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Jianfeng Lin

Publications and source records attributed to Jianfeng Lin.

At least 37 records · Page 2Linked to original sources
arXiv2025

$π_1$-injective bounding and application to 3- and 4-manifolds

Suppose a closed oriented $n$-manifold $M$ bounds an oriented $(n+1)$-manifold. It is known that $M$ $π_1$-injectively bounds an oriented $(n+1)$-manifold $W$. We prove that $π_1(W)$ can be residually finite if $π_1(M)$ is, and $π_1(W)$ can be finite if $π_1(M)$ is. In particular, each closed 3-manifold $M$ $π_1$-injectively bounds a 4-manifold with residually finite $π_1$, and bounds a 4-manifold with finite $π_1$ if $π_1(M)$ is finite. Applications to 3- and 4-manifolds are given: (1) We study finite group actions on closed 4-manifolds and $π_1$-isomorphic cobordism of 3-dimensional lens spaces. Results including: (a) Two lens spaces are $π_1$-isomorphic cobordant if and only if there is a degree one map between them. (b) Each spherical 3-manifold $M\ne S^3$ can be realized as the unique non-free orbit type for a finite group action on a closed 4-manifold. (2) The minimal bounding index $O_b(M)$ for closed 3-manifolds $M$ are defined, %and bounding Euler charicteristic $χ_b(M)$. the relations between finiteness of $O_b(M)$ and virtual achirality of aspherical (hyperbolic) $M$ are addressed. We calculate $O_b(M)$ for some lens spaces $M$. Each prime is realized as a minimal bounding index. (3) We also discuss some concrete examples:Surface bundle often bound surface bundles, and prime 3-manifolds often virtually bound surface bundles, $W$ bounded by some lens spaces realizing $O_b$ is constructed.

math.GT↗
arXiv2025

Probabilistic approach to feedback control enhances multi-legged locomotion on rugged landscapes

Achieving robust legged locomotion on complex terrains poses challenges due to the high uncertainty in robot-environment interactions. Recent advances in bipedal and quadrupedal robots demonstrate good mobility on rugged terrains but rely heavily on sensors for stability due to low static stability from a high center of mass and a narrow base of support. We hypothesize that a multi-legged robotic system can leverage morphological redundancy from additional legs to minimize sensing requirements when traversing challenging terrains. Studies suggest that a multi-legged system with sufficient legs can reliably navigate noisy landscapes without sensing and control, albeit at a low speed of up to 0.1 body lengths per cycle (BLC). However, the control framework to enhance speed on challenging terrains remains underexplored due to the complex environmental interactions, making it difficult to identify the key parameters to control in these high-degree-of-freedom systems. Here, we present a bio-inspired vertical body undulation wave as a novel approach to mitigate environmental disturbances affecting robot speed, supported by experiments and probabilistic models. Finally, we introduce a control framework which monitors foot-ground contact patterns on rugose landscapes using binary foot-ground contact sensors to estimate terrain rugosity. The controller adjusts the vertical body wave based on the deviation of the limb's averaged actual-to-ideal foot-ground contact ratio, achieving a significant enhancement of up to 0.235 BLC on rugose laboratory terrain. We observed a $\sim$ 50\% increase in speed and a $\sim$ 40\% reduction in speed variance compared to the open-loop controller. Additionally, the controller operates in complex terrains outside the lab, including pine straw, robot-sized rocks, mud, and leaves.

cs.RO↗
arXiv2025

On the mapping class groups of 4-manifolds with 1-handles

We develop a framework that generalizes Budney-Gabai's $W_3$ invariant on $π_0\textrm{Diff}(S^1\times D^3,\partial)$ to 4-manifolds with 1-handles. As applications, we show that if $M=(S^1\times D^3)\natural \hat M$ where $\hat M$ either has the form $I\times Y$ or is a punctured aspherical manifold, then the center of the mapping class group of $M$ is of infinite rank.

math.GT↗
arXiv2024

The monodromy diffeomorphism of weighted singularities and Seiberg--Witten theory

