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Attributing outputs from Large Language Models (LLMs) in adversarial settings-such as cyberattacks and disinformation-presents significant challenges that are likely to grow in importance. We investigate this attribution problem using formal language theory, specifically language identification in the limit as introduced by Gold and extended by Angluin. By modeling LLM outputs as formal languages, we analyze whether finite text samples can uniquely pinpoint the originating model. Our results show that due to the non-identifiability of certain language classes, under some mild assumptions about overlapping outputs from fine-tuned models it is theoretically impossible to attribute outputs to specific LLMs with certainty. This holds also when accounting for expressivity limitations of Transformer architectures. Even with direct model access or comprehensive monitoring, significant computational hurdles impede attribution efforts. These findings highlight an urgent need for proactive measures to mitigate risks posed by adversarial LLM use as their influence continues to expand., Comment: 7 pages, 1 figure

The precision measurement of the tritium $\beta$-decay spectrum performed by the KATRIN experiment provides a unique way to search for general neutrino interactions (GNI). All theoretical allowed GNI terms involving neutrinos are incorporated into a low-energy effective field theory, and can be identified by specific signatures in the measured tritium $\beta$-spectrum. In this paper an effective description of the impact of GNI on the $\beta$-spectrum is formulated and the first constraints on the effective GNI parameters are derived based on the 4 million electrons collected in the second measurement campaign of KATRIN in 2019. In addition, constraints on selected types of interactions are investigated, thereby exploring the potential of KATRIN to search for more specific new physics cases, including a right-handed W boson, a charged Higgs or leptoquarks.

The projected sensitivity of the effective electron neutrino-mass measurement with the KATRIN experiment is below 0.3 eV (90 % CL) after five years of data acquisition. The sensitivity is affected by the increased rate of the background electrons from KATRIN's main spectrometer. A special shifted-analysing-plane (SAP) configuration was developed to reduce this background by a factor of two. The complex layout of electromagnetic fields in the SAP configuration requires a robust method of estimating these fields. We present in this paper a dedicated calibration measurement of the fields using conversion electrons of gaseous $^\mathrm{83m}$Kr, which enables the neutrino-mass measurements in the SAP configuration., Comment: 19 pages, 11 figures

The fact that neutrinos carry a non-vanishing rest mass is evidence of physics beyond the Standard Model of elementary particles. Their absolute mass bears important relevance from particle physics to cosmology. In this work, we report on the search for the effective electron antineutrino mass with the KATRIN experiment. KATRIN performs precision spectroscopy of the tritium $\beta$-decay close to the kinematic endpoint. Based on the first five neutrino-mass measurement campaigns, we derive a best-fit value of $m_\nu^{2} = {-0.14^{+0.13}_{-0.15}}~\mathrm{eV^2}$, resulting in an upper limit of $m_\nu < {0.45}~\mathrm{eV}$ at 90 % confidence level. With six times the statistics of previous data sets, amounting to 36 million electrons collected in 259 measurement days, a substantial reduction of the background level and improved systematic uncertainties, this result tightens KATRIN's previous bound by a factor of almost two., Comment: 61 pages, 20 figures, 2 tables

We study a model of machine teaching where the teacher mapping is constructed from a size function on both concepts and examples. The main question in machine teaching is the minimum number of examples needed for any concept, the so-called teaching dimension. A recent paper [7] conjectured that the worst case for this model, as a function of the size of the concept class, occurs when the consistency matrix contains the binary representations of numbers from zero and up. In this paper we prove their conjecture. The result can be seen as a generalization of a theorem resolving the edge isoperimetry problem for hypercubes [12], and our proof is based on a lemma of [10]., Comment: 14 pages, 1 figure

In traditional machine teaching, a teacher wants to teach a concept to a learner, by means of a finite set of examples, the witness set. But concepts can have many equivalent representations. This redundancy strongly affects the search space, to the extent that teacher and learner may not be able to easily determine the equivalence class of each representation. In this common situation, instead of teaching concepts, we explore the idea of teaching representations. We work with several teaching schemas that exploit representation and witness size (Eager, Greedy and Optimal) and analyze the gains in teaching effectiveness for some representational languages (DNF expressions and Turing-complete P3 programs). Our theoretical and experimental results indicate that there are various types of redundancy, handled better by the Greedy schema introduced here than by the Eager schema, although both can be arbitrarily far away from the Optimal. For P3 programs we found that witness sets are usually smaller than the programs they identify, which is an illuminating justification of why machine teaching from examples makes sense at all., Comment: 16 pages, 3 figures, 3 tables

