Non-stationary sequences may exhibit changing effective memory. We study the Learnable-Order Fractional Recurrent Network (LOFT-RNN), a recurrent block in which the order αt ∈ (0, 1) of a type-I Caputo derivative is generated from the evolving state and input. The hidden trajectory follows 0[C]Dt[α(t)]h(t)=fθ(h(t),x(t)), with α(t)=αmin+(αmax-αmin)σ(gϕ(h(t),x(t))). The theoretical scope is deliberately limited. We give (i) a represented-class approximation proposition, conditional on a finite-dimensional fractional-state realization and uniform continuous dependence of its solution map; (ii) a uniform consistency estimate for the exact-weight L1 formula, together with a separate interpolation-error term for the order grid; (iii) a variable-order bounded-input bounded-state estimate under dissipativity, with a Mittag-Leffler refinement only for constant order; and (iv) a regret result for an auxiliary one-dimensional reset-OGD tracker under convex surrogate losses and explicit detection assumptions. The auxiliary tracker is not identified with end-to-end neural-gate training. We also state the boundary assumptions at t=0, explain the choice of the Caputo derivative, and show that the untruncated history convolution costs O(N[2]d) over a length-N trajectory. The archived aggregate experiments cover a delimited-copy task, regime-switching ARFIMA sequences, Bonn EEG segment classification, and S&P 500 volatility forecasting. Because seed-level outputs, split manifests, executable code, and some requested baselines are absent from the supplied archive, the empirical comparisons are reported descriptively and no statistical-significance or state-of-the-art claim is made.

Bimetallic nanoparticles are catalysts for reactions such as COx hydrogenation or propane dehydrogenation. Recently, gallium has been identified as a promoter, which enables dispersion of transition metal sites, increasing their activity and selectivity. However, quantitative information on alloying dynamics under reaction conditions is not readily available, and a general computational method to access such information is lacking. Here, an ab initio molecular dynamics workflow with enhanced sampling methods is used to probe the alloying behavior of Ni-, Pd-, and Pt-Ga nanoparticles under operating conditions (T = 600 °C) in the presence of H2 or CO. The three metals display different alloying behaviors with Ga: Ni forms a core surrounded by gallium, while Pd and Pt form different alloyed structures. Both H2 and CO shift the alloying states to different extents. A set of three descriptors is then proposed to compare and quantify the alloying behavior of these catalyst models: (i) the position α[min] of the most stable alloying state; (ii) the curvature η of the free energy at α[min], referred to as the alloying hardness; and (iii) the skew κ of the free energy at α[min], which relates to its propensity to alloy or segregate. The cost of alloy reorganization, which correlates with alloy hardness, is a major part of the free energy barriers of propane dehydrogenation. Since the alloying behavior of a catalyst is a critical parameter that is overlooked in catalyst design, quantitative descriptors are the first step in designing alloys with set catalytic properties.

A linear spot-type multipass cell-enhanced fiber-optic photoacoustic gas microprobe is proposed. To further reduce the volume of the gas chamber and enhance the photoacoustic signal, we designed the cross section of the photoacoustic tube as a slit with a height of 10 mm and a width of 1.5 mm. The volume of the gas chamber is only 210 μL. Through theoretical analysis and multiphysical field simulation, the photoacoustic intensity of the slit cross section is more than 6 times that of traditional circular cross section. A cantilever beam is integrated into the photoacoustic microprobe and forms a Fabry-Perot (FP) interferometer with an optical fiber, achieving enhanced photoacoustic detection. By adjusting the angle of the collimator, the light passes through the photoacoustic cell 26 times, and 13 linear spots are formed on the reflecting surface. The photoacoustic signal with multiple linear reflections is 12.4 times that of a single reflection. The gas enters the sensor in a freely diffused manner, and the response time of the sensing system is 54 s. When the averaging time is 400 s, the detection limit of the designed sensor for acetylene gas reaches 1.5 ppb. The minimum detectable absorption coefficient (αmin) and the normalized noise equivalent absorption coefficient (NNEA) are 1.7 × 10[-8] cm[-1] and 1.9 × 10[-9] Wcm[-1]/Hz[1/2], respectively.

