Cover Mapping Research Articles

Infinitely many noncontractible closed magnetic geodesics on non-compact manifolds

In this paper we study the existence and multiplicity of periodic orbits of exact magnetic flows with energy levels above the Mañé critical value of the universal cover on a non-compact manifold from the viewpoint of Morse theory.

Extending mixture of experts model to investigate heterogeneity of trajectories: When, where, and how to add which covariates.

Researchers are usually interested in examining the impact of covariates when separating heterogeneous samples into latent classes that are more homogeneous. The majority of theoretical and empirical studies with such aims have focused on identifying covariates as predictors of class membership in the structural equation modeling framework. In other words, the covariates only indirectly affect the sample heterogeneity. However, the covariates' influence on between-individual differences can also be direct. This article presents a mixture model that investigates covariates to explain within-cluster and between-cluster heterogeneity simultaneously, known as a mixture-of-experts (MoE) model. This study aims to extend the MoE framework to investigate heterogeneity in nonlinear trajectories: to identify latent classes, covariates as predictors to clusters, and covariates that explain within-cluster differences in change patterns over time. Our simulation studies demonstrate that the proposed model generally estimates the parameters unbiasedly, precisely, and exhibits appropriate empirical coverage for a nominal 95% confidence interval. This study also proposes implementing structural equation model forests to shrink the covariate space of the proposed mixture model. We illustrate how to select covariates and construct the proposed model with longitudinal mathematics achievement data. Additionally, we demonstrate that the proposed mixture model can be further extended in the structural equation modeling framework by allowing the covariates that have direct effects to be time-varying. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Serre-invariant stability conditions and Ulrich bundles on cubic threefolds

We prove a general criterion which ensures that a fractional Calabi--Yau category of dimension $\leq 2$ admits a unique Serre-invariant stability condition, up to the action of the universal cover of $\text{GL}^+_2(\mathbb{R})$. We apply this result to the Kuznetsov component $\text{Ku}(X)$ of a cubic threefold $X$. In particular, we show that all the known stability conditions on $\text{Ku}(X)$ are invariant with respect to the action of the Serre functor and thus lie in the same orbit with respect to the action of the universal cover of $\text{GL}^+_2(\mathbb{R})$. As an application, we show that the moduli space of Ulrich bundles of rank $\geq 2$ on $X$ is irreducible, answering a question asked by Lahoz, Macr\`i and Stellari.

Effects of distribution patterns of karst landscapes on runoff and sediment yield in karst watersheds

Aquatic karst landscapes are highly heterogeneous and vulnerable to environmental conditions due to carbonate rock dissolution by flowing water, freshwater movement and sediment transport. However, the landscape metrics commonly used in landscape ecology do not consider the spatial distribution of carbonate rocks in karst watersheds because these metrics are derived from land use/land cover maps. Therefore, this study investigated the effects of distribution patterns of karst landscapes on annual runoff and sediment yield in 40 heterogeneous karst watersheds in southwest China. The results show that the distribution patterns of karst landscapes significantly influenced annual runoff and sediment yield. A general linear model explained 74% of the runoff variations, indicating that the distribution pattern was the principal factor affecting runoff. Although these patterns significantly affected sediment yield, the general linear model accounted for only 52% of the sediment yield variations. Thus, the distribution patterns showed larger effects on runoff than sediment yield. This may be because landscape metrics of karst distribution patterns could not fully reflect the three-dimensional (3D) hydrogeological structure of karst watersheds. It is necessary to investigate the effects of 3D hydrogeological structures and hydrological and sediment connectivity on sediment yield. This will facilitate a more in-depth understanding of soil erosion mechanisms in karst watersheds.

Covariant dynamics on the momentum space

A geometrical interpretation of Schrödinger's kinetic and potential energy operators is proposed, allowing for a covariant momentum space formulation of the dynamics that is relevant for the theories with the deformation of the momentum space structure. Some specific examples are discussed in the context of flat space deformations and the Euclidean Snyder (spherical momentum space) model. In this formulation the dynamics for the deformations of the flat momentum space becomes trivial, while different versions of the Snyder model turn out to be dynamically equivalent.

