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We commonly refer to an extremal K\"{a}hler metric with finitely many singularities on a compact Riemann surface as an HCMU (Hessian of the Curvature of the Metric is Umbilical) metric. In this study, we specifically classify non-CSC HCMU metrics on the K-surfaces $S^2_{\{\alpha\}}$ and $S^2_{\{\alpha,\beta\}}$., Comment: 22 pages. Comments are welcome

Multiple access is the cornerstone technology for each generation of wireless cellular networks and resource allocation design plays a crucial role in multiple access. In this paper, we present a comprehensive tutorial overview for junior researchers in this field, aiming to offer a foundational guide for resource allocation design in the context of next-generation multiple access (NGMA). Initially, we identify three types of channels in future wireless cellular networks over which NGMA will be implemented, namely: natural channels, reconfigurable channels, and functional channels. Natural channels are traditional uplink and downlink communication channels; reconfigurable channels are defined as channels that can be proactively reshaped via emerging platforms or techniques, such as intelligent reflecting surface (IRS), unmanned aerial vehicle (UAV), and movable/fluid antenna (M/FA); and functional channels support not only communication but also other functionalities simultaneously, with typical examples including integrated sensing and communication (ISAC) and joint computing and communication (JCAC) channels. Then, we introduce NGMA models applicable to these three types of channels that cover most of the practical communication scenarios of future wireless communications. Subsequently, we articulate the key optimization technical challenges inherent in the resource allocation design for NGMA, categorizing them into rate-oriented, power-oriented, and reliability-oriented resource allocation designs. The corresponding optimization approaches for solving the formulated resource allocation design problems are then presented. Finally, simulation results are presented and discussed to elucidate the practical implications and insights derived from resource allocation designs in NGMA., Comment: 69 pages, 10 figures, 5 tables

Phytoplankton, a crucial component of aquatic ecosystems, requires efficient monitoring to understand marine ecological processes and environmental conditions. Traditional phytoplankton monitoring methods, relying on non-in situ observations, are time-consuming and resource-intensive, limiting timely analysis. To address these limitations, we introduce PhyTracker, an intelligent in situ tracking framework designed for automatic tracking of phytoplankton. PhyTracker overcomes significant challenges unique to phytoplankton monitoring, such as constrained mobility within water flow, inconspicuous appearance, and the presence of impurities. Our method incorporates three innovative modules: a Texture-enhanced Feature Extraction (TFE) module, an Attention-enhanced Temporal Association (ATA) module, and a Flow-agnostic Movement Refinement (FMR) module. These modules enhance feature capture, differentiate between phytoplankton and impurities, and refine movement characteristics, respectively. Extensive experiments on the PMOT dataset validate the superiority of PhyTracker in phytoplankton tracking, and additional tests on the MOT dataset demonstrate its general applicability, outperforming conventional tracking methods. This work highlights key differences between phytoplankton and traditional objects, offering an effective solution for phytoplankton monitoring., Comment: 13pages,eleven figures

This paper proposes a joint active and passive beamforming design for reconfigurable intelligent surface (RIS)-aided wireless communication systems, adopting a piece-wise near-field channel model. While a traditional near-field channel model, applied without any approximations, offers higher modeling accuracy than a far-field model, it renders the system design more sensitive to channel estimation errors (CEEs). As a remedy, we propose to adopt a piece-wise near-field channel model that leverages the advantages of the near-field approach while enhancing its robustness against CEEs. Our study analyzes the impact of different channel models, including the traditional near-field, the proposed piece-wise near-field and far-field channel models, on the interference distribution caused by CEEs and model mismatches. Subsequently, by treating the interference as noise, we formulate a joint active and passive beamforming design problem to maximize the spectral efficiency (SE). The formulated problem is then recast as a mean squared error (MSE) minimization problem and a suboptimal algorithm is developed to iteratively update the active and passive beamforming strategies. Simulation results demonstrate that adopting the piece-wise near-field channel model leads to an improved SE compared to both the near-field and far-field models in the presence of CEEs. Furthermore, the proposed piece-wise near-field model achieves a good trade-off between modeling accuracy and system's degrees of freedom (DoF)., Comment: 28pages

