Stable Maps Research Articles

One-shot entorhinal maps enable flexible navigation in novel environments.

Animals must navigate changing environments to find food, shelter or mates. In mammals, grid cells in the medial entorhinal cortex construct a neural spatial map of the external environment1-5. However, how grid cell firing patterns rapidly adapt to novel or changing environmental features on a timescale relevant to behaviour remains unknown. Here, by recording over 15,000 grid cells in mice navigating virtual environments, we tracked the real-time state of the grid cell network. This allowed us to observe and predict how altering environmental features influenced grid cell firing patterns on a nearly instantaneous timescale. We found evidence that visual landmarks provide inputs to fixed points in the grid cell network. This resulted in stable grid cell firing patterns in novel and altered environments after a single exposure. Fixed visual landmark inputs also influenced the grid cell network such that altering landmarks induced distortions in grid cell firing patterns. Such distortions could be predicted by a computational model with a fixed landmark to grid cell network architecture. Finally, a medial entorhinal cortex-dependent task revealed that although grid cell firing patterns are distorted by landmark changes, behaviour can adapt via a downstream region implementing behavioural timescale synaptic plasticity6. Overall, our findings reveal how the navigational system of the brain constructs spatial maps that balance rapidity and accuracy. Fixed connections between landmarks and grid cells enable the brain to quickly generate stable spatial maps, essential for navigation in novel or changing environments. Conversely, plasticity in regions downstream from grid cells allows the spatial maps of the brain to more accurately mirror the external spatial environment. More generally, these findings raise the possibility of a broader neural principle: by allocating fixed and plastic connectivity across different networks, the brain can solve problems requiring both rapidity and representational accuracy.

Gromov-Witten Invariants in Complex and Morava-Local K-Theories

AbstractGiven a closed symplectic manifold X, we construct Gromov-Witten-type invariants valued both in (complex) K-theory and in any complex-oriented cohomology theory $\mathbb{K}$ which is Kp(n)-local for some Morava K-theory Kp(n). We show that these invariants satisfy a version of the Kontsevich-Manin axioms, extending Givental and Lee’s work for the quantum K-theory of complex projective algebraic varieties. In particular, we prove a Gromov-Witten type splitting axiom, and hence define quantum K-theory and quantum $\mathbb{K}$-theory as commutative deformations of the corresponding (generalised) cohomology rings of X; the definition of the quantum product involves the formal group of the underlying cohomology theory. The key geometric input of these results is a construction of global Kuranishi charts for moduli spaces of stable maps of arbitrary genus to X. On the algebraic side, in order to establish a common framework covering both ordinary K-theory and Kp(n)-local theories, we introduce a formalism of ‘counting theories’ for enumerative invariants on a category of global Kuranishi charts.

EVALUATION OF REMOTE CHECK IN CHILDREN WITH COCHLEAR IMPLANTS

ObjectiveThis study evaluates the feasibility of reducing in-person appointments by utilizing Remote Check (RC) in pediatric cochlear implant (CI) recipients and investigates the most suitable age range for implementing RC. MethodsFifty-eight pediatric CI recipients, aged 1 to 17 years, were evaluated using a web-based RC application by audiologists. Most (84.5%) used verbal communication. Inclusion criteria required stable map status, caregiver tech proficiency, and a compatible phone. ResultsRemote assessments were beneficial, with 89.7% of participants successfully completing RC. Aided threshold tests (ATT) were completed in 73.2% of participants, while speech-in-noise tests (Digit Triplet Test, DTT) were completed in 47.3%. Children as young as 4 successfully completed ATT, while a minimum age of 7 was required for DTT. A significant relationship between age and test success was demonstrated. Verbally communicative children had higher completion success rates. Parental education was significantly correlated with DTT success, with higher success rates in children whose parents had undergraduate degrees. With RC use, 69% of children did not need clinic visits, emphasizing the need for personalized and remote support for optimal cochlear implant performance. In-person appointments were primarily required due to concerns about the duration of device usage. ConclusionThe study confirms the effectiveness and feasibility of using RC in pediatric CI users, even as young as one year old with stable aided hearing. The findings advocate for the integration of RC into routine follow-up protocols, offering a more accessible option for enhanced patient care.

