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It is common in nature to see aggregation of objects in space. Exploring the mechanism associated with the locations of such clustered observations can be essential to understanding the phenomenon, such as the source of spatial heterogeneity, or comparison to other event generating processes in the same domain. Log-Gaussian Cox processes (LGCPs) represent an important class of models for quantifying aggregation in a spatial point pattern. However, implementing likelihood-based Bayesian inference for such models presents many computational challenges, particularly in high dimensions. In this paper, we propose a novel likelihood-free inference approach for LGCPs using the recently developed BayesFlow approach, where invertible neural networks are employed to approximate the posterior distribution of the parameters of interest. BayesFlow is a neural simulation-based method based on "amortized" posterior estimation. That is, after an initial training procedure, fast feed-forward operations allow rapid posterior inference for any data within the same model family. Comprehensive numerical studies validate the reliability of the framework and show that BayesFlow achieves substantial computational gain in repeated application, especially for two-dimensional LGCPs. We demonstrate the utility and robustness of the method by applying it to two distinct oral microbial biofilm images.

Effective parking management is essential for ensuring accessibility, safety, and convenience in master-planned communities, particularly in active adult neighborhoods experiencing rapid growth. Accurately assessing parking utilization is a crucial first step in planning for future demand, but data collection methods can be costly and labor-intensive. This paper presents a low-cost yet highly accurate methodology for measuring parking utilization using road tubes connected to portable traffic counters from JAMAR Technologies, Inc. By integrating results from JAMAR's analysis tool with custom Python scripting, the methodology enables precise parking lot counts through parameter optimization and automated error correction. The system's efficiency allows for scalable deployment without significant manual observation, reducing both costs and disruptions to daily operations. Using Tellico Village as a case study, this research demonstrates that community planners can obtain actionable parking insights on a limited budget, empowering them to make informed decisions about capacity expansion, traffic flow improvements, and facility scheduling. The findings underscore the feasibility of leveraging cost-effective technology to optimize infrastructure planning and ensure long-term resident satisfaction as communities grow.

Turbulent flow fields are characterized by extreme events that are statistically intermittent and carry a significant amount of energy and physical importance. To emulate these flows, we introduce the extreme variational Autoencoder (xVAE), which embeds a max-infinitely divisible process with heavy-tailed distributions into a standard VAE framework, enabling accurate modeling of extreme events. xVAEs are neural network models that reduce system dimensionality by learning non-linear latent representations of data. We demonstrate the effectiveness of xVAE in large-eddy simulation data of wildland fire plumes, where intense heat release and complex plume-atmosphere interactions generate extreme turbulence. Comparisons with the commonly used Proper Orthogonal Decomposition (POD) modes show that xVAE is more robust in capturing extreme values and provides a powerful uncertainty quantification framework using variational Bayes. Additionally, xVAE enables analysis of the so-called copulas of fields to assess risks associated with rare events while rigorously accounting for uncertainty, such as simultaneous exceedances of high thresholds across multiple locations. The proposed approach provides a new direction for studying realistic turbulent flows, such as high-speed aerodynamics, space propulsion, and atmospheric and oceanic systems that are characterized by extreme events.

The Hadean, once thought to be uninhabitable and tumultuous, has more recently been recontextualized as a clement time in which oceans, land, and life likely appeared on Earth. This non-exhaustive chapter follows multiple threads from planet formation to the origin of life. We place significant emphasis on the solar system context for the Earth, the timing and nature of crustal formation and the evolution of the surface and atmosphere. Several scenarios for prebiotic chemistry are also discussed including atmospheric photochemistry, wet-dry and freeze-thaw cycles, and hydrothermal vent systems. We attempt to draw connections between the large-scale, planetary processes and various origin of life pathways to illustrate possible overlaps and correlations. In detail, we conclude with and discuss the "impact of impacts" to show how asteroid and comet impacts during the Hadean may have affected many of these processes and scenarios, from generating land to altering the chemical composition and oxidation state of the early Earth's atmosphere and surface., Comment: 18 pages, 5 figures, accepted for publication in "The Archean Earth" (ed.: M. Homan, P. Mason, R. Ernst, T. Lyons, C. Heubeck, D. Papineau, E. Stueeken, R. Mazumder, A. Webb, W. Altermann), Elsevier

