arXiv Math @arxiv_math@qoto.org

In the realm of 5G communication systems, the accuracy of Channel State Information (CSI) prediction is vital for optimizing performance. This letter introduces a pioneering approach: the Spectral-Temporal Graph Neural Network (STEM GNN), which fuses spatial relationships and temporal dynamics of the wireless channel using the Graph Fourier Transform. We compare the STEM GNN approach with conventional Recurrent Neural Network (RNN) and Long Short-Term Memory (LSTM) models for CSI prediction. Our findings reveal a significant enhancement in overall communication system performance through STEM GNNs. For instance, in one scenario, STEM GNN achieves a sum rate of 5.009 bps/Hz which is $11.9\%$ higher than that of LSTM and $35\%$ higher than that of RNN. The spectral-temporal analysis capabilities of STEM GNNs capture intricate patterns often overlooked by traditional models, offering improvements in beamforming, interference mitigation, and ultra-reliable low-latency communication (URLLC).

The A-channel is a noiseless multiple access channel in which users simultaneously transmit Q-ary symbols and the receiver observes the set of transmitted symbols, but not their multiplicities. An A-channel is said to be unsourced if, additionally, users transmissions are encoded across time using a common codebook and decoding of the transmitted messages is done without regard to the identities of the active users. An interesting variant of the unsourced A-channel is the unsourced A-channel with erasures (UACE), in which transmitted symbols are erased with a given independent and identically distributed probability. In this paper, we focus on designing a code that enables a list of transmitted codewords to be recovered despite the erasures of some of the transmitted symbols. To this end, we propose the linked-loop code (LLC), which uses parity bits to link each symbol to the previous M symbols in a tail-biting manner, i.e., the first symbols of the transmission are linked to the last ones. The decoding process occurs in two phases: the first phase decodes the codewords that do not suffer from any erasures, and the second phase attempts to recover the erased symbols using the available parities. We compare the performance of the LLC over the UACE with other codes in the literature and argue for the effectiveness of the construction. Our motivation for studying the UACE comes from its relevance in machine-type communication and coded compressed sensing.

Due to 5G deployment, there is significant interest in LDPC decoding. While much research is devoted on efficient hardwiring of algorithms based on Belief Propagation (BP), it has been shown that LDPC decoding can be formulated as a combinatorial optimization problem, which could benefit from significant acceleration of physical computation mechanisms such as Ising machines. This approach has so far resulted in poor performance. This paper shows that the reason is not fundamental but suboptimal hardware and formulation. A co-designed Ising machine-based system can improve speed by 3 orders of magnitude. As a result, a physical computation approach can outperform hardwiring state-of-the-art algorithms. In this paper, we show such an augmented Ising machine that is 4.4$\times$ more energy efficient than the state of the art in the literature.

In this article we consider 2-dimensional surfaces. We define some new operators which enable us to evaluate quantities of the surface, such invariants, in a more systematic way.

Perceptive mobile network (PMN) is an emerging concept for next-generation wireless networks capable of conducting integrated sensing and communication (ISAC). A major challenge for realizing high performance sensing in PMNs is how to deal with spatially separated asynchronous transceivers. Asynchronicity results in timing offsets (TOs) and carrier frequency offsets (CFOs), which further cause ambiguity in ranging and velocity sensing. Most existing algorithms mitigate TOs and CFOs based on the line-of-sight (LOS) propagation path between sensing transceivers. However, LOS paths may not exist in realistic scenarios. In this paper, we propose a cooperation based joint active and passive sensing scheme for the non-LOS (NLOS) scenarios having asynchronous transceivers. This scheme relies on the cross-correlation cooperative sensing (CCCS) algorithm, which regards active sensing as a reference and mitigates TOs and CFOs by correlating active and passive sensing information. Another major challenge for realizing high performance sensing in PMNs is how to realize high accuracy angle-of-arrival (AoA) estimation with low complexity. Correspondingly, we propose a low complexity AoA algorithm based on cooperative sensing, which comprises coarse AoA estimation and fine AoA estimation. Analytical and numerical simulation results verify the performance advantages of the proposed CCCS algorithm and the low complexity AoA estimation algorithm.

We developed a pilot course focused on mathematical modeling within the tertiary education framework, with a distinct emphasis on sustainability and sustainable development. While an applicable textbook exists for this liberal arts course, it is noticeable that numerous examples within it are not directly aligned with sustainability concerns. To address this gap, our study strategically integrated the teaching and learning of modeling by carefully selecting classroom examples that closely align with the context of sustainability. By employing an innovative and adaptable approach to the course content delivery, we fostered interdisciplinary collaboration among students, improved their comprehension, and enhanced their interdisciplinary skills.

This paper considers a nonlinear model for population dynamics with age structure. The fertility rate with respect to age is non constant and has the form proposed by [17]. Moreover, its multiplicative structure and the multiplicative structure of mortality makes the model separable. In this setting it is shown that the number of births in unit time is given by a system of nonlinear ordinary differential equations. The steady state solution together with the equilibrium solution is found explicitly.