NPFormer: Interpretable rotating machinery fault diagnosis architecture design under heavy noise operating scenarios

While existing models have achieved significant progress on fault diagnosis tasks, what interpretable temporal dependencies they capture to resist noise remains unclear. Previous studies have ignored the inherent non-stationary property of fault data, which is the basis for capturing reliable temporal dependencies under heavy noise operating scenarios. To tackle the aforementioned problems, we propose a non-stationary perception network (NPFormer). Firstly, we revisit the large kernel design in the early stage of the network, and we demonstrate that this can make the attention map more stable for modeling non-stationary series, which can be a more powerful paradigm with heavy noise interference. Secondly, an adaptive non-stationarity embedding block is developed, which breaks the raw data into multiple components and adaptively attenuates the non-stationarity of mechanical signals for better predictability. Finally, we design multi-scale fusion attention to capture fine-grained features with the global scope, while achieving localized spatial–temporal correlations. Extensive experiments have been conducted on three public datasets and the practical aero-engine engineering application, showing that NPFormer significantly outperforms existing state-of-the-art methods. The weight information is visualized to reveal how NPFormer works, which can demonstrate that the stable attention map is a clear clue of anti-noise. We quantitatively reveal the effect of noise on the model, and the model’s anti-noise clues, during model inference. Code and models will be available for further study.

Development of an Automatic Feature Point Classification Method for Three-Dimensional Mapping Around Slewing and Derricking Cranes

Crane automation requires a three-dimensional (3D) map around cranes that should be reconstructed and updated quickly.In this study, a high-precision classification method was developed to distinguish stationary objects from moving objects in moving images captured by a monocular camera to stabilize 3D reconstruction. To develop the method, a moving image was captured while the crane was slewed with a monocular camera mounted vertically downward at the tip of the crane. The boom length and angle data were output from a control device, a controller area network. For efficient development, a simulator that imitated the environment of an actual machine was developed and used. The proposed method uses optical flow to track feature points. The classification was performed successfully, independent of derricking motion. Consequently, the proposed method contributes to stable 3D mapping around cranes in construction sites.

A novel soybean mapping index within the global optimal time window

Efficient soybean mapping is critical for agricultural production and yield prediction. However, current sample-driven soybean mapping methods heavily rely on large representative sample datasets, limiting the interpretability of physical mechanisms. Besides, sample-free methods failed to exploit key features that differentiate soybean from other crops, especially Chlorophyll content. Misclassification errors persist and spatiotemporal generalization remains limited. Therefore, this study develops a novel Soybean Mapping Composite Index (SMCI) within a precise Global Optimal Time Window (GOTW). It integrates unique features of soybean Chlorophyll content, canopy water content, and canopy greenness by coupling three red-edge bands (RE2, RE3, and RE4), one near-infrared band, one shortwave infrared band, and two feature indices (Enhanced Vegetation Index and Green Chlorophyll Vegetation Index). The novel index was applied to soybean mapping at six sites in four major soybean producing countries (China, Argentina, Brazil, and the United States) from 2019 to 2021, using an optimal threshold of 3.25. Within the GOTW, the index responds better to spectral features and improves soybean separability. The average overall accuracy (OA: 91%) and average Kappa coefficient (Kappa: 0.83) for the novel index at all sites outperformed the traditional sample-driven Random Forest (RF) method (OA: 84%, Kappa: 0.70) and the existing sample-free index-based Greenness and Water Content Composite Index (GWCCI) (OA: 81%, Kappa: 0.64). Furthermore, interannual transfer experiments consistently showed high accuracy, demonstrating robust spatiotemporal transferability. The proposed SMCI index meets the need for a lightweight and stable soybean mapping tool and serves as a valuable reference for efficient global crop mapping.

