We present here an overview of the hypermatrix spectral decomposition deduced from the Bhattacharya-Mesner hypermatrix algebra [BM1, BM2]. We describe necessary and sufficient conditions for the existence of a spectral decomposition. We further extend to hypermatrices the notion of resolution of identity and use them to derive hypermatrix analog of matrix spectral bounds. Finally we describe an...

A decomposition of a molecular conformational space into sets or functions (states) allows for a reduced description of the dynamical behavior in terms of transition probabilities between these states. Spectral clustering of the corresponding transition probability matrix can then reveal metastabilities. The more states are used for the decomposition, the smaller the risk to cover multiple conf...

We presents a refined multiscale Shannon entropy for analyzing electroencephalogram (EEG), which reflects the underlying dynamics of EEG over multiple scales. The rationale behind this method is that neurological signals such as EEG possess distinct dynamics over different spectral modes. To deal with the nonlinear and nonstationary nature of EEG, the recently developed empirical mode decomposi...

When a covariance matrix with a Toeplitz structure is written as the sum of a singular one and a positive scalar multiple of the identity, the singular summand corresponds to the covariance of a purely deterministic component of a time-series whereas the identity corresponds to white noise—this is the Carathéodory-Fejér-Pisarenko (CFP) decomposition. In the present paper we study multivariable ...

Spectral decomposition has been rarely used to investigate complex networks. In this work we apply this concept in order to define two types of linkdirected attacks while quantifying their respective effects on the topology. Several other types of more traditional attacks are also adopted and compared. These attacks had substantially diverse effects, depending on each specific network (models a...

For a nite system A of bounded linear operators whose real linear combinations have real spectrum, the monogenic functional calculus is used to associate a function f(A) of the operators with any analytic function f in n real variables deened in a neighbourhood of the monogenic spectrum (A). Here, the existence of projection operators that decompose the functional calculus onto invariant subspa...

In this paper, the authors present new indices for estimating technical change, return to scale, and TFP growth, as well as its decomposition. These indices, Modified General Index (MGI), Generalized Modified General Index (GMGI), and General Time Trend index (GTTI), are generalization of General Index approaches. These approaches were used for productivity decomposition of Iran's barely produc...

In order to elucidate the difference between nitramine energetic materials, such as RDX (1,3,5-trinitro-1,3,5-triazacyclohexane), HMX (1,3,5,7-tetranitro-1,3,5,7-tetraazacyclooctane), and CL-20 (2,4,6,8,10,12-hexanitro-2,4,6,8,10,12-hexaazaisowurtzitane), and their nonenergetic model systems, including 1,4-dinitropiperazine, nitropiperidine, nitropyrrolidine, and dimethylnitramine, both nanosec...