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We initiate a study of the vertex clique covering numbers of Johnson graphs $J(N, k)$, the smallest numbers of cliques necessary to cover the vertices of those graphs. We prove identities for the values of these numbers when $k \leq 3$, and $k \geq N - 3$, and using computational methods, we provide explicit values for a range of small graphs. By drawing on connections to coding theory and combinatorial design theory, we prove various bounds on the clique covering numbers for general Johnson graphs, and we show how constant-weight lexicodes can be utilized to create optimal covers of $J(2k, k)$ when $k$ is a small power of two.

Hierarchical clustering is a powerful tool for exploratory data analysis, organizing data into a tree of clusterings from which a partition can be chosen. This paper generalizes these ideas by proving that, for any reasonable hierarchy, one can optimally solve any center-based clustering objective over it (such as $k$-means). Moreover, these solutions can be found exceedingly quickly and are themselves necessarily hierarchical. Thus, given a cluster tree, we show that one can quickly access a plethora of new, equally meaningful hierarchies. Just as in standard hierarchical clustering, one can then choose any desired partition from these new hierarchies. We conclude by verifying the utility of our proposed techniques across datasets, hierarchies, and partitioning schemes.

Algorithms are increasingly used to automate or aid human decisions, yet recent research shows that these algorithms may exhibit bias across legally protected demographic groups. However, data on these groups may be unavailable to organizations or external auditors due to privacy legislation. This paper studies bias detection using an unsupervised clustering tool when data on demographic groups are unavailable. We collaborate with the Dutch Executive Agency for Education to audit an algorithm that was used to assign risk scores to college students at the national level in the Netherlands between 2012-2023. Our audit covers more than 250,000 students from the whole country. The unsupervised clustering tool highlights known disparities between students with a non-European migration background and Dutch origin. Our contributions are three-fold: (1) we assess bias in a real-world, large-scale and high-stakes decision-making process by a governmental organization; (2) we use simulation studies to highlight potential pitfalls of using the unsupervised clustering tool to detect true bias when demographic group data are unavailable and provide recommendations for valid inferences; (3) we provide the unsupervised clustering tool in an open-source library. Our work serves as a starting point for a deliberative assessment by human experts to evaluate potential discrimination in algorithmic-supported decision-making processes.

We present a comprehensive study of the large-scale structure, jet and outflow morphology, and kinematics of the Class 0/I protostellar binary Ced 110 IRS4, using JWST NIRCam (F150W and F410M) and MIRI MRS observations from the JWST ERC program IceAge, along with ALMA data from the Early Planet Formation in Embedded Disks (eDisk) program. NIRCam images, combined with ALMA continuum and CO data, reveal arc-like structures ($\sim$1100 au), suggesting a dense envelope around the protostars. We detect disk shadows from both protostars in F150W. The MIRI MRS IFU data reveal a jet from both protostars in multiple [Fe II] lines, [Ar II] 6.99 $\mu$m and [Ne II] 12.81 $\mu$m, marking the first detection of a jet from the system. The [Fe II] (5.34 $\mu$m) jet from Ced 110 IRS4A has a width of $\leq$ 51~au at the protostellar location, with a large opening angle of 23\arcdeg{} $\pm$ 4\arcdeg. After inclination correction, the jet velocity is 124 km s$^{-1}$, corresponding to a dynamical timescale of 25 years. The molecular H$_2$ outflow displays a distinct morphology resembling two hemispheres placed back-to-back. The consistent H$_2$ emission extent across transitions, differing from previous observations of protostellar outflows detected with JWST, suggests that MHD disk winds may not drive the observed outflow. We find that the upper limit to the width of the outflow at the protostellar location is 130 $\pm$ 10 au which is smaller than the disk diameter of 183.4 {$\pm$ 0.4 au} but much larger than the width of the [Fe II] jet., Comment: Accepted in Astronomical Journal; 22 pages and 13 Figures

Causal Bayesian networks are 'causal' models since they make predictions about interventional distributions. To connect such causal model predictions to real-world outcomes, we must determine which actions in the world correspond to which interventions in the model. For example, to interpret an action as an intervention on a treatment variable, the action will presumably have to a) change the distribution of treatment in a way that corresponds to the intervention, and b) not change other aspects, such as how the outcome depends on the treatment; while the marginal distributions of some variables may change as an effect. We introduce a formal framework to make such requirements for different interpretations of actions as interventions precise. We prove that the seemingly natural interpretation of actions as interventions is circular: Under this interpretation, every causal Bayesian network that correctly models the observational distribution is trivially also interventionally valid, and no action yields empirical data that could possibly falsify such a model. We prove an impossibility result: No interpretation exists that is non-circular and simultaneously satisfies a set of natural desiderata. Instead, we examine non-circular interpretations that may violate some desiderata and show how this may in turn enable the falsification of causal models. By rigorously examining how a causal Bayesian network could be a 'causal' model of the world instead of merely a mathematical object, our formal framework contributes to the conceptual foundations of causal representation learning, causal discovery, and causal abstraction, while also highlighting some limitations of existing approaches., Comment: 50 pages

