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Motivated by the spectral theory of relativistic atoms, we prove matching upper and lower bounds for the transition density of Hardy perturbations of subordinated Bessel heat kernels. The analysis is based on suitable supermedian functions, in particular invariant functions., Comment: 59 pages

Modelling the scrape-off layer of a stellarator is challenging due to the complex magnetic 3D geometry. The here presented study analyses simulations of the scrape-off layer (SOL) of the stellarator Wendelstein 7-X (W7-X) using spatially varying diffusion coefficients for the magnetic standard configuration, extending our previous study. Comparing the EMC3-Eirene simulations with experimental observations, an inconsistency between the strike-line width (SLW) and the upstream parameters was observed. While to match the experimental SLW a particle diffusion coefficient $D \approx 0.2$ is needed, $D \approx 1$ is needed to get experimental separatrix temperatures of 50\,eV at the given experimental heating power. We asses the impact of physically motivated spatially varying transport coeffients. Agreement with experimental data can be improved, but various differences remain. We show that drifts are expected to help overcome the discrepancies and, thus, the development of SOL transport models including drifts is a necessary next step to study the SOL transport of the W7-X stellarator., Comment: 15 pages, 13 figures. arXiv admin note: substantial text overlap with arXiv:2201.06341

Transparency rendering is problematic and can be considered an open problem in real-time graphics. There are many different algorithms currently available, but handling complex scenes and achieving accurate, glitch-free results is still costly. This paper describes LucidRaster: a software rasterizer running on a GPU which allows for efficient exact rendering of complex transparent scenes. It uses a new two-stage sorting technique and sample accumulation method. On average it's faster than high-quality OIT approximations and only about 3x slower than hardware alpha blending. It can be very efficient especially when rendering scenes with high triangle density or high depth complexity., Comment: 15 pages, 21 figures

Predictive Maintenance (PdM) emerged as one of the pillars of Industry 4.0, and became crucial for enhancing operational efficiency, allowing to minimize downtime, extend lifespan of equipment, and prevent failures. A wide range of PdM tasks can be performed using Artificial Intelligence (AI) methods, which often use data generated from industrial sensors. The steel industry, which is an important branch of the global economy, is one of the potential beneficiaries of this trend, given its large environmental footprint, the globalized nature of the market, and the demanding working conditions. This survey synthesizes the current state of knowledge in the field of AI-based PdM within the steel industry and is addressed to researchers and practitioners. We identified 219 articles related to this topic and formulated five research questions, allowing us to gain a global perspective on current trends and the main research gaps. We examined equipment and facilities subjected to PdM, determined common PdM approaches, and identified trends in the AI methods used to develop these solutions. We explored the characteristics of the data used in the surveyed articles and assessed the practical implications of the research presented there. Most of the research focuses on the blast furnace or hot rolling, using data from industrial sensors. Current trends show increasing interest in the domain, especially in the use of deep learning. The main challenges include implementing the proposed methods in a production environment, incorporating them into maintenance plans, and enhancing the accessibility and reproducibility of the research., Comment: Preprint submitted to Engineering Applications of Artificial Intelligence

This paper analyzes the neutral fluxes in the divertor region of the W7-X standard configuration for different input powers, both under attached and detached conditions. The performed analysis is conducted through EMC3-EIRENE simulations. They show the importance of the horizontal divertor to generate neutrals, and resolve the neutral plugging in the divertor region. Simulations of detached cases show a decrease in the number of generated neutrals compared to the attached simulations, in addition to a higher fraction of the ion flux arriving on the baffles during detachment. As the ionization takes place further inside the plasma during detachment, a larger percentage of the generated neutral particles leave the divertor as neutrals. The leakage in the poloidal and toroidal direction increases, just as the fraction of collected particles at the pumping gap. The fraction of pumped particles increases with a factor two, but stays below one percent. This demonstrates that detachment with the current target geometry, although it improves the power exhaust, is not yet leading to an increased particle exhaust.

