arXiv subjects

David Fischer

Publications and source records attributed to David Fischer.

At least 19 recordsLinked to original sources

arXiv2026

A study of solar energetic particle transport on 30 March 2022 using multi-spacecraft data assimilation

We analyze a unique solar energetic particle event observed simultaneously by the BepiColombo and STEREO-A spacecraft on March 30, 2022. The two spacecraft at heliocentric distances of 0.6 and 1.0 AU are expected to be aligned approximately along the same magnetic field line, providing a valuable opportunity to investigate particle transport processes in the inner heliosphere. Protons with energies above 1.0 MeV exhibit velocity dispersion during the rise phase, suggesting that the energetic particles are produced close to the Sun, possibly associated with a coronal mass ejection. In contrast, protons during the decay phase are characterized by long-lasting time profiles with longer time scales at 1.0 AU than at 0.6 AU, suggesting that the particles deviate from ballistic propagation. By assimilating these multi-spacecraft observation data into numerical simulations of the focused transport equation, for the first time, we estimate the mean free path parallel to the magnetic field as a time series. The inferred mean free path decreases over time and approaches around 0.5-1.0 AU at the STEREO-A location during the decay phase, suggesting an increasing influence of scattering on particle transport. This interpretation is qualitatively supported by independent STEREO-A observations that showed increasing magnetic field fluctuations, suggesting the connection between the particle transport and the local field fluctuations. However, only a fraction of these fluctuations is expected to contribute to particle scattering, which may be due to the multidimensional nature of magnetic field fluctuations.

astro-ph.SR↗

arXiv2025

Induced minors and subpolynomial treewidth

Given a family $\mathcal{H}$ of graphs, we say that a graph $G$ is $\mathcal{H}$-induced-minor-free if no induced minor of $G$ is isomorphic to a member of $\mathcal{H}$, We denote by $W_{t\times t}$ the $t$-by-$t$ hexagonal grid, and by $K_{t,t}$ the complete bipartite graph with both sides of the bipartition of size $t$. We show that the class of $\{K_{t,t},W_{t\times t}\}$-induced minor-free graphs with bounded clique number has subpolynomial treewidth. Specifically, we prove that for every integer $t$ there exist $\epsilon \in (0,1]$ and $c \in \mathbb{N}$ such that every $n$-vertex $\{K_{t,t},W_{t\times t}\}$-induced minor-free graph with no clique of size $t$ has treewidth at most $2^{c\log^{1-\epsilon}n}$.

math.CO↗

arXiv2025

Spatio-Temporal Evolution of the March 2022 ICME Revealed by Multi-Point Observations of Forbush Decreases

Interplanetary coronal mass ejections (ICMEs) cause Forbush Decreases (FDs) effects, which are local decreases in background galactic cosmic rays (GCR). Even though FDs can be observed with simple particle instruments, their amplitude and shape provide physical profiles of passing ICMEs. However, in some cases, previous statistical studies of the heliocentric distance dependence of FD changes associated with ICME propagation have found no strong correlation. We need the criteria for evaluating the relationship between ICMEs structure and FD, necessary for FDs statistical analysis. This study investigates the effect of evolutions and interactions of ICMEs on FDs profiles in the inner Solar System, using multipoint comparisons. We focus on multipoint ICME observations by Solar Orbiter, BepiColombo, and near-Earth spacecraft from March 10-16, 2022, when these spacecraft were ideally located for studying the radial and longitudinal evolutions of ICME and accompanying FDs. We compared GCR variations with the multiple in-situ data and ICME model, clarifying the correspondence between the evolution of each ICME structure in radial and azimuthal directions and the depth and gradients of the FD. The radial comparison revealed decreases in FD intensities and gradients associated with the expansion of the ICME. The longitudinal difference found in FD intensity indicates longitudinal variations of the ICMEs shielding effect. These results suggest that accurate multi-point FD comparisons require determining the relationship between the observers position and the inner structure of the passing ICMEs.

