Miracle-dz/UniFAR-FTUs huggingface dataset:
Estimates for sums of eigenfunctions of elliptic pseudo-differential operators on compact Lie groups

We extend the estimates proved by Donnelly and Feﬀerman and by Lebeau and Robbiano for sums of eigenfunctions of the Laplacian (on a compact manifold) to estimates for sums of eigenfunctions of any positive and elliptic pseudodiﬀerential operator of positive order on a compact Lie group. Our criteria are imposed in terms of the positivity of the corresponding matrix-valued symbol of the operator. As an application of these inequalities in the control theory, we obtain the null-controllability for diﬀusion models for elliptic pseudo-diﬀerential operators on compact Lie groups.
Frequency Distribution of Prime Numbers between an Integer and its Square: A Case Study

The chronicle of prime numbers travel back thousands of years in human history. Not only the traits of prime numbers have surprised people, but also all those endeavors made for ages to find a pattern in the appearance of prime numbers has been captivating them. Until recently, it was firmly believed that prime numbers do not maintain any pattern of occurrence among themselves. This statement is conferred not to be completely true. This paper is also an attempt to discover a pattern in the occurrence of prime numbers. This work intends to introduce some mathematical well-known equations that point to the existence of a simplistic pattern in the number of primes within the range of a number and its square. We assume that the rigorous evaluation of the perceived pattern may benefit in many aspects such as applications of encryption, algorithms concerning prime numbers, and many more.
Hebbian Deep Learning Without Feedback

Recent approximations to backpropagation (BP) have mitigated many of BP's computational inefficiencies and incompatibilities with biology, but important limitations still remain. Moreover, the approximations significantly decrease accuracy in benchmarks, suggesting that an entirely different approach may be more fruitful. Here, grounded on recent theory for Hebbian learning in soft winner-take-all networks, we present multilayer SoftHebb, i.e. an algorithm that trains deep neural networks, without any feedback, target, or error signals. As a result, it achieves efficiency by avoiding weight transport, non-local plasticity, time-locking of layer updates, iterative equilibria, and (self-) supervisory or other feedback signals -- which were necessary in other approaches. Its increased efficiency and biological compatibility do not trade off accuracy compared to state-of-the-art bio-plausible learning, but rather improve it. With up to five hidden layers and an added linear classifier, accuracies on MNIST, CIFAR-10, STL-10, and ImageNet, respectively reach 99.4%, 80.3%, 76.2%, and 27.3%. In conclusion, SoftHebb shows with a radically different approach from BP that Deep Learning over few layers may be plausible in the brain and increases the accuracy of bio-plausible machine learning. Code is available at https://github.com/NeuromorphicComputing/SoftHebb.
Material Prediction for Design Automation Using Graph Representation Learning

Successful material selection is critical in designing and manufacturing products for design automation. Designers leverage their knowledge and experience to create high-quality designs by selecting the most appropriate materials through performance, manufacturability, and sustainability evaluation. Intelligent tools can help designers with varying expertise by providing recommendations learned from prior designs. To enable this, we introduce a graph representation learning framework that supports the material prediction of bodies in assemblies. We formulate the material selection task as a node-level prediction task over the assembly graph representation of CAD models and tackle it using Graph Neural Networks (GNNs). Evaluations over three experimental protocols performed on the Fusion 360 Gallery dataset indicate the feasibility of our approach, achieving a 0.75 top-3 micro-F1 score. The proposed framework can scale to large datasets and incorporate designers’ knowledge into the learning process. These capabilities allow the framework to serve as a recommendation system for design automation and a baseline for future work, narrowing the gap between human designers and intelligent design agents.
MIMO Integrated Sensing and Communication: CRB-Rate Tradeoff

