Related papers: A calculus for flow categories
Constructions of spectra from symmetric monoidal categories are typically functorial with respect to strict structure-preserving maps, but often the maps of interest are merely lax monoidal. We describe conditions under which one can…
Why do we move forward when we walk? Our legs undergo periodic motion and thus possess no net change in position; however, our bodies do possess a net change in position and we are propelled forward. From a geometric perspective, this…
Generalizing a construction of A. Weil, we introduce a topological invariant for flows on compact, connected, finite dimensional, abelian, topological groups. We calculate this invariant for some examples and compare the invariant with…
Scene flow estimation is the task of describing 3D motion between temporally successive observations. This thesis aims to build the foundation for building scene flow estimators with two important properties: they are scalable, i.e. they…
A flow is a directed space structure on a homotopy type. It is already known that the underlying homotopy type of the realization of a precubical set as a flow is homotopy equivalent to the realization of the precubical set as a topological…
In this paper is presented a new approach to the axiomatic homotopy theory in categories, which offers a simpler and more useful answer to this old question: how two objects in a category (without any topological feature) can be deformed…
In Persistent Homology and Topology, filtrations are usually given by introducing an ordered collection of sets or a continuous function from a topological space to $\R^n$. A natural question arises, whether these approaches are equivalent…
We propose a new algorithm to obtain max flow for the multicommodity flow. This algorithm utilizes the max-flow min-cut theorem and the well known labeling algorithm due to Ford and Fulkerson [1]. We proceed as follows: We select one…
We prove an equivalence of categories from formal complex structures with formal holomorphic maps to homotopy algebras over a simple operad with its associated homotopy morphisms. We extend this equivalence to complex manifolds. A complex…
The problem of resolving virtual method and interface calls in object-oriented languages has been a long standing challenge to the program analysis community. The complexities are due to various reasons, such as increased levels of class…
We report a theory deriving bulk flow scaling for canonical wall-bounded flows. The theory accounts for the symmetries of boundary geometry (flat plate channel versus circular pipe) by a variational calculation for a large-scale energy…
An adaptive model for the description of flows in highly heterogeneous porous media is developed in~\cite{FP21,FP23}. There, depending on the magnitude of the fluid's velocity, the constitutive law linking velocity and pressure gradient is…
This thesis presents an overview of the flow equations recently introduced by Wegner. The little known mathematical framework of the flow in the manifold of unitarily equivalent matrices, as discovered in the mathematical literature before…
We introduce a new category of higher-dimensional automata in which the morphisms are functional homotopy simulations, i.e. functional simulations up to concurrency of independent events. For this, we use unfoldings of higher-dimensional…
We show that the category of log homotopy types is a full subcategory of a category of homotopy types with modulus.
In this paper we study similarity measures for moving curves which can, for example, model changing coastlines or retreating glacier termini. Points on a moving curve have two parameters, namely the position along the curve as well as time.…
This paper aims at building a unified framework to deal with a wide class of local and nonlocal translation-invariant geometric flows. First, we introduce a class of generalized curvatures, and prove the existence and uniqueness for the…
This series explores a new notion of T-homotopy equivalence of flows. The new definition involves embeddings of finite bounded posets preserving the bottom and the top elements and the associated cofibrations of flows. In this third part,…
We report part of our recent work on viscous hydrodynamics with consistent phase space distribution $f(x,\p)$ for freeze out. We develop the gradient expansion formalism based on kinetic theory, and with the constraints from the comparison…
Let f be a smooth map between unit spheres of possibly different dimensions. We prove the global existence and convergence of the mean curvature flow of the graph of f under various conditions. A corollary is that any area-decreasing map…