arXiv subjects

Johan Thunberg

Publications and source records attributed to Johan Thunberg.

At least 19 recordsLinked to original sources

arXiv2026

Scalable Intention Sharing for ETSI VAMs

Efficient maneuver coordination in dense V2X environments requires accurate short-term prediction while maintaining low communication and computational overhead. Current European Telecommunications Standards Institute (ETSI)-compliant approaches rely on intention detection and trajectory vector transmission, which scale poorly with neighborhood size and prediction horizon. This paper revisits maneuver coordination from an intention sharing perspective and investigates geometric encodings that enable scalable communication. First, we analyze three ETSI-compliant encodings, trajectory vectors, N-polygons, and uncertainty ellipses, through complexity analysis and simulation-based CPU measurements. Results show that uncertainty ellipses reduce computational complexity by an order of magnitude compared with trajectory vectors while maintaining a constant message size. Building on this, an Extended Kalman Filter is used to generate short-horizon predictions, which are encoded as uncertainty ellipses to represent the intended maneuver. The prediction pipeline is evaluated using real-world GNSS trajectories collected from cyclist maneuvers on a controlled test track, demonstrating that the approach achieves reliable multisecond prediction horizons while maintaining scalability for dense V2X environments.

cs.NI↗

arXiv2026

A necessary and sufficient condition for discrete-time consensus on star boundaries

It is intuitive and well known, that if agents in a multi-agent system iteratively update their states in the Euclidean space as convex combinations of neighbors' states, all states eventually converge to the same value (consensus), provided the interaction graph is sufficiently connected. However, this seems to be also true in practice if the convex combinations of states are mapped or radially projected onto any unit $l_p$-sphere or even boundaries of star-convex sets, herein referred to as star boundaries. In this paper, we present insight into this matter by providing a necessary and sufficient condition for asymptotic consensus of the normalized states (directions) for strongly connected directed graphs, which is equivalent to asymptotic consensus of states when the star boundaries are the same for all agents. Furthermore, we show that when asymptotic consensus occurs, the states converge linearly and the point of convergence is continuous in the initial states. Assuming a directed strongly connected graph provides a more general setting than that considered, for example, in gradient-based consensus protocols, where symmetric graphs are assumed. Illustrative examples and a vast number of numerical simulations showcase the theoretical results.

math.OC↗

arXiv2026

Projection-based discrete-time consensus on the unit sphere

We address discrete-time consensus on the Euclidean unit sphere. For this purpose we consider a distributed algorithm comprising the iterative projection of a conical combination of neighboring states. Neighborhoods are represented by a strongly connected directed graph, and the conical combinations are represented by a (non-negative) weight matrix with a zero structure corresponding to the graph. A first result mirrors earlier results for gradient flows. Under the assumptions that each diagonal element of the weight matrix is more than $\sqrt{2}$ larger than the sum of the other elements in the corresponding row, the sphere dimension is greater or equal to 2, and the graph, as well as the weight matrix, is symmetric, we show that the algorithm comprises gradient ascent, stable fixed points are consensus points, and the set of initial points for which the algorithm converges to a non-consensus fixed point has measure zero. The second result is that for the unit circle and a strongly connected graph or for any unit sphere with dimension greater than or equal to $1$ and the complete graph, only for a measure zero set of weight matrices there are fixed points for the algorithm which do not have consensus or antipodal configurations.

math.OC↗

arXiv2025

Two-dimensional Decompositions of High-dimensional Configurations for Efficient Multi-vehicle Coordination at Intelligent Intersections