Integrated sensing and communication (ISAC) is envisioned as a key pillar for enabling the upcoming sixth generation (6G) communication systems, requiring not only reliable communication functionalities but also highly accurate environmental sensing capabilities. In this paper, we design a novel networked ISAC framework to explore the collaboration among multiple users for environmental sensing. Specifically, multiple users can serve as powerful sensors, capturing back scattered signals from a target at various angles to facilitate reliable computational imaging. Centralized sensing approaches are extremely sensitive to the capability of the leader node because it requires the leader node to process the signals sent by all the users. To this end, we propose a two-step distributed cooperative sensing algorithm that allows low-dimensional intermediate estimate exchange among neighboring users, thus eliminating the reliance on the centralized leader node and improving the robustness of sensing. This way, multiple users can cooperatively sense a target by exploiting the block-wise environment sparsity and the interference cancellation technique. Furthermore, we analyze the mean square error of the proposed distributed algorithm as a networked sensing performance metric and propose a beamforming design for the proposed network ISAC scheme to maximize the networked sensing accuracy and communication performance subject to a transmit power constraint. Simulation results validate the effectiveness of the proposed algorithm compared with the state-of-the-art algorithms., Comment: Received by IEEE Internet of Things Journal

The recently proposed orthogonal time frequency space (OTFS) modulation, which is a typical Delay-Doppler (DD) communication scheme, has attracted significant attention thanks to its appealing performance over doubly-selective channels. In this paper, we present the fundamentals of general DD communications from the viewpoint of the Zak transform. We start our study by constructing DD domain basis functions aligning with the time-frequency (TF)-consistency condition, which are globally quasi-periodic and locally twisted-shifted. We unveil that these features are translated to unique signal structures in both time and frequency, which are beneficial for communication purposes. Then, we focus on the practical implementations of DD Nyquist communications, where we show that rectangular windows achieve perfect DD orthogonality, while truncated periodic signals can obtain sufficient DD orthogonality. Particularly, smoothed rectangular window with excess bandwidth can result in a slightly worse orthogonality but better pulse localization in the DD domain. Furthermore, we present a practical pulse shaping framework for general DD communications and derive the corresponding input-output relation under various shaping pulses. Our numerical results agree with our derivations and also demonstrate advantages of DD communications over conventional orthogonal frequency-division multiplexing (OFDM).

Self-supervised contrastive learning strategy has attracted remarkable attention due to its exceptional ability in representation learning. However, current contrastive learning tends to learn global coarse-grained representations of the image that benefit generic object recognition, whereas such coarse-grained features are insufficient for fine-grained visual recognition. In this paper, we present to incorporate the subtle local fine-grained feature learning into global self-supervised contrastive learning through a pure self-supervised global-local fine-grained contrastive learning framework. Specifically, a novel pretext task called Local Discrimination (LoDisc) is proposed to explicitly supervise self-supervised model's focus towards local pivotal regions which are captured by a simple-but-effective location-wise mask sampling strategy. We show that Local Discrimination pretext task can effectively enhance fine-grained clues in important local regions, and the global-local framework further refines the fine-grained feature representations of images. Extensive experimental results on different fine-grained object recognition tasks demonstrate that the proposed method can lead to a decent improvement in different evaluation settings. Meanwhile, the proposed method is also effective in general object recognition tasks., Comment: 11 pages, submitted

In the last decade, Convolutional Neural Network with a multi-layer architecture has advanced rapidly. However, training its complex network is very space-consuming, since a lot of intermediate data are preserved across layers, especially when processing high-dimension inputs with a big batch size. That poses great challenges to the limited memory capacity of current accelerators (e.g., GPUs). Existing efforts mitigate such bottleneck by external auxiliary solutions with additional hardware costs, and internal modifications with potential accuracy penalty. Differently, our analysis reveals that computations intra- and inter-layers exhibit the spatial-temporal weak dependency and even complete independency features. That inspires us to break the traditional layer-by-layer (column) dataflow rule. Now operations are novelly re-organized into rows throughout all convolution layers. This lightweight design allows a majority of intermediate data to be removed without any loss of accuracy. We particularly study the weak dependency between two consecutive rows. For the resulting skewed memory consumption, we give two solutions with different favorite scenarios. Evaluations on two representative networks confirm the effectiveness. We also validate that our middle dataflow optimization can be smoothly embraced by existing works for better memory reduction.

