34,265 research outputs found

    A New ±\pm Iwasawa Theory and Converse of Gross-Zagier and Kolyvagin Theorem (with an Appendix by Yangyu Fan)

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    Let p>3p>3 be a prime. In this paper we develop a new kind of anticyclotomic local ±\pm-Iwasawa theory at pp for Hecke characters of quadratic imaginary fields which is valid for all ramification types of pp (split, inert and ramified). As an application we deduce the converse of Gross-Zagier-Kolyvagin theorem for these CM forms, which states that Selmer rank one implies analytic rank one. To carry out the Iwasawa theory argument we employ a recent construction of a new type of pp-adic LL-function by Andreatta-Iovita, and generalized by Yangyu Fan to Shimura curves in the Appendix, and a ``virtual Heenger family'' made via a limiting procedure from a Heegner family along Coleman-Mazur eigencurve constructed by Jetchev-Loeffler-Zerbes.Comment: with an appendix by Yangyu Fa

    Geometric Properties of the 2-D Peskin Problem

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    The 2-D Peskin problem describes a 1-D closed elastic string immersed and moving in a 2-D Stokes flow that is induced by its own elastic force. The geometric shape of the string and its internal stretching configuration evolve in a coupled way, and they combined govern the dynamics of the system. In this paper, we show that certain geometric quantities of the moving string satisfy extremum principles and decay estimates. As a result, we can prove that the 2-D Peskin problem admits a unique global solution when the initial data satisfies a medium-size geometric condition on the string shape, while no assumption on the size of stretching is needed

    The Metaverse: Survey, Trends, Novel Pipeline Ecosystem & Future Directions

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    The Metaverse offers a second world beyond reality, where boundaries are non-existent, and possibilities are endless through engagement and immersive experiences using the virtual reality (VR) technology. Many disciplines can benefit from the advancement of the Metaverse when accurately developed, including the fields of technology, gaming, education, art, and culture. Nevertheless, developing the Metaverse environment to its full potential is an ambiguous task that needs proper guidance and directions. Existing surveys on the Metaverse focus only on a specific aspect and discipline of the Metaverse and lack a holistic view of the entire process. To this end, a more holistic, multi-disciplinary, in-depth, and academic and industry-oriented review is required to provide a thorough study of the Metaverse development pipeline. To address these issues, we present in this survey a novel multi-layered pipeline ecosystem composed of (1) the Metaverse computing, networking, communications and hardware infrastructure, (2) environment digitization, and (3) user interactions. For every layer, we discuss the components that detail the steps of its development. Also, for each of these components, we examine the impact of a set of enabling technologies and empowering domains (e.g., Artificial Intelligence, Security & Privacy, Blockchain, Business, Ethics, and Social) on its advancement. In addition, we explain the importance of these technologies to support decentralization, interoperability, user experiences, interactions, and monetization. Our presented study highlights the existing challenges for each component, followed by research directions and potential solutions. To the best of our knowledge, this survey is the most comprehensive and allows users, scholars, and entrepreneurs to get an in-depth understanding of the Metaverse ecosystem to find their opportunities and potentials for contribution

    Multi-modal Facial Affective Analysis based on Masked Autoencoder

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    Human affective behavior analysis focuses on analyzing human expressions or other behaviors to enhance the understanding of human psychology. The CVPR 2023 Competition on Affective Behavior Analysis in-the-wild (ABAW) is dedicated to providing high-quality and large-scale Aff-wild2 for the recognition of commonly used emotion representations, such as Action Units (AU), basic expression categories(EXPR), and Valence-Arousal (VA). The competition is committed to making significant strides in improving the accuracy and practicality of affective analysis research in real-world scenarios. In this paper, we introduce our submission to the CVPR 2023: ABAW5. Our approach involves several key components. First, we utilize the visual information from a Masked Autoencoder(MAE) model that has been pre-trained on a large-scale face image dataset in a self-supervised manner. Next, we finetune the MAE encoder on the image frames from the Aff-wild2 for AU, EXPR and VA tasks, which can be regarded as a static and uni-modal training. Additionally, we leverage the multi-modal and temporal information from the videos and implement a transformer-based framework to fuse the multi-modal features. Our approach achieves impressive results in the ABAW5 competition, with an average F1 score of 55.49\% and 41.21\% in the AU and EXPR tracks, respectively, and an average CCC of 0.6372 in the VA track. Our approach ranks first in the EXPR and AU tracks, and second in the VA track. Extensive quantitative experiments and ablation studies demonstrate the effectiveness of our proposed method

    Heat kernel-based p-energy norms on metric measure spaces

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    We focus on heat kernel-based p-energy norms (1<p<\infty) on bounded and unbounded metric measure spaces, in particular, weak-monotonicity properties for different types of energies. Such properties are key to related studies, under which we generalise the convergence result of Bourgain-Brezis-Mironescu (BBM) for p\neq2. We establish the equivalence of various p-energy norms and weak-monotonicity properties when there admits a heat kernel satisfying the two-sided estimates. Using these equivalences, we verify various weak-monotonicity properties on nested fractals and their blowups. Immediate consequences are that, many classical results on p-energy norms hold for such bounded and unbounded fractals, including the BBM convergence and Gagliardo-Nirenberg inequality.Comment: 39 pages with 1 figur