Corrigendum: A geometric model for the module category of a gentle algebra

Abstract In this note we correct an oversight in [A geometric model for the module category of a gentle algebra, Int. Math. Res. Not. IMRN 2021, no. 15, 11357–11392] regarding morphisms between indecomposable modules of a gentle algebra. The oversight only occurs when bands are involved, which can be easily corrected by considering infinite periodic strings associated to bands and the universal cover of the surface associated to the gentle algebra.

A general framework to obtain seamless seasonal–directional extreme individual wave heights—Showcase Ekofisk

Extreme wave climate provides the basis for safe design of offshore structures and is crucial for planning and executing offshore operations. Covariate modeling of extremes significantly enriches and improves estimates of return levels and exceedance probabilities of extreme sea states. Based on novel observational and hindcast datasets, we formulate a seasonal–directional extreme value model for individual wave heights and present exceedance probabilities for the Ekofisk oil and gas field, a location in the Central North Sea. Subsequently, we elucidate how to downscale estimates of monthly exceedance probabilities and return levels to daily maxima and illustrate how to retrieve consistent results on seamless directional sectors and different seasons, or for the entire covariate space. We conclude with a versatile statistical framework to obtain seasonal–directional extreme waves and reveal a strong seasonal and directional dependence of extreme individual waves at Ekofisk with the highest waves coming from northwest during winter. Moreover, we apply our approach to normalized wave heights and show noticeable variability depending on season and direction with implications for offshore design.

Morphisms determined by objects under Galois G-covering theory

The theory of morphisms being determined by objects was originally investigated by Auslander, and can be seen as the culmination part of Auslander-Reiten theory. This theory provides a more general frame for working with the Auslander-Reiten theory. In this paper, we will study the behavior of morphisms determined by objects under G-coverings in the sense of Asashiba, which is a generalization of Gabriel's Galois coverings. As an application, we reformulate Bautista and Liu's framework that normal G-coverings preserve sink maps and source maps. We also show that there is a G-covering between two relative stable categories, which unifies Asashiba, Hafezi, Vahed and Mahdavi's work on the stable categories. This is applied to the discussion on the existence of Serre functors by G-coverings of triangulated categories.

Functioning trends of the state banks of Ukraine in the current conditions

This article is devoted to the consideration of current trends in the functioning of state-owned banks in Ukraine. The main internal and external problems faced by Ukrainian banking institutions, including state ones, with the beginning of a large-scale invasion and military aggression, are identified. The nationalization and liquidation of banks operating profitably in Ukraine (in particular Alfa-Bank JSC), which was carried out for the first time due to political factors caused by the war, is described. The owners of such banks were citizens of the aggressor country, were under sanctions and could negatively affect the stability of the Ukrainian banking sector.The strategic goals of state banks during the period of martial law and post-war economic recovery are given. The main performance indicators of state-owned banks have been analyzed for the last time. It is noted that state banks attract more than half of all deposits from clients of the country's banking sector, but they invest the majority of their assets in state securities, thus minimizing the risks of their own active operations and helping to finance state budget projects. State banks are leaders in the implementation of state preferential programs, in particular, «Affordable loans 5–7–9%» and «eOselya», which help restore credit and investment financing of economic development processes. The share of state banks in the country's banking sector in various areas of their activity has been determined. The possibilities and potential contribution of state-owned banks to the post-war recovery of the Ukrainian economy are described. It is the state banks that are the leaders in the market of banking services in Ukraine, which enable the state authorities in the extremely difficult conditions of the war to react quickly and implement the necessary changes in the work of the banking sector, with the aim of stabilizing it and influencing the dynamics of monetary policy in the country. Ukrainian state banks work according to a universal business model and cover customer service of all market segments, but potentially they should become state development banks that will contribute to economic growth and sustainable development of our country.

On the structure of metabelian Galois coverings of complex algebraic varieties

We describe the general structure of metabelian branched covers of smooth complex algebraic varieties. The main question that we consider is the following: given a smooth algebraic variety $Y$, which “building data” on $Y$ determine a metabelian cover $f:

Minimal Euler characteristics for even-dimensional manifolds with finite fundamental group

Abstract We consider the Euler characteristics $\chi (M)$ of closed, orientable, topological $2n$ -manifolds with $(n-1)$ -connected universal cover and a given fundamental group G of type $F_n$ . We define $q_{2n}(G)$ , a generalised version of the Hausmann-Weinberger invariant [19] for 4–manifolds, as the minimal value of $(-1)^n\chi (M)$ . For all $n\geq 2$ , we establish a strengthened and extended version of their estimates, in terms of explicit cohomological invariants of G. As an application, we obtain new restrictions for nonabelian finite groups arising as fundamental groups of rational homology 4–spheres.

