arXiv subjects
Publications and source records attributed to Niklas Müller.
In this short note we provide a characterisation of ball quotients among all minimal smooth projective varieties of general type purely in terms of their characteristic numbers. This generalises earlier work of Miyaoka, Yau and Greb--Kebekus--Peternell--Taji.
In this paper we present, for any integers $0\leq \nu \leq n$, a set of inequalities satisfied by the Chern classes of any minimal complex projective variety of dimension $n$ and numerical dimension $\nu$. In the cases where $\nu$ is either very small or very large compared with $n$, this recovers many previously known results. We demonstrate that our inequalities are sharp by providing an explicit characterisation of those varieties achieving the equality; our proof, in particular, resolves the Abundance conjecture in this situation. Additionally, we provide some new examples of varieties with extremal Chern classes that demonstrate the optimality of our results.
In this paper, we establish a structure theorem for minimal projective klt varieties $X$ that satisfiy Miyaoka's equality $3c_2(X) = c_1(X)^2$. Specifically, we prove that the canonical divisor $K_X$ is semi-ample and that the Kodaira dimension $κ(K_X)$ is either $0$, $1$, or $2$. Furthermore, based on this abundance result, we show that a maximally quasi-étale cover of $X$ is smooth, and we describe explicitly the structure of the Iitaka fibration. Additionally, we prove a similar result for projective klt varieties with a nef anti-canonical divisor.
In this note, we show that if $f\colon M\rightarrow X$ is a germ of a projective Lagrangian fibration from a holomorphic symplectic manifold $M$ onto a normal analytic variety $X$ with isolated quotient singularities, then $X$ is smooth. In particular, if $f\colon M\rightarrow X$ is a Lagrangian fibration from a hyper-K\"ahler fourfold $M$ onto a normal surface $X$, then $X\cong \mathbb{P}^2$, which recovers a recent result of Huybrechts--Xu and Ou.
Up to finite étale cover, any smooth complex projective variety $X$ with nef anti-canonical bundle is a holomorphic fibre bundle over a $K$-trivial variety with locally constant transition functions. We show that this result is optimal by proving that any projective fibre bundle with locally constant transition functions over a $K$-trivial variety has a nef anti-canonical bundle. Moreover, we complement some results on the structure theory of varieties whose tangent bundle admits a singular hermitean metric of positive curvature.
Let $(X, Δ)$ be a klt threefold pair with nef anti-log canonical bundle $-(K_X+Δ)$. We show that $κ(X, -(K_X+Δ))\geq 0$. To do so, we prove a more general equivariant non-vanishing result for anti-log canonical bundles, which is valid in any dimension.
The phase-resolved imaging of confined light fields by homodyne detection is a cornerstone of metrology in nano-optics and photonics, but its application in electron microscopy has been limited so far. Here, we report the mapping of optical modes in a waveguide structure by illumination with femtosecond light pulses in a continuous-beam transmission electron microscope. Multi-photon photoemission results in a remanent charging pattern which we image by Lorentz microscopy. The resulting image contrast is linked to the intensity distribution of the standing light wave and quantitatively described within an analytical model. The robustness of the approach is showcased in a wider parameter range and more complex sample geometries including micro- and nanostructures. We discuss further applications of light-interference-based charging for electron microscopy with in-situ optical excitation, laying the foundation for advanced measurement schemes for the phase-resolved imaging of propagating light fields.
Humor is a substantial element of human social behavior, affect, and cognition. Its automatic understanding can facilitate a more naturalistic human-AI interaction. Current methods of humor detection have been exclusively based on staged data, making them inadequate for "real-world" applications. We contribute to addressing this deficiency by introducing the novel Passau-Spontaneous Football Coach Humor (Passau-SFCH) dataset, comprising about 11 hours of recordings. The Passau-SFCH dataset is annotated for the presence of humor and its dimensions (sentiment and direction) as proposed in Martin's Humor Style Questionnaire. We conduct a series of experiments employing pretrained Transformers, convolutional neural networks, and expert-designed features. The performance of each modality (text, audio, video) for spontaneous humor recognition is analyzed and their complementarity is investigated. Our findings suggest that for the automatic analysis of humor and its sentiment, facial expressions are most promising, while humor direction can be best modeled via text-based features. Further, we experiment with different multimodal approaches to humor recognition, including decision-level fusion and MulT, a multimodal Transformer approach. In this context, we propose a novel multimodal architecture that yields the best overall results. Finally, we make our code publicly available at https://www.github.com/lc0197/passau-sfch. The Passau-SFCH dataset is available upon request.
