Search Results (44)

The Automatic Identification System (AIS) frequently suffers from data loss and irregular report intervals in real maritime environments, compromising the reliability of downstream navigation, monitoring, and trajectory reconstruction tasks. To address these challenges, we propose BAARTR (Boundary-Aware Adaptive Regression for Kinematically Consistent Vessel Trajectory Reconstruction), a novel kinematically consistent interpolation framework. Operating solely on time, latitude, and longitude inputs, BAARTR explicitly enforces boundary velocities derived from raw AIS data. The framework adaptively selects a velocity-estimation strategy based on the AIS reporting gap: central differencing is applied for short intervals, while a hierarchical cubic velocity regression with a quadratic acceleration constraint is employed for long or irregular gaps to iteratively refine endpoint slopes. These boundary slopes are subsequently incorporated into a clamped quartic interpolation at a 1 s resolution, effectively suppressing overshoots and ensuring velocity continuity across segments. We evaluated BAARTR against Linear, Spline, Hermite, Bezier, Piecewise cubic hermite interpolating polynomial (PCHIP) and Modified akima (Makima) methods using real-world AIS data collected from the Mokpo Port channel, Republic of Korea (2023–2024), across three representative vessels. The experimental results demonstrate that BAARTR achieves superior reconstruction accuracy while maintaining strictly linear time complexity ($\mathit{O}\left(\mathit{N}\right)$). BAARTR consistently achieved the lowest median Root Mean Square Error (RMSE) and the narrowest Interquartile Ranges (IQR), producing visibly smoother and more kinematically plausible paths-especially in high-curvature turns where standard geometric interpolations tend to oscillate. Furthermore, sensitivity analysis shows stable performance with a modest training window (n ≈ 16) and minimal regression iterations (m = 2–3). By reducing reliance on large training datasets, BAARTR offers a lightweight, extensible foundation for post-processing in Maritime Autonomous Surface Ship (MASS) and Vessel Traffic Service (VTS), as well as for accident reconstruction and multi-sensor fusion. Full article

With the growing number of applications in embedded systems—such as IoT modules, smart sensors, and wearable devices—there is an increasing demand for fast and accurate computations on resource-constrained platforms. In this paper, we present a new method for computing n-th roots in floating-point arithmetic based on an initial estimate generated by a “magic constant,” followed by one or two iterations of a modified Newton–Raphson or Householder algorithm. For cubic and quartic roots, we provide C implementations operating in single-precision floating-point format. The proposed algorithms are evaluated in terms of maximum relative error and execution time on selected microcontrollers. They exhibit high accuracy and noticeably reduced computation time. For example, our methods for computing cubic roots outperform the standard library function cbrtf() in both speed and precision. The results may be useful in a variety of fields, including biomedical and biophysical applications, statistical analysis, and real-time image and signal processing. Full article

Intrinsic optical bi-stability in dense two-level systems is developed for the bad cavity limit where electromagnetic modes are adiabatically eliminated. Each atom interacts via dipole–dipole forces with its nearby spatial distribution of atoms. The theory is developed into two parts, corresponding to the short sample, with dimensions shorter than the wavelength, and the long sample. In both cases, the local field corrections modify the Maxwell–Bloch equations, so that cubic or quartic equations are obtained for the inversion of population as a function of the external light intensity, thus leading to intrinsic bi-stability. The effects of noise sources on intrinsic bi-stability were treated, and I found that while the observability of bi-stability was not obtained experimentally for a simple two-level system, there were many observations of bi-stability obtained through the ‘up-conversion’ of rare earth excited crystals. I show the differences between these two systems. Full article

In this paper we study the properties of Kasner cosmological solutions in Lovelock gravity. Recent progress in the investigation of flat cosmological models in Lovelock gravity unveiled the fact that in quadratic (Gauss–Bonnet) and cubic Lovelock gravities, the higher-order power-law solutions could play the role of both future and past asymptotes, and under some conditions, there could exist a smooth transition between them. So it is natural to question if this feature is unique to Gauss–Bonnet and cubic Lovelock gravities, or if it is a general feature of Lovelock gravity. Our analysis suggests that starting from quartic and in all higher-order Lovelock gravities, the high-order Kasner solution cannot play the role of a past asymptote, not only preventing the abovementioned transition from happening, but also potentially hindering the possibility of reaching viable compactification. Full article

