Inverse Polynomial Research Articles

Comparative Analysis of the Equations Used in Modeling Individual Lactation Curves in Anatolian Water Buffalo (Bubalus bubalis)

In this study, the equations used in modeling the individual lactation curves of Anatolian Water Buffalo were comparatively examined and the most suitable model or models were tried to be determined. For this purpose, individuals with 8, 9 and 10 lactation records were selected among 8057 Anatolian Water Buffalo and a total of 1591 individual lactation curves were modeled. Guo-Salve, Grossman, Cappio-Borlino, Parabolic Exponential, Cobby and Le Du, Logarithmic Quadratic, Wilmink, Logarithmic Linear, Quadratic, Inverse Polynomial and Wood equations were used in the study. When comparing the models, coefficient of determination, mean squared error, Durbin-Watson autocorrelation test, the Akaike Information Criterion were considered. Among the models used in the study, the Cobby and Le Du, Wood and Logarithmic Quadratic models gave the best results, as opposed to the Guo-Salve model.

Attached prime ideals over skew Ore polynomials

In this paper, we investigate the attached prime ideals of inverse polynomial modules over skew Ore polynomials.

Development and implementation of innovative higher order inverse polynomial method for tackling physical models in epidemiology

Development and implementation of innovative higher order inverse polynomial method for tackling physical models in epidemiology

A direct and analytical method for inverse problems under uncertainty in energy system design: combining inverse simulation and Polynomial Chaos theory

This article introduces and formalizes a novel stochastic method that combines inverse simulation with the theory of generalized Polynomial Chaos (gPC) to solve and study inverse problems under uncertainty in energy system design applications. The method is particularly relevant to design tasks where only a deterministic forward model of a physical system is available, in which a target design quantity is an input to the model that cannot be obtained directly, but can be quantified reversely via the outputs of the model. In this scenario, the proposed method offers an analytical and direct approach to invert such system models. The method puts emphasis on user-friendliness, as it enables its users to conduct the inverse simulation under uncertainty directly in the gPC domain by redefining basic algebra operations for computations. Moreover, the method incorporates an optimization-based approach to integrate supplementary constraints on stochastic quantities. This feature enables the solution of inverse problems bounding the statistical moments of stochastic system variables. The authors exemplify the application of the proposed method with proof-of-concept tests in energy system design, specifically performing uncertainty quantification and sensitivity analysis for a Multi-Energy System (MES). The findings demonstrate the high accuracy of the method as well as clear advantages over conventional sampling-based methods when dealing with a small number of stochastic variables in a system or model. However, the case studies also highlight the current limitations of the proposed method such as slow execution speed due to the optimization-based approach and the challenges associated with, for example, the curse of dimensionality in gPC.

Hyperbolic discounting underpins response curves of mammalian avoidance behaviour.

As humans clear natural habitat, they are brought into increased conflict with wild animals. Some conflict is direct (e.g. elevated exposure of people to predators), some indirect (e.g. abandoning suitable habitat because of human activity). The magnitude of avoidance is expected to track frequency of human activity, but the type of response is an open question. We postulated that animals do not respond passively to increased disturbance nor does response follow a power law; instead, their ability to estimate magnitude leads to 'discounting' behaviour, as in classic time-to-reward economic models in which individuals discount larger value (or risk) in more distant time. We used a 10-year camera dataset from southern California to characterize response curves of seven mammal species. Bayesian regressions of two non-discounting models (exponential and inverse polynomial) and two discounting models (hyperbolic and harmonic) revealed that the latter better fit response curves. The Arps equation, from petroleum extraction modelling, was used to estimate a discount exponent, a taxon-specific 'sensitivity' to humans, yielding a general model across species. Although discounting can mean mammal activity recovers rapidly after disturbance, increased recreational pressure on reserves limits recovery potential, highlighting a need to strike a balance between animal conservation and human use.

