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Martin Svensson

Publications and source records attributed to Martin Svensson.

16 recordsLinked to original sources
arXiv2024

Hierarchical Delay Attribution Classification using Unstructured Text in Train Management Systems

EU directives stipulate a systematic follow-up of train delays. In Sweden, the Swedish Transport Administration registers and assigns an appropriate delay attribution code. However, this delay attribution code is assigned manually, which is a complex task. In this paper, a machine learning-based decision support for assigning delay attribution codes based on event descriptions is investigated. The text is transformed using TF-IDF, and two models, Random Forest and Support Vector Machine, are evaluated against a random uniform classifier and the classification performance of the Swedish Transport Administration. Further, the problem is modeled as both a hierarchical and flat approach. The results indicate that a hierarchical approach performs better than a flat approach. Both approaches perform better than the random uniform classifier but perform worse than the manual classification.

cs.LG↗
arXiv2019

Harmonic surfaces in the Cayley plane

We consider the twistor theory of nilconformal harmonic maps from a Riemann surface into the Cayley plane $\mathbf{O} P^2=F_4/\mathrm{Spin}(9)$. By exhibiting this symmetric space as a submanifold of the Grassmannian of $10$-dimensional subspaces of the fundamental representation of $F_4$, techniques and constructions similar to those used in earlier works on twistor constructions of nilconformal harmonic maps into classical Grassmannians can also be applied in this case. The originality of our approach lies on the use of the classification of nilpotent orbits in Lie algebras as described by D. Djoković.

math.DG↗
arXiv2018

Nonlinear Effects of Gravity in Cosmology

We consider some nonlinear effects of gravity in cosmology. Possible physically interesting consequences include: non-requirement of dark matter and dark energy, asymmetric gravitational matter-creation, emergent homogeneity/isotropy & asymptotic flatness, resolution of "cosmic coincidence" Omega_m \sim Omega_lambda, effective cutoff of gravitational interaction at the scale of cosmic voids.

physics.gen-ph↗
arXiv2017

Continuous deformations of harmonic maps and their unitons

We consider harmonic maps on simply connected Riemann surfaces into the group $\mathrm{U}(n)$ of unitary matrices of order $n$. It is known that a harmonic map with an associated algebraic extended solution can be deformed into a new harmonic map that has an $S^1$-invariant associated extended solution. We study this deformation in detail and show that the corresponding unitons are smooth functions of the deformation parameter and real analytic along any line through the origin.

math.FA↗
arXiv2015

Complete minimal submanifolds of compact Lie groups

We give a new method for manufacturing complete minimal submanifolds of compact Lie groups and their homogeneous quotient spaces. For this we make use of harmonic morphisms and basic representation theory of Lie groups. We then apply our method to construct many examples of compact minimal submanifolds of the special unitary groups.

math.DG↗
arXiv2014

Harmonic maps into the exceptional symmetric space $G_2/SO(4)$

We show that a harmonic map from a Riemann surface into the exceptional symmetric space $G_2/{\mathrm SO}(4)$ has a $J_2$-holomorphic twistor lift into one of the three flag manifolds of $G_2$ if and only if it is `nilconformal', i.e., has nilpotent derivative. Then we find relationships with almost complex maps from a surface into the 6-sphere; this enables us to construct examples of nilconformal harmonic maps into $G_2/{\mathrm SO}(4)$ which are not of finite uniton number, and which have lifts into any of the three twistor spaces. Harmonic maps of finite uniton number are all nilconformal; for such maps, we show that our lifts can be constructed explicitly from extended solutions.

math.DG↗
arXiv2014

Harmonic morphisms from four dimensional Lie groups

We consider four dimensional Lie groups with left-invariant Riemannian metrics. For such groups we classify left-invariant conformal foliations with minimal leaves of codimension two. These foliations produce local complex-valued harmonic morphisms.