Transformer-based models are becoming deeper and larger recently. For better scalability, an underlying training solution in industry is to split billions of parameters (tensors) into many tasks and then run them across homogeneous accelerators (e.g., GPUs). However, such dedicated compute cluster is prohibitively expensive in academia and moderate companies. An economic replacement is to aggregate existing heterogeneous devices and share resources among multi-tenants. Nevertheless, static hardware configurations and dynamic resource contention definitely cause straggling tasks, which heavily slows down the overall training efficiency. Existing works feature contributions mainly tailored for traditional data parallelism. They cannot work well for the new tensor parallelism due to strict communication and correctness constraints. In this paper we first present ZERO-resizing, a novel dynamic workload balancing technique without any data migration. We tune workloads in real-time by temporarily resizing matrices involved in core tensor-related computations. We particularly design data imputation and priority selection policies to respectively satisfy consistency constraint required by normal training and reduce the accuracy loss. We also give a lightweight data migration technique without loss of accuracy, to cope with heavy heterogeneity. Our final SEMI-migration solution is built on top of these two techniques and can adaptively distinguish their respective balancing missions, to achieve an overall success in efficiency and accuracy. Extensive experiments on the representative Colossal-AI platform validate the effectiveness of our proposals., Comment: 13 pages

Studying the existence of rational functions with given branching datum is a classical problem in the field of complex analysis and algebraic geometry. This problem dates back to Hurwitz and remains open to this day. In this paper, we utilize complex analysis to establish a property of rational functions with 3 branching points on the Riemann sphere. Given two compact Riemann surfaces $M$ and $N$, a pair $(d,\mathcal{D})$ of an integer $d\geq2$ and a collection $\mathcal{D}$ of nontrivial partitions of $d$ is called a candidate branching datum if it satisfies the Riemann-Hurwitz formula. And a candidate branching datum is exceptional if there does not exist a rational function realization it. As applications, we present some new types of exceptional branching datum. These results cover some previous results mentioned in \cite{EKS84,PP06,Zhu19}. We also deduce the realizability of a certain type of candidate branching datum on the Riemann sphere., Comment: 9 pages. We have revised certain sentences, corrected several errors, and added additional content to enhance the clarity and depth of our paper. Comments are welcome

The integration of sensing and communication enables wireless communication systems to serve environment-aware applications. In this paper, we propose to leverage sensing to enhance physical layer security (PLS) in multiuser communication systems in the presence of a suspicious target. To this end, we develop a two-phase framework to first estimate the location of the potential eavesdropper by sensing and then utilize the estimated information to enhance PLS for communication. In particular, in the first phase, a dual-functional radar and communication (DFRC) base station (BS) exploits a sensing signal to mitigate the sensing information uncertainty of the potential eavesdropper. Then, in the second phase, to facilitate joint sensing and secure communication, the DFRC BS employs beamforming and artificial noise to enhance secure communication. The design objective is to maximize the system sum rate while alleviating the information leakage by jointly optimizing the time allocation and beamforming policy. Capitalizing on monotonic optimization theory, we develop a two-layer globally optimal algorithm to reveal the performance upper bound of the considered system. Simulation results show that the proposed scheme achieves a significant sum rate gain over two baseline schemes that adopt existing techniques. Moreover, our results unveil that ISAC is a promising paradigm for enhancing secure communication in wireless networks., Comment: 9 pages,3 figures

This paper investigates the bit error rate (BER) minimum pre-coder design for an orthogonal time frequency space (OTFS)-based integrated sensing and communications (ISAC) system, which is considered as a promising technique for enabling future wireless networks. In particular, the BER minimum problem takes into account the maximized available transmission power and the required sensing performance. We devise the precoder from the perspective of delay-Doppler (DD) domain by exploiting the equivalent DD channel. To address the non-convex design problem, we resort to minimizing the lower bound of the derived average BER. Afterwards, we propose a computationally iterative method to solve the dual problem at low cost. Simulation results verify the effectiveness of our proposed precoder and reveal the interplay between sensing and communication for dual-functional precoder design.

