Cover Mapping Research Articles

Universally irreducible subvarieties of Siegel moduli spaces

Abstract A subvariety of a quasi-projective complex variety X is called “universally irreducible” if its preimage inside the universal cover of X is irreducible. In this paper we investigate sufficient conditions for universal irreducibility. We consider in detail complete intersection subvarieties of small codimension inside Siegel moduli spaces of any finite level. Moreover, we show that, for g ≥ 3 {g\geq 3} , every Siegel modular form is the product of finitely many irreducible analytic functions on the Siegel upper half-space ℍ g {{\mathbb{H}}_{g}} . We also discuss the special case of singular theta series of weight 1 2 {\frac{1}{2}} and of Schottky forms.

On the coadjoint Virasoro action

The set of coadjoint orbits of the Virasoro algebra at level 1 is in bijection with the set of conjugacy classes in a certain open subset SL˜(2,R)+ of the universal cover of SL(2,R). We strengthen this bijection to a Morita equivalence of quasi-symplectic groupoids, integrating the Poisson structure on vir1⁎(S1) and the Cartan-Dirac structure on SL˜(2,R)+, respectively.

Improving the Hosmer-Lemeshow goodness-of-fit test in large models with replicated Bernoulli trials

The Hosmer-Lemeshow (HL) test is a commonly used global goodness-of-fit (GOF) test that assesses the quality of the overall fit of a logistic regression model. In this paper, we give results from simulations showing that the type I error rate (and hence power) of the HL test decreases as model complexity grows, provided that the sample size remains fixed and binary replicates (multiple Bernoulli trials) are present in the data. We demonstrate that a generalized version of the HL test (GHL) presented in previous work can offer some protection against this power loss. These results are also supported by application of both the HL and GHL test to a real-life data set. We conclude with a brief discussion explaining the behavior of the HL test, along with some guidance on how to choose between the two tests. In particular, we suggest the GHL test to be used when there are binary replicates or clusters in the covariate space, provided that the sample size is sufficiently large.

Improving conformalized quantile regression through cluster-based feature relevance

Conformalized quantile regression, a cutting-edge and model-agnostic algorithm, has emerged as a recent innovation to generate valid prediction intervals on finite samples while addressing heteroscedasticity. It starts by employing quantile regression to estimate conditional quantiles. Subsequently, these estimated conditional quantiles undergo a rectification process using conformal prediction. Under the assumption of exchangeability, a slightly weaker form of independent and identically distributed (i.i.d.) data, the resulting prediction intervals are valid in finite samples. However, a drawback of the proposed conformalization step is identified: it lacks the capacity to adapt to heteroscedasticity due to its independence from the input. To overcome this limitation, we propose an improvement that involves partitioning the covariates space into clusters, assigning higher weights to features with greater predictive power. Following that, within each cluster, a conformal step is applied, leveraging a rectification that is reliant on the input cluster-wise.To demonstrate the superiority of our improved version over the classic version of conformalized quantile regression, we conducted a comprehensive comparison of their respective prediction intervals using synthetic data.

Integrating remote sensing temporal trajectory and survey statistics to update land use/land cover maps

ABSTRACTRemote sensing and land resource surveys have been used in recent decades for land use/land cover (LULC) mapping; however, keeping the developed LULC up-to-date and consistent with land survey statistics remains challenging. This study developed a practical and effective framework to automatically update existing LULC products and bridge the gap between remote sensing classification results and land survey data. This study employed Landsat imagery time series, change detection algorithms, sample migration, and random forests to develop a framework for updating existing LULC products in China from 1980–2015 to 1980–2022. The updated LULC maps reflect the post-2015 LULC changes well and maintain continuity with the pre-2015 products. Additionally, a statistical space allocation method based on the minimum cross-entropy strategy was proposed to optimize the LULC maps, increasing the correlation coefficient (r) with China’s second and third national land survey statistics from 0.41–0.89 to 0.86–0.99. Thus, the framework and products developed in this study provide valuable tools for sustainable land use and policy planning.

