We identify pairs of (twisted) multiplicative Hitchin fibrations which are "dual" in the sense that their bases are identified and their generic fibres are dual Beilinson $1$-motives. More precisely, we match the following: (1) an untwisted multiplicative Hitchin fibration associated with a simply-laced semisimple group $G$ with an untwisted multiplicative Hitchin fibration associated with the Langlands dual group $G^\vee$; (2) a twisted multiplicative Hitchin fibration associated with a simply-laced and simply-connected semisimple group $G$, without factors of type $\mathsf{A}_{2\ell}$, and a diagram automorphism $\theta \in \mathrm{Aut}(G)$ with an untwisted multiplicative Hitchin fibration associated with the Langlands dual group $H^\vee$ of the invariant group $H=G^\theta$; (3) two twisted multiplicative Hitchin fibrations associated with $G=\mathrm{SL}_{2\ell +1}$ and two special automophisms of order $2$ and $4$, respectively. These results are consistent with a conjecture of Elliott and Pestun (arXiv:1812.05516).

We derive a lower bound, independent of the initial condition, for the solution of the KPZ equation on the torus through its representation as the value function of a (conditional) stochastic control problem. With the same techniques, we also prove a bound for its oscillation, again independent of initial conditions, from which a Harnack type inequality for the rough heat equation (on the torus) can be obtained.

Computing accurate yet efficient approximations to the solutions of the electronic Schr\"odinger equation has been a paramount challenge of computational chemistry for decades. Quantum Monte Carlo methods are a promising avenue of development as their core algorithm exhibits a number of favorable properties: it is highly parallel, and scales favorably with the considered system size, with an accuracy that is limited only by the choice of the wave function ansatz. The recently introduced machine-learned parametrizations of quantum Monte Carlo ansatzes rely on the efficiency of neural networks as universal function approximators to achieve state of the art accuracy on a variety of molecular systems. With interest in the field growing rapidly, there is a clear need for easy to use, modular, and extendable software libraries facilitating the development and adoption of this new class of methods. In this contribution, the DeepQMC program package is introduced, in an attempt to provide a common framework for future investigations by unifying many of the currently available deep-learning quantum Monte Carlo architectures. Furthermore, the manuscript provides a brief introduction to the methodology of variational quantum Monte Carlo in real space, highlights some technical challenges of optimizing neural network wave functions, and presents example black-box applications of the program package. We thereby intend to make this novel field accessible to a broader class of practitioners both from the quantum chemistry as well as the machine learning communities.

A generalized understanding of protein dynamics is an unsolved scientific problem, the solution of which is critical to the interpretation of the structure-function relationships that govern essential biological processes. Here, we approach this problem by constructing coarse-grained molecular potentials based on artificial neural networks and grounded in statistical mechanics. For training, we build a unique dataset of unbiased all-atom molecular dynamics simulations of approximately 9 ms for twelve different proteins with multiple secondary structure arrangements. The coarse-grained models are capable of accelerating the dynamics by more than three orders of magnitude while preserving the thermodynamics of the systems. Coarse-grained simulations identify relevant structural states in the ensemble with comparable energetics to the all-atom systems. Furthermore, we show that a single coarse-grained potential can integrate all twelve proteins and can capture experimental structural features of mutated proteins. These results indicate that machine learning coarse-grained potentials could provide a feasible approach to simulate and understand protein dynamics.

We introduce several improvements to the penalty-based variational quantum Monte Carlo (VMC) algorithm for computing electronic excited states of Entwistle $\textit{et al.}$ [M. T. Entwistle $\textit{et al.}$, Nat. Commun. $\textbf{14}$, 274 (2023)], and demonstrate that the accuracy of the updated method is competitive with other available excited-state VMC approaches. A theoretical comparison of the computational aspects of these algorithms is presented, where several benefits of the penalty-based method are identified. Our main contributions include an automatic mechanism for tuning the scale of the penalty terms, an updated form of the overlap penalty with proven convergence properties, and a new term that penalizes the spin of the wave function, enabling the selective computation of states with a given spin. With these improvements, along with the use of the latest self-attention-based ansatz, the penalty-based method achieves a mean absolute error below 1 kcal/mol for the vertical excitation energies of a set of 26 atoms and molecules, without relying on variance matching schemes. Considering excited states along the dissociation of the carbon dimer, the accuracy of the penalty-based method is on par with that of natural-excited-state (NES) VMC, while also providing results for larger sections of the potential energy surface. Additionally, the accuracy of the original penalty-based method is improved for a conical intersection of ethylene, with the predicted angle of the intersection agreeing well with both NES-VMC and multi-reference configuration interaction.