For multi-vehicle complex traffic scenarios in shared spaces such as intelligent intersections, safe coordination and trajectory planning is challenging due to computational complexity. To meet this challenge, we introduce a computationally efficient method for generating collision-free trajectories along predefined vehicle paths. We reformulate a constrained minimum-time trajectory planning problem as a problem in a high-dimensional configuration space, where conflict zones are modeled by high-dimensional polyhedra constructed from two-dimensional rectangles. Still, in such a formulation, as the number of vehicles involved increases, the computational complexity increases significantly. To address this, we propose two algorithms for near-optimal local optimization that significantly reduce the computational complexity by decomposing the high-dimensional problem into a sequence of 2D graph search problems. The resulting trajectories are then incorporated into a Nonlinear Model Predictive Control (NMPC) framework to ensure safe and smooth vehicle motion. We furthermore show in numerical evaluation that this approach significantly outperforms existing MILP-based time-scheduling; both in terms of objective-value and computational time.

eess.SY↗

arXiv2025

How to Brake? Ethical Emergency Braking with Deep Reinforcement Learning

Connected and automated vehicles (CAVs) have the potential to enhance driving safety, for example by enabling safe vehicle following and more efficient traffic scheduling. For such future deployments, safety requirements should be addressed, where the primary such are avoidance of vehicle collisions and substantial mitigating of harm when collisions are unavoidable. However, conservative worst-case-based control strategies come at the price of reduced flexibility and may compromise overall performance. In light of this, we investigate how Deep Reinforcement Learning (DRL) can be leveraged to improve safety in multi-vehicle-following scenarios involving emergency braking. Specifically, we investigate how DRL with vehicle-to-vehicle communication can be used to ethically select an emergency breaking profile in scenarios where overall, or collective, three-vehicle harm reduction or collision avoidance shall be obtained instead of single-vehicle such. As an algorithm, we provide a hybrid approach that combines DRL with a previously published method based on analytical expressions for selecting optimal constant deceleration. By combining DRL with the previous method, the proposed hybrid approach increases the reliability compared to standalone DRL, while achieving superior performance in terms of overall harm reduction and collision avoidance.

cs.RO↗

arXiv2025

Power Control of Multi-Layer Repeater Networks (POLARNet)

In this letter we introduce POLARNet -- power control of multi-layer repeater networks -- for local optimization of SNR given different repeater power constraints. We assume relays or repeaters in groups or layers spatially separated. Under ideal circumstances SISO narrow-band communication and TDD, the system may be viewed as a dual to a deep neural network, where activations, corresponding to repeater amplifications, are optimized and weight matrices, corresponding to channel matrices, are static. Repeater amplifications are locally optimized layer-by-layer in a forward-backward manner over compact sets. The method is applicable for a wide range of constraints on within-layer power/energy utilization, is furthermore gradient-free, step-size-free, and has proven monotonicity in the objective. Numerical simulations show significant improvement compared to upper bounds on the expected SNR. In addition, power distribution over multiple repeaters is shown to be superior to optimal selection of single repeaters in the layers.

eess.SY↗

arXiv2024

Isometric Multi-Shape Matching

Finding correspondences between shapes is a fundamental problem in computer vision and graphics, which is relevant for many applications, including 3D reconstruction, object tracking, and style transfer. The vast majority of correspondence methods aim to find a solution between pairs of shapes, even if multiple instances of the same class are available. While isometries are often studied in shape correspondence problems, they have not been considered explicitly in the multi-matching setting. This paper closes this gap by proposing a novel optimisation formulation for isometric multi-shape matching. We present a suitable optimisation algorithm for solving our formulation and provide a convergence and complexity analysis. Our algorithm obtains multi-matchings that are by construction provably cycle-consistent. We demonstrate the superior performance of our method on various datasets and set the new state-of-the-art in isometric multi-shape matching.

cs.CV↗

arXiv2024

Channel Orthogonalization with Reconfigurable Surfaces: General Models, Theoretical Limits, and Effective Configuration

