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Background Advanced adaptive randomised clinical trials are increasingly used. Compared to their conventional counterparts, their flexibility may make them more efficient, increase the probability of obtaining conclusive results without larger samples than necessary, and increase the probability that individual participants are allocated to more promising interventions. However, limited guidance is available on designing and evaluating the performance of advanced adaptive trials. Methods We summarise the methodological considerations and provide practical guidance on the entire workflow of planning and evaluating advanced adaptive trials using adaptive stopping, adaptive arm dropping, and response-adaptive randomisation within a Bayesian statistical framework. Results This comprehensive practical guide covers the key methodological decisions for advanced adaptive trials and their specification and evaluation using statistical simulation. These considerations include interventions and common control use; outcome type and generation; analysis timing and outcome-data lag; allocation rules; analysis model; adaptation rules for stopping and arm dropping; clinical scenarios assessed; performance metrics; calibration; sensitivity analyses; and reporting. The considerations are covered in the context of realistic examples, along with simulation code using the adaptr R package. Conclusions This practical guide will help clinical trialists, methodologists, and biostatisticians design and evaluate advanced adaptive trials., Comment: 63 pages (30 without appendices), 5 figures (3 without appendices), 3 tables

Machine learning (ML) systems have become vital in the mobile gaming industry. Companies like King have been using them in production to optimize various parts of the gaming experience. One important area is in-app purchases: purchases made in the game by players in order to enhance and customize their gameplay experience. In this work we describe how we developed an ML system in order to predict when a player is expected to make their next in-app purchase. These predictions are used to present offers to players. We briefly describe the problem definition, modeling approach and results and then, in considerable detail, outline the end-to-end ML system. We conclude with a reflection on challenges encountered and plans for future work.

Influenced by the complexity of volumetric imaging, there is a shortage of established datasets useful for benchmarking volumetric deep-learning models. As a consequence, new and existing models are not easily comparable, limiting the development of architectures optimized specifically for volumetric data. To counteract this trend, we introduce MozzaVID - a large, clean, and versatile volumetric classification dataset. Our dataset contains X-ray computed tomography (CT) images of mozzarella microstructure and enables the classification of 25 cheese types and 149 cheese samples. We provide data in three different resolutions, resulting in three dataset instances containing from 591 to 37,824 images. While being general-purpose, the dataset also facilitates investigating mozzarella structure properties. The structure of food directly affects its functional properties and thus its consumption experience. Understanding food structure helps tune the production and mimicking it enables sustainable alternatives to animal-derived food products. The complex and disordered nature of food structures brings a unique challenge, where a choice of appropriate imaging method, scale, and sample size is not trivial. With this dataset we aim to address these complexities, contributing to more robust structural analysis models. The dataset can be downloaded from: https://archive.compute.dtu.dk/files/public/projects/MozzaVID/.

Isolation levels, consistency guarantees among concurrently execution transactions in local- and distributed systems, have been formalized in a number of models. Thus far, no model can reason about executable implementations of databases or local transaction libraries providing weak isolation levels. Weak isolation levels are characterized by being highly concurrent and, unlike their stronger counterpart serializability, they are not equivalent to the consistency guarantees provided by a transaction library implemented using a global lock. In this paper, we formalize three weak isolation levels in separation logic, namely read uncommitted, read committed, and snapshot isolation. We define modular separation logic specifications that are independent of the underlying transaction library implementation. Historically, isolation levels have been specified using examples of executions between concurrent transactions that are not allowed to occur, and we demonstrate that our specifications correctly prohibit such examples. To show that our specifications are realizable, we formally verify that an executable implementation of a key-value database running the multi-version concurrency control algorithm from the original snapshot isolation paper satisfies our specification of snapshot isolation. Moreover, we prove implications between the specifications -- snapshot isolation implies read committed and read committed implies read uncommitted -- and thus the verification effort of the database serves as proof that all of our specifications are realizable. All results are mechanised in the Coq proof assistant on top of the Iris separation logic framework.

We propose a nanodevice based on multi-terminal Josephson junctions for the creation and detection of poor man's Majorana (PMM) modes. The device consists of a double three-terminal Josephson junction (3TJJ) embedded in a planar semiconductor that engineers a two-site Kitaev chain. We identify the conditions necessary for the emergence of PMM modes by precisely tuning the superconducting phases of the terminals and the inter-junction coupling between the 3TJJs. To validate our findings, we perform numerical simulations that account for disorder in a more general geometry, and test experimentally feasible protocols based on conductance measurements to reliably detect these modes. Unlike traditional approaches that rely on magnetic fields, our design eliminates the need for such fields, potentially increasing the energy-level resolution and significantly expanding the range of compatible semiconductor materials, such as Ge-based heterostructures., Comment: 19 pages, 9 figures

These notes contain -- apart from some physics -- scattered reminiscences of everyday life at the Institute for Theoretical Physics in G\"oteborg in the early eighties. The text has been in the making for many years. Some of it was written inspired by the Lars Brink 70-fest at The Solvay Institute in Brussels in 2014, but was never finished or published. Parts of the old text has now been replaced by a review of the quite unexpected recent renaissance for light-front higher spin theory. Lars sadly did not live to experience more than the very beginnings of this quite remarkable development. The text was finalized in the spring of 2023., Comment: Contribution to a memorial volume for Lars Brink, to be published by World Scientific

This papers consider a two terminal problem, where Alice and Bob jointly want to perform a measurement on a bipartite quantum system \(\rho^{AB}\). Alice can transmit the results of her measurements to Bob on a classical channel, and Alice and Bob have common randomness. The question is what is the minimum amount of communications and common randomness needed. The paper derives an achievable rate region.