Pine caterpillar (Dendrolimus) infestations threaten pine forests, causing severe ecological and economic impacts. Identifying the driving factors behind these infestations is essential for effective forest management. This study uses the APCIRD framework combined with an improved random forest model to analyze spatiotemporal changes in infestation risk and the driving effects of habitat factors in Northeast China. From 2019 to 2024, we applied SHapley Additive exPlanations (SHAP), frequency analysis, fitting functions, and GeoDetector to quantify the impact of key drivers, such as snow cover and soil, on infestation risk. The findings include (1) the APCIRD framework with the MLP-random forest model (MRF) accurately assesses infestation risks. MRF is composed of MLP and random forest. Between 2019 and 2024, areas with high infestation risk declined, shifting from higher to lower levels, with Eastern Heilongjiang and Southwest Liaoning remaining as key concern areas; (2) snow cover and soil factors are critical to infestation risk, with eight key habitat factors significantly affecting the risk. Their relationships with infestation risk follow complex, non-monotonic quartic and cubic patterns; (3) factors triggering high infestation risks are mostly at low to moderate levels. High-risk areas tend to have low to moderate elevation (<800 m), moderate to high solar radiation and temperature, gentle slopes (<30°), low to moderate evaporation, shallow snow depth (<0.02), moderate snow temperature (266.73–275), low to moderate soil moisture (0.2–0.3), moderate to high soil temperature (276.73–286.92), low to moderate rainfall, moderate wind speed, low leaf area index, high vegetation type, low vegetation cover, low population density, and low surface runoff. Interactions between factors provide a stronger explanation of infestation risk than individual factors. The APCIRD framework, combined with MRF, offers valuable insights for understanding the drivers of pine caterpillar infestations. Full article

Space-borne gravitational wave detection missions demand ultra-precise inertial sensors with acceleration noise below $3\times {10}^{-15} \mathrm{m}/{\mathrm{s}}^2/\sqrt{\mathrm{H}\mathrm{z}}$. Patch field effects, arising from surface contaminants and nonuniform distribution of potential on the test mass (TM) and housing surfaces, pose critical challenges to sensor performance. Existing studies predominantly focus on nonuniform potential distributions while neglecting bulge effects (surface deformation caused by the adhesion of pollutants or oxides, production and processing defects, and other factors) and rely on commercial software with limited flexibility for customized simulations. This paper presents a novel boundary element partitioning and octree-based simulation algorithm to address these limitations, enabling efficient simulation of both electrostatic and geometric impacts of patch fields with low spatiotemporal complexity ($O\left(n\right)$). Leveraging this framework, we systematically investigate the influence of single patches on the TM electrostatic force ($\Delta F_x$) and stiffness ($\Delta K_{xx}$) through parametric studies. Key findings reveal that $\Delta F_x$ and $\Delta K_{xx}$ exhibit linear dependence on patch potential variation ($\Delta u$) and can be fitted by a quartic polynomial (which can be simplified in some cases, such as only a cubic term) about patch radius ($rₘ$). The proposed method’s capability to concurrently model geometric bulges and potential nonuniformity offers significant advantages over conventional approaches, providing critical insights for gravitational wave data analysis. These results establish a foundation for optimizing mitigation strategies against patch-induced noise in future space missions. Full article

This study presents a comprehensive investigation of cubic–quartic solitons within birefringent optical fibers, focusing on the effects of the Kerr law on the refractive index. The researchers have derived soliton solutions analytically using the sine-Gordon function technique. To validate their analytical results, the study employs the improved Adomian decomposition method, a numerical technique known for its efficiency and accuracy in solving nonlinear problems. This method effectively approximates solutions while minimizing computational errors, allowing for reliable numerical simulations that corroborate the analytical findings. The insights gained from this research contribute to a deeper understanding of the symmetry properties involved in nonlinear wave propagation in optical fibers. The study highlights the significant role of nonlinearities in shaping the behavior of waves within these systems. The use of proposed method not only serves as a checking mechanism for the sine-Gordon solutions but also illustrates its potential applicability to other nonlinear systems exhibiting complex symmetry behaviors. This versatility could lead to new exploration fronts in nonlinear optics and photonics, expanding the toolkit available for researchers in these rapidly evolving fields. Full article