We envision a future in which multi-antenna technology effectively exploits the spatial domain as a set of non-interfering orthogonal resources, allowing for flexible resource allocation and efficient modulation/demodulation. We may refer to this paradigm as orthogonal space-division multiplexing (OSDM). On the other hand, reconfigurable intelligent surface (RIS) has emerged as a promising technology which allows shaping the propagation environment for improved performance. This paper studies the ability of three extended types of reconfigurable surface (RS), including the recently proposed beyond diagonal RIS (BD-RIS), to achieve perfectly orthogonal channels in a general multi-user multiple-input multiple-output (MU-MIMO) scenario. We consider practical implementations for the three types of RS consisting of passive components, and obtain the corresponding restrictions on their reconfigurability. We then use these restrictions to derive closed-form conditions and explicit expressions for achieving arbitrary (orthogonal) channels. We also study the problem of exploiting the degrees of freedom (DoFs) from the channel orthogonality constraint to maximize the channel gain while maintaining the passive RS constraints, and we propose some initial methods with satisfying performance. Finally, we provide some channel estimation and RS configuration techniques within this framework, where the computations are assumed to be performed at the BS, and we derive some limits on the amount of overhead required to achieve channel orthogonalization with RSs. The numerical results confirm the theoretical findings, showing that channel orthogonality with passive RSs can be effectively achieved in practical environments as long as the direct channel is not significant with respect to the RS cascaded channel. We thus take some important steps towards realizing OSDM.

cs.IT↗

arXiv2023

Hybrid Precoder Design for Angle-of-Departure Estimation with Limited-Resolution Phase Shifters

Hybrid analog-digital beamforming stands out as a key enabler for future communication systems with a massive number of antennas. In this paper, we investigate the hybrid precoder design problem for angle-of-departure (AoD) estimation, where we take into account the practical constraint on the limited resolution of phase shifters. Our goal is to design a radio-frequency (RF) precoder and a base-band (BB) precoder to estimate AoD of the user with a high accuracy. To this end, we propose a two-step strategy where we first obtain the fully digital precoder that minimizes the angle error bound, and then the resulting digital precoder is decomposed into an RF precoder and a BB precoder, based on the alternating optimization and the alternating direction method of multipliers. Besides, we derive the quantization error upper bound and analyse the convergence behavior of the proposed algorithm. Numerical results demonstrate the superior performance of the proposed method over state-of-the-art baselines.

cs.IT↗

arXiv2023

Non-Negative Spherical Relaxations for Universe-Free Multi-Matching and Clustering

We propose a novel non-negative spherical relaxation for optimization problems over binary matrices with injectivity constraints, which in particular has applications in multi-matching and clustering. We relax respective binary matrix constraints to the (high-dimensional) non-negative sphere. To optimize our relaxed problem, we use a conditional power iteration method to iteratively improve the objective function, while at same time sweeping over a continuous scalar parameter that is (indirectly) related to the universe size (or number of clusters). Opposed to existing procedures that require to fix the integer universe size before optimization, our method automatically adjusts the analogous continuous parameter. Furthermore, while our approach shares similarities with spectral multi-matching and spectral clustering, our formulation has the strong advantage that we do not rely on additional post-processing procedures to obtain binary results. Our method shows compelling results in various multi-matching and clustering settings, even when compared to methods that use the ground truth universe size (or number of clusters).

stat.ML↗

arXiv2022

High-dimensional Kuramoto models on Stiefel manifolds synchronize complex networks almost globally

The Kuramoto model of coupled phase oscillators is often used to describe synchronization phenomena in nature. Some applications, e.g., quantum synchronization and rigid-body attitude synchronization, involve high-dimensional Kuramoto models where each oscillator lives on the n-sphere or SO(n). These manifolds are special cases of the compact, real Stiefel manifold St(p,n). Using tools from optimization and control theory, we prove that the generalized Kuramoto model on St(p,n) converges to a synchronized state for any connected graph and from almost all initial conditions provided (p,n) satisfies p<=2n/3-1 and all oscillator frequencies are equal. This result could not have been predicted based on knowledge of the Kuramoto model in complex networks over the circle. In that case, almost global synchronization is graph dependent; it applies if the network is acyclic or sufficiently dense. This paper hence identifies a property that distinguishes many high-dimensional generalizations of the Kuramoto models from the original model.

