Team:USP-UNESP-Brazil/Associative Memory/Background

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=Background=
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===Hopfield Associative Memory Networks===
===Hopfield Associative Memory Networks===
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The main model of the project is the associative memory network made by J.J. Hopfield in the 80’s. On this model, the system tends to converge to a pre-determined equilibrium, restoring the same pattern when exposed to variations of this same pattern.
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The idea of this project is based on the associative memory network introduced by J.J. Hopfield in the 80’s [http://en.wikipedia.org/wiki/Hopfield_network]. The structure of a Hopfield network is simple, all neurons are interconnected, and that brings about some interesting memory properties and provides a model for understanding human memory.
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We have chosen to built a Hopfield network because of its simplicity and robustness. The same methodology can be used to the construction of networks with different architectures, such as the called “perceptrons” [http://en.wikipedia.org/wiki/Perceptron]. In contrast to a Hopfield network, a perceptron is commonly used as a classifier.
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===Biological Mechanism===
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In a biological neural network, cells occupy a specific location and the information is passed through direct physical contact - the neuron axonal projections. In our case, a population of bacteria represents a single neuron and the information is transmitted by a quorum sensing molecule (QSM). Because of that, each "neuron" has its own QSM and the number of neurons is limitated by the number of different QSM. A comparison between a biological neural network and our design is presented in Fig 1.
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{{:Team:USP-UNESP-Brazil/Templates/RImage | image=Figura0020.jpg | caption=Fig 1. Comparison between a biological neural network and "bacterial neural network" | size=600px}}
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In order to evaluate if one population is active, we have designed the construction of a device that keeps each population of bacteria in a fixed position and enables the communication between different populations via QSM - Figure 2. This device can be built using a plate of 96 wells with membranes attached to their bottom. The membranes allow the diffusion of the quorum sensing substances but prevent the flux of bacterial populations.
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The architecture, or geometry of the system, is composed in a way that all neurons are connected .In math terms, a Hopfield Network can be represented as an “Energy” (E) function:
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{{:Team:USP-UNESP-Brazil/Templates/RImage | image=Physicalsystemforbacterialnetwork.png | caption=Fig 2. Device that will be used to measure the output. | size=600px}}
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[[File:equation1.jpg|center|300px|caption|]]
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====Genetic Construction====
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Equation 1
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Where “w” values are chosen such that the stored settings are the minima of the function “E”. The variable “x” is the state of the neuron “i”.
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The state of a given neuron “I”(active or silent) can be mathematically  represented as follows: Given that “xi“ is the state of neuron, 1 if is activated or 0 if silent, and a neuron turns active if the sum of all received stimulus (exciting or inhibiting) is more than 0. Mathematically we can represent the state of the neuron xi as:
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Each population of bacteria ("neuron") is defined by the way it interacts within the network and by its own QSM. Hence, the number of "neurons" is limited to the number of QSM. As a proof of concept we designed two populations of bacteria that communicate in a repressive manner. In order to make the network visually interesting, we used our 3x3 wells device and designed the population network to recognize two patterns - Figure 3. Since they are complementary, only two different population of bacteria are needed to represent the patterns "X" and "O". In this case, each population placed at the letter "X" inhibits all the ones placed at the letter “O” and activates the positions of its own pattern (and vice-versa).
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[[File:equation2.jpg|center|400px|caption|]]
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Equation 2
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In this equation, “wij” is the wheight
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Where "wij" is the weight assigned to the connection from neuron i to neuron j. The summation over j is the sum of all connections made by the neuron i. This dynamics (equation 2) is sufficient  for the network to converge the most similar memorized pattern.  
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{{:Team:USP-UNESP-Brazil/Templates/RImage | image=0019.JPG | caption=Fig. 3. Representation of the input and output in the 3x3 wells device. | size=600px}}
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The so called “learning” of a neural network consists on the choice of “w” weights. There are several ways  to choose them, what, actually, defines different learning methods
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In the Registry of Parts [http://partsregistry.org/Main_Page] there are four well characterized quorum sensing systems. However, there is a strong activation crosstalk between two of them (Las and Rhl). Therefore, we decided to use the system Cin and Rhl.
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Set "i" and "j" such as the wheight "wij" is defined as:
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In our system, the QSM signals trigger the transcription of an activator (or an inhibitor) of the transcription of GFP - this is our system activation reporter. Simultaneous inhibitions and activations of a bacterial population will be converted to a molecular competition of activators and inhibitors by the promoter that controls the production of GFP. It is this molecular competition who "chooses" the pattern stored in the system that is most similar to the input.
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[[File:equation3.png|center|400px|caption|]]
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As an example, if an input activates more positions at the “X” pattern than those at the “O”, a greater number of "X-activators" will be produced, and it is more likely that other "X" positions become activated, due to this competition for promoters at each position. Meanwhile, in the “O” pattern positions, the opposite occurs: a lesser number of initially activated positions implies less "O-activators", and the outcome is that "X wins over O" - the network reproduces the "X" pattern.
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Equation 3
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The Figure 1w shows the selection process of weights of connections between adjacent cells. To add more patterns, we have to sum the network of weights of the new pattern to the old network. (as shown in the Figure 2)
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This multi-regulated promoter, with an activator and an inhibitor, is called Prm. Its inhibitor is the transcriptional factor cl434 and its activator is the cl factor. The genetic design of the positions of the patterns “X” and “O” can be seen in Figure 4.
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[[File:009.JPG|center|570px|caption|]]
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This construction that uses the signal transduction containing cl434 and cl allows to create different systems of associative memory, limited only by the number of quorum sensing systems available. Figure 4 shows how this generic system would work and elucidates how this system could be applied to different functions involving genetic control.
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Figure 1
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The Hopfield model for the construction of an associative memory network using bacteria is a good choice because of its simplicity and strength. The same methodology can be used to the construction of networks with other architectures, such as the “perceptrons”. One step forward is the way how to deal with continuous biological variables, because the standard model uses discrete ones.
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<!--[[File:0022.png|center|600px|caption=Fig. 4|]] -->
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{{:Team:USP-UNESP-Brazil/Templates/RImage | image=0022.png | caption=Fig. 4. Genetic construction. | size=600px}}
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[[File:0018.JPG|center|620px|caption|]]
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Figure 2
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Latest revision as of 03:47, 27 September 2012