Channel estimation (CE) plays a key role in reconfigurable intelligent surface (RIS)-aided multiple-input multiple-output (MIMO) communication systems, while it poses a challenging task due to the passive nature of RIS and the cascaded channel structures. In this paper, a partially decoupled atomic norm minimization (PDANM) framework is proposed for CE of RIS-aided MIMO systems, which exploits the three-dimensional angular sparsity of the channel. In particular, PDANM partially decouples the differential angles at the RIS from other angles at the base station and user equipment, reducing the computational complexity compared with existing methods. A reweighted PDANM (RPDANM) algorithm is proposed to further improve CE accuracy, which iteratively refines CE through a specifically designed reweighing strategy. Building upon RPDANM, we propose an iterative approach named RPDANM with adaptive phase control (RPDANM-APC), which adaptively adjusts the RIS phases based on previously estimated channel parameters to facilitate CE, achieving superior CE accuracy while reducing training overhead. Numerical simulations demonstrate the superiority of our proposed approaches in terms of running time, CE accuracy, and training overhead. In particular, the RPDANM-APC approach can achieve higher CE accuracy than existing methods within less than 30 percent training overhead while reducing the running time by tens of times., Comment: 38 pages, 10 figures. This work is accepted by IEEE Transactions on Wireless Communications. A preliminary version of this work was presented in part at the IEEE Global Communications Conference (GLOBECOM), 2023

This paper addresses the problem of direction-of-arrival (DOA) estimation for constant modulus (CM) source signals using a uniform or sparse linear array. Existing methods typically exploit either the Vandermonde structure of the steering matrix or the CM structure of source signals only. In this paper, we propose a structured matrix recovery technique (SMART) for CM DOA estimation via fully exploiting the two structures. In particular, we reformulate the highly nonconvex CM DOA estimation problems in the noiseless and noisy cases as equivalent rank-constrained Hankel-Toeplitz matrix recovery problems, in which the Vandermonde structure is captured by a series of Hankel-Toeplitz block matrices, of which the number equals the number of snapshots, and the CM structure is guaranteed by letting the block matrices share a same Toeplitz submatrix. The alternating direction method of multipliers (ADMM) is applied to solve the resulting rank-constrained problems and the DOAs are uniquely retrieved from the numerical solution. Extensive simulations are carried out to corroborate our analysis and confirm that the proposed SMART outperforms state-of-the-art algorithms in terms of the maximum number of locatable sources and statistical efficiency.

In this paper, we study the pulse shaping for delay-Doppler (DD) communications. We start with constructing a basis function in the DD domain following the properties of the Zak transform. Particularly, we show that the constructed basis functions are globally quasi-periodic while locally twisted-shifted, and their significance in time and frequency domains are then revealed. We further analyze the ambiguity function of the basis function, and show that fully localized ambiguity function can be achieved by constructing the basis function using periodic signals. More importantly, we prove that time and frequency truncating such basis functions naturally leads to approximate delay and Doppler orthogonalities, if the truncating windows are periodic within the support. Motivated by this, we propose a DD Nyquist pulse shaping scheme considering signals with periodicity. Finally, our conclusions are verified by using various strictly or approximately periodic pulses.

The bistatic integrated sensing and communication (ISAC) system model avoids the strong self-interference in a monostatic ISAC system by employing a pair of physically separated sensing transceiver and maintaining the merit of co-designing radar sensing and communications on shared spectrum and hardware. Inspired by the appealing benefits of bistatic radar, we study bistatic ISAC, where a transmitter sends a message to a communication receiver and a sensing receiver at another location carries out a decoding-and-estimation(DnE) operation to obtain the state of the communication receiver. In this paper, both communication and sensing channels are modelled as state-dependent memoryless channels with independent and identically distributed time-varying state sequences. We consider a rate of reliable communication for the message at the communication receiver as communication metric. The objective of this model is to characterize the capacity-distortion region, i.e., the set of all the achievable rate while simultaneously allowing the sensing receiver to sense the state sequence with a given distortion threshold. In terms of the decoding degree on this message at the sensing receiver, we propose three achievable DnE strategies, the blind estimation, the partial-decoding-based estimation, and the full-decoding-based estimation, respectively. Based on the three strategies, we derive the three achievable rate-distortion regions. In addition, under the constraint of the degraded broadcast channel, i.e., the communication receiver is statistically stronger than the sensing receiver, and the partial-decoding-based estimation, we characterize the capacity region. Examples in both non-degraded and degraded cases are provided to compare the achievable rate-distortion regions under three DnE strategies and demonstrate the advantages of ISAC over independent communication and sensing., Comment: 40 pages, 7 figures

