Lower Bound Research Articles

Stochastic aspects of reversed aging intensity function of random quantiles

This paper studies some stochastic properties of random quantiles according to the newly defined reliability measure called reversed aging intensity function. Preservation property of reversed aging intensity order under random quantile is obtained and using it, a lower bound and an upper bound for the reversed aging intensity function of a random quantile are derived. Preservation of two related monotonic reliability classes under random quantiles is also studied. We finally apply our results for reliability analysis of series systems with heterogeneous component lifetimes. Examples are included to examine and analyze the obtained results.

Measuring the Impact of Unconventional Monetary Policies on the U.S. Banking and Bond Markets at the Lower Bound

Measuring the Impact of Unconventional Monetary Policies on the U.S. Banking and Bond Markets at the Lower Bound

Energy-harvesting recursive filtering for delayed systems with amplify-and-forward relays: Cooperative communication manner

The recursive filtering problem is explored for a class of nonlinear time-delayed systems with amplify-and-forward (AF) relay and energy-harvesting (EH) technology. In order to enhance the signal quality of the remote transmission in wireless communication, the relay under the AF protocol is introduced that posing the merits of low complexity, less energy consumption and fast transmission rate. Meanwhile, to further alleviate the fading and improve the robustness of the signals, the cooperative communication manner is employed, which is different from the commonly encountered two-hop one. In the cooperative communication, the maximal ratio combining (MRC) method is utilized to make sure that the signal-to-noise ratio of the combined output can reach theoretical maximum. In addition, in order to achieve sustainable power supply in harsh environments, the EH sensors and relays are deployed, which can collect energy from external environments with certain probabilities. The aim of this paper is to develop a proper filter so as to reduce the impacts caused by the channel fading and insufficient energy. Furthermore, a minimized upper bound of the filtering error covariance is gained through appropriately designing the filter parameters. Then, the exponential boundedness is analyzed with regard to filtering error. Finally, a numerical example is exhibited to test the validity of the proposed filtering scheme.

SOS decomposition for general Bell inequalities in two qubits systems and its application to quantum randomness

Bell non-locality is closely related with device independent quantum randomness. In this paper, we present a kind of sum-of-squares (SOS) decomposition for general Bell inequalities in two qubits systems. By using the obtained SOS decomposition, we can then find the measurement operators associated with the maximal violation of considered Bell inequality. We also practice the SOS decomposition method by considering the (generalized) Clauser-Horne-Shimony-Holt (CHSH) Bell inequality, the Elegant Bell inequality, the Gisin inequality and the Chained Bell inequality as examples. The corresponding SOS decompositions and the measurement operators that cause the maximum violation values of these Bell inequalities are derived, which are consistent with previous results. We further discuss the device independent quantum randomness by using the SOS decompositions of Bell inequalities. We take the generalized CHSH inequality with the maximally entangled state and the Werner state that attaining the maximal violations as examples. Exact value or lower bound on the maximal guessing probability using the SOS decomposition are obtained. For Werner state, the lower bound can supply a much precise estimation of quantum randomness when p tends to 1.

Graph Burning in Community-based Networks

Graph burning is a deterministic, discrete-time process that can be used to model how influence or contagion spreads in a graph. In the graph burning process, each node starts as dormant, and becomes informed/burned over time; when a node is burned, it remains burned until the end of the process. In each round, one can burn a new node (source of fire) in the network. Once a node is burned in round $t$, in round $t+1$, each of its dormant neighbors becomes burned. The process ends when all nodes are burned; the goal is to minimize the number of rounds.We study a variation of graph burning in order to model spreading processes in community-based networks. With respect to a specific piece of information, a community is {\em satisfied} when this information reaches at least a prescribed number of its members. Specifically, we consider the problem of identifying a minimum length sequence of nodes that, according to a graph burning process, allows to satisfy all the communities of the network. We investigate this NP-hard problem from an approximation point of view, showing both a lower bound and a matching upper bound. We also investigate the case when the number of communities is constant and show how to solve the problem with a constant approximation factor.Moreover, we consider the problem of maximizing the number of satisfied groups, given a budget $k$ on the number of rounds.