We present a quantum algorithm for portfolio optimisation. Specifically, We present an end-to-end quantum approximate optimisation algorithm (QAOA) to solve the discrete global minimum variance portfolio (DGMVP) model. This model finds a portfolio of risky assets with the lowest possible risk contingent on the number of traded assets being discrete. We provide a complete pipeline for this model and analyses its viability for noisy intermediate-scale quantum computers. We design initial states, a cost operator, and ans\"atze with hard mixing operators within a binary encoding. Further, we perform numerical simulations to analyse several optimisation routines, including layerwise optimisation, utilising COYBLA and dual annealing. Finally, we consider the impacts of thermal relaxation and stochastic measurement noise. We find dual annealing with a layerwise optimisation routine provides the most robust performance. We observe that realistic thermal relaxation noise levels preclude quantum advantage. However, stochastic measurement noise will dominate when hardware sufficiently improves. Within this regime, we numerically demonstrate a favourable scaling in the number of shots required to obtain the global minimum -- an indication of quantum advantage in portfolio optimisation., Comment: 35 pages, 23 figures

For certain values of the wave speed parameter, evolution equations for the temperature of a region of fuel admit traveling wave solutions describing fire fronts. We consider such a system in the form of a nonlinear reaction-diffusion equation with a first-order forcing term capturing the combined effects of ambient and fire-induced wind. The fire-induced wind is introduced by way of a piecewise continuous function that ``switches'' in space. We demonstrate that, in the case of a spatially dependent wind, traveling wave solutions corresponding to fire fronts exist for a continuum of wave speeds rather than for a single unique speed. Using geometric methods, we determine the range of allowable speeds, refine this range to only those fronts which will persist in nature, and develop a selection mechanism to identify the specific wind configuration corresponding to the most stable solution. For this spectrally preferred front, we find that the wind switch occurs ahead of the fireline in a manner consistent with the physics of air entrainment. Even when the wind is not coupled to the temperature and is instead imposed as an external forcing, the conditions on the existence and stability of front solutions force the wind term in to a configuration reflective of physical reality.

Spatio-temporal area-level datasets play a critical role in official statistics, providing valuable insights for policy-making and regional planning. Accurate modeling and forecasting of these datasets can be extremely useful for policymakers to develop informed strategies for future planning. Echo State Networks (ESNs) are efficient methods for capturing nonlinear temporal dynamics and generating forecasts. However, ESNs lack a direct mechanism to account for the neighborhood structure inherent in area-level data. Ignoring these spatial relationships can significantly compromise the accuracy and utility of forecasts. In this paper, we incorporate approximate graph spectral filters at the input stage of the ESN, thereby improving forecast accuracy while preserving the model's computational efficiency during training. We demonstrate the effectiveness of our approach using Eurostat's tourism occupancy dataset and show how it can support more informed decision-making in policy and planning contexts., Comment: 23 pages, 4 figures

We investigate two asymmetric loss functions, namely LINEX loss and power divergence loss for optimal spatial prediction with area-level data. With our motivation arising from the real estate industry, namely in real estate valuation, we use the Zillow Home Value Index (ZHVI) for county-level values to show the change in prediction when the loss is different (asymmetric) from a traditional squared error loss (symmetric) function. Additionally, we discuss the importance of choosing the asymmetry parameter, and propose a solution to this choice for a general asymmetric loss function. Since the focus is on area-level data predictions, we propose the methodology in the context of conditionally autoregressive (CAR) models. We conclude that choice of the loss functions for spatial area-level predictions can play a crucial role, and is heavily driven by the choice of parameters in the respective loss.

