Search Results (59)

Ultrasonic wave attenuation in biological tissues arises from complex interactions between mechanical, structural, and fluidic properties, making it essential to identify dominant mechanisms for accurate simulation and device design. This work introduces a novel integration of experimentally measured tissue parameters into time-explicit nonlinear acoustic wave simulations, in which the equations are directly solved in the time domain using an explicit solver. This approach captures the full transient waveform without relying on frequency-domain simplifications, offering a more realistic representation of ultrasound propagation in heterogeneous media. The study estimates both sound diffusivity and viscous damping parameters (dynamic and bulk viscosity) for a broad range of ex vivo tissues (skin, adipose tissue, skeletal muscle, trabecular/cortical bone, liver, myocardium, kidney, tendon, ligament, cartilage, and gray/white brain matter). Four regression models (power law, linear, exponential, logarithmic) were applied to characterize their frequency dependence between 0.5 and 5 MHz. Results show that attenuation is more strongly driven by bulk viscosity than dynamic viscosity, particularly in fluid-rich tissues such as liver and myocardium, where compressional damping dominates. The power-law model consistently provided the best fit for all attenuation metrics, revealing a scale-invariant frequency relationship. Tissues such as cartilage and brain showed weaker viscous responses, suggesting the need for alternative modeling approaches. These findings not only advance fundamental understanding of attenuation mechanisms but also provide validated parameters and modeling strategies to improve predictive accuracy in therapeutic ultrasound planning and the design of non-invasive, tissue-specific acoustic devices. Full article

In this paper, time series of length T are seen as frequency distributions. Each distribution is defined with respect to a statistical variable having T observed values. A methodological system based on Gini’s approach is put forward, so the statistical model through which time series are handled is a frequency distribution studied inside a linear system. In addition to the starting frequency distributions that are observed, other frequency distributions are treated. Thus, marginal distributions based on the notion of proportionality are introduced together with joint distributions. Both distributions are statistical models. A fundamental invariance property related to marginal distributions is made explicit in this research work, so one can focus on collections of marginal frequency distributions, identifying multiple frequency distributions. For this reason, the latter is studied via a tensor. As frequency distributions are practical realizations of nonparametric probability distributions over $\mathbb{R}$, one passes from frequency distributions to discrete random variables. In this paper, a mathematical model that generates time series is put forward. It is a stochastic process based on subjective previsions of random variables. A subdivision of the exchangeability of variables of a statistical nature is shown, so a reinterpretation of principal component analysis that is based on the notion of proportionality also characterizes this research work. Full article

In a previous work, we identified the importance of rotation invariance in the standard complex-valued theory of linear time-invariant (LTI) systems and proposed a generalized vector-valued (VV) definition of convolution that reinterprets the complex-valued product of the traditional formalism as a scale rotation within the framework of geometric algebra. Based on this convolution definition, we characterized linear rotation-invariant time-invariant (LRITI) systems by defining and using a VV impulse response—effectively generalizing time-domain analysis for VV signals and LRITI systems. In this work, we provide a compatible frequency-domain analysis for VV signals and LRITI systems. First, VV bivector exponential signals are shown to be eigenfunctions of LRITI systems. A Fourier transform is defined, and we propose two generalized definitions of frequency response: the first valid for bivector exponentials in an arbitrary plane and the second valid for a general signal decomposed into a set of totally orthogonal planes (TOPs). Finally, we establish a convolution property for the Fourier transform with respect to TOPs. Together, these results provide compatible time-domain and frequency-domain analyses, thereby enabling a more comprehensive analysis of VV signals and LRITI systems. Full article

The acoustic scattering of targets in shallow-sea waveguides exhibits complex features such as multipath propagation and intricate echo components, with its acoustic field properties remaining incompletely understood. This study employs a hybrid method combining normal modes and scattering functions to numerically model the acoustic scattering of targets in waveguide channels. We analyze the coupling mechanisms of multipath acoustic waves and derive precise predictive formulas for the bright–dark interference fringe patterns in range–frequency spectra based on the physical mechanisms governing acoustic field interference. By tracking the peak trajectories of these interference fringes in range–frequency spectra, we investigate the variations of the waveguide invariant with frequency, range, and depth, revealing statistical patterns of the waveguide invariant in target–waveguide coupled scattering fields under different water depths. The results demonstrate that, under constant channel conditions, waveguide properties exhibit a weak correlation with target material characteristics. In shallow water environments, waveguide invariant values display broader distributions with higher probability density peaks, whereas increasing water depth progressively narrows the distribution range and monotonically reduces the peak magnitudes of the probability density function. Experimental validation via scaled elastic target echo testing confirms the observed trends of waveguide invariant variation with water depth. Full article

