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Jakob Hansen

Publications and source records attributed to Jakob Hansen.

At least 19 recordsLinked to original sources
arXiv2026

Human-in-the-Loop Atlas-Based 3D Asset Segmentation for Interactive Content Workflows

Segmenting 3D assets into meaningful regions remains challenging, especially when segmentation criteria are application-dependent and require user control. We present a human-in-the-loop pipeline for generating a segmented 2D parameterized atlas from a 3D model for interactive media, game, and XR content workflows. Our method first selects a compact set of rendered views using a greedy set cover strategy over sampled surface points, and then supports interactive segmentation of these views with SAM~2 and Label Studio. The resulting masks are back-projected onto the model's UV parameterization to produce a unified segmented atlas that supports downstream production tasks such as segment-wise material assignment, style transfer, and semantic labeling. We assess the pipeline through a demonstration-based technical evaluation on eight cultural heritage objects. The results show that the approach can generate usable segmented atlases across diverse geometries while revealing recurring sources of manual correction, particularly fine structures, cavities, and weak appearance boundaries. The code is available at https://github.com/saptarshineil/ai_assisted_atlas_segmentation

cs.CV↗
arXiv2025

FUV to FIR SED modelling of NGC 205

New far ultraviolet imaging of the galaxy NGC 205 is presented, which shows the emission is significantly offset ($\sim5^{\prime\prime}$ NW) from the optical and infrared centers of the galaxy. Spectral energy distribution (SED) modelling is applied to investigate the spatial dependence of the star formation history (SFH) of NGC 205, using data from far ultraviolet to far infrared. The SED model includes young and old stellar populations, gas emission, dust emission and dust absorption. The old stellar population has a total mass of $1.1\times10^8$ M$_{\odot}$ whereas the young population has a much smaller total mass of 3200 M$_{\odot}$. The best forms of SFH for old and young stars are found to be exponentially declining bursts with start times $t_0$ yr ago and e-folding times $\tau$ yr. The old stellar population has uniform $t_0$=9.5 Gyr, with $\tau$ decreasing with radius from 1 Gyr to 500 Myr. The young stellar population has $t_0$=900 Myr and $\tau$=800 Myr, both uniform across NGC 205. The young and old stellar mass surface densities are exponential in radius with scale lengths of 40 and 110 pc, respectively. The dust heating has a $\sim$40\% contribution from young stars and $\sim$60\% from old stars.

astro-ph.GA↗
arXiv2023

A Cosheaf Theory of Reciprocal Figures: Planar and Higher Genus Graphic Statics

This paper introduces cellular sheaf theory to graphical methods and reciprocal constructions in structural engineering. The elementary mechanics and statics of trusses are derived from the linear algebra of sheaves and cosheaves. Further, the homological algebra of these mathematical constructions cleanly and concisely describes the formation of 2D reciprocal diagrams and 3D polyhedral lifts. Additional relationships between geometric quantities of these dual diagrams are developed, including systems of impossible edge rotations. These constructions generalize to non-planar graphs. When a truss embedded in a torus or higher genus surface has a sufficient degree of axial self stress, we show non-trivial reciprocal figures and non-simply connected polyhedral lifts are guaranteed to exist.

math.AT↗
arXiv2023

Knowledge Sheaves: A Sheaf-Theoretic Framework for Knowledge Graph Embedding

Knowledge graph embedding involves learning representations of entities -- the vertices of the graph -- and relations -- the edges of the graph -- such that the resulting representations encode the known factual information represented by the knowledge graph and can be used in the inference of new relations. We show that knowledge graph embedding is naturally expressed in the topological and categorical language of \textit{cellular sheaves}: a knowledge graph embedding can be described as an approximate global section of an appropriate \textit{knowledge sheaf} over the graph, with consistency constraints induced by the knowledge graph's schema. This approach provides a generalized framework for reasoning about knowledge graph embedding models and allows for the expression of a wide range of prior constraints on embeddings. Further, the resulting embeddings can be easily adapted for reasoning over composite relations without special training. We implement these ideas to highlight the benefits of the extensions inspired by this new perspective.

cs.LG↗
arXiv2022

Multidimensional Persistence Module Classification via Lattice-Theoretic Convolutions

Multiparameter persistent homology has been largely neglected as an input to machine learning algorithms. We consider the use of lattice-based convolutional neural network layers as a tool for the analysis of features arising from multiparameter persistence modules. We find that these show promise as an alternative to convolutions for the classification of multidimensional persistence modules.

math.AT↗
arXiv2020

Sheaf Neural Networks

We present a generalization of graph convolutional networks by generalizing the diffusion operation underlying this class of graph neural networks. These sheaf neural networks are based on the sheaf Laplacian, a generalization of the graph Laplacian that encodes additional relational structure parameterized by the underlying graph. The sheaf Laplacian and associated matrices provide an extended version of the diffusion operation in graph convolutional networks, providing a proper generalization for domains where relations between nodes are non-constant, asymmetric, and varying in dimension. We show that the resulting sheaf neural networks can outperform graph convolutional networks in domains where relations between nodes are asymmetric and signed.