We introduce Pura Vida Neutrosophic Algebra, an algebraic structure consisting of neutrosophic numbers equipped with two binary operations namely addition and multiplication. The addition can be calculated sometimes with the function min and other times with the max function. The multiplication operation is the usual sum between numbers. Pura Vida Neutrosophic Algebra is an extension of both Tropical Algebra (also known as Min-Plus, or Min-Algebra) and Max-Plus Algebra (also known as Max-algebra). Tropical and Max-Plus algebras are algebraic structures included in semirings and their operations can be used in matrices and vectors. Pura Vida Neutrosophic Algebra is included in Neutrosophic semirings and can be used in Neutrosophic matrices and vectors

Integrated sensing and communication (ISAC) is considered as the potential key technology of the future mobile communication systems. The signal design is fundamental for the ISAC system. The reference signals in mobile communication systems have good detection performance, which is worth further research. Existing studies applied the single reference signal to radar sensing. In this paper, a multiple reference signals collaborative sensing scheme is designed. Specifically, we jointly apply channel state information reference signal (CSI-RS), positioning reference signal (PRS) and demodulation reference signal (DMRS) in radar sensing, which improve the performance of radar sensing via obtaining continuous time-frequency resource mapping. Crámer-Rao lower bound (CRLB) of the joint reference signal for distance and velocity estimation is derived. The impacts of carrier frequency and subcarrier spacing on the performance of distance and velocity estimation are revealed. The results of simulation experiments show that compared with the single reference signal sensing scheme, the multiple reference signals collaborative sensing scheme effectively improves the sensing accuracy. Moreover, because of the discontinuous OFDM symbols, the accuracy of velocity estimation could be further improved via compressed sensing (CS). This paper has verified that multiple reference signals, instead of single reference signal, have much more superior performance on radar sensing, which is a practical and efficient approach in designing ISAC signal.

In a recent paper "Solvability of equations in elementary functions" [arXiv:1911.10409] the insolvability in elementary functions of equation $\tan(x) - x = a$ was proved. This work applies the same topological method to prove the insolvability of equation $x^x = a$.

Understanding the linear growth of disturbances due to external forcing is crucial for flow stability analysis, flow control, and uncertainty quantification. These applications typically require a large number of forward simulations of the forced linearized dynamics, often in a brute-force fashion. When dealing with simple steady-state or periodic base flows, there exist powerful and cost-effective solution operator techniques. Once constructed, these operators can be used to determine the response to various forcings with negligible computational cost. However, these methods are not applicable to problems with arbitrarily time-dependent base flows. This paper develops and investigates reduced-order modeling with time-dependent bases (TDBs) to build low-rank solution operators for forced linearized dynamics with arbitrarily time-dependent base flows. In particular, we use forced optimally time-dependent decomposition (f-OTD), which extracts the time-dependent correlated structures of the flow response to various excitations. We also demonstrate that in the case of a steady-state mean flow subject to harmonic forcing, the f-OTD subspace converges to the dominant resolvent analysis modes. The demonstration includes four cases: a toy model, the Burgers equation, the 2D temporally evolving jet, and two-dimensional decaying isotropic turbulence. In these cases, we demonstrate the utility of the low-rank operator for (i) identifying the excitation that leads to maximum amplification, and (ii) reconstructing the full-state flow without incurring additional cost.

Wireless backhaul offers a more cost-effective, time-efficient, and reconfigurable solution than wired backhaul to connect the edge-computing cells to the core network. As the amount of transmitted data increases, the low-rank characteristic of Line-of-Sight (LoS) channel severely limits the growth of channel capacity in the point-to-point backhaul transmission scenario. Orbital Angular Momentum (OAM), also known as vortex beam, is considered a potentially effective solution for high-capacity LoS wireless transmission. However, due to the shortcomings of its energy divergence and the specificity of multi-mode divergence angles, OAM beams have been difficult to apply in practical communication systems for a long time. In this work, a novel multi-mode convergent transmission with co-scale reception scheme is proposed. OAM beams of different modes can be transmitted with the same beam divergent angle, while the wavefronts are tailored by the ring-shaped Airy compensation lens during propagation, so that the energy will converge to the same spatial area for receiving. Based on this scheme, not only is the Signal-to-Noise Ratio (SNR) greatly improved, but it is also possible to simultaneously receive and demodulate OAM channels multiplexed with different modes in a limited space area. Through prototype experiments, we demonstrated that 3 kinds of OAM modes are tunable, and different channels can be separated simultaneously with receiving power increasing. The measurement isolations between channels are over 11 dB, which ensures a reliable 16-QAM multiplexing wireless transmission demo system. This work may explore the potential applications of OAM-based multi-mode convergent transmission in LoS wireless communications.