An efficient and generalisable approach for mapping paddy rice fields based on their unique spectra during the transplanting period leveraging the CIE colour space

As one of the most important staple foods globally, rice sustains nearly half of the world's population. Accurate and timely paddy rice mapping is, thus, essential for rice-related policy-making to ensure food security in the context of anthropogenic, environmental and climate changes. However, paddy rice mapping remains a challenging task since it usually has similar spectral characteristics to other land covers. In this research, for the first time, an entirely new approach, called RiceTColour, was proposed for mapping rice fields within the Commission Internationale de l'Eclairage (CIE) colour space based on their unique spectra during the rice transplanting period as observed in remotely sensed imagery. We demonstrate that transplanted rice fields, representing a mixture of soil, water and rice seedlings, consistently exhibit relatively low spectral values in both SWIR and NIR bands across various geographical locations, leading to their unique dark green colours in the false-colour image composed of SWIR, NIR and Red bands. Based upon this, we transformed these three spectral bands into the CIE colour space where paddy rice was found to be readily and completely separated from the other land covers. Straightforward, but specific classification criteria were established within the CIE colour space to differentiate paddy rice from the other land covers. The proposed RiceTColour, thus, represents a new approach for paddy rice identification, that is mapping paddy rice using the CIE colour space based upon the previous underexplored remotely sensed spectra of paddy fields during the transplanting season. The effectiveness of the proposed method was investigated over five rice-planting regions distributed across different geographical regions, characterised by different climates, rice cropping intensities, irrigation schemes and cultural practices. Specifically, the mapping criteria established in a training site (S1) were directly generalised to the other four sites (S2 to S5) for paddy rice mapping. Experimental results demonstrated that the RiceTColour method consistently achieved the most accurate and balanced classifications across all five sites compared with four benchmark comparators: a SAR-based method, an index-based method and two supervised classifier-based methods. In particular, the RiceTColour method performed relatively stable, producing an overall accuracy exceeding 95% in the training site (S1) as well as the four generalised sites (S2 to S5), which is an encouraging result. Such efficient yet stable rice mapping results across various rice-planting regions suggest a very strong generalisation capability of the proposed RiceTColour method. In consideration of the relatively large planting area of paddy rice fields globally, the proposed parameter-free, efficient, and generalisable RiceTColour method, thus, holds great potential for widespread application in various rice-planting areas worldwide.

Growth characterization of mesophotic rhodoliths in the northern Gulf of Mexico using radiocarbon dating

Boxwork rhodoliths are characterized by a multitaxonomic composition and excessive void spaces, and they are distributed from intertidal to mesophotic depths. Growth rates and patterns in rhodoliths from shallower depths and simpler morphologies have been assessed using incremental and geochemical analyses, but rhodoliths from mesophotic depths have been harder to access and require more studies. Boxwork rhodoliths have proved too structurally complex for age and growth rate assessment techniques such as stable oxygen isotopes profiling or elemental mapping. We therefore utilized sequential radiocarbon analysis for growth characterization of mesophotic boxwork rhodoliths. Rhodoliths were collected from the Flower Garden Banks National Marine Sanctuary in the northern Gulf of Mexico from one location at 48–72 m and another at 103 m. Specimens were extensively sampled for radiocarbon concentrations from predicted nucleation points and along growth axes. From depths of 48–72 m, nucleation ages ranged from 795 ± 20 to 3270 ± 25 14C yr B·P. From depths of 103 m, nucleation ages ranged from 8960 ± 110 to 13,050 ± 150 14C yr B.P., dating back to the end of the Pleistocene in some cases. Several rhodoliths contained evidence of growth hiatuses, with deeper samples displaying age reversals that complicated the apparent growth history. We define age reversals to be non-sequential ages within a sampling sequence, typically a singular age before the return to normal age sequence. The research presented here includes the oldest known living rhodoliths, with the oldest rhodoliths grown before and after Holocene sea-level stabilization. These results have implications for the use of rhodoliths as paleoenvironmental indicators, and provide better understanding of the range and volume of carbonate production in these habitats.