We consider spaces of smooth functions obtained by relaxing Gevrey-type regularity and decay conditions. It is shown that these classes can be introduced by using the general framework of the weighted matrices approach to ultradifferentiable functions. We examine alternative descriptions of Gelfand–Shilov spaces related to the extended Gevrey regularity and derive their nuclearity. In addition to the Fourier transform invariance property, we present their corresponding symmetric characterizations. Finally, we consider some time–frequency representations of the introduced classes of ultradifferentiable functions. Full article

The Banach Gelfand Triple $(S_0,L^2,S_0^{\prime })$ consists of the Feichtinger algebra $S_0\left(R^d\right)$ as a space of test functions, the dual space $S_0^{\prime }\left(R^d\right)$, known as the space of mild distributions, and the intermediate Hilbert space $L^2\left(R^d\right)$. This Gelfand Triple is very useful for the description of mathematical problems in the area of time-frequency analysis, but also for classical Fourier analysis and engineering applications. Because the involved spaces are Banach spaces, we speak of a Banach Gelfand Triple, in contrast to the widespread concept of rigged Hilbert spaces, which usually involve nuclear Frechet spaces. Still, both concepts serve very similar purposes. Based on the manifold properties of $S_0\left(R^d\right)$, it has found applications in the derivation of mathematical statements related to Gabor Analysis but also in providing an alternative and more lucid description of classical results, such as the Shannon sampling theory, with a potential to renew the way how Fourier and time-frequency analysis, but also signal processing courses for engineers (or physicists and mathematicians) could be taught in the future. In the present study, we will demonstrate that one could choose a relatively large variety of similar Banach Gelfand Triples, even if one wants to include key properties such as Fourier invariance (an extended version of Plancherel’s Theorem). Some of them appeared naturally in the literature. It turns out, that $S_0\left(R^d\right)$ is the smallest member of this family. Consequently $S_0^{\prime }\left(R^d\right)$ is the largest dual space among all these spaces, which may be one of the reasons for its universal usefulness. This article provides a study of the basic properties following from a short list of relatively simple assumptions and gives a list of non-trivial examples satisfying these basic axioms. Full article

Recently, several papers identified technical issues related to equivalent time-domain and frequency-domain “characterization of the n–block or transmission” feedback capacity formula and its asymptotic limit, the feedback capacity, of additive Gaussian noise (AGN) channels, first introduce by Cover and Pombra in 1989 (IEEE Transactions on Information Theory). The main objective of this paper is to derive new results on the Cover and Pombra characterization of the n–block feedback capacity formula, and to clarify the main points of confusion regarding the time-domain results that appeared in the literature. The first part of this paper derives new equivalent time-domain sequential characterizations of feedback capacity of AGN channels driven by non-stationary and non-ergodic Gaussian noise. It is shown that the optimal channel input processes of the new equivalent sequential characterizations are expressed as functionals of a sufficient statistic and a Gaussian orthogonal innovations process. Further, the Cover and Pombra n–block capacity formula is expressed as a functional of two generalized matrix difference Riccati equations (DREs) of the filtering theory of Gaussian systems, contrary to results that appeared in the literature and involve only one DRE. It is clarified that prior literature deals with a simpler problem that presupposes the state of the noise is known to the encoder and the decoder. In the second part of this paper, the existence of the asymptotic limit of the n–block feedback capacity formula is shown to be equivalent to the convergence properties of solutions of the two generalized DREs. Further, necessary and or sufficient conditions are identified for the existence of asymptotic limits, for stable and unstable Gaussian noise, when the optimal input distributions are asymptotically time-invariant but not necessarily stationary. This paper contains an in-depth analysis, with various examples, and identifies the technical conditions on the feedback code and state space noise realization, so that the time-domain capacity formulas that appeared in the literature, for AGN channels with stationary noises, are indeed correct. Full article

Underwater acoustic channel (UWAC) is characterized by significant multipath effects, strong time-varying properties and complex noise environments, which make achieving high-rate and reliable underwater communication a formidable task. To address the above adverse challenges, this study first presents a novel, robust and efficient polar code construction (NREPCC) method using the base-adversarial polarization weight (BPW) algorithm tailored for typical ocean channel models, including invariable sound velocity gradient (ISVG) channels, negative sound velocity gradient (NSVG) channels, and positive sound velocity gradient (PSVG) channels. Subsequently, a robust and reliable polar-coded UWAC system model based on the orthogonal frequency division multiplexing (OFDM) technique is designed using the $t$-distribution noise model in conjunction with real sea noise data fitting. Then, an enhanced time synchronization and packet detection algorithm based on $t$-distribution is proposed for the performance optimization of the polar-coded UWAC OFDM system. Finally, extensive numerical simulation results confirm the excellent performance of the proposed NREPCC method and polar-coded UWAC OFDM system under a variety of channel conditions. Specifically, the NREPCC method outperforms low-density parity-check (LDPC) codes by approximately 0.5~1 dB in PSVG and ISVG channels while maintaining lower encoding and decoding complexity. Moreover, the robustness of the NREPCC method under $t$-distribution noise with varying degrees of freedom is rigorously validated, which renders vital technical support for the design of high-precision and high-robustness UWAC systems. Full article