The mechanism of adjusting the low-frequency ultra-wide band gap within lightweight spherical superstructue

Conventional resonant structures can be effective in obtaining broadband, but it is still a challenge to design small-sized and lightweight acoustic metamaterials with a low-frequency ultra-wideband. This paper proposes a new approach of designing a lightweight spherical localized resonance superstructure with adjustable stiffness ratio, and the mechanism of adjusting the low-frequency ultra-wide forbidden band is revealed. Then, the correlation between the zero value of its dynamic equivalent mass and the stiffness ratio of the system is studied. It is found that not only is the upper bound of the negative mass effectively broadened, but also the lower bound is successfully lowered only by adjusting the stiffness ratio of the sphere. Most importantly, based on the regulation mechanism with adjustable stiffness ratio, the lower boundary of the band gap is lowered from 171 Hz to 141 Hz, and the upper boundary is increased from 445 Hz to 710 Hz. Therefore, the low-frequency ultra-wideband of 141–710 Hz is obtained only by adjusting the stiffness ratio of the system and the Finite Element Method, which is highly consistent with theoretical analyses. Obviously, the mechanism of obtaining the low-frequency wideband through adjusting the stiffness ratio not only provides a novel idea for adjusting the low-frequency ultra-wideband, but also provides theoretical guidance for the developing the small-size and lightweight acoustic devices, so it would have potential application in the field of vibration and noise reduction.

Understanding elliptical galaxies with warm dark matter

We fit the solution of hydrostatic equations to the observed total and baryonic mass densities ρtot(r) and ρb(r) of 23 massive elliptical galaxies. Our purpose is to investigate how well these measurements constrain the cusp or core of elliptical galaxies, and the dark matter comoving temperature-to-mass ratio, or equivalently, the adiabatic invariant vhrms(1), of dark matter. These studies reinforce the view that the lower bound of the measured distribution of the comoving thermal velocity vhrms(1) is of cosmological origin, in agreement with studies of spiral and dwarf galaxies.

A refined first-order expansion formula in [formula omitted]: Application to interpolation and finite element error estimates

The aim of this paper is to derive a refined first-order expansion formula in Rn, the goal being to get an optimal reduced remainder, compared to the one obtained by usual Taylor’s formula. For a given function, the formula we derived is obtained by introducing a linear combination of the first derivatives, computed at n+1 equally spaced points. We show how this formula can be applied to two important applications: the interpolation error and the finite elements error estimates. In both cases, we illustrate under which conditions a significant improvement of the errors can be obtained, namely how the use of the refined expansion can reduce the upper bound of error estimates.

Revealing the Dark Side of Non-Local Attention in Single Image Super-Resolution.

Single Image Super-Resolution (SISR) aims to reconstruct a high-resolution image from its corresponding low-resolution input. A common technique to enhance the reconstruction quality is Non-Local Attention (NLA), which leverages self-similar texture patterns in images. However, we have made a novel finding that challenges the prevailing wisdom. Our research reveals that NLA can be detrimental to SISR and even produce severely distorted textures. For example, when dealing with severely degrade textures, NLA may generate unrealistic results due to the inconsistency of non-local texture patterns. This problem is overlooked by existing works, which only measure the average reconstruction quality of the whole image, without considering the potential risks of using NLA. To address this issue, we propose a new perspective for evaluating the reconstruction quality of NLA, by focusing on the sub-pixel level that matches the pixel-wise fusion manner of NLA. From this perspective, we provide the approximate reconstruction performance upper bound of NLA, which guides us to design a concise yet effective Texture-Fidelity Strategy (TFS) to mitigate the degradation caused by NLA. Moreover, the proposed TFS can be conveniently integrated into existing NLA-based SISR models as a general building block. Based on the TFS, we develop a Deep Texture-Fidelity Network (DTFN), which achieves state-of-the-art performance for SISR. Our code and a pre-trained DTFN are available on GitHub for verification.

