Role of Graph Theory in Computational Neuroscience

Role of Graph Theory in Computational Neuroscience

Hitesh Marwaha, Anurag Sharma, Vikrant Sharma
DOI: 10.4018/978-1-7998-7433-1.ch005
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Abstract

Neuroscience is the study of the brain and its impact on behavior and cognitive functions. Computational neuroscience is the subfield that deals with the study of the ability of the brain to think and compute. It also analyzes various electrical and chemical signals that take place in the brain to represent and process the information. In this chapter, a special focus will be given on the processing of signals by the brain to solve the problems. In the second section of the chapter, the role of graph theory is discussed to analyze the pattern of neurons. Graph-based analysis reveals meaningful information about the topological architecture of human brain networks. The graph-based analysis also discloses the networks in which most nodes are not neighbors of each other but can be reached from every other node by a small number of steps. In the end, it is concluded that by using the various operations of graph theory, the vertex centrality, betweenness, etc. can be computed to identify the dominant neurons for solving different types of computational problems.
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Introduction To Neuroscience

The only discipline that can help you understand how you think and process knowledge in your brain is computational neuroscience. Computational neuroscience's ultimate aim is to understand how electrical and chemical signals in the brain are used to represent and process information. It covers biophysical computation processes in neurons, computer simulations of neural circuits, and learning models. In general, Before the start of any routine task say reading a book, going to the office or going to market, etc. there are few perceptions that our brain might consider, like why to read or go, What would be the outcome, etc. It's all the mathematics, permutations, and chemical equations that are going on within our brains. Eric L. Schwartz coined the term “computational neuroscience” at a conference to provide a study of a discipline that had previously been known by several names, including “neural modeling,” “brain theory,” and “neural networks.” Neuroscience covers a wide range of disciplines, including molecular and cellular research as well as human psychophysics and psychology. Computational neuroscience aims to explain how the brain interprets and processes information using electrical and chemical signals. Although this goal is not recent, a lot has changed in the last decade. Because of developments in neuroscience, more information about the brain is now available, more computational power is available for practical simulations of neural systems, and new perspectives are being derived from the analysis of simplified models of large networks of neurons. The challenge of understanding the brain is attracting a rising number of scientists from various disciplines. Although there has been an explosion of findings of the structure of the brain at the cellular and molecular levels over the last few decades, we still don't know how the nervous system allows us to see, hear, learn, remember, and plan those acts. Computational neuroscience is a branch of neuroscience that creates models to incorporate large amounts of data in order to better understand how the brain works(Teeters et al., 2008).

A growing number of neuroscience databases are being created and made publicly accessible on the internet. In particular, there has been important progress in the collection and representation of neuroanatomical association patterns. Researchers can now access extensive data sets of connectional relationships between individual neurons or brain areas thanks to these efforts. The availability of such data sets necessitates the development of appropriate analytical resources for thorough and principled research. Graph theory, a branch of mathematics and combinatorics with many applications in various fields, such as R. Kötter (ed.), Neuroscience Data Analysis, provides one avenue for such an analysis(Sporns, 2003).

While using similar analytical methods, the computational neuroscience and systems biology research groups have relatively little contact. In this study, I reconstruct the past of the two disciplines and argue that this helps to understand why they grew up so far apart. It's a shame that they're separated because both fields would benefit from each other. Several examples are given, ranging from sociological to software technological to methodological. Computational neuroscience has more experience with multiscale modeling and the study of information processing by biological systems, whereas systems biology, is a better-structured culture that is very good at sharing resources(De Schutter, 2008).

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