The Regularity of the Linear Drift in Negatively Curved Spaces

We show that the linear drift of the Brownian motion on the universal cover of a closed connected smooth Riemannian manifold is C k − 2 C^{k-2} differentiable along any C k C^{k} curve in the manifold of C k C^k Riemannian metrics with negative sectional curvature. We also show that the stochastic entropy of the Brownian motion is C 1 C^1 differentiable along any C 3 C^{3} curve of C 3 C^3 Riemannian metrics with negative sectional curvature. We formulate the first derivatives of the linear drift and stochastic entropy, respectively, and show they are critical at locally symmetric metrics.

A comparison of three approaches to covariate effects on latent factors

In educational and psychological research, it is common to use latent factors to represent constructs and then to examine covariate effects on these latent factors. Using empirical data, this study applied three approaches to covariate effects on latent factors: the multiple-indicator multiple-cause (MIMIC) approach, multiple group confirmatory factor analysis (MG-CFA) approach, and the structural equation model trees (SEM Trees) approach. The MIMIC approach directly models covariate effects on latent factors. The MG-CFA approach allows testing of measurement invariance before latent factor means could be compared. The more recently developed SEM Trees approach partitions the sample into homogenous subsets based on the covariate space; model parameters are estimated separately for each subgroup. We applied the three approaches using an empirical dataset extracted from the eighth-grade U.S. data from the Trends in International Mathematics and Science Study 2019 database. All approaches suggested differences among mathematics achievement categories for the latent factor of mathematics self-concept. In addition, language spoken at home did not seem to affect students’ mathematics self-concept. Despite these general findings, the three approaches provided different pieces of information regarding covariate effects. For all models, we appropriately considered the complex data structure and sampling weights following recent recommendations for analyzing large-scale assessment data.

Weil–Petersson geodesics on the modular surface

We consider the Weil–Petersson (WP) metric on the modular surface. We lift WP geodesics to the universal cover of the modular surface, and analyse geometric properties of a lift as a path in the hyperbolic metric on the universal cover. For any pair of distinct points in the thick part of the universal cover, we prove that the WP and hyperbolic geodesic segments that connect the pair, fellow-travel in the thick part and all deviations between these segments arise during cusp excursions. Furthermore, we give a quantitative analysis of the deviation during an excursion. We leverage the fellow traveling to derive a correspondence between recurrent WP and hyperbolic rays from a base-point. We show that the correspondence can be promoted to a homeomorphism on the circle of directions. By analysing cuspidal winding of a typical WP geodesic ray, we show that the homeomorphism pushes forward a Lebesgue measure on the circle to a singular measure. In terms of continued fraction coefficients, the singularity boils down to a comparison that we prove, namely, the average coefficient is bounded along a typical WP ray but unbounded along a typical hyperbolic ray.

A global Weinstein splitting theorem for holomorphic Poisson manifolds

We prove that if a compact K\"ahler Poisson manifold has a symplectic leaf with finite fundamental group, then after passing to a finite \'etale cover, it decomposes as the product of the universal cover of the leaf and some other Poisson manifold. As a step in the proof, we establish a special case of Beauville's conjecture on the structure of compact K\"ahler manifolds with split tangent bundle.

Count lifts of non-maximal closed horocycles on $$SL_N(\mathbb {Z}) \backslash SL_N(\mathbb {R})/SO_N({\mathbb {R}})$$

A closed horocycle $$\mathcal {U}$$ on $$SL_N(\mathbb {Z}) \backslash SL_N(\mathbb {R})/SO_N({\mathbb {R}})$$ has many lifts to the universal cover $$SL_N(\mathbb {R})/SO_N({\mathbb {R}})$$ . Under some conditions on the horocycle, we give a precise asymptotic count of its lifts of bounded distance away from a given base point in the universal cover. This partially generalizes previous work of Mohammadi–Golsefidy.

