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The rising severity and frequency of wildfires in recent years in the United States have raised numerous concerns regarding the improvement in wildfire emergency response management and decision-making systems, which require operational high temporal and spatial resolution monitoring capabilities. Satellites are one of the tools that can be used for wildfire monitoring. However, none of the currently available satellite systems provide both high temporal and spatial resolution. For example, GOES-17 geostationary satellite fire products have high temporal (1–5 min) but low spatial resolution (≥2 km), and VIIRS polar orbiter satellite fire products have low temporal (~12 h) but high spatial resolution (375 m). This work aims to leverage currently available satellite data sources, such as GOES and VIIRS, along with deep learning (DL) advances to achieve an operational high-resolution, both spatially and temporarily, wildfire monitoring tool. Specifically, this study considers the problem of increasing the spatial resolution of high temporal but low spatial resolution GOES-17 data products using low temporal but high spatial resolution VIIRS data products. The main idea is using an Autoencoder DL model to learn how to map GOES-17 geostationary low spatial resolution satellite images to VIIRS polar orbiter high spatial resolution satellite images. In this context, several loss functions and DL architectures are implemented and tested to predict both the fire area and the corresponding brightness temperature. These models are trained and tested on wildfire sites from 2019 to 2021 in the western U.S. The results indicate that DL models can improve the spatial resolution of GOES-17 images, leading to images that mimic the spatial resolution of VIIRS images. Combined with GOES-17 higher temporal resolution, the DL model can provide high-resolution near-real-time wildfire monitoring capability as well as semi-continuous wildfire progression maps. [ABSTRACT FROM AUTHOR]

For a finite group G$G$, a G$G$‐crossed braided fusion category is a G$G$‐graded fusion category with additional structures, namely, a G$G$‐action and a G$G$‐braiding. We develop the notion of G$G$‐crossed braided zesting: an explicit method for constructing new G$G$‐crossed braided fusion categories from a given one by means of cohomological data associated with the invertible objects in the category and grading group G$G$. This is achieved by adapting a similar construction for (braided) fusion categories recently described by the authors. All G$G$‐crossed braided zestings of a given category C${\mathcal {C}}$ are G$G$‐extensions of their trivial component and can be interpreted in terms of the homotopy‐based description of Etingof, Nikshych, and Ostrik. In particular, we explicitly describe which G$G$‐extensions correspond to G$G$‐crossed braided zestings. [ABSTRACT FROM AUTHOR]

Understory biomass plays an important role in forests, and explicit characterizations of live and dead understory vegetation are critical for wildland fuel characterization and to link understory vegetation to ecosystem processes. Current methods to accurately model understory fuel complexity in 3D rely on expensive and often inaccessible technologies. Structure-from-motion close-range photogrammetry, in which ordinary photographs or video stills are overlaid to generate point clouds, is promising as an alternative method to generate 3D models of fuels at a fraction of the cost of more traditional field surveys. In this study, we compared the performance of close-range photogrammetry with field sampling surveys to assess the utility of this alternative technique for quantifying understory fuel structure. Using a commercially available GoPro camera, we generated 3D point cloud models from video-derived image stills of 138 sampling plots across two western ponderosa pine and two southeastern slash pine sites. We directly compared structural metrics derived from the photogrammetry to those derived from field sampling, then evaluated predictive models of biomass calibrated by means of destructive sampling. Photogrammetry-derived measures of occupied volume and fuel height showed strong agreements with field sampling (Pearson's R = 0.81 and 0.86, respectively). While we found weak relationships between photogrammetry metrics and biomass 0 to 10 cm in height, occupied volume and a novel metric to characterize the vertical profile of vegetation produced the strongest relationships with biomass above the litter layer (i.e., >10 cm) across different fuel types (R2 = 0.55–0.76). The application of this technique has the potential to provide managers with an accessible option for inexpensive data collection and can lay the groundwork for the rapid collection of input datasets to train landscape-scale fuel models. [ABSTRACT FROM AUTHOR]