astro-ph.SR↗

arXiv2025

String Graph Obstacles of High Girth and of Bounded Degree

A string graph is the intersection graph of curves in the plane. Kratochv\'il previously showed the existence of infinitely many obstacles: graphs that are not string graphs but for which any edge contraction or vertex deletion produces a string graph. Kratochv\'il's obstacles contain arbitrarily large cliques, so they have girth three and unbounded degree. We extend this line of working by studying obstacles among graphs of restricted girth and/or degree. We construct an infinite family of obstacles of girth four; in addition, our construction is $K_{2,3}$-subgraph-free and near-planar (planar plus one edge). Furthermore, we prove that there is a subcubic obstacle of girth three, and that there are no subcubic obstacles of high girth. We characterize the subcubic string graphs as having a matching whose contraction yields a planar graph, and based on this characterization we find a linear-time algorithm for recognizing subcubic string graphs of bounded treewidth.

math.CO↗

arXiv2025

A $(4/3+\varepsilon)$-Approximation for Preemptive Scheduling with Batch Setup Times

We consider the $\mathcal{NP}$-hard problem $\mathrm{P} \mathbf{\vert} \mathrm{pmtn, setup=s_i} \mathbf{\vert} \mathrm{C_{\max}}$, the problem of scheduling $n$ jobs, which are divided into $c$ classes, on $m$ identical parallel machines while allowing preemption. For each class $i$ of the $c$ classes, we are given a setup time $s_i$ that is required to be scheduled whenever a machine switches from processing a job of one class to a job from another class. The goal is to find a schedule that minimizes the makespan. We give a $(4/3+\varepsilon)$-approximate algorithm with run time in $\mathcal{O}(n^2 \log(1/\varepsilon))$. For any $\varepsilon < 1/6$, this improves upon the previously best known approximation ratio of $3/2$ for this problem. Our main technical contributions are as follows. We first partition any instance into an "easy" and a "hard" part, such that a $4/3 T$-approximation for the former is easy to compute for some given makespan $T$. We then proceed to show our main structural result, namely that there always exists a $4/3 T$-approximation for any instance that has a solution with makespan $T$, where the hard part has some easy to compute properties. Finally, we obtain an algorithm that computes a $(4/3+\varepsilon)$-approximation in time n $\mathcal{O}(n^2 \log(1/\varepsilon))$ for general instances by computing solutions with the previously shown structural properties.

cs.DS↗

arXiv2025

Robust Scheduling on Uniform Machines -- New Results Using a Relaxed Approximation Guarantee

We consider the problem of scheduling $n$ jobs on $m$ uniform machines while minimizing the makespan ($Q||C_{\max}$) and maximizing the minimum completion time ($Q||C_{\min}$) in an online setting with migration of jobs. In this online setting, the jobs are inserted or deleted over time, and at each step, the goal is to compute a near-optimal solution while reassigning some jobs, such that the overall processing time of reassigned jobs, called migration, is bounded by some factor $\beta$ times the processing time of the job added or removed. We propose Efficient Polynomial Time Approximation Schemes (EPTASs) with an additional load error of $\mathcal{O}(\varepsilon p_{\max})$ for both problems, with constant amortized migration factor $\beta$, where $p_{\max}$ is the maximum processing time in the instance over all steps. As an intermediate step, we obtain Efficient Parameterized Approximation Schemes (EPASs) for both problems, $(1+\varepsilon)$-competitive algorithms parameterized by $p_{\max}$ and the number of different processing times $d$ in an instance, with $\beta$ bounded in a function of $p_{\max}$, $d$ and $\varepsilon$. This is the first result in the direction of a polynomial time approximation scheme in the field of online scheduling with bounded reassignment on uniform machines; before, such results were known only for the considered problems on identical machines. Crucial to our result is a division of the machines into large and small machines depending on the current approximate objective value, allowing for different approaches on either machine set, as well as a new way of rounding the instance that does not depend on the current objective value.