TreeKernel: interpretable kernel machine tests for interactions between -omics and clinical predictors with applications to metabolomics and COPD phenotypes

BackgroundIn this paper, we are interested in interactions between a high-dimensional -omics dataset and clinical covariates. The goal is to evaluate the relationship between a phenotype of interest and a high-dimensional omics pathway, where the effect of the omics data depends on subjects’ clinical covariates (age, sex, smoking status, etc.). For instance, metabolic pathways can vary greatly between sexes which may also change the relationship between certain metabolic pathways and a clinical phenotype of interest. We propose partitioning the clinical covariate space and performing a kernel association test within those partitions. To illustrate this idea, we focus on hierarchical partitions of the clinical covariate space and kernel tests on metabolic pathways.ResultsWe see that our proposed method outperforms competing methods in most simulation scenarios. It can identify different relationships among clinical groups with higher power in most scenarios while maintaining a proper Type I error rate. The simulation studies also show a robustness to the grouping structure within the clinical space. We also apply the method to the COPDGene study and find several clinically meaningful interactions between metabolic pathways, the clinical space, and lung function.ConclusionTreeKernel provides a simple and interpretable process for testing for relationships between high-dimensional omics data and clinical outcomes in the presence of interactions within clinical cohorts. The method is broadly applicable to many studies.

Sentinel-2 Data for Land Use/Land Cover Mapping: A Meta-analysis and Review

Sentinel-2 Data for Land Use/Land Cover Mapping: A Meta-analysis and Review

Environmental Hazards and Structural Covariates of US Homicide Rates: Methodological Considerations When Investigating the “Ecology” of Violence

ABSTRACT Environmental hazards such as air pollutants have increasingly been investigated as macro-level correlates of violent criminal activity, including rates of homicide across space. Such efforts highlight the growing appreciation in the social sciences of the interaction between humans and the natural environment, particularly within the subfields of environmental sociology and green criminology. However, while such investigations broaden the scope of relevant social scientific inquiry, they often fail to appreciate the theoretical and methodological contributions from prior crime and deviance scholars. Given the expansive history within the social sciences of investigating structural covariates of homicide rates, this effort seeks to determine whether differential levels of particulate matter with aerodynamic diameters smaller than 2.5 μm (PM2.5) can be observed as unique predictor of lethal violence in the US after simplifying the dimensionality of the regressor space. Results indicate that while air pollution levels share covariate space with population size and density, their combined influence represents a robust predictor of county-level homicide rates in the various spatial econometric models estimated.

Galois correspondence for Galois coverings of tropical curves

We define Galois coverings of tropical curves for which a Galois correspondence and a universal mapping property hold.

RCD*(K,N) spaces are semi-locally simply~connected

Abstract It was shown in [A. Mondino and G. Wei, On the universal cover and the fundamental group of an RCD * ⁢ ( K , N ) {\rm RCD}^{*}(K,N) -space, J. reine angew. Math. 753 2019, 211–237] that any RCD * ⁢ ( K , N ) {\mathrm{RCD}^{*}(K,N)} space ( X , d , 𝔪 ) {(X,d,\mathfrak{m})} has a universal cover. We prove that for any point x ∈ X {x\in X} and R > 0 {R>0} , there exists r < R {r<R} such that any loop in B r ⁢ ( x ) {B_{r}(x)} is contractible in B R ⁢ ( x ) {B_{R}(x)} ; in particular, X is semi-locally simply connected and the universal cover of X is simply connected. This generalizes the earlier work in [J. Wang, Ricci limit spaces are semi-locally simply connected, preprint 2021] that any Ricci limit space is semi-locally simply connected.

Integrating GIS and remote sensing for land use/land cover mapping and groundwater potential assessment for climate-smart cocoa irrigation in Ghana

Although Ghana is a leading global cocoa producer, its production and yield have experienced declines in recent years due to various factors, including long-term climate change such as increasing temperatures and changing rainfall patterns, as well as drought events. With the increasing exposure of cocoa-producing regions to extreme weather events, the vulnerability of cocoa production is also expected to rise. Supplemental irrigation for cocoa farmers has emerged as a viable adaptation strategy to ensure a consistent water supply and enhance yield. However, understanding the potential for surface and groundwater irrigation in the cocoa-growing belt remains limited. Consequently, this study aims to provide decision-support maps for surface and groundwater irrigation potential to aid planning and investment in climate-smart cocoa irrigation. Utilizing state-of-the-art geospatial and remote sensing tools, data, and methods, alongside in-situ groundwater data, we assess the irrigation potential within Ghana's cocoa-growing areas. Our analysis identified a total area of 22,126 km2 for cocoa plantations and 125.2 km2 for surface water bodies within the cocoa-growing regions. The multi-criteria analysis (MCA) revealed that approximately 80% of the study area exhibits moderate to very high groundwater availability potential. Comparing the MCA output with existing borehole locations demonstrated a reasonable correlation, with about 80% of existing boreholes located in areas with moderate to very high potential. Boreholes in very high potential areas had the highest mean yield of 90.7 l/min, while those in low groundwater availability potential areas registered the lowest mean yield of 58.2 l/min. Our study offers a comprehensive evaluation of water storage components and their implications for cocoa irrigation in Ghana. While groundwater availability shows a generally positive trend, soil moisture and surface water have been declining, particularly in the last decade. These findings underline the need for climate-smart cocoa irrigation strategies that make use of abundant groundwater resources during deficit periods. A balanced conjunctive use of surface and groundwater resources could thus serve as a sustainable solution for maintaining cocoa production in the face of climate change.

