Related papers: Conformal covariance and the split property
We study topological properties of semi-group actions on the circle by orientation-preserving homeomorhisms. We prove that a generic action either possesses a forward-invariant interval-domain (i.e. a finite union of disjoint circle arcs),…
An important problem in network analysis is predicting a node attribute using both network covariates, such as graph embedding coordinates or local subgraph counts, and conventional node covariates, such as demographic characteristics.…
We show that the fractal curvature measures of invariant sets of one-dimensional conformal iterated function systems satisfying the open set condition exist, if and only if the associated geometric potential function is nonlattice.…
We discuss the Bisognano-Wichmann property for local Poincar\'e covariant nets of standard subspaces. We give a sufficient algebraic condition on the covariant representation ensuring the Bisognano-Wichmann and Duality properties without…
We investigate possible quantifications of the Dunford-Pettis property. We show, in particular, that the Dunford-Pettis property is automatically quantitative in a sense. Further, there are two incomparable mutually dual stronger versions…
Rationality of the Wightman functions is proven to follow from energy positivity, locality and a natural condition of global conformal invariance (GCI) in any number D of space-time dimensions. The GCI condition allows to treat correlation…
The self-similarity properties of fractals are studied in the framework of the theory of entire analytical functions and the $q$-deformed algebra of coherent states. Self-similar structures are related to dissipation and to noncommutative…
The time-dependent scaling of the two-time autocorrelation function of spin systems without disorder undergoing phase-ordering kinetics is considered. Its form is shown to be determined by an extension of dynamical scaling to a local…
We consider an involutive automorphism of the conformal algebra and the resulting symmetric space. We display a new action of the conformal group which gives rise to this space. The space has an intrinsic symplectic structure, a…
In the first part of the paper, we study conformal groups that act properly discontinuously and cocompactly on simply connected, non-flat homogeneous plane waves. We show that proper cocompact similarity actions that are not isometric can…
The conformal covariance of correlation functions is checked in the second-order transition induced by random bonds in the two-dimensional 8-state Potts model. The decay of correlations is obtained {\it via} transfer matrix calculations in…
We introduce a new algebraic structure called \textit{local biquandles} and show how colorings of oriented classical link diagrams and of broken surface diagrams are related to tribracket colorings. We define a (co)homology theory for local…
We discuss dynamics of skew product maps defined by circle diffeomorphisms forced by expanding circle maps. We construct an open class of such systems that are robust topologically mixing and for which almost all points in the same fiber…
We study conformal gravity as an alternative theory of gravitation. For conformal gravity to be phenomenologically viable requires that the conformal symmetry is not manifest at the energy scales of the other known physical forces. Hence we…
Spherical convolutional neural networks (Spherical CNNs) learn nonlinear representations from 3D data by exploiting the data structure and have shown promising performance in shape analysis, object classification, and planning among others.…
We study local normal forms for completely integrable systems on Poisson manifolds in the presence of additional symmetries. The symmetries that we consider are encoded in actions of compact Lie groups. The existence of Weinstein's…
Conformal prediction is a general distribution-free approach for constructing prediction sets combined with any machine learning algorithm that achieve valid marginal or conditional coverage in finite samples. Ordinal classification is…
Hidden symmetries of non-relativistic $\mathfrak{so} (2,1)\cong \mathfrak{sl}(2, {\mathbb R})$ invariant systems in a cosmic string background are studied using the conformal bridge transformation. Geometric properties of this background…
We describe a coordinate-free perspective on conformal nets, as functors from intervals to von Neumann algebras. We discuss an operation of fusion of intervals and observe that a conformal net takes a fused interval to the fiber product of…
Most existing examples of full conformal predictive systems, split-conformal predictive systems, and cross-conformal predictive systems impose severe restrictions on the adaptation of predictive distributions to the test object at hand. In…