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This work explores the use of Surface-Enhanced Raman Spectroscopy (SERS) combined with artificial neural network (ANN) models to detect and quantify growth hormone (GH) and testosterone (TE) in the blood of Sprague Dawley (SD) rats. SERS spectra were recorded from blood samples of SD rats injected with GH, TE, both hormones, and non-injected controls using 785 nm laser excitation. The samples were mixed with silver nanoparticles (AgNPs) synthesized in distilled water, applied onto a microscope slide, and air-dried. The resulting SERS spectra displayed similar profiles with intensity variations depending on the hormone, revealing specific bands at 658, 798, 878, 914, 932, 1064, 1190, 1354, 1410, and 1658 cm-1. PCA analysis indicated time-dependent intensity changes in bands centered around 1378 (all groups), 658 and 1614 cm-1 (GH-injected rats), and others for different hormone combinations. These variations reflect subtle biochemical changes induced by hormone injections. The ANN models, trained with six PCA scores of blood spiked with various hormone concentrations, showed high accuracy, with coefficients of determination greater than 87.71% and low root mean square error (RMSE) values below 0.6436. The hormone levels in injected rats increased initially and later declined, a trend confirmed by ELISA kits. Although ELISA and SERS produced similar results, SERS offered advantages such as rapid analysis (about two minutes), simple sample preparation, small sample volumes, and non-specificity to hormones. This suggests that SERS, combined with ANN models, could be used to detect exogenous sports dopants. These findings expand the potential applications of SERS in sports science, clinical diagnostics, and biomedical research.

This technical report introduces Docling, an easy to use, self-contained, MIT-licensed open-source package for PDF document conversion. It is powered by state-of-the-art specialized AI models for layout analysis (DocLayNet) and table structure recognition (TableFormer), and runs efficiently on commodity hardware in a small resource budget. The code interface allows for easy extensibility and addition of new features and models.

This paper presents a theoretical study of the enhancement of Zou-Wang-Mandel (ZWM) interferometry through cavity-enhanced spontaneous parametric down-conversion (SPDC) processes producing frequency-entangled biphotons. The ZWM interferometry shows the capability to generate interference effects between single signal photons via indistinguishability between the entangled idler photons. This paper extends the foundational principles of ZWM interferometry by integrating cavity-enhanced SPDCs, aiming to narrow photon bandwidths for improved coherence and photon pair generation efficiency, which is critical for applications in quantum information technologies, quantum encryption, and quantum imaging. This work explores the theoretical implication of employing singly resonant optical parametric oscillators within the ZWM interferometer to produce narrow-band single photons. By combining cavity-enhanced SPDCs with ZWM interferometry, this study fills a gap in current theoretical proposals, offering significant advancements in quantum cryptography and network applications that require reliable, narrow-band single photons., Comment: 11 pages, one figure, 35 references

Radiation from a localized, oscillating charge distribution can have angular momentum that cannot be explained in classical electrodynamics. We consider the simplest example -- electric dipole radiation of a single photon -- and show that this angular momentum is attributable to zero-point oscillations in unexcited states of the dipole source.

We present a path-based design model and system for designing and creating visualisations. Our model represents a systematic approach to constructing visual representations of data or concepts following a predefined sequence of steps. The initial step involves outlining the overall appearance of the visualisation by creating a skeleton structure, referred to as a flowpath. Subsequently, we specify objects, visual marks, properties, and appearance, storing them in a gene. Lastly, we map data onto the flowpath, ensuring suitable morphisms. Alternative designs are created by exchanging values in the gene. For example, designs that share similar traits, are created by making small incremental changes to the gene. Our design methodology fosters the generation of diverse creative concepts, space-filling visualisations, and traditional formats like bar charts, circular plots and pie charts. Through our implementation we showcase the model in action. As an example application, we integrate the output visualisations onto a smartwatch and visualisation dashboards. In this article we (1) introduce, define and explain the path model and discuss possibilities for its use, (2) present our implementation, results, and evaluation, and (3) demonstrate and evaluate an application of its use on a mobile watch., Comment: 11 pages, 14 figures, accepted for publication in IEEE Transactions on Visualization and Computer Graphics

