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The second coefficient of the Alexander polynomial as a satellite obstruction
(2024)arXivA set P of links is introduced, containing positive braid links as well as arborescent positive Hopf plumbings. Inspired by work of Ito, it is shown that for links in P, the leading and the second coefficient of the Alexander polynomial have opposite sign. It follows that certain satellite links, such as (n,1)-cables, are not in P.Working Paper -
A new concordance homomorphism from Khovanov homology
(2024)arXivThe universal Khovanov chain complex of a knot modulo an appropriate equivalence relation is shown to yield a homomorphism on the smooth concordance group, which is strictly stronger than all Rasmussen invariants over fields of different characteristics combined.Working Paper -
Cosmological constraints from combined probes with the three-point statistics of galaxies at one-loop precision
(2023)arXivWe present cosmological constraints from a joint analysis including the power spectrum and bispectrum of BOSS galaxies based on the Effective Field Theory of Large-Scale Structure predictions at one-loop order, in combination with CMB data from Planck, Supernovae from Pantheon+, and BAO from eBOSS and 6dF/MGS. Limits on $Λ$CDM parameters are in good agreement, and on average $\sim 5-10\%$ tighter, compared to former results including ...Working Paper -
Tracking SARS-CoV-2 variants of concern in wastewater: an assessment of nine computational tools using simulated genomic data
(2023)bioRxivWastewater-based surveillance (WBS) is an important epidemiological and public health tool for tracking pathogens across the scale of a building, neighbourhood, city, or region. WBS gained widespread adoption globally during the SARS-CoV-2 pandemic for estimating community infection levels by qPCR. Sequencing pathogen genes or genomes from wastewater adds information about pathogen genetic diversity which can be used to identify viral ...Working Paper -
Electric-field-resolved detection of localized surface plasmons at petahertz-scale frequencies
(2023)arXivWe present a novel electric-field-resolved approach for probing ultrafast dynamics of localized surface plasmons in metallic nanoparticles. The electric field of the broadband carrier-envelope-phase stable few-cycle light pulse employed in the experiment provides access to time-domain signatures of plasmonic dynamics that are imprinted on the pulse waveform. The simultaneous access to absolute spectral amplitudes and phases of the interacting ...Working Paper -
Inferring Atmospheric Properties of Exoplanets with Flow Matching and Neural Importance Sampling
(2023)Earth and Planetary PhysicsAtmospheric retrievals (AR) characterize exoplanets by estimating atmospheric parameters from observed light spectra, typically by framing the task as a Bayesian inference problem. However, traditional approaches such as nested sampling are computationally expensive, thus sparking an interest in solutions based on machine learning (ML). In this ongoing work, we first explore flow matching posterior estimation (FMPE) as a new ML-based ...Working Paper -
On unknotting fibered positive knots and braids
(2023)arXivThe unknotting number $u$ and the genus $g$ of braid positive knots are equal, as shown by Rudolph. We prove the stronger statement that any positive braid diagram of a genus $g$ knot contains $g$ crossings, such that changing them produces a diagram of the trivial knot. Then, we turn to unknotting the more general class of fibered positive knots, for which $u = g$ was conjectured by Stoimenow. We prove that the known ways to unknot braid ...Working Paper -
On the asymptotic Plateau problem for cycles in the Tits boundary of a Hadamard space
(2023)arXivThe dimension of cycles in the Tits boundary of a proper Hadamard space is bounded by the asymptotic rank m of the space minus one. Kleiner and Lang proved that for (m-1)-dimensional cycles in the Tits boundary, the asymptotic Plateau problem can be solved. We prove that the asymptotic Plateau problem can be solved for so called strongly immovable cycles in the Tits boundary of a proper Hadamard space. The class of strongly immovable ...Working Paper -
Modyn: A Platform for Model Training on Dynamic Datasets With Sample-Level Data Selection
(2023)arXivMachine learning training data is often dynamic in real-world use cases, i.e., data is added or removed and may experience distribution shifts over time. Models must incorporate this evolving training data to improve generalization, adapt to potential distribution shifts, and adhere to privacy regulations. However, the cost of model (re)training is proportional to how often the model trains and on how much data it trains on. While ML ...Working Paper -
Skin conductance predicts earnings in a market bubble-and-crash scenario
(2023)OSF PreprintsIn financial markets, profit is usually associated with risk-taking, as those who take risks, use the opportunities that markets present.However, during market bubbles, risk-taking might lead to losses, whereas risk aversion can lead to more profit. Emotion-based warning signals might play a role here by helping to recognize when risk aversion is preferable. To study this, we used a trading simulator, where 27 male participants traded on ...Working Paper