We report an extensive rotational spectroscopic analysis of singly deuterated methyl mercaptan (CH$_{2}$DSH) using both millimeter and far-infrared synchrotron spectra to achieve a global torsional analysis of the three lowest torsional substates (e$_{0}$, e$_{1}$, and o$_{1}$) of this non-rigid species. A fit including 3419 millimeter wave transitions along with 43 infrared torsional subband centers was performed with root mean square deviations of 0.233 MHz and 0.270 cm$^{-1}$, respectively, resulting in 68 fit parameters. A spectroscopic catalogue built from this analysis for a temperature of 125 K has led to the first interstellar detection of CH$_{2}$DSH towards the Solar-like protostar IRAS 16293-2422 B. We report the identification of 46 transitions, including eight relatively unblended lines, resulting in a derived column density of (3.0$\pm$0.3)$\times$10$^{14}$ cm$^{-2}$. The column density ratio for HDCS/CH$_{2}$DSH compared to HDCO/CH$_{2}$DOH suggests a difference in the interstellar chemistry between the sulphur and oxygen complex organics, in particular a different link between H$_{2}$CO and CH$_{3}$OH and between H$_{2}$CS and CH$_{3}$SH. This is the first interstellar detection of a deuterated sulphur-bearing COM and therefore an important step into understanding the chemical origin of sulphur-based prebiotics., Comment: Accepted for publication in Astrophysical Journal Letters (ApJL)

With the use of Hida's white noise space theory space theory and spaces of stochastic distributions, we present a detailed analytic continuation theory for classes of Gaussian processes, with focus here on Brownian motion. For the latter, we prove and make use a priori bounds, in the complex plane, for the Hermite functions; as well as a new approach to stochastic distributions. This in turn allows us to present an explicit formula for an analytically continued white noise process, realized this way in complex domain. With the use of the Wick product, we then apply our complex white noise analysis in a derivation of a new realization of Hilbert space-valued stochastic integrals

Big data present new opportunities for modern society while posing challenges for data scientists. Recent advancements in sensor networks and the widespread adoption of IoT have led to the collection of physical-sensor data on an enormous scale. However, significant challenges arise in high-quality big data analytics. To uncover big data challenges and enhance data quality, it is essential to quantitatively unveil data characteristics. Furthermore, the existing studies lack analysis of the specific time-related characteristics. Enhancing the efficiency and precision of data analytics through the big data lifecycle requires a comprehensive understanding of data characteristics to address the hidden big data challenges. To fill in the research gap, this paper proposes a systematic data characteristic framework based on a 6Vs model. The framework aims to unveil the data characteristics in terms of data volume, variety, velocity, veracity, value, and variability through a set of statistical indicators. This model improves the objectivity of data characteristic understanding by relying solely on data-driven indicators. The indicators related to time-related characteristics in physical-sensor data are also included. Furthermore, the big data challenges are linked to each dimension of the 6Vs model to gain a quantitative understanding of the data challenges. Finally, a pipeline is developed to implement the proposed framework, and two case studies are conducted to illustrate the process of understanding the physical-sensor data characteristics and making recommendations for data preprocessing to address the big data challenges. The proposed framework is able to analyze the characteristics of all physical-sensor data, therefore, identifying potential challenges in subsequent analytics, and providing recommendations for data preprocessing.

Public transportation is a major source of greenhouse gas emissions, highlighting the need to improve bus fuel efficiency. Clustering algorithms assist in analyzing fuel efficiency by grouping data into clusters, but irrelevant features may complicate the analysis and choosing the optimal number of clusters remains a challenging task. Therefore, this paper employs the Gaussian mixture models to cluster the solo fuel-efficiency dataset. Moreover, an integration method that combines the Silhouette index, Calinski-Harabasz index, and Davies-Bouldin index is developed to select the optimal cluster numbers. A dataset with 4006 bus trips in North Jutland, Denmark is utilized as the case study. Trips are first split into three groups, then one group is divided further, resulting in four categories: extreme, normal, low, and extremely low fuel efficiency. A preliminary study using visualization analysis is conducted to investigate how driving behaviors and route conditions affect fuel efficiency. The results indicate that both individual driving habits and route characteristics have a significant influence on fuel efficiency.

A systematic pipeline for data processing and knowledge discovery is essential to extracting knowledge from big data and making recommendations for operational decision-making. The CRISP-DM model is the de-facto standard for developing data-mining projects in practice. However, advancements in data processing technologies require enhancements to this framework. This paper presents the DataPro (a standardized data understanding and processing procedure) model, which extends CRISP-DM and emphasizes the link between data scientists and stakeholders by adding the "technical understanding" and "implementation" phases. Firstly, the "technical understanding" phase aligns business demands with technical requirements, ensuring the technical team's accurate comprehension of business goals. Next, the "implementation" phase focuses on the practical application of developed data science models, ensuring theoretical models are effectively applied in business contexts. Furthermore, clearly defining roles and responsibilities in each phase enhances management and communication among all participants. Afterward, a case study on an eco-driving data science project for fuel efficiency analysis in the Danish public transportation sector illustrates the application of the DataPro model. By following the proposed framework, the project identified key business objectives, translated them into technical requirements, and developed models that provided actionable insights for reducing fuel consumption. Finally, the model is evaluated qualitatively, demonstrating its superiority over other data science procedures.

We present a systematic study of the family of positive definite (p.d.) kernels with the use of their associated feature maps and feature spaces. For a fixed set $X$, generalizing Loewner, we make precise the corresponding partially ordered set $Pos\left(X\right)$ of all p.d. kernels on $X$, as well as a study of its global properties. This new analysis includes both results dealing with applications and concrete examples, including such general notions for $Pos\left(X\right)$ as the structure of its partial order, its products, sums, and limits; as well as their Hilbert space-theoretic counterparts. For this purpose, we introduce a new duality for feature spaces, feature selections, and feature mappings. For our analysis, we further introduce a general notion of dual pairs of p.d. kernels. Three special classes of kernels are studied in detail: (a) the case when the reproducing kernel Hilbert spaces (RKHSs) may be chosen as Hilbert spaces of analytic functions, (b) when they are realized in spaces of Schwartz-distributions, and (c) arise as fractal limits. We further prove inverse theorems in which we derive results for the analysis of $Pos\left(X\right)$ from the operator theory of specified counterpart-feature spaces. We present constructions of new p.d. kernels in two ways: (i) as limits of monotone families in $Pos\left(X\right)$, and (ii) as p.d. kernels which model fractal limits, i.e., are invariant with respect to certain iterated function systems (IFS)-transformations.