Exploration of the polarization angle variability of the Crab Nebula with POLARBEAR and its application to the search for axionlike particles

The Crab Nebula, also known as Tau A, is a polarized astronomical source at millimeter wavelengths. It has been used as a stable light source for polarization angle calibration in millimeter-wave astronomy. However, it is known that its intensity and polarization vary as a function of time at a variety of wavelengths. Thus, it is of interest to verify the stability of the millimeter-wave polarization. If detected, polarization variability may be used to better understand the dynamics of Tau A, and for understanding the validity of Tau A as a calibrator. One intriguing application of such observation is to use it for the search of axionlike particles (ALPs). Ultralight ALPs couple to photons through a Chern-Simons term, and induce a temporal oscillation in the polarization angle of linearly polarized sources. After assessing a number of systematic errors and testing for internal consistency, we evaluate the variability of the polarization angle of the Crab Nebula using 2015 and 2016 observations with the 150 GHz P instrument. We place a median 95% upper bound of polarization oscillation amplitude A<0.065° over the oscillation frequencies from 0.75 year−1 to 0.66 hour−1. Assuming that no sources other than ALP are causing Tau A’s polarization angle variation, that the ALP constitutes all the dark matter, and that the ALP field is a stochastic Gaussian field, this bound translates into a median 95% upper bound of ALP-photon coupling gaγγ<2.16×10−12 GeV−1×(ma/10−21 eV) in the mass range from 9.9×10−23 eV to 7.7×10−19 eV. This demonstrates that this type of analysis using bright polarized sources is as competitive as those using the polarization of cosmic microwave background in constraining ALPs. Published by the American Physical Society 2024

Enhancing solar energy conversion efficiency: Thermophysical property predicting of MXene/Graphene hybrid nanofluids via bayesian-optimized artificial neural networks

Accurately predicting thermo-physical properties (TPPs) of MXene/graphene-based nanofluids is crucial for photovoltaic/thermal solar systems, driving focused research on developing precise TPP predictive models. This study presents optimized multi-layer perceptron neural network (MLPNN) models, leveraging Bayesian optimization to refine architectural and training hyperparameters, including hidden layers, neurons, activation functions, standardization, and regularization terms. A comparative analysis of Bayesian acquisition functions—the probability of improvement (POI), lower confidence bound (LCB), expected improvement (EI), expected improvement plus (EIP), expected improvement per second plus (EIPSP), and expected improvement per second (EIPS)—demonstrated that the POI-MLPNN achieves the most accurate results, as evidenced by the lowest MAPE of 1.0923 % and exceptional consistency with an R-value of 0.99811. The EI-MLPNN and EIP-MLPNN models recorded the same outputs. The EI/EIP-MLPNN (R = 0.99668) model excels in consistency over LCB-MLPNN (R = 0.99529) and EIPSP-MLPNN (R = 0.99667). The optimized models offer a reliable, cost-efficient alternate for experimental and computational TPP analyses. Leveraging insights from these models enables better control over nanofluid TPPs in solar systems, enhancing energy conversion efficiency.

On the characterization of reflective surfaces using dual-polarization GNSS-R

Global navigation satellite systems reflectometry (GNSS-R) is a technique to extract information from reflecting surfaces by the reflected GNSS signals. GNSS-R has garnered increasing attention in the scientific literature due to its continuous global coverage and its superior spatial resolution. Moreover, operating in the L-band renders GNSS-R relatively immune to adverse weather conditions and affords high sensitivity to soil electrical properties. This work introduces a new approach with a dual-polarization antenna, left-hand circular polarized (LHCP) and right-hand circular polarized (RHCP), receiving the reflected signal from a sufficiently smooth surface so that all reflected energy arrives from the specular reflection point. The objective is to characterize the reflecting surface by extracting the relative permittivity and conductivity from the reflected signal. In contrast to other studies found in the literature, the reflection of the GNSS signal on different materials, including dielectric and conductive materials is considered. We derive a maximum likelihood estimator (MLE) for estimating the dielectric parameters of the reflective surface and other parameters of the reflected signal. We also derive the respective Cramer–Rao Lower Bound (CRLB) evaluating the performance of the MLE. The attained results are assessed based on the signal-to-noise ratio (SNR) and the angle of reflection of the reflected signal, which are the parameters that predominantly influence the proposed approach. Lower elevation angles, for instance, lead to higher estimation accuracy, while for reflective surfaces composed of metallic materials a higher SNR is needed to yield favorable estimation performance. Regarding dielectric materials, the estimation results are encouraging and thus enable diverse remote sensing applications by GNSS-R using the proposed setup.