Machine learning (ML) has the potential to revolutionize various domains, but its adoption is often hindered by the disconnect between the needs of domain experts and translating these needs into robust and valid ML tools. Despite recent advances in LLM-based co-pilots to democratize ML for non-technical domain experts, these systems remain predominantly focused on model-centric aspects while overlooking critical data-centric challenges. This limitation is problematic in complex real-world settings where raw data often contains complex issues, such as missing values, label noise, and domain-specific nuances requiring tailored handling. To address this we introduce CliMB-DC, a human-guided, data-centric framework for LLM co-pilots that combines advanced data-centric tools with LLM-driven reasoning to enable robust, context-aware data processing. At its core, CliMB-DC introduces a novel, multi-agent reasoning system that combines a strategic coordinator for dynamic planning and adaptation with a specialized worker agent for precise execution. Domain expertise is then systematically incorporated to guide the reasoning process using a human-in-the-loop approach. To guide development, we formalize a taxonomy of key data-centric challenges that co-pilots must address. Thereafter, to address the dimensions of the taxonomy, we integrate state-of-the-art data-centric tools into an extensible, open-source architecture, facilitating the addition of new tools from the research community. Empirically, using real-world healthcare datasets we demonstrate CliMB-DC's ability to transform uncurated datasets into ML-ready formats, significantly outperforming existing co-pilot baselines for handling data-centric challenges. CliMB-DC promises to empower domain experts from diverse domains -- healthcare, finance, social sciences and more -- to actively participate in driving real-world impact using ML., Comment: Saveliev, Liu & Seedat contributed equally

Bootstrapping is often applied to get confidence limits for semiparametric inference of a target parameter in the presence of nuisance parameters. Bootstrapping with replacement can be computationally expensive and problematic when cross-validation is used in the estimation algorithm due to duplicate observations in the bootstrap samples. We provide a valid, fast, easy-to-implement subsampling bootstrap method for constructing confidence intervals for asymptotically linear estimators and discuss its application to semiparametric causal inference. Our method, inspired by the Cheap Bootstrap (Lam, 2022), leverages the quantiles of a t-distribution and has the desired coverage with few bootstrap replications. We show that the method is asymptotically valid if the subsample size is chosen appropriately as a function of the sample size. We illustrate our method with data from the LEADER trial (Marso et al., 2016), obtaining confidence intervals for a longitudinal targeted minimum loss-based estimator (van der Laan and Gruber, 2012). Through a series of empirical experiments, we also explore the impact of subsample size, sample size, and the number of bootstrap repetitions on the performance of the confidence interval.

We present a method for augmenting a Large Language Model (LLM) with a combination of text and visual data to enable accurate question answering in visualization of scientific data, making conversational visualization possible. LLMs struggle with tasks like visual data interaction, as they lack contextual visual information. We address this problem by merging a text description of a visualization and dataset with snapshots of the visualization. We extract their essential features into a structured text file, highly compact, yet descriptive enough to appropriately augment the LLM with contextual information, without any fine-tuning. This approach can be applied to any visualization that is already finally rendered, as long as it is associated with some textual description.

We explore scattering amplitudes on the Coulomb branch of maximally supersymmetric Yang-Mills theory. We introduce a particular pattern of scalar vacuum expectation values that allow us to define amplitudes with a different mass pattern compared to what was studied previously. This is motivated by an extension of the Amplituhedron that leads to infrared-finite four-particle amplitudes involving massive particles. We work out the Feynman rules on the Coulomb branch and use them, together with generalized unitarity techniques, to perform consistency checks on the Amplituhedron expectations for the one- and two-loop integrands for the four-particle amplitude. We present details of the computation of the required two-loop four-point integrals via a four-dimensional version of the differential equations method. Finally, we study the Regge limit of the four-point amplitude, including the first power suppressed terms. We find that when organized in terms of a suitable expansion parameter, the subleading power term exponentiates, with the exponent matching the anomalous dimension of a cusped Wilson line with a local operator insertion. The latter is known from integrability, which leads to a prediction at higher loop orders in the Regge limit., Comment: 36 pages, 4 figures, 4 ancillary files + readme

Purpose : Planning a transition towards sustainable carbon neutrality at the organization level raises several accounting challenges. This paper aims to shed light on key challenges, highlight answers from current accounting standards and guidance, point out potential inconsistencies or limits, and outline potential solutions from the industrial ecology community through systemic environmental assessment tools, such as life cycle assessment (LCA) and environmentally-extended input-output (EEIO) analysis. Results and discussion: We propose a Measure-Reduce-Neutralize-Control sequence allowing organizations to plan their sustainable net-zero strategy, and discuss 24 accounting challenges occurring within this sequence. We then outline ways forward for organizations planning their carbon neutrality trajectory, pointing to existing resources, and for guidelines providers and the industrial ecology communities to address current limitations in the development of future accounting methods and guidelines. Overarching solutions to many accounting issues are to develop comprehensive, open-source, and high-quality life cycle inventory databases, to enable improved dynamic assessments and prospective LCA through integrated assessment models, to refine methods for assessing mineral scarcity and environmental impacts, the supply in some metals being expected to be a bottleneck to the energy transition, and to identify the appropriate climate metrics for planning sustainable carbon neutrality pathways at the organizational level.

In this paper, we reschedule the duties of train drivers one day before the operation. Due to absent drivers (e.g., because of sick leave), some trains have no driver. Thus, duties need to be rescheduled for the day of operation. We start with a feasible crew schedule for each of the remaining operating drivers, a set of unassigned tasks originally assigned to the absent drivers, and a group of standby drivers with fixed start time, end time, start depot, and end depot. Our aim is to generate a crew schedule with as few canceled or changed tasks as possible. We present a tabu-search-based approach for crew rescheduling. We also adapt a column-generation approach with the same objective function and equivalent restrictions as the benchmark for comparing the results, computational time, and space usage. Our tabu-search-based approach needs both less computation time and space than the column-generation approach to compute an acceptable result. We further test the performance of our approach under different settings. The data used in the experiments originated from a regional passenger-train system around Stockholm, Sweden and was provided by M\"alart\r{a}g.

The vertical shear instability and the streaming instability are two robust sources of turbulence in protoplanetary disks. The former has been found to induce anisotropic turbulence that is stronger in the vertical than in the radial dimension and to be overall stronger compared to the largely isotropic turbulence caused by the streaming instability. In this study, we shed light on the dust diffusion by the vertical shear instability and the streaming instability separately and together, and in particular on the direction- and scale-dependence of the diffusion. To this end, we employ two-dimensional global models of the two instabilities either in isolation or in combination. The vertical shear instability in isolation diffuses dust more strongly in the vertical direction than the streaming instability in isolation, resulting in a wave-shaped dust layer in our two-dimensional simulations. Compared with this large-scale diffusion, though, our study highlights that the vertical shear instability causes substantially weaker or even negligible small-scale diffusion. We validate this result using previously published three-dimensional simulations. In particular when simulating centimetre-sized dust, the undulating dust layer becomes internally razor-thin. In contrast, the diffusion owing to the streaming instability exhibits only a marginal scale-dependence, with the dust layer possessing a Gaussian shape. In models including both instabilities, the undulating mid-plane layer is broadened to a width set by the intrinsic diffusion level caused by the streaming instability., Comment: 15 pages, 8 figures, 2 tables; accepted for publication in Astronomy & Astrophysics

