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This paper introduces the concept of Fractal Frenet equations, a set of differential equations used to describe the behavior of vectors along fractal curves. The study explores the analogue of arc length for fractal curves, providing a measure to quantify their length. It also discusses fundamental mathematical constructs, such as the analogue of the unit tangent vector, which indicates the curve's direction at different points, and the analogue of curvature vector or fractal curvature vector, which characterizes its curvature at various locations. The concept of torsion, describing the twisting and turning of fractal curves in three-dimensional space, is also explored. Specific examples, like the fractal helix and the fractal snowflake, illustrate the application and significance of the Fractal Frenet equations.

We use both chirped-pulse Fourier transform and frequency modulated absorption spectroscopy to study the rotational spectrum of 2-methoxyethanol in several frequency regions ranging from 8.7-500 GHz. The resulting rotational parameters permitted a search for this molecule in Atacama Large Millimeter/submillimeter Array (ALMA) observations toward the massive protocluster NGC 6334I as well as source B of the low-mass protostellar system IRAS 16293-2422. 25 rotational transitions are observed in the ALMA Band 4 data toward NGC 6334I, resulting in the first interstellar detection of 2-methoxyethanol. A column density of $1.3_{-0.9}^{+1.4} \times 10^{17}$ cm$^{-2}$ is derived at an excitation temperature of $143_{-39}^{+31}$ K. However, molecular signal is not observed in the Band 7 data toward IRAS 16293-2422B and an upper limit column density of $2.5 \times 10^{15}$ cm$^{-2}$ is determined. Various possible formation pathways--including radical recombination and insertion reactions--are discussed. We also investigate physical differences between the two interstellar sources that could result in the observed abundance variations., Comment: Accepted for publication in The Astrophysical Journal Letters

Young protostellar binary systems, with expected ages less than $\sim$10$^5$ years, are little modified since birth, providing key clues to binary formation and evolution. We present a first look at the young, Class 0 binary protostellar system R CrA IRAS 32 from the Early Planet Formation in Embedded Disks (eDisk) ALMA large program, which observed the system in the 1.3 mm continuum emission, $^{12}$CO (2-1), $^{13}$CO (2-1), C$^{18}$O (2-1), SO (6$_5$-5$_4$), and nine other molecular lines that trace disk, envelope, shocks, and outflows. With a continuum resolution of $\sim$0.03$^{\prime\prime}$ ($\sim$5 au, at a distance of 150 pc), we characterize the newly discovered binary system with a separation of 207 au, their circumstellar disks, and a circumbinary disk-like structure. The circumstellar disk radii are 26.9$\pm$0.3 and 22.8$\pm$0.3 au for sources A and B, respectively, and their circumstellar disk dust masses are estimated as 22.5$\pm$1.1 and 12.4$\pm$0.6 M$_{\Earth}$. The circumstellar disks and the circumbinary structure have well aligned position angles and inclinations, indicating formation in a smooth, ordered process such as disk fragmentation. In addition, the circumstellar disks have a near/far-side asymmetry in the continuum emission suggesting that the dust has yet to settle into a thin layer near the midplane. Spectral analysis of CO isotopologues reveals outflows that originate from both of the sources and possibly from the circumbinary disk-like structure. Furthermore, we detect Keplerian rotation in the $^{13}$CO isotopologues toward both circumstellar disks and likely Keplerian rotation in the circumbinary structure; the latter suggests that it is probably a circumbinary disk., Comment: 33 pages, 29 figures, 6 tables

Based on Berenstein and Retakh's notion of noncommutative polygons we introduce and study noncommutative frieze patterns. We generalize several notions and fundamental properties from the classic (commutative) frieze patterns to noncommutative frieze patterns, e.g. propagation formulae and $\mu$-matrices, quiddity cycles and reduction formulae, and we show that local noncommutative exchange relations and local triangle relations imply all noncommutative exchange relations and triangle relations. Throughout, we allow coefficients, so we obtain generalizations of results from our earlier paper on frieze patterns with coefficients from the commutative to the noncommutative setting., Comment: 18 pages. v2: reference added to a paper by Bergeron and Reutenauer