Planet host stars with well-constrained ages provide a rare window to the time domain of planet formation and evolution. The NASA K2 mission has enabled the discovery of the vast majority of known planets transiting stars in clusters, providing a valuable sample of planets with known ages and radii. We present the discovery of two planets transiting K2-264, an M2 dwarf in the intermediate age (600-800 Myr) Praesepe open cluster (also known as the Beehive Cluster, M44, or NGC 2632), which was observed by K2 during Campaign 16. The planets have orbital periods of 5.8 and 19.7 days, and radii of $2.2 \pm 0.2$ and $2.7 \pm 0.2$ $R_\oplus$, respectively, and their equilibrium temperatures are $496 \pm 10$ and $331 \pm 7$ $K$, making this a system of two warm sub-Neptunes. When placed in the context of known planets orbiting field stars of similar mass to K2-264, these planets do not appear to have significantly inflated radii, as has previously been noted for some cluster planets. As the second known system of multiple planets transiting a star in a cluster, K2-264 should be valuable for testing theories of photoevaporation in systems of multiple planets. Follow-up observations with current near-infrared (NIR) spectrographs could yield planet mass measurements, which would provide information about the mean densities and compositions of small planets soon after photoevaporation is expected to have finished. Follow-up NIR transit observations using Spitzer or large ground-based telescopes could yield improved radius estimates, further enhancing the characterization of these interesting planets.

We propose a novel wave function partitioning method that integrates deep-learning variational Monte Carlo with ansätze based on generalized product functions. This approach effectively separates electronic wave functions (WFs) into multiple partial WFs representing, for example, the core and valence domains or different electronic shells. Although our ansätze do not explicitly include correlations between individual electron groups, we show that they accurately reproduce the underlying physics and chemical properties, such as dissociation curve, dipole moment, reaction energy, ionization energy, or atomic sizes. We identify the optimal number of core electrons and define physical core sizes for Li to Mg atoms. Our results demonstrate that core electrons can be effectively decoupled from valence electrons. We show that the core part of the WF remains nearly constant across different molecules and their geometries, enabling the transfer and reuse of the core part in WFs of more complex systems. This work provides a general framework for WF decomposition, offering potential advantages in computing and studying larger systems, and possibly paving the way for ab-initio development of effective core potentials. Though currently limited to small molecules due to scaling, we highlight several directions for extending our method it to larger systems.

The International Semantic Web Research School (ISWS) is a week-long intensive program designed to immerse participants in the field. This document reports a collaborative effort performed by ten teams of students, each guided by a senior researcher as their mentor, attending ISWS 2023. Each team provided a different perspective to the topic of creative AI, substantiated by a set of research questions as the main subject of their investigation. The 2023 edition of ISWS focuses on the intersection of Semantic Web technologies and Creative AI. ISWS 2023 explored various intersections between Semantic Web technologies and creative AI. A key area of focus was the potential of LLMs as support tools for knowledge engineering. Participants also delved into the multifaceted applications of LLMs, including legal aspects of creative content production, humans in the loop, decentralised approaches to multimodal generative AI models, nanopublications and AI for personal scientific knowledge graphs, commonsense knowledge in automatic story and narrative completion, generative AI for art critique, prompt engineering, automatic music composition, commonsense prototyping and conceptual blending, and elicitation of tacit knowledge. As Large Language Models and semantic technologies continue to evolve, new exciting prospects are emerging: a future where the boundaries between creative expression and factual knowledge become increasingly permeable and porous, leading to a world of knowledge that is both informative and inspiring.