This paper studies a multiple-input multiple-output (MIMO) integrated sensing and communication (ISAC) system, in which a multi-antenna base station (BS) sends unified wireless signals to estimate one sensing target and communicate with a multi-antenna communication user (CU) simultaneously. We consider both the point and extended target models. For the point target case, the BS estimates the target angle and we adopt the Cram\'er-Rao bound (CRB) for angle estimation as the sensing performance metric. For the extended target case, the BS estimates the complete target response matrix, and we consider three different sensing performance metrics including the trace, the maximum eigenvalue, and the determinant of the CRB matrix for target response matrix estimation. For each of the four scenarios with different CRB measures, we investigate the fundamental tradeoff between the CRB for estimation and the data rate for communication, by characterizing the Pareto boundary of the achievable CRB-rate (C-R) region. In particular, we formulate a new MIMO rate maximization problem for each scenario, by optimizing the transmit covariance matrix at the BS, subject to a different form of maximum CRB constraint and its maximum transmit power constraint. For these problems, we obtain their optimal solutions in semi-closed forms by using advanced convex optimization techniques. For the point target case, the optimal solution is obtained by diagonalizing a \emph{composite channel matrix} via singular value decomposition (SVD) together with water-filling-like power allocation over these decomposed subchannels. For the three scenarios in the extended target case, the optimal solutions are obtained by diagonalizing the \emph{communication channel} via SVD, together with proper power allocation over two orthogonal sets of subchannels. Numerical results are conducted to validate the proposed design.
Meta-Learning a Cross-lingual Manifold for Semantic Parsing

Localizing a semantic parser to support new languages requires effective cross-lingual generalization. Recent work has found success with machine-translation or zero-shot methods, although these approaches can struggle to model how native speakers ask questions. We consider how to effectively leverage minimal annotated examples in new languages for few-shot cross-lingual semantic parsing. We introduce a first-order meta-learning algorithm to train a semantic parser with maximal sample efficiency during cross-lingual transfer. Our algorithm uses high-resource languages to train the parser and simultaneously optimizes for cross-lingual generalization to lower-resource languages. Results across six languages on ATIS demonstrate that our combination of generalization steps yields accurate semantic parsers sampling ≤10% of source training data in each new language. Our approach also trains a competitive model on Spider using English with generalization to Chinese similarly sampling ≤10% of training data.1
An Optimization-Based IMU/Lidar/Camera Co-calibration Method

Recently, multi-sensors fusion has achieved significant progress in the field of automobility to improve navigation and position performance. As the prerequisite of the fusion algorithm, the demand for the extrinsic calibration of multi-sensors is growing. To calculate the extrinsic parameter, many researches have been dedicated to the two-step method, which integrates the respective calibration in pairs. It is inefficient and incompact because of losing sight of the constrain of all sensors. With regard to remove this burden, an optimization-based IMU/Lidar/Camera co-calibration method is proposed in the paper. Firstly, the IMU/camera and IMU/lidar online calibrations are conducted, respectively. Then, the corner and surface feature points in the chessboard are associated with the coarse result and the camera/lidar constraint is constructed. Finally, construct the co-calibration optimization to refine all extrinsic parameters. We evaluate the performance of the proposed scheme in simulation and the result demonstrates that our proposed method outperforms the two-step method.
Asset Pricing and Deep Learning

Traditional machine learning methods have been widely studied in ﬁnancial innovation. My study focuses on the application of deep learning methods on asset pricing. I investigate various deep learning methods for asset pricing, especially for risk premia measurement. All models take the same set of predictive signals (ﬁrm characteristics, systematic risks and macroeconomics). I demonstrate high performance of all kinds of state-of-the-art (SOTA) deep learning methods, and ﬁgure out that RNNs with memory mechanism and attention have the best performance in terms of predictivity. Furthermore, I demonstrate large economic gains to investors using deep learning forecasts. The results of my comparative experiments highlight the importance of domain knowledge and ﬁnancial theory when designing deep learning models. I also show return prediction tasks bring new challenges to deep learning. The time varying distribution causes distribution shift problem, which is essential for ﬁnancial time series prediction. I demonstrate that deep learning methods can improve asset risk premium measurement. Due to the booming deep learning studies, they can constantly promote the study of underlying ﬁnancial mechanisms behind asset pricing. I also propose a promising research method that learning from data and ﬁguring out the underlying economic mechanisms through explainable artiﬁcial intelligence (AI) methods. My ﬁndings not only justify the value of deep learning in blooming ﬁntech development, but also highlight their prospects and advantages over traditional machine learning methods.
A Unified Approach for Beam-Split Mitigation in Terahertz Wideband Hybrid Beamforming