Reliable probabilistic production forecasts are required to better manage the uncertainty that the rapid build-out of wind power capacity adds to future energy systems. In this article, we consider sequential methods to correct errors in power production forecast ensembles derived from numerical weather predictions. We propose combining neural networks with time-adaptive quantile regression to enhance the accuracy of wind power forecasts. We refer to this approach as Neural Adaptive Basis for (time-adaptive) Quantile Regression or NABQR. First, we use NABQR to correct power production ensembles with neural networks. We find that Long Short-Term Memory networks are the most effective architecture for this purpose. Second, we apply time-adaptive quantile regression to the corrected ensembles to obtain optimal median predictions along with quantiles of the forecast distribution. With the suggested method we achieve accuracy improvements up to 40% in mean absolute terms in an application to day-ahead forecasting of on- and offshore wind power production in Denmark. In addition, we explore the value of our method for applications in energy trading. We have implemented the NABQR method as an open-source Python package to support applications in renewable energy forecasting and future research.

State-of-the-art JWST observations are unveiling unprecedented views into the atmospheres of substellar objects in the infrared, further highlighting the importance of clouds. Current forward models struggle to fit the silicate clouds absorption feature at ~$10\,\mu$m observed in substellar atmospheres. In the MSG model, we aim to couple the MARCS 1D radiative-convective equilibrium atmosphere model with the 1D kinetic, stationary, non-equilibrium, cloud formation model DRIFT, to create a new grid of self-consistent cloudy substellar atmosphere models with microphysical cloud formation. We aim to test if this new grid is able to reproduce the silicate cloud absorption feature at ~$10\,\mu$m. We model substellar atmospheres with effective temperatures in the range 1200-2500 K and with $\log(g)=4.0$. We compute atmospheric structures that self-consistently account for condensate cloud opacities based on microphysical properties. We present an algorithm based on control theory to help converge such self-consistent models. Synthetic atmosphere spectra are computed for each model to explore the observable impact of the cloud microphysics. We additionally explore the impact of choosing different nucleation species (TiO$_2$ or SiO) and the effect of less efficient atmospheric mixing on these spectra. The new MSG cloudy grid using TiO$_2$ nucleation shows spectra which are redder in the near-infrared compared to the currently known population of substellar atmospheres. We find the models with SiO nucleation, and models with reduced mixing efficiency are less red in the near-infrared. The grid is unable to reproduce the silicate features similar to those found in recent JWST observations and Spitzer archival data. We thoroughly discuss further work that may better approximate the impact of convection in cloud-forming regions and steps that may help resolve the silicate cloud feature., Comment: Accepted for publication in A&A

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

We study the collective photon decay of multiple quantum emitters embedded in a thin high-index dielectric layer such as hexagonal boron nitride (hBN), with and without a metal substrate. We first explore the significant role that guided modes including surface plasmon modes play in the collective decay of identical singlephoton emitters (super- and subradiance). Surprisingly, on distances relevant for collective emission, the guided or surface-plasmon modes do not always enhance the collective emission. We identify configurations with inhibition, and others with enhancement of the dipole interaction due to the guided modes. We interpret our results in terms of local and cross densities of optical states. In the same structure, we show a remarkably favorable configuration for enhanced F\"orster resonance energy transfer between a donor and acceptor in the dielectric layer on a metallic substrate. We compare our results to theoretical limits for energy transfer efficiency., Comment: 16 pages, 6 figures. To be published in Nanophotonics

We present a comprehensive analysis of a planetary microlensing event OGLE-2015-BLG-1609. The planetary anomaly was detected by two survey telescopes, OGLE and MOA. Each of these surveys collected enough data over the planetary anomaly to allow for an unambiguous planet detection. Such survey detections of planetary anomalies are needed to build a robust sample of planets that could improve studies on the microlensing planetary occurrence rate by reducing biases and statistical uncertainties. In this work, we examined different methods for modeling microlensing events using individual datasets, particularly we incorporated a Galactic model prior to better constrain poorly defined microlensing parallax. Ultimately, we fitted a comprehensive model to all available data, identifying three potential typologies, with two showing comparably high Bayesian evidence. Our analysis indicates that the host of the planet is a brown dwarf with a probability of 34%, or a low-mass stellar object (M-dwarf) with the probability of 66%., Comment: 12 pages, 7 figures

In this paper we study 2D Fourier expansions for a general class of planar measures $\mu$, generally singular, but assumed compactly supported in $\mathbb{R}^2$. We focus on the following question: When does $L^2(\mu)$ admit a 2D system of Fourier expansions? We offer concrete conditions allowing an affirmative answer to the question for a large class of Borel probability measures, and we present an explicit Fourier duality for these cases. Our 2D Fourier analysis relies on a detailed conditioning-analysis. For a given $\mu$, it is based on the corresponding systems of 1D measures consisting of a marginal measure and associated family of conditional measures computed from $\mu$ by the Rokhlin Disintegration Theorem. Our identified $L^2(\mu)$-Fourier expansions are special in two ways: For our measures $\mu$, the Fourier expansions are generally non-orthogonal, but nonetheless, they lend themselves to algorithmic computations. Second, we further stress that our class of 2D measures $\mu$ considered here go beyond what exists in the literature. In particular, our measures do not require affine iterated function system (IFS) properties, but we do study grid IFS measures in detail and provide some technical criteria guaranteeing their admission of Fourier expansions. Our analyses make use of estimates for the Hausdorff dimensions of the measure supports. An important class of examples addressed in this paper is fractal Bedford-McMullen carpets.