Modeling construction and demolition waste quantities in Tanta City, Egypt: a synergistic approach of remote sensing, geographic information system, and hybrid fuzzy neural networks

A waste management strategy needs accurate data on the generation rates of construction and demolition waste (CDW). The objective of this study is to provide a robust methodology for predicting CDW generation in Tanta City, one of the largest and most civilized cities in Egypt, based on socioeconomic and waste generation statistics from 1965 to 2021. The main contribution of this research involves the fusion of remote sensing and geographic information systems to construct a geographical database, which is employed using machine learning for modeling and predicting the quantities of generated waste. The land use/land cover map is determined by integrating topographic maps and remotely sensed data to extract the built-up, vacant, and agricultural areas. The application of a self-organizing fuzzy neural network (SOFNN) based on an adaptive quantum particle swarm optimization algorithm and a hierarchical pruning scheme is introduced to predict the waste quantities. The performance of the proposed models is compared against that of the FNN with error backpropagation and the group method of data handling using five evaluation measures. The results of the proposed models are satisfactory, with mean absolute percentage error (MAPE), normalized root mean square error (NRMSE), determination coefficient, Kling–Gupta efficiency, and index of agreement ranging between 0.70 and 1.56%, 0.01 and 0.03, 0.99 and 1.00, 0.99, and 1.00. Compared to other models, the proposed models reduce the MAPE and NRMSE by more than 92.90% and 90.64% based on fivefold cross-validation. The research findings are beneficial for utilizing limited data in developing effective strategies for quantifying waste generation. The simulation outcomes can be applied to monitor the urban metabolism, measure carbon emissions from the generated waste, develop waste management facilities, and build a circular economy in the study area.

Lagrangian Reduction by Stages in Field Theory

We propose a category of bundles in order to perform Lagrangian reduction by stages in covariant Field Theory. This category plays an analogous role to Lagrange–Poincaré bundles in Lagrangian reduction by stages in Mechanics and includes both jet bundles and reduced covariant configuration spaces. Furthermore, we analyze the resulting reconstruction condition and formulate the Noether theorem in this context. Finally, a model of a molecular strand with rotors is seen as an application of this theoretical frame.

Spatial GARCH models for unknown spatial locations – an application to financial stock returns

ABSTRACT Spatial GARCH models, like all other spatial econometric models, require the definition of a suitable weight matrix. This matrix implies a certain structure for spatial interactions. GARCH-type models are often applied to financial data because the conditional variance, which can be translated as financial risks, is easy to interpret. However, when it comes to instantaneous/spatial interactions, the proximity between observations has to be determined. Thus, we introduce an estimation procedure for spatial GARCH models under unknown locations employing the proximity in a covariate space. We use one-year stock returns of companies listed in the Dow Jones Global Titans 50 index as an empirical illustration. Financial stability is most relevant for determining similar firms concerning stock return volatility.

Modeling Land Use/Land Cover Change in Berau Pantai Forests, Berau Regency, East Kalimantan Province

Land demands increase with the rise of population and regional development. This results in considerable pressure on forest resources which is characterized by an increasing rate of deforestation. To further explore the impact of deforestation and forest management in regional planning process, this study specifically aimed 1) to identify patterns of land use/land cover changes, 2) to analyze driving factors and 3) to model future land use/land cover. This study employed Landsat imageries to construct land use/land cover maps and their variation across time. Driving factors were analyzed using binary logistic regression. Land use prediction was made through Artificial Neural Network approach. Multitemporal analysis indicated that the research area experienced a decreasing trend of natural forest and shrubs, with substantial extension of existing plantation forests, plantations, agricultural lands and settlements. Indicated driving factors included accessibility, slope class, soil type, forest permit, forest function, RTRW and population density. A forecast in 2030 suggested that natural forests and built-up land would increase from current figures.

