Merge pull request #9 from BarzanyAntares/Paper-Edits

Paper edits

paper.md

@@ -13,9 +13,10 @@ The classical alpha rhythm is an approximately 8-12Hz oscillatory activity patte
 
 A central criterion around which we base this investigation is the requirement that the models of interest should be expressed in concrete mathematical language, as well as being implemented in numerical simulations and/or quantitative analytic computations. Specifically, we consider a particular class of neurophysiological model - neural population models (NPMs) - that amongst the different mathematical formulations used over the past half century of efforts to model and understand alpha activity (Fig. 1C) are the one that has been used most routinely  [@da1977cortical;@grimbert2006bifurcation;@jansen1995electroencephalogram;@liley2001spatially;@bhattacharya2011thalamo;@david2003neural;@hartoyo2019parameter;@robinson2003neurophysical]. 
 
-We focus on four extensively studied NPMs that are commonly used to describe EEG alpha activity in the neuroimaging, neurophysiology, and computational neuroscience literature: the Jansen-Rit (JR; {cite:alt}`jansen1995electroencephalogram`), Moran-David-Friston (MDF; {cite:alt}`david2003neural;moran2007neural`), Liley-Wright (LW;  {cite:alt}`liley1999continuum;liley2001spatially`), and Robinson-Rennie-Wright (RRW; {cite:alt}`robinson2002dynamics;robinson2003neurophysical`) models. These shorthand terms reference certain key individuals who contributed to the conception and/or development of several prominent strands in the research literature. We do note however that they are imperfect ones - both because all of the models studied here build directly on the earlier work of other important theoreticians (e.g. Freeman, Zetterberg, Lopes Da Silva, Cowan, Nunez), and also in some cases each other (e.g. MDF is an indirect extension of JR). 
-We begin over the next few sections with a description of general elements present in the JR, MDF, LW, and RRW models, and a summary of their individual  characteristics. Direct comparisons between each of them are then made, first in the context of the alpha regime, and then extending into other oscillatory regimes at non-alpha frequencies.
-A central objective in this work is to identify common patterns between the models, using numerical simulations across a broad parameter space to identify the effects of rate constants, inter-population connectivity structure, and other factors on oscillatory dynamics. These similarities and differences across models constitute the points of agreement and divergence across current theories of alpha rhythmogenesis, and it is the mapping of this theoretical landscape that is our main aim in the present paper. The origin, biological significance, and validity of their parameters, as well as the functional forms of their equations, are also considered when discussing the respective limitations and advantages of each candidate model. 
+We focus on four extensively studied NPMs that are commonly used to describe EEG alpha activity in the neuroimaging, neurophysiology, and computational neuroscience literature: the Jansen-Rit [@jansen1995electroencephalogram], Moran-David-Friston [@david2003neural; @moran2007neural], Liley-Wright[@liley1999continuum; @liley2001spatially], and Robinson-Rennie-Wright (RRW; [@robinson2002dynamics; @robinson2003neurophysical]) models. These shorthand terms reference certain key individuals who contributed to the conception and/or development of several prominent strands in the research literature. We do note, however, that they are imperfect ones—both because all of the models studied here build directly on the earlier work of other important theoreticians (e.g., Freeman, Zetterberg, Lopes Da Silva, Cowan, Nunez), and also in some cases each other (e.g., MDF is an indirect extension of JR).
+We begin over the next few sections with a description of general elements present in the JR, MDF, LW, and RRW models, and a summary of their individual characteristics. Direct comparisons between each of them are then made, first in the context of the alpha regime and then extending into other oscillatory regimes at non-alpha frequencies.
+A central objective in this work is to identify common patterns between the models, using numerical simulations across a broad parameter space to identify the effects of rate constants, inter-population connectivity structure, and other factors on oscillatory dynamics. These similarities and differences across models constitute the points of agreement and divergence across current theories of alpha rhythmogenesis, and it is the mapping of this theoretical landscape that is our main aim in the present paper. The origin, biological significance, and validity of their parameters, as well as the functional forms of their equations, are also considered when discussing the respective limitations and advantages of each candidate model.
+
 
 
 ## Alpha origins and rhythmogenesis: current theories