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Compact Ultramassive Antenna Array (CUMA) is a pioneering paradigm that leverages the flexibility of the Fluid Antenna System (FAS) to enable a simple multiple access scheme for massive connectivity without the need for precoding, power control at the base station or interference mitigation in each user's equipment. In order to overcome the mathematical intricacy required to analyze their performance, we use an asymptotic matching approach to relax such complexity with a remarkable accuracy. First, we analyze the performance of the CUMA network in terms of the outage probability (OP) and the ergodic rate (ER), deriving simple and highly accurate closed-form approximations to the channel statistics. Then, we evaluate the potential of the CUMA scheme to provide secure multi-user communications from a physical layer security perspective. Leveraging a tight approximation to the signal-to-interference-ratio (SIR) distribution, we derive closed-form expressions for the secrecy outage probability (SOP). We observe that the baseline CUMA (without side information processing) exhibits limited performance when eavesdroppers are equipped with a CUMA of the same type. To improve their secure performance, we suggest that a simple imperfect interference cancellation mechanism at the legitimate receiver may substantially increase the secrecy performance. Monte Carlo simulations validate our approximations and demonstrate their accuracy under different CUMA-based scenarios.

This paper examines the impact of emerging fluid antenna systems (FAS) on reconfigurable intelligent surface (RIS)-aided secure communications. Specifically, we consider a classic wiretap channel, where a fixed-antenna transmitter sends confidential information to an FAS-equipped legitimate user with the help of an RIS, while an FAS-equipped eavesdropper attempts to decode the message. To evaluate the proposed wireless scenario, we first introduce the cumulative distribution function (CDF) and probability density function (PDF) of the signal-to-noise ratio (SNR) at each node, using the central limit theorem and the Gaussian copula function. We then derive a compact analytical expression for the secrecy outage probability (SOP). Our numerical results reveal how the incorporation of FAS and RIS can significantly enhance the performance of secure communications.

This paper investigates a two-user downlink system for integrated sensing and communication (ISAC) in which the two users deploy a fluid antenna system (FAS) and adopt the nonorthogonal multiple access (NOMA) strategy. Specifically, the integrated sensing and backscatter communication (ISABC) model is considered, where a dual-functional base station (BS) serves to communicate the two users and sense a tag's surrounding. In contrast to conventional ISAC, the backscattering tag reflects the signals transmitted by the BS to the NOMA users and enhances their communication performance. Furthermore, the BS extracts environmental information from the same backscatter signal in the sensing stage. Firstly, we derive closed-form expressions for both the cumulative distribution function (CDF) and probability density function (PDF) of the equivalent channel at the users utilizing the moment matching method and the Gaussian copula. Then in the communication stage, we obtain closed-form expressions for both the outage probability and for the corresponding asymptotic expressions in the high signal-to-noise ratio (SNR) regime. Moreover, using numerical integration techniques such as the Gauss-Laguerre quadrature (GLQ), we have series-form expressions for the user ergodic communication rates (ECRs). In addition, we get a closed-form expression for the ergodic sensing rate (ESR) using the Cramer-Rao lower bound (CRLB). Finally, the accuracy of our analytical results is validated numerically, and we confirm the superiority of employing FAS over traditional fixed-position antenna systems in both ISAC and ISABC.

This article investigates the qualitative aspects of dark solitons of one-dimensional Gross-Pitaevskii equations with general nonlocal interactions, which correspond to traveling waves with subsonic speeds. Under general conditions on the potential interaction term, we provide uniform bounds, demonstrate the existence of symmetric solitons, and identify conditions under which monotonicity is lost. Additionally, we present new properties of black solitons. Moreover, we establish the nonlocal-to-local convergence, i.e. the convergence of the soliton of the nonlocal model toward the explicit dark solitons of the local Gross-Pitaevskii equation.