We prove that the monodromy diffeomorphism of a complex 2-dimensional isolated hypersurface singularity of weighted-homogeneous type has infinite order in the smooth mapping class group of the Milnor fiber, provided the singularity is not a rational double point. This is a consequence of our main result: the boundary Dehn twist diffeomorphism of an indefinite symplectic filling of the canonical contact structure on a negatively-oriented Seifert-fibered rational homology 3-sphere has infinite order in the smooth mapping class group. Our techniques make essential use of analogues of the contact invariant in the setting of $\mathbb{Z}/p$-equivariant Seiberg--Witten--Floer homology of 3-manifolds.

math.GT↗
arXiv2024

Addition of a peristaltic wave improves multi-legged locomotion performance on complex terrains

Characterized by their elongate bodies and relatively simple legs, multi-legged robots have the potential to locomote through complex terrains for applications such as search-and-rescue and terrain inspection. Prior work has developed effective and reliable locomotion strategies for multi-legged robots by propagating the two waves of lateral body undulation and leg stepping, which we will refer to as the two-wave template. However, these robots have limited capability to climb over obstacles with sizes comparable to their heights. We hypothesize that such limitations stem from the two-wave template that we used to prescribe the multi-legged locomotion. Seeking effective alternative waves for obstacle-climbing, we designed a five-segment robot with static (non-actuated) legs, where each cable-driven joint has a rotational degree-of-freedom (DoF) in the sagittal plane (vertical wave) and a linear DoF (peristaltic wave). We tested robot locomotion performance on a flat terrain and a rugose terrain. While the benefit of peristalsis on flat-ground locomotion is marginal, the inclusion of a peristaltic wave substantially improves the locomotion performance in rugose terrains: it not only enables obstacle-climbing capabilities with obstacles having a similar height as the robot, but it also significantly improves the traversing capabilities of the robot in such terrains. Our results demonstrate an alternative actuation mechanism for multi-legged robots, paving the way towards all-terrain multi-legged robots.

cs.RO↗
arXiv2024

Bird-inspired tendon coupling improves paddling efficiency by shortening phase transition times

Drag-based swimming with rowing appendages, fins, and webbed feet is a widely adapted locomotion form in aquatic animals. To develop effective underwater and swimming vehicles, a wide range of bioinspired drag-based paddles have been proposed, often faced with a trade-off between propulsive efficiency and versatility. Webbed feet provide an effective propulsive force in the power phase, are light weight and robust, and can even be partially folded away in the recovery phase. However, during the transition between recovery and power phase, much time is lost folding and unfolding, leading to drag and reducing efficiency. In this work, we took inspiration from the coupling tendons of aquatic birds and utilized tendon coupling mechanisms to shorten the transition time between recovery and power phase. Results from our hardware experiments show that the proposed mechanisms improve propulsive efficiency by 2.0 and 2.4 times compared to a design without extensor tendons or based on passive paddle, respectively. We further report that distal leg joint clutching, which has been shown to improve efficiency in terrestrial walking, did not play an major role in swimming locomotion. In sum, we describe a new principle for an efficient, drag-based leg and paddle design, with potential relevance for the swimming mechanics in aquatic birds.

cs.RO↗
arXiv2024

On four-dimensional Dehn twists and Milnor fibrations

We study the monodromy diffeomorphism of Milnor fibrations of isolated complex surface singularities, by computing the family Seiberg--Witten invariant of Seifert-fibered Dehn twists using recent advances in monopole Floer homology. More precisely, we establish infinite order non-triviality results for boundary Dehn twists on indefinite symplectic fillings of links of minimally elliptic surface singularities. Using this, we exhibit a wide variety of new phenomena in dimension four: (1) smoothings of isolated complex surface singularities whose Milnor fibration has monodromy with infinite order as a diffeomorphism but with finite order as a homeomorphism, (2) robust Torelli symplectomorphisms that do not factor as products of Dehn--Seidel twists, (3) compactly supported exotic diffeomorphisms of exotic $\mathbb{R}^4$'s and contractible manifolds.