Divisors and curves on logarithmic mapping spaces

We determine the rational class and Picard groups of the moduli space of stable logarithmic maps in genus zero, with target projective space relative a hyperplane. For the class group we exhibit an explicit basis consisting of boundary divisors. For the Picard group we exhibit a spanning set indexed by piecewise-linear functions on the tropicalisation. In both cases a complete set of boundary relations is obtained by pulling back the WDVV relations from the space of stable curves. Our proofs hinge on a controlled technique for manufacturing test curves in logarithmic mapping spaces, opening up the topology of these spaces to further study.

A many-to-many matching with externalities solution for parallel task offloading in IoT networks

The efficient and timely execution of tasks is a fundamental challenge in the realm of future Internet of Things (IoT) networks. To address this challenge, fog devices are often deployed close to end devices to facilitate task processing on behalf of IoT nodes. One strategy for improving task computational delay is to employ parallel task offloading, in which tasks are subdivided into subtasks and sent to different fog devices for execution in parallel. However, allocating computational resources to fog nodes and mapping these resources to IoT subtasks is a key challenge in this area. This work models the parallel task offloading problem as a graph-matching problem and utilizes a many-to-many matching technique to achieve a stable mapping of IoT subtasks to fog node resources. Unfortunately, the proposed solution is subject to the problem of externalities due to the dynamic preference profiling of fog nodes. To address this issue, we employ an iterative algorithm to resolve any blocking pairs that may arise. Our results demonstrate that the proposed technique reduces the task latency by 29% as compared to other matching-based techniques available in the literature.

Exponential Decay Estimates and Smoothness of the Moduli Space of Pseudoholomorphic Curves

The compacified moduli space of bordered stable maps carries a Kuranishi structure with boundary. Smoothness of Kuranishi structure along the boundary requires smoothness of coordinate changes along the boundary. The proof of smoothness is written by the authors in [AMS/IP Stud. Adv. Math., 46.1, 2009, xii+396 pp.], [AMS/IP Stud. Adv. math., 46.2, 2009, pp. i–xii and 397–805], and [Surv. Differ. Geom., vol. 22, pp. 133–190, 2018] based on some uniform exponential decay estimates of the stable maps with respect to a parameter T T , the length of the gluing cylindrical neck, near the boundary of the moduli space. In this paper we establish this exponential decay estimates in a precise manner by carefully examining the dependence on the parameter T T of the gluing construction in the setting of bordered Riemann surfaces with boundary punctures. We also show that the smoothness of the collar follows from the aforementioned exponential estimates by taking s = 1 / T s = 1/T as the radial coordinate of the collar.

Synergistic olfactory processing for social plasticity in desert locusts

Desert locust plagues threaten the food security of millions. Central to their formation is crowding-induced plasticity, with social phenotypes changing from cryptic (solitarious) to swarming (gregarious). Here, we elucidate the implications of this transition on foraging decisions and corresponding neural circuits. We use behavioral experiments and Bayesian modeling to decompose the multi-modal facets of foraging, revealing olfactory social cues as critical. To this end, we investigate how corresponding odors are encoded in the locust olfactory system using in-vivo calcium imaging. We discover crowding-dependent synergistic interactions between food-related and social odors distributed across stable combinatorial response maps. The observed synergy was specific to the gregarious phase and manifested in distinct odor response motifs. Our results suggest a crowding-induced modulation of the locust olfactory system that enhances food detection in swarms. Overall, we demonstrate how linking sensory adaptations to behaviorally relevant tasks can improve our understanding of social modulation in non-model organisms.

