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Estimating the rate of rare conformational changes in molecular systems is one of the goals of molecular dynamics simulations. In the past few decades, a lot of progress has been done in data-based approaches toward this problem. In contrast, model-based methods, such as the Square Root Approximation (SqRA), directly derive these quantities from the potential energy functions. In this article, we demonstrate how the SqRA formalism naturally blends with the tensor structure obtained by coupling multiple systems, resulting in the tensor-based Square Root Approximation (tSqRA). It enables efficient treatment of high-dimensional systems using the SqRA and provides an algebraic expression of the impact of coupling energies between molecular subsystems. Based on the tSqRA, we also develop the projected rate estimation, a hybrid data-model-based algorithm that efficiently estimates the slowest rates for coupled systems. In addition, we investigate the possibility of integrating low-rank approximations within this framework to maximize the potential of the tSqRA. [ABSTRACT FROM AUTHOR]

We present a Wave Operator Minimization (WOM) method for calculating the Fermi–Dirac density matrix for electronic structure problems at finite temperature while preserving physicality by construction using the wave operator, i.e., the square root of the density matrix. WOM models cooling a state initially at infinite temperature down to the desired finite temperature. We consider both the grand canonical (constant chemical potential) and canonical (constant number of electrons) ensembles. Additionally, we show that the number of steps required for convergence is independent of the number of atoms in the system. We hope that the discussion and results presented in this article reinvigorate interest in density matrix minimization methods. [ABSTRACT FROM AUTHOR]

Numerical roots play a crucial role in real or complex equations, as well as in various mathematical models involving differentiation, integration, and other mathematical relationships. In the realm of mathematics, there is a growing trend of utilizing new formulas that incorporate non-classical numbers, such as neutrosophic and refined neutrosophic numbers. The objective of this research is to establish precise and comprehensive mathematical procedures for dealing with refined neutrosophic roots within mathematical formulas, be it equations or other mathematical constructs. This paper presents an extensive study on 2-refined neutrosophic numbers, focusing on the square root of a 2-refined neutrosophic real or complex number. Additionally, this work introduces the concept of 2-refined neutrosophic real or complex polynomials and explores the process of finding the refined neutrosophic roots to solve 2-refined neutrosophic equations. To illustrate these concepts, several examples have been provided. [ABSTRACT FROM AUTHOR]

Let F be a field with characteristic not equal to 2, and S ∈ M 2 n (F) be skew-symmetric and nonsingular. For X ∈ M 2 n (F) , we show that X has a ϕ S polar decomposition if and only if (a) ϕ S (X) X has a ϕ S -symmetric square root, (b) X ϕ S (X) is similar to ϕ S (X) X , and (c) rank [ X ϕ S (X) ] t X is even for all nonnegative integers t. [ABSTRACT FROM AUTHOR]

In this work, we investigate the poroelastic waves by solving the time‐domain Biot‐JKD equation with an efficient numerical method. The viscous dissipation occurring in the pores depends on the square root of the frequency and is described by the Johnson‐Koplik‐Dashen (JKD) dynamic tortuosity/permeability model. The temporal convolutions of order 1/2 shifted fractional derivatives are involved in the time‐domain Biot‐JKD model, causing the problem to be stiff and challenging to be implemented numerically. Based on the best relative Chebyshev approximation of the square‐root function, we design an efficient algorithm to approximate and localize the convolution kernel by introducing a finite number of auxiliary variables that satisfy a local system of ordinary differential equations. The imperfect hydraulic contact condition is used to describe the interface boundary conditions and the Runge‐Kutta discontinuous Galerkin (RKDG) method together with the splitting method is applied to compute the numerical solutions. Several numerical examples are presented to show the accuracy and efficiency of our approach. [ABSTRACT FROM AUTHOR]

During hot forging and heat treatment of 40Cr steel, a decarburized layer emerges on the surface, affecting fatigue life. However, the decarbonization of 40Cr steel has not been reported so far. The experiment mainly studies the effect of holding temperature and time on decarbonization. The 40Cr steel undergoes complete decarburization at 700 and 750 °C while experiencing a combination of complete and partial decarburization at 800 °C, transitioning solely to partial decarburization above 850 °C. The decarburized layer thickness measured at 750 and 800 °C is 140 and 200 μm respectively; the total decarburization layer thickness exhibits an exponential increase with the temperature. The thickness of the completely decarburized layer, influenced by varying factors across temperature ranges, initially rises and subsequently declines with the escalation of temperature, reaching its maximum at ≈750 °C. The maximum value of complete decarburization is 146 μm. Simultaneously, the total depth of decarburization is found to be proportional to the square root of time, adhering to Fick's second law. The fitting result is expressed as x = 165.47t1/2 at 750 °C. Notably, the existence of the decarburized layer results in a decrement in both the tensile strength and yield strength of the component, albeit accompanied by a marginal improvement in ductility. [ABSTRACT FROM AUTHOR]

Data on hyperuricemia-related changes in coronary atherosclerosis are limited, especially in sex difference. This study evaluated the association between hyperuricemia and coronary artery calcification (CAC) progression in asymptomatic Korean men and women. We analysed the data of 12,316 asymptomatic adults (51.7 ± 8.5 years; 84.2% men) with a mean follow-up of 3.3 years. Participants were divided into two groups: those with and without hyperuricemia (serum uric acid levels > 7.0 mg/dL for men and > 6.0 mg/dL for women). CAC progression was defined as a difference of ≥ 2.5 between the square roots of the baseline and follow-up coronary artery calcium score (CACS) (Δ√transformed CACS). The incidence of CAC progression was higher in men with hyperuricemia than in those without the condition (37.9% vs. 32.3%, P < 0.001); however, no significant difference in the incidence of CAC progression was observed in women with and without hyperuricemia (20.2% vs. 15.8%, P = 0.243). After adjusting for age, hypertension, diabetes, dyslipidaemia, obesity, current smoking status, serum creatinine, baseline CACS, and inter-scan periods, hyperuricemia was associated with increased risk of CAC progression in men (odds ratio [OR]: 1.20, 95% confidence interval [CI]: 1.06 − 1.36, P = 0.004); however, hyperuricemia was not significantly associated with the risk of CAC progression in women (OR: 0.73, 95% CI: 0.36 − 1.49, P = 0.385). In conclusion, hyperuricemia is more closely associated with CAC progression in men than in women among asymptomatic Korean adults. [ABSTRACT FROM AUTHOR]