math.GT↗
arXiv2024

Data-Driven Real-time Coupon Allocation in the Online Platform

Traditionally, firms have offered coupons to customer groups at predetermined discount rates. However, advancements in machine learning and the availability of abundant customer data now enable platforms to provide real-time customized coupons to individuals. In this study, we partner with Meituan, a leading shopping platform, to develop a real-time, end-to-end coupon allocation system that is fast and effective in stimulating demand while adhering to marketing budgets when faced with uncertain traffic from a diverse customer base. Leveraging comprehensive customer and product features, we estimate Conversion Rates (CVR) under various coupon values and employ isotonic regression to ensure the monotonicity of predicted CVRs with respect to coupon value. Using calibrated CVR predictions as input, we propose a Lagrangian Dual-based algorithm that efficiently determines optimal coupon values for each arriving customer within 50 milliseconds. We theoretically and numerically investigate the model performance under parameter misspecifications and apply a control loop to adapt to real-time updated information, thereby better adhering to the marketing budget. Finally, we demonstrate through large-scale field experiments and observational data that our proposed coupon allocation algorithm outperforms traditional approaches in terms of both higher conversion rates and increased revenue. As of May 2024, Meituan has implemented our framework to distribute coupons to over 100 million users across more than 110 major cities in China, resulting in an additional CNY 8 million in annual profit. We demonstrate how to integrate a machine learning prediction model for estimating customer CVR, a Lagrangian Dual-based coupon value optimizer, and a control system to achieve real-time coupon delivery while dynamically adapting to random customer arrival patterns.

econ.EM↗
arXiv2024

A Progressive Framework of Vision-language Knowledge Distillation and Alignment for Multilingual Scene

Pre-trained vision-language (V-L) models such as CLIP have shown excellent performance in many downstream cross-modal tasks. However, most of them are only applicable to the English context. Subsequent research has focused on this problem and proposed improved models, such as CN-CLIP and AltCLIP, to facilitate their applicability to Chinese and even other languages. Nevertheless, these models suffer from high latency and a large memory footprint in inference, which limits their further deployment on resource-constrained edge devices. In this work, we propose a conceptually simple yet effective multilingual CLIP Compression framework and train a lightweight multilingual vision-language model, called DC-CLIP, for both Chinese and English context. In this framework, we collect high-quality Chinese and English text-image pairs and design two training stages, including multilingual vision-language feature distillation and alignment. During the first stage, lightweight image/text student models are designed to learn robust visual/multilingual textual feature representation ability from corresponding teacher models, respectively. Subsequently, the multilingual vision-language alignment stage enables effective alignment of visual and multilingual textual features to further improve the model's multilingual performance. Comprehensive experiments in zero-shot image classification, conducted based on the ELEVATER benchmark, showcase that DC-CLIP achieves superior performance in the English context and competitive performance in the Chinese context, even with less training data, when compared to existing models of similar parameter magnitude. The evaluation demonstrates the effectiveness of our designed training mechanism.

cs.CV↗
arXiv2024

TFCounter:Polishing Gems for Training-Free Object Counting

Object counting is a challenging task with broad application prospects in security surveillance, traffic management, and disease diagnosis. Existing object counting methods face a tri-fold challenge: achieving superior performance, maintaining high generalizability, and minimizing annotation costs. We develop a novel training-free class-agnostic object counter, TFCounter, which is prompt-context-aware via the cascade of the essential elements in large-scale foundation models. This approach employs an iterative counting framework with a dual prompt system to recognize a broader spectrum of objects varying in shape, appearance, and size. Besides, it introduces an innovative context-aware similarity module incorporating background context to enhance accuracy within messy scenes. To demonstrate cross-domain generalizability, we collect a novel counting dataset named BIKE-1000, including exclusive 1000 images of shared bicycles from Meituan. Extensive experiments on FSC-147, CARPK, and BIKE-1000 datasets demonstrate that TFCounter outperforms existing leading training-free methods and exhibits competitive results compared to trained counterparts.

cs.CV↗
arXiv2023

Beyond Text: Unveiling Multimodal Proficiency of Large Language Models with MultiAPI Benchmark