The Multimodal Sentiment Analysis Challenge (MuSe) 2024 addresses two contemporary multimodal affect and sentiment analysis problems: In the Social Perception Sub-Challenge (MuSe-Perception), participants will predict 16 different social attributes of individuals such as assertiveness, dominance, likability, and sincerity based on the provided audio-visual data. The Cross-Cultural Humor Detection Sub-Challenge (MuSe-Humor) dataset expands upon the Passau Spontaneous Football Coach Humor (Passau-SFCH) dataset, focusing on the detection of spontaneous humor in a cross-lingual and cross-cultural setting. The main objective of MuSe 2024 is to unite a broad audience from various research domains, including multimodal sentiment analysis, audio-visual affective computing, continuous signal processing, and natural language processing. By fostering collaboration and exchange among experts in these fields, the MuSe 2024 endeavors to advance the understanding and application of sentiment analysis and affective computing across multiple modalities. This baseline paper provides details on each sub-challenge and its corresponding dataset, extracted features from each data modality, and discusses challenge baselines. For our baseline system, we make use of a range of Transformers and expert-designed features and train Gated Recurrent Unit (GRU)-Recurrent Neural Network (RNN) models on them, resulting in a competitive baseline system. On the unseen test datasets of the respective sub-challenges, it achieves a mean Pearson's Correlation Coefficient ($ρ$) of 0.3573 for MuSe-Perception and an Area Under the Curve (AUC) value of 0.8682 for MuSe-Humor.
Recent advancements in electron microscopy have introduced innovative techniques enabling the inelastic interaction of fast electrons with tightly confined and intense light fields. These techniques, commonly summarized under the term photon-induced nearfield electron microscopy now offer unprecedented capabilities for a precise mapping of the characteristics of optical near-fields with remarkable spatial resolution but their spectral resolution were only scarcely investigated. In this study, we employ a strongly chirped and temporally broadband light pulse to investigate the interaction between free electrons and light at the edge of a MoS2 thin film. Our approach unveils the details of electron-light coupling, revealing a pronounced dependence of the coupling strength on both the position and photon energy. Employing numerical simulations of a simplified model system we identify these modulations to be caused by optical interferences between the incident and reflected field as well as an optical mode guided within the transition metal dichalcogenide film.
In a recently developed methodology termed photon induced near-field electron microscopy (PINEM), the inelastic scattering of electrons off illuminated nanostructures provides direct experimental access to the structure of optical near-field modes and their population. Whereas the inelastic scattering probability can be quantitatively linked to the near field distribution, analytical results for simple light scattering geometries are scarce. Here we derive a fully analytical expression for the coupling strength between free electrons and optical near-fields in planar geometries representing dielectric thin films. Contributions to the overall coupling from the electric field above, below and within the sample are analyzed in detail. By carefully choosing the relative angles between electron beam, light and thin film and by accounting for a broad spectrum of photon energies, we demonstrate that one can imprint optical material properties like the reflectivity onto the electron energy distribution.