This work focuses on the ice features toward the binary protostellar system Ced 110 IRS 4A and 4B, and observed with JWST as part of the Early Release Science Ice Age collaboration. We aim to explore the JWST observations of the binary protostellar system Ced~110~IRS4A and IRS4B to unveil and quantify the ice inventories toward these sources. We compare the ice abundances with those found for the same molecular cloud. The analysis is performed by fitting or comparing laboratory infrared spectra of ices to the observations. Spectral fits are carried out with the ENIIGMA fitting tool that searches for the best fit. For Ced~110~IRS4B, we detected the major ice species H$_2$O, CO, CO$_2$ and NH$_3$. All species are found in a mixture except for CO and CO$_2$, which have both mixed and pure ice components. In the case of Ced~110~IRS4A, we detected the same major species as in Ced~110~IRS4B, as well as the following minor species CH$_4$, SO$_2$, CH$_3$OH, OCN$^-$, NH$_4^+$ and HCOOH. Tentative detection of N$_2$O ice (7.75~$\mu$m), forsterite dust (11.2~$\mu$m) and CH$_3^+$ gas emission (7.18~$\mu$m) in the primary source are also presented. Compared with the two lines of sight toward background stars in the Chameleon I molecular cloud, the protostar has similar ice abundances, except in the case of the ions that are higher in IRS4A. The clearest differences are the absence of the 7.2 and 7.4~$\mu$m absorption features due to HCOO$^-$ and icy complex organic molecules in IRS4A and evidence of thermal processing in both IRS4A and IRS4B as probed by the CO$_2$ ice features. We conclude that the binary protostellar system Ced~110~IRS4A and IRS4B has a large inventory of icy species. The similar ice abundances in comparison to the starless regions in the same molecular cloud suggest that the chemical conditions of the protostar were set at earlier stages in the molecular cloud., Comment: 33 pages, 19 Figures. Accepted for publication in Astronomy & Astrophysics

The main result of this paper is that there is sometimes a triangulated equivalence between $D_Q( A )$, the $Q$-shaped derived category of an algebra $A$, and $D( B )$, the classic derived category of a different algebra $B$. By construction, $D_Q( A )$ consists of $Q$-shaped diagrams of $A$-modules for a suitable small category $Q$. Our result concerns the case where $Q$ consists of shifts of indecomposable projective modules over a self-injective $\mathbb{Z}$-graded algebra $\Lambda$. A notable special case is the result by Iyama, Kato, and Miyachi that $D_N( A )$, the $N$-derived category of $A$, is triangulated equivalent to $D( T_{ N-1 }A )$, the classic derived category of $T_{ N-1 }( A )$, which denotes upper diagonal $( N-1 ) \times ( N-1 )$-matrices over $A$. Several other special cases will also be discussed., Comment: Reference added. 10 pages

We present an approach for retartgeting off-the-shelf Virtual Reality (VR) trackers to effectively teleoperate an upper-body humanoid while ensuring self-collision-free motions. Key to the effectiveness was the proper assignment of trackers to joint sets via modified task Jacobians and relaxed barrier functions for self-collision avoidance. The approach was validated on Apptronik's Astro hardware by demonstrating manipulation capabilities on a table-top environment with pick-and-place box packing and a two-handed box pick up and handover task., Comment: First Prize Winner of Horizons of an extended robotics reality Workshop at International Conference on Intelligent Robots and Systems, 2022

In this paper, a recently developed snapshot hyperspectral imaging (HSI) system based on Computed Tomography Imaging Spectroscopy (CTIS) is utilized to determine Brix and pH values in Sheegene 20 table grapes through Partial Least Squares Regression (PLSR) modeling. The performance of the CTIS system is compared with that of a state-of-the-art line scan HSI system by imaging 100 grapes across both platforms. Reference measurements of Brix and pH values are obtained directly using a refractometer and a pH meter, as these parameters are essential for assessing the quality of table and wine grapes. The findings indicate that the spectra captured by the CTIS camera correlate well with the reference measurements, despite the system's narrower spectral range. The CTIS camera's advantages, including its lower cost, portability, and reduced susceptibility to motion errors, highlight its potential for promising in-field applications in grape quality assessment., Comment: 15 pages, 10 figures

Context. To date, more than 5000 exoplanets have been discovered. The large majority of these planets have a mass between 1 and 17 {M_\oplus}, making them so-called super-Earths and mini-Neptunes. The exact formation process for this abundant planet population has not yet been fully constrained. Aims. Recent studies on the formation of these planets make various assumptions with regard to the disk. The primary mass budget, held in pebbles, is either assumed to have a constant size or is parametrized as a flux. Simplifications of the temperature structure, in the form of a static power law, do not consider the temperature evolution and high magnitudes of heating in the inner part of the disk. In this study, we aim to investigate the effect these simplifications of temperature and pebble sizes have on the pebble densities and resulting planet populations. Methods. To constrain the timescales needed to form super-Earths, we developed a model for exploring a large parameter space. We included the effect of two different temperature prescriptions on a viscously accreting and spreading disk. We formed a pebble reservoir utilizing a simplified conversion timescale with a time- and radially dependent Stokes number for the dust. We then tracked the temporal evolution of the surface densities of gas, dust, and pebbles. Pebbles were allowed to drift and be accreted onto a growing protoplanet. As a planet grows, it exerts a torque on the disk, carving out a gap and affecting the pebble drift, before halting the growth of the planet., Comment: Accepted by A&A. Comments welcome