The proliferation of Large Language Models like ChatGPT has significantly advanced language understanding and generation, impacting a broad spectrum of applications. However, these models predominantly excel in text-based tasks, overlooking the complexity of real-world multimodal information. This study introduces MultiAPI, a pioneering comprehensive large-scale API benchmark dataset aimed at expanding LLMs' proficiency in multimodal contexts. Developed collaboratively through ChatGPT, MultiAPI consists of 235 diverse API calls and 2,038 contextual prompts, offering a unique platform evaluation of tool-augmented LLMs handling multimodal tasks. Through comprehensive experiments, our findings reveal that while LLMs demonstrate proficiency in API call decision-making, they face challenges in domain identification, function selection, and argument generation. What's more, we surprisingly notice that auxiliary context can actually impair the performance. An in-depth error analysis paves the way for a new paradigm to address these challenges, suggesting a potential direction for future LLM research.

cs.CL↗
arXiv2023

Homological instability for moduli spaces of smooth 4-manifolds

We prove that homological stability fails for the moduli space of any simply-connected closed smooth 4-manifold in any degree of homology, unlike what happens in all dimensions $\neq 4$. We detect also the homological discrepancy between various moduli spaces, such as topological and smooth moduli spaces of 4-manifolds, and moduli spaces of 4-manifolds with positive scalar curvature metrics. To prove these results, we use the Seiberg-Witten equations to construct a new characteristic class of families of 4-manifolds, which is unstable and detects the difference between the smooth and topological categories in dimension 4.

math.GT↗
arXiv2023

Configuration space integrals and formal smooth structures

Watanabe disproved the 4-dimensional Smale conjecture by constructing topologically trivial $D^{4}$-bundles over spheres and showing that they are smoothly nontrivial using configuration space integrals. In this paper, we define a new version of configuration space integrals that only relies on a formal smooth structure on the $D^{4}$-bundle (i.e., a vector bundle structure on the vertical tangent microbundle). It coincides with Watanabe's definition when the $D^{4}$-bundle is smooth. We obtain several applications. First, we give a lower bound (in terms of the graph homology) on the dimension of the rational homotopy and homology groups of $\textrm{Top}(4)$ and $\textrm{Homeo}(S^4)$ (the homeomorphism group of $\mathbb{R}^4$ and $S^4$). In particular, this implies that $\textrm{Top}(4)$ and $\textrm{Homeo}(S^4)$ are not rationally equivalent to any finite-dimensional CW complexes. Second, we discover a generalized Miller-Morita-Mumford class $κ_θ(π)\in H^{3}(B;\mathbf{Q})$, which is defined for any topological 4-manifold bundle $X\to E\to B$. This class obstructs the existence of a formal smooth structure on the bundle. Third, we show that for any compact, orientable, smooth 4-manifold $X$ (possibly with boundary), the inclusion map from its diffeomorphism group to its homeomorphism group is not rationally $2$-connected (hence not a weak homotopy equivalence). This implies that the space of smooth structures on $X$ has a nontrivial rational homotopy group in dimension 2.

math.GT↗
arXiv2023

Design and Stiffness Analysis of a Bio-inspired Soft Actuator with Bi-direction Tunable Stiffness Property

Modulating the stiffness of soft actuators is crucial for improving the efficiency of interaction with the environment. However, current stiffness modulation mechanisms are hard to achieve high lateral stiffness and a wide range of bending stiffness simultaneously. Here, we draw inspiration from the anatomical structure of the finger and propose a bi-directional tunable stiffness actuator (BTSA). BTSA is a soft-rigid hybrid structure that combines air-tendon hybrid actuation (ATA) and bone-like structures (BLS). We develop a corresponding fabrication method and a stiffness analysis model to support the design of BLS. The results show that the influence of the BLS on bending deformation is negligible, with a distal point distance error of less than 1.5 mm. Moreover, the bi-directional tunable stiffness is proved to be functional. The bending stiffness can be tuned by ATA from 0.23 N/mm to 0.70 N/mm, with a magnification of 3 times. The addition of BLS improves lateral stiffness up to 4.2 times compared with the one without BLS, and the lateral stiffness can be tuned decoupling within 1.2 to 2.1 times (e.g. from 0.35 N/mm to 0.46 N/mm when the bending angle is 45 deg). Finally, a four-BTSA gripper is developed to conduct horizontal lifting and grasping tasks to demonstrate the advantages of BTSA.