The sixth generation networks envision the deployment of terahertz (THz) band as one of the key enabling property thanks to its abundant bandwidth. However, the ultra-wide bandwidth in THz causes beam-split phenomenon due to the use of a single analog beamformer (AB). Specifically, beam-split makes different subcarriers to observe distinct directions since the same AB is adopted for all subcarriers. Previous works mostly employ additional hardware components, e.g., time-delayer networks to mitigate beam-split by realizing virtual subcarrier-dependent ABs. This article introduces an efficient and unified approach, called beam-split-aware (BSA) hybrid beamforming. In particular, instead of virtually generating subcarrier-dependent ABs, a single AB is used and the effect of beam-split is computed and passed into the digital beamformers, which are subcarrier-dependent while maximizing spectral efficiency. Hence, the proposed BSA approach effectively mitigates the impact of beam-split and it can be applied to any hybrid beamforming architecture. Manifold optimization and orthogonal matching pursuit techniques are considered for the evaluation of the proposed approach in multi-user scenario. Numerical simulations show that significant performance improvement can be achieved as compared to the conventional techniques.
Numerical techniques for dynamic resistive networks

We consider approaches to the numerical difficulties posed by modelling resistive networks with dynamically changing resistances according to a set of coupled ordinary differential equations (ODEs). The prototype problem is autoregulation on a cerebral microvascular network. In this network the amount of perfusion, or tissue blood supply, is determined by the resistance of the vascular network. This resistance can be dynamically altered to regulate the amount of blood flow and hence maintain a balance of chemicals and nutrients in the tissue. The mechanisms responsible for this are primarily local, and are due to various chemical pathways to the vascular smooth muscle cells lining the arterioles and arteries in the vasculature. These cells contract and dilate, which alters the radii and hence resistance of the vessels. Because of the global coupling induced by the resistive network, the resulting stiff system of ODEs has a dense Jacobian which precludes the direct application of traditional implicit numerical solution methods. We consider a means of remedying this problem by taking a block diagonal Jacobian approximation which allows use of an implicit method but retains the desirable property of explicit solvers of linear solution time scaling with problem size. precludes the direct application of traditional implicit numerical solution methods. We consider a means of remedying this problem by taking a block diagonal Jacobian approximation which allows use of an implicit method but retains the desirable property of explicit solvers of linear solution time scaling with problem size.
Towards Direct Comparison of Community Structures in Social Networks

Community detection algorithms are in general evaluated by comparing evaluation metric values for the communities obtained with different algorithms. The evaluation metrics that are used for measuring quality of the communities incorporate the topological information of entities like connectivity of the nodes within or outside the communities. However, while comparing the metric values it loses direct involvement of topological information of the communities in the comparison process. In this paper, a direct comparison approach is proposed where topological information of the communities obtained with two algorithms are compared directly. A quality measure namely Topological Variance (TV) is designed based on direct comparison of topological information of the communities. Considering the newly designed quality measure, two ranking schemes are developed. The efficacy of proposed quality metric as well as the ranking scheme is studied with eight widely used real-world datasets and six community detection algorithms.
NDD: A 3D Point Cloud Descriptor Based on Normal Distribution for Loop Closure Detection