Our aim in this paper is to refine the orbital and physical parameters of the HATS-2 planetary system and study transit timing variations and atmospheric composition thanks to transit observations that span more than ten years and that were collected using different instruments and pass-band filters. We also investigate the orbital alignment of the system by studying the anomalies in the transit light curves induced by starspots on the photosphere of the parent star. We analysed new transit events from both ground-based telescopes and NASA's TESS mission. Anomalies were detected in most of the light curves and modelled as starspots occulted by the planet during transit events. We fitted the clean and symmetric light curves with the JKTEBOP code and those affected by anomalies with the PRISM+GEMC codes to simultaneously model the photometric parameters of the transits and the position, size, and contrast of each starspot. We found consistency between the values we found for the physical and orbital parameters and those from the discovery paper and ATLAS9 stellar atmospherical models. We identified different sets of consecutive starspot-crossing events that temporally occurred in less than five days. Under the hypothesis that we are dealing with the same starspots, occulted twice by the planet during two consecutive transits, we estimated the rotational period of the parent star and, in turn the projected and the true orbital obliquity of the planet. We find that the system is well aligned. We identified the possible presence of transit timing variations in the system, which can be caused by tidal orbital decay, and we derived a low-resolution transmission spectrum., Comment: 23 pages, 21 figures, Accepted for publication in Astronomy & Astrophysics

Advanced machine learning algorithms are increasingly utilized to provide data-based prediction and decision-making support in Industry 4.0. However, the prediction accuracy achieved by the existing models is insufficient to warrant practical implementation in real-world applications. This is because not all features present in real-world datasets possess a direct relevance to the predictive analysis being conducted. Consequently, the careful incorporation of select features has the potential to yield a substantial positive impact on the outcome. To address the research gap, this paper proposes a novel hybrid framework that combines the feature importance detector - local interpretable model-agnostic explanations (LIME) and the feature interaction detector - neural interaction detection (NID), to improve prediction accuracy. By applying the proposed framework, unnecessary features can be eliminated, and interactions are encoded to generate a more conducive dataset for predictive purposes. Subsequently, the proposed model is deployed to refine the prediction of electricity consumption in foundry processing. The experimental outcomes reveal an augmentation of up to 9.56% in the R2 score, and a diminution of up to 24.05% in the root mean square error.

The transportation sector remains a major contributor to greenhouse gas emissions. The understanding of energy-efficient driving behaviors and utilization of energy-efficient driving strategies are essential to reduce vehicles' fuel consumption. However, there is no comprehensive investigation into energy-efficient driving behaviors and strategies. Furthermore, many state-of-the-art AI models have been applied for the analysis of eco-friendly driving styles, but no overview is available. To fill the gap, this paper conducts a thorough literature review on ecological driving behaviors and styles and analyzes the driving factors influencing energy consumption and state-of-the-art methodologies. With a thorough scoping review process, the methodological and related data are compared. The results show that the factors that impact driving behaviors can be summarized into eleven features including speed, acceleration, deceleration, pedal, and so on. This paper finds that supervised/unsupervised learning algorithms and reinforcement learning frameworks have been popularly used to model the vehicle's energy consumption with multi-dimensional data. Furthermore, the literature shows that the driving data are collected from either simulators or real-world experiments, and the real-world data are mainly stored and transmitted by meters, controller area networks, onboard data services, smartphones, and additional sensors installed in the vehicle. Based on driving behavior factors, driver characteristics, and safety rules, this paper recommends nine energy-efficient driving styles including four guidelines for the drivers' selection and adjustment of the vehicle parameters, three recommendations for the energy-efficient driving styles in different driving scenarios, and two subjective suggestions for different types of drivers and employers.

