We derive explicit inversion formulae for the attenuated geodesic and horocyclic ray transforms of functions and vector fields on two-dimensional manifolds equipped with the hyperbolic metric. The inversion formulae are based on a suitable complexification of the associated vector fields so as to recast the reconstruction as a Riemann Hilbert problem. The inversion formulae have a very similar ...

Agent-based modeling is used to study many kind of complex systems in different fields such as biology, ecology, or sociology. Visualization of the execution of a such complex systems is crucial in the capacity to apprehend its dynamics. The ever increasing complexification of requirements asked by the modeller has highlighted the need for more powerful tools than the existing ones to represent...

In [5] the author proved that if there is a free algebraic circle action on a nonsingular real algebraic variety X then the fundamental class is trivial in any nonsingular projective complexification i : X → XC. The Kähler forms on C and CP naturally induce symplectic structures on complex algebraic affine or projective varieties and in case they are defined over reals, their real parts, if not...

We calculate the exact values of the holomorphic observables of N = 4 supersymmetric SU(N) Yang-Mills theory deformed by mass terms which preserve N = 1 SUSY. These include the chiral condensates in each massive vacuum of the theory as well as the central charge which determines the tension of BPS saturated domain walls interpolating between these vacua. Several unexpected features emerge in th...

This paper describes a novel way of complexifying artificial neural networks through topological reorganization. The neural networks are reorganized to optimize their neural complexity, which is a measure of the information-theoretic complexity of the network. Complexification of neural networks here happens through rearranging connections, i.e. removing one or more connections and placing them...

We study complex product structures on nilpotent Lie algebras, establishing some of their main properties, and then we restrict ourselves to 6 dimensions, obtaining the classification of 6-dimensional nilpotent Lie algebras admitting such structures. We prove that any complex structure which forms part of a complex product structure on a 6-dimensional nilpotent Lie algebra must be nilpotent in ...

Recently the correlation functions of the so–called Itzykson-Zuber/Harish-Chandra integrals were computed (by one of the authors and collaborators) for all classical groups using an integration formula that relates integrals over compact groups with respect to the Haar measure and Gaussian integrals over a maximal nilpotent Lie subalgebra of their complexification. Since the integration formula...

We show that and how the centrifugal-singularity paradox [first formulated by Jevicki and Rodriguez in Phys. Lett. B 146 (1984) 55, partially resolved by Das and Pernice in Nucl. Phys. B 561 (1999) 357 and covering, as its l = 0 special case, also the half-oscillator problem discussed, recently, by Gangopadhyaya and Mallow (arXiv: hep-th/0206133) and by Das and Pernice in their subsequent comme...

From the partial differential Calogero’s (three-body) and Smorodinsky-Winternitz (superintegrable) Hamiltonians in two variables we separate the respective angular Schrödinger equations and study the possibilities of their “minimal” PT symmetric complexification. The simultaneous loss of the Hermiticity and solvability of the respective angular potentials V (φ) is compensated by their replaceme...