Learning a stable approximation of an existing but unknown inverse mapping: application to the half-time circular Radon transform

Supervised deep learning-based methods have inspired a new wave of image reconstruction methods that implicitly learn effective regularization strategies from a set of training data. While they hold potential for improving image quality, they have also raised concerns regarding their robustness. Instabilities can manifest when learned methods are applied to find approximate solutions to ill-posed image reconstruction problems for which a unique and stable inverse mapping does not exist, which is a typical use case. In this study, we investigate the performance of supervised deep learning-based image reconstruction in an alternate use case in which a stable inverse mapping is known to exist but is not yet analytically available in closed form. For such problems, a deep learning-based method can learn a stable approximation of the unknown inverse mapping that generalizes well to data that differ significantly from the training set. The learned approximation of the inverse mapping eliminates the need to employ an implicit (optimization-based) reconstruction method and can potentially yield insights into the unknown analytic inverse formula. The specific problem addressed is image reconstruction from a particular case of radially truncated circular Radon transform (CRT) data, referred to as ‘half-time’ measurement data. For the half-time image reconstruction problem, we develop and investigate a learned filtered backprojection method that employs a convolutional neural network to approximate the unknown filtering operation. We demonstrate that this method behaves stably and readily generalizes to data that differ significantly from training data. The developed method may find application to wave-based imaging modalities that include photoacoustic computed tomography.

Effect of preheating on extending lean extinction limit of ammonia/air combustion in a two-section porous burner

Ammonia utilization is promising way to reduce greenhouse gases emissions. We propose the concept of reactants preheating to achieve stable combustion of lean NH3 in two-layer porous burner, this concept is validated by numerical study with full kinetics. Calculations are conducted over wide range of preheating temperature (Tpre) and mass flow rate (m″) to gain insight in stable map, with special emphasis on effect of Tpre on extending lean extinction limit (LEL). It is shown that Tpre has vital effect in expending LEL. LEL is continually extended for different m″ with preheating, the LEL for NH3/air is successfully extended from equivalence ratio (ϕ) of 0.54 to 0.08 with increasing Tpre from 400 K to 1000 K. It is found that there exist three distinct mechanisms (Ⅰ, Ⅱ and Ⅲ) with respect to ϕ. When ϕ is close to one, self-sustaining combustion is realized without preheating (Ⅲ). The combustion is becoming unstable when ϕ is decreased, stable combustion can only be achieved with preheating (Ⅰ). Flame extinction takes place even with the preheating (Ⅱ) when the Tpre is lower than critical one for the given ϕ. The results present guidelines for burner operating with lean NH3 mixture over wide parameters range.

GRLN: Gait Refined Lateral Network for gait recognition

Gait recognition aims to identify individuals at a distance based on their biometric gait patterns. While offering flexibility in network input, existing set-based methods often overlook the potential of fine-grained local feature by solely utilizing global gait feature and fail to fully exploit the communication between silhouette-level and set-level features. To alleviate this issue, we propose Gait Refined Lateral Network(GRLN), featuring plug-and-play Adaptive Feature Refinement modules (AFR) that extract discriminative features progressively from silhouette-level and set-level representations in a coarse-to-fine manner at various network depths. AFR can be widely applied in set-based gait recognition models to substantially enhance their gait recognition performance. To align with the extracted refined features, we introduce Horizontal Stable Mapping (HSM), a novel mapping technique that reduces model parameters while improving experimental results. To demonstrate the effectiveness of our method, we evaluate GRLN on two gait datasets, achieving the highest recognition rate among all set-based methods. Specifically, GRLN demonstrates an average improvement of 1.15% over the state-of-the-art set-based method on CASIA-B. Especially in the coat-wearing condition, GRLN exhibits a 5% improvement in performance compared to the contrast method GLN.