In this study, we focus on the effects of fuel bed representation and fire heat and smoke distribution in a coupled fire-atmosphere simulation platform for two landscape-scale fires: the 2018 Camp Fire and the 2021 Caldor Fire. The fuel bed representation in the coupled fire-atmosphere simulation platform WRF-Fire currently includes only surface fuels. Thus, we enhance the model by adding canopy fuel characteristics and heat release, for which a method to calculate the heat generated from canopy fuel consumption is developed and implemented in WRF-Fire. Furthermore, the current WRF-Fire heat and smoke distribution in the atmosphere is replaced with a heat-conserving Truncated Gaussian (TG) function and its effects are evaluated. The simulated fire perimeters of case studies are validated against semi-continuous, high-resolution fire perimeters derived from NEXRAD radar observations. Furthermore, simulated plumes of the two fire cases are compared to NEXRAD radar reflectivity observations, followed by buoyancy analysis using simulated temperature and vertical velocity fields. The results show that while the improved fuel bed and the TG heat release scheme have small effects on the simulated fire perimeters of the wind-driven Camp Fire, they affect the propagation direction of the plume-driven Caldor Fire, leading to better-matching fire perimeters with the observations. However, the improved fuel bed representation, together with the TG heat smoke release scheme, leads to a more realistic plume structure in comparison to the observations in both fires. The buoyancy analysis also depicts more realistic fire-induced temperature anomalies and atmospheric circulation when the fuel bed is improved. [ABSTRACT FROM AUTHOR]

Electromagnetic radiation at 1550 nm is highly absorbed by water and offers a novel way to collect fuel moisture data, along with 3D structures of wildland fuels/vegetation, using lidar. Two terrestrial laser scanning (TLS) units (FARO s350 (phase shift, PS) and RIEGL vz-2000 (time of flight, TOF)) were assessed in a series of laboratory experiments to determine if lidar can be used to estimate the moisture content of dead forest litter. Samples consisted of two control materials, the angle and position of which could be manipulated (pine boards and cheesecloth), and four single-species forest litter types (Douglas-fir needles, ponderosa pine needles, longleaf pine needles, and southern red oak leaves). Sixteen sample trays of each material were soaked overnight, then allowed to air dry with scanning taking place at 1 h, 2 h, 4 h, 8 h, 12 h, and then in 12 h increments until the samples reached equilibrium moisture content with the ambient relative humidity. The samples were then oven-dried for a final scanning and weighing. The spectral reflectance values of each material were also recorded over the same drying intervals using a field spectrometer. There was a strong correlation between the intensity and standard deviation of intensity per sample tray and the moisture content of the dead leaf litter. A multiple linear regression model with a break at 100% gravimetric moisture content produced the best model with R2 values as high as 0.97. This strong relationship was observed with both the TOF and PS lidar units. At fuel moisture contents greater than 100% gravimetric water content, the correlation between the pulse intensity values recorded by both scanners and the fuel moisture content was the strongest. The relationship deteriorated with distance, with the TOF scanner maintaining a stronger relationship at distance than the PS scanner. Our results demonstrate that lidar can be used to detect and quantify fuel moisture across a range of forest litter types. Based on our findings, lidar may be used to quantify fuel moisture levels in near real-time and could be used to create spatial maps of wildland fuel moisture content. [ABSTRACT FROM AUTHOR]