Loop closure detection is a key technology for long-term robot navigation in complex environments. In this paper, we present a global descriptor, named Normal Distribution Descriptor (NDD), for 3D point cloud loop closure detection. The descriptor encodes both the probability density score and entropy of a point cloud as the descriptor. We also propose a fast rotation alignment process and use correlation coefficient as the similarity between descriptors. Experimental results show that our approach outperforms the state-of-the-art point cloud descriptors in both accuracy and efficency. The source code is available and can be integrated into existing LiDAR odometry and mapping (LOAM) systems.
An Asymptotically Optimal Batched Algorithm for the Dueling Bandit Problem

We study the $K$-armed dueling bandit problem, a variation of the traditional multi-armed bandit problem in which feedback is obtained in the form of pairwise comparisons. Previous learning algorithms have focused on the $\textit{fully adaptive}$ setting, where the algorithm can make updates after every comparison. The"batched"dueling bandit problem is motivated by large-scale applications like web search ranking and recommendation systems, where performing sequential updates may be infeasible. In this work, we ask: $\textit{is there a solution using only a few adaptive rounds that matches the asymptotic regret bounds of the best sequential algorithms for $K$-armed dueling bandits? }$ We answer this in the affirmative $\textit{under the Condorcet condition}$, a standard setting of the $K$-armed dueling bandit problem. We obtain asymptotic regret of $O(K^2\log^2(K)) + O(K\log(T))$ in $O(\log(T))$ rounds, where $T$ is the time horizon. Our regret bounds nearly match the best regret bounds known in the fully sequential setting under the Condorcet condition. Finally, in computational experiments over a variety of real-world datasets, we observe that our algorithm using $O(\log(T))$ rounds achieves almost the same performance as fully sequential algorithms (that use $T$ rounds).
Viscosity effects on waves in partially and fully ionized plasma in magnetic field

Viscosity is discussed in multicomponent partially and fully ionized plasma, and its effects on two very different waves (Alfven and Langmuir) in solar atmosphere. A full set of viscosity coefficients is presented which includes coefficients for electrons, protons and hydrogen atoms. These are applied to layers with mostly magnetized protons in solar chromosphere where the Alfven wave could in principle be expected. The viscosity coefficients are calculated and presented graphically for the altitudes between 700 and 2200 km, and required corresponding cross sections for various types of collisions are given in terms of altitude. It is shown that in chromosphere the viscosity plays no role for the Alfven wave, which is only strongly affected by ion friction with neutrals. In corona, assuming the magnetic field of a few Gauss, the Alfven wave is more affected by ion viscosity than by ion-electron friction only for wavelengths shorter that 1-30 km, dependent on parameters and assuming the perturbed magnetic field of one percent of its equilibrium value. For the Langmuir wave the viscosity-friction interplay in chromosphere is shown to be dependent on altitude and on wavelengths. In corona the viscosity is the main dissipative mechanism acting on the Langmuir mode.
Deep Manifold Hashing: A Divide-and-Conquer Approach for Semi-Paired Unsupervised Cross-Modal Retrieval

Hashing that projects data into binary codes has shown extraordinary talents in cross-modal retrieval due to its low storage usage and high query speed. Despite their empir-ical success on some scenarios, existing cross-modal hashing methods usually fail to cross modality gap when fully-paired data with plenty of labeled information is nonex-istent. To circumvent this drawback, motivated by the Divide-and-Conquer strategy, we propose Deep Manifold Hashing (DMH), a novel method of dividing the problem of semi-paired unsupervised cross-modal retrieval into three sub-problems and build-ing one simple yet efﬁciency model for each sub-problem. Speciﬁcally, the ﬁrst model is constructed for obtaining modality-invariant features by complementing semi-paired data based on manifold learning, whereas the second model and the third model aim to learn hash codes and hash functions respectively. Extensive experiments on three benchmarks demonstrate the superiority of our DMH compared with the state-of-the-art fully-paired and semi-paired unsupervised cross-modal hashing methods. results on three real-world datasets demonstrate that our DMH can more
Feature-Rich Long-term Bitcoin Trading Assistant