    Robust Multiview Multimodal Driver Monitoring System Using Masked Multi-Head Self-Attention

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    Driver Monitoring Systems (DMSs) are crucial for safe hand-over actions in Level-2+ self-driving vehicles. State-of-the-art DMSs leverage multiple sensors mounted at different locations to monitor the driver and the vehicle's interior scene and employ decision-level fusion to integrate these heterogenous data. However, this fusion method may not fully utilize the complementarity of different data sources and may overlook their relative importance. To address these limitations, we propose a novel multiview multimodal driver monitoring system based on feature-level fusion through multi-head self-attention (MHSA). We demonstrate its effectiveness by comparing it against four alternative fusion strategies (Sum, Conv, SE, and AFF). We also present a novel GPU-friendly supervised contrastive learning framework SuMoCo to learn better representations. Furthermore, We fine-grained the test split of the DAD dataset to enable the multi-class recognition of drivers' activities. Experiments on this enhanced database demonstrate that 1) the proposed MHSA-based fusion method (AUC-ROC: 97.0\%) outperforms all baselines and previous approaches, and 2) training MHSA with patch masking can improve its robustness against modality/view collapses. The code and annotations are publicly available.Comment: 9 pages (1 for reference); accepted by the 6th Multimodal Learning and Applications Workshop (MULA) at CVPR 202

    Optimal Control of the Landau-de Gennes Model of Nematic Liquid Crystals

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    We present an analysis and numerical study of an optimal control problem for the Landau-de Gennes (LdG) model of nematic liquid crystals (LCs), which is a crucial component in modern technology. They exhibit long range orientational order in their nematic phase, which is represented by a tensor-valued (spatial) order parameter Q=Q(x)Q = Q(x). Equilibrium LC states correspond to QQ functions that (locally) minimize an LdG energy functional. Thus, we consider an L2L^2-gradient flow of the LdG energy that allows for finding local minimizers and leads to a semi-linear parabolic PDE, for which we develop an optimal control framework. We then derive several a priori estimates for the forward problem, including continuity in space-time, that allow us to prove existence of optimal boundary and external ``force'' controls and to derive optimality conditions through the use of an adjoint equation. Next, we present a simple finite element scheme for the LdG model and a straightforward optimization algorithm. We illustrate optimization of LC states through numerical experiments in two and three dimensions that seek to place LC defects (where Q(x)=0Q(x) = 0) in desired locations, which is desirable in applications.Comment: 26 pages, 9 figure

    Self-Supervised Learning to Prove Equivalence Between Straight-Line Programs via Rewrite Rules

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    We target the problem of automatically synthesizing proofs of semantic equivalence between two programs made of sequences of statements. We represent programs using abstract syntax trees (AST), where a given set of semantics-preserving rewrite rules can be applied on a specific AST pattern to generate a transformed and semantically equivalent program. In our system, two programs are equivalent if there exists a sequence of application of these rewrite rules that leads to rewriting one program into the other. We propose a neural network architecture based on a transformer model to generate proofs of equivalence between program pairs. The system outputs a sequence of rewrites, and the validity of the sequence is simply checked by verifying it can be applied. If no valid sequence is produced by the neural network, the system reports the programs as non-equivalent, ensuring by design no programs may be incorrectly reported as equivalent. Our system is fully implemented for a given grammar which can represent straight-line programs with function calls and multiple types. To efficiently train the system to generate such sequences, we develop an original incremental training technique, named self-supervised sample selection. We extensively study the effectiveness of this novel training approach on proofs of increasing complexity and length. Our system, S4Eq, achieves 97% proof success on a curated dataset of 10,000 pairs of equivalent programsComment: 30 pages including appendi

    Copy-paste data augmentation for domain transfer on traffic signs

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    City streets carry a lot of information that can be exploited to improve the quality of the services the citizens receive. For example, autonomous vehicles need to act accordingly to all the element that are nearby the vehicle itself, like pedestrians, traffic signs and other vehicles. It is also possible to use such information for smart city applications, for example to predict and analyze the traffic or pedestrian flows. Among all the objects that it is possible to find in a street, traffic signs are very important because of the information they carry. This information can in fact be exploited both for autonomous driving and for smart city applications. Deep learning and, more generally, machine learning models however need huge quantities to learn. Even though modern models are very good at gener- alizing, the more samples the model has, the better it can generalize between different samples. Creating these datasets organically, namely with real pictures, is a very tedious task because of the wide variety of signs available in the whole world and especially because of all the possible light, orientation conditions and con- ditions in general in which they can appear. In addition to that, it may not be easy to collect enough samples for all the possible traffic signs available, cause some of them may be very rare to find. Instead of collecting pictures manually, it is possible to exploit data aug- mentation techniques to create synthetic datasets containing the signs that are needed. Creating this data synthetically allows to control the distribution and the conditions of the signs in the datasets, improving the quality and quantity of training data that is going to be used. This thesis work is about using copy-paste data augmentation to create synthetic data for the traffic sign recognition task
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