Mathematics
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On The Number of Unlabeled Bipartite Graphs
(2016)Let $I$ and $O$ denote two sets of vertices, where $I\cap O =\Phi$, $I = n$, $O = r$, and $B_u(n,r)$ denote the set of unlabeled graphs whose edges connect vertices in $I$ and $O$. It is shown that the following ... 
Mathematical Models of Quorum Sensing
(2016)Mathematical models of biological phenomena are constructed in order to further the understanding of the known and unknown interactions that result in the behaviors of dynamical systems. We present mathematical models ... 
PROCESSING INFORMATION ON INTERMEDIATE TIMESCALES WITHIN RECURRENT NEURAL NETWORKS
(2016)The cerebral cortex has remarkable computational abilities; it is able to solve prob lems which remain beyond the most advanced manmade systems. The complexity arises due to the structure of the neural network which ... 
Conic Economics
(2016)Modern general equilibria under uncertainty are modeled based on the recognition that all risks cannot be eliminated, perfect hedging is not possible, and some risk exposures must be tolerated. Therefore, we need to define ... 
Phase transitions in gene networks evolved under different selection rules
(2016)Mathematical models of gene regulation are a powerful tool for understanding the complex features of genetic control. While various modeling efforts have been successful at explaining gene expression dynamics, much less ...