This study investigates the integration of Broadband Cavity Enhanced Absorption Spectroscopy (BBCEAS) with High-Performance Liquid Chromatography (HPLC) to detect synthetic antioxidants; BHA, BHT, and TBHQ in the deep-UV region below 300 nm. The research addresses the need for more sensitive and cost-effective detection methods in HPLC systems, particularly for low analyte concentrations, by exploring BBCEAS as a superior alternative to conventional detectors that often fall short in sensitivity. The sensitivity of the HPLC-BBCEAS system is assessed by calculating the minimum detectable change in the absorption coefficient (αmin) and comparing with those obtained using conventional HPLC and single-wavelength HPLC-CRDS methods. The findings demonstrate that the HPLC-BBCEAS system achieves αmin values of 1.8 × 10[-5] cm[-1] for BHA, 2.8 × 10[-5] cm[-1] for BHT, and 1.9 × 10[-5] cm[-1] for TBHQ at 280 nm, with Limits of Detection (LOD) and Quantification (LOQ) up to 30 times lower than conventional HPLC systems.

We present the measurement and analysis of the 2OH stretching band of methanol between 7165 cm[-1] and 7230 cm[-1] cooled down to 26 ± 12 K in a buffer gas cooling experiment. Measurements were performed with a cavity ring-down spectrometer having a detection limit αmin = 2 × 10[-10] cm[-1]. A total of 350 rovibrational transitions were assigned and 62 rovibrational transitions were tentatively assigned. This assignment was performed using the pattern recognition method developed by Rakvoský et al. [Phys. Chem. Chem. Phys., 2021, 23, 20193-20200]. In this work, we extended their method by using information on the relative intensities of the transitions to add one criterion to the validation of the assignments, allowing us to firmly assign 188 additional rovibrational transitions and to tentatively assign 14 more compared to the ir work.

A miniaturized optical fiber photoacoustic gas sensor enhanced by dense multibutterfly spots is reported for the first time. The principle of space light transmission of neglecting paraxial approximation is theoretically analyzed for designing a dense multibutterfly spots-based miniature multipass cell. In a multipass photoacoustic tube with a diameter of 16 mm, the light beam is reflected about a hundred times. The light spots on the mirror surfaces at both ends of the photoacoustic tube form a dense multibutterfly distribution. The volume of the micro multipass gas chamber is only 5.3 mL. An optical fiber cantilever based on F-P interference is utilized as a photoacoustic pressure detector. Compared with that of the single-pass structure, the gas detection ability of the photoacoustic system with dense multibutterfly spots is improved by about 50 times. The proposed miniaturized sensor realizes a detection limit of 3.4 ppb for C2H2 gas with an averaging time of 100 s. The recognized coefficients of minimum detectable absorption (αmin) and normalized noise equivalent absorption are 1.9 × 10[-8] cm[-1] and 8.4 × 10[-10] W cm[-1] Hz[-1/2], respectively.