Generative AI (GenAI) models have demonstrated remarkable capabilities in a wide variety of medical tasks. However, as these models are trained using generalist datasets with very limited human oversight, they can learn uses of medical products that have not been adequately evaluated for safety and efficacy, nor approved by regulatory agencies. Given the scale at which GenAI may reach users, unvetted recommendations pose a public health risk. In this work, we propose an approach to identify potentially harmful product recommendations, and demonstrate it using a recent multimodal large language model., Comment: CVPR 2024 Responsible Generative AI (ReGenAI) workshop

We study for a dynamical system $f:X\longrightarrow X$ some of the principal topological recurrence-kind properties with respect to the induced maps $\overline{f}:\mathcal{K}(X)\longrightarrow\mathcal{K}(X)$, on the hyperspace of non-empty compact subsets of $X$, and $\hat{f}:\mathcal{F}(X)\longrightarrow\mathcal{F}(X)$, on the space of normal fuzzy sets consisting of the upper-semicontinuous functions $u:X\longrightarrow [0,1]$ with compact support and such that $u^{-1}(\{1\})\neq\varnothing$. In particular, we characterize the properties of topological and multiple recurrence for the extended systems $(\mathcal{K}(X),\overline{f})$ and $(\mathcal{F}(X),\hat{f})$. Special attention is given to the case where the underlying space is completely metrizable, for which we obtain some stronger point-recurrence equivalences., Comment: 17 pages

We introduce and characterize the operational diversity order (ODO) in fading channels, as a proxy to the classical notion of diversity order at any arbitrary operational signal-to-noise ratio (SNR). Thanks to this definition, relevant insights are brought up in a number of cases: (i) We quantify that in dominant line-of-sight scenarios an increased diversity order is attainable compared to that achieved asymptotically, even in the single-antenna case; (ii) this effect is attenuated, but still visible, in the presence of an additional dominant specular component; (iii) the decay slope in Rayleigh product channels increases very slowly, never fully achieving unitary slope for a finite SNR.

This paper investigates the performance of physical layer security (PLS) in fluid antenna-aided communication systems under arbitrary correlated fading channels. In particular, it is considered that a single fixed-antenna transmitter aims to send confidential information to a legitimate receiver equipped with a planar fluid antenna system (FAS), while an eavesdropper, also taking advantage of a planar FAS, attempts to decode the desired message. For this scenario, we first present analytical expressions of the equivalent channel distributions at the legitimate user and eavesdropper by using copula, so that the obtained analytical results are valid for any arbitrarily correlated fading distributions. Then, with the help of Gauss-Laguerre quadrature, we derive compact analytical expressions for the average secrecy capacity (ASC), the secrecy outage probability (SOP), and the secrecy energy efficiency (SEE) for the FAS wiretap channel. Moreover, for exemplary purposes, we also obtain the compact expression of ASC, SOP, and SEE by utilizing the Gaussian copula under correlated Rayleigh fading channels as a special case. Eventually, numerical results indicate that applying the fluid antenna with only one activated port to PLS can guarantee more secure and reliable transmission, when compared to traditional antenna systems (TAS) exploiting maximal ratio combining (MRC) and antenna selection (AS) under selection combining (SC).

We construct continuous (and even invertible) linear operators acting on Banach (even Hilbert) spaces whose restrictions to their respective closed linear subspaces of chain recurrent vectors are not chain recurrent operators. This construction completely solves in the negative a problem posed by Nilson C. Bernardes Jr. and Alfred Peris on chain recurrence in Linear Dynamics. In particular: we show that the non-invertible case can be directly solved via relatively simple weighted backward shifts acting on certain unrooted directed trees; then we modify the non-invertible counterexample to address the invertible case, but falling outside the class of weighted shift operators; and we finally show that this behaviour cannot be achieved via classical (unilateral neither bilateral) weighted backward sifts (acting on $\mathbb{N}$ and $\mathbb{Z}$ respectively) by noticing that a classical shift is a chain recurrent operator whenever it admits a non-zero chain recurrent vector., Comment: 17 pages

Motivated by recent investigations of Sophie Grivaux and \'Etienne Matheron on the existence of invariant measures in Linear Dynamics, we introduce the concept of locally bounded orbit for a continuous linear operator $T:X\longrightarrow X$ acting on a Fr\'echet space $X$, and we use this new notion to construct (non-trivial) $T$-invariant probability Borel measures on $(X,\mathscr{B}(X))$., Comment: 22 pages