We study Online Linear Programming (OLP) with batching. The planning horizon is cut into $K$ batches, and the decisions on customers arriving within a batch can be delayed to the end of their associated batch. Compared with OLP without batching, the ability to delay decisions brings better operational performance, as measured by regret. Two research questions of interest are: (1) What is a lower bound of the regret as a function of $K$? (2) What algorithms can achieve the regret lower bound? These questions have been analyzed in the literature when the distribution of the reward and the resource consumption of the customers have finite support. By contrast, this paper analyzes these questions when the conditional distribution of the reward given the resource consumption is continuous, and we show the answers are different under this setting. When there is only a single type of resource and the decision maker knows the total number of customers, we propose an algorithm with a $O(\log K)$ regret upper bound and provide a $\Omega(\log K)$ regret lower bound. We also propose algorithms with $O(\log K)$ regret upper bound for the setting in which there are multiple types of resource and the setting in which customers arrive following a Poisson process. All these regret upper and lower bounds are independent of the length of the planning horizon, and all the proposed algorithms delay decisions on customers arriving in only the first and the last batch. We also take customer impatience into consideration and establish a way of selecting an appropriate batch size.

We present symplectic structures on the shape space of unparameterized space curves that generalize the classical Marsden-Weinstein structure. Our method integrates the Liouville 1-form of the Marsden-Weinstein structure with Riemannian structures that have been introduced in mathematical shape analysis. We also derive Hamiltonian vector fields for several classical Hamiltonian functions with respect to these new symplectic structures., Comment: 30 pages, 2 figures

Natural climate solutions (NCS) are critical for mitigating climate change through ecosystem-based carbon removal and emissions reductions. NCS implementation can also generate biodiversity and human well-being co-benefits and trade-offs ("NCS co-impacts"), but the volume of evidence on NCS co-impacts has grown rapidly across disciplines, is poorly understood, and remains to be systematically collated and synthesized. A global evidence map of NCS co-impacts would overcome key barriers to NCS implementation by providing relevant information on co-benefits and trade-offs where carbon mitigation potential alone does not justify NCS projects. We employ large language models to assess over two million articles, finding 257,266 relevant articles on NCS co-impacts. We analyze this large and dispersed body of literature using innovative machine learning methods to extract relevant data (e.g., study location, species, and other key variables), and create a global evidence map on NCS co-impacts. Evidence on NCS co-impacts has grown approximately ten-fold in three decades, although some of the most abundant evidence is associated with pathways that have less mitigation potential. We find that studies often examine multiple NCS pathways, indicating natural NCS pathway complements, and each NCS is often associated with two or more coimpacts. Finally, NCS co-impacts evidence and priority areas for NCS are often mismatched--some countries with high mitigation potential from NCS have few published studies on the broader co-impacts of NCS implementation. Our work advances and makes available novel methods and systematic and representative data of NCS co-impacts studies, thus providing timely insights to inform NCS research and action globally., Comment: 28 pages, 5 figures

We propose an autoregressive framework for modelling dynamic networks with dependent edges. It encompasses the models which accommodate, for example, transitivity, density-dependent and other stylized features often observed in real network data. By assuming the edges of network at each time are independent conditionally on their lagged values, the models, which exhibit a close connection with temporal ERGMs, facilitate both simulation and the maximum likelihood estimation in the straightforward manner. Due to the possible large number of parameters in the models, the initial MLEs may suffer from slow convergence rates. An improved estimator for each component parameter is proposed based on an iteration based on the projection which mitigates the impact of the other parameters (Chang et al., 2021, 2023). Based on a martingale difference structure, the asymptotic distribution of the improved estimator is derived without the stationarity assumption. The limiting distribution is not normal in general, and it reduces to normal when the underlying process satisfies some mixing conditions. Illustration with a transitivity model was carried out in both simulation and a real network data set., Comment: 27 pages, 2 tables, 4 figures

We propose the notion of Attention-Aware Visualizations (AAVs) that track the user's perception of a visual representation over time and feed this information back to the visualization. Such context awareness is particularly useful for ubiquitous and immersive analytics where knowing which embedded visualizations the user is looking at can be used to make visualizations react appropriately to the user's attention: for example, by highlighting data the user has not yet seen. We can separate the approach into three components: (1) measuring the user's gaze on a visualization and its parts; (2) tracking the user's attention over time; and (3) reactively modifying the visual representation based on the current attention metric. In this paper, we present two separate implementations of AAV: a 2D data-agnostic method for web-based visualizations that can use an embodied eyetracker to capture the user's gaze, and a 3D data-aware one that uses the stencil buffer to track the visibility of each individual mark in a visualization. Both methods provide similar mechanisms for accumulating attention over time and changing the appearance of marks in response. We also present results from a qualitative evaluation studying visual feedback and triggering mechanisms for capturing and revisualizing attention.

