If P y (t ) (x ) is the probability that the system transitions from y to x in t time steps, i.e., P y (t ) (x ) = Pr [ X t 0 + t = x | X t 0 = y ], then the steady-state distribution π of X t is defined by π (x ) = lim t → ∞ P k (t ) (x ) for any initial state k ∈ X.
(8) r x y (k ) = ∑ t = 1 N − k (x t − x ¯ ) (y k + t − y ¯ ) ∑ t = 1 N − k (x t − x ¯ ) 2 ∑ t = 1 N − k (y k + t − y ¯ ) 2 where x t is the expression signal of a known gene at time t, and x ¯ is the mean of x t. y k+t is the expression level of a gene at time k+t, and y ¯ is the mean of y y+t.
We took the absolute value of (| x t − x 1|) and subtracted the absolute value of (| x t − x 2|).
These sets of vertices (X t ) t ∈ V T have to satisfy the following conditions: (i) ⋃ t ∈ V T X t = V (ii) (v i, v j ) ∈ E ⇒ ∃ t ∈ V T : { v i, v j } ⊆ X t (iii) v ∈ X t 1 ∧ v ∈ X t 2 ∧ t 3 ∈ path (t 1, t 2 ) ⇒ v ∈ X t 3 A set X t is also called the bag for the vertex t.
For continuous-phase modulation (CPM), Equation (1) can be rewritten as x ( t ) = A T ( t ̄ ) e i ω c t = A 0 e i ( T Δ f c ) ∫ - ∞ t ̄ d τ a T e i ω c t, (16).
That is, if x t shows the value of a series at time t, then the seasonal differencing of order 52 is x t - x t -52.
Roughly speaking, the change of the x vector at each iteration is calculated by x t + 1 = x t − (F x ′ (x, u ) − 1 F (x, u ), with F x ′ (x, u ) = ∂ F (x, u ) ∂ x.
Therefore, at the transmitter, the transmitted signal after the additive hyperchaos masking (digital modulation) is S ( t ) = x ( t ) + d ( t ), (2).
Temperature dependence of g ¯ X (T ) is determined by the choice of the parameter Q 10, g ¯ X : g ¯ X → g ¯ X (Δ T ) = g ¯ X · Q 10, g ¯ X Δ T 10, X ∈ { N a, K, L, A }.
The free undirected graph on x consists of x, s(x), t(x), and g(x), with the pair x, g(x) constituting the two one-way lanes of a two-lane highway between s(x) = t(g(x)) and and t(x) = s(g(x)).
Given a state of the network x t (x t ′), all the states x t ′ (x t ) such that T(x t, x t ′)=1 are the successor (predecessor) states of the state x t (x t ′).