This paper introduces a strategic planning tool for master-planned communities designed specifically to quantify residents' subjective preferences about large investments in amenities and infrastructure projects. Drawing on data obtained from brief online surveys, the tool ranks alternative plans by considering the aggregate anticipated utilization of each proposed amenity and cost sensitivity to it (or risk sensitivity for infrastructure plans). In addition, the tool estimates the percentage of households that favor the preferred plan and predicts whether residents would actually be willing to fund the project. The mathematical underpinnings of the tool are borrowed from utility theory, incorporating exponential functions to model diminishing marginal returns on quality, cost, and risk mitigation., Comment: 13 pages, 14 figures

Rate-induced tipping (R-tipping) occurs when a ramp parameter changes rapidly enough to cause the system to tip between co-existing, attracting states, while noise-induced tipping (N-tipping) occurs when there are random transitions between two attractors of the underlying deterministic system. This work investigates R-tipping and N-tipping events in a carbonate system in the upper ocean, in which the key objective is understanding how the system undergoes tipping away from a stable fixed point in a bistable regime. While R-tipping away from the fixed point is straightforward, N-tipping poses challenges due to a periodic orbit forming the basin boundary for the attracting fixed point of the underlying deterministic system. Furthermore, in the case of N-tipping, we are interested in the case where noise is away from the small noise limit, as it is more appropriate for the application. We compute the most probable escape path (MPEP) for our system, resulting in a firm grasp on the least action path in an asymmetric system of higher scale. Our analysis shows that the carbon cycle model is susceptible to both tipping mechanisms when using the standard formulations.

This paper describes how a time-varying Markov model was used to forecast housing development at a master-planned community during a transition from high to low growth. Our approach draws on detailed historical data to model the dynamics of the market participants, producing results that are entirely data-driven and free of bias. While traditional time series forecasting methods often struggle to account for nonlinear regime changes in growth, our approach successfully captures the onset of buildout as well as external economic shocks, such as the 1990 and 2008-2011 recessions and the 2021 post-pandemic boom. This research serves as a valuable tool for urban planners, homeowner associations, and property stakeholders aiming to navigate the complexities of growth at master-planned communities during periods of both system stability and instability., Comment: 18 pages, 10 figures, 3 Appendices

Metal carbides, nitrides, or carbonitrides of early transition metals, better known as MXenes, possess notable structural, electrical, and magnetic properties. Analyzing electronic structures by calculating structural stability, band structure, density of states, Bader charge transfer, and work functions utilizing first principle calculations, we revealed that titanium nitride Mxenes, namely Ti$_2$N and Ti$_3$N$_2$, have excess anionic electrons in their pseudo-atomic structure inside the crystal lattice, making them MXene electrides. Bulk Ti$_3$N$_2$ has competing antiferromagnetic (AFM) and ferromagnetic(FM) configurations with slightly more stable AFM configurations, while the Ti$_2$N MXene is nonmagnetic. Although Ti$_3$N$_2$ favors AFM configurations with hexagonal crystal systems having $6/mmm$ point group symmetry, Ti$_3$N$_2$ does not support altermagnetism. The monolayer of the Ti$_3$N$_2$ MXene is a ferromagnetic electride. These unique properties of having non-nuclear interstitial anionic electrons in the electronic structure of titanium nitride MXene have not yet been reported in the literature. Density functional theory calculations show TiN is neither an electride, MXene, or magnetic.

Projecting sea-level change in various climate-change scenarios typically involves running forward simulations of the Earth's gravitational, rotational and deformational (GRD) response to ice mass change, which requires high computational cost and time. Here we build neural-network emulators of sea-level change at 27 coastal locations, due to the GRD effects associated with future Antarctic Ice Sheet mass change over the 21st century. The emulators are based on datasets produced using a numerical solver for the static sea-level equation and published ISMIP6-2100 ice-sheet model simulations referenced in the IPCC AR6 report. We show that the neural-network emulators have an accuracy that is competitive with baseline machine learning emulators. In order to quantify uncertainty, we derive well-calibrated prediction intervals for simulated sea-level change via a linear regression postprocessing technique that uses (nonlinear) machine learning model outputs, a technique that has previously been applied to numerical climate models. We also demonstrate substantial gains in computational efficiency: a feedforward neural-network emulator exhibits on the order of 100 times speedup in comparison to the numerical sea-level equation solver that is used for training.

