Let $X$ be a smooth projective variety over $\mathbb{C}$ with a simple normal crossings divisor $D\subset X$. We compare the notions of stable log maps to $(X,D)$ in algebraic geometry and symplectic topology. In particular, we prove an equivalence between fine (basic) algebraic log maps and symplectic log maps, and we define the symplectic analogue of fine saturated algebraic log maps by refining the notion of log Gromov convergence.
Thomas Monninger, Zihan Zhang, Steffen Staab
et al.
Accurate environmental representations are essential for autonomous driving, providing the foundation for safe and efficient navigation. Traditionally, high-definition (HD) maps are providing this representation of the static road infrastructure to the autonomous system a priori. However, because the real world is constantly changing, such maps must be constructed online from on-board sensor data. Navigation-grade standard-definition (SD) maps are widely available, but their resolution is insufficient for direct deployment. Instead, they can be used as coarse prior to guide the online map construction process. We propose NavMapFusion, a diffusion-based framework that performs iterative denoising conditioned on high-fidelity sensor data and on low-fidelity navigation maps. This paper strives to answer: (1) How can coarse, potentially outdated navigation maps guide online map construction? (2) What advantages do diffusion models offer for map fusion? We demonstrate that diffusion-based map construction provides a robust framework for map fusion. Our key insight is that discrepancies between the prior map and online perception naturally correspond to noise within the diffusion process; consistent regions reinforce the map construction, whereas outdated segments are suppressed. On the nuScenes benchmark, NavMapFusion conditioned on coarse road lines from OpenStreetMap data reaches a 21.4% relative improvement on 100 m, and even stronger improvements on larger perception ranges, while maintaining real-time capabilities. By fusing low-fidelity priors with high-fidelity sensor data, the proposed method generates accurate and up-to-date environment representations, guiding towards safer and more reliable autonomous driving. The code is available at https://github.com/tmonnin/navmapfusion
SangHyun Lee, Ali Danandeh Mehr, Daniel Moriasi
et al.
Abstract High‐resolution gridded data sets provide valuable opportunities to enhance drought forecasting, but applying complex machine learning algorithms across large spatial domains is computationally challenging. This study presents a novel hybrid approach for forecasting the gridded Standardized Precipitation‐Evapotranspiration Index (SPEI) across the U.S. Southern Plains (SP), with lead times of 1 and 3 months. We developed a clustering‐based method using 21 centroid grid cells, each representing a unique cluster of similar grid cells based on various hydrologic characteristics, to train and evaluate multilayer perceptrons (MLPs), long short‐term memory (LSTM), and genetic programming (GP). Based on the superior performance of the trained MLPs in terms of Nash‐Sutcliffe efficiency and root‐mean‐square error, they were extended to corresponding grid cells for each cluster, enabling spatially adaptive drought prediction at a high resolution. The use of discrete wavelet transform (DWT) further enhanced model accuracy by capturing key temporal patterns in the SPEI series. Notably, our results showed that physical and hydrologic attributes strongly influenced input selections. While a 12‐month lag period worked well in regions with weaker seasonality, areas with strong seasonality benefited from selection of effective lags by using mutual information. For 3‐month‐ahead forecasts, including decomposed potential evapotranspiration in addition to precipitation as inputs improved accuracy in drier regions but decreased accuracy in humid areas. The forecast maps based on the hybrid DWT‐MLP models effectively captured the spatial variability of drought, with high correlations to observed values, demonstrating their effectiveness for regional drought early warning systems to inform water resources management adaptations.
In response to the application scenarios of modernized Traditional Chinese Medicine (TCM) diagnostic and treatment equipment moving towards the user end, an effort has been made to enhance the user-friendliness of TCM diagnostic and treatment devices. This involves introducing the concept of edge computing into the mobile tongue diagnosis instrument, shifting the tasks of tongue image acquisition and analysis to portable auxiliary diagnostic devices. To improve the efficiency of edge computing devices in handling tongue image analysis tasks, a multi-task network model based on a lightweight network backbone is proposed. The model utilizes the lightweight feature extraction backbone of MobileNet to provide feature encoding for both the semantic segmentation branch and the multi-label classification branch. The semantic segmentation branch adopts a skip-layer connection structure with multi-scale feature maps, and an attention mechanism is incorporated into the classification branch to fuse the feature maps from the segmentation branch. This achieves tongue segmentation and multi-label classification tasks in a computationally efficient environment. The model achieves a pixel accuracy of 85.3% in semantic segmentation and an accuracy of 95.6% in multi-label classification. The network’s forward propagation speed on edge computing platforms reaches 7 frames per second (FPS). The proposed lightweight network backbone multi-task network model ensures a significant improvement in processing efficiency while maintaining the accuracy of segmentation and classification tasks. Additionally, the model exhibits advantages in terms of quantity and scale, saving both storage and computational resources. It not only enhances the accuracy and efficiency of tongue image real-time analysis in edge computing scenarios but also reduces the processing time, providing excellent precision and inference speed.