For a long time predicting, studying and analyzing financial indices has been of major interest for the financial community. Recently, there has been a growing interest in the Deep-Learning community to make use of reinforcement learning which has surpassed many of the previous benchmarks in a lot of fields. Our method provides a feature rich environment for the reinforcement learning agent to work on. The aim is to provide long term profits to the user so, we took into consideration the most reliable technical indicators. We have also developed a custom indicator which would provide better insights of the Bitcoin market to the user. The Bitcoin market follows the emotions and sentiments of the traders, so another element of our trading environment is the overall daily Sentiment Score of the market on Twitter. The agent is tested for a period of 685 days which also included the volatile period of Covid-19. It has been capable of providing reliable recommendations which give an average profit of about 69%. Finally, the agent is also capable of suggesting the optimal actions to the user through a website. Users on the website can also access the visualizations of the indicators to help fortify their decisions.
Gravitational waves in bimetric MOND

I consider the weak field limit (WFL) of bimetric MOND (BIMOND): the lowest order in the small departures Hmn and H'mn from double Minkowski space-time. In particular, I look at propagating solutions, for a favorite subclass of BIMOND. The WFL splits into two sectors for two linear combinations, Hmn+ and Hmn-, of Hmn and H'mn. The Hmn+ sector is equivalent to the WFL of general relativity (GR), with its gauge freedom, and has the same vacuum gravitational waves. The Hmn- sector is fully nonlinear even for the weakest Hmn-, and inherits none of the coordinate gauge freedom. The equations of motion are scale invariant in the deep-MOND limit of purely gravitational systems. In these last two regards, the BIMOND WFL is greatly different from that of other bimetric theories studied to date. Despite the strong nonlinearity, an arbitrary pair of harmonic GR wave packets of Hmn and H'mn moving in the same direction, is a solution of the (vacuum) BIMOND WFL.
Wide-Area Geolocalization with a Limited Field of View Camera

Cross-view geolocalization, a supplement or replacement for GPS, localizes an agent within a search area by matching images taken from a ground-view camera to overhead images taken from satellites or aircraft. Although the viewpoint disparity between ground and overhead images makes crossview geolocalization challenging, significant progress has been made assuming that the ground agent has access to a panoramic camera. For example, our prior work (WAG) introduced changes in search area discretization, training loss, and particle filter weighting that enabled city-scale panoramic cross-view geolocalization. However, panoramic cameras are not widely used in existing robotic platforms due to their complexity and cost. Non-panoramic cross-view geolocalization is more applicable for robotics, but is also more challenging. This paper presents Restricted FOV Wide-Area Geolocalization (ReWAG), a cross-view geolocalization approach that generalizes WAG for use with standard, non-panoramic ground cameras by creating pose-aware embeddings and providing a strategy to incorporate particle pose into the Siamese network. ReWAG is a neural network and particle filter system that is able to globally localize a mobile agent in a GPS-denied environment with only odometry and a 90° FOV camera, achieving similar localization accuracy as what WAG achieved with a panoramic camera and improving localization accuracy by a factor of 100 compared to a baseline vision transformer (ViT) approach.
On Robustness of Double Linear Trading With Transaction Costs

A trading system is said to be robust if it generates a positive return regardless of market direction. To this end, a consistently positive expected trading gain is often used as a robustness metric for a trading system. In this letter, we propose a new class of trading policies called the double linear policy in an asset trading scenario when transaction costs are involved. Unlike many existing papers, we first show that the desired robust positive expected gain may disappear when transaction costs are involved. Then we quantify under what conditions the desired positivity can still be preserved. In addition, we conduct heavy Monte-Carlo simulations for an underlying asset whose prices are governed by a geometric Brownian motion with jumps to validate our theory. A more realistic backtesting example involving historical data for cryptocurrency Bitcoin-USD is also studied.