Obtaining accurate ground and low-lying excited states of electronic systems is crucial in a multitude of important applications. One ab initio method for solving the Schr\"odinger equation that scales favorably for large systems is variational quantum Monte Carlo (QMC). The recently introduced deep QMC approach uses ansatzes represented by deep neural networks and generates nearly exact ground-state solutions for molecules containing up to a few dozen electrons, with the potential to scale to much larger systems where other highly accurate methods are not feasible. In this paper, we extend one such ansatz (PauliNet) to compute electronic excited states. We demonstrate our method on various small atoms and molecules and consistently achieve high accuracy for low-lying states. To highlight the method's potential, we compute the first excited state of the much larger benzene molecule, as well as the conical intersection of ethylene, with PauliNet matching results of more expensive high-level methods.

We study the Fadell-Husseini index of the configuration space F(R^d,n) with respect to different subgroups of the symmetric group S_n. For p prime and d>0, we completely determine Index_{Z/p}(F(R^d,p);F_p) and partially describe Index{(Z/p)^k}(F(R^d,p^k);F_p). In this process we obtain results of independent interest, including: (1) an extended equivariant Goresky-MacPherson formula, (2) a complete description of the top homology of the partition lattice Pi_p as an F_p[Z_p]-module, and (3) a generalized Dold theorem for elementary abelian groups. The results on the Fadell-Husseini index yield a new proof of the Nandakumar & Ramana Rao conjecture for a prime. For n=p^k a prime power, we compute the Lusternik-Schnirelmann category cat(F(R^d,n)/S_n)=(d-1)(n-1). Moreover, we extend coincidence results related to the Borsuk-Ulam theorem, as obtained by Cohen & Connett, Cohen & Lusk, and Karasev & Volovikov.

Name-oriented networks introduce the vision of an information-centric, secure, globally available publish-subscribe infrastructure. Current approaches concentrate on unicast-based pull mechanisms and thereby fall short in automatically updating content at receivers. In this paper, we argue that an inclusion of multicast will grant additional benefits to the network layer, namely efficient distribution of real-time data, a many-to-many communication model, and simplified rendezvous processes. These aspects are comprehensively reflected by a group-oriented naming concept that integrates the various available group schemes and introduces new use cases. A first draft of this name-oriented multicast access has been implemented in the HAMcast middleware.

Machine learning and specifically deep-learning methods have outperformed human capabilities in many pattern recognition and data processing problems, in game playing, and now also play an increasingly important role in scientific discovery. A key application of machine learning in the molecular sciences is to learn potential energy surfaces or force fields from ab-initio solutions of the electronic Schr\"odinger equation using datasets obtained with density functional theory, coupled cluster, or other quantum chemistry methods. Here we review a recent and complementary approach: using machine learning to aid the direct solution of quantum chemistry problems from first principles. Specifically, we focus on quantum Monte Carlo (QMC) methods that use neural network ansatz functions in order to solve the electronic Schr\"odinger equation, both in first and second quantization, computing ground and excited states, and generalizing over multiple nuclear configurations. Compared to existing quantum chemistry methods, these new deep QMC methods have the potential to generate highly accurate solutions of the Schr\"odinger equation at relatively modest computational cost.

We investigate the representation of symmetric polynomials as a sum of squares. Since this task is solved using semidefinite programming tools we explore the geometric, algebraic, and computational implications of the presence of discrete symmetries in semidefinite programs. It is shown that symmetry exploitation allows a significant reduction in both matrix size and number of decision variables. This result is applied to semidefinite programs arising from the computation of sum of squares decompositions for multivariate polynomials. The results, reinterpreted from an invariant-theoretic viewpoint, provide a novel representation of a class of nonnegative symmetric polynomials. The main theorem states that an invariant sum of squares polynomial is a sum of inner products of pairs of matrices, whose entries are invariant polynomials. In these pairs, one of the matrices is computed based on the real irreducible representations of the group, and the other is a sum of squares matrix. The reduction techniques enable the numerical solution of large-scale instances, otherwise computationally infeasible to solve.