Background: Both insulin resistance and hyperglycemia are important risk factors for atherosclerosis. While the characteristics of atherosclerosis are obviously different according to established diabetes, little has been known regarding the risk of coronary artery calcification (CAC) progression related to the biomarkers of atherogenic index of plasma (AIP), triglyceride glucose (TyG) index, and hemoglobin A1C (HbA1C) in conditions with and without diabetes. Methods: We analyzed 12,326 asymptomatic Korean adults (mean age 51.7 ± 8.5 years; 84.2% males; 15.8% with diabetes) over a median follow-up period of 3.0 years. AIP was defined as the base-10 logarithm of the ratio of triglyceride concentration (mmol/L) to high-density lipoprotein cholesterol (mmol/L). The TyG index was calculated as ln (fasting triglycerides [mg/dL] × fasting glucose [mg/ dL]/2). CAC progression was defined using the SQRT method, as a difference of ≥ 2.5 between the square roots (√) of baseline and follow-up coronary artery calcium scores (CACS) (Δ√transformed CACS). Logistic regression models adjusted for interscan periods were used to estimate the odds ratio (OR). Results: The levels of AIP, TyG index, and HbA1C were significantly higher in diabetics than in non-diabetics. CAC progression was more frequently observed in diabetics (46.9%) than in non-diabetics (28.0%). After adjusting for age, sex, hypertension, hyperlipidemia, obesity, current smoking status, serum creatinine levels, baseline CACS, and interscan period, AIP (per-0.1 unit increase) was associated with CAC progression in only non-diabetics (OR: 1.04, 95% confidence interval [CI]: 1.02 − 1.06; P < 0.001). In contrast, HbA1C level (per-1% increase) was significantly associated with CAC progression in only diabetics (OR: 1.19, 95% CI: 1.08 − 1.32; P = 0.001). The TyG index (per-1 unit increase) was associated with CAC progression in both non-diabetics (OR: 1.32, 95% CI: 1.19 − 1.46; P < 0.001) and diabetics (OR: 1.33, 95% CI: 1.10 − 1.60; P = 0.003). Conclusions: The associations between AIP, TyG index, and HbA1C levels with CAC progression vary according to established diabetes. Of these biomarkers, TyG index is independently associated with CAC progression irrespective of established diabetes. [ABSTRACT FROM AUTHOR]

Stochastic and secular variations in the spin frequency |$\nu$| of a rotation-powered pulsar complicate the interpretation of the measured braking index, n , in terms of a power-law spin-down torque |$\propto \nu ^{n_{\rm pl}}$|⁠. Both categories of variation can lead to anomalous braking indices, with |$\vert n \vert = \vert \nu \ddot{\nu } / \dot{\nu }^2 \vert \gg 1$|⁠ , where the overdot symbolizes a derivative with respect to time. Here, we quantify the combined effect of stochastic and secular deviations from pure power-law spin-down on measurements of n. Through analytical calculations, Monte Carlo simulations involving synthetic data, and modern Bayesian timing techniques, it is shown that the variance of n satisfies the predictive, falsifiable formula |$\langle n^{2} \rangle = (n_{\rm pl}+\dot{K}_{\rm dim})^{2}+\sigma _{\rm dim}^{2}$|⁠ , where |$\dot{K}_{\rm dim}$| is inversely proportional to the time-scale |$\tau _K$| over which the proportionality constant of the power-law spin-down torque varies, |$\sigma _{\rm dim}$| is proportional to the timing noise amplitude and inversely proportional to the square root of the total observing time, and the average is over an ensemble of random realizations of the timing noise process. The anomalous regime |$\langle n^2 \rangle \gg 1$| occurs for |$\dot{K}_{\rm dim} \gg 1$|⁠ , |$\sigma _{\rm dim} \gg 1$|⁠ , or both. The sign of n depends in part on the sign of |$\dot{K}_{\rm dim}$|⁠ , so it is possible to measure unequal numbers of positive and negative n values in a large sample of pulsars. The distinguishable impact of stochastic and secular anomalies on phase residuals is quantified to prepare for extending the analysis of synthetic data to real pulsars. [ABSTRACT FROM AUTHOR]

We show weighted non-autonomous L q (L p) maximal regularity for families of complex second-order systems in divergence form under a mixed regularity condition in space and time. To be more precise, we let p , q ∈ (1 , ∞) and we consider coefficient functions in C t β + ε with values in C x α + ε subject to the parabolic relation 2 β + α = 1. If p < d α , we can likewise deal with spatial H x α + ε , d α regularity. The starting point for this result is a weak (p , q) -solution theory with uniform constants. Further key ingredients are a commutator argument that allows us to establish higher a priori spatial regularity, operator-valued pseudo differential operators in weighted spaces, and a representation formula due to Acquistapace and Terreni. Furthermore, we show p -bounds for semigroups and square roots generated by complex elliptic systems under a minimal regularity assumption for the coefficients. [ABSTRACT FROM AUTHOR]

In this paper, a delayed predator–prey model with a square root functional response is structured and analyzed. Through a discussion of the time delay and an analysis of the characteristic equations, the local stability of the boundary equilibrium and the positive equilibrium and the existence of Hopf bifurcation are investigated. On this basis, the critical value of the Hopf bifurcation is derived. According to the central manifold theorem and normal form theory, the nature of the Hopf bifurcation is obtained. Finally, by conducting numerical simulations, it is observed that incorporating a time delay can influence the stability of the predator and prey populations, causing periodic oscillations in the number of two populations. [ABSTRACT FROM AUTHOR]

Lithium‐ion batteries have been a major energy source in electric vehicles because of their strong adaptability in operating conditions. Accurate estimation of state of charge (SOC) for lithium‐ion batteries can efficiently improve the efficiency of battery energy utilization. However, SOC estimation is complicated in operating conditions with unknown model parameters. This study proposes an adaptive square root central difference Kalman filter (ASRCDKF) algorithm based on the equivalent circuit model to achieve high‐precision estimation of SOC. First of all, to avoid an open‐circuit voltage test, a linear Kalman filter is constructed to realize real‐time estimation of unknown parameters in the measurement equation. Then, to improve the stability of the algorithm, a square root method is used to ensure a positive semi‐definite of the error covariance matrix that is based on the adaptive central difference Kalman filter algorithm. Model parameters are considered as the state to be estimated, and the joint estimation of the model parameters and SOC is realized by an ASRCDKF algorithm. After that, the linear Kalman filter is coupled with the ASRCDKF to realize the accurate estimation of SOC in the case of both the state equation and the measurement equation including unknown parameters. Last, the ASRCDKF algorithm is compared with the adaptive central difference Kalman filter algorithm and the adaptive cubature Kalman filter algorithm under two sets of operating conditions. The results show that the SOC estimation of the ASRCDKF algorithm is more significantly accurate than other algorithms under different operating conditions. [ABSTRACT FROM AUTHOR]