In this work, we report on studies of graphene exposed to tritium gas in a controlled environment. The single layer graphene on a $\textrm{SiO}_2$/Si substrate was exposed to 400 mbar of $\textrm{T}_2$ for a total time of $\approx$ 55 h. The resistivity of the graphene sample was measured $\textit{in situ}$ during tritium exposure using the Van der Pauw method. We found that the sheet resistance increases by three orders of magnitude during the exposure, suggesting significant chemisorption of tritium. After exposure, the samples were characterised $\textit{ex situ}$ via spatio-chemical mapping with a confocal Raman microscope, to study the effect of tritium on the graphene structure (tritiation yielding T-graphene), as well as the homogeneity of modifications across the whole area of the graphene film. The Raman spectra after tritium exposure were comparable to previously observed results in hydrogen-loading experiments, carried out by other groups. By thermal annealing we also could demonstrate, using Raman spectral analysis, that the structural changes were largely reversible. Considering all observations, we conclude that the graphene film was at least partially tritiated during the tritium exposure, and that the graphene film by and large withstands the bombardment by electrons from the $\beta$-decay of tritium, as well as by energetic primary and secondary ions., Comment: Published in Nanoscale Advances (RSC), 22 pages, 5 figures

Imagine a learner L who tries to infer a hidden concept from a collection of observations. Building on the work [4] of Ferri et al., we assume the learner to be parameterized by priors P(c) and by c-conditional likelihoods P(z|c) where c ranges over all concepts in a given class C and z ranges over all observations in an observation set Z. L is called a MAP-learner (resp. an MLE-learner) if it thinks of a collection S of observations as a random sample and returns the concept with the maximum a-posteriori probability (resp. the concept which maximizes the c-conditional likelihood of S). Depending on whether L assumes that S is obtained from ordered or unordered sampling resp. from sampling with or without replacement, we can distinguish four different sampling modes. Given a target concept c in C, a teacher for a MAP-learner L aims at finding a smallest collection of observations that causes L to return c. This approach leads in a natural manner to various notions of a MAP- or MLE-teaching dimension of a concept class C. Our main results are: We show that this teaching model has some desirable monotonicity properties. We clarify how the four sampling modes are related to each other. As for the (important!) special case, where concepts are subsets of a domain and observations are 0,1-labeled examples, we obtain some additional results. First of all, we characterize the MAP- and MLE-teaching dimension associated with an optimally parameterized MAP-learner graph-theoretically. From this central result, some other ones are easy to derive. It is shown, for instance, that the MLE-teaching dimension is either equal to the MAP-teaching dimension or exceeds the latter by 1. It is shown furthermore that these dimensions can be bounded from above by the so-called antichain number, the VC-dimension and related combinatorial parameters. Moreover they can be computed in polynomial time.

An unavoidable category of molecular species in large-scale tritium applications, such as nuclear fusion, are tritium-substituted hydrocarbons; these form by radiochemical reactions in the presence of (circulating) tritium and carbon (mainly from the steel of vessels and tubing). Tritiumsubstituted methane species, CQ$_4$ (with Q = H , D , T), are often the precursor for higher-order reaction chains, and thus are of particular interest. Here we describe the controlled production of CQ$_4$ carried out in the CAPER facility of the Tritium Laboratory Karlsruhe (TLK), exploiting catalytic reactions and species-enrichment via the CAPER-integral permeator. CQ4 was generated in substantial quantity (>1000 cm$^3$ at ~850 mbar, with CQ$_4$ - content of up to ~20 %). These samples were analyzed using laser Raman and mass spectrometry, to determine the relative isotopologue composition and to trace the generation of tritiated chain-hydrocarbons., Comment: 10 pages, 4 figures. This article has been accepted for publication in Fusion Science and Technology, published by Taylor & Francis

In this work we present a keV-scale sterile-neutrino search with the first tritium data of the KATRIN experiment, acquired in the commissioning run in 2018. KATRIN performs a spectroscopic measurement of the tritium $\beta$-decay spectrum with the main goal of directly determining the effective electron anti-neutrino mass. During this commissioning phase a lower tritium activity facilitated the search for sterile neutrinos with a mass of up to $1.6\, \mathrm{keV}$. We do not find a signal and set an exclusion limit on the sterile-to-active mixing amplitude of down to $\sin^2\theta < 5\cdot10^{-4}$ ($95\,\%$ C.L.), improving current laboratory-based bounds in the sterile-neutrino mass range between 0.1 and $1.0\, \mathrm{keV}$.