Standing as one of the most significant barriers to reaching quantum advantage, state-preparation fidelities on noisy intermediate-scale quantum processors suffer from quantum-gate errors, which accumulate over time. A potential remedy is pulse-based state preparation. We numerically investigate the minimal evolution times (METs) attainable by optimizing (microwave and exchange) pulses on silicon hardware. We investigate two state preparation tasks. First, we consider the preparation of molecular ground states and find the METs for H$_2$, HeH$^+$, and LiH to be 2.4 ns, 4.4 ns, and 27.2 ns, respectively. Second, we consider transitions between arbitrary states and find the METs for transitions between arbitrary four-qubit states to be below 50 ns. For comparison, connecting arbitrary two-qubit states via one- and two-qubit gates on the same silicon processor requires approximately 200 ns. This comparison indicates that pulse-based state preparation is likely to utilize the coherence times of silicon hardware more efficiently than gate-based state preparation. Finally, we quantify the effect of silicon device parameters on the MET. We show that increasing the maximal exchange amplitude from 10 MHz to 1 GHz accelerates the METs, e.g., for H$_2$ from 84.3 ns to 2.4 ns. This demonstrates the importance of fast exchange. We also show that increasing the maximal amplitude of the microwave drive from 884 kHz to 56.6 MHz shortens state transitions, e.g., for two-qubit states from 1000 ns to 25 ns. Our results bound both the state-preparation times for general quantum algorithms and the execution times of variational quantum algorithms with silicon spin qubits., Comment: 9 + (7) pages, 6 figs, comments are welcomed

Crossed optical dipole traps (ODTs) provide three-dimensional confinement of cold atoms and other optically trappable particles. However, the need to maintain the intersection of the two trapping beams poses strict requirements on alignment stability, and limits the ability to move the trap. Here we demonstrate a novel crossed ODT design that features inherent stability of the beam crossing, allowing the trap to move and remain aligned. The trap consists of a single high-power laser beam, imaged back onto itself at an angle to form a crossed trap. Self-aligning behavior results from employing an imaging system with positive magnification tuned precisely to unity. We employ laser-cooled samples of $^6$Li atoms to demonstrate that the trap remains well-aligned over a 4.3 mm travel range along an axis approximately perpendicular to the plane containing the crossed beams. Our scheme can be applied to bring an atomic cloud held in a crossed ODT close to a surface or field source for various applications in quantum simulation, sensing, and information processing., Comment: 9 pages, 5 figures

We prove that the combination of a target network and over-parameterized linear function approximation establishes a weaker convergence condition for bootstrapped value estimation in certain cases, even with off-policy data. Our condition is naturally satisfied for expected updates over the entire state-action space or learning with a batch of complete trajectories from episodic Markov decision processes. Notably, using only a target network or an over-parameterized model does not provide such a convergence guarantee. Additionally, we extend our results to learning with truncated trajectories, showing that convergence is achievable for all tasks with minor modifications, akin to value truncation for the final states in trajectories. Our primary result focuses on temporal difference estimation for prediction, providing high-probability value estimation error bounds and empirical analysis on Baird's counterexample and a Four-room task. Furthermore, we explore the control setting, demonstrating that similar convergence conditions apply to Q-learning.

A central problem in quantum information is determining quantum-classical boundaries. A useful notion of classicality is provided by the quasiprobability formulation of quantum theory. In this framework, a state is called classical if it is represented by a quasiprobability distribution that is positive, and thus a probability distribution. In recent years, the Kirkwood-Dirac (KD) distributions have gained much interest due to their numerous applications in modern quantum-information research. A particular advantage of the KD distributions is that they can be defined with respect to arbitrary observables. Here, we show that if two observables are picked at random, the set of classical states of the resulting KD distribution is a simple polytope of minimal size. When the Hilbert space is of dimension $d$, this polytope is of dimension $2d-1$ and has $2d$ known vertices. Our result implies, $\textit{e.g.}$, that almost all KD distributions have resource theories in which the free states form a small and simple set., Comment: 12 pages

The SALTUS Probe mission will provide a powerful far-infrared (far-IR) pointed space observatory to explore our cosmic origins and the possibility of life elsewhere. The observatory employs an innovative deployable 14-m aperture, with a sunshield that will radiatively cool the off-axis primary to <45K. This cooled primary reflector works in tandem with cryogenic coherent and incoherent instruments that span the 34 to 660 micron far-IR range at both high and moderate spectral resolutions., Comment: 49 pages, 10 figures, 3 tables, submitted to SPIE JATIS

