Stable Maps Research Articles

Clinical significance and potential pathogenesis of VCAN in adult non-cystic fibrosis bronchiectasis: a retrospective study

BackgroundThe pathogenesis of adult non-cystic fibrosis (CF) bronchiectasis is complex, and the relevant molecular mechanism remains ambiguous. Versican (VCAN) is a key factor in inflammation through interactions with adhesion molecules. This study constructs a stable panoramic map of mRNA, reveals the possible pathogenesis of bronchiectasis, and provides new ideas and methods for bronchiectasis.MethodsPeripheral blood and tissue gene expression data from patients with bronchiectasis and normal control were selected by bioinformatics analysis. The expression of VCAN in peripheral blood and bronchial tissues of bronchiectasis were obtained by transcriptome sequencing. The protein expression levels of VCAN in serums were verified by the enzyme-linked immunosorbent assay (ELISA). The mRNA expression levels of VCAN in co-culture of Pseudomonas aeruginosa and bronchial epithelial cells were verified by real-time quantitative polymerase chain reaction (RT-qPCR). In addition, the biological function of VCAN was detected by the transwell assay.ResultsThe expression of VCAN was upregulated in the bronchiectasis group by sequencing analysis (P < 0.001). The expression of VCAN in the bronchial epithelial cell line BEAS-2B was increased in P. aeruginosa (P.a), which was co-cultured with BEAS-2B cells (P < 0.05). The concentration of VCAN protein in the serum of patients with bronchiectasis was higher than that in the normal control group (P < 0.05). Transwell experiments showed that exogenous VCAN protein induced the migration of neutrophils (P < 0.0001).ConclusionsOur findings indicate that VCAN may be involved in the development of bronchiectasis by increasing the migration of neutrophils and play an important role in bronchial pathogenesis.

Computations of Gromov–Witten invariants of toric varieties

We present the Julia package ToricAtiyahBott.jl, providing an easy way to perform the Atiyah–Bott formula on the moduli space of genus 0 stable maps M‾0,m(X,β) where X is any smooth projective toric variety, and β is any effective 1-cycle. The list of the supported cohomological cycles contains the most common ones, and it is extensible. We provide a detailed explanation of the algorithm together with many examples and applications. The toric variety X, as well as the cohomology class β, must be defined using the package Oscar.jl.

A stable mapping of nmODE

Adversarial attacks pose significant challenges to the reliability and performance of neural networks. Despite the development of several defense mechanisms targeting various types of adversarial perturbations, only a few manage to strike a balance between theoretical soundness and practical efficacy. nmODE (neural memory ordinary differential equation) is a recently proposed model with several intriguing properties. By delving into the rare attribute of global attractors inherent in nmODE, this paper unveils its stable mapping, thereby conferring certified defense capabilities upon it. Moreover, a novel quantitative approach is proposed, establishing a mathematical link between perturbations and nmODE’s defense proficiency. Additionally, a training technique termed as nmODE+ is put forward, enhancing the defense capability of nmODE without imposing additional training burdens. Extensive experiments demonstrate nmODE’s resilience to various perturbations, showcasing its seamless integration with neural networks and existing defense mechanisms. These findings offer valuable insights into leveraging differential equations for robust neural network security.

Genus 0 logarithmic and tropical fixed‐domain counts for Hirzebruch surfaces

AbstractFor a non‐singular projective toric variety , the virtual logarithmic Tevelev degrees are defined as the virtual degree of the morphism from the moduli stack of logarithmic stable maps to the product . In this paper, after proving that Mikhalkin's correspondence theorem holds in genus 0 for logarithmic virtual Tevelev degrees, we use tropical methods to provide closed formulas for the case in which is a Hirzebruch surface. In order to do so, we explicitly list all the tropical curves contributing to the count.