Airborne Laser Scanners (ALS) and Terrestrial Laser Scanners (TLS) are two lidar systems frequently used for remote sensing forested ecosystems. The aim of this study was to compare crown metrics derived from TLS, ALS, and a combination of both for describing the crown structure and fuel attributes of longleaf pine (Pinus palustris Mill.) dominated forest located at Eglin Air Force Base (AFB), Florida, USA. The study landscape was characterized by an ALS and TLS data collection along with field measurements within three large (1963 m2 each) plots in total, each one representing a distinct stand condition at Eglin AFB. Tree-level measurements included bole diameter at breast height (DBH), total height (HT), crown base height (CBH), and crown width (CW). In addition, the crown structure and fuel metrics foliage biomass (FB), stem branches biomass (SB), crown biomass (CB), and crown bulk density (CBD) were calculated using allometric equations. Canopy Height Models (CHM) were created from ALS and TLS point clouds separately and by combining them (ALS + TLS). Individual trees were extracted, and crown-level metrics were computed from the three lidar-derived datasets and used to train random forest (RF) models. The results of the individual tree detection showed successful estimation of tree count from all lidar-derived datasets, with marginal errors ranging from −4 to 3%. For all three lidar-derived datasets, the RF models accurately predicted all tree-level attributes. Overall, we found strong positive correlations between model predictions and observed values (R2 between 0.80 and 0.98), low to moderate errors (RMSE% between 4.56 and 50.99%), and low biases (between 0.03% and −2.86%). The highest R2 using ALS data was achieved predicting CBH (R2 = 0.98), while for TLS and ALS + TLS, the highest R2 was observed predicting HT, CW, and CBD (R2 = 0.94) and HT (R2 = 0.98), respectively. Relative RMSE was lowest for HT using three lidar datasets (ALS = 4.83%, TLS = 7.22%, and ALS + TLS = 4.56%). All models and datasets had similar accuracies in terms of bias (<2.0%), except for CB in ALS (−2.53%) and ALS + TLS (−2.86%), and SB in ALS + TLS data (−2.22%). These results demonstrate the usefulness of all three lidar-related methodologies and lidar modeling overall, along with lidar applicability in the estimation of crown structure and fuel attributes of longleaf pine forest ecosystems. Given that TLS measurements are less practical and more expensive, our comparison suggests that ALS measurements are still reasonable for many applications, and its usefulness is justified. This novel tree-level analysis and its respective results contribute to lidar-based planning of forest structure and fuel management. [ABSTRACT FROM AUTHOR]

Accurate estimation of fuels is essential for wildland fire simulations as well as decision-making related to land management. Numerous research efforts have leveraged remote sensing and machine learning for classifying land cover and mapping forest vegetation species. In most cases that focused on surface fuel mapping, the spatial scale of interest was smaller than a few hundred square kilometers; thus, many small-scale site-specific models had to be created to cover the landscape at the national scale. The present work aims to develop a large-scale surface fuel identification model using a custom deep learning framework that can ingest multimodal data. Specifically, we use deep learning to extract information from multispectral signatures, high-resolution imagery, and biophysical climate and terrain data in a way that facilitates their end-to-end training on labeled data. A multi-layer neural network is used with spectral and biophysical data, and a convolutional neural network backbone is used to extract the visual features from high-resolution imagery. A Monte Carlo dropout mechanism was also devised to create a stochastic ensemble of models that can capture classification uncertainties while boosting the prediction performance. To train the system as a proof-of-concept, fuel pseudo-labels were created by a random geospatial sampling of existing fuel maps across California. Application results on independent test sets showed promising fuel identification performance with an overall accuracy ranging from 55% to 75%, depending on the level of granularity of the included fuel types. As expected, including the rare—and possibly less consequential—fuel types reduced the accuracy. On the other hand, the addition of high-resolution imagery improved classification performance at all levels. [ABSTRACT FROM AUTHOR]

We study the Witt classes of the modular categories s o (2 r) 2 r associated with quantum groups of type Dr at (4 r − 2) -th roots of unity. From these classes we derive infinitely many Witt classes of order 2 that are linearly independent modulo the subgroup generated by the pointed modular categories. In particular, we produce an example of a simple, completely anisotropic modular category that is not pointed whose Witt class has order 2, answering a question of Davydov, Müger, Nikshych and Ostrik. Our results show that the trivial Witt class [ Vec ] has infinitely many square roots modulo the pointed classes, in analogy with the recent construction of infinitely many square roots of the Ising Witt classes modulo the pointed classes constructed in a similar way from certain type Br modular categories. We compare the subgroups generated by the Ising square roots and [ Vec ] square roots and provide evidence that they also generate linearly independent subgroups. [ABSTRACT FROM AUTHOR]