Although Virtual Reality (VR) has undoubtedly improved human interaction with 3D data, users still face difficulties retaining important details of complex digital objects in preparation for physical tasks. To address this issue, we evaluated the potential of visuohaptic integration to improve the memorability of virtual objects in immersive visualizations. In a user study (N=20), participants performed a delayed match-to-sample task where they memorized stimuli of visual, haptic, or visuohaptic encoding conditions. We assessed performance differences between these encoding modalities through error rates and response times. We found that visuohaptic encoding significantly improved memorization accuracy compared to unimodal visual and haptic conditions. Our analysis indicates that integrating haptics into immersive visualizations enhances the memorability of digital objects. We discuss its implications for the optimal encoding design in VR applications that assist professionals who need to memorize and recall virtual objects in their daily work.

We present a polynomial-time reduction from max-average constraints to the feasibility problem for semidefinite programs. This shows that Condon's simple stochastic games, stochastic mean payoff games, and in particular mean payoff games and parity games can all be reduced to semidefinite programming.

Tracking mouse body parts in video is often incomplete due to occlusions such that - e.g. - subsequent action and behavior analysis is impeded. In this conceptual work, videos from several perspectives are integrated via global exterior camera orientation; body part positions are estimated by 3D triangulation and bundle adjustment. Consistency of overall 3D track reconstruction is achieved by introduction of a 3D mouse model, deep-learned body part movements, and global motion-track smoothness constraint. The resulting 3D body and body part track estimates are substantially more complete than the original single-frame-based body part detection, therefore, allowing improved animal behavior analysis.

We report the discovery of a new ultra-short period hot Jupiter from the Next Generation Transit Survey. NGTS-6b orbits its star with a period of 21.17~h, and has a mass and radius of $1.330^{+0.024}_{-0.028}$\mjup\, and $1.271^{+0.197}_{-0.188}$\rjup\, respectively, returning a planetary bulk density of 0.711$^{+0.214}_{-0.136}$~g~cm$^{-3}$. Conforming to the currently known small population of ultra-short period hot Jupiters, the planet appears to orbit a metal-rich star ([Fe/H]$=+0.11\pm0.09$~dex). Photoevaporation models suggest the planet should have lost 5\% of its gaseous atmosphere over the course of the 9.6~Gyrs of evolution of the system. NGTS-6b adds to the small, but growing list of ultra-short period gas giant planets, and will help us to understand the dominant formation and evolutionary mechanisms that govern this population.

In the framework of time series analysis with recurrence networks, we introduce a self-adaptive method that determines the elusive recurrence threshold and identifies metastable states in complex real-world time series. As initial step, we introduce a way to set the embedding parameters used to reconstruct the state space from the time series. We set them as the ones giving the maximum Shannon entropy for the first simultaneous minima of recurrence rate and Shannon entropy. To identify metastable states, as well as the transitions between them, we use a soft partitioning algorithm for module finding which is specifically developed for the case in which a system shows metastability. We illustrate our method with two complex time series examples. Finally, we show the robustness of our method for identifying metastable states. Our results suggest that our method is robust for identifying metastable states in complex time series, even when introducing considerable levels of noise and missing data points.

Characterizing macromolecular kinetics from molecular dynamics (MD) simulations requires a distance metric that can distinguish slowly-interconverting states. Here we build upon diffusion map theory and define a kinetic distance for irreducible Markov processes that quantifies how slowly molecular conformations interconvert. The kinetic distance can be computed given a model that approximates the eigenvalues and eigenvectors (reaction coordinates) of the MD Markov operator. Here we employ the time-lagged independent component analysis (TICA). The TICA components can be scaled to provide a kinetic map in which the Euclidean distance corresponds to the kinetic distance. As a result, the question of how many TICA dimensions should be kept in a dimensionality reduction approach becomes obsolete, and one parameter less needs to be specified in the kinetic model construction. We demonstrate the approach using TICA and Markov state model (MSM) analyses for illustrative models, protein conformation dynamics in bovine pancreatic trypsin inhibitor and protein-inhibitor association in trypsin and benzamidine.