Many real-world problems, such as Markov Logic Networks (MLNs) with evidence, can be represented as a highly symmetric graphical model perturbed by additional potentials. In these models, variational inference approaches that exploit exact model symmetries are often forced to ground the entire problem, while methods that exploit approximate symmetries (such as by constructing an over-symmetric ...

The analysis of complex networks is usually based on key properties such as small-worldness and vertex degree distribution. The presence of symmetric motifs on the other hand has been related to redundancy and thus robustness of the networks. In this paper we propose a method for detecting approximate axial symmetries in networks. For each pair of nodes, we define a continuous-time quantum walk...

in this paper mathematical structure of time-dependent lagrangian systems and their symmetries are extended and the explicit relation between constants of motion and infinitesimal symmetries of time-dependent lagrangian systems are considered. starting point is time-independent lagrangian systems ,then we extend mathematical concepts of these systems such as equivalent lagrangian systems to the...

Modern spectroscopic data on light non-strange meson spectrum is analyzed. It is argued that the observed regularities of experimental spectrum for highly excited states favour a partial restoration of all approximate classical symmetries of QCD Lagrangian (conformal, chiral and axial) broken by the quantum corrections. The rate of restoration of classical symmetries is estimated. The dependenc...

Symmetries of nth-order approximate stochastic ordinary differential equations SODEs are studied. The determining equations of these SODEs are derived in an Itô calculus context. These determining equations are not stochastic in nature. SODEs are normally used tomodel nature e.g., earthquakes or for testing the safety and reliability of models in construction engineering when looking at the imp...

The theory of anisotropic elasticity was originally motivated by applications to crystals, where geometric symmetries hold with high precision. In contrast, symmetries of the effective elastic responses of heterogeneous materials are usually approximate due to various imperfections of microgeometry. A related issue is that available data on the elastic constants may be incomplete or imprecise; ...

This paper is mainly a review concerning singular perturbation methods by means of Lie group analysis which has been presented by the author. We make use of a particular type of approximate Lie symmetries in those methods in order to construct reduced systems which describe the longtime behavior of the original dynamical system. Those methods can be used in analyzing not only ordinary different...