Interfacial spalling is a common failure mode in fiber-reinforced polymer (FRP) strengthened concrete structures, and interfacial bonding defects are one of the major causes of such damage. These early-stage defects are difficult to identify through visual inspection, highlighting the importance of developing non-contact, non-destructive testing (NDT) methods for detecting interfacial bonding. In this study, the digital image correlation (DIC) technique was employed to detect early bonding at the interface of FRP-strengthened concrete beams. Deformation was induced by varying the surface temperature of the specimens, and image stitching and analysis were performed to obtain second principal strain maps during thermal loading. The interfacial bonding defects were identified based on strain concentration zones in the strain field. A finite element model was developed to simulate the thermal loading process, and the simulation results were found to be consistent with experimental observations. The study confirms the feasibility of using DIC-based thermal deformation analysis for detecting interfacial bonding in FRP-strengthened concrete structures. The results show that larger defect size and greater defect thickness lead to more pronounced strain concentration. Thinner FRP layers improve defect detectability, while the effect of anchorage method on detection results is negligible.
Materials of engineering and construction. Mechanics of materials
We discuss Iitaka's theory of quasi-Albanese maps in details. We also give a detailed proof of Kawamata's theorem on the quasi-Albanese maps for varieties of the logarithmic Kodaira dimension zero. Note that Iitaka's theory is an application of Deligne's mixed Hodge theory for smooth algebraic varieties.
We consider the class of interval maps with dense set of periodic points CP and its closure Cl(CP) equipped with the metric of uniform convergence. Besides studying basic topological properties and density results in the spaces CP and Cl(CP) we prove that Cl(CP) is dynamically characterized as the set of interval maps for which every point is chain-recurrent. Furthermore, we prove that a strong topological expansion property called topological exactness (or leo property) is attained on the open dense set of maps in CP and on a residual set in Cl(CP). Moreover, we show that every second category set in CP and Cl(CP) is rich in a sense that it contains uncountably many conjugacy classes. An analogous conclusion also holds in the setting of interval maps preserving any fixed non-atomic probability measure with full support. Finally, we give a detailed description of the structure of periodic points of generic maps in CP and Cl(CP) and show that generic maps in CP and Cl(CP) satisfy the shadowing property.
In this note, we study non-uniqueness for minimizing harmonic maps from $B^3$ to $§^2$. We show that every boundary map can be modified to a boundary map that admits multiple minimizers of the Dirichlet energy by a small $W^{1,p}$-change for $p<2$. This strengthens a remark by the second-named author and Strzelecki. The main novel ingredient is a homotopy construction, which is the answer to an easier variant of a challenging question regarding the existence of a norm control for homotopies between $ W^{1,p} $ maps.
We have used a Ligand Knowledge Base for bidentate P,P-donor ligands of potential interest to homogeneous catalysis to compare three dimensionality reduction techniques, namely Principal Component Analysis (PCA), Uniform Manifold Approximation and Projection (UMAP) and t-distributed Stochastic Neighbor Embedding (t-SNE). While our previous work on Ligand Knowledge Bases has focused on PCA, here we compare this approach with more recently-published approaches and assess the information retention, visualization, clustering and interpretability which can be achieved for each approach. We find that potential advantages of t-SNE are not realized with a database of the current size (275 entries), and that there is a degree of complementarity between PCA and UMAP. The statistics underlying PCA rely on linear relationships, making interpretation of the resulting plots comparatively straightforward. Since much of chemistry relies on linear structure-property relationships and low-dimensional visualization, the explainability and information retention achieved is attractive. UMAP proved more challenging to interpret, but achieved clear clustering which was often chemically meaningful, and it would be a useful approach for ensuring that distinct subsets of compounds are sampled in a machine-learning context. This analysis also highlighted that the tunability of catalysis achieved through ligand exchange maps well onto some areas of chemical space where closely related ligands cluster, while others represent outliers; these arise from different combinations of steric and electronic effects which chemists will find intuitive.