In Mediterranean countries of Southern Europe, the climatic conditions are usually favourable to cultivate greenhouse vegetables but not always for workers. The aim of this study was to design a network of weather stations capable of gathering data of environmental parameters related to the wellbeing of workers in greenhouses in south-eastern Spain. The unevenness of the thermal environment was studied both vertically as well as horizontally following guideline ISO 7726. The results indicate that the greenhouse should be considered a heterogeneous environment, implying that, for an evaluation of the environmental conditions related to thermal stress of the workers inside the greenhouse, measurements should be taken at different points within the greenhouse at three heights (ankle, abdomen, and head)., Comment: 47 pages, 15 figures

This letter investigates the application of the emerging fluid antenna (FA) technology in multiuser communication systems when side information (SI) is available at the transmitters. In particular, we consider a K-user dirty multiple access channel (DMAC) with non-causally known SI at the transmitters, where K users send independent messages to a common receiver with a FA capable of changing its location depending on the channel condition. By connecting Jakes' model to copula theory through Spearman's {\rho} rank correlation coefficient, we accurately describe the spatial correlation between the FA channels, and derive a closed-form expression for the outage probability (OP) under Fisher-Snedecor F fading. Numerical results illustrate how considering FA can improve the performance of multiuser communication systems in terms of the OP and also support a large number of users using only one FA at the common receiver in a few wavelengths of space.

We solve in the negative two open problems, related to the linear and topological structure of the set of recurrent vectors, asked by Sophie Grivaux, Alfred Peris and the first author of this paper. Firstly, we show that there exist recurrent operators whose set of recurrent vectors is not dense lineable; and secondly, we construct operators which are reiteratively recurrent and cyclic, but whose set of reiteratively recurrent vectors is meager., Comment: 17 pages

This paper investigates the performance of a single-user fluid antenna system (FAS), by exploiting a class of elliptical copulas to describe the dependence structure amongst the fluid antenna positions (ports). By expressing the well-known Jakes' model in terms of the Gaussian copula, we consider two cases: (i) the general case, i.e., any arbitrary correlated fading distribution; and (ii) the specific case, i.e., correlated Nakagami-$m$ fading. For both scenarios, we first derive analytical expressions for the cumulative distribution function (CDF) and probability density function (PDF) of the equivalent channel in terms of multivariate normal distribution. Then we obtain the outage probability (OP) and the delay outage rate (DOR) to analyze the performance of FAS. By employing the popular rank correlation coefficients such as Spearman's $\rho$ and Kendall's $\tau$ , we measure the degree of dependency in correlated arbitrary fading channels and illustrate how the Gaussian copula can be accurately connected to Jakes' model in FAS. Our numerical results demonstrate that increasing the size of FAS provides lower OP and DOR, but the system performance saturates as the number of antenna ports increases. In addition, our results indicate that FAS provides better performance compared to conventional single-fixed antenna systems even when the size of fluid antenna is small.

In this work, we analyze how the use of companding techniques, together with digital predistortion (DPD), can be leveraged to improve system efficiency and performance in simultaneous wireless information and power transfer (SWIPT) systems based on power splitting. By taking advantage of the benefits of each of these well-known techniques to mitigate non-linear effects due to power amplifier (PA) and energy harvesting (EH) operation, we illustrate how DPD and companding can be effectively combined to improve the EH efficiency while keeping unalterable the information transfer performance. We establish design criteria that allow the PA to operate in a higher efficiency region so that the reduction in peak-to-average power ratio over the transmitted signal is translated into an increase in the average radiated power and EH efficiency. The performance of DPD and companding techniques is evaluated in a number of scenarios, showing that a combination of both techniques allows to significantly increase the power transfer efficiency in SWIPT systems., Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible

As new wireless standards are developed, the use of higher operation frequencies comes in hand with new use cases and propagation effects that differ from the well-established state of the art. Numerous stochastic fading models have recently emerged under the umbrella of generalized fading conditions, to provide a fine-grain characterization of propagation channels in the mmWave and sub-THz bands. For the first time in literature, this work carries out an experimental validation of a class of such ray-based models, in a wide range of propagation conditions (anechoic, reverberation and indoor) at mmWave bands. We show that the independently fluctuating two-ray (IFTR) model has good capabilities to recreate rather dissimilar environments with high accuracy. We also put forth that the key limitations of the IFTR model arise in the presence of reduced diffuse propagation, and also due to a limited phase variability for the dominant specular components., Comment: 14 pages, 13 figures

We provide an analytical characterization of the coverage region of simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS)-aided two-user downlink communication systems. The cases of orthogonal multiple access (OMA) and non-orthogonal multiple access (NOMA) are considered, under the energy-splitting (ES) protocol. Results confirm that the use of STAR-RISs is beneficial to extend the coverage region, and that the use of NOMA provides a better performance compared to the OMA counterpart.

In this letter, we study the performance of a single-user fluid antenna system (FAS) under arbitrary fading distributions, in which the fading channel coefficients over the ports are correlated. We adopt copula theory to model the structure of dependency between fading coefficients. Specifically, we first derive an exact closed-from expression for the outage probability in the most general case, i.e., for any arbitrary choice of fading distribution and copula. Afterwards, for an important specific case, we analyze the performance of the outage probability under correlated Nakagami-$m$ fading channels by exploiting popular Archimedean copulas, namely, Frank, Clayton, and Gumbel. The results demonstrate that FAS outperforms the conventional single fixed-antenna system in terms of the outage probability. We also see that the spatial correlation dependency structure for the FAS is a key factor to determine its performance, which is natively captured through the choice of copula.

We introduce and characterize the Multi-cluster Two-Wave (MTW) fading model, which generalizes \textit{both} the Durgin's Two-Wave with Diffuse Power (TWDP) and the $\kappa$-$\mu$ models under a common umbrella. The MTW model consists of an arbitrary number of clusters of waves each of which may include one or two dominant (specular) components. The chief probability functions of the MTW fading model are obtained, including the probability density function, the cumulative distribution function and the generalized moment-generating function. \textcolor{black}{The proposed model is empirically validated using channel measurements in the sub-THz band and} a number of applications are exemplified, including the outage probability in noise-limited and interference-limited scenarios and the energy detection probability. %Exact expressions for the outage capacity are also obtained. A composite Inverse Gamma (IG)/MTW model is also investigated, thus extending the proposed propagation model to include shadowing., Comment: This work has been submitted to the IEEE for publication. Copyright may be transferred without notice, after which this version may no longer be accessible

The existence and decay properties of dark solitons for a large class of nonlinear nonlocal Gross-Pitaevskii equations with nonzero boundary conditions in dimension one has been established recently in [de Laire and S. L\'opez-Mart\'inez, Comm. Partial Differential Equations, 2022]. Mathematically, these solitons correspond to minimizers of the energy at fixed momentum and are orbitally stable. This paper provides a numerical method to compute approximations of such solitons for these types of equations, and provides actual numerical experiments for several types of physically relevant nonlocal potentials. These simulations allow us to obtain a variety of dark solitons, and to comment on their shapes in terms of the parameters of the nonlocal potential. In particular, they suggest that, given the dispersion relation, the speed of sound and the Landau speed are important values to understand the properties of these dark solitons. They also allow us to test the necessity of some sufficient conditions in the theoretical result proving existence of the dark solitons., Comment: 33 figures

We present a generalization of the notoriously unwieldy second-order scattering fading model, which is helpful to alleviate its mathematical complexity while providing an additional degree of freedom. This is accomplished by allowing its dominant specular component associated to line-of-sight propagation to randomly fluctuate. The statistical characterization of the newly proposed model is carried out, providing closed-form expressions for its probability and cumulative distribution functions, as well as for its generalized Laplace-domain statistics and raw moments. We exemplify how performance analysis can be done in this scenario, and discuss the role of the fading model parameters on system performance., Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible

We propose an algorithm for joint precoding and user selection in multiple-input multiple-output systems with extremely-large aperture arrays, assuming realistic channel conditions and imperfect channel estimates. The use of long-term channel state information (CSI) for user scheduling, and a proper selection of the set of users for which CSI is updated allow for obtaining an improved achievable sum spectral efficiency. We also confirm that the effect of imperfect CSI in the precoding vector design and the cost of training must be taken into consideration for realistic performance prediction., Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible

Single molecule localization microscopy relies on the precise quantification of the position of single dye emitters in a sample. This precision is improved by the number of photons that can be detected from each molecule. It is therefore recommendable to increase illumination times for the recording process. Particularly recording at cryogenic temperatures dramatically reduces photobleaching and thereby allows a massive increase in illumination times to several seconds. As a downside, microscope instabilities may well introduce jitter during such long illuminations, deteriorating the localization precision. In this paper, we theoretically demonstrate that a parallel recording of fiducial marker beads together with a novel fitting approach accounting for the full drift trajectory allows for largely eliminating drift effects for drift magnitudes of several hundred nanometers per frame., Comment: 12 pages, 7 figures

We study the spaceability of the set of recurrent vectors $\text{Rec}(T)$ for an operator $T:X\longrightarrow X$ on a Banach space $X$. In particular: we find sufficient conditions for a quasi-rigid operator to have a recurrent subspace; when $X$ is a complex Banach space we show that having a recurrent subspace is equivalent to the fact that the essential spectrum of the operator intersects the closed unit disc; and we extend the previous result to the real case. As a consequence we obtain that: a weakly-mixing operator on a real or complex separable Banach space has a hypercyclic subspace if and only if it has a recurrent subspace. The results exposed exhibit a symmetry between the hypercyclic and recurrence spaceability theories showing that, at least for the spaceable property, hypercyclicity and recurrence can be treated as equals., Comment: 24 pages

We study, for a continuous linear operator $T$ on an F-space $X$, when the direct sum operator $T\oplus T$ is recurrent on $X\oplus X$. In particular: we establish the analogous notion, for recurrence, to that of (topological) weak-mixing for transitivity/hypercyclicity, namely quasi-rigidity; and we construct a recurrent but not quasi-rigid operator on each separable infinite-dimensional Banach space, solving the $T\oplus T$-recurrence problem in the negative way. The quasi-rigidity notion is closely related to the dense lineability of the set of recurrent vectors, and using similar conditions we study the lineability and dense lineability properties for the set of $\mathcal{F}$-recurrent vectors, under very weak assumptions on the Furstenberg family $\mathcal{F}$., Comment: 37 pages

We introduce a new class of fading channels, built as the superposition of two fluctuating specular components with random phases, plus a clustering of scattered waves: the Multi-cluster Fluctuating Two-Ray (MFTR) fading channel. The MFTR model emerges as a natural generalization of both the fluctuating two-ray (FTR) and the $\kappa$-$\mu$ shadowed fading models through a more general yet equally mathematically tractable model. This generalization enables the presence of additional multipath clusters in the purely ray-based FTR model, and the convenience of the new underlying fading channel model is discussed in depth. Then, we derive all the chief probability functions of the MFTR model (e.g., probability density function (PDF), cumulative density function (CDF), and moment generation function) in closed-form, having {a mathematical complexity similar to} other fading models in the state-of-the-art. We also provide two additional analytical formulations for the PDF and the CDF: (i) in terms of a continuous mixture of $\kappa$-$\mu$ shadowed distributions, and (ii) as an infinite discrete mixture of Gamma distributions. Such expressions enable to conduct performance analysis under MFTR fading by directly leveraging readily available results for the $\kappa$-$\mu$ shadowed or Nakagami-$m$ cases, respectively. The performance of wireless communications systems undergoing MFTR fading is exemplified in terms of a classical benchmarking metric like the outage probability, both in exact and asymptotic forms, and the amount of fading., Comment: This work was submitted to the IEEE for publication on May 31, 2022. Copyright may be transferred without notice, after which this version may no longer be accessible