For multi-variable finite measure spaces, we present in this paper a new framework for non-orthogonal $L^2$ Fourier expansions. Our results hold for probability measures $\mu$ with finite support in $\mathbb{R}^d$ that satisfy a certain disintegration condition that we refer to as ``slice-singular''. In this general framework, we present explicit $L^{2}(\mu)$-Fourier expansions, with Fourier exponentials having positive Fourier frequencies in each of the d coordinates. Our Fourier representations apply to every $f \in L^2(\mu)$, are based on an extended Kaczmarz algorithm, and use a new recursive $\mu$ Rokhlin disintegration representation. In detail, our Fourier series expansion for $f$ is in terms of the multivariate Fourier exponentials $\{e_n\}$, but the associated Fourier coefficients for $f$ are now computed from a Kaczmarz system $\{g_n\}$ in $L^{2}(\mu)$ which is dual to the Fourier exponentials. The $\{g_n\}$ system is shown to be a Parseval frame for $L^{2}(\mu)$. Explicit computations for our new Fourier expansions entail a detailed analysis of subspaces of the Hardy space on the polydisk, dual to $L^{2}(\mu)$, and an associated d-variable Normalized Cauchy Transform. Our results extend earlier work for measures $\mu$ in one and two dimensions, i.e., $d=1 (\mu $ singular), and $d=2 (\mu$ assumed slice-singular). Here our focus is the extension to the cases of measures $\mu$ in dimensions $d >2$. Our results are illustrated with the use of explicit iterated function systems (IFSs), including the IFS generated Menger sponge for $d=3$.

Uncertainty Quantification (UQ) is vital to safety-critical model-based analyses, but the widespread adoption of sophisticated UQ methods is limited by technical complexity. In this paper, we introduce UM-Bridge (the UQ and Modeling Bridge), a high-level abstraction and software protocol that facilitates universal interoperability of UQ software with simulation codes. It breaks down the technical complexity of advanced UQ applications and enables separation of concerns between experts. UM-Bridge democratizes UQ by allowing effective interdisciplinary collaboration, accelerating the development of advanced UQ methods, and making it easy to perform UQ analyses from prototype to High Performance Computing (HPC) scale. In addition, we present a library of ready-to-run UQ benchmark problems, all easily accessible through UM-Bridge. These benchmarks support UQ methodology research, enabling reproducible performance comparisons. We demonstrate UM-Bridge with several scientific applications, harnessing HPC resources even using UQ codes not designed with HPC support., Comment: Add Benjamin Kent as co-author in accordance with the paper's published version

In this paper, we compare the impact of iterated and direct approaches to sensitivity computation in fixed-step explicit singly diagonally-implicit Runge-Kutta (ESDIRK) methods when applied to optimal control problems (OCPs). We use the principle of internal numerical differentiation (IND) strictly for the iterated approach, i.e., reusing the iteration matrix factorizations, the number of Newton-type iterations, and Newton iterates, to compute the sensitivities. The direct method computes the sensitivities without using the Newton schemes. We compare the impact of the iterated and direct sensitivity computations in OCPs for the quadruple tank system. We benchmark the iterated and direct approaches with a base case. This base case is an OCP that applies an ESDIRK method that refactorizes the iteration matrix in every Newton iteration and uses a direct approach for sensitivity computations. In these OCPs, we vary the number of integration steps between control intervals and we evaluate the performance based on the number of SQP and QPs iterations, KKT violations, and the total number of function evaluations, Jacobian updates, and iteration matrix factorizations. The results indicate that the iterated approach outperforms the direct approach but yields similar performance to the base case., Comment: 6 pages, 5 figures, 2 tables. Submitted for European Control Conference 2024 (ECC2024). Stockholm, Sweden

Digitalization is challenging in heavy industrial sectors, and many pi-lot projects facing difficulties to be replicated and scaled. Case studies are strong pedagogical vehicles for learning and sharing experience & knowledge, but rarely available in the literature. Therefore, this paper conducts a survey to gather a diverse set of nine industry cases, which are subsequently subjected to analysis using the business model canvas (BMC). The cases are summarized and compared based on nine BMC components, and a Value of Business Model (VBM) evaluation index is proposed to assess the business potential of industrial digital solutions. The results show that the main partners are industry stakeholders, IT companies and academic institutes. Their key activities for digital solutions include big-data analysis, machine learning algorithms, digital twins, and internet of things developments. The value propositions of most cases are improving energy efficiency and enabling energy flexibility. Moreover, the technology readiness levels of six industrial digital solutions are under level 7, indicating that they need further validation in real-world environments. Building upon these insights, this paper proposes six recommendations for future industrial digital solution development: fostering cross-sector collaboration, prioritizing comprehensive testing and validation, extending value propositions, enhancing product adaptability, providing user-friendly platforms, and adopting transparent recommendations.