For any arc-weighted oriented graph $D=(V(D), A(D),w)$, we write ${\rm fas}_w(D)$ to denote the minimum weight of a feedback arc set in $D$. In this paper, we consider upper bounds on ${\rm fas}_w(D)$ for arc-weight oriented graphs $D$ with bounded maximum degrees and directed girth. We obtain such bounds by introducing a new parameter ${\rm fasd}(D)$, which is the maximum integer such that $A(D)$ can be partitioned into ${\rm fasd}(D)$ feedback arc sets. This new parameter seems to be interesting in its own right. We obtain several bounds for both ${\rm fas}_w(D)$ and ${\rm fasd}(D)$ when $D$ has maximum degree $\Delta(D)\le \Delta$ and directed girth $g(D)\geq g$. In particular, we show that if $\Delta(D)\leq~4$ and $g(D)\geq 3$, then ${\rm fasd}(D) \geq 3$ and therefore ${\rm fas}_w(D)\leq \frac{w(D)}{3}$ which generalizes a tight bound for an unweighted oriented graph with maximum degree at most 4. We also show that ${\rm fasd}(D)\geq g$ and ${\rm fas}_w(D) \leq \frac{w(D)}{g}$ if $\Delta(D)\leq 3$ and $g(D)\geq g$ for $g\in \{3,4,5\}$ and these bounds are tight. However, for $g=10$ the bound ${\rm fasd}(D)\geq g$ does not always hold when $\Delta(D)\leq 3$. Finally we give some bounds for the cases when $\Delta$ or $g$ are large.

Erd{\H o}s (1963) initiated extensive graph discrepancy research on 2-edge-colored graphs. Gishboliner, Krivelevich, and Michaeli (2023) launched similar research on oriented graphs. They conjectured the following generalization of Dirac's theorem: If the minimum degree $\delta$ of an $n$-vertex oriented graph $G$ is greater or equal to $n/2$,then $G$ has a Hamilton oriented cycle with at least $\delta$ forward arcs. This conjecture was proved by Freschi and Lo (2024) who posed an open problem to extend their result to an Ore-type condition. We propose two conjectures for such extensions and prove some results which provide support to the conjectures. For forward arc maximization on Hamilton oriented cycles and paths in semicomplete multipartite digraphs and locally semicomplete digraphs, we obtain characterizations which lead to polynomial-time algorithms.

In this paper we study the evolution of radiative fluxes, flux radii and observable dust masses in protoplanetary discs, in order to understand how these depend on the angular momentum budget and on the assumed heat sources. We use a model that includes the formation and viscous evolution of protoplanetary gas discs, together with the growth and radial drift of the dust component. We find that we are best able to match the observed fluxes and radii of class 0/I discs when we assume (i) an initial total angular momentum budget corresponding to a centrifugal radius of 40 au around solar-like stars, and (ii) inefficient viscous heating. Fluxes and radii of class II discs appear consistent with disc models with angular momentum budgets equivalent to centrifugal radii of both 40 au or 10 au for solar like stars, and with models where viscous heating occurs at either full efficiency or at reduced efficiency. During the first 0.5 Myr of their evolution discs are generally optically thick at a wavelength of 1.3 mm. However, after this discs are optically thin at mm-wavelengths, supporting standard means of dust mass estimates. Using a disc population synthesis model, we then show that the evolution of the cumulative evolution of the observable dust masses agrees well with that observed in young star forming clusters of different ages., Comment: 12 pagers, 12 figures

Carnot famously showed that engine operation is chiefly characterised by the magnitude of the temperature ratio $T_\mathrm{h}/T_\mathrm{c}$ between its hot and cold reservoirs. While temperature ratios ranging between $1.3-2.8$ and $2-10$ are common in macroscopic commercial engines and engines operating in the microscopic regime, respectively, the quest is to test thermodynamics at its extremes. Here we present the hottest engine on earth, with temperature ratios as high as $110$. We achieve this by realising an underdamped single-particle engine using a charged microparticle that is electrically levitated under vacuum conditions. Noisy electric fields are used to synthesise reservoir temperatures in excess of $10^7$ K. As a result, giant fluctuations show up in all thermodynamic quantities of the engine, such as heat exchange and efficiency. Moreover, we find that the particle experiences an effective position dependent temperature, which gives rise to dynamics that drastically deviates from that of standard Brownian motion. We develop a theoretical model accounting for the effects of this multiplicative noise and find excellent agreement with the measured dynamics. The high level of control over the presented experimental platform opens the door to emulate the stochastic dynamics of cellular and biological processes, and provides thermodynamic insight required for the development of nanotechnologies.

Big data presents potential but unresolved value as a source for analysis and inference. However,selection bias, present in many of these datasets, needs to be accounted for so that appropriate inferences can be made on the target population. One way of approaching the selection bias issue is to first estimate the propensity of inclusion in the big dataset for each member of the big dataset, and then to apply these propensities in an inverse probability weighting approach to produce population estimates. In this paper, we provide details of a new variant of existing propensity score estimation methods that takes advantage of the ability to integrate the big data with a probability sample. We compare the ability of this method to produce efficient inferences for the target population with several alternative methods through an empirical study., Comment: Paper presented at the 2024 International Conference on Establishment Statistics in Glasgow, United Kingdom

Charge transport in materials has an impact on a wide range of devices based on semiconductor, battery or superconductor technology. Charge transport in sliding Charge Density Waves (CDW) differs from all others in that the atomic lattice is directly involved in the transport process. To obtain an overall picture of the structural changes associated to the collective transport, the large coherent X-ray beam generated by an X-ray free-electron laser (XFEL) source was used. The CDW phase can be retrieved over the entire sample from diffracted intensities using a genetic algorithm. For currents below threshold, increasing shear deformation is observed in the central part of the sample while longitudinal deformation appears above threshold when shear relaxes. Shear thus precedes longitudinal deformation, with relaxation of one leading to the appearance of the other. Moreover, strain accumulates on surface steps in the sliding regime, demonstrating the strong pinning character of these surface discontinuities. The sliding process of nanometric CDW is based on an impressive spatial coherence involving the macroscopic sample dimensions., Comment: 20 pages, 5 figures