cs.DS↗

arXiv2025

A simple layered-wheel-like construction

In recent years, there has been significant interest in characterizing the induced subgraph obstructions to bounded treewidth and pathwidth. While this has recently been resolved for pathwidth, the case of treewidth remains open, and prior work has reduced the problem to understanding the layered-wheel-like obstructions -- graphs that contain large complete minor models with each branching set inducing a path; exclude large walls as induced minors; exclude large complete bipartite graphs as induced minors; and exclude large complete subgraphs. There are various constructions of such graphs, but they are all rather involved. In this paper, we present a simple construction of layered-wheel-like graphs with arbitrarily large treewidth. Three notable features of our construction are: (a) the vertices of degree at least four can be made to be arbitrarily far apart; (b) the girth can be made to be arbitrarily large; and (c) every outerstring induced subgraph of the graphs from our construction has treewidth bounded by an absolute constant. In contrast, among several previously known constructions of layered wheels, none achieves (a); at most one satisfies either (b) or (c); and none satisfies both (b) and (c) simultaneously. In particular, this is related to a former conjecture of Trotignon, that every graph with large enough treewidth, excluding large walls and large complete bipartite graphs as induced minors, and large complete subgraphs, must contain an outerstring induced subgraph of large treewidth. Our construction provides the first counterexample to this conjecture that can also be made to have arbitrarily large girth.

math.CO↗

arXiv2024

A coronal mass ejection encountered by four spacecraft within 1 au from the Sun: Ensemble modelling of propagation and magnetic structure

Understanding and predicting the structure and evolution of coronal mass ejections (CMEs) in the heliosphere remains one of the most sought-after goals in heliophysics and space weather research. A powerful tool for improving current knowledge and capabilities consists of multi-spacecraft observations of the same event, which take place when two or more spacecraft fortuitously find themselves in the path of a single CME. Multi-probe events can not only supply useful data to evaluate the large-scale of CMEs from 1D in-situ trajectories, but also provide additional constraints and validation opportunities for CME propagation models. In this work, we analyse and simulate the coronal and heliospheric evolution of a slow, streamer-blowout CME that erupted on 23 September 2021 and was encountered in situ by four spacecraft approximately equally distributed in heliocentric distance between 0.4 and 1 au. We employ the Open Solar Physics Rapid Ensemble Information (OSPREI) modelling suite in ensemble mode to predict the CME arrival and structure in a hindcast fashion and to compute the "best-fit" solutions at the different spacecraft individually and together. We find that the spread in the predicted quantities increases with heliocentric distance, suggesting that there may be a maximum (angular and radial) separation between an inner and an outer probe beyond which estimates of the in-situ magnetic field orientation (parameterised by flux rope model geometry) increasingly diverge. We discuss the importance of these exceptional observations and the results of our investigation in the context of advancing our understanding of CME structure and evolution as well as improving space weather forecasts.

astro-ph.SR↗

arXiv2024

Extent of the Magnetotail of Venus From the Solar Orbiter, Parker Solar Probe and BepiColombo Flybys

We analyze data from multiple flybys by the Solar Orbiter, BepiColombo, and Parker Solar Probe (PSP) missions to study the interaction between Venus' plasma environment and the solar wind forming the induced magnetosphere. Through examination of magnetic field and plasma density signatures we characterize the spatial extent and dynamics of Venus' magnetotail, focusing mainly on boundary crossings. Notably, we observe significant differences in boundary crossing location and appearance between flybys, highlighting the dynamic nature of Venus' magnetotail. In particular, during Solar Orbiter's third flyby, extreme solar wind conditions led to significant variations in the magnetosheath plasma density and magnetic field properties, but the increased dynamic pressure did not compress the magnetotail. Instead, it is possible that the increased EUV flux at this time rather caused it to expand in size. Key findings also include the identification of several far downstream bow shock (BS), or bow wave, crossings to at least 60 Rv (1 Rv = 6,052 km is the radius of Venus), and the induced magnetospheric boundary to at least 20 Rv. These crossings provide insight into the extent of the induced magnetosphere. Pre-existing models from Venus Express were only constrained to within ~5 Rv of the planet, and we provide modifications to better fit the far-downstream crossings. The new model BS is now significantly closer to the central tail than previously suggested, by about 10 Rv at 60 Rv downstream.

