Recurrence plots provide a graphical representation of the recurrent patterns in a timeseries, the quantification of which is a relatively new field. Here we derive analytical expressions which relate the values of key statistics, notably determinism and entropy of line length distribution, to the correlation sum as a function of embedding dimension. These expressions are obtained by deriving t...

If T is a numerical semigroup with maximal ideal N , define associated semigroups B(T ) := (N −N) and L(T ) = ∪{(hN −hN) : h ≥ 1}. If S is a numerical semigroup, define strictly increasing finite sequences {Bi(S) : 0 ≤ i ≤ β(S)} and {Li(S) : 0 ≤ i ≤ λ(S)} of semigroups by B0(S) := S =: L0(S), Bβ(S)(S) := N =: Lλ(S)(S), Bi+1(S) := B(Bi(S)) for 0 < i < β(S), Li+1(S) := L(Li(S)) for 0 < i < λ(S). ...

The main goal of the project A/6983/06, sponsored by the Spanish Agency for Latin America Collaboration, is analyzing and predicting electrocardiography signals of people which suffer post-traumatic stress. In order to make the prediction stage of this research, different techniques have been used. On the one hand, autoregressive moving average models which have been intensively used during dec...

We design an algorithm to embed graph metrics into `p with dimension and distortion bothdependent only upon the bandwidth of the graph. In particular we show that any graph ofbandwidth k embeds with distortion polynomial in k into O(log k) dimensional `p, 1 ≤ p ≤ ∞.Prior to our result the only known embedding with distortion independent of n was into highdimensional `1 and had d...

Let R = k[x1, . . . , xr] be the polynomial ring in r variables over an infinite field k, and let M be the maximal ideal of R. Here a level algebra will be a graded Artinian quotient A of R having socle Soc(A) = 0 : M in a single degree j. The Hilbert function H(A) = (h0, h1, . . . , hj) gives the dimension hi = dimk Ai of each degree-i graded piece of A for 0 ≤ i ≤ j. The embedding dimension o...

Multi-task learning employs shared representation of knowledge for learning multiple instances from the same or related problems. Time series prediction consists of several instances that are defined by the way they are broken down into fixed windows known as embedding dimension. Finding the optimal values for embedding dimension is a computationally intensive task. Therefore, we introduce a ne...

chaos theory discusses unstable and non-periodic behavior of non-linear fluctuating dynamicsystems. since evaporation level variations of lakes have a dynamic identity, chaos theory can have a uniquerole in collecting data of these variations. therefore it is an important and challenging problem in the field ofplanning and qualitative and quantitative management of urmia lake to verify whether ...