arXiv subjects

Alexander Kastner

Publications and source records attributed to Alexander Kastner.

12 recordsLinked to original sources

arXiv2026

A dataset of rated conceptual arguments

Large language models have improved rapidly on tasks with verifiable answers, such as mathematics and programming. Much less is known about their ability to reason about what we call conceptual questions: questions for which no ground truth is realistically accessible and no widely accepted resolution methodology exists, but on which progress can still be made by debating arguments. Most philosophical questions are of this kind, as are central components of questions in AI safety, decision theory, and social choice. Our approach is based on the view that while bottom-line conclusions on such questions are hard to evaluate, individual contextualized arguments can be evaluated far more reliably. We therefore introduce a dataset of 951 argumentative critiques of 442 position texts, spanning topics from AI safety and decision theory to ethics and politics, with 1,458 ratings by six expert raters along dimensions including centrality, strength, correctness, and clarity. We propose two scoring functions and benchmark a range of models. Performance tracks general capability rankings.

cs.AI↗

arXiv2025

Benchmarking Gaussian and non-Gaussian input states with a hybrid sampling platform

The original boson sampling paradigm-consisting of multiple single-photon input states, a large interferometer, and multi-channel click detection-was originally proposed as a photonic route to quantum computational advantage. Its non-Gaussian resources, essential for outperforming any classical system, are provided by single-photon inputs and click detection. Yet the drive toward larger experiments has led to the replacement of experimentally demanding single-photon sources with Gaussian states, thereby diminishing the available non-Gaussianity-a critical quantum resource. As the community broadens its focus from the initial sampling task to possible real-world applications, it becomes crucial to quantify the performance cost associated with reducing non-Gaussian resources and to benchmark sampling platforms that employ different input states. To address this need, we introduce the Paderborn Quantum Sampler (PaQS), a hybrid platform capable of performing sampling experiments with eight Gaussian or non-Gaussian input states in a 12-mode interferometer within a single experimental run. This architecture enables direct, side-by-side benchmarking of distinct sampling regimes under otherwise identical conditions. By employing a semi-device-independent framework, offering certification that does not rely on prior knowledge of the interferometer or the input states, we verify that the observed data cannot be reproduced by any classical model-a prerequisite for demonstrating quantum advantage. Applying this framework, we observe clear performance gains arising from non-Gaussian input states.

quant-ph↗

arXiv2024

Borel Families of Games

We give an elementary proof that in a Borel family of games, the set of games for which player II has a winning strategy is Baire measurable, universally measurable, and completely Ramsey in the case where $X = [\mathbb{N}]^{\aleph_0}$.

math.LO↗

arXiv2023

Baire Measurable Matchings in Non-Amenable Graphs

We prove that every Schreier graph of a free Borel action of a finitely generated non-amenable group admits a Baire measurable perfect matching, and that the Schreier graph of a free computable action of a finitely generated non-amenable group admits a computable perfect matching. These results were previously only known in the bipartite setting. To prove them, we establish variants of Tutte's theorem on perfect matchings in non-bipartite graphs. We also prove that every Borel non-amenable bounded-degree graph with only even degrees admits a Baire measurable balanced orientation.

math.LO↗

arXiv2021

Observation of photoelectron circular dichroism using a nanosecond laser

Photoelectron circular dichroism (PECD) is a fascinating phenomenon both from a fundamental science aspect but also due to its emerging role as a highly sensitive analytic tool for chiral recognition in the gas phase. PECD has been studied with single-photon as well as multi-photon ionization. The latter has been investigated in the short pulse limit with femtosecond laser pulses, where ionization can be thought of as an instantaneous process. In this contribution, we demonstrate that multiphoton PECD still can be observed when using an ultra-violet nanosecond pulse to ionize chiral showcase fenchone molecules. Compared to femtosecond ionization, the magnitude of PECD is similar, but the lifetime of intermediate molecular states imprints itself in the photoelectron spectra. Being able to use an industrial nanosecond laser to investigate PECD furthermore reduces the technical requirements to apply PECD in analytical chemistry.

physics.chem-ph↗

arXiv2020

High-resolution resonance-enhanced multiphoton photoelectron circular dichroism

Photoelectron circular dichroism (PECD) is a highly sensitive enantiospecific spectroscopy for studying chiral molecules in the gas phase using either single-photon ionization or multiphoton ionization. In the short pulse limit investigated with femtosecond lasers, resonance-enhanced multiphoton ionization (REMPI) is rather instantaneous and typically occurs simultaneously via more than one vibrational or electronic intermediate state due to limited frequency resolution. In contrast, vibrational resolution in the REMPI spectrum can be achieved using nanosecond lasers. In this work, we follow the high-resolution approach using a tunable narrow-band nanosecond laser to measure REMPI-PECD through distinct vibrational levels in the intermediate 3s and 3p Rydberg states of fenchone. We observe the PECD to be essentially independent of the vibrational level. This behaviour of the chiral sensitivity may pave the way for enantiomer specific molecular identification in multi-component mixtures: one can specifically excite a sharp, vibrationally resolved transition of a distinct molecule to distinguish different chiral species in mixtures.