Warm Saturn type exoplanets orbiting M-dwarfs are particularly suitable for in-depth cloud characterisation through transmission spectroscopy due to their favourable stellar to planetary radius contrast. However, modelling cloud formation consistently within the 3D atmosphere remains computationally challenging. The aim is to explore the combined atmospheric and micro-physical cloud structure, and the kinetic gas-phase chemistry for the warm Saturn HATS0-6b orbiting an M-dwarf. A combined 3D cloudy atmosphere model is constructed by iteratively executing the 3D General Circulation Model (GCM) expeRT/MITgcm and a kinetic cloud formation model, each in its full complexity. Resulting cloud particle number densities, sizes, and compositions are used to derive the local cloud opacity which is then utilised in the next GCM iteration. The disequilibrium H/C/O/N gas-phase chemistry is calculated for each iteration to assess the resulting transmission spectrum in post-processing. The cloud opacity feedback causes a temperature inversion at the sub-stellar point and at the evening terminator at gas pressures higher than 0.01 bar. Furthermore, clouds cool the atmosphere between 0.01 bar and 10 bar, and narrow the equatorial wind jet. The transmission spectrum shows muted gas-phase absorption and a cloud particle silicate feature at approximately 10 micron. The combined atmosphere-cloud model retains the full physical complexity of each component and therefore enables a detailed physical interpretation with JWST NIRSpec and MIRI LRS observational accuracy. The model shows that warm Saturn type exoplanets around M-dwarfs are ideal candidates to search for limb asymmetries in clouds and chemistry, identify cloud particle composition by observing their spectral features, and identify the cloud-induced strong thermal inversion that arises on these planets specifically., Comment: 21 pages, 15 figures, Accepted by A&A

This paper studies a non-commutative generalisation of Coxeter friezes due to Berenstein and Retakh. It generalises several earlier results to this situation: A formula for frieze determinants, a $T$-path formula expressing the Laurent phenomenon, and results on gluing friezes together. One of our tools is a non-commutative version of the weak friezes introduced by Canakci and Jorgensen., Comment: Updated references. 26 pages and 16 figures

Signals with varying periodicity frequently appear in real-world phenomena, necessitating the development of efficient modelling techniques to map the measured nonlinear timeline to linear time. Here we propose a regression model that allows for a representation of periodic and dynamic patterns observed in time series data. The model incorporates a hidden strictly increasing stochastic process that represents the instantaneous frequency, allowing the model to adapt and accurately capture varying time scales. A case study focusing on age estimation of narwhal tusks is presented, where cyclic element signals associated with annual growth layer groups are analyzed. We apply the methodology to data from one such tusk collected in West Greenland and use the fitted model to estimate the age of the narwhal. The proposed method is validated using simulated signals with known cycle counts and practical considerations and modelling challenges are discussed in detail. This research contributes to the field of time series analysis, providing a tool and valuable insights for understanding and modeling complex cyclic patterns in diverse domains.

The purpose of the present paper is to address multiple aspects of the Fuglede question dealing (Fourier spectra vs geometry) with a variety of $L^2$ contexts where we make precise the interplay between the three sides of the question: (i) existence of orthogonal families of Fourier basis functions (and associated spectra) on the one hand, (ii) extensions of partial derivative operators, and (iii) geometry of the corresponding domains, stressing systems of translation-tiles. We emphasize an account of old and new developments since the original 1974-paper by Bent Fuglede where the co-authors and Steen Pedersen have contributed.

Efficiently evaluating the performance of text-to-image models is difficult as it inherently requires subjective judgment and human preference, making it hard to compare different models and quantify the state of the art. Leveraging Rapidata's technology, we present an efficient annotation framework that sources human feedback from a diverse, global pool of annotators. Our study collected over 2 million annotations across 4,512 images, evaluating four prominent models (DALL-E 3, Flux.1, MidJourney, and Stable Diffusion) on style preference, coherence, and text-to-image alignment. We demonstrate that our approach makes it feasible to comprehensively rank image generation models based on a vast pool of annotators and show that the diverse annotator demographics reflect the world population, significantly decreasing the risk of biases.

We provide a cyclone model for dynamical simulations in the pyro-process of cement production. The model is given as an index-1 differential-algebraic equation (DAE) model based on first engineering principle. Using a systematic approach, the model integrates cyclone geometry, thermo-physical aspects, stoichiometry and kinetics, mass and energy balances, and algebraic equations for volume and internal energy. The paper provides simulation results that fit expected dynamics. The cyclone model is part of an overall model for dynamical simulations of the pyro-process in a cement plant. This model can be used in the design of control and optimization systems to improve energy efficiency and reduce CO2 emission., Comment: 7 pages, 6 figures, 8 Tables

Extended Berkeley Packet Filter (eBPF) is a runtime that enables users to load programs into the operating system (OS) kernel, like Linux or Windows, and execute them safely and efficiently at designated kernel hooks. Each program passes through a verifier that reasons about the safety guarantees for execution. Hosting a safe virtual machine runtime within the kernel makes it dynamically programmable. Unlike the popular approach of bypassing or completely replacing the kernel, eBPF gives users the flexibility to modify the kernel on the fly, rapidly experiment and iterate, and deploy solutions to achieve their workload-specific needs, while working in concert with the kernel. In this paper, we present the first comprehensive description of the design and implementation of the eBPF runtime in the Linux kernel. We argue that eBPF today provides a mature and safe programming environment for the kernel. It has seen wide adoption since its inception and is increasingly being used not just to extend, but program entire components of the kernel, while preserving its runtime integrity. We outline the compelling advantages it offers for real-world production usage, and illustrate current use cases. Finally, we identify its key challenges, and discuss possible future directions., Comment: 22 pages, 6 figures

Bratteli diagrams with countably infinite levels exhibit a new phenomenon: they can be horizontally stationary. The incidence matrices of these horizontally stationary Bratteli diagrams are infinite banded Toeplitz matrices. In this paper, we study the fundamental properties of horizontally stationary Bratteli diagrams. In these diagrams, we provide an explicit description of ergodic tail invariant probability measures. For a certain class of horizontally stationary Bratteli diagrams, we prove that all ergodic tail invariant probability measures are extensions of measures from odometers. Additionally, we establish conditions for the existence of a continuous Vershik map on the path space of a horizontally stationary Bratteli diagram., Comment: 26 pages, 2 figures, the exposition is reworked, typos are corrected, references are added