Quantum K-theory of incidence varieties

We prove a conjecture of Buch and Mihalcea in the case of the incidence variety X=Fl(1,n-1;n)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$X=\ extrm{Fl}\\hspace{0.55542pt}(1,n-1;n)$$\\end{document} and determine the structure of its (T-equivariant) quantum K-theory ring. Our results are an interplay between geometry and combinatorics. The geometric side concerns Gromov–Witten varieties of 3-pointed genus 0 stable maps to X with markings sent to Schubert varieties, while on the combinatorial side are formulas for the (equivariant) quantum K-theory ring of X. We prove that the Gromov–Witten variety is rationally connected when one of the defining Schubert varieties is a divisor and another is a point. This implies that the (equivariant) K-theoretic Gromov–Witten invariants defined by two Schubert classes and a Schubert divisor class can be computed in the ordinary (equivariant) K-theory ring of X. We derive a positive Chevalley formula for the equivariant quantum K-theory ring of X and a positive closed formula for Littlewood–Richardson coefficients in the non-equivariant quantum K-theory ring of X. The Littlewood–Richardson rule in turn implies that non-empty Gromov–Witten varieties given by Schubert varieties in general position have arithmetic genus 0.

Rubber tori in the boundary of expanded stable maps

AbstractWe investigate torus actions on logarithmic expansions in the context of enumerative geometry. Our main result is an intrinsic and coordinate‐free description of the higher rank rubber torus appearing in the boundary of the space of expanded stable maps. The rubber torus is constructed canonically from the tropical moduli space, and its action on each stratum of the expanded target is encoded in a linear tropical position map. The presence of 2‐morphisms in the universal target forces expanded stable maps differing by the rubber action to be identified. This provides the first step towards a recursive description of the boundary of the expanded moduli space, with future applications including localisation and rubber calculus.

The virtual intersection theory of isotropic Quot schemes

Isotropic Quot schemes parameterize rank r isotropic subsheaves of a vector bundle equipped with symplectic or symmetric quadratic form. We define a virtual fundamental class for isotropic Quot schemes over smooth projective curves. Using torus localization, we prescribe a way to calculate top intersection numbers of tautological classes, and obtain explicit formulas when r=2. These include and generalize the Vafa-Intriligator formula. In this setting, we compare the Quot scheme invariants with the invariants obtained via the stable map compactification.

A Framework for Fine-Grained Land-Cover Classification Using 10 m Sentinel-2 Images

Land-cover mapping plays a crucial role in resource detection, ecological environmental protection, and sustainable development planning. The existing large-scale land-cover products with coarse spatial resolution have a wide range of categories, but they suffer from low mapping accuracy. Conversely, land-cover products with fine spatial resolution tend to lack diversity in the types of land cover they encompass. Currently, there is a lack of large-scale land-cover products simultaneously possessing fine-grained classifications and high accuracy. Therefore, we propose a mapping framework for fine-grained land-cover classification. Firstly, we propose an iterative method for developing fine-grained classification systems, establishing a classification system suitable for Sentinel-2 data based on the target area. This system comprises 23 fine-grained land-cover types and achieves the most stable mapping results. Secondly, to address the challenges in large-scale scenes, such as varying scales of target features, imbalanced sample quantities, and the weak connectivity of slender features, we propose an improved network based on Swin-UNet. This network incorporates a pyramid pooling module and a weighted combination loss function based on class balance. Additionally, we independently trained models for roads and water. Guided by the natural spatial relationships, we used a voting algorithm to integrate predictions from these independent models with the full classification model. Based on this framework, we created the 2017 Beijing–Tianjin–Hebei regional fine-grained land-cover product JJJLC-10. Through validation using 4254 sample datasets, the results indicate that JJJLC-10 achieves an overall accuracy of 80.3% in the I-level validation system (covering seven land-cover types) and 72.2% in the II-level validation system (covering 23 land-cover types), with kappa coefficients of 0.7602 and 0.706, respectively. In comparison with widely used land-cover products, JJJLC-10 excels in accurately depicting the spatial distribution of various land-cover types and exhibits significant advantages in terms of classification quantity and accuracy.

Multi-season mobile monitoring campaign of on-road air pollution in Bengaluru, India: High-resolution mapping and estimation of quasi-emission factors