physics.chem-ph↗

arXiv2018

Photoelectron circular dichroism with two overlapping laser pulses of carrier frequencies $ω$ and $2ω$ linearly polarized in two mutually-orthogonal directions

Using a model methane-like chiral system, we theoretically demonstrate a possibility to access photoelectron circular dichroism (PECD) by a single experiment with two overlapping laser pulses of carrier frequencies $ω$ and $2ω$, which are linearly polarized in two mutually-orthogonal directions. Depending on the relative phase, the resulting electric field can be tailored to have two different rotational directions in the upper and lower hemispheres along the polarization of the $ω$-pulse. We predict a strong forward/backward asymmetry in the emission of photoelectrons from randomly oriented samples, which has an opposite sign in the upper and lower hemispheres. The predicted PECD effect is phase- and enantiomer-sensitive, providing new insight in this fascinating fundamental phenomenon. The effect can be optimized by varying relative intensities of the pulses.

physics.atm-clus↗

arXiv2017

Generalized bipyramids and hyperbolic volumes of tiling links

We present explicit geometric decompositions of the complement of tiling links, which are alternating links whose projection graphs are uniform tilings of the 2-sphere, the Euclidean plane or the hyperbolic plane. This requires generalizing the angle structures program of Casson and Rivin for triangulations with a mixture of finite, ideal, and truncated (i.e. ultra-ideal) vertices. A consequence of this decomposition is that the volumes of spherical tiling links are precisely twice the maximal volumes of the ideal Archimedean solids of the same combinatorial description. In the case of hyperbolic tiling links, we are led to consider links embedded in thickened surfaces S_g x I with genus g at least 2. We generalize the bipyramid construction of Adams to truncated bipyramids and use them to prove that the set of possible volume densities for links in S_g x I, ranging over all g at least 2, is a dense subset of the interval [0, 2v_{oct}], where v_{oct}, approximately 3.66386, is the volume of the regular ideal octahedron.

math.GT↗

arXiv2017

Intermediate state dependence of the photoelectron circular dichroism of fenchone observed via femtosecond resonance-enhanced multi-photon ionization

The intermediate state dependence of photoelectron circular dichroism (PECD) in resonance-enhanced multi-photon ionization of fenchone in the gas phase is experimentally studied. By scanning the excitation wavelength from 359 to 431 nm we simultaneously excite up to three electronically distinct resonances. In the PECD experiment performed with a broadband femtosecond laser their respective contributions to the photoelectron spectrum can be resolved. High-resolution spectroscopy allows us to identify two of the resonances as belonging to the B- and C-bands, which involve excitation to states with 3s and 3p Rydberg character, respectively. We observe a sign change in the PECD signal depending on which electronic state is used as an intermediate. Additionally, scanning the laser wavelength reveals a decrease of PECD magnitude with increasing photoelectron energy for the 3s state.

physics.chem-ph↗

arXiv2016

On conservative sequences and their application to ergodic multiplier problems

The conservative sequence of a set $A$ under a transformation $T$ is the set of all $n \in \mathbb{Z}$ such that $T^n A \cap A \not = \varnothing$. By studying these sequences, we prove that given any countable collection of nonsingular transformations with no finite invariant measure $\{T_i\}$, there exists a rank-one transformation $S$ such that $T_i \times S$ is not ergodic for all $i$. Moreover, $S$ can be chosen to be rigid or have infinite ergodic index. We establish similar results for $\mathbb{Z}^d$ actions and flows. Then, we find sufficient conditions on rank-one transformations $T$ that guarantee the existence of a rank-one transformation $S$ such that $T \times S$ is ergodic, or, alternatively, conditions that guarantee that $T \times S$ is conservative but not ergodic. In particular, the infinite Chacón transformation satisfies both conditions. Finally, for a given ergodic transformation $T$, we study the Baire categories of the sets $E(T)$, $\bar{E}C(T)$ and $\bar{C}(T)$ of transformations $S$ such that $T \times S$ is ergodic, ergodic but not conservative, and conservative, respectively.

math.DS↗

arXiv2016

Partially Bounded Transformations have Trivial Centralizer

We prove that for infinite rank-one transformations satisfying a property called "partial boundedness," the only commuting transformations are powers of the original transformation. This shows that a large class of infinite measure-preserving rank-one transformations with bounded cuts have trivial centralizers. We also characterize when partially bounded transformations are isomorphic to their inverse.

math.DS↗

arXiv2015

Volume and Determinant Densities of Hyperbolic Rational Links

The volume density of a hyperbolic link is defined as the ratio of hyperbolic volume to crossing number. We study its properties and a closely-related invariant called the determinant density. It is known that the sets of volume densities and determinant densities of links are dense in the interval [0,v_{oct}]. We construct sequences of alternating knots whose volume and determinant densities both converge to any x in [0,v_{oct}]. We also investigate the distributions of volume and determinant densities for hyperbolic rational links, and establish upper bounds and density results for these invariants.

math.GT↗