Diffusion models, widely used in image generation, rely on iterative refinement to generate images from noise. Understanding this data evolution is important for model development and interpretability, yet challenging due to its high-dimensional, iterative nature. Prior works often focus on static or instance-level analyses, missing the iterative and holistic aspects of the generative path. While dimensionality reduction can visualize image evolution for few instances, it does preserve the iterative structure. To address these gaps, we introduce EvolvED, a method that presents a holistic view of the iterative generative process in diffusion models. EvolvED goes beyond instance exploration by leveraging predefined research questions to streamline generative space exploration. Tailored prompts aligned with these questions are used to extract intermediate images, preserving iterative context. Targeted feature extractors trace the evolution of key image attribute evolution, addressing the complexity of high-dimensional outputs. Central to EvolvED is a novel evolutionary embedding algorithm that encodes iterative steps while maintaining semantic relations. It enhances the visualization of data evolution by clustering semantically similar elements within each iteration with t-SNE, grouping elements by iteration, and aligning an instance's elements across iterations. We present rectilinear and radial layouts to represent iterations and support exploration. We apply EvolvED to diffusion models like GLIDE and Stable Diffusion, demonstrating its ability to provide valuable insights into the generative process.

We investigate the lattice of clones that are generated by a set of functions that are induced on a finite field $\mathbb{F}$ by monomials. We study the atoms and coatoms of this lattice and investigate whether this lattice contains infinite ascending chains, or infinite descending chains, or infinite antichains. We give a connection between the lattice of these clones and semi-affine algebras. Furthermore, we show that the sublattice of idempotent clones of this lattice is finite and every idempotent monomial clone is principal.

In organic semiconductors charge transport typically takes place via slow hopping processes. Molecular aggregation can lead to enhanced exciton and charge transport through coupling of the transition dipole moments. In this work, we investigate the optical, morphological, and electronic properties of thin films of a merocyanine dye, that aggregates due to its high ground-state dipole moment. The degree of aggregation of spin-coated thin films can be easily tuned by thermal annealing. We demonstrate the relationship between charge carrier mobility and the degree of aggregation. The mobility is increased by approximately three orders of magnitude due to aggregation. We combine variable angle spectroscopic ellipsometry and polarization-resolved absorption spectroscopy with density functional theory to demonstrate that the aggregated molecules are oriented in an upright, standing configuration relative to the substrate surface. This arrangement involves a co-facial orientation of the molecular pi-systems which is advantageous for lateral charge transport. By utilizing highly oriented pyrolytic graphite as an ordered substrate, we are able to template the growth of the merocyanine layer in vapor phase deposition, and to improve the in-plane morphological order drastically. By correlating atomic force microscopy and photoluminescence microspectroscopy we observe oriented domains of 100s of {\mu}m^2 in size, emitting linearly polarized light, whereby maintaining the edge-on molecular arrangement. This promises a further significant enhancement of lateral charge carrier mobility.

A brief overview of some computer algebra methods for computations with nested integrals is given. The focus is on nested integrals over integrands involving square roots. Rewrite rules for conversion to and from associated nested sums are discussed. We also include a short discussion comparing the holonomic systems approach and the differential field approach. For simplification to rational integrands, we give a comprehensive list of univariate rationalizing transformations, including transformations tuned to map the interval $[0,1]$ bijectively to itself.

In the pursuit of developing expressive music performance models using artificial intelligence, this paper introduces DExter, a new approach leveraging diffusion probabilistic models to render Western classical piano performances. In this approach, performance parameters are represented in a continuous expression space and a diffusion model is trained to predict these continuous parameters while being conditioned on the musical score. Furthermore, DExter also enables the generation of interpretations (expressive variations of a performance) guided by perceptually meaningful features by conditioning jointly on score and perceptual feature representations. Consequently, we find that our model is useful for learning expressive performance, generating perceptually steered performances, and transferring performance styles. We assess the model through quantitative and qualitative analyses, focusing on specific performance metrics regarding dimensions like asynchrony and articulation, as well as through listening tests comparing generated performances with different human interpretations. Results show that DExter is able to capture the time-varying correlation of the expressive parameters, and compares well to existing rendering models in subjectively evaluated ratings. The perceptual-feature-conditioned generation and transferring capabilities of DExter are verified by a proxy model predicting perceptual characteristics of differently steered performances.

