We present an efficient basis for imaginary time Green's functions based on a low-rank decomposition of the spectral Lehmann representation. The are simply set well-chosen exponentials, so corresponding expansion may be thought as discrete form representation using effective density which is sum $\ensuremath{\delta}$ functions. determined only by upper bound product $\ensuremath{\beta}{\ensurem...

We consider the (projective) representations of the group of holomorphic automorphisms of a symmetric tube domain V ⊕ iΩ that are obtained by analytic continuation of the holomorphic discrete series. For a representation corresponding to a discrete point in the Wallach set, we find the decomposition under restriction to the identity component of GL(Ω). Using Riesz distributions, an explicit int...

We introduce graphical time series models for the analysis of dynamic relationships among variables in multivariate time series. The modelling approach is based on the notion of strong Granger causality and can be applied to time series with non-linear dependencies. The models are derived from ordinary time series models by imposing constraints that are encoded by mixed graphs. In these graphs ...

Dislocation networks and their evolution are known to control the mechanical properties of metal samples. However, lack computationally efficient statistically rigorous descriptors for such defect systems has hindered development adoption rational protocols optimal design these material systems. This study presents a framework statistical quantification low dimensional representation dislocatio...

We present a new method for time-frequency representation (TFR), which combines a Fourier Bessel (FB) series expansion and the Wigner-Ville distribution (WVD). The FB series decomposes a multi-component signal into a number of single component signals before the WVD is applied. and then WVD is applied on the single component signals to analyze its time-frequency distribution (TFD). The simulati...

We introduce graphical time series models for the analysis of dynamic relationships among variables in multivariate time series. The modelling approach is based on the notion of strong Granger causality and can be applied to time series with non-linear dependencies. The models are derived from ordinary time series models by imposing constraints that are encoded by mixed graphs. In these graphs,...

5 For graphs G and F , write G → (F )` if any coloring of the edges of G with ` colors yields 6 a monochromatic copy of the graph F . Let positive integers h and d be given. Suppose S 7 is obtained from a graph S with s vertices and maximum degree d by subdividing its edges h 8 times (that is, by replacing the edges of S by paths of length h+ 1). We prove that there exits 9 a graph G with no mo...