The complexity of modern electro-mechanical systems require the development of sophisticated diagnostic methods like anomaly detection capable of detecting deviations. Conventional anomaly detection approaches like signal processing and statistical modelling often struggle to effectively handle the intricacies of complex systems, particularly when dealing with multi-variate signals. In contrast, neural network-based anomaly detection methods, especially Auto-Encoders, have emerged as a compelling alternative, demonstrating remarkable performance. However, Auto-Encoders exhibit inherent opaqueness in their decision-making processes, hindering their practical implementation at scale. Addressing this opacity is essential for enhancing the interpretability and trustworthiness of anomaly detection models. In this work, we address this challenge by employing a feature selector to select features and counterfactual explanations to give a context to the model output. We tested this approach on the SKAB benchmark dataset and an industrial time-series dataset. The gradient based counterfactual explanation approach was evaluated via validity, sparsity and distance measures. Our experimental findings illustrate that our proposed counterfactual approach can offer meaningful and valuable insights into the model decision-making process, by explaining fewer signals compared to conventional approaches. These insights enhance the trustworthiness and interpretability of anomaly detection models., Comment: 8 pages, 6 figures, 6 tables, conference proceeding

We prove the following local strengthening of Shearer's classic bound on the independence number of triangle-free graphs: For every triangle-free graph $G$ there exists a probability distribution on its independent sets such that every vertex $v$ of $G$ is contained in a random independent set drawn from the distribution with probability $(1-o(1))\frac{\ln d(v)}{d(v)}$. This resolves the main conjecture raised by Kelly and Postle (2018) about fractional coloring with local demands, which in turn confirms a conjecture by Cames van Batenburg et al. (2018) stating that every $n$-vertex triangle-free graph has fractional chromatic number at most $(\sqrt{2}+o(1))\sqrt{\frac{n}{\ln(n)}}$. Addressing another conjecture posed by Cames van Batenburg et al., we also establish an analogous upper bound in terms of the number of edges. To prove these results we establish a more general technical theorem that works in a weighted setting. As a further application of this more general result, we obtain a new spectral upper bound on the fractional chromatic number of triangle-free graphs: We show that every triangle-free graph $G$ satisfies $\chi_f(G)\le (1+o(1))\frac{\rho(G)}{\ln \rho(G)}$ where $\rho(G)$ denotes the spectral radius. This improves the bound implied by Wilf's classic spectral estimate for the chromatic number by a $\ln \rho(G)$ factor and makes progress towards a conjecture of Harris on fractional coloring of degenerate graphs., Comment: 11 pages, comments welcome

Ergotropy -- the maximal amount of unitarily extractable work -- measures the ``charge level'' of quantum batteries. We prove that in large many-body batteries ergotropy exhibits a concentration of measure phenomenon. Namely, the ergotropy of such systems is almost constant for almost all states sampled from the Hilbert--Schmidt measure. We establish this by first proving that ergotropy, as a function of the state, is Lipschitz-continuous with respect to the Bures distance, and then applying Levy's measure concentration lemma. In parallel, we showcase the analogous properties of von Neumann entropy, compiling and adapting known results about its continuity and concentration properties. Furthermore, we consider the situation with the least amount of prior information about the state. This corresponds to the quantum version of the Jeffreys prior distribution -- the Bures measure. In this case, there exist no analytical bounds guaranteeing exponential concentration of measure. Nonetheless, we provide numerical evidence that ergotropy, as well as von Neumann entropy, concentrate also in this case., Comment: 8+4 pages, 2 figures; comments are welcome

We study reinforcement learning (RL) for decision processes with non-Markovian reward, in which high-level knowledge of the task in the form of reward machines is available to the learner. We consider probabilistic reward machines with initially unknown dynamics, and investigate RL under the average-reward criterion, where the learning performance is assessed through the notion of regret. Our main algorithmic contribution is a model-based RL algorithm for decision processes involving probabilistic reward machines that is capable of exploiting the structure induced by such machines. We further derive high-probability and non-asymptotic bounds on its regret and demonstrate the gain in terms of regret over existing algorithms that could be applied, but obliviously to the structure. We also present a regret lower bound for the studied setting. To the best of our knowledge, the proposed algorithm constitutes the first attempt to tailor and analyze regret specifically for RL with probabilistic reward machines., Comment: 35 pages

Accurate uncertainty information associated with essential climate variables (ECVs) is crucial for reliable climate modeling and understanding the spatiotemporal evolution of the Earth system. In recent years, geoscience and climate scientists have benefited from rapid progress in deep learning to advance the estimation of ECV products with improved accuracy. However, the quantification of uncertainties associated with the output of such deep learning models has yet to be thoroughly adopted. This survey explores the types of uncertainties associated with ECVs estimated from deep learning and the techniques to quantify them. The focus is on highlighting the importance of quantifying uncertainties inherent in ECV estimates, considering the dynamic and multifaceted nature of climate data. The survey starts by clarifying the definition of aleatoric and epistemic uncertainties and their roles in a typical satellite observation processing workflow, followed by bridging the gap between conventional statistical and deep learning views on uncertainties. Then, we comprehensively review the existing techniques for quantifying uncertainties associated with deep learning algorithms, focusing on their application in ECV studies. The specific need for modification to fit the requirements from both the Earth observation side and the deep learning side in such interdisciplinary tasks is discussed. Finally, we demonstrate our findings with two ECV examples, snow cover and terrestrial water storage, and provide our perspectives for future research.

An adaptive data-driven controller is proposed and analysed for the class of infinite-horizon optimal control of positive linear system problems presented in [1]. This controller is synthesized from the solution of a "data-driven algebraic equation" constructed from the model-free Bellman equation used in Q-learning. This algebraic equation is driven by data correlation matrices that does not scale in the number of data points, making for an efficient online implementation. As a result, a sufficient condition that ensures stability and robustness against unmodeled dynamics in the plant is extracted. The derived results also allows for a quantitative characterization of the interplay between explorations and robustness to unmodeled dynamics. The class of optimal control problems considered here bears equivalence to Stochastic Shortest Path (SSP) problems, allowing for a performance comparison between the proposed adaptive policy and model-free algorithms for learning the stochastic shortest path, as presented in the numerical experiment., Comment: Submitted to L4DC