We present a 2D model for a grate belt cooler in the pyro-section of a cement plant. The model is formulated as an index-1 differential-algebraic equation (DAE) model based on first engineering principles. The model systematically integrates thermo-physical aspects, transport phenomena, reaction kinetics, mass and energy balances, and algebraic volume and energy relations. The model is used for dynamic simulation of the cooler and the paper provides dynamic and steady-state simulation results matching the expected behavior. The cooler model is one part of a full pyro-section model for dynamical simulations. The model can serve as a basis for the design of optimization and control systems towards improving energy efficiency and CO2 emission., Comment: 7 pages, 6 figures, 4 tables

We present the theory and implementation of a fully variational wave function -- density functional theory (DFT) hybrid model, which is applicable to many cases of strong correlation. We denote this model the multiconfigurational self-consistent on-top pair-density functional theory model (MC-srPDFT). We have previously shown how the multi-configurational short-range DFT hybrid model (MC-srDFT) can describe many multiconfigurational cases of any spin symmetry, and also state-specific calculations on excited states (Hedeg{\aa}rd et al. J. Chem. Phys. 148, 2018, 214103). However, the srDFT part of the MC-srDFT has some deficiencies that it shares with Kohn-Sham DFT; in particular (1) self-interaction errors (albeit reduced because of the range separation), (2) that different M$_S$ states incorrectly become non-degenerate, and (3) that singlet and non-singlet states dissociating to the same open-shell fragments incorrectly lead to different electronic energies at dissociation. The model we present in this paper corrects these deficiencies by introducing the on-top pair density as an auxiliary variable replacing the spin density. Unlike other models in the literature, our model is fully variational and employs a long-range version of the on-top pair density. The implementation is a second-order optimization algorithm ensuring robust convergence to both ground- and excited states. We show how MC-srPDFT solves the mentioned challenges by sample calculations on the ground state singlet curve of H$_2$, N$_2$, and Cr$_2$ and the lowest triplet curves for N$_2$ and Cr$_2$. Furthermore, the rotational barrier for ethene is investigated for the S$_0$ and T$_1$ states. The calculations show correct degeneracy between the singlet and triplet curves at dissociation and the results are invariant to the choice of M$_S$ value for the triplet curves.

While some research fields have a long history of collaborating with domain experts outside academia, many quantitative researchers do not have natural avenues to meet experts in areas where the research is later deployed. We explain how conversations -- interviews without a specific research objective -- can bridge research and practice. Using collaborative autoethnography, we reflect on our experience of conducting conversations with practitioners from a range of different backgrounds, including refugee rights, conservation, addiction counseling, and municipal data science. Despite these varied backgrounds, common lessons emerged, including the importance of valuing the knowledge of experts, recognizing that academic research and practice have differing objectives and timelines, understanding the limits of quantification, and avoiding data extractivism. We consider the impact of these conversations on our work, the potential roles we can serve as researchers, and the challenges we anticipate as we move forward in these collaborations., Comment: Accepted for publication at the fourth ACM Conference on Equity and Access in Algorithms, Mechanisms, and Optimization (EAAMO'24)

The SPARC tokamak is a compact high-field device that will operate at high plasma density with the aim to demonstrate net fusion energy. The experimentally unexplored plasma conditions in SPARC will require a carefully selected set of diagnostics for plasma monitoring and control. Here we explore conceptual design options and potential measurement capabilities of a collective Thomson scattering diagnostic at SPARC. We show that a 140 GHz X-mode CTS system is the most attractive option in terms of optimizing the signal-to-noise ratio and limiting sensitivity to refraction, as well as from a technological readiness perspective. Such a setup can provide core-localized measurements of the fusion -born alpha distribution function, main-ion temperature and toroidal rotation, fuel-ion ratio, and 3He content with relevant spatio-temporal resolution. Our proposed diagnostic layout can in principle be integrated into SPARC and could provide a valuable addition to its diagnostic suite at limited development costs and time., Comment: 26 pages, 10 figures, submitted to Nuclear Fusion

In recent years, the building sector has experienced an increasing legislative pressure to reduce the energy consumption. This has created a global need for affordable building management systems (BMS) in areas such as lighting-, temperature-, air quality monitoring and control. BMS uses 2D and 3D building representations to visualize various aspects of building operations. Today the creation of these visual building representations relies on labor-intensive and costly computer-aided design (CAD) processes. Hence, to create affordable BMS there is an urgent need to develop methods for cost-effective automatic creation of visual building representations. This paper introduces an automatic, metadata-driven method for constructing building visualizations using metadata from existing smart building infrastructure. The method presented in this study utilizes a Velocity Verlet integration-based physics particle simulation that uses metadata to define the force dynamics within the simulation. This process generates an abstract point cloud representing the organization of BMS components into building zones. The developed system was tested in two buildings of respectively 2,560 m2 and 18,000 m2. The method successfully produced visual building representations based on the available metadata, demonstrating its feasibility and cost-effectiveness., Comment: 15 pages, 11 figures

The retrofitting of existing buildings with building management systems presents significant challenges, primarily due to the need for labor and cost efficiency. Wireless technology offers a promising solution to these challenges by minimizing the need for extensive wiring and structural alterations. However, achieving retrofitting in a cost-effective manner necessitates the use of low-cost wireless technologies. This paper introduces a framework for constructing a Zigbee gateway using open-source tools combined with low-cost hardware. The proposed architecture addresses large-scale IoT deployments within the Zigbee ecosystem. By leveraging edge computing with the robustness and scalability offered by Zigbee technology, this architecture significantly reduces the economic barriers to retrofit buildings with building management systems. The results underscore the potential of open-source Zigbee technology in aligning with sustainability goals, providing a cost-effective pathway for retrofitting buildings into smart, energy-efficient living environments.