Structural breaks occur in timeseries data across a broad range of fields, from economics to nanosciences. For measurements of single-molecule break junctions, structural breaks in conductance versus displacement data occur when the molecular junction ruptures. This moment is significant because the molecule is likely in its most extended geometry, and therefore resembles most closely the geometry used in theoretical predictions. Conventional single-molecule break junction data analysis, on the other hand, typically uses the entire molecular plateau to estimate the single-molecule conductance, which skews the estimate when the plateau is sloped. Borrowing from econometrics, where the study of structural breaks is well established, we present change point detection (CPD) as a tool to search for junction rupture in single-molecule break junction data, and improve estimates in single-molecule conductance. We demonstrate that using CPD instead of the conventional 1D conductance histogram to determine the mean molecular conductance yields a standard deviation in the estimate of typically half that of the conventional approach, greatly improving accuracy. We apply CPD to three separate data sets, two on 4,4'-bipyridine and one on a silane, two at room temperature and one at 4 K, two in one lab, one in another, to show the wide applicability of even the simplest of CPD algorithms: the Chow test. This versatility and better accuracy will propagate into more accurate theoretical simulations. These improved metrics, in turn, will further improve any downstream analyses, including all emerging machine learning approaches., Comment: 33 pages and 11 figures and supporting material of 8 pages and 3 figures

The index in triangulated categories plays a key role in the categorification of cluster algebras; specifically, it categorifies the notion of $g$-vectors. For an object $C$ in a triangulated category $\mathcal{C}$, the index of $C$ was originally defined as $[X_0] - [X_1]$ when $X_1 \to X_0 \to C \to \Sigma X_1$ is a triangle with the $X_i$ in a cluster tilting subcategory $\mathcal{X}$ of $\mathcal{C}$. Using the theory of extriangulated categories, the index was later generalised to the case where $\mathcal{X}$ is a contravariantly finite subcategory which is rigid, that is, satisfies $\mathcal{C}( \mathcal{X},\Sigma \mathcal{X} ) = 0$. This paper generalises further by dropping the assumption that $\mathcal{X}$ is rigid, vastly increasing the potential choice of $\mathcal{X}$. We show that this version of the index still has the key property of being additive on triangles up to an error term., Comment: Minor corrections, 13 pages

Electric vehicles are expected to significantly contribute to CO2-eq. emissions reduction, but the increasing number of EVs also introduces chal-lenges to the energy system, and to what extent it contributes to achieving cli-mate goals remains unknown. Static modeling and assumption-based simula-tions have been used for such investigation, but they cannot capture the realistic ecosystem dynamics. To fill the gap, this paper investigates the impacts of two adoption curves of private EVs on the electricity distribution grids and national climate goals. This paper develops a multi-agent based simulation with two adoption curves, the Traditional EV charging strategy, various EV models, driv-ing patterns, and CO2-eq. emission data to capture the full ecosystem dynamics during a long-term period from 2020 to 2032. The Danish 2030 climate goal and a Danish distribution network with 126 residential consumers are chosen as the case study. The results show that both EV adoption curves of 1 million and 775k EVs by 2030 will not satisfy the Danish climate goal of reducing transport sector emissions by 30% by 2030. The results also show that the current resi-dential electricity distribution grids cannot handle the load from increasing EVs. The first grid overload will occur in 2031 (around 16 and 24 months later for the 1 million and 775k EVs adopted by 2030) with a 67% share of EVs in the grid.