The quantum phase transitions of dipoles confined to the vertices of two dimensional (2D) lattices of square and triangular geometry is studied using path integral ground state quantum Monte Carlo (PIGS). We analyze the phase diagram as a function of the strength of both the dipolar interaction and a transverse electric field. The study reveals the existence of a class of orientational phases of quantum dipolar rotors whose properties are determined by the ratios between the strength anisotropic dipole-dipole interaction, the strength of the applied transverse field, and the rotational constant. For the triangular lattice, the generic orientationally disordered phase found at zero and weak values of both dipolar interaction strength and applied field, is found to show a transition to a phase characterized by net polarization in the lattice plane as the strength of the dipole-dipole interaction is increased, independent of the strength of the applied transverse field, in addition to the expected transition to a transverse polarized phase as the electric field strength increases. The square lattice is also found to exhibit a transition from a disordered phase to an ordered phase as the dipole-dipole interaction strength is increased, as well as the expected transition to a transverse polarized phase as the electric field strength increases. In contrast to the situation with a triangular lattice, on square lattices the ordered phase at high dipole-dipole interaction strength possesses a striped ordering. The properties of these quantum dipolar rotor phases are dominated by the anisotropy of the interaction and provide useful models for developing quantum phases beyond the well-known paradigms of spin Hamiltonian models, realizing in particular a novel physical realization of a quantum rotor-like Hamiltonian that possesses an anisotropic long range interaction.

Drafting, i.e., the selection of a subset of items from a larger candidate set, is a key element of many games and related problems. It encompasses team formation in sports or e-sports, as well as deck selection in many modern card games. The key difficulty of drafting is that it is typically not sufficient to simply evaluate each item in a vacuum and to select the best items. The evaluation of an item depends on the context of the set of items that were already selected earlier, as the value of a set is not just the sum of the values of its members - it must include a notion of how well items go together. In this paper, we study drafting in the context of the card game Magic: The Gathering. We propose the use of a contextual preference network, which learns to compare two possible extensions of a given deck of cards. We demonstrate that the resulting network is better able to evaluate card decks in this game than previous attempts.

Anti-Muslim hate speech has emerged within memes, characterized by context-dependent and rhetorical messages using text and images that seemingly mimic humor but convey Islamophobic sentiments. This work presents a novel dataset and proposes a classifier based on the Vision-and-Language Transformer (ViLT) specifically tailored to identify anti-Muslim hate within memes by integrating both visual and textual representations. Our model leverages joint modal embeddings between meme images and incorporated text to capture nuanced Islamophobic narratives that are unique to meme culture, providing both high detection accuracy and interoperability.

We show that independent and uniformly distributed sampling points are as good as optimal sampling points for the approximation of functions from the Sobolev space $W_p^s(\Omega)$ on bounded convex domains $\Omega\subset \mathbb{R}^d$ in the $L_q$-norm if $q

A hybrid system of a semiconductor quantum dot single photon source and a rubidium quantum memory represents a promising architecture for future photonic quantum repeaters. One of the key challenges lies in matching the emission frequency of quantum dots with the transition frequency of rubidium atoms while preserving the relevant emission properties. Here, we demonstrate the bidirectional frequency-tuning of the emission from a narrow-linewidth (close-to-transform-limited) quantum dot. The frequency tuning is based on a piezoelectric strain-amplification device, which can apply significant stress to thick bulk samples. The induced strain shifts the emission frequency of the quantum dot over a total range of $1.15\ \text{THz}$, about three orders of magnitude larger than its linewidth. Throughout the whole tuning process, both the spectral properties of the quantum dot and its single-photon emission characteristics are preserved. Our results show that external stress can be used as a promising tool for reversible frequency tuning of high-quality quantum dots and pave the wave towards the realisation of a quantum dot -- rubidium atoms interface for quantum networking.