physics.space-ph↗

arXiv2024

Improved modelling of SEP event onset within the WSA-Enlil-SEPMOD framework

Multi-spacecraft observations of solar energetic particle (SEP) events not only enable a deeper understanding and development of particle acceleration and transport theories, but also provide important constraints for model validation efforts. However, because of computational limitations, a given physics-based SEP model is usually best-suited to capture a particular phase of an SEP event, rather than its whole development from onset through decay. For example, magnetohydrodynamic (MHD) models of the heliosphere often incorporate solar transients only at the outer boundary of their so-called coronal domain -- usually set at a heliocentric distance of 20-30 $R_{\odot}$. This means that particle acceleration at CME-driven shocks is also computed from this boundary onwards, leading to simulated SEP event onsets that can be many hours later than observed, since shock waves can form much lower in the solar corona. In this work, we aim to improve the modelled onset of SEP events by inserting a "fixed source" of particle injection at the outer boundary of the coronal domain of the coupled WSA-Enlil 3D MHD model of the heliosphere. The SEP model that we employ for this effort is SEPMOD, a physics-based test-particle code based on a field line tracer and adiabatic invariant conservation. We apply our initial tests and results of SEPMOD's fixed-source option to the 2021 October 9 SEP event, which was detected at five well-separated locations in the inner heliosphere -- Parker Solar Probe, STEREO-A, Solar Orbiter, BepiColombo, and near-Earth spacecraft.

astro-ph.SR↗

arXiv2024

On the Mesoscale Structure of CMEs at Mercury's Orbit: BepiColombo and Parker Solar Probe Observations

On 2022 February 15, an impressive filament eruption was observed off the solar eastern limb from three remote-sensing viewpoints, namely Earth, STEREO-A, and Solar Orbiter. In addition to representing the most-distant observed filament at extreme ultraviolet wavelengths -- captured by Solar Orbiter's field of view extending to above 6 $R_{\odot}$ -- this event was also associated with the release of a fast ($\sim$2200 km$\cdot$s$^{-1}$) coronal mass ejection (CME) that was directed towards BepiColombo and Parker Solar Probe. These two probes were separated by 2$^{\circ}$ in latitude, 4$^{\circ}$ in longitude, and 0.03 au in radial distance around the time of the CME-driven shock arrival in situ. The relative proximity of the two probes to each other and to the Sun ($\sim$0.35 au) allows us to study the mesoscale structure of CMEs at Mercury's orbit for the first time. We analyse similarities and differences in the main CME-related structures measured at the two locations, namely the interplanetary shock, the sheath region, and the magnetic ejecta. We find that, despite the separation between the two spacecraft being well within the typical uncertainties associated with determination of CME geometric parameters from remote-sensing observations, the two sets of in-situ measurements display some profound differences that make understanding of the overall 3D CME structure particularly challenging. Finally, we discuss our findings within the context of space weather at Mercury's distances and in terms of the need to investigate solar transients via spacecraft constellations with small separations, which has been gaining significant attention during recent years.

astro-ph.SR↗

arXiv2023

Relativistic electron precipitation events driven by solar wind impact on the Earth's magnetosphere

Certain forms of solar wind transients contain significant enhancements of dynamic pressure and may effectively drive magnetosphere dynamics, including substorms and storms. An integral element of such driving is the generation of a wide range of electromagnetic waves within the inner magnetosphere, either by compressionally heated plasma or by substorm plasma sheet injections. Consequently, solar wind transient impacts are traditionally associated with energetic electron scattering and losses into the atmosphere by electromagnetic waves. In this study, we show the first direct measurements of two such transient-driven precipitation events as measured by the low-altitude Electron Losses and Fields Investigation (ELFIN) CubeSats. The first event demonstrates storm-time generated electromagnetic ion cyclotron waves efficiently precipitating relativistic electrons from >300 keV to 2 MeV at the duskside. The second event demonstrates whistler-mode waves leading to scattering of electrons from 50 keV to 700 keV on the dawnside. These observations confirm the importance of solar wind transients in driving energetic electron losses and subsequent dynamics in the ionosphere.

