34,265 research outputs found
A New Iwasawa Theory and Converse of Gross-Zagier and Kolyvagin Theorem (with an Appendix by Yangyu Fan)
Let be a prime. In this paper we develop a new kind of anticyclotomic
local -Iwasawa theory at for Hecke characters of quadratic imaginary
fields which is valid for all ramification types of (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 -adic -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
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
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
Recommended from our members
Ensuring Access to Safe and Nutritious Food for All Through the Transformation of Food Systems
Multi-modal Facial Affective Analysis based on Masked Autoencoder
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
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
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
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 . Equilibrium LC states correspond to functions
that (locally) minimize an LdG energy functional. Thus, we consider an
-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
) 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
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
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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