Road roughness significantly impacts vehicle safety and dynamic responses. For nonlinear suspension systems, the nonlinear characteristics often make it challenging for estimators to identify the actual road roughness accurately. This paper proposes a hybrid road roughness identification algorithm based on nonlinear auto-regressive with exogenous inputs (NARX) and a process noise adaptive square root cubature Kalman filter (PASCKF) to address this issue. Driven by vehicle acceleration data, an NARX-based road roughness identification system is constructed to mitigate the model uncertainties. Furthermore, a hybrid strategy is proposed. On the one hand, the accurate road roughness estimated by the NARX is converted into process noise covariance, enhancing the estimator's accuracy and convergence rate. Another switching strategy is proposed to optimize the non-convergence issues of the PASCKF. Finally, simulation and actual vehicle experiment data demonstrate that this approach offers superior identification accuracy and adaptability compared to the standalone SCKF algorithm. [ABSTRACT FROM AUTHOR]

For a graph G with vertex set V G = { v 1 , v 2 , ... , v n } and edge set E G = { e 1 , e 2 , ... , e m } , let S G denotes the subdivision graph of G with vertex set V G ∪ E G . In S G , replace each vertex v i , i = 1 , 2 , ... , n , by n 1 vertices and join every vertex to the neighbors of v i . Then in the resulting graph, replace each vertex e j , j = 1 , 2 , ... , m , by m 1 vertices and join every vertex to the neighbors of e j . The resulting graph is denoted by S G (n 1 , m 1). This generalizes the construction of the subdivision graph S G to S G (n 1 , m 1) of a graph G. In this paper, we provide the complete information about the spectrum of S G (n 1 , m 1) using the spectrum of S G . Further, we determine the Laplacian spectrum of S G (n 1 , m 1) using the Laplacian spectrum of G , when G is a regular graph. Also, we find the Laplacian spectrum of S G (n 1 , m 1) using the Laplacian spectrum of S G when n 1 = m 1 . The energy of a graph G is defined as the sum of the absolute values of the eigenvalues of G. The incidence energy of a graph G is defined as the sum of the square roots of the signless Laplacian eigenvalues of G. Finally, as an application, we show that the energy of the graph S G (n 1 , m 1) is completely determined by the incidence energy of the graph G. [ABSTRACT FROM AUTHOR]

Activation functions(AFs) are crucial components in neural networks for deep learning. Piecewise linear functions(PLFs) have been widely employed to act as AFs, thanks to their computational efficiencies and simplicities. However, PLFs are not completely differentiable, have potential problems of training. The analytical expressions of AFs based on pure PLFs can be smoothed via mollified square root function(MSRF) method, inspired by SquarePlus method of ReLU approximation. In this paper, we propose a proposition defining AFs as maximum or minimum of two PLFs, and transform the results into a smoothed function via MSRF method. Based on MSRF, we modify the well-known AFs composed of two PLFs, three or four PLFs to regularized ones systematically, including ReLU, LReLU, vReLU, Step, Biplolar, BReLU(Bounded ReLU), Htanh(Hard Tanh), Pan(Frying pan function), STF(Soft Thresholding Formulas), HTF(Soft Thresholding Formulas), SReLU(S-shaped ReLU), MReLU(Mexican hat type ReLU), TSF(Trapezoid-shaped function) functions. Additionally, according to the equivalences of SquarePlus and SoftPlus functions, some classic compound AFs, such as ELU, Swish, Mish, SoftSign Logish and DLU functions, can be expressed via MSRF method also. The derivatives of their mollified versions demonstrate their smoothness properties. The proposed method can be extended to AFs composed of multiple PLFs easily, which will be investigated deeply in the future. [ABSTRACT FROM AUTHOR]

This paper experimentally studied water jets issued vertically downward from rectangular nozzles into still ambient air. Two rectangular nozzles having the same aspect ratio but different cross-sectional areas were tested under different water flow rates. The water jet surface characteristics while falling were explored using a high-speed camera. The phenomenon of axis switching was observed under both rectangular nozzles. The magnitude of the jet surface fluctuation with falling distance was found to follow an exponential growth. The breakup length was found linearly increasing with the square root of the liquid Weber number. The diameters of the droplets released from jet breakup were analyzed and were mostly around 2 cm. Practical Applications: This investigation studied the characteristics of water jets issued from two rectangular nozzles, including the axis-switching phenomenon, surface wave disturbance, jet breakup length, and diameter of droplets. The outcomes of this study contribute to a better understanding of rectangular jet flows in practical applications. For example, the water flow discharged from spillway gates can be approximated as a large rectangular water jet, the breakup features of such water flows can be estimated, which are closely related to the total dissolved gas level downstream of the dam. Also, the flow inside a dropshaft can be approximated as a rectangular water jet. The results of jet breakup length in this study can provide design reference for noncircular jets. [ABSTRACT FROM AUTHOR]

We provide a framework to analyze control policies for the restless Markovian bandit model under both finite and infinite time horizons. We show that when the population of arms goes to infinity, the value of the optimal control policy converges to the solution of a linear program (LP). We provide necessary and sufficient conditions for a generic control policy to be (i) asymptotically optimal, (ii) asymptotically optimal with square root convergence rate, and (iii) asymptotically optimal with exponential rate. We then construct the LP-index policy that is asymptotically optimal with square root convergence rate on all models and with exponential rate if the model is nondegenerate in finite horizon and satisfies a uniform global attractor property in infinite horizon. We next define the LP-update policy, which is essentially a repeated LP-index policy that solves a new LP at each decision epoch. We conclude by providing numerical experiments to compare the efficiency of different LP-based policies. Funding: This work was supported by Agence Nationale de la Recherche [Grant ANR-19-CE23-0015]. [ABSTRACT FROM AUTHOR]

The calibration of hydrological models through the use of automatic algorithms aims at identifying parameter sets that minimize the deviation of simulations from observations (often streamflows). Further, the choice of objective function (i.e. the criterion or combination of criteria for optimization) can significantly impact the parameter set values identified as optimal by the algorithm. This article discusses how mathematical transformations, which are sometimes applied to the target variable before calculating the objective function, impact model simulations. Such transformations, for example square root or logarithmic, aim at increasing the weight of errors made in specific ranges of a hydrograph. We show in a catchment set that the impact of these transformations on the obtained time series can sometimes be different from their expected behaviour. Extreme transformations, such as squared or inverse squared transformations, lead to models that are specialized for extreme streamflows but show poor performance outside the range of the targeted streamflows and are less robust. Other transformations, such as the power 0.2 and the Box–Cox and logarithmic transformations, can be categorized as more generalist and show good performance for the medium range of streamflows, along with acceptable performance for extreme streamflows. [ABSTRACT FROM AUTHOR]

