Related papers: Morse moves in flow categories
Categorical symplectic geometry is the study of a rich collection of invariants of symplectic manifolds, including the Fukaya $A_\infty$-category, Floer cohomology, and symplectic cohomology. Beginning with work of Wehrheim and Woodward in…
The two-fluid Maxwell system couples frictionless electron and ion fluids via Maxwell's equations. When the frequencies of light waves, Langmuir waves, and single-particle cyclotron motion are scaled to be asymptotically large, the…
Self-similar stable mixed moving average processes can be related to nonsingular flows through their minimal representations. Self-similar stable mixed moving averages related to dissipative flows have been studied, as well as processes…
Let $B$ be a M\"obius band and $f:B \to \mathbb{R}$ be a Morse map taking a constant value on $\partial B$, and $\mathcal{S}(f,\partial B)$ be the group of diffeomorphisms $h$ of $B$ fixed on $\partial B$ and preserving $f$ in the sense…
Let S be an ergodic measure-preserving automorphism on a non-atomic probability space, and let T be the time-one map of a topologically weak mixing suspension flow over an irreducible subshift of finite type under a Holder ceiling function.…
Despite their popularity, to date, the application of normalizing flows on categorical data stays limited. The current practice of using dequantization to map discrete data to a continuous space is inapplicable as categorical data has no…
It is shown that the Holographic Renormalization Group can be formulated universally within Quantum Field Theory as (the quantization of) the Hamiltonian flow on the cotangent bundle to the space of gauge-invariant single-trace operators…
This paper connects two seemingly different ways of studying knots: quantum group invariants and the dynamics of Morse flows. For fibered knots, we define a two-variable series invariant by counting Morse flow loops in the complement. This…
In this paper, we illustrate the behaviour of the mean curvature flows starting from principal orbits of any commuting Hermann action of cohomogeneity two on irreducible rank two Riemannian symmetric spaces of compact type by using…
Flow models are a cornerstone of modern machine learning. They are generative models that progressively transform probability distributions according to learned dynamics. Specifically, they learn a continuous-time Markov process that…
In this paper we give a complete topological classification of orientation preserving Morse-Smale diffeomorphisms on orientable closed surfaces. For MS diffeomorphisms with relatively simple behaviour it was known that such a classification…
We show that the symmetric track group, which is an extension of the symmetric group associated to the second Stiefel- Withney class, acts as a crossed module on the secondary homotopy group of a pointed space. An application is given to…
The observation of strongly-correlated states in moir\'e systems has renewed the conceptual interest in magnetic systems with higher SU(4) spin symmetry, e.g. to describe Mott insulators where the local moments are coupled spin-valley…
In this article, a spectral sequence analysis of a filtered Novikov complex $(\mathcal{N}_{\ast}(f),\Delta)$ over $\mathbb{Z}((t))$ is developed with the goal of obtaining results relating the algebraic and dynamical settings. Specifically,…
We propose using Normalizing Flows as a trainable kernel within the molecular dynamics update of Hamiltonian Monte Carlo (HMC). By learning (invertible) transformations that simplify our dynamics, we can outperform traditional methods at…
In this paper we relate dynamics associated to zero-sum games (Fictitious play) to Hamiltonian dynamics. It turns out that the Hamiltonian dynamics which is induced from fictitious play, has properties which are rather different from those…
We prove that the geodesic flow on a locally CAT(-1) metric space which is compact, or more generally convex cocompact with non-elementary fundamental group, can be coded by a suspension flow over an irreducible shift of finite type with…
A family of the so-called Maxwell times which arises in the contexto of Higher-Order Generalized Hydrodynamics (also called Mesoscopic Hydro-Thermodynamics) is evidenced. This is done in the framework of a HOGH build within a statistical…
Let $f:M \rightarrow \mathbb{R}$ be a Morse-Bott function on a finite dimensional closed smooth manifold $M$. Choosing an appropriate Riemannian metric on $M$ and Morse-Smale functions $f_j:C_j \rightarrow \mathbb{R}$ on the critical…
Examples of Morse functions with integrable gradient flows on some classical Riemannian manifolds are considered. In particular, we show that a generic height function on the symmetric embeddings of classical Lie groups and certain…