Longitudinal imaging allows for the study of structural changes over time. One approach to detecting such changes is by non-linear image registration. This study introduces Multi-Session Temporal Registration (MUSTER), a novel method that facilitates longitudinal analysis of changes in extended series of medical images. MUSTER improves upon conventional pairwise registration by incorporating more than two imaging sessions to recover longitudinal deformations. Longitudinal analysis at a voxel-level is challenging due to effects of a changing image contrast as well as instrumental and environmental sources of bias between sessions. We show that local normalized cross-correlation as an image similarity metric leads to biased results and propose a robust alternative. We test the performance of MUSTER on a synthetic multi-site, multi-session neuroimaging dataset and show that, in various scenarios, using MUSTER significantly enhances the estimated deformations relative to pairwise registration. Additionally, we apply MUSTER on a sample of older adults from the Alzheimer's Disease Neuroimaging Initiative (ADNI) study. The results show that MUSTER can effectively identify patterns of neuro-degeneration from T1-weighted images and that these changes correlate with changes in cognition, matching the performance of state of the art segmentation methods. By leveraging GPU acceleration, MUSTER efficiently handles large datasets, making it feasible also in situations with limited computational resources.

We study the dynamic structure factor $S(k,\omega)$ of the spin-1/2 chain with long-range, power-law decaying unfrustrated (sign alternating) Heisenberg interactions $J_r \sim (-1)^{r-1} r^{-\alpha}$ by means of stochastic analytic continuation (SAC) of imaginary-time correlations computed by quantum Monte Carlo calculations. We do so in both the long-range antiferromagnetic (AFM, for $\alpha \lesssim 2.23$) and quasi ordered (QLRO, for $\alpha \gtrsim 2.23$) ground-state phases, employing different SAC parametrizations of $S(k,\omega)$ to resolve sharp edges characteristic of fractional quasi-particles and sharp peaks expected with conventional quasi-particles. In order to identify the most statistically accurate parametrization, we apply a newly developed cross-validation method as "model selection" tool. We confirm that the spectral function contains a power-law divergent edge in the QLRO phase and a very sharp (likely $\delta$-function) magnon peak in the AFM phase. From our SAC results, we extract the dispersion relation in the different regimes of the model, and in the AFM phase, we extract the weight of the magnon pole. In the limit where the model reduces to the conventional Heisenberg chain with nearest-neighbor interactions, our $S(k,\omega)$ agrees well with known Bethe ansatz results. In the AFM phase the low-energy dispersion relation is known to be nonlinear, $\omega_k \sim k^z$, and we extract the corresponding dynamic exponent $z(\alpha)$, which in general is somewhat above the form obtained in linear spin-wave theory. We also find a significant continuum above the magnon peak. This study serves as a benchmark for SAC/QMC studies of systems with a transition from conventional to fractionalized quasi-particles., Comment: 22 pages, 28 figures

The continuous scaling of metal-oxide-semiconductor field-effect transistors (MOSFETs) has led to device geometries where charged carriers are increasingly confined to ever smaller channel cross sections. This development is associated with reduced screening of long-range Coulomb interactions. To accurately predict the behavior of such ultra-scaled devices, electron-electron (e-e) interactions must be explicitly incorporated in their quantum transport simulation. In this paper, we present an \textit{ab initio} atomistic simulation framework based on density functional theory, the non-equilibrium Green's function formalism, and the self-consistent GW approximation to perform this task. The implemented method is first validated with a carbon nanotube test structure before being applied to calculate the transfer characteristics of a silicon nanowire MOSFET in a gate-all-around configuration. As a consequence of e-e scattering, the energy and spatial distribution of the carrier and current densities both significantly change, while the on-current of the transistor decreases owing to the Coulomb repulsion between the electrons. Furthermore, we demonstrate how the resulting bandgap modulation of the nanowire channel as a function of the gate-to-source voltage could potentially improve the device performance. To the best of our knowledge, this study is the first one reporting large-scale atomistic quantum transport simulations of nano-devices under non-equilibrium conditions and in the presence of e-e interactions within the GW approximation.

Functional methods can be applied to the quantum effective action to efficiently determine counterterms and matching conditions for effective field theories. We extend the toolbox to two-loop order and beyond and show how to evaluate the expansion of the path integral in a manifestly gauge-covariant manner. We also generalize the method to theories with mixed spin statistics and prove the validity of the hard-region matching formula to all loop orders. The methods are exemplified with a two-loop matching calculation of the Euler-Heisenberg Lagrangian resulting from decoupling the electron in QED., Comment: 63 pages, 5 figures

Mixed integer linear programming (MILP) solvers ship with a staggering number of parameters that are challenging to select a priori for all but expert optimization users, but can have an outsized impact on the performance of the MILP solver. Existing machine learning (ML) approaches to configure solvers require training ML models by solving thousands of related MILP instances, generalize poorly to new problem sizes, and often require implementing complex ML pipelines and custom solver interfaces that can be difficult to integrate into existing optimization workflows. In this paper, we introduce a new LLM-based framework to configure which cutting plane separators to use for a given MILP problem with little to no training data based on characteristics of the instance, such as a natural language description of the problem and the associated LaTeX formulation. We augment these LLMs with descriptions of cutting plane separators available in a given solver, grounded by summarizing the existing research literature on separators. While individual solver configurations have a large variance in performance, we present a novel ensembling strategy that clusters and aggregates configurations to create a small portfolio of high-performing configurations. Our LLM-based methodology requires no custom solver interface, can find a high-performing configuration by solving only a small number of MILPs, and can generate the configuration with simple API calls that run in under a second. Numerical results show our approach is competitive with existing configuration approaches on a suite of classic combinatorial optimization problems and real-world datasets with only a fraction of the training data and computation time.

Structure determination is essential to a mechanistic understanding of diseases and the development of novel therapeutics. Machine-learning-based structure prediction methods have made significant advancements by computationally predicting protein and bioassembly structures from sequences and molecular topology alone. Despite substantial progress in the field, challenges remain to deliver structure prediction models to real-world drug discovery. Here, we present NeuralPLexer3 -- a physics-inspired flow-based generative model that achieves state-of-the-art prediction accuracy on key biomolecular interaction types and improves training and sampling efficiency compared to its predecessors and alternative methodologies. Examined through newly developed benchmarking strategies, NeuralPLexer3 excels in vital areas that are crucial to structure-based drug design, such as physical validity and ligand-induced conformational changes.