cs.LG↗
arXiv2020

Expansion in Matrix-Weighted Graphs

A matrix-weighted graph is an undirected graph with a $k\times k$ positive semidefinite matrix assigned to each edge. There are natural generalizations of the Laplacian and adjacency matrices for such graphs. These matrices can be used to define and control expansion for matrix-weighted graphs. In particular, an analogue of the expander mixing lemma and one half of a Cheeger-type inequality hold for matrix-weighted graphs. A new definition of a matrix-weighted expander graph suggests the tantalizing possibility of families of matrix-weighted graphs with better-than-Ramanujan expansion.

math.CO↗
arXiv2020

Opinion Dynamics on Discourse Sheaves

We introduce a novel class of Laplacians and diffusion dynamics on discourse sheaves as a model for network dynamics, with application to opinion dynamics on social networks. These sheaves are algebraic data structures tethered to a network (or more general space) that can represent various modes of communication, including selective opinion modulation and lying. After introducing the sheaf model, we develop a sheaf Laplacian in this context and show how to evolve both opinions and communications with diffusion dynamics over the network. Issues of controllability, reachability, bounded confidence, and harmonic extension are addressed using this framework.

math.DS↗
arXiv2019

Toward a Spectral Theory of Cellular Sheaves

This paper outlines a program in what one might call spectral sheaf theory --- an extension of spectral graph theory to cellular sheaves. By lifting the combinatorial graph Laplacian to the Hodge Laplacian on a cellular sheaf of vector spaces over a regular cell complex, one can relate spectral data to the sheaf cohomology and cell structure in a manner reminiscent of spectral graph theory. This work gives an exploratory introduction, and includes results on eigenvalue interlacing, sparsification, effective resistance, and sheaf approximation. These results and subsequent applications are prefaced by an introduction to cellular sheaves and Laplacians.

math.AT↗
arXiv2017

Gravitational radiation driven capture in unequal mass black hole encounters

The gravitational radiation driven capture (GR capture) between unequal mass black holes without spins has been investigated with numerical relativistic simulations. We adopt the parabolic approximation which assumes that the gravitational wave radiation from a weakly hyperbolic orbit is the same as that from the parabolic orbit having the same pericenter distance. Using the radiated energies from the parabolic orbit simulations, we have obtained the critical impact parameter ($b_{\rm crit}$) for the GR capture for weakly hyperbolic orbit as a function of initial energy. The most energetic encounters occur around the boundary between the direct merging and the fly-by orbits, and can emit several percent of initial total ADM energy at the peak. When the total mass is fixed, energy and angular momentum radiated in the case of unequal mass black holes are smaller than those of equal mass black holes having the same initial orbital angular momentum for the fly-by orbits. We have compared our results with two different Post-Newtonian (PN) approximations, the exact parabolic orbit (EPO) and PN corrected orbit (PNCO). We find that the agreement between the EPO and the numerical relativity breaks down for very close encounters ($\it{e.g.}$, $b_{\rm crit} \lesssim 100$ M), and it becomes worse for higher mass ratios. For instance, the critical impact parameters can differ by more than $50\%$ from those obtained in EPO if the relative velocity at infinity $v_{\infty}$ is larger than 0.1 for the mass ratio of $m_{1}/m_{2}=16$. The PNCO gives more consistent results than EPO, but it also underestimates the critical impact parameter for the GR capture at $b_{\rm crit} \lesssim40$ M.

gr-qc↗
arXiv2016

Consistency constraints for overlapping data clustering

We examine overlapping clustering schemes with functorial constraints, in the spirit of Carlsson--Memoli. This avoids issues arising from the chaining required by partition-based methods. Our principal result shows that any clustering functor is naturally constrained to refine single-linkage clusters and be refined by maximal-linkage clusters. We work in the context of metric spaces with non-expansive maps, which is appropriate for modeling data processing which does not increase information content.

cs.LG↗
arXiv2015

Charged black holes in string-inspired gravity: II. Mass inflation and dependence on parameters and potentials

We investigate the relation between the existence of mass inflation and model parameters of string-inspired gravity models. In order to cover various models, we investigate a Brans-Dicke theory that is coupled to a U(1) gauge field. By tuning a model parameter that decides the coupling between the Brans-Dicke field and the electromagnetic field, we can make both of models such that the Brans-Dicke field is biased toward strong or weak coupling directions after gravitational collapses. We observe that as long as the Brans-Dicke field is biased toward any (strong or weak) directions, there is no Cauchy horizon and no mass inflation. Therefore, we conclude that to induce a Cauchy horizon and mass inflation inside a charged black hole, either there is no bias of the Brans-Dicke field as well as no Brans-Dicke hair outside the horizon or such a biased Brans-Dicke field should be well trapped and controlled by a potential.

hep-th↗
arXiv2014

Charged black holes in string-inspired gravity: I. Causal structures and responses of the Brans-Dicke field