We provide sharp two-sided estimates of the heat kernel of the Dirichlet fractional Laplacian on the half-line perturbed by the Hardy potential., Comment: 20 pages

As software projects rapidly evolve, software artifacts become more complex and defects behind get harder to identify. The emerging Transformer-based approaches, though achieving remarkable performance, struggle with long code sequences due to their self-attention mechanism, which scales quadratically with the sequence length. This paper introduces SparseCoder, an innovative approach incorporating sparse attention and learned token pruning (LTP) method (adapted from natural language processing) to address this limitation. Compared to previous state-of-the-art models CodeBERT, RoBERTa, and CodeT5, our experiments demonstrate that SparseCoder can handle significantly longer input sequences--at least twice as long, within the limits of our hardware resources and data statistics. Additionally, SparseCoder is four times faster than other methods measured in runtime, achieving a 50% reduction in floating point operations per second (FLOPs) with a negligible performance drop of less than 1% compared to Transformers using sparse attention (Sparse Atten). Plotting FLOPs of model inference against token lengths reveals that SparseCoder scales linearly, whereas other methods, including the current state-of-the-art model CodeT5, scale quadratically. Moreover, SparseCoder enhances interpretability by visualizing non-trivial tokens layer-wise., Comment: 34 pages, 9 figures, pre-print

Biology is perhaps the most complex of the sciences, given the incredible variety of chemical species that are interconnected in spatial and temporal pathways that are daunting to understand. Their interconnections lead to emergent properties such as memory, consciousness, and recognition of self and non-self. To understand how these interconnected reactions lead to cellular life characterized by activation, inhibition, regulation, homeostasis, and adaptation, computational analyses and simulations are essential, a fact recognized by the biological communities. At the same time, students struggle to understand and apply binding and kinetic analyses for the simplest reactions such as the irreversible first-order conversion of a single reactant to a product. This likely results from cognitive difficulties in combining structural, chemical, mathematical, and textual descriptions of binding and catalytic reactions. To help students better understand dynamic reactions and their analyses, we have introduced two kinds of interactive graphs and simulations into the online educational resource, Fundamentals of Biochemistry, a multivolume biochemistry textbook that is part of the LibreText collection. One type is available for simple binding and kinetic reactions. The other displays progress curves (concentrations vs time) for both simple reactions and more complex metabolic and signal transduction pathways, including those available through databases using systems biology markup language (SBML) files. Users can move sliders to change dissociation and kinetic constants as well as initial concentrations and see instantaneous changes in the graphs. They can also export data into a spreadsheet for further processing, such as producing derivative Lineweaver-Burk and traditional Michaelis-Menten graphs of initial velocity (v0) vs substrate concentration., Comment: 17 pages, 2 tables, 8 figures. Submitted to Biochemistry and Molecular Biology Education. Funding: MiniSidewinder: NIH/NIGMS (Grant R01-GM123032-04) LibreText: Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot

Explainable Artificial Intelligence (XAI) fills the role of a critical interface fostering interactions between sophisticated intelligent systems and diverse individuals, including data scientists, domain experts, end-users, and more. It aids in deciphering the intricate internal mechanisms of ``black box'' Machine Learning (ML), rendering the reasons behind their decisions more understandable. However, current research in XAI primarily focuses on two aspects; ways to facilitate user trust, or to debug and refine the ML model. The majority of it falls short of recognising the diverse types of explanations needed in broader contexts, as different users and varied application areas necessitate solutions tailored to their specific needs. One such domain is Predictive Maintenance (PdM), an exploding area of research under the Industry 4.0 \& 5.0 umbrella. This position paper highlights the gap between existing XAI methodologies and the specific requirements for explanations within industrial applications, particularly the Predictive Maintenance field. Despite explainability's crucial role, this subject remains a relatively under-explored area, making this paper a pioneering attempt to bring relevant challenges to the research community's attention. We provide an overview of predictive maintenance tasks and accentuate the need and varying purposes for corresponding explanations. We then list and describe XAI techniques commonly employed in the literature, discussing their suitability for PdM tasks. Finally, to make the ideas and claims more concrete, we demonstrate XAI applied in four specific industrial use cases: commercial vehicles, metro trains, steel plants, and wind farms, spotlighting areas requiring further research., Comment: 51 pages, 9 figures

Dzyaloshinskii-Moriya interaction (DMI) manifesting in asymmetric layered ferromagnetic films gives rise to non-colinear spin structures stabilizing magnetization configurations with nontrivial topology. In this work magnetization reversal, domain structure, and strength of DMI are related with the structure of W/Co/Pt multilayers grown by molecular beam epitaxy. Applied growth method enables fabrication of layered systems with higher crystalline quality than commonly applied sputtering techniques. As a result, a high value of D coefficient was determined from the aligned magnetic domain stripe structure, substantially exceeding 2 mJ/m2. The highest value of DMI value D$_{eff}$ = 2.64mj/m2 and strength of surface DMI parameter DS = 1.83pJ/m for N=10 has been observed. Experimental results coincide precisely with those obtained from structure based micromagnetic modelling and density functional theory calculations performed for well-defined layered stacks. This high value of DMI strength originates from dominating contributions of the interfacial atomic Co layers and additive character from both interface types.

