be the non-vanishing polarization density, where the charge density ρ and the (average) dipole length δ are real quantities. The charge density wave function σ(x) is (1)The phase θ(x) is…

(1) (2) Fig. 1 (a) A graph whose vertices (squares) are connected by unidirectional edges (arrows). (b) Network structure corresponding to graph (a). The black solid and dashed arrows indicate excitatory…

, , and , whose dynamics are given by (1)where and are the overall excitatory and inhibitory couplings between the neural oscillators. During reinforcement, the coupling strengths and are changed…

which consists of two sectors: ‘sector 1’ is a Hilbert space , while ‘sector 2’ is a tensor product Hilbert space . Let us now consider the membership weights of…

. The spins recorded in each trial are realizations of random variables A and B, which, in the simplest case, can attain two values each: a 1 or a 2…

(1) where J ij denotes a connection from the j-th to i-th neuron, is an input pattern of input strength γ, and μ is index of learned mappings. For a…

Fig. 1 A two domain-model for ion concentration dynamics in the intra- and extracellular space. The ICS is represented as a cylindrical cable (I), coated by ECS (E). The geometry is…

is formed by the m-dimension vectors and , where . The max distance between X i and X j can be calculated by (1) Given a threshold r and each ,…

or , respectively. Here, p c regulates the total number of connections in the network, q c controls the fraction of inter-modular connections among all connections in the network, and…

(1) (2) (3)where represents the total input to the ith neuron and represents the noise intensity. The quantity J ij represents the absolute strength of the connection from the jth…