The Cartan development takes a Lie algebra valued 1-form satisfying the Maurer-Cartan equation on a simply connected manifold $M$ to a smooth mapping from $M$ into the Lie group. In this paper this is generalized to infinite dimensional $M$ for infinite dimensional regular Lie groups. The Cartan development is viewed as a generalization of the evolution map of a regular Lie group. The tangent mapping of a Cartan development is identified as another Cartan development., Comment: 14 pages. arXiv admin note: text overlap with arXiv:math/0609077, arXiv:math/9801007

A large electric field is typically present in anodic or passive oxide films. Stresses induced by such a large electric field are critical in understanding the breakdown mechanism of thin oxide films and improving their corrosion resistance. In this work, we consider electromechanical coupling through the electrostrictive effect. A continuum model incorporating lattice misfit and electric field-induced stresses is developed. We perform a linear stability analysis of the full coupled model and show that, for typical oxides, neglecting electrostriction underestimates the film's instability, especially in systems with a large electric field. Moreover, a region where electrostriction can potentially provide a stabilizing effect is identified, allowing electrostriction to enhance corrosion resistance. We identified an equilibrium electric field intrinsic to the system and the corresponding equilibrium film thickness. The film's stability is very sensitive to the electric field: a 40 percent deviation from the equilibrium electric field can change the maximum growth rate by nearly an order of magnitude. Moreover, our model reduces to classical morphological instability models in the limit of misfit-only, electrostatic-only, and no-electrostriction cases. Finally, the effect of various parameters on the film's stability is studied.

Due to the potential benefits of parallelization, designing unbiased Monte Carlo estimators, primarily in the setting of randomized multilevel Monte Carlo, has recently become very popular in operations research and computational statistics. However, existing work primarily substantiates the benefits of unbiased estimators at an intuitive level or using empirical evaluations. The intuition being that unbiased estimators can be replicated in parallel enabling fast estimation in terms of wall-clock time. This intuition ignores that, typically, bias will be introduced due to impatience because most unbiased estimators necesitate random completion times. This paper provides a mathematical framework for comparing these methods under various metrics, such as completion time and overall computational cost. Under practical assumptions, our findings reveal that unbiased methods typically have superior completion times - the degree of superiority being quantifiable through the tail behavior of their running time distribution - but they may not automatically provide substantial savings in overall computational costs. We apply our findings to Markov Chain Monte Carlo and Multilevel Monte Carlo methods to identify the conditions and scenarios where unbiased methods have an advantage, thus assisting practitioners in making informed choices between unbiased and biased methods., Comment: 35 pages

There is a large and growing interest in observations of small-scale structure in dark matter. We propose a new way to probe dark matter structures in the $\sim 10 - 10^8 \, M_\odot$ range. This allows us to constrain the primordial power spectrum over shorter distances scales than possible with direct observations from the CMB. For $k$ in the range $\sim 10 - 1000 \, {\rm Mpc}^{-1}$ our constraints on the power spectrum are orders of magnitude stronger than previous bounds. We also set some of the strongest constraints on dark matter isocurvature perturbations. Our method relies on the heating effect such dark matter substructures would have on the distribution of stars in an ultra-faint dwarf galaxy. Many models of inflation produce enhanced power at these short distance scales and can thus be constrained by our observation. Further, many dark matter models such as axion dark matter, self-interacting dark matter and dissipative dark matter, produce dense structures which could be constrained this way., Comment: 15 pages, 8 figures

The solution to Poisson's equation arise in many Markov chain and Markov jump process settings, including that of the central limit theorem, value functions for average reward Markov decision processes, and within the gradient formula for equilibrium Markovian rewards. In this paper, we consider the problem of numerically computing the solution to Poisson's equation when the state space is infinite or very large. In such settings, the state space must be truncated in order to make the problem computationally tractable. In this paper, we provide the first truncation approximation solution to Poisson's equation that comes with provable and computable a posteriori error bounds. Our theory applies to both discrete-time chains and continuous-time jump processes. Through numerical experiments, we show our method can provide highly accurate solutions and tight bounds.