math.OC↗

arXiv2021

Sparse Quadratic Optimisation over the Stiefel Manifold with Application to Permutation Synchronisation

We address the non-convex optimisation problem of finding a sparse matrix on the Stiefel manifold (matrices with mutually orthogonal columns of unit length) that maximises (or minimises) a quadratic objective function. Optimisation problems on the Stiefel manifold occur for example in spectral relaxations of various combinatorial problems, such as graph matching, clustering, or permutation synchronisation. Although sparsity is a desirable property in such settings, it is mostly neglected in spectral formulations since existing solvers, e.g. based on eigenvalue decomposition, are unable to account for sparsity while at the same time maintaining global optimality guarantees. We fill this gap and propose a simple yet effective sparsity-promoting modification of the Orthogonal Iteration algorithm for finding the dominant eigenspace of a matrix. By doing so, we can guarantee that our method finds a Stiefel matrix that is globally optimal with respect to the quadratic objective function, while in addition being sparse. As a motivating application we consider the task of permutation synchronisation, which can be understood as a constrained clustering problem that has particular relevance for matching multiple images or 3D shapes in computer vision, computer graphics, and beyond. We demonstrate that the proposed approach outperforms previous methods in this domain.

math.OC↗

arXiv2019

Synchronisation of Partial Multi-Matchings via Non-negative Factorisations

In this work we study permutation synchronisation for the challenging case of partial permutations, which plays an important role for the problem of matching multiple objects (e.g. images or shapes). The term synchronisation refers to the property that the set of pairwise matchings is cycle-consistent, i.e. in the full matching case all compositions of pairwise matchings over cycles must be equal to the identity. Motivated by clustering and matrix factorisation perspectives of cycle-consistency, we derive an algorithm to tackle the permutation synchronisation problem based on non-negative factorisations. In order to deal with the inherent non-convexity of the permutation synchronisation problem, we use an initialisation procedure based on a novel rotation scheme applied to the solution of the spectral relaxation. Moreover, this rotation scheme facilitates a convenient Euclidean projection to obtain a binary solution after solving our relaxed problem. In contrast to state-of-the-art methods, our approach is guaranteed to produce cycle-consistent results. We experimentally demonstrate the efficacy of our method and show that it achieves better results compared to existing methods.

cs.CV↗

arXiv2019

Higher-order Projected Power Iterations for Scalable Multi-Matching

The matching of multiple objects (e.g. shapes or images) is a fundamental problem in vision and graphics. In order to robustly handle ambiguities, noise and repetitive patterns in challenging real-world settings, it is essential to take geometric consistency between points into account. Computationally, the multi-matching problem is difficult. It can be phrased as simultaneously solving multiple (NP-hard) quadratic assignment problems (QAPs) that are coupled via cycle-consistency constraints. The main limitations of existing multi-matching methods are that they either ignore geometric consistency and thus have limited robustness, or they are restricted to small-scale problems due to their (relatively) high computational cost. We address these shortcomings by introducing a Higher-order Projected Power Iteration method, which is (i) efficient and scales to tens of thousands of points, (ii) straightforward to implement, (iii) able to incorporate geometric consistency, (iv) guarantees cycle-consistent multi-matchings, and (iv) comes with theoretical convergence guarantees. Experimentally we show that our approach is superior to existing methods.