Existence of generating families on Lagrangian cobordisms

For an embedded exact Lagrangian cobordism between Legendrian submanifolds in the 1-jet bundle, we prove that a generating family linear at infinity on the Legendrian at the negative end extends to a generating family linear at infinity on the Lagrangian cobordism after stabilization if and only if the formal obstructions vanish. In particular, a Lagrangian filling with trivial stable Lagrangian Gauss map admits a generating family linear at infinity.

P-Parabolicity and a Generalized Bochner’s Method with Applications

The notions of function growth and sharp global integral estimates in p-harmonic geometry in Wei (Contemp Math 756:247–269, 2020) and Wei et al. (Sharp estimates on A\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {A}$$\\end{document}-harmonic functions with applications in biharmonic maps) naturally lead to a generalized uniformization theorem and a generalized Bochner’s method. These tools enable one to explore various geometric and variational problems in complete noncompact manifolds of arbitrary dimensions. In particular, we find the first set of nontrivial geometric quantities that are p-subharmonic and p-superharmonic functions (cf. Sect. 4.2). As further applications, we establish Liouville theorems for nonnegative A\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {A}}$$\\end{document}-superharmonic functions (cf. Theorem 2.1) and for p-harmonic morphisms (cf. Theorem 4.3), Picard type theorems (cf. Sect. 4.3), existence theorems of harmonic maps (cf. Theorem 4.6), and a solution of the generalized Bernstein problem under p-parabolicity condition (without any volume growth condition, cf. Theorem 5.1) or under p-moderate volume growth (2.4) (cf. Corollary 5.1). These findings generalize and extend the work of Schoen–Simon–Yau under volume growth condition (0.1) which is due to (i)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$({\ ext {i}})$$\\end{document} Corollary 2.1(iv), which states that a manifold with p-moderate volume growth (2.4) must be p-parabolic (generalizing a result of Cheng and Yau (Commun Pure Appl 28(3):333–354, 1975) for the case p=2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p=2$$\\end{document}, F(r)≡1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$F(r)\\equiv 1$$\\end{document}), (ii)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$({\ ext {ii}})$$\\end{document} Example 2.1 of a p-parabolic manifold with exponential volume growth, and (iii)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$({\ ext {iii}})$$\\end{document} volume growth condition (0.1) ⟹(implies)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\overset{(\ ext {implies})}{\\Longrightarrow }$$\\end{document}p-moderate volume growth (2.4). Furthermore, we offer applications to p-harmonic maps and stable p-harmonic maps. Notably, these outcomes address an intriguing question posed by Kobayashi if p-subharmonic functions are valuable tools for studying p-harmonic maps or related topics (cf. in: Kobayashi, Midwest Geometry Conference, University of Oklahoma, Oklahoma, 2006. Private Communication, 1996), and answer in the affirmative. Other applications of the notions and estimates to biharmonic maps, isometric immersions, holomorphic functions on Kähler manifolds, generalized harmonic forms, and Yang–Mills fields on complete noncompact manifolds can be found in Wei et al. (Sharp estimates on A\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal A$$\\end{document}-harmonic functions with applications in biharmonic maps), Chen and Wei (Glasg Math J 51(3):579–592, 2009), Wei (Bull Transilv Univ Brasov Ser III 1(50):415–453, 2008), Wei (Growth estimates for generalized harmonic forms on noncompact manifolds with geometric applications, Contemp Math 756 American Mathematical Society, Providence, 247–269, 2020), Wei (Sci China Math 64(7):1649–1702, 2021) and Wei (Isolation phenomena for Yang–Mills fields on complete manifolds). We generate the work of Schoen–Simon–Yau under p-parabolic condition, in which the result can be used in other types of new manifolds we found, by an extrinsic average variational method we proposed (cf. Wei in Rom J Math Comput Sci 13(2):100–124, 2023; in: Wei, Connecting Poincare inequality with Sobolev inequality on Riemannian manifolds, Int Electron J Geom 17(1):290–305, 2024).