cs.RO↗
arXiv2022

A Bioinspired Bidirectional Stiffening Soft Actuator for Multimodal, Compliant, and Robust Grasping

The stiffness modulation mechanism for soft robotics has gained considerable attention to improve deformability, controllability, and stability. However, for the existing stiffness soft actuator, high lateral stiffness and a wide range of bending stiffness are hard to be provided at the same time. This paper presents a bioinspired bidirectional stiffening soft actuator (BISA) combining the air-tendon hybrid actuation (ATA) and a bone-like structure (BLS). The ATA is the main actuation of the BISA, and the bending stiffness can be modulated with a maximum stiffness of about 0.7 N/mm and a maximum magnification of 3 times when the bending angle is 45 deg. Inspired by the morphological structure of the phalanx, the lateral stiffness can be modulated by changing the pulling force of the BLS. The lateral stiffness can be modulated by changing the pulling force to it. The actuator with BLSs can improve the lateral stiffness about 3.9 times compared to the one without BLSs. The maximum lateral stiffness can reach 0.46 N/mm. And the lateral stiffness can be modulated decoupling about 1.3 times (e.g., from 0.35 N/mm to 0.46 when the bending angle is 45 deg). The test results show the influence of the rigid structures on bending is small with about 1.5 mm maximum position errors of the distal point of actuator bending in different pulling forces. The advantages brought by the proposed method enable a soft four-finger gripper to operate in three modes: normal grasping, inverse grasping, and horizontal lifting. The performance of this gripper is further characterized and versatile grasping on various objects is conducted, proving the robust performance and potential application of the proposed design method.

cs.RO↗
arXiv2022

The Family Seiberg-Witten Invariant and nonsymplectic loops of diffeomorphisms

By extending a result of Kronheimer-Mrowka to the family setting, we prove a gluing formula for the family Seiberg-Witten invariant. This formula allows one to compute the invariant for a smooth family of 4-manifolds by cutting it open along a product family of 3-manifolds and studying the induced maps on monopole Floer (co)homology. When the cutting 3-manifold is an L-space, this formula implies a relation between the family Seiberg-Witten invariant, the Seiberg-Witten invariant of the fiber and the index of the family Dirac operator. We use this relation to calculate the Seiberg-Witten invariant of families of 4-manifolds that arise when resolving an ADE singularity using a hyperkähler family of complex structures near the singularity. Several applications are obtained. First, we establish a large family of simply-connected 4-manifolds $M$ (e.g. all elliptic surfaces) such that $π_{1}(\textrm{Diff}(M))$ has a $\mathbb{Z}^{\infty}$-summand . For such $M$, the product $S^{2}\times M$ smoothly fibers over $S^{2}$ with fiber $M$ in infinitely many distinct ways. Second, we show that on any closed symplectic 4-manifold that contains a smoothly embedded sphere of self-intersection $-1$ or $-2$, there is a loop of diffeomorphisms that is not homotopic to a loop of symplectormorphisms. This generalizes a previous result by Smirnov and confirms a conjecture by McDuff in dimension 4. It also provides many new examples of 4-manifolds whose space of symplectic forms has a nontrivial fundamental group or first homology group.

math.GT↗
arXiv2022

Isotopy of the Dehn twist on K3#K3 after a single stabilization

Kronheimer-Mrowka recently proved that the Dehn twist along a 3-sphere in the neck of $K3\#K3$ is not smoothly isotopic to the identity. This provides a new example of self-diffeomorphisms on 4-manifolds that are isotopic to the identity in the topological category but not smoothly so. (The first such examples were given by Ruberman.) In this paper, we use the Pin(2)-equivariant Bauer-Furuta invariant to show that this Dehn twist is not smoothly isotopic to the identity even after a single stabilization (connected summing with the identity map on $S^{2}\times S^{2}$). This gives the first example of exotic phenomena on simply connected smooth 4-manifolds that do not disappear after a single stabilization.

math.GT↗