cs.CV↗

arXiv2018

A state-space approach to sparse dynamic network reconstruction

Dynamic network reconstruction has been shown to be challenging due to the requirements on sparse network structures and network identifiability. The direct parametric method (e.g., using ARX models) requires a large amount of parameters in model selection. Amongst the parametric models, only a restricted class can easily be used to address network sparsity without rendering the optimization problem intractable. To overcome these problems, this paper presents a state-space-based method, which significantly reduces the number of unknown parameters in model selection. Furthermore, we avoid various difficulties arising in gradient computation by using the Expectation Minimization (EM) algorithm instead. To enhance network sparsity, the prior distribution is constructed by using the Sparse Bayesian Learning (SBL) approach in the M-step. To solve the SBL problem, another EM algorithm is embedded, where we impose conditions on network identifiability in each iteration. In a sum, this paper provides a solution to reconstruct dynamic networks that avoids the difficulties inherent to gradient computation and simplifies the model selection.

eess.SY↗

arXiv2018

Towards Almost Global Synchronization on the Stiefel Manifold

A graph $\mathcal{G}$ is referred to as $\mathsf{S}^1$-synchronizing if, roughly speaking, the Kuramoto-like model whose interaction topology is given by $\mathcal{G}$ synchronizes almost globally. The Kuramoto model evolves on the unit circle, \ie the $1$-sphere $\mathsf{S}^1$. This paper concerns generalizations of the Kuramoto-like model and the concept of synchronizing graphs on the Stiefel manifold $\mathsf{St}(p,n)$. Previous work on state-space oscillators have largely been influenced by results and techniques that pertain to the $\mathsf{S}^1$-case. It has recently been shown that all connected graphs are $\mathsf{S}^n$-synchronizing for all $n\geq2$. The previous point of departure may thus have been overly conservative. The $n$-sphere is a special case of the Stiefel manifold, namely $\mathsf{St}(1,n+1)$. As such, it is natural to ask for the extent to which the results on $\mathsf{S}^{n}$ can be extended to the Stiefel manifold. This paper shows that all connected graphs are $\mathsf{St}(p,n)$-synchronizing provided the pair $(p,n)$ satisfies $p\leq \tfrac{2n}{3}-1$.

math.OC↗

arXiv2018

A Lifting method for analyzing distributed synchronization on the unit sphere

This paper introduces a new lifting method for analyzing convergence of continuous-time distributed synchronization/consensus systems on the unit sphere. Points on the d-dimensional unit sphere are lifted to the (d+1)-dimensional Euclidean space. The consensus protocol on the unit sphere is the classical one, where agents move toward weighted averages of their neighbors in their respective tangent planes. Only local and relative state information is used. The directed interaction graph topologies are allowed to switch as a function of time. The dynamics of the lifted variables are governed by a nonlinear consensus protocol for which the weights contain ratios of the norms of state variables. We generalize previous convergence results for hemispheres. For a large class of consensus protocols defined for switching uniformly quasi-strongly connected time-varying graphs, we show that the consensus manifold is uniformly asymptotically stable relative to closed balls contained in a hemisphere. Compared to earlier projection based approaches used in this context such as the gnomonic projection, which is defined for hemispheres only, the lifting method applies globally. With that, the hope is that this method can be useful for future investigations on global convergence.

math.OC↗

arXiv2017

Experimental design trade-offs for gene regulatory network inference: an in silico study of the yeast Saccharomyces cerevisiae cell cycle

Time-series of high throughput gene sequencing data intended for gene regulatory network (GRN) inference are often short due to the high costs of sampling cell systems. Moreover, experimentalists lack a set of quantitative guidelines that prescribe the minimal number of samples required to infer a reliable GRN model. We study the temporal resolution of data vs quality of GRN inference in order to ultimately overcome this deficit. The evolution of a Markovian jump process model for the Ras/cAMP/PKA pathway of proteins and metabolites in the G1 phase of the Saccharomyces cerevisiae cell cycle is sampled at a number of different rates. For each time-series we infer a linear regression model of the GRN using the LASSO method. The inferred network topology is evaluated in terms of the area under the precision-recall curve AUPR. By plotting the AUPR against the number of samples, we show that the trade-off has a, roughly speaking, sigmoid shape. An optimal number of samples corresponds to values on the ridge of the sigmoid.

q-bio.QM↗