We introduce a new class of algorithms for finding a short vector in lattices defined by codes of co-dimension $k$ over $\mathbb{Z}_P^d$, where $P$ is prime. The co-dimension $1$ case is solved by exploiting the packing properties of the projections mod $P$ of an initial set of non-lattice vectors onto a single dual codeword. The technical tools we introduce are sorting of the projections followed by single-step pairwise Euclidean reduction of the projections, resulting in monotonic convergence of the positive-valued projections to zero. The length of vectors grows by a geometric factor each iteration. For fixed $P$ and $d$, and large enough user-defined input sets, we show that it is possible to minimize the number of iterations, and thus the overall length expansion factor, to obtain a short lattice vector. Thus we obtain a novel approach for controlling the output length, which resolves an open problem posed by Noah Stephens-Davidowitz (the possibility of an approximation scheme for the shortest-vector problem (SVP) which does not reduce to near-exact SVP). In our approach, one may obtain short vectors even when the lattice dimension is quite large, e.g., 8000. For fixed $P$, the algorithm yields shorter vectors for larger $d$. We additionally present a number of extensions and generalizations of our fundamental co-dimension $1$ method. These include a method for obtaining many different lattice vectors by multiplying the dual codeword by an integer and then modding by $P$; a co-dimension $k$ generalization; a large input set generalization; and finally, a "block" generalization, which involves the replacement of pairwise (Euclidean) reduction by a $k$-party (non-Euclidean) reduction. The $k$-block generalization of our algorithm constitutes a class of polynomial-time algorithms indexed by $k\geq 2$, which yield successively improved approximations for the short vector problem.

We discuss the implications of generative AI on education across four critical sections: the historical development of AI in education, its contemporary applications in learning, societal repercussions, and strategic recommendations for researchers. We propose ways in which generative AI can transform the educational landscape, primarily via its ability to conduct assessment of complex cognitive performances and create personalized content. We also address the challenges of effective educational tool deployment, data bias, design transparency, and accurate output verification. Acknowledging the societal impact, we emphasize the need for updating curricula, redefining communicative trust, and adjusting to transformed social norms. We end by outlining the ways in which educational stakeholders can actively engage with generative AI, develop fluency with its capacities and limitations, and apply these insights to steer educational practices in a rapidly advancing digital landscape., Comment: This is a preprint version of an edited book chapter to appear in Kourkoulou, D., O. Tzirides, B. Cope, M. Kalantzis, (eds) (2024). Trust and Inclusion in AI-Mediated Education: Where Human Learning Meets Learning Machines, Springer

This paper studies the optimization of Markov decision processes (MDPs) from a risk-seeking perspective, where the risk is measured by conditional value-at-risk (CVaR). The objective is to find a policy that maximizes the long-run CVaR of instantaneous rewards over an infinite horizon across all history-dependent randomized policies. By establishing two optimality inequalities of opposing directions, we prove that the maximum of long-run CVaR of MDPs over the set of history-dependent randomized policies can be found within the class of stationary randomized policies. In contrast to classical MDPs, we find that there may not exist an optimal stationary deterministic policy for maximizing CVaR. Instead, we prove the existence of an optimal stationary randomized policy that requires randomizing over at most two actions. Via a convex optimization representation of CVaR, we convert the long-run CVaR maximization MDP into a minimax problem, where we prove the interchangeability of minimum and maximum and the related existence of saddle point solutions. Furthermore, we propose an algorithm that finds the saddle point solution by solving two linear programs. These results are then extended to objectives that involve maximizing some combination of mean and CVaR of rewards simultaneously. Finally, we conduct numerical experiments to demonstrate the main results., Comment: Risk-seeking optimization of CVaR in MDP

Large Language Models (LLMs) are being adopted at an unprecedented rate, yet still face challenges in knowledge-intensive domains like biomedicine. Solutions such as pre-training and domain-specific fine-tuning add substantial computational overhead, requiring further domain expertise. Here, we introduce a token-optimized and robust Knowledge Graph-based Retrieval Augmented Generation (KG-RAG) framework by leveraging a massive biomedical KG (SPOKE) with LLMs such as Llama-2-13b, GPT-3.5-Turbo and GPT-4, to generate meaningful biomedical text rooted in established knowledge. Compared to the existing RAG technique for Knowledge Graphs, the proposed method utilizes minimal graph schema for context extraction and uses embedding methods for context pruning. This optimization in context extraction results in more than 50% reduction in token consumption without compromising the accuracy, making a cost-effective and robust RAG implementation on proprietary LLMs. KG-RAG consistently enhanced the performance of LLMs across diverse biomedical prompts by generating responses rooted in established knowledge, accompanied by accurate provenance and statistical evidence (if available) to substantiate the claims. Further benchmarking on human curated datasets, such as biomedical true/false and multiple-choice questions (MCQ), showed a remarkable 71% boost in the performance of the Llama-2 model on the challenging MCQ dataset, demonstrating the framework's capacity to empower open-source models with fewer parameters for domain specific questions. Furthermore, KG-RAG enhanced the performance of proprietary GPT models, such as GPT-3.5 and GPT-4. In summary, the proposed framework combines explicit and implicit knowledge of KG and LLM in a token optimized fashion, thus enhancing the adaptability of general-purpose LLMs to tackle domain-specific questions in a cost-effective fashion., Comment: 29 pages, 5 figures, 1 table, 1 supplementary file