The growing shift towards a Smart Grid involves integrating numerous new digital energy solutions into the energy ecosystems to address problems arising from the transition to carbon neutrality, particularly in linking the electricity and transportation sectors. Yet, this shift brings challenges due to mass electric vehicle adoption and the lack of methods to adequately assess various EV charging algorithms and their ecosystem impacts. This paper introduces a multi-agent based simulation model, validated through a case study of a Danish radial distribution network serving 126 households. The study reveals that traditional charging leads to grid overload by 2031 at 67% EV penetration, while decentralized strategies like Real-Time Pricing could cause overloads as early as 2028. The developed multi-agent based simulation demonstrates its ability to offer detailed, hourly analysis of future load profiles in distribution grids, and therefore, can be applied to other prospective scenarios in similar energy systems.

Power-to-Hydrogen is crucial for the renewable energy transition, yet existing literature lacks business models for the significant excess heat it generates. This study addresses this by evaluating three models for selling electrolyzer-generated heat to district heating grids: constant, flexible, and renewable-source hydrogen production, with and without heat sales. Using agent-based modeling and multi-criteria decision-making methods (VIKOR, TOPSIS, PROMETHEE), it finds that selling excess heat can cut hydrogen production costs by 5.6%. The optimal model operates flexibly with electricity spot prices, includes heat sales, and maintains a hydrogen price of 3.3 EUR/kg. Environmentally, hydrogen production from grid electricity could emit up to 13,783.8 tons of CO2 over four years from 2023. The best economic and environmental model uses renewable sources and sells heat at 3.5 EUR/kg

This paper addresses the critical integration of electric vehicles (EVs) into the electricity grid, which is essential for achieving carbon neutrality by 2050. The rapid increase in EV adoption poses significant challenges to the existing grid infrastructure, particularly in managing the increasing electricity demand and mitigating the risk of grid overloads. Centralized EV charging strategies are investigated due to their potential to optimize grid stability and efficiency, compared to decentralized approaches that may exacerbate grid stress. Utilizing a multi-agent based simulation model, the study provides a realistic representation of the electric vehicle home charging ecosystem in a case study of Strib, Denmark. The findings show that the Earliest-deadline-first and Round Robin perform best with 100% EV adoption in terms of EV user satisfaction. The simulation considers a realistic adoption curve, EV charging strategies, EV models, and driving patterns to capture the full ecosystem dynamics over a long-term period with high resolution (hourly). Additionally, the study offers detailed load profiles for future distribution grids, demonstrating how centralized charging strategies can efficiently manage grid loads and prevent overloads.

Motivated by questions in quantum theory, we study Hilbert space valued Gaussian processes, and operator-valued kernels, i.e., kernels taking values in B(H) (= all bounded linear operators in a fixed Hilbert space H). We begin with a systematic study of p.d. B(H)-valued kernels and the associated of H-valued Gaussian processes, together with their correlation and transfer operators. In our consideration of B(H)-valued kernels, we drop the p.d. assumption. We show that input-output models can be computed for systems of signed kernels taking the precise form of realizability via associated transfer block matrices (of operators analogous to the realization transforms in systems theory), i.e., represented via 2\times2 operator valued block matrices. In the context of B(H)-valued kernels we present new results on regression with H-valued Gaussian processes.

MoonLITE (Lunar InTerferometry Explorer) is an Astrophysics Pioneers proposal to develop, build, fly, and operate the first separated-aperture optical interferometer in space, delivering sub-mas science results. MoonLITE will leverage the Pioneers opportunity for utilizing NASA's Commercial Lunar Payload Services (CLPS) to deliver an optical interferometer to the lunar surface, enabling unprecedented discovery power by combining high spatial resolution from optical interferometry with deep sensitivity from the stability of the lunar surface. Following landing, the CLPS-provided rover will deploy the pre-loaded MoonLITE outboard optical telescope 100 meters from the lander's inboard telescope, establishing a two-element interferometric observatory with a single deployment. MoonLITE will observe targets as faint as 17th magnitude in the visible, exceeding ground-based interferometric sensitivity by many magnitudes, and surpassing space-based optical systems resolution by a factor of 50 times. The capabilities of MoonLITE open a unique discovery space that includes direct size measurements of the smallest, coolest stars and substellar brown dwarfs; searches for close-in stellar companions orbiting exoplanet-hosting stars that could confound our understanding and characterization of the frequency of Earth-like planets; direct size measurements of young stellar objects and characterization of the terrestrial planet-forming regions of these young stars; measurements of the inner regions and binary fraction of active galactic nuclei; and a probe of the very nature of spacetime foam itself. A portion of the observing time will also be made available to the broader community via a guest observer program. MoonLITE takes advantage of the CLPS opportunity and delivers an unprecedented combination of sensitivity and angular resolution at the remarkably affordable cost point of Pioneers., Comment: 13 pages, 8 figures, SPIE Astronomical Telescopes + Instrumentation 2024

The Big Fringe Telescope (BFT) is a facility concept under development for a next-generation, kilometer-scale optical interferometer. Observations over the past two decades from routinely operational facilities such as CHARA and VLTI have produced groundbreaking scientific results, reflecting the mature state of the techniques in optical interferometry. However, routine imaging of bright main sequence stars remains a surprisingly unexplored scientific realm. Additionally, the three-plus decade old technology infrastructure of these facilities leads to high operations \& maintenance costs, and limits performance. We are developing the BFT, based upon robust, modern, commercially-available, automated technologies with low capital construction and O\&M costs, in support of kilometer-scale optical interferometers that will open the door to regular `snapshot' imaging of main sequence stars. Focusing on extreme angular resolution for bright objects leads to substantial reductions in expected costs through use of COTS elements and simplified infrastructure., Comment: 11 pages, 3 figures, SPIE Astronomical Telescopes + Instrumentation 2024