In this work, we study the Wasserstein gradient flow of the Riesz energy defined on the space of probability measures. The Riesz kernels define a quadratic functional on the space of measure which is not in general geodesically convex in the Wasserstein geometry, therefore one cannot conclude to global convergence of the Wasserstein gradient flow using standard arguments. Our main result is the exponential convergence of the flow to the minimizer on a closed Riemannian manifold under the condition that the logarithm of the source and target measures are H{ö}lder continuous. To this goal, we first prove that the Polyak-Lojasiewicz inequality is satisfied for sufficiently regular solutions. The key regularity result is the global in-time existence of H{ö}lder solutions if the initial and target data are H{ö}lder continuous, proven either in Euclidean space or on a closed Riemannian manifold. For general measures, we prove using flow interchange techniques that there is no local minima other than the global one for the Coulomb kernel. In fact, we prove that a Lagrangian critical point of the functional for the Coulomb (or Energy distance) kernel is equal to the target everywhere except on singular sets with empty interior. In addition, singular enough measures cannot be critical points.

In this paper we study the local wellposedness of the solution to a non-linear parabolic-dispersive coupled system which models a Micro-Electro-Mechanical System (MEMS). A simple electrostatically actuated MEMS capacitor device has two parallel plates separated by a gas-filled thin gap. The nonlinear parabolic-dispersive coupled system modelling the device consists of a quasilinear parabolic equation for the gas pressure and a semilinear plate equation for gap width. We show the local-in-time existence of strict solutions for the system, by combining a local-in-time existence result for the dispersive equation, Hölder continuous dependence of its solution on that of the parabolic equation, and then local-in-time existence for a resulting abstract parabolic problem. Semigroup approaches are vital for both main parts of the problem.

In this paper we improve and complement a result by Móricz and Siddiqi \cite{Mor}. In particular, we prove that their estimate of the Nörlund means with respect to the Vilenkin system holds also without their additional condition. Moreover, we prove a similar approximation result in Lebesgue spaces for any $1\leq p<\infty$.

In this article, thermal bioconvection in a rotating phototactic medium is analyzed with a stress-free top and rigid upper boundary. The suspension rotates with a uniform angular velocity around a vertical axis. Utilizing MATLAB's bvp$4$c solver, neutral and growth rate curves are analyzed, emphasizing the impacts of parameters such as the Taylor number, thermal Rayleigh number, Lewis number, and critical total intensity. It is observed that generally critical bioconvection Rayleigh number increases with increasing Taylor number and Lewis number while decreasing with higher thermal Rayleigh number and critical total intensity. The critical thermal Rayleigh number appears to remain unaffected by variations in the critical total intensity and Lewis number. However, it is notably influenced by changes in the Taylor number.

The aim of the present paper is to prove whose smallness conditions being necessary in order to get the final result of existence of a solution. In the first part, we present the model for a proton exchange membrane fuel cell (PEMFC) single cell and we clarify the interactions of the different components namely, velocity, pressure, density, temperature and potential. The final mathematical model is a quasilinear elliptic system where the cross effects have a strong interlink. It consists of the Stokes--Darcy system altogether with thermoelectrochemical system under some non-standard interface and boundary conditions. The proof of existence of weak solutions relies on the Tychonof fixed point theorem, by providing some regularity and some smallness conditions. The actual system is divided into two systems of equations and they are separately studied. The novelty of the present work is to establish quantitative estimates for improving the technical hypotheses and, in particular, the smallness conditions in the two-dimensional case. Indeed, the smallness conditions only can be explicit if quantitative estimates are established. To this aim, we establish quantitative estimates for the Poincaré and Sobolev inequalities and for some trilinear terms.

In this paper we are interested in the coupled wave and Klein-Gordon equations in $\mathbb{R}^+\times\mathbb{R}^2$. We want to establish the global well-posedness of such system by showing the uniform boundedness of the energy for the global solution without any compactness assumptions on the initial data. In addition, we also demonstrate the pointwise asymptotic behavior of the solution pair. In order to achieve that we apply a modified Alinhac's ghost weight method together with a newly developed normal-form framework to remedy the lack of the space-time scaling vector field. Finally we show the global solutions scatter linearly strongly for the Klein-Gordon field $ϕ$ and weakly for the wave field $n$ as $t\to+\infty$. To our best knowledge such scattering phenomenon is novel in the literature.

Each point of a simplex is expressed as a unique convex combination of the vertices. The coefficients in the combination are the barycentric coordinates of the point. For each point in a general convex polytope, there may be multiple representations, so its barycentric coordinates are not necessarily unique. There are various schemes to fix particular barycentric coordinates: Gibbs, Wachspress, cartographic, etc. In this paper, a method for producing sparse barycentric coordinates in polytopes will be discussed. It uses a purely algebraic treatment of affine spaces and convex sets, with barycentric algebras. The method is based on a certain decomposition of each finite-dimensional convex polytope into a union of simplices of the same dimension.

In this paper, we consider the fractional Navier-Stokes equations. We extend a previous non-uniqueness result due to Cheskidov and Luo, found in [5], from Navier-Stokes to the fractional case, and from $L^1$-in-time, $W^{1,q}$-in-space solutions for every $q > 1$ to $L^s$-in-time, $W^{1,q}$-in-space solutions for appropriate ranges of $s,q$.