Decision trees are a popular machine learning method, known for their inherent explainability. In Explainable AI, decision trees can be used as surrogate models for complex black box AI models or as approximations of parts of such models. A key challenge of this approach is determining how accurately the extracted decision tree represents the original model and to what extent it can be trusted as an approximation of their behavior. In this work, we investigate the use of the Probably Approximately Correct (PAC) framework to provide a theoretical guarantee of fidelity for decision trees extracted from AI models. Based on theoretical results from the PAC framework, we adapt a decision tree algorithm to ensure a PAC guarantee under certain conditions. We focus on binary classification and conduct experiments where we extract decision trees from BERT-based language models with PAC guarantees. Our results indicate occupational gender bias in these models., Comment: Accepted at AAAI 2025

We study the single photon purity of a resonantly driven single-photon source in the realistic scenario where the excitation laser can leak into the detection path. We find that the duration of the excitation pulse strongly influences the quality of the single-photon source. We calculate the influence of this on the effective parameters describing the most relevant properties, including the two-photon component and Hong-Ou-Mandel (HOM) visibility. Furthermore, we analyze how these properties can be strongly affected by frequency filtering of the outgoing field. Our results highlight that the relation between the two-photon component of the emission and the HOM visibility is more complicated than typically assumed in the literature, and depends on the specific details of the source., Comment: 14 pages, 9 figures + appendix

Graph states are the key resources for measurement- and fusion-based quantum computing with photons, yet their creation is experimentally challenging. We optimize a hybrid graph-state generation scheme using a single quantum emitter and linear optics Bell-state measurements, called fusions. We first generate a restricted class of states from a single quantum emitter and then apply fusions to create a target graph state, where we use a dynamic programming approach to find the construction that requires the lowest possible number of fusions. Our analysis yields a lookup table for constructing $\sim 2.8\times 10^7$ non-isomorphic graph states with the minimum number of fusions. The lookup table covers all graph states with up to eight qubits and several other ones with up to 14 qubits. We present construction protocols of selected graph states and provide the lookup table. For large graph states that are not in the lookup table, we derive bounds for the required number of fusions using graph-theoretic properties. Finally, we use the lookup table to search for the best graph codes for loss-tolerant encodings, given a fixed number of fusions for their construction.

Plasma shape is a significant factor that must be considered for any Fusion Pilot Plant (FPP) as it has significant consequences for plasma stability and core confinement. A new simulator, NSFsim, has been developed based on a historically successful code, DINA, offering tools to simulate both transport and plasma shape. Specifically, NSFsim is a free boundary equilibrium and transport solver and has been configured to match the properties of the DIII-D tokamak. This paper is focused on validating the Grad-Shafranov (GS) solver of NSFsim by analyzing its ability to recreate the plasma shape, the poloidal flux distribution, and the measurements of the simulated diagnostic signals originating from flux loops and magnetic probes in DIII-D. Five different plasma shapes are simulated to show the robustness of NSFsim to different plasma conditions; these shapes are Lower Single Null (LSN), Upper Single Null (USN), Double Null (DN), Inner Wall Limited (IWL), and Negative Triangularity (NT). The NSFsim results are compared against real measured signals, magnetic profile fits from EFIT, and another plasma equilibrium simulator, GSevolve. EFIT reconstructions of shots are readily available at DIII-D, but GSevolve was manually ran by us to provide simulation data to compare against., Comment: 12 pages, 7 figures

Until now, it has been difficult for volumetric super-resolution to utilize the recent advances in transformer-based models seen in 2D super-resolution. The memory required for self-attention in 3D volumes limits the receptive field. Therefore, long-range interactions are not used in 3D to the extent done in 2D and the strength of transformers is not realized. We propose a multi-scale transformer-based model based on hierarchical attention blocks combined with carrier tokens at multiple scales to overcome this. Here information from larger regions at coarse resolution is sequentially carried on to finer-resolution regions to predict the super-resolved image. Using transformer layers at each resolution, our coarse-to-fine modeling limits the number of tokens at each scale and enables attention over larger regions than what has previously been possible. We experimentally compare our method, MTVNet, against state-of-the-art volumetric super-resolution models on five 3D datasets demonstrating the advantage of an increased receptive field. This advantage is especially pronounced for images that are larger than what is seen in popularly used 3D datasets. Our code is available at https://github.com/AugustHoeg/MTVNet, Comment: 14 pages, 8 Figures with supplementary material

Pb on Si(111)-(7x7) shows surprising nucleation and mass transport dynamics at odds with standard theories. To create local imbalances on stable Pb islands we use the tip of a scanning force microscope. We enforce a short, local contact between the island and our tip. The subsequent island height growth and the local contact potential difference are studied via scanning force microscopy and Kelvin probe force microscopy. Though the island has a large volume increase after the contact, we observe that its surrounding wetting layer shows the same Pb density decrease as the global wetting layer. This indicates a collective density thinning of the wetting layer., Comment: 9 pages, 2 figures in main text and 5 figures in the Appendix; Paper accepted by Physical Review B: https://journals.aps.org/prb/accepted/5e078Yf5E3015a8088ba499754fdeefbd71da71aa

This letter presents the measurement of the energy-dependent neutrino-nucleon cross section in tungsten and the differential flux of muon neutrinos and anti-neutrinos. The analysis is performed using proton-proton collision data at a center-of-mass energy of $13.6 \, {\rm TeV}$ and corresponding to an integrated luminosity of $(65.6 \pm 1.4) \, \mathrm{fb^{-1}}$. Using the active electronic components of the FASER detector, $338.1 \pm 21.0$ charged current muon neutrino interaction events are identified, with backgrounds from other processes subtracted. We unfold the neutrino events into a fiducial volume corresponding to the sensitive regions of the FASER detector and interpret the results in two ways: We use the expected neutrino flux to measure the cross section, and we use the predicted cross section to measure the neutrino flux. Both results are presented in six bins of neutrino energy, achieving the first differential measurement in the TeV range. The observed distributions align with Standard Model predictions. Using this differential data, we extract the contributions of neutrinos from pion and kaon decays.