Mobile monitoring can supplement regulatory measurements, particularly in low-income countries where stationary monitoring is sparse. Here, we report results from a ~ year-long mobile monitoring campaign of on-road concentrations of black carbon (BC), ultrafine particles (UFP), and carbon dioxide (CO2) in Bengaluru, India. The study route included 150 unique kms (average: ~22 repeat measurements per monitored road segment). After cleaning the data for known instrument artifacts and sensitivities, we generated 30 m high-resolution stable ‘data only’ spatial maps of BC, UFP, and CO2 for the study route. For the urban residential areas, the mean BC levels for residential roads, arterials, and highways were ~ 10, 22, and 56 μg m−3, respectively. A similar pattern (highways being characterized by highest pollution levels) was also observed for UFP and CO2. Using the data from repeat measurements, we carried out a Monte Carlo subsampling analysis to understand the minimum number of repeat measures to generate stable maps of pollution in the city. Leveraging the simultaneous nature of the measurements, we also mapped the quasi-emission factors (QEF) of the pollutants under investigation. The current study is the first multi-season mobile monitoring exercise conducted in a low or middle -income country (LMIC) urban setting that oversampled the study route and investigated the optimum number of repeat rides required to achieve representative pollution spatial patterns characterized with high precision and low bias. Finally, the results are discussed in the context of technical aspects of the campaign, limitations, and their policy relevance for our study location and for other locations. Given the day-to-day variability in the pollution levels, the presence of dynamic and unorganized sources, and active government pollution mitigation policies, multi-year mobile measurement campaigns would help test the long-term representativeness of the current results.

Quantifying the Role of Model Internal Year-to-Year Variability in Estimating Anthropogenic Aerosol Radiative Effects

The model internal year-to-year variability (hereafter, internal variability) is a significant source of uncertainty when estimating anthropogenic aerosol effective radiative forcing (ERF). In this study, we investigate the impact of internal variability using large ensemble simulations (600 years in total) with the same climate model under prescribed anthropogenic aerosol forcings. A comparison of the magnitudes (i.e., standard deviation, Std) of these influences confirms that internal variability has negligible impacts on the instantaneous radiative forcing (RF) diagnosed by double radiation calls but has considerable impacts on estimating ERF through rapid adjustments (ADJ). Approximately half of the model grids exhibit a strong internal variability influence on ERF (Std &gt; 5 W m−2). These strong internal variabilities lead to a 50% probability that the 30-year linear change can reach 2 W m−2 and the 10-year linear change can reach 4 W m−2. A 50-year simulation can provide a relatively stable annual mean map of ERF (ERF = ADJ + RF), but it fails for ADJ. The statistically significant areas in the annual mean maps of both ERF and ADJ from a 10-year simulation exhibit instability with evident chaotic features. The insights derived from our analysis aid in assessing the stability of modeled ERF and contribute to the design of comparative experiments.

Controlling surface wetting in high-alkaline electrolytes for single facet Pt oxygen evolution electrocatalytic activity mapping by scanning electrochemical cell microscopy.

Scanning electrochemical cell microscopy (SECCM) has been used to explore structure-electrocatalytic activity relationships through high-resolution mapping of local activities of electrocatalysts. However, utilizing SECCM in strongly alkaline conditions presents a significant challenge due to the high wettability of the alkaline electrolyte leading to a substantial instability of the droplet in contact with the sample surface, and hence to unpredictable wetting and spreading of the electrolyte. The spreading phenomena in SECCM is confirmed by the electrochemical response of a free-diffusing redox probe and finite element method (FEM) simulations. Considering the significance of alkaline electrolytes in electrocatalysis, these wetting issues restrict the application of SECCM for electrocatalyst elucidation in highly alkaline electrolytes. We resolve this issue by incorporating a small percentage of polyvinylpyrrolidone (PVP) in the electrolyte inside the SECCM capillary to increase the surface tension of the electrolyte. To demonstrate successful wetting mitigation and stable SECCM mapping, we performed oxygen evolution reaction (OER) mapping on polycrystalline Pt by using 1 M KOH with an optimized PVP concentration. The OER activity maps correlated with the orientation of the exposed facets determined by electron backscatter diffraction and reveal different activities between Pt facets, hence confirming our methodology for exploring electrocatalytic activities in single facet scale in concentrated alkaline media. Interestingly, the maximum OER current density was highest for (110) and (111) which contradicts the activity trends in acidic electrolyte for which (100) is most active for the OER.