Earlier studies acknowledged that the design speed does not principally assure consistency in the design of highway geometric elements. Methodologies for estimating operating speeds are limited to specific or local traffic conditions and design standards, as in various studies conducted on two-lane and multi-lane highways. The present study develops operating speed models of the vehicle types observed on horizontal curves and tangent sections on two-lane highways in southern parts of India. Geometric features of the curve section and adjacent tangent sections, such as the radius of the curve, curve length, deflection angle, degree of curvature, gradient, carriageway width, and shoulder width, are obtained from the field. The speed data collected at 24 locations on the highway, including curved and tangent gradient sections, are used to analyze and model operating speed. The results indicate that the inverse of the square root of the radius appears to be an influencing parameter for modeling the operating speed of vehicles. The operating speed is sensitive for a curve radius of up to 600 m; thereafter, the operating speed appears insignificant. On tangent sections, the gradient has a larger influence on the operating speeds of all vehicle types. The operating speed models are validated and compared with models available in the literature. The proposed models developed in the present study are helpful to traffic engineers for predicting the operating speed on two-lane highways. [ABSTRACT FROM AUTHOR]

Speech separation is crucial for effective speech processing in multi-talker conditions, especially in real-time, low-latency applications. In this study, the Time-Domain Audio Separation Network (TasNet) and Dual-Path Recurrent Neural Network were used to perform a time-domain multiple-speaker speech separation challenge. One-dimensional conventional recurrent neural networks (RNNs) are not capable of accurately simulating long sequences. When their receptive length exceeds the sequence field, 1-D CNNs cannot recreate utterance-level sequences. Dual-Path Recurrent Neural Network (DPRNN) breaks up the lengthy sequential input that progressively performs intra- and inter-chunk operations with input lengths proportional to the square root of the beginning sequence length. Model outputs are more efficient than earlier systems, improving performance on the Libri Mix dataset. Investigations show that the DPRNN, sample-level modeling, and time-domain audio separation network can replace present methods. EEND-SS and other separation algorithms perform worse than DPRNN. The suggested model was able to achieve (12.376) SI-SDR, (0.969) STOI (short-time objective intelligibility), (12.363) SDR, (9.363) DER, and (97.193) SCA. [ABSTRACT FROM AUTHOR]

The well-known twin-field quantum key distribution (TF-QKD) protocol is the first one to overcome the fundamental rate-distance limit without quantum repeaters. It encodes the key information into phases of the light, and has a secret key rate scaling with the square root of the transmission transmittance by taking advantage of single-photon interference. Inspired by the idea in TF-QKD, we proposed a polarization encoding protocol to break the rate-distance limit by the property of the two states with orthogonal polarizations, named no-interfering QKD (NI-QKD). Two effective events are defined in which no interference happens. Simulation results show that the proposed protocol also holds the capacity of surpassing the Pirandola–Laurenza–Ottaviani–Banchi (PLOB) bound. Moreover, it has a better performance than no-phase-postselection TF-QKD (NPP-TF-QKD), one of TF-QKD's variants, and its communication distance can reach at most 424 km. The relationships between the performance and the polarization misalignment, the phase mismatch are discussed. It turns out that one event is very robust against polarization misalignment while the other is not, and both events are sensitive to phase mismatch. The mutual information of the effective events under collective attack is also calculated, which is lower than that of NPP-TF-QKD. This new protocol provides a new angle of exploring QKD and improving the secret rate. [ABSTRACT FROM AUTHOR]

Acceleration of objects in fluids widely exists in biological propulsions and contains rich unsteady fluid mechanisms. In this paper, the instantaneous drag force on accelerating normal flat plates (circular, elliptical, square, and rectangular plates) in a wide range of dimensionless acceleration ( a * = 1 6 ∼ 2) is measured, and the underlying mechanism for force generation is investigated. At first, we find that the drag force coefficient generally scales with the square root of a * when a * < 1.0 , coinciding with the scaling law given by Reijtenbagh et al. (PRL. 2023,130,174001). However, the drag force coefficient more linearly scales with a * rather than a * when a * > 1.0 , thereby indicating acceleration plays two distinct roles on the force generation depending on a * . Moreover, two scaling laws are built to quantitatively describe the two distinct roles of a * on the drag force generation. Based on fluid impulse, the drag force is largely contributed by the added mass of the accelerating plates (added mass force) and vorticity generation fed by the shear layer on the edge of the plates (vortex creation force). When a * < 1.0 , the vortex creation force scales with a * and almost contributes to the total drag force. When a * > 1.0 , the added mass force scaling with a * contributes to most of the drag force. Furthermore, the two force generation mechanisms associated with acceleration ( a * ) are independent, and a criterion based on the energy ratio is proposed to identify the transition of the two force generation mechanisms. The present results uncover the role of acceleration in force generation and explain the inconsistencies of using one quasi-steady model in describing the force on accelerating plates. [ABSTRACT FROM AUTHOR]

Using adaptive filtering to estimate the frequency of power systems has become a popular trend. In recent years, however, few studies have been performed on adaptive frequency estimations in non-stationary noise environments. In this paper, we propose the distributed complex inverse square root algorithm and distributed augmented complex inverse square root algorithm for the frequency estimation of power systems based on the widely linear model and the inverse square root cost function, where the function can restrain both positive and negative large errors, based on its symmetry. Moreover, the wireless sensor networks support monitoring and adaptation for the frequency estimation in the distributed networks, and the proposed approach can ensure good robustness of the balanced or unbalanced three-phase power system with the help of a local complex-value voltage signal generated by Clark's transformation. In addition, the bound of step size is driven by the global vectors, and that low computation complexity do not hinder those performances. The results of several experiments demonstrate that our algorithms can effectively estimate the frequency in impulsive noise environments. [ABSTRACT FROM AUTHOR]

To navigate changes within a highly dynamic and complex environment, it is crucial to compare current visual representations of a scene to previously formed representations stored in memory. This process of mental comparison requires integrating information from multiple sources to inform decisions about changes within the environment. In the present article, we combine a novel systems factorial technology change detection task (Blunden et al., 2022) with a set size manipulation. Participants were required to detect 0, 1, or 2 changes of low and high detectability between a memory and probe array of 1–4 spatially separated luminance discs. Analyses using systems factorial technology indicated that the processing architecture was consistent across set sizes but that capacity was always limited and decreased as the number of distractors increased. We developed a novel model of change detection based on the statistical principles of basic sampling theory (Palmer, 1990; Sewell et al., 2014). The sample size model, instantiated parametrically, predicts the architecture and capacity results a priori and quantitatively accounted for several key results observed in the data: (a) increasing set size acted to decrease sensitivity (d′) in proportion to the square root of the number of items in the display; (b) the effect of redundancy benefited performance by a factor of the square root of the number of changes; and (c) the effect of change detectability was separable and independent of the sample size costs and redundancy benefits. [ABSTRACT FROM AUTHOR]

