Causal structure discovery in complex dynamical systems is an important challenge for many scientific domains. Although data from (interventional) experiments usually limited, large amounts of observational time series sets are available. Current methods that learn causal often assume linear relationships. Hence, they may fail realistic settings contain nonlinear relations between the variables...

Let Fq be a finite field and consider the polynomial ring Fq [X]. Let Q ∈ Fq [X]. A function f : Fq [X] → G, where G is a group, is called strongly Q-additive, if f(AQ + B) = f(A) + f(B) holds for all polynomials A,B ∈ Fq [X] with degB < degQ. We estimate Weyl Sums in Fq [X] restricted by Q-additive functions. In particular, for a certain character E we study sums of the form X P E(h(P )), wher...

In three experiments, we examined connections between item-recognition memory and memory for item-position information. With sequences of compound gratings as study and probe items, subjects made either item-position judgments (Experiments 1 and 2), by identifying the serial position of the study item that matched the probe, or recognition judgments (Experiment 3), by judging whether the probe ...

We address the distinction between dynamical and additive noise in time series analysis by making a joint evaluation of both the statistical continuity of the series and the statistical differentiability of the reconstructed measure. Low levels of the latter and high levels of the former indicate the presence of dynamical noise only, while low values of the two are observed as soon as additive ...

In this paper, a new identification of the Lagrange multipliers by means of the Sumudu transform, is employed to  btain a quick and accurate solution to the fractional Black-Scholes equation with the initial condition for a European option pricing problem. Undoubtedly this model is the most well known model for pricing financial derivatives. The fractional derivatives is described in Caputo sen...