Stable Arterial Perforators Mapping in Lower Leg Using Color-Coded Doppler Sonography, Acoustic Doppler, and Thermal Imaging Camera in Patients Undergoing Digital Subtraction Angiography

Abstract Background Chronic defects in the lower leg present significant challenges in plastic surgery due to their diverse etiologies and association with impaired peripheral circulation. This study describes the localization of stable perforators and assesses their changing velocities after digital subtraction angiography (DSA) and alterations of flow characteristics. Methods Ten patients with lower extremity defects requiring DSA had undergone examinations by using standard methods. The localization of 40 stable perforators originating from the anterior tibial artery, posterior tibial artery, fibular artery, and medial sural artery was performed before and after angiography. Where stenoses or occlusions were observed, percutaneous transluminal angioplasty (PTA) was conducted, and velocity changes following reperfusion were measured. Results Angiographic abnormalities were observed in all of patients, thus necessitating PTA interventions. Prior to PTA, handheld acoustic Dopplers detected 37 out of 40 perforators (90%), whereas color-coded sonography detected 35 out of 40 perforators (87.5%). After PTA, these numbers increased to 38 out of 40 (95%) and 37 out of 40 (92.5%), respectively. The diameter of the perforators ranged between 1.14 and 1.16 mm. The mean flow characteristics included the peak systolic velocities (PSV) of 21.9 and 27.2, end-diastolic velocities (EDV) of 9.4 and 11.4, and resistance indexes (RI) of 0.63 and 0.71, respectively. In the postintervention period, 16 microvessels exhibited enlarged lumen diameters ranging from 1 to 3 mm, resulting in increased perfusion values for PSV in 85.2% (21.9/27.2) and EDV in 88.2% (9.4/11.4) of the patients. The RI increased from 0.63 to 0.71. However, two perforators showed decreases in flow velocity after PTA. Conclusion In most patients with chronic lower leg wounds and other comorbidities, adequate perforators for reconstruction can be identified by using conventional methods. PTA interventions positively impact blood flow in perforators, although they are not necessarily required prior to reconstruction.

Transcranial magnetic stimulation mapping of the motor cortex: comparison of five estimation algorithms.

There are currently five different kinds of transcranial magnetic stimulation (TMS) motor mapping algorithms available, from ordinary point-based algorithms to advanced field-based algorithms. However, there have been only a limited number of comparison studies conducted, and they have not yet examined all of the currently available algorithms. This deficiency impedes the judicious selection of algorithms for application in both clinical and basic neuroscience, and hinders the potential promotion of a potential superior algorithm. Considering the influence of algorithm complexity, further investigation is needed to examine the differences between fMRI peaks and TMS cortical hotspots that were identified previously. Twelve healthy participants underwent TMS motor mapping and a finger-tapping task during fMRI. The motor cortex TMS mapping results were estimated by five algorithms, and fMRI activation results were obtained. For each algorithm, the prediction error was defined as the distance between the measured scalp hotspot and optimized coil position, which was determined by the maximum electric field strength in the estimated motor cortex. Additionally, the study identified the minimum number of stimuli required for stable mapping. Finally, the location difference between the TMS mapping cortical hotspot and the fMRI activation peak was analyzed. The projection yielded the lowest prediction error (5.27 ± 4.24 mm) among the point-based algorithms and the association algorithm yielded the lowest (6.66 ± 3.48 mm) among field-based estimation algorithms. The projection algorithm required fewer stimuli, possibly resulting from its suitability for the grid-based mapping data collection method. The TMS cortical hotspots from all algorithms consistently deviated from the fMRI activation peak (20.52 ± 8.46 mm for five algorithms). The association algorithm might be a superior choice for clinical applications and basic neuroscience research, due to its lower prediction error and higher estimation sensitivity in the deep cortical structure, especially for the sulcus. It also has potential applicability in various other TMS domains, including language area mapping and more. Otherwise, our results provide further evidence that TMS motor mapping intrinsically differs from fMRI motor mapping.

Linear hyperelliptic Hodge integrals

We provide a closed form expression for linear Hodge integrals on the hyperelliptic locus. Specifically, we find a succinct combinatorial formula for all intersection numbers on the hyperelliptic locus with one λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda $$\\end{document}-class, and powers of a ψ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\psi $$\\end{document}-class pulled back along the branch map. This is achieved by using Atiyah–Bott localization on a stack of stable maps into the orbifold P1/Z2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\left[ {\\mathbb {P}}^1/{\\mathbb {Z}}_2\\right] $$\\end{document}.

Topology of Fold Map Germs from mathbb R^3 to mathbb R^5

Let f:(mathbb R^3,0)rightarrow (mathbb R^5,0) be an analytic map germ with isolated instability. Its link is a stable map which is obtained by taking the intersection of the image of f with a small enough sphere S^4_epsilon centered at the origin in mathbb R^5. If f is of fold type, we define a labeled tree associated to its link and prove that is a complete topological invariant for it. As an application we obtain the complete topological classification of map germs contained in the mathcal {A}^2-class (x,y,z^2,xz,0).