When introducing physics-constrained deep learning solutions to the volumetric super-resolution of scientific data, the training is challenging to converge and always time-consuming. We propose a new hierarchical sampling method based on octree to solve these difficulties. In our approach, scientific data is preprocessed before training, and a hierarchical octree-based data structure is built to guide sampling on the latent context grid. Each leaf node in the octree corresponds to an indivisible subblock of the volumetric data. The dimensions of the subblocks are different, making the number of sample points in each randomly cropped training data block to be adaptive. We reconstruct the octree at intervals according to loss distribution to perform the multi-stage training. With the Rayleigh-B\'enard convection problem, we deploy our method to state-of-the-art models. We constructed adequate experiments to evaluate the training performance and model accuracy of our method. Experiments indicate that our sampling optimization improves the convergence performance of physics-constrained deep learning super-resolution solutions. Furthermore, the sample points and training time are significantly reduced with no drop in model accuracy. We also test our method in training tasks of other deep neural networks, and the results show our sampling optimization has extensive effectiveness and applicability. The code is publicly available at https://github.com/xinjiewang/octree-based_sampling.

This paper proposes an integrated sensing, navigation, and communication (ISNC) framework for safeguarding unmanned aerial vehicle (UAV)-enabled wireless networks against a mobile eavesdropping UAV (E-UAV). To cope with the mobility of the E-UAV, the proposed framework advocates the dual use of artificial noise transmitted by the information UAV (I-UAV) for simultaneous jamming and sensing to facilitate navigation and secure communication. In particular, the I-UAV communicates with legitimate downlink ground users, while avoiding potential information leakage by emitting jamming signals, and estimates the state of the E-UAV with an extended Kalman filter based on the backscattered jamming signals. Exploiting the estimated state of the E-UAV in the previous time slot, the I-UAV determines its flight planning strategy, predicts the wiretap channel, and designs its communication resource allocation policy for the next time slot. To circumvent the severe coupling between these three tasks, a divide-and-conquer approach is adopted. The online navigation design has the objective to minimize the distance between the I-UAV and a pre-defined destination point considering kinematic and geometric constraints. Subsequently, given the predicted wiretap channel, the robust resource allocation design is formulated as an optimization problem to achieve the optimal trade-off between sensing and communication in the next time slot, while taking into account the wiretap channel prediction error and the quality-of-service (QoS) requirements of secure communication. Simulation results demonstrate the superior performance of the proposed design compared with baseline schemes and validate the benefits of integrating sensing and navigation into secure UAV communication systems., Comment: 30 pages, 20 figures, submitted to an IEEE journal for possible publication

Image-text retrieval in remote sensing aims to provide flexible information for data analysis and application. In recent years, state-of-the-art methods are dedicated to ``scale decoupling'' and ``semantic decoupling'' strategies to further enhance the capability of representation. However, these previous approaches focus on either the disentangling scale or semantics but ignore merging these two ideas in a union model, which extremely limits the performance of cross-modal retrieval models. To address these issues, we propose a novel Scale-Semantic Joint Decoupling Network (SSJDN) for remote sensing image-text retrieval. Specifically, we design the Bidirectional Scale Decoupling (BSD) module, which exploits Salience Feature Extraction (SFE) and Salience-Guided Suppression (SGS) units to adaptively extract potential features and suppress cumbersome features at other scales in a bidirectional pattern to yield different scale clues. Besides, we design the Label-supervised Semantic Decoupling (LSD) module by leveraging the category semantic labels as prior knowledge to supervise images and texts probing significant semantic-related information. Finally, we design a Semantic-guided Triple Loss (STL), which adaptively generates a constant to adjust the loss function to improve the probability of matching the same semantic image and text and shorten the convergence time of the retrieval model. Our proposed SSJDN outperforms state-of-the-art approaches in numerical experiments conducted on four benchmark remote sensing datasets.

In the 6G era, space-air-Ground integrated networks (SAGIN) are anticipated to deliver global coverage, necessitating support for a diverse array of emerging applications in high-mobility, hostile environments. Under such conditions, conventional orthogonal frequency division multiplexing (OFDM) modulation, widely employed in cellular and Wi-Fi communication systems, experiences performance degradation due to significant Doppler shifts. To overcome this obstacle, a novel two-dimensional (2D) modulation approach, namely orthogonal time frequency space (OTFS), has emerged as a key enabler for future high-mobility use cases. Distinctively, OTFS modulates information within the delay-Doppler (DD) domain, as opposed to the time-frequency (TF) domain utilized by OFDM. This offers advantages such as Doppler and delay resilience, reduced signaling latency, a lower peak-to-average ratio (PAPR), and a reduced-complexity implementation. Recent studies further indicate that the direct interplay between information and the physical world in the DD domain positions OTFS as a promising waveform for achieving integrated sensing and communications (ISAC). In this article, we present an in-depth review of OTFS technology in the context of the 6G era, encompassing fundamentals, recent advancements, and future directions. Our objective is to provide a valuable resource for researchers engaged in the field of OTFS., Comment: Survey paper on OTFS, accepted by China Communications; Cover paper of the 6th issue