Leveraging NAIP Imagery for Accurate Large-Area Land Use/land Cover Mapping: A Case Study in Central Texas

Large-area land use land cover (LULC) mapping using high-resolution imagery remains challenging due to radiometric differences between scenes, the low spectral depth of the imagery, landscape heterogeneity, and computational limitations. Using a random forest (RF)- supervised machine-learning algorithm, we present a geographic object-based image analysis approach to classifying a large mosaic of 220 National Agriculture Imagery Program orthoimagery into lulc categories. The approach was applied in central Texas, USA, covering over 6000 km2. We generated 36 variables for each object and accounted for spatial structures of sample data to determine the distance at which samples were spatially independent. The final rf model produced 94.8% accuracy on independent stratified random samples. In addition, vegetation and water indices, the mean and standard deviation of principal components, and texture features improved classification accuracy. This study demonstrates a cost-effective way of producing an accurate multi-class land use/land cover map using high-spatial/low-spectral resolution orthoimagery.

Local Search for Efficient Causal Effect Estimation

Causal effect estimation from observational data is a challenging problem, especially with high dimensional data and in the presence of unobserved variables. The available data-driven methods for tackling the problem either provide an estimation of the bounds of a causal effect (i.e. nonunique estimation) or have low efficiency. The major hurdle for achieving high efficiency while trying to obtain unique and unbiased causal effect estimation is how to find a proper adjustment set for confounding control in a fast way, given the huge covariate space and considering unobserved variables. In this paper, we approach the problem as a local search task for finding valid adjustment sets in data. We establish the theorems to support the local search for adjustment sets, and we show that unique and unbiased estimation can be achieved from observational data even when there exist unobserved variables. We then propose a data-driven algorithm that is fast and consistent under mild assumptions. We also make use of a frequent pattern mining method to further speed up the search of minimal adjustment sets for causal effect estimation. Experiments conducted on extensive synthetic and real-world datasets demonstrate that the proposed algorithm outperforms the state-of-the-art criteria/estimators in both accuracy and time-efficiency.

Simultaneous Measurements of Noncommuting Observables: Positive Transformations and Instrumental Lie Groups.

We formulate a general program for describing and analyzing continuous, differential weak, simultaneous measurements of noncommuting observables, which focuses on describing the measuring instrument autonomously, without states. The Kraus operators of such measuring processes are time-ordered products of fundamental differential positive transformations, which generate nonunitary transformation groups that we call instrumental Lie groups. The temporal evolution of the instrument is equivalent to the diffusion of a Kraus-operator distribution function, defined relative to the invariant measure of the instrumental Lie group. This diffusion can be analyzed using Wiener path integration, stochastic differential equations, or a Fokker-Planck-Kolmogorov equation. This way of considering instrument evolution we call the Instrument Manifold Program. We relate the Instrument Manifold Program to state-based stochastic master equations. We then explain how the Instrument Manifold Program can be used to describe instrument evolution in terms of a universal cover that we call the universal instrumental Lie group, which is independent not just of states, but also of Hilbert space. The universal instrument is generically infinite dimensional, in which case the instrument's evolution is chaotic. Special simultaneous measurements have a finite-dimensional universal instrument, in which case the instrument is considered principal, and it can be analyzed within the differential geometry of the universal instrumental Lie group. Principal instruments belong at the foundation of quantum mechanics. We consider the three most fundamental examples: measurement of a single observable, position and momentum, and the three components of angular momentum. As these measurements are performed continuously, they converge to strong simultaneous measurements. For a single observable, this results in the standard decay of coherence between inequivalent irreducible representations. For the latter two cases, it leads to a collapse within each irreducible representation onto the classical or spherical phase space, with the phase space located at the boundary of these instrumental Lie groups.

Spatial prediction of groundwater level change based on the Third Law of Geography

Spatial prediction methods are an important means of predicting the spatial variation of groundwater level change. Existing methods extract spatial or statistical relationships from samples to represent the study area for inference and require a representative sample set that is usually in large quantity and is distributed across geographic or covariate space. However, samples for groundwater are usually sparsely and unevenly distributed. In this paper, an approach based on the Third Law of Geography is proposed to make predictions by comparing the similarity between each individual sample and unmeasured site. The approach requires no specific number or distribution of samples and provides individual uncertainty measures at each location. Experiments in three different watersheds across the U.S. show that the proposed methods outperform machine learning methods when available samples do not well represent the area. The provided uncertainty measures are indicative of prediction accuracy by location. The results of this study also show that the spatial prediction based on the Third Law of Geography can also be successfully applied to dynamic variables such as groundwater level change.

On the holomorphic convexity of reductive Galois coverings over compact Kähler surfaces

This article generalizes the result of Katzarkov and Ramachandran from algebraic surfaces to Kähler surfaces. We follow their argument to prove the holomorphic convexity of a reductive Galois covering over a compact Kähler surface which does not have two ends, except that we replace the p-adic factorization theorem by an analysis of the singularities of the continuous subanalytic plurisubharmonic exhaustion function.