physics.space-ph↗

arXiv2023

Exponential Quantum Speedup for Simulation-Based Optimization Applications

The simulation of many industrially relevant physical processes can be executed up to exponentially faster using quantum algorithms. However, this speedup can only be leveraged if the data input and output of the simulation can be implemented efficiently. While we show that recent advancements for optimal state preparation can effectively solve the problem of data input at a moderate cost of ancillary qubits in many cases, the output problem can provably not be solved efficiently in general. By acknowledging that many simulation problems arise only as a subproblem of a larger optimization problem in many practical applications however, we identify and define a class of practically relevant problems that does not suffer from the output problem: Quantum Simulation-based Optimization (QuSO). QuSO represents optimization problems whose objective function and/or constraints depend on summary statistic information on the result of a simulation, i.e., information that can be efficiently extracted from a quantum state vector. In this article, we focus on the LinQuSO subclass of QuSO, which is characterized by the linearity of the simulation problem, i.e., the simulation problem can be formulated as a system of linear equations. By cleverly combining the quantum singular value transformation (QSVT) with the quantum approximate optimization algorithm (QAOA), we prove that a large subgroup of LinQuSO problems can be solved with up to exponential quantum speedups with regards to their simulation component. Finally, we present two practically relevant use cases that fall within this subgroup of QuSO problems.

quant-ph↗

arXiv2022

The Software Stack That Won the Formula Student Driverless Competition

This report describes our approach to design and evaluate a software stack for a race car capable of achieving competitive driving performance in the different disciplines of the Formula Student Driverless. By using a 360{\deg} LiDAR and optionally three cameras, we reliably recognize the plastic cones that mark the track boundaries at distances of around 35 m, enabling us to drive at the physical limits of the car. Using a GraphSLAM algorithm, we are able to map these cones with a root-mean-square error of less than 15 cm while driving at speeds of over 70 kph on a narrow track. The high-precision map is used in the trajectory planning to detect the lane boundaries using Delaunay triangulation and a parametric cubic spline. We calculate an optimized trajectory using a minimum curvature approach together with a GGS-diagram that takes the aerodynamics at different velocities into account. To track the target path with accelerations of up to 1.6 g, the control system is split into a PI controller for longitudinal control and model predictive controller for lateral control. Additionally, a low-level optimal control allocation is used. The software is realized in ROS C++ and tested in a custom simulation, as well as on the actual race track.

cs.RO↗

arXiv2022

Approximation algorithms for coupled task scheduling minimizing the sum of completion times

In this paper we consider the coupled task scheduling problem with exact delay times on a single machine with the objective of minimizing the total completion time of the jobs. We provide constant-factor approximation algorithms for several variants of this problem that are known to be NP-hard, while also proving NP-hardness for two variants whose complexity was unknown before. Using these results, together with constant-factor approximations for the makespan objective from the literature, we also introduce the first results on bi-objective approximation in the coupled task setting.