Spatial homoscedasticity of the error term is commonly assumed in mixed geographically weighted regression analysis. In many practical situations, however, rarely can we know a priori whether the error term is homoscedastic or not. Therefore, it is necessary to first detect the spatial heteroscedasticity of the error term before the mixed geographically weighted regression model is used. In this paper, a statistic is constructed based on the square root of the absolute value of the residuals obtained by the two step estimation. The three moment $ \chi ^2 $ χ 2 approximation is applied to compute the p value of the test. Furthermore, simulation results show that the proposed test method has high accuracy and satisfactory power in detecting spatial heteroscedasticity, even when the model errors follow non-normal distributions. A real-world data set is analysed to demonstrate the application of the proposed test method and the paper is ended with a conclusion. [ABSTRACT FROM AUTHOR]

In order to overcome the uncertainty in hyperspectral estimation of soil organic matter content, this paper aim to establish a grey information relational estimation model of soil organic matter content based on hyperspectral data and grey information theory. Based on 76 samples in Zhangqiu District of Jinan City, Shandong province of China, the spectral data are first transformed by the nine methods such as square root, first order differentiation of the logarithm reciprocal, and so on, the correlation coefficient is calculated, and the estimation factors are selected by using the principle of great maximum correlation. Then, according to the principle of increasing information and taking maximum method, the spectral estimation factors of each sample are sorted from small to large, and the grey information sequence is formed, and the grey relational estimation model of soil organic matter content is constructed based on the information chain. Finally, the estimation results based on different information chains are fused twice, and compared with the commonly used estimation methods. The results of the method in this paper show that the average relative error of the 12 test samples is 5.576%, and the determination coefficient R2 is 0.934, and the estimation accuracy is higher than that of commonly used methods such as multiple linear regression, BP neural network and support vector machine. The results show that the grey information relational estimation model using hyperspectral data proposed in this paper is feasible and effective, and it provides a new way for hyperspectral estimation of soil organic matter and other soil properties. [ABSTRACT FROM AUTHOR]

The time of concentration is an important concept in hydrology. It provides a characteristic hydrological response time (CHRT) useful in many applications. Estimation of the time of concentration is challenging because small watersheds (<100 km2) with sub-daily flow and precipitation records are uncommon. Many practitioners therefore use empirical equations developed from watersheds exposed to different climates and with different attributes. The main objective of this study is to develop an approach to estimate the CHRT from physiographic characteristics for small watersheds located in Ontario, Québec and the northeastern USA. Regression trees are used to identify the physiographic characteristics associated with CHRT. The fraction of lakes and wetlands was identified as the most significant attribute related to CHRT, followed by the ratio between the main watercourse length and the square root of the main watercourse slope. Uncertainties on estimated CHRT values based on regression tree are also provided. [ABSTRACT FROM AUTHOR]

Guyon and Lekeufack (Quant. Finance 23:1221–1258, 2023) recently proposed a path-dependent volatility model and documented its excellent performance in fitting market data and capturing stylised facts. The instantaneous volatility is modelled as a linear combination of two processes; one is an integral of weighted past price returns and the other is the square root of an integral of weighted past squared volatility. Each weighting is built using two exponential kernels reflecting long and short memory. Mathematically, the model is a coupled system of four stochastic differential equations. Our main result is the wellposedness of this system: the model has a unique strong (non-explosive) solution for all parameter values. We also study the positivity of the resulting volatility process and the martingale property of the associated exponential price process. [ABSTRACT FROM AUTHOR]

In this paper, we show that Hilbert space-valued stochastic models are robust with respect to perturbations, due to measurement or approximation errors, in the underlying volatility process. Within the class of stochastic-volatility-modulated Ornstein–Uhlenbeck processes, we quantify the error induced by the volatility in terms of perturbations in the parameters of the volatility process. We moreover study the robustness of the volatility process itself with respect to finite-dimensional approximations of the driving compound Poisson process and semigroup generator, respectively, when considering operator-valued Barndorff-Nielsen and Shephard stochastic volatility models. We also give results on square root approximations. In all cases, we provide explicit bounds for the induced error in terms of the approximation of the underlying parameter. We discuss some applications to robustness of prices of options on forwards and volatility. [ABSTRACT FROM AUTHOR]

Quantum computers have the capacity to solve certain complex problems more efficiently than classical computers. To fully leverage these quantum advantages, adapting classical arithmetic for quantum systems in a circuit level is essential. In this paper, we introduce a depth-optimized quantum circuit of Gauss–Jordan elimination for matrices in binary. This quantum circuit is a crucial module for accelerating Information Set Decoding (ISD) using Grover's algorithm. ISD is a cryptographic technique used in analyzing code-based cryptographic algorithms. When combined with Grover's search, it achieves a square root reduction in complexity. The proposed method emphasizes the potential for parallelization in the quantum circuit implementation of Gauss–Jordan elimination. We allocate additional ancilla qubits to enable parallel operations within the target matrix and further reuse these ancilla qubits to minimize overhead from our additional allocation. The proposed quantum circuit for Gauss–Jordan elimination achieves the lowest Toffoli depth compared to the-state-of-art previous works. [ABSTRACT FROM AUTHOR]

This study aimed to use MTB-Task Cards to remediate the learning gaps in Grade 7 mathematics, ultimately leading to the creation of a handbook for developing, producing, and utilizing these cards. It investigated the least mastered learning competencies based on MELCs for the first and second quarters of the 2023-2024 school year, assessed students' performance before and after the implementation of MTB-Task Cards, and determined the mean gain performance. The study also examined whether there was a significant difference between actual accomplishment and the target level of mastery after implementing the MTB-Task Cards. Employing a quasi-experimental design, the research utilized pre-test and post-test evaluations to measure the intervention's impact on a non-random group of 135 Grade 7 students at Emilio V. Quizon National High School. Data were gathered through a researcher-made test and validated MTB-Task Cards, focusing on competencies students struggled with the most. Findings revealed substantial improvements in mathematical competencies such as fundamental operations on integers, estimating square roots, and evaluating algebraic expressions. Students' performance levels increased significantly post-intervention, with mastery levels exceeding 80% in the second quarter, indicating the effectiveness of MTB-Task Cards. The analysis showed a significant difference between actual accomplishment and the target mastery level, with a p-value of 0.000. The study proposed a handbook outlining rules and guidelines for the development, production, and utilization of MTB-Task Cards, emphasizing the importance of standardization, curriculum alignment, quality production, and effective classroom use. Recommendations included continuous monitoring of student progress, professional development for educators, innovative engagement strategies, and ongoing research to enhance the instructional efficacy of MTB-Task Cards. [ABSTRACT FROM AUTHOR]