Beamforming design for intelligent reflecting surface (IRS)-assisted multi-user communication (IRS-MUC) systems critically depends on the acquisition of accurate channel state information (CSI). However, channel estimation (CE) in IRS-MUC systems causes a large signaling overhead for training due to the large number of IRS elements. In this paper, taking into account user mobility, we adopt a deep learning (DL) approach to implicitly learn the historical line-of-sight (LoS) channel features and predict the IRS phase shifts to be adopted for the next time slot for maximization of the weighted sum-rate (WSR) of the IRS-MUC system. With the proposed predictive approach, we can avoid full-scale CSI estimation and facilitate low-dimensional CE for transmit beamforming design such that the signaling overhead is reduced by a scale of $\frac{1}{N}$, where $N$ is the number of IRS elements. To this end, we first develop a universal DL-based predictive beamforming (DLPB) framework featuring a two-stage predictive-instantaneous beamforming mechanism. As a realization of the developed framework, a location-aware convolutional long short-term memory (CLSTM) graph neural network (GNN) is developed to facilitate effective predictive beamforming at the IRS, where a CLSTM module is first adopted to exploit the spatial and temporal features of the considered channels and a GNN is then applied to empower the designed neural network with high scalability and generalizability. Furthermore, in the second stage, based on the predicted IRS phase shifts, an instantaneous CSI-aware fully-connected neural network is designed to optimize the transmit beamforming at the access point. Simulation results demonstrate that the proposed framework not only achieves a better WSR performance and requires a lower CE overhead compared with state-of-the-art benchmarks, but also is highly scalable in the numbers of users., Comment: 30 pages, 14 figures, journal paper

A conformal metric ${\rm d}s^{2}$ with finitely many conical singularities of constant Gaussian curvature $K=1$ on a compact Riemann surface is referred to as a spherical conical metric. When the associated monodromy group of ${\rm d}s^{2}$ is diagonalizable, we refer to ${\rm d}s^{2}$ as a reducible spherical conical metric. The simplest case of a reducible spherical conical metric is a `football', which denotes a 2-sphere with a spherical conical metric that has precisely two singularities separated by a distance of $\pi$. This study delves into the intrinsic geometric structure and existence of reducible spherical conical metrics on compact Riemann surfaces. We demonstrate that any such spherical surface can be divided into a finite number of pieces by cutting along a set of suitable geodesics, which connect the conical singularities and some smooth points of the metric. Especially, each piece is isometric to a portion obtained by cutting a football along a geodesic that joins the two conical singularities. As an application, an angle condition for the existence of such a metric is presented. Most notably, our study demonstrates the existence of a reducible spherical conical metric where all the saddle points of a Morse function are located on the same geodesic., Comment: 47 pages, 17 figures

The first two parts of this tutorial on orthogonal time frequency space (OTFS) modulation have discussed the fundamentals of delay-Doppler (DD) domain communications as well as some advanced technologies for transceiver design. In this letter, we will present an OTFS-based integrated sensing and communications (ISAC) system, which is regarded as an enabling technology in next generation wireless communications. In particular, we illustrate the sensing as well as the communication models for OTFS-ISAC systems. Next, we show that benefiting from time-invariant DD channels, the sensing parameters can be used for inferring the communication channels, leading to an efficient transmission scheme. As both functionalities are realized in the same DD domain, we briefly discuss several promising benefits of OTFS-based ISAC systems, which have not been completely unveiled yet. Finally, a range of potential applications of OTFS for the future wireless networks will be highlighted., Comment: 5 pages, 2 figures, submitted to IEEE Communications Letters