SHACL is a W3C-proposed schema language for expressing structural constraints on RDF graphs. Recent work on formalizing this language has revealed a striking relationship to description logics. SHACL expressions can use three fundamental features that are not so common in description logics. These features are equality tests; disjointness tests; and closure constraints. Moreover, SHACL is peculiar in allowing only a restricted form of expressions (so-called targets) on the left-hand side of inclusion constraints. The goal of this paper is to obtain a clear picture of the impact and expressiveness of these features and restrictions. We show that each of the four features is primitive: using the feature, one can express boolean queries that are not expressible without using the feature. We also show that the restriction that SHACL imposes on allowed targets is inessential, as long as closure constraints are not used. In addition, we show that enriching SHACL with "full" versions of equality tests, or disjointness tests, results in a strictly more powerful language.

The formation of the radial electric field, $E_{\rm r}$ in the SOL has been experimentally studied for attached divertor conditions in stellarator W7-X. The main objective of this study is to test the validity in a complex 3D island divertor of simple models, typically developed in tokamaks, relating $E_{\rm r}$ to the sheath potential drop gradient at the target. Additionally, we investigate the effect of the edge $E_{\rm r}$ shear on the reduction of density fluctuation amplitude, a well-established phenomenon according to the existing bibliography. The main diagnostic for measurements in the SOL is a V-band Doppler reflectometer that can provide the measurement of the $E_{\rm r}$ and density fluctuations with good spatial resolution. Three-dimensional measurements of divertor parameters has been carried out using infrared cameras, with $\lambda_{\rm q}$ resulting a suitable proxy for the model-relevant $\lambda_{\rm T}$. In the investigated attached regimes, it is shown for the first time that the formation of the $E_{\rm r}$ in the SOL depends on parameters at the divertor, following a $E_{\rm r} \propto T_{\rm e} /\lambda_q$ qualitatively similar to that found in a tokamak. Then, from the analyzed plasmas, the observed $E_{\rm r}$ shear at the edge is linked to a moderate local reduction of the amplitude of density fluctuations.

In this study, we develop a multi criteria model to identify dengue outbreak periods. To validate the model, we performed a simulation using dengue transmission-related data in Sri Lanka's Western Province. Our results indicated that the developed model can be used to predict a dengue outbreak situation in a given region up to one month in advance.

We obtain Gr\"onwall type estimates for the gradient of the harmonic functions for a L\'evy operator with order strictly larger than 1 and minimal assumptions of its L\'evy measure.

We give local in time sharp two sided estimates of the heat kernel associated with the relativistic stable operator perturbed by a critical (Hardy) potential.

We consider non-local Schr\"odinger operators $H=-L-V$ in $L^2(\mathbf{R}^d)$, $d \geq 1$, where the kinetic terms $L$ are pseudo-differential operators which are perturbations of the fractional Laplacian by bounded non-local operators and $V$ is the fractional Hardy potential. We prove pointwise estimates of eigenfunctions corresponding to negative eigenvalues and upper finite-time horizon estimates for heat kernels. We also analyze the relation between the matching lower estimates of the heat kernel and the ground state near the origin. Our results cover the relativistic Schr\"odinger operator with Coulomb potential., Comment: 28 pages

We consider the fractional Burgers equation $ \Delta^{\alpha/2} u + b\cdot \nabla (u|u|^{(\alpha-1)/\beta})$ on ${\mathbf R}^d$, $d\geq2$, with {$\alpha \in (1,2)$ and} $\beta>1$ and prove the existence of a solution for a large class of initial conditions, which contains functions that do not belong to any $L^p({\mathbf R}^d)$, $1\leq p\leq\infty$. Next, we apply the general results to the initial condition $u_0(x)=M|x|^{-\beta}$, $1<\beta

A study of time homogeneous, real valued Markov processes with a special property and a non-atomic initial distribution is provided. The new notion of a function of evolution of distribution which determines the dependency between one dimensional distributions of a process is introduced. This, along with the notion of bridge operators which determine the backward structure, as opposed to the forward structure determined by the usual semi-group operators, paves a way to the new approach for dealing with finite-dimensional distributions of Markov processes. This, in particular, produces explicit formulas which effectively simplify the computations of finite-dimensional distributions, giving an alternative to the standard approach based on computations using the chain rule of transition densities. Various examples illustrating the new approach are presented.

We give ground-state representation for the fractional Laplacian with Dirichlet condition on the half-line