A bstract We go “back to basics”, studying accelerating systems in 2 + 1 AdS gravity ab initio . find three classes of geometry, which we interpret by holographically their physical parameters. From these, construct stationary, point particles; one-parameter extensions the BTZ family resembling an black hole; and new solutions including a novel “BTZ geometry” not continuously connected hole as ...

Any geometric algorithm can be dissected into combinatorial parts and geometric parts. The two parts intertwine in both the description and the implementation of the algorithm. We consider the benefits of relaxing this tight coupling. Coordinate freedom is widely considered the most important principle in designing and implementing geometric systems. By ensuring that client code not manipulate ...

We extend our previous studies of shock waves and shock-free solutions in thin accretion and winds in pseudo-Newtonian geometry to the case when the flow is two-dimensional and around a Kerr black hole. We present equations for fully general relativistic viscous transonic flows and classify the parameter space according to whether or not shocks form in an inviscid flow. We discuss the behaviors...

Several recent works have explored stochastic gradient methods for variational inference that exploit the geometry of the variational-parameter space. However, the theoretical properties of these methods are not well-understood and these methods typically only apply to conditionallyconjugate models. We present a new stochastic method for variational inference which exploits the geometry of the ...

BACKGROUND Epithelial junctional networks assume packing geometries characterized by different cell shapes, neighbor number distributions and areas. The development of specific packing geometries is tightly controlled; in the Drosophila wing epithelium, cells convert from an irregular to a hexagonal array shortly before hair formation. Packing geometry is determined by developmental mechanisms ...

D-decomposition technique is targeted to describe the stability domain in parameter space for linear systems, depending on parameters. The technique is very simple and effective for the case of one or two parameters. However the geometry of the arising parameter space decomposition into root invariant regions has not been studied in detail; it is the purpose of the present paper. We prove that ...

Several recent works have explored stochastic gradient methods for variational inference that exploit the geometry of the variational-parameter space. However, the theoretical properties of these methods are not well-understood and these methods typically only apply to conditionallyconjugate models. We present a new stochastic method for variational inference which exploits the geometry of the ...

We study the properties of a particular one-parameter family of circle maps called offcenter reflections defined in §2. This map, in its 2-dimensional version, is first introduced in an open problem by S. T. Yau, [Y, problem 21], who suggests a cross study of the dynamics and geometry. In this article, we attempt to explore the possible link between the dynamics of this family of circle maps an...

Information geometry provides a tool to systematically investigate the parameter sensitivity of the state of a system. If a physical system is described by a linear combination of eigenstates of a complex (that is, non-Hermitian) Hamiltonian, then there can be phase transitions where dynamical properties of the system change abruptly. In the vicinities of the transition points, the state of the...