Icy dust particles emerge in star-forming clouds and are subsequently incorporated in protoplanetary disks, where they coagulate into larger pebbles up to mm in size. In the disk midplane, ices are shielded from UV radiation, but moderate levels of disk turbulence can lift small particles to the disk surface, where they can be altered, or destroyed. Nevertheless, studies of comets and meteorites generally find that ices at least partly retained their interstellar medium (ISM) composition before being accreted onto these minor bodies. Here we model this process through hydrodynamical simulations with VSI-driven turbulence in the outer protoplanetary disk. We use the PLUTO code in a 2.5 D global accretion setup and include Lagrangian dust particles of 0.1 and 1 mm sizes. In a post-processing step, we use the RADMC3D code to generate the local UV radiation field to assess the level of ice processing of pebbles. We find that a small fraction ($\sim$17$\%$) of 100 $\mu$m size particles are frequently lifted up to $Z/R=0.2$ which can result in the loss of their pristine composition as their residence time in this layer allows for effective CO and water photodissociation. The larger 1 mm size particles remain UV-shielded in the disk midplane throughout the dynamical evolution of the disk. Our results indicate that the assembly of icy bodies via the accretion of drifting mm-size icy pebbles can explain the presence of pristine ice from the ISM, even in VSI-turbulent disks. Nevertheless, particles $\leq$ 100 $\mu$m experience efficient UV processing and may mix with unaltered icy pebbles, resulting in a less ISM-like composition in the midplane., Comment: Accepted to A&A

Hash-based sampling and estimation are common themes in computing. Using hashing for sampling gives us the coordination needed to compare samples from different sets. Hashing is also used when we want to count distinct elements. The quality of the estimator for, say, the Jaccard similarity between two sets, depends on the concentration of the number of sampled elements from their intersection. Often we want to compare one query set against many stored sets to find one of the most similar sets, so we need strong concentration and low error-probability. In this paper, we provide strong explicit concentration bounds for Tornado Tabulation hashing [Bercea, Beretta, Klausen, Houen, and Thorup, FOCS'23] which is a realistic constant time hashing scheme. Previous concentration bounds for fast hashing were off by orders of magnitude, in the sample size needed to guarantee the same concentration. The true power of our result appears when applied in the local uniformity framework by [Dahlgaard, Knudsen, Rotenberg, and Thorup, STOC'15].

In the trace reconstruction problem our goal is to learn an unknown string $x\in \{0,1\}^n$ given independent traces of $x$. A trace is obtained by independently deleting each bit of $x$ with some probability $\delta$ and concatenating the remaining bits. It is a major open question whether the trace reconstruction problem can be solved with a polynomial number of traces when the deletion probability $\delta$ is constant. The best known upper bound and lower bounds are respectively $\exp(\tilde O(n^{1/5}))$ and $\tilde \Omega(n^{3/2})$ both by Chase [Cha21b,Cha21a]. Our main result is that if the string $x$ is mildly separated, meaning that the number of zeros between any two ones in $x$ is at least polylog$n$, and if $\delta$ is a sufficiently small constant, then the trace reconstruction problem can be solved with $O(n \log n)$ traces and in polynomial time.

The CHaracterising ExOPlanet Satellite (CHEOPS) is a partnership between the European Space Agency and Switzerland with important contributions by 10 additional ESA member States. It is the first S-class mission in the ESA Science Programme. CHEOPS has been flying on a Sun-synchronous low Earth orbit since December 2019, collecting millions of short-exposure images in the visible domain to study exoplanet properties. A small yet increasing fraction of CHEOPS images show linear trails caused by resident space objects crossing the instrument field of view. To characterize the population of satellites and orbital debris observed by CHEOPS, all and every science images acquired over the past 3 years have been scanned with a Hough transform algorithm to identify the characteristic linear features that these objects cause on the images. Thousands of trails have been detected. This statistically significant sample shows interesting trends and features such as an increased occurrence rate over the past years as well as the fingerprint of the Starlink constellation. The cross-matching of individual trails with catalogued objects is underway as we aim to measure their distance at the time of observation and deduce the apparent magnitude of the detected objects. As space agencies and private companies are developing new space-based surveillance and tracking activities to catalogue and characterize the distribution of small debris, the CHEOPS experience is timely and relevant. With the first CHEOPS mission extension currently running until the end of 2026, and a possible second extension until the end of 2029, the longer time coverage will make our dataset even more valuable to the community, especially for characterizing objects with recurrent crossings., Comment: 9 pages, 8 figures, Special Issue of the Journal of Space Safety Engineering

Morbidelli, Kleine & Nimmo (2024) (MKN) recently published a critical analysis on whether the terrestrial planets in the Solar System formed by rapid pebble accretion or by the classical route of multiple giant impacts between planetary embryos after the dissipation of the protoplanetary disc. They arrive at the conclusion that the terrestrial planets did not form by pebble accretion. Although we welcome debate on this topic, we want to emphasize here several points that we disagree on. We will not address in detail every claim made in MKN, but rather stick to four main points. Our conclusion is that pebble accretion remains a viable mechanism to drive significant growth of protoplanets in the protoplanetary disc, with as much as 70% of Earth formed by pebble accretion. This rapid growth phase must nevertheless have been followed by an extended period of collisional growth after the end of the protoplanetary disc phase, likely culminating with the moon-forming giant impact. We emphasize here an important recent result from Olson & Sharp (2023), namely that significant growth by pebble accretion can be reconciled with the Hf-W decay system even for a canonical moon-forming giant impact with a Mars-mass protoplanet and a low equilibration efficiency - a more massive impactor, as proposed in Johansen et al. (2023), is not necessary. Given that terrestrial planet formation naturally involves both pebble accretion and a combination of small and large impactors, this challenges the very notion of making an either/or distinction between the classical collision model and the pebble accretion model., Comment: Comment on arXiv:2411.09271 (slight correction to abstract here), 6 pages, 1 figure, comments and questions welcome

The purpose of this work is to demonstrate a robust and clinically validated method for correcting sound speed aberrations in medical ultrasound. We propose a correction method that calculates focusing delays directly from the observed two-way distributed average sound speed. The method beamforms multiple coherence images and selects the sound speed that maximizes the coherence for each image pixel. The main contribution of this work is the direct estimation of aberration, without the ill-posed inversion of a local sound speed map, and the proposed processing of coherence images which adapts to in vivo situations where low coherent regions and off-axis scattering represents a challenge. The method is validated in vitro and in silico showing high correlation with ground truth speed of sound maps. Further, the method is clinically validated by being applied to channel data recorded from 172 obstetric Bmode images, and 12 case examples are presented and discussed in detail. The data is recorded with a GE HealthCare Voluson Expert 22 system with an eM6c matrix array probe. The images are evaluated by three expert clinicians, and the results show that the corrected images are preferred or gave equivalent quality to no correction (1540m/s) for 72.5% of the 172 images. In addition, a sharpness metric from digital photography is used to quantify image quality improvement. The increase in sharpness and the change in average sound speed are shown to be linearly correlated with a Pearson Correlation Coefficient of 0.67., Comment: Supplementary GIF images are found at the project page following https://andersvra.github.io/research/coherenceaberration/