A survey of compositional inverses of permutation polynomials over finite fields

A survey of compositional inverses of permutation polynomials over finite fields

Lactation Curves of Mastitic Vrindavani Cattle: A Statistical Approach

Mastitis is one of the important animal disease which causes huge economic loss. The present study was aimed to find the best lactation curve model that describes the milk production pattern of Vrindavani cattle suffered from mastitis. In the study, test day milk yield data of 161 mastitic Vrindavani cattle (incidence of the disease occurring within the three months of parturition) was collected from Cattle and Buffalo Farm, LPM section, ICAR‑IVRI over 5 years (2009-2014). Eight lactation curve models [Inverse quadratic polynomial model (ND), Incomplete Gamma function (WD), Linear decline model (CL), Wilmink model (WL) Mixed log model (ML), Mitscherlich x Exponential (ME), Morant and Gnanasakthy model (MG) and Ali & Schaeffer lactation curve model (AS)] were fitted. The best model was selected based on different goodness of fit criteria and the Durbin-Watson test was used to examine the presence of autocorrelation present in the data set. Kolmogorov-Smirnova test and Shapiro-Wilk were used to test the normality of the residuals. Based on the various goodness of fit test it was observed that the Mixed Log (ML) model was the best fitted model to describe the lactation pattern of mastitic Vrindavani cattle.

Inverses for Fourth-Degree Permutation Polynomials Modulo 32Ψ or 96Ψ, with Ψ as a Product of Different Prime Numbers Greater than Three

In this paper, we address the inverse of a true fourth-degree permutation polynomial (4-PP), modulo a positive integer of the form 32kLΨ, where kL∈{1,3} and Ψ is a product of different prime numbers greater than three. Some constraints are considered for the 4-PPs to avoid some complicated coefficients’ conditions. With the fourth- and third-degree coefficients of the form k4,fΨ and k3,fΨ, respectively, we prove that the inverse PP is (I) a 4-PP when k4,f∈{1,3} and k3,f∈{1,3,5,7} or when k4,f=2 and (II) a 5-PP when k4,f∈{1,3} and k3,f∈{0,2,4,6}.

Local method for compositional inverses of permutation polynomials

In this paper, we provide a local method to find compositional inverses of all PPs, some new PPs and their compositional inverses are given.

Inverse polynomials of numerical semigroup rings

We study the defining ideal of a numerical semigroup ring k[H] using the inverse polynomial attached to the Artinian ring k[H]/(th). We give a criterion for H to be symmetric or almost symmetric using the annihilator of the inverse system. Also we give characterizations of symmetric numerical semigroups with small multiplicity and give a new proof of Bresinsky's Theorem for symmetric semigroups generated by 4 elements.

Impact of Spatial Rainfall Scenarios on River Basin Runoff Simulation a Nan River Basin Study Using the Rainfall-Runoff-Inundation Model

This study aims to investigate the impact of spatial rainfall distribution scenarios from ground observation stations on runoff simulation using hydrological modeling specific to the Rainfall-Runoff-Inundation (RRI) model. The RRI model was applied with six different spatial distribution scenarios of input rainfall, including Inverse Distance Weight (IDW), Thiessen polygon (TSP), Surface Polynomial (SPL), Simple kriging (SKG), and Ordinary kriging (OKG), to simulate the runoff of a 13,000 km2 watershed, namely the Nan River Basin in Thailand. This study utilized data from the 2014 storm event, incorporating temporal information from 28 rainfall stations to estimate rainfall in the spatial distribution scenarios. The six statistics, Volume Bias, Peak Bias, Root Mean Square Error, Correlation, and Mean Bias, were used to determine the accuracy of the estimated rainfall and runoff. Overall, the Simple kriging (SKG) method outperformed the other scenarios based on the statistical values to validate with measured rainfall data. Similarly, SKG demonstrated the closest match between simulated and observed runoff, achieving the highest correlation (0.803), the lowest Root Mean Square Error (164.48 cms), and high Nash-Sutcliffe Efficiency coefficient (0.499) values. This research underscores the practical significance of spatial interpolation methods, such as SKG, in combination with digital elevation models (DEMs) and landuse/soil type datasets, in delivering reliable runoff simulations considering the RRI model on the river basin scale.