We propose improvements to the Artificial Neural Network (ANN) method of determining electron scattering cross-sections from swarm data proposed by coauthors. A limitation inherent to this problem, known as the inverse swarm problem, is the non-unique nature of its solutions, particularly when there exists multiple cross-sections that each describe similar scattering processes. Considering this, prior methods leveraged existing knowledge of a particular cross-section set to reduce the solution space of the problem. To reduce the need for prior knowledge, we propose the following modifications to the ANN method. First, we propose a Multi-Branch ANN (MBANN) that assigns an independent branch of hidden layers to each cross-section output. We show that in comparison with an equivalent conventional ANN, the MBANN architecture enables an efficient and physics informed feature map of each cross-section. Additionally, we show that the MBANN solution can be improved upon by successive networks that are each trained using perturbations of the previous regression. Crucially, the method requires much less input data and fewer restrictive assumptions, and only assumes knowledge of energy loss thresholds and the number of cross-sections present.

We place limits on dark matter made up of compact objects significantly heavier than a solar mass, such as MACHOs or primordial black holes (PBHs). In galaxies, the gas of such objects is generally hotter than the gas of stars and will thus heat the gas of stars even through purely gravitational interactions. Ultrafaint dwarf galaxies (UFDs) maximize this effect. Observations of the half-light radius in UFDs thus place limits on MACHO dark matter. We build upon previous constraints with an improved heating rate calculation including both direct and tidal heating, and consideration of the heavier mass range above $10^4 \, M_\odot$. Additionally we find that MACHOs may lose energy and migrate in to the center of the UFD, increasing the heat transfer to the stars. UFDs can constrain MACHO dark matter with masses between about $10 M_\odot$ and $10^8 M_\odot$ and these are the strongest constraints over most of this range., Comment: 19 Pages, 6 Figures

Many models of dark matter include self-interactions beyond gravity. A variety of astrophysical observations have previously been used to place limits on the strength of such self-interactions. However, previous works have generally focused either on short-range interactions resulting in individual dark matter particles scattering from one another, or on effectively infinite-range interactions which sum over entire dark matter halos. In this work, we focus on the intermediate regime: forces with range much larger than dark matter particles' inter-particle spacing, but still shorter than the length scales of known halos. We show that gradients in the dark matter density of such halos would still lead to observable effects. We focus primarily on effects in the Bullet Cluster, where finite-range forces would lead either to a modification of the collision velocity of the cluster or to a separation of the dark matter and the galaxies of each cluster after the collision. We also consider constraints from the binding of ultrafaint dwarf galaxy halos, and from gravitational lensing of the Abell 370 cluster. Taken together, these observations allow us to set the strongest constraints on dark matter self-interactions over at least five orders of magnitude in range, surpassing existing limits by many orders of magnitude throughout., Comment: 10 pages, 2 figures

We consider a scalar QED model for the frictional force and the momentum fluctuations of a polarizable particle in thermal equilibrium with radiation or in hyperbolic motion in a vacuum. In the former case the loss of particle kinetic energy due to the frictional force is compensated by the increase in kinetic energy associated with the momentum diffusion, resulting in the Planck distribution when it is assumed that the average kinetic energy satisfies the equipartition theorem. For hyperbolic motion in vacuum the frictional force and the momentum diffusion are similarly consistent with a thermal equilibrium at the Davies-Unruh temperature. The quantum fluctuations of the momentum imply that it is only the average acceleration that is constant when the particle is subject to a constant applied force.