The MuSe 2023 is a set of shared tasks addressing three different contemporary multimodal affect and sentiment analysis problems: In the Mimicked Emotions Sub-Challenge (MuSe-Mimic), participants predict three continuous emotion targets. This sub-challenge utilises the Hume-Vidmimic dataset comprising of user-generated videos. For the Cross-Cultural Humour Detection Sub-Challenge (MuSe-Humour), an extension of the Passau Spontaneous Football Coach Humour (Passau-SFCH) dataset is provided. Participants predict the presence of spontaneous humour in a cross-cultural setting. The Personalisation Sub-Challenge (MuSe-Personalisation) is based on the Ulm-Trier Social Stress Test (Ulm-TSST) dataset, featuring recordings of subjects in a stressed situation. Here, arousal and valence signals are to be predicted, whereas parts of the test labels are made available in order to facilitate personalisation. MuSe 2023 seeks to bring together a broad audience from different research communities such as audio-visual emotion recognition, natural language processing, signal processing, and health informatics. In this baseline paper, we introduce the datasets, sub-challenges, and provided feature sets. As a competitive baseline system, a Gated Recurrent Unit (GRU)-Recurrent Neural Network (RNN) is employed. On the respective sub-challenges' test datasets, it achieves a mean (across three continuous intensity targets) Pearson's Correlation Coefficient of .4727 for MuSe-Mimic, an Area Under the Curve (AUC) value of .8310 for MuSe-Humor and Concordance Correlation Coefficient (CCC) values of .7482 for arousal and .7827 for valence in the MuSe-Personalisation sub-challenge.
To any compact K\"ahler manifold $(X, \omega)$ one may associate a bundle of affine spaces $Z_X\rightarrow X$ called a \emph{canonical extension} of $X$. In this paper we prove that if the tangent bundle of $X$ is nef, then the total space $Z_X$ is a Stein manifold. This partially answers a question raised by Greb-Wong of whether these two properties are actually equivalent. We also complement some known results for surfaces in the converse direction.
The Multimodal Sentiment Analysis Challenge (MuSe) 2022 is dedicated to multimodal sentiment and emotion recognition. For this year's challenge, we feature three datasets: (i) the Passau Spontaneous Football Coach Humor (Passau-SFCH) dataset that contains audio-visual recordings of German football coaches, labelled for the presence of humour; (ii) the Hume-Reaction dataset in which reactions of individuals to emotional stimuli have been annotated with respect to seven emotional expression intensities, and (iii) the Ulm-Trier Social Stress Test (Ulm-TSST) dataset comprising of audio-visual data labelled with continuous emotion values (arousal and valence) of people in stressful dispositions. Using the introduced datasets, MuSe 2022 2022 addresses three contemporary affective computing problems: in the Humor Detection Sub-Challenge (MuSe-Humor), spontaneous humour has to be recognised; in the Emotional Reactions Sub-Challenge (MuSe-Reaction), seven fine-grained `in-the-wild' emotions have to be predicted; and in the Emotional Stress Sub-Challenge (MuSe-Stress), a continuous prediction of stressed emotion values is featured. The challenge is designed to attract different research communities, encouraging a fusion of their disciplines. Mainly, MuSe 2022 targets the communities of audio-visual emotion recognition, health informatics, and symbolic sentiment analysis. This baseline paper describes the datasets as well as the feature sets extracted from them. A recurrent neural network with LSTM cells is used to set competitive baseline results on the test partitions for each sub-challenge. We report an Area Under the Curve (AUC) of .8480 for MuSe-Humor; .2801 mean (from 7-classes) Pearson's Correlations Coefficient for MuSe-Reaction, as well as .4931 Concordance Correlation Coefficient (CCC) and .4761 for valence and arousal in MuSe-Stress, respectively.
Transmission electron microscopy is an excellent experimental tool to study the interaction of free electrons with nanoscale light fields. However, up to now, applying electron microscopy to quantum optical investigations was hampered by the lack of experimental platforms which allow a strong coupling between fast electrons and high-quality resonators. Here, as a first step, we demonstrate the broad-band excitation of optical whispering-gallery modes in silica microresonators by fast electrons. In the emitted coherent cathodoluminescence spectrum, a comb of equidistant peaks is observed, resulting in cavity quality factors larger than 700. These results enable the study of quantum optical phenomena in electron microscopy with potential applications in quantum electron-light metrology.