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τ=inf{t>a:X(t)>L}was considered, describing the first exit time of a stochastic processX(t) outside from the interval[-L, L]with starting pointx0att0=0. The expression for the Laplace transform of theFPTdistribution used in [82] is more complicated than (19) and has the form Z...
Given the matrix Kij, let Q denote the number of non-zero Kij, i.e Q = Σij I(Kij > 0) where I is here the indicator function. We then define the network entropy as where we have rescaled Kij(t) by 1/n in order to ensure that Σij Kij(t) = 1. Note that the entropy ...
Thus, local signalling entropy around node i is close to zero. (b) Estimation of signalling entropy. An overall measure of signalling promiscuity of the cell is given mathematically by the signalling entropy rate (SR), which is a weighted average of local signaling entropies Si over all the ...
any set of existing collisions (q.v., the discussion of Lorentz and Boltzmann in Sect.5below). Later on, Maxwell asserted that there are such reciprocal collisions if the colliding objects are perfectly elastic (or perhaps point-like) molecules acting through central forces ([175], p. 537)...
l In 2016, invited as the first guest dancer of Hong Kong Dance Company to co-create and perform Zero《零》 in the Japan Arts Festival and 8/F Platform, Hong Kong. l In 2015, the invited work FROM IN by Young Artists Platform of Dance of China Dancers Association was premiered at th...
-lor--lamd: Specify the weight for L1 or L2 regularization. Default value is zero, meaning no regularization. Regularization is typically used to avoid over-fitting. -ror--reg: Specify the type of regularization. Default is L2 regularization. L1 and L2 are supported. ...
Information will be zero when the probability of an event is 1.0 or a certainty, e.g. there is no surprise. Let’s make this concrete with some examples. Consider a flip of a single fair coin. The probability of heads (and tails) is 0.5. We can calculate the information for flipping...
Furthermore, for arbitrary graph we have \(c_2=0\) for the Laplacian. Hence if a graph has a bounded degree, then we can simply utilize Theorem 5 in this scenario. While considering Laplacian matrices we need to assume that a matrix is singular. More specifically, the number of zero ...
Therefore, the rank of is 1 and has exactly one nonzero eigenvalue Having obtained the principal eigenvalue λ, we continue to determine its corresponding eigenvector . Obviously, λ and satisfy the following relation: which can be reexpressed as a system of equations: where is the ith ...