Energy load disaggregation can contribute to balancing power grids by enhancing the effectiveness of demand-side management and promoting electricity-saving behavior through increased consumer awareness. However, the field currently lacks a comprehensive overview. To address this gap, this paper con-ducts a scoping review of load disaggregation domains, data types, and methods, by assessing 72 full-text journal articles. The findings reveal that domestic electricity consumption is the most researched area, while others, such as industrial load disaggregation, are rarely discussed. The majority of research uses relatively low-frequency data, sampled between 1 and 60 seconds. A wide variety of methods are used, and artificial neural networks are the most common, followed by optimization strategies, Hidden Markov Models, and Graph Signal Processing approaches.

Complex organic molecules (COMs) have been detected ubiquitously in protostellar systems. However, at shorter wavelengths (~0.8mm) it is more difficult to detect larger molecules than at longer wavelengths (~3mm) because of the increase of millimeter dust opacity, line confusion, and unfavorable partition function. We aim to search for large molecules (>8 atoms) in the ALMA Band 3 spectrum of IRAS 16293-2422 B. We search for more than 70 molecules and identify as many lines as possible in the spectrum. The spectral settings were set to specifically target three-carbon species such as propanol and glycerol. We identify lines of 31 molecules including many oxygen-bearing COMs such as CH3OH and c-C2H4O and a few nitrogen- and sulfur-bearing ones such as HOCH2CN and CH3SH. The largest detected molecules are gGg-(CH2OH)2 and CH3COCH3. We do not detect glycerol or propanol but provide upper limits for them which are in line with previous laboratory and observational studies. The line density in Band 3 is only ~2.5 times lower in frequency space than in Band 7. From the detected lines in Band 3 at a $\gtrsim 6\sigma$ level, ~25-30% of them could not be identified indicating the need for more laboratory data of rotational spectra. We find similar column densities and column density ratios of COMs (within a factor ~2) between Band 3 and Band 7. The effect of dust optical depth for IRAS 16293-2422 B at an off-source location on column densities and column density ratios is minimal. Moreover, for warm protostars, long wavelength spectra are not only crowded, but also take longer integration times to reach the same sensitivity limit. The 3mm search has not yet resulted in detection of larger and more complex molecules in warm sources. A full deep ALMA Band 2-3 (i.e., 3-4 mm) survey is needed to assess whether low frequency data have the potential to reveal more complex molecules in warm sources., Comment: Accepted for publication in A&A

Improving energy efficiency in industrial production processes is crucial for competitiveness, and compliance with climate policies. This paper introduces a data-driven approach to identify optimal melting patterns in induction furnaces. Through time-series K-means clustering the melting patterns could be classified into distinct clusters based on temperature profiles. Using the elbow method, 12 clusters were identified, representing the range of melting patterns. Performance parameters such as melting time, energy-specific performance, and carbon cost were established for each cluster, indicating furnace efficiency and environmental impact. Multiple criteria decision-making methods including Simple Additive Weighting, Multiplicative Exponential Weighting, Technique for Order of Preference by Similarity to Ideal Solution, modified TOPSIS, and VlseKriterijumska Optimizacija I Kompromisno Resenje were utilized to determine the best-practice cluster. The study successfully identified the cluster with the best performance. Implementing the best practice operation resulted in an 8.6 % reduction in electricity costs, highlighting the potential energy savings in the foundry.

It is known from Earth that ionizing high-energy radiation can lead to ion-induced nucleation of cloud condensation nuclei in the atmosphere. Since the amount of high-energy radiation can vary greatly based on the radiative environment of a host star, understanding the effect of high-energy radiation on cloud particles is critical to understand exoplanet atmospheres. This study aims to explore how high-energy radiation affects the aggregation and charging of mineral cloud particles. We present experiments conducted in an atmosphere chamber on mineral SiO$_2$ particles with diameters of 50 nm. The particles were exposed to gamma radiation in either low-humidity (RH $\approx$ 20%) or high-humidity (RH $>$ 50%) environments. The aggregation and charging state of the particles were studied with a Scanning Mobility Particle Sizer. We find that the single SiO$_2$ particles (N1) cluster to form larger aggregates (N2 - N4), and that this aggregation is inhibited by gamma radiation. We find that gamma radiation shifts the charging of the particles to become more negative, by increasing the charging state of negatively charged particles. Through an independent T-test we find that this increase is statistically significant within a 5% significance level for all aggregates in the high-humidity environment, and for all except the N1 particles in the low-humidity environment. For the positively charged particles the changes in charging state are not within the 5% significance level. We suggest that the overall effect of gamma radiation could favor the formation of a high number of small particles over a lower number of larger particles., Comment: Accepted to ApJ, 19 pages, 9 figures