Stable multivariate lesion symptom mapping.

Multivariate lesion-symptom mapping (MLSM) considers lesion information across the entire brain to predict impairments. The strength of this approach is also its weakness-considering many brain features together synergistically can uncover complex brain-behavior relationships but exposes a high-dimensional feature space that a model is expected to learn. Successfully distinguishing between features in this landscape can be difficult for models, particularly in the presence of irrelevant or redundant features. Here, we propose stable multivariate lesion-symptom mapping (sMLSM), which integrates the identification of reliable features with stability selection into conventional MLSM and describe our open-source MATLAB implementation. Usage is showcased with our publicly available dataset of chronic stroke survivors (N=167) and further validated in our independent public acute stroke dataset (N = 1106). We demonstrate that sMLSM eliminates inconsistent features highlighted by MLSM, reduces variation in feature weights, enables the model to learn more complex patterns of brain damage, and improves model accuracy for predicting aphasia severity in a way that tends to be robust regarding the choice of parameters for identifying reliable features. Critically, sMLSM more consistently outperforms predictions based on lesion size alone. This advantage is evident starting at modest sample sizes (N>75). Spatial distribution of feature importance is different in sMLSM, which highlights the features identified by univariate lesion symptom mapping while also implicating select regions emphasized by MLSM. Beyond improved prediction accuracy, sMLSM can offer deeper insight into reliable biomarkers of impairment, informing our understanding of neurobiology.

Dual NWP wind speed correction based on trend fusion and fluctuation clustering and its application in short-term wind power prediction

With the continuous growth of grid-connected installed capacity of wind power, the inevitable gap, volatility and randomness of wind power pose challenges to the stability of real-time operation of power system. Accurate wind power prediction (WPP) can effectively ensure the safe and stable operation of power system. At present, the main input of short-term power prediction based on data-driven model is numerical weather prediction (NWP), and its prediction accuracy leads to the failure to effectively improve the accuracy of short-term power prediction. To solve this problem, this paper proposes a dual NWP wind speed (WS) correction method based on trend fusion and fluctuation clustering. First, the WS trend is used to construct a new input feature, and the NWP WS error distribution is determined to establish a more correct and stable mapping relationship with the NWP WS error. Secondly, the error is decomposed by Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN), and the trend and fluctuation components are defined by Pearson coefficient. The trend curve features in the short 24h period were extracted from the two dimensions of time and value, and the trend and fluctuation curve databases under different scenarios were formed by K-Medoids clustering. Finally, the trend component is modified by the Attention-GRU model, and the corresponding trend component is searched and matched from the database to correct the fluctuation component. The NWP WS is modified by the superposition of the two components and the short-term WPP is made. Two wind farms in Mengxi, China were used for example analysis, and the prediction accuracy was improved by 10 % and 13.1 % respectively, which demonstrated the effectiveness of the proposed method.

Towards personalized precision functional mapping in infancy

Abstract The precise network topology of functional brain systems is highly specific to individuals and undergoes dramatic changes during critical periods of development. Large amounts of high-quality resting state data are required to investigate these individual differences, but are difficult to obtain in early infancy. Using the template matching method, we generated a set of infant network templates to use as priors for individualized functional resting-state network mapping in two independent neonatal datasets with extended acquisition of resting-state functional MRI (fMRI) data. We show that template matching detects all major adult resting-state networks in individual infants and that the topology of these resting-state network maps is individual-specific. Interestingly, there was no plateau in within-subject network map similarity with up to 25 minutes of resting-state data, suggesting that the amount and/or quality of infant data required to achieve stable or high-precision network maps is higher than adults. These findings are a critical step towards personalized precision functional brain mapping in infants, which opens new avenues for clinical applicability of resting-state fMRI and potential for robust prediction of how early functional connectivity patterns relate to subsequent behavioral phenotypes and health outcomes.