Some extensions of the Standard Model of Particle Physics allow for Lorentz invariance and Charge-Parity-Time (CPT)-invariance violations. In the neutrino sector strong constraints have been set by neutrino-oscillation and time-of-flight experiments. However, some Lorentz-invariance-violating parameters are not accessible via these probes. In this work, we focus on the parameters $(a_{\text{of}}^{(3)})_{00}$, $(a_{\text{of}}^{(3)})_{10}$ and $(a_{\text{of}}^{(3)})_{11}$ which would manifest themselves in a non-isotropic beta-decaying source as a sidereal oscillation and an overall shift of the spectral endpoint. Based on the data of the first scientific run of the KATRIN experiment, we set the first limit on $\left|(a_{\text{of}}^{(3)})_{11}\right|$ of $< 3.7\cdot10^{-6}$ GeV at 90\% confidence level. Moreover, we derive new constraints on $(a_{\text{of}}^{(3)})_{00}$ and $(a_{\text{of}}^{(3)})_{10}$.

The Karlsruhe Tritium Neutrino (KATRIN) experiment is designed to measure a high-precision integral spectrum of the endpoint region of T2 beta decay, with the primary goal of probing the absolute mass scale of the neutrino. After a first tritium commissioning campaign in 2018, the experiment has been regularly running since 2019, and in its first two measurement campaigns has already achieved a sub-eV sensitivity. After 1000 days of data-taking, KATRIN's design sensitivity is 0.2 eV at the 90% confidence level. In this white paper we describe the current status of KATRIN; explore prospects for measuring the neutrino mass and other physics observables, including sterile neutrinos and other beyond-Standard-Model hypotheses; and discuss research-and-development projects that may further improve the KATRIN sensitivity., Comment: Contribution to Snowmass 2021. 70 pages excluding references; 35 figures. Author list updated June 2023

We report on the direct cosmic relic neutrino background search from the first two science runs of the KATRIN experiment in 2019. Beta-decay electrons from a high-purity molecular tritium gas source are analyzed by a high-resolution MAC-E filter around the kinematic endpoint at 18.57 keV. The analysis is sensitive to a local relic neutrino overdensity of 9.7e10 (1.1e11) at a 90% (95%) confidence level. A fit of the integrated electron spectrum over a narrow interval around the kinematic endpoint accounting for relic neutrino captures in the Tritium source reveals no significant overdensity. This work improves the results obtained by the previous kinematic neutrino mass experiments at Los Alamos and Troitsk. We furthermore update the projected final sensitivity of the KATRIN experiment to <1e10 at 90% confidence level, by relying on updated operational conditions., Comment: 7 pages, 7 figures

We present the results of the light sterile neutrino search from the second KATRIN measurement campaign in 2019. Approaching nominal activity, $3.76 \times 10^6$ tritium $\beta$-electrons are analyzed in an energy window extending down to $40\,$eV below the tritium endpoint at $E_0 = 18.57\,$keV. We consider the $3\nu+1$ framework with three active and one sterile neutrino flavor. The analysis is sensitive to a fourth mass eigenstate $m_4^2\lesssim1600\,$eV$^2$ and active-to-sterile mixing $|U_{e4}|^2 \gtrsim 6 \times 10^{-3}$. As no sterile-neutrino signal was observed, we provide improved exclusion contours on $m_4^2$ and $|U_{e4}|^2$ at $95\,$% C.L. Our results supersede the limits from the Mainz and Troitsk experiments. Furthermore, we are able to exclude the large $\Delta m_{41}^2$ solutions of the reactor antineutrino and gallium anomalies to a great extent. The latter has recently been reaffirmed by the BEST collaboration and could be explained by a sterile neutrino with large mixing. While the remaining solutions at small $\Delta m_{41}^2$ are mostly excluded by short-baseline reactor experiments, KATRIN is the only ongoing laboratory experiment to be sensitive to relevant solutions at large $\Delta m_{41}^2$ through a robust spectral shape analysis., Comment: 14 pages, 8 figures, 2 tables

In a graph, a perfect matching cut is an edge cut that is a perfect matching. Perfect Matching Cut (PMC) is the problem of deciding whether a given graph has a perfect matching cut, and is known to be NP-complete. We revisit the problem and show that PMC remains NP-complete when restricted to bipartite graphs of maximum degree 3 and arbitrarily large girth. Complementing this hardness result, we give two graph classes in which PMC is polynomial time solvable. The first one includes claw-free graphs and graphs without an induced path on five vertices, the second one properly contains all chordal graphs. Assuming the Exponential Time Hypothesis, we show there is no $O^*(2^{o(n)})$-time algorithm for PMC even when restricted to $n$-vertex bipartite graphs, and also show that PMC can be solved in $O^*(1.2721^n)$ time by means of an exact branching algorithm.

