huán)上后,環(huán)流作為主要的驅(qū)動力驅(qū)使系統(tǒng)做周期振蕩運(yùn)動。我們發(fā)現(xiàn)環(huán)流力可能為不同記憶間的聯(lián)系提供了驅(qū)動力。接下來,我們利用地貌理論探討了一個與做決定相關(guān)的神經(jīng)網(wǎng)絡(luò)。與關(guān)聯(lián)記憶的網(wǎng)絡(luò)相似,如做決定等大腦認(rèn)知功能可以通過吸引子動力學(xué)所描述。然而相應(yīng)量化的吸引子地貌卻仍然沒有給出過。這里我們量化了做決定過程的勢能地貌并在地貌中量化了從未決定態(tài)到?jīng)Q定態(tài)這一做決定過程的最優(yōu)路徑。我們定量討論了做決定時速度,準(zhǔn)確性與能量消耗三者間的權(quán)衡問題。此外,我們也討論了做決定過程中改變主意的機(jī)制。我們還將勢能地貌與環(huán)流理論應(yīng)用到了基底節(jié)神經(jīng)環(huán)路這一運(yùn)動調(diào)控網(wǎng)絡(luò)來探索其相應(yīng)機(jī)制,特別是帕金森癥里出現(xiàn)的異常同步振蕩活動的相應(yīng)機(jī)制。我們發(fā)現(xiàn)因多巴胺耗竭而出現(xiàn)異常振蕩活動時,網(wǎng)絡(luò)的勢能地貌是一個墨西哥草帽狀的閉合環(huán)形山谷。量化的地貌和環(huán)流可以直接反映出網(wǎng)絡(luò)中突觸連接和外部輸入變化是如何影響系統(tǒng)的動力學(xué)行為的。我們定量研究了腦深部刺激術(shù)(DBS)對帕金森癥的治療機(jī)制,即其可以有效減小環(huán)路中的同步振蕩活動。我們的方法為定量研究神經(jīng)網(wǎng)絡(luò)提供了一個普適的方法,其也可能有助于發(fā)現(xiàn)更有效的治療運(yùn)動障礙的療法。
[Abstract]:Understanding the functioning of the human brain has always been a major goal of today's scientific community. In recent years, great achievements have been made in the field of theoretical and experimental neuroscience. Although a lot of meaningful work has been done, understanding the global and physical aspects of brain behavior and function remains a huge challenge. In this paper, in order to face this challenge, we construct a universal nonequilibrium neural network geomorphology and circulation theory to further establish the relationship between theoretical prediction results and experimental observation results. In previous studies, the brain's memory and learning processes were quantitatively described by the energy of the equilibrium state constructed in the symmetrically connected neural network. Different energy attractors store different memories. The dynamic process of memory retrieval is determined by the gradient force of energy. However, in real neural networks, the connections between neurons are usually asymmetric, and oscillatory behaviors associated with physiological prosody regulation do not occur in symmetric neural networks. Here we first develop a set of universal nonequilibrium geomorphology and circulation theory for ordinary neural network systems. In order to quantify the global stability and function of the network system, we quantitatively solve the potential energy geomorphology and the corresponding Lyapunov function related to the steady probability distribution of the system. We find that the oscillatory activity of neurons in the brain is determined not only by the gradient force of the geomorphology but also by the circulation. We find that the circumferential circulation originates from the asymmetric connection of the network. The physiognomy of neural oscillations shows the topological shape of a closed ring attractor. After being attracted to the ring by the gradient force of the potential geomorphology, the circulation drives the system to oscillate periodically as the main driving force. We find that the circulation force may provide a driving force for the relationship between different memories. Next, we discuss a decision-making neural network using geomorphological theory. Similar to the network of associated memory, cognitive functions such as decision making can be described by attractor dynamics. However, the corresponding quantized attractor geomorphology has not been given. Here we quantify the potential energy geomorphology of the decision making process and quantify the optimal path of the decision making process from the never determined state to the decision state in the geomorphology. We quantitatively discuss the tradeoff between speed, accuracy and energy consumption in making decisions. In addition, we discussed the mechanism of change of mind in the process of making a decision. We also apply the theory of potential energy geomorphology and circulation to the basal ganglion loop to explore the corresponding mechanism, especially the mechanism of abnormal synchronous oscillation in Parkinson's disease. We found that the potential energy landform of the network is a closed circular valley in the shape of a Mexican straw cap when abnormal oscillations occur due to the depletion of dopamine. The quantitative geomorphology and circulation can directly reflect how the changes of synaptic connections and external inputs in the network affect the dynamic behavior of the system. We quantitatively studied the therapeutic mechanism of deep brain stimulation (DBS) for Parkinson's disease, that is, it can effectively reduce the synchronous oscillation activity in the loop. Our method provides a general method for quantitative study of neural networks, which may also contribute to the discovery of more effective treatments for dyskinesia.
【學(xué)位授予單位】：吉林大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2016
【分類號】：O175;TP183

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