Trajectory planning and control of large robotic excavators based on inclination-displacement mapping

This paper proposes a trajectory planning and control method for heavy-duty manipulators based on inclination-displacement mapping. In this method, inclination sensors are employed to detect the excavator's orientation. By establishing a mapping relationship between joint inclination and cylinder displacement, the cylinder displacement is indirectly derived. Subsequently, considering the typical excavation operation process, the spatial trajectory of the excavator bucket is planned. The displacement of the driving cylinder is determined using kinematic inverse solutions and cubic polynomials. The cylinder displacement is then controlled using a position-velocity (PV) strategy. This method is tested on a 95-ton large excavator, and the results demonstrate several advantages, including easy installation, low maintenance requirements, smooth trajectory planning, and high tracking accuracy. These qualities make it suitable for the demands of intelligent operations in large excavators. Thus, this paper offers valuable insights for the intelligent transformation of heavy excavators.

A rapidly mixing Markov chain from any gapped quantum many-body system

We consider the computational task of sampling a bit string x from a distribution π(x)=|⟨x|ψ⟩|2, where ψ is the unique ground state of a local Hamiltonian H. Our main result describes a direct link between the inverse spectral gap of H and the mixing time of an associated continuous-time Markov Chain with steady state π. The Markov Chain can be implemented efficiently whenever ratios of ground state amplitudes ⟨y|ψ⟩/⟨x|ψ⟩ are efficiently computable, the spectral gap of H is at least inverse polynomial in the system size, and the starting state of the chain satisfies a mild technical condition that can be efficiently checked. This extends a previously known relationship between sign-problem free Hamiltonians and Markov chains. The tool which enables this generalization is the so-called fixed-node Hamiltonian construction, previously used in Quantum Monte Carlo simulations to address the fermionic sign problem. We implement the proposed sampling algorithm numerically and use it to sample from the ground state of Haldane-Shastry Hamiltonian with up to 56 qubits. We observe empirically that our Markov chain based on the fixed-node Hamiltonian mixes more rapidly than the standard Metropolis-Hastings Markov chain.

Uncertainty quantification in low-probability response estimation using sliced inverse regression and polynomial chaos expansion

For wave energy converters (WECs), wind turbines, etc., estimation of response extremes over a selected exposure time is important during design. Sources of uncertainty arising from background slowly-varying environmental conditions and from shorter time-scale fluctuations in ocean winds, turbulence, etc. must all be considered. Together, these different sources can comprise a high-dimensional vector of stochastic variables (often on the order of hundreds or thousands). To accurately propagate the influence of these uncertainty sources to model outputs, conventional surrogate model building approaches such as polynomial chaos expansion (PCE), stochastic collocation, low-rank tensor approximations, etc. must consider dimension reduction. We explore the use of sliced inverse regression (SIR) combined with polynomial chaos expansion. SIR first reduces the original high-dimensional problem to a low-dimensional one; then, an optimal polynomial PCE model is proposed and applied on “effective” components in the low-dimensional space. SIR-PCE can mitigate the curse of dimensionality. It is employed here in the prediction of the long-term extreme response of offshore structures; it is demonstrated using classical benchmark analytical functions as well as offshore applications including extreme waves and the response of a wave energy converter. Efficiency and accuracy gains over Monte Carlo simulation and other methods in literature are found.

Research on the scene design of virtual reality technology in film and television animation

Abstract In this paper, firstly, we study the modeling of film and television animation based on virtual reality technology and use quadratic polynomial inverse to control the intensity of light source to establish the lighting model. The image alignment is designed for the scene based on multi-resolution decomposition, and the filtered image layer is obtained by calculating the difference between two layers of Gaussian filtered images, and the Laplace pyramid is established to match the image resolution consistently. Then the scene is chunked and locally rendered, and a smooth transition between geometry and texture is achieved by morphing the geometry next to the texture. Finally, the scene effect, LOD detail level and interactive experience effect before and after simplification are compared and analyzed. The scene design of virtual reality technology basically scores 5-6 on each index, while the scene design of common technology only scores 3-4, indicating that the scene design of virtual reality technology works well.