We present the results of the ALMA Large Program Early Planet Formation in Embedded disks observations of the Class 0 protostar GSS30 IRS3. Our observations included 1.3 mm continuum with a resolution of 0.''05 (7.8 au) and several molecular species including $^{12}$CO, $^{13}$CO, C$^{18}$O, H$_{2}$CO and c-C$_{3}$H$_{2}$. The dust continuum analysis unveiled a disk-shaped structure with a major axis size of $\sim$200 au. We observed an asymmetry in the minor axis of the continuum emission suggesting that the emission is optically thick and the disk is flared. On the other hand, we identified two prominent bumps along the major axis located at distances of 26 and 50 au from the central protostar. The origin of the bumps remains uncertain and might be due to an embedded substructure within the disk or the result of the temperature distribution instead of surface density due to optically thick continuum emission. The $^{12}$CO emission reveals a molecular outflow consisting of three distinct components: a collimated one, an intermediate velocity component exhibiting an hourglass shape, and a wider angle low-velocity component. We associate these components with the coexistence of a jet and a disk-wind. The C$^{18}$O emission traces both a Keplerian rotating circumstellar disk and the infall of the rotating envelope. We measured a stellar dynamical mass of 0.35$\pm$0.09 M$_{\odot}$., Comment: 25 pages, 19 figures. Accepted for publication in A&A

This study focuses on the numerical discretization methods for the continuous-time discounted linear-quadratic optimal control problem (LQ-OCP) with time delays. By assuming piecewise constant inputs, we formulate the discrete system matrices of the discounted LQ-OCPs into systems of differential equations. Subsequently, we derive the discrete-time equivalent of the discounted LQ-OCP by solving these systems. This paper presents three numerical methods for solving the proposed differential equations systems: the fixed-time-step ordinary differential equation (ODE) method, the step-doubling method, and the matrix exponential method. Our numerical experiment demonstrates that all three methods accurately solve the differential equation systems. Interestingly, the step-doubling method emerges as the fastest among them while maintaining the same level of accuracy as the fixed-time-step ODE method.

In this paper, we present a nonlinear model predictive control (NMPC) algorithm for systems modeled by semi-explicit stochastic differential-algebraic equations (DAEs) of index 1. The NMPC combines a continuous-discrete extended Kalman filter (CD-EKF) with an optimal control problem (OCP) for setpoint tracking. We discretize the OCP using direct multiple shooting. We apply an explicit singly diagonal implicit Runge-Kutta (ESDIRK) integration scheme to solve systems of DAEs, both for the one-step prediction in the CD-EKF and in each shooting interval of the discretized OCP. The ESDIRK methods use an iterated internal numerical differentiation approach for precise sensitivity computations. These sensitivities are used to provide accurate gradient information in the OCP and to efficiently integrate the covariance information in the CD-EKF. Subsequently, we present a simulation case study where we apply the NMPC to a simple alkaline electrolyzer stack model. We use the NMPC to track a time-varying setpoint for the stack temperature subject to input bound constraints.

This study presents the design, discretization and implementation of the continuous-time linear-quadratic model predictive control (CT-LMPC). The control model of the CT-LMPC is parameterized as transfer functions with time delays, and they are separated into deterministic and stochastic parts for relevant control and filtering algorithms. We formulate time-delay, finite-horizon CT linear-quadratic optimal control problems (LQ-OCPs) for the CT-LMPC. By assuming piece-wise constant inputs and constraints, we present the numerical discretization of the proposed LQ-OCPs and show how to convert the discrete-time (DT) equivalent into a standard quadratic program. The performance of the CT-LMPC is compared with the conventional DT-LMPC algorithm. Our numerical experiments show that, under fixed tunning parameters, the CT-LMPC shows better closed-loop performance as the sampling time increases than the conventional DT-LMPC.

We present Atacama Large Millimeter/submillimeter Array (ALMA) observations of the binary Class 0 protostellar system BHR 71 IRS1 and IRS2 as part of the Early Planet Formation in Embedded Disks (eDisk) ALMA Large Program. We describe the $^{12}$CO ($J$=2--1), $^{13}$CO ($J$=2--1), C$^{18}$O ($J$=2--1), H$_2$CO ($J=3_{2,1}$--$2_{2,0}$), and SiO ($J$=5--4) molecular lines along with the 1.3 mm continuum at high spatial resolution ($\sim$0.08" or $\sim$5 au). Dust continuum emission is detected toward BHR 71 IRS1 and IRS2, with a central compact component and extended continuum emission. The compact components are smooth and show no sign of substructures such as spirals, rings or gaps. However, there is a brightness asymmetry along the minor axis of the presumed disk in IRS1, possibly indicative of an inclined geometrically and optically thick disk-like component. Using a position-velocity diagram analysis of the C$^{18}$O line, clear Keplerian motions were not detected toward either source. If Keplerian rotationally-supported disks are present, they are likely deeply embedded in their envelope. However, we can set upper limits of the central protostellar mass of 0.46 M$_\odot$ and 0.26 M$_\odot$ for BHR 71 IRS1 and BHR 71 IRS2, respectively. Outflows traced by $^{12}$CO and SiO are detected in both sources. The outflows can be divided into two components, a wide-angle outflow and a jet. In IRS1, the jet exhibits a double helical structure, reflecting the removal of angular momentum from the system. In IRS2, the jet is very collimated and shows a chain of knots, suggesting episodic accretion events., Comment: 38 pages, 29 figures, accepted in ApJ