In this paper, we present a “non-linear” factorization of a family of non-normal operators arising from Gribov’s theory of the following form: ${\displaystyle H_{{\lambda }^{\prime },\mu ,\lambda }={\lambda }^{\prime }{A}^{{*}^2}{A}^2+\mu A^{*}A+i\lambda A^{*}}$$(A+A^{*})A,$ where the quartic Pomeron coupling ${\lambda }^{\prime }$, the Pomeron intercept $\mu$ and the triple Pomeron coupling $\lambda$ are real parameters, and $i^2=-1$. $A^{*}$ and A are, respectively, the usual creation and annihilation operators of the one-dimensional harmonic oscillator obeying the canonical commutation relation $[A,A^{*}]=I$. In Bargmann representation, we have ${\displaystyle A⟷\frac{d}{dz}}$ and ${\displaystyle A^{*}⟷z}$, $z=x+iy$. It follows that ${\displaystyle H_{{\lambda }^{\prime },\mu ,\lambda }}$ can be written in the following form: ${\displaystyle H_{{\lambda }^{\prime },\mu ,\lambda }=p\left(z\right)\frac{d^2}{d{z}^2}+q\left(z\right)\frac{d}{dz},}$ where $p\left(z\right)={\lambda }^{\prime }{z}^2+i\lambda z$ and $q\left(z\right)=i\lambda z^2+\mu z.$ This operator is an operator of the Heun type where the Heun operator is defined by $H=p\left(z\right){\displaystyle \frac{d^2}{d{z}^2}}+q\left(z\right){\displaystyle \frac{d}{dz}}+v\left(z\right),$ where $p\left(z\right)$ is a cubic complex polynomial, $q\left(z\right)$ and $v\left(z\right)$ are polynomials of degree at most 2 and 1, respectively, which are given. For $z=-iy$, $H_{{\lambda }^{\prime },\mu ,\lambda }$ takes the following form: $H_{{\lambda }^{\prime },\mu ,\lambda }=-a\left(y\right){\displaystyle \frac{d^2}{d{y}^2}}+b\left(y\right){\displaystyle \frac{d}{dz}},$ with $a\left(y\right)=y(\lambda -{\lambda }^{\prime }y)$ and ${\displaystyle b\left(y\right)=y(\lambda y+\mu ).}$ We introduce the change of variable $y={\displaystyle \frac{\lambda }{2{\lambda }^{\prime }}}(1-cos\left(\theta \right))$, $\theta \in [0,\pi ]$ to obtain the main result of transforming ${\displaystyle H_{{\lambda }^{\prime },\mu ,\lambda }}$ into a product of two first-order operators: ${\displaystyle {\tilde{H}}_{{\lambda }^{\prime },\mu ,\lambda }={\lambda }^{\prime }(\frac{d}{d\theta }+\alpha \left(\theta \right))(-\frac{d}{d\theta }+\alpha \left(\theta \right)),}$ with $\alpha \left(\theta \right)$ being explicitly determined. Full article

The risk-neutral density is a fundamental concept in pricing financial derivatives, risk management, and assessing financial markets’ perceptions over significant political or economic events. In this paper, we propose a new nonparametric method for estimating the risk-neutral density using natural cubic splines (NCS). The estimated density is twice continuously differentiable with linear tails at both ends. Our method targets the logarithm of the underlying asset price, releasing the restriction to the positive domain. We theoretically prove the consistency of our NCS method. We conduct a comprehensive empirical study comparing the proposed NCS method with a piecewise constant method, a uniform quartic B-spline method, and a cubic spline method from the literature using 20 years of S&P 500 index option data. The empirical results show that our NCS method is more robust than the piecewise constant method, which can only produce a discontinuous density, especially for options with maturities longer than six months. Moreover, our NCS method outperforms other historical continuous methods in terms of optimization feasibility and option price estimation. Full article

Succinic anhydride, a crucial chemical intermediate, finds widespread applications in pharmaceuticals, polymers, and agrochemicals. The carbonylation of acetylene presents a promising route for succinic anhydride synthesis, offering environmental advantages and process efficiency. This study focuses on the empirical modeling of the carbonylation process to optimize the gas ratio of carbon monoxide (CO) to acetylene (C₂H₂), a critical parameter influencing product yield. Regression Analysis was applied to experimental data to develop a predictive model that can be used to predict the yield of succinic anhydride based on the ratio of carbon monoxide (CO) to acetylene (C₂H₂). The linearity connection between the analytical variables was determined by plotting the (CO:C₂H₂) ratio (independent variable) and the yield of the process (dependent variable) against each other. However, the plot’s curvilinear form suggested polynomial regression, showing that the connection was not linear. The R² values were 0.9219, 0.9563, and 0.9874 for the data in quadratic, cubic, and quartic models. These findings with statistical tests showed that the quartic model is the best empirical model for explaining the observed data variance (by a margin of 98.74%). The verification of experimental data to validate model acceptability showed an error of less than 0.05. Thus, using this model and changing the ratio of (CO:C₂H₂) from 1.1 to 4.0, the yield of succinic anhydride increased. The insights of this study would contribute to the advancement of sustainable and efficient chemical processes with potential applications in various industries. Full article