The dynamics of excitonic energy transfer in molecular complexes triggered by interaction with laser pulses offers a unique window into the underlying physical processes. The absorbed energy moves through the network of interlinked pigments and in photosynthetic complexes reaches a reaction center. The efficiency and time-scale depend not only on the excitonic couplings, but are also affected by the dissipation of energy to vibrational modes of the molecules. An open quantum system description provides a suitable tool to describe the involved processes and connects the decoherence and relaxation dynamics to measurements of the time-dependent polarization.

Varying the angle Theta between applied field and the conducting planes of a layered superconductor in a small interval close to the plane-parallel field direction, a large number of superconducting states with unusual properties may be produced. For these states, the pair breaking effect of the magnetic field affects both the orbital and the spin degree of freedom. This leads to pair wave functions with finite momentum, which are labeled by Landau quantum numbers 0\infty of the paramagnetic vortex states to the FFLO-limit is analyzed and the physical reason for the occupation of higher Landau levels is pointed out.

In this work we present the computer algebra package HarmonicSums and its theoretical background for the manipulation of harmonic sums and some related quantities as for example Euler-Zagier sums and harmonic polylogarithms. Harmonic sums and generalized harmonic sums emerge as special cases of so-called d'Alembertian solutions of recurrence relations. We show that harmonic sums form a quasi-shuffle algebra and describe a method how we can find algebraically independent harmonic sums. In addition, we define a differentiation on harmonic sums via an extended version of the Mellin transform. Along with that, new relations between harmonic sums will arise. Furthermore, we present an algorithm which rewrites certain types of nested sums into expressions in terms of harmonic sums. We illustrate by nontrivial examples how these algorithms in cooperation with the summation package Sigma support the evaluation of Feynman integrals.

Six-loop massive scheme renormalization group functions of a d=3-dimensional cubic model (J.M. Carmona, A. Pelissetto, and E. Vicari, Phys. Rev. B vol. 61, 15136 (2000)) are reconsidered by means of the pseudo-epsilon expansion. The marginal order parameter components number N_c=2.862(5) as well as critical exponents of the cubic model are obtained. Our estimate N_c<3 leads in particular to the conclusion that all ferromagnetic cubic crystals with three easy axis should undergo a first order phase transition.

We analyze univariate oscillatory integrals defined on the real line for functions from the standard Sobolev space $H^s({\mathbb{R}})$ and from the space $C^s({\mathbb{R}})$ with an arbitrary integer $s\ge1$. We find tight upper and lower bounds for the worst case error of optimal algorithms that use $n$ function values. More specifically, we study integrals of the form $$I_k^\rho (f) = \int_{ {\mathbb{R}}} f(x) \,e^{-i\,kx} \rho(x) \, {\rm d} x\ \ \ \mbox{for}\ \ f\in H^s({\mathbb{R}})\ \ \mbox{or}\ \ f\in C^s({\mathbb{R}})$$ with $k\in {\mathbb{R}}$ and a smooth density function $\rho$ such as $\rho(x) = \frac{1}{\sqrt{2 \pi}} \exp( -x^2/2)$. The optimal error bounds are $\Theta((n+\max(1,|k|))^{-s})$ with the factors in the $\Theta$ notation dependent only on $s$ and $\rho$.

The areas of machine learning and knowledge discovery in databases have considerably matured in recent years. In this article, we briefly review recent developments as well as classical algorithms that stood the test of time. Our goal is to provide a general introduction into different tasks such as learning from tabular data, behavioral data, or textual data, with a particular focus on actual and potential applications in behavioral sciences. The supplemental appendix to the article also provides practical guidance for using the methods by pointing the reader to proven software implementations. The focus is on R, but we also cover some libraries in other programming languages as well as systems with easy-to-use graphical interfaces.

