Related papers: Configuration Space Based Recurrence Relations for…
Applications of a method recently suggested by one of the authors (R.L.) are presented. This method is based on the use of dimensional recurrence relations and analytic properties of Feynman integrals as functions of the parameter of…
This is a book on higher-categorical diagrams, including pasting diagrams. It aims to provide a thorough and modern reference on the subject, collecting, revisiting and expanding results scattered across the literature, informed by recent…
We show that the problem of solving recurrence relations for L-loop (R+1)-point Feynman integrals within the method of integration by parts is equivalent to the corresponding problem for (L+R)-loop vacuum or (L+R-1)-loop propagator-type…
We study the problem of solving integration-by-parts recurrence relations for a given class of Feynman integrals which is characterized by an arbitrary polynomial in the numerator and arbitrary integer powers of propagators, {\it i.e.}, the…
This study involves definitions for multiple-counting regular and summation sequences of rho. My paper introduces and proves recurrent relationships for multiple-counting sequences and shows their association with Fermat's little theorem. I…
Using high resolution Cluster satellite observations, we show that the turbulent solar wind is populated by magnetic discontinuities at different scales, going from proton down to electron scales. The structure of these layers resembles the…
We formulate a framework of polynomial diagrams, which are a generalisation of power diagrams (PDs) and anisotropic power diagrams (APDs) allowing for boundaries between cells to be algebraic curves of a prescribed degree. We show that they…
We derive semiclassical laser equations valid in all orders of nonlinearity. With the help of a diagrammatic representation, the perturbation series in powers of electric field can be resummed in terms of a certain class of diagrams. The…
We present the results for two-loop massive kite master integrals with elliptics in terms of iterated integrals with algebraic kernels. The key ingredients are new integral representations for sunset subgraphs in $d=4-2\epsilon$ and…
We provide new methods to straightforwardly obtain compact and analytic expressions for epsilon-expansions of functions appearing in both field and string theory amplitudes. An algebraic method is presented to explicitly solve for…
Compound graphs are networks in which vertices can be grouped into larger subsets, with these subsets capable of further grouping, resulting in a nesting that can be many levels deep. In several applications, including biological workflows,…
This work focuses on the study of the reconfiguration strategies available for uniformly distributed satellite constellations and slotting architectures. Particularly, this manuscript deals with the cases of reducing, maintaining, and also…
Unordered, variable-sized inputs arise in many settings across multiple fields. The ability for set- and multiset-oriented neural networks to handle this type of input has been the focus of much work in recent years. We propose to represent…
We present a study of the structure of phase diagrams for matter-radiation systems, based on the use of coherent states and the catastrophe formalism, that compares very well with the exact quantum solutions as well as providing analytical…
Cosmological correlators are important observables in cosmology. They are often approximated by de Sitter space correlators. In this paper, we give a first precise diagrammatical computation of higher loop diagrams to all orders for a…
We propose an algorithm, that scales with the fifth power of the system size, for computing the second-order dispersion energy for monomers described with multiconfigurational wave functions. This scaling can be achieved when the number of…
The large scale reflector array of programmable metasurfaces is capable of increasing the power efficiency of backscatter communications via passive beamforming and thus has the potential to revolutionize the low-data-rate nature of…
Magnetic reconnection drives a wide range of astrophysical phenomena, including geomagnetic storms, solar flares, and activity in blazars. However, direct measurement of key reconnection observables remains challenging due to the remote and…
In this paper is discussed description of some algebraic structures in quantum theory by using formal recursive constructions with "complex Poincar\'e group" ISO(4,C).
We obtain extensions of the Poincar\'e and Perron theorems for higher order recurrence relations and apply them to obtain an inverse type theorem for row sequences of (type II) Hermite-Pad\'e approximation of a vector of formal power…