We propose a geometric construction of three-dimensional birational maps that preserve two pencils of quadrics. The maps act as compositions of involutions, which, in turn, act along the straight line generators of the quadrics of the first pencil and are defined by the intersections with quadrics of the second pencil. On each quadric of the first pencil, the maps act as two-dimensional QRT maps. While these maps are of a pretty high degree in general, we find geometric conditions which guarantee that the degree is reduced to 3. The resulting degree 3 maps are illustrated by two known and two novel Kahan-type discretizations of three-dimensional Nambu systems, including the Euler top and the Zhukovski-Volterra gyrostat with two non-vanishing components of the gyrostatic momentum.
<b>Background:</b> The mechanisms of atrial tachycardia (AT) related to the left atrial anterior wall (LAAW) are complex and can be challenging to map in patients after catheter ablation for atrial fibrillation (AF) or cardiac surgery. We aimed to investigate the electrophysiological characteristics AT and to devise an ablation strategy. <b>Methods and Results:</b> We identified 31 scar-related LAAW reentrant ATs in 22 patients after catheter ablation for AF or cardiac surgery. Activation maps of the left atrium (LA) or both atria were obtained using a high-density mapping system, and the precise mechanism and critical area for each AT were analyzed. Patients were followed up regularly in a clinic. After analyzing the activation and propagation of each AT, the scar-related LAAW ATs were classified into three types, based on mechanisms related to: (1) LAAW conduction gap(s) in 19 LA macro-reentrant ATs; (2) LAAW epicardial connection(s) in 11 LA or bi-atrial ATs; and (3) LAAW local micro-reentry in 1 LAAW AT. Multiple ATs were identified in seven patients. Effective ablation (termination or circuit change of AT) was obtained in 30 ATs by targeting the critical area identified by the mapping system. During 16.0 ± 7.6 months follow-up, recurrent AT occurred in two patients. <b>Conclusions:</b> Three mechanisms of scar-related AT of LAAW were identified, most of which were related to LAAW conduction gaps. Notably, epicardial AT or bi-atrial AT comprised a nonnegligible proportion. A high-density mapping system could make it possible to determine the accurate mechanism of AT and serve as a guide following ablation.
Diseases of the circulatory (Cardiovascular) system
In 2014-2019, geoarchaeological research of the ancient city Nea Paphos and the Paphos region (SW Cyprus) was carried out. One of the aims was to determine the environmental factors for the location and functioning of this city in the period from 4th BC to 4th AD. Based on the field survey and thematic maps, physico-geographical mapping of geosystems of various orders was carried out. Next typology and regionalization were carried out on two levels: geocomplexes (“uroczysko”) and landscapes (terrains). The separated geocomplexes was grouped into 162 subtypes and 13 types, and then five landscapes were grouped into two types. As a result of the evaluation of separated landscapes, the landscape 1 - the lowest uplifted marine terrace is the most suitable for ancient Nea Paphos settlement. It is characterized by high heterogeneity, a relatively high presence of valleys (15%), the presence of monadnocks and rock walls (quarries) and the presence of sandy clay soils (pottery). In the light of geographical analyzes, it seems that during the location of the ancient Nea Paphos, environmental factors were not as important as economic and political conditions.