We investigate gravitational collapses of charged black holes in string-inspired gravity models, including dilaton gravity and braneworld model, as well as f(R) gravity and the ghost limit. If we turn on gauge coupling, the causal structures and the responses of the Brans-Dicke field depend on the coupling between the charged matter and the Brans-Dicke field. For Type IIA inspired models, a Cauchy horizon exists, while there is no Cauchy horizon for Type I or Heterotic inspired models. For Type IIA inspired models, the no-hair theorem is satisfied asymptotically, while it is biased to the weak coupling limit for Type I or Heterotic inspired models. Apart from string theory, we find that in the ghost limit, a gravitational collapse can induce inflation by itself and create one-way traversable wormholes without the need of other special initial conditions.

hep-th↗
arXiv2013

Applying the $\chi^2$ Regularization Parameter Estimator by Downsampling Through Relations with The Singular Value Expansion

The solution, $x$, of the linear system of equations $A x\approx b$ arising from the discretization of an ill-posed integral equation with a square integrable kernel $H(s,t)$ is considered. The Tikhonov regularized solution $ x(\lambda)$ is found as the minimizer of $J( x)=\{ \|A x - b\|_2^2 + \lambda^2 \|L x\|_2^2\}$. $ x(\lambda)$ depends on regularization parameter $\lambda$ that trades off the data fidelity, and on the smoothing norm determined by $L$. Here we consider the case where $L$ is diagonal and invertible, and employ the Galerkin method to provide the relationship between the singular value expansion and the singular value decomposition for square integrable kernels. The resulting approximation of the integral equation permits examination of the properties of the regularized solution $ x(\lambda)$ independent of the sample size of the data. We prove that estimation of the regularization parameter can be obtained by consistently down sampling the data and the system matrix, leading to solutions of coarse to fine grained resolution. Hence, the estimate of $\lambda$ for a large problem may be found by downsampling to a smaller problem, or to a set of smaller problems, effectively moving the costly estimate of the regularization parameter to the coarse representation of the problem. Moreover, the full singular value decomposition for the fine scale system is replaced by a number of dominant terms which is determined from the coarse resolution system, again reducing the computational cost. Numerical results illustrate the theory and demonstrate the practicality of the approach for regularization parameter estimation using generalized cross validation, unbiased predictive risk estimation and the discrepancy principle applied for both the system of equations, and the augmented system of equations.

math.NA↗
arXiv2013

Inside and outside stories of black-branes in anti de Sitter space

In this paper, we investigate the dynamics inside and outside of black-branes in anti de Sitter space by numerical simulations using double-null formalism. We prepare a charged planar matter shell which, due to a negative cosmological constant, collapses and dynamically forms a black-brane with an apparent horizon, a singularity and a Cauchy horizon. The gravitational collapse cannot form a naked overcharged black-brane and hence weak cosmic censorship is safe. Although mass inflation occurs, the effect is much milder than in the case of charged black holes; hence, strong cosmic censorship seems not to be safe. We observed the scalar field dynamics outside the horizon. There should remain a non-trivial scalar field combination - 'charge cloud' - between the horizon and the boundary. This can give some meaning in terms of the AdS/CFT correspondence.

hep-th↗
arXiv2013

Non-negatively constrained least squares and parameter choice by the residual periodogram for the inversion of electrochemical impedance spectroscopy

The inverse problem associated with electrochemical impedance spectroscopy requiring the solution of a Fredholm integral equation of the first kind is considered. If the underlying physical model is not clearly determined, the inverse problem needs to be solved using a regularized linear least squares problem that is obtained from the discretization of the integral equation. For this system, it is shown that the model error can be made negligible by a change of variables and by extending the effective range of quadrature. This change of variables serves as a right preconditioner that significantly improves the condition of the system. Still, to obtain feasible solutions the additional constraint of non-negativity is required. Simulations with artificial, but realistic, data demonstrate that the use of non-negatively constrained least squares with a smoothing norm provides higher quality solutions than those obtained without the non-negative constraint. Using higher-order smoothing norms also reduces the error in the solutions. The L-curve and residual periodogram parameter choice criteria, which are used for parameter choice with regularized linear least squares, are successfully adapted to be used for the non-negatively constrained Tikhonov least squares problem. Although these results have been verified within the context of the analysis of electrochemical impedance spectroscopy, there is no reason to suppose that they would not be relevant within the broader framework of solving Fredholm integral equations for other applications.

math.NA↗
arXiv2011

A new method for reconstructing the density distribution of matter in the disks of spiral galaxies from the rotation velocity curve in it

In this paper we propose a new method for reconstructing the surface density of matter in flat disks of spiral galaxies. The surface density is expressed through observational rotation velocity curves of visible matter in the disks of spiral galaxies. The new method is not based on quadrature of special functions. The found solution is used for processing and analysis of observational data from several spiral galaxies. The new method can be used to more accurately estimate the amount of dark matter in spiral galaxies.

astro-ph.GA↗