Wildfires are an essential part of a healthy ecosystem, yet the expansion of the wildland-urban interface, combined with climatic changes and other anthropogenic activities, have led to the rise of wildfire hazards in the past few decades. Managing future wildfires and their multi-dimensional impacts requires moving from traditional reactive response to deploying proactive policies, strategies, and interventional programs to reduce wildfire risk to wildland-urban interface communities. Existing risk assessment frameworks lack a unified analytical method that properly captures uncertainties and the impact of decisions across social, ecological, and technical systems, hindering effective decision-making related to risk reduction investments. In this paper, a conceptual probabilistic wildfire risk assessment framework that propagates modeling uncertainties is presented. The framework characterizes the dynamic risk through spatial probability density functions of loss, where loss can include different decision variables, such as physical, social, economic, environmental, and health impacts, depending on the stakeholder needs and jurisdiction. The proposed approach consists of a computational framework to propagate and integrate uncertainties in the fire scenarios, propagation of fire in the wildland and urban areas, damage, and loss analyses. Elements of this framework that require further research are identified, and the complexity in characterizing wildfire losses and the need for an analytical-deliberative process to include the perspectives of the spectrum of stakeholders are discussed. [ABSTRACT FROM AUTHOR]

Summary: The dead foliage of scorched crowns is one of the most conspicuous signatures of wildland fires. Globally, crown scorch from fires in savannas, woodlands and forests causes tree stress and death across diverse taxa. The term crown scorch, however, is inconsistently and ambiguously defined in the literature, causing confusion and conflicting interpretation of results. Furthermore, the underlying mechanisms causing foliage death from fire are poorly understood. The consequences of crown scorch – alterations in physiological, biogeochemical and ecological processes and ecosystem recovery pathways – remain largely unexamined. Most research on the topic assumes the mechanism of leaf and bud death is exposure to lethal air temperatures, with few direct measurements of lethal heating thresholds. Notable information gaps include how energy transfer injures and kills leaves and buds, how nutrients, carbohydrates, and hormones respond, and what physiological consequences lead to mortality. We clarify definitions to encourage use of unified terminology for foliage and bud necrosis resulting from fire. We review the current understanding of the physical mechanisms driving foliar injury, discuss the physiological responses, and explore novel ecological consequences of crown injury from fire. From these elements, we propose research needs for the increasingly interdisciplinary study of fire effects. [ABSTRACT FROM AUTHOR]

We develop categorical and number-theoretical tools for the classification of super-modular categories. We apply these tools to obtain a partial classification of super-modular categories of rank 8. In particular we find three distinct families of prime categories in rank 8 in contrast to the lower rank cases for which there is only one such family. [ABSTRACT FROM AUTHOR]

Methods to accurately estimate spatially explicit fuel consumption are needed because consumption relates directly to fire behavior, effects, and smoke emissions. Our objective was to quantify sparkleberry (Vaccinium arboretum Marshall) shrub fuels before and after six experimental prescribed fires at Fort Jackson in South Carolina. We used a novel approach to characterize shrubs non-destructively from three-dimensional (3D) point cloud data collected with a terrestrial laser scanner. The point cloud data were reduced to 0.001 m–3 voxels that were either occupied to indicate fuel presence or empty to indicate fuel absence. The density of occupied voxels was related significantly by a logarithmic function to 3D fuel bulk density samples that were destructively harvested (adjusted R 2 =.32, P <.0001). Based on our findings, a survey-grade Global Navigation Satellite System may be necessary to accurately associate 3D point cloud data to 3D fuel bulk density measurements destructively collected in small (submeter) shrub plots. A recommendation for future research is to accurately geolocate and quantify the occupied volume of entire shrubs as 3D objects that can be used to train models to map shrub fuel bulk density from point cloud data binned to occupied 3D voxels. [ABSTRACT FROM AUTHOR]

A braided fusion category is said to have Property F if the associated braid group representations factor through a finite group. We verify integral metaplectic modular categories have property F by showing these categories are group-theoretical. For the special case of integral categories 𝒞 with the fusion rules of SO (8) 2 we determine the finite group G for which Rep (D ω G) is braided equivalent to 𝒵 (𝒞). In addition, we determine the associated classical link invariant, an evaluation of the 2-variable Kauffman polynomial at a point. [ABSTRACT FROM AUTHOR]

We give a complete classification of modular categories of dimension p³m where p is prime and m is a square-free integer relatively prime to p. When p is odd, all such categories are pointed. For p = 2 one encounters modular categories with the same fusion ring as orthogonal quantum groups at certain roots of unity, namely SO(2m)2. We also classify the more general class of modular categories with the same fusion rules as SO(2N)2 with N odd. [ABSTRACT FROM AUTHOR]