Introduction. Measles infection in recent years has become particularly relevant in connection with the registration of outbreaks of this disease in various territoriesof the Russian Federation and abroad.The aim of the study is to characterize the epidemic process of measles in a large industrial city in the near and long term with the use of modern mathematical modeling technologies for making new management decisions on infection control at the elimination stage.Materials and methods. The research materials were data from statistical reports of measles incidence in Yekaterinburg from 1950 to 2019 (70 years of follow-up), medical documentation of measles cases, population vaccination data (form No. 6 for 2000—2018 and outpatient maps of children under two years of age vaccinated against measles), results of screening for measles IgG ofmedical organizations, data of planned serological monitoringof population immunity to measles in «indicator» groups in the period from 2013 to 2017 and the results of mathematical modeling of measles incidence in different scenarios of its prevention.Results. Under the influence of vaccination, the epidemic process of measles in Yekaterinburg — a city with a population of 1.5million inhabitants-has undergone significant changes. During the observation period, the incidence decreased to sporadic levels, there was no indigenous measles, drifts from endemic areas had no consequences, the epidemic process was under control. However, outbreaks of 72 cases in 2016 and 90 cases in 2019 have changed our view of measles as a eradicated infection.Of the factors that led to the spread of infection in the foci, the most significant were the presence of measles-susceptible children and adults, including those previously vaccinated, mainly in the periods remote from vaccination and revaccination, defects in the clinical diagnosis of measlesin the first and subsequent cases, and violations in the organization and conduct of anti-epidemic measures. Conclusion. Based on the data of mathematical modeling of the epidemic process of measles with different combinations of its determinants, for the elimination of infection, it is necessary to ensure vaccination against measles at the age of 1 year and 6 years in 95—97.5%. In vulnerable groups for infection to discuss the introduction of routine revaccination among people up to 50 years of age with an interval of 10 years.
As an open artificial ecosystem, the development of a city requires the continuous input and output of material and energy, which is called urban metabolism, and includes catabolic (material-flow) and anabolic (material-accumulation) processes. Previous studies have focused on the catabolic and ignored the anabolic process due to data and technology problems. The combination of remote-sensing technology and high-resolution satellite images facilitates the estimation of cumulative material amounts in urban systems. This study focused on persistent accumulation, which is the metabolic response of urban land use/urban land expansion, building stock, and road stock to land-use changes. Building stock is an extremely cost-intensive and long-lived component of cumulative metabolism. The study measured building stocks of Jinchang, China’s nickel capital by using remote-sensing images and field-research data. The development of the built environment could be analyzed by comparing the stock of buildings on maps representing different time periods. The results indicated that material anabolism in Jinchang is a distance-dependent function, where the amounts and rates of material anabolism decrease with changes in distance to the central business district (CBD) and city administration center (CAC). The cumulative metabolic rate and cumulative total metabolism were observed to be increasing, however, the growth rate has decreased.
Underwater images suffer from different types of quality degradation, including haze, blur, low contrast, and color distortion, owing to light scattering and absorption. This article proposes a novel underwater image restoration algorithm based on the complete underwater image formation model (UIFM). Although the majority of the existing methods consider the direct transmission and backward scattering components only, this study, in addition, includes forward scattering in the UIFM. We estimate the transmission map based on the observation that the scene distance is inversely proportional to the geodesic color distance from the background light. We also approximate the point spread function in the forward scattering term to estimate the scene radiance more faithfully. Moreover, we obtain the optimal parameters of the UIFM required for transmission estimation and scene radiance restoration by minimizing a cost function composed of the sharpness, information loss, and dark background prior. The experimental results confirm that the proposed algorithm considerably improves the quality of the estimated transmission maps and restores scene radiance compared with the existing state-of-the-art methods.
We introduce a class of integrable dynamical systems of interacting classical matrix-valued fields propagating on a discrete space-time lattice, realized as many-body circuits built from elementary symplectic two-body maps. The models provide an efficient integrable Trotterization of non-relativistic $\sigma$-models with complex Grassmannian manifolds as target spaces, including, as special cases, the higher-rank analogues of the Landau-Lifshitz field theory on complex projective spaces. As an application, we study transport of Noether charges in canonical local equilibrium states. We find a clear signature of superdiffusive behavior in the Kardar-Parisi-Zhang universality class, irrespectively of the chosen underlying global unitary symmetry group and the quotient structure of the compact phase space, providing a strong indication of superuniversal physics.
In this paper, we study the dynamics of Newton maps for arbitrary polynomials. Let $p$ be an arbitrary polynomial with at least three distinct roots, and $f$ be its Newton map. It is shown that the boundary $\partial B$ of any immediate root basin $B$ of $f$ is locally connected. Moreover, $\partial B$ is a Jordan curve if and only if ${\rm deg}(f|_B)=2$. This implies that the boundaries of all components of root basins, for all polynomials' Newton maps, from the viewpoint of topology, are tame.