Modeling microstructure evolution in electrochemical systems is vital for understanding the mechanism of various electrochemical processes. In this work, we propose a general phase field framework that is fully variational and thus guarantees that the energy decreases upon evolution in an isothermal system. The bulk and interface free energies are decoupled using a grand potential formulation to enhance numerical efficiency. The variational definition of the overpotential is used, and the reaction kinetics is incorporated into the evolution equation for the phase field to correctly capture capillary effects and eliminate additional model parameter calibrations. A higher-order kinetic correction is derived to accurately reproduce general reaction models such as the Butler-Volmer, Marcus, and Marcus-Hush-Chidsey models. Electrostatic potentials in the electrode and the electrolyte are considered separately as independent variables, providing additional freedom to capture the interfacial potential jump. To handle realistic materials and processing parameters for practical applications, a driving force extension method is used to enhance the grid size by three orders of magnitude. Finally, we comprehensively verify our phase field model using classical electrochemical theory.

We develop a general description of how information propagates through a magnetohydrodynamic (MHD) system based on the method of characteristics and use that to formulate numerical boundary conditions (BCs) that are intrinsically consistent with the MHD equations. Our formulation includes two major advances for simulations of the Sun. First, we derive data-driven BCs that optimally match the state of the plasma inferred from a time series of observations of a boundary (e.g., the solar photosphere). Second, our method directly handles random noise and systematic bias in the observations, and finds a solution for the boundary evolution that is strictly consistent with MHD and maximally consistent with the observations. We validate the method against a Ground Truth (GT) simulation of an expanding spheromak. The data-driven simulation can reproduce the GT simulation above the photosphere with high fidelity when driven at high cadence. Errors progressively increase for lower driving cadence until a threshold cadence is reached and the driven simulation can no longer accurately reproduce the GT simulation. However, our characteristic formulation of the BCs still requires adherence of the boundary evolution to the MHD equations even when the driven solution departs from the true solution in the driving layer. That increasing departure clearly indicates when additional information at the boundary is needed to fully specify the correct evolution of the system. The method functions even when no information about the evolution of some variables on the lower boundary is available, albeit with a further decrease in fidelity., Comment: Submitted for publication to the Astrophysical Journal; 77 pages, 12 figures

Strong motivation for investing in quantum sensing arises from the need to investigate phenomena that are very weakly coupled to the matter and fields well described by the Standard Model. These can be related to the problems of dark matter, dark sectors not necessarily related to dark matter (for example sterile neutrinos), dark energy and gravity, fundamental constants, and problems with the Standard Model itself including the Strong CP problem in QCD. Resulting experimental needs typically involve the measurement of very low energy impulses or low power periodic signals that are normally buried under large backgrounds. This report documents the findings of the 2023 Quantum Sensors for High Energy Physics workshop which identified enabling quantum information science technologies that could be utilized in future particle physics experiments, targeting high energy physics science goals., Comment: 63 pages, 8 figures, Quantum Sensors for HEP workshop report, April 26-28, 2023

Let $J(\cdot)$ be a compound Poisson process with rate $\lambda>0$ and a jumps distribution $G(\cdot)$ concentrated on $(0,\infty)$. In addition, let $V$ be a random variable which is distributed according to $G(\cdot)$ and independent from $J(\cdot)$. Define a new process $W(t)\equiv W_V(t)\equiv V+J(t)-t$, $t\geq0$ and let $\tau_V$ be the first time that $W(\cdot)$ hits the origin. A long-standing open problem due to Iglehart (1971) and Cohen (1979) is to derive the moments of the functional $\int_0^\tau W(t)\,{\rm d}t$ in terms of the moments of $G(\cdot)$ and $\lambda$. In the current work, we solve this problem in much greater generality, i.e., first by letting $J(\cdot)$ belong to a wide class of spectrally-positive L\'evy processes and secondly, by considering more general class of functionals. We also supply several applications of the existing results, e.g., in studying the process $x\mapsto \int_0^{\tau_x}W_x(t)\,{\rm d}t$ defined on $x\in[0,\infty)$.

The advent of low cost, accessible, and high performance augmented reality (AR) has shed light on a situated form of analytics where in-situ visualizations embedded in the real world can facilitate sensemaking based on the user's physical location. In this work, we identify prior literature in this emerging field with a focus on situated analytics. After collecting 47 relevant situated analytics systems, we classify them using a taxonomy of three dimensions: situating triggers, view situatedness, and data depiction. We then identify four archetypical patterns in our classification using an ensemble cluster analysis. We also assess the level which these systems support the sensemaking process. Finally, we discuss insights and design guidelines that we learned from our analysis., Comment: 19 pages