math.OC↗

arXiv2022

Exponentially faster fixed-parameter algorithms for high-multiplicity scheduling

We consider so-called $N$-fold integer programs (IPs) of the form $\max\{c^T x : Ax = b, \ell \leq x \leq u, x \in \mathbb Z^{nt}\}, where $A \in \mathbb Z^{(r+sn)\times nt} consists of $n$ arbitrary matrices $A^{(i)} \in \mathbb Z^{r\times t}$ on a horizontal, and $n$ arbitrary matrices $B^{(j)} \in \mathbb Z^{s\times t} on a diagonal line. Several recent works design fixed-parameter algorithms for $N$-fold IPs by taking as parameters the numbers of rows and columns of the $A$- and $B$-matrices, together with the largest absolute value $\Delta$ over their entries. These advances provide fast algorithms for several well-studied combinatorial optimization problems on strings, on graphs, and in machine scheduling. In this work, we extend this research by proposing algorithms that additionally harness a partition structure of submatrices $A^{(i)}$ and $B^{(j)}$, where row indices of non-zero entries do not overlap between any two sets in the partition. Our main result is an algorithm for solving any $N$-fold IP in time $nt log(nt)L^2(S_A)^{O(r+s)}(p_Ap_B\Delta)^{O(rp_Ap_B+sp_Ap_B)}$, where $p_A$ and $p_B$ are the size of the largest set in such a partition of $A^{(i)}$ and $B^{(j)}$, respectively, $S_A$ is the number of parts in the partition of $A = (A^{(1)},..., A^{(n)}), and $L = (log(||u - \ell||_\infty)\cdot (log(max_{x:\ell \leq x \leq u} |c^Tx|))$ is a measure of the input. We show that these new structural parameters are naturally small in high-multiplicity scheduling problems, such as makespan minimization on related and unrelated machines, with and without release times, the Santa Claus objective, and the weighted sum of completion times. In essence, we obtain algorithms that are exponentially faster than previous works by Knop et al. (ESA 2017) and Eisenbrand et al./Kouteck{\'y} et al. (ICALP 2018) in terms of the number of job types.

cs.DS↗

arXiv2022

Structural Results for High-Multiplicity Scheduling on Uniform Machines

Parameterizing by the largest processing time $p_{max}$ and the number of different job processing times $d$, we propose a proximity technique for High-Multiplicity Scheduling on Uniform Machines for the objectives Makespan Minimization ($C_{max}$) and Santa Claus ($C_{min}$) to obtain new structural results for these problems. The novelty in our approach is that we deal with a fractional solution for only a sub-instance, where the sub-instance itself is not known a priori. While the construction and computation of the fractional solution -- in contrast to usual proximity techniques -- is not done in polynomial time, this also allows us to formulate a comparably strong and general proximity statement. Eventually, this allows us to reduce the number of jobs that need to be distributed to a polynomial in $p_{max}$ for each machine and job type, by preassigning jobs according to the fractional solution, essentially returning a bounded number (at most $O(p_{max}^{O(d^2)})$) of kernels, one for each (guessed) sub-instance. We can use our structural results to obtain an algorithm with running time is $p_{max}^{O(d^2)}poly|I|$, matching the best-known so far by Knop et al. (Oper. Res. Lett. '21). Moreover, we propose an $p_{max}^{O(d^2)} poly |I|$ time algorithm for Envy Minimization $C_{envy}$ in the High-Multiplicity Setting on Uniform Machines, showing that this problem is \textsc{fpt} in $p_{max}$. Eventually, we also propose a general mechanism to bound the largest coefficient in the Configuration ILP for so called \emph{Load Balancing Problems} by $(dp_{max})^{O(d)}$, which we hope to be of interest for the development of algorithms.

cs.DS↗

arXiv2021

Talaria: A Framework for Simulation of Permissioned Blockchains for Logistics and Beyond

In this paper, we present Talaria, a novel permissioned blockchain simulator that supports numerous protocols and use cases, most notably in supply chain management. Talaria extends the capability of BlockSim, an existing blockchain simulator, to include permissioned blockchains and serves as a foundation for further private blockchain assessment. Talaria is designed with both practical Byzantine Fault Tolerance (pBFT) and simplified version of Proof-of-Authority consensus protocols, but can be revised to include other permissioned protocols within its modular framework. Moreover, Talaria is able to simulate different types of malicious authorities and a variable daily transaction load at each node. In using Talaria, business practitioners and policy planners have an opportunity to measure, evaluate, and adapt a range of blockchain solutions for commercial operations.

cs.CR↗