Related papers: Directed algebraic topology and higher dimensional…
It has been found empirically that quasi-Monte Carlo methods are often efficient for very high-dimensional problems, that is, with dimension in the hundreds or even thousands. The common explanation for this surprising fact is that those…
Higher-order topological phases (HOTPs) hold gapped bulk bands and topological boundary states localized in boundaries with codimension higher than one. In this paper, we provide a unified construction and topological characterization of…
A three-dimensional integrable generalization of the St\"ackel systems is proposed. The classification of such systems is obtained which results in two families. The first one is the direct sum of the two-dimensional case which is…
A deformed differential calculus is developed based on an associative star-product. In two dimensions the Hamiltonian vector fields model the algebra of pseudo-differential operator, as used in the theory of integrable systems. Thus one…
We discuss the higher-order topological field theory and response of topological crystalline insulators with no other symmetries. We show how the topology and geometry of the system is organised in terms of the elasticity tetrads which are…
We identify Whittaker vectors for $\mathcal{W}_k(\mathfrak{g})$-modules with partition functions of higher Airy structures. This implies that Gaiotto vectors, describing the fundamental class in the equivariant cohomology of a suitable…
A notion of dual curve for pseudoholomorphic curves in 4--manifolds turns out to be possible only if the notion of almost complex structure structure is slightly generalized. The resulting structure is as easy (perhaps easier) to work with,…
We construct a monoidal category of open transition systems that generate material history as transitions unfold, which we call situated transition systems. The material history generated by a composite system is composed of the material…
Formalising the pi-calculus is an illuminating test of the expressiveness of logical frameworks and mechanised metatheory systems, because of the presence of name binding, labelled transitions with name extrusion, bisimulation, and…
Many theoretical treatments of transport in heterogeneous Darcy flows consider advection only. When local-scale dispersion is neglected, flux-weighting persists over time; mean Lagrangian and Eulerian flow velocity distributions relate…
In this thesis, we study quantum phase transitions and topological phases in low dimensional fermionic systems. In the first part, we study quantum phase transitions and the nature of currents in one-dimensional systems, using field…
This thesis splits into two major parts. The connection between the two parts is the notion of "categorification" which we shortly explain/recall in the introduction. In the first part of this thesis we extend Bar-Natan's cobordism based…
Declarative modeling uses symbolic expressions to represent models. With such expressions one can formalize high-level mathematical computations on models that would be difficult or impossible to perform directly on a lower-level simulation…
This article is aimed at studying the effects of the dimensional crossover (DC) on physical properties of condensed systems near phase transition and critical points. Here we consider the following problems: (1) the theoretical provisions…
Based on the combinatorial description of the moduli spaces of curves provided by Strebel differentials, Witten and Kontsevich have introduced combinatorial cohomology classes $W_{(m_0,m_1,m_2,\dots),n}$, and conjectured that these can be…
We present an approach to modeling computational calculi using higher category theory. Specifically we present a fully abstract semantics for the pi-calculus. The interpretation is consistent with Curry-Howard, interpreting terms as typed…
The Shape Calculus is a bio-inspired calculus for describing 3D shapes moving in a space. A shape forms a 3D process when combined with a behaviour. Behaviours are specified with a timed CCS-like process algebra using a notion of channel…
Most Machine Learning (ML) methods, from clustering to classification, rely on a distance function to describe relationships between datapoints. For complex datasets it is hard to avoid making some arbitrary choices when defining a distance…
Topological condensed matter systems from class A and class AII of the classification table have received classical electromagnetic and mechanical analogs and protected wave-guiding with such systems has been demonstrated experimentally.…
Tracking of reference signals is addressed in the context of a class of nonlinear controlled systems modelled by $r$-th order functional differential equations, encompassing inter alia systems with unknown "control direction" and dead-zone…