Related papers: Higher-order perturbation theory for highly-improv…
Time series analysis has gained significant attention due to its critical applications in diverse fields such as healthcare, finance, and sensor networks. The complexity and non-stationarity of time series make it challenging to capture the…
Synchronization processes play critical roles in the functionality of a wide range of both natural and man-made systems. Recent work in physics and neuroscience highlights the importance of higher-order interactions between dynamical units,…
In this work I apply a recently proposed improvement procedure, originally conceived to reduce finite lattice spacing effects in transfer matrices for dilute Fermi systems, to tuning operators for the calculation of observables. I…
The recent promises of Model Predictive Control in robotics have motivated the development of tailored second-order methods to solve optimal control problems efficiently. While those methods benefit from strong convergence properties,…
Symplectic integration methods based on operator splitting are well established in many branches of science. For Hamiltonian systems which split in more than two parts, symplectic methods of higher order have been studied in detail only for…
We discuss interplay between the high-twist (HT) terms in the operator-product expansion and the next-to-next-to-leading-order (NNLO) QCD corrections to the deep-inelastic-scattering structure functions in analysis of the high-precision…
I give a review of existing frameworks, which are designed to analyse lattice data in the three-particle sector. A particular emphasis is laid on the foundations of the theory, where the separation of the short- and long-range effects plays…
Models for what may lie behind the Standard Model often require non-perturbative calculations in strongly coupled field theory. This creates opportunities for lattice methods, to obtain quantities of phenomenological interest as well as to…
This paper provides an extension of the constructive loop vertex expansion to stable matrix models with interactions of arbitrarily high order. We introduce a new representation for such models, then perform a forest expansion on this…
A method is described to solve the nonlinear Langevin equations arising from quadratic interactions in quantum mechanics. While, the zeroth order linearization approximation to the operators is normally used, here first and second order…
In this thesis, we argue that (order-) lattice-based multi-agent information systems constitute a broad class of networked multi-agent systems in which relational data is passed between nodes. Mathematically modeled as lattice-valued…
We calculate an effective Polyakov line action of QCD at large Nc and large Nf from a combined lattice strong coupling and hopping expansion working to second order in both, where the order is defined by the number of windings in the…
I review recent progress in heavy quarkonium physics from an effective field theory perspective. In this unifying framework, I discuss advances in perturbative calculations for low-lying quarkonium observables and in lattice calculations…
A higher dimensional lattice space can be decomposed into a number of four-dimensional lattices called as layers. The higher dimensional gauge theory on the lattice can be interpreted as four-dimensional gauge theories on the multi-layer…
The work relates to a new way for analysis of one-dimensional stochastic systems, based on consideration of its higher order difference structure. From this point of view, the deterministic and random processes are analyzed. A new numerical…
The dynamics of an extremely diluted neural network with high order synapses acting as corrections to the Hopfield model is investigated. As in the fully connected case, the high order terms may strongly improve the storage capacity of the…
The idea of adaptive perturbation theory is to divide a Hamiltonian into a solvable part and a perturbation part. The solvable part contains the non-interacting sector and the diagonal elements of Fock space from the interacting terms. The…
The complicated mesoscopic configurations of composite plate and shell structures requires a huge amount of computational overhead for directly simulating their mechanical problems. In this paper, a unified high-order multi-scale method,…
We derive strong estimates for Schatten norms of operator derivatives along paths of contractions and apply them to prove existence of higher order spectral shift functions for pairs of contractions.
We construct a higher lattice gauge theory based on the representation of 2-groups described by a category of crossed modules on a lattice model described by path 2-groupoids. Using these lattice gauge representations, an exactly solvable…