A $k$-leaf power of a tree $T$ is a graph $G$ whose vertices are the leaves of $T$ and whose edges connect pairs of leaves whose distance in $T$ is at most $k$. A graph is a leaf power if it is a $k$-leaf power for some $k$. Over 20 years ago, Nishimura et al. [J. Algorithms, 2002] asked if recognition of leaf powers was in P. Recently, Lafond [SODA 2022] showed an XP algorithm when parameterized by $k$, while leaving the main question open. In this paper, we explore this question from the perspective of two alternative models of leaf powers, showing that both a linear and a star variant of leaf powers can be recognized in polynomial-time.

The minimum height of vertex and edge partition trees are well-studied graph parameters known as, for instance, vertex and edge ranking number. While they are NP-hard to determine in general, linear-time algorithms exist for trees. Motivated by a correspondence with Dasgupta's objective for hierarchical clustering we consider the total rather than maximum depth of vertices as an alternative objective for minimization. For vertex partition trees this leads to a new parameter with a natural interpretation as a measure of robustness against vertex removal. As tools for the study of this family of parameters we show that they have similar recursive expressions and prove a binary tree rotation lemma. The new parameter is related to trivially perfect graph completion and therefore intractable like the other three are known to be. We give polynomial-time algorithms for both total-depth variants on caterpillars and on trees with a bounded number of leaf neighbors. For general trees, we obtain a 2-approximation algorithm., Comment: Full version, 19 pages

We report the results of the second measurement campaign of the Karlsruhe Tritium Neutrino (KATRIN) experiment. KATRIN probes the effective electron anti-neutrino mass, $m_{\nu}$, via a high-precision measurement of the tritium $\beta$-decay spectrum close to its endpoint at $18.6\,\mathrm{keV}$. In the second physics run presented here, the source activity was increased by a factor of 3.8 and the background was reduced by $25\,\%$ with respect to the first campaign. A sensitivity on $m_{\nu}$ of $0.7\,\mathrm{eV/c^2}$ at $90\,\%$ confidence level (CL) was reached. This is the first sub-eV sensitivity from a direct neutrino-mass experiment. The best fit to the spectral data yields $m_{\nu}^2 = (0.26\pm0.34)\,\mathrm{eV^4/c^4}$, resulting in an upper limit of $m_{\nu}<0.9\,\mathrm{eV/c^2}$ ($90\,\%$ CL). By combining this result with the first neutrino mass campaign, we find an upper limit of $m_{\nu}<0.8\,\mathrm{eV/c^2}$ ($90\,\%$ CL)., Comment: 19 pages, 10 figures, 5 tables

The KATRIN experiment is designed for a direct and model-independent determination of the effective electron anti-neutrino mass via a high-precision measurement of the tritium $\beta$-decay endpoint region with a sensitivity on $m_\nu$ of 0.2$\,$eV/c$^2$ (90% CL). For this purpose, the $\beta$-electrons from a high-luminosity windowless gaseous tritium source traversing an electrostatic retarding spectrometer are counted to obtain an integral spectrum around the endpoint energy of 18.6$\,$keV. A dominant systematic effect of the response of the experimental setup is the energy loss of $\beta$-electrons from elastic and inelastic scattering off tritium molecules within the source. We determined the \linebreak energy-loss function in-situ with a pulsed angular-selective and monoenergetic photoelectron source at various tritium-source densities. The data was recorded in integral and differential modes; the latter was achieved by using a novel time-of-flight technique. We developed a semi-empirical parametrization for the energy-loss function for the scattering of 18.6-keV electrons from hydrogen isotopologs. This model was fit to measurement data with a 95% T$_2$ gas mixture at 30$\,$K, as used in the first KATRIN neutrino mass analyses, as well as a D$_2$ gas mixture of 96% purity used in KATRIN commissioning runs. The achieved precision on the energy-loss function has abated the corresponding uncertainty of $\sigma(m_\nu^2)<10^{-2}\,\mathrm{eV}^2$ [arXiv:2101.05253] in the KATRIN neutrino-mass measurement to a subdominant level., Comment: 12 figures, 18 pages; to be submitted to EPJ C