We consider the task of recovering a Sobolev function on a connected compact Riemannian manifold $M$ when given a sample on a finite point set. We prove that the quality of the sample is given by the $L_\gamma(M)$-average of the geodesic distance to the point set and determine the value of $\gamma\in (0,\infty]$. This extends our findings on bounded convex domains [IMA J. Numer. Anal., 44:1346--1371, 2024]. As a byproduct, we prove the optimal rate of convergence of the $n$-th minimal worst case error for $L_q(M)$-approximation for all $1\le q \le \infty$. Further, a limit theorem for moments of the average distance to a set consisting of i.i.d.\ uniform points is proven. This yields that a random sample is asymptotically as good as an optimal sample in precisely those cases with \gamma&lt;\infty. In particular, we obtain that cubature formulas with random nodes are asymptotically as good as optimal cubature formulas if the weights are chosen correctly. This closes a logarithmic gap left open by Ehler, Gräf and Oates [Stat. Comput., 29:1203-1214, 2019].

Plants are dynamic systems that are integral to our existence and survival. Plants face environment changes and adapt over time to their surrounding conditions. We argue that plant responses to an environmental stimulus are a good example of a real-world problem that can be approached within a reinforcement learning (RL)framework. With the objective of controlling a plant by moving the light source, we propose GrowSpace, as a new RL benchmark. The back-end of the simulator is implemented using the Space Colonisation Algorithm, a plant growing model based on competition for space. Compared to video game RL environments, this simulator addresses a real-world problem and serves as a test bed to visualize plant growth and movement in a faster way than physical experiments. GrowSpace is composed of a suite of challenges that tackle several problems such as control, multi-stage learning,fairness and multi-objective learning. We provide agent baselines alongside case studies to demonstrate the difficulty of the proposed benchmark.

Gr\"atzer and Lakser asked in the 1971 {\sl Transactions of the American Mathematical Society} if the pseudocomplemented distributive lattices in the amalgamation class of the subvariety generated by ${\bf 2}^n\oplus{\bf 1}$ can be characterized by the property of not having a $*$-homomorphism onto ${\bf 2}^i\oplus{\bf 1}$for$1

Graph autoencoders (GAE) and variational graph autoencoders (VGAE) emerged as two powerful groups of unsupervised node embedding methods, with various applications to graph-based machine learning problems such as link prediction and community detection. Nonetheless, at the beginning of this Ph.D. project, GAE and VGAE models were also suffering from key limitations, preventing them from being adopted in the industry. In this thesis, we present several contributions to improve these models, with the general aim of facilitating their use to address industrial-level problems involving graph representations. Firstly, we propose two strategies to overcome the scalability issues of previous GAE and VGAE models, permitting to effectively train these models on large graphs with millions of nodes and edges. These strategies leverage graph degeneracy and stochastic subgraph decoding techniques, respectively. Besides, we introduce Gravity-Inspired GAE and VGAE, providing the first extensions of these models for directed graphs, that are ubiquitous in industrial applications. We also consider extensions of GAE and VGAE models for dynamic graphs. Furthermore, we argue that GAE and VGAE models are often unnecessarily complex, and we propose to simplify them by leveraging linear encoders. Lastly, we introduce Modularity-Aware GAE and VGAE to improve community detection on graphs, while jointly preserving good performances on link prediction. In the last part of this thesis, we evaluate our methods on several graphs extracted from the music streaming service Deezer. We put the emphasis on graph-based music recommendation problems. In particular, we show that our methods can improve the detection of communities of similar musical items to recommend to users, that they can effectively rank similar artists in a cold start setting, and that they permit modeling the music genre perception across cultures.