On the Dimension of Limit Sets on ℙ(ℝ3) via Stationary Measures: Variational Principles and Applications

Abstract This paper investigates the (semi)group action of $\textrm{SL}_{n}({\mathbb R})$ on ${\mathbb P}({\mathbb R}^{n})$, a primary example of non-conformal, non-linear, and non-strictly contracting action. We establish variational principles of the affinity exponent for two main examples: the Borel Anosov representations and the Rauzy gasket. In [ 32], they obtain a dimension formula for the stationary measures on ${\mathbb P}({\mathbb R}^{3})$. Combined with our result, it allows us to study the Hausdorff dimension of limit sets of Anosov representations in $\textrm{SL}_{3}({\mathbb R})$ and the Rauzy gasket. It yields the equality between the Hausdorff dimensions and the affinity exponents in both settings, generalizing the classical Patterson–Sullivan formula. In the appendix, we improve the numerical lower bound of the Hausdorff dimension of Rauzy gasket to $1.5$.

Aberration-robust monocular passive depth sensing using a meta-imaging camera

Depth sensing plays a crucial role in various applications, including robotics, augmented reality, and autonomous driving. Monocular passive depth sensing techniques have come into their own for the cost-effectiveness and compact design, offering an alternative to the expensive and bulky active depth sensors and stereo vision systems. While the light-field camera can address the defocus ambiguity inherent in 2D cameras and achieve unambiguous depth perception, it compromises the spatial resolution and usually struggles with the effect of optical aberration. In contrast, our previously proposed meta-imaging sensor1 has overcome such hurdles by reconciling the spatial-angular resolution trade-off and achieving the multi-site aberration correction for high-resolution imaging. Here, we present a compact meta-imaging camera and an analytical framework for the quantification of monocular depth sensing precision by calculating the Cramér–Rao lower bound of depth estimation. Quantitative evaluations reveal that the meta-imaging camera exhibits not only higher precision over a broader depth range than the light-field camera but also superior robustness against changes in signal-background ratio. Moreover, both the simulation and experimental results demonstrate that the meta-imaging camera maintains the capability of providing precise depth information even in the presence of aberrations. Showing the promising compatibility with other point-spread-function engineering methods, we anticipate that the meta-imaging camera may facilitate the advancement of monocular passive depth sensing in various applications.

An algorithmic construction of union-intersection-bounded families

In this paper, we present lower bounds and algorithmic constructions of union-intersection-bounded families of sets. The lower bound is established using the Lovász Local Lemma. This bound matches the best known bound for the size of union-intersection-bounded families of sets. We then use the variable framework for the Lovász Local Lemma, to discuss an algorithm that outputs explicit constructions that attain the lower bound. The algorithm has polynomial complexity in the number of points in the family.

The upper bound of the buckling stress of axially compressed carbon steel circular cylindrical shells

Abstract The buckling stress of axially compressed circular cylindrical shells (CCSs) is highly sensitive to imperfections. The literature proved that it is hard to generalize the imperfections and the designers are encouraged by the Eurocode EN 1993:1-6 (2007) to conduct geometric and material nonlinear with imperfections analysis (GMNIA) considering different possible forms of imperfections for the shell under design. As GMNIA type of analysis is difficult and requires highly skilled engineers, knowledge of the upper limit of the buckling stress serves as a guide and prevents the overestimation of the shell buckling resistance. It also encourages average skill designers to attempt GMNIA as far as the maximum possible limit is known. Thus, the objective of this study is to provide the upper bound of the buckling stress of carbon steel CCSs. Geometric and material nonlinear analysis (GMNA) of perfect circular cylindrical shells for a wide range of R/t ratio is conducted. It has been found that for cases of small and intermediate R/t values the buckling stress can be predicted by GMNA while the elastic buckling controls those of larger R/t values. The limiting R/t values depend on the steel grade and have been derived for the available standard grades of carbon steel. The obtained results are presented in terms of simplified formulas and a design chart to be used by engineers. Application of the proposed upper bound in simplified design approaches using knock down factor (KDFs) has also been discussed.