The Phubbing Scale (PS) is an instrument used to measure the frequency and extent of the behavior of ignoring someone you are with and giving attention to your mobile phone instead. However, there is insufficient evidence about the psychometric adequacy of the Spanish version of the instrument. The main goal of this research was to analyze the psychometric properties of PS in a representative sample of Spanish adolescents and young adults. A total of 1351 participants comprised the sample (42.78% females, age range = 12–21). Students were selected from different levels of education such as secondary school, high school, vocational training, or university. A convenient sample was used. The reliability of the scores was calculated by means of McDonald’s Omega. The evidence of the internal structure of the questionnaire was analyzed by means of confirmatory factor analysis (CFA). The measurement invariance of the instrument by gender and educational level was also calculated. In addition, Pearson’s correlations between phubbing and other indicators of mental health were also calculated. The goodness-of-fit indices for the two-factor model were good. The McDonald’s Omega coefficient for the total score was 0.787. Measurement invariance both by gender and educational level was found. The phenomenon of phubbing was found to have statistically significant correlations with emotional well-being, other mental health indicators, and with Problematic Internet Use (PIU), with the sole exception of the hyperactivity subscale of the SDQ. This study provided validity evidence for the Spanish version of the Phubbing Scale (PS), suggesting that PS is a reliable tool for quantifying phubbing in Spanish adolescents. Full article

Mucosal-associated invariant T cells (MAIT cells) are a subset of T cells with innate, effector-like properties that play an essential role in the immune response to microbial infections. In humans, MAIT cells are detectable in the blood, liver, and lungs, but little is known about the frequency of these cells in the bone marrow. Also, the pathogenic role, if any, of MAIT cells in the development of aplastic anemia, a disease with an exquisite origin in the bone marrow, is currently unknown. We investigated the frequency and clinical relevance of bone marrow MAIT cells in a cohort of 14 patients (60.6 ± 23 and 57% women) with aplastic anemia. MAIT cells in the bone marrow samples obtained at diagnosis were evaluated by flow cytometry, and their association with various blood cell parameters and the patients’ clinical features was analyzed. MAIT cells were detectable in the bone marrow of all patients, with considerable variations among them. Bone marrow MAIT cells expressing the activator receptor natural killer group 2D - NKG2D (NKG2D+ MAIT cells) were significantly more abundant in the specimens of the aplastic anemia patients than in patients with bone marrow failure distinct from aplastic anemia. In addition, the NKG2D+ MAIT cells positively correlated with whole blood cell counts (WBC), platelet counts, and neutrophil counts, as well as with various inflammatory markers, including neutrophil-to-lymphocyte rate (NLR), platelet-to-lymphocyte rate (PLR), and systemic inflammatory index (SII). In functional studies, bone marrow CD34+ hematopoietic cells exposed to phytohemagglutinin or bacterial-derived lipopolysaccharide and acetyl-6-formylpterin upregulated MR1 (major histocompatibility complex, class I-related, known to interact with MAIT cells) and MICA/B (MHC class I chain-related gene A, a ligand of NKG2D) proteins on their cell surface, suggesting that under stress conditions, CD34+ hematopoietic cells are more likely to interact with NKG2D+ MAIT cells. In addition, NKG2D+ MAIT cells upregulated perforin and granzyme B in response to their interaction with recombinant MICA protein in vitro. This study reports for the first time the frequency of MAIT cells in the bone marrow of patients with aplastic anemia and assesses the potential implications of these cells in the pathogenesis or progression of aplastic anemia. Full article