In this paper we showcase the strengths of polarized neutron imaging as a magnetic imaging technique through a case study on field-cooled multifilamentary YBCO tape carrying a transport current while containing a trapped magnetic field. The measurements were done at J-PARC's RADEN beamline, measuring a radiograph of a single polarization component, to showcase the analysis potential with minimal acquisition time. Regions of internal damage are easily and accurately identified as the technique probes the internal magnetic field of the sample, thereby avoiding surface-smearing effects. Quantitative measurements of the integrated field strength in various regions are acquired using time-of-flight information. Finally, we estimate the strength of the screening currents in the superconductor during the experiment by simulating an experiment with a model sample and comparing it to the experimental data. With this, we show that polarized neutron imaging is not only a useful tool for investigating magnetic structures but also for investigating samples carrying currents., Comment: 6 pages, 4 figures with total of 6 or 7 images (some bundles, some seperate)

The steep dose gradients obtained with pencil beam scanning allow for precise tumor targeting at the cost of high sensitivity to uncertainties. Robust optimization is commonly applied to mitigate uncertainties in density and patient setup, while its application to motion management, called 4D-robust optimization (4DRO), is typically accompanied by other motion mitigation techniques. In particular, current commercial implementations of 4DRO do not model the interplay effect between the delivery time structure and the patient's motion. Previously, it has been shown that Interplay-robust optimization (IPRO) can mitigate the interplay effect given uncertainty in the patient's breathing frequency. In this study, we investigate and evaluate IPRO in the context where the motion uncertainty is extended to also include variations in breathing amplitude. We model the patients' motion using synthetic 4DCTs, each created by deforming a reference CT based on a motion pattern obtained with 4DMRI. Each synthetic 4DCT contains multiple breathing cycles, partitioned into two sets for scenario generation: one for optimization and one for evaluation. Motion scenarios are then created by randomly concatenating breathing cycles varying in period and amplitude. In addition, a method considering a single breathing cycle for generating optimization scenarios (IPRO-1C) is developed to investigate to which extent robustness can be achieved with limited information. IPRO and IPRO-1C increased the target coverage for all patient cases in terms of the near-worst-case (5th percentile) CTV D98, compared to 4DRO. After normalization of plan doses to equal target coverage, IPRO with 49 scenarios resulted in the greatest decreases in OAR dose, with near-worst-case (95th percentile) improvements averaging 4.2 %. IPRO-1C with 9 scenarios, with comparable computational demands as 4DRO, decreased OAR dose by 1.7 %.

We present a spectral element model for general-purpose simulation of non-overturning nonlinear water waves using the incompressible Navier-Stokes equations (INSE) with a free surface. The numerical implementation of the spectral element method is inspired by the related work by Engsig-Karup et al. (2016) and is based on nodal Lagrange basis functions, mass matrix-based integration and gradient recovery using global $L^2$ projections. The resulting model leverages the high-order accurate -- possibly exponential -- error convergence and has support for geometric flexibility allowing for computationally efficient simulations of nonlinear wave propagation. An explicit fourth-order accurate Runge-Kutta scheme is employed for the temporal integration, and a mixed-stage numerical discretization is the basis for a pressure-velocity coupling that makes it possible to maintain high-order accuracy in both the temporal and spatial discretizations while preserving mass conservation. Furthermore, the numerical scheme is accelerated by solving the discrete Poisson problem using an iterative solver strategy based on a geometric $p$-multigrid method. This problem constitutes the main computational bottleneck in INSE models. It is shown through numerical experiments, that the model achieves spectral convergence in the velocity fields for highly nonlinear waves, and there is excellent agreement with experimental data for the simulation of the classical benchmark of harmonic wave generation over a submerged bar. The geometric $p$-multigrid solver demonstrates $O(n)$ computational scalability simulations, making it a suitable efficient solver strategy as a candidate for extensions to more complex, real-world scenarios., Comment: 27 pages, 20 figures

The ICH E9(R1) addendum provides guidelines on accounting for intercurrent events in clinical trials using the estimands framework. However, there has been limited attention on the estimands framework for meta-analysis. Using treatment switching, a well-known intercurrent event that occurs frequently in oncology, we conducted a simulation study to explore the bias introduced by pooling together estimates targeting different estimands in a meta-analysis of randomized clinical trials (RCTs) that allowed for treatment switching. We simulated overall survival data of a collection of RCTs that allowed patients in the control group to switch to the intervention treatment after disease progression under fixed-effects and random-effects models. For each RCT, we calculated effect estimates for a treatment policy estimand that ignored treatment switching, and a hypothetical estimand that accounted for treatment switching by censoring switchers at the time of switching. Then, we performed random-effects and fixed-effects meta-analyses to pool together RCT effect estimates while varying the proportions of treatment policy and hypothetical effect estimates. We compared the results of meta-analyses that pooled different types of effect estimates with those that pooled only treatment policy or hypothetical estimates. We found that pooling estimates targeting different estimands results in pooled estimators that reflect neither the treatment policy estimand nor the hypothetical estimand. This finding shows that pooling estimates of varying target estimands can generate misleading results, even under a random-effects model. Adopting the estimands framework for meta-analysis may improve alignment between meta-analytic results and the clinical research question of interest.

This paper concerns control of a class of systems where multiple dynamically stable agents share a nonlinear and bounded control-interconnection. The agents are subject to a disturbance which is too large to reject with the available control action, making it impossible to stabilize all agents in their desired states. In this nonlinear setting, we consider two different anti-windup equipped proportional-integral control strategies and analyze their properties. We show that a fully decentralized strategy will globally, asymptotically stabilize a unique equilibrium. This equilibrium also minimizes a weighted sum of the tracking errors. We also consider a light addition to the fully decentralized strategy, where rank-1 coordination between the agents is introduced via the anti-windup action. We show that any equilibrium to this closed-loop system minimizes the maximum tracking error for any agent. A remarkable property of these results is that they rely on extremely few assumptions on the interconnection between the agents. Finally we illustrate how the considered model can be applied in a district heating setting, and demonstrate the two considered controllers in a simulation.