Groundwater has a significant influence on the mechanical properties of surrounding rock. Aiming at the large deformation of surrounding rock of red layer soft rock tunnel affected by groundwater, the uniaxial graded loading tests were carried out on red beds soft rock with different water content. The failure process of the specimen was monitored by acoustic emission (AE) and the crack evolution law was analyzed, and the scanning electron microscopy (SEM) was used to compare the microstructure of the specimens before and after immersion. Combined with fractal theory, the monofractal and multifractal characteristics of AE ringing count during the loading process of red beds soft rock were analyzed. The results show that, with the gradual increase of water content, the AE ringing count before the yield stage gradually decreased, and the corresponding cumulative ringing count at the same time gradually decreased, and the decrease was large in the early stage of immersion, and decreased in the later stage. The cumulative ringing curve gradually slowed down, the internal crack appeared earlier, the cumulative ringing curve stepped significantly, the AE signal amplitude gradually weakened, and the bandwidth of each frequency band gradually decreased. The failure of red beds soft rock with different water content is dominated by shear crack, and with the gradual increase of water content, the proportion of shear crack increases gradually, and the AE b value decreases gradually. With the gradual increase of the relative peak strength, the correlation dimension D of red beds soft rock with different water content increases first and then decreases. At 80% of the relative peak strength, the correlation dimension D reaches its maximum value and then drops sharply until it is maintained at a relatively low level, and the correlation dimension D gradually decreases with the water content. The fitting correlation coefficients of different water content (lnC(r), lnr) are all above 0.9, indicating that the AE ringing count of water-bearing red beds soft rock has fractal characteristics, and the higher the correlation coefficient, the higher the self-similarity of AE ringing count sequence. As the weight q gradually increases, the generalized fractal dimension D(q) gradually decreases. When q ≠ 0, under the condition of the same q, D(q) presents a trend of first increasing and then decreasing. The multifractal characteristics of AE ringing count of red beds soft rock with different water content is inverted 'U' shape. From the natural state to immerse 1 d, the ∆α gradually increases, and from 1 to 7 d, the ∆α gradually decreases, where Δα = αmax - αmin represents the spectral width of the multifractal spectrum. When saturation is not reached, ∆f < 0 indicates that the number of cracks in the specimen is small, when saturation is reached, ∆f > 0 indicates that a large number of cracks are generated inside the specimen and macro cracks are formed, where Δf = f (αmax) - f (αmin) represents the frequency relationship between different signals of different sizes. This research can provide a reliable theoretical basis for the construction and maintenance of large deformation of water-rich soft rock tunnel excavation, and have certain engineering significance.

Entropy-based and fractal-based metrics derived from heart rate variability (HRV) have enriched the way cardiovascular dynamics can be described in terms of complexity. The most commonly used multifractal testing, a method using q moments to explore a range of fractal scaling in small-sized and large-sized fluctuations, is based on detrended fluctuation analysis, which examines the power-law relationship of standard deviation with the timescale in the measured signal. A more direct testing of a multifractal structure exists based on the Shannon entropy of bin (signal subparts) proportion. This work aims to reanalyze HRV during cognitive tasks to obtain new markers of HRV complexity provided by entropy-based multifractal spectra using the method proposed by Chhabra and Jensen in 1989. Inter-beat interval durations (RR) time series were obtained in 28 students comparatively in baseline (viewing a video) and during three cognitive tasks: Stroop color and word task, stop-signal, and go/no-go. The new HRV estimators were extracted from the f/α singularity spectrum of the RR magnitude increment series, established from q-weighted stable (log-log linear) power laws, namely: (i) the whole spectrum width (MF) calculated as αmax - αmin; the specific width representing large-sized fluctuations (MFlarge) calculated as α0 - αq+; and small-sized fluctuations (MFsmall) calculated as αq- - α0. As the main results, cardiovascular dynamics during Stroop had a specific MF signature while MFlarge was rather specific to go/no-go. The way these new HRV markers could represent different aspects of a complete picture of the cognitive-autonomic interplay is discussed, based on previously used entropy- and fractal-based markers, and the introduction of distribution entropy (DistEn), as a marker recently associated specifically with complexity in the cardiovascular control.