Remarks on the Coefficients of Inverse Cyclotomic Polynomials

Cyclotomic polynomials play an imporant role in discrete mathematics. Recently, inverse cyclotomic polynomials have been defined and investigated. In this paper, we present some recent advances related to the coefficients of inverse cyclotomic polynomials, including a practical recursive formula for their calculation and numerical simulations.

A proposed sixth order inverse polynomial method for the solution of non-linear physical models

A proposed sixth order inverse polynomial method for the solution of non-linear physical models

Joint Blind Reconstruction of the Cyclic Codes and Self-Synchronous Scramblers in a Noisy Environment

Reverse analysis of the intercepted signal to reconstruct the communication scheme used by the transmitter is a key problem in the non-cooperative context. In this paper, we propose a new algorithm for the joint blind reconstruction of the cyclic codes and self-synchronous scramblers directly using soft-decision sequences. First, we derive the conclusion that if the parity polynomial of the factor of the generator polynomial of the cyclic code and the feedback polynomial of the self-synchronous scrambler are multiplied, then the vector corresponding to the inverse polynomial of this product forms a parity-check relation with the row vector of the self-synchronously scrambled cyclic code bit matrix, which is constructed by the sequence of self-synchronously scrambled cyclic codes. To detect this parity-check relation, the concept of average parity-check probability (APCP) is defined, which uses the intercepted soft-decision sequence to measure the reliability of the parity-check relation. An optimal threshold based on the minimum error criterion is then derived. When the APCP is greater than this optimal threshold, the parity-check relation is considered to be detected, i.e., the corresponding irreducible polynomial is a factor of the generator polynomial of the cyclic code and the corresponding candidate feedback polynomial is the feedback polynomial of the self-synchronous scrambler. Therefore, the blind reconstruction problem in this paper is exactly equivalent to the hypothesis-testing problem. Simulation results show that the algorithm is more fault-tolerant than existing algorithms in noisy environments.

A new modification of an iterative method based on inverse polynomial for solving Cauchy problems

This paper introduces a new modification to an iterative method for solving Cauchy problems (IVPs) based on an inverse polynomial technique. The proposed method is proven to be consistent, stable, and convergent. We also demonstrate the consistency property of the One-stage scheme and the Two-stage scheme, as well as the stability property of the proposed method. To validate the accuracy of our approach, we conduct several numerical experiments and present the results graphically. Our findings show that the proposed method outperforms existing approaches in terms of accuracy and efficiency. Additionally, we discuss the implications of our results for future research in this field. Overall, this paper provides a valuable contribution to the numerical solution of IVPs and lays the groundwork for further exploration in this area.

Joint blind reconstruction of cyclic codes and self‐synchronous scramblers

AbstractThe inverse analysis of the intercepted signals to reconstruct the communication scheme used by the transmitter is a key problem in the non‐cooperative context. In this paper, the problem of blind reconstruction of cyclic codes and self‐synchronous scramblers is considered. There is no existing solution to this problem. To solve this problem, a joint blind reconstruction method for cyclic codes and self‐synchronous scramblers is proposed in this paper. A lemma is proposed and proved theoretically that the maximum common factor of the inverse polynomial of the polynomial form of the dual vectors of the self‐synchronous scrambled bit matrix is the product of the parity polynomial of the cyclic code and the feedback polynomial of the self‐synchronous scrambler. Using this lemma, the joint blind reconstruction of the cyclic code and the self‐synchronous scrambler is completed. Finally, a Gaussian elimination based on random column exchange and soft information (GERCESI) method is proposed, which can apply the proposed method to a noisy environment. Simulations prove that the fault‐tolerance performance of the GERCESI method proposed in this paper is at least 0.5 dB higher than that of the GJETP method.