In topological quantum computing, information is encoded in "knotted" quantum states of topological phases of matter, thus being locked into topology to prevent decay. Topological precision has been confirmed in quantum Hall liquids by experiments to an accuracy of 10-10 and harnessed to stabilize quantum memory. In this survey, we discuss the conceptual development of this interdisciplinary field at the juncture of mathematics, physics, and computer science. Our focus is on computing and physical motivations, basic mathematical notions and results, open problems and future directions related to and/or inspired by topological quantum computing. [ABSTRACT FROM AUTHOR]

Abstract: Understanding how hillslope topography modulates ecosystem dynamics across topoclimatic gradients is critical for predicting future climate change impacts on vegetation function. We examined the influence of hillslope topography on ecosystem productivity, structure, and photosynthetic activity across a range of water and energy availability using three independent methods in a forested watershed (Montana, USA): 308 tree cores; light detection and ranging quantification of stem density, basal area, foliar biomass, and total biomass; and the enhanced vegetation index (EVI; 1984–2012). Multiple linear regression analysis across three conifer species revealed significant increases in measured basal area increment growth rates (from 56 to 2,058 mm2/yr) with increasing values of the topographic wetness index and decreases in the climatic water deficit. At the watershed scale, we observed strong gradients in total biomass (e.g., 52 to 75 Mg/ha), which increased from ridgelines to convergent hollows. The most predominant topographic organization of forest biomass occurred along locations of climatically driven water limitations. Similarly, an analysis of growing season EVI indicated enhanced photosynthetic activity and a prolonged growing season in convergent hillslope positions. Collectively, these analyses confirm that within water‐limited landscapes, meter‐scale differences in topographic position can mediate the effects of the local energy balance and contribute to large differences in local hydrometeorological processes that are a necessary consideration for quantifying spatial patterns of ecosystem productivity. Further, they suggest that local topography and its topology with regional climate may become increasingly important for understanding spatial patterns of ecosystem productivity, mortality, and resilience as regional climates become more arid. [ABSTRACT FROM AUTHOR]

We study representations of the loop braid group LBn from the perspective of extending representations of the braid group $\mathcal{B}$n. We also pursue a generalization of the braid/Hecke/Temperlely–Lieb paradigm – uniform finite dimensional quotient algebras of the loop braid group algebras. [ABSTRACT FROM AUTHOR]

We study spin and super-modular categories systematically as inspired by fermionic topological phases of matter, which are always fermion parity enriched and modelled by spin topological quantum field theories at low energy. We formulate a 16-fold way conjecture for the minimal modular extensions of super-modular categories to spin modular categories, which is a categorical formulation of gauging the fermion parity. We investigate general properties of super-modular categories such as fermions in twisted Drinfeld doubles, Verlinde formulas for naive quotients, and explicit extensions of PSU(2)4m+2 with an eye towards a classification of the low-rank cases. [ABSTRACT FROM AUTHOR]

The feasibility of a classification-by-rank program for modular categories follows from the Rank-Finiteness Theorem. We develop arithmetic, representation theoretic and algebraic methods for classifying modular categories by rank. As an application, we determine all possible fusion rules for all rank=5 modular categories and describe the corresponding monoidal equivalence classes. [ABSTRACT FROM AUTHOR]

Understanding fine-scale variability in understory fuels is increasingly important as physics-based fire behavior models drive needs for higher-resolution data. Describing fuelbeds 3Dly is critical in determining vertical and horizontal distributions of fuel elements and the mass, especially in frequently burned pine ecosystems where fine-scale fuels arrangement drives fire intensity and resulting fire effects. Here, we describe research involving the use of highly resolved 3D models. We create fuelbeds using individual grass, litter, and pinecone models designed from field measurements. These fuel models are distributed throughout the fuelbed to replicate fuel distribution in rectified nadir photography taken for each plot. The simulated fuelbeds are converted into voxel arrays and biomass is estimated from calculated surface area between mesh vertices for each voxel. We compare field-based fuel depth and biomass with simulated estimates to demonstrate similarities and differences. Biomass distributions between simulated fuel beds and terrestrial laser scan data correlated well using Weibull shape parameters (r= 0.86). Our findings indicate that integration of field, simulated, and terrestrial laser scanner data will improve characterization of fuel mass, type, and spatial allocations that are important inputs to physics-based fire behavior models. [ABSTRACT FROM PUBLISHER]

