Related papers: On the strong convolution singularity property

In this note, we prove that the abstract gradient flow introduced by Baird-Fardoun-Regbaoui \cite{BFR}is well-posed on a closed Riemann surface with conical singularity. Long time existence and convergence of the flow are proved under…

A theorem of Mumford states that, on complex surfaces, any normal isolated singularity whose link is diffeomorphic to a sphere is actually a smooth point. While this property fails in higher dimensions, McLean asks whether the contact…

We consider the reduced density matrix of a large block of consecutive spins in the ground states of the XY spin chain on an infinite lattice. We derive the spectrum of the density matrix using the expression of the Renyi entropy in terms…

We investigate the properties of the combinatorial Ricci flow for surfaces, both forward and backward -- existence, uniqueness and singularities formation. We show that the positive results that exist for the smooth Ricci flow also hold for…

The gradient flow is the evolution of fields and physical quantities along a dimensionful parameter~$t$, the flow time. We give a simple argument that relates this gradient flow and the Wilsonian renormalization group (RG) flow. We then…

We suggest an approach to microrheology based on optical traps in order to measure fluid fluxes around singular points of fluid flows. We experimentally demonstrate this technique, applying it to the characterization of controlled flows…

We describe all possible topological structures of typical one-parameter bifurcations of gradient flows on the 2-sphere with holes in the case that the number of singular point of flows is at most six. To describe structures, we separatrix…

This article discusses a relatively new geometric flow, called the hypersymplectic flow. In the first half of the article we explain the original motivating ideas for the flow, coming from both 4-dimensional symplectic topology and…

Goldman defined a symplectic form on the smooth locus of the $G$-character variety of a closed, oriented surface $S$ for a Lie group $G$ satisfying very general hypotheses. He then studied the Hamiltonian flows associated to $G$-invariant…

Normalising flows offer a flexible way of modelling continuous probability distributions. We consider expressiveness, fast inversion and exact Jacobian determinant as three desirable properties a normalising flow should possess. However,…

We obtain sufficient conditions for an invariant splitting over a compact invariant subset of a $C^1$ flow $X_t$ to be dominated. In particular, we reduce the requirements to obtain sectional hyperbolicity and hyperbolicity.

Fluid deformation and strain history are central to wide range of fluid mechanical phenomena ranging from fluid mixing and particle transport to stress development in complex fluids and the formation of Lagrangian coherent structures…

We propose a new strategy for the determination of the step scaling function $\sigma(u)$ in finite size scaling studies using the Gradient Flow. In this approach the determination of $\sigma(u)$ is broken in two pieces: a change of the flow…

The landslide flow, introduced in [5], is a smoother analog of the earthquake flow on Teichm\"uller space which shares some of its key properties. We show here that further properties of earthquakes apply to landslides. The landslide flow…

The transition into a strongly-correlated regime of 3 fermions trapped in a one-dimensional harmonic potential is investigated. This interesting, but little-studied system, allows us to identify characteristic features of the regime, some…

We impose the first strong-lensing constraints on a wide class of modified gravity models where an extra field that modifies gravity also couples to photons (either directly or indirectly through a coupling with baryons) and thus modifies…

Recently, 3D Gaussian Splatting has emerged as a promising approach for modeling 3D scenes using mixtures of Gaussians. The predominant optimization method for these models relies on backpropagating gradients through a differentiable…

We classify combinations of isolated singularities that can occur on complex cubic threefolds generalizing analogous results for cubic surfaces due to Schl\"{a}fli and Bruce--Wall. In addition, we provide concise combinatorial description…

We show that, for the scalar field cosmology with exponential potential, the set of values of the coupling parameter for which the solutions undergo a transient period of acceleration is much larger than the set discussed in the literature.…

The inverse eigenvalue problem of a graph studies the real symmetric matrices whose off-diagonal pattern is prescribed by the adjacencies of the graph. The strong spectral property (SSP) is an important tool for this problem. This note…