Matrix diagonalization is almost always involved in computing the density matrix needed in quantum chemistry calculations. In the case of modest matrix sizes (≲4000), performance of traditional dense diagonalization algorithms on modern GPUs is underwhelming compared to the peak performance of these devices. This motivates the exploration of alternative algorithms better suited to these types of architectures. We newly derive, and present in detail, an existing Chebyshev expansion algorithm [Liang et al., J. Chem. Phys. 119, 4117–4125 (2003)] whose number of required matrix multiplications scales with the square root of the number of terms in the expansion. Focusing on dense matrices of modest size, our implementation on GPUs results in large speed ups when compared to diagonalization. Additionally, we improve upon this existing method by capitalizing on the inherent task parallelism and concurrency in the algorithm. This improvement is implemented on GPUs by using CUDA and HIP streams via the MAGMA library and leads to a significant speed up over the serial-only approach for smaller (≲1000) matrix sizes. Finally, we apply our technique to a model system with a high density of states around the Fermi level, which typically presents significant challenges. [ABSTRACT FROM AUTHOR]

We generalize a microscopic statistical mechanical theory of the activated dynamics of dilute spherical penetrants in glass-forming liquids to study the influence of crosslinking in polymer networks on the penetrant relaxation time and diffusivity over a wide range of temperature and crosslink fraction (fn). Our calculations are relevant to recent experimental studies of a nm-sized molecule diffusing in poly-(n-butyl methacrylate) networks. The theory predicts the penetrant relaxation time increases exponentially with the glass transition temperature, Tg(fn), which grows roughly linearly with the square root of fn due to the coupling of local hopping to longer-range collective elasticity. Moreover, Tg is also found to be proportional to a geometric confinement parameter defined as the ratio of the penetrant diameter to the mean network mesh size. The decoupling ratio of the penetrant and Kuhn segment alpha times displays a complex non-monotonic dependence on fn and temperature that is well collapsed based on the variable Tg(fn)/T. A model for the penetrant diffusion constant that combines activated relaxation and entropic mesh confinement is proposed, which results in a significantly stronger suppression of mass transport with degree of effective supercooling than predicted for the penetrant alpha time. This behavior corresponds to a new network-based type of "decoupling" of diffusion and relaxation. In contrast to the diffusion of larger nanoparticles in high temperature rubbery networks, our analysis in the supercooled regime suggests that for the penetrants studied the mesh confinement effects are of secondary importance relative to the consequences of crosslink-induced slowing down of activated hopping of glassy physics origin. [ABSTRACT FROM AUTHOR]

The given text is a technical document discussing mathematical equations and algorithms related to remote sensing and linear equation systems. It provides a precise definition of the rhombus convergence property and discusses the enhancement of Algorithm 2 for calculating vectors. The document demonstrates the application of algorithms to solve diagonal QUBO problems and includes examples using exact rational expressions. While the text may not be directly relevant to specific research topics, it may be useful for researchers studying remote sensing and mathematical algorithms. [Extracted from the article]

Office environments play a critical role in employee wellbeing and productivity. While the benefits of incorporating nature into workspaces have been recognized, the specific visual characteristics that contribute to restorativeness remain unclear. This study investigates how visual characteristics of office environments, specifically the presence of greenery and color complexity, are associated with perceived restorativeness. In Study 1, we developed a scale based on Attention Restoration Theory to measure the restorative characteristics of office environments, consisting of three subscales: Being Away, Fascination, and Extent. In Study 2, we used this scale to examine the correlation between the restorative characteristics of offices and the visual properties of office photographs. The results showed that the square root of the percentage of green area, the color fractal dimension, and the brightness fractal predicted perceived restorativeness. Notably, the color fractal dimension often showed a stronger effect than the amount of greenery per se. These findings suggest that both the presence of greenery and the overall complexity of color transitions in office spaces contribute to their restorative potential. Our study provides insights for designing more restorative office environments, emphasizing the importance of not only increasing greenery but also mimicking natural color patterns. The predictive model developed provides a practical tool for estimating the restorative potential of office designs. Although there are limitations such as the use of photographic assessments and the inability to fully explain the Extent component of restorativeness, this study contributes to our understanding of how to create more psychologically supportive work environments. [ABSTRACT FROM AUTHOR]

Leaf nitrogen content (LNC) is an important indicator for scientific diagnosis of the nutrition status of crops. It plays an important role in the growth, yield and quality of wolfberry. This study aimed to develop new spectral indices (NSIs) and constructed machine learning regression (MLR) models for predicting wolfberry tree LNC. By utilizing four smoothing methods and five mathematic transformation methods, we obtained the original spectral dataset and five spectral transformation datasets for quantitative analysis and model establishment. Subsequently, published vegetation indices (PVIs) were acquired, sensitive wavelengths (SWs) were screened and NSIs were calculated based on SWs. Then MLR models were constructed by combining NSIs from six spectral datasets with three machine learning algorithms. Finally, a comparison was made among the MLR models. The study indicated that the application of mathematical transformation highlighted the differences in spectra, the square root, first-derivative and second-derivative transformation improved the prediction accuracy of MLR models constructed based on NSIs (MLR-NSIs models). However, these transformations had little impact on improving the prediction ability of MLR models constructed based on PVIs (MLR-PVIs models). Additionally, The optimal model for predicting the LNC of wolfberry tree was obtained by using the Random Forest (RF) algorithm combined with NSIs developed by first-derivative transformation spectra. The determination coefficient of validation (Rv2) and ratio of percentage deviation (RPD) was 0.71 and 1.90, respectively. In conclusion, this study has demonstrated that the combination of hyperspectral transformation and machine learning is useful for improving the accuracy of LNC estimation in wolfberry trees. [ABSTRACT FROM AUTHOR]

