We introduce a novel framework to approximate the aggregate frequency dynamics of coherent generators. By leveraging recent results on concentration tightly connected networks, and weighted balanced truncation, hierarchy reduced-order models is developed. This provides increasing accuracy in approximation system response, outperforming existing aggregation techniques.

We emphasize some properties of coherent state groups, i.e. groups whose quotient with the stationary groups, are manifolds which admit a holomorphic embedding in a projective Hilbert space. We determine the differential action of the generators of the representation of coherent state groups on the symmetric Fock space attached to the dual of the Hilbert space of the representation. This permit...

Characteristic uncertainty relations and their related squeezed states are briefly reviewed and compared in accordance with the generalizations of three equivalent definitions of canonical coherent states. The standard SU(1, 1) coherent states are shown to be the unique states that minimize the Schrödinger uncertainty relation for every pair of the three generators and the Robertson relation fo...

Representations of coherent state Lie algebras on coherent state manifolds as first order differential operators are presented. The explicit expressions of the differential action of the generators of semisimple Lie groups determine for linear Hamiltonians in the generators of the groups first order differential equations of motion with holomorphic polynomials coefficients. For hermitian symmet...

The concept of intentional controlled islanding (ICI) is introduced as a proactive measure to safeguard the power system against blackouts in event significant disturbances. It involves strategically partitioning into self-healing islands, thereby mitigating impact such This study introduces new framework for creating stable, islands systems with large-scale wind plants. proposed strategy takes...

Many applications such as experimental evaluations of clustering algorithms require the existence of a significant reference clustering. This task is dual to finding significant clusterings of a given graph. We present several generators for pre–clustered graphs based on perturbation and geometry. In an experimental evaluation we confirm the applicability of our generators. Furthermore, the pre...

The generalization of A r statistics, including bosonic and fermionic sectors, is performed by means of the so-called Jacobson generators. The corresponding Fock spaces are constructed. The Bargmann representations are also considered. For the bosonic A r statistics, two inequivalent Bargmann realizations are developed. The first (resp. second) realization induces, in a natural way, coherent st...

Robertson intelligent states which minimize the Schrödinger-Robertson uncertainty relation are constructed as eigenstates of a linear combination of Weyl generators of the su(3) algebra. The construction is based on the analytic representations of su(3) coherent states. New classes of coherent and squeezed states are explicitly derived. ∗Permanent adress: LPMC, Faculty of Sciences, University I...

The self-similarity properties of fractals are studied in the framework of the theory of entire analytical functions and the q-deformed algebra of coherent states. Self-similar structures are related to dissipation and to noncommutative geometry in the plane. The examples of the Koch curve and logarithmic spiral are considered in detail. It is suggested that the dynamical formation of fractals ...