math.DG↗
arXiv2013

New constructions of twistor lifts for harmonic maps

We show that given a harmonic map $φ$ from a Riemann surface to a classical compact simply connected inner symmetric space, there is a $J_2$-holomorphic twistor lift of $φ$ (or its negative) if and only if it is nilconformal. In the case of harmonic maps of finite uniton number, we give algebraic formulae in terms of holomorphic data which describes their extended solutions. In particular, this gives explicit formulae for the twistor lifts of all harmonic maps of finite uniton number from a surface to the above symmetric spaces.

math.DG↗
arXiv2011

Timelike Constant Mean Curvature Surfaces with Singularities

We use integrable systems techniques to study the singularities of timelike non-minimal constant mean curvature (CMC) surfaces in the Lorentz-Minkowski 3-space. The singularities arise at the boundary of the Birkhoff big cell of the loop group involved. We examine the behaviour of the surfaces at the big cell boundary, generalize the definition of CMC surfaces to include those with finite, generic singularities, and show how to construct surfaces with prescribed singularities by solving a singular geometric Cauchy problem. The solution shows that the generic singularities of the generalized surfaces are cuspidal edges, swallowtails and cuspidal cross caps.

math.DG↗
arXiv2010

The Geometric Cauchy Problem for Surfaces With Lorentzian Harmonic Gauss maps

The geometric Cauchy problem for a class of surfaces in a pseudo-Riemannian manifold of dimension 3 is to find the surface which contains a given curve with a prescribed tangent bundle along the curve. We consider this problem for constant negative Gauss curvature surfaces (pseudospherical surfaces) in Euclidean 3-space, and for timelike constant non-zero mean curvature (CMC) surfaces in the Lorentz-Minkowski 3-space. We prove that there is a unique solution if the prescribed curve is non-characteristic, and for characteristic initial curves (asymptotic curves for pseudospherical surfaces and null curves for timelike CMC) it is necessary and sufficient for similar data to be prescribed along an additional characteristic curve that intersects the first. The proofs also give a means of constructing all solutions using loop group techniques. The method used is the infinite dimensional d'Alembert type representation for surfaces associated with Lorentzian harmonic maps (1-1 wave maps) into symmetric spaces, developed since the 1990's. Explicit formulae for the potentials in terms of the prescribed data are given, and some applications are considered.

math.DG↗
arXiv2010

Filtrations, factorizations and explicit formulae for harmonic maps

We use filtrations of the Grassmannian model to produce explicit algebraic formulae for all harmonic maps of finite uniton number from a Riemann surface, and so all harmonic maps from the 2-sphere, to the unitary group for a general class of factorizations by unitons. We show how these specialize to give explicit formulae for such harmonic maps to each of the classical compact Lie groups and their inner symmetric spaces - the nonlinear sigma-model of particle physics. Our methods also give an explicit Iwasawa decomposition of the algebraic loop group.

math.DG↗
arXiv2007

Harmonic morphisms from solvable Lie groups

In this paper we introduce two new methods for constructing harmonic morphisms from solvable Lie groups. The first method yields global solutions from any simply connected nilpotent Lie group and from any Riemannian symmetric space of non-compact type and rank $r\ge 3$. The second method provides us with global solutions from any Damek-Ricci space and many non-compact Riemannian symmetric spaces. We then give a continuous family of 3-dimensional solvable Lie groups not admitting any complex valued harmonic morphisms, not even locally.

math.DG↗
arXiv2006

Harmonic morphisms from the Grassmannians and their non-compact duals

In this paper we give a unified framework for the construction of complex valued harmonic morphisms from the real, complex and quaternionic Grassmannians and their non-compact duals. This gives a positive answer to the corresponding open existence problem in the real and quaternionic cases.

math.DG↗
arXiv2006

On the existence of harmonic morphisms from certain symmetric spaces

In this paper we give a positive answer to the open existence problem for complex-valued harmonic morphisms from the non-compact irreducible Riemannian symmetric spaces $SL_n(R)/SO(n)$, $SU^*(2n)/Sp(n)$ and their compact duals $SU(n)/SO(n)$ and $SU(2n)/Sp(n)$. Furthermore we prove the existence of globally defined, complex-valued harmonic morphisms from any Riemannian symmetric space of type IV.

math.DG↗