Recently, there has been growing interest in lifting MAP inference algorithms for Markov logic networks (MLNs). A key advantage of these lifted algorithms is that they have much smaller computational complexity than propositional algorithms when symmetries are present in the MLN and these symmetries can be detected using lifted inference rules. Unfortunately, lifted inference rules are sound bu...

Isospin is an approximate symmetry which treats the up and down quarks as different eigenstates of the same particle. The mathematical structure for describing the isospin of a system is identical to that of angular momentum. We explore the implications of isospin. Specifically, we use isospin to predict the ratios of cross-sections in pion-nucleon scattering with incredible accuracy. We also d...

In this chapter we show how to compute the Discrete Fourier Transform using a Fast Fourier Transform (FFT) algorithm, including not-so special case situations such as when the data to be transformed are real. In those situations, we speed up the transforms by about a factor of two by exploiting symmetries in the data and the coefficients. We end this chapter by showing how to approximate the de...

in this paper, heir-equations method is applied to investigate nonclassical symmetries and new solutions of the black-scholes equation. nonlinear self-adjointness is proved and infinite number of conservation laws are computed by a new conservation laws theorem.

It has been argued that the energy content in time varying spacetimes can be obtained by using the approximate Lie symmetries of the geodesics equations in that spacetime. When applied to cylindrical gravitational waves, it gives a self-damping of the waves. According to this proposal the energy of the waves go to zero asymptotically as the radial distance to the two-thirds power. If true, this...

In quasicrystals, there are not only conventional, but also phason displacement fields and associated Burgers vectors. We have calculated approximate solutions for the elastic fields induced by two-, threeand fivefold straight screwand edge-dislocations in infinite icosahedral quasicrystals by means of a generalized perturbation method. Starting from the solution for elastic isotropy in phonon ...

Vortices in superfluid 3He-B have been observed to undergo a core transition. We discuss the analog phenomenon in relativistic field theories which admit embedded global domain walls, vortices and monopoles with a core phase structure. They are present in scalar field theories with approximate global symmetries which are broken both spontaneously and in parts explicitly. For a particular range ...

In this study symmetry analysis is carried out for a system dealing with nonreactive pollutant transport along a single channel. Constitutive equations obeying a power law fluid are used in the description of the mathematical problem. We obtain forms of the source term for which the governing system admits extra point symmetries. Invariant solutions which satisfy physical boundary conditions ar...

We present an exact collapsing solution to 2+1 gravity with a negative cosmological constant minimally coupled to a massless scalar field, which exhibits physical properties making it a candidate critical solution. We discuss its global causal structure and its symmetries in relation with those of the corresponding continously self-similar solution derived in the Λ = 0 case. Linear perturbation...