Objective: This study aimed to evaluate the relationship between the weight-adjusted waist circumference index (WWI) and the frailty in American adults aged over 60 years. Methods: We utilized data from the National Health and Nutrition Examination Surveys (NHANES) spanning from 2007 to 2018. WWI was calculated using the square root of waist circumference (cm) divided by body weight (kg). The frailty index > 0.25 was employed to assess frailty. Weighted multivariate logistic regression was conducted to explore the association between WWI and frailty. Generalized Additive Modeling (GAM) was used to explore potential non-linear relationships. Receiver operating characteristic curve (ROC) analysis was used to assess the predictive ability of WWI for frailty. Results: The study encompassed 7765 participants. Higher WWI was significantly associated with higher odds of frailty. In the fully adjusted model, each unit increase of WWI was associated with an 82% increased odds of frailty (OR: 1.82, 95% CI: 1.61 -2.06; P < 0.001). GAM found significant nonlinear relationships and threshold effects. Conclusion: The study presented a robust correlation between elevated WWI and increased odds of frailty among American older adults. However, these findings require further validation in large-scale, prospective studies. [ABSTRACT FROM AUTHOR]

Background: Experimental studies of wound healing often use survival analysis and time to event outcomes or differences in wound area at a specific time point. However, these methods do not use a potentially large number of observations made over the course of a trial and may be inefficient. A model-based approach can leverage all trial data, but there is little guidance on appropriate models and functional forms to describe wound healing. Methods: We derive a general statistical model and review a wide range of plausible mathematical models to describe wound healing. We identify a range of possible derived estimands and their derivation from the models. Using data from a trial of an intervention to promote ulcer healing in patients affected by leprosy that included three measurement methods repeated across the course of the study, we compare the goodness-of-fit of the models using a range of methods and estimate treatment effects and healing rate functions with the best-fitting models. Results: Overall, we included 5,581 ulcer measurements of 1,578 unique images from 130 patients. We examined the performance of a range of models. The square root, log square root, and log quadratic models were the best fitting models across all outcome measurement methods. The estimated treatment effects magnitude and sign varied by time post-randomisation, model type, and outcome type, but across all models there was little evidence of effectiveness. The estimated effects were significantly more precise than non-parametric alternatives. For example, estimated differences from the three outcome measurements at 42-days post-randomisation were − 0.01 cm2 (-0.77, 0.74), -0.44 cm2 (-1.64, 0.76), and 0.11 cm2 (-0.87, 1.08) using a non-parametric method versus − 0.03 cm2 (-0.14, 0.06), 0.06 cm2 (-0.05, 0.17), and 0.03 cm2 (-0.07, 0.17) using a square-root model. Conclusions: Model-based analyses can dramatically improve the precision of estimates but care must be taken to carefully compare and select the best fitting models. The (log) square-root model is strongly recommended reflecting advice from a century ago. [ABSTRACT FROM AUTHOR]

Extensive research is currently underway to determine the security of existing ciphers in light of the advancements in quantum computing. Against symmetric key cryptography, Grover's search algorithm is a prominent attack, capable of reducing search costs to the square root. For using Grover's algorithm, it is imperative to embed the target cipher into a quantum circuit. Even so, this area of research is relatively new; it has garnered significant attention from the research community. In this study, we provide the first estimation of the cost of Grover's key search attack against the AES-based AEAD schemes Rocca-S, AEGIS-128, and Tiaoxin-346. Our analysis considers circuit depth restrictions specified in NIST's PQC standardization process. Considering NIST's maximum depth constraints, We present the overall cost of these attacks using gate count and depth-times-width metrics. We observed that for MAXDEPTH = 2 40 , Rocca-S, AEGIS-128, and Tiaoxin-346 can be retrieved using Grover's search algorithm with gate count of 1.09 × 2253, 1.14 × 2124, and 1.22 × 2124 respectively. Concerning the current updated values by NIST, these ciphers are secure in terms of the cost of implementing Grover's attack for key recovery. The quantum circuits of these ciphers are implemented using QISKIT, an open-source software development kit (SDK) designed for working with quantum computers running on the IBM Quantum Experience platform. [ABSTRACT FROM AUTHOR]

The article in Pharmacotherapy delves into the pharmacokinetics/pharmacodynamics analysis and optimal dosing regimens of unbound cefmetazole for patients with ESBL-E. Revised tables and figures are included to enhance reader understanding, evaluating the probability of target attainment in plasma against MICs of ESBL-E for cefmetazole regimens. The study offers valuable insights for clinical practice by presenting data on the probability of target attainment for cefmetazole regimens against ESBL-E isolate populations, with tables showing response rates for various dosing regimens based on body weight, creatinine clearance, and albumin levels. The document also includes abbreviations and notes on the probability of target attainment, with figures illustrating the data from the tables. [Extracted from the article]

The matrix square root is widely encountered in many fields of mathematics. In this paper, based on the properties of M-matrix and quadratic matrix equations, we study the square root of M-matrix, and prove that for a regular M-matrix there always exists a regular M-matrix as its square root. In addition, a structure-preserving doubling algorithm is proposed to compute the square root. Theoretical analysis and numerical experiments are given to show that our method is feasible and is effective under certain conditions. [ABSTRACT FROM AUTHOR]

A comprehensive process model for 4H‐SiC oxidation is created and calibrated against a very large collection of experimental data. The model reproduces measured oxide thickness for Si‐face, C‐face, and a‐face SiC wafers, in the temperature range 950–1500 °C, in the pressure range 0.25–4.0 atm, in the thickness range 3–1600 nm, and for SiC doping ranging between 1019 cm−3 n‐type and 1019 cm−3 p‐type. The model is based on the Massoud model: Oxidation is driven by oxidants (O2, H2O) which are present in the gas phase, diffuse through the oxide, and form SiO2 at the oxide–SiC interface. For thin oxides, the interface reaction rate includes empirical correction terms which add to the oxidation rate, and which asymptotically approach zero with increasing oxide thickness. For dry oxidation, a remarkable dependence on the O2 partial pressure is discovered: For thick oxides, the oxidation rate scales linearly with the pressure, but the correction term for thin oxides scales with the square root of the pressure. This suggests that the atomistic processes responsible for the fast initial growth of oxides involve the splitting of O2 molecules into two O atoms. [ABSTRACT FROM AUTHOR]

Multiplication, division, and square root operations introduce significant challenges in digital signal processing (DSP) systems, traditionally requiring multiple operations that increase execution time and hardware complexity. This study presents a novel approach that leverages binary logarithms to perform these operations using only addition, subtraction, and shifts, enabling a unified hardware implementation—a marked departure from conventional methods that handle these operations separately. The proposed design, involving logarithm and antilogarithm calculations, exhibits an algebraically symmetrical pattern that further optimizes the processing flow. Additionally, this study introduces innovative log-domain correction terms specifically designed to minimize computation errors—a critical improvement over existing methods that often struggle with precision. Compared to standard hardware implementations, the proposed design significantly reduces hardware resource utilization and power consumption while maintaining high operational frequency. [ABSTRACT FROM AUTHOR]