This letter is the first part of a three-part tutorial on orthogonal time frequency space (OTFS) modulation, which is a promising candidate waveform for future wireless networks. This letter introduces and compares two popular implementations of OTFS modulation, namely the symplectic finite Fourier transform (SFFT)- and discrete Zak transform (DZT)-based architectures. Based on these transceiver architectures, fundamental concepts of OTFS modulation, including the delay-Doppler (DD) domain, DD domain information multiplexing, and its potential benefits, are discussed. Finally, the challenges ahead for OTFS modulation are highlighted. Parts II and III of this tutorial on OTFS modulation focus on transceiver designs and integrated sensing and communication (ISAC), respectively., Comment: 6 pages, 2 figures, submitted to IEEE Communications Letters

The fundamental concepts and challenges of orthogonal time frequency space (OTFS) modulation have been reviewed in Part I of this three-part tutorial. In this second part, we provide an overview of the state-of-the-art transceiver designs for OTFS systems, with a particular focus on the cyclic prefix (CP) design, window design, pulse shaping, channel estimation, and signal detection. Furthermore, we analyze the performance of OTFS modulation, including the diversity gain and the achievable rate. Specifically, comparative simulations are presented to evaluate the error performance of different OTFS detection schemes, and the advantages of coded OTFS systems over coded orthogonal frequency-division multiplexing (OFDM) systems are investigated., Comment: 5 pages, 5 figures, submitted to IEEE Communications Letters

In \cite{WeiWu22-3} (J.Geom.Anal.32, 199(2022)), we classified HCMU surfaces in 3-dimensional Euclidean space as Weingarten surfaces by holomorphic functions. In this paper, using a totally different method from \cite{WeiWu22-3}, we will classify HCMU surfaces in 3-dimensional space forms as Weingarten surfaces. Moreover we will give a criteria of a Weingarten surface which is also an HCMU surface., Comment: 12pages

In this paper, an intelligent reflecting surface (IRS) is introduced to assist an unmanned aerial vehicle (UAV) communication system based on non-orthogonal multiple access (NOMA) for serving multiple ground users. We aim to minimize the average total system energy consumption by jointly designing the resource allocation strategy, the three dimensional (3D) trajectory of the UAV, as well as the phase control at the IRS. The design is formulated as a non-convex optimization problem taking into account the maximum tolerable outage probability constraint and the individual minimum data rate requirement. To circumvent the intractability of the design problem due to the altitude-dependent Rician fading in UAV-to-user links, we adopt the deep neural network (DNN) approach to accurately approximate the corresponding effective channel gains, which facilitates the development of a low-complexity suboptimal iterative algorithm via dividing the formulated problem into two subproblems and address them alternatingly. Numerical results demonstrate that the proposed algorithm can converge to an effective solution within a small number of iterations and illustrate some interesting insights: (1) IRS enables a highly flexible UAV's 3D trajectory design via recycling the dissipated radio signal for improving the achievable system data rate and reducing the flight power consumption of the UAV; (2) IRS provides a rich array gain through passive beamforming in the reflection link, which can substantially reduce the required communication power for guaranteeing the required quality-of-service (QoS); (3) Optimizing the altitude of UAV's trajectory can effectively exploit the outage-guaranteed effective channel gain to save the total required communication power enabling power-efficient UAV communications.

For decades, people are developing efficient numerical methods for solving the challenging quantum many-body problem, whose Hilbert space grows exponentially with the size of the problem. However, this journey is far from over, as previous methods all have serious limitations. The recently developed deep learning methods provide a very promising new route to solve the long-standing quantum many-body problems. We report that a deep learning based simulation protocol can achieve the solution with state-of-the-art precision in the Hilbert space as large as $2^{1296}$ for spin system and $3^{144}$ for fermion system , using a HPC-AI hybrid framework on the new Sunway supercomputer. With highly scalability up to 40 million heterogeneous cores, our applications have measured 94% weak scaling efficiency and 72% strong scaling efficiency. The accomplishment of this work opens the door to simulate spin models and Fermion models on unprecedented lattice size with extreme high precision., Comment: Massive ground state optimizations of CNN-based wave-functions for $J1$-$J2$ model and $t$-$J$ model carried out on a heterogeneous cores supercomputer

By constructing an ODE through a kind of meromorphic 1-forms, we will give an explicit construction of a kind of conformal metrics of constant curvature on Riemann surfaces with singularities. As an application, we will classify constant curvature one metrics on $S^{2}$ with two conical singularities, which was first proved by Troyanov in \cite{Tr89} by using projective connection., Comment: 8 pages