The transmit/receive-receive (T/R-R) synergetic High Frequency Surface Wave Radar (HFSWR) has increasingly attracted attention due to its high localization accuracy, but multi-target pairing needs to be performed before localization in multi-target scenarios. However, existing multi-target parameter matching methods have primarily focused on track association, which falls under the category of information-level fusion techniques, with few methods based on detected points. In this paper, we propose a multi-target pairing method with high computational efficiency based on angle information for T/R-R synergetic HFSWR. To be more specific, a dual-receiving array signal model under long baseline condition is firstly constructed. Then, the amplitude and phase differences of the same target reaching two subarrays are calculated to establish the cross-correlation matrix. Subsequently, in order to extract the rotation factor matrices containing pairing information and improve angle estimation performance, we utilize the conjugate symmetry properties of the uniform linear array (ULA) manifold matrix for generalized virtual aperture extension. Ultimately, azimuths estimation and multi-target pairing are accomplished by combining the propagator method (PM) and the ESPRIT algorithm. The proposed method relies solely on angle information for multi-target pairing and leverages the rotational invariance property of Vandermonde matrices to avoid peak searching or iterations, making it computationally efficient. Furthermore, the proposed method maintains superb performance regardless of whether the spatial angles are widely separated or very close. Simulation results validate the effectiveness of the proposed method. Full article

A precise interpretation of the universe wave function is forbidden in the spirit of the Copenhagen School since a precise notion of measure operation cannot be satisfactorily defined. Here, we propose a Bohmian interpretation of the isotropic universe quantum dynamics, in which the Hamilton–Jacobi equation is restated by including quantum corrections, which lead to a classical trajectory containing effects of order ${\hslash }^2$. This solution is then used to determine the spectrum of gauge-invariant quantum fluctuations living on the obtained background model. The analysis is performed adopting the wave function approach to describe the fluctuation dynamics, which gives a time-dependent harmonic oscillator for each Fourier mode and whose frequency is affected by the ${\hslash }^2$ corrections. The properties of the emerging spectrum are discussed, outlining the modification induced with respect to the scale-invariant result, and the hierarchy of the spectral index running is discussed. Full article

This paper proposes a novel algorithm, termed Mixed Riccati–Lyapunov Balanced Truncation (MRLBT), tailored for order reduction of Linear Time-Invariant Continuous-Time Descriptor Systems (LTI-CTD), commonly encountered in electrical and electronic circuit modeling. The MRLBT approach synergistically combines the advantages of balanced truncation (BT) and positive-real balanced truncation (PRBT) techniques while mitigating their limitations. Unlike BT, which preserves stability but not passivity, and PRBT, which retains passivity at the expense of larger reduction errors, MRLBT ensures the preservation of both stability and passivity inherent in the original system. Additionally, MRLBT achieves reduced computational complexity and minimized order reduction errors compared to PRBT. The proposed algorithm transforms the system into an equivalent Mixed Riccati–Lyapunov Balanced form, enabling the construction of a reduced-order model that retains the critical physical properties. Theoretical analysis and proofs are provided, establishing an upper bound on the global order reduction error. The efficacy of MRLBT is demonstrated through a numerical example involving an RLC ladder network, showcasing its superior performance over BT and PRBT in terms of reduced errors in the time and frequency domains. Full article

THz radiation has gained great importance due to its potential applications in a wide variety of fields. For this reason, continuous efforts have been made to develop technological tools for use in this versatile band of the electromagnetic spectrum. Here, we propose a reflecting device with long focusing performances in the sub-THz band, using a bimirror device in which the relative angle is mechanically adjusted with the displacement of one of the mirrors. Despite the simplicity of the setup, the performance of this device is satisfactory down to a frequency of 0.1 THz. Theory and experience confirm that the bimirror is capable of focusing 0.1 THz radiation with a 2× magnification of the maximum input intensity while maintaining a longitudinal full width at half maximum (FWHM) of about 6 mm, which is about 12 times the depth of focus of a cylindrical optical element of the same focal length. In the absence of suitable THz equipment, the invariance property of the Fresnel diffraction integral allowed the predicted behavior to be tested in the THz range using conventional equipment operating at visible frequencies. Full article

Fractional derivative operators are finding applications in a wide variety of fields with their ability to better model certain phenomena exhibiting spatial and temporal nonlocality. One area in which these operators are applicable is in the field of electromagnetism, thereby modelling transient wave propagation in complex media. To apply fractional derivative operators to electromagnetic problems, the operator must adhere to certain principles, like the trigonometric functions invariance property. The Grünwald–Letnikov and Marchaud fractional derivative operators comply with these principles and therefore could be applied. The fractional derivative arises when modelling frequency-dispersive dielectric media. The time-domain convolution integral in the relation between the electric displacement and the polarisation density, containing an empirical extension of the Debye model, is approximated directly. A common approach is to recursively update the convolution integral by approximating the time series by a truncated sum of decaying exponentials, with the coefficients found through means of optimisation or fitting. The finite-difference time-domain schemes using this approach have shown to be more computationally efficient compared to other approaches using auxiliary differential equation methods. Full article