Constraining Logarithmic f(R, T) Model Using Dark Energy Density Parameter Ω_Λ and Hubble parameter H_0

Of many extended theories of gravity, f(R, T) gravity has gained reasonable interest in recent times as it provides interesting results in cosmology. Logarithmic corrections in modified theories of gravity have been studied extensively. In this work, we considered logarithmic correction to the trace term T and took the functional form as f(R, T) = R+16πGαlnT where α is a free parameter. The free parameter is constrained using dark energy density parameter ΩΛ and Hubble parameter H0. The lower bound is found to be α ≥ −9.85×10−29. The cosmological implications are also studied.

A simple two-phase approach to predict moisture-dependent thermal conductivity for porous materials

This study develops a generalized solution for moisture-dependent thermal conductivity (λeff) in porous media, utilizing readily available parameters. By introducing arbitrary dry and saturated phases, the tri-phase model (solid, gas, and water) is simplified into a two-phase model. Seven analytical solutions are adapted, including series-parallel, Maxwell-Eucken, Landauer's, exponential, and Somerton's relations. The proposed method requires only two parameters to predict λeff under different degrees of saturation (Sr): effective dry thermal conductivity (λdry, where Sr = 0) and effective saturated thermal conductivity (λsat, where Sr = 1). In the absence of direct λsat measurement, this λsat can be obtained using λdry and the parallel relation for highly porous media, and using Landauer's relation for medium-density materials. Validation results indicate that both Landauer's and exponential relations provide the upper bound and lower bounds, respectively, for λeff. For medium-density materials, the upper bound aligns with the parallel relation and the lower bound aligns with Landauer's relation.

Reproducibility and Repeatability of US Shear-Wave and Transient Elastography in Nonalcoholic Fatty Liver Disease.

Background US shear-wave elastography (SWE) and vibration-controlled transient elastography (VCTE) enable assessment of liver stiffness, an indicator of fibrosis severity. However, limited reproducibility data restrict their use in clinical trials. Purpose To estimate SWE and VCTE measurement variability in nonalcoholic fatty liver disease (NAFLD) within and across systems to support clinical trial diagnostic enrichment and clinical interpretation of longitudinal liver stiffness. Materials and Methods This prospective, observational, cross-sectional study (March 2021 to November 2021) enrolled adults with NAFLD, stratified according to the Fibrosis-4 (FIB-4) index (≤1.3, >1.3 and <2.67, ≥2.67), at two sites to assess SWE with five US systems and VCTE with one system. Each participant underwent 12 elastography examinations over two separate days within 1 week, with each day's examinations conducted by a different operator. VCTE and SWE measurements were reported in units of meters per second. The primary end point was the different-day, different-operator reproducibility coefficient (RDCDDDO) pooled across systems for SWE and individually for VCTE. Secondary end points included system-specific RDCDDDO, same-day, same-operator repeatability coefficient (RCSDSO), and between-system same-day, same-operator reproducibility coefficient. The planned sample provided 80% power to detect a pooled RDCDDDO of less than 35%, the prespecified performance threshold. Results A total of 40 participants (mean age, 60 years ± 10 [SD]; 24 women) with low (n = 17), intermediate (n = 15), and high (n = 8) FIB-4 scores were enrolled. RDCDDDO was 30.7% (95% upper bound, 34.4%) for SWE and 35.6% (95% upper bound, 43.9%) for VCTE. SWE system-specific RDCDDDO varied from 24.2% to 34.3%. The RCSDSO was 21.0% for SWE (range, 13.9%-35.0%) and 19.6% for VCTE. The SWE between-system same-day, same-operator reproducibility coefficient was 52.7%. Conclusion SWE met the prespecified threshold, RDCDDDO less than 35%, with VCTE having a higher RDCDDDO. SWE variability was higher between different systems. These estimates advance liver US-based noninvasive test qualification by (a) defining expected variability, (b) establishing that serial examination variability is lower when performed with the same system, and (c) informing clinical trial design. ClinicalTrials.gov Identifier NCT04828551 © RSNA, 2024 Supplemental material is available for this article.

The Contribution of Foreign Holdings of U.S. Treasury Securities to the U.S. Long-Term Interest Rate: An Empirical Investigation of the Impact of the Zero Lower Bound

The Contribution of Foreign Holdings of U.S. Treasury Securities to the U.S. Long-Term Interest Rate: An Empirical Investigation of the Impact of the Zero Lower Bound