This paper investigates the consequences of encoding a $K$-valued categorical variable incorrectly as $K$ bits via one-hot encoding, when using a Na\"{\i}ve Bayes classifier. This gives rise to a product-of-Bernoullis (PoB) assumption, rather than the correct categorical Na\"{\i}ve Bayes classifier. The differences between the two classifiers are analysed mathematically and experimentally. In our experiments using probability vectors drawn from a Dirichlet distribution, the two classifiers are found to agree on the maximum a posteriori class label for most cases, although the posterior probabilities are usually greater for the PoB case., Comment: 7 pages, 3 figures

This paper presents an overview of the Milky Way and nearby galaxies science case for the \textit{Single Aperture Large Telescope for Universe Studies} (SALTUS) far-infrared NASA probe-class mission concept. SALTUS offers enormous gains in spatial resolution and spectral sensitivity over previous far-IR missions, thanks to its cold ($<$40~K) 14-m primary mirror. Key Milky Way and nearby galaxies science goals for SALTUS focus on understanding the role of star formation in feedback in the Local Universe. In addition to this science case, SALTUS would open a new window to to of Galactic and extragalactic communities in the 2030s, enable fundamentally new questions to be answered, and be a far-IR analog to the near- and mid-IR capabilities of JWST. This paper summarizes the Milky Way and nearby galaxies science case and plans for notional observing programs in both guaranteed and guest (open) time., Comment: Resubmitted to JATIS as part of a special issue on SALTUS

This paper presents an overview of the high-redshift extragalactic science case for the Single Aperture Large Telescope for Universe Studies (SALTUS) far-infrared NASA probe-class mission concept. Enabled by its 14m primary reflector, SALTUS offers enormous gains in spatial resolution and spectral sensitivity over previous far-IR missions. SALTUS would be a versatile observatory capable of responding to the scientific needs of the extragalactic community in the 2030s, and a natural follow-on to the near- and mid-IR capabilities of JWST. Key early-universe science goals for SALTUS focus on understanding the role of galactic feedback processes in regulating galaxy growth across cosmic time, and charting the rise of metals and dust from the early universe to the present. This paper summarizes these science cases and the performance metrics most relevant for high-redshift observations., Comment: Submitted to JATIS as part of a special issue on SALTUS. Key performance metrics in Figs. 1 and 2

We investigate the viscoelastic relaxation to equilibrium of a disordered planar epithelium described using the cell vertex model. In its standard form, the model is formulated as coupled evolution equations for the locations of vertices of confluent polygonal cells. Exploiting the model's gradient-flow structure, we use singular-value decomposition to project modes of deformation of vertices onto modes of deformation of cells. We show how eigenmodes of discrete Laplacian operators (specified by constitutive assumptions related to dissipation and mechanical energy) provide a spatial basis for evolving fields, and demonstrate how the operators can incorporate approximations of conventional spatial derivatives. We relate the spectrum of relaxation times to the eigenvalues of the Laplacians, modified by corrections that account for the fact that the cell network (and therefore the Laplacians) evolve during relaxation to an equilibrium prestressed state, providing the monolayer with geometric stiffness. While dilational modes of the Laplacians capture rapid relaxation in some circumstances, showing diffusive dynamics, geometric stiffness is typically a dominant source of monolayer rigidity, as we illustrate for monolayers exposed to unsteady stretching deformations., Comment: 8 figures

We explore covert communication of qubits over the lossy thermal-noise bosonic channel, which is a quantum-mechanical model of many practical channels, including optical. Covert communication ensures that an adversary is unable to detect the presence of transmissions, which are concealed in channel noise. We show a \emph{square root law} (SRL) for quantum covert communication similar to that for classical: $\propto\sqrt{n}$ qubits can be transmitted covertly and reliably over $n$ uses of an optical channel. Our achievability proof uses photonic dual-rail qubit encoding, which has been proposed for long-range repeater-based quantum communication and entanglement distribution. Our converse employs prior covert signal power limit results and adapts well-known methods to upper bound quantum capacity of optical channels. Finally, we believe that the gap between our lower and upper bounds for the number of reliable covert qubits can be mitigated by improving the quantum error correction codes and quantum channel capacity bounds., Comment: 12 pages