Spatiotemporal Land Use/Land Cover Mapping and Prediction Based on Hybrid Modeling Approach: A Case Study of Kano Metropolis, Nigeria (2020–2050)

The change dynamics of land use/land cover (LULC) is a vital factor that significantly modifies the natural environment. Therefore, mapping and predicting spatiotemporal LULC transformation is crucial in effectively managing the built environment toward achieving Sustainable Development Goal 11, which seeks to make cities all-inclusive, sustainable, and reliable. The study aims to examine the change dynamics of LULC in Kano Metropolis, Nigeria from 1991 to 2020 and predict the city’s future land uses over the next 15 and 30 years, i.e., 2035 and 2050. The maximum likelihood algorithm (MLA) of the supervised classification method was utilized to classify the study area’s land uses using Landsat satellite data and various geographic information system (GIS) techniques. A hybrid simulation model comprising cellular automata and Markov chain (CA-Markov) was then employed in validating and modeling the change dynamics of future LULC. The model integrated the spatial continuity of the CA model with the Markov chain’s ability to address the limitations of individual models in simulating long-term land use prediction. The study revealed substantial changes in the historical LULC pattern of Kano metropolis from 1991 to 2020. It indicated a considerable decline in the city’s barren land from approximately 413.47 km2 in 1991 to 240.89 km2 in 2020. Built-up areas showed the most extensive development over the past 29 years, from about 66.16 km2 in 1991 to 218.72 km2 in 2020. This trend of rapid urban growth is expected to continue over the next three decades, with prediction results indicating the city’s built-up areas expanding to approximately 307.90 km2 in 2035 and 364.88 km2 in 2050. The result also suggests that barren lands are anticipated to decline further with the continuous sustenance of various agricultural activities, while vegetation and water bodies will slightly increase between 2020 and 2050. The findings of this study will help decision-makers and city administrators formulate sustainable land use policies for a more inclusive, safe, and resilient city.

Galois coverings of enriched categories and an extension of Cohen-Montgomery theorem

The purpose of this paper is to give an intrinsic fundamental group and coverings for categories enriched over an abelian symmetric monoidal category (V,⊗,I). We relate this to various categorical constructions such as the universal covering, smash products and connected gradings of a small V-category B. Finally, we apply these methods to obtain an extension of Cohen-Montgomery duality theorem for coactions to the symmetric monoidal category (V,⊗,I).

Bijective enumeration of planar bipartite maps with three tight boundaries, or how to slice pairs of pants

We consider planar maps with three boundaries, colloquially called pairs of pants. In the case of bipartite maps with controlled face degrees, a simple expression for their generating function was found by Eynard and proved bijectively by Collet and Fusy. In this paper, we obtain an even simpler formula for \emph{tight} pairs of pants, namely for maps whose boundaries have minimal length in their homotopy class. We follow a bijective approach based on the slice decomposition, which we extend by introducing new fundamental building blocks called bigeodesic triangles and diangles, and by working on the universal cover of the triply punctured sphere. We also discuss the statistics of the lengths of minimal separating loops in (non necessarily tight) pairs of pants and annuli, and their asymptotics in the large volume limit.

Spatiotemporal dynamics of ecological security in a typical conservation region of southern China based on catastrophe theory and GIS.

Ecological security assessment can effectively reflect the ecological status of a region and reveal its level of sustainable development. In this paper, an ecological security-oriented evaluation system was constructed, and the ecological security level of the Dongjiangyuan region from 2000 to 2020 was evaluated based on catastrophe theory and GIS. The results were as follows: (1) As shown in the land use and cover maps, by 2020, the forestland area had decreased the most, and the artificial surface area had increased the most. (2) The ecological security index of the Dongjiangyuan region showed a low trend in the artificial surface area and its surrounding areas. The quite low values of the ecological security index in 2000 and 2010 were improved in 2020 due to the increase in ecological services capacity. The increased vegetation cover from 2000 to 2020 promoted the improved ecological service capacity. (3) The rapid urbanization process in the Dongjiangyuan region resulted in a lower ecological sensitivity index value. Notably, the ecological sensitivity index of the study area had a slightly decreasing trend. (4) The spatial autocorrelation showed that the proportion of hot and cold spots from 2000 to 2020 decreased by 2.96% and 6.91%, respectively. This study can provide a scientific basis and decision-making guidance for ecological management in the Dongjiangyuan region in the future.