Partial directed coherence

Cortical Connectivity during Isometric Contraction with Concurrent Visual Processing by Partial Directed Coherence... 

Keywords— Partial Directed Coherence, Motor Control, Isometric Contraction, Visual Processing. 

In various multivariate systems the information flow between subsystems is limited to distinct frequency bands. For such systems it is reasonable to transfer the concept of Granger-causality to the frequency domain. Granger-causal relationships can be detected in the frequency domain by means of the partial directed coherence which is based on modeling the investigated multivariate system by vector autoregressive processes [4]. Therefore, PDC is estimated according to (3) with the condition in (2) while the coefficient matrices Ui/r) are estimated by fitting a VAR model of order p as shown in (1). 

Partial directed coherence method was used for the analysis of EEG-EEG coherence because it facilitates the information pathways or direction of human brain activities during the two tasks as explained in the previous section. 

Next, the averaged EEG signals passed through partial directed coherence function that calculated the value of PDC to model the information pathways between EEG signals using the equation in (2). Meanwhile, the last step was... 

Luiz A. Baccala and Koichi Sameshima (2001) Partial Directed Coherence A New Concept in Neural Structure Determination. Biol. Cy-bcrn 84 463-474... 

Descriptions of Physical Objects, Processes, or Abstract Concepts. Eor example, pumps can be described as devices that move fluids. They have input and output ports, need a source of energy, and may have mechanical components such as impellers or pistons. Similarly, the process of flow can be described as a coherent movement of a Hquid, gas, or coUections of soHd particles. Flow is characterized by direction and rate of movement (flow rate). An example of an abstract concept is chemical reaction, which can be described in terms of reactants and conditions. Descriptions such as these can be viewed as stmctured coUections of atomic facts about some common entity. In cases where the descriptions are known to be partial or incomplete, the representation scheme has to be able to express the associated uncertainty. 

Since partial laser phase coherence affects both the direct terms as well as the cross terms, the extent of control is dependent on the laser properties through the relative magnitudes of ( l( ulg) (c02g))l and (l i-(w ) 2)> =1,2. To expose the dependence on the coherence of the pump field denote the terms ckc jF u>jk)dq kj)(E) by a ]- and consider the ratio of the k / j term in Eq. (5.44) to the associated diagonal terms. That is, consider the contrast ratio ... 

Finally, the combined voltammetric and on-line differential electrochemical mass spectrometry measnrements allow a quantitative approach of the ethanol oxidation reaction, giving the partial current efficiency for each product, the total number of exchanged electrons and the global product yields of the reaction. But, it is first necessary to elucidate the reaction mechanism in order to propose a coherent analysis of the DBMS results. In the example exposed previously, it is necessary to state on the reaction products in order to evaluate the data relative to acetic acid production which cannot be directly detected by DBMS measurements. However, experiments carried out at high ethanol concentration (0.5 mol L" ) confirmed the presence of the ethyl acetate ester characterized by the presence of fragments at m/z = 61, 73 and 88 at ratios typical of the ethyl acetate mass spectrum. " This ethyl acetate ester is formed by the following chemical reaction between the electrochemically formed acetic acid and ethanol (Bq. 29) and confirms the formation of acetic acid. 

The mass fraction A is obtained as the solution to a partial differential equation, which comes from the mass balance. In order to derive this we will consider a coherent region of any size, out of which we will imaginarily cut a body in which diffusion takes place, Fig. 2.57a. The volume of the region is V, and its surface area A. A surface element dA, whose normal n is directed outwards as in Fig. 2.57a, has a mass flow... 

The fractions dqi/dCj are the partial derivatives of the competitive isotherms. The fractions dCj/dCi are the directional derivatives, which cannot be derived directly from the experimental data, i.e., from the retention factors k[. However, they can be derived from the coefficients of the isotherm model, by applying the coherence condition (see Chapter 12). In the case of a binary mixture, the retention factors of the perturbations on a plateau of concentrations Cq,i, Cq i are solutions of the... 

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