A categorification of the quantum Lefschetz principle

The quantum Lefschetz formula explains how virtual fundamental classes (or structure sheaves) of moduli stacks of stable maps behave when passing from an ambient target scheme to the zero locus of a section. It is only valid under special assumptions (genus 0, regularity of the section and convexity of the bundle). In this paper, we give a general statement at the geometric level removing these assumptions, using derived geometry. Through a study of the structure sheaves of derived zero loci we deduce a categorification of the formula in the ∞-categories of quasi-coherent sheaves. We also prove that Manolache's virtual pullbacks can be constructed as derived pullbacks, and use them to recover the classical Quantum Lefschetz formula when its hypotheses are satisfied.

Representations on the cohomology of [formula omitted

The moduli space M‾0,n of n pointed stable curves of genus 0 admits an action of the symmetric group Sn by permuting the marked points. We provide a closed formula for the character of the Sn-action on the cohomology of M‾0,n. This is achieved by studying wall crossings of the moduli spaces of quasimaps which provide us with a new inductive construction of M‾0,n, equivariant with respect to the symmetric group action. Moreover we prove that H2k(M‾0,n) for k≤3 and H2k(M‾0,n)⊕H2k−2(M‾0,n) for any k are permutation representations. Our method works for related moduli spaces as well and we provide a closed formula for the character of the Sn-representation on the cohomology of the Fulton-MacPherson compactification P1[n] of the configuration space of n points on P1 and more generally on the cohomology of the moduli space M‾0,n(Pm−1,1) of stable maps.

Poisson stable solutions and solution maps for stochastic functional differential equations

We observe Poisson stable solutions for nonlinear stochastic functional differential equations (SFDEs) with finite delay. Firstly, we prove the existence and uniqueness of bounded (in square-mean sense) solutions and solution maps for SFDEs with finite delay by remoting start (or dissipative method) and classical pull-back attraction method. Then, based on the relationship between the solution and coefficients, we obtain such Poisson stable solutions by using Shcherbakov’s comparability method in character of recurrence. Because the solutions of the delay equations are not-Markov, we employ the solution maps in the appropriate phase space as a viable alternative for studying further asymptotic properties, and we also discuss Poisson stable solution maps and their asymptotic stability. For illustration of our results, we give the application arising from stochastic Lotka–Volterra cooperative systems with distributed delay.

A functor for constructing R$R$‐matrices in the category O$\mathcal {O}$ of Borel quantum loop algebras

AbstractWe tackle the problem of constructing ‐matrices for the category associated to the Borel subalgebra of an arbitrary untwisted quantum loop algebra . For this, we define an invertible exact functor from the category linked to to the one linked to . This functor is compatible with tensor products, preserves irreducibility, and interchanges the subcategories and of Hernandez and Leclerc (Algebra Number Theory 10 (2016) 2015–2052). We construct ‐matrices for by applying on the braidings already found for by Hernandez (Represent. Theory 26 (2022) 179–210). We also use the factorization of the latter intertwiners in terms of stable maps to deduce an analogous factorization for our new braidings. We finally obtain as byproducts new relations for the Grothendieck ring as well as a functorial interpretation of a remarkable ring isomorphism of Hernandez–Leclerc.

Framed cohomological Hall algebras and cohomological stable envelopes

There are multiple conjectures relating the cohomological Hall algebras (CoHAs) of certain substacks of the moduli stack of representations of a quiver Q to the Yangian Y^{Q}_textrm{MO} by Maulik–Okounkov, whose construction is based on the notion of stable envelopes of Nakajima varieties. In this article, we introduce the cohomological Hall algebra of the moduli stack of framed representations of a quiver Q (framed CoHA), and we show that the equivariant cohomology of the disjoint union of the Nakajima varieties {mathcal {M}}_Q(text {v},text {w}) for all dimension vectors text {v} and framing vectors text {w} has a canonical structure of subalgebra of the framed CoHA. Restricted to this subalgebra, the algebra multiplication is identified with the stable envelope map. As a corollary, we deduce an explicit inductive formula to compute stable envelopes in terms of tautological classes.