The symmetries of a Riemann surface $\mathsf{\Sigma }\setminus \left\{a_i\right\}$ with n punctures $a_i$ are encoded in its fundamental group ${\pi }_1\left(\mathsf{\Sigma }\right)$. Further structure may be described through representations (homomorphisms) of ${\pi }_1$ over a Lie group G as globalized by the character variety $\mathcal{C}=\mathrm{Hom}({\pi }_1,G)/G$. Guided by our previous work in the context of topological quantum computing (TQC) and genetics, we specialize on the four-punctured Riemann sphere $\mathsf{\Sigma }=S_2^{\left(4\right)}$ and the ‘space-time-spin’ group $G=S{L}_2\left(\mathbb{C}\right)$. In such a situation, $\mathcal{C}$ possesses remarkable properties: (i) a representation is described by a three-dimensional cubic surface $V_{a,b,c,d}(x,y,z)$ with three variables and four parameters; (ii) the automorphisms of the surface satisfy the dynamical (non-linear and transcendental) Painlevé VI equation (or $P_{VI}$); and (iii) there exists a finite set of 1 (Cayley–Picard)+3 (continuous platonic)+45 (icosahedral) solutions of $P_{VI}$. In this paper, we feature the parametric representation of some solutions of $P_{VI}$: (a) solutions corresponding to algebraic surfaces such as the Klein quartic and (b) icosahedral solutions. Applications to the character variety of finitely generated groups $f_p$ encountered in TQC or DNA/RNA sequences are proposed. Full article

In this work the matrix exponential function is solved analytically for the special orthogonal groups $SO\left(n\right)$ up to $n=9$. The number of occurring k-th matrix powers gets limited to $0\le k\le n-1$ by exploiting the Cayley–Hamilton relation. The corresponding expansion coefficients can be expressed as cosine and sine functions of a vector-norm V and the roots of a polynomial equation that depends on a few specific invariants. Besides the well-known case of $SO\left(3\right)$, a quadratic equation needs to be solved for $n=4,5$, a cubic equation for $n=6,7$, and a quartic equation for $n=8,9$. As an interesting subgroup of $SO\left(7\right)$, the exceptional Lie group $G_2$ of dimension 14 is constructed via the matrix exponential function through a remarkably simple constraint on an invariant, $\xi =1$. The traces of the $SO\left(n\right)$-matrices arising from the exponential function are sums of cosines of several angles. This feature confirms that the employed method is equivalent to exponentiation after diagonalization, but avoids complex eigenvalues and eigenvectors and operates only with real-valued quantities. Full article

In this paper, the new representations of optical wave solutions to fiber Bragg gratings with cubic–quartic dispersive reflectivity having the Kerr law of nonlinear refractive index structure are retrieved with high accuracy. The residual power series technique is used to derive power series solutions to this model. The fractional derivative is taken in Caputo’s sense. The residual power series technique (RPST) provides the approximate solutions in truncated series form for specified initial conditions. By using three test applications, the efficiency and validity of the employed technique are demonstrated. By considering the suitable values of parameters, the power series solutions are illustrated by sketching 2D, 3D, and contour profiles. The analysis of the obtained results reveals that the RPST is a significant addition to exploring the dynamics of sustainable and smooth optical wave propagation across long distances through optical fibers. Full article

The current paper recovers cubic–quartic optical solitons in fiber Bragg gratings having polynomial law of nonlinear refractive index structures. Lie symmetry analysis is carried out, starting with the basic analysis. Then, it is followed through with improved Kudryashov and generalized Arnous schemes. The parameter constraints are also identified for the existence of such solitons. Numerical surface plots support the adopted applied analysis. Full article

We study the transition from integrability to chaos for the three-particle Fermi–Pasta–Ulam–Tsingou (FPUT) model. We can show that both the quartic $\beta$-FPUT model ($\alpha =0$) and the cubic one ($\beta =0$) are integrable by introducing an appropriate Fourier representation to express the nonlinear terms of the Hamiltonian. For generic values of $\alpha$ and $\beta$, the model is non-integrable and displays a mixed phase space with both chaotic and regular trajectories. In the classical case, chaos is diagnosed by the investigation of Poincaré sections. In the quantum case, the level spacing statistics in the energy basis belongs to the Gaussian orthogonal ensemble in the chaotic regime, and crosses over to Poissonian behavior in the quasi-integrable low-energy limit. In the chaotic part of the spectrum, two generic observables obey the eigenstate thermalization hypothesis. Full article