Facing economic challenges due to the diverse objectives of businesses, and consumers, commercial greenhouses strive to minimize energy costs while addressing CO2 emissions. This scenario is intensified by rising energy costs and the global imperative to curtail CO2 emissions. To address these dynamic economic challenges, this paper proposes an architectural design for an energy economic dispatch testbed for commercial greenhouses. Utilizing the Attribute-Driven De-sign method, core architectural components of a software-in-the-loop testbed are proposed which emphasizes modularity and careful consideration of the multi-objective optimization problem. This approach extends prior research by implementing a modular multi-objective optimization framework in Java. The results demonstrate the successful integration of the CO2 reduction objective within the modular architecture with minimal effort. The multi-objective optimization output can also be employed to examine cost and CO2 objectives, ultimately serving as a valuable decision-support tool. The novel testbed architecture and a modular approach can tackle the multi-objective optimization problem and enable commercial greenhouses to navigate the intricate landscape of energy cost and CO2 emissions management., Comment: 19 pages

In machine learning energy potentials for atomic systems, forces are commonly obtained as the negative derivative of the energy function with respect to atomic positions. To quantify aleatoric uncertainty in the predicted energies, a widely used modeling approach involves predicting both a mean and variance for each energy value. However, this model is not differentiable under the usual white noise assumption, so energy uncertainty does not naturally translate to force uncertainty. In this work we propose a machine learning potential energy model in which energy and force aleatoric uncertainty are linked through a spatially correlated noise process. We demonstrate our approach on an equivariant messages passing neural network potential trained on energies and forces on two out-of-equilibrium molecular datasets. Furthermore, we also show how to obtain epistemic uncertainties in this setting based on a Bayesian interpretation of deep ensemble models., Comment: Presented at Advancing Molecular Machine Learning - Overcoming Limitations [ML4Molecules], ELLIS workshop, VIRTUAL, December 8, 2023, unofficial NeurIPS 2023 side-event

Recent work in activation steering has demonstrated the potential to better control the outputs of Large Language Models (LLMs), but it involves finding steering vectors. This is difficult because engineers do not typically know how features are represented in these models. We seek to address this issue by applying the idea of mean-centring to steering vectors. We find that taking the average of activations associated with a target dataset, and then subtracting the mean of all training activations, results in effective steering vectors. We test this method on a variety of models on natural language tasks by steering away from generating toxic text, and steering the completion of a story towards a target genre. We also apply mean-centring to extract function vectors, more effectively triggering the execution of a range of natural language tasks by a significant margin (compared to previous baselines). This suggests that mean-centring can be used to easily improve the effectiveness of activation steering in a wide range of contexts.

Decentralized Finance (DeFi) is reshaping traditional finance by enabling direct transactions without intermediaries, creating a rich source of open financial data. Layer 2 (L2) solutions are emerging to enhance the scalability and efficiency of the DeFi ecosystem, surpassing Layer 1 (L1) systems. However, the impact of L2 solutions is still underexplored, mainly due to the lack of comprehensive transaction data indices for economic analysis. This study bridges that gap by analyzing over 50 million transactions from Uniswap, a major decentralized exchange, across both L1 and L2 networks. We created a set of daily indices from blockchain data on Ethereum, Optimism, Arbitrum, and Polygon, offering insights into DeFi adoption, scalability, decentralization, and wealth distribution. Additionally, we developed an open-source Python framework for calculating decentralization indices, making this dataset highly useful for advanced machine learning research. Our work provides valuable resources for data scientists and contributes to the growth of the intelligent Web3 ecosystem.