Incoherent broadband cavity-enhanced absorption spectroscopy (IBBCEAS) can achieve sensitive measurements at trace concentrations for liquid phase marine samples. The IBBCEAS system consists of a cavity-enhancement module (CEM) and a transmission hyperspectral module (THM). The CEM has cavity-enhancement factors up to 78 at 550 nm. Measurements were obtained over a wide wavelength range (420-640 nm) with a halogen lamp, and the optical cavity was formed by two concave highly reflective mirrors (R=0.99). The minimum detectable absorption coefficient αmin of 7.3×10-7cm-1 at 550 nm corresponds to a limit of detection for nutrients of 780 pM. The spectral resolution of the THM is 3 nm in the wavelength range of 400 to 750 nm. We performed the IBBCEAS measurements for biological and chemical substances, including nutrients, microalgae, and Cy5 dye. The concentrations of nutrients in a deionized water environment and artificial seawater environment were measured at nanomolar levels; the concentration of microalgae phaeocystis was detected with 3.46×104/mL, and fluorescence substances such as Cy5 dye could be measured at 0.03 mg/L. Experimental results show that the IBBCEAS system has the capability for sensitive measurements of biological and chemical substances and has strong potential forin situ ecological marine environmental monitoring function.

We analyze the nonlinear properties of social media activity(SMA) using the multifractal detrended fluctuation analysis (MF-DFA) method. Social media data related to the stock market are gathered from social media platforms. Using data on over 2000 firms in the Korean stock market for 2018-2020, we study social media activity and its differences to evaluate associated nonlinear and statistical properties. We find that the cumulative distribution function of SMA follows a stretched exponential distribution with β = 0.85 . The Hurst exponent of SMA for three datasets (2018, 2019, 2020 year) is larger than 0.9, whereas the Hurst exponents of shuffled time series have values of approximately 0.5. In particular, we find a multifractal structure in both SMA and SMA difference results irrespective of the period and degree of multifractality defined as α max - α min , which reaches a maximum value during the COVID-19 pandemic as a financial crisis.

The present study was done to evaluate chest computed tomography (CT) images of patients with 2019 novel coronavirus disease (COVID-19) by multifractal technique as a new method to find a way for comparing lung infection quantitatively and identifying progression pattern of the disease. The multifractal spectra extracted from analysis of CT images showed that these spectra were correlated with lung infection amount and disease progression so that, multifractal parameters (αmin, αmax, ∆α, f(αmin), f(αmax), ∆f(α), α(q = 0), and f(α) max) were strongly dependent on amount of lung infection. The results demonstrated that multifractality of chest CT images was increased with the increase in lung infection in patients. The interesting and promising result was that capacity dimension (D0) as a new diagnostic parameter varied linearly with progression and reduction of lung infection. A critical value was found for D0, according to which patients with D0 lower than 1.4 can be healed by treatment. Therefore, herein, a way was found for quantitative assessment of lung infection of patients with COVID-19 by analyzing chest CT images using the multifractal method. This method can be very effective for physicians in diagnosis and treatment of pneumonia caused by COVID-19 and timely identification of therapeutic effects.

A special phenomenon of resonance mode separation is observed during the study of a high sensitivity folded-cavity enhanced absorption spectroscopy for the measurement of trace gases. The phenomenon affects the measurement of gas absorption spectrum in the cavity. This resonant mode separation phenomenon of the resonant cavity is different from the resonant modes previously observed in linear-cavity enhanced absorption spectroscopy systems. To explore the mechanism of this phenomenon, a series of hypotheses are proposed. The most likely reason among these hypotheses is based on the different reflectance properties of the plane mirror at the fold of the cavity for S-polarized light and P-polarized light. Based on the matrix calculation method, the different reflectance and phase shift of the plane mirror for S-polarized light and P-polarized light are analyzed theoretically, and the results are in better agreement with the phenomena observed in the experiment. Finally, in order to eliminate the resonant mode separation phenomenon, line polarizers were added. By improving the system, the cavity enhanced absorption spectrum of residual water vapor in the cavity was successfully measured, and a minimum detectable absorption coefficient of αmin = 7.6 × 10-9 cm-1 can be obtained in a single laser scan of 10 s.