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We provide an elementary introduction to topological quantum computation based on the Jones representation of the braid group. We first cover the Burau representation and Alexander polynomial. Then we discuss the Jones representation and Jones polynomial and their application to anyonic quantum computation. Finally we outline the approximation of the Jones polynomial by a quantum computer and explicit localizations of braid group representations. [ABSTRACT FROM AUTHOR]

Terrestrial laser scanning (TLS) was used to collect spatially continuous measurements of fuelbed characteristics across the plots and burn blocks of the 2012 RxCADRE experiments in Florida. Fuelbeds were scanned obliquely from plot/block edges at a height of 20 m above ground. Pre-fire blocks were scanned from six perspectives and four perspectives for post-fire at ,2 cm nominal spot spacing. After processing, fuel height models were developed at one meter spatial resolution in burn blocks and compared with field measurements of height. Spatial bias is also examined. The resultant fuel height data correspond closely with field measurementsofheight and exhibit low spatial bias. They show that field measurements of fuel height from field plots are not representative of the burn blocks as a whole. A translation of fuel height distributions to specific fuel attributes will be necessary to maximise the utility of the data for fire modelling. [ABSTRACT FROM AUTHOR]

The lack of independent, quality-assured field data prevents scientists from effectively evaluating and advancing wildland fire models. To rectify this, scientists and technicians convened in the southeastern United States in 2008, 2011 and 2012 to collect wildland fire data in six integrated core science disciplines defined by the fire modelling community. These were fuels, meteorology, fire behaviour, energy, smoke emissions and fire effects. The campaign is known as the Prescribed Fire Combustion and Atmospheric Dynamics Research Experiment (RxCADRE) and sampled 14 forest and 14 non-forest sample units associated within 6 small replicate (,10 ha) and 10 large operational (between 10 and 1000 ha) prescribed fires. Precampaign planning included identifying hosting agencies receptive to research and the development of study, logistics and safety plans. Data were quality-assured, reduced, analysed and formatted and placed into a globally accessible repository maintained by the US Forest Service Research Data Archive. The success of the RxCADRE project led to the commencement of a follow-on larger multiagency project called the Fire and Smoke Model Evaluation Experiment (FASMEE). This overview summarises the RxCADRE project and nine companion papers that describe the data collection, analysis and important conclusions from the six science disciplines. [ABSTRACT FROM AUTHOR]

Motivated by physical and topological applications, we study representations of the group LB3 of motions of 3 unlinked oriented circles in R3. Our point of view is to regard the three strand braid group B3 as a subgroup of LB3 and study the problem of extending B3 representations. We introduce the notion of a standard extension and characterize B3 representations admitting such an extension. In particular we show, using a classification result of Tuba and Wenzl [Pacific J. Math. 197, 491-510 (2001)], that every irreducible B3 representation of dimension at most 5 has a (standard) extension. We show that this result is sharp by exhibiting an irreducible 6-dimensional B3 representation that has no extensions (standard or otherwise). We obtain complete classifications of (1) irreducible 2-dimensional LB3 representations, (2) extensions of irreducible 3-dimensional B3 representations, and (3) irreducible LB3 representations whose restriction to B3 has abelian image. [ABSTRACT FROM AUTHOR]

We investigate braid group representations associated with unitary braided vector spaces, focusing on a conjecture that such representations should have virtually abelian images in general and finite image provided the braiding has finite order. We verify this conjecture for the two infinite families of Gaussian and group-type braided vector spaces, as well as the generalization to quasi-braided vector spaces of group-type. [ABSTRACT FROM AUTHOR]

We develop a theory of localization for braid group representations associated with objects in braided fusion categories and, more generally, to Yang–Baxter (YB) operators in monoidal categories. The essential problem is to determine when a family of braid representations can be uniformly modelled upon a tensor power of a fixed vector space in such a way that the braid group generators act “locally”. Although related to the notion of (quasi-)fiber functors for fusion categories, remarkably, such localizations can exist for representations associated with objects of non-integral dimension. We conjecture that such localizations exist precisely when the object in question has dimension the square-root of an integer and prove several key special cases of the conjecture. [ABSTRACT FROM PUBLISHER]