Large ensembles of model simulations are frequently used to reduce the impact of internal variability when evaluating climate models and assessing climate change induced trends. However, the optimal number of ensemble members required to distinguish model biases and climate change signals from internal variability varies across models and metrics. Here we analyze the mean, variance and skewness of precipitation and sea surface temperature in the eastern equatorial Pacific region often used to describe the El Niño–Southern Oscillation (ENSO), obtained from large ensembles of Coupled model intercomparison project phase 6 climate simulations. Leveraging established statistical theory, we develop and assess equations to estimate, a priori, the ensemble size or simulation length required to limit sampling‐based uncertainties in ENSO statistics to within a desired tolerance. Our results confirm that the uncertainty of these statistics decreases with the square root of the time series length and/or ensemble size. Moreover, we demonstrate that uncertainties of these statistics are generally comparable when computed using either pre‐industrial control or historical runs. This suggests that pre‐industrial runs can sometimes be used to estimate the expected uncertainty of statistics computed from an existing historical member or ensemble, and the number of simulation years (run duration and/or ensemble size) required to adequately characterize the statistic. This advance allows us to use existing simulations (e.g., control runs that are performed during model development) to design ensembles that can sufficiently limit diagnostic uncertainties arising from simulated internal variability. These results may well be applicable to variables and regions beyond ENSO. Plain Language Summary: Earth's climate naturally fluctuates on intraseasonal to interdecadal timescales, confounding the evaluation of climate models and the detection of trends linked to climate change. To tackle this challenge, scientists produce ensembles of simulations with identical external forcings (e.g., volcanic eruptions, greenhouse gas emissions) but plausibly different initial conditions. In this study, we analyze how these ensembles can be used to reduce the uncertainty of the simulated climate, to help guide the design of future ensembles and optimize the use of available computing resources. Key Points: Large ensembles of climate simulations are analyzed to characterize the sampling uncertainty of El Niño–Southern Oscillation statisticsAs expected, uncertainty of these statistics decreases with the square root of the number of simulated years provided by the ensembleA simple equation developed to predict the ensemble size required to limit this sampling uncertainty to within a given tolerance [ABSTRACT FROM AUTHOR]

Hardy conjectured that the error term arising from approximating the number of lattice points lying in a radius‐R$R$ disc by its area is O(R1/2+o(1))$O(R^{1/2+o(1)})$. One source of support for this conjecture is a folklore heuristic that uses i.i.d. random variables to model the lattice points lying near the boundary and square root cancellation of sums of these random variables. We examine this heuristic by studying how these lattice points interact with one another and prove that their autocorrelation is determined in terms of a random model. Additionally, it is shown that lattice points near the boundary which are "well separated" behave independently. We also formulate a conjecture concerning the distribution of pairs of these lattice points. [ABSTRACT FROM AUTHOR]

In the present paper, we consider the problem of plane wave reflection and transmission at the boundary of two different transversely isotropic microstretch elastic half-spaces. The main purpose of this problem is to examine the effect of microstretch elasticity, microrotation and transverse isotropy on wave propagation. Four reflected and four transmitted waves are produced when a plane wave is incident at the boundary between two different half-spaces. The relations for Amplitude ratios and Energy ratios of reflected and transmitted waves are derived which depends upon the material parameters and angle of propagation. The Amplitude ratios and square root of Energy ratios are plotted against the angle of propagation using MATLAB Software to observe the effect of microstretch elasticity, microrotation and transverse isotropy. Theoretical and numerical results show the significant dependence of microstretch fields, microrotation and transverse isotropy on wave propagation. [ABSTRACT FROM AUTHOR]

Let k ∈ N and suppose we are given k integers 1 ≤ a 1 , ... , a k ≤ n. If a 1 + ... + a k is not an integer, how close can it be to one? When k = 1 , the distance to the nearest integer is ≳ n − 1 / 2. Angluin-Eisenstat observed the bound ≳ n − 3 / 2 when k = 2. We prove there is a universal c > 0 such that, for all k ≥ 2 , there exists a c k > 0 and k integers in { 1 , 2 , ... , n } with 0 < ‖ a 1 + ... + a k ‖ ≤ c k ⋅ n − c ⋅ k 1 / 3 , where ‖ ⋅ ‖ denotes the distance to the nearest integer. This is a case of the square-root sum problem in numerical analysis where the usual cancellation constructions do not apply: already for k = 3 , the problem appears hard. [ABSTRACT FROM AUTHOR]

The exponential growth in internet data usage has created a pressing demand for highly efficient Network Intrusion Detection Systems (NIDS) capable of scaling with ever-increasing bandwidths to safeguard sensitive information. A cornerstone of NIDS, packet inspection, hinges on the ability to rapidly identify and analyze patterns within incoming data streams. The more diverse and extensive the pattern database, the more robust and effective the NIDS becomes. While the parallel failure-less version of the Aho-Corasick (AC) algorithm provides maximum parallelism, it faces significant memory constraints due to the large transition tables generated when dealing with a vast number of patterns. To mitigate this limitation and enhance the scalability of NIDS, we introduce a novel parallel failure-less compressed hashed variation of the Aho-Corasick algorithm. Our proposed approach leverages the power of compression and hashing techniques to significantly reduce memory consumption without compromising performance. Empirical evaluations demonstrate that our algorithm requires only a fraction (approximately the square root) of the memory footprint compared to the original parallel failure-less Aho-Corasick algorithm, making it a more practical and scalable solution for modern NIDS architectures. [ABSTRACT FROM AUTHOR]

In order to investigate the cause of the liquid phase migration (LPM) and the shape distortion when WC-Co cemented carbides (alloys) undergo a temperature gradient during cooling, round bars of WC-10 mass%Co alloys are inserted halfway under the coil of the induction heating furnace and partially heated at 1673 K. The results showed that Co migrated from the higher temperature side to the lower one and increase of Co content and bar diameter occurred in a zone at the outside of the coil. The alloy containing free carbon had a significantly narrow Co-increased zone and the zone located at a lower temperature. The volume transfer (V) of Co during heating changed in proportional to the square root of the heating time (t). It was considered that the phenomenon was the same as the LPM between a couple of alloys having different Co content in our previous report. We have concluded that the Co-increased zone in this study corresponds to the Co solid-liquid coexistence zone during partial heating and the Co increase is caused by the migration pressure occurred in the zone, which we named ΠSL. ΠSL should be generated because FWC/Co(S) derived from γWC/Co(S) and γCo(L)/Co(S) is higher than FWC/Co(L) derived from γWC/Co(L). [ABSTRACT FROM AUTHOR]