We report on the development of a simple, linear optical cavity-based system combining evanescent wave (EW) with high-sensitive cavity ring-down spectroscopy (CRDS) technique using a diode laser at 644 nm and a right-angled prism for evanescent field generation on prism surface. We characterized the setup in detail and achieved an optimum ring-down time of 159.4 ns and a minimum absorption coefficient of αmin = 1.67 × 10-6 cm-1. We utilized this setup to investigate the salt-induced aggregation kinetics of gold (Au) and silver (Ag) nanoparticles (NPs) at the prism interface with high-sensitivity. We evaluated the extinction rates on the surface due to Au and Ag NPs aggregation and examined the variations due to their respective concentrations. To demonstrate the applicability of the developed EW-CRDS prototype setup to different molecular systems, we investigated the urease-bound aggregation kinetics of the Au and Ag NPs which has not been explored earlier by this linear cavity geometry. We finally illustrated the aggregation dynamics through surface imaging, thus demonstrating an alternative analytical approach to monitor interfacial phenomena using EW-CRDS technique.

In this work, acoustic damping performances of double-layer in-duct perforated plates are studied at low Mach (Ma) and Helmholtz number (He) to evaluate the effects of (1) Ma, (2) the porosities (i.e., open-area ratio) σ1 and σ2 of the front and back plates, and (3) the axial distance Lc between these two plates. The orifices' damping is characterized by sound absorption coefficient α denoting the fraction of incident sound energy being absorbed. For this, a quasi-steady acoustic model is developed first and experiments are then conducted. When Ma = 0, α is experimentally found to oscillate with He, whatever the porosities of σ1 and σ2 are set. However, when Ma is increased to and above 0.037, the power absorption troughs, i.e., local αmin of the double-layer plates with σ1,2 ≤ 9% are more separated and shallower. Furthermore, when σ1= 9% or σ2 = 9%, the damping performances are quite different in terms of the local αmax peaks and their number. In addition, increasing Lc with respect to the downstream pipe length Ld gives rise to an increase of αmin and αmax by 10%. Finally, the double-layer plates are shown to involve a larger α than that of single-layer one over a broader He range.

Cavity ring-down spectroscopy (CRDS) is a well-established, highly sensitive absorption technique whose sensitivity and selectivity for trace radical sensing can be further enhanced by measuring the polarization rotation of the intracavity light by the paramagnetic samples in the presence of a magnetic field. In this paper, we highlight the use of this Faraday rotation cavity ring-down spectroscopy (FR-CRDS) for the detection of HO2 radicals. In particular, we use a cold atmospheric pressure plasma jet as a highly efficient source of HO2 radicals and show that FR-CRDS in the near-infrared spectral region (1506 nm) has the potential to be a useful tool for studying radical chemistry. By simultaneously measuring ring-down times of orthogonal linearly polarized light, measurements of Faraday effect-induced rotation angles (θ) and absorption coefficients (α) are retrieved from the same data set. The Faraday rotation measurement exhibits better long-term stability and enhanced sensitivity due to its differential nature, whereby highly correlated noise between the two channels and slow drifts cancel out. The bandwidth-normalized sensitivities are αmin=2.2×10-11 cm-1 Hz-1/2 and θmin=0.62 nrad Hz-1/2. The latter corresponds to a minimum detectable (circular) birefringence of Δnmin=5×10-16 Hz-1/2. Using the overlapping qQ3(N = 4-9) transitions of HO2, we estimate limits of detection of 3.1 × 108 cm-3 based on traditional (absorption) CRDS methods and 6.7 × 107 cm-3 using FR-CRDS detection, where each point of the spectrum was acquired during 2 s. In addition, Verdet constants for pertinent carrier (He, Ar) and bulk (N2, O2) gases were recorded in this spectral region for the first time. These show good agreement with recent measurements of air and values extrapolated from reported Verdet constants at shorter wavelengths, demonstrating the potential of FR-CRDS for measurements of very weak Faraday effects and providing a quantitative validation to the computed rotation angles.